WORKSHOP IN SAMPLING REQUIREMENTS

      FOR MONITORING AND EVALUATION

    OF WATERSHED MANAGEMENT PRACTICES
              Presented by

      Simons, Li & Associates, Inc.

             Daryl B. Simons
               Run-Ming Li -vvO
          Thomas P. Ballestero -MD
            Kenneth G. Eggert
              Sponsored by

  U.S. Environmental Protection Agency
 .^  Environmental Research Laboratory
             Athens, Georgia

           In cooperation with

  U.S. Environmental Protection Agency
         Water Planning Division
Office of Water Regulations and Standards
            Washington, D.C.
             May 20-21, 1981
           Arlington, Virginia

-------
                              TABLE OF CONTENTS
 I.  INTRODUCTION	1.1

     1.1  Course Objectives  	 1.1
     1.2  Physical Processes Governing Watershed Response  	 1.2

          1.2.1   Introduction	1.2
          1.2.2   Spatial Representation of Watersheds  	 1.6
          1.2.3   Model Components  	 1.16

     1.3  Procedures  for Evaluation of a Monitoring Network  .... 1.24
     1.4  References	1.25

II.   CONCEPTUAL  DESIGN OF A MONITORING SYSTEM	2.1

     2.1  Introduction	2.1
     2.2  Data Needs	2.1

          2.2.1   General	2.1
          2.2.2   Specific Needs	2.2

     2.3  Direct Measurements	2.8

          2.3.1   General	2.8
          2.3.2   Collection and  Processing of Surface Water Data .  . 2.8

                 2.3.2.1   Gage Datum	2.9
                 2.3.2.2   Maintenance  of a Gaging Station	2.9
                 2.3.2.3   Recording and Documentation of  Data.  . .  . 2.10
                 2.3.2.4   Servicing Stage Recorders	2.10
                 2.3.2.5   Discharge Measurements  	 2.15
                 2.3.2.6   Equipment	2.17
                 2.3.2.7   Current Meter Measurements 	 2.18
                 2.3.2.8   Velocity  Measurements	 2.18
                 2.3.2.9   Development  of Rating Curves 	 2.21
                 2.3.2.10  Requirement  for Discharge Measurement
                          at  a Range of Stage	2.27
                 2.3.2.11  Operation and Maintenance of Crest-
                          Stage Gages	2.27
                 2.3.2.12  Discharge Measurements  at Low-Flow
                          Partial-Record Stations	2.29

          2.3.3   Collection and Processing of Water Quality Data .  . 2.31

                 2.3.3.1   General	2.31
                 2.3.3.2   Sampling  Techniques	2.32
                 2.3.3.3   Field Evaluations	2.33
                 2.3.3.4   Chemical  Samples  	 2.35
                 2.3.3.5   Sediment  Sampling	2.35
                 2.3.3.6   Site Selection 	 2.36
                 2.3.3.7   Stream  Sampling Stations  	 2.39

-------
                        TABLE OF CONTENTS (continued)

                 2.3.3.8  Total Collection Devices 	 2.39
                 2.3.3.9  Suspended Sediment Samplers and	 2.41
                          Measurements 	 2.41
                 2.3.3.10 Bed-Material Samplers	2.50

     2.4  Meteorological Data	2.52

          2.4.1  Site Requirements	2.52
          2.4.2  Air Temperature	2.54
          2.4.3  Air Humidity	2.55
          2.4.4  Wind	2.56
          2.4.5  Solar Radiation	2.57
          2.4.6  Barometric Pressure 	 2.59
          2.4.7  Rainfall Measurement	2.60

                 2.4.7.1  Site Selection 	 2.61
                 2.4.7.2  Factors Affecting Accuracy 	 2.62
                 2.4.7.3  Nonrecording Gages 	 2.64
                 2.4.7.4  Recording Gages	2.66
                                                               i
     2.5  References	2.68

III. SPATIAL AND TEMPORAL CORRELATION  	 3.1

     3.1  Introduction	3.1
     3.2  Correlation in Time,  the Autocorrelation Function  .... 3.2

          3.2.1  Introduction and Theory	3.2
          3.2.2  Loss of Information by Discretization	3.6

                 3.2.2.1  Discrete Point Sampling  	 3.8
                 3.2.2.2  Average Sampling  	 3.11

          3.2.3  Effect  of the  Sampling Interval  on the Correlogram  3.11
          3.2.4  Miscorrelation:   Effects of the  Misuse of  Data and
                 the Misinterpretation of the Autocorrelation
                 Function	3.14

                 3.2.4.1  Intermittent Processes  	 3.14
                 3.2.4.2  Jumps and Trends  	 3.14
                 3.2.4.3  Measurement Accuracy (Effect of Trunca-
                          tion)  and Autocorrelation	3.17

          3.2.5  Effects of Reservoirs on Correlation Structure  . . 3.18

                 3.2.5.1   Introduction 	 3.18
                 3.2.5.2  Water Quantity Variables 	 3.18
                 3.2.5.3  Water Quality Variables  	 3.22

          3.2.6  Note on Sampling Frequency  Design	3.26

-------
                        TABLE OF CONTENTS (continued)
                 3.2.6.1  Introduction 	 3.26
                 3.2.6.2  Water Quality Sampling Frequency 	 3.26
                 3.2.6.3  Concepts for Designing Sampling Frequency  3.28

          3.2.7  Conclusion for Temporal Correlation 	 3.28

     3.3  Spatial Correlation;  The Cross-Correlation Function  ... 3.28

          3.3.1  Introduction and Theory	3.28
          3.3.2  Effect of Spatial Correlation on the Amount of
                 Information Obtained from a Gaging Network  .  . . .3.31
          3.3.3  Use of Cross Correlation for Network Design and
                 Application to a Raingage Network 	 3.34

                 3.3.3.1  Introduction ... 	 3.34
                 3.3.3.2  Geographic Effects on the Spatial
                          Variability of Rainfall  	 3.34
                 3.3.3.3  Topographic Effects on the Spatial
                          Variability of Rainfall  	 3.42
                 3.3.3.4  Small-Scale Spatial Variability of
                          Precipitation  	 3.44

          3.3.4  Spatial Variability of Streamflow 	 3.48
          3.3.5  Spurious Correlation  	 3.48

     3.4  References	3.50

IV.   QUALITY  OF DATA	   4.1

     4.1  Introduction	   4.1
     4.2  Data  Quality  Assessment Through Physical Process
          Analysis    	   4.2
     4.3  Data  Inhomogeneity	   4.4

          4.3.1   Introduction	   4.4
          4.3.2   Testing for Data Inhomogeneities	   4.4

                 4.3.2.1   Qualitative Test  For Inconsistencies  .  .    4.4
                 4.3.2.2   Testing for a Jump	    4.5
                 4.3.2.3   Detection  of Trends  	    4.16

     4.4  Correction of  Data Inhomogeneities	    4.23

          4.4.1   Introduction	    4.23
          4.4.2   Filling of  Missing  Data	    4.23
          4.4.3   Measurement or  Recording Errors  .........    4.27
          4.4.4   Jumps	    4.27
          4.4.5   Trends	    4.29

     4.5  References	    4.29

-------
                        TABLE OF CONTENTS  (continued)


 V.  PHYSICAL PROCESS  SIMULATION:  I. WATER  AND  SEDIMENT ROUTING  .  .  5.1

     5.1  Introduction	5.1
     5.2  Water and Sediment Routing  	  5.2

          5.2.1  Formulation of the Water  and Sediment Model  ....  5.2
          5.2.2  Formulation of Excess Rainfall  Calculations
                 for MSED1	5.4
          5.2.3  Derivation of Analytical  Kinematic Wave
                 Equations for MSED1	•	5.9
          5.2.4  Sediment Determination for  MSED1   	  5.24

                 5.2.4.1  Overland Sediment  Transport Capacity  .  .  .  5.24
                 5.2.4.2  Channel Sediment Transport Capacity   .  .  .  5.29
                 5.2.4.3  Determination of Sediment Supply  	  5.29
                 5.2.4.4  Determination of Sediment Yield   	  5.30

          5.2.5  Mathematical Derivation of  the  Numerical Kinematic
                 Routing Procedure for MSED3 	  5.30
          5.2.6  Channel Infiltration Routine for MSED3  	  5.35
          5.2.7  Sediment Routine for MSED3  	  5.35

                 5.2.7.1  Governing Equation for Sediment Routing   .  5.36
                 5.2.7.2  Numerical Procedure for Sediment Routing  .  5.38

          5.2.8  MSED2	5.39

     5.3  Water and Sediment Input Data Requirements 	  5.40

     5.4  References	5.41

VI.  PHYSICAL PROCESS SIMULATION:   II.  INTERSTORM AND
     PESTICIDE MODELS   	  6.1

     6.1  General	6.1
     6.2  Interstorm Process 	 . 	  .....  6.1

          6.2.1   Evaporation	6.2
          6.2.2   Evapotranspiration (ET)	6.7
          6.2.3   Electrical Analogue 	  6.13
          6.2.4   Heat Transfer by Convection	6.21

     6.3  Interception and Infiltration  	  6.23

          6.3.1   Interception	6.23
          6.3.2   Infiltration	6.27
          6.3.3   Infiltration Parameters  	  6.33

     6.4  Data  Requirements for  Interstorm Model  	  6.35
     6.5  Pesticide Loading  	  6.36
     6.6  Data  Requirements for  Pesticide  Model   	  6.45
     6.7  References	6.50

-------
                        TABLE OF CONTENTS (continued)


VII.  APPLICATION OF EVALUATION PROCEDURES 	    7.1

     7.1  Introduction	    7.1
     7.2  Data Availability and Data Gaps	    7.1
     7.3  Analysis of Existing Data Network	    7.6

          7.3.1  Geometry and Channel Data	    7.6
          7.3.2  Soil Data	    7.7
          7.3.3  Vegetation Data	    7.14
          7.3.4  Climatic Data	    7.17
          7.3.5  Hydrologic and Hydraulic Data	    7.33
          7.3.6  Nutrients and Herbicides-Pesticides 	    7.49

                 7.3.6.1   Nutrients  	    7.49
                 7.3.6.2   Herbicides-Pesticides  	    7.54

     7.4  References	    7.59

VIII.  CASE STUDY II:  APPLICATION OF A PHYSICAL PROCESS MODEL  .  .    8.1

     8.1  General	    8.1
     8.2  Data Needs	    8.1
     8.3  Available Data  and Gaps	    8.1
     8.4  Model Application and Results Using Collected Data ...    8.3

          8.4.1   General	    8.3
          8.4.2   Small  Watershed Simulation   	 ...    8.3
          8.4.3   Medium Watershed Simulation 	    8.10

     8.5  Use  of  the Model for Data Synthesis and Evaluation .  .  .    8.10

          8.5.1   Time of  Concentration Determination	    8.10
          8.5.2   Sensitivity Analysis	    8.15
          8.5.3   Correlation in Simulated Runs	    8.20

     8.6  Summary	    8.28

     8.7  References	    8.35

-------
I.   INTRODUCTION
1.1  Course Objectives
     The objective of this short course, as the name  implies/  is the design
and evaluation of monitoring networks.  Four points that  are  addressed are:
     1.   If data are to be collected, what will they be  used for?
     2.   If a watershed is to be studied, how is the sampling program
          designed?
                                              •
     3.   If water supply data have been gathered, how are  they interpreted?
          (What do you have ?)
     4.   How are measurements evaluated?
     The design of any monitoring network must be based not only upon the
overall objective (i.e., designing a major hydraulic  structure), of which
monitoring is a part, but also upon the physical processes  governing watershed
response.
     The most overlooked yet the most important aspect of designing a moni-
toring network is that there is usually no adequate available data on the pro-
cesses which are to be monitored (i.e., time series,  maximum  value, minimum
value, variation, etc.).  Sometimes there are regional average values which
can be found or calculated (regional mean rainfall, computing average annual
runoff with mean discharge per square mile, etc.).  Many  recent publications
base network design on statistical data.  Unfortunately the statistics must
come from observed data in order to be computed in the first  place.  A signi-
ficant aid to monitoring network design is the utilization  of physical process
models to synthesize data and then to use the synthesized data for the network
design specificities (what data to collect, what time step, where should the
gages be located, etc.).  Physical process models may not initially have all
the required information in order to synthesize data,  and thus this infor-
mation would necessitate interim monitoring of watershed  processes and charac-
teristics in order to calibrate model parameters, or  some information may be
obtained by borrowing statistical parameters from other watersheds (i.e., soil
permeability).
     The evaluation of a data monitoring network must be  performed in order to
ascertain whether or not the monitoring network is collecting data suitable to
satisfy the monitoring objective.  For example, if the monitoring objective
were to simply detect water quality criteria violations,  the  most important

-------
                                       1.2
monitoring design  consideration to satisfy this  objective is  selection of the
sampling  frequency.   Guidelines have  been suggested for this  case based upon
the average daily  streamflow and the  type of  water quality variable being
measured  (see reference  1).   Other design criteria for  this example would be
the location of the  gage,  homogeneity of  the  data, and  representative nature
of the data (is the  data realistic for the process which it was obtained
from?).   After the gage  has  been in operation, it  may be evaluated to see if
all of the design  considerations have been satisfied and also whether it can
identify  or has identified water quality  violations.  Meeting the monitoring
objectives is very important since usually the overall  objective must base
future decisions on  the  data base. An example might be designing a hydraulic
structure based on three years  of data.   Typically,  in  this case, estimates of
certain magnitude  events are made with probabilistic or physical process
models and the structure is  then designed based  on the  estimates. .The  esti-
mates could not be made  without a data base since  the models  used to estimate
the events must be designed  and calibrated with  observed data.   If the
observed  data is of  poor quality or insufficient,  the hydraulic structure will
be poorly designed (over-  or underdesigned).
     Design and evaluation of monitoring  networks  are integral  parts of
accomplishing watershed  objectives.
     These topics will be  covered in  the  next section.

1.2  Physical Processes  Governing Watershed Response
     1.2.1  Introduction
     The  management  of watersheds and river basins for  the optimum benefit of
the people in general requires  a complete knowledge  of  the interrelations
between ecology and  environment.   The watershed  response to developments,
either natural or man-induced,  must be anticipated correctly  if progress is to
be made toward wise  use  of our  natural resources.   The  increasing interests in
predicting watershed response has accelerated the  progress in the mathematical
modeling  of water hydrographs and yields.   Concern for  protecting the natural
environment has also increased  research in the field  of predicting watershed
sediment  yields.  Further, degradation, aggradation  and movement of sediment
and other pollutants in  watersheds are closely related  to water movement.  In
fact, no  sediment yield  can  be  predicted  without the  knowledge  of water

-------
                                      1.3

routing and yield.  This section describes several methodologies  for  calcu-
lating water yield and storm water routing from watersheds which  were deve-
loped at the Engineering Research Center, Colorado State University,  under the
general direction of Daryl B. Simons and Run-Ming Li.
     The physical processes governing watershed response are very complicated.
Many past studies have utilized a statistical interpretation of observed
response data.  The unit hydrograph method for water routing and  the  hydraulic
geometry equations for stream morphology are examples of- these types  of stud-
ies It is often difficult to predict the response of a watershed  to various
watershed developments or treatments using these methods, because they are
based on the the assumption of homogeneity in time and space.  Mathematical
modeling using the governing physical processes may be used as an alternative
means of estimating the time-dependent response of watersheds to -precipitation
with varying vegetative covers and land use.  The principal advantage of  the
mathematical simulation approach is that the parameters that are  used to  vary
watershed response may be physically defined.  Such a definition  enables  the
user to predict changes in watershed response arising from alterations in the
watershed environment.  The principal disadvantage of the simulation  approach
in comparison to purely statistical methods is size and complexity of simula-
tion models.  However, the speed and availability of modern computers largely
answer this problem.  In addition, the availability of inexpensive and power-
ful hand-held programmable calculators places many sophisticated  simulation
methods in the hands of both researchers and application-oriented engineers.
     Physical process simulation models represent the system being modeled by
decomposing it into its respective components.  By dividing a system  into its
respective components, "lumping" of processes or parameters can be avoided.
By simulating the selected phenomena through separate components,  each indivi-
dual process can be analyzed and refined or altered to meet the needs of  the
user.  Consequently, as each process component is upgraded, the model becomes
more representative of the physical system.  Only a limited number of physical
process models are presented.  However, because they are physical process com-
ponent models, the processes involved are similar between the models.
Differences do exist between some components, making some models  more complex
or versatile than others.  Basically two modeling approaches are  described
below.  The selected water routing approaches are:  (1) high-resolution
watershed storm water routing and yield model, and (2) simplified watershed

-------
                                      1.4

routing and  yield models.   A number  of  other  approaches  are available,  but
research has  shown  that  these cited  models  contain  the most sensitive physical
processes.
     The above general approaches  share essentially the  same basic physical
process.  The main  differences are in the formulation, implementation and
degree of detail that may  be represented.   The  high-resolution model  was  first
developed by Li  (1974) and subsequently published by Simons,  Li and Stevens
(1975) and updated  by Shiao (1978).  The model  routes storm runoff water  from
overland flow surfaces and then  through the channel system of a watershed.
This is done using  mathematical  formulations  of the water  continuity  equations
and certain  assumptions  about the  flow. This model is termed high resolution
because it uses a finite-difference  solution  technique to  solve the water
discharge at selected times and  points  on the overland flow surface and chan-
nel system.  The watershed for this  model can be^subdividecj into numerous
overland flow surfaces and the channel  represented  by several connected
segments.
     The simplified models,  in contrast to  the  high-resolution model, require
a watershed to be represented by a channel  and  two  contributing planes  or a
combination of two-plane and single-plane watersheds connected by a channel
system.  This much  simpler representation of  the watershed provides for easier
application, but may create problems if the watershed is extremely nonhoraoge-
neous or anisotropic.  This model  uses  an analytic  formulation to route water
from the overland flow planes (Simons,  Li and Eggert, 1977).   Use of  the
single two-plane one-channel model is warranted for watersheds that are fairly
homogeneous and are subject to spatially constant_rainfall.   The combined
watershed model may be used for  larger,  more  heterogeneous drainages  that may
be modeled as a group of differing,  yet internally  homogeneous,  subwatersheds.
     Simulation of  continuous time hydrology  requires modeling of the
interstorm period.  The processes  included  in the interstorm model are  eva-
poration, evapotranspiration and soil moisture  redistribution.  This  model is
designed to interface with the storm water  and  sediment  runoff model.  The
interstorm model may be used to  establish initial conditions  for runoff and
predict soil moisture contents required for nutrient and pesticide loading
calculations.
     The interstorm model  is a mechanistically  based simulation requiring
daily meteorological inputs.   It is  based on  a  model originally presented by

-------
                                      1.5

Goldstein, Mankin and Luxmoore (1974) with substantial modifications  to  the
storm infiltration calculations.  This model approaches the
evapotranspiration-soil moisture flow-evaporation problem by utilizing an
electrical circuit analog.  Flow of water through the system is  assumed  analo-
gous to the current, the water as hydraulic potential is assumed analogous to
the voltage, and the plant-soil atmosphere characteristics are parameterized
into resistances to water flow.  In addition, the model uses climatic data to
predict evaporation rates.  Soil water content is updated daily, layer by
layer, to provide correct parameters for infiltration.  Transpiration is
modeled simply by continuity.  Water absorbed by the roots is delivered  to the
atmosphere.  On days when rainfall occurs, the additional hydrologic  processes
of interception and infiltration are simulated.  With initial soil  and inter-
ception conditions specified by the daily routines, interception and  infiltra-
tion calculations are performed on rainfall hyetographs to produce  an excess
rainfall hyetograph to be routed as surface water runoff.  When  using the
interstorm simulation, its infiltration and interception calculations are
substituted for those normally performed in the runoff model.
     Pesticide yields from field surfaces is modeled using a mechanistically
based approach presented by Leonard and Wanchope, 1980.  This model was  deve-
loped on simplified concepts of processes and designed to be responsive  to
different management options.  Foliar- and soil-applied pesticides  are separ-
ately described so that different decay rates can be used for each  source of
the same chemical if necessary.  Usually pesticide residing on foliage dissi-
pates more rapidly than that from soil.  Also decay rates can be made site-
specific if information is available.  Movement of pesticides from  the soil
surface as a result of infiltrating water is estimated using differences of
rainfall and runoff for the storm and pesticide mobility parameters.
Pesticide in runoff is partitioned between the solution or water phase and the
sediment phase.  This aspect is particularly important when examining manage-
ment options that limit sediment yield.
     The discussion of these routing and yield simulations begins in  Section
1.2.2 with a description of the spatial representations required by the  indi-
vidual methods.  This section is followed by a description of the physical
process components and general layout of the simulators.  An important feature
of both the high-resolution and simplified models is the method  used  for esti-
mating excess rainfall.  This method involves both interception  and infiltra-

-------
                                       1.6

tion processes.  The  greatest differences  between the high-resolution and
simplified models  occur in the water  routing methods.  Both kinds of models
use kinematic wave routing for overland and channel flow.   However,  the
simplified models  use the  method of characteristics solution to the  kinematic
wave problem for some or all of the water  routing.  The high-resolution model
uses a numerical solution  to the kinematic wave problem for all water routing.
     All of these  methods  exist as  specific computer programs at SLA; however,
the general theory presented is not intended as a program  description,  but
rather a general approach  that may  be used in a variety of watershed simula-
tion problems.

     1.2.2  Spatial Representation  of Watersheds
     Because most  watersheds are nonhomogeneous in topography,  soils, vegeta-
tion, and other features,  it is necessary  to segment each  watershed  into units
which can be treated  as  being homogeneous.   Similarly,  the  channel system in a
watershed can be represented by one  or  more  segments,  each  having a charac-
teristic location,  shape,  slope and  roughness.
     The location,  area,  length,  and slope of each watershed unit are usually
obtained from the available  topographic maps.  The following steps can be used
in collecting the geometric  data  from topographic  maps.   Two types of
watershed segmentation are considered.   For  the high-resolution model, the
watershed is subdivided  into square  grids of a selected size (Simons, Li and
Ward, 1978).  The size of  these grids or cells is  chosen to conform with the
watershed geometry  and represent  the accuracy of the  input  data and required
output.  Node points  of  the  grid  system represent  sampling  points where
topographic, soils, and  vegetative data are  selected.   The  channel system is
represented by straight  line segments between node points.   The sampled infor-
mation is computer  processed to produce a segmented watershed of overland flow
cells with corresponding length,  slope,  width,  and soil  and vegetative
indices, and a channel system described by lengths, slopes,  and locations.
Gravity flow logic, cell and channel aspect  are used  to  determine flow direc-
tions in the watershed.  On  a much smaller scale,  the  slope,  lengths, widths
and flow directions of roadways can  be  prepared from  maps,  construction plans,
or field measurements.   For  the simplified watershed  models consisting of
planes and channels,  a different  approach is used  to  abstract the geometry for
model input.  This  approach  can be used on small or large watersheds.  On

-------
                                      1.7
large watersheds multiple sets of two-plane one-channel watersheds  may be  pre-
sent (Simons, Li and Sprorik, 1978).  A method is presented below  that  is
applicable to single watersheds or subdivided watersheds.

     Geometric Representation for High-Resolution Model.  The  first problem
encountered in numerical modeling of watershed response is to  determine repre-
sentative response units for mathematical computations.  Simons and Li (1975)
have approached this problem by developing a watershed segmentation program
based on a grid system.  The grid size is chosen so that the watershed boun-
dary and channel segments can be approximated by grid lines  (Figure 1.1).   The
overland flow units are the grid units inside the watershed boundary and the
channel units are segments of channel between grid intersection points.
     From the contour lines, the elevations of the land surface at  the grid
points are determined (Figure 1.2).  These elevations, along with the  loca-
tions and bed elevation of the stream channel, are input to the developed  com-
puter program.  In addition to elevation data, vegetation and  soil  code
numbers can be input for each grid point (Figure 1.2).  The computer program
then performs the following functions:
     1.   The slope and the slope azimuth of each overland flow unit are com-
          puted.
     2.   It is assumed that the water flows in the opposite direction of  the
          slope gradient to the next overland flow unit or to  the adjacent
          channel.  Thus, water cascades from overland unit to overland unit
          and then into the channel system.  The program identifies the
          cascade sequence (arrows in Figure 1.1).
     3,   The computational sequence for the flow is established  by the
          program.  The method employed is simply to follow the logics of  gra-
          vity flow and flow continuity.
     4.   If data on the vegetation type, soil type, canopy cover density,  and
          ground cover density are available, the variations of these  factors
          inside a watershed can be established in the program.   This  is exe-
          cuted by decoding the vegetation and soil codes and  assigning pre-
          viously input parameters to each type code.  These parameters may
          include soil porosity, soil depth, and selected vegetation measures.
     In order to save computer storage capacity and processing time in the
water and sediment routing computations, an additional computer program to
combine small grid units into larger response units is developed.   With this
treatment, the flow is conceptually routed from overland flow  units to channel
units and to the selected watershed outlet.

-------
                                         1.8
Watershed
 boundary
                          Contour
                       Channel
Watershed
boundary
                                                                            • Channel
' \
1
J
1
1
\
X
N
i
X
/
/
\
x
—
i
X
/
/
\
X
—

/
^
1
/
:—
T
Flo
s
/
—
w dire
 a.   Topographic  features
                                                        b.  Segmentated watershed
              Figure  1.1   Example of watershed segmentation.

-------
                            1.9
         (a)  Topographic Map Contour Interval = 40'
         (b)  Soils Map Numbers are soil  type codes
    (c)  Vegetation Map Numbers  are  vegetation type codes
Figure  1.2  Input data for hypothetical watershed.

-------
                                      1.10

     This segmentation method is  essential  not  only in  water  and sediment
routing, but also  for  introducing the information  from  snowineIt computations/
landslide hazard mapping,  forest  fire hazard mapping, forest  inventory studies
and snow avalanche hazard  identification into the  routing model.  Moreover,  if
such factors as soil properties,  vegetation cover,  type of  management treat-
ment, or rainfall  vary within the watershed,  these variations can be handled
easily and with the least  manual  input  by segmenting the  watershed with a grid
system.  The developed segmentation method  provides input data on watershed
geometry and computational sequence required for the simulation model to pre-
dict water and sediment routing and yield from  small watersheds.
     Often the manual  determination of  the  response unit  is preferable for
non-computer oriented  personnel.   Such  a manual determination should follow
the similar logic  used in  the computer  segmentation method.  The flow path can
be drawn perpendicular to  contour lines.  The manual determination of hydro-
logic response unit is subject to the individual's  perception and is time con-
suming for applications to complicated  watersheds.   It  is recommended that the
manual determination be limited in application  to  small and simple watersheds.
     Another characteristic of the channel  system  that  must be numerically
defined is the wetted  perimeter-flow area relationships for each channel
segment.   This relationship is needed  for  use  in  water and sediment routing
in the channel.  The relationship is most often expressed in  the power form  as

          P = a^  1                                                   (1.1)

where  P  is the wetted perimeter,   A   is the flow area,  and a   and  b  are
statistically determined values.   Data  needed for  development of Equation 1.1
are measurements of the channel cross section.  These measurements are the
horizontal distance from a datum  mark or  a  bank to  a point  in the channel and
the elevation change between the  point  and  the  mark.  In  a  complex application
where many stream  cross sections  are involved,  the  values of   a   and  b  for
each channel segment may be found by a  fitting  routine  contained within the
simulation program.  As an alternative,   a
beforehand using a small calculator program.
simulation program.  As an alternative,  a   and  b   may be determined
     Geometric Representation  for Simplified Model.  The two  types  of
simplified watershed simulation use essentially the  same geometric

-------
                                      1.11


 representation.   The  watershed must be  subdivided in such a manner to allow

 approximation of  the  land surface by planes that extend to the watershed boun-

 dary and one or more  interconnecting channels.  The simpler of these two

 models uses  an "open-book" representation wherein the watershed is transformed

 into a single two-plane unit with a central channel.  The more complex model
 uses a number of  such units in combination with single planes and intercon-

 necting channel segments.
      At Colorado  State University these two simplified models have been

 developed and named ANAWAT and MULTWAT.  The former is an acronym for
.Analytical Watershed  Model and is the simpler single open-book representation.

 The latter name is an acronym for Multiple Watershed Model and is the more
 complex formulation.   These acronyms are only introduced here to simplify

 later reference to these two model approaches.  The basic method of trans-

 forming the  contour map geometry into planes and channels, however, is the
 same for both models.  This technique is described below for ANAWAT and then

 extended for the  MULTWAT case.  The process is illustrated by Figure 1.3 and
 presented in a step-by-step form below.

      1a.  Divide  the  watershed into units which can be considered homogeneous
           by using the available topographic, soil type, and vegetation type
           maps for the watershed.  The  size of the division is based on the
           resolution  needed and the availability of data.

      1b.  Divide  the  watershed using the channel system.  This division is
           often at the user's discretion, but should be based on homogeneity
           in the  channel segment or its contributing side slopes.  This homo-
           geneity may be the channel segment gradient or similar soil types on
           the contributing side slopes.

      2.   Delineate the main channel in the unit.  Extend the channels at
           least to the last distinct end points.  Such an end point is often
           noted as the last distinct "V" on the contour line for tributary
           channels.  In small watersheds determining the correct path along
           which to extend the channel may be difficult.  In larger watersheds
           the extension of the channel  may be apparent all the way to the
           basin boundary.  Therefore, the extension of the channel for
           measurement purposes is arbitrary.  A general consideration may be:

           (a)  Small  watersheds - extend the channel to the last distinct "V"
               and no further.

           (b) Medium sized watersheds  - extend the channel from the last "V"
               one-half the distance to the watershed boundary.

-------
                           1.12
                                    Line  E
   (a)    Original  Subwatershed  Topographic  Map
     (b)     Openbook Plane Representation
Figure 1.3.  Geometric representation of a subwatershed unit.

-------
                                 1.13
     (c)  Large watersheds - Extend the channel from the  last  "V"  to  the
          watershed boundary.

     No distinction is made on watershed size as this  is  a  factor  that is
     dictated by experience.  In general, however, a small  watershed  may
     have a maximum size of one hundred acres, medium  would be  100 to
     1000 acres, and large, anything more than 1000 acres.

     If a channel extension is made, the extension must perpendicularly
     cross the contour elevations to insure that the water  is  following
     the shortest path to the channel.  Measure the channel segment
     length.

3.   Sketch in the boundaries between contributing side slopes  to  the
     different channel segments.  The enclosed contributing areas  are now
     the watershed subdivisions.  Each channel has a left and  right sub-
     division when looking downstream.

4.   Determine the channel segment slope as the ratio  of  elevation dif-
     ference at the channel end points to the channel  length.

5.   Determine the area of the left and right contributing  subdivisions
     by using the channel as the dividing line.  For small  and  medium
     sized watersheds, an artificial dividing line may need to  be
     constructed as an extension from the assumed channel end  point to
     the watershed boundary.  Make sure this division  remains perpen-
     dicular to the topographic contours.

6.   Determine each subdivision width as sum of subdivision area divided
     by channel length as determined in Step 4.

7.   Subdivide the channel into several (5-20) equally spaced  sampling
     points.  At each sampling point lay out sampling  lines from the
     channel to the watershed or response unit boundary.  Sampling lines
     are drawn perpendicular to contour lines and represent flow lines
     that cross equipotential lines in a flow net.  The sampling lines
     are the potential routes water would follow when  flowing  across  the
     subdivision.  Determine the slope as elevation change  on  the
     sampling line.  Form the product of sampling line length  times
     slope.  Sum these products for the sampling lines in each  response
     unit.

8.   For small or medium sized watersheds, a single slope sampling line
     will be extended from the end point of the channel.  This  sampling
     line should coincide with the artificial dividing line constructed
     in Step 6.  Because the area above the assumed channel endpoint
     represents an overland flow plane, it is treated  as  being  equally
     divided between the two response units.  To do this, add  the  slope-
     length products for this sampling line to the summed slope-length
     products for each subdivision.  Also add the length  of the sampling
     line to the summed lengths of the sampling lines  of  each  sub-
     division.  These additions will incorporate the effects of this
     headwater overland flow plane into each of the subdivisions.

-------
                                      1.14
     9.   Determine  the  average  slope  of  each  subdivision as  the summed slope-
          length products  for  the  unit divided by the summed  sampling line
          lengths, or
               n
               I  S  x A
          —   i=1
          S = —	                                             (1.2)
                 n
          where  S  is  the  average  of  overland  slope,   n  is  the  number of
          sampling  lines,   S.   is the  slope  of  line   i,   and   Si.   is the
          length of line  i.  The consistent step-by-step procedure  presented
          above will provide  a  digitized watershed amenable to analysis by
          watershed modeling.
     An example of the  above  procedure  is presented  below.
     Example:  Small Watershed  (See  Figure  1.4).
          Area = 4.01 acres
          Length of channel to  "V" = 418 ft
          Slope of channel to "V" =  0.108
                                   Average  Width          Weighted*
                        Acres     	(ft)	        Average  Slope
          Left side   .  2.64          275.5                0.172
          Right side    1.37          142.4                0.205
          *includes artificial  extension 192.5  feet  long with slope of
           0.26.  Ten sampling  lines utilized.
     As mentioned earlier, ANAWAT has the capability of simulating  the storm
water runoff from a single plane or  from the  "open book" geometry as shown in
Figure 1.3.  MULTWAT classifies the  single-plane  units  as planes  and the "open
book" units as subwatersheds.   Storm water  runoff hydrographs from  the ANAWAT
units serve as inputs to  the  interconnecting  channel units.   Water  in the
channels is routed by using a numerical solution  to  the nonlinear kinematic
wave approximation.  A  method to account for  channel losses  due to  infiltra-
tion is included in the channel routing procedure.   The necessity of using a
numerical channel routing routine rather than an  analytical  routine is due to
the occurrence of kinematic shock.   The analytical solution  cannot  be applied
in situations where kinematic shock  occurs.
     There are four types of  response units in  MULTWAT:  (1)  a  single plane
ANAWAT unit, (2) an "open book" ANAWAT unit,  referred to as  a subwatershed,

-------
   M;i i n
                        1.15
                    Art i f\ c i .'i 1  (ili.'innel  lix tens ion
                                             S;i;n|) I i H
                                                1 i n c s
                                 (Ion! DMr I i nc
                    100  feet
Figure 1.4.   Important features for developing a small
              watershed representative  geometry.

-------
                                      1.16   .

(3) a channel, which  is  a  larger  channel  interconnecting  the  other  units,  and
(4) a connection.  A  connection unit  is used when only  the  lowest part  of  a
basin is being modeled and the response of  the upstream portion  of  the  basin
is input as a hydrograph recorded or  simualted at the gaging  station  dividing
the upper and lower parts  of  the  basin.   The method of  obtaining the  size  and
slope of planes and channels  was  given above.  As an example  of  the transfor-
mation of a larger, more heterogeneous watershed into a system of planes and
channels, Figure  1.5  shows a  map  of Walnut  Gulch, Arizona,  a  watershed
selected for development and  testing  of MULTWAT.  The boundaries of the planes
and subwatersheds are marked  to illustrate  how a large  watershed can  be repre-
sented by a system of these units interconnected by channel units.  Figure 1.6
shows a schematic diagram  of  Walnut Gulch Watershed, represented by planes,
subwatersheds, and channels.

     1.2.3  Model Components
     As mentioned earlier,  both the high-resolution and simplified  models  con-
tain essentially the  same  physical process  components;  however,  the implemen-
tation of the process varies  considerably due to the differences in water
routing methods.  The components  and  basic  model structure  are presented
below.  This discussion  is a  description  of existing models,  but may  be used
as a blueprint for the development of similar models.

     High-Resolution Model
     Once the watershed  has been  numerically defined by the above segmentation
procedure, overland flow units and channel  flow units in  the  watershed  can be
determined.  Simons and  Li (1975) developed a watershed sediment model  which
is primarily applicable  for surface erosion simulation.   It simulates the  land
surface hydrologic cycle,  sediment production, and water  and  sediment movement
on small watersheds.  Conceptually, the watershed is divided  into an  overland
flow part and a channel  system part.  Different physical  processes  are  impor-
tant for the two different environments.  In the overland flow loop, processes
of interception, evaporation, infiltration,  and overland  flow water routing to
the nearest channel are  simulated.  In a  channel system loop, water contri-
buted by overland flow is  routed.  A  flow chart presenting  the interrela-
tionship of these processes is shown  in Figure 1.7.  A  brief  summary of the
components is given below.  The model described in Figure 1.7 also  contains
sediment routing and erosion  components.

-------
           0     I     2
 4
-j
                                                      Legend'.

                                                      Watershed  Boundary

                                                      Subdivision Boundary

                                                    •  Major Channels
                  Scolein  miles
Figure 1.5.   Response units for Walnut Gulch,  Arizona, watershed.

-------
                               1.18
    SW-32
    CH-7
 PL-2l|PL-22
    CH-6
  PL-I9|PL-20
   CH-9
PL-25JPL-2S
   CH-IO
PL-27IPL-23
                             CH-8
                          PL-23|PL-24
                             CH- 2   j
                          PL-l5ipl_-!4 j
                                             SV/-29
CH-I
PL-ll|p
,_-!2
Figure 1.6.  Schematic diagram of the Walnut Gulch response units.

-------
                     1.19
  t
Figure 1.7.   Flow chart for the watershed sediment
             and routing model.

-------
                                       1.20
     Overland Flow  Loop
     There are  three  components  in the  overland flow loop:   interception,
infiltration, and overland surface water.
     Interception Component.   In this component the  interception amounts  due
to the crown and forest floor  are computed and the net rainfall is  determined
from the rainfall input.   The  interception loss includes  the constant inter-
ception storage and the continuous evaporation from  the interception surfaces.
The evaporation is  usually negligible during  the storm.  The interception
storage is formulated to  be a  funciton  of  canopy cover density, ground cover
density, and vegetation type.
     Infiltration Component.   This component  of the  model simulates the pro-
cess of infiltration.   The infiltration rate  is computed  by an approximation
of Darcy1s Law assuming that a distinct wetting front exists and is formulated
to be a function of saturated  hydraulic conductivity,  average capillary suc-
tion pressure, soil porosity,  antecedent moisture content,  and moisture con-
tent in the wetted  zone.   Therefore, the rate of rainfall excess can be
determined from the net rainfall and infiltration rates.
     Overland Surface  Water Routing Component.   With this component the
overland surface water runoff  resulting from  the mean rainfall excess is
routed to the nearest  channel.   The routing procedure is  based on the con-
tinuity of water, a momentum equation of kinematic wave approximation,  and  a
set of resistance functions for  different  hydraulic  conditions.  The total
resistance to flow  is  assumed  to be a sum  of  the drag resistance due to ground
cover and the shear stress acting on the soil bed.   The computation is  carried
out by a nonlinear  finite-difference scheme developed by  Li et al.  (1975a)  and
the computation results include  the mean flow depth,  bed  shear stress and flow
discharge at computation  points  as a function of time and space point.
     Channel Water  Routing Component.   This component of  the model  routes the
water down the creeks  in  the channel system and computes  the hydrograph at  the
watershed outlet.   The lateral water inflows  to the  channel system  are  the
overland surface water flows.  The channel  water routing  procedure  and  the
finite-difference scheme  are similar to those used in the overland  flow loop.

     Simplified Models
     The simplified models contain the  same physical  processes listed above,
but these routines  are applied to subunits  that are  in general much larger

-------
                                      1.21

than those of the high-resolution model.  In addition, these routines are
uncoupled in the sense that they are used to calculate the process response
for the entire event on a given unit before passing on to the next physical
process.  For example, infiltration for the entire storm is calculated before
passing the entire rainfall excess function on to overland flow routing.  This
is as opposed to the time step-by-time step calculation of the high-resolution
model.  Therefore, some resolution is sacrificed for a gain in computational
speed.
     The physical processes modeled for each type of unit are shown  in Table
1.1.  The processes involved in the plane and subwatershed units are identical
except for the analytical channel routing performed for the subwatershed
units.  The only processes considered for the channel units are numerical
routing and channel infiltration.
     Much of the rain falling during the first part of a storm is intercepted
by the vegetal ground cover.  Precipitation intercepted by vegetation or other
ground cover eventually evaporates, and the amount of rainfall reaching the
soil surface is less than the recorded amount.  The amount of interception
loss depends on the percentage of the ground that is covered by canopy and
ground cover, and their respective water holding capacities.  It is  assumed
that interception starts at the beginning of a storm and continues until the
potential intercepted volume is filled.
     A portion of the rainfall reaching the ground moves through the soil sur-
face into the soil.  This process is defined as infiltration.  The model used
to simulate this process is based on the Green and Ampt infiltration equation
(Li, Simons and Eggert, 1976).
     Using an approximate explicit solution to the Green-Ampt equation for
time-varying rainfall given by Eggert, Li and Simons (1979), a function for
infiltration with respect to time is developed.  Thus, the infiltration
occurring during a selected time period can be determined if the soil charac-
teristics are known.
     An analytical solution to the continuity, momentum, and cross section
geometry equations is used to route water in the plane and subwatershed units.
The method presented is identical to the routing scheme presented by Simons,
Li and Eggert (1977).  However, the routing of water with the conditions of

-------
                                1.22
Table 1.1.  Physical Processes Considered for Each Type of  Unit
                     Plane
Subwatershed
                 2.  Overland
                    Infil-
                    tration

                 3.  Analytical
                    Overland
                    Routing
2. Overland
   Infil-.
   tration

3. Analytical
   Overland
   Routing

4. Analytical
   Channel
   Routing
  Channel
Physical
Processes
Considered
1. Inter-
ception

1. Inter-
ception

1 . Channel
Infil-
tration
2.  Overland
   Channel
   Routing

-------
                                      1.23
                                           o-
continuous infiltration is developed and incorporated.  Due  to  the  assumed
"open book" geometry, both overland and channel routing are  required.   Excess
rainfall, the amount of rainfall not intercepted or infiltrated,  serves as the
input to the overland flow routing scheme.  Results of the overland flow
routing are then used as the lateral inflow into either a subwatershed or a
channel unit.
     The partial differential equations for overland  flow are solved by the
method of characteristics.  The characteristic paths  along which  the solution
is valid can be calculated in either the upstream or  downstream direction.
This allows a user to find the discharge at the downstream boundary for any
given time.
     A numerical procedure for water routing developed by Li, Simons and
Stevens (1975) is used for the channel units.  Routing is accomplished by a
second-order nonlinear scheme developed to  numerically solve the  kinematic
wave equation.  A numerical routing procedure rather  than an analytical proce-
dure is used for the channel units because  analytical solutions are restricted
by the formation of kinematic shock.  Kinematic shock results when  charac-
teristic paths intersect.  Physically this  may be described  as  a  faster moving
parcel of water overtaking a slower moving  parcel of  water as they  both travel
downstream.  Analytic solutions for problems that have kinematic  shock display
discontinuities in the hydrographs.  Due to this restriction, a simple numeri-
cal routing procedure is necessary for the  channel units.
     Stability of a numerical procedure refers to whether the computational
errors, due to the finite-difference approximation of the partial differential
equations, accumulate to an unbounded error.  If the  errors  do  not  grow
unbounded, the procedure is stable.  The numerical scheme that  is used has
proved to be unconditionally stable and can be used with a wide range of time
to space increment ratios without loss of significant accuracy.  However, the
physical significance of the time and space intervals should be considered
when selecting their values.
     An infiltration routine is combined with the numerical  channel routing
procedure to account for channel seepage losses.  The channel infiltration
procedure is similar to the overland infiltration procedure  because both are
based on the Green-Ampt infiltration equation  (1911). The major  difference
between the two routines is that the depth  of the water in the  channel
situation cannot be neglected as in the overland situation.

-------
                                       1.24
     This  description has listed the components of a MULTWAT model.   The same
description applies  to the simple ANAWAT model up to the  numerical channel
routing scheme.   Since the single open-book representation does not  require an
upstream inflow to any channel  segment,  a numerical channel routing  is not
required.

1.3  Procedures for  Evaluation  of a  Monitoring Network
     The methodology discussed  in this workshop combines  graphical,  statisti-
cal, and physical process modeling techniques  to analyze  and evaluate existing
and proposed data collection networks.   Graphs are used extensively  since they
rapidly display the  relationships between data types,  sampling sites, data and
time.  Plots of input and output measurements, such as rainfall and  runoff,
water and  sediment discharge, and nutrient concentrations and soil depth, per-
mit comparison of the physical  link  between the measured  quantities.   Analyses
based on the distance between stations at a fixed sampling interval  show the
spatial variation in data while analyses based on time at a selected site show
the temporal variation of the data.   A combination of  the two allows a better
understanding of  the network and the data.   Similarly, mass accumulation
curves, such as used for  rainfall, show  both temporal  and spatial  rela-
tionships  between sites.   Trend graphs and data compared  to time allow
appraisal  of key  sampling times and  uptrend or downtrend  shifts in values.
     Graphic procedures provide rapid insight  into a data collection system
when there is existing information at several  sites.   However,  for sparse or
proposed systems this type of information may  not exist.   In such  cases,  use
of physical process  models can  aid design and  evaluation  by simulating and
analyzing  data at selected sites and times.  This information can  be  used in
lieu of the actual data if the  physical  process model  accuratley represents
the system being evaluated.   Physical process  models  can  also provide useful
information regarding system variability,  travel time  of  floods, magnitudes
and durations of flow,  sediment transport,  nutrient movement,  changes in soil
moisture,  and fluctuations in climate.   Not only can process models  be used to
simulate the output  data  but also to detect and check  the accuracy of input
data.
     By combining visual  techniques  including  graphical presentation  and use
of physical-process  models,  a unified approach to evaluate data collection
networks can be achieved.   in this way,  collection networks can be evaluated.

-------
                                      1.25
This method is applicable to many situations.

     General data network evaluation procedures consist of  the  following

steps.

     1.   Data needs should be identified for intended application  or
          modeling.

     2.   Data needs should be compared with measured data.

     3.   Data gaps must be identified, and it must be determined if missing
          data can be derived from the measured data or from  other  records.

     4.   Graphical and statistical techniques should be utilized to compare
          data between sites at different sampling intervals  and with  time.
          Statistical techniques include autocorrelation, cross correlation,
          maximum values, minimum values, means, standard deviations,  ranges
          of data, linear and nonlinear relationships between data, and order
          of magnitude comparisons.  Graphical comparisons  can  be time series
          plots, such as hydrographs auto and cross-correlograms relating
          correlation coefficients with time, space, or both  (Lecture  3),
          dimensionless mass accumulation curves, changes in  magnitude of a
          measured variable with location, bar graph distributions, and rela-
          tionships between two variables.

     5.   Correlograms and other graphical and statistical  aids can be used  to
          check on the spatial and temporal adequacy and the  physical  signifi-
          cance of the data.

     6.   Erroneous data should be checked, eliminated, or  modified so physi-
          cally inconsistent data are not used in further analyses.

     7.   If data are not available at certain locations and  for specified
          times, then mathematical models may need to be employed to generate
          records for those sites or times.  For example, if  a  discharge
          measurement station is to be built at a certain location  or  if a
          current station records stage height every hour,  a  stream flow simu-
          lation model can generate hydrographs at the station  resulting from
          different levels of storm input for analysis.

     8.   The simulated data base by physical process simulation models may  be
          used to conduct the same analyses as listed in Step 4.

1.4  References

Grimsrud, G.P., et al., 1976, User Handbook for the Allocation  of Compliance
     Monitoring Resources, Office of Air, Land, and Water Use,  USEPA,  Document
     EPA-600/5-76-012, Washington, D.C., December, pg. 9.

-------
                                       2.1

II.  CONCEPTUAL DESIGN OF A MONITORING SYSTEM
2.1  Introduction
     In order for any monitoring network to be designed and implemented, the
overall objective as well as the monitoring objective should be analyzed to
assess what type of data is required to fulfill these objectives.  An overall
objective is of broad scope; for example, a water supply system or a sewage
treatment system.  A much smaller objective which is formulated under the
overall objective., is the monitoring objective.  Examples are:  streamflow
measurement; water quality measurements; precipitation measurements; etc.  It
must be kept in mind that the overall objective determines the nature of the
monitoring objective.  For example, if the overall objective was enforcement
of water quality laws, the monitoring objective would be to monitor the water
quality variables in the jurisdiction area; but how is the monitoring to be
done?  In this case, sampling every night may miss industrial pollution loads,
and monitoring upstream of industrialized areas would do the same.  Here the
overall objective conceptually defines the sampling frequency and spatial
location of the monitoring network.  The exact number, location and sampling
frequency for monitoring stations must bow to social, political, legal and
financial considerations.
     When computer modeling is the overall objective (or an objective on a
higher level than the monitoring objective), there are certain specific data
which are required by the model(s) and these needs must be fulfilled through
the monitoring objective.  In the light of any constraints placed on the moni-
toring network (financial, legal, etc.), data measurements may be made
directly or indirectly.  These types of measurements will be discussed after
describing data needs.  Details of performing direct measurements of hydro-
logic parameters are discussed in following sections.

2.2  Data Needs
     2.2.1  General
     Data for water, sediment and chemical yields from agricultural lands can
be divided into several groups including watershed and channel geometry, soil,
vegetation, climate and meteorology, hydrology, hydraulics, and man's
influence.  As models vary so do the specific inputs for each.  Specific needs
will be discussed in following subsections.

-------
                                       2.2

     Data needs should not be determined carelessly because of the time,
money, and instrumentation necessary to collect information.  Careful con-
sideration must be made so that each piece of information is justified and
prioritized with respect to other data.  Modeling needs are usually dictated
by the model inputs.  So, the person using the model must know the essential
model inputs.
     Typical data for modeling are listed in Table 2.1.  Although general,
this list shows there are numerous factors' to consider in designing a data
collection system.  Typical data collection methodologies are listed in Table
2o2.  Although the list is brief, it does indicate that a number of measure-
ment devices are needed for data collection.
     Data for modeling of rainfall, runoff, sediment yield, dissolved oxygen,
and nutrient transport in agricultural watersheds require complex collection
networks.  Seldom are enough data collected to fully meet most users' needs.
Consequently, some models may be untested or unverified.  Therefore, it is
important to define data needs, data priorities, and data availability to
determine linkage between data collection and ultimate use.  The first step is
to define the specific data needs.

     2.2.2  Specific Needs
     Data needs vary from model to model.  For example, the models being
developed at Colorado State University that describe rainfall, runoff, sedi-
ment yield, dissolved oxygen, and nutrient processes require specific infor-
mation (Simons et al., 1979).  Four separate models comprise the overall
mathematical model.  The primary model is a water balance and evapotranspira-
tion model that computes infiltration of layered soils and operates on a daily
basis in the watershed.  If a rainfall event occurs on a certain day, control
is passed to an event-based water and sediment routing and yield model that
used antecedent conditions from the water balance model.  In addition to these
hydrologic-hydraulic models there are two water quality models.  One is for
dissolved oxygen and thermal loading and the other is for nitrogen and
phosphorous.  These models also use inputs from the two water and sediment
models.  As indicated in Table 2.3, data needs vary among models and not all
data are used for inputs.  Some are used for calibration and/or verification
of the model.  Fortunately, use of a physical process model allows calibration
with a limited number of events with measured data.

-------
                                       2.3
       Table 2.1.   Data Parameters for Modeling Water and Sediment Yield
   I.   Watershed and Channel Geometry Data

       1.  Area of watershed
       2.  Slopes and  lengths of channels and  land surfaces
       3.  Channel cross sections
       4.  Geological  or man-made control
       5.  Watershed and channel network

  II.   Soil Characteristics

       1.  Soil type
       2.  Distribution of types
       3.  Porosity
       4.  Grain size  distribution
       5.  Infiltration characteristics
       6.  Soil moisture data->.

 III.   Vegetative Cover Data

       1.  Density or  coverage
           a.  Canopy  cover
           b.  Ground  cover
       2.  Cover interception of rainfall
           a.  Canopy  cover
           b.  Ground  cover

  IV.   Climatic Data

       1.  Rainfall hyteographs
       2.  Snowmelt rate
       3.  Evaporation rate
       4.  Air temperature
       5.  Humidity
       6.  Wind
       7.  Solar radiation

  V.   Hydrologic and Hydraulic Data*

       1.  Water discharge hydrographs
           a.   Timing
           b.   Peak
           c.   Volume
       2.  Resistance to flow parameters
       3.  Sediment yield
       4.  Grain size analysis of transported sediment

*Most of this catagory of data are required for model calibration and/or
verification.

-------
                                        2.4
                  Table 2.2.  Typical Data Collection Methods
      Type of data
                Methodology
 Rainfall

 Evaporation
 Solar Radiation
 Air Temperature
 Soil Temperature
.Infiltration
 Flow Discharge

 Water Surface Elevation

 Flow Velocity

 Sediment Discharge

 Flow Resistance Parameter

 Location of the Channel

 Channel  Cross Section Geometry

 Channel  Bed Profile

 Rock Outcrops and Man-made Control

 Bed and  Bank Samples
 Watershed Geometry
 Vegetation Distribution

 Soil Type Distribution

 Soil Moisture

 Sediment Source
 Measured by automatic  recording  rain
 gauge or meteorological radar
 Measured by evaporation pan
 Measured by radiometer
 Measured by thermometer
 Measured by thermometer
 Measured by infiltrometer
 Measured by weir, current meter, or
 rating table for a calibrated section
 Measured by an automatic recording
 bubble gauge or in a stilling well
 Measured by current meter or dye
 dilution method
 Measured by automatic  pump sampler or
 standard depth-integrating samplers
 Manning's equation, comparison to USGS
 publication, equation  for 'n1
 Measured by plane surveys or from
 USGS maps or aerial photographs
 Measured by hand level-survey rod,
 sag tape, or transit-stadia rod
 Measured by sonic soundings and
 transit-stadia rod
 Measured by geological survey or
 from available geological maps
 Determined by composite soil samples
 Determined from topographic maps
 Determined from aerial photographs or
 a vegetation map
 Determined from soil survey maps and
 field investigations
 Measured by neutron probe or gypsum
blocks
Color infrared or black and white
photographs

-------
                                       2.5
  Table 2.3.  Data Needs for Colorado State University Physical Process Models

Water
balance
Data group model
Geometry and Channel Data
Watershed area
Length of overland slopes X
Width of overland slopes X
Gradients of overland slopes
Length of channel sections
Gradient of channel sections
Measured, representative channel
Water and
sediment
storm model
X
X
X
X
X
X
X
Dissolved
Nutrient oxygen
model'. model
i.. •
X X
X X
X X



    cross sections
  Elevation of watershed             X
Soil Data
  Distribution of  soils              X
  Types of soils                      X
  Number of soil layers              X
  Thickness of layers                 X
  Initial water content of  layers    X
    or top layer
  Saturated hydraulic  conductivity   X
    of each layer  or top layer
  Tensiometer  measurements            X
    (desorption curve)  for  each layer
  Temperature  for  tensiometer  data   X
  Field moisture capacity for  each   X
    layer
  Intrinsic permeability of top layer
  Porosities of soil layers on top   X
    layer
  Specific  gravity of  soil
  Temperature  of top layer
  Thermal conductivity of soil
  Grains  size  analysis  of top  layer
X
X
X
             X
             X
                         X
                         X
X
X
X
X

-------
                                        2.6
                            Table 2.3.  (Continued)
         Data group
 Water
balance
 model
 Water and
 sediment
storm model
Nutrient
  model
                                                                     Dissolved
                                                                      oxygen
                                                                       model
 Soil  Data  (continued)
   Concentrations of nitrogen  and
    phosphorus  species  in  soil
    and  litter  layer
 Vegetation Data
   Types                              X
   Distribution                       X
   Density of ground cover            X
   Density of canopy cover            X
   Storage of ground cover            X
   Maximum and minimum storage        X
    of canopy cover
   Albedo of vegetation               X
   Yearly growth cycle of canopy      X
   Average leaf length of dominant    X
    species
   Maximum and minimum leaf area      X
   Root cross sectional area per      S
    unit area of soil in each layer
   Fraction of roots in each layer    X
   Annual litter input to ground
    surface
   Litter layer thickness
   Average litter temperature
   Nitrogen content of litter
   Phosphorous content of litter
   Specific gravity of litter
Climatic Data
  Daily solar radiation              X
  Average daily temperature          X
  Average daily humidity or          X
     vapor pressure
               X
               X
               X
               X
               X
               X
                            X
                            X
                            X
                            X
                            X
                            X
                            X
                             X
                             X

-------
                                        2.7
                           Table 2.3.  (Continued)
        Data group
                                   Water
                                  balance
                                   model
        Water and
         sediment
       storm model
Nutrient
  model
Dissolved
 oxygen
  model
Climatic Data (continued)
  Total daily precipitation          X
  Average wind speed                 X
  Air pressure—for year as          X
    function of altitude
  Specific heat of air               X
  Rainfall storm hyetographs         X
  Nitrogen species input from
    rainfall
  Surface water temperature
Hydrologic and Hydraulic Data
  Storm and daily runoff hydrographs X
  Overland flow resistance
  Channel flow resistance
  Storm sediment yield
  Sediment yield from litter layer
  Runoff temperature
  Grain size and analyses of sediment
  Sediment detachment coefficient
    for rainfall and runoff
  Dissolved oxygen content in runoff
  Nutrient concentration in runoff
  Rate of addition of BOD in runoff
Man's Influence
  Cropping patterns
  Land use changes
  Timbering activities
  Modification of drainages
  Nitrogen application
  Phosphorous application
                          X
                                     X
            X
            X
            X
            X
            X
            X
                                     X
                                     X
Man's influence may affect all of the
physical qualities controlling water
runoff, sediment yield, and nutrient
transport from watersheds.  The effects
can be quantitized by assessing the
impact of man's activities on the
different measurable variables.

-------
                                       2.8

     It is not always possible or necessary to collect every piece of iden-
tifiable data.  Several types of data can be estimated or synthesized from a
single measurement or description as well as from experience or data from a
nearby watershed.  For example, a soil type description such as sandy loam or
sandy clay allows initial estimates of erosion potential, porosity, moisture
conditions, and hydraulic properties.  These estimates may be refined later
with measurements or through model calibration.  Sensitivity analyses of the
model with respect to the different inputs will aid in determining the most
important data.

2.3  Direct Measurements
     2.3.1  General
     Direct measurement of a process is defined as the procurement of data for
a variable by measuring the variable itself.  An example of this is measure-
ment of precipitation by use of a rain gage.  Direct measurements are the most
important type of data since any model based upon the. measured data may be
calibrated with the use of the direct measurements.  For example, rainfall-
runoff models may be calibrated on observed storm rainfall and the resultant
hydrograph.  Often this calibration occurs through model parameters which are
vaiables that are measured indirectly or insufficiently.  Indirect measurement
will be treated in the next section.  Insufficient measurement of a variable
means exactly what its name implies, that there is not enough information
about the variable to support concrete statements, but that the information
available is used for generalized statements.  For example, soil properties,
(conductivity, porosity, etc.) may be measured at two or three locations in a
watershed and then they (or their averages) may be assumed to be represen-
tative for the entire watershed.  Due to this coarse treatment of variables,
model calibration occurs through the adjustment of indirectly or insuf-
ficiently measured variables.
     Considerable care must be taken to obtain accurate data.  Proper applica-
tion of the techniques of data gathering are an important feature of any data
collection system.  Accepted methods for direct measurement of stream flow,
water quality and meteorologic data are now discussed.

     2.3.2  Collection and Processing of Surface Water Data
     The USGS has formulated standard methods for stream flow data collection.

-------
                                       2.9

These methods involve the general operation and maintenance of a gaging sta-
tion such that data are available for establishing the stage-discharge rela-
tion and other flow characteristics at a given location on a river or stream.
Accomplishing this objective includes:
   - datum control to maintain the accuracy of stream flow records
   - Maintenance and collection of a complete and accurate continuous stage
     record
   - current meter measurements at a range of stages to adequately define
     yearly fluctuations
   - development and continual verification of the stage-discharge relation to
     reflect current physical conditions
   - computation of mean daily discharges, volumes, and peak flow discharges

     2.3.2.1  Gage Datum
     Maintaining gages at correct elevations requires periodic checking of all
station reference marks and gages with a surveying level.  Levels should be
run at least once a year regardless of the apparent permanency of the gage or
reference mark.  Greater frequency of verification is required at stations
where it is known or suspected that poor foundations or vertical movement
exist.

     2.3.2.2  Maintenance of a Gaging Station
     Equipment maintenance is an important aspect in obtaining accurate data.
A visual inspection can often identify potential problems that might prevent
continuation of measurement activities.  The required maintenance to resolve
problems can be classed as minor or major maintenance.  Minor maintenance
includes the minor repairs necessary to keep the gaging station operational,
safe, and to maintain its appearance.  Major maintenance is defined as repair
or services necessary to make the station operational after being inoperative
due to vandalism, damage or major stream channel changes.
     Minor repairs include, but are not limited to, replacement of defective
recorders and timers which cannot be repaired in the field, replacement of
outside staff gages which have been damaged by debris or vandalism, relocation
of bubble-gage tubing and orifices (temporarily in order to get a continuing
record, and permanently when field schedules permit), replacement of defective

-------
                                      2.10
floats, and repainting and repairing the shelter as required.  Maintenance of
shelter and surrounding area includes keeping the shelter clean, oiling
hinges, locks, and hasps, clipping weeds and grass around the station and in
high-water measuring section to ensure more accurate discharge measurements,
removing debris, and generally keeping the area clean.
     Major repairs include, but are not limited to, extensive rebuilding of
the gage house, replacement of stilling wells, and complete replacement of
instrumentation.  If the station is destroyed, a temporary reference point
should be set and a local observer hired (if possible) to take daily or more
frequent gage readings until the station can be repaired.  This is par-
ticularly important if the gage is inundated or destroyed by flood so that
these gage readings be obtained during hte flood or on the recession to reduce
the period of missing record to a minimum.

     2.3.2.3  Recording and Documentation of Data
     Standard recording procedures and documentation are an essential aspect.
of producing quality data.  The data and information collected initially and
throughout station servicing shall include:
     a.   Station name, in full.
     b.   Date:  month (name, not number), day, and year.
     c.   Time:  watch time using 24-hour time system.
     d.   Pen time of analog recorder, punch time on digital recorder.
     e.   Types of inside and outside gages and gage height.
     f.   Gage height by float tape or manometer dial, the reference gage, and
          the recorders.
     g.   Initials of contractor( s).
     h.   Additional remarks related to station conditions, including control
          conditions.

     2.3.2.4  Servicing Stage Recorders
     Servicing of stage recorders is performed prior to discharge measurements
to insure proper operation after new tapes are installed.  Following this pro-
cedure minimizes the possibility of record loss due to common mistakes (i.e.,

-------
                                      2.11

leaving pen up or clock stoppage after winding).  The following procedures are
useful as a guide to servicing analog and digital recorders:

     a.   Check to see if the clock and/or timer is running and mark the
          recorder charts.

          1.   By marking the point where the pen or pencil is resting on the
               strip-chart recorder (adjust timer if needed or replace if
               timer has been malfunctioning), or

          2.   By watching the instrument punch the digital tape and drawing a
               line across the digital tape/ using the top of the punch block
               as the straight edge.

     b.   Compare gage readings and recorded gage heights and check to see if
          there is a malfunction of the equipment such as:

          1.   If the stilling well intakes are plugged

          2.   If there are any malfunctions in the gas-purge system of the
               bubble gage or if the orifice lines are plugged

          3.   If there has been any oil loss from an oil cylinder, and

          4.   If there are any inconsistencies between the recorded and
               reference gage heights, note them so that adjustments can be
               made to the recorded gage height.  In stations equipped with a
               bubble gage, check the counter.

     c.   Records shall be removed from each recorder at intervals not to
          exceed two months.  Change the record from each recorder as follows:

          1.   Analog recorder

               a.   At the time of initial inspection the time shall be indi-
                    cated by a vertical mark of the pen or pencil.  The float
                    tape or cable should be grasped between the float and the
                    float wheel and lifted a few hundredths and gradually
                    released.  The mark should not be made by rocking the
                    float wheel because it places undue strain on the float
                    wheel bearing.  If equipped with a bubble gage, the
                    contractor shall mark the chart by pushing the up or down
                    switch so that the pen trace is changed a few hundredths.

               b.   Advance the chart about one inch.  Run a reversal mark and
                    adjust if necessary.

               c.   Blot the ink at the end of the recording to prevent
                    smears.

               d.   Identify the chart by printing the name of the station,
                    date, time, gage height readings and initials of person.

-------
                            2.12


     e.   Cut and remove the chart, leaving at least one full day in
          addition to the day of the visit on the end of the chart
          to provide ample room for joining the pieces in the
          office.

     f.   Wind clock or negator spring.

     g.   Check the amount of paper left on the supply roll and make
          certain that there is more than enough to last the inter-
          val between visits.

     h.   Flush intakes or purge orifice line.

     i.   Rethread the chart into take-up rolls and run reversals,
          read all gages again, and record all data and observations
          on the chart.

     j.   Reset pen to agree with the gage height indicated by the
          reference gage, and advance chart to agree with watch
          time, and make a vertical mark.  Be certain that pen is
          not in reversal.

     k.   Check the ink supply of the pen and replenish it if
          necessary.

     m.   Unroll and examine the chart in an effort to detect any
          recorder malfunction or clock stoppage since the last
          visit, and if found, note range line.

2.   Digital recorder:  When arriving at a station, look at the face
     of the timer to see if a punch would occur in about the next
     five minutes, the time it would take to remove the punched
     record and reset the tape.  If so, it would be better to wait
     until the punch has occurred before starting the tape removal
     procedure.  Fill in the removal block of the inspection slip.
     When ready to remove the punched record, follow the steps
     listed below.

     a.   Turn the take-up roll to advance the tape about nine
          inches beyond the last punch, cut the tape with a knife or
          razor blade just above the upper paper guide bar.

     b.   Slip the roll of punched tape off the take-up roll.

     c.   Note the date, watch time, clock time and gage height on
          the tape just removed but do not take the time for ela-
          borate notes until after the tape has been reset.

     d.   Check battery voltage or amperage and record.  Replace
          battery if no load voltage is less than 7.0 volts.

     e.   Flush intakes or purge orifice line.

-------
                                 2.13

          f.   Thread the paper onto the take-up roll.  Care should be
               exercised not to elongate the large feed holes in the tape
               on the pins protruding on the tape drive drum by turning
               the take-up roll too hard.  Advance the tape until the
               printed line on the tape just above the punch block is
               about eight readings earlier than watch time.  (On the
               15-minute tape, this would be two hours earlier than watch
               time).

          g.   Record the station name, station number, date, time and
               gage height on the beginning of the new tape and start new
               inspection slip.

          h.   Reset the punch mechanism, if necessary, to agree with the
               gage height indicated by the reference gage.

          i.   Punch sufficient test punches so that the next punch
               caused by a properly set cam will be at the correct time.

          j.   Draw a penciled line across the top of the punch block so
               that later the test punches can be separated from the
               automatically recorded data.  If the preset action has
               already taken place before the line was drawn, the line
               will pass through the last test punch; if not, the line
               will be above the last est punch.  Care must be exercised
               not to tear the paper with the pencil.

          k.   After resetting the tape, record the station name and the
               remaining notes on the tape just removed.  At this point
               take time to superficially examine the last portion fo the
               tape just removed for any obvious trouble which would call
               for action before leaving the station.  This examination
               should include rolling the tape back about three feet to
               check damaged or poorly spaced holes in the tape or places
               where feed holes are skipped (these can be seen most
               easily by looking at the reverse side of the tape).  Gross
               time errors and timer stoppages can be found by checking
               day numbers against calendar days.  Attach inspection slip
               to removed tape with a rubber band.  Prior to leaving the
               station, check to see that there is sufficient tape on the
               supply roll.  If the amount of tape on the supply roll is
               in question, remove the left flange on the supply roll
               holder and measure the thickness of the paper remaining.
               The following table (Table 2.4) gives the approximate
               thickness against days of tape remaining.

          m.   When visiting the station but not changing tape or chart,
               note recorder readings and base reference gage readings on
               tape leader and chart, but do not advance tape or chart.

d.   If the station consists of a stilling well with a float-operated
     recorder,

-------
                     2.14
Table 2.4.  Days Remaining on Supply Roll
Thickness of
remaining tape
on supply roll
1/4 inch
7/16 inch
9/16 inch
11/16 inch
5 min
10
20
30
40
Days remaining on supply roll
Reading Frequency
15 min 30 min 60 min
30
60
90
120
60
120
180
240
120
240
360
480

-------
                                      2.15


          1.   Check the float for leaks.

          2.   Check the float-clamp screw to make sure that there can be no
               slippage of the float tape where it joins the float*

          3.   Check the well for unduly large accumulations of sediment and
               remove such material.

          4.   Check the depth of oil in the oil tube, if there is one, to
               detect any oil leaks and if any oil should be added.

          5.   Flush the intakes regularly if the well is equipped with a
               flushing system, or if there is no such system, force clean the
               intake with a plumber's snake, and

          6.   If there has been a high discharge since the last visit, check
               the stilling well, both inside and out, for high-water marks as
               a check on the peak stage shown on the recorder.  If the equip-
               ment malfunctioned since the last visit, the high-water mark
               information is used to estimate missing record.  After this
               check, clean the marks off to prevent confusion with later
               high-water marks.

     e.   If the station is equipped with a bubble gage sensor, there are
          several other checks that are necessary:

          1.   Inspect the bubble orifice to make sure it is not buried by
               sediment.

          2.   Keep a log of gas-feed rate, gas consumption, and gas-cylinder
               replacement to insure a continuous supply of gas and to help
               check for leaks in the system, and

          3.   If a high discharge has occurred since the last visit, look for
               a high-water mark near the base reference gage as another check
               on the recorded peak stage.   Record gage height of outside
               high-water mark on measurement front sheet.

     After making the necessary measurement, the initial steps (involving
basic checks on the operation of the recorder) are repeated to insure opera-
tion of the recorder.
     2.3.2.5  Discharge Measurements
     Discharge measurements consist generally of making velocity and depth
measurements at a number of verticals in a channel cross section near a stream
gage.  The basic equipment for most conditions includes a current meter for
measuring velocity and a wading rod for measuring depths and holding the
current meter or some type of hanging weight and current meter assembly when

-------
                                      2.16

measurements are made from a boat, bridge or cablecar.  When unusual con-
ditions prevail such as very small flows, a small flume may be used.  Other
conditions may best be gaged by dye dilution or float techniques.  When direct
discharge measurements are either missed or impossible due to flooding,
indirect techniques are used such as the slope-area method.
     After servicing of the gaging station, preparation for the discharge
measurement begins.  Sometime before the measurement begins, the contractor
would have determined the method to be used (wading, cablecar, boat, bridge,
etc.) beforehand so as to have all necessary equipment on hand.  Possibly a
specific location would have been given by the USGS.  If not, a proper section
must be selected by the contractor.  The section where the actual measurement
is to take place should: (1) be in a stable location to minimize scour and
fill, (2) not be where a large amount of turbulence or backwater conditions
exist, (3) be close to the gage, (4) and be in a relatively straight reach for
the most uniform flow.  These conditions may not all be possible, but all
efforts need to be made to insure that discharge measurements are as accurate
as possible.
     At the beginning of the measurement, after the equipment is prepared, the
stream gager prepares the discharge measurement notes.  The required infor-
mation includes the following:
     1.   Station
     2.   Data
     3.   Party
     4.   Meter information:  date rated, spin time
     5.   Type of measurement (wading, boat, etc.)
     6.   Gage height at beginning and end of measurement (during, if stages
          are noted to be changing)
     7.   Location of section with respect to the gage
     8.   Quality of measurement (excellent, good, fair, poor)
     9.   Cross-section information (bed forms, uniformity, etc.)
    10.   Air and water temperature
    11.   Control
    12.   Remarks
    13.   Gage height of zero flow
During the measurement, depths, widths, velocities, horizontal angles, etc.
are recorded.

-------
                                      2.17
     2.3.2.6  Equipment
     The current meter generally employed by the USGS is the Price AA current
meter.  This meter is a vertical axis meter with six cone-shaped cups which
rotate with the stream velocity.  Each meter has been calibrated in a test
flume and a tally is made which relates the number of revolutions of the
bucket wheel in a given time increment (ranging from 40 to 70 seconds) to the
velocity of the flow.  When shallow depths are encountered, the Price Pygmy
meter can be used.  It is scaled to be 2/5 as large as the AA meter and does
not have a tailpiece.
     The standard Price AA current meter has an eccentric cam which makes an
electric contact once each revolution and a penta-gear reduction which makes
contact once each five revolutions where velocities are high.  This contact is
heard as a click in a headphone assembly or one count on a counting, box.
These counts are again made over a 40 to 70 second interval which is converted
to velocity by using the rating table or equation.
     Current meter measurements can be made by wading, from a boat, bridge or
cablecar.  Wading is generally preferred since it is the easiest and fastest
method, but when the product of depth times velocity ranges from 5 to 7 or
higher, a person cannot safely wade a stream.  The next preferred gaging
method is" from a cablecar.  The cablecar is generally in a selected location
for gaging and is perpendicular to the flow.  Instead of the wading rod, a
reel with cable is used to hold the current meter.  A short distance below the
hanging current meter a lead weight such as the Columbus sounding weights
holds the cable in a near vertical position.  These weights range from 15 to
300 pounds depending on flow conditions.  A reel with a depth indicator is
used to raise and lower the meter and weight and to measure depth.
     Stream gaging from a bridge uses a similar arrangement as the cablecar
method.  A reel and weight system suspends the current meter.  For small
streams a handline can be substituted for a reel.  For larger streams, one of
several types of cranes or booms mounted on a truck is used to hold the reel,
cable meter and weight assembly.  Horizontal angle corrections need to be
applied since the bridge may not be perpendicular to the flow.  Discharge
measurement notes can be used in determining the angle correction.
     When a bridge or cablecar is not available, a boat may be used.  For
smaller streams, a cable may be stretched across the river and a special boom

-------
                                      2.18
and crosspiece is attached to the bow of the boat.  This assembly attaches to
the cable stretched across the river to hold the boat in place.  Again a reel,
cable, meter and weight arrangement is used to raise and lower the meter and
measure depths.

     2.3.2.7  Current Meter Measurements
     A current meter measurement entails measuring the incremental width,
depth and velocity at about 10 to 30 verticals in a cross section.  The total
discharge is then the sum of the individual areas  (a.)  times the velocities
(v.).
          Q = E (aiv±)                                               (2.1)

Widths are measured by stringing a tag line across the river or tape along a
bridge or marks on the cable of a cablecar.  The discharge at partial sections
is computed by the midsection method as shown in Figure 2.1 (after Buchanan
and Somers, 1969).
                                           ,  „
          qi * V - 2 - + - 2 - J  di

                  rbi-M " bi-1,  „
             - v±[ - - - ]  d±

where     q. = partial discharge through section  i
                                                                     (2.2)
          v. = mean velocity of location  i
        b
          .  . = distances from initial point to locations  i-1
          b. = distances from initial point to locations  i  and
        b    = distances from initial point to locations  i+1
          d. = depth at location  i.

     2.3.2.8  Velocity Measurements
     The velocity of a stream generally varies logarithmically with depth.
Because time constraints do not allow measuring a more complete vertical velo-
city profile at each site, the velocity is measured at certain depths depend-
ing on flow conditions.
     Three basic methods are used under most conditions.  When the depths are
between 0.3 ft and 2.5 ft the velocity is measured at a depth 0.6 of the depth
below the water surface or 0.4 times the depth above the bed.  This depth is

-------
                                         2.19
Initial
point    i'
                            EXPLANATION

              1,2.3,      n       Observation points

              fa,, b2,b3,       bn    Distance, in feet, from the initial
                                   point to the observation point

              di'd2-d3-       d"    Depth of water, in feet, at the
                                   observation point
              Dashed lines          Boundary of partial sections: one
                                   heavily outlined discussed in text
       Figure 2.1.  Definition  sketch of midsection method  of
                      computing cross-section area for  discharge
                      measurements (after Buchanan and  Somers, 1969).

-------
                                      2.20

used because when integrating the logarithmic velocity profile over depth to
find the mean velocity,  the mean velocity occurs  0.6d  below the surface.
     Another method  is to take two velocity measurements at each vertical, one
0.2d  below the surface  and one  O.Sd  below the surface*  The arithmetic mean
is then computed for the mean velocity.  This method is used when the depths
are over 2.5 ft and  is called the two-point method.
     A third method  incorporates the previous two where velocities are
measurable at  0.2d,  0.6d  and  O.Sd  below the surface.  Generally the velo-
cities at  0.2d  and  O.Sd  are averaged and the result is averaged with the
O.Sd  measurement to compute the mean velocity.  This method is used when the
vertical velocity distribution is abnormal, such as when caused by obstruction
on the bed.
     Other modifications of these procedures may be resumed under adverse flow
conditions.  For example, if stages are changing rapidly, the 0.6 method may
be used over depths of 2.5 ft to reduce the time of the measurement.  Debris
or ice may preclude the  use of the 0.2 depth measurement.  If the weight can't
hold the meter in position at  O.Sd  due to high velocities and large depths,
a  0.6d  method or a  0.2d  method with a correction may be used.  When a
meter cannot be used, the float technique is used to estimate discharge.
Velocities are measured  over a premeasured distance (100 ft at least) at
various locations across the channel.  Areas are multiplied by the velocities
and summed to obtain the total discharge.  Low-flow measurements may be made
by Pygmy meter or portable flume or weir.
     A few precautions must be taken in order to assure accurate discharge
measurements.  Allow a few seconds for the current meter to reach an
equilibrium velocity after putting it in position in the stream before start-
ing the actual measurement.  When wading, keep a good distance (downstream and
to the side) from the current meter with the feet and legs to minimize inter-
ference.  Whenever the tagline (cablecar, bridge, etc.) is not perpendicualr
to the flow, the horizontal correction must be made.  Periodically, check the
free spin time of the meter during the measurement to insure proper meter
operation.  When stream  gaging an alluvial, sand-bed river, note the bed forms
if at all possible and water surface conditions since often a distinct shift
in the stage-discharge relation occurs when the stream bed changes from lower
to upper regime.  Before starting the measurement, check the chart or tape at
the stream gage for rate of rise or fall of the stage.  If the stage is rising

-------
                                      2.21
       0'
or falling rapidly, a quick  0.6d  measurement may be required or at least
frequent monitoring of the gage height would be necessary.
     At the end of each measurement, the stream gager will check the measure-
ment by plotting the stage and discharge on a field rating curve to see if the
new measurement follows the previous trends.  If a significant difference
exists, a recheck of computations is performed.  If the computations are
correct, a remeasurement with a separate set of equipment is in order if no
obvious physical reason for the discrepancy is observed.  A return visit by
the stream gager and supervisory personnel may be required.

     2.3.2.9  Development of Rating Curves
     The development of rating curves requires tabulation of the following
data:
     1.   Measurement number
     2.   Date
     3.   By whom
     4.   Width
     5.   Area
     6.   Mean velocity
     7.   Gage height
     8.   Discharge
     9.   Rating shift
    10.   Percent difference
    11.   Method of velocity determination in vertical
    12.   Number of verticals
    13.   Gage height change
    14.   Measurement rating
    15.   Air temperature
    16.   Water temperatuare
    17.   Remarks
     Following the compilation of data, the rating table of stage or gage
height versus discharge can be developed.  This development of the rating
table follows procedures given in Surface Water Techniques of the USGS,
Book 1, Chapter 12, Discharge Rating at Gaging Stations.
     First the discharge versus stage is plotted from the compilation of
measurements on an appropriate scale.  Previous graphs at each station can

-------
                                      2.22

serve as a guide.  The points on the curve are plotted as prescribed with a
3/32 inch circle and with a 0.8 inch guide line starting 0.2 inches from the
circle at a 45° angle.
     Points that don't plot within +5 percent of the rating curve must be
given attention.  These points may be valid measurements indicating a shift or
may be more temporary in nature.  A reason for the departures should be
explained.  For example, when developing a rating curve for a sand-bed chan-
nel, changing bed forms can drastically change resistance to flow, which in
turn changes the stage for a given discharge.  The resistance to flow may be
on the order of 0.035 (Manning's n) for dunes, but as flow increases and
changes the bed forms to plane bed in upper regime, the  n  value may drop to
0.012.  An example is given in Figure 2.2.
     Note how the bed form observation and corresponding change in resistance
to flow can explain deviations in a stage-discharge relation.
     Stages or depths may also vary during the passage of a flood wave due to
a lag in bed form changes due to rapidly changing hydraulic conditions as
shown in a number of laboratory experiments by Simons and Richardson (1962)
(see Figure 2.3).  Again, relatively large changes in stage or depth can occur
at a given discharge.  For these reasons, all efforts should be made to
observe bed forms during discharge measurements.
     Dynamic effects due to unsteady nonuniform flow can create a hysteresis
loop in the stage-discharge relationship.  This occurs again during an unsteady
flow event or when stages are rising or falling.  A common method used by the
USGS to correct discharge measured during a period when stages are changing is
the Boyer method.  The ratio of the measured discharge to the corrected
discharge is found by the following equation.

where  Q   is the measured discharge,  Q   is the corrected discharge,  U  is
the velocity of the flood wave,  S   is the constant stage slope for the stage
at which the measurement was made and  dh/dt  is the rate of change of stage.
The velocity of the flood wave is computed by
                     S         S    	
          U = 1.3 V  -2 + (1 - -£) /gd                               (2.4)
                   m S         S
                      o         o

-------
                        2.23
      500
              tOOO     2OOO     4OOO  6OOO   IODOO

             Ditchorgt (0) In cubic f»«t p«r second
Figure 2.2.   Relation of depth to discharge for
              Elkhorn River near Waterloo, Nebraska
              (after Beckman and Furness, 1962).

-------
                                        2.24
  0.8
  0.7
  0.6
  0.5







1
V
1

r"
rT
I







X

X





X



Ripples an
developing






Rising
stage —

v
x
—
X

X
^


/


"t
L
Ripples and dui
developing,

es









>- —




-------
                                      2.25
where  S   is the slope of the stream at high stages,  V   is the mean velo-
        o                                               m
city,  g  is the acceleration of gravity and  d  is the mean depth.
     Another method was presented by Simons et al. (1977) which computes  in
more detail the relationship of stage to discharge during the passage of  a
flood wave to correct for the hysteresis loop due to unsteady nonuniform  flow.
In this method the full dynamic momentum equation given in Equation  2.5 is
solved in terms of the geoemtry of the particular cross section, resistance to
flow and rate of change of stage.
          S  = S    2-*- - —-  x '-  - -— -l£                             (2 5 )
           f    o   3x   gA   3x    gA 3t                             \**=»
where  S   is the friction slope,   S   is the channel bed slope,  y   is the
depth of flow,  x  is the downstream distance,  g  is the gravitational
acceleration,  A  is the cross-sectional area of flow,  Q  is the discharge,
and t  is the time.
     Figures 2.4 and 2.5 show application of the method on the Mississippi
River.  Significant changes in stage can occur for a given discharge  simply
due to flow dynamics.
     Careful consideration to physical processes such as flow dynamics,
changes in bed form and of course changes in cross section due to scour and
fill must be given in developing the rating curve and table for each  station.
     A new rating table is required when a definite shift occurs backed up by
an understanding of the physical process causing the shift.  After a  suf-
ficient number of new measurements is made and plotted, a manual method of
developing the rating table from the curve is used.  From the low end of  the
rating curve where the relation is usually quite curvilinear, discharges  are
tabulated at 0.1-ft stage increments.  Where a rating curve is close  to linear
the discharges are read at 1.0-ft intervals.  Values are then to be inter-
polated between the points picked from the curve.  The table must then be com-
pared at all values to the rating curve and adjustments made if needed.   The
rating table should be as complete as the curve and give discharge of 0.1-ft
increments.
     Instead of developing a new rating table whenever some natural phenomenon
causes a change in a rating curve, a shifting control correction may  be made.
This correction involves computing the gage height that would produce the

-------
        o
        o
        O
        o
        .c
1200



1100



1000



 9OO



 8OO



 700



 600



 500



 400



 300



 200



 100
                         2.26
                                  o  Observed


                                     Computed
                   10  20   30  40   50  60

                         Time,  days
Figure 2.4.  Discharge hydrograph for the Mississippi

             River, Tarbert Landing, LA (2/9/66 -4/11/66)
    50



    45


    40



 r  35


 «" 30
 o»
 o

 tr>  25


    20
                  o  Observed

                  	Computed
    15

     200     400     600     800     1000    1200

                  Discharge ,  1000 cfs
Figure 2.5.  Stage-discharge relations for Mississippi River,

             Tarbert Landing, LA (2/9/66-4/11/66).

-------
                                      2.27
                                                                             0'
measured discharge from the original data.   The shift is then the difference
between the observed gage height and the computed gage height.  Care must be
taken to apply the shift with the correct sign.
     If the computed gage height is less than the observed gage height, the
shift is negative; if more, it is positive.
     When applying shift corrections on a daily gage height record to obtain
daily discharge, the shifts may be applied prorated in time or as a function
of gage height or a combination of the two.

     2.3.2.10  Requirement for Discharge Measurement at a Range of Stage
     In order to develop a rating curve that is as complete as possible,
discharge measurements should be made so as to cover as wide a range of stages
as possible for given hydrologic conditions.  Efforts to make measurements at
high flows will be made in addition to regular monthly measurements.  Such
extra measurements may be made during one flood event.  To accomplish this,
timely and sufficient rainfall and snowmelt information must be acquired.

     2.3.2.11  Operation and Maintenance of Crest-Stage Gages
     A crest-stage gage marks the highest water-surface elevation that occurs
between servicing by cork particles adhering to a staff gage within the gage
pipe.  Observations of the gage and possible changes such as debris, erosion,
deposition or man-made changes are to be noted.  Datum control is also impor-
tant for maximum accuracy.  Specific steps for site maintenance are listed.
     1.   If the stage at the time of inspection is below the datum pin,
          a.   Remove the cap at the top of the gage pipe.
          b.   Remove the staff and if cork particles indicate a peak has
               occurred, mark the cork line with a pencil line, then remove
               all cork particles.  If a cork line is found at the same eleva-
               tion as the vent hole, the gage may have been toppled.  Always
               verify such a mark by outside high-water marks.
          c.   Enter the date of the inspection on the penciled line and
               measure the distance from the line to the bottom of the staff
               (to the nearest 0.01 foot).
          d.   Remove the lower cap and flush out any silt that might have
               collected;  make sure all intake and vent holes are
               unobstructed.

-------
                                 2.28
     e.   Place one tablespoon of granulated cork in the bottom cap, and
          secure the cap with a pipe wrench.  Caps that are easily
          removed are often taken by children of all ages.  Make sure the
          intake system is positioned so that the five closely-spaced
          holes face upstream.

     f.   Replace the top cap (with a wrench), and make sure all bracket
          bolts and lag screws are tight.

     g.   Determine the present water surface at the gages (to the
          nearest 0.01 foot) if over-the-road flow exists.

     h.   Remove debris that might have collected on the gage.

     io   Carefully describe and measure any debris that might have
          collected.  Try to estimate the location of the debris at the
          time of the peak flow (floating, lodged in the entrance, etc.).
          Draw a diagram of the obstruction.  Remove the debris and
          record any resultant change in"the present water surface eleva-
          tion at the gage.

     j.   Document the outside high-water marks and any changes in chan-
          nel properties.  If a peak stage has not occurred since the
          previous visit, the cork supply in the gage will be adequate.
          Never assume the gage is fully charged because ants or wind
          will sometimes remove the cork.
                                                                        x
2.   If the present water surface elevation is higher than the datum pin
     and the stage is falling, the above procedure should be modified as
     follows.

     a.   Perform steps a to c above as described.

     b.   Carefully pour a teaspoon of cork (half of the amount used when
          servicing the gage from the bottom cap) into the gage pipe.
          Wipe the staff completely dry and lower it very slowly into the
          pipe.  Make it a practice to determine the present water-
          surface elevation by measuring outside the pipe.

     c.   Perform steps g to j above as described.

3.   If the water surface is high and rising, use the following procedure:

     a.   Remove the top cap.

     b.   Do not remove the staff from the gage.  The removal of the
          staff may cause an erroneous mark if the stream is near its
          peak stage.

     c.   Determine the present water surface by measuring the distance
          between the top of the gage pipe and the water surface or the
          datum pin, if possible.

-------
                                      2.29
          d.   Indicate the rising trend of the stream on the note sheets
               along with the time of day.
          e.   Replace the top cap and try to identify the control for the
               present flow.
     4.   The USGS Technical Officer should be notified immediately if the
          recorded peak stage is such as to warrant an indirect determination
          of peak flow.  Pre-flood plans should be made as to type of indirect
          to be made and best location for indirect.
     2.3.2.12  Discharge Measurements at Low-Flow Partial-Record Stations
     Periodic seepage runs are an excellent method for explaining the signi-
ficant low-flow gains or losses along an extended reach or length of stream.
Accordingly, a series of discharge measurements on selected stream reaches can
be used to define low-flow variations in regions of actual or anticipated coal
mining development.  To maximize information, seepage runs should be coordi-
nated so that monthly inspections, discharge measurements, and sampling at
other sites in the same stream basin are all made within a 36-hour period or
less and during a period of uninterrupted base flow.  Measurement of seepage
runs follow the general techniques used for surface water discharge evaluation
(Section 2.3.2.8).
     The objectives of a study influence selection of a runoff measuring
device.  For example, if a water budget is studied in an area where runoff
accounts for only about five percent of the water budget, 95 percent of the
funds should not be spent on measurement of runoff.  More funds should be
directed to other parts of the hydrologic cycle.  If the objective of a study,
on the other hand, is to measure the effect of land treatment on the water
supply derived from a watershed, a precalibrated runoff measuring device would
be required.  Fewer funds and less time should be directed to other parts of
the hydrologic cycle.
     Selection of a device and location for measuring runoff depends on such
factors as the peak runoff rate, distribution of runoff volume by categories
of flow rate, absence or presence of sediment or woody trash, or both,  in the
flow, whether backwater submergence will affect flow through the device, icing
conditions,  foundation conditions, material availability, and economics.
Location of gages is also affected by the objectives of the study, site
accessibility and stability and the range of discharges to be measured.

-------
                                      2.30

     The term "runoff" normally is used to distinguish surface flows from
ground water contributions to a streamflow.  This distinction generally is
derived through analysis of hydrographs since independent measurement is not
feasible.  The terms  "runoff" and "streamflow" are used interchangeably here.
They refer to all the flow, regardless of origin, that passes through the
control at the point of measurement.
     In open channels, a control is a cross section or length of reach above
which the water level is a stable index of the discharge rate.  All sections
have equal capacity to pass a flow.  In natural streams the control may shift
from one point to another with changes in stage.  For use as a runoff station,
a control must be selected, altered, or constructed to provide a stable head-
discharge relationship.
     Many considerations influence selection of a control for flow me'asure-
ments.  The ultimate objective is to provide a stable relationship between the
depth of water and the rate of flow.  Since the rate of flow equals the pro-
duct of average velocity and the cross-sectional area, controls should be
selected for stability of cross section and such factors as slope, con-
figuration, channel roughness, and absence of tailwater, which affects velo-
city.
     Quantitative evaluation of flow is easier if the flow passes from subcri-
tical to supercritical around the control section.  Precalibrated devices use
this advantage.  Natural controls that maintain critical flow at all stages
are unusual.  They are selected, therefore, to provide subcritical velocities
at all depths since changes in depth are approximately equal to changes in
specific energy.  Measurement of flow at critical depth should be avoided
since it presents so many difficulties.  This sometimes can be accomplished by
converting to subcritical flow through impoundment or manipulation of the
channel gradient.  The flow subsequently can pass through critical downstream
of the point of head measurement.
     For some purposes the control must be located so that gaged streamflow
represents the entire flow from the watershed—none escapes beneath or around
the control.  Cutoff walls extending vertically in impervious strata and
laterally in floodplains may be needed to prevent flow from bypassing the
gaging station.  Bypassing flow may be unimportant for some studies and at
some locations.
     Other considerations in selecting a control include capacity needed for

-------
                                      2.31

major flows; silt, ice and debris content of expected flows; and structural
requirements such as footings and protection against frost heaving.  Controls
are classified herein as (1) precalibrated devices, (2) existing structures
adapted to calibration, and (3) natural controls, such as cross sections or
channel reaches with suitable hydraulic characteristics for calibration.
     Selection of sites should not necessarily be based on the assumptions of
a rigid boundary channel and steady flow conditions.  An additional analysis
is required to answer some critical questions.  First, the effect of potential
bank and bed erosion on stage-discharge relations should be evaluated.
Secondly, the rate of rise and fall of discharge may create a looped stage-
discharge relation.  The effects of loop rating curves on accuracy of flood
discharge should be determined.  Furthermore, the selection of sites must con-
sider the need for erosion protection.  This requires the analysis of erosion
and sedimentation utilizing river mechanics and sediment transport concepts.
     Analysis of potential gage sites should consider the stage-discharge
relationship, including the effect of rise and fall of discharge, the effect
of potential bank and bed erosion, and the sensitivity of the relationship at
various levels of discharges.  The analysis of potential erosion and sedimen-
tation at a site may be particularly important.  Errors in using the original
stage-discharge relationship under conditions of changed channel cross section
are evaluated.  Stage-discharge relationships with a cutoff point above which
the relationships can no longer be considered valid should be identified.

     2.3.3  Collection and Processing of Water Quality Data
     2.3.3.1  General
     Collection and processing of water quality data requires samples for
chemical and sediment analysis.  Samples collected for chemical analysis
include those for laboratory analysis and those for field analysis.
Laboratory samples require preparation, filtration, preservation and shipment
while field samples require measurement for selected water-quality parameters
and biological observations.  Samples collected for sediment analysis require
preparation and shipment.
     Prior to collecting samples, initial observations on weather conditions,
streamflow, color of the water, condition of the site, etc. must be made and
documented.  Current discharge measurements are required at the time of water
quality data collection or at least an estimate based on stage and the rating

-------
                                      2.32
curve or other information.
     The sampling site location is extremely important to obtaining quality
data.  Sections of streams that are not thoroughly mixed or where differences
in composition exist should be avoided.  This condition often exists
downstream of the confluence of major tributaries.  A good sampling section
should show fairly uniform measurements or observations in the channel cross
section (Middelburg, 1979) when the proper sampling technique has been
applied.

     2.3.3.2  Sampling Techniques
     The sampling technique should produce a sample that is as representative
as possible of the average condition of the water quality variables for a
given time and location.  Sampling techniques can be categorized as point or
integrating methods.  Different sampling devices or instruments are used to
obtain different types of samples.  The same samplers used for fluvial sedi-
ment are used for water quality with slight modifications to reduce con-
tamination.  Water sample bottles for the sampling devices must be washed and
thoroughly rinsed.
     The equal discharge interval technique (EDI) is one of two depth-
integrated cross-sectional composite methods.  The EDI method consists of the
collection of equal amounts of water at the centroids of equal discharge
increments of the stream.  The discharge pattern must be established by
measurement prior to water quality sampling, or from previous discharge
measurements.  For narrow streams (up to 15 meters) with good mixing, the
discharge profile can be divided into three to five equal parts.  For larger
streams, five to ten sections are required.  A depth-integrating sampler is
used to get approximately an equal amount of water from the centroid of each
section.  The depth-integrating sampler is lowered to the bottom (or maximum
depth for the sampler being used) and then raised again.  The down rate does
not need to equal the up rate; however, the travel rates should be constant
and less than 0.4 times the velocity.  The bottle should be filled 3/4 full or
less.  Repeated vertical transects can be used to get an adequate amount of
water.  The amount collected at each section depends on what is required for
the analysis techniques.  The proper amount can be determined by computing the
amount needed for analysis plus two to three liters (for rinsing purposes and
waste) divided by the number of sections.  As the sampler bottle becomes full

-------
                                      2.33

it is composited into a larger second container.  The same bottle should be
used throughout the cross section to prevent the cumulative error introduced
by the loss of particulate matter that is not rinsed from the sample bottle to
the composite container.
     The equal width increment (EWI) is the second procedure available to pro-
duce a depth-integrated cross-sectional composite sample.  It can be used with
or without dicharge measurements and for braided streams (the EDI should not
be used for braided streams).  The sampling procedures are the same as the EDI
method, except equal distance is used between verticals regardless of the
discharge, although the distance should be selected so that no more than ten
percent of the discharge passes between two verticals.  One vertical rate is
used resulting in different amounts of sample collected at each cross section,
depending on the depth and velocity.  Therefore, it is difficult to predict
how many verticals are needed.  If a sufficient sample is collected, the EWI
section can be repeated.  The second pass can use a different cross-sectional
spacing if necessary.
     If the sample bottle cannot go down and back without overfilling, a
point-integrating sampler must be used.  Point-integrating samplers use an
electric value to allow vertical transects in one direction, up to approxi-
mately 30 ft.  Repeated vertical transects each covering a different depth can
be used for greater depths.  The point-integrating sampler can be used for
either the EDI or the EWI procedures.

     2.3.3.3  Field Evaluations
     Field evaluations are made on samples or directly in the stream to
establish certain water quality parameters prior to any potential change.
Field measurements on pH, acidity, alkalinity, dissolved oxygen, specific con-
ductance air and water temperature are generally required.  The USGS has
established strict procedures'on these tests.  These procedures are available
in TWRI Book 5,  Chapter A1 and "Field Measurement of Water Quality"
(Middelburg, 1979).  A brief review is presented below.
     Field measurements of pH are often made using the glass electrode method.
A water sample is taken and pH measurement is made promptly to avoid possible
changes due to chemical or biological activity.  Standard pH buffers used in
calibration should be kept at the same temperature as the sample.  A brief
procedure outline follows.

-------
                                      2.34

     1.   Perform battery check.
     2.   Add 25 ml pH 7 buffer to a clean 50 ml beaker.  Measure temperature.
     3.   Place electrode in buffer.  Measure pH and standardize.
     4.   Clean electrode with distilled water and continue calibration with
          pH 4 and pH 10 buffers.
     5.   Measure pH of sample in a clean beaker or plastic cup that has been
          rinsed with sample water.  While measuring pH set the temperature
          dial according to measured sample temperature.
     After establishing the pH, the appropriate test for alkalinity/acidity
can be performed.  These tests are chemical titrations used to establish the
concentrations of major constituents.  The appropriate reagents to titrate
with, the procedures followed and the formulas used to determine the consti-
tuents are detailed in TWRI Book 5, Chapter A1.
     Dissolved oxygen can also be evaluated by chemical titration or by
electrode instruments.  The procedures set forth in USGS Quality of Water
Branch Technical Memorandum 79.10 may serve as a guide.
     Specific conductance is measured by a battery powered Wheatstone Bridge.
Specific conductance should be measured in the field.  After a sample is
taken, the procedure is as outlined below:
     1.   Perform battery check
     2.   Clean cells
     3.   Check calibration
     4.   Rinse cell with sample water and then fill
     5.   Measure temperature
     6.   Measure conductivity
     7.   Correct measurement to 25°C.
     Temperature is an important parameter in water quality data collection.
Temperature is generally measured by thermometer or thermistor.
     Air temperatures are measured using a dry thermometer in a shaded area.
The thermometer should be exposed to sufficient air circulation without being
subject to strong winds.  Let the thermometer sit for ten or more minutes
before reading.  Record temperature and time of day.
     Water temperatures should be measured at about five verticals in the
stream and averaged to obtain a mean value.  Thermistors should be allowed to
stabilize for three minutes and thermometers for one.  All temperature

-------
                                      2.35
measuring devices should be adequately calibrated to insure correct readings.

     2.3.3.4  Chemical Samples
     Chemical samples must be prepared, filtered, packaged, labelled and
shipped by the most expedient method available on the same day of collection.
USGS procedures specify volumes required for each subsample, the types of con-
tainers to be used, the type of treatment and/or preservation and the sample
designation.

     2.3.3.5  Sediment Sampling
     The Agricultural Research branch of the U.S. Science and Education
Administration has compiled many of the techniques used for monitoring sedi-
ment yields from watersheds.  The following discussion is from Brakensiek et
al., 1979.
     Sedimentation is the detachment, entrainment, transportation, and deposi-
tion of eroded soil.  Techniques and procedures described are limited to those
used in fluvial sedimentation research on agricultural lands.  Sedimentation
in major rivers, large reservoirs, estuaries, and harbors is not considered in
this manual.
     Although no single phase of the sedimentation cycle can be treated as an
entity, the natural sequence of the cycle is as follows:  Soil erosion-
transportation-deposition.  Soil erosion has been defined as the detachment
and movement of soil from the land surface by wind or running water.
     Most of the damage caused by sediment is the result of accelerated ero-
sion, defined as erosion in excess of the geologic norm.  Accelerated erosion
is usually induced by activities of man such as:  deforestation, cultivation
and overgrazing, reshaping the land surface for construction or mining, and
disturbance of the natural drainage system.
     In agriculture, sediment sources are classified as:  (1) sheet and rill
erosion, (2) erosion from gullies, arroyos, roads, rights of way and construc-
tion sites, and (3) channel bed and bank erosion.  In most regions, sheet and
rill erosion is usually the largest source of sediment.
     In addition to being erosive forces, wind and water are the transporting
agents for sediment.  Although significant amounts of sediment are moved by
wind, particularly in the arid regions, water is the major transporting agent.
Sediment transported in a stream or watercourse is usually subdivided into two

-------
                                      2.36

categories according to the dominant mode of transport, suspended load, and
bed load.  Total sediment load is the sum of the two.  Other paired terms such
as washload, bed-material load, measured and unmeasured load, and sampled and
unsampled load are also used to describe sediment transport.  Figure 2.6 gives
the relative location of these descriptive terms in the stream vertical.
     Since sedimentation processes are completely linked to the quantity and
character of runoff, it is necessary that fluvial sedimentation data be asso-
ciated with corresponding runoff for many interpretive anlayses.
     A variety of instruments and techniques has been developed for field
measurement of soil erosion, sediment movement, and sediment deposition.  In
general, three basic types of measurements are required:  (1) measurements of
sediment in surface runoff from small experimental plots and watersheds and in
stream channels, (2) measurements of eroded areas to determine the volume of
material removed, and (3) measurements of the volume and density of sediment
deposits.  Instruments, equipment, and techniques typical of those used in
sedimentation research on agricultural lands are discussed in this section.

     2.3.3.6  Site Selection
     The objectives of the experiment and the type of data to be obtained
determine the location of the experimental site.  Other considerations include
the availability of land, access to the area, topography, facilities for
cultivating the land if cropping practices are a part of the experiment,
availability of servicing personnel, management control of the experimental
area, drainage and vertical head requirements for instruments, and sampling
equipment.
     Generally, fractional-acre plots and small watersheds a few acres in size
are used to study basic erosion rates of various soil-cover complexes which
are representative of a land resource area.  This requires location of the
experimental area on a specific soil type with the desired topography.
Vegetative cover, except forest cover, is usually easily established within a
relatively short time.  Replicate plots are sometimes required to obtain
representative data due to such factors as inherent errors in measurement and
variations within soil types.  For most experiments, tenure of the land is
needed for ten years or more to cover the normal range in weather patterns.
     Plot shape is determined by the objective of the study and can range from
a small rectangular area to a naturally shaped watershed.  Plot length should

-------
                         2.37
                   BY
                METHOD OF
                TRANSPORT
   BY
SAMPLING
CAPABILITY
                                              Total
                                              Load
Figure 2.6   Schematic diagram of  stream vertical
             showing relative position of sediment
             load terms, from Brakensiek et al, 1979.

-------
                                      2.38

represent the length of  slope on which soil losses occur.  Lengths commonly
used in feet are 36.3, .72.6, 92.0,  145.2, and 400 (11, 22.1, 28, 44.3 and 122
m).  Plot widths may vary from six  feet  (1.8 m) for hand-tilled plots to 20
feet (6 m) or more when  conventional farm machinery is used.  Computations of
results are aided when length times width results in a simple fraction of an
acre (72.6 ft (22/ra) length x 6 ft  (1.8 m) width = 435.6 ft2 (40.5 m2) = 0.01
acre (0.004 ha)).
     Sites should be selected to represent the range of slopes encountered in
the general farming area.  Plots on natural slopes are best because reshaped
slopes usually  do not contain normal soil profiles.  Larger plots and small
watersheds may  have natural slopes ranging from convex to concave.  Slopes low
enough to cause soil deposition above the measurement site should be avoided,
unless special provision is made for measurement.
     Heavy-gage sheet metal may be used for borders on small plots.  Metal
borders are easily removed when cultivation of the plots is required.  Earthen
ridges may be used on plots wide enough .for farm equipment normally used in
farming operations.  Terrace interval plots may be used only with the terraces
at the upper and lower boundaries, with a grassed waterway to route flow from
the lower end of the rows to the point of measurement.
     Small watersheds usually do not require borders except dikes at the lower
edge to direct  flow to the point of measurement.  Plots of all sizes are
equipped with a trough or other collecting device to route the soil-water mix-
ture to the sampling site.  Sheet metal is used for the collecting trough on
small plots.  A concrete channel or earth dike may be used on large plots and
small watersheds.  Sheet metal borders, particularly those on the lower boun-
dary, should be installed deep enough to prevent piping and tunneling under-
neath by rodents.
     When land use and conservation practices are to be evaluated, they must
be considered when the site is selected.  Cropping treatments may vary from
continuous fallow (bare soil) to continuous sod or forest.  Fallow soil serves
as a basis for evaluating other treatments and provides a measure of the
inherent erodibility of the soil.  Cropping systems that employ a crop rota-
tion patern should have all years of the rotation represented on separate
plots at all times after the rotation is fully established.  Conservation
practices may include terraces, minimum tillage, strip cropping, contour
plowing, and others.

-------
                                      2.39
     2.3.3.7  Stream Sampling Stations
     Generally, sites selected for water discharge measurements in natural
channels are adequate for suspended sediment measurements.  In addition to the
usual requirements of access and availability, a straight channel reach with
uniform velocity and sediment distribution is desirable.  Consideration is
also given to the construction of walkways, cables, and bridges and to the
installation of sampling equipment.
     Sampling equipment has not been perfected that will sample the entire
depth of flow in a natural channel.  Conventional depth-integrating samplers
are limited to sampling the flow from the water surface to about 0.3 ft (9.1
cm) above the streambed.  Therefore, artificial or natural grade controls
which provide an overfall and permit sampling through the entire flow vertical
are necessary if total load sampling is to be accomplished.  Artificial or
natural turbulence sections which uniformly suspend transported sediments also
provide an alternative approach to total load sampling.  Many flow-measuring
devices such as weirs, rectangular notches and flumes can be designed to pro-
vide sufficient overfall for total load sampling.  Highway box culverts and
other hydraulic structures may also be used.
     Sediment investigations in a land resource area may require measurements
of sediment yield from channels, gullies, and other major sediment sources.
Typical sites may not exist, but sites selected should represent local con-
ditions as nearly as possible.  There must be access to instrumentation to
install and service sampling equipment.  Detailed topographic surveys may be
needed.
     No attempt has been made to cover all sediment sampling and measuring
devices and equipment.  Only those used most commonly in sedimentation
research on agricultural lands are discussed.  Variations and adaptations of
basic instruments are often made to fit local conditions.

     2.3.3.8  Total Collection Devices
     A simple total collection device for very small plots may be constructed
to measure erosion by installing a suitable collection tank large enough to
contain the total runoff (water and sediment) expected in a 24- or 48-hour
period.  The weight or volume, or both, of the water-sediment mixture is then
determined and the material sampled for subsequent laboratory analysis and
computation of the weight or volume of sediment.

-------
                                      2.40

     Total collection devices are not generally recommended for erosion stu-
dies because runoff storage requirements are excessive even for very small
drainage areas.  Small drainage areas, in turn, are not normally represen-
tative of large, complex field conditions.  Slot-type samplers, which collect
a known portion of the runoff-sediment mixture, are preferred because they can
be used on larger areas, and the sample volume is reduced to manageable quan-
tities.
     Slot-type samplers are used in basic erosion studies on small plots and
watersheds.  These samplers are automatic in the sense that no attendant is
required during the sampling operation, and sampling is continuous during the
runoff event.  The samplers provide a storm-integrated or discharge weighted
sample for determining sediment yield.  The multislot divisor, with a sta-
tionary slot, and the Coshocton wheel sampler, with a revolving slot, have
been used extensively.
     The Multislot Divisor.  Runoff is routed from the collector through the
conveyance channel to a sludge tank where the heavier sediment particles are
deposited.  Overflow from the sludge tank is routed through the multislot
divisor, where an aliquot sample is obtained from a single slot and routed to
a sample storage tank.  A second or third sample storage tank may be connected
to the first if additional sample storage is needed.
     Many investigators prefer to install a small, removable intertank
directly below the inflow spout in the sludge and sample (aliquot) tanks.
This greatly reduces the time and labor required to sample and clean up after
small storms which do not overflow the small intertanks.  It also improves the
accuracy of volume measurements.
     The size and capacity of the sampling apparatus are determined by the
anticipated maximum rate and amount of runoff and sediment to be sampled.  For
small fraction-acre plots it is assumed for design purposes that maximum
runoff rate will equal the maximum five-minute rainfall rate.  Sample storage
based on 100 percent runoff should be provided for a 100-year, 48-hour storm.
     Sediment storage requirements vary greatly with location, soil type, land
use, and climatic conditions.  Sediment rates as high as 50 tons per acre have
been recorded from single runoff events under adverse conditions.  Bulk den-
sities of trapped sediment may range from 40 to 100 lb/ft3.  The size and
geometry of the collector trough and conveyance channel are determined by the
maximum flow requirements.  Flow velocities in conveyance channels should be

-------
                                      2.41

fast enough to prevent sediment deposition through a wide range of flows*
Minimum velocities of 2 ft/s at flow rates of about one-fifth of the maximum
will prevent excessive deposition for most soils.
     The collector acts as a weir at the end of the plot.  It is installed so
that the elevation can be adjusted to the plot surface as erosion occurs.  It
is attached to an end plate which should extend at least eight inches into the
soil below the collector trough.  Although the collector and end plate may
extend'across the entire length of the plot, it is best to concentrate runoff
before it reaches the collector on wide plots.
     The depth is usually the same as the conveyance channel with about 0.4
foot (0.12 m) freeboard.  The width may vary but should be wide enough to
clean easily, 8 to 10 inches (20-25 cm).  The bottom should slope to the
center by at least five percent.  Screens of one-half or one inch (1.3 to 2.5
cm) mesh should be installed over the collector to keep trash out of the
system.
     Coshocton-Type Runoff Sampler.  The Coshocton-type runoff sampler is
constructed to form a single unit with the small H flume.  Three basic models,
N-1, N-2 and N-3, have been designed for use with the 0.5, 1.0 and 1.5-foot H
flumes.  Models N-1 and N-2 have been used extensively in the field.
     Capacities, sampling rates, and other pertinent information on Coshocton-
type samplers are given in Table 2.5.  Sampler size and capacity for a given
experiment are determined by the capacity of the H flume required to measure
peak runoff rates.  Slightly oversized flumes and samplers are recommended
because the sampling error increases significantly at discharges above 80 per-
cent of flume capacity.  For small plot studies the maximum runoff rate is
assumed to equal the maximum expected five-minute rainfall rate.  Sample
storage capacity is provided for the aliquot sample from the maximum 48-hour
runoff event.

     2.3.3.9  Suspended Sediment Samplers and Measurements
     The development of suspended sediment sampling equipment and procedures
and techniques for making field measurements of sediment discharge in streams
and rivers has been well documented.  Suspended sediment samplers currently
used by most U.S. Government agencies were developed by the Federal
Inter-Agency Sedimentation Project now located at the St. Anthony Falls
Hydraulics Laboratory, Minneapolis, Minnesota.

-------
                     2.42
Table 2.5.   Size Schedule for Coshocton-
             type Runoff Samplers
Head-
Sampler Wheel . room ...
,. ,. Capacity . Aliquot
No. diameter " require-
ment
N-l
N-2 . .
N-3

Ft
1
0
3

Ft- is Ft Pet
'/3 1 '/* 1
2 2' a ''2
5'/2 33,4 ''3
Approxi-
mate
weight
Lb
26
85
270
  Source: Parsons

-------
                                      2.43

     Suspended sediment samplers are designed to obtain samples of the water-
sediment mixture.  Two basic types have been developed; depth integrating and
point integrating.  Basic requirements of suspended sediment samplers have
been reported as follows:
     Depth-Integrating Samplers.  Depth-integrating samplers are designed to
continuously extract a sample as they are lowered from the water surface to
the streambed and returned at a constant rate of travel.  Ascending and
descending speeds need not be the same, but the rate of travel must be
constant in each direction.  As the sample is collected, air in the container
is compressed so that the pressure balances the hydrostatic pressure at the
air exhaust and the inflow velocity is approximately equal to the stream velo-
city.
     If the sampler is lowered too fast, pressurization will not equal
hydostatic pressure and the inflow velocity will exceed stream velocity.
Raising the sampler too rapidly will result in the opposite phenomenon.
Inflow through the exhaust port may also occur.  If the sampler transit speed
is too slow, the sample container will overfill before the sampler is returned
to the surface, circulation will occur, and the sample will be enriched.
Ideally, the sample container should be from two-thirds to three-fourths full
when depth integration is completed.
     Point-Integrating Samplers.  Point-integrating samplers are equipped with
an electrically controlled rotary valve which opens and closes the sampler on
command.  They are designed to take a sample at any point in a stream over a
short time interval.  The diving bell principle is used to balance the air
pressure in the sample container with the hydrostatic pressure at the nozzle
to prevent an initial in rush of water when the valve is opened.  With the
control valve fixed in the open position, these samplers are also used to
obtain depth-integrated samples.  One-way depth-integrated samples may be
obtained by opening the valve with the sampler at the water surface and
lowering it to the streambed at constant speed.  This permits sampling to
greater depths.
     Brief descriptions of suspended sediment samplers most frequently used by
U.S. Government agencies are given in Table 2.6.  All of these samplers,
fabricated from cast aluminum or bronze, are streamlined with tail fins to
orient the sampler so that the intake nozzle points directly into the
approaching flow.  Round or square glass milk bottle sample containers are

-------
                                  2.44
Table 2.6.  Suspended Sediment Samplers from Brakensiek et al,  1979.


u


u





Sampler
designation

.S. DH^tS ..Depth-
integrating

.S. D^19 	 Depth-
integrating




U.S. DH-59 __ Depth—



integrating


U.S. D-74 	 Depth—




U








U.








integrating



.S. P-61-A1 Point-
integrating







S. P-63 	 Point-
integrating







Sample „ ,
iif • u. i _n_ i Sample
Weight Length nozzle .
6 6 . volume
sizes
Lb In h,
4.5 13 3/.e 1 pt
and
V<
62 24 '/s 1 pt
3/.6
'/«



22 15 '/s 1 pt
3/16
'/4

60 24 »/• 1 pt
3/is and/or
'/« 1 qt


105 28 3/is 1 pt
and/or
Iqt






200 34 3/,e 1 pt
and/or
Iqt






Sampling conditions
and operation

Wading depths &
velocities.

Depths 15 to 18 ft. Low
to moderate flow
velocities. Sampler is
usually operated from
a bridge, cableway or
truck-mounted rig.
Moderate depths & flow
velocities. Sampler is
usually operated from
bridge or cableway.
Depths 15 to 18 ft. with
1 pt container.
Usually operated
from bridge, cableway
or truck.
Point-integrated
samples to 150 ft.
Also used to obtain 2-
way depth-integrated
samples to 18 ft in
moderate velocities.
Usually operated
from bridge, cableway
or truck-mounted rig.
Point-in tejrrated
samples to 180 ft
depth-integrated
samples in deep high
velocity streams.
Usually operated
from bridge, cableway
or truck-mounted rig.

Auxiliary
equipment
required

Sampler is affixed to
standard 1;2-in rod or
small diameter pipe.
'/s-in steel cable, reel &
crane.




Hand line or long
suspension rod.


'/8-in steel cable, reel.
and crane.



Vs-in steel, 2-conductor
electrical suspension
cable, reel & crane. 48
V d.c. power source to
operate sampler
valve. Additional
power source &
electric motor to
operate reel.
Rugged 2-conductor
steel suspension
cable, reel & crane. 48
V d.c. power source to
operate sampler
valve. Additional
power source &
electric motor to
operate reel.

-------
                                      2.45

inserted directly into the sampler body cavity.  The bottles are easily
removed after the sample has been collected.  Plastic bottles can be used in
some of these samples, but some can be equipped with teflon nozzles and
bushings to minimize contact between the sample and metal surfaces.
     Suspended Sediment Discharge Measurement.  Sediment measurement involves
sampling the water-sediment mixture to determine the mean suspended sediment
concentration, particle size distribution,  specific gravity, temperature of
the water sediment mixture, and other physical and chemical properties of the
transported solids.  Suspended sediment concentration in a natural stream
varies from the water surface to the streambed and laterally across the
stream.  Concentration generally increases from a minimum at the water surface
to a maximum at or near the streambed.  Vertical distribution of both sediment
and flow velocity in a typical stream vertical is illustrated in Figure 2.7.
     Coarse particles, sand size and larger, account for most of the
variation.  Fine particles, silt and clay,  are usually fairly evenly distri-
buted throughout the stream cross section.   Variations and fluctuations in
concentration in the vertical are affected by stream turbulence, velocity,
depth, temperature, the particle size of the bed material, concentration of
fine material, and some chemical properties of water.  Lateral concentration
in stream cross sections varies with channel geometry, slope and alignment,
velocity, depth, bed form, and sediment particle size.
     Suspended sediment discharge in a stream is the produce of the water
discharge and the mean suspended sediment concentration.  Symbolically,
suspended sediment discharge,  G  ,  may be defined as:
                                ss
                w=w y=d
          G=//CUdydx=Cy                              (2.6)
           Ss     /»   r              m
                w-0 y=6
where     w = the stream width
          d = the stream depth
          C and u are the concentration and velocity, respectively, at any
              point (x,y)  above the streambed
          6 = an indefinite point above the streambed, usually a few times the
              mean size of the bed sediment
         C  = the mean suspended sediment concentration (discharge-weighted)
          Q = the stream discharge.
     The suspended sediment discharge per unit width  g    is:
                                                       SS

-------
                        2.46
                   Water Surface
     Q.
     0)
     Q
             Channel |  Bed
                Concentration
     a.
     0)
     Q
                   Flow
                   Velocity
                   Velocity
Figure  2.7.
Vertical  sediment concentration and
flow velocity distribution in a
typical stream cross section, from
Brakensiek,  et al, 1979.

-------
                                      2.47

          ^ = /cu dy= c^                                       (2.7)
                s
in which  q  is the water discharge per unit of width and  C   is the
suspended sediment discharge concentration (discharge-weighted) at the ver-
tical where  C  and  U  were measured.
     The mean spatial concentration,  C,  for the sampled zone in the stream
vertical is:
          _             d
          C = 1/(d - a) / C dy                                       (2.8)
                        a
in which  a  is the distance from the bed to the lowest sampling point.  By
plotting the point concentration  C  against the position of  y  above the
bed, the mean concentration is readily determined.  In the absence of a
measured velocity distribution, the spatial concentration may be used as an
approximation of  C .  However, in most field work discharge-weighted con-
                   m
centrations are needed for computations of sediment transport.
     In most streams the sediment concentration and flow velocity vary ver-
tically and laterally, and sometimes erratically, and samples must be
collected systematically at selected points to be representative- of the flow
cross section.
     "Equal Transit Rate Method".  In this method the samples are collected at
equally spaced verticals in the flow cross section. . The transit rate of the
depth-integrating sampler must be uniform and the same at all verticals.  The
composite sample from all verticals will then represent the mean (discharge-
weighted) cross section concentration.  Suspended sediment discharge is then
computed as the product of the mean cross section concentration and the total
water discharge.  The number of sampling verticals required, normally 6 to 12
for most small streams, to obtain a representative sample depends upon the
accuracy desired, the channel width, the velocity distribution and the sedi-
ment concentration and particle size distribution.  This is the most commonly
used method on small agricultural streams.
     Depth-Integrated Samples at Uniformly Spaced Verticals.  In this method a
relatively large number of depth-integrated samples is taken at the midpoint
of equal fractions of the stream width.  This method gives a good indication
of the distribution of sediment across the stream.  Mean sediment con-

-------
                                      2.48

centration in the stream is determined by weighting the mean concentration in
each sampling vertical with respect to stream discharge in the vertical.
Suspended sediment discharge is then computed as the product of mean cross
section concentration and total water discharge.
     Depth-Integrated Samples at Centroids of Equal Water Discharge.  This
method requires depth-integrated samples at selected sampling verticals which
represent areas of equal discharge across the stream as determined by water
discharge measurements.  The sampling vertical is then located at the centroid
of each section (area).  Location of the sampling verticals may be determined
graphically.  The water discharge for individual sections is determined and
cumulated for the stream cross section.  Cumulated discharge in percent of the
total for various water stages is then plotted against the lateral distance of
each vertical from a fixed reference point.
     Table 2.7 gives the cumulative percentage of water discharge in the
stream cross section for selected numbers of sampling verticals.  After
selecting the number of sampling intervals, the location of each interval is
determined from the percentage values given in Table 2.7 and the graph of
cumulated water discharge versus location in the stream cross section.
     For example, if six verticals are selected, the first sampling vertical
would be at the point (distance from reference point) representing eight per-
cent of the total flow, the second vertical at the point representing 25 per-
cent of the total flow, etc.  The mean cross section concentration is the
average of the concentrations of the verticals, and the suspended sediment
discharge is computed as the product of mean concentration and water
discharge.
     Point-Integrated Samples at Selected Depths in Stream Verticals
Representing Areas of Equal or Known Water Discharge.  In this method, samples
are taken at selected points in the stream vertical which represent areas of
equal or known water discharge.  Samples representing areas of equal water
discharge may be averaged to determine the mean vertical concentration.
     The number of point samples required to determine the mean concentration
will depend upon the accuracy desired, the particle size distribution, stream
velocity, and turbulence.  Obviously, the accuracy of the method increases
with the number of samples.  Fewer samples are required for streams
transporting mostly fine materials since the concentration of clays and silt
will not vary significantly in the stream vertical.

-------
                         2.49
Table 2.7.   Cumulative  Percentage of Stream-
              flow in Cross Sections,  from
              Brakensiek,  et all, 1979.
Number
of
sampling
verticals
Cumulative stream discharge — percent of
total
Vertical number
1 2 3 4 5 6 7 8 9 10 11 12 13 14
    2	25 75
    4 	12 38 62 88
    6 		  8 25 42 58 75 92
    8 .	 6 19 31 44 56 69 81 94
   10  		 5152535455565758595
   12  _		 4 12 21 29 38 46 54 62 71 79 88 96
   14 _.     ... 4 11 18 25 32 39 46 54 61 68 75 82 89 96
     Source: Federal Inter-Agency River Basin Committee
   on Water Resource:

-------
                                      2.50
     This method is rarely used on small upland streams.  It is best suited to
large streams with relatively steady flow and rated streams where cross sec-
tion geometry remains  relatively constant.  Point sampling is not normally
used for depths shallow enough for depth integration.

     2.3.3.10  Bed-Material Samplers
     Bed-material samplers are designed to collect samples from the bed of a
stream, or from lake or reservoir deposits.  Some of the most frequently used
samplers for bed material, which is predominantly sand or sand and gravel, are
described below.  These samplers were developed by the Federal Inter-Agency
Sedimentation Project, and are described in detail in Brakensiek et al.
(1979).
     U.S. BMH-60 Hand-Line Bed-Material Sampler.  This lightweight sampler is
approximately 22 inches long.  If constructed from cast aluminum, it is 30
pounds.  Because of its light weight, the sampler is only used in tranquil
streams and moderate to slightly compacted bed materials.
     A spring-loaded sampling bucket, which holds about 10.7 in^ of material,
is located on the bottom side of the sampler.  In the cocked position the
sampling bucket is fully retracted within the sampler body.  It remains in
this position ready for sampling as long as tension is maintained on the sup-
porting handline.  When the sampler is lowered into the stream and touches
bottom, tension on the handline is released and the bucket snaps closed.  In
closing, it penetrates the streambed and completely encloses a sample from the
top 1.5 to 2 inches of the bed matrial.  Gaskets prevent the loss or con-
tamination of the trapped  sample as the sampler is raised to the surface.  A
safety yoke is provided to lock the sampling bucket in the open position for
removing the sample.
     U.S. BM-54 Bed-Material Sampler.  This 100-pound, 22-inch long cast steel
sampler is used to collect samples from the bed of a stream or reservoir of
any depth.  It is equipped with a spring-loaded scoop-type sampling bucket
located on the bottom  side of the sampler body.  The sampler is suspended by a
steel cable and raised and lowered by a suitable reel and crane.  Operation is
the same as that for the U.S. BM-60 sampler described above.
     U.S. BM-53 Piston-Type Bed-Material Hand Sampler.  This is a lightweight
piston-type sampler which  is used to sample bed material in streams or reser-
voirs shallow enough for wading.  It is constructed of readily available steel

-------
                                      2.51

pipe and fittings.  The sampling cylinder is 2 inches in diameter and 8 inches
long.  A handle is provided at the top of the sampler frame for pressing the
cylinder into the streambed.  As the sampler is forced into the streambed, a
piston in the cylinder is retracted.  Suction created by the piston holds the
sample in place.  Upon removal from the stream, the piston is used to force
the sample out of the cylinder.
     Bed-load Samplers.  Suspended sediment samplers will only sample to a
point about 0.3 foot above the streambed.  The sediment transported in the
unsampled zone is composed of both suspended load and bed load.  The bed load
portion is composed of particles having a density or grain size which pre-
cludes movement far above or for long distances out of contact with the
streambed.
     In wide sand-bed streams with shallow flow depths and high sand con-
centrations, more sediment may be transported in the unsampled zone than in
the sampled zone.  As flow depth increases, the proportion of sediment in the
unsampled zone becomes smaller, often accounting for only a small fraction of
the total sediment load.
     The bed-load portion of sediment discharge in uncontrolled stream chan-
nels is the most difficult to sample.  Although many portable samplers have
been constructed and tested, none have proved entirely satisfactory for all
conditions.  For this reason and because the use of portable bed-load samplers
in uncontrolled stream cross sections requires a detailed study and evaluation
of the site conditions, these samplers are not discussed.
     At controlled stream cross sections, fixed bed-load samplers can some-
times be developed to provide an adequate sample.  The Tombstone Automatic
Bedload Sampler is an example of instrumentation designed for a specific loca-
tion.  This sampler was designed to take a sample of bed load (sand and
gravel) on the downstream side of a concrete measuring flume.
     The 1-inch by 12-inch sampling slot, powered by an electric motor, tra-
verses back and forth through half of the flow cross section extracting a
sample from the bottom 12 inches of flow.  The water sediment mixture passing
through the slot is routed through a series of graded sieves where the coarse
bed-material particles are trapped.  The trapped sediment is subsequently
removed, measured and packaged for laboratory analysis.  The sample includes
only particle sizes larger than the smallest sieve opening.
     The preferred method of sampling bed load is in restricted turbulent

-------
                                      2.52

stream cross sections or overfalls where the total sediment load is in suspen-
sion and suspended sediment samplers can be used.  The sheet piling grade
control structure with footbridge and manually operated sampling device is
typical of instrumentation that may be developed for total load sampling.  A
U.S. DH-4S suspended sediment sampler is attached to a rigid strut and raised
and lowered by a cable and reel arrangement.  The sampler passes through the
entire flow vertical on the downstream side of the sheet piling control.  It
is moved across the channel on a dolly attached to the bridge hand rails.

2.4  Meteorological Data
     The collection of meteorologic data is essential to prediction of pesti-
cides, nutrients, sediment and water runoff as well as estimates of evapo-
transpiration.  The following discussion is from Brakensiek (1979), which has
compiled many of the basic methods of measurement for these data.

     2.4.1  Site Requirements
     A central meteorological station should be located to be as represen-
tative as possible of the macroclimate of the study area.  When watershed con-
ditions cover a wide range, such as in mountainous areas, several base
stations may be needed to adequately sample the mesoscale regimes making up
the watershed climate.  These base stations could be supplemented with data
from temporary substations on less important areas that could be correlated
with from the base station.  Microclimatology, the precise definition of the
meteorological variables in a vertical section over a point, may be useful in
special studies at the facility, but is usually not part of the routine data
collection program.
     In any event, most meteorological observations are point measurements
that will be used to represent an area.  Thus, there is an assumption of spa-
tial conformity, more true for some variables than for others.
     Exact specifications for locating a climatological station cannot be
given.  A site away from the immediate influence of nearby trees and buildings
is necessary.  It should not be on a steep slope, on a sharp ridge, or in a
narrow valley.  The site should be such that the exposure will not be changed
over a long period.  The ideal selection is an open, grassy area isolated from
buildings, trees, and other obstructions by a horizontal distance of at least
four times their height.  In arid areas, a sparsely vegetated site would be

-------
                                      2.53

more natural.
     Instruments at the climatological station should be installed to provide
a good exposure for each instrument, primarily in terms of isolation from
other instruments.  Important to consider are such details as having the door
of the instrument shelter open to the north, locating obstructions such as
electric poles to the north of the plot to avoid shading the instruments, and
maintaining a fence that will protect the site from animals.
     Areas of concrete or gravel under or near instruments should be kept to a
minimum.  The fence should not exceed three feet in height, should be made of
large mesh wire at the top with smaller mesh below, and should be supported on
posts with a small cross section.  A perch higher than the other instruments
may attract birds that would otherwise roost on the sensors.  Extra space
should be reserved in the plot for installation of additional instruments not  '
planned for when the plot was established.
     Whenever feasible, recording instruments should be used in lieu of
instruments requiring manual observations.  These instruments furnish con-
tinuous observations over weekends and holidays—data that might be missed
otherwise.  Local standard time should be used for all observations.  Daily
averages, where required, should be for the calendar day.  New stations should
adopt the metric system for their observations.
     A permanent record of the station should be kept in a looseleaf notebook.
Such data should be entered as the latitude and longitude of the station, date
established, a map showing the physical layout including electric lines and
water lines, and the ground elevation of the point where the rain gage is
installed.  The record book should contain a series of photographs that
clearly show the exposure of the plot and the relationship of the instruments
to each other.  A record should be kept of instruments added to or removed
from the plot.  Names of observers and dates of service should be noted.
Notes should be kept on general operations such as dates of mowing and
painting of shelters.  A separate page may be reserved for each instrument,
with notes on serial and model numbers used, calibration data, problems in
operation and their solution, and repairs or replacements made.
     Extensive climatological data compiled over the years by the National
Weather Service should not be overlooked.  Many meteorological readings, such
as air humidity, are conservative in that the average of a series of readings
taken at one location may be fairly representative of the daily average at

-------
                                      2.54

another location some miles away.  Frequency arrays from a long-term record
can be used to judge the normalcy of climate observed for a short period at a
nearby experimental site if the records at the two locations are correlated.
The assistance of the National Weather Service should be sought when questions
on long-term records arise.  A file of daily weather maps and local clima-
tological data sheets from one or two nearby long-term National Weather
Service stations will prove useful.
     The instrumentation suggested in this section may be considered minimal
for most facilities for watershed research.  The system described herein will
insure that sufficient meteorological data are collected so that the research
results of a facility may be compared on a climatic basis with results of
nearby National Weather Service stations or other watershed facilities.  The
data collected should be sufficient to enable a calculation of potential eva-
potranspiration on a daily basis.  If further detail is needed for a special
study, the installations can be expanded accordingly.

     2.4.2  Air Temperature
     Temperature of the air is one of the most commonly measured meteorologi-
cal variables at a research station in agricultural hydrology.  Air tem-
perature is so intimately related to evaporation, transpiration, soil freezing
and thawing, and snowmelt that its measurement is almost mandatory.  Daily
maximum and minimum temperatures are needed to determine mean daily air tem-
perature, a statistic required in most methods of computing daily potential
evapotranspiration.  A trace of the daily march of air temperature from a
thermograph or hygrothermograph is useful in studies of snowmelt and as a
backup system for maximum and minimum measurements.
     Separate liquid-in-glass maximum and minimum thermometers mounted on the
cross board of a shelter with a thermometer support (such as those used by the
National Weather Service) are recommended for obtaining daily extremes of air
temperature.  The maximum thermometer has a mercury-filled bulb exposed in a
nearly horizontal position—the bulb end about 5° above the horizontal.  The
metal backing of the maximum thermometer is clamped securely to the lower
(longer) shaft of the support at a point 3.5 inches from the high temperature
end of the back and with the bulb end to the left.  A rise in temperature for-
ces the mercury through the constricted part of the bulb into the graduated
portion.  The mercury remains in this part even though the temperature falls,

-------
                                      2.55

thus permitting a maximum-temperature reading.
     The minimum thermometer has an alcohol-filled tube exposed with the bulb
end about 5° below the horizontal.  The metal back of the minimum thermometer
is clamped securely to the upper (shorter) shaft of the support, slightly less
than half the length from the high temperature end and with the bulb end to
the left.  The bore of the thermometer contains a dark dumbbell-shaped piece
of glass called an "index."  As the temperature rises, the alcohol expands and
flows around the index without displacing it.  Further cooling causes the top
of the column to move nearer the bulb, carrying the index with it.  When the
temperature rises again,  the alcohol column moves toward the top of the bore
without moving the index, thereby leaving the index to indicate the lowest
temperature reached.
     Besides the maximum and minimum thermometers, a recording hygrother-
mograph should be operated on the floor of the shelter house.  This will fur-
nish a continuous trace record of the air temperature and relative humidity.
A weekly time scale is adequate.  Temperature pen readings are checked against
maximum and minimum thermometer readings made in the same shelter.
Adjustments are made to the pen setting whenever its error is more than 2° F.
Separate winter and summer charts a"re used in localities having wide ranges of
seasonal air temperatures.  Winter charts cover a range in temperature from
-30° to 70° F, while the summer chart range is 10° to 110° F.

     2.4.3.  Air Humidity
     Humidity of the air near the surface has a definite influence on the rate
of evaporation from lakes and ponds and on evapotranspiration from land areas.
The basic process in evaporation and evapotranspiration is the physical change
of water from the liquid to the gaseous phase.  This process occurs more
rapidly as the difference between the saturated vapor pressure at the water
surface and the actual vapor pressure of the adjacent air increases.  Thus,
evaporation occurs more rapidly in dry air than in air with a high relative
humidity.  Several techniques for computing potential evapotranspiration
require a measure of air humidity such as dew point or relative humidity.
     Instruments commonly used for measuring air humidity near the earth's
surface fall into two general categories:  (1) those using thermodynamic prin-
ciples and (2) those using the change in dimensions of hygroscopic substances.
Instruments using thermodynamic principles are called psychrometers.

-------
                                      2.56

Essentially they consist of two mercury thermometers, one of which has its
bulb covered with a piece of muslin or wicking for wetting.  These ther-
mometers are mounted together on a common backing with the wet-bulb ther-
mometer slightly lower than the dry-bulb thermometer.
     Techniques for ventilating the thermometers can be classed into three
general categories:  (1) natural ventilation, (2) moving thermometers rapidly
through the air, and (3) forcing air movement over the thermometer bulbs with
a fan or other device.  The first method is characteristic of simple psychro-
meters that are mounted in a. fixed position; these are sometimes designated
"hygrometers."  The second method is used by the sling psychrometer, which is
a widely used portable psychrometer.  The third method is represented by
several instruments, but the best known is the Assmann psychrometer.
     The most common instrument based on the change in hygroscopic substances
to measure air humidity is the hair-element hygrograph.  This instrument con-
tains a banjo set of human hair that expands .and contracts with changes in
atmospheric moisture.  Movement caused by expansion and contraction actuates a
pen that records relative humidity on a chart.  This chart is rotated in time
by a clock movement.  Usually the hair hygrograph is coupled with a device for
recording temperature on the same chart.  This combination instrument is
called a hygrothermograph.
     Several other instruments use special animal membrane elements to measure
air humidity.  These usually contain a dial and a needle that is linked to the
membrane and calibrated so that relative humidity can be read directly.  Thus,
they are designated hygrometers.  All of these instruments are very difficult
to calibrate and they are subject to considerable error.

     2.4.4  Wind
     Wind is important in both agriculture and hydrology.  Agriculturally,
excessive gusts of wind can damage many crops.  Hydrologically, wind influen-
ces the magnitude of evapotranspiration.  Wind speed and wind direction also
influence rain gage catch and the removal and deposition of soil and snow.
The total run of wind for each day is the minimum measurement of wind that
should be made at a hydrologic research station.  A chart trace showing the
direction of wind and the variability of wind velocities throughout the day
will prove useful at most stations.
     Many commercially available anemometers are satisfactory for routine

-------
                                      2.57

measurements of wind movement.  Readings should be recorded continuously so
that a permanent record of velocities is available.  The anemometer also
should record on a counting device to eliminate the necessity of counting tick
marks on the chart or integrating the chart trace to obtain a daily total.
     The standard anemometer is equipped with three conical, beaded cups
mounted on a rotor with a turning diameter of 17 inches.  The rotor assembly
drives a spindle that operates counter and a pair of wheels.  The wheels are
equipped with pins that close an electrical contact for every statute mile
(1.6 km) of wind and every 1/60 mile (26.8 m) of wind.  Electrical contacts
are wired to a recorder for a continuous trace of windspeed and wind direc-
tion.
     The wind transmitter operates from a 36-inch single-panel metal vane.
Eight of the ten switches are used to record direction continuously to  16
points.  The event recorder notes time of occurrence and duration of wind from
eight directions.  A simultaneous recording of two directions, such as  S and
SW, indicates that wind was from the intermediate direction, SSW.  A separate
pen records each mile of wind so that average velocity can be determined for
any period.  The remaining pen may be wired to record every 1/60 mile of wind
or movement of wind during precipitation or other special events.
     The use of a series of counters to record the total miles (or km)  of wind
movement on a calendar-day basis should be considered.  A timing clock  can be
used to activate a stepping switch every midnight.  The stepping switch shunts
the incoming signal from one counter to the next.  The time saving is con-
siderable compared to counting tick marks from a chart.

     2.4.5  Solar Radiation
     Solar radiation provides the energy that drives regional and global
hydrologic cycles.  Radiation is generally the most important factor in the
evaporation and transpiration processes.  The energy for plant growth and pro-
duction of dry matter is supplied by solar radiation.
     Several methods for determining potential evapotranspiration use solar
radiation data.  The usefulness of such equations is being extended by  studies
to establish coefficients that account for stage of crop development and other
plant and soil factors.  These coefficients permit the conversion of calcu-
lated potential evapotranspiration to realistic estimates of actual
evapotranspiration.

-------
                                      2.58

     Evaporation and transpiration are more closely related to  net  radiation
than to solar radiation  because a fraction of solar radiation is reflected
back to the atmosphere and  is not used in the conversion of radiant energy to
the latent heat of vaporization.  In the eastern states and irrigated areas of
the western states, evapotranspiration frequently uses over 80  percent of the
net radiation.
     The best estimates  of  evapotranspiration amounts, particularly for short
periods, usually are obtained with equations that involve net radiation as a
term.  Several equations are available for predicting evapotranspiration where
water is not limiting.   Equations using net radiation data, plant cover, and
other information are being developed to estimate actual evapotranspiration
under field conditions.  Evapotranspiration rates determined from meteorologi-
cal measurements by the  Bowen ratio method require net radiation data as an
essential element.
     Total incoming shortwave radiation is commonly measured with pyranome-
ters, sometimes called solarimeters.  They sense the intensity  of radiation of
wavelengths, less than 4\i from the sun and sky, that falls on a horizontal
plane.  (These instruments  are often erroneously referred to as pyrheliome-
ters.  A pyrheliometer measures direct solar radiation only.)
     The portion of the  total radiation of all wavelengths that is  transformed
into other forms of energy  is termed "net radiation."  Net radiometers measure
this difference between  the incoming (downward) radiation of all wavelengths
and the outgoing (upward) radiation of all wavelengths.
     The electrical output  from a radiation sensing device often is recorded
on a strip chart recorder fitted with an integrator.  Data reduction is
simplified if the integrator pulses are accumulated on counters.  Two or more
counters per recorder should be used, with an automatic mechanism for
switching integrator pulses from one counter to another at midnight.  Thus,
the integrated 24-hour value displayed on a counter can be read the next day
at the observer's convenience.  Because net radiation varies from incoming to
outgoing between day and night, it is sometimes desirable to integrate these
fluxes separately.  This is accomplished by having separate counters for the
plus and minus integrations.
     Electronic integrating systems are commercially available  that amplify
low-level signals, integrate the resulting current, and display the amount in
digital form for visual  readout.  These integrating systems are available with

-------
                                      2.59

single-stage amplification for use with circuits where the current does not
vary in polarity (such as with a pyranometer) and with two-stage amplification
for circuits where polarity reverses from time to time (such as with a net
radiometer).  They have an overall accuracy of about two percent, which is
adequate for many applications.
     Pyranometers and net radiometers must be installed so that the solar beam
is not obstructed at any time of the day, nor during any season.  The view of
the horizon from the instrument location should not be obstructed by nearby
objects such as trees and buildings.  In addition, glare or reflections should
not be directed toward the instruments.
     The site over which the net radiometer is exposed should be typical of
the situation under investigation.  This poses problems when mixed vegetation
or other nonhomogeneities exist at watershed sites.  Locating the instrument
high above such a site gives a representative measure of the net radiation of
the heterogeneous area because of the large field of view of the instrument.
     Instrument heights much greater than 3.3 ft cause some errors due to
radiation divergence.  These errors cause actual net radiation at instrument
height to differ from that at the surface.  Despite this theoretical dif-
ference, it is often best to expose net radiometers at a height of 3.3 to 9.8
ft when heterogeneous conditions exist.  When the sensor is  Z  meters above a
level surface, it receives 90 and 99 percent of its upward flux from areas
with a radius of 3Z and 10Z meters, respectively.

     2.4.6  Barometric Pressure
     The need for barometric pressure measurements will be determined by the
research program.  Measurements are incidental to the biological processes
important in agriculture and are not directly related to hydrological activi-
ties except in special situations.
     An estimate of the standard barometric pressure at the facility is
required in calculating potential evapotranspiration by the combination
method.  This value probably can be supplied by the nearest National Weather
Service office with sufficient accuracy, after allowances are made for dif-
ferences in elevation.  A barometric pressure term appears in the psychro-
metric formula, but a standard barometric pressure term should be used in
computing dew points unless extreme accuracy is required.
     The water level in a well penetrating a confined or partly confined

-------
                                      2.60

aquifer may rise and fall  inversely with atmospheric pressure.  If this effect
is possible at the facility, a recording microbarograph should be used.
     Some laboratory experiments may be affected by atmospheric pressure when
air is entrapped in a water column, thus necessitating the recording of baro-
metric pressure.  The value of the barometric chart in making short-range
weather predictions may be enough justification for operating a barograph.
     A microbarograph is recommended for routine readings of atmospheric
pressure at the facility.  A file of chartos from which a selection of data
that are pertinent to current needs should be maintained, rather than using
one or two visual readings noted during a day.  The microbarograph is not as
reliable as a mercury barometer for indicating absolute pressure, but it gives
a useful indication of pressure changes with time.  It is sufficiently
accurate for most hydrological and agricultural purposes.  If absolute
pressure values are required, they can be obtained from a mercury barometer
once a day and intermediate values can be interpolated from the corrected
microbarograph chart.

     2.4.7  Rainfall Measurement
     Of all the meteorological measurements, rainfall has the greatest effect
on runoff from small watersheds.  In its simplest form, a precipitation gage
is an open-mouthed can with straight sides.  Gages are installed with the open
end upward and the sides vertical.  Improved gages measure small amounts and
record the time and intensity of precipitation.  Rain gages are used in (1)
climatology, in which nonrecording gages are often used, (2) hydrology, in
which forecasting of runoff requires self-recording gages and totalizers, and
(3) hydrometeorological studies, in which a rain gage must show rates and
amounts of rainfall.
     For most climatological studies, today's rain gages are adequate.  For
hydrological purposes, such as runoff forecasting, the recording gages are
satisfactory although measurement of precipitation is limited by such factors
as gage sensitivity and network density.  For hydrometeorological studies in
which rates of rainfall and amounts must be shown accurately for short inter-
vals, today's networks of  recording gages are frequently inadequate.
     A wide variety of gages has been developed to measure precipitation; some
gages were developed for a special purpose.  Two types of gages (nonrecording
and recording) are used primarily in the United States.  The nonrecording gage

-------
                                      2.61

retains the total precipitation between observations; the recording gage gives
the time of precipitation so that intensities can be computed.

     2.4.7.1  Site Selection
     Installation should be geared to conditions of operation and maintenance.
Climatic factors, physical conditions of the site, and the anticipated type of
observer should be considered.  Usually simplicity of operation  is the best
guarantee of satisfactory performance.  Simplicity of procedure  insures ade-
quate observations.  Where procedures are complicated, the duties of the
observer should be reduced to a step procedure.  Provision in the installation
design often can facilitate such reduction.  Gage sites should be selected,
designed, and located to provide unconfounded records.
     The location of the gage is the primary consideration for obtaining
accurate precipitation measurements.  An ideal exposure would eliminate all
turbulence and eddy currents near the gage.  Individual trees, buildings, fen-
ces, or other small groups of isolated objects near the gage may set up
serious eddy currents, especially when their height above the gage is appre-
ciable.  As a general rule, an isolated obstruction should not be closer to
the gage than twice (preferably four times) its height above the gage.
Obstructing objects usually provide a more accurate catch when they are so
numerous and extensive that prevailing windspeed in the vicinity of the gage
has been reduced and, consequently, the turbulence and eddy currents also have
been reduced.  The best exposures often are found, therefore, in orchards, in
openings in a grove of trees or bushes, or where fences and other objects form
an effective windbreak.
     Sites on a slope or on ground sloping sharply away in one direction
should be avoided especially if this direction is the same as that of the pre-
vailing wind.  The surrounding ground can be covered with short  grass or be of
gravel or shingle, but a hard, flat surface, such as concrete, causes
excessive splashing and abnormally high surface temperatures.
     The growth of vegetation, trees, and shrubbery, and man-made alterations
to the surroundings may make an excellent exposure unsatisfactory in a relati-
vely short time.  The angle from the gage orifice to the top of  any nearby
object should not exceed 30°, thus allowing for growth of vegetation.  Under
no circumstances should an obstruction be nearer to the gage than its own
height (45°).  Wilson felt, however, that a small clearing in uniform forests,

-------
                                      2.62

having a diameter about equal to the height of the trees, was best because the
measurement would gain- more  from the reduction of wind than it would  lose from
interception.
     To place a gage in a  forest opening of 60-foot trees, a clearing of about
1/4 acre is required.  If  no such openings exist on a watershed or on control
watersheds where no cutting  is allowed, measuring rainfall at the surface of
the tree crown should  be considered.
                                                      ..•           •
     2.4.7.2  Factors  Affecting Accuracy
     Rain gages measure the  amount of precipitation that reaches the  ground.
Accuracy depends on inherent inaccuracies in the gage itself, wind velocity at
the orifice of the gage, and form of precipitation.  Inherent errors  can
result from bent, damaged, or deformed knife edge and orifice, leak in  storage
container; inaccurate  calibration of measuring container or dip stick,  tilted
orifice due to settling or improper installation, or evaporation between the
end of precipitation and when the gage is ready.
     The most common errors  result from evaporation, adhesion, color, inclina-
tion of the gage, splash,  wind, faulty technique in measuring catch,  and phy-
sical damage to the gage.  Errors in measurements have been estimated as
follows:
                                             Percent
                    Evaporation               -1.0
                    Adhesion                 -0.5
                    Color                     -0.5
                    Inclination               -0.5
                    Splash                   +1.0
                         Subtotal             -1.5
                    Wind                  -5.0 to -80.0
     The greatest amount of  error in rain-gage catch results from wind.  Under
exposed conditions, rain-gage catch generally is deficient.  This error is
related to windspeed and to  the type of precipitation.  The decrease  in catch
increases as wind velocity increases and is greater for light rain than for
heavy rain.  Wind increases  pressure on the windward side of the gage,
decreases pressure over the  gage, and sets up eddy currents over and  within
the orifice.  Since windspeed increases the height above a surface, the higher
the gage orifice is above  the ground, the greater will be catchment errors due

-------
                                      2.63

to exposure.
     Some inherent errors are caused by the gage being out of calibration,
binding or sticking parts in the weighing mechanism, bent, damaged, or
malformed orifice ring, or other mechanical damage to the gage.  The cause of
these errors, except gage calibration, can be detected by brief inspection
during routine visits to the station.  The observer should watch constantly
for errors and correct them as soon as possible to maintain high-quality
records.
     Sizable errors may occur in recording total catch.  They may or may not
be compensating and often change sign amount at the pen reversals.  Therefore,
the total catch in the bucket should be measured at the end of the storm.
     A properly installed pit gage accurately measures rainfall at a point.
When the rain gage is placed in a pit with its orifice at ground level, the
gage no longer obstructs air movement and the effects of turbulent wind around
the orifice are diminished.  Conventionally exposed gages, even when shielded,
catch less rainfall than pit gages.  Pit gages are inadequate for snow
measurements, however, because of problems with drifting snow under windy con-
ditions.  Trash and sediment also tend to collect in pit gages.  For extensive
rain-gage networks, increased accuracy usually does not warrant the increased
cost of installing and maintaining pit gages.
     The possibility of inaccurate measurements resulting from vertically
placed rain gages in watersheds of steep and complex topography was pointed
out by several investigators.  Errors were assumed to be due to the incidence
of different volumes of precipitation on sloping surfaces of several areas and
exposures where wind prevented the rain from falling vertically.  It was
recommended that gages be placed with their orifice parallel to the slope of
the land.  Rain-gage catch was divided by the cosine of the gage inclination
so that the volume would be on a horizontal area.
     The main sources of error will be inaccurate measures or dip rods,
spilling of some water when transferring it to the measure, and inability to
transfer all water from the receiver to the measure.
     Losses by evaporation also can occur.  Evaporation errors are most
serious in dry climates and in areas where gages are visited infrequently.
Losses can be reduced by placing oil in the receiver (this forms a film over
the water) or by designing the gage so that (1) only a small surface is
exposed, (2) the ventilation is small, and (3) the internal temperature of

-------
                                      2.64

the gage does not become excessive.  The receiving surface of the gage must be
smooth so that the raindrops do not adhere to it.  It never should be painted.
     In winter, rains often are followed immediately by freezing weather.
Damage to the receiver and subsequent loss by leakage can be prevented by
adding an antifreeze solution, especially when gages are visited infrequently.
Allowance for the solution added must be made when measuring the results.  All
gages should be tested regularly for possible leaks.
     Correct timing of the recorded precipitation trace and the ability to
estimate any errors in the record are important.  Three causes of error that
can affect timing of the record are backlash, clock rate, and change in chart
dimension.
     Backlash between the chart drum and the clock spindle delays the start of
the record and causes a constant error once the record has started.  Backlash
in the timing gears can be taken up by turning the drum until the indicated
time is about three hours fast and then turning it back to the correct time.
     Another error may be caused by the clock rate or the use of an unsuitable
time scale on the chart.  If the difference is small, the rate of drum revolu-
tion can be adjusted with the clock regulator.  All errors of this type pro-
bably cannot be removed by adjusting the regulator because clock rate will
vary according to temperature and humidity.
     Errors due to change in chart dimensions are caused by variation in humi-
dity.  Charts expand and contract as relative humidity increases and
decreases, and most chart papers will change more in one direction than in
another.  Whether changes due to humidity are greater in the time scale or the
depth scale, depending on how the paper is cut.  These changes easily can
exceed one percent and can amount to a 15- or 20-iainute error in the time
scale or several hundredths of an inch in the depth scale.  Charts also creep
up the drum because of expansion and contraction.  Therefore, the bottom of
the chart may be above the bottom flange of the drum in an amount equal to the
creep.
     All errors can be recognized and corrected if accurate time marks and
zero checks are made when the charts are put on and taken off the drum, and at
intermediate times when convenient.

     2.4.7.3  Nonrecording Gages
     Nonrecording rain gages usually consist of a collector above a funnel

-------
                                      2.65
leading into a receiver.  In the United States these gages have been  standar-
dized to the shape of a right circular cylinder with an eight-inch collector
orifice diameter.  Important requirments of nonrecording gages are:
     1.   The rim of the collector should fall away vertically inside and be
          steeply beveled outside.  The gage for measuring snow should be
          designed to minimize errors due to constriction of the aperture.
          Constriction is caused by the accumulation of wet snow above the
          rim.
     2.   The area of the orifice should be known to the nearest 0.5  percent,
          and it should remain constant.
     3.   The collector should prevent rain from splashing in or out.  This
          can be done by having the vertical wall sufficiently deep and the
          slope of the funnel sufficiently steep (at least 45°).
     4.   The receiver should have a narrow neck and should be protected suf-
          ficiently from radiation to minimize loss of water by evaporation.
          Rain gages used in places where daily readings are impracticable
          should be similar to gages used daily but should have a receiver of
          larger capacity.
     Precipitation in nonrecording rain gages usually is measured by  pouring
from the gage into a calibrated container or by using a calibrated dip stick,
or both.
     The calibrated container should be made of clear glass with a low coef-
ficient of expansion and should be marked clearly with the size of gage with
which it will be used.  Its diameter shold not be more than about one-third
the diameter of the rim of the gage and can be made less than this.   The gra-
duations should be finely engraved; generally, they should be marked  at 0.01,
0.05 and 0.10 inch.  For accuracy, the maximum error of the graduations should
not exceed 0.005 inch.
     To achieve this accuracy with small amounts of rainfall, the inside of
the measuring cylinder should be tapered off at its base.  In all measure-
ments, the bottom of the water meniscus should be taken as the defining line.
The measure must remain vertical, and parallax errors must be avoided.  It is
helpful if the main graduation lines are repeated on the back of the  measure.
     Dip rods should be made of cedar wood or other material that absorbs
little water and reduces capillarity.  Wooden dip rods are unsuitable if oil
has been added to the collector to suppress evaporation of the catch.
Therefore, use rods of metal or other material from which oil can be  cleaned.
These rods should have a brass foot to avoid wear and should be graduated

-------
                                      2.66

according to the cross  section of the gage orifice and the receiving  can,
allowing for displacement  due to the rod itself.  Marks should be  show-n  for at
least every 0.02 inch.  The maximum error in the dip-rod graduation should not
exceed +0.005 inch at any  point.

     2.4.7.4  Recording Gages
     Three types of recording precipitation gages in general use are  weighing,
tipping bucket, and float.  The only satisfactory instrument for measuring
both liquid and solid precipitation is the weighing-type gage.
     Several rainfall intensity recorders have been designed and used for spe-
cial purposes.  They are not recommended for general networks, however,
because of their complexity.  A satisfactory record of rainfall intensity can
be determined from a float- or weigh-in-type recorder by providing the proper
time scale.
     Whether the rainfall  recorder operates by weighing the rise of a float,
the tipping of a bucket, or other method, these movements must be  converted
into a form that can be stored and analyzed later.  The simplest method  of
recording is to move a  time chart by a spring or electrically driven  clock
past a pen that moves as the float or weighing device moves.  Two  main types
of charts are:
     1.   The drum chart,  which is secured around a drum that should  revolve
          once a day (exactly), once a week, or another period as  desired;
     2.   The strip chart, which is driven on rollers past the pen arm.  By
          altering chart speed, the recorder can operate from one  week to a
          month, or even longer.  The time scale on this chart can be large
          enough to calculate intensity easily.
     The movement of a  float, bucket, or weighing mechanism also can  be  con-
verted into an electric signal.  This signal can be transmitted by radio or
wire to a distant receiver where records can be made from several  rain recor-
ders on data-logging equipment.
     Most clocks for rain  gages can be geared to provide one drum  revolution
in 6, 12, 24 or 192 hours.  The time scale selected will depend on the storm
characteristics being studied, the shortest interval to be read from  the
charts, and the frequency  or ease of servicing gages.  Table 2.8 is a guide
for deciding which time scale to use.  Generally, the shorter the  interval,
the more difficult it is to extract data from the charts because of the

-------
                     2.67
Table 2.8.  Guide for Selecting Time Scale
            for Recording Rain-gage Clocks,
            from Brakensiek, et all, 1979.
Time for 1
revolution of drum
(hours)

6
12 	
24
192 	 	 	
Shortest interval
between chart
time lines
Minutes
5 	 . _
10 	
20 „ .
120 	 	
Shortest
interval
on chart
Minutes
I
2
5
30

-------
                                      2.68
crossing and recrossing of  trace lines between chart changes.  For ease in
chart reading, use the longest  interval that is compatible with the  study

objectives.


2.5  References

Al-Shaik-Ali, K. S., D. B.  Simons and R. M. Li, 1978.  Effect of sediment on
resistance to flow in cobble and boulder bed rivers, Civil Engineering
Department, Colorado State  University, Fort Collins, Colorado,
CER77-78KSA-DBS-RML-46.

Beckman, E. W., and L. W. Furness,  1962.  Flow characteristics of Elkhorn
River near Waterloo, Nebraska,  U.S. Geological Survey Water Supply Paper
1498-B.

Brakensiek, D. L., H. B. Osborne and W. J. Rawls, 1979.  Field Manual for
Research in Agricultural Hydrology, Agricultural Handbook No. 224, Science and
Education Administration, Washington, O.C.

Carter, R. W., and I. F. Anderson,  1963.  Accuracy of current meter  measure-
ments, Journal of the Hydraulics Division, ASCE, Vol. 89, No. HY4, Proc. Paper
3572, pp. 105-115, July.

Colby, B. R., 1960.  Discontinuous rating curves for Pigeon Roose and Cuffawa
Creeks in northern Mississippi, U.S. Department of Agriculture, Agricultural
Research Service Report 41-46,  31 pp.

Corbett, D. M., 1943.  Stream gaging procedure, Geological Survey Water Supply
Paper 888, U.S. Government  Printing Office, Washington.

Corps of Engineers, 1968.   Missouri River channel regime studies, MRD Sediment
Series No. 13A, Omaha, Nebraska.

Dawdy, D. R., 1961.  Depth-discharye relations of alluvial streams - discon-
tinuous rating curves, U.S. Geological Survey Water Supply Paper 1498-C, 16
pp.

Fread, D. L., 1973.  A dynamic  model of stage-discharge relations affected by
changing discharge, NOAA Technical Memorandum NWS Hydro 16, November.

Henderson, F. M., 1966.  Open Channel Flow, MacMillan, London.

Li, R. M., G. O. Brown and  D. B. Simons, 1979.  Computer simulation  of river
stages, Colorado State University, Fort Collins, prepared for Summer Computer
Simulation Conference in Toronto, Canada.

Senturk, F., 1969.  Nehir hidroligi, DSI Publication No. 66/X/64, Ankara.

Simons, D. B., and E. V. Richardson, 1961.  The effect of bed roughness on
depth-discharge resionation in  alluvial channels, Geological Survey  Water
Supply Paper 1498-E,  U.S. Government Printing Office, Washington.

-------
                                      2.69
Simons, D. B., M. A. Stevens and J. H. Duke, 1973.  Predicting stages of sand-
bed rivers, Journal of the Waterways, Harbors and Coastal Engr. Division,
ASCE, Vol. 99, No. WW2, Proc. Paper 9731, pp. 231-243, May.

Simons, R. K., 1977.  A modified kinematic approximation for water and seid-
ment routing, M.S. Thesis, Department of Civil Engineering, Colorado State
University, Fort Collins, Colorado.

Simons, R. K., R. M. Li and D. B. Simons, 1977.  On stage discharge relation
of rivers, Proceedings Congress IAHR, Baden-Baden.

-------
                                       3.1
III.  SPATIAL AND TEMPORAL CORRELATION
3.1  Introduction
     Any set of data has information stored in it and there  are  various ways
to usurp this information.  Data collected at regular intervals  in time are
known as a time series.  A simple method to grasp overview characteristics of
a time series is to simply plot the measured values versus time.   In this way
information such as variability and periodicity  (i.e.,  daily,  monthly,  seaso-
nal, or annual fluctuations) of the time series  may be  inferred.   Raw sta-
tistics of the data (mean, standard deviation, skewness,  etc.) are
mathematical transformations of the data which result with a reduction of the
total volume of data to a few numbers.  Statistics of mean and standard
deviation are helpful in designing and sizing structures.  For example the
mean organic load to a sewage treatment plant aids in the sizing of the
plant's components.  The mathematical transformation of data in  order to com-
pute the mean does not create any additional information, it simply reveals
information which is present in the data.  This  concept is true  for all forms
of data transformation (mathematical, graphical, etc.).
     Peculiar to most time series data is that the smaller the sampling inter-
val (frequent sampling), the more similar each data point is to  previously
measured points.  This fact indicates that a relationship exists between con-
secutive data points and this relationship is called the  data (or process, or
system) "memory."  "No memory" indicates that one data  point has no rela-
tionship to previous or subsequent points.  An example  of this is flipping a
coin and recording heads or tails.  Large memory means  that  there is a high
degree of relationship between consecutive points.  Average  daily streamflow
on the Delaware River at Philadelphia has a large memory  since the average
daily discharge does not considerably change over 24 hours.   The degree of
memory in a data series can be found by utilizing a mathematical transforma-
tion called the autocorrelation function.  The autocorrelation function com-
putes the relation (correlation) between the points of  a  data series.  This
mathematical transformation is discussed in Section 3.2.
     Information which is also present 'in a data set is the  relationship bet-
ween one data set and another.  An example of this type of relationship is a
rating curve.  The rating curve reveals the relationship  between river stage
and river discharge.  The stage and discharge are both  time  series, and by
plotting concurrent points of stage and discharge the familiar power function

-------
                                       3.2
relationship can be observed.  There  is a mathematical transformation  for data
sets which can compute  the  relationship or independence of the data sets and
it is called the cross-correlation function.  The cross-correlation function
is described in Section 3.3.
3.2  Correlation In Time, the Autocorrelation Function
     3.2.1  Introduction and Theory
     Temporal correlation essentially is a mapping of the relationship of data
of one gage with itself, when considering various time  lags between data
points (correlogram).   Figure 3.1 depicts an observed time series  and its
corresponding correlogram.  Autocorrelation theory has  been derived for con-
tinuous as well as discrete time.  Due to the fact that most hydrologic data
is taken only at regular time intervals/ only the discrete case will be
treated herein.  Errors induced by discretization of a  continuous  series will
be treated in a later section.
     The sample .autocorrelation function (r ) is:
                                           JC
               cov (x
           (var  (x.) var  (x    )}
                                  1/2
         N-k
                                 2 /N-k   \/N-k
               Nk
                                       1/2
N-k
                                                  N-k
                                                      i+k
                                                                      (3.1)
                                  1/2
where:  x = observed hydrologic variable; k = the number of  lags between data
points; and N = the total  number of observed points.  Computationally, this
equation can be simplified by multiplying both numerator and denominator by
(N-k)^ .  For a finite sample, as  k  increases, there  is  less data  to compute
the
r   value (N-k values) and therefore there is less reliability in the
 K.
estimates of  r  for large values of  k  [k a error in estimate] .
               K

-------
                             3.3
      K.I93I ' 32 ' 33  34 ' 35 '36  37  38  39 ' 4O '  41 ' 42  43 ' 44 ' 45
 3000
      1946- 47  48   49  50  51  52  53  54  55  56   57  58   59  6O
                                       k, months
Figure 3.1.   The hydrograph and correlogram of monthly river
              flows of the Middle Fork of the American River
              near Auburn, California  (1931-1960)(after
              Yevjevich).

-------
                                       3.4

     Significant properties of the autocorrelation plot are:
          r  =  1.0
           o
          r, =  r
           k    -k
   =  What physically  occurs during the computation of any autocorrelation
coefficient (also called the serial correlation coefficient),  r  ,  is to view
                                                                 K
the one data set as two.  This is depicted in Table 3.1.   Column one is simply
the observation period,  for the purpose of this example this can be  assumed to
be one day.  The second  column is the observed streamflow for the respective
sampling period.  Columns three and four represent the two series',  derived
from the original series in column 2, used for computing the lag zero auto-
correlation coefficient   (r )  .  The q's are substituted for the x's in
Equation 3.1, where in this case,  k=0 .  Since the two series'  (columns 3 and
4) are identically the same,  cov(q. ,q. ) = var(q. ) , thus the numerator and
denominator of  Equation  3.1 are the same and  r =1.  This is always  true.
Columns five and six  are the data series'  used in computation of the lag one
autocorrelation coefficient  (r1) •  Here, values from one time period are
related to the  values from the following time period.  Since there is only a
finite set of data points (N=15), the total length of the series' used for
computation of  r   is N-k (15-1=14).  The two series are not identically the
                 K
same, as they were for  r  , thus cov(q. ,q   ) £ var(q.)  .  In fact,
cov(q. ,q.  ) <  var(q.)  .  Without loss of generality, it can be assumed that
var(q. ) = var(q .) . Thus the denominator of Equation 3.1  is equal to
var(q. ) .  The  numerator  (cov(q. ,q .,.))  is the relationship between how the
     1    .                       1.
product of two corresponding points  of the correlated data series',  q.  x
q    (i.e., in columns  five  and six,  line 7,  i=7,  k=1,  q.  = q  = 18 and
 1" JC                                                     1    /
^•+1, = ^a = 17)' relate to the product of the mean of each series (mean of
column five times mean  of  column six).  With  perfect correlation, i.e.,  r ,
                                                                          o
q. x q     is always  positive (even  when negative  values are measured) and has
 !L    1 •" 1C
the same value as  q. 2 .   This means that q.   and  q.    move  about their
respective means in perfect  synchronization,  thus  when  q.  is  greater than
its mean,   1.

-------
                                3.5
Table 3.1.  Data Series'  Used for Calculating the Lags Zero, One
            and Two Autocorrelation Coefficients.
Discharge
Observation q
Time
1
2
3
4
5
6
7
3
9
10
11
12
13
14
15
(cfs)
10
12
17
18
18.5
18
18
17
16
15
13
11
17
22
24
Lag Zero
Autocorrelation
Data Series'
qi
10
12
17
18
18.5
18
18
17
16 .
15
13
11
17
22
24
qi
10
12
17
18
18.5
18
18
17
16
15
13
11
17
22
24
Lag One
Autocorrelation
Data Series'
qi
10 ~
12
17
18
18.5
18
18
17
16
15
13
11
17
22

qi+1
12
17
18
18.5
18
18
17
16
15
13
11
17
22
24

Lag Two
Autocorrelation
Data Series'
qi
10
12
17
18
18.5
18
18
17
16
15
13
11
17


qi+2
17
18
18.5
18
18
17
16
15
13
11
17
22
24



-------
                                       3.6

     Mathematically,  the  correlogram of  various processes  have  been iden-
tified.  The correlogram  for random  independent variables  (Gaussian process,
white noise) is very  important  since the disaggregation  of stochastic pro-
cesses is directed  towards  reducing  a series  to white  noise and also other
processes can be compared to this process in  order  to  test for  any significant
correlation.  Figure  3.2  shows  the correlogram for  a random process.  Since
the sample is only  a  few  observations of the  total  population of random num-
bers, all  r   can  have non-zero values.   The value of the gaussian  r  , for
            JC                                                          K-
k > 0 , will fall below error limits based upon the total  number of obser-
vation and the lag.   The  equation for the 95% confidence bands  is:

               _ -1.0  + 1.96 (N-k -  1)1/2
           k   ~ 	N^k(3.2)
           kg5            N k

This limit is based on the  assumption that the  r,  are  normally distributed
                                                  JC
about the population  value   (p  = 0  for  all k > 0).  Recognize  that the 95%
confidence limit indicates  that 95%  of the time   r  <  Lfc   .  Therefore,  for
                                                  i\.     y o
twenty computed values of  r   it would  be expected that one value be outside
of the 95% limits.  Physical consideration should be given as to whether the
r    values outside of confidence limits should represent  something other than
 1C
sampling variability.  For  example   r   may usually be significant for most
hydrologic phenomena  which  are  monitored at regular intervals less than one
month.  If a monthly  measuring  basis is  used, it  is quite  possible for  r  >
       , this would  indicate  annual  cyclicity.
   -O
     The correlograms of  other processes have been  theoretically derived,
i.e., Autoregressive, Moving  Average, Autoregressive Moving  Average,  etc.,  and
correlograms from observed data  can  be  compared with them to identify the
underlying process by association.

     3.2.2  Loss of  Information  by Discretization
     The loss of information  by  discretizing a continuous process has been
studied (2) and some of the results  are presented here.   Out of  three types of
data measuring/reporting  methods, viz.  discrete point  sampling,  average
sampling, and quantization (reporting of data in class  intervals analogous  to
measurement errors of truncation or  accuracy), the  information loss  due  to
quantization sampling was negligible compared to the losses  introduced when

-------
                               3.7
                                    	Theoretical  Independent
                                        Process

                                     	95% Confidence  Band

                                    	Observed  Data
               \
                Lag
Figure 3.2.  Correlogram for an  independent process.

-------
                                       3.8

sampling in time.  This  implies  that  more frequent  sampling is  more important
than accurately  sampling.
     An example  of these  three types  of  data  measurement  is presented here.
In this case, samples  are  made from a continuous  uniform  distribution (there
is equal probability of  selecting  any real number between zero  and one.   When
sampling and reporting by  quantizing,  any sample  is  rounded off to the
measurement accuracy,  i.e.,  if the instrument can only measure  to the nearest
tenth, a sampled value of  0.1732 is reported  as 0.2.   Discrete  sampling
reports a measurement  as  it  is measured  at regular  intervals.   Average
sampling reports the average value of a  process over  some time  interval,  i.e.,
average daily discharge.   Six thousand data points  were selected from the uni-
form distribution and  these  were considered as bi-hourly  values.   Every
twelfth value was reported as the  daily  value.  These two types of sampling
represent discrete sampling. Every twelve values were averaged and reported
for average sampling.. Quantization was  used  on every twelfth point with  two
accuracy levels, accuracy  to the nearest tenth (0.0,  0.1,  0.2,..., 1.0) and
accuracy to the  nearest  hundredth  (0.00,  0.01, 0.02,  ...,  0.99,  1.00).  The
statistical results of the five  sampling schemes  compared to the population
parameters are presented  in  Table  3.2  and the empirical distributions for
four of the sampling schemes (exclude  quantization  sampling to  the nearest
tenth) are found in Figure 3-.3.
     Notice how  averaging  totally  transforms  the  uniform  distribution into a
normal distribution.   Thus it is evident that average sampling  aids in esti-
mating the mean  but is actually  detrimental to estimating the standard
deviation.  As this example  worked with  an independent process  (no relation
between two values), it  has  very limited application  to hydrologic problems.
The results of discrete  and  average sampling  of river data is presented in the
next two sections.

     3.2.2.1  Discrete Point Sampling
     Increasing  the sampling interval  from 2  up to  24 hours, for river flows,
does not introduce any significant information loss  in estimating the mean.
The same can be  said about estimation of the  process  variation  and autocorre-
lation with sampling intervals less than six  hours,  in this instance
increasing to daily sampling results  with about 60%  loss  of information.   The
information loss when  estimating extremal events  can  be significant.  The

-------
                             3.9
Table 3.2.  Statistical Results of Various Sampling Methods
            on the Uniform Distribution
Sampling
Method
Population
Discrete
Discrete
Average
Quantizing (0.10)
Quantizing (0.01)
Sampling
Interval
Continuous
Bi-hourly
Daily
Daily
Daily
Daily

Mean
0.500
0.502
0.494
0.502
0.491
0.494
Standard
Deviation
0.289
0.287
0.296
0.080
0.302
0.297
Skew
Coefficient
0.000
-0.014
-0.052
0.013
-0.032
-0.052

-------
      e.s
            	  II-HOURLV DISCRETE
             	  DAILY QUANTIZATION SAflPUINC (TO THE NEWEST HUNDREDTH)
            	DAILY DISCRETE SArtPLINC
            	DAILY AVERAGE SAnPUMG
      e.3
P(S)
       e.i
                               .*\
                          	f
                       .-if-l
                                            ,..«••••
V^
                ^
          e.e
                                                  •.a
                                                STORAGE
                                                                      J.2
                                             t.4
l.C
              Figure 3.3.  Empirical distributions  from various samples of
                           the uniform distribution between zero and  one

-------
                                     3.11
marginal information loss tends to decrease with sampling  intervals  larger
than four hours .

     3.2.2.2  Average Sampling
     When the mean is the only data statistic of interest, average sampling
can occur in intervals up to 24 hours without significant  loss  of information.
Unfortunately, estimation of the variance and autocovariance  functions  are
severely impaired by average sampling.  With a sampling interval of  only four
hours, a great degree of bias is introduced.  On a daily sampling interval,
the information loss in estimating the variance was three  orders of  magnitude
larger than when using discrete point sampling.
     For estimation of extreme events, an increase in the  sampling interval
yielded information losses similar to discrete point sampling (usually  larger
losses though).

     3.2.3  Effect of the Sampling Interval on the Correlogram
     The further apart data is taken in time, the more likely the measurements
are to be independent of each other.  This effect can be visualized  with the
aid of Figure 3.4 which plots the correlograms for the Terror River,  Alaska
for various sampling intervals.  Recognize that the first  serial correlation
coefficient for monthly sampling (r ) is equal on the average to the thirtieth
serial correlation coefficient for the daily sampling (r   ) and also the fif-
teenth serial correlation coefficient (r1c) when sampling  every other day.
Another way of presenting the gradual independence with time  is to plot the
relation of the average first serial correlation coefficient, r ,  with
sampling interval, this occurs in Figure 3.5.  Interesting in Figure 3.5 is
that r  for 120-day sampling is negative.  This represents the  seasonality of
the river where there is evidently distinctive high and low flow seasons of
the year.  Also, there appears to be large annual correlation,  possibly owing
to the long season of melt-runoff ( 6 months) .
     As previously mentioned, the first serial correlation coefficient  of
annual sampling (r ) is equal, on the average, to the 365th autocorrelatin
coefficient (r~365) of the daily sampling autocorrelation function.   If  yearly
sampling were done on October 30, r  would most likely be much  higher  than
r     .   This is due to normally low flows during this time of  the  year  and
 Joo
thus less variation of the flow.  If annual sampling were to  occur  on  April 5,

-------
                    3.12
                             Daily Sampling
                             Sampling Every Other Day
                            Weekly Sampling
                            Monthly Sampling
                                   8
                  Lag
Figure 3.4.   Correlograms for the Terror River,
             Alaska due to various sampling
             intervals.

-------
      t.e
             	 UXCR  BS» LiniT
             	 UPPER  B5» LIHIT
-P
c
0)
•H
CJ
•H
0)
8
c
o
-P
(0
8
o
+J
U)
M
•H
CM


8.
id
M
0)

I
                                                                                                           M
                                                                                                           OJ
-1.5
      -l.t
                                                     Illlillilllllitllilll
                               IM
                                                                                              4M
                                           Sampling Interval
              Figure  3.5.   Correlogram for  the Terror River daily flow  series.

-------
                                      3.14

r   would most likely  be  much  lower  than  r     owing  to  high  variability in the
timing of snowmelt and  the  more  numerous precipitation  events  during the
spring.  Thus, low variability creates  high annual  correlation and the con-
verse is also true, and r_._  for the  daily series simply  averages this effect
                          3oo
for every day of the  year .

     3.2.4  Miscorrelation:   Effects  of the Misuse  of Data  and the
            Misinterpretation of the  Autocorrelation Function
     3.2.4.1  Intermittent  Processes
     Improper use of  the correlogram  can lead  to misinterpretation of a phy-
sical process.  Take  for example Figure 3.6, which  plots  correlograms for the
Rio Puerco, New Mexico.   The  use of the daily  flow  series results in extremely
high correlation structure.   Recognize, though, that the  Rio Puerco is an
intermittant stream with an average of  205 days per year  without  any flow.
This data produced the  top  most  curve in Figure 3.6.  If  data  generation were
to be based on such a correlation structure, severe errors  would  result due to
the implication of strong watershed memory.  If the intermittancy was
accounted for by deleting all zero flow values from the historic  record, thus
placing all storm hydrographs end to  end, the  resulting correlation structure
would be smaller than the initial approach but higher than  the true watershed
memory.  This is due  to the fact that the first one or  two  and the last four
or five values of the hydrographs are very small, causing a higher overall
correlation due to effects  which physically should  not  have any relation.  A
truer representation  of watershed memory would be to average the  r  values for
                                                                   k
each hydrograph of non-zero discharge (lowest  curve in  Figure  3.6).  Similar
types of tniscorrelation may be inferred when analyzing  precipitation data/-
water quality data with a seasonal polluter (i.e.,  apple  processing,  etc.); or
any other intermittant  process.   A significant aid  to screen such types of
data is a plot of the time  series itself.  Such plots qualitatively indicate:
mean, variability, seasonality,  and intermittancy.

     3.2.4.2  Jumps and Trends
     Data inhomoegeneity is produced  by jumps  and trends  in the data set.  A
positive data jump is depicted in Figure 3.7a, and  in general  the jump can be
positive or negative.   Jumps  can be caused by  various factors,  for example:
construction of a dam,  stream capture,  change  in measurement techniques, etc.

-------
    Rio Puerco
                                  3.15
 1.0
0.5
 0
            I       2      3

              Lag (Days)
-e— All Values

-a— Neglecting Zero's (Placing  all flows
                          in one array)
-£»— Neglecting Zero's
       Figure 3.6.  Correlograms for the daily flow series of the
                    Rio Puerco.

-------
                                    3.16
o>
»_
a
-5
en
a
o
3
C
Mean of each series
before  and after the Jump.

Overall  Mean
 I960
 1965           1970

           Time (Years)
1975
1980
       Figure 3.7a.
     Effect of a constant jump  on  an annual flow series.

     6  is the jump in the mean for data before and after

     the jump.
             _ Mean of entire series

             . . Linear Trend
 a>


 a

 o
 a
 3
 C
 I960
 1965           1970

           Time (Years)
1975
1980
         Figure 3.7b.  Effect of a linear trend on an annual flow series.

-------
                                     3.17

A classic example of a jump is the change in the annual  flow  of  the Nile River
due to the construction of Aswan Dam.  The effect of a jump on the data is to
change all statistics (12), i.e., mean, standard deviation, skewness,  and
serial correlation.  The mean changes with the type of jump  (increasing jump,
increasing mean) and the variance increases with the magnitude of  the  jump
(large jump, large increase of the variance).  The autocorrelation function
decreases with the magnitude of the jump.  A simple example of this is to
visualize a jump in a constant process, here the correlogram  will  change from
r,  = 1.0 for all k > 1 to r,  < 1.0 for all k >1 .
 k                 —       k
     A linear increasing trend is depicted in Figure 3.7b.  The  nature of
trends can be increasing or decreasing and linear or nonlinear and they may be
caused by various factors, i.e., watershed urbanization,  industrialization,
revegetation, etc.  An example of a trend is the water use time  series of a
growing city, each year more and more water is demanded  due to an  increase in
the number of users.  Trends also change all data statistics.  The mean and
variance changes with a trend are the same as for the constant jump.   The
effect of the trend on the autocorrelation coefficients  is to increase them.
This increase is due to the fact that the trend represents an increase in the
deterministic part of the data set, thus there is more relation  between points
due to the trend.  Trends and jumps will be considered further in  the  next
chapter.

     3.2.4.3  Measurement Accuracy (Effect of Truncation) and Autocorrelation
     There is no instrument which can exactly measure a  process.   Measurement
errors arise from misreading, improper calibration, accuracy  of  the instru-
ment, and even use of the instrument itself may disturb  the process being
measured such that a true reading is not possible.  All  of these errors,
except the measurement accuracy, are random errors in the data series.  The
measurement accuracy is a constant error that may or may not  effect the repre-
sentation of the process which is being measured.  Usually measurement
accuracy is tied to the cost of the measuring instrument, the more accurate
the measurement the more costly the instrument.  If the  measurement is too
coarse, the process being measured is not well monitored, i.e.,  if one was
interested in the acidic Ph fluctuations in a river in order  to  detect cri-
teria violations, not much information would be obtained if the  measuring
instrument read either acidic or basic (as does litmus paper).   Contrary to

-------
                                      3.18

this last example, if  one  wanted  to  measure  the  Mississippi  River Discharge at
New Orleans, it would  be foolish  to  measure  to  -?0.0001  cfs  since not much
information would be obtained  by  this  accuracy.   Section I-B dealt with data
accuracy when data sampling  by quantization  was  discussed.   In this case,
accuracy can change most of  the statistics of a  data  set.   Increasing accuracy
will not significantly change  the mean and will  slightly decrease the standard
deviation, also the serial correlation coefficients will be  slightly higher.
A decrease in accuracy can be  viewed as a process with  many  small jumps,  here
the effects on the data statistics are opposite  to those of  increasing
accuracy.

     3.2.5  Effects of Reservoirs on Correlation Structure
     3.2.5.1  Introduction
     Man's influence on hydrologic variables can be quite significant,  espe-
cially in the case of  reservoirs. The effect of a reservoir,  in a hydrologic
system, is to increase water residence time.  This effect results with lower
water velocities  (causing  sediment deposition),  increased mixing of water,  and
a decrease in the discharge  range (maximum minus minimum discharge).  The
magnitude of the effect of reservoirs  on  hydrologic variables  is a function of
the relative size of the reservoir compared  to the mean annual reservoir
inflow.

     3.2.5.2  Water Quantity Variables
     Water storage in  reservoirs  creates  an  increased correlation structure of
the water quantity variables.   This  is due to the fact  that  flood peaks are
stored for later release,  and  also that drought  flows are augmented.  These
effects produce a very slow  change in  reservoir  outflow from one day to the
next, which may be quite contrary to the  inflow  time  series.   Figure 3.8
graphs the monthly time series' of inflows and outflows for  the Bonny
Reservoir which is located on  the South Fork of  the Republican River (SFRR)  in
northeast Colorado.  The inflow series is a  combination of the SFRR, gaged  at
Idalia, and Landsman Creek.  Landsman  Creek  supplies  about 9%  of the total
annual inflow.  The reservoir  outflow  is  gaged on the SFRR at  Hale, and there
is a major diversion at the  dam which  is  not accounted  for.  The correlograms
for each individual component  and for  combined components occur in Figures  3.9
and 3.10.  Figure 3.9  indicates that the  SFRR at Idalia does not reveal a

-------
sae  r-
            S. f. R. R. AT HALE
            COMBINED INFLOU
                                                                                                           to
                                                                                                           M
                                                                                                           VO
                                                                                        zse
                               Tine (BOHTHS)  T-«  IS OCTOIER 19SI
         Figure 3.8.  Hydrologic variables for the Bonny  Reservoir.

-------
     1.0 r
A
U
T
0
C
0
R
R
E
I
A
T
I
0
h
C
0
E
F
F
1
C
1
E
N
T
 e.s
    0.0
-e.s
    -1.0
                 SFRfl AT IDALIA
                 LAflDSHAN CREEK
                 SFRR AT HALE
                 LOUER 95* LiniT
                 UPPER 95* LlfllT
                                                                                                              lo
                                                                                                              O
            i.	I   1   1   I   1   I	1	 j	I	|	I	I	j '  I	i	I	I
                                                            30
                                                                                               50
                                             LAC (FIOMTHS)
       Figure  3.9.   Correlograms  for the  Bonny  Reservoir hydrologic  variables.

-------
     t.e
A
U
T
0
C
0
R
R
E
I
A
T
I
0
N
C
0
E
r
r
l
c
I
E
N
T
e.s
-e.s
    -i.e
            	 SFRR AT HALE

            	 COnilMED RESERVOIR INFLOW

            	 LOUER 95* LIMIT

            	 UPPER 95* LIMIT
                                                                                                            OJ

                                                                                                            to
                                                           30
                                            LAO (nOHTHS)
       Figure  3.10.  Correlogram for the Bonny Reservoir hydrologic variables.

-------
                                      3.22

strong seasonal component.   This  is  due  to  the  influence  of  thunder shower
activity and many  irrigation diversions  and return  flows  above the gage.
Contrary to this,  on  the  smaller  Landsman Creek watershed, there is definitely
a seasonal factor  evidenced by large r    and r   .   The  reservoir outflows show
the greatest seasonality  effects  and this results from  seasonal operation
rules for filling  and emptying the reservoir.   Such rules can be observed in
Figure 3.8, where  outflows  are increased before the large inflow periods  in
order to reserve storage  space.   Bonny began filling June 6,  1950, construc-
tion was completed May 4,  1951, and  it was  first filled March 29,  1954.   Since
this time, the outflow hydrograph begins drawing down before  the high inflow
season and also after large flood events.

     3.2.5.3  Water Quality Variables
     The.effect of reservoirs on  water quality  variables  is  similar to the
effect on water quantity  variables,  and  this is smoothing of  the inflow
series.  Another effect of  the reservoir, though, is to become a sink for che-
micals, pollutants, etc.  As previously  mentioned,  low  reservoir water veloci-
ties result in a depositional environment for sediments.   This would include
insoluble chemicals as well as chemicals attached to the  sediment, i.e.,
phosphorus, etc.   In  addition,  the location of  sedimentation  may be suitable
for an aquatic environment  which  utilizes incoming  nutrients  and soluble  che-
micals, i.e., swamps.   This type  of  environment has been  evidenced by reser-
voir and lake eutrophication.
     Three water quality  time series were selected  at two stations on the Rio
Grande.  The Otowi Bridge gage is 26 miles  upstream of  Cochiti Dam and the San
Felipe Gage is 15  miles below the dam.   These gages are part  of the USGS  sur-
veillance network  and thus  many chemicals,  nutrients and  other water quality
variables are regularly monitored at each.   The three variables chosen for the
purposes of this analysis are Ph, total  nitrogen (N)  and  total phosphorus (P).
The Ph time series of Figure 3.11 indicate  that the reservoir decreases the Ph
and also introduces a lag of 1-2  months. The correlograms of these series
displays a fairly  independent inflow process, yet the outflow series has
strong correlation extending over three  months.  The total nitrogen and total
phosphorus series  of  Figures 3.12 and 3.13  indicate that  the  reservoir does
act as a sink for  these chemicals, but also there is a  large  loading mechanism
below the dam.  The correlograms, for the same  figures, indicates  that these

-------
                                          •3.23
is.e
             RIO GRANDE AT OTOUI BRIDGE
             RIO CRAMDC AT SAN  FELIPE
12.5
ie.e
 7.5
 s.e
 2.5
 e.e
                                       j_
                                                         I
                                       40               69

                                Tine  tnoMTHS)  T-e is JULY 1975
              A
              U
              T
              0
              C
              0
              R
              R
              E
              {.
              A
              T
              I
              0
              M
              C
              0
              E
              F
              F
              I
              C
              :
              E
              M
              T
                                OTOUI BRIDGE .. .
                                SAM FELIPE ...PH
                                LOUER 9SX UNIT
                                UPPER 9S» LIPIIT
-1
                                    I
                                             IB          15


                                              LAC  CnONTHSJ
                                                                   2«
            Figure 3.11.
        Smoothing of  the Ph monthly time series of
        the Rio Grande due  to Cochiti Reservoir.

-------
                                              3.24
T
0
T
A
L
M
I
T
R
0
C
E
                  RIO GRANDE AT OTOUI BRIDGE
                  BIO GRANDE AT SAN FELIPE
                                            40
                                     Tine
                                                             66

                                                  T-e is  JULY I»TS
                                                                               8«
                                        OTOUI IRIDCC ...TOTAL  NITROGEN
                                        SAM FELIPE ...TOTAL  MITRO&EN
                                        LOUER 95* LIMIT
                                        UPPER BS» LiniT
                      A
                      U
                      T
                      0
                      C
                      0
                      8
                      a
                      E
                      I
                      A
                      T
                      I
                      0
                      N
                      C
                      0
                      e
                      F
                      T
                      I
                      C
                      I
                      E
                      N
                      T
-1
                         I
                                    I
                                                    !•         IS

                                                     LAQ  (HONTHS)
                Figure  3.12.
     Effect of Cochiti Reservoir  on the monthly
     total nitrogen  time  series.

-------
                              3.25
   RIO GRANDE AT OTOUI BRIDGE
   RIO GRANDE AT SAN FELIPE
                             4«                66

                     Tine cnoHTHS)  T-»  is JULV
                     OTOUI »RIDC£'"TOTftl- PHOSPHORUS
                     SAN FELIPE... TOTAL PHOSPHORUS
                     LOUCR 9SX LiniT
                     UPPER 95* UniT
   A
   U
   T
   0
   C
   0
   R
   R
   E
   L
   A
   T
   1
   0
   M
   C
   0
   E
   F
   F
   I
   C
   I
   E
   N
   T
 1  i-
-1
                                             IS
                              LAG
Figure 3.13.
       Effect  of Cochiti Reservoir  on the  monthly
       total phosphorus time series.

-------
                                     3.26

time series are fairly independent processes.  For all three variables,  there
does not appear to be any  strong  seasonal or annual cyclic component.

     3.2.6  Note on Sampling  Frequency Design
     3.2.6.1  Introduction
     The design of any monitoring system is greatly affected by  legal,
logistical, political, and administrative considerations.  The design and
operation are further confined by economic constraints.  Thus the total  number
of stations and the sampling  interval tend to counteract each other.  Many
stations may not leave enough personnel and/or money for a productive sampling
frequency  (see Figure 3.14).
     The selection of the  sampling frequency itself must be related to the
objective of the monitoring network  itself.  Examples of water quality objec-
tives are:  computation of the total load of a certain material, i.e.,
sediment; detection of criteria violations; maintaining effluent standards;
aid in mathematical model  calibration; designing  temporal criteria based upon
the temporal loading; identification of loading mechanisms; aid  in the design
of structural measures for water  quality control; definition of  natural
background levels prior to construction or watershed management practices.
Examples of water quantity objectives are:  water budget identification; aid
in the design of hydraulic structures; analysis of the system variability/-
legal partitioning of ownership;  minimum stream standards; aid in calibration
of hydrologic/hydraulic models; frequency analysis for design criteria.

     3.2.6.2  Water Quality Sampling Frequency
     Pomeroy and Orlob based  the  design of water quality frequency on the size
and water quantity variability (Q   .   /O  . .    ) of watersheds.  Sanders
          ^-                       maximum  minimum
et.al. (3) have based water quality monitoring frequency on the  importance of
any of the three objectives of:   measuring extremes; measuring trends; and
measuring means and the distributions of the variables.  All of  Sanders'
objectives can be conveniently placed on probabilistic terms and thus this
method is more attractive  as  far  as  formulating sampling frequency on the
water quality variables themselves rather than on water quantity variables.
What the probabilistic statements enable are a direct computation of the
number of samples per time period given the amount of acceptable error of the

-------
                                     3.27
o
o
                            Sampling  Interval
  Figure  3.14.  Comparison  of  a continuous process with its discrete time

                representation.

-------
                                      3.28

measured parameter.  Unfortunately,  the method  requires apriori  knowledge  of
the mean and variance of  the  process which  is to be  sampled.

     3.2.6.3  Concepts  for  Designing Sampling Frequency
     It must be borne in  mind that  if a sampling station  does  not  fulfill  the
monitoring requirements of  the objective the station is almost worthless.
Without any data, the sampling frequency must be determined by scrutinizing
the objective.  For example,  if the  objective is to  be able to minitor  the
mean of a process, monthly  monitoring may be feasible if  the process  is not a
rapidly varying process.  If  the objective  is to be  able  to identify  periodi-
cities, the process may have  to be monitored six times a  day in  order to
detect daily, weekly, monthly and annual cyclicities.  Once the  sampling fre-
quency is set and after some  data is obtained,  the data may be analyzed to
test whether or not it  is fulfilling the objective.  For  example,  the auto-
correlation function may  indicate too high  a correlation  between successive
measurements, thus a data redundancy is present and  the sampling interval
could be reduced.

     3.2.7  Conclusion  for  Temporal  Correlation
     The use of the correlogram can  indicate much about a physical process.
Inferences on system memory or process cyclicity can be'made based upon corre-
lograms.  Also inferences of  the actual time series  process can  be made by
comparing a computed correlogram to  theoretical correlograms.  Data gaps in a
station's records could be  filled by knowledge  of the underlying process and
the correlation function.

3.3. Spatial Correlation;   The Cross-Correlation Function
     3.3.1  Introduction  and  Theory
     Considering two separate time series (x,y), measuring one variable at two
stations or measuring two different  variables at one station,  the  cross-
correlation function can  identify the relationship between the two series  at
various time lags.  A common  form of cross-correlation is the  usage of
regression, i.e., a water discharge-sediment discharge relationship.  The  two
time series used in regression analysis are usually  regressed  by using  values
measured at the same time,  the R  value (coefficient of determination or
explained variance) obtained  from the regression analysis is the square of the

-------
                                     3.29
lag zero cross-correlation coefficient (/R2 = r  (x,y)), which  is  commonly
called the coefficient of correlation (r) (see Lecture 4).  The cross-
correlation function allows computation of the correlation  between points at
any desired lag, similar to the autocorrelation  function.   When the records  of
two stations are analyzed by using cross-correlation at lags other than zero,
the analysis occurs over time and space.
     The equation for the cross-correlation function is:
          rk(x,y)
                         COv(VyU*}
   1/2
                                         N
N-k L i*i+k " ~2 L i L *i
N k i=1 l i+k N2 i=1 1 i=1 1
U ? X2 _i /? xvi
N • -, 1 »2 I >. . L
I 1=1 N \i=1 / J
1/2

N
" Z,

yt

                                                                      (3.3)
                       '  (\    \  21
                      7  Uyi)   J
1/2
Recognize that the records for each time series must have the  same  length.
This equation is very similar to that of the autocorrelation function
(Equation 3.1).  Figure 3.15 displays the cross-correlogram for  the Bonny
Reservoir inflow and outflow series (found in Figure 3.8).  The  positive lags
[r (x,y), k > 0]  relate future outflows to the present  inflows,  these  indi-
cate the water residence time of the reservoir.  The negative  lags  (r   x,y)
                                                                     ™1C
physically are relating the inflow series (x) to preceding values of the
outflow series.  Since physically there should be no relationship between
outflows and inflows which have not yet occurred, the r   (x,y) values are  not
                                                       "™ K
significantly different from those of an independent series (p (x,y) =  0 for
                                                               K,
all k).  The exception to this, in Figure 3.15, is r  (x,y), which  is above
the 95% limit for independent x and y processes.  Recall that  the first serial
correlation coefficient for the SFRR at Hale (the Bonny  Reservoir outflows)
was very large (r  = 0.563, Figure 3.10).  Thus the reservoir  outflow from the
present period has a lot of relation to the outflow in the next  period.
Correspondingly, the lag zero cross-correlation coefficient between the inflow
and outflow series [r (x,y)]  is also very large ([r (x,y) = 0.500],  Figure
3.15).  Thus,  with strong dependence between successive outflows and strong

-------
 R (X.V)
 LOUCR SS» LtniT
 UPPER 9S» UiniT
                                      Illllllllllllll
                                                                                                CJ
                                                                                                o
                            uw
Figure 3.15.   Cross-correlogram between the Bonny Reservoir inflows
               and outflows.

-------
                                       3.31

 dependence of inflow and outflow at the same time period, there  is  some degree
 of dependence between present outflow and inflow of the  next  period due to the
 reservoir memory.  This type of carryover relation is depicted  in Figure 3.16
 where strong, physical dependences are marked by solid arrows and implied
 dependence, caused by the reservoir memory and cross-dependence  structure, is
 marked with a broken arrow.
      It is important to note that the cross-correlation  function (similarly as
 does the autocorrelation function) is measuring the degree  of variability of
 points at a certain lag with their respective mean, thus there  is no implica-
 tion of scale or cause and effect in the cross-correlation  function.  Figures
 3.17 and 3.18 exemplify this point.  Two independent time series are depicted
 in Figure 3.17.  Note that although the two series have  a large  difference in
 magnitude and variability, their movements about their respective means is
 quite similar.  This latter fact is evidenced by the large  lag  zero cross-
. correlation coefficient in Figure 3.18 [r (A,B) = 0.944].
      Cross-correlograms aid in identifying relationships between .time series
 of two variables.  Examples are:  travel time between two locations on a
 river; relation between discharge and water quality variables;  influence of
 atmospheric phenomena on streamflow, i.e., cloud cover,  convective
 precipitation; etc.  Also, cross correlograms can detect independence of two
 time series', i.e., sunspots and runoff; time between storm events  and inten-
 sity of storms; etc.

      3.3.2  Effect of Spatial Correlation on the Amount  of  Information
             Obtained from a Gaging Network
      What any correlation coefficient indicates is the amount of information
 present in two sets of data.
      Considering two raingages to be situated in one watershed,  if  the objec-
 tive is to obtain the most amount of precipitation information  with the two
 gages for use in hydrologic simulation models, the two gages  should be placed
 far apart from each other as well as being well within the  watershed boun-
 daries.  If the gages were placed right next to each other, it  is farily
 obvious that there would be a huge redundancy of information.   This would
 be indicated by a large r (x,-y) coefficient.  The farther away  the  gages are
 placed, the lower r (x,y) and the more information obtained on  the  spatial
 variability of rainfall.  The following hypothetical example  results from the

-------
                             3.32
             Reservoir Inflows
             Reservoir Outflows
                  3456
                        Time (months)
                                   8
Figure 3.16.
Relationship between reservoir  inflow  and outflow
time series.  Solid arrow indicates  strong,
physical relationships.   Broken arrow  indicates a
relationship caused by other dependence  structures.

-------
                                 3.33
             Process A
  20--
x
CO
"c
                             10           15
                         Time (months)
 20
       Figure 3.17.  Two time series'  (A,B) measured in units of  x .
                       (A,B)
                                                     rk(A,B)
                                              	Upper 95% Limit
       -4   -3   -2
345
                           Lag (months)
  Figure 3.18.   Cross-correlogram  for the two time  series of Figure 3.17.

-------
                                      3.34

work of Yevjevich and  Karplus (4).
     Within a fixed  area,  assume  a  network  of  raingages  exists.   Also assume
that the lag zero cross-correlation coefficient  between  stations  (p..)  is uni-
form.  Due to the interstation dependence,  the information from a set number
of dependent stations  is  equal to the  same  amount  of  information  from a much
smaller number of independent stations (p (x,y)  =0).  This smaller number of
independent stations is known as  the effective number  of stations (n ):

          n  =	^	                                         (3.4)
               1 + p±.  (n-1)

where
       n = the total number  of stations  and
     p.. = the average  lag  zero  cross-correlation  coefficient  between all  sta-
tions.  The effect of station  interdependence  is found in  Table  3.3  and
graphed in Figure 3.19.
     This last example  may  aid in  the  design of systems and  this is  because
with the knowledge of interstation correlation, a  system may be  designed to
obtain the maximum amount of information  for the fewest number of stations.
More importantly, the trade-off  between the amount of  obtainable information
and the degree of desired interstation correlation (in order to  fill data
gaps, etc.) may be assessed for  their  separate marginal benefits with respect
to the overall network  and  the budget  for the  network.

     3.3.3  Use of Cross Correlation for  Network"Design and  Application to a
            Raingage Network
     3.3.3.1  Introduction
     Numerous studies have  been  conducted which deal with  the  spatial variabi-
lity of precipitation.  Precipitation, used here,  refers exclusively to rain-
fall, although special  notes are made  with regards to  snow.  This section  will
be broken down in such  a manner  as to  identify and present the factors which
affect precipitation from large-scale  down to  small-scale  or local effects.
Example of the large-scale'to  small-scale sequence is:   watershed geographic
location, watershed topographic  location,  gage location in the watershed.

     3.3.3.2  Geographic Effects on the Spatial Variability  of Rainfall
     The spatial variability of  rainfall  is significantly  affected by the

-------
                              3.35
Table 3.3.  Effect of Station Interdependence on the Effective
            Number of Stations (n ).  The Entries in the Body
            of the Table are  n   Based on the Number of
            Stations, n, and the Average Interstation Lag Zero
Iross-Correlation, p . . .

n
2
5
10
20
50

0.2
1.67
2.78
3.57
4.17
4.63

Pij
0.5
1.33
1.67
1.82
1.90
1.96

0.8
1.11
1.19
1.22
1.23
1.24

-------
                       3.36
                                                   =0-2
                                             «>  ^=0.5
                                             ©  />ij=0.8
10
           15   20  25   30   35  40  45  50  55   60
                Number of  Stations (n)
Figure 3.19.  Graphical representation of Table 3.3.

-------
                                     3.37

location of a watershed in the continental United States*  Much  of  this  effect
results from the origination and travel of moisture.  Figure  3.20 depicts  the
origin locations of storms and their numbers and average January paths for the
years of 1892-1912 (Geoff Love, personal communication).   If  geographic  loca-
tion was the sole measure of the spatial variability of rainfall, it would be
expected that the least amount of spatial variation would  occur  along the
storm paths.  Orthogonal movements from the storm paths would result with  the
largest spatial variation of precipitation.  This knowledge alone can aid  in
the siting of precipitation gages.  For example, if a sampling network were to
be designed to monitor the increse in rainfall acidity due to industrializa-
tion, the maximum effects would of course be realized in the  general downwind
direction, and in this direction monitoring gages can be spaced  farther  apart
than in other directions.  If the monitoring gages were placed upwind from the
industrialized region, effects of industrialization may be masked by
background rainfall acidity which, in upwind areas, may be as large as the
degree of industrial-caused acidity.
     The effect of geography on the spatial correlation of precipitation in
the midwestern United States was studied by Yevjevich and  Karplus  (5).   The
study areas (Figure 3.21, Region I and Figure 3.22, Region II) have minimal
topographic effects, and by observing the storm traces of  Figure 3.20, it  is
seen that storm movements are fairly uniform over the areas.   The interstation
lag zero cross-correlation coefficients (r (x,y)) were computed  between  all
precipitation stations in the study area by utilizing at least 40 years  of
monthly data for the correlation coefficient computations.  The  r  (x,y) data
were then plotted against the interstation distance and ten mathematical
models were analyzed for their fit to the data.  An example of one  of the
mathematical models which was fitted to the data is presented in Figure  3.23.
The three best fitting models are presented in Table 3.4 with the corres-
                                                                       2
ponding optimized parameters (A,n), and coefficient of determination (R  )  for
each region.  Although the mathematical fit to the data is very  good, it is
believed that even better fit could be made by weighting the  interstation
distance by its bearing (i.e., for E-W bearing the weighting  coefficient is
1.0 and for N-S bearing the weighting coefficient is 1.25, then  all bearings
between these two bearings would have a weighting coefficient between 1.0  and
1.25) .

-------

                                          .   ?•*••.*.  "ip^,11 :r^-^j ^'*VT*^
                                       i     " \  »   _? <""v   ^i ji  •  -^/° °
 'A  t'Vy  '  jf

-------
                             3.39
                       100,00 "w
                            92.5O°W
 Figure 3.21.
 Location within U.S.A. of Region I, used as the
 example for the regionalization of parameters
 of monthly precipitation series, (after Yevjevich
 and Karplus)
                       99.5O°W
                           96.0O*
                                            42.50°
                                          	. 40.00°
Figure 3.22.
Location within U.S.A. of Region II used as
the second example for the regionalization
of parameters of monthly precipitation
series, (after Yevjevich and Karplus)

-------
                        3.40
0.90
0.8O
0.7O
0.6O
0.50
0.4O
0.30
01 n
nnn
i/*
*fc
^
•^








V _. .
^
<<•








s^.
y&j
•r>?>
•V..









•Zfc
. **








^
•^••^








'. — -
^v"7

•










d
                 5O  IOO 150 200 250 3OO 350
                         miles
Figure 3.23.
Fit of the equation r  =  (l-Ad)~n
to the data for Region I  (Figure
3.21) , with corresponding 95%
tolerance limits  (after Yevjevich
and Karplus.

-------
                               3.41
Table 3.4.  Mathematical Fit of Interstation Correlation  (r } and
            Interstation Distance (d-miles) Data for the Mid-
            western United States (after Yevjevich and Karplus)
Region

I


I

I

II

II

II
Model
-1
r = (1 + Ad)
0
—n
r = (1 + Ad)
o
r = (1 + Ad)~1/2
o
r = (1 + Ad)~1
0
r = (1 + Ad)~n
o
r = (1 + Ad)~V2
R2

89.8


90.8

91.6

91.0

92.0

92.2
Fitted Coefficients
A n

0.006


0.016

0.018

0.007

0.015

0.018

— —


0.534

__

__

0.571

—

-------
                                      3.42

     3.3.3.3  Topographic  Effects  on the Spatial Variability of Rainfall
     It is a. well  recognized fact  that  precipitation variability in space is
significantly controlled by the  relief  of  the  earth's surface.   One common
effect is the release  of moisture  on the windward  side of  mountain ranges, and
a "rainshadow" on  the  leeward side.   Physically, as  moist  air masses are
lifted, the amount of  total moisture the air mass  can hold decreases.   Once a
lifted air parcel  reaches  saturation, any  further  lifting  can result in preci-
pitation.  Thus, when  incoming air masses  approach the mountains,  most of the
moisture deposits  on the windward  slopes.  When the  air mass passes over the
mountain peaks and begins  descending, its  total moisture has not only been
reduced, but the amount  of total moisture  that the air can hold is increasing.
Thus on the leeward mountain slopes,  only  strong convective or  frontal systems
can squeeze-out more moisture from the  air.  Studies of this effect for speci-
fic locations are  found  in references (7)  and  (8).  The result  of topography
on the spatial correlation of precipitation is to  modify the correlation
structure prescribed by  the geographic  location  (presented in the last
section).  These two effects combine to form regional spatial variability
effects in precipitation.
     The topographic/geographic  effects on the spatial correlation of  precipi-
tation is found in Figure  3.24 (reference  6).  The ellipses represent the
major and minor axes of  correlation,  highest correlation in space is the major
axis (C ) and the  direction of lowest correlation  is the minor  axis (C ).  The
quotient of the major  and  minor  axes (C /C ) is written below each ellipse.  A
quotient of 1.0 indicates  isotropic  variations and as the  quotient approaches
zero the ellipse approaches a line.   If the general  moisture movement over the
continental United States  were assumed  to  be west  to east,  all  of the  ellipses
would be aligned with  their major  axis  in  this direction.   Topographic effects
can shift this alignment a full  90°.  The  90°  shift  can first be seen at the
west coast and is  attributable to  the orographic influences of  the Cascade,
Sierra Nevada, and Coast Ranges.   This  alignment indicates less spatial
variation in the North-South direction, perpendicular to the general moisture
movement (6).  A similar re-orientation of the major and minor  ellipse axes
occurs at the Rocky Mountains.  Once these orographic controls  have been
passed, the orientation  of the major and minor correlation ellipse axes beco-
mes aligned to the West-East moisture flow.  Exceptions to this occur  near the

-------
                          3.43
                                     ^
                       ? / -  »   I3i  15   1.7
                                             >
"  ^°"?.\?  *-..
'  .«*fc£M» 07'
3 •* v^V-i-i.-r 4 *.?.w
  „   -«7 ^ Ux, ^ - - "*" '  V»
5 * w&it
-    /v-'  ' *"r
    AJ^»u    *^ '
    /        \

-~e*  *'
   _ ** "*• o., 0«
   ^^O ST I
            1
                                                      -3'
               ,"* »*
.^
          -tff—J&—**—&
          ^•< 0*4  oa> als
                   o«-^ '^ Oil-©- ^- ^ _:
                        OS*  07> I OTT 07T OT3 O«^
                  J®r& -   '         *
  Figure 3.24.
            Regional distribution of the azimuths of the axes of the
            maximal correlation coefficients and the values of the
            ratio (C /C_) for the annual precipitation variable.
            (after Caffey)

-------
                                      3.44

Great Lakes and  the  Gulf  of  Mexico,  which bodies  of  water  also act as moisture
sources  (6).

     3.3.3.4  Small-Scale Spatial Variabilty of Precipitation
     The elements  causing small  scale  (i.e., watershed)  variability in preci-
pitation are local topography and climatic regime.   Topographic influences
were presented in  the  last section and they tend  to  re-orient the alignment of
the spatial correlation structure set-up  by the general  flow  of moisture.
Climatic regime  will be discussed in this section.   Specifically, the climatic
regime will deal with  the various types of precipitation events which occur in
a region, viz.,  thunderstorms, steady  rains, air  mass  storms,  etc.   These  cli-
matic regimes can  be further subdivided by:  season  (time  of  year);  depth  of
rainfall; sampling interval;  storm duration; etc.  It  would be expected large
storms produce less  spatial  variability than small storms.  For example, a •
thunderstorm would only affect one or  two gages in a watershed whereas a tro-
pical depression may affect  all  gages  on  a watershed.  Along  this line, it
would be expected  that longer duration and larger rainfall depth storms would
produce less spatial variability than  short duration and small depth storms
(steady rain versus  thundershowers).   Two studies which  have  verified these
observations are references  10 and 11.  Huff and  Shipp (10) found that the
large variability  of thunderstorm rainfall depth  reduces the  overall spatial
correlation when analyzing the spatial variabiity of rainfall depth (Figure
3.25).  In Figure  3.25, rainfall depths of 0.01 - 0.10 inches were mostly
attributable to  large  scale  storms producing drizzle and light, extensive
rain, also the storms  with a total depth  greater  than  1.0  inch mostly resulted
from large storm systems.  Thundershower  activity, in  general, yielded depths
of 0.1 -1.0 inches.  Other correlations for Illinois,  found by. Huff and Shipp
(10), are found  in Figures 3.26, 3.27,  and 3.28.  These  figures plot the lag
zero cross-correlation coefficient against the distance  between raingages.
All of the plots are for  May through September storms.  Huff  and Shipp found
that the cold weather  precipitation  events (October-April)  in general yielded
larger cross-correlations than the warm weather storms.  For  concluding
remarks, they described the  required interstation distance for various rain-
fall monitoring  objectives (i.e., total rainfall  depth,  type  of storm, fixed
storm duration,  etc.)  given  a desired  interstation correlation of 0.866 (75%

-------
                      3.45
            Total Storm Rainfall  Depth (inches)
          345    ~-—	_.    9
                                  ^\Zf —.—.
                         678

             Interstation  Distance  (miles)
                                                 0.51 - I .CO
                                                 0.26-0.50
10
 0.11-0.25
Figure 3.25.   Effects of total rainfall depth with
              interstation correlation.

-------
                                   3.46
     1.0
    0.8-•
                                                       Storm Duration (hours)
                                                              6.1-12.0
    0.6  -
                                                               3.1-6.0
*-   0.4-
    0.2-
                       3456789
                         Interstation  Distance (miles)
                                   10
          Figure 3.26.
Effect of storm duration and interstation
correlation for May through September
storms in Illinois, (after Huff and Shipp)

-------
                                   3.47
    1.0


   0.8


^ 0.6
x~
   0.2
                                                       h
      0123
4   5   6  7  8   9  10  II   12  13  14  15  16  17
     Interstation Distance (miles)
     Figure  3.27.   Overall  spatial correlation of precipitation for
                    May  through September storms in Illinois.
                    (after Huff and Shipp)
    I.O-c
 Time Step tor  Rainfall Rate  Averaging
                          "" -o lOmin.
                                I min.
                                           -4-
                            6       8      10
                          Interstation  Distance  (miles)
       Figure 3.28.
 Effect of the time step for reporting average
 rainfall depth on the interstation correlation
 for May through September storms  in Illinois.
 (after Huff and Shipp)

-------
                                      3.48

explained variance).   Depending  on the  objective/  raingages would then have to
be spaced between  0.3  miles  to  12  miles apart.
     In a similar  study in Vermont,  Hendrick and Comer (11) found results
similar to those of Huff and Shipp.   Their  desired interstation correlation
was 0.90 (81% explained variance)  and this  correlation required raingages to
be 2.5 to 4 miles  apart (depending on the objective).

     3.3.4  Spatial Variability  of Streamflow
     The spatial variability of  streamflow  is much smaller  than that of preci-
pitation.  This is due to water  storage (in rivers,  on the  surface,  and
underground) in the watershed which acts to smooth the precipitation input.
This means that gages  can be placed farther apart  on a river and yet maintain
a relatively high  correlation.   Depending on the sampling interval and the
water velocity, the largest  cross-correlation coefficient between two series
may occur at any lag  (r (x,y), r.(x,y),  r (x,y), etc.)  and  the largest cross-
                        o        l        2
correlation coefficient would indicate  the  travel  time between gages.
Recognize, that high cross-correlation  between  two streams  on the same
watershed does not indicate  a cause  and effect  relationship (when one stream
is flooding the other  must also  be flooding,  etc.).   What the high correlation
means in this case is  that both  streams most likely have  flows owing to the
same type of causal factor  (i.e.,  groundwater recharge, precipitation,
snowmelt, etc.).  Thus independent variables are uncorrelated, but uncorre-
lated variables are not necessarily independent.   Dependence in correlated
variables does not have to be a  physical or cause  and effect dependence.

     3.3.5  Spurious Correlation
     It is possible to create an apparent correlation between two variables
when there is in fact  no correlation present between their  data sets, this is
called spurious correlation. Two  types of  spurious correlation which can
exist are data clustering and presence  of one variable in both data sets.
Data clustering is depicted  in Figure 3.29.   The overall  cross-correlation
between x and y is large, yet the  correlation within each cluster is essen-
tially zero.  Any prediction of  y  by   x   would be dangerous since there is
an implied relationship by the unpartitioned data  set.  A.n  example of this may
occur with water versus sediment discharge  in an intertnittant stream with
seasonal runoff from snowmelt and  thundershowers.   The snowmelt runoff may

-------
                    3.49
       IOO              200               300
 Average  Monthly Water Discharge (AF/month)
Figure 3.29.   Spurious correlation caused  by
              data clustering.

-------
                                      3.50

have low flows with  low  sediment  concentrations and the thundershowers would

produce highly variable  flows with  large sediment  loads.

     The second type of  spurious  correlation arises when data  is  being stan-

dardized or nondimensionalized.   In these cases, two variables  (X and Y) which

are initially independent, may each be divided or  multiplied by a third

variable (Z) such that X/Z and Y/Z  (or XZ and YZ)  show significant  correla-

tion.  This is a spurious correlation caused by a  common random variable.

Corrections for common variables  in a correlation  relationship  have been

determined and tabulated (such as in reference 13).


3.4  References


Yevjevich, V.,  1972, "Stochastic  Processes  in Hydrology,"  Water Resources
Publications, Fort Collins,  CO.

Dyhr-Nielsen, M., 1972,  Loss of Information by Discretizing Hydrologic
Series, Hydrology Paper  No.  54, Colorado State University,  Fort Collins,
CO, October.

Sanders, T. G., ed., 1980, Principals for Network  Design for Water
Duality Monitoring,  Colorado State  University, Fort Collins, CO,  July.

Pomeroy, R. D. and G. T. Orlob,  1967, "Problems of Setting Standards and
of Surveillance for  Water Quality Control," California State Water
Quality Control Commission,  Pub.  No. 36, Sacramento, California,  May.

Yevjevich, V. and A. K.  Karplus,  1973, Area-Time Structure of  the Monthly
Precipitation Process, Hydrology  Paper No.  64, Colorado State  University,
Fort Collins, CO, August.

Caffey, J. E.,  1965, Inter-Station  Correlations in Annual  Precipitation
and in Annual Effective  Precipitation, Hydrology Paper No.  6,  Colorado
State University, Fort Collins, CO, June.

Burns, J. I., 1953,  "Small-Scale  Topographic Effects on Precipitation
Distribution in San  Dimas Experimental Forest," Trans., Am. Geoph.  Union,
Vol. 34, No. 5, pp.  761-766, October.

Smallshaw, J.,  1953, "Some Precipitation-Altitude  Studies  of the
Tennessee Valley Authority," Trans., Am. Geoph. Union, Vol. 34, No. 4,
pp. 583-588, August.

Neter, J. and W. Wasserman,  1974, Applied Linear Statistical Models,
Richard D. Irwin, Inc.

Huff, F. A. and W. L. Shipp,  1969,  "Spatial Correlations of Storm,
Monthly, and Seasonal Precipitation," Jour, of Applied Meteorology, Vol.
3, pp. 542-550, August.

-------
                                     3.51


Hendric, R. L. and G. H. Comer, 1970, "Space Variations of Precipitation
and Implications for Raingage Network Design," Jour, of Hydrology, Vol.
10, pp. 151-163, October.

Yevjevich, V. and R. I. Jeng, 1969, Properties of Non-Homogeneous
Hydrologic Series, Hydrology Paper No. 32, Colorado State University,
Fort Collins, CO, April.

Haan, C. T.,  1977, Statistical Methods in Hydrology, The Iowa State
University Press, Ames, IA.

-------
                                      4.1

IV.  QUALITY OF DATA
4.1  Introduction
     Data quality is defined as the accuracy and homogeneity of  a  data  set.  (\0(y   .y
                                                                              AT    ^
Without exact measures of the quality of data  (i.e., 99% pure, etc.), the     \r*6
                                                                             I ) TV
assessment of what exactly the quality of a data set may be is difficult to  ^
describe.  Some data errors may be easily discerned by looking at  the physical
processes involved.  Other data inhomogeneities may be statistically tested
for or discovered by use of a physical process model.  These methods are pre-
sented in this chapter.
     Data are assumed to be of good quality if they represent the  measured
variables, do not fluctuate so widely that they cannot be interpreted,  have  an
acceptable level of error, and are physically realistic.  Data quality  is
affected by several factors.  These factors include:  sensitivity  of the
measurement technique, errors in the measurements, incomplete sampling, and
selection of the wrong variable to measure.  An example of incomplete sampling
and poor selection is encountered in rainfall measurements when  only daily
rainfall totals are recorded.  If the selected model requires rainfall  inform-
tion by five minute increments, then the daily rainfall is incomplete indi-
cating a poor selection of sampling interval.  However, if the daily water
balance is desired, then the daily total is perfectly acceptable.
     If data are difficult to measure or the measurement device  is insen-
sitive, there is the possibility of significant errors and lower quality data.
Hard-to-measure data may occur because of natural variability or the selected
measurement technique.  Natural variability of soils produces large differen-
ces in soil infiltration rates between otherwise similar sites.  Therefore,
infiltration rates are usually calibrated in the model using a representative
starting point.  Measurements are also sensitive to the technique  used.  For
example, discharge computed from a rating curve and stage height may substan-
tially differ from directly measured discharge if the measurement  device is
not responsive or sensitive enough to changes in flow depth.
     Errors in measurements can occur from human, mechanical or  technical
sources.  Human errors, such as not starting the measurement instrument
correctly and without proper calibration, or missing a reading can be caused
by inexperience in data collection and can usually be improved after proper
training.  Mechanical errors such as clock stoppage, plugging of stilling
basins, or the loss of sampling equipment during large runoff events can be

-------
                                       4.2

minimized through proper  design and maintenance.  Errors caused by measurement
techniques are often hard to  detect unless the limitations imposed by adopted
techniques are known.  An example of error common in reporting discharges is
created through use of average stage values.  This type of error is also
related to parameter sensitivity.  An  approach often used is to average hourly
stage values for a day, then  convert the stage/ often adjusting for a shift,
to an averge daily discharge.  This approach may be unacceptable because the
relationship between stage and discharge is often highly nonlinear.  The
stage-discharge relationship  can be written as

          Q = a Sb                                                   (4.1)
where  Q  is discharge,   S is stage,  and  a  and  b  are statistically fitted
parameters.  Many natural channels and most flow measurement devices have  b
parameters greater than,  or equal to,  1 varying from about 1 to 4 or 5.  A
typical value may be from 1.5 to 3.0 to provide enough sensitivity for
measurement.  The relative error in  Q can be found from

          ^«>5f

where  dQ/Q  is the relative  change in discharge and  dS/S  is the relative
change in stage.  Because  b  is usually greater than 1, an error in  S  due
to improper averaging is  magnified to  produce a greater error in  Q .  If
average stages are used to determine average discharges, there may be a signi-
ficant difference between that value and one obtained by computing each
discharge and then averaging.
     Although there are many  sources of error that can affect data quality,
the primary causes can be eliminated or reduced.  However, complete elimina-
tion of error is practically  and economically infeasible; therefore, an accep-
table amount of error must be allowed.  In this way, data can be of high
quality at an acceptable  cost.

4.2  Data Quality Assessment  through Physical Process Analysis
     As stated in the notes for the previous lecture (Spatial and Temporal
Correlation), some information contained within a data set may be extracted by
a simple plot of the data.  This also  holds true for misinformation present in
data.  The time series plot of data will depict any extreme (large or small)

-------
                                     4.3

values present in the data set.  With prior knowledge of the physical charac-
teristics, of the system from which the data came, it can be qualitatively
assessed as to whether or not any observed extreme values are physically
possible.  For example, if a large discharge value may be a reporting error,
if it has also been determined that:  no high water in low-lying areas was
reported, no large discharges into the river occurred elsewhere, and/or no
drastic watershed changes occurred.
     Another form of data error is detectable by knowledge of the physical
limits of the variable being measured.  In such a case, a data set may look
homogeneous with no extreme events, yet the entire data set may be wrong due
to improper recording and/or reporting.  For example, if the monthly pan eva-
poration for Cincinnati was reported over a five-year period with values
always'within a range of ten to thirty inches per month, the data is obviously
wrong since calculation of the average monthly evaporation by physical models
using the maximum solar radiation available could not consistently yield such
high values (the average annual evaporation for Cincinnati is about 34 inches
per year1).  Many data sets can be qualitatively assessed by comparing
reported values with published long-term regional average values.  Knowledge
of system variability will aid in determining the degree of extreme values
which should occur in a data set.  Also, simple calculations can be made in
order to compute the general values of a process.  For example, using mean
annual rainfall on the rational formula to get mean annual discharge.
     Of special importance in detection of data errors is the physical rela-
tionship  between variables in the watershed system.  Plotting two time series
in one figure can reveal errors.  For example, water discharge is usually
related with sediment discharge, typically through a sediment rating curve.
Plotting the two time series on the same graph can aid in visualizing this
relationship.  Physically, there cannot be any fluvial sediment discharge when
there is no streamflow.  In addition, there should be no sediment con-
centrations very much larger than the total sediment conveyance capacity for a
given discharge.
     These aforementioned types of qualitative assessment can be made without
mathematical transformation of the data and should be included in the first
phases of any modeling or data analysis procedures.  It is especially important
to recognize and identify the physical processes which act within the moni-
toring network and to assess the relative megnitude and importance of each.

-------
                                      4.4

Since data acquisition is usually a subset of larger objectives  (i.e.,
watershed model, evaluation of environmental practices, etc.), errors in the
data set will be present in any future usage of the data.  Thus  the data pro-
vides a foundation for large scale objectives and should be of as high a
quality as feasible.

4.3  Data Inhomogeneity
     4.3.1  Introduction
     Webster's definition of homogeneity is, "like in nature or  kind; uniform
in structure of composition."  In order to obtain relevant information from a
data gathering station, the collected data should be homogeneous.  Jumps and
trends tend to create inhomogeneities in data.  Any inhomogeneity manifested
by the data is also present in any subsequent use of the data (i.e., struc-
tural design, etc.).  Detection of data inhomogeneities can lead to remedial
measures to form a more homogeneous data set.
     The qualitative detection of data inconsistency (inhomogeneity) was
described in the last section whereby knowledge of the physical process being
monitored aided in detecting inconsistent or incorrect data.  This section
will deal with mathematical measures which are used to detect data inhomoge-
neities.

     4.3.2  Testing for Data Inhomogeneities
     4.3.2.1  Qualitative Test for Inconsistencies
     A qualitative method to isolate data inhomogeneities starts with plotting
the time series data and computing the mean and standard deviation (Equations
4.3 and 4.4) of the data.   [Both equations are unbiased estimates of
          Mean = x = -   I  x±                                         (4.3)

                                     1 N      2-21/2
          Standard Deviation = s =  [—-  £  (x. - x )]                (4.4)

the population parameters, N = total number of observations,  x. = observation
at time i.]   Next, the mean of the data is plotted on the same graph with the
time series data, and then lines one standard deviation above and below the
mean are plotted.  This  allows identification of single extreme points, jumps

-------
                                      4.5
and trends.  The single points must be  separately assessed as to their vali-
dity and admissibility into the data set.  For  example,  if an extremely large
BOD load was recorded in the daily BOD  time  series/  but  surrounding data
points were not exceptionally large, this data  point would be questionable (it
was found to be more than one standard  deviation  away from the mean daily BOD
value).  If it was discovered that an upstream  rendering plant had dumped a
large amount of organic wastes into the river due to plant malfunctions, this
data point is validated.  If the objective of the monitoring network is to
discover criteria violations, then the  data  point is admissible into the data
set.  If the objective of monitoring is to gather data in order to model the
background and typical BOD loading mechanisms,  this  data point may be deleted
from the data set.
     A jump in data observations is detected by this method in that for
example, with an increasing data jump,  the part of the data series before the
jump will be mostly below the overall mean and  the data  after the jump will be
mostly above the mean.  The case of a decreased jump is  simply the reverse of
the increased jump.  Trends show similar effects  as  jumps, only there will not
be a sharp delineation as with jumps.   Another  way to discern a trend is to
plot the running mean through time (compute  a new mean each time a new obser-
vation is made) and compare this to the overall mean. A trend will have these
two means equal only at the end of a record.  Crossing over the overall mean
by the running mean would not definitely identify a  trend.  This method is
depicted in Figure 4.3 for an example in the next section.

     4.3.2.2  Testing for a Jump
     Jumps may be caused by many factors, i.e., a change in a measuring tech-
nique, movement of a gage to a nearby location, a rapid  and substantive change
in the causal factors of the process being measured,  or  a change in the pro-
cess itself.  The major problem in detection of a jump is trying to decide
whether or not the jump is significant. For instance, if a raingage were
moved two feet from its original location in order to laydown some underground
phone lines, the jump of data may not be detectable  at all.  In fact, the data
set can be logically assumed to be a homogeneous  set. If the gage were to be
moved 300 feet and near to some large cottonwood  trees,  there may be quite a
significant change in the data due to sheltering  of  the  gage by the trees.  In
order to tell whether or not there is a significant  change in data due to a

-------
                                      4.6
jump, the procedures described in the next paragraph should be followed.
     The first step for the detection of jumps is to determine when the jump
has occurred.  This can be done by plotting the data and visually detecting
the jump, or by knowing when the physical changes were made in the monitoring
network or the process (i.e., when the gage was moved, when cloud seeding
began, etc.).  Once the time of the jump has been identified, the data must
then be partitioned into pre- and post-jump data sets.  With these two data
sets, the mean and standard deviation for each is computed (x ,x ,s..,s_).
What is to be done now is to test the hypothesis that both sample means
(x" ,x" ) are the same.  If the test fails, the means are statistically dif-
ferent (subject to a criterial level, i.e., at the 95% level), and if the test
passes, the means are statistically the same.  In other words, if the computed
means are assumed to be the same (the hypothesis) and that their only dif-
ference is due to sampling variability, a test is performed to test whether
the hypothesis is true or false.  The mathematical formulation of the hypothe-
sis is based on the true population parameters (y = mean, a = standard
deviation) of which the sample values are estimates (x~  estimates U-, etc.).
Thus the hypothesis that there is no jump and that sample statistics are
derived from one population is
          P1 = U2 = U  and  01 = o2 = a    .                         (4.5)

The test for this hypothesis requires that all sample statistics be incor-
porated into one test statistic:  the  t  variable.  Here,
                 x  - x
          t = 	     ;                                     (4.6)
              °t
 /TTT
/ N1   N2
where  N   is the subsample size of the data before the jump,  N   is the sub-
sample size after the jump, and  a   is the pooled variance compute with
                          - 2          *                             (4'7)

The  t  variable has special significance since its distribution is known
(Student's t-distribution) and the distribution is only a function of the

-------
                                      4.7

number of degrees of freedom left in the data.  The  number  of degrees of
freedom (2) is equal to the sample size  (N) minus  the  number of estimated
population parameters/  (k), v = N-k .   If a  data  set  has N values,  it has N
degrees of freedom (v = N) as it is.  When the  mean  is computed, by using the
mean to represent the data there is one  less  degree  of freedom (v = N-1).
When the standard deviation is computed  and used to  represent the data,
another degree of freedom is lost (one for using the mean to compute the stan-
dard deviation and one for using the standard deviation itself); thus v = N-2;
and for the  t  statistic,  v = N  + N   - 2  .
     In order to use the t-statistic in  a test  format, the  t-distribution must
first be described.  Figure 4.1 depicts  the t-distribution  with a value
t  marked-off on the t-axis.  The area under  the entire curve is of course
 P
one.  The area under the curve from -» to t   is p, where 0  < p < 1,  and the
                                           p                -   -
area from t  to +°° is 1-p (or a).  Since the  t-distribution is symmetric,
t  = I -t  I .  If the area under the curve between  -t  to t   is p, each area
 P   '   P '          .                                 P     P
outside of this is (1-p)/2, or the area  from  -» to -t   = the area from t  to
                                                     p                  p
<*> = a/2.  These two concepts are important in the  actual test, for what the
test does is to compare Equation 4.6 to  values  of  t  .   Depending upon how t
compares to t  indicates acceptance or rejection of  the hypothesis.   There are
             P
two types of tests:  a one-tailed test and a  two-tailed test.  The manner in
which Equation 4.5 has set up the hypothesis  is a  two-tailed test.  Here the
test is to see if the two means are the  same  or not, and it implicitly assumes
that it is not known whether the jump was an  increase  or a  decrease.  Thus t
will be compared with -t  and t :
                        P      P
          if  -t  < t < t     then the hypothesis  is accepted (u =p =y);
                p —   —  p                                       12
          if  | t | > t         then the hypothesis  is rejected (U1^ M~) •

The power of the test is related to p.  The usual  values for p for strong
testing are 0.95 to 0.99.
     A stronger test, in the case of a suspected jump, is a one-tailed test.
In the case of an increasing jump, the hypothesis  can  be set up the same as in
Equation 4.5, but the acceptance or rejection of the hypothesis is simply:

-------
                                 4.8
   PERCENTILE VALUES (£P)
               for
  STUDENT'S t DISTRIBUTION
     with v degrees of freedom
        (shaded area = p)
1 F
1
(«,
63.66
2 1 9.92
3 6.84
4 4.60
5 4.03
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
60
120
"
3.71
3.50
3.36
3.25
3.17
3.11
3.06
3.01
2.98
2.95
2.92
2.90
2.88
2.86
2.84
2.83
2.82
2.81
2.80
2.79
2.78
2.77
2.76
2.76
2.75
2.70
2.66
2.62
2.58
(n
31.82
6.96
4.54
3.75
3.36
3.14
3.00
2.90
2.82
2.76
2.72
2.68
2.65
2.62
2.60
2.58
2.57
2.55
2.54
2.53
2.52
2.51
2.50
2.49
2.48
2.48
2.47
2.47
2.46
2.46
2.42
2.39
2.36
2.33
t.m
12.71
4.30
3.18
2.78
2.57
2.45
2.3G
2.31
2.26
2.23
2.20
2.18
2.16
2.14
2.13
2.12
2.11
2.10
2.09
2.09
2.08
2.07
2.07
2.06
2.06
2.06
2.05
2.05
2.04
2.04
2.02
2.00
1.98
1.96
(.»
6.31
2.92
2.35
2.13
2.02
1.94
1.90
1.86
1.83
1.81
1.80
1.78
1.77
1.76
1.75
1.75
1.74
1.73
1.73
1.72
1.72
1.72
1.71
1.71
1.71
1.71
1.70
1.70
1.70
1.70
1.68
1.67
1.66
1.645
t.m
3.08
1.89
1.64
1.53
1.48
1.44
1.42
1.40
1.38
1.37
1.36
1.36
1.35
1.34
1.34
1.34
1.33
1.33
1.33
1.32
1.32
1.32
1.32
1.32
1.32
1.32
1.31
1.31
1.31
1.31
1.30
1.30
1.29
1.28
(w
1.376
1.061
.978
.941
.920
.906
.896
.889
.883
.879
.876
.873
.870
.868
.866
.865
.863
.862
.861
.860
.859
.858
.858
.857
.856
.856
.855
.855
.854
.854
.851
.848
.845
.842
<.,,
1.000
.816
.765
.741
.727
.718
.711
.706
.703
.700
.697
.695
.694
.692
.691
.690
.689
.688
.688
.687
.686
.686
.685
.685
.684
.684
.684
.683
.683
.683
.681
.679
.677
.674
t,.
.727
.617
.584.
.569
.559
.553
.549
.646
.543
.542
.540
.539
.538
.537
.536
.535
.534
.634
.533
.633
.532
.532
.532
.631
.531
.531
.631
.630
.530
.630
.629
.527
.626
.524
£«
.325
.289
.277
.271
.267
.265
.263
.262
.261
.260
.260
.259
.259
.258
.258
.258
.257
.257
.257
.257
.257
.256
.256
.256
.256
.256
.256
.256
.256
.256
.255
.254
.254
.253
t.u
.158
.142
.137
.134
.132
.131
.130
.130
.129
.129
.129
.128
.128
.128
.128
.128
.128
.127
.127
.127
.127
.127
.127
.127
.127
.127
.127
.127
.127
.127
.126
.126
.126
.126
Figure 4.1.  Percentile values  (tp) for student's  t  distribution
             with  v  degrees of freedom  (shaded area = p).

-------
                                      4.9

          if  t >^ -t       then the hypothesis is accepted  (M  =y  =p);

          if  t < -t       then the hypothesis is rejected  (p.,*p,.,
                    P                                         '  2
                           in fact, y1 < u2)«

Again, this decision structure is based upon an increasing  jump (a  decrease
jump would test with t  and reject with t > t ) and what  is then  being tested
                      P                      P
is not simply \i  * p  but \i  < \i .  This is because Equation 4.6  will  yield a
negative value of t since it is already known that x  < x  (increase jump).
     To find the t  value, Figure 4.1 is used with the knowledge  of the number
of degrees of freedom.  For the one-tailed test, t  is simply  found by finding
the column of the desired t  value (t  = t nr. for a 95% test,  etc.) and then
                           P         P    «95
locating the row with the correct v.  For example, for a  one-tailed test at
the 95% level and v = 20, t  = t. _, = 1.72.  The two-tailed test requires a
                           p    o .ys
little manipulation in order to use the table in Figure 4.1.  In  this  case,
since there is an a/2 rejection region at either tail of  the t distribution,
the desired t  value is found by looking under the column heading of t    ._.
             p                                                         p+a/2
For example, in a two-tailed test at the 95% level with v — 10, a = 0.05 (and
thus a/2 = 0.025), since p = 0.95, p + a/2 = 0.975 and the  t  value for
                                                             P
testing is found in the t  = t      column (here t.. „_.. = 2.23).   Thus, the
                         p    u.y/j               u.y/D
two-tailed test in this case is whether or not -2.23 £ t  £  2.23.
     An example of t testing for the detection of a jump  is presented here.
Monthly evaporation from April through October has been recorded  at the Bonny
Lake gage since 1949.  The original type of recording instrument  was the stan-
dard USWB 4-foot diameter sunken pan.  From 1965 through  1976,  the  measuring
device was a sunken 3-foot diameter pan which was painted black.   The  location
of the Bonny Lake gage is in northeast Colorado (Figure 4.2).   The  time series
of the monthly pan evaporation data is found in Figure 4.3, and it  appears
that either regional evaporation has decreased sometime near when the  gage was
changed or the change in the gage technique affected the  data  collection.
Comparing the Bonny data with long-term average regional  evaporation values
(2) revealed that there was no significant deviations from  the long-term
monthly means.  After the instrument change, the running  mean  in  Figure 4.3
decreased and started to level off in 1971.  The records  at the nearby Enders
Dam gage (Figure 4.4) show that during this time, evaporation  showed a slight
decrease.  This decrease is not found in the data of the  nearby Tribune 1W

-------
                                                nrn--
                                                  L::, i   /
                                                   •O-   •..!••
                                   ltfrrh. .. PLATTE  DRANAGE
7V./N  ••	o/Z.^npr-rZ1',. rLAIIt un«pvt    - *»,«^
— IUta ,,,,_« f./-»U.-"l (>1» O I '         _J      /

\MSifcsSDterfH  /      !
                                                   X J"
                                                   ^.-..T
         -«•! ^.ri'B1^
            /   C..I. I_J
            / K.-W-" . 1
         ——
                            T" T» I "^  "8-
                            AffKANSAS DRAINAGE     I
                          •r  R—f—r	1
"	^
                                                   COLORADO
                                Fi
           1.2.

-------
                nCASORED EVAPORATION
                RUNNING HEAH
e
v
A
P
0
R
A
T
I
0
N
I
N
C
H
E
S
                                       19S1-1B76
gaging method changed
                       Figure 4.3.  Bonny Dam evaporation series.

-------
E
U
A
P
0
R
A
T
I
0
N
                                            Bonny gage changed
                                                                                                     to
   Figure 4.4.  Pan evaporation for the Enders Dam gage during the growing season.

-------
                                      4.13
gage (Figure 4.5).  Thus, with evidence from nearby gages that  there  was  no
significant decrease in evaporation, the Bonny Lake gage -shows  a  decrease jump
during the time after the monitoring equipment was changed.   A  one-tailed test
was then performed on the two subsamples of before and after  the  gage change.
The two means of each data subset are found plotted in Figure 4.6.
Calculations for the one-tailed test are found on below.
                 Bonny Lake Evaporation Test for a Data Jump
                          Mean      Standard Deviation      Sample  Size
      Before Change      11.63             2.58                  65
      After Change        9.93             1.96                  57
          o  = 2.330 and t = 4.02
          since t = 4.02 > t     = 2.36  the means are  statistically
                                          different at  the  99%  level.
This test means that the data before and after the change are essentially from
two different populations and thus the data set is inhomogeneous .
     Since the Enders Dam gage also showed a small decrease jump  during the
same time, this data set was tested simlarly to the Bonny Lake  data in order
to see if the decrease might be some type of regional trend:
      Before Change
      After Change
          a.  = 2.153
           t
          since t = 0.973 < t. gg = 2.36  the means are  statistically the
                                          the same at  the 99%  level.
     The conclusion is that the Bonny Lake evaporation data  is not  a  homoge-
neous set due to the change in the measuring device in 1965.   The decrease
jump in the Bonny data was also found to not be  due to a regional decrease in
evaporation.
     Another way to show that there was no regional decrease in evaporation
after 1965 is to plot the concurrent data of the Bonny gage  against that of a
nearby gage.  If there were a regional factor causing  lower  evaporation, the
Mean
9.62
9.24
. = 0.973
Standard
2
1
fc0.99
Deviation
.30
.93
= 2.36
Sample Size
65
57


-------
B3.5
29.e
17.5
15. e
12.5
                      gage moved 80'  North from
                      elev.  3612'  to  3620'
                                                                              mean  for the series
                                                                              and also for 1951-1964
                                                                              and 1965-1976
19.9
          Figure 4.5.  Pan  evaporation for'the tribune 1W gage during the growing season.

-------
17.5 (-
                                         gaging method  changed
 a.s
                                                                                  11.63 mean for 1951-1964
                                                                                  10.84 mean for entire series
                                                                                   9.93 mean for 1965-1976
                                                                                                               (Jl
                                    Tine
            Figure 4.6.  Pan evaporation for the Bonny Dam  gage  during the growing season.

-------
                                      4.16
points of  this plot  will be randomly scattered about a regression line through
all of the  data.   If there is no regional factor for the evaporation decrease
and the decrease was only due to the change of the Bonny gage,  then data about
a regression  line  will  be partitioned into two sets:   most points above the
regression  line will be from before  the  change and most points  below the
regression  line will be after the change.  This partitioning results from the
fact that  the Bonny  gage will have a lower evaporation value for a post-change
value ~of the  Enders  or  Tribune gages than a pre-change value.  This effect can
be observed in Figure 4.7 for the Bonny  Lake and Tribune 1W data.  More evi-
dence of the  partitioning is found in the coefficient of determination (R )
                           2
for all data  compared to R  values for each data subset (Table  4.1).
     The t  test is one  of the best methods to test the significance of a jump.
It is based on sampling theory and gives a level of accuracy of the test
itself.
     There  are many  ways to detect a jump and they are:   plotting of the data,
computation and plotting of the running  mean,  interstation plots (such as
Figure 4.7),  knowledge  of the movement of a gage or change in the gaging
method.  Another general method to detect jumps is the double mass analysis,
and this method will be presented in the next section,  dealing  with trends.

     4.3.2.3  Detection of Trends
     A trend  in a  process (see Figure 3.7b of the last lecture)  is found in
the systematic and continuous change over an entire sample of that process.
This produces a systematic and continuous change in the  estimated parameters
of that process.   The trend can be viewed as an added deterministic (predict-
able) component in any  hydrologic process,  i.e.,  the  increase in water demand
through time  due to  population growth can be predicted,  but exact values can-
not be predicted due to random variations.   The effects  of trends on sample
statistics  was discussed in Section  2.4.2 of the last lecture.
     A simple qualitative method to  detect trends is  to  plot the time series,
its overall mean,  and its running mean.   A series with a quantity trend will
have a running mean  which continuously changes in a consistant  manner (i.e.,
always increasing, etc.).  There are trends in which  the mean can stay
constant yet  the standard deviation  changes.   There will be no  crossing-over
of the running and overall means (except for the first three of  four values)
with a quantity trend in the data.   The  trend causing a  change  in the mean

-------
I
0
N
N
V

D
A
H

E
y
A
p
o
R
A
T
 t
0
N
IS
                                      X  X
                                         i
                                                    i
                                         !•               IS

                                  TBIIUNC 1U  CVAPOdATION (INCHES)
     Figure 4.7.   Regression of Bonny Dam evaporation on tribune 1W  evaporation.

-------
                                      4.18
         Table 4.1.  Linear Regression Equations and Coefficients of
                     Determination (R2) for the Data of Figure 4.7
                     [Bonny Evaporation = a  + a  (Tribune 1W Evaporation)]
ao
1 R2
All Data (1951 - 1976)           2.01               0.70               0.707

Before Bonny Gage Change
    (1951 - 1964)                1.95               0.77               0.816

After Bonny Gage Change
    (1965-1976)                  2.18               0.62               0.812

-------
                                      4.19

will be exclusively analyzed from this point on.  The implication of the trend
by plotting the mean should be verified by an inspection of the causal factors
which could produce such data.  If the trend is due to measurement errors/ a
trend in the process does not truly exist.  It is not altogether uncommon for
hydrologic processes to have trends.  A more quantitative method to assess the
degree of a trend is the use of the doublemass analysis.
     The doublemass analysis (DMA) essentially assesses interstation rela-
tionships in order to detect, data inhomegeneities at one station.  This is
done by computing and then plotting the cumulative value of data through time
for the station in question versus a group of nearby or strongly correlated
stations.  If there were no data inhomogeneities, the plot would be fairly
linear (some scatter may exist due to the variaiblity of most hydrologic pro-
cesses), see Figure 4.8a.  If there was an isolated data inhomogeneity (i.e.,
the reporting of a very large rainfall at only one station, on one day), there
would be a noticeable jump in the relationship between the one station and the
group of stations (Figure 4.8b).  If there were many isolated inhomogeneities,
the DMA may not actually indicate an inhomogeneous data set, but rather imply
poor correlation between the gage in question and the group of gages (Figure
4.8c).  In the case of a data jump, the DMA will show two distinct lines which
intersect at the point in time when the jump began (Figure 4.8d).  Finally,
for a trend, the DMA will show a progressive movement away from the linear
relationship (Figure 4.8e.).
     The major drawback to the doublemass analysis is that there is no test of
significance associated with it.  Weiss and Wilson (1953) use an analysis of
variance technique to discern whether or not slope changes from a DMA are
significant or simply due to chance.  This method would require severe slope
changes to detect a trend or jump with only one or two points, and this may
not be true with most trends.
     Once a trend is discovered in data, the physical process and its causal
factors should be analyzed in order to ascertain whether or not the trend is
physially based (i.e., watershed management causing slow decrease of sediment
dishcarge, tree growing near a precipitation gage causing a decrease in preci-
pitation records, surface mining within the watershed causing gradual river pH
changes, etc.).  The trend may be tested by partitioning the data set into
three groups:  Zone I, unaffected, homogeneous data subset; Zone II, tran-
sition data subset;  Zone III, subset of obvious trend (Figure 4.9).  With this

-------
                                   4.20
II
^^L fl)
'5 =
2°
a. c
«: o
II
               Cumulative  Precipitation for the Group of Gages
    Figure 4.8a.
Double mass curve for well correlated stations indicating
homogeneous data sets.
 o»
'£ a
15
o
               Cumulative  Precipitation for the Group of Gages
    Figure 4.8b.   Double mass analysis indicating an isolated inhomogeneity.
ll
•— to
•^ o
So
li
o
                                       A
             A/
               Cumulative Precipitation  for the  Group of Gages
    Figure 4.8c.   Double mass analysis   indicating poorly correlated
                  stations .

-------
                         4.21
o -S.
"5
       Cumulative Precipitation for  the Group of  Gages
    Figure 4.3d.  Double mass analysis  indicating  a  jump.
II
o
        Cumulative Precipitation for the Group of Gages
     Figure  4.8e.  Double mass  analysis indicating a trend.

-------
                                      4.22
                 •Trend
o>
I
u
w
             Zone I
        Homogeneous   Data
 Zone n
Transition
  Zone  m
Definite Trend
                                     Time (Years)
       Figure 4.9.  Triple partition of a data set  for testing of a trend.

-------
                                      4.23

partitioning, the data sets before and after the transition  region  can  be
tested as a jump would be tested.  It must be emphasized that  there should be
at least ten points in the trend and unaffected series, otherwise the   t
                                                                        P
values will be very large, thus producing tests which cannot significantly
detect statistical differences due to too little data.

4.4  Correction of Data Inhomogeneities
     4.4.1  Introduction
     Data inhomogeneities may be corrected by various techniques.   Any  speci-
fic technique selected for correction of data inhomogeneities  is a  function of
the type of inhomogeneity, the data available and the availability  of physical
process models.  If it is known that an isolated data inhomogeneity is  due to
simple recording error (i.e., reading water stage as 13.72 feet and reporting
it as 3.72 feet), the correction procedure may be quite obvious, especially if
the values from previous and successive observations were all  consistently
below or above the suspected observation and there is a large  memory in the
process.  If a stream gage were knocked out during a flood event, it would be
possible to estimate the flood hydrograph with a watershed model, or backing
into the flood peak with information on the high-water marks and use of a
slope-area backwater technique.  In the absence of a physical  process model,
data may be estimated with the aid of data from a nearby station that has  high
interstation correlation with the knocked out gage.  The methods for correc-
tion of an inhomogeneous data set are presented in this chapter.

     4.4.2  Filling of Missing Data
     Data gaps represent a specific type of data inhomogeneity in which data
for certain time periods is missing from the data set.  Physical process
models can fill data gaps by modeling the causal factors of  a  process.
Knowledge of system inputs and use of the physical process model allow  a
reproduction of data points surrounding the data gap as well as points  in  the
gap itself.  For example, if a flood hydrograph was not recorded, a watershed
model can be run with knowledge of antecedent storm conditions (baseflow,
antecedent moisture, etc.), watershed pre-storm physical characteristics
(vegetative cover, impervious area, soil type, etc.), and the  rainfall
hyetograph in order to reproduce the flood hdyrograph.  When the data required
for the physical process model is unavailable or gaps also exist in the input

-------
                                      4.24

data  (i.e., malfunctioning  rain  gage/ etc.), reasonable  estimates  must  be  made
for the input data, or  it may be possible  to use  statistical  methods  to fill
these data gaps.  Physical  process modeling is to be covered  in  the next two
lectures.
     With strong interstation correlation, it is  possible to  transfer the
information from other  gages  to  fill data  gaps.   This is very similar to
regression relationships.   Here, an analysis is performed between  one or more
variables to find the relationship between the variables  (i.e.,  linear  rela-
tionship between nearby raingages, power function relationship between  water
and sediment discharges, etc.).  This regression  relationship allows  predic-
tion of one variable by the other variable(s) in  the regression  relationship;
thus when data for one  variable  are missing, the  regression relationship is
used to predict the missing data.  Regression with one independent variable
will be treated here.   Descriptions and examples  of the  use of multiple
regression can be found in  any of the many books  on regression,  such  as
Reference 4.
     Regression analysis produces the statistical relation between two
variables.  Unlike a functional  relation (i.e., y=3x+ 5),  the statistical
relation is not perfect.  The statistical  relation has a functional part and a
random part (i.e., y =  2x + 1 +  e,  where  (2x +  5)  is  the functional
(deterministic) part and  e  is  the random part).  A regression  analysis finds
the best fitting functional part and the random part is  described  by  the
degree of correlation (coefficient of determination - R^) between  the two
variables in the analysis.  If the functional part is very strong  compared to
the random part, a high correlation exists.  If the random part  is much larger
than the functional part, a very low correlation  exists.  A special note here
is that if the functional part is strong,  yet the form of the regression
relationship is improperly  chosen, the correlation will  be very  low.  A
classic example is trying to  fit the data  from a  perfect circle  by a  linear
regression relation, in this  case the correlation is zero because  the data
were fitted by an equation  of the form  y  = a  +  a  x (a  and a    are
constants) instead of the equation  y  = a - x .  An aid to  picking  the
correct regression relation is to either physically analyze what the  relation
should be (i.e., the relation between two  nearby  precipitation gages  should be
linear since meteorologic events usually cover an area in a uniform fashion;
theoretically sediment  discharge is a function of velocity to some power,

-------
                                      4.25
therefore a power function for sediment discharge versus water discharge  is
expected) or to plot the data and see what type of graphical transformation
(i.e., plotting on log paper, etc.) best linearizes the data.
     The linear regression function for the dependent variable   y  regressed
on the independent variable  x  is:

          yi = ao + aixi + ei                                         (4'8)

where  a   and  a   are constants and  e  is a random error term which  is
independent and normally distributed with mean zero and variance of   a  2
which is equal to the variance of  y  (reference 4, page 31).  Figure 4.10
describes the significance of each term in Equation 4.8.  The estimates of
a   and  a   are
                N          N      N
                I  x y  -  I  x   I  y
               1=1        1=1    1=1
                                	                             (4-9)
                   V   *    V   *
                   E  Xi •  L  Xi
                  i= 1      i= 1
                              N

                   £  yi-ai  I  V                                 (4-10)
                  1=1         1=1
where  N  is the total number of data points.  The use of the linear
regression equation as a predictor takes the form

          yi = ao + aixi                                              (4'11)
       A
where  y.  is the predicted value of  y  at time period  i  given the observed
value of  x. .  The measure of the goodness of fit of a regression relation is
the coefficient of determination  R2.  R2  is a ratio of the explained
variation (by the regression equation) to the total variation (variation of  y
to its own mean) .  If every data point were to be exactly predicted by the
regression equation,  the explained variation would be equal to the total
variation and  R2  would equal unity (in this case the unexplained variance is
zero).  R2  is computed by Equation 4.12.

-------
                               4.26
Figure 4.10.
Example of a linear regression fit to data (y.
and the actual scatter of the data about the
regression line.
a  + a,  x. )
 o    1   i

-------
                                      4.27
                N         N
                I  (y± -  I  y±)2
                \
                1=1

                             N
An example of the use of linear regression between two  stations  was presented
in Section B.2 for the Bonny Lake and Tribune  1W evaporation  gages (Table 4.1,
Figure 4.7) .
     Other forms of nonlinear regression relations may  be  found  in books
covering the regression topic.

     4.4.3.  Measurement or Recording Errors
     If a measurement or recording error has been determined  as  an inhomoge-
neity in a data set (i.e., 20 inches of rain on a cloudless day),  the inhomo-
geneity may be adjusted with the knowledge of  how the error might  have been
made, or the inhomogeneity may simply be treated as a data gap.
     Knowledge of how the error was made can be obtained by checking back with
the original records or by analyzing the values of correlated variables during
that time (i.e., a discharge of 19,700 cfs at  a time when  river  stage was not
above bankfull, a stage that allows only 2000  cfs, indicates  that  the actual
discharge may have been 1970 cfs; the complete hydrograph  should be plotted to
verify the correct value though) .
     If the data homogeneity is treated as a data gap,  a physical  process
model or a regression relationship may be able to fill  the gap.

     4.4.4  Jumps
     The effect of a jump is to essentially be monitoring  two different pro-
cesses.  What is needed is to extract information from  the data  set in spite
of the jump.  The treatment of data, in light  of a data jump,  is based upon
the specific objective of the monitoring network.  For  example,  if a moni-
toring network is to detect water quality criteria violations, the jump may
have resulted from better treatment practices, but the  data set  need not be
changed in any way to account for the jump.  Contrary to this, if  a river
discharge data set showed an increased jump and the data were to be used for
the design of a flood control project, use of  the entire data set  can lead to

-------
                                      4.28

significant underdesign.   In  this  last  example,  the  easiest  method to correct
for the data inhomogeneity is to neglect  the  first part  of the  data.   In such
a case, though, the information contained within the pre-jump data is
discarded and this results in a design  on less data,  resulting  in hydraulic
structures with less reliability in  regulating the system.   Thus,  in  the case
of jumps, the information  contained  in  the  entire data set is very useful in
satisfying design objectives.  The abstraction of the information from an
inhomogeneous data set  is  performed  by  first  converting  the  data  set  to homo-
geneous form.
     As with measurement and  recording  errors, data  jumps may be  handled by
treating the unrepresentative portion of  the  data as a data  gap.   In  this
case, the data gap may  be  filled by  a physical process model or by regression
relations.  The physical process model  can  be calibrated on  the representative
data subset, and then reproduce data for  the  unrepresentative data subset with
knowledge of the input  parameters  during  that time.   For regression relations,
it would probably be best  to  use the form of  the regression  equation  which
includes the random component term (i.e., Equation 4.8)  and  then  to generate
many equally likely traces of the  missing data.   In  this manner,  structures
can be designed in a probabilistic framework.
     The last form of correction of  data  inhomogeneity due to a jump  is to
transform the unrepresentative data  subset  to conform to the representative
subset.  This is done by reducing  the unrepresentative data  to  just its random
part by removing the deterministic components.   This is  termed  standardizing
the data.  The most common form of standardization is to subtract the mean
from each value in a data  set and  then  divide these  values by the standard
deviation (Equation 4.13):

               x. - x
          ?.=  V-                                                 (4.13)
                  x
where  £.  is the residuals which  are usually normally distributed with mean
zero and variance of one.   For a jump,  the  mean  and  standard deviation are
computed for each subset (before and after  the jump). The residuals  from the
unrepresentative subset are then multiplied by the standard  deviation of the
representative subset and  added to the  representative subset mean. Now the
entire data set is in homogeneous  form.   This method is  presented in  the

-------
                                     4.29

following example•
     The evaporation data for the Bonny Reservoir gage  (1952-1976) has been
determined to have a jump (1965-1976) due to the change in the type of gage
(III-B-2).  The post-jump data (1965-1976) yield lower evaporation readings
than the pre-jump data (1952-1964) and the post-jump data are the unrepresen-
tative data subset since the common USWB sunken pan was not used during  this
time*  The subset statistics for pre- and post-jump data are presented in
Table 4.2, and these statistics were used to standardize the post-jump data
and then transform it to a form more homogeneous to that of the pre-jump data.
The two time series are then plotted in Figure 4.11.  Statistics of the  entire
data sets (before and after correction 'for the jump) are found in Table  4.3.
This type of reconstructed record can be used to check the results of a  physi-
cal process model.

     4.4.5  Trends
     Once a trend has been identified, the part of the data which is affected
by the trend can be deleted and then this period may be treated as a data  gap
(just as the jump was).  Thus, physical process or regression models may be
employed to fill this gap.
     It is possible to treat all of the data as one homogeneous set when the
trend is removed.  This is done by recognizing the trend as a deterministic
component in the time series (Equation 4.14):
          x.  = T  + D  + E.                                           (4.14)
           i    x    x    i
where  x.   is the value of the stochastic process at time  i,  T   is the
        i                                                       x
trend in  x  (constant increase, nonlinear change, etc.),  D   is the deter-
ministic part of  x  (seasonal mean, annual mean, etc.), and  E  is the  random
component for time period  i.  With Figure 4.9 in mind, it is easy to see  that
for a homogeneous data set  T  =0.  This is also true for the part of the
                             X
data set unaffected by the trend.  Thus, an inhomogeneous data set caused  by a
trend can be made homogeneous by simply removing the trend component from  the
part of the data which owns the trend.

4.5  References
Linsley, R. K. Jr., M. A. Kohler and J. L. H. Paulhus,  1975, Hydrology for
Engineers, Second Edition, McGraw-Hill Book Company, New York, New York, page
173.

-------
                                  4.30
        Table 4.2.  Historic Statistics for the Bonny Reservoir
                    Evaporation Time Series
          All data (1951 - 1976)          10.84          2.46

          Before (1949 - 1964) Jump       11.63          2.58

          After (1965 - 1976) Jump         9.93          1.96
Table 4.3.  Comparative Statistics for the Bonny Reservoir Evaporation
            Time Series When Correcting for Data Inhomogeneity
       All data (inhomogeneous set)          10.84          2.46

       All data (homogeneous set)            11.63          2.57

-------
9Z.6T-2S6T JT
                                      Auuog JTOJ  sajjas  CUT)
•91
     •81
        ISHiNOU) 3UI1


MI         M        M
                                 I
                                                      I
                                                                                       •t
                                                                                       SI
                                                                              M
                                                                              0
                                                                              I
                                                                              1
                                                                              «
                                                                              a
                                                                              o
                                                                              d
                                                                              W
                                                                              A
                                                                              3
                                                                                                                  to

-------
                                     4.32
Meyer, A. P.,  1942, Evaporation from Lakes and Reservoirs, Minnesota Water
Resources Commission, St. Paul, Minn., June.

Neter, J., and W. Wasserman,  1974, Appleid Linear Statistical Models, Richard
D. Irwin, Inc., Homewood, Illinois.

Weiss, L. L., and W. T. Wilson, 1953, "Evaluation of Slope Changes in
Double-Mass Curves," Transactions of the American Geophysical Union, Volume
34, No. G, December, pages 893-896.

-------
                                      5.1
V.   PHYSICAL PROCESS SIMULATION:  I. WATER AND  SEDIMENT  ROUTING
5.1  Introduction
     A variety of simulations may be used to evaluate and extend  data collec-
tion systems.  The primary requirement for such  a model is  that it must repre-
sent the physical process active in the watershed.  Such  a  model  is sensitive
to management activities in the simulation area  and can be  expected to
correctly reflect at least trends in watershed response with  a minimum of  data
for calibration.  A model meeting these requirements was  developed at Colorado
State University and at Simons, Li & Associates, Inc. for the purpose of exa-
mining a variety of nonpoint source pollution problems.   Elements of this  mode
have been implemented for the purpose of this short course.
     The data base and collection system examined as a case study for this
short course was the Four Mile Creek Watershed near Traer,  Iowa.   Data was
available from this watershed for the years 1976-1978 (Johnson,  1977;  1978).
For the purposes of this course, the processes simulation were water and sedi-
ment runoff, and nonpoint source loading from pesticides.  Conclusions drawn
regarding these processes are by and large applicable to  the  problem of esti-
mating non-conservative processes such as nutrient loading  as well as conser-
vative processes such as pesticide yields.  In particular,  the
characterization of runoff hydrology and sediment transport are key elements
in a proper understanding of the transport of all water quality constituents.
Synthesis of water quality and quantity records  can require not only the
calculation of water and sediment hydrographs, but the estimation of
interstorm phenomena such as evapotranspiration  and soil  water movement as
well.  Interstorm processes are of considerable  importance  to the modeling of
nutrient and pesticide processes through the estimation of  soil moisture
changes.
     Therefore, the elements of nonpoint source  pollution modeling discussed
here in detail are as follows:
     1.   Water runoff, including
          o interception
          o infiltration
          o overland and channel routing
     2.   Sediment runoff, including
          o erosion processes
          o sediment transport

-------
                                      5.2

           o aggradation and degradation
      3.    interstorm processes
           o evapotranspiration
           o vertical soil moisture movement
      4.    pesticide yields
           o pesticide uptake by runoff
           o pesticide incorporation in  soil.
      The chapter will present the theoretical foundation for the water and
 sediment runoff model and in this short course.  The following chapter will
.present  the interstorm process model which in combination with the water and
 sediment model and other nonpoint source pollutants (NFS) models constitute
 the  NPS  model used in this short course.  Nonpoint source components are dri-
 ven  by the routing and interstorm models in a roughly similar manner.  A
 pesticide routing component is used as  an example of such a component.  It is
 felt that conclusions reached about the quality and appropriateness of data
 with respect to the above mentioned components encompass most of thos appli-
 cable to other water quantity and quality components.

 5.2   Water and Sediment Routing
      In  order to correctly represent the processes encountered in estimating
 water and pollutant runoff from watersheds, a runoff event model was imple-
 mented.   This model may be incorporated into (or "driven" by) an interstorm
 model such as the one to be described in the next chapter to form a continuous
 time simulation.  However, simulation of transport of materials from
 watersheds requires careful attention to the hydraulics of water and sediment
 runoff.   The runoff model used here was developed by Li, et al., 1979 and has
 been refined to its present form by Fullerton, 1980.  It is incorporated into
 a  group.of programs called MULTSED, which consists of 3 subprograms, MSED1,
 MSED2 and MSED3.

      5.2.1  Formulation of the Water and Sediment Model
      The theoretical background for physical process components used in
 MULTSED  is presented below.  In the derivation of the basic equations used in
 the  model, the following assumptions are made:
      1.    Subwatersheds may be represented by an "open book" approximation
           (see Figure 5.1).

-------
                         5.3
     c
     o>
    -   2
     o
     or
        0
      (a)
                                     V, = INTERCEPTED  VOLUME
          0   10   20   30  40   50  60

                       Time in minutes
Original   hyetograph.
                            70  80
*- o
d
c
>» 4.
*— ^
"t/i
c
0)
"c
o
c
o
o:
n









i













.1




















i i i
         0   10   20   30   40  50  60   70  80

                      Time in minutes

     (b)      Rainfall reaching the ground.
Figure 5.1.  Effects of interception on rainfall hyetograph.

-------
                                       5.4
     2.   Soil characteristics  are isotropic  and homogeneous for a single unit
          (or side  of  a subwatershed).
     3.   Canopy  cover and ground cover  are homogeneous for a single unit (or
          side of a subwatershed).
     4.   Rainstorm events are  spatially homogeneous  within a unit and cover
          the entire plane or subwatershed unit.
     5.   Initial conditions such as  soil moisture are uniform within a unit
          (or side  of  a subwatershed).
     6.   Evaporation  processes are neglected for the runoff event.
     7.   streams within the watershed are ephemeral, and the movement of sub-
          surface flow and ground water  flow  are negligible as far as surface
          water runoff is concerned.
     8.   The kinematic-wave approximation for flow routing is valid, i.e.,
          the gradients due to  local  and convective accelerations are negli-
          gible and the energy  slope  is  nearly equal  to the bed slope.  (If  an
          appropriate  estimate  of the energy  slope can be made, it may be
          substituted  for the bed slope  to relax this restriction.)
     9.   Water and sediment yield simulation are based on a single  storm.

     5.2.2  Formulation of Excess Rainfall Calculations for MSED1
     Much of the  rain  falling during  the first part of a storm is intercepted
by the ground cover.   Precipitation intercepted by vegetation or other ground
cover eventually  evaporates,  and the  amount of rainfall reaching the soil sur-
face is less than the  recorded  amount.   The amount of interception loss
depends on the percentage of the ground  that  is covered by canopy and ground
cover, and their  respective water holding capacities.  The total intercepted
volume can be written  as:
          V. = C  V + C  V                                          (5.1)
           i    c   c    g  g
where  V.  is the total potential intercepted volume  per unit area,   C   is
        i                                                              c
the canopy cover  density  (0  <  C  < 1),   V   is the potential storage volume
                                 c         c
per unit area of  canopy cover interception,   C   is the ground cover density
(0 < C  < 1), and   V   is the potential  storage volume per unit area of ground
cover interception.  The values of V    and   V   are  a function of types of
vegetation and corresponding leaf  area.
     The interception  volume given by Equation 5.1  is subtracted from the
rainfall hyetograph.   This is done by assuming that no rainfall is available
for infiltration  or overland flow until  the total interception volume has been
filled.  Effects  of interception on the  rainfall hyetograph are shown in
Figure 5.1.

-------
                                      5.5
     A portion of the rainfall reaching the  ground  moves  through the soil sur-
face into the soil by infiltration.  The model used to  simulate this process
is based on the Green and Ampt (1911) infiltration  equation.   Development of
the infiltration model is based on the following  assumptions:
     1.   The effect of the displacement of  air from soil has  negligible
          effect on the infiltration process.
     2.   Infiltration may be regarded as purely  vertical,  and the movement of
          water through the soil may be described by a  distinct piston wetting
          front (Figure 5.2).
     3.   Soil compaction due to rainfall impact  is neglected.
     4.   Hysteresis effects in the saturation-desaturation process may be
          neglected.
     5.   Depth of overland flow is sufficiently  small  that it has little
          influence on the infiltration process.
     The derivation is essentially the same  as presented  by Eggert (1976),
with minor changes.  Under the assumptions stated,  Darcy's  Law may be
applied.  That is
          V  = -K  ^                        '                         (5.2)
           z     w dz
where  V   is the water velocity in the vertical  direction,  K   is the
        Z                                                      W
hydraulic conductivity in the wetted zone,   h  is the piezometric head and  z
is the vertical dimension.
     Due to the assumed piston wetting front shown  in Figure 5.2,  the piezo-
metric head may be expressed as
          h = -z  - ty                                                 (5.3)
                o
where  z   is the gravitational head and  ty  is the capillary  suction head.
     Darcy's Law can be rewritten as
                  (z  + \\>)
          V  = K  —	                                            (5.4)
           z    w   z
                     o
Further, by continuity,  it is easy to see that
          f = Vz                                                      (5.5)
where  f  is the rate of infiltration that is defined in  the following
equation:
          f-H                                                      (5.6)
where  F  is the total volume of infiltration at  time  t.
     The value of  ZQ  (Figure 5.2) can be written  as

-------
                                 5.6
  Soil
Surface  z = 0
                        Degree   of  Saturation
Si
                                     >w
                                 Piston  Wetting Front
                          Actual Wetting Front
1.0
                                          -r—* S
          Figure 5.2.  Approximation of soil moisture profile.

-------
                                      5.7
          Zo = 4, (S  - S.)                                            (5'7)
                   w    i
where  4  is soil porosity,  S   is the degree  of  soil  saturation in the
                              w
wetted zone, and  S.  is the initial degree of  saturation.   Using Equations
5.5, 5.6 and 5.7, Equation 5.4 may be rewritten as

          f=Kw(1+F)                                             (5'8)
where  y  is defined as
          Y = i|> <|> (Sw - S±)                                           (5.9)
This is essentially the equation proposed by Green and  Ampt (1911).
     Equation 5.8 can be rearranged so
            * ^
          ,
          (F +
                    K  dt                                             (5.10)
Integrating this equation between zero and a  time   t  results in
                           K
          - - in (1 + -) = — t                                       (5.11)
          Y           Y    Y
     If at any .time  t  the infiltrated volume  is   F(t),   then at some later
time  t + At  the infiltrated volume is
          F(t + At) = F(t) + AF                                       (5.12)
in which  AF  is the change in infiltrated volume  that occurs during the time
increment  At.  An expression for  AF,  obtained from Equation 5.12, is
          AF = F(T + At) - F(t)                                       (5.13)
Substituting  F[(t) + At]   for  F  in Equation  5.11  results in

          F(t + At) -An   1 +
              Y               L    Y    J       Y
Substituting  F(t)  for  F  in Equation 5.11  and subtracting this equation
from Equation 5.14 yields
                                     F(t + At)
          F(t + At) - F(t)	Y      = _w
                 Y         "        1 + F(t)     Y
                                          Y
The above equation can be simplified, by using  Equation 5.13, to the following
form:
          AF              AF        w
          "^   »  '-      "•*•   -  _ 	IL A4.                              / c 1 c. \
                                 — 	 At                              lo . 1b)

-------
                                      5.8

     Equation 5.16 gives a.  relationship between the infiltrated volume   F(t)
and time, but due to its implicit nature, the equation is very difficult to
use.  An explicit solution  can be obtained by using a power'  series  expansion
to approximate the logarithmic term in Equation 5.16.  The result is
                                       2AF
          *n (1 +         ' - £n  1 +

AF
— Z
Y

AF
- Y + F(t)
„ , AF
' ' Y + F(t)

- W At
ut
Y

     Truncating Equation 5.17 after the second term and substituting  into
Equation 5.16, one obtains
                                                                      (5.18)
Equation 5.18 is simplified  into the following quadratic equations  for  AF:
          AF2 +  [2F(t) - K   At] AF - 2 K  At  [7 + F(t)] = 0           (5.19)
                          w             w
which has a solution with
               -[2F(t) - K At] +  [(2F(t) - K At)2 + 8K At (y + F(t))] /2
          AF =	—	  (5.20)

Since only the positive root of Equation 5.19 has any physical meaning, the
negative root is ignored. • Equation 5.20 provides an explicit function  for
infiltration with respect to time.  The infiltration  AF  occurring during
time  At  can be determined  knowing the soil characteristics  (K    and  y)
                                                                w
and the previous infiltration  volume  F(t).
     Once interception and infiltration have been calculated, the final rain-
fall excess can be determined.  The following discussion presumes the rain-
storm considered is spatially  uniform over each subwatershed or plane unit but
varies in time.  This type of  storm can be represented by a hyetograph  as
shown in Figure 5.1a.  After the effects of interception have been  subtracted
from the rainfall hyetograph (Figure 5.1b), the average rainfall intensity
occurring during a time increment  At  is compared to the average infiltration
rate  f.  Then the average infiltration rate or  f  can be found by dividing
the change in infiltrated volume  AF  given in Equation 5.20 by a time  incre-
ment  At  or
          f-f*                                                      (5.2,,

-------
i. = f.
3 3
I. = r.
3 :
if

if

r. > f.
3 3
r. < ~£.
3 3
                                      5.9

This average infiltration rate is the maximum of potential average  rate  that
occurs when there is a continuous supply of water, i.e., when there is more
water available than can be infiltrated.  The actual infiltration rate depends
on the rainfall intensity and has a range from a minimum of  zero to a maximum
equal to the potential rate.  If the rainfall intensity exceeds the potential
rate  f  (Equation 5.21), excess rainfall is generated.  The actual average
infiltration rate  i  is given by
                                                                     (5.22)

                                                                     (5.23)
where the subscript  j  denotes the jth time increment of a  storm hyetograph
and  r.  is the jth rainfall intensity in units of length per unit  time.  The
excess rainfall intensity during the jth time increment can  be calculated as
          e. = r. - I.                                               (5.24)

     The infiltration process continues after the termination of rainfall
until all available water has either run off or been infiltrated.   To approxi-
mate this process, the excess rate is set to the negative of the hydraulic
conductivity in the wetted zone.  In other words, the water  continues to
infiltrate at a rate equal to the hydraulic conductivity.  The method of
characteristics can easily handle the negative excess as long as it is the
last excess.

     5.2.3  Derivation of Analytical Kinematic Wave Equations for MSED1
     This portion of the section clarifies the analytical kinematic routing
component of the watershed model.  The derivation is essentially the one given
by Harley, Perkins, and Eagleson (1970), or Simons, Li, and  Eggert  (1976).
This routing procedure is used for the plane and subwatershed units of MSED1
to determine the upstream and lateral inflows into the channel units of  MSED3.
     A single routing procedure is presented to compute both overland flow
(used by the plane and subwatershed units), and channel flow (used  only  by the
subwatershed units).  Other than a few minor changes needed  to switch the pro-
cedure between overland and channel flow, the derivations are identical.
     The analytical solution to the kinematic wave approximation is based on
the continuity and momentum equations in the absence of all  dynamic interac-

-------
                                       5.10
  0
tion.  The continuity  equation  for overland  flow  is
          9q    9y                                                     / f-  oc,
          —a +  TT = e                                                 (5.25)

where  q  is the discharge  per  unit width,   x  is the  downstream  dimension,   y
is the depth,   t  is time and   e  is the lateral  inflow.   In  this case,   e   is
the excess rainfall function presented earlier.
     The Darcy-Weisbach  resistance equation  for overland  flow is
                   2
          Sf =  f -^-j                                                 (5.26)
                 8gy
where  s   is the friction  slope,  f   is the Darcy-Weisbach friction  factor
and  g  is the  acceleration due to gravity.  By neglecting dynamic effects,
the momentum equation  for a kinematic  wave becomes
          S,  = S                                                     (5.27)
          .f     o
in which  S   is the average land slope.  (For slopes  in  excess of 20 percent,
the sine of the slope  angle, not the tangent, should be used).
     Substituting Equation  5.26 into Equation 5.27 and rearranging, the  fol-
lowing expression for  discharge as a function of  depth is
           2    8gS
          q  = -f-2 y                                                 (5.28)

Many researchers, most recently Chen (1976), have shown that   f   may  be  repre-
sented as
          f = f-                                                      (5.29)
              £\
                e
where  R   is the Reynolds  number and  K  is a constant directly  dependent on
resistance.   The Reynolds number may be expressed as
          Nr=*                                                      (5.30)

where  v  is the kinematic  viscosity of water.  Equations 5.29 and 5.30  may
be substituted  into Equation 5.28 to give
              8gS,
                 o  3
                 - y                                                  (5.3D
Discharge is often assumed to be a power function of depth.
          q = ay6                                                     (5.32)

-------
                                      5.11
Therefore, in the case of overland flow  3 = 3  and  a  is expressed as

          a = -^                                                    (5.33)
Substituting Equation 5.32 into Equation 5.25 yields
          a3y^~1 :p + |^ = e                                          (5.34)
This partial differential equation may be solved by the method  of  charac-
teristics.  The total differential of  y(x,t)  is given by:
          ,    3y ,    3y ,                                           ,_„,..
          dy = TT dt + — dx                                          (5.35)
Equations 5.34 and 5.35 form a system of two equations in two unknowns, and
may be written in matrix form as:
           a3y
            dx
                         1
                        dt

"!/
3x
ly.
at
=
e
dy
                                                                      (5.36)
     The characteristic paths along which the solution is valid  are  found by
determining the loci of indeterminancy of the solution.  These loci  are
obtained by equating the determinant of the coefficient matrix with  zero.  The
resulting characteristic equation is
          dX    --*'1                                                 (5.37)
Integrating Equation 5.37 with respect to time yields

                          "1 dt'
          x - x  =
               o
t
/
                                                                      (5.38)
     The invariants of this solution are found by substituting  the  right-hand
side of Equation 5.36 for each column of the coefficient matrix and equating
the determinant of the resulting matrix to zero.  The invariants are
          dt   dx
or by integrating Equation 5.39
          y - yo = / edf
                   t
                    o
                                                                      (5.39)
                                                                      (5.40)
or

-------
                                      5.12
                   X
          q - q  = / edx1                                            (5.41)
                   x
                    o
By substituting Equation 5.40 into Equation 5.38, the following expression for
the characteristic path is obtained.

                                                                     (5.42)
= 00(7    /    edo + yj 3~1
     Theoretically, if the functional form of  e(t)  is known, then Equation
5.42 will give the characteristics in the  xt  plane.  When  e(t)  is a
histogram, then with reference to Equation 5.40, Equation 5.42 may be evalu-
ated in pieces.
     The procedure that calculates the characteristic paths is illustrated in
Figure 5.3.  From any point   (x. , t. )  on characteristic  C,  the value of
x.    on  C  corresponding to time, t     may be calculated by Equation 5.42
expressed as
                                   (t< " V + yi]    dt'             (5>43)
                           i
From Equation 5.40 it may  be  seen  that
          yi+i - yi + ei+i (Vi - V                               {5-44)
Integrating Equation 5.43  yields
                           C(y  +      (     -    )B - y  ]           (5-45)
For a given plane of length  L,  values of  x.    are calculated until
x.   > L.  Time of arrival of the characteristic at the downstream boundary
t   is found by solving Equation 5.45 for  t   in terms of  t.  and  x..
                                            ij                3        3
          t, = t. +
                      1
                             e   (L-x  )        1/6
                                                    (5-461
For cases where  e    = 0,  Equations 5.45 and 5.46 may be rederived from
Equation 5.42, yielding
                                                                      (5-47)
and

-------
                               5.13
Excess
Intensity
Histogram
_Upstream
 Boundary
Downstream
Boundary
                                                          (L,tL)
 Figure 5.3.  Method of characteristics solution domain  illustrating
             calculation of characteristics in downstream direction.

-------
                                      5.14
          x±+1 = x± + aBy    (t±+1 - t.)                             (5.48)
     Equations 5.45 through 5.48 are used serially,  until a characteristic
reaches the downstream boundary after the final time of interest for the
hydrograph.  At this time, additional characteristics are not required.   If  a
characteristic contains the final negative excess, it may never cross the
downstream boundary.  This happens when the infiltration process is given suf-
ficient time to remove all the excess surface water, after the termination of
rainfall.  The characteristic path in this case is represented by an upward
slope until it eventually reaches vertical.  At this point all runoff has been
infiltrated.  For the case when this occurs before the final time increment  of
the hydrograph, the time when the last characteristic reaches the boundary is
estimated by an iterative procedure.  The remaining portion of the storm
hydrograph is set equal to zero.  Figure 5.4 illustrates the characteristic
solution domain.
     As previously stated, the channel routing for the subwatersheds scheme  is
nearly identical to the overland flow routing.  The continuity equation  for
channel flow is

          £*£-«.
where  Q  is the total discharge,  A  is the cross-sectional area of the chan-
nel and  q   is the lateral inflow to the channel.
     When using Manning's equation, the kinematic wave approximation to  the
momentum equation can be written as
in which  S   is bed slope,  S   is energy slope,   n  is  Manning's  roughness
coefficient,  g  is the gravitational acceleration and  R  is  the hydraulic
radius.  By definition the hydraulic radius is:
          R = |                                                      (5.51)
in which P  is the wetted perimeter and usually can be represented  as a power
function of flow area, or

          P = a1 A 1                                                 (5.52)
in which  a   and  b   are constants that vary with the shape  of a  cross-

-------
                                    5.15
Upstream    t
Boundary
  Excess
  Intensity
  Histogram
                                              Downstream
                                              Boundary
Last  Characteristic
to Reach Boundary
    Figure 5.4.   Method of characteristics solution domain illustrating a
                set  of characteristics for an arbitrary excess rainfall
                histogram.

-------
                                      5.16
sectional area.  Simons,  Li  and Ward  (1977)  devised a computer program  to
estimate  a.  and  b   providing  the  cross section of the channel  is  known.
     If the Chezy relationship is employed,  the momentum equation  becomes
                       2
          So 5 Sf =
    A2C2 R
                                                     (5.53)
in which  C  is the Chezy  coefficient.
     The flow cross-sectional  area can be expressed as a power  function of
discharge
          Q = cxA3                                                     (5.54)
in which  a  and   3  are coefficients with values dependent on  channel shape,
roughness and slope.
     If Manning's  equation is  applied, the corresponding  a  and  3   are
determined by using Equations  5.50, 5.51, 5.52 and 5.54.  The values  are
                           V2
                                                                      (5.55)
S (2.21)
 o	
 2  4/3
and
              5 - 2b
                     1
                                                                      (5.56)
     If the Chezy relationship is used, the  a  and  g  values are determined
using Equations 5.51, 5.52,  5.53 and 5.54.  The values are:
                      V2
                                                                      (5.57)
and
              3 - b
           e =
                    1
                                                     (5.58)
     The user may also assume  that the two planes of the Wooding watershed
configuration meet to form  a triangular channel.  The wetted perimeter of that
channel  P  (Figure 5.5) may be expressed as

                                                                      (5.59)
where the subscripts refer  to plane  1 and plane 2.  Since  t   and  t   may be
expressed as

-------
                                      5.17
           1   c;   '   w?   c
           1   S1      2   S2

Equation 5.59 may be written:
                                                                      (5.60)
          P = y
                                                                      (5.61)
                         /      \
Referring to Figure 5.5, the cross-sectional area of the channel may  be
expressed:
or
            = j y [t1 + t2]

                                                                      (5.62)
                                                                      (5.63)
                     1    2
Solving Equation 5.63 for  y  and substituting the result  into  Equation  5.61
yields the following expression for  P  in terms of A:
                  ^
          P = a  A
allowing
     The
                                       1
                                                              V2
                                                                      (5.64)
                                                                      (5.65)
                                                                      (5.66)
                       calculated in this manner may then be used  to  obtain
a  and  3  by substitution into either Equations 5.55, 5.56, 5.57 or  5.58
                                                                             If
 1
    and  b   are not input to the program, they will be calculated  in MULTSED
as in Equations 5.65 and 5.66.
     Equations for water routing are again Equations 5.45 through  5.48.
Excess  e  is replaced by lateral inflow or discharge per unit  width   q0
                                                                           The
                                                                           A
parameters  a  and  3  are defined above, and  y  and  q  are  replaced  by
and  Q,  respectively.  Since there are two planes, lateral  inflow  to the
channel consists of the sum of the two overland flow discharge  hydrographs.
     A problem in constructing an open-book catchment simulation  using  the
method of characteristics solution for kinematic wave routing  lies  in the
timing of the overland flow feeding the channel.  In order to  preserve  as much
generality as possible, the two planes must be allowed to differ  in geometric
and hydraulic properties.  When using the method of calculating charac-

-------
                         5.18
Figure 5.5.  Definition sketch of triangular channel.

-------
                                      5.19

teristics, one selects a time on the upstream boundary of  the  solution domain,
t   (Figure 5.4) and proceeds to determine points on the characteristic until
the downstream boundary is reached.  Time of arrival of that characteristic at
the downstream boundary  t   is a function of the lateral  inflow  and the
                          L
hydraulic and geometric properties of the plane.  Therefore, for  the selection
of the same set of  t 's,  different planes produce different  sets  of  t 's.
                     o                                                   L
     This situation poses no particular difficulty until it is desired to com-
bine the overland flow discharges to produce the lateral inflow for channel
routing.  It might be suggested that the difficulty may be easily handled by
simply interpolating each onto a common time line.  This solution is valid,
though an unknown amount of error in each discharge occurs due to inter-
polation.  If, on the other hand, it is possible to pick the time on the
downstream boundary and then calculate  t   on the upstream boundary, the two
                                         o
overland flow hydrographs could simply be added, time by time,  to obtain the
desired lateral inflow to the channel.  Further, in this case,  there would be
no error included in forming the inflow hydrograph.  A subroutine was devel-
oped to find the  t   corresponding to a selected  t_,  and it is based on the
                   O                                Li
theory presented below.
     The equation for a general characteristic path is:
                t.
          L
          — =   f
          ™«     J
               t
                o
(a
      3-1
                       o
dt1                           (5.67)
where  L  is the length of the slope being routed  and   t'   and  a  are dummy
variables of integration.  The problem here  is  to  solve Equation 5.67 for  t
                                                                             o
when everything else is known.  Lateral  inflow  q    is  generalized;  therefore,
Equation 5.67 may be used for both overland  and channel flow.   For simplicity
of discussion, the method will continue  to be developed for overland flow;
however, it will be directly applicable  to channel flow simply by specifying
the appropriate  a,  B  and  q .  For overland  flow, the lateral inflow  q
                              Xf                                            XT
is defined as the excess rainfall after  satisfying infiltration and intercep-
tion,  e.  This function is assumed to exist in the form of a  histogram and is
displayed vertically along the upstream  boundary in Figure  5.4.
     Since  e(t)  has the form of a histogram,  excess rainfall during the  jth
time increment  t. - t.    is constant.   In  addition, the form of Equation
5.67 may be simplified by noticing the inner integration, i.e., the integra-

-------
                                      5.20
tion of  o  is simply  the  difference  between  the  cumulative  excess at time
t   and the cumulative excess  at  time  t  .  That  is,
 L                                      o
          /  e(o) do = E(t  }  - E(t  )
                                                                      (5.68)
where  E  represents  the  cumulative  excess.
     With this notation in mind and  taking advantage  of  the  histogram form of
e(t),  Equation 5.67  may  be "rewritten  as
L
~Z
ct3
, ^-
k+1
                              ^-i^
                              k+1  k
                                            -.uit   +  e-j.-t-  ~  E.]p   dt'
                                            j+1 o    3+1  j     j
              k      i
            i=j+2 t.  .
                                                                         dt'
                                                              I3"1  dt1   (5.69)
     Equation 5.69 consists  of nothing more  than  a  series  of  simple integra-
tions of the form
          / (at1 + b)3"1  dt1  = J-T-  (at1 + b)6
          J                    a3
                                                                      (5.70)
Integrating as in Equation  5.70 and  introducing   A.   as  defined below,
          A. =-e. t.  , + E.  ,+e.  , t.  -  E.
           i     ii-1     i-1     J+1   D     J
Equation 5.69 may be written  as:
                                                                      (5.71)
                            t1 + A
                                            V
                                                    K
                           ! .  t' +
                                            V
               ej+1e
                                           t .
                                                                      (5.72)
     Since Equation A-72 may be explicitly differentiated  with  respect to   t ,
                                                                             o

-------
                                      5.21
a Newton-Raphson technique can be used to obtain a. solution.   The subroutine
developed uses a second-order routine to speed convergence.   The routine pro-
ceeds by rewriting Equation A-72 as
                                                           t.
          f(v  - -
+   E
  i=j+2
                          K i I
                                    Ai
                                                                     (5.73)
The first and second derivatives of  f(t )  with respect to  t   are,
                                        o                    o
respectively,
          ft(V
                             Ak+1  - ej+1to)
                                           3-1
                                (e.t.  + A.  -
                   i=j+2   i
                   (e.t.  .  + A.  - e._t )
                     ii-1     i     3+1  o
                                         3-1
and
                                                                     (5.74)
                        (3-1)
                    Jc i l
                                           J-2

-------
                                      5.22
                      k    e2
                                                                      (5.75)

The second-order Newton's method  is based on truncating a Taylor's  series
                                                                 *
expansion of  f(t  )  about  a  trial value of  t  ,  defined as  t   ,   after  the
                 o                            o                o
third term.  Thus,  f(t  )   is written as
                       o
                                        *    (to - V2
          f(to) -  f(to)  -  
-------
                                 5.23
  E
  o
 c
 a>
 UJ
                           Upper Bounding
                            Characteristic
                                      Lower Bounding
                                      Characteristic
                       to be Calculated
Selected
  t,
Figure 5.6.   Method of characteristics solution  domain illustrating
              upstream calculation of characteristics between
              bounding characteristics previously calculated in
              downstream direction.

-------
                                      5.24
are known.
     This technique provides  a rapid means of finding  t  's  corresponding  to
a given  t .  Three iterations of Newton's method have seemed  sufficient  for
          L
n = 0.001.  Knowing  t   and  t  ,  the depth may be evaluated  at the down-
                      O        L
stream boundary at time  t    by using Equation 5.40.  This depth is used  to
                          L
determine the discharge at the downstream boundary at time  t   by using
                                                             LI
Equation 5.32.
     5.2.4  Sediment Determination for MSED1
     Erosion and sediment  yields are processes of balancing  soil erosion rates
and transporting rate of the  transporting medium.  Generally,  sediment  yield
from a watershed can be divided into processes related to the  flow conditions,
such as overland flow and  channel flow.  The following is a  discussion  of
sediment supply due to erosion by both rainfall and runoff,  and the transport-
ing rate by overland flow  and channel flow in upstream subwatersheds.

     5.2.4.1  Overland Sediment Transport Capacity
     After a runoff rate   q   is known, the overland sediment transport  capa-
city rate can be calculated.  This is accomplished after determination  of
several intermediate steps.   First, the overall flow resistance is assumed  to
be:

          Kg - K* + (Kh *  V °g                  .                    (5'78)
where  K   is the parameter describing the overall flow resistance associated
with ground cover effects,  K  is the parameter describing  the maximum
resistance for the area  (C •= 1.0),  and  C   is the percent  of ground cover.
An increase in  C   produces  a rapid increase in  K ,  as seen in Figure 5.7.
These values closely agree with those found in Woolhiser's (1975) work  in
unsteady overland flow modeling.
     Both  q  and  K   are then used to find the average flow  depth as
               qK^v 1/3
                   )                                                  (5.79)
                  o
where  y  is the flow depth,  v  is the kinematic viscosity of water,  g   is
     icceleration of gravity anc
     The mean flow velocity is
the acceleration of gravity and  S   is the slope of the ground surface.
                                  o

-------
                          5.25
Kg
I     I    I     I    I	I    I	I     I
   0.2      0.4       0.6      0.8
         Cg , Ground Cover
                                                      .0
   Figure 5.7.  Assumed variation of overall resistance
               with ground  cover.

-------
                                      5.26
          V =                                                         (5.80)
              y
The flow parameters calculated above are  then  used to  determine  sediment
transport capacity.  The procedure  for determining sediment  transport capacity
given by Simons, Li and Stevens  (1975) is used in this report.
     The first sediment transport parameter that should be determined is  the
tractive force or boundary  shear stress.  Effective boundary shear  stress
acting on a grain can be determined by
                          V
          T = 5- f p V2 = 1 -°-  vp V2                                    (5.81)
              o         O q
where  T  is the effective  boundary shear stress,  f   is  the Darcy-Weisbach
friction factor for grain resistance,  p  is the density  of  water and K   is
                                                                        o
the parameter describing grain resistance.
     The boundary shear stress  T',  considering total resistance (form and
grain resistance) , is
          T1 = yySQ                                                   (5.82)
where  y  i-s tne specific weight of water.  It should  be  noted that  T"   is
usually much larger than  T.  The shear velocity  U^   is  then
          U* =                                                        (5.83)
     The sediment transport  capacity rate  is an  integral of  all  the  individual
sediment size transport rates or  in discrete form
                N
          a  =  Z   (q+^i  )                                            (5.84)
               i=1
where  a   is the total transport capacity rate,  a  .   is the potential
transport rate for  each size,  i   is the  percentage of each sediment size of
                                s
bed material and  N is the  total number of sizes considered.  Each  individual
size transport  q    is composed of bed-load transport  q    and suspended
load transport  q .  ,  or
                 S 1
          *ti = qbi + qsi                                             (5'85)
The bed-load transport rate  can be calculated using the Meyer-Peter,  Muller
formulation (USSR,  1960) as
                12.85 ,       J.5
          qb± = — — (T - T )                                        (5.86)
                 /p
where  T   is the critical shear  force  for the given particle size.   Though

-------
                                      5.27
the Meyer-Peter, Muller equation was used here, other  suitable  bed-load for-
mulations could be easily substituted into the model.  The  critical shear
force for particle movement is determined by the  Shields  criteria  of
          T  = 6y(S  - 1) d .                                          (5.87)
           C       S       SI
where  6  is the parameter depending on flow conditions,  S  is the specific
                                                            s
gravity of the sediment, and  d  .  is the sediment  size in  question.  The
value of  S   usually ranges from 2.60 to 2.70, but 6  is  dependent on flow
conditions and should be calibrated to the actual field situation.   If  T   is
                                                                          c
greater than  T  there is no sediment movement.
     For steep slopes, the critical shear stress  must  be  reduced to account
for the lessened component of gravity in the direction normal to the land sur-
face.  This correction factor is expressed as
          k = cos9  /1 -   "                                          (5.88)
The variable  6  is the slope angle of the land surface,  $   is  the angle of
repose of the material (assumed to be 40°), and  k  is the correction factor.
The critical shear stress is multiplied by this factor.
     The suspended load is determined using the Einstein method  (1950),  or
                       sw-1    v
          q   = C U.a 	 [(£- + 2.5) J  + 2.5 J ]                 (5.89)
                      (1-S)     *
where  C   is the sediment concentration at distance  a  above the  land  sur-
        a
face,  and  S,  A,  a,  J   and  J   are given below.
     The concentration term is related to the bed-load transport as
          q, .  = 11.6 C U.a                                            (5.90)
           DI         a "
     The distance  a  is assumed to be 0.2 feet for particles which are  less
than 0.1 foot in diameter.  For larger particles, the distance   a  is set
equal to twice the particle size.  The 0.2-foot value was chosen based on a
calibration with Colby's method for sand sizes.  If twice the sediment
diameter is used for small particles, such as sand, the transport rates  become
unrealistically large.  The dimensionless parameters relate flow depth to
sediment size as
          S = -                                                       (5.91)
The dimensionless parameter  w  relates the in-water settling velocity of the

-------
                                      5.28
sediment to the shear velocity, or
                                                                     (5.92)
where  V   is the settling velocity of the sediment and  K  is von Karman's
number, taken as 0.40.
     Settling velocities are a function of particle size and water properties
and can be formulated  (ASCE, 1975) as
               2.9517  d  .2
          V  = - —    when  d .  < 0.0002 feet                (5.93)
           s       v                 si
or
                                  1/2
               (36.064 d3. + 36v2)   - 6v
          V  = - ^j -    when  d .  > 0.0002 ft
           s             d  .                        si
                          si
The terms  J   and  J   are integrals resulting from integration of the equa-
tion describing the vertical concentration of sediment in the flow.  The first
integral  J   is given as
               1        w
          J1 = / ( — ^-2)  da                                         (5.94)
               S
where  a  is a dimensionless relative position,

          a = ^                                                      (5.95)
and  e  is the distance above the land surface in the flow.  The other
integral is similar and is given as
               1            w
          J2 = / Una ( — — )  do                                     (5.96)
               S
These two integrals can be evalauted by successive integrations of a power
series expansion given by Li (1974).  Rearranging Equation 5.89 and substi-
tuting into Equation 5.88 gives a simpler form or

          *si - TIT! -^—z [(u; + 2-5)  Ji + 2-5 J2]                  (5-97)
The total potential transport rate,  Equation A-85,  becomes
                N
          qt *  *  (qsi+ qbi> S                                    (5-98)

-------
                                      5.29
The potential transport capacity can be found as
                    f
                    / q  dt                                           (5.99)
           fc

where  T  is the top width of the channel,  At  is the duration  of  runoff  and
V    is the nonporous volume of potential transport.

Channel Sediment Transport Capacity
     After the overland flow runoff is known, the sediment transporting  capa-
city of the channel can be calculated.  Although the physics  of  sediment
transport for the channel are much the same as those for overland flow,  rela-
tions describing channel sediment capacity are altered.
     The resistance factor  f  is calculated for each sediment size based  upon
the ratio of sediment diameter to hydraulic radius.  The expression used is
          f = [1.69 + 2 * log (2 * R/d .)]~2                          (5.100)
in which  R  is the hydraulic radius.  This is an empirical expression shown
to be valid for calculating flow resistance in open channels  when the flow is
in the turbulent range.  According to the equation, for a given  depth the
larger particles will have a larger resistance.  Since the resistance on a
selected particle size also depends on the size of the particles surrounding
it, the resistance factor is not allowed to fall below half the  value computed
for the largest sizes.  In addition, the friction factor is not  allowed  to
fall out of the range between 0.1 and 0.01.

     5.2.4.3  Determination of Sediment Supply
     Potential sediment transport represents the capacity of  the system.  Sup-
ply of sediment comes from two mechanisms:  detachment by raindrop  splash  and
detachment by overland and channel flow.  For a plane of width and  length   L,
raindrop splash detachment can be formulated as a simple power function  of
rainfall intensity (Meyer, 1971):
          Vr = a^2 LW (1 - ) Aj^                                     (5.101)
where  V   is the nonporous volume of detached material by raindrop splash,
a.   is an empirically determined constant describing erodibility of the  soil,
and  A^  is an area reduction factor.
     The variable  A   represents the fraction of unprotected or bare soil in

-------
                                      5.30
•the area and is given as
          A, =  1 - C  -C   + (C  C  )                                   (5.102)
           £>        g    c     g C
where   (C C )  accounts for areas of  cover  overlap.   Sediment  supply by over-
         g c
land flow detachment is determined by
          Vf = Df (Vfc - Vr>                                          (5.103)
where  V   is detachment by overland  flow and   D    is the  flow detachment
coefficient.  An equation similar to  that used  in  overland flow detachment  is
used for channel flow detachment.  For many cases,  however,  the flow detach-
ment coefficient for channels is assumed to be  zero due  to natural  armoring,
riprap or other forms of bed and bank protection.   This  is especially true  for
man-made channels.
     If  V  < V   there is  no flow detachment because the  transport rate is
limited by the transporting capacity.  The  total available sediment supply
V   is
 a
          V  = V  + V                                                 (5.104)
     5.2.4.4  Determination of  Sediment Yield
     Once the supply and  capacity  for  each  size  fraction  has  been  calculated
and summed over the entire event,  the  actual sediment  yield can  be determined.
This is done by comparing the transporting  capacity  and supply for each  size
fraction.  If the transporting  capacity is  greater than the total  available
sediment supply,  V  > V  ,  then the sediment  yield  for that  size  fraction is
                   t    di
equal to  V .  However, if  V   < V ,   then  the yield for  that size fraction is
           a                 t     a
equal to  V .

     5.2.5  Mathematical  Derivation of the  Numerical Kinematic Routing
            Procedure for MSED3
     The numerical and analytical  kinematic wave routing  schemes are  governed
by the same equations:  the equation of continuity,  the momentum equation and
the equations describing  channel geometry and  flow resistance.   The following
numerical kinematic routing procedure  is used  by MSED3 for the channel units.
     The derivation for the discharge-area  relationship is slightly different.
In MSED3 the relationship is expressed as
          A = a' QS                                                   (5.105)
instead of

-------
                                      5.31
          Q = a AP                                                    (5.106)
as in MSED1.  This is due to the use of the numerical method  in  MSED3.
Usually  3'  is less than 1.0 and has a value of  1/3 for  Reynolds  numbers  less
than 900.  Consequently, if discharge is computed incorrectly, the relative
error in the flow area is smaller than the relative error in  the discharge.
On the other hand, the error in the discharge estimation  is magnified if the
numerical computations are performed on the flow area (Li, Simons  and Stevens,
1975).  In the case of MSED1 it is more convenient to compute discharge as a
function of flow area.
     If Manning's equation is applied, the corresponding   a1  and   3"  are
                 a 4/3n2\  \10-<
                .2:21-8-'     '                                        (5-107)
                       o
and
          3' =   ^                                                    (5.108)

     If the Chezy relationship is used, the  a1  and   3"  values  are

                 V~ 1          1                                     (5.109)
                \C2S /
                \   o'
and
          3' = 33jj-                                                   (5.110)

     The water continuity equation for the channel can be expressed as
          Ix" + It = q£                                                (5.111)
in which  Q  is water discharge,  x  is the downslope  distance,   A  is  the
flow area,  t  is time and  q   is the lateral inflow.  The  lateral inflow
                             J6
rate  q   for the channel units is obtained from the overland  flow in the
adjacent plane units calculated in MSED1.
     The problem of water routing becomes a matter of  solving  Equations 5.105
and 5.111.  A nonlinear scheme with an iterative procedure was used in  this
study.  A linear scheme was used to obtain the initial estimate of the  unknown
discharge for the nonlinear scheme.  The linear scheme may be  used as is, with
no iterations, to solve for the unknown discharge if the accuracy is

-------
                                      5.32
satisfied.
     The finite difference form of Equation 5.111 can be represented as
           n+1    n+1    n+1    n
                                    ='^'
in which  Q.   is the quantity  q  at grid point  x = jAx  and  t = nAt,
where  Ax  is the space increment and  At  is the time increment.  The rec-
tangular network shown in Figure 5.8 illustrates the  x-t  grid system.
     Unknowns in Equation 5.112 are  (Q .   )     and  (A   )    ,  but the  dis-
charge bears a definite relation with the flow area, as indicated by Equation
5.105.  with two equations, the values of the two unknowns can be obtained.
     Substitution of Equation 5.105 into Equation 5.112 yields
                                 At  n+1 _,_ nn     At ,  n+1   _._  n
                                         +      + T (       +
     The right side of Equation 5.113 contains known quantities and is  denoted
by  Q  which can be expressed as
                         n. At. n+1     n.                     ,-..,.,.>
               n+1
          r = Q
               j+1
and

              Ax
then the left side of Equation 5.113 is expressed as
          f(r) = 9r + a'r^                                           (5.115)
The solution of Equation 5.113 satisfies the condition
                         8'
          f(r) = 9r + ct'rp  = i2                                      (5.116)
An approximate solution to this nonlinear equation is obtained by the follow-
ing iterative scheme.
     If  r   is the value of  r  at the kth iteration,  the Taylor Series
expansion of the function  f(r)  around  f   is
          f(r) = f(rk) + (r - rk) f (rk) + ^ (r - rk)2 f" (rk)
               + j (r - rk)3 f" (rk) + ...                          (5.117)
                 o
              k            k
in which  f'(r )  and  f"(r )  are values of  the first and second derivatives

-------
                       5.33
                   *  Known Grid  Points
                   o  Unknown Grid Point
      n -n
   0>
   £'
™r
  At
      h-Ax-^
      !       !
       1   x
                    Space
Figure 5.8.  Definition sketch for channel water and
            sediment finite difference  routing
            scheme.

-------
                                      5.34
                      v
of the function at   r .   Dropping  the terms  higher  than  the  second order,  one
obtains
          f(r)  = f(rk)  +  (r  -  rk)  f  (fk) +    
-------
                                      5.35

          "_  "t* ct  p Q      .  =cj_                                      \5o127)
The finite difference form of  Equation  5.127  is given by the expression
                  _n+1
                      + a.g.  i _J_L_:	1— i      _itl
                                                      At

                                                                      (5.128)
            * \ * '+1     * ' + 1 /
so that
                                      /on  +on+^ \ ^'~^
                                                      .  At
                                                                      (5.129)
                                                   -i_ /
                                                  2
     Equation 5.129 uses a linear, scheme  to provide  the best initial estimate
of  r°  for the nonlinear scheme.   However, Equation 5.129 is not applicable
if both  Q.     and  Q.     are 'zero.   When both are zero,  3' = 1  is used in
Equation 5.115 and then
                 n
                e + a1
                                                                      (5.130)
     5.2.6  Channel Infiltration  Routine  for  MSED3
     The channel infiltration  routine  is  similar to the layered infiltration
scheme described earlier in the report, but with one difference.  Since the
depths of flow in the channels are  normally much greater than those for
overland flow, the depth of the water  is  not  ignored.   Thus,  the equations are
the same except for the addition  of  head  due  to  the depth of  flow.

     5.2.7 Sediment Routine for MSED3
     The sediment routing in MSED3 uses the same principle as the sediment
yield calculations in MSED1, the  process  of balancing supply  and capacity for
each sediment size.
     The sediment calculations in MSED3 are different in that the numerical
method used allows for the sediment  to be routed through the  channels at each
time increment and then integrated over the time increments to arrive at a
total yield for each size fraction.  The  method  used in MSED1 can only provide
a total yield for each size fraction,  but cannot truly route  the sediment

-------
5.36
through the  channel.   MSED3 is  able  to route  the  sediment  because  the
balancing of transporting capacity and supply can be  compared at each time  and
space  increment along  the channel due  to  the  use  of the  numerical  scheme.   The
method used  in MSED1 does not allow  for this,  since only conditions  at the
downstream end of  the  channel are calculated.
     Since MSED3 uses  the numerical  method, which requires actual  transport
rates at each time increment, and it needs  to use the yields  calculated in
MSED1 as upstream  and  lateral inflows,  the  yields in  MSED1  must be transformed
into sediment hydrographs.   This  is  accomplished  by distributing the yields
from MSED1 in proportion  to the water  discharge at each  time  increment.  MSED3
could easily be modified  to distribute  the  yields from MSED1  by various  other
schemes.
     The remainder of  this  section will be  devoted to the  governing  equations
for sediment routing and  the development  of the numerical  routing  technique.

     5.2.7.1  Governing Equation  for Sediment  Routing
     In the  channel units the processes which  govern  sediment routing are the
continuity for sediment,  the transport  capacity,  sediment  flow detachment and
armoring.  The continuity equation for  sediment size   i  is
          3G .   3C.A   3TZ.
          —^ + ~dr~  + -rr1 =  g  •                                    <5.13D
           3x      3t      3t    si
in which  i  is the size  fraction index,  G .  is the total sediment transport
rate by volume per unit time,   C.  is  the sediment concentration by  volume,
Z.  is the depth of loose soil,   T  is  the  channel top width,  and  g .   is  the
 1                                                                   SI
lateral sediment inflow.   (Z is in terms  of nonporous soil.   To correct  for
porosity  Z  is divided by  one  minus the  porosity.)
     The concentration of sediment for  a  sediment size  i   is
               G
          CL = -^                                                   (5.132)
The total concentration of  sediment  at  a  cross section is
                N

and the total loose soil  available is
                N
          ZT =  £   Z±                                                 (5.134)
                               (5.133)

-------
                                      5.37

     The sediment transport capacity equations  are  the  same  as  those used for
the channel in MSED1 and described earlier.  The  only difference  is the trans-
port capacity is calculated at segments along the channel  at each time  incre-
ment instead of at the downstream end of  the channel.
     The amount of soil detachment by channel flow  is determined  by comparing
the total sediment transport capacity to  the total  available amount of  loose
soil.  The total sediment transport capacity is
                N
          G  =  E  G .                                                 (5.135)
           C   i=1  C1
Assuming the total sediment transport capacity  G   is  equal to the transport
                                                  C
rate, the total potential change in loose  soil  can  be determined  from Equation
5.131 as
          AZP = || At                                                 (5.136)
                dt
           p
     If  AZ  > -Z,  the loose soil storage is enough for transport and  there
                                                                     P
is no detachment of soil by surface runoff.  Soil is detached if   AZ < -Z.
The amount of detachment can be computed  by
          D = D (AZP + Z)                                             (5.137)
in which  D  is the total amount of detached soil and   D   is a detachment
coefficient which varies from 0.0 to 1.0  depending  on soil erodibility.  If
the channel bed is cemented together by cohesive  material,   D  is equal to
zero.  In a river which has no cohesive material, the value  for  D   is one.
     Two limitations are placed on the loose soil layer.   The first states
that when the loose soil layer has become  greater than  one foot,  the detach-
ment process is controlled by the sediment size with the lowest relative
transport rate (this will be the largest  size present).  The reasoning  which
justifies this procedure is when the loose soil layer has  grown as large as
one foot, the flow cannot effectively interact  any  deeper; therefore, it must
remove the less transportable sediment before it  can move  the more easily
transportable sediment.  As a result, the  detachment process becomes limited
to the rate at which the largest sizes can be detached.  Although the bed is
not armored, the transport rate has become retarded by  the larger sizes when
this occurs.
     The other limitation is when a nontransportable size  exists,  the detach-
ment cannot be larger than the amount of material that  must  be  removed  to

-------
                                      5.38

leave behind a layer of  nontransportable  particles with  a  thickness  of  twice
the nontransportable diameter.   If  there  is  enough nontransportable  material
in the loose soil layer  at  the beginning  of  the time  increment,  then no
detachment at all can occur.
     The accepted value  for the  soil detachment is the lower  of  the  values
computed by Equation 5.137, or the  two  limitations just  described.   The new
amount of loose soil is  then
          Zi = Z. + D F.                                              (5.138)
in which  Z.  is calculated for  each size fraction of sediment.

     5.2.7.2  Numerical  Procedure for Sediment Routing
     A numerical routing procedure  is adopted for determining the sediment
transport rate for each  sediment size.  In this procedure, the sediment con-
tinuity equation is solved  for each size. Equation 5.131  is  rewritten  in
finite difference form and  combined with  Equation 5.132  to yield
                                 <«      * *      "
The sediment transport rate  for each  size at  the outlet of the  reach  for  the
time increment of interest can be approximated by
                                                                      (5.140)
in which  (Qsi'i)     represents  the theoretical transport  capacity  of  the  ith
GT
zn+1
Vl
'~ZTn
J+1
n+1
si . .
:+i
sediment size if the bed was  made only of  that  size material.   The  other  term
represents an approximation of the  fraction of  sediment of the  ith  size in the
loose soil layer at the end of the  time increment.  It is an approximation
since the denominator is the  total  loose soil depth for the previous  time
increment and not the present.  The approximation is good as long as  the  loose
soil layer does not change greatly  during  the time increment.
     The change in the loose  soil layer can be  rewritten as
                      - Zn                                            (5.141)

-------
                                      5.39
     Combining equations 5.139 through 5.141, the new loose soil  layer  can  be
solved for directly by the equation
          Zn+1  = [2n   T + Gn+1    + Cn   A"
                                            3 1
                  At .  n+1
                               »
All the terms on the right-hand side of Equation 5 . 1 42 are known  and  as  a
               _. » 1
result  (Z^.  )     is determined.  Knowing the new loose soil  depth,  the  trans-
port rate can be solved for by Equation 5.140.
     When Equation 5.142 predicts aggradation  (an  increase in the loose  soil
layer) the amount of aggradation is checked against that which  is feasible
given the flow conditions and the settling velocity of the sediment particles.
This is extremely important for the routing of fine materials that will  not
              *
settle out in relatively short reaches of a channel even if the transport
capacity is much smaller than the supply.
     The fraction of sediment that can settle out  based on ideal  settling  and
assuming a simplified sediment concentration profile  (uniform), is given by
          S.  = V   TAx/(2 Q)                                      (5.143)
           f .     s .          n+ 1
            i     i
A factor of 2 is included to account for turbulence .  The  total  amount  of
aggradation predicted by 5.142 and 5.143 is compared  and the  lesser  value
chosen.  If  Sf .  is greater than one, settling cannot  lessen the  aggradation
process.
     When Equation 5.143 controls, the transport  rate is corrected by
including the fraction of sediment that was predicted to be deposited by
Equation 5.142, but could not settle.

     5.2.8  MSED2
     MSED2 mentioned above acts as in interface between the MSED1  and MSED3
components of MULTSED and is necessary to make efficient use  of  computer time
and storage.  As described, MSED1 uses an analytical  routing  method  which
calls for the results for each unit (plane or subwatershed) to be  calculated
for the whole event before proceeding to calculate  any  results for the  next
unit in the computational sequence.  However, MSED3 uses a numerical procedure

-------
                                      5.40

which works most efficiently when the results for a single itme increment of
the event are calculated for all units before proceeding to the next time
increment.  Since MSED1 provides the lateral and upstream inflows for MSED3
the space time orientation of the results must be switched.  MSED2 reads the
files created in MSED1 and then executes the switch.  In addition, MSED2
separates the discharge hydrographs from the sediment yield results.

5.3  Water and Sediment Input Data Requirements
     Data requirements for the water and sediment routing model are summarized
in the list below.  Other mechanistic water and sediment models require simi-
lar data input and therefore this list of inputs summarizes the data that must
be provided in order to provide a data base for simulating water and sediment
impacts from man's activities in the watershed.
     Geometry and Channel Data
       Watershed area
       Length of overland slopes
       Width of overland slopes
       Gradients of overland slopes
       Length of channel sections
       Gradient of channel sections
       Measured, representative channel cross sections
       Extent of impervious areas

     Soil Data
       Distribution of soils
       Types of soils
       Initial water content of soil
       Saturated hydraulic conductivity of soil
       Porosities of soil
       Specific gravity of sol
       Grains size analysis of soil and channels
       Rainfall storm hyetographs
     Hydrologic and Hydraulic Data
       Storm and daily runoff hydrographs
       Overland flow resistance

-------
                                      5.41


       Channel flow resistance
       Storm sediment yield
       Grain size and analyses of sediment
       Sediment detachment coefficient for rainfall and runoff
     Vegetation Data
       Types
       Distribution
       Density of ground cover
       Density of canopy cover
       Storage of ground cover
       Maximum and minimum storage of canopy cover

     Climatic Data
       Average daily temperature

5.4  References
American Society of Civil Engineers, 1975, Sedimentation Engineering, prepared
     by the ASCE Task Committee of the Hydraulics Division.

Einstein, H.A., 1950, The Bed Load Function for Sediment Transportation in
     Open Channel Flows, USDA Technical Bulletin No. 1026, Washington, D.C.

Fullerton, W.T., 1980, Water and Sediment Routing Model for Complex Watersheds
     and Its Application, unfinished Masters Thesis, Department of Civil
     Engineering, Colorado State University, Fort Collins, Colorado.

Green, W.H. and G. A. Ampt, 1911, "Studies on Soil Physics, Part I:  The Flow
     of Air and Water through Soils," Journal of Agriculture Science, May.

Harley, B.M., F.E. Perkins, and T.S. Eagleson, 1970, A Modular Distributed
     Model of Catchment Dynamics, Massachusetts Institute of Technology,
     Hydrodynamics, Report No. 133.

Johnson, R., N. Crawford, P. Grimsrud, T. Barnwell, and L. Mulkey, 1979,
     Hydrologic Simulation Program-Fortran Workshops, sponsored by the
     Environmental Protection Agency and Hydrocomp Inc., Mountain View,
     California.

Li, R.M., 1974, Mathematical Response from Small Watersheds, Ph.D.
     Dissertation, Department of Civil Engineering, Colorado State University,
     Fort Collins, Colorado.

Li, R.M., D.B. Simons, W.T. Fullerton, K.G. Eggert, and B.E. Sprank, 1979,
     "Simulation of Water Runoff and Sediment Yield from a System of Multiple
     Watersheds," XVIII Congress International Association for Hydraulic
     Research, Cagliani, Italy.

Li, R.M., D.B. Simons, and M.A. Stevens, 1975a, "A Nonlinear Kinematic Wave
     Approximation for Water Routing," Water Resources Research, Vol. 11.

Meyer, L.D., 1971, "Soil Erosion by Water on Upland Areas," in River
     Mechanics, Vol. II, ed. by H.W. Shen, Fort Collins, Colorado.

-------
                                      5.42


Simons, D.B., R.M. Li, and K.G. Eggert, "Storm Water and Sediment Runoff
     Simulation for Upland Watersheds Using Analytical Routing Technique,"
     Volume I—Water Routing and Yield, Colorado State University Report
     CER77-78DBS-RML-DGE16, prepared for USDA Forest Service, Rocky Mountain
     Forest and Range Experiment Station, Flagstaff, Arizona, April 1977.

Simons, D.B., R.M. Li, and M.A. Stevens,  1975, Development of Models for
     Predicting Water and Sediment Routing and Yield from Storms on Small
     Watersheds, prepared for USDA Forest Service, Rocky Mountain Forest and
     Range Experiment Station.

Simons, D.B., R.M. Li, and T.J. Ward, 1977a, Estimation of Parameters for
     Describing Channel Geometry for Watershed Modeling, prepared for the USDA
     Forest Service, Rocky Mountain Forest and Range Experiment Station,
     Flagstaff, Arizona.

United States Bureau of Reclamation, 1960, "Investigation of Meyer-Peter,
     Muller Bedload Formulas," Sedimentation Section, Hydrology Branch,
     Division of Project Investigations, U.S. Department of Interior,
     Washington, D.C.

Woolhiser, D.A., 1975, "Simulation of Unsteady Overland Flow," in Unsteady
     Flow in Open Channels, ed. by K. Mahmood and V. Yevjevich, Water
     Resources Publications, Fort Collins, Colorado.

-------
                                       6.1

VI.  PHYSICAL PROCESS SIMULATION:  II.  INTERSTORM AND PESTICIDE MODELS
6.1  General
     This chapter discusses two physical-process simulations, an interstorm
model for simulating soil moisture changes, and a pesticide loading model  for
predicting pesticide yields and residues from managed fields.  The interstorm
model may be used in conjunction with the water and sediment model, as well as
water quality components such as the pesticide model, in two ways.  First,  the
simulation of soil moisture levels is important for determination of  initial
moisture condition for runoff and pesticide yield.  Secondly, knowledge of  the
variation in soil moisture with time is required for modeling of nutrient
changes.  The case study to be discussed in the next two chapters largely
deals with the final use of the interstorm model, and therefore the following
discussion will emphasize the use of the interstorm model for estimation of
moisture condition between storms.
     The pesticide model chosen for the purposes of this course was developed
by the Science and Education Administration - Agricultural Research (Leonard
and Wanchope, 1980), and presented in Knisel (1980).  This loading model was
chosen as appropriate for the data available and represents a mechanistically
based approach to computation of pesticide yields and residues.  It is coupled
to the water and sediment routing model which provides required runoff and
sediment yield calculations.

6.2  Interstorm Process
     Teare (1977) observed that two significant advances in describing plant-
water relationships occurred in this century.  One advance was the realization
that the movement of water from cell to cell within a plant is not wholly
controlled by osmotic pressure gradients, but rather by gradients in  total
water potential.  The second advance was the recognition of the analogy bet-
ween electrical circuits and the flow of water in the soil-plant-atmosphere
system.  The analogy is a natural outgrowth of the form of the steady-state
equations for flux density of a quantity through a medium.  This relationship
has the form
          J. = -K	                                                (6.1)
           1       dS

where  J.  is the flux density of quantity  i,  K.  is the conductivity of  the

-------
                                       6.2

medium for  i,  and   3.   to the electrical  voltage drop.
This analogy has  been applied to  the daily  water balance processes by a  number
of authors, notably Cowan  (1965), Sutcliffe (1968),  Huff et al.  (1977),  and
Goldstein and Mankin  (1972).   The code for  the water balance  components  of
the simulation was in large part  taken from that developed  by Goldstein,
Mankin and Luxmoore (1974).   Their code directly implements the  basic theory
to follow.  Some  special assumptions and  computational  details of their  imple-
mentation will be discussed later.
     6.2.1  Evaporation
     As pointed out by Eagleson  (1970),  evaporation  is  a  combination of  dif-
fusive and convective processes.   In  the presence  of an absolutely still
atmosphere, vapor transport  away  from the  free  surface  would  be  entirely a
diffusion process.  Fick's first  law  of  diffusion  has the form of  Equation
6.1, where  3./9s  is the concentration gradient  of substance  i   in a  medium
and  K.  is the molecular diffusivity of substance  i  into the  medium.   In a
diffusion process,  K.   is a property of the  substance  and the medium, and a
function of their physical state.   However, under  other than  laboratory  con-
ditions, evaporation seldom  occurs  by pure diffusion.
     Heating of the earth's  surface and  the interaction of wind  motion with
surface roughness combine to introduce vertical air  motion.   The presence of
turbulence in the layer  of air above  that  immediately adjacent to  the earth or

-------
                                       6.3

the evaporating surface means that water vapor is convected away from the sur-
face.  Convection in general transports materials orders of magnitude more
quickly than diffusion alone.  Therefore, convection is the dominant process
when the atmosphere may not be assumed at rest.  Convective processes may also
be modeled using equations having the form of Equation 6.1.  The flux density
of material  i  is still represented by  J. ,   and  9./3s  still represents
the concentration gradient of  i.  However,  in this case the constant of pro-
portionality  K.  may be shown to depend on the flow of the transporting
medium as well as of the medium.  Prandtl's mixing length theory may be viewed
as an example in which  K.   is a function of turbulent structure.
     For convective processes, the constant  K  is usually called an eddy dif-
fusivity, and in general its value, not being purely properties of the medium,
is not known.  However, examination of the flow may be used to calculate values
of the eddy diffusivity.  Another quantity transferred by convection is momen-
tum.  The flux of momentum is generally known as the Reynolds stress, and is
given by

          T - 'Km £                                                 (6'4)
where  T  is the Reynolds stress,  p  is the density of air,  u  is the hori-
zontal wind speed,  z  is distance measured vertically and  K   is the kinema-
                                                             m
tic eddy diffusivity.  Using the Reynolds stress as an example, and assuming
adiabatic (neutral or nonbuoyant) conditions,

          r-~
          dZ   
          u  - u  = — (In —)                                       (6.7)
           
-------
                                     6.4
and by combination with Equation 6.6,

          uf = K  — - -                                           (6.9)
           *    m z2 - z 1

By solving Equation 6.7 for  u^,   and  substituting the result into Equation
6.9, the following expression for  K   may be obtained:

              <2 (u  - u ) (z  - z )
          K = - - - !— — -f - -                                (6.10)
                           2
                      (in-)

Therefore, the kinematic eddy diffusivity for momentum may be directly related
to measurable properties of the flowing air.
     The relevance of Equation 6.10 to the evaporation process may be seen  by
assuming that water vapor is transported in proportion to momentum, and the
eddy diffusivity of water vapor  K  may be equated to the kinematic eddy dif-
fusivity  K .  Therefore,  evaporation  'flux density  E  given by
where  q  is the specific humidity of  the  air, may be written
                p< (u  - u )  (z  - z )
          E- —    .; ,  2    'if
                     (In — )
                         Z1
In integrated form,  Equation  6.12 is written
      p
E =
                p<  (u2 - u
                  (In — )
                      Z1
Equations of the form given by Equation 6.13 have been used to estimate poten-
tial evapotranspiration.  Equations  of this type represent the profile method
of estimating vapor flow.   The utility of Equation 6.13, however, is limited
by the necessity to measure  q ,   the specific humidity at the leaf surface.
This difficulty may be avoided by use of the energy balance and an expression

-------
                                     6.5

for the heat (and mass) transfer from leaf surfaces-
     Since energy must be conserved, the energy equation provides  a mathemati-
cal means to calculate energy available for evaporation.   Ignoring such small
terms as energy storage in the canopy, the energy equation may be  written on
a daily basis as
          R+AE+G+A=0                                         (6.14)
           n
where  R   is the net daily radiation input to the evapotranspiration surface,
        n
X   is the latent heat of vaporization of water,  G   is the  energy used in
heating the soil, and  A  is the sensible heat or heat convected from the sur-
face of the atmosphere.  Equation 6.14 is written for daily  flux density to  a
surface that is assumed a uniform, homogeneous site of evaporation.   For
cropped surfaces, the surface represents an integration of the leaf area. In
a forest, the surface must represent leaf area as well as  ground area subject
to evaporation.
     The net radiation  R   may be calculated  from
                         n
          R  = R (1 - A ) + R,
           n    s      v     L,
(6.15)
where  R   is the incoming shortwave energy,  A   is the albedo  of  the  vegeta-
tion, and  R   is the net longwave or re-radiated energy input to the  surface.
            Li
Net radiation  R   may be calculated by measuring  R   and  calcualting   R
                n                                   S                     L
from temperature measurements, or it may be measured directly by using  a net
radiometer (Reifsnyder and Lull, 1965).  The energy transferred  daily to the
soil may be estimated by functions such as given by Van Wijk and DeVries
(1963),
          G = G  + G  sin (2"n))                                  (6.16)
where  G   is the mean daily heat flux to the soil,  G    is  the  maximum  daily
variation of  G  from the mean,  D  is the Julian day number and  q   is  a
phase shift to compensate for the cycle not being at value   G   on the first
                                                              m
day of the year.
     The sensible heat transfer is a convective process and  may  be expressed
by:
                      T  - T
                       2    1
          A = -pc  K  -                                         (6.17)
                 P  h z  - Z

-------
                                      6.6
where  c   is the  specific  heat  of  air  at  constant pressure ,   K   is  the  eddy
diffusivity of heat,  T   is  the temperature of air at distance   (z -z  )   from
                       ^                                           fi   I
the surface,  T    is  the  temperature  of the surface, and   z    is  the  height  of
the surface relative  to some  datum.   Again by  assuming that  the heat  trans-
ferred to the atmosphere  is in proportion  to the momentum  transfer,   K   may
be taken as equal  to  the  kinematic  eddy diffusivity, allowing  sensible  heat
transfer to be estimated  as a function  of  atmospheric conditions.  However,  as
in the case of the specific humidity  of the surface, the temperature  of the
surface is usually not known.  Transport equations such as Equations  6.4,  6.11
and 6.17 may be placed in a more useful form by assuming further  that the flow
is steady.  Under  this condition K ,   K  and K   may be assumed constant,
                                    m     v        n
and using the flow of sensible heat as  an  example, Equation  6.17  may  be writ-
ten as:
              pc   (T  - T )
          A -   P   \ - 2-                                          (6.18)
                   > a
where  r "  is known as  the  diffusion  resistance to heat transport  and  is
        a
equal to  (z -z  )/K.  The form of Equation 6.18 may also be used for Equation
6.13, resulting  in

                 ql " q2
          E = p  — - -                                               (6.19)
                   a
or
              P   ~ P
               V1 _ V2
          E = -                                               (6.20)
                  a
where  p   is vapor density.  Equations 6.18 and 6.20  still contain surface
temperature and  humidity, which are difficult to measure.  However,  a com-
bination of Equations 6.20 and 6.14 is often used to predict potential  eva-
potranspiration,  PE,  which is the maximum amount of  water that can be
evaporated and transpired for the given set of micrometeorological  conditions
and energy available.  The necessity of measuring the  state of vapor at the
surface is avoided by assuming there are no horizontal gradients and that the
energy entering  a control volume at height  z   is equal to that leaving at
height  z .  The energy  balance is therefore written for a control  volume in

-------
                                     6.7-

close proximity to the evapotranspiration surface, as observed by Van Bavel
(1966) and Tanner and Pelton (1960).  It is possible to eliminate the
necessity of measuring at two points above the surface by using the aerodyna-
mic arguments introduced in the derivation of  K  .  This result is very advan-
tageous since it allows calculation of evaporation by using only standard
meteorologic measurements.

     6.2.2  Evapotranspiration (ET)
     From the standpoint of simulating soil moisture losses through eva-
potranspiration, two problems still remain:  (1) evapotranspiration seldom
proceeds at the potential rate, and (2) the formulations present3d are not
sensitive to plant type.  In ET calculations the actual evapotranspiration
E   rate is usually related to the potential rate by a multiplicative crop-
soil factor.  That is,
          Efc = CetPE                                                 (6.21)

The difficulty with this approach is the estimate of  C    and predicting its
                                                       st
sensitivity to management activities.  Further,  C    depends on the moisture
status of the plants and soils.  In order to address this problem, several
authors (Tanner and Pelton, 1960, and Slatyer, 1967) have proposed linking the
energy and aerodynamic methods with a mechanistic leaf model.
     A detailed discussion of the structure of plant leaves is beyond the
scope of this discussion; however, a brief description of a mesophyte leaf is
useful for hydraulic analysis.  As pointed out by Slatyer (1967), the leaf of
most mesophytes (plants having intermediate water requirements) is usually
between 100 and 200 y in thickness, and consists of between 10 and 15 cell
layers.  The upper and lower surfaces of the leaf are formed by the cuticle
layer of waxy substance known as cutin that is essentially impervious to vapor
transport.  Immediately below the cuticle is a layer of epidermal cells whose
outer walls are also impregnated with cutin.  The cuticle and epidermis
completely sheath the leaf except for many small openings called stomata.
     The stomata are pores in the sheath that permit air to ventilate the leaf
interior.  A stoma is formed by a pair of guard cells, and the size of the
individual stoma depends on the turgor of the guard cells.  During periods
when there is insufficient water for plant needs, guard cells lose turgor and
the stomata may completely close.  When water is plentiful, the guard cells

-------
                                     6.8

are fully hydrated and the  stomata are open.  Therefore,  the  stomata  functions
as a type of valve sensitive  to plant moisture  stress.
     The actual site of  evaporation  in a  leaf is  the mesophyll  tissue inside
the epidermis.  The liquid  flow of water  is conducted along the cell  walls and
through the cell cytoplasm.   Mesophyll tissue consists of a sponge-like  struc-
ture of cells and interconnects air  passageways.  Evaporation occurs  on  the
interface between the cells and air.  Since the mesophyll also  contains  most
of the plant chlorophyll, it  is also the  site of  most plant photosynthesis.
Therefore, the regulation of  water vapor, oxygen, and carbon  dioxide  by  the
stomata is vital to plant life functions.
     The flow of water from the plant occurs largely in the vapor phase.
However, the water enters the leaf in liquid form via the petiole or  through
leaf sheaths.  Liquid water is distributed throughout the leaf  to the
mesophyll by a system of veins and vascular strands, branding into progressi-
vely smaller dimensions.  The capillary tensions  developed in the leaf may
reach values lower than  -100  bars, which  combined with the cohesive nature of
water, explains the ability of very  tall  trees  to lift water  to great heights.
     From this very brief description of  leaf morphology, it  may be seen that
the stomata exert considerable control over the evapotranspiration process.
Therefore, models such as Equation 6.20 are' inadequate, since they do not
incorporate the plant's  ability to regulate transpiration.  Researchers
including Slatyer (1967), Cowan (1965), and Cowan and Milthorpe (1968) have
presented equations having  the 'form
                  ~ P
                 -
where site 1 is within the  leaf and  r   is the resistance of  the  leaf  to
                                      Xt
vapor flux back through the cuticle and through the  stomata.   Since  the stoma-
tal aperture is a function  of plant water  status , the evapotranspiration rate
as given by Equation 6.22a  is a function of atmospheric as well  as plant water
status.
     The vapor concentration adjacent to the evaporation  surface within the
leaf,  pv ,  is usually somewhat  less than the saturated  vapor pressure at
ambient conditions; however, the  relative  humidity within the  spongy mesophyll
is seldom less than 0.80  and is likely to  be greater than 0.95 in  non-

-------
                                     6.9




transpiring plants (Slatyer, 1967).  Therefore, the assumption that  pv   is


equal to the vapor density at saturation  ps   is justified.  Equation 6.22a


may be restated as



              P   ~ P

               S1    V2
          E = 	—	                                               (6.22b)

               ra   ra



     The diffusive resistance to vapor transport  r   may be approximated
                                                   a

using heat transfer analysis as follows.  If Equation 6.17 is written in the


form



          A = k,  (T. - T0)                                            (6.23)
               hi    2



k   is defined as a local heat transfer coefficient, and may by equating terms


with Equation 6.17 be expressed as
                                                                      (6.24)
As presented in Holman (1972), the nondimensional Nusselt number may be used


to describe convective heat transfer.  The Nusselt number for flow  in  the   x


direction  N,,   is described as follows:
            ux


                k, x


          Nu  =—                                                   (6'25)
            X



where  k  is the thermal conductivity of the convecting fluid,  in this case


air.  For a flat plate heated over its entire length, the Nusselt number may


be represented as




          N   = 0.332 P1/3 R1/2                                       (6.26)
           u           re
            x                x



where  P   is the Prandtl number,  P  = v/D,  v  being kinematic viscosity  and


D  being thermal diffusivity; and  Rg   is the Reynolds number  in the  x


direction.  Combining Equations 6.23 and 6.24 gives an expression for  It




          k.  = - (0.332 PV3 R1/2)                                    (6.27)
           h   x         re
                               x



Or, for a plate of down-wind length  b,

-------
                                     6.10

                         -5 i/2
          It = 4.57  x  10   -T7T-                                     (6.28)
            n                , 1/2
                            b
where  u  is the wind  speed and the  constant  reflects units of
cal/cm   sec    °C   .   The average value of   )t ,   It,  is twice the local
value, or

                         -5 u172
          k, = 9.15  x  10   —7-7T                                      (6.29)
            n
Slatyer  (1967) noted  that  a cylindrical  body perpendicular  to the flow has an
average  heat transfer coefficient of
                              1/3
          k, = 1.03 x 10~   — — r— •                                   (6.30)
           ^                (2r)2/3
where  r is the radius  of the  cylindrical  body in centimeters.
     From Equations 6.18 and 6.23 it may be seen that
               pc
                a
               pc
or
          r» =                                                        (6.32)

     Further, the resistance  to heat  transfer  may be  related to water vapor
transfer by noting that

          r^ = |                                                      (6.33)

where  d  is the thickness  of  the boundary layer  next to  the surface.
Similarly, the resistance to  water  vapor  transfer may be  expressed as

          ra * 5"                                                     (6'34)
                w
where  D   is the diffusivity of water vapor in air.   Therefore,

          ra - §- ra                                                  (6'35)
                w

-------
                                    6.11
and finally, using Equation 6.29 with  r   for the constant
                      ()                                             (6.36)
                       U
The values of  D,  D ,   p  and  c   are constant at normal temperatures/  so
that Equation 6.36 may be written
                   b
          ra = r, (-)                                                 (6.37)

     Cowan and Milthorpe (1968) presented an additional function for  randomly
oriented leaves having the form of Equation 6.37.
                    0.25
          r  = 2.6                                                    (6.38)
           a        u . D
                   u
where  A  is the individual leaf area and the units are in cgs system.
Goldstein, Mankin and Luxmoore (1974) used
          ra = 3.3 — '                                               (6.39)
                   u
where  Si  is a representative leaf length.  This expression is currently used
in the simulation.
     Using expressions developed above, vapor flux to the atmosphere  may be
directly related to commonly measured meteorologic data and plant moisture
status (noting that Equation 6.22 includes the leaf resistance to vapor flux
which is itself a function of leaf hydraulic potential) .  Combining Equations
6.22, 6.18 and 6.14 and assuming that  r "  is essentially equal to   r  ,  the
                                        a                             a
following expression for ET flux to the atmosphere may be derived by  elimi-
nating  p *  and  T ,
               (R  - G )r A
              r  n    s  a  ,  ,  *     , i
              { - ^ - + (P2 - P2)}
          E- -    -                              (6.40)
where

-------
                                    6.12

              T  - T
               1    2
          A = —	                                                 (6.41)
              P1 - P2
Assuming the air and water  vapor mixture behaves like an ideal gas,
              T1 - T2 _ dp*    T  de*
          A = ^~^ = d^-F?dF-                                 (6'42)

where  R   is the gas constant  for water vapor and  e*  is the saturation
vapor pressure.  Several expressions for saturation vapor pressure and the
slope of the saturation vapor pressure curve exist as functions of ambient
temperataure  T ,  the Goff-Gratch equation being among the most accurate
(Smithsonian Institute, 1966).  Equation 6.42 is similar in form to that pre-
sented by Monteith (1965) for latent heat transfer.
     The resistance of leaves to vapor release is a combination of stomatal
resistance, cuticle resistance, cellular transport, and resistance within the
leaf itself (Cowan and Milthorpe, 1968).  Leaf resistance has been success-
fully related to xylem hydraulic potential, water vapor deficit, incident
radiation, leaf temperature, and intercellular  CO   concentration (Ehleringer
and Miller, 1976; Running,  Waring and Rydell, 1975; Running, 1976; Slatyer,
1967; and Jarvis, 1976).  The subject has inspired considerable research in
the last two decades since  it appears that stomata regulation exerts  the
greatest control over plant transpiration of all plant processes (Thompson and
Hinckley, 1977; Slatyer, 1967).  Of all the factors that affect stomatal
resistance, leaf water potential is the most attractive for simulation, since
if it dominates stomatal aperture, the coupling of the atmospheric con-
siderations discussed above to  a hydraulic plant and soil model would be
complete.  Unfortunately, stomatal resistance is apparently a complex function
of all of the above factors (Jarvis, 1976).  However, many researchers have
successfully shown that stomatal resistance can be related to leaf water
potential, although with considerable scatter.  Goldstein and Mankin  (1972)
used a function of the form

                                     p(W
          rn = r.  +(r    -r.)e         ,   I Y , I  <   I ^  I      (6.43)
           Si    mm     max    mm                '  !L '      '  c '
where  r .   is the minimum leaf resistance assumed to represent resistance
        mm
when stomata are fully open,  r    is the maximum value of resistance when
                        c       max

-------
                                    6.13

stomata are closed,  4*   is the critical leaf water potential at which the
stomata are closed, and  p  is an empirical factor.
     An equation of this form incorporates most of the essential features of
stomatal response to moisture stress, if not the exact mechanism.  At high
moisture stress ( | ¥  | > | ¥  | ),  the guard cells lose turgor and close.
                    jir      C
Under this condition the flux of water vapor continues, but at a greatly
reduced rate, since it must pass through the leaf cuticle.  Cuticle resistance
r      and critical leaf water potential  ¥   are available in the literature
 max                           c           c
for a number of species.  Under conditions of full hydration the guard cells
fully open the stomata and the flux of vapor is predominantly along that path.
The resistance  r .   represents this flow condition.
                 mm    ^
     A similar equation has been presented by Reed and Waring (1975), for sto-
matal resistance as a function of leaf infiltration pressure.  Running,
Waring, and Rydell (1975) show a figure relating pre-dawn plant moisture
stress to leaf conductance for conifers that would fit an equation like
Equation 6.43.  However, the best models of leaf resistance as a function of a
single variable are based on CO  concentration or vapor pressure deficit  (Tan,
Black and Nuyamak, 1977; Slatyer, 1967).  Also according to Slatyer (1967),
transpiration estimates based on water potential alone in general give good
first approximation results.  Further, intercellular CO  concentration and
vapor pressure deficit require a more basic physiological model including
plant photosynthesis processes.  Therefore, Equation 6.43 is judged to give a
reasonable or first-order approximation for stomatal control of transpiration.
     6.2.3  Electrical Analogue
     The remaining details of the soil-plant interaction were developed  by
Goldstein, Mankin, and Luxmoore (1974), and for clarity they are presented  in
this section.  The basic concept of the soil and plant flow model  is  that this
part of the system may be modeled by an electrical circuit analogue.  While
the details of this part of the simulation were developed by Goldstein and
Mankin (1972), the analogue concept has been presented by many  authors,
including Cowan (1965), Cowan and Milthorpe (1968), Sutcliffe  (1968)  and
Slatyer (1967).
     The central assumption is that there is not storage in the plant in par-
ticular at the interface between the atmosphere and the plant tissues con-
taining liquid water.  Under this assumption the leaf water potential appears

-------
                                     6.14

as the  independent  variable in both the  atmospheric analysis presented above
and the electrical  soil-plant analogue described below.   If there is no
storage at the  liquid-vapor interface, the  mass flow of  vapor by ET flux from
the interface must  be  equal to the  delivery mass flow rate to the interface.
A method therefore  is  established by which  the leaf potential may be calcu-
lated as a function of measurable atmospheric  conditions and known soil
moisture status.  The  expressions are written  for the flux of water to the ET
surface in terms of the potential of the soil  layers and the unknown potential
of the ET surface.   As discussed  above,  the flux away from the ET to the
atmosphere is calculated using combined  aerodynamic and  energy balance
approach.  The  flux away from the surface is also a function of the liquid-
vapor interface potential  '•¥   through the  expression for resistance to vapor
                             J6
flux from the ET interface.   If the mass flux  to the interface is called
H(4! ),  and the flux to the surface is assumed to be equal to the flux away
   X-
from the surface, then
          E(«P4) = H(f£)                                               (6.44)

H(7 )  represents a function of   '•?    derived by circuit  analysis of the repre-
   **                              JC
sentative soil-plant  electrical  analog.   An  example  of  the function  H(¥_)   is
derived below for the current model  implementation.   From the functional form
of  H(f )  and  E( ¥  ) ,   from Equations 6.40  and 6.43 it will be clear that
       J6           Jt
Equation 6.44 is a nonlinear expression  for   Y  .   In addition,  it is func-
                                              JC
tionally desirable to separate the expressions  for vapor flux away from the ET
interface and water flow to  the  interface so that  their forms may be altered
to fit the application.   Therefore,  Equation 6.44  is solved numerically by  a
linear fractional iteration  scheme.  This scheme seeks  to find a zero of the
function  F('¥ )  where
                               )                                       (6.45)

     The model provides  for  up to  five  soil  layers.   The  current model for-
mulation assumes that  there  are  five  layers  but  the  four  lowest layers are
assumed to have the same properties due  to a lack  of data.   As stated earlier,
the form of  H( H* )  is dependent on the  electrical analog used to represent
the soil-plant system.   The  current form is  based  on the  representation shown
in Figure 6.1.  The resistance definitions for Figure 6.1  appear in Table 6.1.
Here the plant roots are assumed to be  distributed only in the top two soil

-------
                               6.15
         ET Surface
                                      RA + RX
                          RLIT
         Soil Surface
                         :RSI
Infiltration to Layer I
                RSBLI
                                 RSR
Infiltration to Layer 2
                RSBL2
                                 RSR2
Infiltration to Layer 3
                RSBL3
Infiltration to Layer4-
                RSBL4
Infiltration to Layer 5
                     To Drainage
                                                        =Y
                                                 RP
                                                'RRI/2
                                                              Layer I
                                                 RR2 + RRI/2
                                              I
                                                             Layer 2
                                                             Layer 3
                                                             Layer 4
                                                             Layer  5
    Figure 6.1.  Electrical analogue for water balance calculations.

-------
                                     6.16
              Table 6.1.   Resistance  Definitions for Figure 6.1
Resistance
Resistance
in Figure 2
  Verbal
Description
 Defining Expression
or Resistance Value in
Current Implementation
                  RLIT
                resistance of
                litter layer
                            200,000
                  RS1
                resistance to soil
                layer 1
                                                                  2 K..
    's2
                  RS2
                resistance to soil
                layer 2
                                                                  2 K,,
                  RR1
                resistance of roots
                in layer 1
                                                                 2 A ,K .
                                                                    r1  r1
   'r2
                  RR2
                resistance of roots
                in layer 2
                                                                 2 A ,,K „
                                                                    r2 r2
    'srl
    'sr2
                  RSR1
                  RSR2
                  RP
                resistance to soil
                water uptake by
                roots in layer 1

                resistance to soil
                water uptake by
                roots in layer 2

                above ground plant
                resistance
                             Vr1
                             f1AIK1
                             d2Ar2

                             f2AIK2
                              5,000

-------
                                    6.17

layers of a five-layer soil column.  The schematic of  Figure  6.1  may be
redrawn as shown in Figure 6.2a with resistance values as  defined below and in
Table 6.1.  In Table 6.1  d.  is the thickness of soil layer   i,   K.  is
hydraulic conductivity of soil layer  i,  f.  is the fraction of  roots in soil
layer  i,  Ar.  is the cross-sectional area of roots in layer  i.   The conduc-
tivity of roots in layer  i  is assumed to be linearly related to the soil
conductivity by
          Kr  = C1 K±                                                 (6.46)
            i
where  C.  is an empirically derived constant having the value of 101* in the
current implementation.  The resistance to water flow  between soil layers is
represented by  RSBL.  in Figure 6.1.  To simplify the resistance expressions
the above resistances are regrouped as illustrated in  Figure  6.2a.  Resistance
equivalences between Figure 6.1 and Figure 6.2a are as follows:
          R1 = RSBL1
          R2 = RSR2 + (RR2 + RR1/2) g(A )
          R3 = RS1                                                    (6.47)
          R4 = RP + RR1/2
          R5 = (RSR1) g(AJ)
     The numerical value of 200,000 for  r   was obtained  by  calibration by
                                          X»
Goldstein, Mankin and Luxmoore (1974).  The value of 5000  appearing in this
expression for the above-ground-plant resistance  r    was  obtained from Cowan
                                                   P
(1965).  Both values represent possible calibration parameters for ET flux.
     A  A-Y  transformation is performed on the lower   A  of  Figure 6.2a to
produce the equivalent circuit of Figure 6.2b.  The  A-Y  transform gives an
equivalent circuit element with resistances given by
          RT1 =
          RT2 =
                R1 + R5 + R2
                                                                      (6.48)
                   R1 R2
                R1 + R5 + R2
and
or
                              R5 R2
          RT4 = RT3 - RR = 	                               (6.49)
                           R1 + R5 + R2                               io.**j
          RT3 = R1   R5 + R2 + **                                     (6'50>

-------
                                     6.18
R3 + RLIT
                RA + RX
RR
                                   A-Y
                                        RA + RX
RR
                                                                RT3-RR=RT4
                 Figure  6.2.  Circuit diagram of Figure A-l and
                             first A-Y transformation.

-------
                                    6.19
     Noting that the loop of the circuit  of  Figure  6.2b  may be redrawn as

Figure 6.3a, another  A-Y  transformation may be  applied again to give the

final equivalent circuit shown in Figure  6.3b.  Equivalent  resistances are

given by

                          pm-1
    m
RRC -
                RT1 + RT3 + R3 + RLIT

                - (R3 + RLIT) RT3 -
                RT1 + RT3 + R3 + RLIT

                   (R3 + RLIT) RT1
                RT1 + RT3 + R3 + RLIT
     Knowing potentials  V   and  V   from  the previous  calculation,  the flux

to the ET surface,  H(f )  may be expressed in terms  of  ET  surface potential

Y  by Kirchoff's current law applied at node A (Figure 6.3).   Allowing  ¥   to
                                                                          A
represent the potential at node A, and using the  convention the flux  away from

the node is negative ,
          H(V =-- + --                                   <6-54)
However, from Ohm's Law,

                  f  - ¥
          H(>iV =  ^RRB A                                             (6.55)

Therefore,

                  (RRA + RRC)¥  - RRA V  -  RRC V
          H(4/Jl) =    RRC RRA + (RRA + RRC)  RRB                        (6.56)

or
            v -
where  D = RRA + RRC.  This is the form of  H(f  )   found  in  subroutines EVAL
                                               X-
and SUBEV.  This derivation is presented to indicate  how  the form of  HC? )
                                                                          X
depends on the circuit representation and may be used as  a guide if a dif-

ferent representation such as three or more soil layers of differing proper-

ties is desired.

-------
                                 6.20
                RX+RA
RX+RA
  R3+RLIT
*,
     RTI
r >
^
<
<
4
X
<
<
4
<
<
4
<
<
4
<
<
4

• Y
H(Y)f«
>RT3 A~Y RT2 j
» J' i
^RSBL2 <
i \lf i
> RSBL3 <
4
1 \lf |
' <
1 }]/ j

• Y
RRB
A
RRA
RT2
i ii/
»
>RSBL2
• \i/
> RSBL3
i \1^
^RSBL4
1*.
                   Figure 6.3.  Second A-Y transformation.

-------
                                    6.21
     6.2.4  Heat Transfer by Convection
     The rate of transfer of heat energy by convection  A  from the evapo-
transpiration surface is given by
          A = [oC p(T. - T )1/r                                       (6.58)
                 P    I    ^    CL
where  C   is the specific heat of air at constant pressure,  p  is the den-
sity of air,  T   is the temperature of the evapotranspiration (ET) surface,
T   is the ambient air temperature, and  r   is the resistance to the transfer
of sensible heat from the evapotranspiration surface to the atmosphere.  All
of these parameters have been defined above with the exception of  a,  the
ratio of convection area to evapotranspiration area.  For this implementation,
a  is given by
                   A
          a=1+ T-±—                                               (6.59)
                   Imax
where  A  'is the current leaf area index and  A,     is the maximum value of
        I                                       Imax
V
     Convection occurs throughout the canopy.  Since the evapotranspiration
surface is a combination of soil surface, litter surface and leaf area, the
evapotranspiration surface does not reflect the vertical structure of the
canopy.  Therefore,  o  is given this simple form to allow for greater convec-
tion than would be possible from a simple plane and relates convection area to
canopy growth.

     6.2.5  Implementation Specific to Vegetation Type
     The parameters of Equation 6.43 are evaluated internally.  Stomatal
resistance at full hydration is given by
               = 6_l_^_M5._	IT-^-|                         (6.60)
                                   'off  on
where  T  is the Julian day number,  T    is the Julian day the  canopy has
emerged 50 percent, and the  T f   is the Julian day the canopy  has  fallen
below 50 percent emergence.
     It should be noted that the expression for  r_,  the resistance to vapor
                                                  X
flux from the evapotranspiration surface, is related to canopy growth through
the expression for  r .  .  This functional relationship can account  for obser-

-------
                                     6.22

vations that the number of  open  stomata varies during the  year and  that mini-
mum stomatal resistance per unit area varies with  leaf area.  Therefore,  if
changes to this function  are made, these variations may need  to  be  considered.
     Swift et al.  (1975)  modified the energy flux  equation originally  imple-
mented by Goldstein, Mankin and  Luxmoore (1974) to account for leaf area  being
much greater than  ground  surface area.  However, the leaf  area index is not
directly used since not all of the canopy is equally effective in evapo-
transpiration at any given  time.  An effective leaf area function   f(A )   is
implemented to compensate for this effect.  This variable  has the form

                                                                      (6.61)
     In addition,  f(L  )   is  used  in  the energy balance calculation  of  evapo-
transpiration flux given  by
          RN =  [f (L  ) +1] XE +  [af(Lx) +1] A + G                    (6.62)

where  R   is the net incoming solar  radiation,  X   is the  latent  heat  of
vaporization of water,  A is the  convective heat flow,  E  is the vapor flux,
and  G  is the daily change in soil heat storage.  The functional  form  of
f(L )  was selected  for experimental  data obtained at the Coweeta  Hydrological
Laboratory and is discussed in Swift  et al. (1975).  If such data  are avail-
able in the area to  be modeled,  the formulation could be changed.
     The electrical  analog representation discussed  below assumes  that  plant
transpiration characteristics may  be  lumped into a single resistance to water
flux for each watershed plane.   Therefore, active roots, stems and leaves  are
assumed to be homogeneously distributed across the plane.   This  assumption is
probably most valid  under the condition of a closed  canopy.  However, for
management activities such as crop growth in agricultural watersheds, timber
replacement and regrowth,  or  under natural conditions of low canopy  cover,  a
closed canopy cannot be assumed.   Since number of transpiration  paths per  unit
ground area is reduced for low values of leaf area index, the resistance to
transpiration water  flux  should  increase during these periods.   Swift et al.
(1975) presented a function of the form

-------
                                    6.23
          g(LT) = — 5 - r-                                           (6.63)
where  A   and  k  are calibrated parameters, to accomplish the  increase  in
resistance.  The transpiration resistances are therefore divided by   g(L  ).

6. 3  Interception and Infiltration
     6.3.1  Interception
     The processes of interception and infiltration have been discussed in
Chapter 5; however, some modifications of these routines are incorporated into
the interstorm model.  When coupling the event water and sediment model with
the interstorm model, the interstorm routines perform more sophisticated
interception and infiltration calculations in order to generate  excess rain-
fall on any given day.  The interception process is modified to  incorporate
evaporation.  The infiltration model is reformulated to provide  for  layered
soils.
     A portion of rainfall is intercepted by canopy foliage, ground  cover,  and
forest litter.  Part of this water eventually reaches the ground by  stem  flow
or by dripping from vegetation; however, the water that is held  on these  sur-
faces never reaches the soil and is for the most part lost to evaporation.  In
many conditions of light rainfall or in dense forests this process cannot be
ignored.  For this purpose of this simulation the intercepting area  is taken
to be equal to the area of the evapotranspiration surface.  Maximum  and mini-
mum values of interception storage per unit canopy-covered area  are  assumed
to be provided data, and therefore potential interception storage is a volume
of water related to evapotranspiration surface size and the amount of water
already existing in interception storage.
     On a day when rainfall occurs, an amount of water equal to  the  available
interception storage or the volume of rainfall, whichever is smaller, is
removed from the storm water available for infiltration.  Some or all of  this
water is evaporated during the day.  Any water left in interception  storage
decreases the amount of interception potential for the next day  to the dif-
ference between the maximum potential storage and the amount of  water left  in
storage.  In addition, since the storage of energy available for evaporation
in the forest environment is assumed negligible with respect to  the  daily

-------
                                    6.24

energy fluxes, the energy required to evaporate water from  interception
storage should be deducted  from the daily influx of solar radiation  before
evapotranspiration is calculated.  This approach works well for  determining
daily water balance; however, it must be augmented in order to modify the
rainfall hyetographs into throughfall needed for infiltration and  subsequent
surface water routing calcualtions, particularly when a  storm lasts  for more
than one day.
     In order to modify the  rainfall histogram, the following procedure is
adopted.  On the day the rainfall begins, a volume of water equal  to that
day1s potential interception volume is removed from the  beginning  of the rain-
fall hydrograph.  Of course, if this volume is greater than the  day's precipi-
tation volume, no throughfall will occur on this day, and the remaining
interception volume, after  evaporation, forms a part of  the potential inter-
ception volume for the next  day.  The rationale for removing the interception
volume from the beginning of the storm on the first day  of  the event is based
on the concept that at the  beginning of a storm the potential interception
volume represents a reservoir that must be filled before throughfall can reach
the ground.  Processes of stemflow and dripping are ignored for  the  purposes
of this simulation.  If there is insufficient rainfall volume to satisfy the
interception volume on the  first day of the storm, all of that day's rainfall
is intercepted.  The remaining unfilled interception volume is added to the
day's evaporation loss from  interception, and this volume becomes  the poten-
tial initial interception loss for the next day, and so  forth through the
storm.  The change in the beginning of the storm to reflect initial  intercep-
tion losses is illustrated  in Figure 6.4.
     If the storm lasts for  more than one day, significant  changes in poten-
tial interception volume may occur as a result of evaporation.   Evaporation
losses from the interception storage are assumed to be made up by  interception
on the following day.  Since evaporation losses are distributed  throughout the
day, these losses are not subtracted from the beginning  of  that  day's rain-
fall, but are assumed to be  made up uniformly during the next day.   The
distribution of interception storage losses and the subsequent modification of
rainfall after the initial  storage is satisfied as illustrated in  Figure 6.4.
     Equations 6.64 and 6.65 below are used to calcualte the initial and
distributed evaporation interception volumes per unit area,  respectively.

-------
                             6.25
    «

    c
    o
    OC
            •Initial Interception
                  Volum
                                  o
                                  cr
             Time Before
              (a)    Initial  Interception
                                            Time After
   r>
   c
   a
   '
   cr
       Initial Interception
        /    Volume
               Day I
                         Evaporation from

                         Interception on

                         Day
                             Day 2

                           Time  Before
                                                Evaporation from

                                                Interception on Day 2
Day 3
>»

°5


jjE


"5

c
"6
cr
                                    ft.
             Day I





             (b)    Multiple  Day  Storms
                              Day 2

                          Time  After
Day 3
Figure 6.4.  Transformation of hyetograph by interception process.

-------
                                    6.26
          VT =  [— - - V     C  + V      (1 - C  )] - V                  (6.64)
           I

          VT =  (-^) D                                                 (6.65)
           IDs
                 s
where  V   is the potential interception volume per unit watershed area,
V      is the potential  interception volume per unit area completely  covered
by canopy,  V_  .   is the potential interception volume per unit  area not
             Imin
covered by canopy,  L    is the canopy leaf area index,  L       is the maximum
                     X                                   Xmax
value of  L ,  C   is the fraction of watershed area covered by canopy, and
           X    C
Vj .   is the residual water stored in interception as a result of  insufficient
evaporation on the previous day.  The residual interception  Vj .  is  assumed
to be evenly distributed between canopy covered and uncovered ground.   Since
V   varies with canopy leaf area index, it is mathematically possible that
case  V   is assumed to  be zero.
     In Equation 6.65,   E   is the daily evaporation loss from  interception
storage and  D   is the  duration of the non-zero portion of a storm on a given
              S
day.  Equation 6.65 appears unsimplified to illustrate that the intensity
(E /D )  is subtracted from the hyetograph intensities to provide for a uni-
form distribution in time of the evaporation losses from interception.
Evaporation losses are assumed to be evenly distributed between leaf  area and
uncovered ground.
     A short comment on  the definition  of some of the above quantities is
relevant at this point.  Leaf area index is usually defined as  the ratio bet-
ween the total watershed leaf area and  the watershed ground area.  Leaf area
index as a function of time may be viewed to give the growth curve for the
plan tspecies.  Some authors, e.g. Rutter (1967), have used leaf  area index to
describe species-specific response.  The difficulty with the definition as it
usually appears is that  if strictly interpreted, it would also  be affected by
cover density.  For crops and dense forests, there usually is no  problem,
since crown closure may  be assumed.  However, where cover densities are signi-
ficantly less than one,  that is, where  there are clearings in the forest or
thinning has been performed, a more rigid definition is necessary.  For the
purposes of this model,  leaf area index as measured in a closed canopy will be
assumed to be the same as the ratio between the leaf area of an individual and

-------
                                    6.27

the ground covered by that individual.  This definition effectively makes the
leaf area index function-specific to the plant type and not to the particular
watershed.  This assumption is imperfect as well/ since it does not allow for
species response to different environments; however, it provides a more
workable definition.
     Secondly, that definition of canopy cover density for current purposes
needs some clarification.  The present simulation is made up of watershed
response subunits .consisting of planes and channels.  Precise detail of para-
meter distributions within the planes is not made.  That is, the cover density
is taken to be uniformly distributed across the plane.  For example, an 80
percent canopy cover is taken to mean that at any given point in the plane,
there is an 80 percent probability of being covered by canopy.  This applies '
to a representation of a real watershed having 80 percent of its surface con-
tinuously covered with closed canopy and 20 percent continuous clearing, as
well as a closed canopy that has been 20 percent thinned.  This definition
also extends to ground cover and allows expressions of set theory to be
applied to combinations of cover.

     6.3.2  Infiltration
     The infiltration scheme chosen is a time-explicit formulation for the
Green and Ampt infiltration equation as presented by Eggert, Li and Simons
(1979).  This method is an extension to layered soils with hydraulically homo-
geneous layers of a time-explicit formulation presented by Eggert (1976).  The
derivation of the layered scheme for layered soils parallels that for a homo-
geneous soil.  For clarity the derivation will be briefly discussed.  Modern
interpretation of the Green-Ampt (1911) formulation as provided by Mein and
Larson (1973), assumes that as rainfall infiltrates the soil, a wetting front
advances like a piston so that the rate of change of volume behind the wetting
front equals the infiltration rate at the surface.  The situation is
illustrated by Figure 6.5.  Here the location of the wetting front at time  t
is shown by the dashed line of depth  z  from the surface.  At the beginning
of the storm, the wetting front is assumed to be at the surface.  It moves
downward through the soil column as water infiltrates, filing the volume of
pore space not already occupied by water initially in the layers at the
beginning of throughfall.

-------
                        6.28
                           .Soil Surface
                         X Soil Layer I
    <>
                                         K-l
r
              Wetting "Front       f"

       	  K
Figure 6.5.   Definition sketch for infiltration process.

-------
                                    6.29

     To formulate the equation of infiltration, it is assumed  that  the wetting
front as mentioned before is already at depth  z  as shown in  Figure  6.5.   The
total hydraulic head at depth  z  is
               k-1
          hT =  E  Al^ + Ahk                               .           (6.66)
               i=1
where  h   is the total head at  z,  Ah.  is the head loss in  the   i     fully-
wetted layer , and  Ah   is the head loss Jin the  k   " layer  containing the
wetting front.  For flow above the wetting front, Darcy's law  for the i
layer may be written
                                                                      (6'67)
where  Q  is the total volume inflow of water per unit area,  A_   is  the
                                                               G
ground area,  q  is the Darcian velocity,  K.  is the hydraulic conductivity
in the wetted zone of the  i    layer,  Ah.  is the change  in head in the
i    layer, and  Az.  is the thickness of the  i    layer.  Solving Equation
6.67 for  Ah.  for each  i = i,k  and substituting the results into Equation
6.66 yields an expression for the total hydraulic head at   z  as  a function  of
the Darcian flux  q
                  k-1 Az
          \ = q ( Z  — + £- )                                        (6-68)
                  i=1  i     k
where  i  is the distance that the wetting front has penetrated the  k
layer.  However, the total hydraulic head may also be written as  the  sum of
the gravitational and capillary suction heads such that
                                                                   (6.69)

               gravitational       capillary
                  head              pressure
                                      head
where  V   is the capillary suction head across the wetting front  in the   k
layer.  Therefore,  Equation 6.69 may be substituted into Equation  6.68
yielding an expression for  q,  that is,

-------
                                    6.30
              k-1
               Z  Az
                k-i   .    ,
                 z  — - + —
                .  , K.    K,
                1=1  i     k
If  F  is allowed to be the total infiltrated water volume  above the wetting
front at  z,  it may be expressed as
              k-1
          F =  Z  . AS. Az. + <)>  AS I                               (6.71)
              ,  -   1   1   1    JC   K

where  .  is the porosity of the  i    layers and  AS.   is the difference
between the percent of pore space in the  i    layer filled with water  at
saturation and the percent of pore space filled with water  initially or the
initial degree of saturation deficit of the  i    layer.  The  product of poro-
sity and degree of saturation deficit is the potential change  of dimensionless
water content or for the  i    layer,  A0 .  = .A5..  Allowing  the summation
term of Equation 6.71 to be represented as   F   ,   the length   &  may be
                                             K.~ I
expressed as
              F -  F
          * =      k"1                                               (6'72)
Using Equations 6.71 and 6.72 and noting that  q = dF/dt   by  continuity,
Equation 6.70 may be written as
          i -Vi ae" * F ' he.'* A9k                          <«•">
                   W.  . A6.  +      k~1
                    k-1   k

where
                 k-1
          z,    =  E  Az.
and
                 k-1 Az.
          W    =  E
                 i-1 Ki

In order to simplify algebra it may be noticed that  for  flow  in the   k
layer

-------
                                    6.31
          A 9,  (z,  H  + V )  - F,  ,  = c,  = constant
            k   k-1     k     k-1 .    k
                 Wk-1 A9k *      - dk - constant
                                                                     (6.74)
Therefore, for flow in the  k    layer,  Equation 6.73 may be written as
          ,_   c,  + F
          I -   -T-                                          ,.    '«•»>
Suitable rearrangement of Equation 6.75 and integration within the  k    layer
yields the following nonlinear expression for  F:

          (dk-iC>  ln (1 + c7)  - (dk-r> ln (1  +^~)
                 k           k           k            k
                                                                     (6.76)
                 F - F
where  t  is the time after the beginning of the event when the total
infiltrated volume equals  F,   and  t     is the time when the total
                                     1C™ I
infiltrated volume was  F     (or when the wetting front was at z = z   ) .   In
                         K~ i                                          k~ I
order to obtain an approximate solution to Equation 6.76,  it is noted that
within the  k    layer the infiltrated volume at some time  t .+ At  may be
expressed as
          F(t + At)  = F(t) + AF                                      (6.77)
where  AF  is the change in  F  occurring between  t  and  t + At.  If
Equation 6.76 is written for  F(t + At)  and  F(t)  and subtraction is per-
formed, an expression for  AF  as a function of  F(t)  results:
                c
                 k             A F        A F
          (dk ' ^  ln [1 + ck + F(t)]  + ^ * At                     (6'78)

The logarithmic term may be expressed using a standard series expansion for
ln(a+x) ,

          ln(a+x) = In a + 2 b^r~x~ + 3 ( 2a + x}   + ' "]             (6.79)

If only the first two terms of Equation 6.79 are used, insignificant error

-------
                                     6.32

results  (Li, Simons and  Stevens,  1976).   Noting  that   a  =  1,   Equation 6.78
may be approximately rewritten and  simplified  to become

          AF2 +  UKd  + 2F(t) -  KAt] AF
              - 2K At  [c   +  F(t)] =  0                                 (6.80)
                  K.     K.
Equation 6.80 may be immediately  recognized as  a quadratic  equation  for • AFi
All other quantities in Equation  6.80 are  known at  time   t  +  At;   therefore
the change in infiltrated  volume  between time   t  and  t  +  At  may be  calcu-
lated from
          AF = —	1	L                                          (6.81)
where
          0 = 2K d  + 2F(t) - K At
          Y = -2K At[c  + F(t)]

and only the positive root  is physically meaningful.
     Equation 6.81 provides a time-explicit formulation for the  change  in
infiltrated volume occurring between  t  and  t + At.  The formulation  is
written for flow in the  k    layer.  However, this presents  no  computational
problems since initially  F = 0  and the flow is in the first layer.  As the
event proceeds in time, water enters the upper soil surface of the  soil and
the wetting front travels down through the soil.  One  need only  keep  track of
the location of the wetting front at any time and appropriately  update  the
values of  F(t),  wv_,,  zv_i'  ^9,,  ^v-'  Fv 1'  and  Kk  depending  on the
location of the wetting front.  The only apparent difficulty  is  the implicit
nature of the problem, since the depth of the wetting  front at any  time is
directly related to the infiltrated volume.  However,  the problem is  easily
solved due to the explicit  nature of Equation 6.81.  The change  in  infiltrated
volume  AF  given by Equation 6.81 represents a potential volume that will
infiltrate if there is sufficient supply of water at the surface.   If there is
insufficient throughfall during  At  to satisfy the potential volume, then the
infiltration is controlled by rainfall and
          AF = i At                                                   (6.82)

-------
                                    6.33

     6.3.3  Infiltration Parameters
     The Greeri-Ampt layered infiltration model described- above  is  essentially
a two-parameter model:  (1) K.  the hydraulic conductivity  in the  wetted zone
of the  i    layer and (2) 4*.  the average capillary suction head  of  the  i
layer.  A possible third parameter is the porosity of the   i     soil  layer
.,  but this parameter is bound to the initial saturation  deficit AS.   which
is discussed below, and is assumed not to change as a function  of  moisture
content.  The hydraulic conductivity of the soil layer is a function  of  the
layer moisture content.  However, the Green- Ampt formulation is based on the
saturated conductivity of the wetted zone  K .  This parameter  does not  appre-
                                            s
ciably vary with moisture content.  The average suction  head, however, is a
direct function of initial degree of saturation.  This parameter is evaluated
by taking the weighted mean of the capillary suction between the initial
degree of saturation and the final degree of saturation  using the  relative
conductivity as a weighting function.  The approach was  suggested  by  Mein and
Larson (1973).  The equation for average head takes the  form
          Y  = .  /    fdk                                             (6.83)
               *,(S.)
                k  i
where  k  is the relative hydraulic conductivity of the  k     layer;  that  is,
k (S) = K. ( s ) /K
 k       k     sk  where  Ks   is the saturated hydraulic conductivity  of
the  k    layer, and  K (S)  is hydraulic conductivity of the   k     layer  at
                       K
saturation  S;  S   is the final or wetted soil degree of saturation, usually
taken as 1.0,  and  S.  is the initial degree of saturation.  As examples,
graphs of  ¥  as a function of  S.  are shown in Figure 6.6.   For  degrees  of
saturation near 1.0,   7  is obviously a sensitive function of   S..   For this
reason the value of  ¥ .   is updated based on the value of  S.   on  the day
prior to the storm by reevaluating Equation 6.83.  Therefore,  the  initial
degree of saturation serves as an initial condition affecting  the  saturation
deficit AS.  and the average suction head.  All of the parameters  mentioned
above are determined by a soil routine of the daily water flux  model  or are
supplied as changing inputs from daily moisture content calculations.
     The soil routine for initially determining the soil moisture-soil  tension
and soil moisture relative conductivity terms is borrowed from  the Goldstein,
Mankin and Luxmoore (1974) model.  This routine uses theory presented by Green

-------
                                6.34
   20
   18
                         Muren Fine Clay
(A
0)

U
c
I 12
u
tn

| 10
'a.
o
0}
0>
o
^
0)
    Q
    8
             Columbia Sandy Loam
                   Plainfield Sand
          Poudre Fine Sand
                            Ida Silt Loam
                                                         Nickel Gravel-
                                                         Sand Loam
     0.2     0.3
                     0.4     0.5     0.6     0.7     0.8

                     Initial Degree  of Saturation, S|
0.9
1.0
        Figure 6.6.   Average  capillary  suction head as a function
                     of initial moisture content.

-------
                                    6.35
and Corey (1971).  The method allows calculation of full soil hydraulic pro-

perties from the porosity and a simple laboratory tensiometer-moisture content

experiment.

     The above discussion with reference to Appendix A completes a description

of the portion of the model necessary to simulate evapotranspiration, soil

water balance, interception, and infiltration.  In short, those routines
necessary to calculate time-dependent excess rainfall function on a con-

tinuous basis.  This model may be used to simulate on a daily basis any period

of time for which environmental data are provided.


6.4  Data Requirements for Interstorm Model
     Simulation of the interstorm processes requires a variety of data.

Measurements of soil, meteorological, geometric and vegetative parameters are
required for input and calibration.  Usually daily values are necessary for

meteorological variables used in obtaining meaningful estimates of soil
moisture variation.  The following list details the data requirements for

simulation of daily soil moisture.

Geometry and Channel Data
     Length of overland slopes
     Width of overland slopes
     Elevation of watershed

Soil Data
     Distribution of soils
     Types of soils
     Number of soil layers
     Thickness of layers
     Initial water content of layers or top layer
     Saturated hydraulic conductivity of each layer or top layer
     Tensiometer measurements (desorption curve) for each layer
     Temperature for tensiometer data
     Field moisture capacity for each layer
     Porosities of soil layers on top layer

Vegetation Data
     Types
     Distribution
     Density of ground cover
     Density of canopy cover
     Storage of ground cover
     Maximum and minimum storage of canopy cover
     Albedo of vegetation
     Yearly growth cycle of canopy
     Average leaf length of dominant species

-------
                                    6.36
     Maximum and minimum leaf area
     Root cross-sectional area per unit area of soil in each layer
     Fraction of roots in each layer
Climatic Data
     Daily solar radiation
     Average daily temperature
     Average daily humidity or vapor pressure
     Total daily precipitation
     Average wind speed
Climatic Data
     Air pressure—for year as function of altitude
     Specific heat of air
     Rainfall storm hyetographs
Hydrologic and Hydraulic Data
     Storm and daily runoff hydrographs
Man's influence may affect all of the physical qualities controlling water
runoff, sediment yield, and nutrient transport from watersheds.  The effects
can be quantified By assessing the impact of man's activities on the different
measurable variables.
6.5  Pesticide Loading
     The pesticide model chosen for this study is a simple mechanistically
based model developed by the Science and Education Administration -
Agricultural Research (Knisel, 1980).  It is directly coupled to the water and
sediment yield model through the use of water and sediment runoff volumes as
inputs.  The model also requires an estimate of the initial moisture deficit
in the soil, therefore, the interstorm model may be used to generate daily
changes in initial moisture content.  The following discussion is taken from
Leonard and Wanchope, 1980  (Knisel, 1980).
     The pesticide submodel was developed on simplified concepts of processes
and designed to be responsive to different management options.  Foliar- and
soil-applied pesticides are separately described so that different decay rates
can be used for each source of the same chemical if necessary.  Usually pesti-
cide residing on foliage dissipates more rapidly than that from soil.  Also
decay rates can be made site specific if information is available.  Movement
of pesticides from the soil surface as a result of infiltrating water is
estimated using differences of rainfall and runoff for the storm and pesticide
mobility parameters.  Pesticide in runoff is partitioned between the solution
or water phase and the sediment phase.  This aspect is particularly important

-------
                                    6.37

when examining management options that limit sediment yield.
     A simple conceptualization of the runoff system is  shown  in  Figure  6.7.
The primary source of pesticide available to enter the runoff  stream is
visualized as a surface layer of soil defined arbitrarily as having  a depth of
one centimeter.  This definition is based on observations by Leonard et  al.
(1979) that runoff concentrations of both dissolved and  adsorbed  pesticides
were strongly correlated with pesticide concentrations in this  layer.
Actually the thickness of this layer depends on many factors.   Pesticide
extraction by raindrop splash and interrill soil movement may  occur  in a very
shallow layer, whereas extraction from rills may extend  several centimeters
deep.  In models by Bruce et al. (1975) and Frere et al. (1975),  rill and
interrill extractions were described separately, but here the  process was con-
ceptually combined for simplicity.  Others have defined  this effective
thickness to be about 0.5 cm and 2.5 cm (Crawford and Davigan,  1974;  Steachius
and Walter, 1978).
     Washoff of pesticide applied to foliage is another  source  that  may  enter
the runoff stream.  In this model, the fraction of applied pesticide inter-
cepted by foliage is specified initially.  Dislodgeable  residue remaining on
the foliage at the time of rainfall is estimated from information given  in
Knisel (1980).  The fraction of this dislodgeable residue removed by rainfall
is then added to the soil surface 0 to 1 cm zone and a new concentration for
this zone is computed for the runoff event.
     Pesticide dissipates from the surface zone primarily by degradation and
volatilization processes.  During rainfall events, pesticide may  move  below
the surface zone in the infiltrating water and across the surface in runoff.
In the model, initial concentrations of unincorporated pesticides are  computed
as if they were uniformly incorporated into the 0 to 1 cm depth.   Concen-
trations of incorporated pesticides are computed based on their incorporation
depth and efficiency of incorporation.  A simplified schematic  of the  pesti-
cide submodel is shown in Figure 6.8.
     As stated previously, the source zone for extraction into  runoff  was
arbitrarily defined as the 0 to 1 cm depth increment of  the soil  surface.
Concentrations are computed in units of micrograms/gram  or parts  per million.
For pesticides applied directly to the soil surface the  concentration
resulting from the application,  C ,  is

-------
                           6.38
                                                    •,>.:•:
                                       SPLASH AND    •"*>
                                        INTERRILL   ?•*,
                                        EROSION AND I'
                                        PESTICIDE .•.;':.-'
                                        EXTRACTION".:'/!
  V SOURCE OF
    PESTICIDE
    FOR RUNOFF
    (SOIL SURFACE
    ZONE)
SURFACE
RUNOFF
PESTICIDE»MOVEMENT
      FROM   __
  SURFACE LAYER

      DEPTH OF SOIL
      INCORPORATED
      PESTICIDE
Figure 6.7.   Schematic representation of the conceptualized
           ;   runoff process.   (from Leonard and  Wanchope,
              1980)

-------
                              . 6.39
 FRACTION ON  SOIL
        (C,)
ADD  INITIAL RESIDUES
        (C2)
      COMPUTE
   CONCENTRATION
    OF  RESIDUE
        (C4)
    ADJUST FOR
DOWNWARD  MOVEMENT
      COMPUTE
     AVAILABLE
      RESIDUE
     FOR STORM
                             PESTICIDE
                            APPLICATION
                             (R OR  CQ)
                             RAINFALL,
                         RUNOFF, SEDIMENT
                         (HYDROLOGY AND
                         EROSION MODELS)
 FRACTION  ON FOLIAGE
         (M,)
 ADD INITIAL RESIDUES
         (M2)
       COMPUTE
        MASS
     OF  RESIDUE
         (M4)
       WASHOFF
      FRACTION
(FROM OTHER MODELS)
   CONCENTRATIONS
      IN WATER
  AND SEDIMENT AND
     TOTAL MASS
         Figure 6.8.   Simplified schematic representation of
                     the pesticide model.

-------
                                     6.40
          Cl=Rx                                                    (6.84)

where  BD  is the bulk density of the  surface  soil  layer and   R   is  the appli-
cation rate in units of  kilograms/hectares.  Assuming an average   BD of  1.5,
                                                             !>
          C1 = R x 6.7                                                (6.85)
For soil incorporated pesticides,
          C1 = 6.7 R x EF/ID                                          (6.86)

where  EF  is a unitless  factor to compensate  for nonuniform  incorporation and
ID  is the incorporation  depth.  If uniform mixing  is assumed,  EF = 1;
however, experience has  shown that uniform mixing is rarely achieved (Smith et
al., 1978).  Concentrations in the surface 0 to  1 cm layer are usually higher
than computed assuming uniformity so that  EF  probably ranges from  1 to  3.
In situations where pesticide is injected or banded below the  soil surface,
                                                                  9
EF  may be less than 1.   A range of 0.5 to 1 is  suggested.  Normally EF
would be assigned a value of 1 unless  information is available on the incor-
poration pattern in a specific situation of interest.  If some pesticide  resi-
due,  C ,  was initially  present in the soil at  the time of application,  the
total or net concentration wold be  C  = C9 +  C..
     When pesticides are  applied to foliage, the areal concentration expressed
in units of milligrams/square meters is
          M  = R x FF x  100                                           (6.87)

where  FF  is the fraction of the application  intercepted by  the  foliage.  M
is not concentration on the leaf surface, but  a  concentration  based  on the
projected ground area.  Unless the canopy is dense  with complete  closure, a
fraction of the application,  SF,  will also be  intercepted by the soil sur-
face.  Soil concentration resulting from this  application is  computed as  above
as  C  = R x SF.  When aerial applications are made, losses by drift and  vola-
tilization may occur so that  FF + SF  will not  equal one.
     Residues of the same pesticide from previous applications, if present in
either the soil or foliage compartment, are added to that resulting  from  the
new application for the total residue  level.   At the beginning of the model
application period, any initial residues present are specified.   When pesti-
cide residues are redistributed in the soil by major tillage, a new  model

-------
                                    6.41

application period should be begun, with the resultant surface  concentration
input as initial residue for this period.  The surface concentrations  at  the
beginning of the period may be estimated • from the residue remaining  and the
tillage depth.
     A simple exponential dissipation rate is assumed for both  soil  and foliar
residues throughout the model application period.  For soil residue,   C ,  the
concentration remaining at time  t  in days after application of  the pesticide
or in days after specifying the concentration of initial residue  is:
                  -k t
          C, = CLe  S                                                 (6.88)
           4    3
Likewise, mass remaining on foliage,  M. , at time  t  is:
                  -kft
          M  = Me                                                    (6.89)
          or
                    0.693t
          M, = Me                                                    (6.90)
           4    3
where  C  .   is the "half life" or half concentration time of  the  foliar  resi-
due in days.  In the model, the mass of foliar pesticide of  concern  is  that
"dislodgeable" or potentially removed by rainfall.
     Little information is available in patterns of pesticide  removal by  rain-
fall.  In the model, the assumption is made that once rainfall exceeds  a
threshold value corresponding to the amount that can be retained as  droplets
on the canopy, the fraction potentially dislodgeable is removed during  the
event.  This amount is then added to the soil pesticide residue present at the
time of the event.  For computation of concentrations consistent with the con-
ceptual thickness of the soil surface, this mass is distributed evenly  in the
0 to 1 cm zone.  In reality, washoff may occur during the storm such that
foliar contributions may fall directly into the runoff stream  and  be
transported off the field.  Also, spatial patterns of washoff  are  likely  not
uniform and washoff may fall into rills under the plant formed by  previous
rainfall.  Therefore, the assumptions made may tend to underestimate the
foliar contribution to runoff.
     Some pesticides, particularly dust formulations, may reach the  soil  sur-
face by dry fall between runoff events.  Also, drop losses from heavy dew may
remove pesticide from foliage.

-------
                                     6.42

     Runoff potential  of  mobile  pesticides  is  reduced as  infiltrating water
moves some of the pesticide  below  the  soil  surface  (Baldwin et  al.,  1975).
Pesticide mobility  in  soil has been  studied extensively using thin-layer chro-
matography technique  (Davidson et  al.,  1975).   With  this  technique,  mobility
is expressed relative  to  the movement  of water  (R    values).   R  values are
related to  K ,  a  coefficient describing distribution of pesticide  between
the solution phase  and the soil  phase,  defined as a  constant for a simple
linear adsorption isotherm as:         *
          Kd=                                                        (6.91)
                w
where at equilibrium   C    is  the  concentration, micrograms/gram,  in the  soil
                       s
or solid phase and  C   is the  concentration  in solution,  micrograms/milli-
liter.  Other procedures  for  estimating  K    for  a  number  of  common pesticides
in soil, along with limitations and possible  inherent  errors  in  its use,  are
also discussed in Knisel  (1980).
     The following algorithm  was  developed  to estimate vertical  movement  of
pesticide from the soil surface.
     The rate of change of pesticide mass   Z   in  the soil  surface is
          -dZ = C  f dt                                               (6.92)
                 w
where  C   is the pesticide concentration in  water  or  mobile  phase  and  f is
the water flux.  At saturation,
          Z = C  p+C  (1-p)D                                     (6.93)
               w       s
where  p  is the soil porosity,  C   is the concentration  of  the  adsorbed or
                                  S
immobile phase, and  D  is the particle density.  Introducing C  = K C    and
                                                                 s    d w
rearranging the equation  above becomes:

          Cw = p H- DKd(1-p)                                           <
     The rate equation can now be written:

          ~dZ = p + DKd?1-P)dt                                        (6'95)
and integrated between limits of  Z ,  t   and  Z,  t  to  yield
                                   o    o

-------
                                    6.43
           Z = Z e                                                    (6.96)
                o
where  Z   is the mass of pesticide present per unit volume  of  soil surface  at
the beginning of the storm.  The water flux through the  surface during a storm
                  •
is

          f = ** - *° - S                            ,                 (6.97)

where  RF  is the amount of rainfall,  RO  is runoff,  S  is the surface
storage or initial abstraction to reach saturation, and   t  is  the  storm dura-
tion.  Making the substituting for  f,  t  can be eliminated so that
                   RF - RO - S
                 ~1DK (1-p) + p'
          Z = Z e                                                     (6.98)
               o
The value of  S  is estimated from porosity and the average  soil water content
plus canopy stored water.  In the model,  C  x BD = Z    and   Z  = C    x BD
where  C    is the runoff available pesticide concentration  and  C.  is as
        AV                                                        *«
previously described.
     Where pesticide is foliar applied, the amount assumed to reach the soil
by washof f is added to the surface pesticide residue before  estimation of ver-
tical translocation.  This method provides only a crude  approximation of the
process compared to other methods (Genuchten et al., 1974).   However,  it is
developed for use where only total storm rainfall and  runoff amounts are
available.  Its primary function is to reduce surface  concentrations of those
compounds with high soil mobility.  Since the amount of  vertical translocation
will be small in a single storm for relatively insoluble compounds, this
calculation is bypassed in the model if the compound solubility is  < 1 vig/g.
     The source zone supplying pesticide to runoff was defined  as the  surface
( 0 to 1 cm) depth increment.  At the time of runoff, this increment of soil
contains a pesticide residue specified in the model as the concentration of
"available residue."  This is the concentration computed using  the  appropriate
decay functions, adding any foliar washof f, and allowing for vertical translo-
cation.  The concentration units are expressed in micrograms/gram of dry soil
as is the convention when a soil sample is removed and analyzed for its pesti-
cide content.

-------
                                     6.44

     Pesticide  is  extracted by water flowing over the surface and by disper-
sion and  mixing of -the soil material by the flow and by raindrop impact.
Instantaneous pressure gradients at the surface caused by raindrop impact on a
water-saturated soil  could also contribute to exchange of pesticide between
the soil  water  and the flowing water.   At the interface between the soil
matrix and  the  runoff stream,  some mass of soil is "extracted" or is effective
in supplying pesticide to some volume  of  runoff.  The mass of pesticide in
this mass of soil  is:
          Y = B C                                                     (6.99)
                 AV
where  B  is the soil mass per unit volume and  C    is the concentration of
available residue.  As this soil mass  mixes or "equilibrates" with the runoff
stream
          Y = (C  V)  + (C  B)                                         (6.100)
                 w         s
where  C    is the  pesticide concentration in the water,   V  is the volume of
        w
water per unit  volume of  runoff interface,  and  C   is the pesticide con-
                                                  S
centration  remaining  in the soil or solid phase.  Ignoring the volume occupied
by the soil mass compared to the larger volume of water,  that is,   V =  total
unit volume of  runoff interface = 1,

          Cw +  Cs  B =  B CAV                                          (6.101)
By assuming that the  distribution between the solution and the soil is
approximated by the equilibrium expression:
          Kd =                                                        (6.102)
                w
                B CAV
          °  =
           W    1 + B K
                      d
or
          °S =  1   B K                                         •       (6
                      d
In these expressions it  can  be  seen  that  when   K, =  0,   then  C   =  B C  ;
                                                d              w      AV
e.g., if 100 g  of soil containing  1  yg/g  of pesticide  that  partitions comple-
tely to the solution phase is extracted by or  is dispersed  in one liter of
water,  C  = 100 jjg/1.   Also, as   K,   becomes  larger,   C = C ...  The
         w                         as     Av

-------
                                    6.45

numerical value of the parameter  B  in the above  equation  cannot be obtained
by direct measurement, and probably is dependent on  runoff  conditions.
However, it will be shown later that the value ranges  from  0.05  to 0.2,  with
0.1 giving adequate fit in most situations.
     As material flows from the field, it is assumed that the  pesticide  con-
                                          •
centration in the runoff solution is equal to  C .   However, not all the
                                                w
affected soil material will become sediment at the field edge.   The coarser
soil material will be deposited or left in place.  As  a result,  the
transported soil will have a higher per unit mass  adsorptive capacity and
adsorbed pesticide concentration than that of the  whole soil.  Therefore, an
enrichment factor is required.
     Total storm loads are computed as:  mass in solution phase  = C  x storm
                                                                    w
runoff volume, and mass in sediment phase = C  x enrichment factor x sediment
                                             s
yield.
     The approach taken by these procedures differs  from other models in that
the runoff stream is not forced to equilibrate at  the  soil/water ratio deter-
mined by the composition of the saturated soil matrix  (Frere et  al., 1975)  nor
at a ratio determined by the concentration of the  transported  sediment,
assuming sediment has the same adsorptive capacity as  the soil (Crawford and
Donigan, 1974).  The weakest assumption, probably, is  that  associated with
using  K   to partition between the solution and the soil phase.  In addition
to the limitations discussed in Knisel (1980) the  runoff process is dynamic,
and true equilibration is probably never reached.  Also, pesticide apparently
partitions differently depending on time of contact  with the soil (Smith et
al., 1978); that is, the "apparent  K," based on observed partitioning in
                                     a
runoff from experimental watersheds differs from the laboratory  determined
values and increases throughout the observation period.  For this reason,
may be best used to differentiate between behavior of  pesticide  classes,  with
K,  ranges differii
 d
100, and so forth.
values and increases throughout the observation period.  For  this  reason,   K,
                                                                             a

K   ranges differing perhaps by orders of magnitude, that  is,  1  to 10,  10  to
6.6  Data Requirements for Pesticide Model
     Hydrologic inputs required are rainfall and runoff volume.   These  are
obtaiend from the hydrology model or input as observed data.   Sediment  yield
is also obtained from the model, experimental observations, or other

-------
                                    6.46

estimates*  The  other  data requirements are  detailed as  follows.  . Most are
specific to the  chemical applied.
     Application Rate.   The desired pesticide  rate  for a given application
usually is specified within certain limits by  the registration data on the
label or is obtained as  recommendations from the supplier or  extension spe-
cialists.  The number  of applications  for some pesticides,  particularly
foliar-applied insecticides,  will  depend on  extent  of insect  infestation or
established spray schedules.   Application rate is input  in units  of
kilograms/hectare.
     Depth of Pesticide  Incorporation.  Pesticides  often are  incorporated by
double-disking,  rotary tillers, and other equipment for  harrowing or smoothing
the soil surface.   Depth of pesticide  incorporation will depend on the type of
tillage equipment  used and soil conditions.  Depth  of incorporation normally
ranges from about  8 to 15 cm (3 to 6 inches).   When the  pesticide is incor-
porated, select  the depth based on the tillage equipment used.  For surface-
applied chemicals,  a value of 1 cm is  input  as the  incorporation  depth since
the surface is defined arbitrarily as  having a depth of  1 cm.
     Efficiency  Factor for Incorporation.  Most incorporation devices do not
mix the applied  pesticide uniformly throughout the  entire depth.   The con-
centration remaining at  the surface may be significantly higher than at lower
depths.  Injected  pesticides may have  a low  surface concentration due to their
placement below  the surface.   The  efficiency factor can  be used to adjust the
surface concentration  based on known patterns  of incorporation.   If an incor-
poration device  leaves a concentration in the  surface of twice  that achieved
by uniform mixing,  for example, an efficiency  factor equal to  half the incor-
poration depth could be  used.  For injected  pesticides,  an efficiency factor
of less than one  will  reduce the surface concentration in proportion.   Since
this type of information usually is unavailabale, a value of  1  would be input
with the assumption that uniform mixing was  achieved.
     Fraction on Soil  and Foliage.  When crops are  treated with pesticides
applied to the plant canopy,  some  of the application, depending on degree of
canoy closure, will reach the surface  of the soil directly, some  will  remain
on the foliage,  and the  rest will  be lost by drift  and volatilization.   At
full canopy, about  75+20 percent and 50+20 percent  of the ground  and aerial
applications, respectively,  reach  the  canopy.   If the amounts  reaching soil
directly are assumed negligible at full canopy, about 25 to 50  percent can be
lost by drift and  volatilization during application. For incomplete canopy,

-------
                                    6.47
               tr
the fraction reaching soil should be somewhat proportional to  the  extent  of
ground cover, although insufficient information is available to provide any
functional relationship.  The actual distribution between soil, foliage,  and
off-target loss will be highly variable and dependent on atmospheric  con-
ditions, path of application, and canopy characteristics.  If  site-specific
                                                                 •
information is unavailable, at full canopy closure use 0.4 to  0.6  on  foliage
for aerial applications and 0.7 to 0.8 on foliage for ground applications.
Assume an insignificant fraction reaching the soil.  For less  than full clo-
sure, use a fraction for soil interception in proportion to exposed ground
surface.  For example, suppose an aerial application is made to cotton that,
on projection, covers 50 percent of the ground surface.  The fraction on
foliage would be 0.3 and the fraction on soil would be 0.3, with the  rest,
0.4, assumed as off-target losses.
     Initial Foliar Residues.  Pesticides normally dissipate from  foliage such
that a residue will not be present at the beginning of a model application
period.  This option is provided, however, so that the model can be applied  on
any date.  To estimate an initial residue from a previous application, assume
interception fraction, as was suggested, and use equations given in Knisel
(1980) to estimate dissipation with time.  Rates of foliar dissipation are
discussed in a following section.  The value input should be in units of
milligrams of pesticide per square meter of ground surface.  Initial  residue
can be determined best by direct measurement, but this procedure usually  is
not practical except for research.
     Initial Soil Residue.  As for foliar residue, the amount  of pesticide
present in soil at the beginning of a model application period is  best deter-
mined by sampling and analysis.  Little residue of nonpersistent pesticides
would be expected at the beginning of a growing season.  When  persistent
pesticides, such as organochlorines, have been used for several years on  a
site, however, a significant residue will be present.  If sampling and analy-
sis cannot be accomplished, published data should be sought on residues in the
soils of the area.  The input value should be in units of micrograms  per  gram
(ppm).  If the initial residue cannot be determine by measurement  or  cannot  be
estimated from published information such as that found in the Pesticide
Monitoring Journal, levels of initial residue may be estimated by  using the
values in Kniser (1980).
     The initial residue parameter also provides a service for updating the

-------
                                    6.48

concentration of pesticide  in  the  surface of  the  soil  as  a  result  of  redistri-
bution caused by major tillage.  Persistent pesticide  may accumulate  at  the
soil surface during an application season.  This  accumulated  residue  would be
predicted as output from  the model.  At the time  of  tillage,  a  new value for
the concentration at the  surface of the soil  can  be  computed, based on the
accumulated residue and tillage depth, and can  be entered as  an initial  soil
residue for a new model application period.
     Foliar Washoff Threshold.  This parameter  estimates  the  amount of rain-
fall required to exceed the capacity of the canopy to  intercept and retain
rainfall as droplets on the leaf surfaces.  Once  this  amount  of rainfall is
exceeded, pesticide washoff is assumed.  The  value of  this  parameter  probably
ranges from about 0.1 cm  to 0.3 cm for a dense  crop  canopy.
     Washoff Fraction.  Little information is available on  extent  and patterns
of pesticide washoff from foliage.  The efficiency of  the washoff  process may
be related to several factors.  Information in  Knisel  (1980)  suggests that
rainfall can remove about 60 percent of the dislodgeable  residue of most
pesticides.  Organochlorines,  and  possibly other  pesticides,  however, are
exceptions.  Less than 10 percent  of these compounds is removed by rainfall.
Values of 0.6 to 0.7 are  suggested, therefore,  for all except the  organo-
chlorines, where values in  the range of 0.05  to 0.1  should  be used.
     Water Solubility.  Pesticide  solubilities  can be  found in  many handbooks
on pesticide properties.  In the model, solubility serves two functions.  If
solubility is < 1 ppm, the  vertical transport computation is  bypassed.
Secondly, the predicted runoff concentration  in solution  is compared  to  solu-
bility.  If solubility is exceeded, the solution  concentration  is  limited to
the water solubility.  Solubility  is, therefore,  a critical input  parameter
only for the relatively insoluble  pesticides.
     Foliar Residue Half  Life.  Knisel (1980) presented estimates  for half-
life values of pesticides on foliage.  Pesticides generally are not as per-
sistent on foliage as in  soil.
     Extraction Ratio.  This parameter describes  the efficiency of the runoff
stream in removing or extracting pesticide.   Conceptually,  it is the  ratio of
soil:water in the mixing  zone.  Tests with the  model indicate that values in
the range of 0.05 to 0.2  are needed—the higher values for  conditions of
excessive runoff and erosion.  Predicted runoff concentrations  of  those  pesti-
cides transported entirely  in  solution vary in  direct  proportion to the  value

-------
                                    6.49
                                       u
of the extraction ratio.  As sediment transport becomes more  significant,  sen-
sitivity to this parameter decrases.  A value of 0.1 gives adequate prediction
in most situations.
     Soil Decay Constant.  Value sof rate constants,  k ,  are tabulated
(Knisel, 1980) for the assumed expoential decay function applied  to several
pesticides and conditions.  Because dissipation rates are affected by climatic
factors, the results of individual experiemnts also should be reviewed before
making a final selection.  Many pesticides dissipate more rapidly at  the  sur-
face of the soil than from the soil bulk.  The  k   values for surface dissi-
                                                 s
pation are more appropriate for runoff prediction, but more results have  been
reported on persistence in the soil bulk.  Where  k   values  are  given for
                                                   s
soil bulk but not for surface, differences reported for similar compounds
maybe used in making a subjective judgment on how the surface  k   might
differ from the reported bulk soil  k .
     Additional information is provided in Knisel (1980) on how   k    values
can be estimated based on properties of the pesticides and their  environment.
In addition to a better perspective of factors influencing dissipation rates,
methods are provided by which  k   values can be estimated where  little
                                S
experiemntal data are available.
     In some instances, the first-order decay equation poorly describes dissi-
pation of a pesticide.  No direct method is provided in the present model for
substituting these equations for the first-order decay equation.  The  k
values can be updated, however, using different values for different  times
after application.  A best-fit equation could be used to compute  k    values
for shorter time segments of the linear log c vs t relationship assumed.
     Distribution Coefficient  K,.  Knisel (1980) discusses how   K,   is deter-
     	d                                 d
mined, the factors affecting its value for different pesticides and soils, and
how to estimate  K,  for a specific situation.  Tables are presented  that list
                  d
mean  K,  with standard deviations for several pesticides.  These tables  also
       d
provide for estimating  K,  as a function of soil texture and organic matter
                         d
content, thus tying  k   to both the pesticidal properties and controlling
                      a
site-specific characteristics of the soils.  Additional relationships  for
estimating  K   are b
pesticide solubility.
     Some assumptions
pesticide between solution and adsorbed phases.  Users should  compare
estimating  K   are based on observed soil thin-layer chromatography and
            Lu
     Some assumptions are discussed for using  K   to predict distribution of

-------
                                     6.50


potential errors due  to  linearity  and  other  assumptions  in  relation  to  the

accuracy of required  output  to  achieve the objectives  of  their  simulation.

Since the effect of these  assumptions  on  the validity  of  model  output is

uncertain,  K  values for  an order of  magnitude mgiht  be  warranted when
             d
distinguishing major  behavioral differences.   Expressing  K  values expli-

citly as per reference may be useful to analyze certain problems  or

situations, using model  simulations to compare effects of different  management

alternatives on the same site.


6.7  References
Baldwin, F.L., P.W. Santelmann, and J.M. Davidson,  1975,  "Movement of
Fluometuron across and  through the Soil," Journal of Environmental Quality,
4:191-194.

Bruce, R.R., L.A. Harper,  R.A. Leonard, W.M.  Snyder, and  A.W. Thomas,  1975,  " A
Model for Runoff of Pesticides from Small Upland Watersheds," Journal  of
Environmental Quality,  4:541-548.

Cowan, I.R., 1965, "Transport of Water  in the Soil-Plant  Atmosphere  System,"
Journal of Applied Ecology, 2:221.

Cowan, I.R. and F.L. Milthorpe, 1968, "Plant  Factors Influencing  the Water
Status of Plant Tissues,"  in Water Deficits and Plant Growth, Vol. I,  ed.  by
T.T. Kozlawski, Academic Press, New York.

Crawford, N.H. and A.S. Donigian, Jr.,  1974,  "Pesticide Transport and  Runoff
Model for Agricultural  Lands," Hydrocomp, Inc., Palo Alto, California, pre-
pared for U.S. Environmental Protection Agency, Athens, Georgia,  Publication
No. EPA-600/2-74-013, 211  pp.

Davidson, J.M., G.H. Brusewitz, D.R. Baker, and A.L. Wood, 1975,  "Use  of Soil
Parameters for Describing  Pesticide Movement  through Soils," U.S.
Environmental Protection Agency, Publication  No. USEPA-660/2-75-009, 149 pp.

Eagleson, P.S., 1970, Dynamic Hydrology, McGraw-Hill, New York.

Eggert, K.G., 1976, Modeling the Unsteady Infiltration Process, Master's
Thesis, Department of Civil Engineering, Colorado State University,  Fort
Collins, Colorado.

Eggert, K.G., R.M. Li,  and D.B. Simons, 1979,  "The  Explicit Formulation of the
Green-Ampt Infiltration Equation," 18th Congress of International Association
for Hydraulic Research, Vol. 5, Cagliari, Italy, pp. 145-152.

Ehleringer, J.R. and P.C.  Miller, 1975, "A Simulation Model of Plant Water
Relations and Production in the Alpine  Tundra, Colorado," Oceologia, Vol.  19,
pp. 177-193.

-------
                                    6.51
Frere, M.H., C.A. Onstad, and H.N. Holtan,  1975, ACTMO, An Agricultural
Chemical Transport Model, U.S. Department of Agriculture, Agricultural
Research Service, Headquarters, ARS-H-3, 54 pp.  (Series discontinued;
Agricultural Research Service now Science and Education
Administration-Agricultural Research.)

Genuchten, M.Th.van, J.M. Davidson, and P.J. Wierengen, 1974,  "An Evaluation
of Kinetic and Equilibrium Equatins for the Prediction of Pesticide  Movement
through Porous Media," Soil Science Society of America Proceedings,  38:29-35.

Green, R.E. and I.e. Corey, 1971, "Calculation of Hydraulic Conductivity:   A
Further Evaluation of Some Predictive Methods,"  Soil Science Society of
America Proceedings, Vol. 35, pp. 3-8.

Green, W.H. and G.A. Ampt, 1911, "Studies on Soil Physics, Part  I: The Flow of
Air and Water through Soils," Journal of Agriculture Science,  May.

Huff, D.D., R.J. Luxmoore, J.B. Mankin, and C.L. Begovich, 1977, TEHM; A
Terrestrial Ecosystem Hydrology Model, Oak Ridge National Laboratory,
EDFB/1BP-76/8, Oak Ridge, Tennessee.

Jarvis, P.G., 1976, "The Interpretation of the Variations in Leaf Water
Potential and Stomatal Conductance Found in Canopies in the Field,"  Phil.
Trans. Royal Soc. Lond., Vol. 273, pp. 593-610.

Knisel, W.G., 1980, "A Field Scale Model for Chemicals, Runoff,  and  Erosion
from Agricultural Management Systems," for U.S.  Department of  Agriculture,
Conservation Research Report #26.

Leonard, R.A., G.W. Langdale, and W.G. Fleming,  1979, "Herbicide Runoff from
Upland Piedmont Watersheds - Data and Implications for Modeling  Pesticide
Transport, Journal of Environmental Quality, Vol. 8, pp. 223-229.

Leonard, R.A., R.D. Wanchope, 1980, "The Pesticide Submodel,"  in U.S.
Department of Agriculture, Conservation Research Report #26.

Li, R.M., M.A. Stevens, and D.B. Simons, 1976, "Solutions to Green-Ampt
Infiltration Equation," Journal of Irrigation and Drainage, ASCE, Vol.  102,
pp. 239-248.

Mein, R.G. and C.L. Larson, 1973, "Modeling Infiltration During  a Steady
Rain," Water Resources Research, Vol. 9.

Monteith, J.L., 1965, "Evaporation and Environment," Symposium Society of
Environmental Biology, Vol. 19, pp. 206-234.

Reed, K.L. and R.H. Waring, 1975, "Coupling Environment to Plant Response,"
Ecology, Vol. 55, pp. 62-72.

Reeves, M. and E.E. Miller, 1975, "Estimating Infiltration for Erratic
Rainfall," Water Resources Research, Vol. 11, No. 1, pp. 102-110.

-------
                                    6.52


Reifsynder, W.E.  and H.W.  Lull,  1965,  Radiant  Energy in  Relation  to  Forests,
U.S. Department of  Agriculture Technical  Paper No.  1344,  Washington,  D.C.

Running,  S.W.,  1976,  "Environmental Control  of Leaf  Water Conductance in
Conifers," Canadian Journal of Forest  Research,  Vol.  6,  No.  1,  pp.   104-112.

Running,  S.W., R.H.  Waring, and  R.A. Rydell,  1975,  "Physiological Control  of
Water  Flux in Conifers," Oceologia, Vol.  18, pp. 1-16.

Rutter, A.J., 1967,  "An Analysis of Evaporation from a Stand of Scots Pine,"
Forest Hydrology, ed.  by W.E. Sopper and  H.W.  Lull,  Pergamon Press,  Oxford,
England,  pp. 403-415.

Slatyer,  R.O.,  1967, Plant-Water Relationships,  Academic  Press, New  York.

Smith, C.N., R.A. Leonard,  G.W.  Langdale,  and  G.W. Bailey,  1973,  "Transport of
Agricultural Chemicals from Small Upland  Piedmont Watersheds,"  U.S.
Environmental Protection Agency,  Athens,  Georgia, and U.S.  Department of
Agriculture, Watkinsville,  Georgia, Final Report on  Interagency Agreement  No.
D6-0381,  Publication No. EPA 600/3-78-056, 363 pp.

Smithsonian Institute,  1966, Smithsonian  Meteorological  Tables, Vol.  69,
No. 1, Washington,  D.C.

Steenhuis, T.S.,  and M.F.  Walter,  1978, "Closed Form Solution for Pesticide
Loss in Runoff Water,"  American  Society of Agricultural  Engineers Technical
Paper No. 78-2031,  presented at  the 1978  summer meeting  of  the  American
Society of Agricultural Engineers, Logan,  Utah,  June  27-30.

Sutcliffe, J., 1968, Plants and  Water, Studies in Biology No. 14, Institute of
Biology,  St. Martins Press, New  York.

Swift, L.W., Jr., W.T.  Swank, J.B. Mankin, R.J.  Luxmoore,  and R.A. Goldstein,
1975,  "Simulation of Evapotranspiration and  Drainage  from Mature  and Clear-Cut
Deciduous Forests and  Young Pine Plantation,"  Water  Resources Research,  Vol.
II, No. 5.

Tan, C.S., T.A. Black,  and J.V.  Nuyamak,  1977,  "Characteristics of Stomatal
Diffusion Resistance in a  Douglas Fir  Forest Exposed  to  Soil  Water Deficits,"
Canadian Journal  of  Forest Research, Vol.  7, pp. 595-604.

Tanner, C.B. and  W.L.  Pelton, 1960, "Potential Evapotranspiration Estimate by
the Approximate Energy Balance Method  of  Penman," Journal of  Geophysical
Research, Vol. 7, pp.  400-409.

Thompson, D.R. and  T.M. Hinckley,  1977, "A Simulation of  Water  Relations of
White Oak Based on  Soil Moisture and Atmospheric Evaporative  Demand,"
Canadian Journal of Forest Research, Vol.  7, pp. 400-409.

Van Bavel, C.H.M.,  1966, "Potential Evaporation:  The Combination Concept  and
Its Experimental Verification,"  Water  Resources  Research, Vol.  2, pp.
455-467.

-------
                                    6.53


Van Wijk, W.R. and D.A. DeVries, 1963, "Periodic Temperature Variations in a
Homogeneous Soil," in Physics of Plant Environment, ed. by W.R. Van Wijk,
North-Holland Company, Amsterdam.

-------
VII. APPLICATION OF EVALUATION PROCEDURES
7.1  Introduction
     The methodologies described previously were applied to  an  agricultural
watershed in Iowa.  This watershed is located near Traer,  Iowa,  and  is  called
Four-Mile Creek (Figure 7.1).  The watershed covers an area  of  19.51  square
miles and contains several smaller watersheds and numerous data measurement
sites.  The watershed is characterized by glacial till covered  by  loess up to
35 feet thick.  Average temperature is about 47.6°F and annual  precipitation
averages 32.4 inches.  The watershed is about 90 percent agriculture  with 65
percent row crop and 25 percent pasture, meadow, and small grains.  There are
three U.S. Geological Survey gages in the watershed, designated as Four-Mile
Creek near Traer, Four-Mile Creek near Lincoln, and Half-Mile Creek  near
Gladbrook.  In addition, Iowa State University  (ISU) in cooperation with the
U.S. Environmental Protection Agency (EPA) has  installed and is currently
collecting data at three field size watersheds  ranging in  size  from  about  14
to 19 acres, and two larger sites about 370 and 700 acres  each.  -There  are
five recording rain gages in the total watershed.  A weather station  with a
recording rain gage is located just outside the watershed  boundary.   Fifteen
permanent channel cross section measurement sites are maintained in  the main
channel and one additional cross section site is located on  Half-Mile Creek.
In addition to these typical measurement sites, ISU maintains tile drain
sampling stations, nutrient and herbicide soil  collection  stations, pump
smaplers for collecting sediment, nutrient, and herbicide  outflow with  runoff,
vegetation observation points, and erosion markers.  Details of the entire
collection system were presented in-two annual  reports (Johnson, 1977;  1978),
and are not repeated in this study.  Application of the data network  eva-
luation methodology to Four-Mile Creek is presented in the following  sections.
Each piece of data was not evaluated because of time and financial limita-
tions.  However, every data type was examined using some or  all of the  tech-
niques presented herein.

7.2  Data Availability and Data Gaps
     Model requirements for data listed in Table 2.1 were  compared to those
available as outlined in the previously cited annual reports.   Of the 69 items
listed, available data was identified for 35 (Table 7.1).  Although  35  items
were identified, this does not indicate these data were accurate or  sufficient

-------
                                                  Four-Mile  Creek  Wolershed  Instrumenlolion
                                                     A   Gaging Station
                                                     •   Rain Gouge Location
                                                     O   Tile Outlet Location
                                                     -••   Cooperotor's  Farm and  ISU  Weather  Station
                                                     |    Channel Measurement  Station
                                                                                                     36
                                                                                                             to
Figure  7.1.   Sampling sites in the  Four-Mile Creek Watershed.

-------
                                    7.3
           Table 7.1.  Available Data for Colorado State University
                       Physical Process Models
            Data''groups                                   Data availability^
Geometry and channel data
     Watershed area                                                +
     Length of overland slopes                                     +
     Width of overland slopes                                      +
     Gradients of overland slopes                                  +
     Length of channel sections                                    +
     Gradient of channel sections                                  +
     Measured, representative channel cross sections               +
     Elevation of watershed                                        +
                     •t
Soil data
     Distribution of soils                                         +
     Types of soils                                                +
     Number of soil layers                                         +
     Thickness of layers                                           +
     Initial water content of layers or top layer                  +
     Saturated hydraulic conductivity of each layer
        or top layer
     Tensiometer measurements (desorption curve) for
        each layer
     Temperature for tensiometer data
     Field moisture capacity for each layer
     Intrinsic permeability of top layer
     Porosities of soil layers o  top layer
     Specific gravity of soil
     Temperature of top layer  -                                    +
     Thermal conductivity of soil
     Grain size analysis of top layer
     Concentrations of nitrogen and phosphorus species             +
        in soil layers

-------
                                     7.4
           Table 7.1.   Available Data for Colorado State University
                       Physical Process Models (continued)
            Data groups                                   Data availability''
Vegetation data
     Types                                                         +
     Distribution                                                  +
     Density of ground cover
     Density of canopy cover                                       +
     Storage of ground cover
     Maximum and minimum storage of canopy cover
     Albedo of vegetation
     Yearly growth cycle of canopy                                 +
     Average leaf length of dominant species
     Maximum and minimum leaf area
     Root cross-sectional area per unit area of soil
        in each layer
     Fraction of root in each layer
     Annual litter input to ground surface
     Litter layer thickness
     Average litter temperature
     Nitrogen content of litter
     Phosphorous content of litter
     Specific gravity of litter
Climatic data
     Daily solar radiation                                         +
     Average daily temperature                                     +
     Average daily humidity or vapor pressure                      +
     Total daily precipitation                                     +
     Average wind speed                                            +
     Air pressure — for year as function of altitude
     Specific heat of air
     Rainfall storm hyetographs                                    +
     Nitrogen species input from rainfall
     Surface water temperature

-------
                                   7.5
        Table 7.1.  Available Data for Colorado State University
                    Physical Process Models (continued)
            Data groups               "                    Data availability1'
Hydrologic and hydraulic data
     Storm and daily runoff hydrographs                            +
     Overland flow resistance
     Channel flow resistance
     Storm sediment yield                                        •  +
     Sediment yield from litter layer
     Runoff temperature
     Grain size and analyses of sediment                           +
     Sediment detachment coefficient for rainfall
        and runoff
     Dissolved oxygen content in runoff
     Nutrient concentration in runoff                              +
     Rate of addition of BOD in runoff
Man's influence
     Cropping patterns                                             +
     Land use changes                                              +
     Timbering activities
     Modification of drainages                                     +
     Nitrogen application                                          +
     Phosphorus application                                        +
  + Yes, this item has been identified in the annual reports
  - No, this item has not been identified in the annual reports

-------
                                      7.6

for modeling.  For example,  although  cropping patterns were  detailed  for  the
small field sized plots,  only very  generalized  information for  the  entire
watershed was provided.   More detailed  descriptions  of data  accuracy  and  ade-
quacy are included for each  data  category.   In  general,  the  data  base as  it
now exists is deficient  in some key items.   This makes model application  dif-
ficult.  The model may still be applied but  with "best estimates" of  the
missing data.

7.3  Analysis of Existing Data Network
     Data can be subdivided  into  several groups as evidenced by Table 7.1.  To
facilitate discussion, groupings  of data will be utilized and analysis of
selected specific data is presented for illustrative purposes.

     7.3.1  Geometry and Channel  Data
     This group of data  is complete because  most of  the  measures  can  be
acquired from topographic maps.   U.S. Geological Survey  7-1/2 minute
quadrangle sheets were used  to define most of the data listed within  this
group, excpet for determination of  channel cross sections.   In  addition,
topographic maps for the  three field  size watersheds were included  in the
annual reports.  These topogaphic maps  yielded  the detail necessary for the
small watersheds.  A complete description of the geometric measures is
included in the model application section.
     The detail on the topographic  maps proved  to be sufficient to  satisfy
requirements at this time.
     Channel cross-sectional measurements taken at the 16 collection  sites
show a substantial change in channel  shape between 1967  and  1977.   These  types
of changes must be taken  into account if water  and sediment  routing is to be
correctly computed.  An  example of  the  changes  that  occurred over a shorter
period can be found by comparing  the  1977 measurements to those of  1978.  It
is appropriate to compare those measures of  the channel  cross-sectional
geometry that are used in the proposed  model.   In this instance the parameters
a  and  b  of the wetter  perimeter  (P)  and flow area   (A)   relationship:

     P = a Ab                                                          (7.1)
are considered.  Theory and  experience  show  that  a  and b   are  inversely
related.  In addition,  b usually  ranges from  0.3 to 0.6 for many  channels,

-------
                                      7.7
whereas  a  can be quite variable.  As cross sections change with time and
location on the stream, so do the  a  and  b  parameters.  Figure 7.2 shows
variation in these parameters as a function of distance from the outlet of
Four-Mile Creek.  Note that parameter  b  increases toward 0.5, a value asso-
                                                                o
ciated with swale or triangular sections, but parameter  a  decreases in the
upsteam direction.  Similar trends are seen in Figure 7.3 which can  also be
compared to Figure 7.2.  Changes in  a  and  b  parameters between 1977 and
1978 measurements indicate the channel is relatively active in the lower and
middle portions, as might be expected, but less active near the upper end of
the channel.  Although the changes are relatively small in absolute  values,
they can significantly effect water routing and sediment transport.  In this
case, the  a  and  b  parameters are used in the water routing portion of the
model to find flow area  A  from discharge  Q.  An error in parameter  a  of
10 percent, for example, creates a similar error in the flow area, whereas an
error in  b  may be magnified several times depending on flow conditions
(Simons, Li and Ward, 1978).  Fortunately,  b  is less variable than a  for
most channels.  It is important, then, that the  a  and  b  parameters be
accurately evaluated.  In the Four-Mile Creek channel, the downstream and
yearly changes in cross-sectional geometry suggest the need for additional
measurement sites that may be maintained on an annual or semi-annual schedule.
These additional stations and shorter sampling interval may help indicate
channel changes and necessary model adjustments.
     Watershed geometry data is relatively good.  Some additional emphasis on
cross section measurements can help in selecting proper model parameters and
making correct adjustments with time and distance.  In addition, reproduction
of cross section plots in the annual summaries was poor in some cases making
it difficult to correctly choose distances and elevations.

     7.3.2  Soil Data
     Soil data were examined with respect to hydrologic properties,  sedimen-
tologic characteristics, and nutrient and herbicide-pesticide indices.  Silt
loam soils predominate in the watershed, primarily derived from the  loess
deposits.  Their distribution and types for the small field size watersheds
are presented in the annual reports.  However, soils distribution maps for the
entire watershed were not presented.  Depth information from the nutrient and
herbicide-pesticide sampling sites can be used.  However, these measurements

-------
                                   7.8
   0
1
1 1 1 1
1 1 1 1
                    234567
                 Distance   from   Mouth  of Watershed,  miles
8
Figure 7.2.   Cross section parameters  a  and  b  for 1976-1977  measurements.

-------
  10 r
   8
I  6
E
a
I  5
4^
o
0)
14
                                                            1976-1977
                                                            1977-1978
                      234567
                        Distance from Mouth of Watershed (miles)
8
           Figure 7.3.  Cross  section parameters  a  and  b  for 1976-1978
                        and  1978-1979 measurements.
                                                                                                     D

-------
                                      7.10

are taken to a depth  of  only 60  inches.  This  is  probably  adequate  for most
modeling unless deep  ground water  flow  is analyzed,  then a better measure of
soil depth is needed.  In  addition,  the  sampling,  by necessity,  is  done at
preselected depth ranges that may  or may not be related to specific soil hori-
zons if there are any.   A  better description of a typical  soil profile for
each type would be useful  in determining from  which  horizon or layer the soil
samples are taken.  Although such  information  may be available elsewhere, a
summarized description would be  helpful.
     One useful piece of information derived from nutrient and herbicide-
pesticide soil measurements is the water content  of  the soil layers.   This
type of information,  for the small watersheds  at  least, can be used to deter-
mine antecedent conditions needed  for infiltration computations.  The model
being developed at Colorado State  University for  predicting the  effects of
best management practices  can use  soil moisture measurements as  a check to
keep simulated interstorm  soil moisture  levels realistic.   Soil  temperature
data is collected at  the ISU weather station (number 36) at several depths.
Similar measurements  have  been made  at  Site 1  (field watershed)  and based on a
very limited winter sampling, the  measurements indicate that both sites have
similar temperature profiles.  More  data is needed before  conclusions about
the correlation of these two stations can be made.
     Additional soil  temperatures  for the surface  1  to 2 cm of depth were made
for pesticide studies.   These temperatures are also  beneficial since they
depict the diurnal variations in surface conditions.  Concentrations of
nutrients and herbicides-pesticides  in the soil are  also necessary  for
modeling the origin and  fate .of  these constituents.   One type of information
that is valuable is the  change in  constituent  concentrations with depth.
Figures 7.4a, b and c show the changes  in concentration of the herbicide para-
quat with depth for three  sample sites in field watershed  1  (ISU 1).   These
figures show the spatial distribution in two directions:   planar and with
depth; and the temporal  variations.   The concentrations are plotted at the
midpoint of the soil  layer sampling  interval.  These figures show that the
concentration of Paraquat  generally  increases  then decreases with depth.   This
is important because  Paraquat readily absorbs  to  and is transported on soil
particles.  If the surface layers  have lower concentrations than the subsur-
face layers, this should be considered  in soil loss  and pesticide loss
modeling.  If the soil is  disturbed  to a depth of  15 cm, more paraquat may be

-------
                            7.11
                        Paraquat, kg/ha
                             1.0
                                    4-22-77
                                    5-23-77
                                    5-31-77
                                    6-  10-77
                                    6-20-77
                                    7-06-77
                                 O  8-  18-77
25 L
         Figure 7.4a.
Temporal and spatial variation of
Paraquat site 1-1 corn, 1977.

-------
                                7.12
    0
     0
0.5
Paraquat, kg/ha
     1.0
1.5
2.0
   10
£
o
CL
a>
Q
   15
  20
  25 L
                  A   4-22-77
                  D   5-23-77
                  
-------
                              7.13
                 0.5
   Paraquat,  kg/ha
        1.0
       1.5
2.0
.c
a.
Q
  15
 20
           A
           a
           <]
           O
           o
4-22-77
5-23-77
5-31-77
6-  10-77
6-20-77
7-06-77
8-  18-77
 25 L
          Figure 7.4c.
Temporal and spatial variation of
Paraquat site 1-3 corn, 1977.

-------
                                      7.14

lost during erosion events,   similarly,  soil loss during certain times of  the
year will have more effect on paraquat concentrations than others.  Figure
7.4a shows that the paraquat  concentration  is more than twice as high in July
than in April for the  7.5 to  15  cm  soil  layer, but more than four times higher
in the surface layer.   Such information  is  needed for correctly estimating the
timing of constituent  movements.  More discussion on nutrients and  herbicides-
pesticides is presented in a  later  section.
     Key soil measures missing from the  data base are those related to the
hydrologic properties.   These have  previously been identified in Table 7.1  and
include hydraulic conductivity,  tensiometer data, specific gravity, grain  size
distribution, and porosity.   Such information is essential for determining
infiltration and sediment transport parameters.  Some of this information  may
be contained in other  publications  unavailable for review in this study.   It
typcially is not included and therefore  needs to be collected to provide
better estimations of  key model  parameters.  Infiltrometer tests, carefully
collected soil samples,  sieve analyses,  and saturation-desaturation tests  need
to be conducted.  As stated in the  1977-1978 annual report, sediment size  ana-
lyses for the on-site  soil sampels  are being conducted for inclusion in the
data base.  Other sedimentalogical  aspects  of the soil are covered  in a later
section.

     7.3.3  Vegetation Data
     Vegetation data,  like soils information, is rather sparse in certain
areas.  Considerable effort has  been expanded in monitoring canopy  cover
growth for the field size watersheds.  Spatial and temporal changes in leaf
canopy for watersheds  1  and 2 are shown  in  Figures 7.5 and 7.6 for  1976 and
1977.  These plots show the increase in  leaf area during the growing season
and the plant litter left after  harvest, basic information necessary when
modeling.  Such detailed work has not been  expended on other sub-watersheds
nor on the entire watershed.  This  creates  a problem when modeling  the respon-
ses of the entire watershed,  particularly when canopy and ground cover changes
can significantly affect water and  sediment yields.  The extent of  the
description of vegetation for the entire watershed is limited to percent areas
of different crops grown during  the year.  A complete vegetation distribution
map for the entire watershed  is  not available, however, using physical process
models it is possible  to transfer parameters from one watershed to  another.

-------
  lOOr
 o!90-
 o
 c
 o

°80-
o
QJ
   70-
"S 60-
i_
O)

o
   50--
 o
 O)
< 40--
 o>
 o
 o
   30--
    0--
&  Site I - Soybean

O  Site 2-Corn
                                                                                               •^j
                                                                                               •


                                                                                               en
                                              	1	1	

                                              .1.  JJ_"    >-f;


                                               I 976
         Figure 7.5.  Variation of leaf canopy  cover for 1976, sites  1  and 2.

-------
 IOOT
Q.
O
           O  Site I " Corn
           A  Site 2- Soybeon
       JAN.    FEB.  MARCH APRIL    MAY   JUNE  JULY   AUG   SEPT   OCT    NOV    DEC

                                            1977
         Figure 7.6.   Variation of  leaf  canopy cover for 1977, sites 1 and 2.

-------
                                      7.17
This can be done for soils, vegetation, and other data types.   Unfortunately,
there is a limit to the amount of transferability that can be  attained.   If
the vegetation types and patterns are similar between watersheds,  then such  a
transfer can be made with acceptable reason.  Conversely, if the watersheds
are dissimilar such a transfer is risky.  More detail on transferability is
presented in the model application.
     Information is needed on the specific characteristics of  each vegetation
type, specifically the growth characteristics, transpiration rates,  amount of
litter produced, and interception properties.  Much of this information can
probably be derived from published sources.  However, additional critical
information, may need to be collected for accurate model applications.

     7.3.4  Climatic Data
     Of all data types, climatic data is usually the most abundant,  but not
necessarily the most complete or accurate.  Primary climatic data  for  modeling
include precipitation, temperature, solar radiation, humidity,  and wind speed.
Considerable effort has been spent in collecting climatic data  for the
Four-Mile Creek watershed.  Six recording rain gages are in use for  measuring
precipitation, specifically rainfall events.  In addition to these gages, one
site (Number 36) has been instrumental for measurement of several  climatic
variables including daily maximum and minimum temperatures, solar  radiation,
average wind speed, relative humidity, and pan evaporation.
     Because of numerous rainfall events in the area, rainfall  records  are the
most numerous type of data available for climatic information.  Two  types
exist, daily total rainfall and storm accumulations.  The storm accumulation
records can be analyzed to yield volume-duration or hyetograph  values  that may
be used in modeling.  Analyses of rainfall records should compare  stations
both temporally and spatially.  Daily rainfall values are often a  key  input  to
water yield models.  Therefore extensive daily records are collected at all
six stations.  However, simple spatial correlations of daily rainfall  between
the stations indicated that the readings were very similar.  Results of  these
correlations are shown in computer produced figures (Figures 7.7,  7.8,  7.9,
7.10, 7.11 and 7.12) for each of the stations.  The lowest correlation is be-
tween stations 31 and 34 as seen in Figures 7.7 and 7.8 with a  correlation
value of about 0.79.  The highest correlation are for gage 32  (Figure  7.8).
Key gage numbers 33 and 36 also have correlations usually greater  than 0.85.

-------
D
A
I
L
V

u
0
L
U
H
e

c
o
R
R
E
L
A
T
1
0
N

C
0
E
F
F
I
C
I
E
N
T
 .95
 .9*
I.BS
 .80
        .75
                        32
                                                               35
                                                                                             00
                                         I
                                                       I
                          a               4              t              •

                              DISTANCE FRO* REFERENCE RAIN CAGE IN RILE*


                  REFERENCE GAGE  FOR  THIS FIGURE  IS  NUMBER 31
    Figure 7.7.  Spatial correlation of daily rainfall volumes between base gage
                 (number 31) and other gages.

-------
D
A
I
L
V

V
0
L
U
n.
E

C
0
R
R
E
L
A
T
I
0
N

C
0
E
F
F
I
C
I
E
M
T
35
      ».8S»
                       1234

                              DISTANCE FROM RCFERCNCC RAIN QACC IN HIUS



                  REFERENCE GAGE  FOR THIS  FIGURE  IS  NUMBER 33
    Figure 7.8.   Spatial correlation of daily rainfall volumes between base  gage
                 (number 32) and other gages.

-------
D
A
I
L
V

U
0
L
U
H
C

c
0
R
R
E
L
A
T
I
0
N

C
0
e
F
F
I
C
1
E
                                                                  35
                                                                                            -~J

                                                                                            o
«.8S -
       I.M
                          t              «              3              4

                              DISTANCE FROfl RCFCRCNCE RAIN CAGE IN HIUS



                  REFERENCE GAGE  FOR THIS FIGURE IS  NUMBER 33
     Figure 7.9.  Spatial correlation of  daily rainfall volumes between base gage
                 (number 33) and other gages.

-------
D
A
I
I
V

U
0
L
u
n
E

C
0
R
R
C
L
A
T
I
0
n

c
0
c
F
F
1
C
I
E
N
T
36
                          1              E              3              4

                              DISTANCE FROfl REFERENCE RAIN CACE IN HIIES



                  REFERENCE GAGE  FOR  THIS  FIGURE IS  NUMBER  34
                              (0
    Figure 7.10.  Spatial correlation of daily rainfall volumes between base gage
                  (number 34)  and other gages.

-------
D
A
I
L
V

U
0
L
U
n
E

c
0
R
R
t
I
A
T
I
0
N

C
0
£
F
F
I
C
I
C
N
T
32
                                                to
                                                NJ
                                        4             C

                              DISTANCE FRO* REFERENCE (WIN CACE IN RIICS
                  REFERENCE GAGE FOR THIS FIGURE IS  NUMBER 35
     Figure 7.11.  Spatial correlation of daily rainfall volumes between  base gage
                  (number 35)  and other gages.

-------
       i.ee v
D
A
I
L
Y

U
0
L
U
n
E

C
0
R
R
E
L
A
T
I
0
M

C
0
C
F
F
I
C
I
C
M
T
e.95  -
                                               32
                                                                                            to
                                                                                            CO
•.re  -
       e.s«
                          3461

                              DISTM1CC FDOfl REFCRCnCC MIN CACC IN HIUS


                  REFERENCE GAGE  FOR  THIS  FIGURE  IS NUMBER  36
    Figure 7.12.  Spatial correlation of daily rainfall volumes between base gage
                  (number 36)  and other gages.

-------
                                      7.24

This analysis  indicates two things.   First,  gage 32  should be maintained to
help fill missing  records,  and second,  the  high corelations suggest a redun-
dancy  in measurements  for daily rainfall totals.  This does not suggest that
certain stations be  abandoned, as following analyses show, only that there is
oversampling of daily  rainfall with  the present network.   Another comparison
of daily snowfall  amounts for stations  33 and 36 produced a correlation of
1.0.   Apparently,  this strong relationship  was also  noted by ISU personnel as
•"station 33 was discontinued for snowfall measurements.
     Storm events  were too numerous  for complete analyses.  Therefore about
five storms with the highest volumes at station 33 were selected for each year
(1976, 1977, 1978) as  a comparison basis.  The first noticeable result was
that of the 15 storms;  only four had records at all  six stations (Table 7.2).
Station 32 which was previously identified  as being  highly correlated was
missing eight  of fifteen records.  Table 7.2 indicates that the variability in
rainfall volumes and length of storm can be  quite large for the watershed.
Table  7.3 lists the  statistics of  the 15 storms.   Ranges  where all six gage
records are available,  particularly  for the  storm of 5/28/76,  demonstrate the
need for a good network of recording gages.   Interestingly,  the patterns of
the storms at  the  six  gages were very similar as shown in Figures 7.13,  7.14,
7.15 and 7.16.  The  5/28/76 storm exhibits  an advanced-delayed pattern with
periods of low intensity or no rainfall. Normally such a storm would be sub-
divided into two parts  if the intermittent  break were larger than two hours.
It is  included in  total here for demonstration purposes.   The  5/12/78 storm is
of an  intermediate pattern  as shown  in  Figure 7.15,  while Figures 7.14 and
7.16 indicate  that the  6/13/76 and 6/20/78  storms have patterns typical of
thunderstorm events.   Although durations and volumes vary from station to sta-
tion,  the dimensionless time-volume  distribution is  similar between stations
for a  particular storm.   This is helpful if  recordings are lost and must be
synthesized.   No attempt was made  to correlate storm values or durations
because of lack of complete six station data sets.
     In order  to better understand the  characteristics of storms over the
watershed, 95  storms at station 33 were analyzed for key  statistics of volume
and duration.  The mean volume was 0.508 inches  with a standard deviation of
0.448.  The range was  0.01  to 2.55 inches.   For  duration,  the  mean was 4.558
hours, the standard  deviation was  4.359 hours,  with  a range  of 0.01  to 23.17
hours.  Figures 7.17 and 7.18 show that the  distribution  of volume and

-------
                         Table 7.2.   Characteristics of Fifteen  Large  Rainfall  Storms
CAGE NUNIIEK
Date
04-17-76
04-20-76
05-28-76
06-13-76
07-28-76
07-28-77
08-15-77
08-27-77
09-17-77
10-07-77
04-05-78
04-17-78
05-12-78
05-27-78
06-20-78
31
B E V
No Record
Not Complete
19.42 7.4 21.84 '
18.32 22.22 36.83
2.0 7.33 33.53
No Record
17.83 .67* 47.75
19.8 9.33 21.39
19.12 22.93 34.62
No Record
13.85 18.45 19.78
11.67 6.83- 59.18
19.90 6.90* 36.07
No Record
.35 4.58 29.21
32
B E V
No Record
No Record
22.75 7.93 16.0
18.42 22.33 43.69
2.45 9.08 22.61
No Record
No Record
No Record
No Record
7.00 18.00 22.86
No Record
No Record
19.92 6.97* 35.81
16.08 17.00 26.67
.30 5.83 38.10

B
17.75
11.75
19.5
18.3
2.22
16.6
18.00
19.97
19.33
7.42
11.72
11.83
19.83
16.40
.58
33
E
7.38
1.00
. 7.67
21.58
6.5
19.08
. 88*
10.17
23.20
20.58
2.00
6.83*
7.00*
17.23
4.58

B
38.35
26.35
37.34
35.56
27.94
29.97
37.85
28.19
28.05
27.43
27.94
63.96
36.83
28.45
30.23

B


22.33
18.47
2.55
16.55
18.00
19.87
19.33
7.42
11.75
11.83
20.17
16.00
.53
34
E
No Record
No Record
7.6
22.42
4.93
19.33
.50*
8.58
22.90
19.08
1.42
7 . 00*
7.17*
17.22
4.33

V


13.97
35.36
26.42
41.66
37.34
28.96
49.53
27.18
29.21
60.20
37.08
31.50
32.00

B
17.67

22.25
18.5
2.47
16.58
18.17
19.93
19.25
7.33
11.25
10.50
19.75

.47
35
E
4.58
No Record
8.0
23.5
7.55
18.67
1 . 1 7*
9.42
22.97
21.17
1.37
5.67*
6.38*
No Record
6.33

V
29.89

37.85
37.59
25.15
40.64
36.32
35.31
60.68
28.7
31.5
67.51
50.80

42.16

B

11.17
22.5
18.58

16.58
18.17
19.98
19.30
7.33
11.25
10.73
19.75

.83
36
E
No Record
20.67
8.0 .
23.0
No Record
18.42
.67*
9.25
23.03
20.83
2.00
5.57*
6.38*
No Record
5.67

V

30.48
27.18
40.64

39.37
36.31
35.56
60.28 ^
28.7 to
Ul
31.24
60.15
45.72

39.12
* = next day. B = beginning time (military time in decimal hours), E = ending lime, V = volume in mm of depth

-------
                          7.26
Table 7.3.  Statistics of Fifteen Large Rainfall Storms

Date
04-17-76
04-20-76
05-28-76
06-13-76
07-28-76
07-28-77
08-15-77
08-27-77
09-17-77
10-07-77
05-05-78
04-17-78
05-12-78
05-27-78
06-20-78
// of
gages
2
2
6
6
5
4
5
5
5
5
5
5
6
3
6

Mean
12.50
11.63
10.31
4.08
4.74
2.30
6.67
12.86
3.74
12.63
13.67
19.07
10.99
.99
4.71
Mean
8.72
Duration
Std. dev.
•
2.24
3.01
1.38
.58
1.57
.42
.25
1.36
.11
1.23
1.29
.15
.18
1.01
.85
Std. dev.
5.19
(hr)
Range
10.91-14.08
9.50-13.75
9.18-12.17
3.28- 5.00
2.38- 6.63
1.84- 2.78
6.50- 7.00
10.61-14.20
3.57- 3.87
11.00-13.84
11.45-14.75
18.84-19.17
10.63-11.17
.83- 1.22
3.80-5.87

Mean
1.34
1.12
1.01
1.59
1.07
1.49
1.54
1.18
1.84
1.06
1.13
2.45
1.59
1.14
1.38
Mean
1.40
Rainfall
Std. dev.
.24
.11
.406
.178
.160
.212
.190
.232
.585
.095
.135
.137
.249
.096
.211
Std. dev.
.382
(in.)
Range
1.18-1.50
1.04-1.20
.55-1.49
1.40-1.86
.89-1.32
1.18-1.64
1.43-1.88
.84-1.40
1.10-2.30
.90-1.13
.91-1.24
2.33-2.66
1.41-2.00
1.05-1-24
1.15-1.66

-------
                         7.27
0    O.I    0.2   0.3   0.4   0.5   0.6   0.7   0.8   0.9    1.0
           ACCUMULATED  TIME,  dimensionless
 Figure 7.13.  Dimensionless mass  accumulation curve for
              rainfall event of 5/28/76.

-------
                        7.28
1 .U

0.9
U)
t»
° S7 ^0gA ' D ' **
O

j» ^7 ^
0 ^7 ^

. ^ <§-^* ^J^
^* fjT
	 ^k n
— \Qr$9 *
^7 ^^ * • ^ -n a
g * A «?
o ^
0 S? «^ D
O _ •* D
°2> D|=I
C57 o ^a w Rain Gauge
O ^o
• 3I
A7 ^ /\ 32
_ A
-o /vd a 33
/^ ^s^—^
o o 34
- «A 0 35
/*_
.^ ^36

a .....,,,.
0   O.I   0.2   0.3  0.4  0.5   0.6   0.7  0.8  0.9
         ACCUMMULATED  TIME,  dimensionless
                                                         .0
Figure  7.14.  Dimensionless mass accumulation for
             rainfall event of 6/13/76.

-------
                        7.29




CO

^
Z)
o
o
<



1 .w

0.9


0.8


0.7
0.6

0.5

0.4


0.3

0.2


O.I

n
1 1 1 1 1 1 1 i 1 /vQ]
o ^P
• 05^0 °
•A ^^
w\  O O 35
puX^
/^»"Vs ,-, -j/^
'JO " 36
(5^
So
iy"^ i I i i i i i t i
0   O.I   0.2   0.3  0.4   0.5   0.6  0.7   0.8   0.9
         ACCUMMULATED  TIME,  dimensionless
1.0
 Figure 7.15.  Dimensionless mass accumulation for
             rainfall event of 5/12/78.

-------
                        7.30
1 .U
0.9
imensionless
p o
->!' CO
-o
- 0.6
^ 0.5
a:
LU
3 0.3
o 0.2
o
**
O.I
n
^^/ A ft
<^ ^ oga *
<§ D
'Co^/ JO
o /£ IT
O • °
r^ f>P Rain Gauge
=^ i
.. cr
° ^b • 31
^7 O^b A 32
- »^ a 33
c?9 ° 34
-^oo^ O 35
^P o S7 36
^W^. i i i i t i i i
0   O.I   O.2   0.3   0.4  0.5   0.6   0.7  O.8
         ACCUMMULATED  TIME,  dimensionless
0.9
1.0
Figure 7.16.   Dimensionless mass accumulation for
              rainfall event of 6/20/78.

-------
                               7.31
   30 ••
E
o


"o  20--
0)
o
l_
O)
Q.
    10--
         0-25
0-75
1-25
1-75
2-25
2-75
             0-50      1-00      1-50     2-00      2-50

                   Rainfall  Volume , inches of depth
 Figure 7.17.  Distribution of rainfall volumes by depth classes.

-------
                                 7.32
    40--
    30--
 £
 L-
 o
    20
o>
Q.
    10--
          2-5
7-5
12-5
17-5
22-5
               5-0       10-0      15-0      20-0     25-0


                        Duration, hours
  Figure 7.18.  Distribution of  rainfall durations by hour classes.

-------
                                      7.33
duration are skewed towards zero or smaller durations and  amounts.   These two
distributions are independent and a short duration  storm may  produce a large
rainfall volume.
     In general the rainfall data are fairly complete.  Problems  do  arise when
gages malfunction and only partial coverage results.  However,  the close
correlation for daily volumes and similar storm patterns suggest  that synthe-
sized data may be used to fill gaps.  Not much can  be said about  snowfall data
except that daily volumes appear adequate at this time.
     Other climatic data of temperature, wind, humidity, and  pan  evaporation
appear realistic and reasonable.  Unfortunately, solar radiation  does not.
Several times the reported langleys per day were well over 1000,  such as
6/13/77 (3047), 3/30/78 (2086), and 4/25/78 (2657).  As a  comparison the maxi-
mum solar radiation at the top of the atmosphere for the latitude of Four-Mile
Creek is about 1000 (Eagleson, 1970).  Therefore, the several values above
that level are suspect if not completely false.  For water balance modeling
more care is needed in solar radiation collection.  The other data listed in
Table 7.1 are specific types and must be measured as needed.

     7.3.4  Hydrologic and Hydraulic Data
     Whereas climatic data include the inputs to models, these data  include
the output against which models are checked or calibrated.  Of particular
interest are the daily and storm hydrographs, how they are measured, and
sedimentation characteristics.
     There are not enough gaging stations in the watershed to conduct an
extensive correlation analysis of the flow.  Daily  discharges and storm runoff
must be examined.  Simple analysis of the daily discharge  values  at  the three
U.S. Geological Survey gaging sites (numbers 4, 5,  and 6 in Figure 7.1)  help
define discharge characteristics of the watershed.  A large portion  of the
volume of runoff occurs during the winter snowmelt  and spring rainfall months
as indicated by Figure 7.19 for Four-Mile Creek near Traer, the basin outlet.
It is interesting to note that the last few years were relatively dry,  as evi-
denced by lower flows; indicating that recent efforts may  be  during  a non-
typical runoff regime and not representative of a wide spectrum of conditions.
Comparison of average daily discharges for all three stations (a  measure of
water yield) shows there is significant watershed runoff contribution in the
lower portion of the watershed (Figure 7.20), as would be  expected.   This is

-------
   5r
   4



•£'  3
o
§  2
o:
   0
   62    63    64    65    66    67    68    69
                                                                                                            OJ
 70

Year
71    72    73    74    75    76    77    78
                  Figure 7.19.  Four-Mile Creek near Traer, Iowa monthly runoff in inches.

-------
                                 7.35
30r
                        Line of Perfect
                        Agreement
                         10          15          20
                   Average  Daily  Discharge  at  Traer, cfs
         Figure 7.20.
Comparison of upstream contributions
to downstream flows.

-------
                                      7.36

consistent with other  watersheds.   Peak  discharge  records  are  affected by many
factors including overland flow  contributions,  channel  flow  resistance,  and
the reliability of  the gaging station.   Original graphical comparisons of peak
discharges for the  upstream Lincoln and  downstream Traer sites based on U.S.
Geological Survey gaging  records indicated  some discrepancies.  In particular
the Lincoln peaks were greater for  six of eleven discharges.   Although this
difference may have been  a result of attenuation of intense, short duration
storms, it actually was gaging errors that  were corrected  in the 1977-1978
annual report.
     Figure 7.21 shows the relationship  between the corrected  yearly instan-
taneous peaks at Traer and at Lincoln.   Of  the  eleven events,  four did not
occur on the same day  and one was higher at Lincoln than at Traer  (1963).   In
this case, attenuation of the flood peak or its location may have  caused the
lower downstream discharge.   Graphical analysis helped  pinpoint the fact that
there were mistakes in the peak  discharge records.   Whenever a graphical ana-
lysis shows a trend or relationship that appears different than expected,  the
records should be rechecked.
     The interrelationship of daily flow at Lincoln and Traer  and  the rela-
tionship between stations were checked for  an  "average" water  year based on
the Traer gage.  An average  year is defined here as one in which the annual
mean daily flow is  nearly the same  as the long  term mean daily flow.   As of
the end of the water year (WY) 1977 (October  1  to  September  30), the long term
14 year mean daily  flow was  11 cfs. Water  year 1972 almost matched that with
a 11.1 cfs mean daily  flow and consequently was chosen  for analysis.   A more
complete analysis would require  encoding all data  for Lincoln,  Gladbrook,  and
Traer; a task that was beyond the scope  fo  this project.   However,  this  analy-
sis using WY 1972 can  be  extended if the data obtained  in  a reasonable format.
Figures 7.22 and 7.23  show the autocorrelation  plots or correlograms for
Lincoln and Traer with a  maximum 14 daily lags  (two weeks).  There is a  simi-
larity in shape.  Of particular  interest is the sharp drop in  correlation  be-
tween zero lag and  lag 1  (same day  and previous day).   This  indicates there is
only a moderate relationship  between daily  flow values  due to  large watershed
precipitation variability,  irrigation diversion and return flows.   In a  large
system such as the  lower  Mississippi River, changes occur  more slowly so the
correlation at lag  1 is expected to be higher.  Another interesting obser-
vation is the rise  in  correlation at lag 6  (six days).  This may be particular

-------
                               7.37
   1400
   1200
 . 1000
0)
o
.c
o
»  800
o
0)
CL
O)
o
   600
   400
   200
                                            1974
Line of Perfect
Agreement
      0
                                *  Signifies  that Discharges were

                                   not on the Same Day
       0     200     400     600    800    1000    1200


                      Lincoln, Peak Discharge, cfs
                                   1400
            Figure  7.21.  Comparison of peak discharges at

                         downstream Traer and upstream
                         Lincoln gages.

-------
to
0>


o   1-0'

o


5   09 +
=  O-8-f
 o
Q

H-  0-7
g 0'6 +
'o

it 0-5-

o
0 04-
c
o
   0-2
 0)

 w
 o
 o

    0-
                                                                                                  OJ
                                                                                                  03
                                                     cr	:	95% limit
                                   6    78   9    10   II

                                    Lag , days
                                                              12   13   14
      Figure 7.22.   Autocorrelation for Four-Mile  Creek near Lincoln,

                    WY 1972 daily discharges.

-------
0>
o>
                                                                                                  00
                                                                                                  VO
                                    6789

                                      LAG,  days
10  II    12  13   14
        Figure 7.23.  Autocorrelation  for  Four-Mile  Creek  near  Traer,
                      WY  1972 daily discharges.

-------
                                      7.40
to WY  1972 but may also  indicate  some physical process  such  as  ground water
effluent flow.  Another  cause  for this  relationship  is  the correlation of  the
flows  at the beginning and  end of storm hydrographs.  This analysis  shows  that
daily  flows may not be the  best method  for  characterizing system response
because they cannot be correlated well  enough with previous  records,  i.e.,
     •
information may be lost.  Cross-correlations have similar results (Figure
7.24)  with the zero lag  being  quite  high and lag  1 dropping  appreciably.   This
analysis shows that the  use of daily flow to characterize discharge  is a
choice that may lead  to  problems.  Correlation at lag 6 increases similar  to
the autocorrelation and  this is due  to  the  carryover effect  of  the large auto-
correlation at this lag  for each  gage.
     The cross-correlation  of  the Traer and Lincoln  gages with  a gage outside
of the Four-Mile watershed  was next  assessed.  This  was done to assess the
degree of correlation of  the causal  factors for streamflow and  also  to be  able
to transfer data in case  the need arose.  The Hudson stream  gage on  Blackhawk
Creek  was selected for this correlation.  The gage monitors  303 sq.  mi. and is
located twenty miles  northeast of the Lincoln gage.  The lag zero cross-
correlation coefficient  for monthly  data is 0.937 and 0.902  for the
Hudson-Lincoln and Hudson-Traer gages respectively.  This high  interwatershed
correlation indicates that  the causal processes for runoff are  fairly uniform
over this area.
     Interpolation of the correlograms  indicates a time lag  of  about one hour
at the 0.8 correlation level.  This  coincides with time of travel estimates
for the channel based on  historic flood records, typical channel cross sec-
tions  (a  and  b  parameters), channel  slope, and Manning's   n   value. The
equation used to determine  time of travel was:

          V = a1 Q 1

where  V  is average  velocity,  Q is discharge, and  a  and  b.  are parame-
ters estimated from channel characteristics.  This equation  was derived from
Manning's formula.  Several flood discharges were used  to estimate travel
times.  These discharges  roughly  correspond to 2, 5, 10, 25,  50,  and 100 year
return period flows (based  on  short  records).  The parameters used were slope
of 0.0014, Manning's  n   of 0.04,  average   a   value (from wetted perimeter-
flow area relationship)  of  5.9, and  average b   value  of 0.38.   The  time  of

-------
                                                                  13
                                Lag   K.,  days
Figure 7.24.  Cross-correlation between Four-Mile Creek near Lincoln and near Traer,
              WY 1972 daily discharges.

-------
                                      7.42

travel for the  3.41 miles  between Lincoln and Traer  for a 2 year return period
discharge of 400  cfs  is  about  1.6 hours  while the  100  year peak of 2,000 cfs
requires only one hour.  These  values  are comparable with the lag times
required to yield a high cross  correlation as seen in  Figure 7.24.
Computations show that a one hour,  or  preferably shorter, sampling interval is
                              •
needed to correspond  to  the movement of  the flood  wave.  Because flooding is
not a major concern of the watershed data collection system, such a require-
ment may be excessive.   However,  the above analyses  do show there may be a
need for re-evaluating the sampling interval at  these  stations.
     Similar comparisons of peaks can  be made for  ISU  1 and ISU 8.  These two
watersheds were chosen because  ISU  1 lies inside ISU 8 and records exist for
both.  In addition, raingage 33 which  represents conditions in both areas is
considered as a key gage site  from which other analyses can be conducted.
Figure 7.25 shows a plot of peak  discharge per unit  area at ISU 1 and 8 for
eight events.  As this figure  indicates, there is  some consistency between the
peaks at each of the  stations.  However, it also suggests that at this
watershed scale, there is  a certain degree of "noise"  or natural variability
in rainfall and runoff that creates the  scatter  seen in this figure.  Figure
7.26 shows a comparison  of time to  peak  runoff from  the beginning of rainfall
for the same eight storms.  Although there is a  trend  towards closer values as
time to peak increases,  it appears, using Figure 7.25,  that these are not
associated with resistance effects  as  much as location of storm cells and
movement of the storm.   For example, events 7 and  8  had similar magnitudes of
peak discharge for ISU 1,  but  almost an  order of magnitude difference for
ISU 8.  This would indicate that  these runoff events may be heavily controlled
by the spatial distribution of  the  rainfall.   Inspection of the rainfall
record confirms this  suspicion  as event  7 was only 43  minutes in duration
while event 8 lasted  four  hours.  This would suggest that event 7 may be a
more 'localized, high-intensity short duration event, whereas event 8 may be
more uniform in nature.  Such  comparisons help in  modeling to determine when
certain assumptions,  such  as homogeneity of rainfall,  are invalid.
     In addition to discharge,  there is  available  information for a brief ana-
lysis of sediment data.  Figure 7.27 shows the variation of bed material with
distance along the stream.  For the coarse fraction  larger than 62 microns,
there is no trend along  the channel indicating the material has not been
sorted by stream action.   These coarse sizes indicate  that sediment sampling

-------
                                     7.43
     lOOOr
   
-------
     1000
   c

   1


00  O
 I  0>
Z)  0-
CO  o
H  *-
00
        0
                                     Line of Perfect Agreement
                                      7
                                      e
                       I    I   I  I  I I  I
                                             I   I   I  I  I  I I I
                                     10        ISU-I             100
                                         Time to Peak,  min
                                                                                   I   I  I  I  I I I
                                                                                      1000
                Figure 7.26.  Comparison of time to peak discharge for ISU 1 and  ISU 8.

-------
QJ
                                   6543
                                    Distance  From Outlet (miles)
             Figure 7.27.  Changes in bed material  size  along main channel.

-------
                                      7.46

devices  may  be  needed to collect sand size particles*   This graph also shows
that  a significant  portion of sediment is composed of  fines (less than 0.62 mm
in diameter)  as might be expected for the loessial soils.   Buried, vertical
channel  chains  and  field sediment discs are efficient  ways of checking the
aggradation  and degradation at certain locations.   Field discs are flat pieces
                                                                               •
of plastic that are placed in the field to detemrine the amount of aggradation
in an area.   For the field discs, sieve samples have only shown that most of
the deposited sediments  are silt size and smaller.   However,  sieving will
determine when  larger particles move  and are deposited.   A better
understanding of field sediment processes will  be  provided by continuation of
sieve samples.   Likewise,  the chain surveys and sieve  analyses are useful for
determining  channel transport and aggradation and  degradation.  Use and
testing  of the  sedigraph 5000 for measuring concentrations of fines should be
continued because it appears to be an acceptable method.
      A rating curve of sediment transport rate  versus  water discharge is some-
times developed to  help  in determining sediment outflow.   Figures 7.28 and
7.29  show rating curves  for ISU 1 and the entire watershed.   The relationship
is scattered  up to  some  threshold discharge after  which  there is a rise in
sediment outflow with increasing discharge.  Although  there is a very strong
linear trend  for the higher discharges at ISU 1 (Figure  7.28), there is much
more  randomness at  Traer.   As the data base improves,  more information may
substantiate  these  preliminary relationships.   However,  there is a complex
relationship  between the transport capacity of  the  discharge  and the sediment
supply that must be better understood if the watershed is  to  be properly
modeled.  Such  relationships cannot be adequately  explained by a simple sedi-
ment  transport  rate-water  discharge relationship.
      One other  important aspect of the  hydrologic measurements in the
watershed is  the rating  curves used for converting  stage  readings to
discharge.  Each of the  U.S.  Geological Survey  stations  is a  meter rated sec-
tion.  The ISU  watersheds  1,  2,  and 3 have  four foot H flumes and watersheds 7
and 8 have rated culverts.   For comparison,  the rating curves for each of
these devices was converted to an equation  of the  form
          Q = a Sb
as discussed  in an  earlier section.   Here  S is either  the actual stage or it
has been adjusted by a constant value so that   Q =  0   when S = 0.   This con-

-------
o
cu
   140-



   130-



   120



   I 10+
 - 100+
Q)
CT

o  90+
-C
o
w

5  8
g   7° +
"S   60+
CO

•o   50+
O)
TJ

S   40--
Q.


    30--



    20 •



    I 0--
CO
                                                   10
                                                                     14
                                      Water Discharge, cfs
16
18
20
            Figure 7.28.   Suspended sediment discharge and water discharge at  ISU  1.

-------
o
0)
to
Q)
C7>
140-



130-



120



110



100
_£   90
o
CO

5   80


^
«   70



"   60
C/)
o>   so-
c
0)
 13
O)
    SO



    20



    lOt
                                                                                                        -j


                                                                                                        oo
              ^-
          10   20  30   40  50  60  70  80  90   100  110  120  130  140  150  160  170  180  190  200

                                      Water Discharge (cfs)
           Figure 7-. 29.  Suspended sediment discharge and water discharge at Four-Mile

                         Creek near Traer.

-------
                                      7.49
version makes comparisons of  a  and  b  parameters meaningful.   All of the
points in the published rating curves were  not  used in  this  analysis, only
selected points that help define the relationship.  Figures  7.30,  7.31, and
7.32 show examples of these curves.  The lines  shown  are  for definition only
and are not computed from the equations.  The listed  parameters  should not be
used to compute discharge from stage readings.   Instead,  the parameters in
Table 7.4 show the relative magnitude of the coefficient  and,  more signifi-
cantly, the power  b  parameters.
     As previously discussed, the larger the  b value, the  more sensitive the
computed discharge is to the change in stage.   This will  be  beneficial if low
flows with minor head changes are being gaged.   However,  such benefits can be
minimized if small errors in gage measurements  produce  significantly large
errors in computed discharges.  It is interesting to  note that the ISCJ 8 gage
with a power of  b  of about 1.02 is the least  sensitive  and almost linear.
     In general, the discharge and sediment information is acceptable for
testing the model.  However, there are some problems  with regard to the timing
of measurements for short-term events that  should be  resolved.

     7.3.6  Nutrients and Herbicides-Pesticides
     Nutrient (i.e., fertilizers) and herbicide-pesticide data are not grouped
separately in Table 7.2.  The general types of  data available for  these man-
introduced chemicals are concentration measurements in  the on-site soils and
in the runoff and in the water transported  sediments.   This  information is
collected to show the sources and downstream occurrence of chemicals in the
hydrologic cycle.

     7.3.6.1  Nutrients
     On-site soil samples were taken from selected depths at different sites
in the field size watersheds.  These samples were collected  at various times
during the year.  Combinations of these data illustrate a sequential change in
concentration with time and depth at a site as  previously shown.  Samples are
analyzed for NH -N, NO -N, PO -P, EXT N, available P, and water  content.
Unfortunately, there are no corresponding pH measurements, important infor-
mation when modeling chemical reactions and transport.  Nutrient outflows at
the stream gaging sites and tile drains are measured  to indicate the amounts
lost to hydrologic processes.  These data are presented in a site,  Julian day,

-------
13-0-
12-0-
 1-0-
C- 10-0-
«4—


-------
Ol
CT
O
  4-0-
  3-0-
  2-0-
   i-o-
             10       20       30       40       50       60
                                           Discharge  (cfs)
70       80       90       100
               Figure 7.31.  Stage-discharge relationship for 4-foot H flumes.

-------
                                                                                              -J
                                                                                              Ui
           100     200     300      400     500     600

                                       Discharge (cfs)
700
800
900
Figure 7.32.   Stage-discharge relationship for Four-Mile Creek near Lincoln.

-------
                                7.53
Table 7.4.  Comparative Rating Curve Parameters Based on Selected
            Values from the Four-Mile Creek Watershed
b
Preliminary parameters in Q = a S
Location
ISU 1,2,3
Traer
Lincoln
Gladbrook
ISU 7
ISU 8
Device
4-ft H flume
Rated Section
Rated Section
Rated Section
Box Culvert
Headwall and
a
6.08
6.78
10.51
14.51
21.19
69.39
b Remarks
2.06
2.50 Stage reduced by 6 ft
2.00 Stage reduced by 5.5 ft
2.00 Stage reduced by 3 ft
1.60
1.02
     Culvert

-------
                                      7.54

and time  format.  They also include  NH  -N,  NO  -N,  PO  -P,  TDS,  TDS plus sedi-
ment, and chloride measurements  in ppm.   These data are  useful in showing the
temporal  and spatial  variations  in surface  and ground water  water quality.
However,  it lacks a key element  in that the flow rate at the time the water is
sampled is not  specified.   Without this information it is difficult to
determine concentration changes  affected by flow changes and total yields of
the chemical being measured.  There  are some monthly  flow concentration data
available as shown in Figure  7.33.~  However, such  information  only shows
general responses and is not  sufficiently detailed for use in  modeling.

     7.3.6.2  Herbicides-Pesticides
     Herbicides were  measured similarly to  the nutrients.  Five herbicides
were used and sampled in soils and water.   These were (by their common (trade)
names):  Alachlor (Lasso),  Cyanazine (Blandex),  Metribuzin (Sencor/Lexane),
Paraquat  (Ortho Paraquat),  and Propachlor (Ramrod).   The solubilities of these
herbicides ranges from 171  to 1220 mg/1  at  20°C, except  for  Paraquat which
readily attaches to positive  ions  in the soil.   Paraquat is  seldom detected in
water, unlike the other herbicides that are associated with  water and sedi-
ment.  Like the nutrient samples,  soil  concentrations are measured at several
sites and depths at various times.   Likewise,  water outflow  at sites 1, 2,  and
8 are sampled.  Again,  there  is  no corresponding discharge data presented with
the concentration data.   However,  the 1976-1977  Annual Report  did present
limited data for one  event, that of  6/13/76, for sites 1  and 2.  Figures 7.34,
7.35 and 7.36 show the  variablity  in flow and  concentrations from site 1.
This type of data is  extremely valuable  in  modeling.   Although data sets for
some events may be obtained piecemeal from  various data  sections,  these sets
should be self-contained in the  pesticide section.  In general, the herbicide-
pesticide information lacks detail for  model application.  As  indicated above,
there is some ambiguity with  the runoff  rate and sampled concentration.  This
information, particularly for event-based models,  is  necessary.  The frequency
of soil sampling and  water  chemistry analyses  should  be  better assimilated  to
show the relationship between the  two and to check consistency.  Another
missing item is measurements  of  NH -N and PO -P  attached to  the transported
sediment.  This information helps  pinpoint  a key source  of loss for these che-
micals.  Finally, the loss  of chemicals  from the soil is  a function of tem-
perature and pH, both of which are missing  from the soil  sample data.

-------
                        7.55 .
                                        D P04-P
                                        O N03-N
                                        A NH4-N
   Jan Feb Mar  Apr  May Jun  Jul Aug  Sep Oct  Nov Dec
Figure  7.33.  Four-Mile Creek near  Traer, monthly  yields
             of selected chemicals.

-------
u


o
o
Q
1_

-------
    I80h
    160 -
    140-
E
Q.
Q.
•d   120
0)
§   100
CT
O

O
Q.

     80
     60
     40
      1800
                                                                          ^i
                                                                          Ln
      1900
2000
2100
                                     Time ,   hrs
           Figure 7.35.
ISU 1, Paraquat concentration in sediment from rainfall storm

runoff of 6/13/76.

-------
o
    0.08
   0.07 -
   0.06 -
    0.05
   0.04
o

5   0.03
    0.02
    0.01
       0
       1800
1900
2000
                                                                    Ui
                                                                    00
2100
                                          Time ,  hrs
             Figure  7.36.  ISU 1, Sencor concentration in water from rainfall storm

                          runoff of 6/13/76.

-------
                                     7.59
7.4  References

Simons, D.B., R.M. Li, and T.J. Ward, 1978, "Methods for Estimating  Parameters
     that Describe Channel Geometry," prepared for U.S. Forest Service, Rocky
     Mountain Forest and Range Experiment Station, Flagstaff, Arizona.

Johnson, H..P., 1977, "Development and Testing of Mathematical Models as
     Management Tools for Agricultural Nonpoint Source Pollutants,"  Annual
     Report 1976-1977, Department of Agricultural Engineering, Iowa  State
     University, Ames.

Johnson, H.P., 1978, "Development and Testing of Mathematical Models as
     Management Tools for Agricultural Nonpoint Source Pollutants,"  Annual
     Report 1977-1978, Department of Agricultural Engineering, Iowa  State
     University, Ames.

-------
                                      8.1

VIII.  CASE STUDY II:  APPLICATION OF A PHYSICAL PROCESS MODEL
8.1  General
     An important aspect of data network evaluation requires use of physical
process models.  Since the core of the previously discussed primary model is
rainfall-runoff simulation, this part is" selected for example application.
The processes that simulate the production of sediment and nonpoint source
pollutants are dependent on the results of the rainfall and runoff.  In order
for the former to provide reasonable results, the routing model must provide
realistic results.
     This evaluation uses the multiple watershed rainfall-runoff simulation
model (MULTSED) (Li, et al., 1979) to help analyze the data collection system
at Four-Mile Creek.  MULTSED is used in three areas.  First, a comparison is
made of recorded and simulated hydrographs obtained from the available data to
determine the adequacy of the data collected.  Simulations are carried out on
two sizes of watershed within Four-Mile Creek,, small (ISU 1) and medium (ISU
8) sized subwatersheds with areas of 18.83 acres and 369.6 acres, respec-
tively.  Next, the model is tested for sensitivity to the various input para-
meters to determine the quality of the data being collected, to reduce the
errors in the simulation results, and to help with the calibration of the
model.  Finally, the creation of hydrographs utilizing the model for storms of
specified duration and return periods (not available from recorded data) are
then used in the spatial and temporal analysis of the system.

8.2  Data Needs
     The physical process model MULTSED requires data that represents the phe-
nomena being simulated.  To entirely model the processes would be impractical
due to the immense amount of data required and the resulting complexity of the
model.  Simplifying assumptions must be made to make the model manageable.
Details of the model are presented in Li, et al. (1979) or Simons, et al.
(1979).  The physical processes modeled are interception, infiltration,
overland flow, channel flow, erosion, sediment transport, aggradation and
degradation.  With the model formulated in this manner, the data needs are
specified as listed in Table 8.1.

8.3  Available Data and Gaps
     From the annual reports and several supplemental sources, such as the

-------
                                       8.2
                 Table 8.1.  Input Data for MULTSED Program
  I.  Geometry
      1.  Number of subdivision
      2.  Slope, length, and area for each plane and subwatershed unit
      3.  Slope and length for channel units
      4.  Relationships of:  a) wetted perimeter vs. cross-sectional area,
          and b) top width vs. cross-sectional area for each of the channel
          units

 II.  Soil Characteristics
      1.  Effective hydraulic conductivity
      2.  Porosity
      3.  Initial and final soil moisture
      4.  Average suction head
      5.  Temperature
      6.  Rilling ratio
      7.  Sediment size distribution
      8.  Plastic index

III.  Vegetative Cover
      1.  Density
          a.  Percent canopy cover
          b.  Percent ground cover
      2.  Cover storage
          a.  Canopy cover
          b.  Ground cover

 IV.  Rainfall Data
      1.  Rainfall hyetographs that are spatially consistent over each
          subdivision

  V.  Overland Flow and Channel Flow Data
      1.  Duration of hydrograph
      2.  Time increment used for the calculation of the hydrograph

 VI.  Erosion Data
      1.  Overland flow detachment coefficient
      2.  Channel flow detachment coefficient
      3.  Detachment coefficient for rain drop impact

-------
                                       8.3

U.S. Geological Survey topographic maps and U.S. Weather Service records, most
of the data needs listed in Table 8.1 are satisfied.  Data gaps that exist are
listed in Table 8.2.
     Some data can be estimated by calibration.  This is accomplished by
realistically varying the parameter in question until the simulated
hydrographs are similar to the recorded hydrographs.  Missing 'data for soil
     'p
characteristics and resistance parameters are supplemented by this method.
The technique requires detailed recorded hydrographs which are available for
the small and medimum sized watersheds, but not for the entire watershed.
Therefore, the parameters calibrated in the two smaller watersheds were
extended to cover the entire watershed.  The validity of this procedure cannot
be tested due to the absence of detailed, recorded hydrographs.  However, the
parameters calibrated for ISU 1 were used directly for ISU 8 as a check.

8.4  Model Application and Results Using Collected Data
     8.4.1  General
     The watershed must be divided into subwatershed units, plane units, and
channel units.  A schematic map of the Four-Mile Creek watershed is presented
in Figure 8.1.  The simplified geometry data are presented in Table 8.3.

     8.4.2  Small Watershed Simulation
     The small watershed selected was ISU 1 with an area of 13.83 acres.  This
site was picked because of a recording raingage location near it, available
vegetative cover data, and a recording discharge measurement device located on
its outlet.  Representative storms during 1977 and 1978 which produced
measurable runoff were chosen for simulation.  The storms and their respective
rainfall depths and durations are listed in Table 8.4.
     The soil parameters were adjusted in an attempt to match the recorded
hydrographs.  The results are listed in Table 8.5.  Several of the events did
not model well because of minimal runoff.  It was difficult to calibrate the
model using these events and still produce reasonable agreement with the
larger events.  Because the larger events are usually more significant in
terms of water runoff, sediment,  and nutrient losses, they were used for para-
meter calibration.

-------
                                       8.4


                Table 8.2.  Data Gaps Identified for MULTSED
  I.  Geometry
      1.  No gaps, good quality

 II.  Soil Characteristics
      1.  Effective hydraulic conductivity
      2.  Porosity
      3.  Initial and final soil moisture
      4.  Average suction head

III.  Vegetative Cover
      1.  Data are present, but are not given for the entire watershed,
          therefore, extrapolation methods must be utilized.

 IV.  Rainfall Data
      1.  No gaps

  V.  Overland Flow and Channel Flow Data
      1.  Resistance for channel units
      2.  Resistance to flow for overland units

 VI.  Erosion Data
      1.  Parameters may be estimated.

-------
                                                     	 Boundaries between Units
                                                     	Main Channels
                                                     	Subwatershed Channels
WS - Subwatershed
PL - Plane
CH - Channel
                                                                                                  oo
                                                                                                  01
     Figure 8.1.  Four-Mile  Creek  map showing subdivisions for modeling.

-------
                          8.6
Table 8.3.  Watershed Geometry for Four-Mile Creek
Unit
WS-1L
WS-1CH
WS-1R
WS-2L
WS-2CH
WS-2R
WS-3L
WS-3CH
WS-3R
WS-4L
WS-4CH
WS-4R
WS-5L
WS-5CH
WS-5R
WS-6L
WS-6CH
WS-6R
WS-7L
WS-7CH
WS-7R
PL-1
CH-10
PL- 2
PL-3
CH-9
PL-4
PL- 5
CH-8
PL- 6
PL- 7
CH-6
PL-8
CH-5
PL- 9
CH-4
PL- 10
PL- 11
CH-2
PL- 12
PL- 13
CH-1
PL- 14
PL- 15
CH-7
Length
(feet)
6200
6200
6200
7200
7200
7200
11000
11000
11000
13000
13000
13000
3000
3000
3000
9000
9000
9000
7400
7400
7400
12500
12500
12500
6267
6267
6267
4133
4133
4133
7066
7066
7066
7066
5400
5400
5400
4800
4800
4800
7400
7400
7400
2933
2933
Width
(feet)
3131

1890
1768

2869
1611

3508
3553

1388
2645

2282
1199

1781
3184

1970
2961

2294
1395

1626
2056

4970
2890

1887

1335

3677
2769

3406
2253

4523
1318

Slope
.0147
.00629
.0123
.0162
.00542
.0170
.0278
.00691
.0253
.0266
.00623
.0277
.0330
.0183
.0326
.0455
.0122
.0440
.0355
.0115
.0381
.0322
.00264
.0239
.0412
.00303
.0316
.0367
.00218
.0242
.0388
.00170
.0431
.0017
.0573
.00148
.0488
.0534
.00146
.0454
.0653
.00135
.0495
.0557
.0443
Area
(acres)
446

269
292

474
407

886
1061

414
182

157
248

368
541

335
850

658
201

234
195

472
469

306

166

456
305

375
383

768
89


-------
                          8.7
Table 8.3.  Watershed Geometry for Four-Mile Creek
            (continued)

Unit
PL- 16
PL- 17
CH-3
PL- 18
ISU-Site 1L
ISU-Site 1CH
ISU-Site 1R
Abbreviations :
PL - Plane
CH - Channel
Length Width
(feet) (feet)
2933 948
3467 1034
3467
3467 1580
574.50 494.21
574.50
574.50 554.50



Area ,
Slope (acres)
.0400 m 64
.0652 * 82
.0433
.0488 126
.0453 6.52
.0174
.0456 7.31



WS - Subwatershed
L - Left
R - Right





-------
                      8.8
Table 8.4.  Selected Storms for Simulation
Date
August 15, 1977
September 17, 1977
April 17, 1978
May 12, 1978
May 27, 1978
June 20, 1978
Depth ( inches )
1.48
1.10
2.56
1.43
1.12
1.19
Duration (minutes)
413
232
1390
670
50
240

-------
                                8.9
Table 8.5.  Comparison of Simulated and Recorded Hydrographs for
            the Small Watershed
Peak Discharge (cfs)
Date
8/15/77
9/17/77
4/17/78
5/12/78
5/27/78
6/20/78
Recorded Sim.
10.1
.34
.31
10.1
.39
1.4
Volume (acre-ft)
Recorded Sim.
.22 .36
.01 .09
.06 .10
Negligible recorded runoff - no
2.01
2.15
7.06
1.67
.05 .25
.16 .14
Time to Peak (min)
Recorded Sim.
20:28 22:30
20:06 20:24
23:15 23:20
simulated runoff
16:49 16:48
9:12 1:14

-------
                                       8.10

     8.4.3  Medium Watershed  Simulation
     The medium sized  watershed  selected was  ISO 8 with a planimetered  area of
369.6 acres.   (ISU annual  report states 749 hectares or 368.03 acres).   It was
chosen for the same reason as ISU 1.   In addition, ISU 1 lies within  its boun-
daries so that the parameters calibrated for  ISU 1 could be transferred.  No
calibration was done on the simulations for ISU 8; the paramters  from ISU 1
were directly applied.  The same events as those for ISU 1 were also  used.
The results were presented in Table 8.6.~  Again, events that cannot be  modeled
well are those with little runoff.  The amount of runoff being produced is
smaller than the resolution capability of the model, but for larger events the
results do show that the model can  simulate the rainfall-runoff response ade-
quately with the available and transferred data.

8.5  Use of the Model  for  Data Synthesis and Evaluation
     8.5.1  Time of Concentration Determination
     The time of concentration is an important characteristic when designing a
gaging system because  it provides insight into the watershed's response to a
given rainfall and helps determine at  which intervals readings should be
taken.  Rainfalls with specified return periods were calculated using a
regression method developed from information  in the U.S. Weather  Service
Technical Paper No. 40 (Hershfield, 1963).  The equation and results  are
listed in Table 8.7.
     In order to reach a time of concentration, it is expedient to assume a
constant rainfall excess.   Since interest is  in the time it takes for the
water to travel from the furthest point of the watershed to the outlet,  the
infiltration and interception model components for the time of concentration
simulations are not used.   To account  for infiltration and interception losses
the actual rainfall rate was  multiplied by a factor ranging from  0.1  to 0.4 to
account for losses.  The 0.1  factor is used for the one year storm and  the 0.4
factor was used for the 100 year storm.  The factors for storms with  return
periods between these  values  are calculated by linearly interpolating between
the one and 100 year volumes  according to the storm's actual volume.  For
example, if the one year actual  storm  has a volume of one inch and the  100
year storm has a volume of two inches, a 50 year storm with a rainfall  volume
of 1.5 inches will have a  factor of 0.25 to determine its excess.  The  results
of the runs of ISU 1 and ISU  8 are presented  in Table 8.8 and in  Figure 8.2.

-------
                                  8.11
Table 8.6.  Comparison of Simulated and Recorded Hydrographs for the
            Medium Sized Watershed
Peak Discharge (cfs)
Date
8/15/77
9/17/77
4/17/78
5/12/78
5/27/78
6/20/78
Recorded
51.40
23.60
14.50
0.98
108.40
18.84
Sim.
100.70
8.40
1.56
No runoff
95.28
17.23
Volume (acre-ft) Time to Peak (min)
Recorded
4.12
1.42
5.61
0.30
3.32
2.25
Sim.
8.43
2.10
1.28
No runoff
5.94
3.21
Recorded
22:38
20:32
23:24
4:07
16:55
1:55
Sim.
22:45
22:33
23:29
No Runoff
16:59
2:24

-------
                                      8.12
     Table 8.7.  Four-Mile  Creek Watershed Synthetic Rainfalls Using the
                 Regression Method Developed From  "TP-40"
Duration
{ hour )
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
6.0
9.0
12.0
24.0
Return period ( years )
1
1.01*
1.29
1.45
1.57
1.66
1.73
1.79
1.85
1.90
1.94
2.01
2.18
2.29
2.58
2
1.22
1.57
1.77
1.91
2.02
2.12
2.19
2.26
2.32
2.37
2.46
2.66
2.81
3.15
5
1.50
1.94
2.19
2.37
2.51
2.62
2.72
2.80
2.38
2.94
3.06
3.31
3.49
3.92
10
1.72
2.22
2.51
2.72
2.88
3.01
3.12
3.21
3.30
3.37
3.50
3.80
4.00
4.50
25
2.00
2.59
2.93
3.17
3.36
3.51
3.64
3.76
3.86
3.94
4.10
4.44
4.68
5.27
50
2.22
2.87
3.25
3.52
3.73
3.90
4.04
4.17
4.28
4.38
4.55
4.93
5.20
5.85
100
2.43
3.15
3.57
3.86
4.09
4.28
4.44
4.58
4.70
4.81
5.00
5.41
5.71
6.43
*Rainfall in inches

 PPT = 1.2870 + 0.453 UnY) + (0.4040 + 0.1360 UnY)) SLnT
 PPT = precipitation in inches
   Y = storm duration in hours
   T = return period in years

-------
                                 8.13
    Table 8.8.  Time of Concentration Results,  Four-Mile Creek
Return
Period
( year )
1SU 1
100
50
25
20
5
5
2
1
Duration
Duration
(min)

30
30
30
30
30
60
60
120
Rainfall
Intensity
(in/hr)

1.94
1.58
1.24
0.86
0.61
0.40
0.23
0.079
Time of
Concentration
(min)

16
18
20
24.
30
39
57
112
ISLJ 8
100
50
25
10
10
5
2
2
1
30
60
60
60
120
120
120
180
180
1.94
1.02
0.08
0.56
0.341
0.243
0.138
0.103
0.058
                                                            23
                                                            43
                                                            51
                                                            60
                                                            79
                                                            96
                                                           120
                                                           162
                                                           200

-------
                             8.14
   200 ro
   180-
                                         ISU  I
                                         ISU 8
              0.4      0.8       1.2       1.6
                 Rainfall Intensity  ,  ia/hr
2.0
Figure 8.2.   Simulated time of concentration for ISU 1 and ISU  8
             for different rainfall intensities.

-------
                                     8.15

Considering the entire Four-Mile Creek watershed, the rainfall intensities are
such that the time of concentration is never reached for any of the durations
or return periods.
     The simulated time of concentration for ISU 1 varies between 16 and 112
minutes and for ISU 8 between 28 and 200 minutes depending on the storm's
return period.  An estimate of the time it takes the watershed to completely
respond to a rainfall input is important.  Depending on the number of inter-
mediate points desired between the start of rainfall and the time of con-
centration an idea of the time interval and when discharge reading should be
taken is provided.

     8.5.2  Sensitivity Analysis
     A sensitivity analysis is necessary for two reason.  The analysis is
important in determining the quality of the various data needed in order to
keep errors within acceptable limits.  It is also a useful aid in the calibra-
tion process in that it gives the user an idea about how the simulated
hydrographs response to changes in the parameters being calibrated.
     The sensitivity analysis was carried out on the medium sized watershed
(ISU 8) for two storms.  The storms occurred on May 27, 1978 and on August 15,
1977.  These storms are used since they represent two distinct types of rain-
fall that occur at the site.  The first storm was of short duration, high
intensity and the second was of long duration, low intensity.
     In the analysis, the parameters required as input to the model are varied
one at a time at various percentages of their original values while leaving
all other parameters constant.  The results are graphed in Figures 8.3 and 8.4
for peak flows only.  Volume and duration are similarly affected.  Results
show that the most sensitive parameters are the soil characteristics and the
overland flow resistance which is governed by the percentage of ground cover
and the resistance factor.  This could be signficiant since these two areas
have little data collected for these parameters.  However, the calibration
process can fill in these gaps and still produce reasonable simulations as was
noted earlier.
     Similar sensitivity analysis was performed for sediment yield (Figures
8.5, 8.6).  Changes in parameters such as permeability (or hydraulic
conductivity)  and overland flow resistance are shown to exert considerable
influence on sediment yield as was the case for water yield.  This result is

-------
   200
0)

D>
   160
O


I  120
S   80
Q.
g,  40
c
o
j=
O

*.    0
c
0}
o
w
0)
a.  -40
   -80
              Ground
           -... Cover
                   \
    Overland Flow

    Resistance, Darcey

    Weisbach  Friction Factor   v

    (<  1% Change)
                                   Hydraulic

                                    Conductivity
                             1
               --•""  Initial  Saturation
               Rilling Ratio (Less than 1% Change
-100     -80     -60     -40     -20     0       20     40

                                Percent  Change  in Parameters
                                                                         60
                                                                                 80
100
                                                                                                     CD


                                                                                                     H
                                                                                                     CTi
  Figure 8.3.   Peak discharge sensitivity analysis for watershed ISU 8, storm of May 27, 1978.

-------
0)
o
Cfl
o
0)
Q.
a>
o>
c
o
.c
o
c
0)
o
k.
0)
Q.
   500 r
   400
   300
   200
100
  0
   -100
      -100
Hydraulic Conductivity        	
Suction Head
Initial Saturation
Rilling Ratio No Effect      —
Overland Flow  Resistance
(Coincides with Suction  Head —
on Positive  Side)  Darcey
Weisbach Friction Factor
'••...(
-------
3500r
3000-
                                     100 Year Storm

                                     D  Channel  5

                                     O  Channel  I
                                             100     120     140     160      180     200
                                           Time,  min.
00

H
03
    Figure 8.5.  Simulated hydrographs for 30 minute, 100 year storm.   (Time is  real time.)

-------
7000
6000
5000
in
>*-
o


0)
0>

o
-C
4000
SJ 3000
b



  2000




   1000
    0
                                                 100 Year Storm


                                                 D  Channel  5


                                                 O  Channel  I
                                                                                          00
     0      60     120     180    240    300     360     420    480     540    600

                                       Time, min.
    Figure 8.6.   Simulated hydrographs for 3 hour, 100 year storm.  (Time is real time.)

-------
                                      8.20

not surprising as the hydraulics of flow determines sediment transport,
however, it does further emphasizes the importance of accurate measures of
these parameters.  Figure 8.5 indicates effects of changes in parameters
largely related to overland flow on sediment yield.  Figure 8.6 displays a
similar sensitivity plot for channel patterns based on the same event.  The
channel sensitivity analysis indicates that considerable attention should be
given to these parameters since errors in their estimation can cause con-
siderable differences in estimates of sediment yield.  Since these parameters
are usually guided by calibration within physically reasonable bounds,
measured sediment yields and hydrographs or concentration records are
required.

     8.5.3  Correlation in Simulated Runs
     TO help assess the required spatial and temporal design for the water
discharge gaging stations in the entire watershed, correlations were deter-
mined as to how the discharge varies in space and time.  The available
discharge records along the main channel are such that they are inadequate in
providing the data necessary to make such correlations on a basis any finer
than hourly.  Since most of the events are less than a day in length, this
information is important.  Thus, in order to provide information for such
correlations, the runoff results from the 100-year storm for the entire
watershed were substituted for actual data.  These hydrographs are simulated
for the downstream end of the watershed (channel 1 in the simulation model)
and a point further upstream (channel 5 in the model).  These points
correspond to the U.S. Geological Survey gaging station at Traer and Lincoln,
respectively.  The hydrographs are presented in Figures 8.7 to 8.10.
     Autocorrelations and lagged cross-correlations were made for the
hydrographs.  The lag time was varied to determine how the discharge at dif-
ferent time intervals is correlated.  This was done to help assess the time
increment that would be most useful for taking readings.  For example, if
readings are taken at highly correlated time intervals, little information is
gained by each and excessive data are collected.  However, if readings are
recorded at intervals that have very low correlation, the data is too sparse.
Results are shown in Figures 8.11, 8.12, and 8.13.  Interestingly enough, the
time increment for a 0.8 correlation is on the order of one hour for the two
and three hour storms.  This value is similar to that interpolated from the

-------
  6000
  5000
  4000
o
0>
5 3000
.c
o
(/)
Q
  2000
   1000
      0
              100 Year Storm
              D Channel  5
              O Channel  I
                                  00
                                  to
       0      40      80      120     160    200    240
                                           Time, min.
280
320
360    400
       Figure 8.7.  Simulated hydrographs for 2 hour, 100 year storm.  (Time is real time.)

-------
7000
6000
5000
in



"_


Q)

0>
h»
O



|


b
4000
3000
2000
 1000
    0
                 100 Year Storm

                 D  Channel 5

                 O  Channel I
 CO


'' to
 to
     0      30      60      90     120     150     180     210    240    270     300

                                         Time, min.
   Figure 8.8.  Simulated hydrographs for I hour, 100 year storm.  (Time is real time.)

-------
1.0*
0.9-
   0
15
                                      100 Year Storm
                                      O  30 minute
                                      O    I  hour
                                      D    2 hour
                                      A  ,  3 hour
30
45         60
 Lag  Time, min.
90
                                                                                           00
                                                                                           •

                                                                                           OJ
105
                   Figure 8.9.  Autocorrelation for channel 5.

-------
0
15
30
                                             100  Year  Storm
                                              O   30 minute
                                              O    I  hour
                                              D    2 hour
                                              A    3 hour
45         60
 Lag Time, min .
75
90
                                                                                       00
                                                                                       M
105
               Figure 8.10.  Autocorrelation for channel  1.

-------
0
20
                                                  100 Year Storm
                                                  O   30  minute
                                                        I  hour
                                                       2  hour
                                                       3  hour
40         60        80        100        120
  Time CH-5  Lagged Behind CH-I, min.
140
                                                                                       CD
                                                                                       to
      Figure 8.11.  Lagged cross-correlation of simulated hydrographs.

-------
O.lh
0
   0
                                                100  Year  Storm
                                                 O   30 minute
                                                 O    I  hour
                                                , D    2 hour
                                                 A    3 hour
15
30
45         60
 Lag Time, min .
                                                         75
                                                                                            03
                                                                                            to
                                                                                            CT>
                                                                 105
                    Figure 8.12.  Autocorrelation for channel 1.

-------
0
20
                                                   O
                                        100 Year Storm
                                            30 minute
                                              I  hour
                                              2 hour
                                              3 hour
40         60        80        100
  Time CH-5  Lagged Behind CH-I, min.
120
                                                                                     00
                                                                                     to
140
      Figure 8.13.  Lagged cross-correlation of simulated hydrographs.

-------
                                      8.28

daily discharge correlograms previously shown.
     Similar autocorrelation analysis was performed on the sediment hydro-
graphs (Figures 8.14 to 8.17) for channels 1 and 5.  The results of the analy-
sis in the form of correlograms appear in Figures 8.18 and 8.19.  The
correlation is similar to that performed for water hdyrographs indicating that
a similar sampling frequency may be used for both water and sediment.
     As stated before, there should be an upper and lower "correlation band"
where sample timing and station spacing occurs.  The upper correlation may be
about 0.8.  The lower correlation can be estimated using statistical tech-
niques.  Using a "t" test, the value of correlation below which there is no
significance can be calculated.  At the 95 percent level of significance, the
limiting values of the correlation coefficients range between 0.44 for the 30
minute storm with ten time lags and 0.31 for the three hour storm with no time
lag.  To maintain correlation, the readings should be taken at some increment
that provides a correlation greater than 0.44.  The 30 minute storm provides a
basis for design of the gaging system because this type of short duration-high
intensity storm causes high discharges which in turn may result in large sedi-
ment and nonpoint pollutant yield.  This will result in more data being taken
for longer storms, but it may not be adequate to design the system for longer
storms and then collect poor data for important short storms.  The system
should be designed with higher correlation than the lower limit calculated so
that bad data can be identified using nearby stations or data gaps filled if a
station malfunctions.

8.6  Summary
     Use of physical process models can aid in the design and analysis of data
collection systems.  Process models can be used as a basis for identifying
data gaps and checking data quality.  They can also be used to simulate data
that can be utilized in correlation analyses and design modification.  Use of
models in this fashion allows a more efficient, better conceived collection
network.  Model results indicate that:
     1.   The math model can be used to estimate water discharge from the
          small and medium sized watersheds,
     2.   Data is transferable between sites,
     3.   Sampling intervals are reasonable for the watershed stage recorders,
     4.   Flood peaks may be higher at the watershed mouth than previously

-------
s
E
D
I
n
E
N
T
    xie"

    3.0
    a.s -
a.e  -
    i.s -
     i.e -
    e.s -
     e.e
                CH-1

                CH-5
                                                                                                           00


                                                                                                           VD
                                                                  399
                                                                            3S9
                                         Tine
       Figure 8.14.
                           Simulated sediment hydrographs  for the 30 minute,
                           100 year storm.

-------
   xie
s
E
D
I
n
E
H
T

D
I
S
c
H
A
R
G
E
                 CK-1

                 CH-5
                                                 oo
                                                                                                         w
                                                                                                         o
                 54
                           tea
                                     158       809

                                         Tine (MINUTES i
ese
                    359
   Figure 8.15.   Simulated sediment  hydrographs for the 1 hour, 100 year storm.

-------
  3.0
  a.s
  e.e
  1.5
  i.e
  e.s
             PH-1

             CH-5
       1  1  i
               se
                        let
                                                                                                        CD
                                                                                                        •

                                                                                                        CO
                                  ise
                                                                          35«'
                                      TIHE (HINUTES)
Figure  8.16.  Simulated sediment hydrographs for  the 2 hour,  100 year storm.

-------
 a.e i-
  i.s
 i.e
  8.5
  e.e
             CH-l

             CH-5
                                                                                                         00
                                                                                                         U)
                                                                                                         NJ
               sa
                                   tse        e«e

                                       TIPt (MINUTES)
                                                       ES»
                                                                 3M
                                                                           3S«
                                                                                     40«
Figure  8.17.  Simulated sediment  hydrographs for the  3  hour, 100 year storm.

-------
c
0
E
F
F
I
C
I
E
M
T
    i.se
    1.25
    1.00
                 30-niNUTE DURATION STORfl
                 1-HOUR  DUHftTIOM  STORfl
                 2-HOUR  DURftTION  STORfl
                 3-HOUR  DURATION  STORfl
                 95% LIMIT
    a.75
8.59
    e.es
                                                                                                              00

                                                                                                              Ul
    e.eo
                                                           ••i
                         20
                                      40               60

                                        LAG (MINUTES)
                                                                            80
100
           Figure 8.18.   Autocorrelogram .for channel 5  sediment discharge.

-------
    i.se  i-
A
U
T
0
C
0
R
R
E
L
A
T
I
0
M
C
0
E
F
F
I
C
I
E
N
T
    i.as
1.00
    O.TS
9.50
    9.25
                 30-tlINUTE DURftTION STORH
                 1-HOUR DURflTIOH STORN
                 8-HOUR DURflTIOH STORf!
                 3-HOUR DURflTIOH STORfl
                 95X LIHIT
                                                                                                               00

                                                                                                               U)
    e.ee
                                           j_
                                                             I
                          20
                                        40               60

                                         LAG  (MINUTES)
80
                                                                                               100
           Figure  8.19.   Autocorrelogram for  channel 1 sediment  discharge.

-------
                               8.35
    recorded,

    Sampling intervals on U.S.  Geological Survey gages should be no

    longer than one hour and preferable 30 minutes for smaller events,

    and

    A thirty minute storm may aid in designing future measurement

    installations.
aferences

ield,  D.M.,  1963,  "Rainfall Frequency Atlas of the United States for
aration from 30 Minutes to 24 Hours and Return Periods from 1 to 100
aars," Tech.  Paper No.  40,  U.S.  Weather Bureau.

n,  H.P.,  1978,  "Development and  Testing of Mathematical Models as
anagement Tools for Agricultural Non-Point Pollution Control," for
epartment of Agricultural Engineering,  Iowa State University, Ames.

n.,  D.B.  Simons,  W.T.  Fullerton, K.G. Eggert,  and B.S. Sprank, 1979,
simulation of Water Runoff and Sediment Yield  from a System of Multiple
atersheds,"  XVIII  Congress International Association for Hydraulic
asearch,  Cagliani,  Italy.

-------