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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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-
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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
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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.
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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.
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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.
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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
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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.
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1.12
Line E
(a) Original Subwatershed Topographic Map
(b) Openbook Plane Representation
Figure 1.3. Geometric representation of a subwatershed unit.
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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
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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.
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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
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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.
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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.
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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.
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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
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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
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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.
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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
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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
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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
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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.
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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.
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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.
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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
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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.
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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
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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
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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.
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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
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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.
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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-
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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.
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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:
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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
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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
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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
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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
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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,
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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
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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.
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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
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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
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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.
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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
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L
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0
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H
e
c
o
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32
35
00
I
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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
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E
L
A
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0
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E
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F
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C
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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
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R
E
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T
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0
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e
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35
-~J
o
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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
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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
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E
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e.95 -
32
to
CO
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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
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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.)
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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.
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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.
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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
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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.
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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.
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