EPA/600/9-83/015
d States
jnmental Protection
Environmental Research
Laboratory
Athens GA30613
EPA-600/9-83-015
September 1983
arch and Development
Proceedings of
Stormwater and
Water Quality Model
Users Group Meeting
January 27-28, 1983
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EPA-600/9-83-015
September 1983
PROCEEDINGS
OF
STORMWATER AND WATER QUALITY MODEL
USERS GROUP MEETING
January 27-28, 1983
Edited by
Thomas 0. Barnwell, Jr.
Center for Water Quality Modeling
Environmental Research Laboratory
Athens, Ga. 30613
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GA 30613
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DISCLAIMER
Mention of trade names or commercial products does not constitute endorse-
ment or recommendation for use by the U. S. Environmental Protection Agency.
Similarly, publication of studies reporting better results from one model vis-
a-vis others does not constitute endorsement.
ii
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FOREWORD
A major function of research and development programs is to effectively
and expeditiously transfer technology developed by those programs to the user
community. A corollary function is to provide for the continuing exchange of
information and ideas between researchers and users, and between the users
themselves. The Stormwater and Water Quality Model Users Group, sponsored
jointly by the U.S. Environmental Protection Agency and Environment Canada/
Ontario Ministry of the Environment, was established to provide such a forum.
The group has recently widened its interest to include models other than the
Stormwater Management Model and other aspects of modeling water quality in
urban and natural waters. This report, a compendium of papers presented at
the January 1983 Users Group meeting, is published in the interest of dissemi-
nating to a wide audience the work of group members.
William T. Donaldson
Acting Director
Environmental Research Laboratory
Athens, Georgia
iii
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ABSTRACT
This report includes 17 papers on topics related to the development and
application of computer based mathematical models for water quantity and qua-
lity management presented at the semi-annual meeting of the Joint U.S.-Cana-
dian Stormwater and Water Quality Model Users Group held on January 27-28,1983
in Gainesville, Florida.
Topics covered included an applications of the QUAL-II model in the North-
eastern U.S. and Columbia, South America ; applications of STORM in Singapore
and the Republic of China; and implementation of SWMM in Tunisia. Modeling
pesticides in small ponds and mixing zones in rivers was also discussed, as
well as sizing detention ponds to meet water quality objectives. A program to
assess the impact of forest management practices on water quality was also
presented as was a mechanistic model for nonpoint source simulation. Papers
related to precipitation discussed data management, estimation of missing
values, and areal intensity-duration-frequency curves. The questions of hy-
drological regionalization, snowmelt, and porous pavements were addressed.
Other papers discussed regional Stormwater management facilities and storm
sewer design optimization.
iv
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CONTENTS
Page
FOREWORD i i i
ABSTRACT i v
Project Success - Sensitivity to Project Assumptions 1
Anthony Knepp and Grace Wood
Dames a Moore
Application of the STORM Model to Design Problems in Singapore and Kaoh-
siung, Republic of China 22
Brendan M. Harley
Camp Dresser a McKee Inc.
An Attempt to Implement SWMM in Tunisia 43
Janusz Niemczynowicz
Lund Institute of Technology
The Sediment-Water Interface in Modeling Pesticides in Sedimentation
Ponds 53
Raymond A. Ferrara and Peter Jaffe
Princeton University
A Mixing Zone Model for Conservative Parameters 65
Main R. Hutcheson
Oklahoma Water Resources Board
Some Recent Adaptations and Applications of QUAL-II in the Northeast 87
William W. Walker, Jr.
Environmental Engineer
A Review of Model Use in Evaluating Nonpoint Source Loads from Forest
Management Activities 102
George G. Ice and Raymond C. Whittemore
National Council of the Paper Industry for Air and Stream Improvement
Detention Pond Sizing to Achieve Water Quality Objectives 123
Roger K Wells
HMM Associates, Inc.
A Mechanistic Simulation for Transport of Nonpoint Source Pollutants 146
Daryl B. Simons, Run-Ming Li and Kenneth G. Eggert
Simons, Li a Associates
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Data Management for Continuous Hydrologic Simulation 161
Jy S. Wu
University of North Carolina at Charlotte
Estimation of Missing Values in Monthly Rainfall Series 177
Efi Foufoula
University of Florida
Area! Intensity-Duration-Frequency Curves - A Possible Way of Improving
the Rainfall Input 192
Janusz Niemczynowicz
Lund Institute of Technology
Hydrological Regionalization: A Question of Problem and Scale 202
I. Simmers and E. Seyhan
Free University, Amsterdam
Snowmelt Induced Urban Runoff in Northern Sweden 215
Lars Bengtsson
McMaster University
An Advancement in Hydraulic Modeling of Porous Pavement Facilities 237
Gary Goforth
Espey Huston a Associates Inc.
Planning and Implementation of Regional Stormwater Management Facilities
i n Montgomery County, Maryland 255
John M. Crouse(l), Vincent H. Berg(2) and Linda J. D. Mitchell(l)
vl)Greenhorne a O'Mara and (2)Montgomery County, MD
Storm Sewer Design Optimization 272
Dong Hoang
City of Portland
ATTENDEES 281
vi
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Project Success: Sensitivity to Project Assumptions
"The Medellin Case"
by
Anthony Knepp, P.E.
and
Grace E. Wood
Dames & Moo're, Bethesda, MD
Abstract
The effect of major planning assumptions on the predicted water
quality of the R1o HedelUn 1s Investigated through application
of the dual II model. The R1o HedelUn flows through the center
of MedelUn, the second largest dty In Colombia with a 1980 popu-
lation of over 1.2 million people. Currently, there Is no treatment
of municipal or Industrial waste. The river receives raw sewage
via direct discharge and from numerous polluted tributaries 1n the
developed area. Nonpolnt sources of pollution contribute large
quantities of sediment to the river. Practices such as 1n-stream
gravel mining and direct dumping of solid waste add to the large
sediment and pollutant loads observed during wet weather periods.
All of these factors result not only 1n very poor biochemical
quality of the river, but frequent visual, color, and odor problems.
Public health 1s threatened by the poor quality of the river, and
uses are severely limited.
Preliminary results of a major planning study (Greeley and
Hansen, CCC, 1982) indicate that a configuration of four treat-
ment plants sited along the modeled portion of the Rio MedelUn
would cost-effectively meet specified water quality criteria.
This paper presents the results of a sensitivity analysis
using Qua! II which demonstrates the degree predicted water
quality 1s affected by initial project assumptions, such as:
o Expected ability to control the nonpolnt sources
of pollution, including solid waste and land runoff
o Availability of dilution water
o Likelihood of meeting wastewater collection goals.
The paper examines the Importance of meeting basic assumptions to
the attainment of water quality goals. The sensitivity analysis
was accomplished by establishing a "baseline" condition and
examining the effects on baseline quality of modifying a single
assumption or group of assumptions. Changes to the baseline
condition included variations 1n flow, percent wastewater
collection, dilution water Inflow, nonpolnt source inputs, and
solid waste contributions.
Study Area Location Map
Introduction
Every water resources study team begins a project with the expectation
that it will proceed in a systematic manner from problem identification and
collection of pertinent information, through the development of feasible
solutions, to the determination of their consequences. Final results
usually include the identification of one or, at most, a limited number of
feasible solutions. The decision maker(s) are then expected to arrive at
a final decision concerning implementation of a selected alternative, and
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then proceed to the next problem. Experience suggests that in small pro-
jects such a systematic approach works quite well. However, in many larger
water resources planning projects, such conceptual neatness is brought
closer to reality by the following observations of Loucks (1981):
o A final solution to a water resources problem rarely exists.
o Plans and projects are dynamic and evolve over time.
o The time to study a problem is never adequate to perform "state-
of-the-art" mathematical work. The converse of the above
statement should also be recognized, i.e., if sufficient
time does exist the objectives of the original study will
have shifted by the time the study is completed.
Recognizing that these difficulties exist, a major contribution to the
planning process is obtained when a sensitivity analysis is conducted for
the major project assumptions composing the "Model" used in the analysis of
feasible solutions. "Model" is used here to mean the set of formulae
coefficients, parameters, etc., which reproduces both prototype behavior
and system response to future conditions. In this way, the evolution of
project objectives is enhanced and the feasibility of project solutions is
recognized early in the planning stages. Most importantly, the objectives,
feasibility of alternatives, and the interrelated aspects of the project
are brought into focus for the decision makers. Since most water quality
planning studies are based on at least a 20 year planning horizon, a knowl-
edge of the impact of major assumptions to the overall success of a project
is invaluable to a decision maker as priorities and objectives change from
the time of project inception to the end of the planning horizon.
This paper examines the sensitivity of meeting selected water quality
criteria to the assumed status of major project assumptions. Emphasis is
placed on those project factors which are often classified as assumptions
in a study and which, as demonstrated here, can influence the meeting of
project objectives.
The background for this paper is a water quality management plan
developed for the metropolitan areas in the Aburra Valley surrounding
Medellin, Colombia. As part of an overall study of the valley, a river
model was calibrated, verified, and used to evaluate potential wastewater
treatment plant systems for the area. Aspects of the study Included water
quality sampling, the estimation of nonpoint pollution, hydrology, sediment,
water diversions for dilution, and solid waste studies. The planning
horizon for the sensitivity analysis is the year 2000.
This paper is based on results of a prefeasibility study. Simulation
results are used to illustrate the importance of carefully performing a
sensitivity analysis of major project assumptions with respect to the
information the analysis provides to decision makers for the direction of
the project. Results and conclusions referenced in this paper may change
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considerably during subsequent feasibility and design phases of the project.
Description of Project Area
The Aburra Valley is located in the Andean mountains, 7 north of the
equator at an elevation of 1,500 meters (4,920 ft) above mean sea level
(MSL). The City of Medellin and nine other municipalities comprise most of
the population of the valley. The city of Medellin, the capital of the
Department (state) of Antioquia, is located at the center of the valley
(Figure 1) approximately 205 km (127 mi) from the Pacific Ocean and 295 km
(183 mi) from the Caribbean Sea. It is the second largest city in Colombia
with a 1980 population of over 1.2 million inhabitants. Total population
in the valley is approximately 2 million.
The climate is mild with monthly average temperatures varying only
slightly over the year. The mean temperature is 22.5°C (72.5°F), with
temperatures ranging between 13 C (55°F) and 33°C (91 F). Average annual
rainfall totals 1,450 millimeters (57 inches). Average annual humidity is
70%. Four seasons are distinguishable from changing rainfall patterns.
Two relatively dry seasons occur from December to March and July to August.
Two wet seasons occur from April to June and from September to November.
UNIDAD DE SANEAMIENTO HlDRlCO
HOYA HIDROGRAFICA DEL RIO M£DELUN
Figure 1: Aburra Valley - study area.
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Most of the Aburra Valley is classified as humid subtropical and low
mountain humid forest. The forest that remains is concentrated at the
upper and lower reaches of the valley. In the Medellin area, urban zones
cover most of the available usable land, limited only by steep slopes. The
metropolitan area is an important commercial and industrial center for
textile activity. The non-urban areas are used for livestock grazing and
agriculture.
The Rio Medellin flows north through the urban population centers.
The river is the natural drainage for the valley. It receives flow from
numerous tributaries, the majority having steep slopes in the upstream
sections. Tributary flows range from a few liters per second in the dry
seasons to several cubic meters per second during the wet seasons. The Rio
Medellin extends for approximately 100 km (62 miles) from its headwater
near Primavera to its mouth at the confluence with the Rio Grande. The
river receives 7.7 m /sec (180 MGD) of raw municipal and industrial waste.
Median flow at gage RM-12 (Figure 1) is 25 nr/sec (570 MGD). Current uses
are severely limited and public health is threatened.
The upper reaches of the Rio Medellin from its headwater to Itagui,
approximately 20 km (12 mi), flows through a narrow valley and falls
approximately 200 meters (656 ft) in 13 kilometers (8 mi). The water
quality in this reach is relatively good. It is downstream of this reach
that municipal discharges become significant. Below Itagui the valley
widens, the river slope decreases, and the river passes through the heavily
populated and industrialized area of metropolitan Medellin. The river is
channelized through much of this portion. The water quality in this
stretch is severely degraded due to the large volumes of industrial,
municipal, and domestic effluents being discharged into the river as shown
by high levels of coliform bacteria, oil and grease, detergents, and heavy
metals. The five-day biochemical oxygen demand (BOD5) is very high, reach-
ing 120 mg/1 in the metropolitan area, and the dissolved oxygen (DO)
approaches zero, especially during the dry season. Below the channelized
reach, the water quality continues to be highly degraded due to industrial
and domestic discharges from Medellin and Bello. As a result, the DO
concentration remains near zero. Because of the short travel times and
high pollution load the organic matter from the Medellin area decomposes
only slightly in the river and water quality remains very poor.
The characteristics of the river below gage RM-12 (kilometer 40, mile
26) changes radically. The valley becomes very narrow, the slope increases,
and water flow is very rapid passing through riffle areas and cascades.
This stretch represents a zone of high reaeration, as rapids and cascades
oxygenate the water and sewage discharges are minimized by the small degree
of human development. Thus, oxygen levels increase with distance down-
stream but BOD5, nutrients, toxic substances, and coliform bacteria
concentrations are still elevated.
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Near the mouth of the Rio Medellin, the valley widens and the slope
again decreases. The Rio Grande and the Rio Santiago join the Medellin to
form the Rio Force and dilute the pollutants of the Rio Medellin.
Figures 2 through 5 present water quality measurements taken between
March and August 1981 (Dames & Moore, 1981). Flows were generally above
the average annual levels. Sampling locations are indicated by the vertical
lines and ranges of measurements by short dashes. The sampling points are
connected for clarity.
Figures 2 and 3 indicate the extensive pollution load the river is
currently receiving. Oxygen levels are recorded below 2 mg/1 over a 20-km
(12 mi) reach of the river. BODS'concentrations are greater than secondary
effluent levels (30 mg/1) for nearly 40 kilometers (24 mi). Ammonia
nitrogen and total phosphorus concentrations are well above potential
eutrophication causing levels.
Waste Management Practices in the Aburra Valley
The city of Medellin and the surrounding municipalities are without
facilities necessary for the treatment of domestic, industrial, or
commercial wastewater. Although the metropolitan area is served by
sanitary sewers, these discharge directly to the mainstem or to various
tributaries and open ditches draining the area.
Existing management practices for solid waste disposal also contribute
to the poor quality of the Rio Medellin. The indiscriminate disposal of
solid waste directly into and on the banks of the river and its tributaries
creates obvious visual and odor problems. The organic load from floating
waste and the accumulation of debris creates a potential demand on in-
stream oxygen and elevates the concentration of BODS, thereby adding to
the degradation of the river.
Water Quality Criteria
Quality criteria were established for a range of potential uses of
water from the Rio Medellin. Criteria were developed for two categories
of pollutants: pollutants not significantly affected by the abatement
program, pollutants significantly affected by the abatement of organic
pollution. The organic pollution criteria served a dual purpose. First,
they obviously indicated a concentration of the given pollutant. Second
(and more important) they served to indicate a level (albeit subjective)
of chemical pollution, originating from industrial and commercial
activities in the valley. The implementation program is expected to
alleviate increasingly high percentages of pollution from the above two
sources as higher percentages of the population related pollution is
eliminated.
Water quality parameters included as indicators of organic pollution
were dissolved oxygen, biochemical oxygen demand, ammonia, total phosphorus,
and fecal coliforms.
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URBAN CALDAS ITAGUI M6DELLIN BELLO COPACABANA GIRARDOTA
AREAS
NOTE: Horizontal bars denote
and maximum samples.
40 50 60
RIVER KILOMETERS
Figure 2: Rio Medellin mean dissolved oxygen for March - August, 1981.
URBAN CALDAS ITAGl
AREAS [V3 F?\\
I
r
i
r
s
« 60-
20-
^^\
— —.
1
]f
I
/
Jl MEDELLIN
1 L\\\\\V\V
!
"\
\
/
BELLO COPACABANA GIRARDOTA BARBOSA
rei r^i ^3 R^J
\
\
\
. \
^^
~~~ .
^^^
10 20
NOTE: Horiionul baridenote mrnimum
and meximum umplet.
40 &0 60 70
RIVER KILOMETERS
80 90
Figure 3: Rio Medellin mean biochemical oxygen demand for March - August, 1981.
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URBAN CALDAS ITAGUI MEDELLIN BELLO COPACABANA GIRARDOTA BARBOSA
ixxxxxxxx^ 15^ k\xi R\51 Fx^l
0 10 20
NOTE Horizonial bars denote mm
and maximum samples.
40 50 60
RIVER KILOMETERS
Figure 4: Rio Medellin mean ammonia nitrogen for March - August, 1981.
URBAN CALPAS
AREAS [X^
ITAGUI MEDELLIN BELLO COPACABANA GIRARDOTA
0 10 20
NOTE: Horizontal b»n denote minimurr
and maximum samples.
40 50 60
RIVER KILOMETERS
Figure 5: Rio Medellin mean total phosphorus for March - August, 1981.
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Selected Abatement Strategy
An extensive analysis was performed by the project team (Greeley and
Hansen, and CCC, 1982) to determine the cost-effective abatement strategy
appropriate for the Rio Medellin. Population, land use, solid waste, and
river mining conditions were projected to the design year 2000 to estimate
pollutant loads The Qual II model was used to simulate in-stream quality
resulting from implementation of a given point source treatment plant
configuration and selected non-point source controls. Preliminary results
of the study (Greeley and Hansen, and CCC, 1982) indicate that a configu-
ration of four treatment plants (Figure 6) sited along the modeled portion
of the Rio Medellin would cost-effectively meet selected water quality
criteria. The proposed configuration consists of two large secondary
plants and two additional plants defined as providing preliminary treatment
(screening, grit removal, and chlorination). The interbasin transfer of
high quality water for the purpose of dilution (20.5 m /sec) is also
assumed in the treatment configuration.
SECONDARY TREATMENT PLANT
TREATMENT
PLANT
LOCATIONS
PRELIMINARY TREATMENT PLANT*
LUTION
ATER
PUTS
RIO
MEDELLIN
D = 2.5 cms D
\
0 10
o
= 5 cms
\
20
0
30 40
O
D = 18 cms
\
50 60
0
I I
70 80
R
M
I I
90 100
CITIES
ALONG THE
RIO MEDELLIN
GIRAROOTA
COPACABANA
•PRELIMINARY TREATMENT IS DEFINED AS
SCREENING, GRIT REMOVAL AND CHLORINATION
Figure 6: Point source selected abatement strategy.
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Sensitivity Analysis
Adapting the calibrated model to year 2000 conditions required many
assumptions and projections to be made which describe the expected "state"
of the environment. Foremost among these were the assumptions regarding:
1. Level of naturally occurring base flow used in the screening
of alternatives.
2. Year 2000 status of the interceptor connection program to
the major trunk lines.
3. Availability of an appreciable quantity of dilution water,
particularly during drought periods when dilution water is
most needed.
4. Level of solid waste control possible.
5. Effects of wet weather (nonpoint) sources of pollution on
meeting quality criteria.
The implementation of a comprehensive plan requires a detailed
knowledge of Jiow the quality of the river responds to each of these
assumptions and which among them are impediments to meeting water quality
criteria. The potential range of changes in regard to political and
social forces that are possible over a 20-year planning horizon make an
understanding of the sensitivity of the proposed solution to these
assumptions critical during the implementation phase of the comprehensive
plan.
Sensitivities were developed by modifying either a single assumption
or group of assumptions and using the Qual II model to develop the
associated water quality response (Dames & Moore, 1982e). A "baseline"
simulation was used as a standard to compare the relative sensitivities.
The "baseline" simulation represented a most likely set of assumptions
regarding the development of events influencing water quality. For the
baseline simulation, a treatment plant configuration of four plants was
selected—two secondary plants located at Envigado and Bello, and two
plants providing preliminary treatment at Girardota and Barbosa. The two
secondary plants were assumed to have 92% treatment efficiency for BOD
removal.
The status of the five major assumptions in the Baseline simulation
are:
1. A flow likely to be exceeded 75 percent of the time was
selected as the naturally occurring portion of the flow
used in the baseline simulation.
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2. Seventy-five percent of the domestic, industrial, and
commercial wastewater in the valley is collected
and treated, with 95% collection and treatment of
industrial waste from several major industries in the
valley.
3. High quality dilution water is available to the Rio Medellin.
4. Implementation of a solid waste management program
eliminates the pollutant loadings attributed to unmitigated
solid waste dumping.
5. Nonpoint sources of pollution are minimal under baseline
conditions.
In the following discussion each project assumption is examined
separately. The basis for each is outlined and the project details
surrounding the assumption are discussed, along with the sensitivity of
predicted water quality to a modification of the assumption.
Assumption 1: A flow that is likely to be exceeded 75 percent of
the time was selected as the naturally occurring
portion of the flow used in the baseline simulation.
The selection of a design flow for use with the Qual II model in the
evaluation of the water quality impacts of abatement programs is a major
factor basic to the results of much of the analysis. Currently, no local
institutional or legal constraints exist in Colombia to guide the selection
of this flow.
An analysis of extreme events, the usual procedure for determining a
design low flow, was not possible due to the short length of records avail-
able. The period of record was 2-10 years, with an average of 6 years at
each gage (Dames & Moore, 1982c). Therefore, for purposes of screening
abatement strategies a flow exceeded 75 percent of the time was established
for the analysis. The exceedance frequency was selected in recognition of
the severity of existing conditions and uncertainties in the data.
To demonstrate the sensitivity of this assumption on predicted water
quality, the Qual II inputs were modified to reflect a more severe flow
condition, the average annual 14-consecutive-day low flow. The effect of
modifying the design is shown in Figure 7. The reduced flow corresponds to
an exceedance frequency of 90 percent. The minimal impact on oxygen
reserves of a lower flow is due to the large quantities of dilution water
and sanitary contributions to the total flow in comparison to the smaller
"naturally" occurring base flow portion. The predicted maximum DO sag
level is less than 0.5 mg/1 more severe. The predicted in-stream BOD5
10
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BASELINE SIMULATION (75%)*
20 30
40 50 60
RIVER KILOMETERS
LOW FLOW (90%)*
BASELINE SIMULATION (75%)*
MINIMUM LIMIT
40 50 60
RIVER KILOMETERS
•EXCEEDANCE FREQUENCY
Figure 7: Effect of changes in flow on biochemical oxygen demand and dissolved
oxygen concentrations.
n
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concentrations are only minimally affected. The maximum and minimum limits
shown on Figure 7 are those limits established to minimize odor problems.
With a knowledge of local hydrology, coupled with the low sensitivity
of water quality to changes in the base portion of the design flow, it be-
comes evident that further work in establishing a more restrictive or
reliable design flow should not be a high priority concern in the future
planning process. Water quality is not particularly sensitive to changes
in this factor.
Assumption 2: Seventy-five percent of the domestic, industrial
and commercial wastewater generated in the valley
is collected and treated.
As indicated earlier, although there are no treatment facilities in
the Aburra Valley, portions of Medellin and the surrounding municipalities
are sewered. In 1957 a plan was completed for construction of a sanitary
collection and treatment system for the City of Medellin (Greeley and
Hansen, 1957). Presently, approximately 50 percent of the 152 kilometers
of the major interceptors (94 mi) originally planned are constructed. A
major problem is that many of the trunks and smaller domestic lines are not
connected to the main interceptors and necessary manholes and cleanout
points are not built.
A large-scale retrofit program for the system connections, manholes,
overflow outlets, etc., is necessary as part of the plan for 75 percent
wastewater collection in the valley. A point of concern is whether 75 per-
cent collection is feasible from an engineering and cost standpoint. The
topography of the region, as well as the status of existing housing
conditions, precludes collection of an uncertain percentage of waste flows.
Many of the dwellings in the valley, especially in the upland areas, are
without plumbing or public water supply. Collection of the wastewater
generated from these houses would be difficult to achieve.
The results of changing the collection percentage from 75 to 50 per-
cent is shown in Figure 8. The ability to meet minimum water quality
criteria is strongly influenced by the amount of sewage that can be
collected and treated before release. The oxygen sag drops to a minimum
2.0 mg/1 while the BOD5 increases to a maximum of 48 mg/1. The BOD5
maximum and DO minimum occur near the center of the most populated area.
A major public works program to connect 75 percent of the wastewater
flows to the collection/treatment system must be recognized as a critical
factor in achieving water quality goals. The indicated sensitivity of the
predicted water quality would lead a decision maker to recognize that the
program to connect interceptors to the main trunk lines is a major factor
in the implementation of a comprehensive plan.
12
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50% COLLECTION
BASELINE SIMULATION (75%)*
40 50 60
RIVER KILOMETERS
K
2
MINIMUM LIMIT
BASELINE SIMULATION (75%)
50% COLLECTION
40 50 60
RIVER KILOMETERS
•WASTEWATER COLLECTION
Figure 8: Effect of wastewater collection levels on biochemical oxygen demand
and dissolved oxygen concentrations.
13
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Assumption 3: High quality water is available for dilution of
waste flows entering the Rio Medellin during
critical periods.
Current planning calls for the diversion of water from the neighbor-
ing Rio Grande watershed to the Aburra Valley for hydroelectric power,
water supply, and dilution purposes. The proposed diversion includes the
building of gravity tunnels to the municipalities of Bello and Girardota.
The plan also includes construction of two hydroelectric power plants as
well as a water treatment plant. An average of 35 m /sec (1236 ft3/sec)
would be diverted by the year 2000. Although approximately 12 m /sec (424
ft3/sec) would-be used to meet increasing water demand, the remaining 23
m /sec (812 ft /sec) would be discharged into the river as dilution water
after power generation. The baseline simulations accounted3for the above
by establishing inflows to the Rio Medellin of 5.0 and 18 m /sec (176.6 and
636 ft3/sec) at river kilometers 30 and 54 (miles 19 and 34), respectively.
An additional 2.5 m /sec (88 ft /sec) will be available from another source
at kilometer 20 (mile 12).
Since the availability of dilution water is dependent upon completion
of the rather complex proposed diversion plan, the ability to meet the
initial project assumption is again important to the decision makers. To
test the sensitivity of water quality to the assumption of no dilution
water, all dilution flows were eliminated from the simulation. The results
of this modification are shown for BOD5 and DO in Figure 9, along with the
predicted baseline concentrations. The BOD5 concentrations remain
elevated through the City of Medellin and only begin to decline downstream
as the organic load is diluted, river flows increase, and BOD5 inputs are
reduced. Upstream of river kilometer 20 (mile 12), predicted water quality
is the same for the baseline and modified assumptions simulations. The
simulation of DO is shown to be very sensitive to the availability of
dilution water. Without added dilution water a major zone of anaerobic
conditions is likely to develop, even after construction of the assumed
collection and treatment facilities.
The importance of dilution water to meeting project water quality
criteria is indicated to be very large, particularly near the
population center of Medellin, river kilometers 15 to 35 (miles 9 to 21).
Likewise the importance of the availability of water for dilution to the
success of the project is also large.
Assumption 4: A solid waste management plan is assumed to be
implemented thereby eliminating solid waste as
a cause of water quality degradation.
14
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NO DILUTION WATER
BASELINE SIMULATION
10 20
40 50 60
RIVER KILOMETERS
20 30
40 SO 60
RIVER KILOMETERS
Figure 9: Effect of dilution water on biochemical oxygen demand and dissolved
oxygen concentrations.
15
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In 1980, the total quantity of solid waste produced in the Aburra
Valley was estimated to be approximately 460,000 metric tons (Grandjean,
1980). The collection, treatment, recycling, and disposal of this solid
waste is a complex problem in Medellin and the surrounding municipalities.
Although a significant portion eventually reaches a controlled landfill or
the composting plant for ultimate disposal, in many areas of the valley the
location and methods of disposal are determined by convenience. A common
practice is to dispose of solid waste on the banks of the Rio Medellin or
its tributaries. Eventually, disposal sites adjacent to water courses
extend into the channel and waste is carried downstream during high flow
periods, causing widespread visual and odor problems and degrading in-
stream water quality.
Implementation of a solid waste management program, independent of a
wastewater abatement program, is intended for Medellin. For planning
purposes it was assumed that implementation of such a program would
eliminate solid waste as a cause of water quality degradation. Therefore,
the estimated contribution of solid waste to the total pollution load to
the river from all sources (Dames & Moore, 1982b) was excluded as input to
the QUAL II simulation for the baseline condition.
The above decision assumes a significant change in solid waste
disposal practices in the valley. Solid waste recycling at all levels, at
the street receptacle, on the collection trucks, and at numerous disposal
sites, provides income to thousands of people throughout the valley.
Changing methods of disposal may have serious socioeconomic impacts on
many people, and therefore implementation of a program to completely
eliminate solid waste as a source of water quality degradation may be
quite difficult to achieve.
The sensitivity of water quality to the assumptions regarding solid
waste is shown in Figure 10. Solid waste is assumed to enter the river as
leachate from solid waste sites (a relatively minor source of pollution),
through direct dumping, and by entrainment with the runoff. Figure 10 was
developed assuming a storm flow condition existed. The naturally occurring
base flow of the river was increased to simulate an "average" storm. It is
recognized that Qual II is a hydraulically steady state model and does not
simulate the time varying nature of runoff from a watershed. However, the
model does provide a crude screening suitable for the sensitivity analysis
presented here. Elevated BOD5 concentrations are at almost twice the base-
line concentration along the entire modeled portion of the river. The
dissolved oxygen sag is approximately 1 mg/1 more severe at the point of
minimum DO concentration. Recovery of oxygen to concentrations similar to
the baseline condition occurs downstream of kilometer 51, (mile 32) because
of the addition of 18 m3/sec (636 ft3/sec) of water for dilution.
Meeting water quality criteria is shown to be very dependent on an
effective solid waste management program. The reliance of the predicted
pollution abatement to the assumption regarding the solid waste management
16
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NONPOINT POLLUTION WITH SOLID WASTE
NONPOINT POLLUTION
BASELINE SIMULATION
10 20
40 50
RIVER KILOMETERS
X
o
MINIMUM LIMIT
NONPOINT POLLUTION WITH SOLID WASTE
BASELINE SIMULATION
. NONPOINT POLLUTION
20 30
40 50 60
RIVER KILOMETERS
Figure 10: Effect of nonpoint sources and solid waste on biochemical oxygen demand
and dissolved oxygen concentrations.
17
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program is clearly indicated, particularly with respect to organic
pollutant concentrations. Future implementation of a comprehensive plan
should also rank a solid waste management plan as necessary to achieve
water quality improvements.
Assumption 5: The effect of nonpoint source pollution on water
quality.
By definition here, nonpoint pollution occurs only during rainstorm
events when accumulated pollutants on urban and rural land surfaces are
carried to receiving streams. Hence, this source of pollution is largely
dependent on rainfall patterns, topography, and land use in the region.
Since the selected design flow is a dry weather condition, nonpoint
pollutant loadings would be minimal and were, therefore, excluded as input
to Qual II in selection of an appropriate abatement program.
An important concern to planners, however, is whether nonpoint
pollution in combination with point discharges would be significant enough
that water quality criteria would be violated during wet weather.
To determine the nonpoint contribution to stream pollution, an
estimate was made of diffused, runoff-associated pollutant loads (Dames &
Moore, 1982d). Figure 10 presents the results of the simulation.
Simulated BOD5 concentrations were slightly higher in wet weather relative
to the baseline condition. Below river kilometer 40 (mile 24), concen-
trations were similar to baseline conditions because of the large
quantities of water available for dilution. Dissolved oxygen levels, how-
ever, were high throughout the stream. The sag during wet weather was more
than 1 mg/1 less severe when compared to baseline conditions.
Interestingly, wet weather conditions do not seem to affect seriously
the opportunity to achieve water quality criteria. This is in part due to
the level of the criteria as indicated on Figure 10 and to the averaging
of flows and pollutant loadings required by the methodology followed.
First flush effects of urban areas are not simulated. Results indicate
that for most water quality parameters, nonpoint pollution would have
little impact on achieving water quality criteria at the levels indicated.
Assumption 6: Cumulative Impacts
In the above cases, changes to the baseline conditions included
variations in flow, percent collection, water for dilution, nonpoint
source pollutants, and solid waste pollutants. In a subsequent step, the
cumulative effect of the assumptions impacting water quality was also
evaluated by modifying several assumptions simultaneously. These changes
18
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PEAK-APPROX. 130BOD5 (MILLIGRAMS/LITER)
CUMULATIVE IMPACTS
(LOW FLOW, NO DILUTION WATER, WITH SOLID WASTE)
NONPOINT POLLUTION WITH SOLID WASTE
50% COLLECTION
NO DILUTION WATER
40 50 SO
RIVER KILOMETERS
BASELINE SIMULATION
AND NO DILUTION WATER
CC
2
1 CUMULATIVE IMPACTS
-(LOW FLOW, NO DILUTION WATER, WITH SOLID WASTE)'
40 50 60
RIVER KILOMETERS
Figure 11: Effects of cumulative impacts on biochemical oxygen demand and
dissolved oxygen concentrations.
19
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were chosen to reflect a potential "worst case" picture of resulting water
quality. The simulation was based on the following assumptions, modified
from baseline conditions:
Cumulative Impacts: The simulated flow was changed to the lower flow
as described in Assumption I. All dilution
water inputs were eliminated. No abatement to
the solid waste dumping was included.
Results of this simulation are shown in Figure 11 for DO and BODS. The
results more clearly demonstrate the importance of both dilution water
availability and solid waste abatement. A DO sag to zero occurs for
approximately 50 kilometers.
BODS demands exceeding 30 mg/1 are predicted for approximately 88
kilometers of the 100-kilometer Rio Medellin. Thirty milligrams per liter
of BODS was the maximum permissible concentration to meet minimum water
quality criteria. This concentration was exceeded except in the most up-
stream reach. A peak of 130 mg/1 resulted in the City of Medellin, where
organic loading contributions to the river are the greatest. These results
again illustrate the importance of recognizing the relative importance of
the major assumptions to achieving water quality planning objectives.
Summary
When used correctly, water quality models can enhance the likelihood
of.the success of comprehensive planning efforts. The use of a model to
evaluate the effect on predicted water quality of major project assumptions
provides:
1) Understanding of the relative importance of each project
assumption to the overall abatement program.
2) Basis for informed discussion on the direction the planning
process should follow.
An analysis of project assumptions for Medellin would indicate that in
addition to the extensive point source controls recommended, decision
makers should recognize that the implementation of a sewer connection pro-
gram, the abatement of solid waste, and the provision of dilution water are
very important to maintaining quality criteria during critical periods and
thus to the success of the project as currently planned. Also, in this
case, the sensitivity of projected water quality to nonpoint sources and to
lower flows than used in the screening of abatement alternatives is small.
20
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Acknowledgements
The number of people involved in this study and their valuable contri-
butions are simply too numerous to mention here. Their contributions to the
analysis presented in this paper are gratefully acknowledged. Project
directors from the organizations involved in the study were Messrs. Robert
Zimmerman from Greeley and Hansen, Jaime Rodas from Compania Colombiana
de Consultores, Richard C. Tucker from Dames & Moore, and Dr. Alonso
Palacios from Empresas Publicas de Medellin. The direction provided the
project by their participation shaped the project and helped it successfully
to meet its objectives.
REFERENCES
Dames & Moore, December 1981, "Existing Environmental Conditions," Pollution
Control of the Medellin River and its Tributaries - Memorandum 34-1.
Dames & Moore, April 1982. "Solid Uaste Pollution Assessment," Pollution
Control of the Medellin River and its Tributaries - Memorandum 56-1.
Dames & Moore, May 1982. "Hydro!ogic Studies," Pollution Control of the
Medellin River and its Tributaries - Memorandum 59-1.
Dames & Moore, May 1982. "Nonpoint Pollution Assessment," Pollution Control
of the Medellin River and its Tributaries - Memorandum 25-1.
Dames & Moore, July 1982. "Develop Initial Treatment Arrays," Pollution
Control of the Medellin River and its Tributaries - Memorandum 22-1.
EPA Environmental Research Laboratory, 1977. User's Manual for Stream
Quality Model (Qual II).
EPA, Environmental Research Laboratory, 1977. Computer Program
Documentation for Stream Quality Model (Qual II).
Grandjean, 0, 1980, Estudio Sobre Recoleccion, Trataments y Dispocition
Final de Desectos Solidos en al Area Metropolitano y Oriente Crecano,
Ports 1 y 2. Departmento Administraro de Planeacion y Direccion
Desarollo Metropolitano, Governacion de Antioquia.
Greeley and Hansen, 1957. "Informe Sobre Recoleccion y Disposicion de las
Aquas Negras de Medellin. Medellin, EE. PP. M.
Greeley and Hansen and Compania, Colombiana de Consultores, Ltda., July 1982.
"Initial River Model and Treatment Model Analysis of Treatment
Configurations and Selection of Treatment Configurations for Further
Study," Pollution Control of the Medellin River and its Tributaries,
Memorandum 28-1.
Loucks, Daniel P. et al. Water Resources System Planning and Analysis,
Prentice Hall, 1981.
Orozco, A., 1978. Solid Waste in Medellin and its Metropolitan Area.
Revista Empresas Publicas de Medellin, Monografia Del Rio Medellin. Vol. 3,
Nos. 3 y 4, Julio/Deciembre 1981. ISSN 0120-1239.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
21
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Application of the STORM Model to Design Problems
in Singapore and in Kaohsiung, Republic of China
by
Brendan M. Harley
Camp Dresser & McKee Inc.
Boston, Massachusetts 02108
ABSTRACT
This paper presents two examples of the application of modified versions of
the STORM model to design situations overseas. One of these, involved sim-
ulation of a raw water supply system where flow is captured via diversions
from the storm drainage system. The second application used the model to
evaluate cost-effective CSO control measures in a situation where no separ-
ation of sanitary and storm sewers exist.
INTRODUCTION
Problems in managing urban runoff and combined sewer overflow in rapidly ex-
panding cities in developing countries are generally quite major and, in
some cases, address urgent public health hazards with immediate needs for
solutions. Use of simulation models to assist in developing design criteria
is still quite rare, although a trend towards use of such models is develop-
ing.
Recently, COM has been involved in two overseas projects which presented the
opportunity to apply modified versions of the STORM model to quite different
situations. The first, in Singapore, involved a study where urban stortnwater
runoff from "new town" areas is to be captured and treated for use to augment
the island's water supply. The STORM model was used to evaluate the basin
runoff, to size the diversion/storage/pumping facilities which are spread
throughout the area, and to help determine the effective "safe yield" from
the proposed project. This project is now under construction.
The second application of the STORM model was in the development of design
strategies to control heavily contaminated combined sewer overflows to the
Jen Ai River in the City of Kaohsiung, Republic of China. This city of about
one million people has essentially no sanitary sewerage system at all; all
sanitary wastewater together with stormwater flows via small open ditches and
channels to the river which is presently totally anoxic. The design study
was for a series of major combined sewer overflow structures which, in con-
22
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junction with a single trunk sewer, will reduce BOD loadings on the Jen Ai
River by over 90 percent. Effective use was made of the ability of the
STORM model to simulate the effect of storage and local treatment (simple
detention, swirl separators, etc.) at each of the control facilities.
SELETAR PROJECT - SINGAPORE
BACKGROUND
The expansion of reliable water supply systems is a major requirement in
areas of the world which experience very rapid population growth. Some of
these developing countries lie in regions of the world having limited rain-
fall, many lie in areas of abundant rainfall but possess very limited
capture/storage/transmission capability; in nearly all cases, large capital
investments have to be undertaken to meet the water supply needs.
The island nation of Singapore is handling the population growth demands
through the development of self-contained "new towns" containing both resi-
dential and industrial areas; these "new towns" incorporate separate storm
and sewer systems designed to good modern practice levels. Each "new town"
is, in effect, a small city with a population of 200,000-400,000. This
scheme utilizes runoff from such "new towns" areas to augment the water
supply requirements. The scheme which is presently in the final design and
tender stages involves the following elements:
o Diversions from main storm drains to a series of storage ponds located
throughout the "new towns." Diversion structures include both large
drop-inlets and tightly controlled bascule-gate regulators.
o Pumpage from these ponds to main reservoirs which also accept gravity
drainage from sections of the "new towns."
o Blending of this urban runoff with runoff from undeveloped watersheds.
The development of this scheme, which has a first stage capacity of 30 imgd
and an ultimate safe yield of 60 imgd, included the application of many
hydro!ogic analysis techniques including:
o Generation of long term rainfall records, using disaggregation techniques,
for use in yield studies.
o Generations of design storm events, both for spillway design events and
for the more frequent events where the diversion structures have to oper-
ate effectively.
o- Use of a modified version of the STORM model to evaluate the runoff/diver-
sion/pumping operations.
o Application of the MITCAT model to simulate design event operation of
major components of the system.
23
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o Development of a system simulation model which emulated the operation of
the overall collection/storage/treatment system and which was used to:
- evaluate overall system yield
- set pump station design rates
- develop the integrated operation rules for the multiple reservoirs in
the system
o Evaluation of expected water quality in the various components of the
system.
o Application of air-bubble systems to control undersirable stratification
in the reservoirs.
The overall scope of the project is to develop a water supply to augment the
present supply for municipal uses. Treatment of this water to standards
suitable for municipal uses and its discharge at service pressure into the
distribution system are included in the project.
A shcematic layout of the water supply system is shown in Figure 1. The
reservoirs will receive and hold the runoff to equalize the sometimes high
and very intermittent runoff rates to meet the steady demand on the system
for treated water.
The Seletar Reservoir will be developed by the construction of an earth em-
bankment dam with protecting sluice way across the mouth of the estuary.
The reservoir created by the dam will collect runoff which originates on its
tributary watershed and runoff from collecting systems located in adjacent
catchments. These adjacent catchments are lands which are now being devel-
oped into "new towns" and nearby rural areas. A large sand quarry pit will
form the Bedok Reservoir. It will primarily receive runoff collected from
nearby urban land. Runoff from these catchments will be collected in ponds
or lagoons and conveyed to the Reservoir by pumps and pipelines. The water
collected in the Seletar Reservoir will be pumped either to Bedok Reservoir
or directly to the proposed treatment plant; the pipeline will be about 16km
long.
STORMWATER RUNOFF/CAPTURE ANALYSIS
One of the unique features of this scheme is the use of urban runoff as a
source of water supply. The drainage system consists of a rather complex
group of catchment areas; 23 catchment basins are involved. For twelve
of these, flow by gravity into the reservoirs is infeasible and a capture/
transfer scheme involving pumping is utilized. The response of this system
to rainfall events was evaluated so that overall system yield could be esti-
mated, and the capture/transfer sites could be properly sized.
24
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I
U-l
oc
u.
o
UJ
a:
OAQ
25
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STQRMWATER RUNOFF ANALYSIS
The model chosen to simulate the stormwater runoff characteristics of the
study area is STORM. In this study, STORM was used to compute surface run-
off from precipitation, based on the hydrologic characteristics of the drain-
age basin.
In order to systematically and consistently apply the STORM Model to each
basin, the standard procedure involving the following three steps was employ-
ed:
1. Identification of the most appropriate land use categories for the study
area.
2. Computation, for each drainage basin, of the area in each land use cate-
gory, and
3. Estimation of the STORM Model parameters for each land use.
Within the study area, there are a variety of existing or planned land uses.
To meet the requirements of this study, the usual six general land use cat-
egories were identified as follows: major roads, industrial, institutional,
residential, open space, and natural. Some variations in the development
levels and thus hydrologic features associated with each land use category
exist. However, it was established that the use of six standard land uses
adequately represents the hydrologic conditions. Given the rainfall char-
acteristics of the study area and the STORM parameters, the average annual
percent runoff was established for each of six land uses and using the
standard model parameters for each land use, the STORM Model was systemati-
cally employed to simulate basin runoff conditions.
For a number of drainage basins within the study area, stormwater runoff
cannot be transferred to system reservoirs by natural means. Such cases re-
quire a pumping scheme to lift flows to a reservoir. Rainfall in the area
is characterized by relatively high-intensity short-duration storm events.
Due to the fairly large amount of impervious surface and the short response
time of drainage basins in the study area, this rainfall is transformed into
runoff with no large attenuations. This particular condition requires that
any runoff transfer scheme involving pumping to also include a stormwater
storage facility to retain a portion of the runoff volume for pumping after
the storm has subsided.
A schematic of a typical storage and pumping facility is illustrated in
Figure 2. In the case shown, stormwater flowing along the main drainage
channel is diverted to the storage unit and from there is pumped to the
reservoir. When flows exceed the pumping rate, storage is used to contain
the excess. When flows are less than the pumping rate, the available pumping
rate is used to reduce the storage level. If the storage capacity is ex-
ceeded, any excess flow is not diverted to the storage unit.
It is important to note that Figure 2 illustrates one possible storage
scheme, which is typically referred to as "off-line" storage. An alternative
26
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Drainage
Channel
Diversion
Point
FIGURE 2
SCHEMATIC OF STORMWATER STORAGE AND PUMPING FACILITIES
27
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involves using the main drainage channel as an impoundment for "in-line"
storage; pumping occurs directly from the channel. Performance is based
only on the storage capacity (i.e., volume) irrespective of its location.
An additional component of a stormwater transfer scheme involves the diver-
sion point itself. The facility must include a means of selectively divert-
ing only a portion of the main channel flow for the reasons as follows:
1) during low-flow periods a bypass may be desired based on water quality
conditions, and 2) there may be a maximum hydraulic capacity where excess
flow cannot be diverted.
The stormwater transfer scheme described above has a number of basic design
parameters as follows:
1. For the channel diversion, there is a low-flow bypass and a high-flow
capacity,
2. The storage unit is parameterized by its volume capacity, and
3. The pumping unit has a hydraulic capacity.
Each of these features influences the ultimate capture achieved by the facil-
ity. A primary objective of the study was to define the relationships be-
tween the design parameters (such as storage volumes) and capture rates.
Basic design questions addressed include the following: how much capture is
lost to low-flow bypass, what limits do the diversion capacity place on
capture, and what are the tradeoffs between pumping and storage?
To evaluate the above methods for each basin in the study area, the DIVERT
module for STORM was developed. DIVERT is intended to be a preliminary de-
sign tool to assess the hydraulic performance of a large number of process
configurations.
Storage-treatment was included in the model due to the anticipated quality
of stormwater runoff and potential need for treatment. The DIVERT model was
developed primarily to evaluate capture achieved in schemes such as that in
this project; however, it has a number of very general capabilities.
A schematic representation of the DIVERT model hydraulic components is shown
as Figure 3. System computations are performed on an hourly time step and
are typically carried out for a number of years. Basic model input is an
hourly time series of runoff generated by STORM, and model output is an
hourly time series of system flows, As shown in Figure 3, there are six
basic system flows.
Hourly output time series are processed into relevant summaries (i.e., daily,
monthly, yearly, and simulation totals) for use in assessing system perform-
ance.
The DIVERT model was used extensively in the development of the sizing of
the various diversion/pumping alternatives considered. A typical output
from the simulation studies is the iso-capture plot shown in Figure 4 where
28
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SELECTIVE
DIVERSION
BLOCK
"TREATMENT/
STORAGE
BLOCK
PUMP/
STORAGE
BLOCK
STORJKATER RUNOFF (from STORM)
"RUNOr11
r
Model Output
"OVFLO"
FLOU TO RESERVOIR
FIGURE 3
SCHEMATIC DIAGRAM OF DIVERSION MODEL
29
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10 20
10 15 20 25 30 35
PUMPING CAPACITY, P • Q/{A F) (m3/hour per hectare)
FIGURE 4. CAPTURE NOMOGRAPH, ISO-CAPTURE AS A FUNCTION OF PUMPING
AND STORAGE CAPACITY PER UNIT EFFECTIVE AREA
30
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the capture effectiveness of a diversion site is expressed in terms of stor-
age pond volume and pumping rates. Such a plot, combined with the relevant
cost data, can then be used to select both the optimum volume/pump capacity
at a given site, and also to allocate capture rates between the many sites
in use in this scheme. A number of observations can be made from the data
shown in Figure 4.
1. Overall, the spacing between iso-capture contours steadily increases,
indicating an increasing marginal capacity required for additional
capture.
2. Beyond 50 to 60 percent capture, the marginal capacity requirements be-
come relatively large.
3. Along the vertical axis (i.e., constant storage volume), there is an
abrupt increase in the marginal pump requirements, and beyond about 3
to 5 m3/hour per hectare very large additional pump capacity is required
for further capture.
These figures are specific to hydrologic conditions for this scheme; similar
figures can be readily estimated for other sites.
SELECTIVE DIVERSION
Selective diversion potentially consists of two components - a low-flow by-
pass and high-flow diversion capacity. It is assumed that the bypass must
be satisfied before diversion begins and further that a limited hydraulic
capacity at the diversion structure exists such that excessive flows cannot
be routed to the pump/storage unit. Given this condition, the STORM/DIVERT
model was used to determine the relationship between the quantity of runoff
diverted and the diversion structure parameters. The following general ob-
servations can be made about the results obtained during this study:
1. Overall, there is a steady decrease in the sensitivity of capture to in-
creases in bypass and diversion capacity.
2. For relatively low bypasses there is a vary rapid loss in capture ef-
fectiveness.
3. Beyond a certain maximum diversion capacity very little additional
capture is achieved.
Bypass will be used primarily to exclude low-flows which may contain un-
acceptable water quality constituents. From a capture point of view, re-
sults indicate that a relatively large amount of runoff can potentially be
lost via bypass flows, and thus only the minimum required to satisfy water
quality requirements should be excluded. These are flows which are easily
captured from a hydraulics point of view and should not be bypassed unless
clearly necessary from a water quality perspective.
31
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HATER QUALITY ASPECTS
Numerous water quality issues are important to the implementation of the
proposed scheme. These issues are primarily stormwater runoff quality load-
ings and salinity and TDS levels in the reservoirs. Stormwater runoff qual-
ity is of importance since the water supply system consists primarily of
this urban runoff; these flows are the main source of nutrients to the res-
ervoirs.
In general, storm runoff is characterized by relatively high pollutant load-
ings; these pollutants exist and are washed off from both developed and un-
developed land surfaces. In this particular project, increased emphasis was
placed on runoff quality estimates because of the unusual nature of the
scheme as a whole. A relatively straightforward approach was taken with a
somewhat modified version of the STORM model being used in the simulation of
runoff quality loads. Available local historic hourly rainfall records were
used to drive the STORM simulations, with a three year period of record be-
ing found sufficient to provide reasonable estimates of long term averages;
generally a ten year hourly record was available for use. An important set
of parameters in modeling runoff quality is the pollutant accumulation and
washoff rates for the specific area being studied. Ideally, sampling data
from the area would be used to calibrate these parameters of the simulation
model. Although specific data of this nature was obviously not available
from the yet-to-be-developed "new towns," some data was available for nearby
similar developments. This data, coupled with values available in published
literature was sufficient to enable the team to estimate the long term aver-
age loadings to Total Suspended Solids, Nitrates, Phosphates and Biological
Oxygen Demand resulting from the stormwater runoff. Sensitivity studies
were undertaken to determine the impact of parameter uncertainty on the
loading estimates; the design of the overall system is sufficiently robust
to .adequately handle expected pollutant variations.
The modifications of the STORM model were primarily to enable the model to:
1. Simulate the transfer of pollutants through the diversion components in-
cluding the actual diverters, settling of solids in the small ponds, and
the pump operations.
2. Evaluate the operation of swirl concentrators which were considered for
use at the diversion sites. These were ultimately not recommended for
use.
The runoff from the catchment areas is captured and stored in the reservoirs
prior to treatment. The benthos deposits in the reservoirs are also a major
source of contaminant loadings in the system; in previous similar schemes
they have been a significant operational nuisance. It is expected that
phosphate, chloride and sulphates will be the contaminants of most impor-
tance in this scheme.
32
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SUMMARY
This application required integrated use of many hydrologic modeling techni-
ques in the development of a highly complex system. Their use in this pro-
ject permitted significant increases in the design "safe yield" of the sys-
tem and enabled the design team to evaluate the effectiveness of the many
quantity and quality control options which have to be considered during de-
sign development. Problems do exist in the use of urban runoff for supply
systems; however, in situations where well-designed separate storm drain
systems are available, the runoff can be effectively used as a supply source.
JEN AI RIVER - KAOHSIUNG, REPUBLIC OF CHINA
BACKGROUND
Kaohsiung is a city of about one million people Icoated on the southwest of
the Island of Taiwan.
There are now essentially no sanitary sewers in Kaohsiung. All sanitary
wastewater, together with stormwater, flows via combined sewers and open
channels to the Jen Ai River, a narrow, poorly-flushed tidal estuary. The
resulting very heavy loadings of BOD have rendered the Jen Ai anoxic; the
river is both odorous and an eyesore due to floatables.
The city government is presently undertaking a project to radically improve
the water quality in the Jen Ai. This project has several major components
as follows:
1. Build a trunk sewer of sufficient capacity to intercept all the dry
weather flow (DWF) and some of the wet weather flow at each of 3
principal tributary channels or sewers.
2. Remove the majority of the anoxic sediments from the bottom of the Jen
Ai by dredging.
3. Implement other means to maintain an improved water quality in the river.
At this time, a trunk sewer has been constructed to intercept combined storm
and sanitary sewage from 8 catchment areas, 6 on the east bank of the Jen Ai
River, and 2 on the west bank (see Figure 5). The area drained by the 8
basins is about 5400 ha. The total dry weather flow from the 8 areas is 3
cms, and the total dry weather BOD load is 56000 kg/day.
33
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The total design capacity of the trunk sewer and the pump station at its
downstream end is 6.5 cms, or about twice the combined total dry weather
flow of the 8 areas. Thus all dry weather flow and some storm flow will be
intercepted, but stormwater will still overflow to the river when flows ex-
ceed the trunk sewer capacity.
The analytic work described here was undertaken to evaluate the effective-
ness of the proposed scheme in terms of improvements in D.O. in the Jan Ai
River, and to assist in the sizing of the diversion structure. On the
larger tributaries, the provision of capacity to store significant quanti-
ties of stormwater, until the water can be drained to the sewer following
the storm, greatly reduces the frequency and magnitude of storm overflows,
and the mass of BOD discharged in overflows.
On the smaller tributaries with little or no storage capacity, where much of
the stormwater will have to overflow to the river, the use of swirl concen-
trators to remove TSS and BOD from overflow water before its discharge to
the river was evaluated.
As will be noted, the plan is to divert a significant fraction of the tota1
BOD loads from the overall watershed through use of quite a small intercept-
or, with essentially the whole drainage system diverted through it during
dry weather conditions. The storm discharges from the basin are about 63
cms for a "typical" monthly storm (6mm/hour) and 540 cms for the 5-year
design event; these figures should be contrasted with the 6.5 cms peak
capacity of the interceptor.
APPLICATION OF STORM
The STORM model was used extensively in the following aspects of the study:
(1) To determine runoff rates from the various watersheds.
(2) To determine mass loadings of BOD and TSS from the area.
(3) To assist in sizing the various control facilities required to divert
flows.
(4) To help evaluate long term management strategies for the basin.
Hourly rainfall data was available for 12 years; typical simulations used
6 years of records which included a typical range of wet and dry years. The
climate of Kaohsiung is characterized by an extremely dry winter from Novem-
ber through March followed by a very wet summer season.
Sol-ids buildup in the side drains and street-side ditches tends to be signi-
ficant during the winter months; during this period the flows in the system
are largely sewage and grey water. Little or no flushing of the estuary
occurs during this period.
35
-------
The months of April and May are characterized by moderately intense rain-
falls; these first storms after the dry season flush much of the deposited
solids from the network and dump them in the river. The assimilative capa-
city of the river during this period is overwhelmed by the total magnitude
of the BOD moads.
A modification was made to the STORM model to enable us to simulate the
long term deposition of solids in the "sanitary" system since the system is
not self cleansing as in typical U.S. systems. These depositional factors,
Fl and F2, are the mass fraction of the TSS and BOD in sanitary sewage which
in dry weather settles out of suspension and is deposited in the drains and
watercourses. These deposits are then resuspended and flushed to the inter-
ceptor/river during storms. It was not possible to perform field tests to
determine the actual deposit fraction for TSS and BOD during the course of
the project. The values used for most STORM runs were 0.7 for TSS and 0.3
for BOD. These values are probably conservatively high since channels at
low-flow sites cannot be assumed to be as efficient as primary clarifiers
would be. However, since our concern was with the fraction resuspended dur-
ing the storm events, it was decided to adopt the above figures.
The overall system was evaluated by simulating each individual basin and its
interceptor junction characteristics; the allocation of interceptor capacity
against basins was as further indicated below.
The results of the simulation runs were largely as anticipated. Figure 6
shows the impact of allocated interceptor capacity on the BOD overflowing
to the river from a typical basin; it will be noted that the allocation of
flow capacity above the DWF results in only minor reductions in overflows.
It proved possible to use disused canals as storage basins in several
instances; the impact of such storage on BOD overflows can be significant
and as shown in Figure 7 can reduce the fraction of BOD overflowing to the
river from about 30% to 5% of total BOD loads from the tributary basin.
The impact of using swirl concentrators for grit and solids removal at sev-
eral of the smaller basins is shown in Figure 8. Although effective on a
single site basis, they did not prove cost effective in terms of the overall
Jen Ai control strategy.
Schematic layouts of a typical interceptor structure are shown in Figure
9-11.
Overall, it is estimated that the proposed scheme will reduce BOD loads to
the Jen Ai River by about 90% from existing conditions. Overflows will still
occur about 20-40 times per year; many of the overflows are quite small and
the BOD loads minimal.
The computed reduction in BOD loading to the river is just about adequate to
enable the estuary to achieve a D.O. level of 2 ppm under average month
conditions. Heavy loadings in the spring months will be sufficient to de-
oxygenate the river during these periods. As a result, it is proposed that
a series of air-bubblers be installed to ensure that the estuary remains
fully mixed and surface oxygenation maximized. Simulations indicate that
36
-------
500
ec
400
* 300
cc
LJ
IT
o
>-
o
z
o
CC
Id
200
O 100
o
o
m
SITE D
F = 0.3
NO TREATMENT
NO STORAGE
.05 .10 .13 .tO .25 JO
ALLOCATED TRUNK SEWER CAPACITY, t(CMS)
FIGURE 6. INFLUENCE OF TRUNK CAPACITY, t,
ON BOD OVERFLOW RATE, y
37
-------
o
m
UJ
o
0.6
0.5
0.4
0.3
O.I-
)•
LETTERS DENOTE SITES
H°
.005 .010 JOI5
STORAGE VOLUME
.020
.025
TRIBUTARY AREA X RUNOFF FACTOR
m
FIGURE 7. INFLUENCE OF STORAGE VOLUME
ON BOD OVERFLOW RATIO
o
o
UJ
>
O
O.6
0.5
0.4-
S O3
I ....
O.I -
WASH:do WAS":2;
O.I OlE 0.3 0:4 0:5 0& 0.7 aB
BOD REMOVAL EFFICIENCY
(IN SWIRL CONCENTRATOR FOR OVERFLOWS)
0.9
FIGURE 8. INFLUENCE OF" BOD REMOVAL EFFICIENCY
ON BOD OVERFLOW RATIO
38
-------
6 VERTICAL- LIFT
FLOOD GATES
ALTERNATE
LOCATION A
EXISTING
WORKING
SHAFT
, EXISTING
/ WORKING
SHAFT
ALTERNATE
LOCATION B
FIGURE 9. SITE PLAN FOR INTERCEPTOR STRUCTURE AT "E"
TWO ALTERNATE LOCATIONS ARE SHOWN.
39
-------
UJ
o:
oo
C£
o
I—
D_
LU
O
QL
UJ
U3
40
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01
ID
K-
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p
Q.
C_J
a:
Di
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C£
Qu
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CD
41
-------
this will maintain adequate D.O. levels in the river.
SUMMARY
In this situation, it has proved possible to quickly restore adequate water
quality to an estuary which was grossly overloaded with uncontrolled sani-
tary and stormwater flows. The cost is quite low and well within the means
of developing countries. Of course, the problem is not yet fully solved -
those areas upstream of the interceptor still contain open sewers which will
have to be systematically upgraded over the next 10-20 years.
CONCLUSIONS
Models such as STORM can be effectively used in design situations in devel-
oping countries. In many instances, the problems facing the designer are
much tougher than those encountered in the U.S. - fundamental public health
improvements must be sought with moderate expenditure of funds for construc-
tion. In the cases discussed in this paper, STORM proved to be a very effec-
tive tool in assisting the designers to achieve the design goals.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
42
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AN ATTEMPT TO IMPLEMENT SWMM IN TUNISIA
by Janusz Niemczynowicz
ABSTRACT
In 1980, the University of Lund started a research project in co.operation
with the University of Tunis. The aim of the project, was to implement the
SWMM in Tunis and to teach local research personel how to handle the model.
During the winter season, there are flooding problems in the cities of Tuni-
sia due to high-intensity convective rain storms and underdesigned sewage
systems. The greatest efforts in the city of Tunis until now have been made
to solve the immediate problems as street flooding by constructing a huge
stormwater conduits. This will probably increase already severe pollution
problems in the receiving waters. It is obvious that some kind of system
thinking has to be applyed in this situation. Implementation of SWMM-model
was thought to be one of the masures possible to take in order to assure
meaningful! water management in th cities. In order to obtain the input data
for calibration of the model, a catchment of 20 sq km was instrumented. Dif-
ferences between Swedish and Tunisian urban areas, together with the climat
in Tunisia, couse significant differances in the input parameters in the
model. For example, roughnes in water courses can not be treated as a cons-
tant in Tunisia. During the dry period great amount of garbage is accumulated
in the water corses, during rainy season the garbage and lush vegetation is
succesively removed and the roughnes decreases gradualy. The paper describes
how the difficulties during field work, differances in working routines,
problems with understanding the"model ing philosophy", and problems with model
calibration influence the possibility of model implementation in Tunisia.
INSTRUCTION
The average, yearly precipitation in Tunis is about 450 mm. The major part of
the yearly rainfall occurs during October, November and December, usually as
short, intensive convective rainstorms. These rainstorms often take the form
of thunderstorms. The rest of the year, there is very little precipitation.
Tunis is surrounded by high hills which slope steeply towards the central
part of the town causing severe problems with storm water management.
43
-------
The storm water system presently existing in Tunis is not sufficiently design-
ed to handle storm water runoff resulting in street flooding several times a
year. During the past three years, great efforts have been made to reduce
flooding by constructing a huge storm water conduit which leads water from
the central part of the town to the nearby situated Lac de Tunis lagoon
(Coyne 1974). It is unlikely that even these efforts will significantly im-
prove the situation due to rapidly increasing urbanisation of the suburban
areas. Other problems will occur, i.e. pollution of the lagoon by storm water
discharge.
Most of the cities in Tunisia has the same problems. It is obvious that some
kind of system thinking has to be applyed in this situation in order to as-
sure resonable way to solve the design problems associated with storm water
systems. Implementation of SWMM-model was thought to be one of the measures
possible to take in order to assure meaningful 1 water management in the ci-
ties avoiding all the mistakes previously done in European countries in this
matter.
In 1980, a research project was started in co-operation with the University
of Tunis. The aim was to implement the Storm Water Management Model and to
teach local Tunisian research personnel how to handle this model.
In order to calibrate the model, a large amount of rainfall and runoff data
had to be collected in an environment rather different from the Swedish one.
p
We decided to use the 20 km Guereb-Roriche catchment in the northern part of
Tunis.
CATCHMENT AND INSTRUMENTATION
The Guereb-Roriche catchment consists of two areas: the highly urbanised sec-
tion in the south and the rural area in the north with a few single-family
dwellings.(See Figure 1).
The urbanised area of the catchment is densely populated and housing consists
of multi- and single-family buiIdings andsome industries. The character of
44
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GUEREB-RORICHE
CATCHMENT
INSTRUMENTATION
O Raingouge J/ /L°C de Tunis
* Run off measuring station
0 Quality sampler
*%S Densly populated aerea
^ Water storage dams
Figure 1. Instrumentation of the Guereb-Roriche catchment.
the housing is quite different from European housing, which has significant
hydrological consequences. For example, almost all houses have flat roofs
with elevated edges, which causes roof ponding. Some of the minor streets
are not paved. Roof drainage is rarely connected to the storm water system.
The percentage of impermeable surfaces is very high - up to 60% in some are-
as.
The southern part of the catchment is very flat and varies less than 50 meters
in altitude.
The northern part,on the other hand, is hilly with altitude differences up to
250 meters. Agriculture dominates in this rural area byt the uppermost region
is uninhabited due to severe erosion of the steep hillsides.
The catchment is drained by two periodicly appearing rivers, the Guereb and
the Roriche, which join in the lower part of the catchment and then flow into
the Lac de Tunis lagoon. In the upper part of the catchment, there is no flow
in either river during the dry period. However, there is some baseflow
occuring in the lower part due to the release of waste water from the slum
45
-------
areas. During the wet season, discharge from both revers can be as nigh as 15
m3/s.
The soil type within the catchment is laterit clay. Because of cracks
occuring in this clay during the dry season, it becomes very permeable.
After the first few rainfalls, permeability of the clay reduces drastically
(Infiltration tests made during the dry season have shown that the infiltra-
tion capacity exceeds 50 inches per hour during the next three hours). It
can be expected that infiltration tests made during the wet season will give
quite different results.
Urbanisation of the rural northern regions is proceeding rapidly and it is
expected that the entire catchment will be urbanised within a few years. The
development plans for the northern part include single-family homes, high
multi-family buildings and schools.
In order to take into account the nonhomogeneous character of the catchment,
and achieve rainfall area! characteristic, the runoff and rainfall measuring
stations were installed in 9 tield stations (Figure 1). (Niemczynoiwicz et al
1981).
As the distance between the stations is rather long, and there are no reli-
able telephone lines available, it was decided that all stations shouldrbe
equipped with separate clocks, data-loggers and automatic start-/stop-units.
The rainfall gauges are of the standard tipping-bucket type manufactured by
Rimco, Australia, with a bucket capacity of 0.2 mm. The funnel diameter is
203 mm and the total accuracy is + 1% up to 380 mm/h.
The runoff gauge is an echosounder manufactured by Endress and Mauser, West
Germany. It permits a non-contact continuous measurement of the water level
over the weir.
In addition, there is also a mechanical water level recorder ensuring that
no data are lost during current-failure periods.
46
-------
The datalogger, manufactured by A D Data Systems Inc., USA, Type ML-10, has
an internal quartz-controlled clock and a capability of monitoring up to 10
analogue signals and 32 bits of digital data. The data are recorded in a com-
puter-compatible format on a Philips-type data cassette. Data can be recorded
at pre-selected intervals which are controlled by the digital clock, by a
front-panel manual switch or by external input.
The recording interval is 5 minutes.
The automatic start/stop unit offers two possibilities of starting a recor-
ding sequence.
If the water rises to a certain pre-selected level, the recording starts; if
the raingauge counter reads two or more, the recording is also started...An
additional timer keeps the recording for 2 hours after the last raingauge
tipping to make sure that the whole hydrograph is recorded.
The stations operate on a 220 V 50 Hz supply, but as we have had som bad
experiences with the power supply, especially during rainfalls, we have
changed the stations to battery power.
Figure 2 and 3 show two of the runoff measuring stations.
Figure 2 Runoff station
47
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Figure 3 Runoff station.
RESULTS
During 1981 and 1982, great efforts were made to collect and analyse avail-
able documents and maps in order to gather all data necessary for modeling.
We often discovered that important data were missing or could not be delive-
red by the officials in charge. There were also many maps of conduits that
did not correspond to the actual situation in the field. As a result, a lot
of field work had to be done for verification of necessary data.
The catchment was divided into forty-six subcatchments ranging in size from
22
0.06km to 1.44 km (see Figure 4). The storm water system consists of seven-
ty-seven sewer pipes amd two storages in the upstream region of the catch-
ment (see Figure 5).
After two years of data collection only about 8 rainfalls-runoff occurences
were registratod on more then one station. Only service in the field which
had to be done to assure registration was changing the cassettes, paper
charts ande the batteries in adequate periods of time. Unfortunately, most
of the high intensity rainfalls happen to occur while batteries were empty
or cassettes were full. During the third and final season of registrations
48
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Catchment segmentation
Water divider
Main water course
Water divider between subcatchments
Main conduits
Water storage dams
Figure 4 Guereb-Roriche catchment in Figure 5. Guereb-Roriche catchment.
Tunis Diagram of storm water
system.
the schedule for permanent superintending by Swedish personnel was estab-
lished. This resulted in that sufficient amount of field data to make a reso-
nable calibration of.the model was collected.
MODEL CALIBRATION
In co-operation with two students from the University of Tunis, an attempt
was made to calibrate the model. We discovered that our initial estemates of
the parameters were rather inaccurate.
Fig 6 shows an example of the calibration runs. The first run was completely
49
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different from observed hydrograph. We soon discovered that procentage of
impermeable surfaces taken directly from the maps does not represent the real
situation. Only about 40% of all impermeable surfaces is connected to storm
water system. The main problem however is that this figure changes with time
during the rainy season. The reason is to find in erosion of soil between
paved surfaces, which gradually open small channels connecting new areas to
the system. One of two parameters depression storage or procentage of imper-
meable surfaces must to be treated as a function of time.
M3/S /\
TUNIS ELMENZ4H
EVENT 2Q.Ot.82
TUNIS 9CRUCT
EVENT laot.n
Figure 6 Examples of observed and SWMM-Simulated hydrographs
Thewidthof the overland flow (w-parameter), which influences the shape of
the hydrograph, calculated accordingly to the generally accepted rules, ap-
peared to be far too high. This can be explained by the fact that the surfa-
ces are more undulated than we are used to, which makes the legth of the
overland flow longer. Because of the high values of the infiltration para-
meters, used in the first simulations, no runoff was simulated from perme-
able surfaces. This is probably true for some of the first rainfalls in the
beginning of the rain season. During the rain season, the infiltration capa-
city changes drastically and the infiltration parameters should be changed
50
-------
accordingly. During the first rainfalls, SWMM overestimated the peak flow
and runoff volume, but during the following veeks, the simulations were much
better (see Figure 7). This can probably be explained by the variations of
the roughness in the main water channel. The river Guereb and Roriche, which
drain the catchment, have rather flat sloping sides in the lower part of the
catchment. During the dry season, very lush vegetation covers the slopes of
the channel and most of the vegetation from the side slopes changing the
rouqhness of the channel drastically.
Fiqure 7
Examples of observed and SWMM-simulated hydrographs
In spite of those difficulties and differences in the magnitude of model
parameters it is possible to reproduce the observed hydrograph quite well.
The areal distribution of rainfull has to be taken into account because dif-
ferances in rainfall intensity are very significant.
The one of the goals of the projekt was to implement SWMM on the French com-
puter in the university of Tunis. The Guereb-Roriche catchment
51
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was ment to be only a experimential field for demonstration of model applic-
tion, and for training Tunisien personnel in geting indata, running the model
and making design simulations. With other words, the project was thought to
be demonstration project to teach "modelling philosaphy". The main problems
which we faced in this context was the lack of hydrologists simultaneously
able to run the computer. On the other side there are no computer man who
understand hydrology.
Until now all the computer runs were done in Sweden.
REFERENCES
Coyne et Bellier,1974, Etude de 1'assainissement de Grand Tunis. Etude de
facilite du plan directeur, ICN, Pays-Bas.
Dahlblom, P; Niemczynowicz, J; Hogland, W, 1982, "Significance of Water
Planning in Tunisia". Dept of Water Res. Eng., Lund University, 1982.
Dendrou, S A ; Delleur, J W, 1978, Planning Storm Drainage Systems for Urban
Growth, Journal of the Water Resources Planning and Management Division, Nov.
Hogland, W; Niemczymowicz, J, 1980, Kvantitativ och kvalitativ vattenom-
sattningsbudget for Lunds centralort. Kompletterande matningar och metoder.
Institutionen for teknisk vattenresurslara, LTH/LU, Nr 3038, Lund.
Niemczynowicz, J; Grahn, L, 1981, Hydrological Instrumentation. Fifteenth
Anniversary Report, Department of Water Resources Engineering, University
of Lund, Report No 3053.
The work described in this paper was hot funde'd by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
52
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THE SEDIMENT-WATER INTERFACE IN MODELING PESTICIDES IN SEDIMENTATION PONDS
by
Peter R. Jaffe and Raymond A. Ferrara
Department of Civil Engineering
Princeton University
Princeton, NJ 08544
Introduction
Many pesticides adsorb onto soil particles upon application to fields.
Stormwater runoff then results in the transport of these soil particles with
adsorbed pesticides to the receiving waters. As a result, peak pesticide
concentrations, sometimes reaching acute levels, can occur in receiving
waters during storm events that follow pesticide application. Since parti-
culate material can be removed via sedimentation, the objective of this work
is to study what effect a sedimentation pond may have on the pesticide load
to receiving waters.
The model presented in this study considers that the pesticide fraction
adsorbed onto the sediments will be removed during the sedimentation process,
and incorporated into the bottom sediments. When after several storm events
the dissolved pesticide concentration in the overlying water column decreases,
the bottom sediments will release some of the pesticide contained in them.
The sedimentation pond will then behave like an equalization basin, capable
of buffering peak loads. This buffer capacity is enhanced by the sedimen-
tation process, and the capacity of the bottom sediments to first retain and
then release again a portion of the applied load. Furthermore, if decay
occurs, a pond could be designed to provide sufficient detention time to
decrease the net total load to the receiving water.
Model Development
The water column of the pond is represented as a completely mixed
system. Pesticides are added to the pond during storm runoff in dissolved
and adsorbed phases. These phases are at equilibrium as defined by their
partition coefficient (i.e. a linear Freundlich adsorption isotherm). The
dissolved phase can undergo any of a series of first order transformation
processes, such as chemical or biological degradation or evaporation, all
of which are additive. Other sources and/or sinks of the dissolved phase
are the equilibrium interaction with the phase adsorbed onto sediments,and
diffusion into or out of the bottom sediments. The adsorbed phase can also
undergo any of a series of first order transformation processes in addition
to settling from the water column to the bottom sediments. Consequently,
to model this system, equations are required to describe the changes in
53
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volume, suspended sediments, adsorbed pesticide concentration, dissolved
pesticide concentration, and pesticide concentration in the bottom sediments.
a) change in volume
- E) (l)
V -
2/3
if V £ VM, then QQ = 0
where: A - surface area,
E = evaporation,
K = constant,
L = length of the weir,
P = precipitation,
Q. = inflow,
Q = outflow,
R = change of volume due to the deposition of sediments,
V = volume, and
VM = holding capacity of the pond.
b) suspended sediment
Many chemical and physical properties of individual sediment particles
are dependent on their size distribution (e.g. clay has a higher adsorptive
capacity and a lower settling velocity than sand). Consequently the size
distribution of sediments contained in storm water runoff is important.
Furthermore irregularities in shape require the specification of a settling
velocity distribution for particles which are nominally of the same size
(Ferrara and Salvage, 1982). Then:
3t ' »l Cs1jk - «o Csjk - A \ Csjk
J. L
where: Cs.. = suspended sediment concentration of j size
J fraction with settling velocity vk,
Csi., = Cs., in the inflow, and
j k j k
vk = settling velocity.
then the term R in Equation ( 1 ) is
54
-------
s j k
where: P = density of an average sediment particle, and
= connected porosity.
The sediment-size distribution is divided into n size fractions, j = 1 -> n.
Each size fraction has a velocity distribution that is divided into m velocities,
k = 1 ->• m, but m does not have to be the same for each j. For non-settling
solids (colloids), the velocity is zero.
c) adsorbed pesticide concentration
The change of concentration with respect to time of adsorbed pesticides
in a given size-velocity fraction of the sediments in the water column is:
If (Cajk V> = Qi Caijk - QO Cajk - A vk Cajk -V kj Cajk - Djk (6>
The overall adsorbed concentration is then
^r (V E E Ca,,) = Q. E E Cai . - Qo z E Ca.. - A E E v, Ca ..
01 j k Jk n j k Jk j k Jk j k k Jk
- V E E k'! Ca - £ E D . (7)
j k J Jk j k Jk
where: Ca.k = adsorbed concentration on j sediment fraction
J with settling velocity v, ,
K
Cai., = Ca.. in the inflow,
J K JK
k". = sum of first order reaction rates of the adsorbed
J pesticide, and
D-k = desorption term.
d) dissolved concentration
The equation describing the dissolved concentration in the water column
is:
. Q. -CC) - k1 VC - AJ+ E I D , (8)
IT o .JI.JK
and
55
-------
j = _ A(on + Dr + DT) — + d> v (9)
VN B S I 3x y w '
x=0 x=0
where: C = dissolved pesticide concentration,
k1 = sum of all first order reaction rates,
J = losses into the bottom sediments across the sediment-
water interface (advective plus diffusive flux),
DR = bioturbation coefficient,
D<. = molecular diffusion coefficient,
DT = irrigation coefficient,
v = velocity of water burial below the sediment water
interface, and
D.. = desorption term.
The equilibrium between the dissolved and adsorbed phases is
Cajk - Kj C Csjk (10)
where K. = partition coefficient.
J
Substituting equation (10) into equation (7) to eliminate the adsorbed
concentration and then combining this equation with that for the dissolved
concentration, equation (8) eliminates the desorption terms and yields the
final equation for the dissolved pesticide:
Q C. Z (K. Csi.) - C[Q +Vk;] Z (K. Cs.) - AC Z v K Cs + C Q
f\r 1 1 -• J J 0 JjJJ n-JJJ 11
uu = J sj J
dt V[l + Z K. Cs.]
T J J
( HV dCsi
CQn- k'VC- AJ-
-------
Ca - C Z £ K. Cs., (12)
j k J Jk
and the total pesticide concentration (adsorbed and dissolved) as:
CT = C(l + z z K. Cs.. ) (13)
1 j k J JK
Solution of this system of equations requires knowledge of the dissolved
concentration gradient in the bottom sediments (equation (9)). Therefore
solution of the concentrations in the bottom sediments is also necessary.
e) bottom sediments
The development of the following equations is summarized from the work
of Berner (1980).
The mass balance equation in the sediments is:
3C. 3F
inrs -1*1 + z Ri (14)
where: C. = concentration of solid or liquid component i in terms
1 of mass per unit volume of total sediment,
F. = flux of component i, and
R. = reaction rates affecting i.
and
3C.
F. = - D -r-1 + v C. (15)
18X1
where: D = diffusion coefficient, and
v = velocity of flow relative to the sediment-water interface.
If no compaction or infiltration to the groundwater zone occurs, v is the same
for the solid and liquid component. Then v = v = velocity of burial of
solid particles and/or water below the sediment-water interface.
The diffusion coefficient for the solid component near the sediment-
water interface (bioturbation and/or current mixing) is Dg. For the dis-
solved phase, this same DR plus an irrigation coefficient Dy and a moleular
diffusion coefficient DM which is independent of depth apply.
The concentration of a solid component Ts can be expressed in terms of
mass per unit mass of total solids
57
-------
Cs = (1 -)p Cs (16)
and for the dissolved component the concentration C is expressed as mass per
unit volume of pore water
Cd = 4> C (17)
Then, combining each of equations (16) and (17) with equations (14) and (15)
yields the general equations for the bottom sediments, which for a solid
component is
r
3['0 - *)p. CS] 8(D - -^ - } 3[(1 - *)v p CS]
(1 _ j R
3t 9X 8X v/ S
(18)
where Rs is the reaction rate in mass per mass of solids per time, and for a
dissolved component
v C)
where Rd is the reaction rate in mass per volume of pore water per time.
For sorbing pesticides, equation (18) can be used for the adsorbed pesti-
cide C, and equation (19) for the dissolved pesticide. The partition coef
ficient is used again to describe the equilibrium between the adsorbed and
dissolved phases
C" - Kp C (20)
where K is an average partition coefficient in the bottom sediments (equa-
tions (10) and (20) are equivalent).
Furthermore, a mass balance between the two phases must hold, so that the
sorotion rates R are related to each other by:
Rs = ," * > R. (21)
(1 - 4>JPS d
From the previous equations the final equation that describes the changes
in concentration in the pore water of the bottom sediments is obtained:
58
-------
9[(D
v £k + /_..' \
V ( l
it" 3X 1 + K1 3X w 3X 1 + Kl
(22)
where K1 = (PS(! - 4>) Kp).
This equation is solved numerically via finite difference methods with a
variable boundary condition, which is the dissolved concentration in the
water column. The set of ordinary differential equations describing the
water column is solved using the Runge-Kutta method. Because the two
systems are interacting with each other they are solved in sequence for
each time step.
Results and Discussion
The results of several simulations are shown in the following figures.
Typical values for yearly storm runoff data, including runoff volume, sedi-
ment mass and pesticide load were used (Smith, et. al., 1977). The sediment
size-velocity distributions of the inflow sediments were assumed constant
for all storms, and are listed in Table 1. Using the relationships reported
by Karickhoff, et. al. (1978) the partition coefficients were estimated based
on the organic carbon content of the sediments and a range of typical octanol-
2 4
water partition coefficients (10 -10 ). In the absence of reported data for
mixing coefficients in bottom sediments, reported values for mixing coeffi-
cients in near shore silts were used (Berner, 1980). For the following simu-
lations, a detention capacity of the pond of 2000m and a depth of 2 m was
selected.
The bottom sediments were modeled over a depth of 0.2 m. Bioturbation
and irrigation was considered to occur only in the upper 10 cm while mole-
cular diffusion was modeled over the entire depth of the bottom sediments.
The molecular diffusion coefficient was estimated based on a molecular weight
of 200 and corrected for the tortuosity dividing it by the product of the
porosity and the formation factor. A formation factor of 3 was assumed.
In Figure 1 the inflow (runoff) pesticide concentration is shown over
time, as well as the pesticide concentration in the pond for two different
partition coefficients. The effect of the pond can be seen clearly. The
peak concentration in the pond is about 3% of the peak storm runoff concen-
tration without a pond. As expected, if the partition coefficient is in-
creased the reduction of the peak concentration is even higher, because more
pesticide is in the adsorbed phase, consequently increasing the pesticide
removal efficiency of the sedimentation process. For longer times, the ef-
fect of the pond is to retain and slowly release pesticides. This effect is
increased for higher partition coefficients.
In Figure 2 the total cumulative pesticide load to the receiving waters
for consecutive seasons is shown. As expected, if some decay does occur in
the water column (k = 0.02 day" , for the dissolved phase) the overall
pesticide removal rate is increased. It is interesting to notice that for the
59
-------
case where decay occurs the system reaches its final conditions sooner than
if decay does not occur. For the later case, the final conditions would be
such that the yearly cumulative loads with and without the pond are the same.
The reason for this is that the initial adsorptive capacity of the bottom
sediments is exhausted but a buffering capacity still exists. In other
words, when the system reaches its final conditions, there is no net gain in
pesticide mass in the bottom sediments over a season. This is illustrated in
Figure 3, which represents the concentration profiles in the bottom sediments
at the end of each year for the cases of Figure 2. The fact that the bottom
sediments continue to have a buffering capacity, even if their net yearly
gain of pesticides is negligible, is shown in Figure 4. This figure shows
the pesticide profile in these sediments at the beginning of the second
season, after 50 days, and at the end, for a pesticide with decay.
The effect on the cumulative load of different partition coefficients is
shown in Figure 5 in which a pesticide with decay is modeled. The increase
in pesticide removal efficiency for increased partition coefficients, during
season modeled, results because for higher adsorptivities the influence of
sedimentation increases, and also the bottom sediments have a higher capacity
to retain pesticides.
For all of the previous simulations it was considered that 54% of the
sediments in the inflow are colloidal material or fine clays that will not
settle. Theimproved pesticide removal efficiency when a coagulant is added
reducing the non-settling fraction by 75% is shown in Figure 6. These simu-
lations do not include a decay rate. Similar results were obtained for two
simulations using low (i.e. fine silt) as well as high (i.e. sand) settling
velocities for the coagulated solids.
Summary and Conclusions
The results of these simulations show that sedimentation ponds can be
used effectively to dampen out peak pesticide loads to receiving waters. If
no decay occurs the total yearly load to the receiving waters will be the
same with or without a pond once final conditions (i.e. after a few seasons)
are obtained. If some decay occurs, the total yearly load at final condi-
tions will be less with a pond than without one.
Bottom sediments and their interactions with the water column, often ig-
nored for this type of analysis, have been shown to have an important effect
on the performance of the pond. It would therefore be extremely valuable to
have a better understanding of the mixing conditions in the upper sediment
layers of ponds and lakes, as well as the reactions that occur for pesticides
and other pollutants in adsorbed and dissolved phases in these sediments.
References
Berner, R.A., Early Diagenesis, Princeton University Press, Princeton, NJ,
1980.
Ferrara, R.A., and Salvage, K.M., "Stormwater Pollutant Settleability," in
press.
60
-------
Karickhoff.S.W., Brown, D.S., and Scott, T.A., "Sorption of Hydrophobia Pol-
lutants on Natural Sediments," Water Research, v. 13, pp. 241-248, 1979.
Smith, C.N., et. al., "Transport of Agricultural Chemicals from Small Upland
Piedment Watersheds," USEPA, ORD, Env. Res. Lab., Athens, Georgia, draft
report, 1977.
Table 1
Distribution of the Solid Particles in the Runoff
Particle Size (microns)
% organic
carbon
fraction of
the total
mass
settling
velocity
(m/day)
larger than 150
2.6%
o.ie
2070
0.03
6480
0.01
10800
between 1 and 150
5.3%
0.01
540
0.11
1620
0.04
2880
smaller than 1
4.9%
0.02
195
0.08
580
0.54
0
61
-------
0,06
•t
*
g 0.05
£ 0.04
Z
z
I 0.03
£
g 0.02
<_>
£ 0.01
M
• INFLOW CONCENTRATION
O CONCENTRATION IN THE POND FOR
Ko.W " 10^
ft CONCENTRATION IN THE POND FOR
KO.W » 103
100
200
TIME (DAYS)
300
1.5
1.0
s
J
FIGURE 1. ATTENUATION OP THE CONCENTRATION.
• WITHOUT THE POND
• 2ND YEAR WITHOUT DECAY
j, 1ST YEAR WITHOUT DECAY
• 3RD YEAR WITH DECAY
i
I
w
>
§
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0 1ST YEAR WITH DECAY
•
.
• •
.
X
Jt A *
I £ o °
• 4 o
• • *
• |l*
8
-
•
50 100 150
TIME (DAYS)
FIGURE 2. CUMULATIVE LOAD FOR CONSECUTIVE SEASONS.
62
-------
0
2.5
5
I 7.5
10
12.5
15
17.5
20
X INITIAL CONDITIONS (2 YEAR)
• -50 DAYS LATER
A FINAL CONDITIONS (3 YEARS)
. I . . i . I
0.005 0.010
DISSOLVED CONCENTRATION (MS/*)
0.015
FIGURE 3. PERIODICAL VARIATION OF THE CONCENTRATION
IN THE BOTTOM SEDIMENTS.
I
0
2.5
5.0
7.5
10.0
12.5
15.
17.5
20.
A END OF THE FIRST SEASON/ WITHOUT DECAY
" END OF THE SECOND SEASON, WITHOUT DECAY
OEND OF THE FIRST SEASON, WITH DECAY
»END OF THE SECOND SEASON, PITH DECAY
. I i i . . I . . i .
0.005 0.010
DISSOLVED CONCENTRATION
0.015
FIGURE 4.
EFFECT OF A DECAY RATE ON THE CONCENTRATION IN
THE BOTTOM SEDIMENTS.
63
-------
0.22
0.20
0.18
0.16
i 0.14
| 0.12
> 0.10
3 0.08
CJ
0.06
0.04
0.02
A
•
WITHOUT THE POND
K*S COMESPONDIN6 TO A Ko.M - 102
S CORRESPONDING TO A Kb.tt. - 10*
'S CORRESPONDING TO A KO.N. - 10"
0 •
SO
100
TINE (DAYS)
150
FIGURE 5. EFFECT OF DIFFERENT PARTITION COEFFICIENTS ON THE CUMULATIVE LOAD.
0.22
0.20
0.18
0.16
~ 0.14
3
g 0.12
u 0.10
>
§ 0.08
* 0.06
0.04
0.02
• o*
• MITHOUT THE FOND
O WITH THE P0»
A KITH THE POND AND COAGULANT ADDITION
50
150
100
TINE (DAYS)
FIGURE 6. EFFECT OF INCREASED SEDIMENT REMOVAL ON THE CUMULATIVE LOAD-
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred,.
64
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A MIXING ZONE MODEL FOR CONSERVATIVE PARAMENERS
by
Main R. Hutcheson
Oklahoma Water Resources Board
SECTION 1
INTRODUCTION
There are two basic ways in which point source discharges are regulated.
One way is through the application of technology based permit limits for
dischargers. However, the current administration strongly supports the
water quality based approach to regulating pollutants (Eidsness, 1982). In
this approach a wasteload allocation is performed to determine permit limits
which will protect the water quality standards assigned to the receiving
stream.
The water quality standards apply everywhere outside the mixing zone. In
the past, the thrust has been to ignore mixing zones and perform wasteload
allocations for entire planning segments. However, this approach has not
proven feasible (Hutcheson, 1979). More states are now including mixing
zones. In 1971 twenty-two states mentioned mixing zones, while at present
all but three states include mixing zones in their regulations (Neely,
1982). Therefore, a mixing zone model applicable to single discharges or
dischargers with overlapping mixing zones can have general applicability.
Mixing zones may be defined in many different ways. Several states use an
arbitrary definition involving flow volume, stream width, or distance from
the source. Oklahoma defines a mixing zone as being thirteen times the
stream width, with three quarters of the flow volume protected as a zone of
passage, which effectively limits the mixing zone to about a fourth of the
stream width (Figure 1).
In order to assign discharge permit limits (to an industrial point source,
for example) which will protect water quality standards outside the mixing
zone, it is necessary to employ a dispersion model in the wasteload allo-
cation process. The dispersion model predicts pollutant concentrations in
the receiving stream. The most basic and widely used model is the mass
balance approach, wherein a steady state system exists and pollutant is
mixed uniformly throughout the receiving stream. There are several problems
with this approach, the most important being its inability to protect the
zone of passage (depicted in Figure 1). Another major problem with the mass
65
-------
balance approach is verification. Usually the pollutant becomes uniformly
distributed within the stream so far downstream that the signal to noise
level is too low to relate the effects of the discharge to the instream
concentration. Sometimes resuspension, nonpoint sources, partitioning and
sedimentation contribute significantly to the concentration of conservative
parameters. If the mixing zone is arbitrarily defined, as is the case in
many states, then the assumption of uniform mixing through the stream at the
end of the mixing zone may be invalid. In Oklahoma complete mixing at the
end of the defined mixing zone occurs only on very small streams, so in
Mixing lone
Portion of the nixing zone
which is also a zone of passage
Figure 1
Portion of receiving stream in which water quality
standards are not valid for an isolated discharge
general, the concentration outside the mixing zone is much greater than
predicted by mass balance (Hutcheson and Gopal, 1981a).
Since dispersion across a stream must be taken into
zone, applicable models must include this effect.
methods for accounting for cross stream dispersion.
that the concentration due to a
half-normally distributed across
occurs.
for with
concentration distribution is
(Hutcheson and Gopal, 1981b).
account in the mixing
There are two basic
The easier one assumes
steady state point source on the banks is
a stream until reflection from the far bank
Due to the principle of superposition, reflection may be accounted
a virtual point source. The assumption of a half-normal (Gaussian)
generally reasonable in Oklahoma streams
There are many situations where a wasteload
allocation methodology based on a Gaussian dispersion model will adequately
determine discharge wasteloads (from which permit limits may be derived)
which will allow instream concentrations specified by the water quality
standards to be met. There are, however, situations where the observed
distributions in Oklahoma do not approximate normal ones. Furthermore, it
has been shown that the dispersion mechanism is dependent both upon the
turbulence of the stream and the configuration of the pollution (Hutcheson,
66
-------
1979b). In other words, turbulent eddies disperse different sized plumes at
differing rates. Therefore, the Gaussian model may not predict concen-
tration distributions as well as a numerical solution to the dispersion
equation which computes new dispersion coefficients at various distances
from the source does. Furthermore, processes affecting the concentration
distribution which depend on the hydrology of the stream are better handled
with a numerical solution. An example is partitioning and sedimentation.
In general, conservative elements settle out of the water column when the
flow speed is slow, not uniformly as would be assumed in a Gaussian model.
Therefore, it is deemed worthwhile to pursue a numerical solution to the
dispersion equation. This type of model is more amenable to incorporation
of other mechanisms affecting pollutant concentration besides dispersion.
The objective of this report is to describe the development of a wasteload
allocation process which incorporates a numerical solution to the dispersion
equation, and to demonstrate the utility of the process. The development
consists of the following steps. First, the dispersion equation is simpli-
fied through the use of assumptions so that it may be solved numerically.
Then a relationship between the standard deviation of a Gaussian distri-
bution and the dispersion coefficient is derived. Dye studies are used to
determine the standard deviations. A relationship for the standard
deviation, hence the dispersion coefficient is developed based on hydrology
and plume dimensions. The dispersion equation is solved numerically for
pollutant concentration at grid points throughout the mixing zone. The
maximum concentration at the end of the mixing zone or on the boundary of
the zone of passage, the related source strength, the background concen-
tration and the water quality standard are used to determine the wasteload
allocation which will protect the water quality standard. This process is
applicable to multiple discharges as well as isolated ones, using the super-
position principle.
SECTION 2
DERIVATION OF THE APPROPRIATE DISPERSION EQUATION
Dye studies performed in Oklahoma showed that the Natural coordinate system
is appropriate for dispersion modeling. The Natural Coordinate system,
advocated by Yotsukura and Sayre (1976), features curvilinear horizontal
coordinates. The x direction is along the thalweg of the stream, the hori-
zontal coordinate perpendicular to this is the cumulative discharge, q, and
the vertical component, y, is stream depth. The cumulative discharge is
defined as the discharge from the injection bank to a point in the stream.
The maximum q is the total stream discharge.
Hutcheson and Gopal (1981b) showed that, in general, dye concentrations are
more like normal distributions when the Natural coordinate system is used
rather than a Cartesian coordinate system. Yoksukura and Sayre (1976) also
observed this to be the case. Therefore, the Natural system yields better
estimates of the dispersion coefficient. Another important reason for using
the Natural system in Oklahoma is the definition of the zone of passage.
One quarter of the flow volume occurs at the point at which the ratio of
cumulative to total discharge is one quarter. Therefore, in a coordinate
system using cumulative discharge, the physical dimensions of the zone of
passage may be easily determined.
67
-------
The standard diffusion equation is expressed in the Cartesian system. A
coordinate transformation is required to convert to the Natural system, and
many assumptions may be made to simplify the equation to facilitate a
numerical solution.
In Cartesian coordinates the dispersion equation may be written (Yotsukura
and Sayre, 1976)
afl 3(6wv) 8(6vO
where 6 is instantaneous concentration, and w , w and w are flow speeds
in the x (downstream along the bank), y (ve&iccrl) and zz (transverse)
directions. Steady state conditions are assumed to exist. Therefore, (1)
may be reduced to a three dimensional equation by time averaging (Hutcheson,
1980). The gradient transfer hypothesis (concentration flux proportional to
concentration gradient) is assumed valid because the Oklahoma Water
Resources Board (OWRB) dye studies showed that the concentration distri-
butions were more or less Gaussian. Further simplification of the
dispersion equation requires the assumption of uniform mixing in the
vertical. It has been shown that vertical mixing is complete at a distance
downstream from the source equal to 50 to 100 times the depth of the
discharge point. In shallow Oklahoma streams the assumption of uniform
vertical mixing is valid virtually throughout the mixing zone. It is also
assumed that the mean velocity is along the thalweg (x direction) and that
longitudinal dispersion has negligible influence on steady state mixing.
While longitudinal dispersion is the primary dispersion mechanism in non-
steady state situations, the longitudinal gradients for the concentration
distribution which evolves from a steady state source renders the longi-
tudinal dispersion mechanism ineffective.
Using the above assumptions, dispersion in the q direction and advection in
the x direction are the only mechanisms which must be accounted for in order
to predict concentration distributions of conservative parameters in a
mixing zone. Therefore, employing the appropriate coordinate transfor-
mations, (1) becomes (Hutcheson, 1980)
If • f^x"2"^'' (2)
where c is the time and vertically averaged plume concentrations, h is
stream depth, u is stream velocity in the x direction, K is the dispersion
coefficient and m is a factor introduced to correct for differences between
distances along curved coordinate lines and those measured along the x axis.
Along the thalweg m = o, and at other locations the approximation of
Yotsukura and Sayre ft.976) may be used:
ALv
\ - -s
where AL is the distance between grid points along a constant q. Eq (2)
may be solved if an expression for K can be obtained.
68
-------
SECTION 3
DETERMINATION OF AN EXPRESSION FOR THE DISPERSION COEFFICIENT K
Dispersion of pollution from a steady state point source is dependent upon
the relationshp between the characteristics of the prevalent turbulent
eddies and the size of the pollutant plume. In order to determine the
characteristics of the eddies, perturbation (as opposed to mean) quantities
must be measured and assimilated in a statistical fashion. Because of the
difficulties in accomplishing this, it was decided to use the relationship
between the variance of the concentration distribution and K to determine
the dispersion coefficient indirectly. This approach may be used because
the Oklahoma dye concentration usually approximated a normal distribution in
the Natural coordinate system.
For the conditions under which a normal distribution is valid, h, u and K
are independent of q, and m = 1. Under these conditions (2) may be written
H - Kh2u w = "•
The solution to (4) is the Gaussian plume, expressed by
c = -^_ exp (-3L) (5)
where a2 is the variance of the concentration distribution and S is the
source strength. Substitution of (5) into (4) yields
This is the diffusivity expression required to satisfy (4) for a Gaussian
plume. It will be assumed that it also holds when the concentration distri-
bution is approximately Gaussian.
In order to develop an expression for diffusivity using (6), dye studies
were performed on selected Oklahoma streams (Hutcheson and Gopal , 1981b).
Ten field experiments were conducted on six different stream reaches. The
streams chosen were typical of the larger streams in central Oklahoma. They
were broad, flat, shallow streams with smooth sand or mud bottoms containing
few rocks or other obstructions. Flow velocities were generally on the
order of .5 to 3 feet per second. Dye was injected into the receiving
streams at a rate of .2 to .3 ml /second. Samples for dye concentration
analysis and flow measurements were taken at frequent enough intervals to
adequately define the stream hydrology and plume dimensions to thirteen
stream widths from the source.
To determine the variance of the observed dye concentrations symmetry about
the injection bank must be assumed since a bank release produces a half-
normal distribution. The concentrations observed in the river were placed
at the same distance from the injection banks on the inland side to obtain
the entire normal distribution. The variance of these concentration distri-
butions were computed using a method employed by Meyer (1977), for equally
spaced data
69
-------
I[c.(qq)2]
where c. is the normalized steady state concentration at the cumulative
discharge q. and
Equally spaced concentrations were extracted from normalized distributions
derived from the analyzed samples collected during the dye experiments.
The dye samples were collected on cross sections at various distances from
the source. Therefore, the variances computed using (7) are valid for these
distances. These computed variances at the cross sections (solid lines) are
plotted for seven of the field experiments in Figures 2, 3, 4, 5, 6, 7, and
8 as a function of distance from the source. Data from three experiments
could not be used, due to problems with the dye injector on two occasions,
and because an injection into the middle of the stream, rather than a bank
injection, was attempted once (Hutcheson and Gopal , 1981b).
An examination of Figures 2, 4, 5, 7, and 8 show a tendency for the computed
variance to eventually become quasi-constant at some distance from the
source. However, since the dye must eventually spread uniformly across the
river, the computed variance must continue to increase with distance from
the source. Several theories have been advanced for the behavior displayed
in these figures, but no definitive answer has been found. The most
important behavior displayed in Figures 2-8 is the rapid increase in
variance with distance from the source.
Various mechanisms by which the variance increases have been considered.
Since only gross features of the flow were measured, it is not possible to
relate the dispersion coefficient to turbulence at this time. As shown in
Figures 2-8, the variance increases with distance from the source. In order
to predict variance using distance, it was assumed that
a2 = ax ,
where a and b are arbitrary constants. The constant values may be obtained
using a least squares technique with the computed variances up to the point
they become quasi-constant, so
a2 = .0002 x 2'3. (8)
This equation is used to predict variance, and the results are depicted in
Figures 2-8 as the dashed line, so that predicted and computed variances may
be compared. The dashed lines are identical in each figure, but appear to
shift due to the changing scales.
70
-------
o »^
71
-------
72
-------
73
-------
o2(xlOO ft2)
240 -
2)0 -
180 -
150 -
3000 4000
Distance (ft.)
5000
Figure 8 Observed and Predicted Variance versus Distance from Source
U.S. Highway 177B
The correlation between predicted and observed concentration variance is .7.
This indicates that (8) does not predict the variance very accurately. Even
so, it is tempting to use (8) due to the simple concentration prediction
scheme which would result. The expression for a may be substituted into
(5), and, when the mean flow is known, the concentration may be computed as
a function of position. This is much simpler than trying to predict concen-
trations by solving (2) numerically.
It may be shown that, close to the source, the dispersion coefficient
changes with distance downstream. A constant coefficient implies a2
increases linearly with x, from (6). However, (8) shows the relationship is
not linear. Therefore, K is not constant and, therefore, published dis-
persion coefficients are of little use in predicting concentration distri-
butions near the source.
A relationship between
during the dye studies.
volume of discharge and dispersion was observed
In order to account for upstream dispersion as well
74
-------
as this relationship, the integral of the cumulative discharge to .3 of the
maximum concentration with respect to distance from the source was used as a
predictor. The integrated value is used because the variance of the concen-
tration distribution depends upon the dispersion which has occurred at all
points downstream from the source. The relationship may be expressed as
a2 = a+b/P dx,
where CD is cumulative discharge from the injection banks to the location
where the normalized concentration equals .3 and z* is the distance from the
injection bank to this location. The a and b are arbitrary constants found
by the least squares technique, so that
rn
a2 = 351.9+.02j^f dx. (9)
Again, the constants were evaluated using only variance and cumulative
discharge data up to the point where the increase in variance essentially
stopped.
The correlation between the predicted and observed concentration variance is
.94. This indicates that (9) is more capable of estimating concentration
variance than (8) is. Less than 50% of the variance of a2 is explained by
(8), while (9) explains nearly 90%. Predictions using (q) are depicted as
the dash-dot lines in Figures 2-8. Since the value of the constant in (9)
is immaterial, because the expression will be differentiated to obtain K, a2
is set equal to 0 at x = 0, and = 20 when JCD/z*dx<200.
Although (9) is apparently a good predictor for a2, the physical mechanisms
governing dispersion remain undefined. Therefore, it is anticipated that
much work will be required to adequately predict variance. However, (9)
will be used to show the utility of the dispersion equation.
Note that in Figures 2 and 3 there is an initial slow increase in variance,
then a rapid increase. In both stream reaches the flow was intitally near
the bank opposite the dye injection, and it shifted over to the injection
bank at the point where the concentration variance started its rapid
increase.
In Figures 4 and 5 the rapid increase in variance starts much closer to the
source. In these reaches the thalwegs were near the injection banks at the
injection points. Predictions using (9) are able to anticipate the point at
which the increase in variance starts, while those using (8) cannot.
The same reach is depicted in Figures 7 and 8. Flow conditions are the
same, and the only difference is that in Figure 7 the wind is blowing very
strongly away from the injection bank, while in Figure 8 the wind is blowing
strongly towards the injection bank. This may cause a large enough increase
in turbulence near the dye injector to cause the much greater variances
observed in Figure 8.
If (9) or a similar expression is used to predict variance, then an
analytical expression such as (5) is not appropriate for predicting concen-
75
-------
tration. The variance must be known in order to use (5) to predict the
concentration distribution, but the concentration distribution must be known
in order to determine CD and z*. To resolve this dilemma, the dispersion
equation must be solved using numerical methods. This requires the use of
an expression for dispersion, rather than one for variance. Since the
concentration distributions observed in the dye studies are reasonably
normal in the cross-stream direction, (6) should yield a good estimate of
the dispersion coefficient. Substitution of (9) into (6) yields
K - -01 CD2 ™
K " ** ' U0)
If h and u are constant, then CD = uhz* and (10) reduces to
K = .Oluz*. (11)
Since z* increases as the plume spread across a river, K must always
increase, according to (11). However, K probably becomes constant at some
distance from the source, and at this point (10) will no longer be valid.
However, the distribution has flattened out so much that, as seen from (4),
c changes relatively slowly anyway. Therefore, (10) may be assumed to be
valid for thirteen stream widths downstream from the source without unduly
degrading the concentration distribution prediction.
SECTION 4
NUMERICAL SOLUTION TO THE DISPERSION EQUATION
Once all of the independent variables have been determined, the equation may
be solved for c. Expanding the right hand side (r.h.s.) of (2) and making
the appropriate assumptions about K and m yields
/\
where k = m h2uK.
Eq (12) implies that K and m change slowly enough in the q direction so
that their cross stream gradients are negligible in comparison with the
gradients of u and h2. Certainly the m gradient is negligible so long as a
stream reach is relatively straight, and the manner in which K is derived
requires that it remain constant in the q direction.
In order to solve (12) numerically, it must first be finite differenced. To
avoid stability problems, the Crank-Nicholson finite difference scheme is
employed. In the x direction, forward differencing is used:
9c _ c(m,n+l)-c(m,n)
9x ~ Ax '
where Ax is an incremental distance along the thalweg.
76
-------
The m's indicate locations on the cumulative discharge coordinate (across
the stream) and the n's indicate distance downstream along the thalweg.
In the cross-stream direction,
§c _ c(m+l,n+l)-c(m-
8q 4Aq
and similarly for In h2 and In u. The Aq is the incremental discharge in
the cross-stream direction. Using the same type of finite differencing:
(15)
Since In h2 and In u are known at the grid points, their gradients may be
determined a priori. For this reason
Y
Substituting (13), (14), (15) and (16) into (12), defining \ = kAx/2Aq, and
separating the concentration terms involving the n+1 grid points from those
involving n yields
-l,n) (17)
All the quantities in this equation are known except the concentrations at
the grid points involving n+1. Therefore, a system of M equations in M
unknowns (the concentrations at the n+1 grid points) may be developed.
To solve the system of equations initial and boundary conditions must be
specified. The initial condition is required to obtain the concentration at
the grid points where n = 1. Based upon the dye studies a half- normal
concentration distribution located near the source is the appropriate
initial condition. A half-normal distribution may be expressed by (5) with
S replaced by 2S, to double the concentration (absolute reflection). The
concentration variance must be known in order to use (5). Because concen-
trations were measured in the dye studies and the industry example, the
initial variance is computed from the observed concentration. However, a
prediction for a2 very near the source will be required when concentration
measurements are not available. When the concentration at n = 1 is deter-
mined, (17) may be used in an iterative procedure, so the concentrations at
succeeding distances downstream may be determined.
The boundary conditions may be obtained from the anticipated concentration
distribution. The half-normal distribution implies very small gradients in
concentration at the banks near the source. Far from the source, a uniform
concentration distribution again implies very small gradients. Therefore,
77
-------
the appropriate boundary condition is 9c/3q
this is the case if:
= 0 at the banks. From (14)
c(o,n) = c(2,n), c(o,n+l) =
c(M-l,n) =
Expanding (17) into M equations and employing the boundary conditions yields
a system of simultaneous equations which may be written in the form of a
matrix equation
where t is the column vector
c(M,n+l)
and F is the column vector
(18)
and A is the tridiagonal matrix
•0 0
2\
Aq
78
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Due to the tridiagonal nature of A, it is possible to invert the matrix and
solve for C directly, or an iterative approach may be used.
The mathematical formalism to determine the concentration distribution from
a continuous point source located on the bank is now complete. To reiter-
ate, the concentration is first initiated by assuming a Gaussian distri-
bution. Computation of the dispersion coefficient is accomplished in step
two using (10). Averaged values of h and u are used, and K is incorporated
in the A's in the tridiagonal matrix. Concentration at the next grid
distance downstream is determined using the last computed concentrations,
the newly computed dispersion coefficient, and the required hydrological
parameters which are obtained from the observed flow and stream morphology.
Step 2 is repeated using the new concentration data, establishing an
iterative procedure which is repeated until the concentration at the grid
points farthest from the source is determined.
If the input data is totally consistent, then the procedure described will
yield a concentration distribution which conserves mass. This, however, is
often not the case, and can cause errors in the concentration computations.
In order to ensure conservation of mass, a variational formalism is employed
(Hutcheson, 1981c).
A numerical solution to the diffusion equation is not new, and a computer
program could have been readily obtained from several sources. However, the
concept of allowing the model to determine the dispersion coefficient at
each grid distance downstream based on the dimensions of the plume and the
hydrological characteristics of the portion of the stream affecting dis-
persion is unique. Therefore, it is deemed more efficient to build the
model from basic principles rather than trying to modify an existing
computer program.
SECTION 5
MODEL VERIFICATION
Data obtained during the dye studies is used to verify the dispersion model.
The dye concentrations were measured on cross sections extending to thirteen
stream widths downstream from the source (Hutcheson and Gopal, 1981b). A
comparison of the actual dye concentrations with those predicted is given in
Figures 9-12. Only the best comparisons are shown here. Eighteen others,
some where the comparisons are not nearly so good, are displayed in the Task
111 Final Report (Hutcheson, 1981c). The x's represent the actual dye
concentrations and the solid lines represent the predictions. The vertical
dashed lines represent the point at which the cumulative discharge equals
one-fourth the total discharge, i.e., the edge of the zone of passage.
Initialization occurred on cross section A, using the observed concentration
variance. The cross sections are essentially equidistant from each other,
with A being this distance from the source. The cross sections in Figures
9-12 are 2,770, 2,029, 1,255, and 854 feet from the source, respectively.
79
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t
l NOU*V1N33H<
§ g
E »
| f
80
-------
-s
•s
81
-------
The model adequately reproduces the concentration distributions for the
cases presented. This does not mean that in every instance the measured and
computed concentrations are identical. In some cases major discrepancies
between actual and predicted concentrations exist. More refinement of the
model is required before all concentration distributions can be predicted
accurately.
When no concentration data is available, initialization must occur close to
the source, where the concentration variance is known to be very small. If
the plume occupies only a small portion of the discharge, then small grid
intervals are required in order to have enough points within the plume to
achieve adequate concentration computations. However, smaller grid
intervals require more grid points, which require added manual analysis of
the data and more entries to the computer. Therefore, it is not feasible to
initialize the model on an operational basis unless an objective analysis
scheme is developed to alleviate the manual analysis and data entry problem.
Since the initial variances measured in the two stream reaches examined on
the Washita River are very small, a finer grid mesh than is employed by the
dispersion model is required. For this reason, these cases were not run.
It is very difficult to make the input data compatible with the dispersion
model using a manual analysis. The amount of time required to manually
adjust the flow velocity, depth, and total discharge on a grid dense enough
for use in the dispersion model is prohibitive, especially since m must
also be accounted for. Therefore, an objective analysis scheme which
ensures compatibility between the model and input data must be developed to
ensure conservation of mass.
In order to make the model valid for all situations, a better dispersion
coefficient is required. The K currently used in the model is not related
closely enough to the turbulence of the flow to be useful in all situations.
For example, the effect of bottom roughness on turbulence is not taken into
account. Therefore, the current dispersion coefficient cannot be valid
except for the smooth sand or mud bottoms on which it was developed.
SECTION 6
WASTELOAD ALLOCATION METHODOLOGY
The wasteload allocation technique uses the assimilation capacity of the
receiving stream as a basis for permitting. This is accomplished through
the use of a dispersion model. It is recognized, however, that technology
based permit limits and socio-economic considerations are also vital parts
of the wasteload allocation process. Even when the assimiTation capacity is
virtually unlimited, dischargers should be required to meet some minimal
level of treatment, such as best practicable treatment. In some cases the
assimilation capacity is so small that it is impossible to achieve stringent
water quality standards, so socio-economic factors come into play. These
factors are not considered here, however.
82
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To obtain wasteload allocations, concentrations generated by the dispersion
model must be used. Because the principle of superposition applies to
conservative parameters, it is easy to extend the dispersion model,
developed to predict concentrations for a single source, to multiple
discharges. Therefore, the model may be run for each discharger, and the
results added to determine total concentration at the grid points.
The wasteload allocation process is designed to use the model results to
determine permit limits which restrict discharges so that concentrations on
the boundary do not exceed standards. First the background concentration
must be estimated. This may be done in any one of several ways (Hutcheson,
1982). Next, concentrations on the boundary formed by the mixing zone and
the zone of passage, as shown in Figure 1 are determined using the dis-
persion model. For wasteload allocation purposes, any reasonable source
strength, S,, may be used. However, for multiple discharges the source
strengths must be related to each other so that
S. = a.S1 2
-------
SECTION 7
APPLICATION OF THE WASTELOAD ALLOCATION METHODOLOGY
TO AN INDUSTRIAL POINT SOURCE
Farmland Industries discharges into Skeleton Creek. Velocity, depth, and
water samples were taken at appropriate locations in the mixing zone
(Hutcheson and Gopal, 1981a). The water samples were analyzed for zinc,
chrome, and total dissolved solids (TDS). Farmland Industries does not
discharge continuously. However, its period of discharge is assumed long
enough for a steady state situation to be established within the mixing
zone. Therefore, the wasteload allocation methodology may be applied.
Even though wasteload allocations for three different parameters were per-
formed, it was necessary to run the dispersion model only once to obtain C
for a given S-^ (Hutcheson, 1982). The background concentrations were
obtained from analyzed samples and C1 for each parameter from the Oklahoma
Water Quality Standards. These standards have since been revised. Eq. (20)
was used to obtain the source strength (proposed permit limit) for the three
parameters.
The wasteload allocations for Farmland Industries can be made without the
use of the dispersion model, since the maximum concentrations on the
boundary are known from an analysis of the samples collected. Therefore,
the observed concentrations and observed source strengths may be used in
(20) to determine allowable wasteloads. A comparison of the proposed
allowable loads is shown in Table 1.
Table 1. Comparison of wasteload allocations.
C-B S,
(mg/L) (mg/Sec.)
Wasteload
Using Observed
Concentration
(mg/sec.)
Wasteload Using
Dispersion Model
(mg/sec.)
Chromium
.2435 28.664
.2745 27.56
1619 524,872
4.12
Zinc
499.4
TDS
116,415
6.83
962.1
69,456.5
Wasteloads using the water samples are shown in column three, while those
obtained using the dispersion model are shown in column four. The first two
columns show the difference between the observed maximum concentration on
the boundary and the background, and the observed source strength,
84
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respectively. For chrome and zinc, the allowable wasteload produced using
observed concentrations is smaller than that using the dispersion model.
However, for IDS the allowable wasteload produced using observed concen-
trations is larger.
While there are discrepancies between the wasteload allocations, they are
relatively insignificant. A more important comparison is between the waste-
loads and column 2, which represents the actual wasteload being discharged
at the time of observation. The allowable wasteload (represented by either
column 3 or 4) for chromium and IDS is much lower than the actual wasteload.
Therefore, regardless of which method of computing maximum allowable waste-
load is used, a great reduction in the observed wasteload is required to
meet the water quality standards which were applied. However, the allowable
wasteload for zinc is much larger than the observed wasteload. Therefore,
zinc loading could be increased without violating water quality standards.
SECTION 8
CONCLUSIONS
A wasteload allocation methodology has been developed. It does not rely on
the assumption of a uniform concentration distribution, and can be applied
to either isolated or multiple outfalls. The methodology provides a means
for determining the wasteload allocation required to meet water quality
standards, thereby protecting the beneficial uses assigned to a receiving
stream. The central component of the methodology is a dispersion model for
the mixing zone for conservative parameter discharges.
There are several improvements which should be made to the dispersion model
in order for it to be used on an operational basis in the wasteload allo-
cation procedure. Input to the dispersion model is much too tedious for
operational use, so an objective analysis must be developed to minimize
manipulation of data to make it more compatible with the dispersion model.
The initialization procedure is too dependent upon the judgement of the
person operating the model; it must be made more automatic. The determi-
nation of the dispersion coefficient is not based on physical principles, so
more data should be gathered and a coefficient which explains the dispersion
mechanism more fully should be developed. Other mechanisms which affect
concentration, such as settling, must also be incorporated into the model.
There are many situations in which the wasteload allocation described is not
applicable. Because it is based upon a steady state mixing zone model for
conservative parameters, it cannot be used if the discharge interval is too
short to allow steady state conditions to develop in the mixing zone, if the
pollutant is not "conservative," or if a classical mixing zone is not
appropriate for the receiving water body. This occurs when there is no flow
velocity, as in a lake, or when the discharge forms a majority of the flow.
However, even in its present form, the utility of the wasteload allocation
methodology has been shown. It has been demonstrated that the dispersion
model can predict concentration distributions well enough to develop permit
limits which will allow water quality standards in a receiving stream to be
met.
85
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REFERENCES
Eidsness, Frederic A. 1982. Prepared Text on Water Quality Standards.
Presented at the Governor's Water Conference, Oklahoma City.
Hutcheson, Main R. 1979a. Select and Verify Hydrologic Model(s) for
Conservative Parameters. Final Report, 208 Work Element No. 613,
Oklahoma Water Resources Board.
Hutcheson, Main R. 1979b. Analysis of Ensemble Averaged Concentrations and
Fluxes in a Tracer Puff. EPA-600/4-79-002, National Technical Infor-
mation Service, Springfield, VA.
Hutcheson, Main R. 1980. Refine and Update Model for Conservative
Parameters. Working Paper, 208 Work Element 111. Oklahoma Water
Resources Board.
Hutcheson, Main R. and B. K. Gopal. 1981a. Mixing Zone Survey. Final
Report, 208 Work Element No. 245, Oklahoma Water Resources Board.
Hutcheson, Main R. and B. K. Gopal. 1981b. Model Calibration and
Verification Studies for Conservative Parameters. Final Report, 208
Work Element 232. Oklahoma Water Resources Board.
Hutcheson, Main R. 1981c. Refine and Update Model for Conservative
Parameters. Final Report, 208 Work Element 111. Oklahoma Water
Resources Board.
Hutcheson, Main R. 1982. Develop a Wasteload Allocation Methodology and
Determine Maximum Allowable Loads for Conservative Parameters. Final
Report, 208 Work Element 121. Oklahoma Water Resources Board.
Meyer, W. 1977. Transverse Mixing in the Mobile River, Alabama. Journal
Research, U.S. Geological Survey, Volume 5, No. 1.
Neely, W. Brock. 1982. The Definition and Use of Mixing Zones. Environ.
Sci. Techno!. Vol. 16, No. 9, pp. 518-521.
Oklahoma Water Resources Board. Oklahoma Water Quality Standards (1982).
Yotsukura, Nobuhiro and William W. Sayre. 1976. Transverse Mixing in
Natural Channels. Water Resources Research, Vol. 12, No. 4,
695-704.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
86
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SOME RECENT ADAPTATIONS AND APPLICATIONS OF QUAL-II IN THE NORTHEAST
presented at the
Stormwater and Water Quality Model Users Group Meeting
University of Florida, Gainesville, January 27-28, 1983
by
William W. Walker, Jr., Environmental Engineer
1127 Lowell Road, Concord, Massachusetts 01742
Introduction
The QUAL-II model has an extensive history which can be traced to the
original work of Streeter and Phelps (1925) and has been widely used in
wasteload allocations and other aspects of river basin water quality
management. Several versions of the program have appeared (Texas Water
Development Board, 1970, Water Resources Engineers, 1972, Meta Systems, 1979,
Roesner et al., 1981). Generally, all versions provide a capability for
simulating longitudinal transport and transformation of water quality
components in one-dimensional, vertically-mixed systems with steady-state
hydraulic conditions. This paper describes certain modifications which have
been made in the model structure to improve simulations of dissolved oxygen
conditions in rivers heavily impacted by photosynthesis. The code has also
been adapted for use on microcomputers. The development of this version is
traced to wasteload allocation studies in Vermont (Meta Systems, 1979,
Vermont Department of Water Resources, 1982) and to recent studies in Maine
(Walker, 1982) and Massachusetts (Walker, 1983).
Model Modifications
The simulation of nutrient cycles and algal growth kinetics tend to be
more important in rivers and shallow impoundments with low velocities. In
these situations, photosynthesis by suspended phytoplankton, aquatic plants,
and/or periphyton may represent important components of the oxygen balance.
Several alterations have been made in the QUAL-II structure to improve
simulations of phytoplankton, nutrients, and oxygen under these conditions.
These include:
(1) addition of detrital organic phosphorus and organic nitrogen
compartments;
(2) provision for algal uptake of ammonia and/or nitrate nitrogen (vs.
nitrate only in previous versions);
(3) provision for self-shading by phytoplankton; (computing light
extinction coefficients as a function of chlorophyll introduces an
important feedback control on peak biomass levels in nutrient-rich
environments);
87
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(4) specification of alternative (vs. multiplicative) nutrient limitation
by nitrogen or phosphorus;
Control pathways are depicted in Figure 1. The addition of detrital organic
nutrient compartments essentially closes the nutrient cycles and permits
model calibration and testing against observed total nitrogen and total
phosphorus data, as well as individual nutrient species. The other
modifications are designed to reflect the kinetic formulations used in state-
of-the-art phytoplankton models, as applied to lakes and estuaries (Di Torro
et al., 1977). Details on the equations and functional forms are given
elsewhere (Vermont Department of Water Resources, 1982, VanBenschoten and
Walker, 1982).
Other additions and structural modifications used in the applications
discussed below include:
(1) calculation "Apparent BOD-5" concentrations as a function of
carbonaceous BOD and estimated 5-day algal respiration at 20 deg C
(permits calibration and testing against observed BOD-5 data);
(2) calculation of Secchi depths from chlorophyll and non-algal light
extinction coefficients (also useful in calibration and impact
assessments) ;
(3) output of several diagnostic variables useful for identifying
controlling processes, including breakdowns of oxygen sources and
sinks (g/m3-day) and algal growth factors in each computational
element;
(4) provision for specifying benthic sources and/or sinks for any state
variable by reach in g/m2-day, including plant photosynthesis and
respiration;
(5) provision for including dam reaeration at the downstream end of any
reach;
(6) provision for simulating eddy-diffusive exchanges with downstream
water bodies by specifying far-field concentrations and effective
dispersion rate (useful for simulating fresh-water estuaries or other
backwater situations where the downstream water quality boundary
condition is fixed);
(7) provision for estimating longitudinal dispersion coefficients using a
function developed by Fischer et al. (1979), reportedly more
realistic than the Elder (1959) equation;
(8) provision for simulating diel oxygen fluctuations attributed to
photosynthesis and respiration using an approximate formulation
described by DiTorro (1968);
The last modification permits calculation of daily minimum oxygen
concentrations without applying the model in a non-steady-state mode. Diel
flucutations are calculated around the steady-state solution as a function of
88
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Figure 1
Control Pathways in the Modified QUAL-II Model
ATMOSPHERIC
REAERATION
r+ORGANIC N
AMMONIA N
\
BENTHIC DEMAND
C-BOD
NITRITE N
NITRATE
ORGANIC P
i
DISSOLVED P
CHLOROPHYLL-A
(ALGAE)
BOTTOM SEDIMENT
89
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reaeration rate, photosynthesis rate, and day length.
In the Vermont application, most of the above changes have been
implemented by modifying certain subroutines in the EPA code and adding new
subroutines for simulating detrital organic nutrients and diel oxygen
variations. A SAS (SAS Institute, 1979) interface has also been developed
for manipulating model output and plotting observed and predicted
concentration profiles (Walker, 1980). The interface has been extremely
useful in streamlining calibration, testing, and report writing.
In subsequent applications, the program code has been completely
rewritten and adapted for use on a microcomputer. The micro version is
written in standard FORTRAN and uses overlays to overcome storage
limitations. It has also been run on mainframes. Experimentation indicated
that a version written in intrepreted BASIC would be too slow and storage-
limited to be practical in most applications. Application limits are
determined primarily by the number of computational elements, computer
memory, and the memory overhead consumed by the FORTRAN compiler, linker, and
input/output operations. On a system with approximately 40K of available
storage (64K less overhead), the current version can handle up to 190
computational elements. Provisions for branching or non-steady-state
simulations are not included, primarily because they have not been required
in applications to date. These restrictions could be lifted with additional
code modifications and overlaying. The micro version has been tested against
the modified EPA code using input files developed for the Vermont Winooski
River application. A separate program has also been written for plotting
observed and predicted profiles. Execution times for a typical problem,
including printing and plotting, are on the order of ten minutes on an 8-bit,
4 mhz microcomputer equipped with a special arithmetic chip available for
most systems.
Upgrading of the algal growth kinetics (especially the inclusion of
self-shading) reduces the linearity of the equations has been found to pose
problems for the steady-state solution algorithm, particularly in systems
with long hydraulic residence times. In the current EPA code (Roesner et
al., 1981), convergence is guided and tested based upon algal growth rates.
In the modified code, convergence is tested based upon stability of the state.
variables from one iteration to the next. Certain modifications of the tri-
diagonal matrix formulation have also been successful in improving
convergence properties, especially in systems with long residence times or
significant algal growth limitation by self-shading or nutrients.
Calibration and Testing Procedures
Model inputs may be broadly classified as (1) "boundary conditions" or
(2) "system parameters". Boundary conditions include such factors as river
flows, waste inputs, morphometry, and climate; these can be directly
measured or independently estimated. System parameters include the
fundamental rate and stoichiometric coefficients which are used in process-
level simulations and which are usually difficult to measure directly. In
simulating a given river system, the boundary conditions vary from one time
period to another, depending upon various driving forces, while the system
parameters should be relatively constant.
90
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The development of input estimates within each category is based upon
combinations of the following:
(1) direct monitoring data
(2) empirical functions (e.g. reaeration rate formulae)
(3) literature values and guidance manuals (e.g., Zison et al., 1978,
NACASI, 1980)
(4) empirical adjustment ("tuning") to observed water quality profiles
(5) field reconnaissance
The calibration process would be relatively straight-forward if all inputs
could be directly measured. This is generally infeasible, however, because
of the complexity of the model, implicit nature of some coefficients, and
limitations in monitoring resources and technology. Calibration of this type
of model requires subjective judgments because the feasible ranges of most
coefficients are wide and more than one set of coefficients can often be
selected to fit a given set of field data. Because of these limitations,
user experience and field reconnaissance are valuable assets in model
applications. Sensitivity analysis should be employed to determine the
importance of parametric and structural assumptions.
One test of model generality is based upon stability of the process-
level parameters from one time period to another in a given river. This test
involves simulating observed water quality conditions under at least two
different sets of boundary conditions using a fixed set of parameters. A
more severe test of generality would require parameter stability from one
river to another. A model with this property, while difficult to achieve,
would be extremely useful because it would ease the calibration and testing
requirements for each application.
Because of the desirability of achieving generality and learning more
about the strengths and weaknesses of the model structure, a relatively
conservative approach involving minimal adjustment of system parameters has
been taken in calibrating the model to the systems described below. Most
parameter adjustments have been limited to characteristics which could
logically vary from one river to another, such as benthic photosynthesis or
benthic oxygen demand; these are essentially forcing functions, as opposed to
system parameters. Stoichiometric coefficients (e.g., respiration
equivalents, algae chlorophyll-a and nutrient contents) and many rate
coefficients have been held constant at "reasonable" values, based upon
literature ranges and accumulated experience with the model.
Many parameters have been estimated with the aid of published empirical
relationships (e.g. reaeration rate), rather than adjusted to fit individual
profiles. Direct field measurements of reaeration rate would be preferable,
but are usually infeasible because of time or economic constraints.
Variations in certain process-level parameters, such as algal growth rate,
respiration rate," and settling velocity, from one reach to another in a given
river would introduce too many degrees of freedom in the calibration process
and are less defensible on a scientific basis; accordingly, reach-to-reach
adjustments in these parameters are not part of the calibration procedure.
91
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Applications
The model has been applied in studies of three river basins in the
Northeast: (1) Lower Winooski River, Vermont (VanBenschoten and Walker,
1982); (2) Upper East Branch of the Sebasticook River, Maine (Walker, 1982);
and (3) Sudbury/Concord Rivers, Massachusetts (Walker, 1983). While there
are several unique features associated with each of these applications, all
include low-velocity reaches in shallow impoundments or backwater areas with
high concentrations of algae (generally greater then 30 mg chlorophyll-a/m3)
during critical periods. Key parameter estimates are summarized in Table 1.
Model generality is reflected by the stabilities of some parameters and
instabilities of others from one system to another. Each application is
described briefly below.
The Winooski River originates in the Green Mountains of Vermont and
empties into Lake Champlain. In its last 32 kilometers, the river flows
through the metropolitan Burlington area, where there are two hydropower dams
and several industrial and municipal point sources. Violations of the 6
mg/liter dissolved oxygen standard have generally been observed near the
mouth of the river, where the elevation gradient is relatively small and
where maximum summer algal populations of about 30 mg/m3 are generally found.
The oxygen violations are usually associated with large diel fluctuations (up
to 8 mg/liter), attributed to combined effects of (1) algal photosynthesis
and respiration and (2) daily fluctuations in river flow resulting from
hydropower operations (typically 50 to 1200 cfs). Sustained periods of
oxygen violations have also been observed at various locations under
conditions of maximum temperature (> 30 degrees C) and die-off of algal
blooms.
The Vermont Agency of Environmental Conservation (VAEC, 1980, 1982)
conducted a wasteload allocation study in order to assess possible
requirements for advanced waste treatment. The unsteady flow regimes induced
by hydropower peaking operations posed several potential problems for the
modeling effort. Because of the complexities and extensive data requirements
involved in application of . a non-steady-state hydraulic and water quality
model, the Agency elected to use a steady-state model and to conduct the
allocation runs under steady 7Q10 conditions, under the assumption that the
utilities would be required to pass a minimum of 7Q10 during non-generating
hours. The model described above was calibrated and tested against data from
week-long intensive surveys conducted during two different years. With the
cooperation of the power company, stable flow conditions were maintained
during both surveys to provide suitable data sets for calibration and testing
of a steady-state model. Observed and predicted concentration profiles for
the second survey are shown in Figure 2.
The Sebasticook study (Walker, 1982) examined the impacts of a combined
municipal/industrial discharge on a small stream which discharges into an
inlet of Lake Sebasticook, a eutrophic lake in central Maine. The shallow
inlet is characterized by high algal and aquatic plant densities and
hydraulic exchanges with open lake waters are probably important in
determining concentrations at the lower end. Preliminary model simulations
indicate that the inlet is functioning as an oxidation pond, since oxygen
turnover rates in the water column consist largely of photosynthesis and
respiration by algae and aquatic plants. A detailed evaluation is hindered
by lack of diurnal sampling for dissolved oxygen and limited spatial and
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Table 1
Parameter Estimates Used in Winooski, Sebasticook, and Sudbury Applications
Parameters
Value/Comments
Reaeration Rate
O'Connor & Dobbins (1958) equation
constrained to K2 > 1 / mean depth (Su)
Longitudinal Dispersion Elder(1959) (Wi), Fischer (1979) (Se,Su)
Decay/Oxidation Rates (I/day)
BOD-U
Ammonia N
Nitrite N
Organic N
Organic P
Algal Parameters
Maximum Growth Rate
Respiration Rate
Settling Velocity
Chlorophyll Content
P Content
N Content
Light Extinction
Ammonia Pref. Factor
Photo. Oxygen Equiv.
Resp. Oxygen Equiv.
.2 + bed activity (Zison et al., 1978)
.2-2 (Wi), .3-1 (Se), .6 (Su)
2.0 (Wi.Se), 3.0 (Su)
.1
.1
2.3 I/day (Wi.Su), 2.5 I/day (Se)
.12 I/day
.75 m/day (Wi.Su), .60 m/day (Se)
.010 mg Chl-a / mg Algae
.011 mg P / mg Algae
.080 mg N / mg Algae
43.2 m2/g Chl-a
.9
1.6 mg 02 / mg algae
2.0 mg 02 / mg algae
Half-Saturation Constants
Algal P Uptake .005 g/m3
Algal N Uptake .03 g/m3
Algal Growth vs. Light 1.5 calories/cm2-hr
Benthic Oxygen Fluxes (g/m2-day)
Plant Photosynthesis 0-2 (Wi), 0-2 (Se), 1.5
Plant Respiration 0 (Wi), 0-2 (Se), 1.5
Other Benthic Demand .5 (Wi), .5 (Se), 1
10 (Su)
10 (Su)
3 (Su)*
Other Benthic Fluxes (g/m2-day)
Dissolved P Source ** 0 - .005 (Se,Su)
Ammonia N Source ** 0 -
Ammonia N Sink .05
Nitrate N Sink .10
025 (Su, channel)
(Su, overbank)
(Su, overbank)
Wi = Winooski, Se = Sebasticook, Su = Sudbury
parameters are zero in other applications if some initials are given
parameters are used in all applications if no initials are given
ranges refer to reach-specific values, all rates at 20 degrees C
* plus wetland benthic loading component
** benthic sources of phosphorus and ammonia in impounded reaches
93
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Figure 2
Observed and Predicted Water Quality Profiles
Lower Winooski River 1979
Dissolved Oxygen (mg/liter) 1979
12-
10-
8
6
4-
2
0-i
0 4 8 12 16 20
River Mile
5-Day BOD (mg/liter) 1979
C-BOD
—C-BOD + Algal Respiration
3.5
3.0
2.5-
2.0
1 .5-
1 .0-
0.5
0.0
4,8 12 16 20
River Mile
1979
Chloropbyll-a (ug/liter)
Nitrogen (mg/liter)
Total N
--Total Kjeldahl N
1979
12 16
River Mile
20
Nitrogen (mg/liter) 1979
Nitrate-N + Nitrite-N
Ammonia-N
.10
.08
.06
.04
.02
.00
Phosphorus (mg/liter)
Total P
Dissolved P
1979
20
4 8 12 16 20
River Mile
94
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temporal sampling frequencies for all water quality variables. In this
application, reasonable simulation of observed chlorophyll and afternoon
oxygen (between predicted daily mean and daily maximum) profiles was achieved
with minor adjustments in the parameters used in the Winooski simulations.
The model has been recently applied to the Sudbury/Concord Rivers in
Massachusetts (Walker, 1983), as part of an assessment of the potential
environmental constraints involved in diverting waters from the upper
watershed for water supply purposes. The study extends over 51 river
kilometers, 44 of which consist of a shallow impoundment surrounded by
wetlands, including the Great Meadows National Wildlife Refuge. Both the
model and monitoring data indicate that water quality conditions are
controlled largely by the hydraulic geometry and by interactions with
tributary wetlands and that point sources are of minor importance. Hydraulic
simulations using HEC-II and detailed channel cross-section measurements at
278 locations have been used to define hydraulic geometries in water quality
model.
As a result of the channel and floodplain morphometry and backwater
effects, the river undergoes relatively large changes in width as a function
of flow in certain reaches. Bottom sediments in the channel and overbank
areas are highly organic in nature and reflect the export, settling, and
decay of organic materials from adjacent wetlands. Figure 3 depicts
variations in dissolved oxygen and dissolved oxygen deficit as a function of
river flow measured during summer months at the lower end of the impounded
area most stongly influenced by adjacent wetlands. A unique aspect of this
system is that dissolved oxygen levels tend to be lower (and deficits,
higher) during high-flow periods. The relationships in Figure 3 reflect the
combined influences of (1) higher organic loadings during high-flow periods;
(2) higher benthic demands in overbank areas; (3) less algal growth because
of the increased flushing rate during high-flow periods; (4) die-off and
decay of wetland vegetation during infrequent summer flooding events. The
last condition results in the most severe water quality conditions, including
depression of oxygen levels below 2 mg/liter over most the impoundent. A
significant fishkill was reported in 1938 following the largest recorded July
flood.
Preliminary calibration of the net benthic oxygen demands in each model
reach under high-flow and low-flow conditions indicated that demands
increased with the ratio of tributary wetland area to river surface area and
increased with average basin runoff. Accordingly, a simple mass balance
model linking the apparent benthic demand to tributary wetland areas and
runoff rate has been used to represent wetland interactions. The calibrated
wetland organic export rate of .17 grams of oxygen demand per square meter
per day represents only about 1.3 to 2.1 percent of the literature range for
net primary productivity of freshwater emergent macrophytes on fertile sites
in temperature regions (Wetzel, 1975). The remainder of the organic matter
produced in the" wetlands is apparently decomposed in place or flushed
downstream with little decomposition. Another wetland interaction
considered in the model is benthic uptake of nitrate (.1 g/m2-day) in
overbank areas and is attributed to plant uptake and denitrification
supported by organic substrates, as observed in other wetland systems (Kadlec
and Kadlec, 1978).
The model has been calibrated and tested against data from three
intensive surveys (1) August 1973, summer low-flow; (2) July 1973, summer
95
-------
Figure 3
Summer Dissolved Oxygen Concentration and Deficit
at Route 117 vs. Concord River Flow at Lowell
14.0
12.0
10.0
8.0'
6.0
4.0-
2.0
0.0-i
-range of diel measurements
June - Sept.
o « Concord DNR
x - Mass. DEQE
1.7 2.1 2.5 2.9
LOG(FLOW,CFS)
3.3
10.
I
\
CD 6.
^ 4.
I—
U 2-
£ o.
(=3
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a" -4-
-6.
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0
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0 0
X
o
o '
.7 2.1
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i
o
0
0
o
0
o
o
j — -range of diel measurements
June - Sept.
1 o = Concord DNR
x = Mass. DEQE
2.5 2.9 3.3
LOG(FLOW,CFS)
96
-------
flood; and (3) June 1979, late-spring flood. While the average flows were
similar in the July 1973 and June 1979 surveys, the major hydrologic
difference is that the former occurred a week after a summer storm event of
about seven-year freqency, whereas flows were decreasing seasonally during
the latter, when only flood-tolerant vegetation would have developed in
adjacent wetlands. Over most of the impoundment, diel oxygen fluctuations
were less than 1 g/m3 during the July 1973 survey, as compared with a range
of 2 - 8 g/m3 for the other surveys; this reflects a suppression of plant
photosynthesis associated with summer flooding.
Observed and predicted daily mean oxygen profiles for each survey are
shown in Figure 4. The severe conditions during July of 1973 have been
simulated by setting benthic photosynthesis rates to zero, as compared with a
1.5 - 10 g/m2-day range calibrated to various reaches for the other survey
periods. All other model parameters are fixed for the three simulations. An
oxygen sag attributed to high benthic demands and low velocities is apparent
below river kilometer 48, the approximate upper end of the backwater effects
created by the impoundment at river kilometer 7.
Observed and predicted chlorophyll-a profiles are shown in Figure 5.
Using the same kinetic and stoichiometric parameters used in the Lower
Winooski algal simulations, the model simulates the peak algal densities
observed during the low-flow and spring-flood surveys with reasonable
accuracy, especially considering that the observed points are based upon
single grab samples. For the low-flow survey, the chlorophyll profile is
over-predicted below the Assabet River (RKM 25). The time-of-travel through
the impoundment during that survey was about 20 days and it is possible that
the lower observed chlorophyll levels reflect higher flow conditions previous
to the survey. Other possible explanations include effects of zooplankton
predation (more likely to be important at long residence times but not
simulated by the model), or shading by floating duckweed which have been
observed in this portion of the river. Despite this problem, the model
adequately simulates the observed chlorophyll-a profiles in the upper end of
the impoundment, where the oxygen sag is located.
Conclusions
This paper has described adaptations and applications of QUAL-II to
three New England river basins. Incorporation of organic nutrient
compartments and updating of algal growth kinetics increase the realism and
generality of the model. Interfacing the model output with SAS and plotting
routines facilitates calibration, testing, and statistical analysis of
observed and predicted water quality profiles. The revised code can be used
on microcomputers or mainframes with FORTRAN capability.
Reasonable generality is indicated by model calibration to observed
water quality profiles with minimal adjustment in key parameter estimates
from one application to another, especially in those parameters which
determine nutrient and algal profiles. Relatively large variations in some
parameters, including nitrification rate, benthic oxygen demand, and benthic
photosynthesis, reflect inherent limitations in this type of model and
dictate needs for calibration and testing in each application. Modifications
of the code to permit systematic sensitivity analysis (Walker, 1982a) would
improve user perspectives of key processes and assumptions in a given model
application.
97
-------
Figure 4
Observed and Predicted Mean Dissolved Oxygen Concentrations
Sudbury/Concord Rivers
11.000
10.421
9.842
9.263
8.684
8.105
7.526
6.947
6.368
5.789
5.211
4.632
4.053
3.474
2.895
2.316
1.737
1.158
.579
.000
60
August 1973: Mean Dissolved Oxygen (g/m3)
SUMMER, LOW-FLOW
"oo 53.37 4&!?5 40.12 33.50 26ts7
River Kilometer
2ot25 13.62 7.00
11.000
10.421
9.842
9.263
8.684
8.105
7.526
6.947
6.368
5.789
5.211
4.632
4.053
3.474
2.895
2.316
1.737
1.158
.579
.000
60
July 1973: Mean Dissolved Oxygen (g/m3)
SUMMER, FLOOD
MEAN D . 0
.00 53.37 46.75 4o!l2 Sslso 2&!s7 2ot25 13.62 7^00
River Kilometer
11.000
10.421
9.842
9.263
8.684
8.105
7.526
6.947
6.368
5.789
5.211
4.632
4.053
3.474
2.895
2.316
1.737
1.158
.579
.000
June 1979: Mean Dissolved Oxygen (g/m3)
LATE SPRING,FLOOD
• »•
• >!• 'IT»
»T
53.37
46.75 40.12 33.50 26.J
River Kilometer
2ot25 13.62 ?toO
98
-------
Figure 5
Observed and Predicted Chlorophyll-a Concentrations
Sudbury/Concord Rivers
.037
.035
.033
.031
.029
.027
.025
.023
.021
.019
.018
.016
.014
.012
.010
.008
.006
.004
.002
.000
60"
August 1973: Chlorophyll-a (g/m3)
SUMMER, LOW-FLOW
CHLOROPHYLL-A
00 53.37 46.75 40.12 33.50 26.87 20.25 13.62 7.00
River Kilometer
.037
.035
.033
.031
.029
.027
.025
.023
.021
.019
.018
.016
.014
.012
.010
.008
.006
.004
.002
.000
July 1973: Chlorophyll-a (g/m3)
SUMMER,FLOOD
60.00 53.37 46.75
4ol2 33sO 26
River Kilometer
20.25 13.62
7.00
June 1979: Chlorophyll-a (g/m3)
LATE SPRING, FLOOD
.037
.035
.033
.031
.029
.027
.025
.023
.021
.019
.018
.016
.014
.012
.010
.008
.006
.004
.002
.000
60.00 53.37 46.75
40.12 33.50 26.87
River Kilometer
20.25 13.62
7.00
99
-------
References
DiTorro, D.M., "Algae and Dissolved Oxygen", in "Basic Models of Natural
Systems", prepared for U.S. Environmental Protection Agency by Manhattan
College, New York, 1968.
DiTorro, D.M., Thomann, R.V., O'Connor, D.J., and Mancini, J.L., "Estuarine
Phytoplankton Biomass Models - Verification Analyses and Preliminary
Applications", in The Sea, John Wiley and Sons, Inc., New York, 1977.
Elder, J.W., "The Dispersion of Marked Fluid in Turbulent Shear Flow",
Journal of Fluid Mechanics. Vol. 5, pp. 544-560, 1959.
Fischer, H.B., E.J. List, R.C.Y. Koh, J. Imberger, and N.H. Brooks, Mixing in
Inland and Coastal Waters. Academic Press, New York, 1979.
Kadlec, R.H. and J.A. Kadlec, "Wetlands and Water Quality", in Wetland
Functions and Values: The State of Our Understanding , American Water
Resources Association, November 1978.
Meta Systems, Inc., "Documentation for the Meta Systems Version of the QUAL-
II Water Quality Simulation Model", prepared for U.S. Environmental
Protection Agency, Water Planning Division, 1979.
National Council for Air and Stream Improvement, Inc., "A Review of the
Mathematical Water Quality Model QUAL-II and Guidance for Its Use", Stream
Improvement Technical Bulletin No. 335, 1980.
O'Connor, D.J. and W.E. Dobbins, "Mechanism of Reaeration in Natural
Streams", Trans. ASCE. Vol. 123, 1958.
Roesner, L.A., et al., "Computer Program Documentation for Stream Quality
Model (QUAL-II)", U.S. Environmental Protection Agency, Center for Water
Quality Modeling, Athens Environmental Research Laboratory, Georgia, EPA-
600/9-81-014, 1981.
SAS Institute Inc., "SAS Users Guide", Raleigh, NC, 1979.
Streeter, H.W. and E.B. Phelps, "A Study of the Pollution and Natural
Purification of the Ohio River", U.S. Public Health Service Bulletin 146
(reprinted 1958), 1925.
Texas Water Development Board, "Simulation of Water Quality in Streams and
Canals", Program Documentation and User's Manual, 1970.
VanBenschoten, J.B. and W. W. Walker, "Calibration and Application of QUAL-II
to the Lower Winooski River", draft manuscript submitted to Water Resources
Bulletin. American Water Resources Association, August 1982.
Vermont Agency of Environmental Conservation, "Lower Winooski River Wasteload
Allocation Study - Part A: Report of Data", Department of Water Resources and
Environmental Engineering, Montpelier, December 1980.
100
-------
Vermont Agency of Environmental Conservation, "Lower Winooski River Wasteload
Allocation Study - Part B: Mathematical Modeling Report", Department of Water
Resources and Environmental Engineering, Montpelier, January 1982.
Walker, W. W., "A SAS Interface for QUAL-II", prepared for U.S. Environmental
Protection Agency and Vermont Agency of Environmental Conservation, 1980.
Walker, W. W., "Calibration and Application of QUAL-II to the Upper East
Branch of the Sebasticook River between Corinna and Coburn", prepared for
Kleinschmidt and Dutting, Inc., Pittsfield, Maine, 1982.
Walker, W.W., "A Sensitivity and Error Analysis Procedure for Lake
Eutrophication Modeling", Water Resources Bulletin. American Water Resources
Association, Vol. 18, No. 1, pp. 53-61, February 1982a.
Walker, W. W., "Downstream Water Quality Impacts of Diversions from Sudbury
Reservoir - Model Calibration and Testing", prepared for Interdisciplinary
Environmental Planning, Inc., Parsons Brinkerhoff Quade & Douglas, Inc., and
Metropolitan District Commission, Commonwealth of Massachusetts, January
1983.
Water Resources Engineers, Inc., "Progress Report on Contract No. 68-01-0713,
Upper Mississippi River Basin Model Project", prepared for U.S. Environmental
Protection Agency, September 1972.
Wetzel, R.G., Limnology. W.B. Saunders Company, Philadelphia, 1975.
Zison, S.W., W.B. Mills, D. Deimer, C.W. Chen, "Rates, Constants, and
Kinetics in Surface Water Quality Modeling", U.S. Environmental Protection
Agency, Athens Environmental Research Laboratory, Georgia, EPA-600/3-78-105,
December 1978.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
101
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A REVIEW OF MODEL USE IN EVALUATING
NONPOINT SOURCE LOADS FROM FOREST MANAGEMENT ACTIVITIES
1 2
George G. Ice and Raymond C. Whittemore
INTRODUCTION
The water quality of runoff from forest land is a topic of
continuing interest; particularly regarding the influence of
management activities. Models and predictive techniques are now
being used to compare alternative management strategies. This
paper will discuss: (a) the unique regulatory requirements that
mandate predictions of nonpoint source (NFS) contributions for
forest lands; (b) procedures which are being developed or used to
predict sediment loading to streams; (c) areas of continuing need
for modelling development; and (d) forest industry research to
improve our understanding of forest-water quality relationships
and modelling.
II NEED FOR MODELLING YIELDS FROM SILVICULTURAL NONPOINT SOURCES
There is currently a urgent need to validate procedures to
predict water quality, streambed and stream biota responses to
forest practices. In part this need results from the Clean Water
Act and the diverse silvicultural nonpoint source (NPS) control
programs developed under Section 208. However even more pressing
are the recent questions that have been raised about modelling in
regard to state forest practice acts, state water quality stand-
ards, and legislation covering planning on National Forests. In
addition there is a continuing evolution in the perspective of
forest planners regarding NPS loading which is further compli-
cating both modelling approaches and solutions.
Like other NPS activities, the Clean Water Act required
that, where necessary, control programs for silvicultural activi-
ties be developed by the states. These programs have emphasized
the use of Best Management Practices (BMP's). The development of
BMP's has required an understanding of the mechanisms influencing
NPS loading. For example, in Florida recommended practices under
the voluntary silvicultural NPS control program are based on a
site-sensitivity classification which is a function of steepness-
of-slope, soil erodibility (K-factor from the Universal Soil Loss
Equation), and proximity to open water (1).
1 Research Forester, NCASI, Oregon State University, Corvallis,
Oregon
2 Research Engineer, NCASI, Tufts University, Medford, MA
102
-------
A recent survey of state silvicultural NFS control programs
found that, in general, these programs have been well implemented
and are effective in reducing NPS loading (2). However, as part
of an ongoing process, changes in BMP's continue to be considered.
Using Florida again as an example, some changes in guidelines
have been proposed based on an understanding of "source area
differences" between physiographic provinces (3). In New Mexico,
an extensive BMP development program is ongoing. Robert Brozka,
Water Quality Project Forester for the New Mexico Forestry
Division writes that,
". . . soil movement was quantified by means of the
Modified Universal Soil Loss Equation using procedures
described in the EPA handbook titled "An Approach to
Water Resource Evaluation of Non-Point Silvicultural
Sources'. Soil movement on roads was Quantified sep-
arately utilizing a mathematical sediment yield model
developed specifically for forest roads. This same
model is currently being adapted specifically to the
State by the New Mexico Water Resources Research Insti-
tute. Data is being collected from around the State on
runoff and sediment production rates with a rainfall
simulator. Ultimately, different road designs and
erosion control practices will be evaluated with the
model so that the best alternative can be chosen." (4)
In some states, predictive procedures are being used or are
proposed to be used to indicate appropriate forest management prac-
tices and compare alternatives on a site-specific basis. In
Northern California, where the silvicultural NPS control program
is enforced through the State Forest Practice Act, an Erosion
Hazard Rating (EHR) has been used to identify areas of high erosion
potential. In the past the EHR has combined both surface and mass
wasting (landslide) erosion hazard. Two recent studies (one by
California Division of Forestry and the other by Humbolt State
University) found that the EHR was not a good indicator of observed
erosion rates (5,6). In response to this, the California Board of
Forest has recently adopted a new EHR for surface erosion and is in
the process of developing a new EHR for mass wasting. See Table _!_
for factors considered by the California surface soil EHR. Rules
have recently been adopted in California which require EHRs down
to 10 acre parcels in some cases.
In Idaho, USDA Forest Service operations in one watershed
were recently halted because a USDA Forest Service model pro-
jected that harvesting and reading would result in sediment
loading which would cause a 20 percent reduction in fishery
potential. This projected 20 percent reduction in fishery poten-
tial was interpreted by the Idaho Department of Health and
Welfare as violating state water quality standards that protect
beneficial use.
103
-------
In Oregon, a petition has been submitted to the Board of
Forestry which requests that an erosion model developed by the
Siuslaw National Forest for forest-wide planning be adopted as
part of the Oregon Forest Practice Act to be used in evaluating
Forest Operations along the Oregon Coast. The petition requests
that operations be limited to those that, according to the
Siuslaw model, restrict sediment loading increases to less than
200 percent of the natural rate. A further discussion of the
model is presented later.
TABLE 1 SURFACE SOIL EROSION HAZARD RATING
FORM FOR STATE OF CALIFORNIA
STATE OF CALIFORNIA
DEPARTMENT OF FORESTRY
ESTIMATED SURFACE SOIL
EROSION HAZARD
FORM I (12/81)
L SOIL FACTORS
A. SOIL TEXTURE FINE MEDIUM COARSE
1. DETACHABILITY
RATING
2. PERMEABILITY
RATING
LOW
1-J
SLOW
5-4
MODERATE
10-18
MODERATE
3-2
HIGH
11-30
RAPID
1
FACTOR
RATING
Illlip
B. DEPTH TO RESTRICTIVE LAYER OR BEDROCK
RATING
SHALLOW
f.io"
15-9
MODERATE
20-31"
DEEP
>3"
8-4 j 3-1
p^Tfv j
C. PERCENT SURFACE COARSE FRAGMENTS GREATER THAN 2MM IN SIZE
INCLUDING ROCKS OR STONES
RATING
LOW
<*OX
10-6
MODERATE
^0-70%
5-3
HIGH
70-/OOJJ
2-1
SUB TOTAL!
FACTOR
RATING
II. SLOPE FACTOR
! 5-15%
RATING j 1-3
16-30%
4-6
31-40%^
7-10
41-50% | 51-70%
11-15 | 16-25
>70%
26-35
HI.PROTECTIVE VEGETATIVE COVER REMAINING AFTER DISTURBANCE
RATING
LOW
0-40%
15-6
MODERATE I HIGH
41-80%
7-4
81-100%
3-1
IV. TWO-YEAR, ONE HOUR RAINFALL INTENSITY (HundrtJtb Inch)
See attached map
RATING
LOW
4.40
1-3
MODERATE
40-59
4-7
HIGH
60-69
8-11
EXTREME
>«^
12-15
TOTAL SUM OF F ACTORS |j
EROSION HAZARD RATING
<50
LOW
I 50-65
'MODERATE
66-75
HIGH
>75
EXTREME
i* ,,*v *'
THE DETERMINATION IS |
104
-------
The Forest Service has been the developer and user of
numerous sediment loading models recently because the National
Forests are subject to special planning requirements under the
National Environmental Policy Act of 1969 and National Forest
Management Act (NFMA). Under NFMA the USDA Forest Service is
required to make projections about resource outputs resulting
from management options. The results of these decisions will
influence the availability of timber, particularly for the
Western United States. However a recent evaluations about
available predictive techiques for forest resources found that
11. . . it is impossible to accurately predict [ ] on-site and
offsite effects ..." and the land manager is currently
". . . unable to define limitations to use, if and how manage-
ment practices might be applied, and possible trade-offs in the
various uses and values, even though he is required to do so for
environmental analysis reports" (7).
On top of these regulatory and legislative requirements for
the use of models in forest management planning, the forestry
community (particularly in the West) has recently begun to
consider the consequences of multiple forest operations on water
quality. A California Board of Forestry task force has raised
the concern that ". . . effects may appear to be insignificant
when a harvesting project is viewed alone, but may become cumula-
tive and cause demonstrable damage when the effects of other
harvesting projects are considered" (8). Some of the potential
cumulative effects that have been propose include: (a) peak flow
increases from snow accumulation and melt rate changes in cleared
areas, (b) peak flow increases due to soil compaction and altered
drainage networks, (c) channel changes due to accelerated inputs
of large sediment and organic debris, and (d) channel changes due
to removal of large wood debris and streamside vegetation (9).
in addition to the consideration of multiple operations,
forest planners are now being required to project not only changes
in sediment concentration (the traditional NFS measure for forest
practice impacts on water quality) but also changes in channel
conditions and ultimately the beneficial uses of the water.
From these examples we can summarize that there continues to
be increasing sophistication demanded in projecting the water
quality consequences of forest activities at both the state and
federal level. Models are being used both in long-term planning
on federal lands and by states as a tool to identify general
management practices which are appropriate for use as BMP's. In
order for planning decisions to be the best possible it is
necessary that the models being used be tested and their limita-
tion considered.
105
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Ill PROCEDURES TO EVALUATE WATER PUALITY
RESPONSE TO SILVICULTURAL OPERATIONS
Because sediment is considered to be the most important NPS
contribution from forest activities we will concentrate our dis-
cussion on this parameter. It is recognized, however, that in
other more specific situations nutrients, biochemical oxygen de-
mand, temperature, and herbicides can result in localized non-
point source pollution problems.
A. WRENSS
In 1980, EPA published "An Approach to Water Resources
Evaluation of Nonpoint Silvicultural Sources" (WRENSS) (10).
WRENSS was written by forest hydrologists with the USDA Forest
Service and is now being used (in various modified forms) by sev-
eral states and National Forests Management groups. Because WRENSS
involves many of the modelling elements currently used we will
provide a brief description of the sediment prediction components.
(1) Overview - WRENSS models changes resulting from forest
activities that cause increases in water available for runoff,
and also increases in both surface erosion and landslides. All
these modifications are then considered using sediment-rating
curves to evaluate potential channel geometry changes.
(2) Water Quantity - Water available for runoff is modeled using
a water-balance approach where the change in available water is
a function of changes in interception and evapotranspiration (ET)
resulting from vegetation removal. Modifications in interception
and ET are a function of the change in leaf area index (LAI) or
forest cover density (CD). Response of discharge is given in
terms of either a seasonal hydrograph for snow dominated regions
or a flow duration curve for rain dominated regions.
(3) Surface Erosion - Sediment loading to streams is a function
of three processes; surface erosion, sediment from landslides
(mass wasting), and channel scour. Surface erosion is calculated
with a version of the Universal Soil Loss Equation which has been
modified for application to forest sites.
The modified soil loss model (MSLE) is:
A = R K L S VM
106
-------
where: A = The estimated average annual soil loss
per unit area in tons/acre.
R = The rainfall factor, usually expressed
in units of rainfall-erosivity index,
El, and evaluated from an iso erodent
map.
K = The soil-credibility factor, is usually
expressed in tons/acre/EI units for a
specific soil in cultivated, continuous
fallow, tilled up and down the slope.
L = The slope length factor is the ratio of
soil loss from the actual field slope
length to that from a 72.6-foot (22.1 m)
length plot.
S = The slope gradient factor, is the ratio
of soil loss from a given field gradient
to that from a 9-percent slope.
VM = The vegetation-management factor, is the
ratio of soil loss from land managed
under specified conditions to that from
the fallow condition (10).
A delivery ratio is calculated from the site conditions to
predict the amount of soil loss (A) actually reaching the stream
system. This portion of V7RENSS might be used to predict surface
erosion frorn site-preparation activities as are shown in Figure I.
FIGURE 1
BEDDING AS A SITE
PREPARATION TECHNIQUE
IN FLORIDA
(4) Landslides - In the West, landslides can be major contributor
to the sediment .loading of forest streams. See Figure 2. Of the
two general types of landslides (slump-earth flows which are deep,
slow movements in plastic soils, and debris avalanche-debris flows
which are rapid, shallow failures) it is the debris avalanche-
debris flow type which is most influenced by forest activities.
107
-------
In order to predict landslide rates using WRENSS, a similar nearby
site which has previously experienced comparable management
activities must be inventoried to determine landslides under
undisturbed and man-induced conditions. Site and practice hazard
similarity can be judged using a hazard index based on site condi-
tions. From this first inventory, an accelerator factor (F) is
developed where:
F =
man-induced failures
natural failures
FIGURE 2
I'APS VTASTING IN THE
OPECON CASCADES
Another inventory of the site being modeled, provides the
natural delivery rate which is multiplied by the accelerator
factor to yield the delivery of man-induced mass failure material.
(5) Total Potential Sediment and Channel Modification - System
modifications are combined to predict changes in total sediment.
The following steps are involved.
(a) From the pre and post management flow-duration curves and a
sediment rating curve developed by stream measurements, pre and
post management suspended sediment loads are developed. [Stream
stability may be used in post-management sediment rating curve
adjustments] . This step accounts for channel.-derived sediment
load increases. See Figure 3.
(b) Bedload sediment rating curves are developed as above and the
same type of analysis is used to generate pre and post management
bedload rates.
(c) Coarse and fine sediment contributions are separated from
material delivered to the stream from mass wasting.
108
-------
(d) Total suspended sediment load is determined as the cumulative
yield from rating curve increases, surface erosion increases, and
the wash load from mass failures. All surface erosion material is
assumed to be suspendable.
(e) Total sediment available for transport is determined by
including bedload and coarse mass-wasted material.
(f) The potential for channel modification are assessed by com-
paring maximum bedload transport to introduced coarse material.
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1,000 '
100 ••'::
10 .
1 10 100 1000
INSTANTANEODS DISCHARGE IN CSM
10,000
FIGURE 3
SEDIMENT RATING CURVE WITH STREAM STABILITY
RATING (SSR) ADJUSTMENTS - DEVELOPED FOR FOX
PLANNING UNIT, SIX RIVERS NATIONAL FOREST, CALIFORNIA
(POOR SSR 115; FAIR SSR 115 AND 75; GOOD SSR 75)
109
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B. NCASI Activity Involving WRENSS
Because WRENSS is being applied to an increasing number of
assessments, this procedure and its derivatives will be the
subject of numerous performance evaluations.
Recently, a portion of WRENSS was used to predict baseline
sediment yields from undisturbed basins. As previously mentioned,
the NFMA has necessitated that sediment yields along with other
factors, be considered for planning purposes on National Forests.
For this reason methods which predict changes in sediment yield
are being developed and applied for specific conditions. In 1981,
the USDA Forest Service Northern and Intermountain Regions pre-
pared a working- draft of procedures to predict sediment yields.
However, one problem was the lack of baseline data for most sites
to show sediment yields prior to harvesting (12).
A method was proposed in this document which would estimate
natural sediment yields. Data from undisturbed watersheds (repre-
senting low to high sediment producing landscapes) were reported
to show a range of 10 to 100 tons/mi /year. For undisturbed
forest watersheds "... the source of natural sediment is pri-
marily stream channel erosion processes" (12). The authors
concluded that "since natural surface erosion is considered
insignificant, the variation in natural sediment is assumed
attributable to differences in mass erosion hazards and delivery
differences" (12J- Therefore, using the boundary values of 10
to 100 tons/ mi /year a relationship between average natural
sediment yield and the WRENSS mass erosion hazard rating was
developed.
In order to rapidly evaluate this natural sediment yield
estimating procedure, a USDA Forest Service Pacific Northwest
Region document, "Erosion and Sedimentation Data Catalog of the
Pacific Northwest" was utilized (13). The catalog summarizes the
results and site characteristics for 19 small watershed studies
as well as other erosion plot and large-basin studies. Several of
the summarized studies include data for control (undisturbed)
basins. Using site characteristics listed and knowledge of these
watersheds, hazard ratings were developed and plotted against
measured yields. See Figure 4. The results showed that the
approach could not be applied throughout the Northwest. Further,
the hazard index used could not descriminate between wide ranges
of average outputs even for nearby watersheds.
Although there are many reasons why short periods of sediment
monitoring might not agree with the hazard index, the need to
explore the proposed relationship is apparent.
110
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iiUUU -
N
1
I
Sediment 1
n c
D C
g yw
Z
E
0)
>
4 -
3
9
^
.
! ^
.s*^\
^^ •
•
•
•
...!#
^^
•
X
^
^
y
Function as originally plotted
through single data point.
•
10 20 30 40 50 60
Mass Erosion Hazard Rating
FIGURE 4
COMPARISON OF PREDICTED TO ACTUAL
SEDIMENT YIELDS FOR NORTHWEST STUDIES (20)
NCASI is now collecting information from landslide surveys
which can be used to evaluate predictive methods. This informa-
tion is now being organized into a catalog similar to the "Erosion
and Sedimentation Data Catalog of the Pacific Northwest" which was
refered to earlier. One example of the arrangement of information
is shown below for a survey of landslides in the Mapleton Panger
District. See Table 2.
Until recently WRENSS has involved a laborious, hand calcula-
tion procedure. The USDA Watershed Systems Development Group in
Fort Collins, Colorado has just released a draft copy for review
of computerized WRENSS solutions, WETT.WET and WET.SED. NCASI,
111
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along with others, is now reviewing these programs. (Although the
hydrograph portion of WPENSS is simulated by WETT.WET., the
sediment portion of WRENSS is only partially reproduced.)
C. Other Procedures to Predict Sediment Yields from Silvicultural
Yields
While this discussion has centered on WRENSS there are
numerous other procedures being touted to assist in forest plan-
ning. A recent publication by the USDA Forest Service Pacific
Northwest Region summarized more than 10 different techniques
being used to quantify surface erosion, mass movements (slides),
and sediment delivery (14). See Table 3 for a short description
of these models.
The Siuslaw National Forest provides another example of the
number of models being proposed for use in forest planning.
Passing over the erosion prediction options provided in Table 3,
hydrologist, soil scientists and fisheries biologists on the
Siuslaw National Forest have developed 5 separate procedures to
predict sediment loading to streams and the response of anadrom-
ous fish as a result of forest reading and harvesting. These
procedures included: (a) a forest-wide planning procedure; (b) a
district-wide procedure to estimate cumulative effects; (c) a
district procedure which estimates landslide-only sediment load-
ing; (d) a site-specific procedure which requires on-site esti-
mates of the effectiveness of mitigative measures, and (e) a
steam-threshold procedure to estimate when unacceptable sediment
loading occurs to the stream system.
As previously discussed, the forest-wide procedure for the
Siuslaw National Forest has been proposed as a predictor for
defining appropriate practices under the Oregon Forest Practice
Act. The Siuslaw Model benefits greatly from numerous on-site
studies and landslide inventories and this empirical model is
based in part on these relationships. Components predicted
include natural erosion rates, in-unit failures and volumes, road
related failures and volumes, surface erosion rate (dry ravel
from broadcast burning) and delivery, and effectiveness of pro-
tective measures (leave areas). The procedures weaknesses include
lack of validation, lack of discrimination between a wide range
of practices, and the need for gross generalizations about site
considerations.
NCASI has developed computer programs to solve the Siuslaw
National Forest procedures as well as many of those presented, by
the Pacific Northwest Region in order to compare predicted
sediment loading rates with existing data sets.
112
-------
-------
-------
TABLE 2 EXAMPLE OF MASS WASTING CATALOG
Inventory of Mass Erosion in the Mapleton Ranger District
Siuslaw National Forest and Pacific Northwest Forest and Range Experiment Station
Location: Selected units in the Mapleton Ranger District, Siuslaw National Forest,
Oregon were evaluated. See Mapleton District - Ketcheson and Froehlich for the location
of the of the Mapleton District.
Objective: With improved road building, in-unit slides are- suspected as possibly
becoming more important (proportional) to the overall sediment budget for steep terrain
sites. This is especially true because road right-of-ways occupy only a fraction
(approx. 8%) of the overall area being harvested. Therefore, an inventory of slides
was made to determine the number of failures in forested, in-unit (clearcut) and road
right-of-way sites. The focus of the study was on the most slide-prone soil types in
the Mapleton District.
Site Characteristics; See Mapleton Ranger District - Ketcheson and Froehlich for a
complete description of soil types, topography, and precipitation. This inventory focus-
ed on SRI soil type 47 which is the most slide prone in the Mapleton District (hazard
rating of 5) and has shallow, coarse-textured soils with steep, deeply-incised slopes.
Procedures; Color air photos (scale - 1:15,840) made in 1972 were used to determine
road and in-unit slide frequencies. Field measurements were used to establish the size
distribution of these slides along with dating by dendrochronological methods. In-forest
erosion rates were determined exclusively using field observations. Slide volumes less
than 10 yds were excluded. The inventory covered time periods of 10, 15, and 20 years,
respectively, for clearcut (in-unit), road right-of-way, and natural failures. No
accounting was made of debris torrents following slide entrance into the stream channel.
Results: Comparison of in-field and air photo methods showed good agreement for clearcut,
and road-in-clearcut sites, but poor agreement for road-in-forest sites (due to shadows)
so in-field techniques were used for the forest and road-in-forest calculations. Clear-
cuts adjacent to roads did not significantly increase the-slide rate of road right-of-
ways. Photo inventory methods were found to detect 40 yd or larger slides, while in-
field measurements detected 10 yd or larger failures C< of in-unit slides 40 yd or less).
The frequency of events for in-forest sites was found to be 20x the rate for other sites
studied in the Northwest, but because the average volume was 4% the volume found in
other studies, the in-forest slide erosion rate was similar. A decrease in importance
of roads between this study and the initial Mapleton landslide inventory was noted (change
in the ratio of clearcut area to road failures from 7.3 to 31).
In an Appendix report, debris torrents were surveyed for Cedar Creek which is a
tributary to Sweet Creek and the Siuslaw River, 5.5 miles SW of Mapleton. The analysis
used cumulative acre-years in order to account for changing land-uses ef the period of
records. The authors concluded that a similar adjustment to the Mapleton data could
increase the man-caused rate of sliding 2 to 4 times.
LANDSLIDES FOR FORESTED,
CLEARCUT, AND ROADED SITES
Unit Associated Road Associated
i Slope Class
K
0-58
58-70
70-84
14-100
100-115
1U-
ict
I
St
i
SKI
»jfic«tion
3
18
11
10
14
1}
13
12
II
9
3
20
55
19
3
13.
20.
12.
5.
12.
9.2
K.I
Natural
For
4
15
33
31
8
1.2
4.1
14.3
12.2
16.3
14.3
12.2
11.4
DEBRIS TORRENTS ON
CEDAR CREEK DRAINAGE
FQrevt
ClMrcut
CuMulAtive
34,544
10,751
Debris , Frequency
Torrents ( Event! /Acre- Yr )
5 0.00014
8 0.00074
frequency to
Debris Torrents
For Forest Areas
j.
S.3X
8.0056
o « *
47
others
o.so
0.20
0.33
11.5
5.1
1.4
0.15
0.28
0.17
113
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TABLE 3 AVAILABLE MODELS AND TECHNIQUES FOR COMPUTING ON-SITE
EROSION, MASS MOVEMENT, SEDIMENT DELIVERY INDICES,
AND EROSION HAZARD RATINGS AS LISTED BY THE
USDA FOREST SERVICE PACIFIC NORTHWEST REGION (14)
Technical
Name
EROSON
ONEROS 3
OSLE
MSLE
Hegahan
Time
Trend
Erosion
Model
Region 5
Erosion
Hazard
Rating
System
Region 1
and 5
Guidelines
for
Predicting
Sediment
Yields
VIRENSS
Mass
Erosion
Hazard
Rating
WRENSS
Sediment
Delivery
Model
Region 5
Sediment
Delivery
Model
Description
Program computes maximum erosion hazard
rating in inches of soil lost per year
based on slope, precipitation, and
erodibility coefficients, and a basic
erosion rate. Cover conditions are then
used to estimate actual soil loss.
Modified Musgrave method which is adapted
to forest applications and used to predict
sheet-erosion in tons/acre. Cully erosion
and delivery of on-site erosion to streams
can be included in calculation.
Calculates sheet erosion based on rain-
fall, soil erodibility, slope-lengths,
cover and erosion control factors in tons/
acre (or desired units).
Modified DSLE which uses precipitation,
soil erodibility, topographic, and vegeta-
tion management factors to predict on-site
erosion in tons/acre. (Modified for forest
use).
Forest level planning model which distri-
butes erosion over time in tons/acre based on
long-term normal erosion (no new disturbance),
material available to erode after disturb-
ance, and potential recovery rate.
Point total based on site characteristics
defines hazard rating.
Erosion predicted as a function of land
type and management activity. Guidelines
include functions to deliver eroded
material to streams and route it to criti-
cal areas.
Two erosion hazard ratings (for debris
avalanche and slump-earthflow types fail-
ures) based on site conditions and a point
scale for component hazard
Sediment delivery index based on available
water, texture of eroded material, ground
cover, slope gradient, slope shape, sur-
face roughness, and delivery distance.
Delivery of sediment is a function of soil
erosion hazard rating, drainage dissection,
slope position, vegetation cover, and
entrapment coefficient.
Computer
Solutions
Available
114
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IV AREAS OF CONTINUING NEED FOR MODELLING DEVELOPMENT
A general understanding of many of the basic mechanisms con-
trolling watershed-sediment response to forest-management activi-
ties has been developed and this understanding is incorporated
into some of the predictive techniques discussed. For example,
WRENSS has identified key components including channel scour, mass
wasting, and surface erosion which can contribute to sediment load
changes. However, because of the complexity of forest systems
and the difficulties of quantifying those systems (particularly
the hydrologic cycle), no single model has yet proven to be uni-
versally acceptable. In fact some models are being used prema-
turely without thorough testing simply because immediate answers
and management decisions are required for planning.
The further development of models to predict NFS response to
forest practices will require five steps. First our understanding
of some of the mechanisms currently modelled as cause-and-effect
need to be refined. For example, several models use sediment-
rating curves to predict sediment load response to forest prac-
tices by predicting hydroyraph changes following harvesting. Yet,
it is known from sediment concentration-flow patterns for season,
storm sequence, and position in the storm hydrograph, that flow
is only one of the independent variables influencing sediment
concentration. When discharge is increased, as a result of
reduce evapotranspiration for example, the sediment-rating curve
relationship could overestimate sediment loading because the
rainfall-intensity factors generating material available for trans-
port are overestimated by the flow parameters. Conversely, the
sediment-rating curve relationship could underestimate sediment
loading because practices could make more material available for
transport. Further examples can be drawn from the bulk of re-
search dealing with infiltration and interflow (22).
Second, key mechanisms need to be modelled which have been
avoided to this point. An example is the lack of groundwater
modelling for mass wasting analysis. A special soils task force
reporting to the Oregon State Forester concluded that "nearly all
slope failures in the forest environment occur in response to a
higher than average pore water pressure condition..." and there-
fore the development of engineering groundwater models is nec-
essary to improve road location and design (15).
Hewlett (21), in a recent paper on modelling philosophy,
points out that hydrological modellers are currently "plagued with
an embarrassment of riches "for journals contain numerous attempts
to explain and/or model individual hydrological processes without
providing a clear-cut choice for managers to implement. Hewlett
115
-------
further suggests that decision making should be the "heart of the
research enterprise". Models which simulate nature accurately
may become inefficient in application to decision making because
the cost is prohibitive for collecting input meteorological and/or
hydrological data, and measurement of model parameters.
Difficulties may arise when users attempt to interpret cause
and effect relationships from a model which was not designed to
deterministically simulate the effect of interest or concern. A
surge in concentration of an aerially applied pesticide in storm
flow, for example, may be attributed to basin-wide flushing if an
overland flow model is used to fit the hydrograph. The same
effect, however, could be attributed to stream channel factors if
a subsurface storm water flow model is used. Both models may fit
the hydrograph for predictive purposes, but neither may imitate
the actual runoff process.
Third, complete models providing the linkage between forest
activity, site conditions, and the water quality factors upon which
decisions are based need to be provided. in reviewing research
priorities, Brown noted that the next step for research is
"...integrated, process-level studies of system function. For
example, instead of measuring sediment concentration at the outlet
of a small watershed after clearcutting, sediment production will
be defined as a function of soil disturbance, soil characteristics,
terrain, and climatic variables. The transport and deposition of
sediment in the stream channel will be defined as a function of
the hydraulic factors involved. These conditions then will be
related to the variables that influence aquatic organisms" (16).
Models based on fundamental factors and directed at the key
response parameters will be more transferable and useful. This
system's engineering approach is clearly not a major focus of the
current modelling activity being discussed.
Fourth, and perhaps most importantly, there is a need to
develop workable techniques for collecting the key on-site param-
eters which influence site response. For example, for sites sub-
ject to mass failures, a small change in the depth of soil,
presence or absence of a hardpan, groundwater drainage, or orien-
tation of bedrock bedding planes can make the difference between a
site failing or remaining intact. It needs to be acknowledged
that there may be limits or uncertainty to the information we can
collect and use operationally. Where site-specific information
is not available for key parameters, defacto "best estimate"
data is often used and the modelling problems of this approach
need to be recognized and incorporated in the management decision.
Finally, models need to be thoroughly tested and documented
before operational use to evaluate their accuracy and precision.
This need is similar to that expressed by NCASI concerning point
116
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source water quality models in Technical Bulletin No. 367 (23) .
This technical bulletin addressed the practical concerns of model
selection, calibration, and verification. The findings of this
study show the need to define goodness of fit criteria for eval-
uating models, and to develop a broad enough data base to uncover
and subsequently represent mathematically major physical, chemical,
and biological mechanisms in the basin before making long-range
forecasts.
V RESEARCH TO IMPROVE OUR UNDERSTANDING
OF FOREST WATER QUALITY MODELING
Each year since 1979, about $9,000,000 has been spent on re-
search to address NFS questions (17). This research includes
efforts to provide the basic data necessary to model NFS mechanisms
and also efforts to improve or validate models. An excellent
example of industry, university, and USDA Forest Service research
cooperation is centered in Gainesville, Florida under IMPAC
(Intensive Management Practices Assessment Center) program. This
program is filling a real information need about the effects of
harvesting and site preparation in flatwoods conditions on water
quality. Perhaps some of the most interesting results from this
study have concerned the water quality coming from undisturbed
flatwoods sites.
Many other research programs are scattered throughout the U.S.
and information on these programs can be obtained in an annual
NCASI Technical Bulletin. An example of the type of basic data
gathering research underway is seen in the South Central U.S.
Until recently there has been little or no research on controlling
sediment losses from forest roads in the South Central U.S. Four
road projects are now being conducted by the forest industry, states,
and universities in Oklahoma, Arkansas (2), and Mississippi. See
Figure 5.
Similarly, in the West, studies have been conducted to assess
sediment losses from road and skid trails in Idaho, California,
Oregon, and Wasington. A forest industry conducted study in Idaho
has demonstrated the effectiveness of scattering slash over skid
trails as a BMP to minimize erosion (18). This study has also
been used to compare observed sediment losses from skid trails to
those predicted by commonly used sediment loss equations. See
Figure 6.
A review of non-point source models applicable to the assess-
ment of the effect of silvicultural practices on water quality is
also underway at the Northeast Regional Center of NCASI. The over-
land flow and catchment models described in Tables 4 through 6^
are being examined for their ultimate utility to the pulp and
paper industry. The information in the Tables 4 through 6^ was
assembled in a recent review by Ambrose (24).
117
-------
FIGURE 5
FOREST INDUSTRY STUDY
OF BEST MANAGEMENT
PRACTICES FOR FOREST
ROADS IN THE SOUTH -
A PROPORTIONAL SAMPLER
COLLECTS RUNOFF FROM
THE ROAD
A FIGURE 6 °
FOREST INDUSTRY STUDY OF EROSION FROM SKID TRAILS IN IDAHO
SHOWS THE EFFECTIVENESS OF SCATTERED DEBRIS IN REDUCING EROSION
A; SKID TRAIL WITH SCATTERED DEBRIS B; BARE SKID TRAIL
118
-------
The models can be further segmented for forested areas
according to sophistication by the use of a classification scheme
proposed by Ambrose (24). The segmentation and classification
are provided in Table 7 . The models in Table 7 are the focus of
current NCASI interest.
Physical Properties Spactial Properties
Iirper- Agri- Wet Channel
Model vious cultural Forested lands Single Multiple Routing
TABLE 4
PRE-SCREENED
OVERLAND MODELS-
CATCHMENT PROPERTIES
Model
ACTMO
ACRUN
Amberger
et al.
ANSWERS
ARM-II
CNS
CREAMS
CSU
EPA RRB (URO)
Haith and Tubbs
HSPF
Hydroscience
MRI
MUNP
tfS
OKI -RRB
PTR
80S
SCRAM
SEMSTORM
SOGREAH-
CAREDAS
Simplified
SWMM
STORM
SKMM-Level I
SWMM-II
Texas A 4 M
URS
UTM-TEHM
WEST
HQAM
WRENS
Continuous Event Annual Monthly
X
X
X
X
X
X X
X
X
X X
X
X
X X
X X
X
X
X X
X
X
X
X X
X
X
X • X
X X
X
X
X X
X
X X
X X
Dally
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
ACTMO X X
AGRUN X X
Amberger
et al. X X
ANSWERS X X
ARM-II X X
CNS X X
CREAMS X X
CSU XX X
EPARRB CURD X X X X X
HSPF X X X X X
Haith and
Tubbs X XX
Hydroscience X X
MRI XXX X
MUNP X
NPS X X X X X
OKI-RRB X X
PTR XXX
QQS X X
SCRAM X X
SEMSTORM X X X X X
SOGREAH-
CAREOAS X X
Simplified
SWMM X X
STORM X X X X X
SWMM-Level IX X
SWMM-II X X X X X
Texas MM x X
URS X X
UTM-TEHM XX X
WEST
WQftM X X X X X
WRENS X X
TABLE 5 PRE-SCREENED
OVERLAND MODELS-
TIME DOMAIN*
X
X
X
X
X
X
X
X
•This reflects the effective predictive capability of the model and is
considerably larger than the computational time step.
119
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TABLE 6 PRE-SCREENED
OVERLAND MODELS-
CONSTITUENT SYSTEMS
Model
ACTMO
AGRUN
Amberger
et al.
ANSWERS
ARM-II
OB
CREAMS
CSU
EPA RRB (URI)
Haith and
Tubbs
HSPF
Hydroscience
MR I
HJtf
tes
OKI-RRS
PTR
DOS
SCRAM
SEMSTORM
SOGREAH-
CAREOAS
SimplifiK)
SWrt"t
STORM
SMMM Level I
SMMM-II
Texas A4H
URS
UTM-TEHM
WEST
NQAM
KRENS
Hydro-
logy
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Sed-
iment
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Arb- Pnos- Carbon
itrarv Nitrogen phorus (organics)
1 X X
J
X X
X
XX X X
X X
XXX
XXX X
XXX X
X
XXX X
X
X
X
X
X
X
X
10
X
X
X
X
X
XXX X
X
X
X
X
TABLE 7 NFS MODELS AND SOPHISTICATION LEVEL
MODEL SOPHISTICATION LEVEL
CSU
HSPF
SWMM-II
NPS
SEMSTORM
STORM
WQAM
WRENS
4
4 or 3
4 or 3
3
2
2
1
-1
LEVEL 1 - Totally empirical approach to watershed hydrology and
sediment generation. Useful for long term (annual)
predictions. Handbook approach.
LEVEL 2 - Simplified empirical hydrology simulation via
computer program. No attempt is made to account for moisture
between storm events. The Rational Formula and/or SCS Curve
Number approaches to runoff from impervious and pervious
surfaces are used. Effective temporal resolution is 1 month.
LEVEL 3 - Watershed hydrology is calculated explicitly via a
process oriented approach. Pollutant generation is handled
empirically by link to sediments or the use of washoff
functions. Effective temporal resolution is of the order of
one day or less.
LEVEL 4 - These models treat important hydrologic, nutrientr
and sediment processes in detail. Nutrient interactions can
occur in both particulate and dissolved form. Detail structure
is built into the model to account for various management
strategies. The time resolution is of the order of one day or
less.
120
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VI LITERATURE REFERENCES
(It "Summary of the Current Status of Silvicultural 208 Programs-
1980," Special Report No. 80-12 (December 1980).
(2) "A Summary of Silvicultural Nonpoint Source Control Programs
for the United States-1982," NCASI Special Report 83-01
(January 1983)
(3) Olszewski, R.J., "Streamside Management Zones in Florida and
the Southeast,"Presented in Technical Bulletin No. 389
(November 1982).
(4) Brozka, R.J., Water Quality Project Forester, Forestry
Division, Natural Resources Department, Santa Fe, New Mexico,
Personal Communication (August 4, 1982).
(5) Hauge, C.J., Furniss, M.J. and Euphrat, F.D., "Soil Erosion
in California's Coastal Forest District," Calif. Geo. 32 (6)
120 (June 1979).
(6) Datzman, P.A., "The Erosion Hazard Rating System of the
Coast Forest District: How Valid is it as a Predictor of
Erosion and Can a Better Prediction Equation be Developed?"
M.S. Thesis, Humbolt State Univ., Arcata, California (June
1978).
(7) Nobel, D., "Silver Creek - Field Laboratory in the Idaho
Bathalith," Forest Resources West 4 (November 1980).
(8) O'Leary, S., "Silvicultural 208 Activities in California,"
Presented in Technical Bulletin No. 389 (November 1982).
(9) Swanson, F., "Cumulative Stream Impacts," Paper presented at
Workshop on Stream Management, Oregon State University,
Corvallis, Oregon (May 1982).
(10) "An Approach to Water Resources Evaluation of Nonpoint
Silvicultural Sources; A Procedural Handbook," EPA-600/8-
80-012 (August 1980).
(11) Laven, R.D., and Lehre', A.K., "The Effects of Timber Har-
vest and Roads on Sediment Yield and Channel Morphology in
the Fox Planning Unit," USDA Forest Service, Six Rivers
National Forest (July 1977).
(12) Cline, R. , et al. "Procedure for Predicting Sediment Yiels-
A Working Draft," USDA For. Serv., North Region and Inter-
mountain Region (No Date).
(13) Lassen, K.R., and Sidle, R.C., "Erosion and Sedimentation
Data Catalog of the Pacific Northwest,: USDA For. Serv.,
Pacific Northwest Region R6-WM-050-1981 (September 1981).
(14) Howes, S., and Hughes, D. , "Descriptions of Available Models
and Techniques for Computing On-Site Erosion Losses and Mass
Movement, Sediment Delivery Indices, and Erosion Hazard
Ratings," Forest Soil Horizons 7, USDA For. Serv., Pacific
Northwest Region, Portland, Oregon (May 1981).
(15) Spiesschaert, D. , Carleson, D., Carter, G., Duncan, S.,
Madison, R., Manson, R., and Pyles, M., "Minimizing Debris
Avalanches on Forest Land," A Report to the State Forester,
Oregon State Department of Forestry (December 1982).
(16) "Pollution Control in the Forest Products Industry," EPA
625/3-79-010 Envir. Res. Info. Center, Cincinnati, Ohio
(August 1979) .
(17) "Annual Survey of Ongoing Research on the Impact of Forest
Management Practices on Water Quality and Utility - 1982,"
NCASI Technical Bulletin No. 373 (June 1982).
121
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(18) McGreer, D.J., "A Study of Erosion from Skid Trails in
Northern Idaho," in Measuring and Assessing the Effective-
ness of Alternative Forest Management Practices on Water
Puality, NCASI Technical Bulletin No. 353 (August 1981).
(19) "Factors Affecting Changes in the Percent of Fine Sediment
in Gravel Bedded Channels," NCASI Technical Bulletin No. 354
(August 1981).
(20) McGreer, D., Forest Hydrologist, Potlatch Corp., Lewiston
Idaho, Personal Communication (December 28, 1981).
(21) Hewlett, J., "Models in Land Use Hydrology", Technical
Report No. TR 113, Department of Water Affairs,
Forestry, and Environmental Conservation, Pretoria,
So. Africa (May, 1980).
(22) Novotny, V. and Chesters, G., Handbook of Non-Point
Source Pollution, Van Nostrand Reinhold, New York (1981).
(23) "A Study of the Selection, Calibration, and Verification
of Mathematical Water Quality Models", NCASI Technical
Bulletin No. 367, New York, NY (March, 1982).
(24) Ambrose, R. , et al., "Models for Analyzing Euthrophication
in Watersheds-A Selection Methodology", Chesapeake
Bay Program, US EPA, Annapolis, MD (1981).
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
122
-------
DETENTION POND SIZING TO ACHIEVE WATER QUALITY OBJECTIVES
Roger K. Wells, P.E.
HMM Associates, Inc.
Intr odu ct ion
HMM Associates has recently performed a modeling study of the Black
Warrior River in Tuscaloosa County, Alabama. The study area consisted of
the reach downstream from the Oliver Lock and Dam to the Warrior Lock and
Dam--approximately 75 river miles. The goals of the study were twofold:
(1) to perform the necessary water quality modeling to support an applica-
tion for discharge permit under NPDES and (2) since the reach is water
quality-limited during a portion of the year, to demonstrate the adequacy of
a proposed discharge detention system. As part of (2), the size of the pond
was to be determined.
Overall Method
As part of the effort, several mathematical modeling techniques were
employed. The water quality of the reach was modeled using QUAL-II. Runs
were made with and without the proposed discharge. QUAL-II was used in the
flow augmentation mode to generate data to provide a correlation between
river conditions and allowable discharge. Once this relationship was es-
tablished, a synthetic streamflow model was developed to simulate a realis-
tic sequence of daily flows, and finally a detention pond model was devel-
oped to determine the annual maximum storage requirements for a 50-year
period of simulation. Figure 1 shows an example of the desired frequency
distribution. Extreme value distributions such as this are difficult to
construct solely on the basis of existing records because of the distribu-
tion's skew. Skew is a measure of the third moment, which is greatly in-
fluenced by rare outlying events. Rarely are streamflow records long enough
for reliable estimates of the third moment. Using a reliable estimate of
this relationship, designers can pick the required pond volume with a knowl-
edge of the return period of conditions which may affect facility capacity.
The following sections discuss in turn the analytical steps to develop this
curve.
Model Set-Up and Input Parameters
The first step in setting up a QUAL-II simulation is to schematize the
river so that important waste loads, tributaries, and geometrical charac-
teristics may be accounted for. For this study, a total of 154 1/2-mile
computational elements for the reach between the Oliver Lock and Dam and
the Warrior Lock and Dam downstream were used. These computational
elements were grouped into reaches, each with its own reaction rates, tem-
perature, and geometry. Fifteen reaches with 11 different hydraulic charac-
teristics were incorporated into the model. Each reach also receives dis-
tributed runoff flow. Eleven computational elements were identified as
point source discharges or withdrawals. Small tributary flows were con-
sidered point sources in this study. Figure 2 shows the river schematic
developed for this study.
123
-------
~| -
33
s
^_^ I _
a *
2u
So
Figure 1
124
-------
REACHES
PT
2.0
2.1
3.0
4.o
5.o
Go
7.0
&>
10.Q
ll.O
\.l
OLIVE?
CL£ME\iTS
BJTECSTATC
EA6LE
SUCfcLS
SAklCX CX.
MOUkJO
STATt
ELLIOT6 CR
WV4A.TLCY 6R
CUTOFP
O41LDS
BROW us ec
WlSHWAY-14.
PT
3U
sfo
500
296
292
236
274
210
OIL
GOODRJCW
TUSC^LOOSA STR
IklTMCE
DISCHARGE.
LAWTELK.- CHEMICAL
Noerw
• D^iOTS CR. (vMOUMDVIUL SDUTU LWOOI4)
Figure 2
Black Warrior River Model
125
-------
Hydraulic Data
Hydraulic data were developed as a result of field work which was un-
dertaken in support of this study. The field study is discussed later in
this paper. These data were used to develop trapezoidal approximations of
each section for model verification. Since different flows were necessary
for subsequent model runs, velocity, flow, and depth relationships were de-
rived for later runs. These relationships are of the following form:
V = aQb
D = a(f
where V = stream velocity, in ft/sec;
Q = stream flow, in ft^/sec;
D = stream depth, in ft; and
a, b, a, and 3 are coefficients determined as part of this study.
Table 1 summarizes the coefficients so determined.
Reaction Coefficients
The reaction coefficients which must be specified include the carbon-
aceous BOD reaction rate (Kj), the NH3 oxidation rate (CKNH3), the N02 oxi-
dation rate (CKN02), and the atmospheric reaeration rate (K2).
K_j. The BOD reaction rate is a parameter which expresses the rate (in
units of days"1) of oxidation of carbonaceous BOD. During the field mea-
surement program, a sample was taken near the proposed discharge location
for a 30-day BOD analysis. These data were analyzed for reaction rate using
a non-linear least squares regression technique known as the Gauss-Newton
method. Figure 3 summarizes the results of this analysis. It can be seen
that the oxygen demand is still increasing substantially up to 30 days,
which indicates a low reaction rate. It was also felt that the point at
five days might be invalid because of its low value, so regressions were
performed both with and without this value.
In selecting a reaction coefficient (Kj) for modeling, the values from
Figure 3 were used as limits. The rate was varied until a balance was
struck between measured BODs and measured DOs within this range. The final
rate selected for modeling was 0.02 day"1. This value is considerably below
the values traditionally used for modeling, i.e., 0.1-0.2 day"1. Since this
test is the only known long-term BOD test from this reach of the Black
Warrior River and reasonable agreement was obtained between field measure-
ments and calculations, it was decided to use the value of 0.02 day"1 for
modeling.
CJCNHj. A value of 0.05 day"1 was selected for the ammonia oxidation
rate. This is based on discussions with the regulatory authorities and re-
ports of their work in the Black Warrior River, which indicated that nitri-
fication is not an important oxygen-consuming process in-stream.
CKNO^. The nitrite oxidation rate chosen was 2.0 day"1. This corres-
ponds to the idea that nitrite is merely a short-lived intermediate step in
the process of oxidizing NH, to N03. Without detailed nitrogen measurements
to support the use of another value, the upper end of the range suggested in
the QUAL-II user's manual was chosen.
126
-------
Table 1
Stream Flow Coefficients
Reach
Number
1
1
2
2
3
4
5
6
7
8
9
10
11
11
11
.0
.1
.0
.1
.0
.0
.0
.0
.0
.0
.0
.0
.0
.1
.2
3
3
1
1
3
3
3
2
3
1
2
1
1
1
1
a
.408E-4
.408E-4
.943E-4
.943E-4
.840E-4
.155E-4
.417E-4
.538E-4
.203E-4
.953E-4
.072E-4
.472E-4
.314E-4
.314E-4
.314E-4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
b
.929
.929
.956
.956
.904
.934
.931
.949
.933
.949
.946
.952
.968
.968
.968
11
11
20
20
10
11
8
16
9
21
19
27
29
29
29
a
.085
.085
.407
.407
.054
.368
.756
.817
.496
.187
.240
.066
.237
.237
.237
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
.0523
.0523
.0329
.0329
.0561
.0514
.0617
.0383
.0584
.0320
.0345
.0261
.0245
.0245
.0245
127
-------
30-Day BOD
Time
(days)
5
10
15
20
25
30
BOD
(fflg/1)
0.05
0.65
1.45
1.55
1.75
2.05
2.0
1.5
1.0
0.5
0.0
5 pts
6 pts
0
5
10
15
Days
20
25
30
Data Base
6-point
5-point
Reaction Rate
0.0118
0.0260
Corr. Coeff.
0.91517
0.90644
Figure 3
128
-------
Reaeration Rate
Atmospheric reaeration is the fundamental source to replenish in-
stream DO. Unfortunately, a wide range of estimates of the coefficient
is available. The method of Tsivoglou and Wallace was used for the
calibration/verification, a method recommended by EPA in the QUAL-II docu-
mentation. The form of this estimate is:
K2 = 3600 K Se U
where K2 = reaeration rate, in hour ;
K = a constant - 0.05-0.1 ft"1;
Se = energy gradient slope, in ft/ft; and
U = stream velocity, in ft/sec.
It can be seen that K2 depends on the energy gradient slope. At low flows,
the Warrior Pool becomes more lake-like, with a near-zero energy gradient,
and a method more appropriate for a lake environment is used. Therefore, it
was decided that a method outlined by Brown* would be used. This method re-
lates the surface transfer coefficient K^ to the wind speed:
KL = 0.05 w2
where K, = surface transfer coefficient, in m/day; and
w = wind speed, in m/sec.
For the low flow portion of this study, K^ was estimated to be 0.25 m/day
(0.82 ft/day), based on a 5 mph wind speed. Table 2 summarizes the K2
selected for each reach for the low flow runs.
Initial Conditions
For a steady-state simulation, the only parameter which needs to be
specified is the temperature since it affects the adjusted reaction coeffi-
cient and the saturation value of DO. A value of 85.1°F (29.5°C) was chosen.
This value is the mean August temperature based on daily measurements at
Northport, Alabama, during the most recently published water resources data
period (USGS, as of June 1982).
Headwater Sources
The only headwater considered in this study is the Black Warrior River
at the Oliver Lock and Dam. The USGS in Tuscaloosa was contacted to deter-
mine the most recent estimate of the 7Q^Q. This parameter is significantly
affected by the operating policy of the upstream dams. The current operat-
ing mode was instituted in 1964. The values of 7Q}Q for this period were
obtained from the USGS. The value 605.7 cfs is used as the starting point
for all low flow modeling. As mentioned before, in-stream temperature is
taken to be 85.1°F, and the headwater DO level is taken to be the saturation
value at 85.1°F, or 7.4 mg/1. The value of BOD^ at the headwaters is taken
to be 0.45 mg/1. The source of this estimate consists of measurements taken
during the field study conducted by HMM as part of this study and measure-
*Brown, Russ T. Modeling the Effects of Wind Reaeration. Report No. WR28-
2-520-117. Tennessee Valley Authority. March 1981.
129
-------
Table 2
Reaeration Values (K2) for Each Reach, Based on 5 mph Wind Speed
Reach Number
1,0, 1.1
2.0, 2.1
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0, 11.1, 11.2
Depth (ft)
15.5
25.2
14.4
15.8
13.0
21.5
13.8
26.0
24.0
32.0
34.2
K2 (day"1)
0.053
0.033
0.057
0.052
0.063
0.038
0.059
0.032
0.034
0.026
0.024
130
-------
ments provided by AWIC. Table 3 summarizes these data, as well as measure-
ments of NH3, N03, and P04 (1980 only) included in 1980 and 1981 studies by
AWIC. The mean value of BOD5, N03, and TSS was included in the headwater
concentration levels for these constituents. The concentration of NH3 was
entered as zero, and PC^ was not modeled since all measurements were below
the detection limit.
The QUAL-II model provides for a complete description of the relation-
ship among algae, nutrients, and oxygen. In the field measurement programs
conducted by AWIC in September 1980 and in June-July 1981, numerous oxygen
samples were taken that indicated that the water was supersaturated with
oxygen. This also occurred in the HMM measurements taken in August 1982.
These findings indicate that a net oxygen credit, due to photosynthesis by
algae, is occurring, since this is assumed to be the only process producing
oxygen in-stream. In August 1981 AWIC indicated, in their analysis con-
cerning the Hunt Oil Company expansion, that a net contribution of 0.15 mg/1/
day of oxygen was being made by algal processes. This rate was incorporated
into the HMM modeling effort. The QUAL-II model couples algal growth to the
availability of nutrients and light. It also allows for creating NH^-N
from algae through a coefficient which represents the fraction of respired
algal biomass which is resolubilized as NH3-N by bacterial action. Unless
the reaction rate for NH3-N to N02-N is very low, a net oxygen deficit will
result from these coupled processes. Thus, the supersaturated levels of
oxygen also support the idea that little or no nitrification is occurring
in-stream, an opinion expressed by AWIC when evaluating the Hunt Oil expan-
sion. In QUAL-II, the presence of algae is considered to be represented by
the measurement of chlorophyll A. This was input to the model at 20 ug/1,
which yields an oxygen production rate of 0.15 mg/I/day at the headwaters.
This value rises slightly until about river mile 325, when increasing river
depths limit the availability of light for algal growth, and the downstream
chlorophyll concentration drops to about 5.25 yg/1 at the Warrior Dam,
yielding an oxygen production rate of 0.04 mg/l/day.
Existing Point Source Loads
Point source loadings in QUAL-II include unmodeled tributaries as well
as industrial and municipal discharges. Sources of data on existing dis-
charges include the Tuscaloosa County 208 Report and AWIC. Table 4 summar-
izes the characteristics of all modeled discharges.
New Discharge
The new discharge is subject to new source performance standards. The
following parameters summarize the discharge's characteristics.
QD = 5.028 cfs;
TSS = 201 mg/1;
BOD5 =84.7 mg/1; and
BOD /BODC = 2.62
u 5
Field Measurement Program
On August 3-4, 1982, HMM Associates undertook a field measurement pro-
gram on the Black Warrior River to obtain data necessary to characterize the
131
-------
Table 3
BOD5, N03, NH3, and P04 Near the Headwaters
Date
8/82
6-7/81
9/80
Mean =
Std.
Dev. =
TSS
8.4
3.6
4.4
-
-
-
6
5
6
3
4
11
5.71
2.56
B
0
0
0
1
0
0
0
0
0
0
0
0
0
\J LJ f-
.05
.15
.25
.3
.3
-
.4
.5
.4
.5
.4
.7
.45
.33
River
Mile
311
320
329
337
337
337
337
337
337
337
337
337
Source
NC
3 NH, PO,
Field Study -
Field Study -
Field Study
AWIC
AWIC
AWIC
AWIC
AWIC
AWIC
AWIC
AWIC
AWIC
-
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
-
92 < 1
74 < 1
54 < 1
43 1 -
45
44
42 - < .2
41 - < .2
37 < .2
524
185
132
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hydraulic characteristics of the river, to measure depths in detail in the
vicinity of the intake and discharge areas, and to obtain DO, BOD, TSS, and
color samples throughout the modeled reach of the river. Samples were also
taken from Big Sandy Creek, Elliot's Creek (upstream of the Moundville South
Lagoon), Whatley Branch, and Five Mile Creek.
The hydraulic characteristics were determined by bathymetric measure-
ments taken in the river with a Raytheon DE719B recording fathometer. The
daily discharges at the Northport Gage for the two days of the study were
obtained from the USGS. The flow for August 3 was 6530 cfs, and the flow
for August 4 was 5790 cfs. In modeling, the mean flow of 6160 cfs was used,
since the measurements of DO and BOD spanned the two days. The water qual-
ity parameters were sampled at each bathymetric measurement point. _Tn situ
DO and temperature measurements were taken with a Yellow Springs ModeT 54B
DO meter. Table 5 summarizes the samples taken during the field study.
Modeling Results
Calibration/Verification
The QUAL-II model was set up as described with the measured hydraulic
characteristics as input. Using the data measured on August 3-4 as a ref-
erence, the model was run to verify that reasonable results were produced.
Minor adjustments were made in reaction rates and the method of treating the
hydraulics until reasonable agreement was reached between calculated and
measured DO and BOD. The results of this process are shown in Figure 4. It
should be noted that the City of Tuscaloosa Sewage Treatment Plant (STP) was
not operating properly on the days of measurement. The level of BOD5 in the
STP effluent was at an average level of 211 mg/1. The level of NH3 assumed
in the STP discharge was the permit level of NH? scaled by the ratio of
actual BOD5 to permit BOD5:
NH3 discharge = 20 x 211/30 = 141 mg/1
It can be seen that reasonable agreement was obtained, particularly in the
case of DO. The large amount of scatter in the measured BODs can be
accounted for by incomplete mixing of the STP discharge in the portion of
the river where the greatest changes in BOD levels would be expected.
No Mill
The model was next run with the river flow at the 7Q}Q level of 605.7
cfs and all present dischargers operating at their full permit limits. The
minimum calculated DO was 5.39 mg/1, occurring at the downstream end of the
reach.
With New Discharge
When the new discharge was input at the levels described above and the
river flow was 605.7 cfs, the flow augmentation option was used. In this
case, a total augmentation of 60.9 cfs was required to maintain 5.0 mg/1 of
DO. Several runs were made to provide information necessary for input to
the retention plan analysis. Since the maximum daily discharge permitted
under NSPS is twice the 30-day average, this level is considered to be the
upper limit for the discharge. Computer runs were made at 25%, 50%, 75%,
150%, and 200% of the 30-day average discharge levels to determine the cri-
tical flows for these discharge levels. The results are plotted in Figure 5,
134
-------
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-------
DO Calibration
BOD Calibration
Figure 4
136
-------
Mill Discharge Fraction vs. River Flow
River Flow (cfs)
Discharge Volume (70)
465.0
623.2
666.6.
786.0
877.0
0
75
100
150
200
Note: 100% discharge is 5.028 cfs and 84.7 mg/1 BOD,- or
2300 Ibs/day. D
4-
-H-
t\ '• I !
\0ki OF FULL
Regression Analysis of Critical River Flows
Figure 5
137
-------
and a regression line was calculated for use in subsequent analyses. The
equation of the regression line is given by:
X = 2.0 881 < Q
X = -2.229 + 0.004798 x Q 465 < Q < 881
X = 0 otherwise
where X = fraction of maximum new discharge; and
Q = river flow.
The correlation coefficient is 0.9982.
Persistence of Daily Flows
It is evident from the results reported in the previous sections that
the allowable discharge level is highly dependent on daily river flow val-
ues. Since the current river operating system went into effect in the early
1960's , the daily flow fluctuations have been greatly reduced, and prolonged
periods of low flow are rare. This is evident in the fact that for the
period of record of the Northport Gage (1895-present), the 10-year 7-day low
flow (7Qi0) has risen from approximately 96 cfs to 605.7 cfs. Since the
volume of retention is greatly dependent on day-to-day flow variations, an
analysis has been performed to study the actual persistence of day-to-day
flows. As an example of the issue at hand, the 7Q}Q is 605.7. This could
be taken to mean that for at least 7 days, no discharge could occur (if the
limiting flow happened to be at or above this value), resulting in 7 days of
required storage. However, this 7-day average could also be the result of
the following sequence of flows (in cfs): 248, 248, 1500, 248, 248, 1500,
248--resulting in 2 days of required storage (if the limiting flow was less
than 1500). Thus, modeling the day-to-day variation is fundamental to
studying this problem.
The USGS has supplied statistics on the daily flow records from the
Northport Gage from 1964 to 1981. The distribution of daily flow values is
shown in Figure 6, along with a calculated log normal distribution which
shows that the log normal distribution is a reasonable model of the daily
river flow. The parameters of this distribution are:
logq = 8.31 (mean)
VQ = 1.30 (variance)
N = 6575 (number of samples)
Synthetic Stream Flow Generation
This section presents a method for generating daily stream flows by
computer. These stream flows will correspond to the actual stream flows on
three measures of performance — the mean and the variance of the logarithm of
the daily flows, and the mean annual 7-day low flow. The method used has
been described by Loucks et^ jil_. * A simple autogressive model is used. This
type of model is a first-order Markov process which recognizes that the flow
*Loucks, D. P., J. R. Stedinger, and D. A. Haith. Water Resource Systems
Planning and Analysis. Prentice-Hall. 1981. Chapter 6.
138
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> J
Q
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-5-1
Figure 6
Distribution of Daily Flow Values
139
-------
today is to some degree dependent on the flow yesterday. The generation of
synthetic stream flows requires the marginal distribution of flow on one
day given the flow on the previous day. Thus, if there is a low flow today,
a low flow is more likely than a high flow tomorrow. The preferred method
of generating such flows is to transform the flows to a normally distributed
random variable. In this case, this corresponds to dealing with the logar-
ithms of the flows. A first-order Markov model for such a variable is given
by:
Xt+1 = V + Px(Xt
where X = log Q;
u = mean of X;
p = lag 1 autocorrelation coefficient;
J\.
t = time, in -days;
a = standard deviation of X; and
A.
V = unit normal random variate.
In this case, y = 8.31;
a = /~O" = 1.14; and
J\.
p is varied until the mean annual 7-day low flow is reproduced.
Table 6 summarizes a number of computer runs for various values of p. For
this study, a value of 0.45 is used.
Retention Pond Model
The basic mathematical expression of a detention basin is given by the
following ordinary differential equation:
^| = i(t) - o(to (i)
where s = storage volume;
I = inflow;
0 = outflow; and
t = time.
In this case, I is a constant 3.25 mgd. The problem becomes one of deter-
mining 0(t). The following procedure is used. The flow generation model
described above is used to generate a daily flow value. The relationship
determined previously is used to determine the maximum permissible discharge:
f = 0 QR < 465
f = 0.00478Q - 2.229 465 < QR < 881
f = 2.0 QR > 881
where f = fraction of daily average discharge (3.25 mgd); and
QR = river flow, in cfs.
140
-------
Table 6
Dependence of 7-Day Low Flows on the Lag 1 Autocorrelation Coefficient
p
0
0
0
0
0
0
0
0
.3
.4
.5
.6
.7
.8
.9
.45
Mean 7 -Day Low Flow
1364
1146
959
806
695
631
600
1050.3
USGS value is 1058.11
141
-------
Equation (1), in discrete form and rearranged, is used to compute the
daily change in required storage:
AS = [I - 0]*At
If storage goes negative, it is set equal to zero. Another flow is gener-
ated, and the process repeats. A flow chart representing this procedure is
shown in Figure 7.
An algorithm was written to implement this procedure on a small com-
puter. A run modeling performance for 50 years was made and the resulting
distribution of annual extreme maximum storage volumes plotted. Table 7
contains the results of this run. A Pearson Type III extreme value prob-
ability distribution was fitted to these observations. Using this distri-
bution, a graph was constructed to show the required storage volumes for
different return periods (Figure 8).
Proposed Control Plan
Since development of this plan has been based on the distribution of
low river flows, it is proposed that the level of discharge be controlled
in coordination with present flow levels. In order to do this, river flow
must be measured or estimated locally. Using the measured flow level, the
discharge may be regulated according to the following relationship:
QD = 0 QR < 465
QD = 24.12E-3 x QR - 11.21 465 < QR < 881
QD = 10.06 881 < QR
where Qn = discharge flow, in cfs; and
QR = river flow, in cfs.
The purpose of the discharge control plan is to maintain Black Warrior
water quality while at the same time allowing the facility to operate at
design capacity. To this end, retention storage has been incorporated into
the overall facility design.
Conclusion
A method of generating a time series for the modeling of extreme
values, in this case annual maximum storage volumes, has been presented.
The dependence of these processes on higher moments of the underlying dis-
tribution makes use of existing records unreliable, since rarely are hydro-
logical time sequences long enough for the estimation of higher-order
moments. In the future, models using higher-order autoregressive and/or
moving average parameters may be fruitfully explored.
142
-------
Flow Chart for Retention Pond Performance Computer Program
143
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144
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Storage Requirements for Various Return Periods
Storage Volume Days at Return Period
(acre-feet) 3.25 mgd (years)
27.8 2.79
32.2 3.23
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The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
145
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A MECHANISTIC SIMULATION FOR TRANSPORT OF NONPOINT
SOURCE POLLUTANTS
BY
Daryl B. Simons, President
Ruh-Ming Li, Executive Vice President
Kenneth G. Eggert, Senior Water Resources Engineer
Simons, Li & Associates, Inc.
Fort Collins, Colorado
ABSTRACT
Nonpoint source pollution represents an integration of the behavioral
response of the ecosystem to the impacts of land use activities on indivi-
dual components of the ecosystem. By analyzing basic ecosystem processes
and impacts of land use activities on specific processes governing produc-
tion and transport of nonpoint source pollution, it is possible to predict
cause-effect relationships between these activities and water quality. In
order to accomplish this goal, a simulation model for evaluation of alter-
native management practices as a function of both environmental and manage-
ment parameters is presented.
The simulation may be used to predict watershed response to land use
including both planned management practices and unplanned activities asso-
ciated with catastrophic events. Nonpoint source pollution from these acti-
vities and events may include loading of streams by: 1) sediment from sur-
face erosion, mass wasting, and channel bottom and bank erosion, 2) thermal
energy, 3) biological contaminants, 4) organic debris, 5) nutrients and
dissolved solids, 6) pesticides, and 7) other waste materials either in
solution or adsorbed to sediments. The simulation is composed of the
following components: 1) a soil-plant-atomspheric water simulation for
adjusting soil moisture as a function of evaporation, evapotranspiration,
soil water hydraulics, and snowmelt, 2) a kinematic wave surface water
routing component, 3) a hydraulically-based sediment yield model, 4) a sub-
surface flow component, 5) a temperature and dissolved oxygen component, 6)
pollutant routing, and 7) streambank erosion and forest litter routing
routines.
INTRODUCTION
The theoretical foundation of the watershed simulation component of the
generalized planning model for evaluation of alternative management prac-
tices is described in this paper. The model is a cause-effect simulation
based on mathematical descriptions of watershed processes related to
146
-------
nonpoint source pollution. Nonpoint source pollution represents an integra-
tion of the behavioral response of the ecosystem to the impacts of activi-
ties on individual components of the ecosystem. Management activities
include both planned management practices, such as road construction,
watershed management, stream improvement, low head impoundments, application
of pesticides and fertilizers, foliage production and grazing, mechanical
site preparation, and disposal of wastes by land treatment, and unplanned
activities associated with catastrophic events such as large runoff events.
The model as originally formulated was addressed to management activities
involving timber harvest, timber planting and replacement, grazing, mechan-
cial site preparation and prescribed fire. However, the mechanistic basis
of the model makes it applicable to nearly any watershed activity. Specific
applications to agricultural activities as well as waste land treatment and
disposal are well within the scope of the model formulation.
The watershed process model is structured in modular form. The modules
contain related physical process simulations and are described individually
later in this paper. The basic structure of the model is shown in Figures 1
through 3. The model structure was designed to allow a high level of repre-
sentation of physical processes but still remain within the range of memory
constraints normally encountered at most computing centers. The modular
nature of the model structure also facilitates substitution of new or
improved simulation components as they are developed without extensive revi-
sion of the code. The approach has both advantages and disadvantages. The
basic advantages are the modular nature as described above, and the capabi-
lity of using simulation routines that are not overly limited by computer
storage. The disadvantage of the structure is that input/output sequences
and file management are machine specific and must be tailored to the host
computer. However, the basic file management functions used are generally
available at most computing centers. Presently, the model has been
installed on CDC Cyber 172, HP 1000 and IBM 370 systems. Therefore, the
advantage of a more precise representation of physical processes is felt to
outweigh any disadvantages due to machine specific job control language.
As shown in Figures 1 through 3, the basic model components are as
follows:
1. Water balance
2. Water and sediment routing
3. Pollutant routing
4. Heat and dissolved oxygen routing
5. Streambank erosion
6. Vegetative litter routing
7. Sequential GOAL Programming
WATER BALANCE
Since infiltration exerts a fundamental control on the storm water
runoff hydrograph, any long-term hydrologic simulation must have a component
for calculating the changes in soil moisture content as a function of time.
The primary processes affecting the amount of soil moisture are infiltra-
tion, percolation, evaporation, evapotranspiration and drainage. These
147
-------
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Figure 3. Water and Sediment Routing
150
-------
interrelated processes involve hydrologic, biologic, atmospheric and soil-
specific aspects. Therefore, a physically-based water balance model must
simulate all of these aspects and properly account for their interrelation.
After a literature search for an existing water balance model, a decision
was made to modify and implement a simulation presented by Goldstein and
Mankin (1972). This program, known as PROSPER, has been widely tested in a
variety of locations with generally good results (Swift et al. , 1975;
Luxmoore et al., 1977). The success of these applications is probably based
on the flexibility built into the model. It is possible to adapt model
subroutines to a particular watershed environment by modifying the methods
used to calculate the resistances to water flux through the soil and plant
components.
PROSPER is a plant-atmosphere-soil water flux simulation which imple-
ments an energy balance and aerodynamic calculation of evapotranspiration
using the Penman method with a multilayer Darcian soil model. The model
simulates the fluxes of water through the soil and plants in response to
atmospheric and solar conditions. The simulation uses a time increment of
one day. All hydrologic plant and atmospheric processes are averaged on a
daily basis. The model as implemented uses an electrical circuit analogue
for the soil and plant system. The current in the circuit loop represents
the water flux through the respective soil, plant, or atmospheric component.
Since PROSPER was written for predicting daily variations in water
flux, its formulation was found to be inadequate for the prediction of
infiltration and interception on a storm-by-storm basis. Further, since the
time history of infiltration during a storm is particularly critical when
determining water and sediment runoff, the effects of watershed management
on infiltration parameters could not be properly simulated without modifica-
tion to PROSPER. Therefore, the water balance component was modified to
include modified Green-Ampt infiltration component for layered soils for
more precise determination of storm water runoff and a storm water intercep-
tion routine. Both infiltration and interception components provide greater
sensitivity to management activities in the watershed than the original
PROSPER, and the infiltration routine provides for the interfacing of the
water balance component with the water and sediment routing and water
quality subprograms.
Figure 4, which is modified from Goldstein and Mankin (1972), shows a
schematic representation of the water balance system. Resistances in the
current analogue are formulated in terms of physically defined watershed
moisture parameters. These parameters include soil layer hydraulic conduc-
tivities, root resistance, and empirically measured species specific stoma-
tal resistances. By varying the values of these parameters to fit the phy-
sical setting of the watershed, it is possible to achieve a more precise
representation of physical processes than provided by previous simulation of
similar scope. •
151
-------
Infiltration to Layer I
Layer I
RSBLI .>
RR2 + RRI/2
Infiltration to Layer 2
RSBL2
Infiltration to Layer 3-
RSBL3
Infiltration to Layer4-
RSBL4
Infiltration to Layer 5-
Layer 2
Layer 3
Layer 4
Layer 5
To Drainage
Figure 4. Soil-plant flux schematic.
In many watersheds the most significant contribution to runoff is from
snowmelt. Often the most severe erosion and sedimentation events occur as
combinations of high intensity spring rainfall and snowmelt runoff. This
aspect of the hydrologic cycle is particularly important in high altitude
watersheds of the western United States and in northern latitudes. After
examining available snowmelt models, it was felt that a modified version of
the model developed by Leaf and Brink (1973) would provide the best approach
for incorporation into the generalized planning model. This model is a
simulation originally developed for snowmelt prediction in Colorado
subalpine watersheds. It is a mechanistic approach with data requirements
consistent with previously described planning model components, in par-
ticular, evapotranspiration and water balance components. The snowmelt
model as formulated is designed to provide daily runoff water yields and
therefore, it requires modification to interface with the other water
balance routines.
The snowmelt model is a combination of the fundamental laws of conser-
vation of mass (water balance) and conservation of energy. The thermal
152
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state of the snowpack is described by the calorie deficit of the pack on any
given day. The calorie deficit is defined to be the number of calories (per
unit area) required to bring the pack to an isothermal state at 0°C. It is
assumed that no melt can occur until the pack has reached this state. The
general scheme of computing snowpack accumulation, temperature change, and
melt begins with an assessment of the effects of the day's precipitation, if
any, on the pack. This includes the effect of the snow or rain introduced
to the pack at the average air temperature, as well as the addition of water
to the pack as snow or as rainfall. After the effect of rainfall has been
assessed, an energy balance calculation is begun with a determination of the
net radiation input (or loss) to the snow pack. Depending on the thickness
of the snowpack and the amount of free water existing in the pack, a thermal
diffusion model is used instead of a radiation balance. The new pack tem-
perature is calculated using either the thermal diffusion model or the
radiation balance directly. Based on the new temperature, a new calorie
deficit or melt is calculated, and the simulation proceeds to the next day's
precipitation and radiation data. Water balance relations are adjusted
daily based on the above outcome.
The original Leaf and Brink (1973) snowmelt model was designed to pro-
duce daily runoff water yields. As in the previously discussed case, this
type of runoff description is inadequate for prediction of the water
hydrographs required for simulation of nonpoint source pollution transport.
A means for transforming the melt water volume into a snowmelt hyetograph is
required. Since the melt occurs in response to the input of solar energy,
it seems reasonable to approximate the snowmelt hyetograph by distributing
the melt over the sunshine period using the hourly insolation divided by the
total daily insolation as a weighting function. Since hourly measurements
of insolation at the snowpack are not usually available, it is assumed that
the corresponding ratio of hourly extraterrestrial to total extraterrestrial
radiation will suffice. This insolation weighted meltwater runoff function
is subjected to infiltration at a rate equal to the saturated hydraulic con-
ductivity, and the resulting excess runoff is treated by the routing models
in the same manner as the excess rainfall described above.
WATER AND SEDIMENT ROUTING
The water and sediment routing model is designed to route storm water
and sediment runoff from watersheds of complex geometry. In order to
accomplish this task, the complex watershed geometry must be simplified into
a representation suitable for computer simulation. The geometric approxima-
tion used in this component is an arbitrary number of two plane, one-channel
"open book" subwatersheds and planes linked together by channels. Figure 5
illustrates a sample representation of such a system of planes and channels.
For simplicity, a numerical solution to the kinematic wave problem
could have been used for both the subwatershed units and the linking chan-
nels. However, an analytical solution such as the method of characteristics
approach allows more efficient use of computer storage and usually more
rapid calculation of the runoff hydrograph. Therefore, whenever possible,
analytical solutions are employed. To be consistent, in the portions of the
watershed where the analytical methods is used to route the water, the sedi-
ment yield is also computed by an analytical method. Likewise, in the
153
-------
CH-5
PL -9 PL- 10
|
^\
WS-7 J
V^/
CH-4
PL-7 PL-8
,.
CH-6
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CH-7
PL- 13 PL- 14
1
CH-8
PL-15 PL- 16
i
CH-9
PL-17 PL- 18
J
t
CH-IO
PL-19 PL-20
1
CH-II
PL- 21
Figure 5. Schematic diagram of a typical routing network.
portions where water is routed numerically, sediment yield and transport are
computed by a numerical routing scheme.
Overland Flow and Primary Channels
The two tasks performed by this program are the determination of sedi-
ment yield by size fractions and the routing of water for all plane and
upstream watershed units that form the entire watershed. The water routing
is performed analytically by applying the method of characteristics to the
kinematic wave approximation to the momentum and continuity equations. The
sediment yield is calculated by comparing the supply due to detachment by
both rainfall and runoff, and the potential transporting capacity. The
transport capacity is determined by size fraction. The suspended sediment
transport capacity is calculated using Einstein's (1950) suspended sediment
equation and bed load is calculated using the Meyer-Peter, Muller (USSR,
1960) equation. These methods are used in both the overland flow and pri-
mary channel flow routines.
Main Channel Water Routing
The main channel routing program uses a numerical scheme to route the
water in the downstream main channels. It uses the discharges calculated in
154
-------
the overland flow and primary channel routines as upstream and lateral
inflows into the channel units. In addition, an infiltration routine calcu-
lates the amount of water which infiltrates in the channel units and
subtracts it from the lateral inflow.
Sediment Routing
The sediment routing in the main channel routine uses a similar prin-
ciple to the sediment yield calculations in the overland flow and primary
channel model—the process of balancing supply and capacity for each sedi-
ment size. In addition, the main channel includes the effect of armoring on
the sediment transport rate. The process of armoring occurs because of the
difference in sediment transport capacity between the different sizes,
resulting in a layer of large size fraction formed on the surface. If the
erosion processes continue, this layer of larger size fraction will protect
the smaller one from detaching or dislodging.
The sediment calculations in the main channel are also 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 incre-
ments to arrive at a total yield for each size fraction. The method used in
overland flow and primary channel model can only provide a total yield for
each size fraction, but cannot truly route the sediment through the channel.
The main channel model 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 the overland flow and primary channel does not allow for
this, since only average conditions are determined.
Since the main channel model uses the numerical method, which requires
sediment transport rates at each time increment, and needs to use the yields
calculated in the overland flow and primary channel model as upstream and
lateral inflows, the yields in the latter must be transformed into sediment
hydrographs. This is accomplished by distributing the yields from overland
flow and primary channel model in proportion to the water discharge at each
time increment. A more detailed discussion of the water and sediment
routing component may be found in Li et al (1979).
This water and sediment routing method has been successfully employed
on a variety of watersheds. Results have shown it to provide very accurate
characterization of watershed hydraulics. A considerable degree of emphasis
has been placed on the previously described water balance and the water and
sediment routing components. Pollutants are, of course, chiefly transported
by surface and subsurface flow components. Therefore, the characterization
of the hydraulics of infiltration, overland flow, channel flow, and the
mechanics of sediment yield and transport are critical and of central impor-
tance to accurately estimating pollutant migration. The described hydraulic
components provide the level of accuracy necessary to represent these pro-
cesses and through the model structure remain practical for implementation
on most computing hardware.
POLLUTANT ROUTING
As originally formulated, the pollutant routing module addressed the
routing of nutrients. Nutrient compounds are a source of nonpoint
155
-------
pollutants affecting water quality. Nutrients, such as nitrogen and
phosphorus, are of concern because of their role in eutrophication pro-
cesses. A physical process simulation model was developed for predicting
nutrient losses from forest and agricultural watersheds associated with sur-
face runoff and sediment transport. Mass balance and loading function con-
cepts were the basic principles utilized in formulating this model. The
model was developed to predict loadings of organic nutrients, nitrate, ammo-
nium, and inorganic ortho-phosphorus to streams and rivers.
Natural nutrient input to the ecosystem comes mainly from precipita-
tion, litter fall, and geologic weathering. Precipitation and litter fall
were considered the primary external inputs of nutrients from the
atmosphere. These average inputs were routed into the litter layer where
microbial degradation occurred. The products of degradation were then
routed to the stream and into the soil layer. Within the soil layer, these
products were again evaluated along with plant uptake and soil adsorption.
The products of these processes occurring within the soil were then routed
to the stream. Generally, nutrient constituents cannot move unless
transported by sediment and water and therefore, water and sediment are the
major carriers of nutrients through the ecosystem. Evaluation of these
carrier amounts is necessary for predicting nutrient losses from the
watershed.
The nutrient simulator proposed here is basically a nutrient budget
model. All of the processes mentioned above except the immobilization pro-
cess were taken into account when simulating average nutrient concentrations
in the soil. The quantities of nutrient losses to streams during storms
were predicted by the incorporation of the loading function concept.
As stated earlier, the pollutant model was originally developed, as
described, for nutrient routing. However, it is currently under modifica-
tion to allow the addition of pesticide routing processes. Again, an
existing accepted pesticide model was selected. The pesticide model chosen
for this study is a simple mechanistically based model developed by the
Agricultural Research Service (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, which is obtained directly from the water
balance routines.
The pesticide component (as reported by Knisel, 1980) 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 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. Pesti-
cide in runoff is then partitioned between the solution in water and that
adsorbed to sediment. This aspect is particularly important when examining
management options that may limit sediment yield. Further, the partition
coefficient system used is particularly useful since the coefficients are
lab measurable.
156
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TEMPERATURE AND DISSOLVED OXYGEN ROUTING
Thermal energy content, dissolved oxygen (DO), and biological oxygen
demand (BOD) of runoff water can directly or indirectly affect the tem-
perature and oxygen content in the stream. Based on mass and energy
balance, the temperature and dissolved oxygen model is included in this
simulation. This model is useful to evaluate the thermal and dissolved oxy-
gen loading to the stream through surface runoff.
Overland flows transmit thermal and DO loading from land surfaces to
the stream. Temperature and dissolved oxygen loading of the stream result
from high temperature, high bio-chemical oxygen demand, and low dissolved
oxygen in runoff water. Temperature and DO effects of subsurface flow are
not included in this model.
The three mechanisms of heat transfer, radiation, conduction, and con-
vection, are included in this model. Each mechanism plays a role in the
heat transfer process. Conduction is the only predominant mechanism for
heat transfer between soil layers and heat transmission between soil and
surface flow. Convective heat transfer occurs because of relative motion
betwen various parts of the heated body or fluid. Convection plays an
important role in heat transfer from water surfaces, particularly in eva-
porative processes. In this model, these heat transfer mechanisms are used
to formulate equations for (1) atmospheric processes, (2) canopy-ground
cover processes, and (3) surface runoff processes.
The oxygen concentration in the stream water at any given time is
determined by the solubility of oxygen in the water, the rate at which this
oxygen is consumed by various biological processes (represented by biologi-
cal oxygen demand), and the rate at which this depletion is replenished.
Deoxygenation of the water due to the bacterial decomposition of car-
bonaceous organic material and reaeration caused by the oxygen deficit and
turbulence are the most fundamental processed occurring in natural water.
The basic theory used to describe the deoxygenation and reaeration processes
was proposed by Streeter and Phelps (1925). The rate at which the BOD is
exerted was presumed to be identical to that observed while using the
laboratory BOD test. A proportionality is assumed to exist between the
reaeration rate and certain hydraulic parameters of flow. The DO effects
include concentration reductions due to purging action of gases rising from
the benthal layer, plant aspiration, diffusion into the benthic layer, and
DO addition photosynthesis.
STREAMBANK EP.OSION
Much of the sediment production of watersheds and channel systems ari-
ses from streambank erosion. In the United States it has been estimated
that approximately 500 million tons/year enter the drainage systems of the
country (Barnes, 1963). Therefore, a mathematical model of the process of
streambank erosion by channel widening is included in this simulation. The
predictive capability of the model is enhanced by its pheriomenological
structure, although empirical data are needed in the stream morphology com-
ponent. The model estimates the total amount of streambank erosion and the
fraction of it that goes into suspension. Threshold channel conditions,
157
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bank characteristics, and the hydrologic events are input to the model.
As formulated, the streambank erosion model estimates the total amount
of erosion that is likely to occur in the transition from a condition of
geomorphic equilibrium to another condition of equilibrium. As such, it
does not provide information on the rate of streambank erosion; rather, it
gives a total value assuming the new equilibrium condition is eventually
reached. In practice, however, the rate of streambank erosion is a function
of the time history of hydrologic events which are not explicitly considered
in the present model. Therefore, the calculated values are to be regarded
as estimates of the total amount of streambank erosion that is associated
with a certain level of hydrologic excitation. Further refinements will
need to be implemented if the model is to provide information on the rate of
streambank erosion.
FOREST LITTER
A first approximation to the rill formation and the loading of forest
litter is included in this simulation. The model is based on the assumption
that the amount of forest litter loading is directly proportional to the
areal extent of rilling. This is a reasonable assumption in view of the
demonstrated effectiveness of concentrated flow in transporting sediment and
debris through upland watershed drainage networks. This approach allows the
conversion of the forest litter loading problem into that of determining the
areal extent of rilling (rilling density), given a set of topographic,
hydrologic, and morphologic conditions.
The quantity of forest litter delivered to a stream is a direct func-
tion of the areal extent of rilling and the amount of forest litter produc-
tion. The areal extent of rilling will, in general, be determined by large
events. Smaller subsequent events will not entirely fill the established
rill network. Therefore, the litter washed out of the rill network will be
detached from the area defined by the top width of the flowing water. This
top width may be obtained from an "at a station" relationship provided by
Li, Simons and Stevens (1976).
SEQUENTIAL GOAL PROGRAMMING
The problem of management of a basin depends very much upon the selec-
tion of the best land-use strategy to optimize specified socioeconomic
objectives under certain constraints on water and sediment transport con-
ditions in the stream channels and on water quality standards in the basin.
The quality of a basin management plan depends on the quality and availabi-
lity of data. However, the efficiency of planning depends on the optimiza-
tion tool to be selected and the accuracy of simulation models used to pro-
ject future basin-system response. A review and evaluation of multi-
objective programming techniques used to solve basin planning problems has
been conducted by Loucks (1975) and later by Cohon and Marks (1975). One
technique of increasing popularity often encountered in water resources
literature is goal programming. It is designed to evaluate (possibly
conflicting) goals as well as goals of differing priorities.
The planning model is designed as multi-level. The lower level is used
to select optimal land-use strategies based on different alternative
158
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management practices and subject to some specified land-use constraints. In
this level, the elements of the resource response matrix are calculated by
various land-use process models which use the same type of spatial and tem-
poral information (i.e., same soil-vegetation units and time-step). After
selecting a set of optimal strategies for land-use management, the upper
level is then used to select the best management strategy for the entire
basin system based on different land-use strategies selected from the first
level and the outcomes of hydrologic and water quality component processes,
subject to some specified socioeconomic constraints. In this level, complex
models of water and sediment yields and water quality are used to calculate
the elements of the process response matrix which then serves as the nece-
sary input for the selection of the best basin management strategy.
POTENTIAL APPLICATIONS
Potential applications of the simulation are initially intended to aid
in the evaluation of watershed management alternatives. Management activi-
ties that could be considered initially were vegetation growth (over story
and under story), timber harvest, foliage utilization (grazing), site pre-
paration, waste disposal and prescribed nutrient and pesticide applications.
The linkage of the management activity models, the process models and the
multiple objective programming model form the preliminary generalized
planning model. This preliminary planning model would be useful in eva-
luating selected alternatives as a function of environmental goals.
Environmental goals relate to control of sediment, nutrients, pesticide,
hazardous waste, thermal, and dissolved oxygen pollution. Also, resource
management goals can be identified that maximize income and/or implement the
best management practices. The changes caused by management activities are
reflected in changes in input model parameters. The effects of these
changes may be simulated by adjusting soil and vegetative and chemical para-
meters. Chronological simulation allows those parameters to be varied
either instantaneously or as functions of time. By interfacing with the
planning model, these parameter values may be adjusted in order to select
the best management alternatives and scheduling.
ACKNOWLEDGEMENT
The writers wish to acknowledge Mr. W. T. Fullerton, Mr. J. N-H. Ho,
Dr. N. Duong, and Dr. V. M. Ponce for their valuable contributions to the
formulation of this simulation. Financial support for this study was pro-
vided by the Environmental Protection Agency, Environmental Research
Laboratory, Athens, Georgia; and by the USDA Forest Service, Rocky Mountain
Forest and Range Experiment Station, Flagstaff, Arizona.
REFERENCES
Barnes, R. C., Jr. 1968. Streambank erosion. Soil Conservation
33(6):126-128.
Cohon, J. L., and D. H. Marks. 1975. A Review and Evaluation of
Multiobjective Programming Techniques. Water Resource Research
11(2):208-220.
159
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Einstein, A. H. 1950. The Bed Load Function for Sediment Transportation in
Open Channel Flows. U.S. Department of Agriculture Technical Bulletin
No. 1026.
Goldstein, R. A., and J. B. Mankin. 1972. PROSPER: A Model of Atmosphere-
Soil -Plant Water Flow. Proceedings, Summer Simulation Conference, Los
Angeles, pp. 1176-1181.
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.
Leaf, C. F. and G. E. Brink. 1973. Computer Simulation of Snowmelt Within
a Colorado Subalpine Watershed, USDA Forest Service Research Paper RM-99,
Rocky Mountain Forest and Range Experiment Station, Fort Collins, Colorado.
Li, R. M., D. B. Simons, W. T. Fullerton, K. G. Eggert and B. E. Spronk.
1979. "Simulation of Water Runoff and Sediment Yield from a System of
Multipole Watersheds," presented at the XVIII Congress of the International
Association for Hydraulic Research, Cagliari, Italy.
Li, R. M., D. B. Simons, and M. A. Stevens. 1976. Morphology of Cobble
Streams in Small Watersheds. J. Hydraul. Div., ASCE, 12(HY8):1101-1112.
Loucks, D. P. 1975. Conflict and Choice: Planning for Multiple
Objectives. In: Economy Wide Models and Development Planning, edited by C.
Blitzer, P. Clark, and L. Taylor, Oxford University Press, New York.
Luxmoore, R. J., D. J. Van Roagen, F. D. Hale, J. B. Mankin, and R. A.
Goldstein. 1977. Field Water Balance and Simulated Water Relations of
Prairie and Oak-Hickory Vegetation on Deciduous Forest Soils. Soil Sci.
123(2):77.
Streeter, H. W., and E. B. Phelps. 1925. A Study of the Pollution and
Natural Purification of the Ohio River. Public Health Bulletin 146, U.S.
Public Health Service, Washington, D.C.
Swift, L. W., 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 Plantations. Water Resources
Research 11 (5):667.
U.S. Bureau of Reclamation. 1960. Investigation of Meyer-Peter, Muller
Bedload Formulas. Sedimentation Section, Hydrology Branch, Div. of Project
Investigation, U.S. Department of the Interior.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
160
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DATA MANAGEMENT FOR CONTINUOUS
HYDROLOGIC SIMULATION
Jy S. Wu, Ph.D.1
INTRODUCTION
The use of models to simulate rainfall-runoff events is receiving
considerable attention by water resources planners and engineers. One of
the major reasons for this concern is the limited capability of field
sampling programs in obtaining a continuous data-base which reflects the
watershed responses to changes in hydrologic conditions and management
practices over an extended period of time. The conduct of a continual
field monitoring and sampling program is often quite expensive; even a
well managed sampling program can still be handicapped by the failure of
sampling devices and unexpected difficulties during the sampling period.
Mathematical modeling thus becomes a useful tool for analyzing existing
data and predicting future conditions as a result of implementing watershed
management practices. In some cases, the collected data must be utilized
to statistically generate missing records for calibrating a continuous
hydrologic simulation model. This paper describes the application of the
U.S. EPA's Agricultural Runoff Model (ARM) on one of the agricultural
watersheds of the Chowan River Basin in North Carolina. The technique of
regression analysis was employed to generate missing runoff data as
required for calibrating the ARM model.
WATERSHED DESCRIPTION
The Cutawhiskie Lateral monitoring site is located in Hertford County
of northeastern North Carolina with a total drainage area of 667 acres.
Runoff from this monitoring site drains into the Cutawhiskie Creek which,
in turn, drains into the Chowan River near the North Carolina-Virginia
border. The site is relatively flat with an average overland slope of 0.4%.
Land use is about 50% woodland and 50% cropland of peanut, soybean, cotton
and corn.
The North Carolina State University, in cooperation with the Division
of Environmental Management, has been conducting a field sampling and
monitoring program for selected agricultural watersheds including the
Cutawhiskie site, to assess nonpoint source effects on streams. The program
also calls for the survey of producers within the monitored watersheds to
assess land use, management practices and opinions on 208 planning and
Assistant Professor, Department of Urban and Environmental Engineering,
University of North Carolina at Charlotte, Charlotte, N.C. 28223
161
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implementation options.
have been collected for
A field smapling data-base
a period of three years.
RESEARCH RATIONALE
and survey information
The selected period for hydrologic calibration of the ARM model was
chosen from October, 1980, through September, 1981. The hourly rainfall and
daily evaporation records were incomplete during this particular period. It
was necessary to explore alternate procedures for generating missing records.
Available data from nearby meteorological stations were utilized to construct
isohytes of rainfall and evaporation. Estimations were then based on inter-
polating adjacent isohytes of the study area.
The recorded runoff information was also incomplete. A total of eleven
runoff events having well defined hydrographs were identified. The technique
of multi-regression analysis was employed to generate missing runoff records.
Runoff volume of each event was correlated with rainfall volume of each event,
duration of rainfall, and number of dry days prior to rainfall. A regression
equation was developed and used to calculate the single event, monthly and
annual runoff volumes. This allows calibrating the ARM model based on annual
and monthly water balances and individual storm comparison. A detailed
description of data preparation is given in subsequent sections.
ARM MODEL DESCRIPTION
The ARM model is a continuous hydrologic and water quality simulation
model (Donigian & Harley, 1978). It simulates runoff, sediment, pesticides
and nutrients contribution to stream channels from both surface and sub-
surface sources. Major data requirements for hydrologic simulation include:
A. Rainfall records on 5 minutes, 15 minutes, or hourly intervals.
B. Daily evaporation data, and the following hydrologic parameters:
Nominal upper zone soil moisture storage, UZSN
Initial upper zone soil moisture storage, UZS
Nominal lower zone soil moisture storage, LZSN
Initial lower zone soil moisture storage, LZN
Overland flow length, L
Average overland flow slope, SS
Fraction of impervious area, A
Maximum interception storage, EPXM
Index to actual monthly evaporation, K3
Potential evapotranspiration correction factor, PETMUL
Mean infiltration rate, INFIL
Interflow parameter, INTER
Interflow recession rate, IRC
Fraction of groundwater recharge percolating to deep groundwater, K24L
Groundwater recession rate, KK24
Fraction of watershed area where groundwater is within reach of
vegetation, K24EL
162
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Initial groundwater storage, SWG
Parameter for variable recession rate of groundwater
recharge, KV
Initial interception storage, ICS
Initial overland flow storage, OFS
Initial interflow storage, IPS
Of all the above parameters; LZSN, INFIL, UZSN, INTER, and K3 are the
major parameters subject to calibration. Hydrologic calibration involves
the comparison of simulated and recorded runoff volumes on annual, monthly
and single storm event basis.
INPUT DATA
Rainfall
Rainfall records were obtained from the U. S. Geological Survey
(U.S.G.S.) meteorological station no. 02053175 at Cutawhiskie Creek
tributary near Menola, N.C. The recorded rainfall amounts were found to
fluctuate due to the expansion and contraction effect of the rainwater
collecting devices. It was necessary to compare rainfall records with the
nearby Murfreesboro and Lewiston stations to ensure the probable occurence
of rainfall. If no rain was noted from these two reference stations, the
recorded fluctuations of rainfall amounts were ignored for the Cutawhiskie
site. The U.S.G.S. data provides rainfall records from October through
December of 1980; and from January, April, May, June and July of 1981.
The missing rainfall records for February, March, August and September of
1981 were estimated by constructing rainfall isohytes from recorded data
of the nearby stations. Once the monthly rainfall for those missing months
were estimated, the hourly rainfall records from the Murfreesboro station
were adjusted proportionally and used as the input hourly rainfall for the
Cutawhiskie site. The monthly rainfall data are given in Table 1.
Evapotranspiration
Potential evapotranspiration is assumed to be equal to lake
evaporation estimated from Weather Bureau Class A pan records. The ARM
model allows the use of a single variable to adjust pan evaporation data.
The actual evapotranspiration is computed as a function of the potential
evapotranspiration and soil moisture conditions. Chang (1968) reported
average ratios between potential evapotranspiration and pan evaporation.
These ratios for cotton, grass and corn are summarized in Table 2.
163
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Table 1.
Rainfall Data for Cutawhiskie Site, 1980-1981
Rainfall, in
Month
October
November
December
January
February
March
April
May
June
July
August
September
U.S.G.S.* Cutawhiskie
6.23
3.42
4.59
4.64
5.00
4.88
4.24
4.84
Murfreesboro
4.78
66
13
02
02
02
13
0.94
2.55**
20**
00
55
21
81
7.00**
1.20**
36.11
.65
.42
,29
.16
.35
.29
7.10
1.20
37.57
Lewiston
3.96
.13
.71
.19
2.25
03
58
11
36
98
6.86
Values include effects of equipment expansion and contraction
and may be high.
Estimated from isohytes.
Table 2.
Ratio of Potential Evapotranspiration to Pan Evaporation
(After Chang, 1968)
Ratio
Types of Crop
Cotton
Corn
Grass
Mature Ripening
0.2 0.85-1.00
0.27 0.90
0.84 (average)
0.1-0.4
0.4
164
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There are four meteorological stations recording pan evaporation data near
the study area, namely John H. Kerr Dam in Virginia; Chapel Hill, Aurora
and Hoffman Forest (formerly Maysville) in North Carolina. The following
guidelines were adapted to estimate the evaporation records for the study
area.
1. John H. Kerr Dam is the closest station; therefore, the evaporation
data was taken directly from this station except the missing period
for November and December of 1980 and January through March of 1981.
2. During the missing period, evaporation data from Chapel Hill or
Hoffman Forest was used as the substitution. Preference is given
to Chapel Hill since it is closer to the study area.
Table 3 summarizes the montly evaporation data estimated for the Cutawhiskie
site.
Table 3.
Monthly Evaporation Data, 1980-1981
Monthly Evaporation,in
Month
October
November
December
January
February
March
April
May
June
July
August
September
Cutawhiskie
(Estimated)
John H.
Dam
Kerr
39
89
54(1)
3.39
Chapel
Hill
3.27
2.89
1.86(2)
.24(3)
,98
,16
,98
.23
.60
.45
,16
,98
.23
,60
.45
.86
.69
.58
.51
Hoffman
Forest
3.37
1.97
3.98
6.21
4.80
50.12
4.80
6.08
4.48
7.14
7.22
6.79
4.76
4.86
1) Based on Hoffman Forest data from December 7-20 and
average value from December 7-20 for the remaining days,
2) Based on Hoffman Forest data of 1980.
3) Based on the partial available data from Hoffman Forest
and average value for the remaining days.
165
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Parameter Evaluation
The following summarizes calibrated values of the ARM model parameters for
hydrologic simulation (see previous section for parameter definitions).
UZSN: 0.93 inch
UZS: 0.72 inch
LZSN:
L:
A:
PETMUL:
INTER:
K24L:
K3:
6.60 inch
800.0 ft.
0.00%
0.50
2.00
1.00
0.5,0.5,0
LZS:
SS:
EPXM:
INFIL:
IRC:
6.52 inch
0.40%
0.15 inch
0.05 in/hr
0.50
5,0.5,0.5,0.6,0.67,0.7,0.75,0.8,0.8,0.8,0.65,0.5
KK24,K24E1,SWG,KV,ICC,OFS,IPS: 0.00
The nominal capacity of soil was estimated using the information
provided by the ARM model user's manual and was subsequently fine-tuned
in the calibration process. The pan evaporation data was adjusted by a
factor of 0.5 in accordance with Chang's work (Chang, 1968) as described
in the previous section. It was found during trial runs that values of
greater than 0.5 would cause a large loss of water due to evapotranspiration,
making annual water balance undesirable. The infiltration capacity, INFIL,
was estimated from soil characteristics and was fine-tuned during calibra-
tion. The INTER parameter which controls runoff from interflow and peaking
of runoff hydrographs was initially estimated from guidelines given in the
user's manual and was subject to calibration. The K3 parameter was based
on 50% watershed area with deep vegetation and was varied monthly to re-
flect seasonal cropping periods. Other parameters were estimated following
the guidelines given in the user's manual.
RUNOFF DATA
Calibration involves the comparison of simulated and recorded runoff
volumes. The existence of a good data-base of runoff records is essential
for model calibration. Discharges from the Cutawhiskie site were recorded
by U.S.G.S. The flow records were incomplete for five months and totally
missing for three months. Therefore, it was necessary to generate flow
records using the technique of multi-regression analysis. A similar
analysis was used by the Principal Investigator (Wu and Ahlert, 1978) in a
study to predict total runoff and sediment loads during selected runoff
events.
In this project, runoff volume of each event was correlated with
rainfall volume of each event, number of dry days prior to rainfall, and
duration of rainfall. A total of fifteen runoff hydrographs were obtained;
however, only eleven of them were used in the regression analysis. This is
because the other four hydrographs were recorded during the period in which
rainfall data was estimated from nearby stations. There is no assurance as
166
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to the consistence of the timing of rainfall-runoff events. The following
procedures were used for generating runoff data:
1. Hydrographs were plotted from U.S.G.S. data.
2. Area under the hydrograph was computed to derive the volume of direct
runoff for each event.
3. Number of dry days prior to rainfall and duration of rainfall were
determined from the continuous hourly rainfall records. A minimum
of 3 hours was chosen to define an individual rainfall event.
4. Regression analysis were performed using the Minitab Computer Program
(Ryan et al., 1976) available at the computer center of the University
of North Carolina at Charlotte. Table 4 summarizes runoff data used
for regression analysis. The standard residuals of prediction were also
included in Table 4. Standard residuals normally range from -2 to
+2 for good correlation. Figs. 1-4 illustrate relationships among
recorded runoff, rainfall, dry days, rainfall duration and results of
regression analysis.
Table 4.
Rainfall-Runoff Events for Regression Analysis
Date
Recorded
Runoff
(R).in
Rainfall
(P), in
Dry Days
(D), days
10/19/80
10/25/80
10/30/80
11/21/80
11/24/80
12/10/80
1/21/81
4/05/81
4/19/81
4/24/81
7/03/81
0.043
0.298
0.031
0.017
0.151
0.055
0.045
0.225
0.029
0.010
0.056
32
93
0.52
0.54
1.06
0.99
0.82
0.74
0.66
0.30
0.73
7.
5,
1,
2,
2.
.21
.04
.33
.83
.08
12.42
13.83
6.21
10.63
3.63
0.79
Rainfall
Duration
(RD), hrs
13
14
17
8
6
14
16
5
4
2
3
Standard
Residuals From
Regression
-1
1
.64
.01
0.56
-0.45
0,07
-0.21
0.39
2.13
-0.55
-0.29
-0.79
A regression equation was developed:
R = 0.1676(P) - 0.0031(D) - 0.0043(RD)
This equation was then applied to each rainfall event to calculate the
per storm runoff volume for periods in which missing records were noted.
The-monthly and annual runoff volumes were computed as the summation of
individual storm runoff volume.
167
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0.3
0.2
"S o.i
o
o
a;
c£
0.0
0.5 1.0 1.5
Recorded Rainfall, in
Fig.l Runoff versus Rainfall for Storm
Events Shown in Table 4
2.0
0.3
i •
•- 0.2
o
c
3
o:
-o
O)
•o
o
o
OJ
o:
0.1
0.0
• »i
8
Dry Days, days
12
Fig. 2 Runoff versus Dry Days for Storm
Events Shown in Table 4
16
168
-------
0.3
•^ 0.2
o
c
CtL
O)
"g 0.1
o
o
Ol
0.0
5 10 15 20
Rainfall Duration, hrs
Fig.3 Runoff versus Rainfall Duration for
Storm Events Shown in Table 4
0.0
0.1 0.2 0.3
Predicted Runoff, in
Fig.4 Recorded versus Predicted Runoff
from Regression Analysis
169
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RESULTS AND DISCUSSION
Statistical Analysis
For regression analysis, a good size of sample population is needed
to obtain statistically reliable results. A total of eleven runoff events
were employed in the regression analysis; a majority of them occurred in
the Fall and Spring with only one runoff event recorded in July. Rainfall-
runoff relationships usually vary seasonally; therefore, the regression
results of runoff volume for the Summer season are unlikely to be accurate.
However, due to the fact that a good runoff data-base is unavailable, the
regression technique may serve as a guide for generating missing records to
calibrate the ARM model.
Results of Calibration
A comparison of runoff volumes between the field data and the ARM
model output is given in Table 5. It can be seen that the annual and
monthly runoff volumes compare reasonably well. Figure 5 presents the
model output of monthly rainfall, runoff, evapotranspiration, soil moisture
changes, and groundwater recharge. The per storm comparisons are given in
Figures 6-11 and in Table 6;they also agree reasonably with recorded
hydrographs. Thus, the ARM model has been successfully calibrated for
the Cutawhiskie site. The calibration of water quality parameters could
not be undertaken since there is only one set of water quality data avail-
able for the study period.
Table 5.
Predicted Runoff for the Catawhiskie Site, 1980-1981
ARM
Month Output
October 0.379
November 0.210
December 0.166
January 0.053
February 0.377
March 0.108
April 0.066
May 0.090
June 0.599
July 0.126
August 1.123
September 0.049
3.346
* Partial Records
** Missing Records
Runoff* in
U.S.G.S. Data
+ Regression
0.377
0.153
0.076
0.035
0.552
0.146
0.160
0.299
0.414
0.473
0.903
0.107
3.695
U.S.G.S.
Records
0.372
0.153
0.035*
0.034*
0.552
0.146*
0.160
**
**
0.050*
0.059*
**
170
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CD
Monthly Rainfall, inches
(1980-1981)
Oct Nov Dec Jan Feb Mar Apr May Jim Jul Aug Sep
OJ
-S'
Monthly Runoff, inches
(1980-1981)
Oct Nov Dec Jan Feb Mar Apr May Jim Jul Aug Sep
OJ
•5*
Monthly Actual Evapotranspiration, inches
(1980-1981)
Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
Fig.5 Summary of Simulation Results from ARM Model
171
-------
OJ
o
c
I I
Monthly Soil Moisture Changes, inches
(1980-1981)
-I L
-2
-4
I I
1 I I I
I I i
Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
6
oi 4
-C
(J
c
1 — 1
2
0
, 1 1 1 1 r — • 1 1 1 i '
Monthly Groundwater Recharge, inches
(1980-1981)
.
_
|~ ' 1 1
Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
Fig.5 Summary of Simulation Results from ARM Model
(Cont'd)
172
-------
CFS
60
40
20
0
Simulated by ARM
Recorded
0
CFS
1.2
0.8
0.4
0
8 12 16 20 24 4 8 12
Time, hrs
Fig.6 Hydrograph Comparison for Storm 10/25/80
T
T
T
T
Simulated by ARM
Recorded
0
CFS
1.2
0.8
0.4
0
12 16 20
Time, hrs
24
Fig.7 Hydrograph Comparison for Storm 10/30/80
Simulated by ARM
Recorded
12
0
8 12 16 20 24 4 8
Time, hrs
Fig.8 Hydrograph Comparison for Storm 11/21/80
12
173
-------
CFS
3
Simulated by ARM
Recorded
16
20
16
24 4 8
Time, hrs
Fig.9 Hydrograph Comparison for Storm 11/24/80
20
24
Simulated by ARM
Recorded
8
12 16 20 24 4 8 12
Time, hrs
Fig.10 Hydrograph Comparison for Storm 12/10/80
16
Simulated by ARM
Recorded
16 20 24 4 8 12 16
Time, hrs
Fig.11 Hydrograph Comparison for Storm 1/21/81
174
20
-------
Table 6.
Date
10/25/80
10/30/80
11/21/80
11/24/80
12/10/80
1/21/81
Comparison of Single Runoff Event
from
Recorded Data and ARM Model Output
Peak Time
Recorded Computi
6:30
13:30
13:00
19:20
15:30
5:00
12:00
10:30
18:20
15:00
Peak Discharge. CFS
22:00
19:00
Recorded
53.0
1.0
0.9
20.8
2.8
1.6
Computed
54.5
0.8
0.5
14.2
1.9
0.9
1.
2.
3.
4.
CONCLUSIONS
Use of continuous hydrologic simulation model can be a useful tool
for evaluating the effectiveness of watershed management practices
over an extended period of time. However, it requires the
existence of a good data-base for calibration and verification.
The regression technique can be used to generate missing records
for calibration; however, great care is needed in interpreting
the regression results.
A well planned sampling program is critical so that the collected
data can be utilized and served for its intended purpose of the
sampling and analysis program.
stations in the Chowan
determine the
As there is a few evaporation measuring
Basin, a study is recommended to better
evapotranspiration of the Chowan Basin.
ACKNOWLEDGEMENT
This study was supported by the North Carolina Uater Resources
Res-earch Institute. Appreciation is due Ms. Beverly Young for
providing field data and other pertinent information, and Mr. Robert Davis
for preparing input data and performing computer work.
175
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REFERENCES
Chang, Jen-Hu, "Climate and Agriculture-An Ecological Survey",
Aldine Publishing Company, 1968.
Donigian Jr., A. S. and Harley H. Davis, Jr., "User's Manual
for Agricultural Runoff Management Model", EPA 600/3-78-080,
1978.
Ryan Jr., T. A., et al. "Minitab Student Handbook", Belmont,
California, 1976.
Wu, Jy S. and Robert C. Ahlert, "Assessment of Methods for
Computing Storm Runoff Loads", Water Resources Bulletin,
Vol. 4, No. 2, pp. 429-439, 1978.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
176
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ESTIMATION OF MISSING VALUES
IN MONTHLY RAINFALL SERIES
by
Efi Foufoula-Georgiou
ABSTRACT
Infilling of missing values is often necessary prior to the practical
use of hydrological time series. In this paper, three different types of
infilling methods are considered reflecting the following basic ideas:
(1) the use of regional-statistical information in four simple techniques:
- mean value method (MV),
- reciprocal distance method (RD),
- normal ratio method (NR),
- modified weighted average method (MWA);
(2) the use of a univariate stochastic (ARMA) model which describes the
time correlation of the series;
(3) the use of a multivariate stochastic (ARMA) model which describes the
time and space correlation of the series.
An algorithm for the recursive estimation of the missing values by a
parallel updating of the univariate or multivariate ARMA model is proposed
and demonstrated. All methods are illustrated in a case study using 55 years
of monthly rainfall data from four south Florida stations.
INTRODUCTION
Many different kinds of statistical analyses may be performed on a given
data set, e.g., determination of elementary statistical parameters, auto-
and cross-correlation analysis, spectral analysis, frequency analysis, fitting
time series models. For routine statistics (e.g., calculation of mean,
variance and skewness) missing values are seldom a problem. But for
techniques as common as autocorrelation and spectral analysis missing values
can cause difficulties. In multivariate analysis missing values result in
"wasted information" when only the overlapping period of the time series is
used in the analysis, and in numerical inconsistencies (Valencia and Schaake,
1973; Fiering, 1968; Slack, 1973) when the incomplete series are used. The
evaluation of the estimation methods analyzed has utilized monthly rainfall
records from the South Florida Water Management District (SFWMD), and has
been based upon: a) the statistical comparison of the methods to each other
at a fixed level of percent of missing values, and b) the performance of each
individual method at different levels of percent of missing values. Gaps
(missing values) have been artificially created in the complete record of the
interpolation station (station whose missing values are to be estimated) with
1 Graduate student, Department of Environmental Engineering Sciences,
University of Florida, Gainesville.
177
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the following procedure: First, the lengths of the_gaps have been generated
from a discrete exponential distribution with mean k months. Then, for a
given percent of missing values, m, the mean interevent length (missing
values between two successive gaps), T~, has been calculated as T = k (100-m)/m
and the interevent lengths have been generated ^randomly from an exponential
distribution with mean T. The values used for k and m are based on a
frequency analysis of missing values__in SFWMD monthly rainfall records
(Foufoula-Georgiou, 1982) and are: k = 2.4 months and m = 2, 5, 10, 15 and
20%. Overlapping and concurrent periods of 55 years of monthly rainfall data
of the four SFWMD stations shown in Fig. 1 have been used in the analysis.
TRADITIONAL ESTIMATION TECHNIQUES
Mathematical Representation
In all the following equations y will be used for the interpolation
station and x. for index station j, j = 1, 2, ..., n. An estimated value at
time t is y'.J
Mean Value Method (MV) —
The simplest method simply replaces the missing values with the sample mean:
y^ = y (i)
This method results in a reduced variance and a spurious correlation
coefficient especially at a high percent of missing values.
Reciprocal Distance Method (RD)
A missing value v is estimated as:
y=?aX (2)
The weighting coefficients a^ are calculated from:
_ , i , j \ ^ / V / 1 / J \r
a •
1=1
where d. is the distance between index station j and the interpolation
station, and n is the number of index stations used for the estimation. It
has been concluded (Shearman and Salter, 1975; Wei and McGuinness, 1975;
Dean and Snyder, 1977) that P=2 better approximates the isohyetal map drawn
by conventional methods.
Normal Ratio Method (NR) —
A missing value y is estimated as:
178
-------
T Aa^JJCdtr..... 1
Fig. 1. The four south Florida rainfall stations used in the
analysis.
" A: 6038, Moore Haven Lock 1
1: 6013, Avon Park
2: 6093, Fort Myers WSO AP.
3: 6042, Canal Point USDA
179
-------
where R and R. are the normal annual or monthly rainfall at the interpolation
and index station j respectively. This method is recommended (Paulhus and
Kohler, 1952) when the normal rainfall at any of the index stations differs
from that of the interpolation station by more than 10 percent.
Modified Weighted Average Method (MWA) —
The RD and NR methods may be both written in the general form of a
weighted average scheme:
y; - A xt (5)
where A is_a row vector (1 x n) and Xt is a column vector (n x 1). To
preserve the mean, ~y, and variance, sy, estimated from the available data, a
modified scheme may be used:
(6)
yj = B Xt + (y - B X)
where
B = A^ (7)
V
and s , is obtained from:
Y 2 T n n
s , = A cov[X] A = E I a. a. c.. (8)
7 i=l j=l 1 J 1J
where c-jj is the covariance between elements x^ and xj of the rainfall
series ox the index stations i and j (Kottegoda and Elgy, 1977; Foufoula-
Georgiou, 1982).
Comparison of the Methods
Evaluation of the methods is based on the statistical comparison of the
estimated series (mixture of existing and estimated values) to the incomplete
series (what is really available in practice) and to the actual series
(unknown in practice but known in this artificial case).
The following notation is introduced:
y . s , r = mean, standard deviation and serial correlation coefficient of
e e e
_ the estimated series;
y., s., r. = same as above but for the incomplete series, where
1 x x i=l,2,3,4 and 5 for the five different percentages of
_ missing values;
ya, s , r = parameters of the actual series;
3. 3-
yj. = mean of the residuals (estimated - actual values);
s^, s = variance of the residuals over the whole series and over only
r r'e the estimated values respectively.
180
-------
The criteria used for the comparison of the methods are:
(1) the b±as jun the mean_as measured by
~ and
(2) the bias in the standard deviation as measured by
(a) se/si and (b) s /s ;
(3) the bias in the serial correlation coefficient as measured by re - r ;
(4) _the bias of the estimation model as given by the mean of the residuals,
yr (this is also a way to detect a consistent over- or under-estimation
by a method) ;
(5) the accuracy as determined by the variance of the residuals s^ and s^ ;
(6) the significance of the biases in the mean, standard deviation and 'e
correlation coefficient as determined by the appropriate test statistic
for each.
Regarding comparison of the means the following can be concluded from
Table 1:
(1) the bias in the mean in all cases is not significant at the 5%
significance level as shown by the appropriate t-test;
(2) the bias in the mean of the incomplete series is relatively small but
becomes larger the higher the percent of missing values;
(3) at high percents of missing values the NR method gives the less biased
mean ;
(4) except for the RD method which consistently overestimates the mean (the
bias being larger the higher the percent of missing values) , the other
methods do not show a consistent over or underestimation.
Regarding comparison of the variances the following can be concluded
from Table 2:
(1) although slight, the bias in the standard deviation is always significant,
but this is so because the ratio of variances would have to equal 1.0
exactly to satisfy the F-test (i.e., be unbiased) with as large a number
of degrees of freedom as in this study;
(2) the MV method always gives a reduced variance as compared to the variance
of the incomplete series and of the actual series, the bias being larger
the higher the percent of missing values;
(3) the bias in the standard deviation of the incomplete series is small;
(4) there is no consistent over or under-estimation of the variance by any
of the methods (except the MV method) ;
(5) the MWA method does not give less biased variance even at the higher
percent of missing values tested, as compared to the RD and NR methods.
Regarding comparison of the correlation coefficient the following can be
concluded from Table 3:
(1) the bias in the correlation coefficient is in all cases not significant
at the 5% significance level as shown by the appropriate z-test;
(2) the MV method gives the largest bias in the correlation coefficients, the
bias increasing the higher the percent of missing values;
(3) all methods (except the MWA method) consistently overestimate the serial
correlation coefficient of the incomplete series but not the serial
correlation of the actual series, and therefore this is not considered
181
-------
Table 1. Bias In the Mean.
2%
5%
10%
15%
20%
INC
0.
0.
0.
0.
0.
MV
0.009
-0.012
-0.010
-0.089
0.042
RD
ya
2%
5%
10%
15%
20%
-0.010
-0.013
0.018
0.009
-0.044
-0.001
-0.025
0.008
-0.020
-0.002
-0.002
0.001
0.024
0.051
0.105
-0.012
-0.021
-0.006
0.009
-0.001
-0.013
-0.010
0.001
0.008
0.042
4.126
Table 2. Bias in the Standard Deviation.
2%
5%
10%
15%
20%
2%
5%
10%
15%
20%
INC
1.
1.
1.
1.
1.
1.002
0.999
1.009
0.999
1.008
MV
0.995
0.983
0.972
0.957
0.944
0.997
0.983
0.981
0.956
0.952
RD
se/si
0.998
1.007
0.996
0.988
1.006
s IB
e a
1.000
1.006
1.004
0.988
1.014
NR
0.996
1.001
0.986
0.978
0.973
0.998
1.000
0.994
0.978
0.980
MWA
0.998
1.013
1.005
0.994
1.011
1.000
1.013
1.014
0.994
1.019
si
3.680
3.671
3.705
3.671
3.701
s
a
3.673
182
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Table 3. Bias in the serial correlation coefficient.
INC
MV
RD
NR
MWA
(rl,e - rl,a) rl,a
2%
5%
10%
15%
20%
0.005
0.006
0.013
0.033
0.042
0.001
0.003
0.014
0.006
0.004
0.002
0.001
0.011
0.013
0.011
-0.003 0.366
-0.002
0.010
-0.009
-0.012
Table 4. Accuracy—Mean and Variance of the Residuals,
N = total number of values = 660
N = number of missing values
INC
2%
5%
10%
15%
20%
2%
5%
10%
15%
20%
2%
5%
10%
15%
20%
MV
-0.043
-0.440
0.007
-0.175
0.037
5.037
8.610
7.892
7.620
5.224
0.084
0.406
0.720
1.112
1.016
RD
= (y
r J e
-0.061
0.034
0.156
0.338
0.502
5 = (yQ
r ,e e
2.874
3.656
4.239
4.630
4.891
sr = (ye -
0.048
0.172
0.387
0.675
0.951
NR
- y )/N
a o
-0.570
-0.380
-0.113
0.074
0.038
- y )2/(N -2)
a o
3.149
3.411
3.484
3.958
3.681
v )2/(N-2)
3.
0.053
0.161
0.318
0.577
0.716
MWA
-0.589
-0.176
-0.046
0.105
0.200
4.585
5.340
5.187
5.816
4.898
0.077
0.252
0.473
0.849
0.953
N
o
13
33
62
98
130
183
-------
a problem;
(4) the RD method seems to give the less biased correlation coefficient even
at the higher percentage of missing values .
Regarding accuracy of the methods the following can be concluded from
Table 4:
(1) no method seems to consistently over or underestimate the missing values
at all percent levels, but at high percent levels the missing values are
overestimated by all methods;
(2) the NR method is the most accurate method especially at high percents of
missing values (i.e., it gives the smallest mean and variance of the
residuals) .
ESTIMATION BY A UNIVARIATE STOCHASTIC MODEL
Introduction
The observed monthly rainfall series, y£, is normalized using the square
root transformation (Roesner and Yevjevich, 1966; Stidd, 1970; Delleur and
Kavvas , 1978) and the periodicity is removed by subtracting the monthly
means and dividing by the standard deviations (Kavvas and Delleur, 1975) .
The reduced series, zt, approximately normal and stationary is then modeled
by an ARMA(1,D model:
Zt = * Zt-l ~ 9 at-l + at (9)
where , 6 are the autoregressive and moving average parameters respectively,
and at is a sequence of independent random variables from a normal
distribution with zero mean and unit variance (white noise) .
For an ARMA(1,1) model the minimum mean square error forecasts z'(£) of
Z ,, where £ is the lead time are:
= zt - 6 £t , £=1 (10)
= z^U-1) , £=2, ..., k
as developed by Box and Jenkins (1976).
Proposed Estimation Algorithm
The estimation of the missing values in the series is performed
recursively by the following procedure:
Step 1: The incomplete series S is filled-in with any initial estimates of
the missing values giving the complete series, _£]_.
Step 2; An ARMA(1,1) model is fitted to the series _S, and the maximum
likelihood estimates (MLE) of the parameters and 6 are found.
Step 3; New estimates of the missing values are calculated as forecasts .of
the model M, = (
-------
missing values as well as in the parameters of the model.
The above algorithm will be addressed as RAEMV-U (Recursive Algorithm
for the Estimation of Missing Values - Univariate model) and is schematically
shown in Fig. 2. A FORTRAN program has been developed for the above algorithm
(Foufoula-Georgiou, 1982). Input is the incomplete rainfall series and the
positions of the gaps. Output is the final estimated complete series as well
as the final parameters of the fitted ARMA model.
Results of the Method
Little influence of the method used to determine initial estimates of
missing values was found on the final values of parameters and 6 and on
the final estimates of missing values computed by the recursive scheme. All
methods that were tried yielded identical estimates of missing values and
model parameters after five iterations at 10 percent missing values ( = 0.5095,
6 = 0.4333) and eight iterations at 20 percent missing values (((> = 0.0776,
6 = -0.0293). Moreover, by using zeroes as initial estimates the same
results were obtained, suggesting the latter as a convenient choice.
The RAEMV-U method was assessed using the same statistical measures as
used for the four traditional techniques described previously. Table 5 shows
the bias in the mean, standard deviation and serial correlation coefficient
for the final series (at 10% and 20% missing values). The bias in the mean
and correlation coefficient is not significant at the 5% significance level;
however, the bias in the standard deviation does not pass the stringent
F-test (requiring exact equality of standard deviations) and thus is
significant.
Table 5. Bias in the Mean, Standard Deviation and Serial Correlation
Coefficient-Univariate Model.
10%
20%
ye " ya
-0.021
-0.083
s Is
e a
0.983
0.951
T" — T"
l,e rl,
0.018
0.044
a
The forward mean square error forecasting procedure that was used worked
satisfactorily In the sense that rapid convergence to a statistically
acceptable series occurred. Damsleth (1980) introduced the optimal between-
forecasts as that linear combination of forecasts and backforecasts which
gives the minimum mean square error. For the case of monthly rainfall data
the use of more sophisticated forecasts seems not to be justified. The
parameters and 6 of the fitted AEMA(1,1) model are very close to each
other and the value of § is small as compared to one, thus making the large
white noise variance the predominant term in the calculation of the mean
square forecast error (Box and Jenkins, 1976, p. 154).
185
-------
So
Mo
s.
M,
S2
Mz
f MI -Mj
I §i •* Sj.
II1 l+l
i+l
Fig. 2. Recursive Algorithm for the Estimation of Missing Values—
Univariate model (RAEMV-U). S^ denotes the series, and
Mi the model, (,6)-j_, at the ith iteration.
Fig. 3. Recursive Algorithm for the Estimation of Missing Values-
Bivariate model (RAEMV-B). Sj_ denotes the series, and
KjL the model, (PjQ).^ at the ith iteration.
186
-------
ESTIMATION BY A MULTIVARIATE STOCHASTIC MODEL
Introduction
When the concurrent rainfall series of nearby stations are available,
their correlation with the series of interest may be incorporated in the
model for an improved estimation of the missing values. The lag-one
multivariate autoregressive model (Matalas, 1967) is expressed as:
= P
(12)
where Zt and Z are n-length vectors of the normalized and standardized
variables at time t and t-1, H is an n-length vector of random components
and n is the number of stations used. The above model preserves the lag-zero
(MO) and lag-one (M^) correlation matrices when the coefficient matrices P
and Q are estimated by:
M, M
-1
(13)
Q QT =
(14)
Equation (14) may be solved for Q using a principal component analysis
(Fiering, 1964) or much easier by an upper triangularization technique
(Young, 1968; Young and Pisano, 1968). Missing values in any of the records
may result in no solution at all or a solution that contains complex numbers
since Q Q may not be a positive semidefinite matrix as required for a real
solution to occur (Valencia and Schaake, 1973; Slack, 1973).
The special case considered here is that of a bivariate AR(1) model
between the interpolation station A and the index station 2 (Fig. 1). This
model is written as:
12
Xt-1
52,t-l
quO
n2,,
(15)
Following the Box-Jenkins forecasting procedure, the mean square error
forecasts z' (5,) of z1 ,Q are:
JL 9 U -L j t »jlj
lll,t
P12Z2,t
, a = 2,
(16)
where k is the number of values missing in each gap.
Proposed Estimation Algorithm
An algorithm analogous to the one for the univariate case is also
proposed for the bivariate case. The procedure is exactly the same, except
that now the parameters of the model, M = (P, Q) , are matrices calculated
from equations (13) and (14), and the forecasts are calculated from eqn . (16)
187
-------
The algorithm will be addressed as RAEMV-B (B stands for Bivariate
model) and is shown schematically in Fig. 3. A FORTRAN program is also
available (Foufoula-Georgiou, 1982). Input data are: the incomplete series
of the interpolation station, the position of its gaps, and the complete
series of the index station. Output results are: the final estimated
complete series of the interpolation station, the parameters P and Q of the
fitted bivariate model and the correlation matrices MQ and Mj_.
Results of the Method
Again, the scheme converges rapidly and independently of the method used
to obtain initial estimates of missing values, thus suggesting their
convenient replacement by zeroes to start the algorithm. Also, the conver-
gence of the bivariate scheme seems to be less sensitive to the percentage
of missing values as compared to the univariate one (three to four iterations
were needed in both the 10% and 20% missing values).
Table 6 shows the bias in the mean, standard deviation and serial
correlation coefficient for the final series (at 10% and 20% missing values).
Again, the bias in the mean and correlation coefficient is not significant
at the 5% significance level, but the bias in the standard deviation is.
Table 6. Bias in the Mean, Standard Deviation and Serial Correlation
Coefficient—Bivariate Model.
y - y s /s r-i - r,
e'a ea l,e l,a
10% -0.030 0.983 0.016
20% -0.049 0.959 0.050
CONCLUSIONS
On the basis of the monthly rainfall data from the four south Florida
stations used in the analysis, the following conclusions can be drawn:
(1) All the traditional estimation techniques give unbiased (overall and
monthly) means and correlation coefficients at the 5% significance level
even for as high as 20% missing values.
(2) At high percentages of missing values (greater than 10%) the MV method
gives the more biased (although not significantly so) correlation
coefficients.
(3) All methods give a slightly biased overall variance but unbiased monthly
variance at the 5% significance level, and the MV method gives the most
biased variances for all percentages of missing values.
(4) The NR method gives the most and the MV the least accurate estimates,
at almost all levels of percent missing values.
(5) The proposed recursive algorithm works satisfactorily in both the
univariate and bivariate case. It converges rapidly and independently
of the initial estimates and gives unbiased means and correlation
coefficients at the 5% significance level.
188
-------
(6) The use of a bivariate model as compared to a univariate one did not
improve the estimates except for a slight improvement at 20% missing
values. However, the use of a multivariate model based on three or four
nearby stations is expected to give much better estimates. The use of
three adjacent stations is the main reason for the better performance of
the NR method over the more sophisticated univariate and bivariate ARMA
models which use only zero and one additional stations.
If the purpose of estimation is to calculate the historical statistics
of the series (e.g., mean, standard deviation, and autocorrelations) the
selection of the method matters little, and the simplest one may be chosen.
However, if it is desired to fit an ARMA model to the incomplete series, to
be used, say, to construct forecasts, the estimation of the missing values
and the parameters of the model by the proposed recursive algorithm is
recommended. In this case the equilibrium state (i.e., final series and
parameters of the model) achieved upon convergence is unique, depending only
on the existing information in the system (available data) and not on any
external information added to the system (by the replacement of the missing
values with some estimates derived by an arbitrary chosen method).
ACKNOWLEDGEMENTS
I would like to acknowledge with gratitude Professor Wayne C. Huber
for the invaluable guidance and encouragement he provided along the course
of, this research.
The study was supported in part by the South Florida Water Management
District.
189
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REFERENCES
Box, G.E.P., and Jenkins, G.M., 1976, Time Series Analysis Forecasting and
Control, Holden-Day, San Francisco, Revised ed.
Damsleth, E., 1980, "Interpolating missing values in a time series," Scand.
J. Stat., 7:33-39.
Dean, J.D., and Snyder, W.M., 1977, "Temporally and areally distributed
rainfall," J. of the Irrigation and Drainage Div.. ASCE, 103(IR2):221-229.
Delleur, J.W., and Kawas, M.L., 1978, "Stochastic models for monthly rainfall
forecasting and synthetic generation," J. Appl. Meteor., 17(10):1528-
1536.
Fiering, M.B., 1964, "Multivariate technique for synthetic hydrology,"
J. Hydraul. Div., ASCE, 90(HY5):43-60.
Fiering, M.B., 1968, "Schemes for handling inconsistent matrices," Water
Resour. Res., 4(2):291-297.
Foufoula-Georgiou, E., 1982, Estimation of Missing Values in Monthly Rainfall
Series, Masters Thesis, University of Florida, Gainesville.
Kawas, M. , and Delleur, J., 1975, "Removal of Periodicities by differencing
and monthly mean substraction," J. Hydrol., 26:335-353.
Kottegoda, N.T., and Elgy, J., 1977, "Infilling missing flow data," ^Ln
Modeling Hydrologic Processes, Ed. by Morel-Seytoux, H., Salas, J.D.,
Sanders, T.G., and Smith, R.E., Water Resour. Res. Publications, Fort
Collins, Colorado.
Matalas, N.C., 1967, "Mathematical assessment of synthetic hydrology,"
Water Resour. Res., 3(4):937-945.
Paulhus, J.L.H., and Kohler, M.A., 1952, "Interpolation of missing precipita-
tion records," Mon. Weather Review, 80:129-133.
Roesner, L.A., and Yevjevich, V., 1966, "Mathematical models for time series
of monthly precipitation and monthly runoff," Hydrology paper No. 15,
Colorado State University, Fort Collins, Colorado.
Slack, J.R., 1973, "I would if I could (self-denial by conditional models),"
Water Resour. Res., 9(1):247-249.
Shearman, R.J., and Salter, P.M., 1975, "An objective rainfall interpolation
and mapping technique," Hydrological Sciences Bulletin, 20(3):353-363.
Stidd, C.K., 1970, "The nth root normal distribution of precipitation,"
Water Resour. Res., 6(4):1095-1103.
190
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Valencia, D.R., and Schaake, J.C., Jr., 1973, "Disaggregation processes in
stochastic hydrology," Water Resour. Res., 9(3):580-585.
Wei, T.C., and McGuirtess, J.L., 1973, "Reciprocal distance squared method, a
computer technique for estimating areal precipitation," ARS NC-8, U.S.
Dept. of Agriculture, Washington, D.C.
Young, G.K., 1968, "Discussion of 'Mathematical assessment of synthetic
hydrology' by N.G. Matalas," Water Resour. Res., 4(3):681-682.
Young, G.K., and Pisano, W.C., 1968, "Operational hydrology using residuals,"
J. Hydr. Div., ASCE, 94(HY4):909-923.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
191
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AREAL INTENSITY-DURATION-FREQUENCY CURVES -
A POSSIBLE SAY OF IMPROVING THE RAINFALL INPUT.
by Janusz Niemczynowicz *
1.INTRODUCTION
Intensity-duration-frequency (i-d-f) relationships, usually derived from
point rainfall measurements, have for a long time been used for synthesizing
so-called "design storms". Simple block rain can easily be derived from
i-d-f curves for the desired duration and return period and then be used as
an input for simulation of runoff occurances.
Since i-d-f curves comprise the statistical properties of a long time series
of rainfall data in a comprehensive form, it is easy to believe that rain-
fall input derived from them has a good statistical justification. As lung
as the rational method was used, no proof could be found that statistical
information taken from point i-d-f curves was not always sufficient for
design purposes. Later on. when more sophisticated methods of runoff
prediction come into common use, it was realised that the single block rain
not only gives the wrong picture of a hyetograph, but also the wrong rain-
fall volume. (Arnell 1962)
Furthermore, it was soon realised that the rainfall frequency given by
intensity-duration relationships not correspond to the observed runoff
frequency. (Sieker 1978, Urbonas 1979. James 1981)
During recent years a number of design storms with different shapes have
been developed. (Keifer at al 1957, Amorocho 1981, Arnell 1982) Some of them
tried to reproduce a real shape of observed hyetographs. But these design
storms can not reflect the dynamics of the moving storms and by no means
represent areal properties of the rainfall pattern.
The main reason that there is no simple linear relationship between the
frequencies of rainfall and runoff is probably the fact that the rainfall
frequency comes from point observations, while runoff represents the areal
and dynamical properties of the rainfall. In other words, a similar rain-
fall hyetograph observed by one gauge can give a number of different runoff
occurances. or vice versa.
Convective storms, which are most significant for design purposes, are
rather limited in space. Design storms derived from point i-d-f curves have
no areal dimensions, but are nevertheless used for runoff simulations on
catchments of different sizes. We can reduce this idea "ad absurdum" by
trying to imagine one single design storm falling simultaneously on thou-
sands of square kilometers.
* Department of Water Resources Engineering,
University of Lund, Sweden.
192
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It is obvious that some kind of reduction factors, taking into consideration
the areal properties of a rainfall, have to be used, especially while
modeling runoff from large catchments.
The coprehensivness and convinience of the statistical information in i-d-f
curves, make us to belive that design storms will stay with us for some
time.
One possible way of improving the rainfall input derived from i-d-f curves
is to develop AREAL INTENSITY-DURATION-FREQUENCY curves. Another way is to
develop area-rainfall depth relationships from which factors reducing
rainfall from point to areal values can be obtained for different areas,
durations and return periods. Those factors can then be used to reduce the
design storms from point to areal values.
These solutions are more practical than complete, because neither areal
i-d-f curves nor areal reduction factors describe the dynamics of the moving
storms.
The third and most desirable solution is to develop a statistical model
simulating a rainfall series taking into account temporal, spatial and
dynamical variations of the rainfall pattern. (Bras et al 1976, Amorocho et
al 1977, Gupta et al 1979)
The need for reasonable rainfall input for runoff simulations in big cities
has caused a number of area-rainfall depth relationships to be developed in
different countries. (Abraham et al 1976. Bell 1976, Rodrigues-Iturbe et al
1974) One important problem to face is the lack of sufficiently long time
series of observations on a dense network with good time synchronisation.
The raingauge network installed in Lund in 1978 covers approximately a 25
sqare kilometer area with 12 gauges. More than three years of registered
data is assumed to be sufficient to produce reasonably good statistics for
short term rainfalls. This paper describes point and areal i-d-f curves
derived for the city of Lund. Presented areal relationships will give more
realistc design storms in comparison with design storms derived from point
relationships.
2. THE GAUGING SYSTEM AND DATA PROCESSING
Twelve automatic tipping-bucket gauges were installed in Lund in 1978 to
cover an area of approximately 25 sq km. The depth resolution of the gauges
is 0.035 mm per tipping, the time resolution of registration is one minute.
All gauges are connected via open telephone lines to the receiving station
in the laboratory of the department. Since all gauges are governed by the
same clock, the absolute time synchronisation is achieved. Figure 1. shows
the situation of the raingauges in Lund. The gauging system and the data
collecting procedure have been described before. (Falk et al 1979, Niemczy-
nowicz at al 1981). Collected data was processed according to the flow chart
shown in Figure 2.
193
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LUND
AUTOMATIC RAINGAUGES
Figure 1. Situation of the raingauges in Lund.
The rainfall series from all twelve gauges were divided into rainfall events
with an arbitrarily chosen interval between the events set to 40 minutes.
Since the main goal of this study is to compare the point rainfall statis-
tics with the area! rainfall statistics for short term rainfalls, all events
with low intensity were taken out of the data base. The criterion chosen was
that all events with rainfall depth less than 0.35 mm observed during ten
succesive minutes were excluded from data base. If any of the gauges excee-
ded the criterion, data from all other gauges were accepted for the same
s
:
D
Dj
1IQ
*•
ENT
F1L
FWT.,,: | | „„..„ 1 |«5,
ELL
^
a
«
-*•
IL
me
CCtS
FILE
—
pU 1""
INTtMSITY
» DUfiATIO-*
TRESrtOLD
1, », 1
klk"i_l
Figure 2. Flow chart for rainfall data processing.
194
-------
period of time. It was found that this procedure only eliminated rainfall
events with a very uniform temporal and spatial distribution. All data
suspected to be wrong and all events with less than eight gauges operating
were taken away from the data base. This data base, originally consisting of
about 130 thousands lines was reduced to 20 thousand lines which made file
operations much easier. A total of 588 rainfall events were finaly included
into the data base.
Malfunction of the gauges was observed or suspected about 15 2 of the time
on the average for the 12 gauges. Gauge No 1 was the worst with malfuncti-
ons during 38 Z of the time, gauges No 2.3 and 8 were functioning all the
time. Most of the malfunctions were caused by broken telephone lines.
3. POINT INTENSITY-DURATION-FREQUENCY RELATIONSHIPS
Point i-d-f curves were developed separately for all 12 gauges in Lund. The
one hundred maximum values of rainfall intensity were found for durations of
1,5,10,15,20.30, and 40 minutes. Intensities for each duration were then
ranked and listed for each gauge. The return period for each intensity and
duration was calculated by dividing the total time of operation of the gauge
by the rank number. Descending maximum intensities were than plotted on a
linear scale against return periods for each duration and gauge.
Several investigators have found that the Log-Pearson typ III distribution
function fits well with the maximum rainfall intensity data. (Arnell 1981)
Since our main interest is the differences between point and area! rainfall,
no other distribution functions were tested during this study. A
Log-Pearson distribution function was fitted to the observation points by
method of moments according to the computer program given by Kite. (Kite
1977)
Figure 3. shows an example of the intensity-return period diagram with
observed and fitted distribution function for one of the gauges. Values from
the fitted distribution curves were then rearranged and the usual form of
intensity-durationf requency curves were drawn as shown in Figure 4. The
described procedure was followed for the 12 gauges and resulted in 12
complete i-d-f curves, each of them representing a point value. The mean
point-value i-d-f curve was finally calculated by averaging the values for
all durations and return periods. Figure 5. shows the mean point-value
intensityduration-f requency curves.
4. SPATIAL VARIATIONS OF RAINFALL INTENSITY
TABLE 1. gives the range of differences in maximum intensities observed
between 12 gauges in Lund. The highest (Max), the lowest (Min), the mean
values (Mean), the standard daviations between 12 gauges (s) and the coeffi-
cients of variation (CV = s/mean) are given for different durations and
return periods.
The differances between the highest and the lowest values and standard
deviations decrease quickly for shorter return periods. Coefficient of
195
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£2.0
i/i
3D 40
RAINFALL DURATION MIN.
FIGURE 3. Intensity-return period
diagram for gauge No 8.
FIGURE 4 . Intensity-Duration-
Frequency curves for gauge No 8.
variation seems to be rather constant for all durations within the same
return period, but decreases with shortening return period. Obviously,
extreme intensity values are the most unevenly distributed in space. The
highest values of intensity occur persistently in gauges No. 2,3,4,5 and 12
which are situated in the central part of the town and to the north-east
which is the most prevaling wind direction. The lowest intensity values are
typical for gauges No. 9,1,11, and 6, situated outside of the town. This
effect can perhaps be explained by the influence of the city on precipitati-
on.
5. AREAL INTENSITY-DURATION-FREQUENCY RELATIONSHIPS
In order to extrapolate rainfall data from point measurements to area!
values, specific areas were associated to all gauges. The influence that
different methods of extrapolating point values to area! means have on the
accuracy of area! estimation was investigated by Gottshalk and Jutman
(1982). Results show that the magnitude of error is to a small extent
influenced by the method of extrapolation. For simplicity of calculations,
the method of Thiessen polygons was chosen for this study.
Due to periodical malfunction, the gauges represented slightly different
periods of observations. In order to develop areal relationships, mean
rainfall values from a number of gauges had to be treated simultaneously.
In order to avoid shortening the total length of the record by averaging the
observation period for all gauges, a special routine for reproducing the
missing values was developed.
196
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POINT VALUES
1 GAUGE
LUND
RETURN
PERIOD:
AREAL VALUES
12 GAUSES 25.2 KM2
RETURN
PERIOD:
RAINFALL DURATION MIN.
AREAL VALUES
5 GAUSES ICL5 KM2
LUND
RAINFALL DURATION MIN.
FIGURE 5. Point and areal itensity-duration-f requency curves
for the city of Lund.
The average weighted values from the three nearest functioning gauges were
inserted in place of the missing values for each minute of the data base.
After this procedure, a new point i-d-f relationships were developed for all
12 gauges. No significant changes in results were observed after this
procedure. All further calculations were performed on the same data base
with reproduced missing values.
Areal i-d-f curves were developed by making calculations (described in
chapter 3) on mean weighted values from combinations of the gauges. Each
combination consists of 12 groups of gauges. In each combination, the same
gauge is represented the same number of times.
For example, a mean-value i-d-f curve representing an area of two gauges was
developed as follows: mean value of rainfall intensity for each minute in
the data base was calculated for the arbitrarily chusen group of two gauges.
Intensity-duration-frequency relationships were then developed for this
group. The next group of two gauges was chusen and new relationships were
developed. Calculations proceeded until 12 groups of gauges were treated.
This resulted in 12 different, complete intensity-duration frequency relati-
onships representing different areas of pairs of gauges. Finally, the
mean-value relationship was calculated representing the mean area of 12
pairs of gauges.
197
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TABLE 1. MAXIMUM RAINFALL INTENSITIES OBSERVED IN 12 GAUGES IN LUND DURING A
THREE YEAR PERIOD. (The number of the gauge where the value was observed is
in parenthesis.)
MAXIMUM
INTENSITY
MM/MIN 1
D U
5
RATION
1 0
IN
1 5
M I N U
20
T E S
30
40
RETURN PERIOD 3.0 YEARS
Max 3.19(7) 1.98(2) 1.36(3) 1.00(2) 0.84(3) 0.62(3) 0.55(4)
Min 1 .3
Mean 12
gauges
s
CV
1(9)
2 . 20
0.61
0. 27
1.08(11
1.61
0.51
0 . 24
) 0 . 86
1
0
0
(9)
. 20
. 43
. 26
0. 64 I
0 .
0.
0 .
!9 )
93
. 34
, 32
0.51
0
0
0
(9 )
. 76
. 26
. 37
0 . 40 (
0 .
0 .
0 .
9 )
57
1 8
4 1
0.37(9)
0 .47
0.15
0 . 37
The same procedure for calculating was carryed on for the groups consisting
of 3.4.5,6.8.10 and 12 gauges. Intensity-duration-frequency curves for
point value, and the 10. and 20 sq.km values are shown in Figure 5.
For all intensity-duration-frequency curves was fitted a mathematical
expression of the form:
a
I = * c
T + b
where I - maximum area) rainfall intensity for duration T (mm/h)
T - rainfall duration (min)
a.b.c - constants
The constants a.b. and c were calculated using the least squares criterion
and the optimization routine accordingly to Marquardts method. (Ericsson
1979).
6. AREAL VARIATIONS OF RAINFALL INTENSITY
By rearranging the values from point and areal i-d-f relationships the
statistical areal reduction factors were developed for different durations
and return periods. Factors for 3.0 and 1.0 years return periods are shown
in Figure 6. It is interesting to notice that statisticaly derived areal
reduction factors not only depend on duration, but also on the return
period, which was questioned before. (Bell 1976)
7. CONCLUSIONS
Areal intensity-duration-frequency relationships give different rainfall
values then point i-d-f relationships. Areal rainfall intensity values are
lower for all durations and return periods.
198
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If point i-d-f curves are used for deriving design storms, the error in
average rainfall intensity and rainfall volume will be introduced for
simulation of runoff from real catchments.
The magnitude of error depends on duration, return period and the size of
the catchment.
The most significant differences between point and areal rainfall values can
be found for short durations and long return periods.
Factors reducing point rainfall values to areal values are given in this
paper. The presented relationships will give a more realistic design storms
in comparison with such storms derived from point i-d-f curves.
20 25
AREA KM2
RAINFALL DURATION : 40 MIN.
RETURN
PERIOD:
20 25
AREA KM2
FIGURE 6. Statistical areal reduction factors.
199
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REFERENCES
Abracham.C.,Lyons,T.,C..Schulze,K.,W.,(1976): "Selection of a Design Storm
for Use With Simulation Models". National Symposium on Urban
Hydrology.Hydroulics and Sediment Control, Univ.of Kentucky, July 1976.
Amorocho,J..Wu,B..(1977): "Mathematical Models for the Simulation of Cyclo-
nic Storm Sequences and Precipitation Fields". Journal of Hydrology, 32
1977.
Amorocho,J.,(1981): "Stocastic Modeling of Precipitation in Space and Time".
International Symposium on Rainfall-Runoff Modeling Mississippi State
Univ.,May 1981.
Arnell,W.,(1982): "Rainfall Data for the Design of Sewer Pipe Systems",
Chalmers Institute of Technology, Report series A:8, Goteborg 1962.
Bell,F.,C.,(1976): "The Areal Reduction Factors in Rainfall Frequency
Estimation". Institute of Hydrology, Wallingford, U.K. Report no 39 Decem-
ber 1976. Bras.R.,L.,Rodriguez-Iturbe.L,(1976): "Rainfall Network Design
for Runoff Prediction". Water Resources Research Vol.12 no 6, December 1976.
Ericsson.G.,( 1979): "Numerisk analys". Institutionen for informationsbehand-
ling. Sigma-tryck, Lund 1979.
Falk,J.,J6nsson.O.,Niemczynowicz.J.,(1979): "Measurements of Rainfall
Intensities in Lund". Lund Institute of Technology, Department of Water
Resources Engineering, Report No 3023,1979.
Gottshalk,L.,Jutman,T.,(1982): "Calculation of Areal Means of Meteorologic
Variables for Watersheds" Nordiske Hydrologiske Konferanse, Forde. Juni
1982.
GuptalV..K..Waymire,E.,C.,(1979): "A Stochastic Kinematic Study of Subsynop-
tic Space-Time Rainfall". Water Resources Research Vol. 15 No 3 June 1979.
James,W.,( 1981): "Kinematic Design Storm Incorporating Spatial and Time
Aweraging". Second International Conference on Urban Storm Drainage", Univ.
of Illinois, Urbana, June 1981.
Keifer,C.,U.,Chu,H.,H..( 1957): "Synthetic Storm Pattern for Drainage
Design". Journal of the Hydroulics Div. ASCE, Vol. 83 No Hy4, August 1957.
Kite,G.,W.,( 1977): "Frequency and Risk Analysis in Hydrology". Water
Resources Publications, Fort Collins, Colorado 1977.
Niemczynowicz,J.,Jonsson,0.,(1981): "Extreme Rainfall Events in Lund
1979-1980" Nordic Hydrology, 12. 1981.
200
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Rodrigue2-Iturbe,I.,Mejia,J.,M.,(1974): "On the Transformation of Point
Rainfall to Areal Rainfall". Water Resorces Research Vol.10 No 4 August
1974.
Sieker,F.,(1977): "Statistical Simulation Model Based on Analysis of
Variance". 3-rd International Hydrological Symposium, Fort Collins, June
1977.
Sieker.F.,(1978): "Investigation of the Accuracy of the Postulate "Total
Rainfall Frequency Equal Flood Peak Frequency"", International Conference on
Urban Storm Drainage Univ. of Southampton, April 1978.
Urbonas,8.,(1979): "Reliability of Design Storms in Modeling". Internatio-
nal Symposium on Urban Storm Runoff. Univ. of Kentucky, July 1979.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
201
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HYDROLOGICAL REGIONALISATION : A QUESTION OF PROBLEM AND SCALE
I. Simmers and E. Seyhan : Free University, Amsterdam
Extended Abstract
Quantifying catchment hydrological response and subsequent regionalisation of
resultant information have until now been largely dependent on techniques of:
(a) generalised water balance determinations
(b) regional statistical generation of descriptive variables or model
parameters
(c) lumped catchment models
(d) complex process models which rely on detailed plot or experimental
basin studies for input parameters.
The spectrum of available models does not reflect individual dissatisfaction
with the approach of others, but is a manifestation of two fundamental is-
sues, viz. the type of problem to be solved and the scale at which a solu-
tion is required. It is therefore to be expected that some models are ideal
for initial estimates of a water resource but are unusable in an operational
mode. Others present problems of translation to basins of varying size,
while many have computing requirements which are so great that their prac-
tical application is restricted to research areas where economic criteria
are less dominant.
The classification of an area into distinctive hydrological response units
from natural resource maps is seen as a first step to resolve the obvious
confusion surrounding data regionalisation. Unit identification may be
achieved using multivariate statistics and, dependent on the immediate
problem, can be at any scale.
Preliminary results from a continuing study in east Luxembourg are presented
to demonstrate the technique. Since the problem to be resolved involves pre-
diction of hydrological response consequent upon landuse change, the scale
is small and requires application of a physically based, dynamic contribut-
ing area approach. Data collection was initiated from a regionalised sam-
pling matrix based on topography, vegetation cover, soil and rock type.
The results from several study catchments are encouraging and adequately
define the spatial variability of hydrological response and the varying in-
fluences of physiographic parameters on mechanisms which govern streamflow
generation. Schematic models are presented for both hillslope processes and
total system operation within a larger area. Regionalisation and solution of
the present problem are thus deemed achievable by way of reconstituted re-
sponse (matrix) unit flow diagrams, requiring only verification sampling.
In areas where natural resource maps are available but quantitative data are
scarce, the described approach to regionalisation shows promise and will
certainly minimise instrumental and data collection requirements.
Authors' address
Prof.dr. I. Simmers; Dr.ir. E. Seyhan,
Dept. Hydrogeology and Geographical Hydrology,
Institute of Earth Sciences, Free University,
P.O. Box 7161, 1007 MC Amsterdam, The Netherlands
202
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HYDROLOGICAL REGIONALISATION : A QUESTION OF PROBLEM AND SCALE
I. Simmers and E. Seyhan : Free University, Amsterdam
ABSTRACT
Parameter prediction for ungauged catchments and regionalisation of hydrolo-
gical data are bound by two fundamental issues - the 'problem' to be resolved
and the 'scale' at which a solution is required. The variety of current ap-
proaches to the question suggests that there is a need to develop a simple,
robust method for regionalising hydrological information which can encom-
pass these issues. Classification of an area into distinctive hydrological
response units from natural resource maps is seen as the first step to a so-
lution; unit identification can be at any 'scale' dependent on the 'problem'.
Preliminary results from a continuing study in east Luxembourg are encour-
aging and are presented to illustrate the technique. The 'problem' required
application of a physically based, dynamic contributing area approach and
data collection was initiated from a regionalised sampling matrix technique.
The described approach to regionalisation is shown by this and other studies
to be robust and if combined with remote sensing should minimise instrumental
and data collection requirements.
INTRODUCTION
Quantifying catchment hydrological response and subsequent regionalisation of
resultant information have until now been largely dependent on techniques of:
(a) generalised water balance determinations
(b) regional statistical generation of descriptive variables or model param-
eters
(c) lumped catchment models
(d) complex process models which rely on detailed plot or experimental basin
studies for input parameters.
The spectrum of available response models does not reflect individual dis-
satisfaction with the approach of others, but is a manifestation of two fun-
damental issues, viz. the type of 'problem' to be solved and the 'scale1 at
which a solution is required.
For example, if a 'problem' requires generation of streamflow records from a
longer rainfall time series, a lumped model may prove adequate. However, if
it is necessary to predict the hydrological effects of localised landuse
change, the consequences of spatially variable inputs and outputs, or the
movement of pollutants and sediment through a catchment, then it is necessa-
ry to use a distributed, physically based model. Changes in catchment char-
acteristics are thus directly reflected by changes in the model parameters
(Seven and O'Connell, 1982) - such considerations cannot be satisfactorily
contemplated using spatially averaging models.
Other examples and valid applications of hydrological response models defined
by (a) - (d) above are of course abundantly reported in the literature and
need not be elaborated on here. However, given the heterogeneity of 'problem*
and 'scale' it is therefore to be expected that some models are ideal for
203
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initial estimates of a water resource but are unusable in an operational mode.
Others present problems of translation to basins of varying size, while many
have computing requirements which are so great that their practical applica-
tion is restricted to research areas where economic criteria are less domi-
nant .
Furthermore, the choice of model for even one particular 'problem' is never
simple - there is a marked 'contrast between the complexity of hydrological
reality and the important and often pressing practicality of making manage-
ment decisions based on limited knowledge of that reality' (Beven and
O'Connell, op cit) . Model selection will be based on, inter alia, economic
constraints, hydrological considerations and data availability, with a further
essential prerequisite being to match management problem requirements with
the complexity of model used.
Parameter prediction from ungauged catchments and regionalisation of hydrol-
ogical data are also subject to the same constraints imposed by'problem1 and
'scale'. A number of methods in current use rely on statistical regression of
calibrated model parameters against catchment characteristics (eg. NERC,
1975), with obvious dangers. However, such an approach can resolve only a
limited range of 'problems' and omits the difficulties associated with data
translation at different scales due to variable storage effects.
It is evident, therefore, that there is a need to develop a simple yet robust
method for regionalising hydrological information which can acknowledge these
aspects. The classification of an area into distinctive hydrological response
units from natural resource maps is seen as a first step to resolve the ob-
vious confusion. Unit identification can be achieved by map interpretation
and multivariate statistics and, dependent on the immediate 'problem', can be
at any scale' (see, for example, Body, 1982; Krasovskaia, 1982 (a), (b) ;
Refsgaard and Hansen, 1982; Simmers, et al, 1982 • Seyhan and Hope,1983).
Preliminary results from a continuing study in east Luxembourg are presented
to demonstrate the technique. Since the 'problem' to be resolved involves
prediction of hydrological response consequent upon landuse change, the
'scale' is small and requires the dynamic spatial variation in discharge
source areas to be taken explicitly into account (Beven, et al, 1980; Beven
and Hornberger, 1982; Freeze, 1980; Pilgrim and Bloomfield, 1980; O'Loughlin,
1981). As such, the physically based, dynamic contributing area approach
adopted by Beven and Kirkby (1979) is taken as a basis for the present study.
A full description of the research area, overall project objectives and anal-
yses of data available to date are presented elsewhere (Both and van der
Sommen, in press).
STUDY AREA
Figure 1 displays the area under investigation. Four catchments are involved
thus far; two (labelled C and D) lying within Triassic Keuper formations and
the others (A and B) in exposed or covered Lower Jurassic sandstone. Since
the Luxembourg sandstone is more important from a local water resource point
of view (v. Hoyer,1971), the research project has until now focussed prin-
cipally on the two catchments in this region - viz. Tollbach and Dosbach. The
present paper reflects this priority.
204
-------
LJ map location
^r^f drainage pattern
• village
A Dosbach
B Tollbach
C Deifebach
D Briicherbach
K -y Keuper formation
mX (Km) - Luxembourg
sandstone (Li)
boundary
li exposed Luxembourg
sandstone
[:[••:•:[ Luxembourg
I : 3: I sandstone covered
by Arietenmarls
3 4 km
I I
Figure 1 : East Luxembourg research area
205
-------
The Tollbach lies entirely in exposed sandstone, has an area of 2.54 km2 and
an elevation which varies from 285 to 421 m above sea level. Conversely,
weathered and unweathered Arieten marls cover 66 % of the Dosbach, and the
base of the underlying sandstone is exposed in the channel close to the
lowest flow measurement point. Total catchment area is 1.98 km2 and eleva-
tion varies from 210 to 365 m.
The Arieten marl soils are poorly developed, though arable land areas have a
well ploughed upper zone of loamy clay (~ 30 cm). Beneath this are 1-3 m of
heavy, compact, blue to blue-grey clays, which cap a confined aquifer in
beds of unweathered marls and karstified limestone. Weathering reduces the
Luxembourg sandstone to a brown-yellow loamy sand, the clay content of which
reduces both down slope and with increasing profile depth. The Luxembourg
sandstone aquifer is the most important in Luxembourg and is characterised by
short residence times (~ 1 year - v. Hoyer, 1971) and spring discharges which
reflect, inter alia, the influences of tectonic control and degree of marl
cover.
DATA NETWORK DESIGN
In order to determine the nature and dynamics of runoff production within
each major geological unit data collection was initiated on a regionalised
sampling matrix according to topography, vegetative cover and nature of sur-
ficial deposits, similar to that proposed by Tricker (1981) . The watershed
is thus regarded as a system and is considered to consist of a series of
'homogeneous1 units, each playing their particular role in runoff formation.
slope position :
vegetation :
geology (soil type)
slope position :
1 - downs lope and
riparian zone
2 - midslope
3 - upslope
vegetation :
b - beech forest
p - pine/spruce forest
g - grassland
c - arable land (crop)
geology :
K - Keuper marls
S - Luxembourg
sandstone
A - Arieten marls
Matrix unit
No. (fig. 2)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Matrix
unit
(table 1)
Kb!
Sbl
Sg2
Agl
Kb 2
Sb2
Sp2
Ab2
Sg2
Sc2
Ag2
Ac 2
Ap2
Ag3
Ab3
Ap3
Sg3
Sp3
Spl
Sb3
Sc3
% Dosbach
area
0.6
2.0
0.4
1.0
4.5
5.5
2.0
1 .0
15.5
1 .6
29.7
2.5
4.4
8.7
13.7
4.5
1 .8
0.6
-
-
-
% Tollbach
area
_
1 .0
-
-
-
5.2
30.9
-
-
1.5
-
-
-
-
-
-
-
29.1
1 .0
18.5
12.8
Table 1 : Basic sampling matrix
Table 2 : Dosbach and Tollbach homo-
geneous sampling units
Table 1 gives the basic matrix used, while table 2 and figure 2 show the
resultant division of the Dosbach and Tollbach into relatively homogeneous
sampling units. Such a procedure obviates the necessity for excessive data
206
-------
collection and the derived results may be objectively incorporated into the
Beven and Kirkby (1979) model without the possibility of introduced bias. It
is of interest to note that for the Dosbach eight units allow representative
sampling over 87 % of the total area, and for the Tollbach this decreases to
five units for 97 %.
(i) SLOPE
A:DOSBACH
B: TOLLBACH
N
SLOPE
I u u u I upslope (O-3°)
I m mm I midslope (3-9°)
L. m, I spur/ridge . „..
LJ ll positions {'* >
riparian zone (0-3°)
VEGETATION
I « « » I spruce/pine forest
| o o ° | beech forest
v%/%\ arable land (crop)
grassland
GEOLOGY
I ~I I I Arieten marls
I:: :•:•:•:•:•:] Luxembourg
|x::::::::::::| sandstone
Keuper marls
Figure 2 : Slope (i), vegetation (ii), geology (iii) and sampling matrix
units (iv) for the Dosbach (A) and Tollbach (B) catchments
Data collection was largely in accordance with the indicated division and in-
volved measurement of normal input-output variables, soil moisture levels,
surface-, spring-, well- and soil-water chemistry, piezometric levels and
selected soil hydraulic properties such as infiltration rate and conductivity.
Primary sampling sites for the Dosbach are shown in figure 3.
207
-------
Legend:
• •••• catchment boundary
—J50-— contours (m)
——=r drainage pattern
ffi pond
O* spring
O5 well
©R pluviograph
J V-notch
Wu |_ waterlevel recorder
p piezometer
T tensiometer
Ssoil moisture
chemistry sampler
A—A' transect
X throughfall troughs
N
Figure 3 : Dosbach field measurement and instrumentation network
RESULTS
Streamflow characteristics
Analyses of the basic discharge and precipitation records demonstrate marked
differences in response between the Tollbach and Dosbach. Groundwater from a
number of distinct aquifers plays a dominant role in the total runoff pro-
cess for the Tollbach, with < 2 % of measured precipitation resulting in
quickflow from storms with maximum rainfall intensities which vary from
2.8-20.3 mm/hr. For the Dosbach, with 66 % marl cover, mean baseflow is ~ 45%
of that recorded from the Tollbach, while corresponding quickflow response
varies between 5 and 60 % of storm precipitation. The overall results, when
taken in conjunction with hydro-chemical investigations, confirm the appro-
priateness of present project objectives and methods.
Modelling the runoff process
The existence of various mechanisms for streamflow generation is now widely
accepted and summaries of current knowledge are presented by, inter alia,
Dunne (1978) and Freeze (1980). All recognise the importance of soil param-
eter heterogeneity in space, time and depth governing these mechanisms.
208
-------
Unfortunately insufficient data have as yet been collected or processed to
allow rigorous testing of the complete Beven and Kirkby model, so emphasis is
placed here only on measurements relating to variations in soil moisture, in-
filtration rate, saturated hydraulic conductivity and water table depth for
a number of the proposed sampling units (figure 2). Since surface processes
are relatively less important in the Tollbach principal effort to date has
been on data collection in the Dosbach, though sufficient information is now
available to propose schematic models for both hillslope processes and total
system operation in the Luxembourg sandstone region (figures 4 and 5).
Evidence to support these models is derived in part from measurement tran-
sects AA', BB1 and CC1 shown in figure 3. Piezometers have depths of 0.5 to
3.0 meters and tensiometer pairs are installed at 17 and 35 cm. Saturated
hydraulic conductivities for varying profile depths were determined using the
constant head method and infiltration parameters by sprinkling infiltrometer.
Tables 3 and 4 present a sample of results obtained.
28/9
29
30
1/10
2
3
4
5
6
7
8
D
(mm)
6
-
_
-
2
8
-
1
-
_
-
Matrix unit
A-A'
PI T2
8 s
16 s
29 s
34 s
35 s
26 s
19 s
28 s
31 s
38 s
38 s
15
P2
11
9
1?
10
15
1 1
9
10
1 1
17
20
1 1
P3 T4
1 1 s
8 s
9 s
9 s
10 s
8 s
6 s
5 s
6 s
12 s
16 s
1 1
P4
7
8
8
10
9
6
5
6
7
10
16
1 1
P5 T6
73 52.0
76 51.5
81 51.3
83 50.6
85 50.6
79
75 54.0
84 52.7
82 51.3
86 51.0
88 50.0
4
B-B'
P6
14
1 1
16
24
23
11
12
1 1
12
24
23
14
P7 T8
7 s
5 53.2
9 52.7
10 52.7
13 52.0
2 s
5 s
7 s
7 53.8
14 53.2
21 52.0
1 1
P8
6
2
9
6
6
1
4
4
5
11
14
1 1
P9 T10
44 50.0
33 49.8
48 49.4
54 49.5
60 49.4
24 49.6
36 50.0
49 49.5
43 50.0
58 49.4
66 49.4
4
C-C'
Pll
42
37
41
41
44
40
38
39
40
43
45
14
P12
12
8
13
14
17
8
7
8
7
12
16
9
P13
_
-
20
12
21
20
2
8
8
19
27
9
P14 Til
t -
39.0
1 38.5
o 38.7
o 38.5
2 38.5
A 38.7
38.7
38.6
38.2
38.7
9
P = piezometer (water level depth in cms); T = tensiometer (values at 17 cm
depth expressed as soil moisture content % by volume : s (saturation) = 57%)
Table 3 : Dosbach piezometric head and soil moisture variations (28.9-8.10.81)
Matrix
unit No.
(fig. 2)
4
6
9
11
12
14
15
21
% Area
(table 1)
1.0
5.5
15.5 ]
29.7 j
25\
)
8.7
13.7
12.8
Slope
O
_
25
5
10
7
9
9
3
3
3
-
4
OFV
(mm/hr)
_
-
-~
49
-
320*
170
110
27
-
"~
SD
(mm)
_
7
33
12
14
6*
4
8
7
-
™"
i
o
(mm/hr)
_
83
92
> 105
58
51
53*
43
52
85
-
59
vertical
K
s
(m/d)
20
-
} 3
! 0.1
j
5
-
0.4
~
lateral
K
s
(m/d)
5
-
9
0.007
-
0.1
~
K
s
depth
(cm)
20
-
20
30
-
15
—
209
-------
*= top 20 cm removed; OFV = overland flow velocity parameter; ±Q = final
constant infiltration rate; SD = maximum value of interception and de-
pression store (see Seven and Kirkby, 1979)
Table 4 : Selected saturated hydraulic conductivity (K ) and infiltration
s
parameter estimates - (for table see previous page).
Although statistical verification of suggested interrelationships is not yet
possible a number of points emerge. Allowing for minor surface irregular-
ities water table depths reflect the dominant influences of topographic po-
sition and lithological differences, with up- and down-slope piezometers
showing a strong, rapid head response during and after rain (figure 6). This
is readily explained by the Kg values in table 4 despite saturated soil con-
ditions in the upslope areas. Response is least in the midslope zone, with
shallow water tables and lowest Kc.
o
Infiltration parameters also display considerable spatial variability, with
iQ values which exceed rainfall intensities measured during the observation
period. Marked differences between i and Kg, particularly in unit 11, sug-
gest that despite existing vegetation cover it is unwise to assume equiva-
lence of these parameters in areas subject to ploughing (cf. Anderson and
Burt, 1978). On the Arieten marls i appears strongly related (but not equiv-
alent) to only subsurface Kg, since similar i values are measured for vary-
ing slope angle and landuse (units 11 and 12). However, landuse has a marked
influence on OFV. Conversely, Kg is found to be not a limiting factor for
infiltration on weathered Luxembourg sandstone, slope angle is also unimpor-
tant, and iQ seems to be principally controlled by landuse (units 6, 9 and
21) - highest under grass cover and least with bare soil or crop as expect-
ed. The same conclusion is also reached by Tricker (1981).
DISCUSSION
The above preliminary results, supporting hydrochemical data and field ob-
servations allow a number of generalisations to be made on system operation
within the Luxembourg sandstone.
At the hillslope scale on Arieten marls (figure 4) the most important runoff
producing process is saturated overland flow, initiated in the midslope area
(cf. Krasovskaia, 1982(a), (b)).Channel precipitation will of course con-
tribute. Since the upper weathered zone is relatively permeable infiltration
will occur until storage is filled, this occurring first in the midslope
zone where water table depths and lateral Kg values are least (Freeze, 1980;
O'Loughlin,1981). Growth of the saturated area will be predominantly in a
downslope direction as a result of sheet/rill flow and percolation, with
subsurface flow a minimal component in this rapid response system. The small
peak discharges measured in weathered sandstone areas are attributed to
saturated overland flow from a narrow zone along the channel, 'Horton1 over-
land flow on access tracks, channel precipitation and groundwater response.
Figure 5 defines the hydrological system on a regional scale. Response to
precipitation is primarily controlled by the degree of marl cover, since
Qma + QUJJ » Qgf + Qga and Qbg > Q^sd,,) • Groundwater is the dominant runoff
component from Luxembourg sandstone, and apart from marl cover reflects the
characteristics of thickness and storage capacity of the weathered zone,
structure and local lithological differences. %ws is small, as is
210
-------
downslope midslope upslope
< X X >
ip . L
o ^o |o ^ I o I o
Legend:
sandstone
marls with limestone
weathered marls
•;•;•;•.•.•'.•'.•] saturated zone
unsaturated zone
|p precipitation
E flow lines
Figure 4 : Schematic model of runoff producing processes on hillslopes of
the Dosbach catchment
CONCLUSIONS
Although results reported here represent only the initial investigatory phase
of our ongoing programme they are a source of encouragement . The spatial
variability of hydrological response is adequately defined, as are the vary-
ing influences of physiographic parameters on mechanisms which govern stream-
flow generation.
To solve the immediate 'problem' , testing of the Seven and Kirkby (1979) mod-
el structure under varying input and operation conditions continues and
amendments will be made as necessary. Verification of model components and
results is being based on further field measurements of inter- and intra-
matrix unit input variability in space and time, hydrochemical and isotope
studies, and geophysical surveys.
To address the more general problem posed by the paper title and introduc-
tion, the stratified sampling matrix adopted as a basis for the present over-
all project is found to be an appropriate technique for regionalised data
collection. Regionalisation for purposes of assessing the hydrological ef-
fects of landuse change, both within the same area and elsewhere, is thus
deemed achievable by way of reconstituted response (matrix) unit flow dia-
-------
(T) Arieten marls
(2) Luxembourg sandstone
rr~?
.
|forest |
T
E
OSQ
t
rforest |
Osf < I T *]
Omf
E
t
(Su) Surface zone
ma
Qbu
(Swm) Weathered marls
(Sm) Marls
(Sws)
Weathered
sandstone
Qbm
\r
Lm
Obls(m)
Qbs(m)
i
Notation :
E evapotranspiration
L leakage
P precipitation
Q runoff
S storage
T throughfall
a
b
f
I
m
(m)
s
u
agricultural land
base
forest area
local area
marl formations
formations with marl cover
sandstone formations
surface zone
w weathered material
Figure 5 : Hydrological system of the Luxembourg sandstone region
212
-------
10
E 20
u
SZ 30
40
"§ 50
O
60
70
80
10
20
30
(C)
(a)-upslope ; (b)-midslope ; (c)-downslope
22 24 26 28 30 2 4 6 8 10
September- October 1981
Figure 6 : Mean Dosbach piezometric head variations, sections AA', BB',
CC' (24.9-8.10.81)
grams, a general distributed, physically-based model, and verification sam-
pling. The sampling matrix approach to data regionalisation is also shown to
be robust by the independent successful application of the technique to a
variety of 'problems' at 'scales' which range from five to 1000 km2 (see
Krasovskaia, 1982; Refsgaard and Hansen, 1982; Body, 1982).
In areas where natural resource maps are available but quantitative data are
scarce, this approach to regionalisation shows promise and if combined with
remote sensing will certainly minimise instrumental and data collection re-
quirements .
ACKNOWLEDGEMENTS
This project would not be possible without a team effort. The guidance and
assistance given by both staff and senior students from the Department of
Hydrogeology and Geographical Hydrology, Free University, are gratefully
acknowledged.
REFERENCES
Anderson, M.G. and Burt, T.P. 1978 : The role of topography in controlling
throughflow generation. Earth Surface Processes, 3; 331-344.
Beven, K.J. and Hornberger, G.M. 1982 : Assessing the effect of spatial pat-
tern of precipitation in modelling streamflow hydrographs. Water
Resources Bulletin, 18 (5); 823-829.
Beven, K.J. and Kirkby, M.J. 1979 : A physically based, variable contributing
area model of basin hydrology. Hydrol. Sci. Bull., 24 (1); 43-69.
213
-------
Seven, K.J. and O'Connell, P.E. 1982 : On the role of physically-based dis-
tributed modelling in Hydrology. Institute of Hydrology, Wallingford,
Report No. 81; 36 pp.
Seven, K.J. et al. 1980 : SHE : towards a methodology for physically-based
distributed forecasting in hydrology. IAHS Publication no. 129; 133-137.
Body,D.N. 1982 : The application of results of catchment research in water
resources planning and management. In, Proc. IAHS Symp. on Hydrological
Research Basins and their use in Water Resources Planning, Berne,
Switzerland.
Both, M. and v.d. Sommen, J. in press : Catchment studies for the application
and regionalisation of physically based hydrologic models : Luxembourg
sandstone region. Dept. Hydrogeol. and Geog. Hydrol., Inst. of Earth
Sci., Free University, Amsterdam, Working Paper no. 1.
Dunne, T. 1978 : Field studies of hillslope processes. In, Hillslope hydrol-
ogy, ed. M.J. Kirkby, Wiley Interscience. New York; 227-293.
Freeze, R.A. 1980 : A stochastic-conceptual analysis of rainfall-runoff
processes on a hillslope. Water Resources Research, 16(2); 391-408.
von Hoyer, M. 1971 : Hydrogeologische und hydrochemische Untersuchungen im
Luxemburger Sandstein. Publications du Service Geologlque du Luxembourg
vol. 21; 61 pp.
Krasovskaia, I. 1982(a) : Hypothesis of runoff formation in small watersheds
in Sweden. SMHI FoU-Notiser 19, Norrkoping; 15 pp.
Krasovskaia, I. 1982(b) : Rainfall-runoff relationships in small research
basins in Sweden. In, Proc. IAHS Symp. on Hydrological Research Basins
and their use in Water Resources Planning, Berne, Switzerland.
Natural Environment Research Council (NERC). 1975 : Flood Studies Report,
London, 5 vols.
O'Loughlin, E.M. 1981 : Saturation regions in catchments and their relation
to soil and topographic properties. J. Hydrology 53; 229-246.
Pilgrim, D.H. and Bloomfield, P.H. I'A. 1980 : Problems in determining in-
filtration and soil parameters of runoff models. IAHS Publication no.
129; 271-277.
Refsgaard, J.C. and Stang, 0. 1981 : An integrated groundwater/surface water
hydrological model. Danish Committee for Hydrology, Report SUSA H13;
122 pp.
Refsgaard, J.C. and Hansen, E. 1982 : An integrated surface/subsurface
catchment model. In, Proc. IAHS Symp. on Hydrological Research Basins
and their use in Water Resources Planning, Berne, Switzerland.
Seyhan, E. and Hope, A.S. 1983 : On the estimation of runoff equations and
the classification of catchments in South Africa by multivariate statis-
tical techniques. Water S.A., 8(6) (in press).
Simmers, I., v.d. Sommen, J.J. and Both, M. 1982 : Regionalisation of
hydrological data : a dynamic modelling approach. In, Proc. IAHS Symp.
on Hydrological Research Basins and their use in Water Resources
Planning, Berne, Switzerland.
Tricker, A.S. 1981 : Spatial and temporal patterns of infiltration.
J. Hydrology 49; 261-277.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should-be inferred.
214
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SNOWMELT INDUCED URBAN RUNOFF IN NORTHERN SWEDEN
by
Lars Bengtsson
Computational Hydraulics Group
McMaster University, Hamilton, Ontario
ABSTRACT
Snownelt and runoff data collected during 7 years at different sites in
the Lule region, Sweden is summarized and analyzed. The capacity of a
snowpack to hold liquid water and the effect of refreezing during cold nights
are included in a degree-day approach.
The maximum observed melt flux to the base of a snowpack during one hour
is 4.1 mm/h. The maximum observed daily melt is 40 mm, but the daily melt of
two year return period is only 20 mm. The runoff from small study plots is
(at least in practical considerations) found to be distributed over about 12
hours. Maximum observed runoff from these study plots of hard packed
gravelled or grassed surfaces is about 2 mm/h. In the late phase of a snow-
melt period the daily runoff is shown to closely correspond to the daily melt.
The very maximum runoff values are, however, observed during or seme days
after the snowmelt period. Overland flow or flow just beneath the ground
surface is shown to take place.
Finally some very rough "design criteria" for snowmelt induced runoff are
g iv en.
REVIEW OF THE PROBLEM
Due to the research during the last two decades the frequency of
different rain intensities over different time intervals is rather well known
for populated areas in Europe and North America. From this knowledge and
using physically sound runoff models the runoff due to rain from urban areas
can be computed quite accurately. Computations may be made for a single
rainfall event or as continuous simulation.
Only few studies of snowmelt induced runoff have been made, even if the
snowmelt rate at a popint has been frequently studied and analyzed in detail.
The different energy fluxes, which determine the snowmelt rate is discussed
215
-------
by, for example, Gray and Male (1981), who recently presented the state of the
art of snow hydrology and snow management.
Before any meltwater can leave a snowpack, the snow must first be
saturated above its irreducible liquid content. The meltwater, which
thereafter reaches the base of the snowpack, infiltrates into the ground
unless the infiltration capacity of the ground is reduced -iue to an asphalted
surface or as a consequence of that the ground is frozen and saturated, in
which case runoff can take place along the ground in the snowpack or just
beneath the ground surface. The theory of percolation of meltwater through a
snowpack has been developed to an advanced level through the work of Colbeck
(1978). Once vertical drains develop in the snowpack, it is, however,
difficult to quantify the percolation process.
There are no systematically collected data of snowmelt induced runoff or
even snownelt data at a point from urban areas reported in the literature. A
group within the Swedish Board for Building Research made a state of the art
report of snow management in urban areas in Sweden, Bengtsson et al . (1980).
From a continuation of that work Bengtsson (1981) found that the snowmelt rate
was higher in urban areas than in rural areas. He also found that in the late
phase of a snowmelt period runoff took place also from normally permeable
surfaces. Also the problem of infiltration in frozen soils is summarized in
the snow handbook by Gray and Male.
To be able to estimate the runoff it is of course essential to know in
what way the snow has been redistributed by man. Snow is piled up within the
cities, but large snow masses are also transported away from the cities. The
degree to which snow is transported away depends on if there is space to pile
up the snow within the city, and to a large degree on how much money that has
been reserved for snow management.
The above cited works and 7 years of snowmelt observations at WREL (Water
Resources Engineering, Lulea, Sweden) show that at least for periods less than
6-12 hours rain intensities exceed snowmelt intensities. Still, in northern
Sweden problems with damming in urban areas are much more severe during
snowmelt than during heavy rain storms. After a long period of snowmelt
runoff can take place from normally permeable surfaces. Rainfall during this
period or just after the snow is completely gone may also cause runoff from
these surfaces. When retention storages, perkolation storages or infiltration
surfaces are included in a storm water system, it is possible that at least
seme parts of the system should be designed for snownelt conditions.
In this paper the theory of meltwater flux to the base of a snowpack is
treated. Account is taken for refreezing of the liquid water of the upper
part of the snowpack during cold nights. Comparison is made with measure-
ments. Thereafter snowmelt observations from the Lulea region in northern
Sweden are presented. The degree-day method, but including the capacity of
the snow to hold liquid water, is used on 25 years of data for 13 areas in
Sweden for estimating return periods of snowmelt intensities. Observed runoff
from an all areas in the Lulea region are also presented and compared with the
melt rate. Rain on snow and runoff caused by rainfall just after the snowmelt
period are discussed separately. Finally seme rough rules of thumb are given.
216
-------
All the data presented in this paper has been collected by the staff of
WREL, when the author was head of the department at Water Resources
Engineering, Lulea, Sweden.
SNOWMELT AND MELTWATER FLUX TO THE BASE OF A SNOWPACK
The snovmelt rate at the snow surface can be determined from an energy
budget analysis. The energy balance for a snow surface is dominated by the
radiation balance. A large heat flux of solar radiation and atmospheric
radiation is almost completely compensated for by the reflected solar
radiation and by the longwave radiation from the snow. In Fig. 1 it is shown
how the measured accumulated net radiation followed the accumulated snovmelt
during a snovmelt period at a site near Lulea. Although the radiation balance
dominates the energy balance of a snow cover, the convective sensible heat
flux between the atmosphere and the snow cover determines to a large extent
how intense the snowmelt will be. In fact the degree-day method is quite
accurate for determining daily snowmelt.
When consecutive snow surveys are made or snow plates are used, it is not
the snowmelt at the snow surface which is measured, but how much water that
leaves the snowpack or the meltflux at the base of the snowcover. The
snowpack can hold liquid water. The percolation rate in dry snow is much
slower than the percolation rate in snow above the irreducible liquid
saturation, since rather much meltwater is needed to raise the liquid content
of the dry snow to and above the irreducible value. Since the liquid content,
which corresponds to a certain melt flux, does not deviate very much from the
irreducible liquid content, the propagation rate of the wetting front in dry
snow can as shown by Bengtsson (1982a) approximately be described by
C = i/Q (1 )
where C = propagation rate of wetting front, i = snovmelt intensity, 6^ =
irreducible liquid content (volume/volume) . A typical propagation rate is of
the order cm/h or even less.
The percolation rate in that part of a snowpack, which initially is at
its irreducible liquid content, depends on to which extent vertical flow
channels have developed and on the snowmelt intensity. Observations at WREL
show typical percolation rates in the drains to be at least 0.1 but closer to
0.5 m/h.
Since a snow cover must be saturated above its irreducible liquid content
before it can release any water and since intense snovmelt causes a faster
percolation of meltwater than less intense snowmelt, it is often first when
the surface melt is as most intense that the snow cover starts to release any
water. The melt flux to the base is then close to the surface melt rate. An
example from measurements at WREL is shown in Fig. 2.
From Fig. 2 it is seen that the peak melt flux to the base of the
snowpack exceeds the peak value of the surface melt rate. This might be due
to errors in computing the energy balance, but since the depth of the snow
217
-------
cover decreases less liquid water can be held in the snowpack. Liquid water
previously held in the snow is released. At constant melt rate the meltwater
flux to the bottom of the snow cover is
vb = i (1 + 6i (p/ps» (2)
where v, = meltwater flux to the base of the snowpack, p = density of water,
p = density of snow (not including liquid water). The meltwater flux to the
bottom of the snow cover can exceed the surface melt rate by as much as 155&.
During a snowmelt period the air temperature falls at least during some
nights below freezing. Then the liquid water in the upper part of a snow
cover refreezes. Bengtsson (1982b) has shown that the depth to which
refreezing takes place can be approximately found from the implicit equation
a — 0. 5 T
a
(3)
where zf = refreezing depth, t = time from when refreezing starts at the
surface, k = thermal diffusivity of the snow accounting also for seme convec-
tive effects due to intense winds, T = air temperature above freezing, and
3
a = e_!l e (4)
ps ci *
where F = latent heat of fusion, c. = heat capacity of ice.
For small negative values of T the last term of the denunerator of eq .
(3) can be neglected and the refreezing depth is determined as
zf = Cf N°'5 (5)
where Cf = refreezing coefficient, which is
-5 (6)
and N = number of negative degree- seconds (or more practical negative
degree-hours if Cf is given in appropriate units) defined as
t
N = / -T dt (7)
3
o
Let us now return to the degree-day method, which gives a linear relation
between melt rate and air temperature. From a practical point of view it is
easiest to work with an equilibrium temperature of 0°C. The degree-day
equation is then simply
m = C Ta (8)
d
218
-------
where M = melt rate, C = degree-day coefficient, T = air temperature above
freezing.
The degree-day method is usually used on a daily basis or a 12-h basis
but sometimes also on a monthly basis. When an equilibrium temperature of 0°C
is used, the value of the degree-day coefficient depends on the solar radia-
tion, wind conditions, the atmospheric emissivity and on the properties of the
snow. For forested areas with a high canopy density it can be theoretically
shown that the degree-day coefficient should be between 1.5 -2 mm/ C day,
Bengtsson (1976). This theoretical value has been confirmed by many measure-
ments, e.g. Kuusisto (1980).
For open areas degree-day coefficients determined from eq. (8) varies
from region to region, area to area, and from year to year. Usually the
degree-day coefficient is observed to increase in the course of the snowmelt
period. This result is partly due to that it is not the surface melt but the
amount of water that leaves the snow cover, which is directly or indirectly
measured. But the melt rate does in fact increase. This is primarily due to
the decrease of the albedo of the snow, so that more of the solar radiation is
absorbed in the late phase of a snowmelt period than in the early phase. The
albedo of fresh newly fallen snow is 0.8 or more. When the melt period begins
it is usually 0.6 - 0.7 and drops to 0.4 during the snownelt. In city areas
the snow albedo drops rather fast to 0.2 - 0.3 as reported by Bengtsson
(1981). The absorbed solar energy is almost twice as large in the late as in
the early phase of a melt period.
The degree-day coefficient as determined from eq. (8) and using daily
average air temperatures can well vary within an interval of 2-10 mm/ C day.
In Sweden the degree-day coefficient is usually higher in northern than in
southern Sweden, since the melt period occurs later in spring during a higher
solar intensity in northern than in southern Sweden. Since the rate of
refreezing of meltwater in the snowpack is not linearly proportional to the
air temperature below freezing, the high value of the coefficient is also due
to the frequent large diurnal temperature variations during melt periods in
northern Sweden. For open areas the degree-day coefficient can for most of
Sweden be estimated to 3 mm/ C-day, but in northern Sweden values around 4-6
mm/ C-day are more reasonable.
It is not obvious how a day having air temperatures above and below
freezing should be treated when using the degree-day method on a daily basis.
The degree-day equation gives a linear relation between melt and air temper-
ature above freezing, whereas eq. (5) shows that the refreezing depth is
proportional to the square root of the temperature below freezing. Assuming
that the degree-day method is strictly correct for determining snowmelt, the
average daily air -temperature inserted in the degree-day equation will not
give the correct melt rate, if the air temperature is below freezing during
some part of the day.
Look at the following example. The average daily temperature is +2 C,
but during 12 h of daytime the average temperature is 4°C and during 12 h of
nighttime it is -2°C. The observed snovmelt is 6 mm. When eq. (8) is applied
on a daily basis, the degree-day coefficient is calculated to be 3 mm/ C day.
219
-------
Wlaen refreezing is taken into account and choosing Cf r 50 mm/(°C
day) ' , the refreezing depth is computed to 50 mm. If the irreducible liquid
content is 0.04, about 2 mm of meltwater is needed for saturating the snowpack
to its irreducible value. The actual surface melt is therefore the observed
snowmelt 6 mm plus the above 2 mm. The total of 8 mm melts over a 12 h
period, when the temperature is 4°C. The degree-day coefficient is therefore
2 mm/ C day.
In the above example the degree-day coefficient was overestimated using a
daily average value. If there are rather large negative temperatures during
the night, the snowmelt can be rather much underestimated using the degree-day
method on a daily basis and using a degree-day coefficient derived in periods
of night temperatures above or only slightly below freezing.
The re free zing-degree day method suggested by Bengtsson (1982b) was from
a study in Besbyn Research Basin found to be accurate on a 12 h time basis,
but should be applicable also for a shorter time basis as long as the time for
the water to percolate through the wetted zone of a snowpack is short. The
refreezing method can be summarized as follows:
1. Determine the number of negative degree-hours over a short freezing
period, for example a 24 h period.
2. Compute the refreezing depth using eq. (5) or eq. (3).
3. Compute the amount of meltwater, which is refrozen, using an a priori
value of the irreducible liquid content.
2-3. When eq. (5) is used for computing the refreezing depth, the amount of
refrozen meltwater, M», is
Mf = 9i Cf N°'5 (9)
4. Determine the number of positive degree-hours over a short period pro-
ceeding the short period of freezing air temperatures.
5. Compute the amount of surface melt using the degree-day eq. (8).
6. Deduct the amount of refrozen meltwater, which must be remelted and held
as liquid water in the snowpack before any water can leave the snowpack,
from the computed surface melt to find the amount of meltwater that
reaches the bottom of the snow cover.
It was seen for Fig. 2 that the melt flux to the bottom of the snowcover
was distributed over about 12 hours. Even if there is melt flux also during
nights, most of the meltwater reaches the ground during daytime hours. A typ-
ical runoff hydrograph observed from a snow plate at WREL is shown in Fig. 3.
OBSERVATIONS OF SNOWMELT AT A POINT
The data presented in this chapter regards the meltwater flux to the
220
-------
bottom of a snow cover. Maximun melt intensities for different periods are
given .
Snowmelt Intensities from Temperature and Precipitation Observations
Using 25 years of temperature and precipitation measurements the
frequency of different snownelt intensities has been computed for 13 areas in
Sweden. The procedure for the computations was:
1. Update measured snow precipitation by 30? (= S)
2. Determine the number of positive degree-days during the melt period
(= IT)
3. Determine the degree-day coefficient for the area and for the year as
C r S/ET
4. Multiply the temperature, T, of the warmest day of the melt period by the
degree-day coefficient. The maximum melt rate of that year is m = C.T.
5. Distribute the snowmelt over 12 h so that m = cm/12 h.
6. Update this value by 10% to account for the liquid water, which can be
held by the snowpack.
Extreme value analysis has been used in analyzing the data. The computed
snowmelt intensities are shown in Table 1.
The table can be summarized: Every second year the maximum daily melt is
20 mm/12 h in southern Sweden and 30 in northern Sweden.
Snowmelt Intensities from Snow Surveys
WREL is during snowmelt carrying out snow surveys every second day at a
number of sites around Lulea. Since the energy balance for the snow cover is
computed using measurements of radiation balance and computations of sensible
and latent heat fluxes from profile measurements, eventual observation errors
can be revealed fairly well, and the snowmelt over at least as short time as
2-4 days can be determined quite accurately.
The reduction of the snow cover as water equivalents is shown for 1982
for an open field and a forested area in Bensbyn Research Basin in Fig. 4 and
Fig. 5. Tne snow cover of the forested area is reduced by 5 mm water equiv-
alents per day during most of the melt period. The melt rate of the snow in
the open field is considerably faster. All the snow disappears in the course
of a week. The melt rate is somewhat more than 15 mm/day. In 1982 the
snowmelt process in Lulea was, however, more even than usualy with no single
day of intense snowmelt.
Observations of the snowmelt have been made in Bensbyn and also at For son
near WREL's laboratories since 1976. The observed maximum melt rates for
different years are summarized in Table 2. The shown values, which are melt
221
-------
TABLE 1
Recurrence interval of snowmelt runoff with intensities in mm/12 h.
Region
Karesuando
Haparanda
Stensele
Harnosand
Ostersund
Falun
Stockholm
Karlstad
LinkOping
GOteborg
Visby
Vaxj'6
Lund
2 year
37
33
22
20
28
24
23
21
20
21
21
20
22
5 year
53
11
28
30
42
41
35
30
30
30
30
25
36
1 0 year
63
46
32
36
51
52
43
35
36
36
36
30
46
50 year
84
57
42
51
71
76
59
46
50
50
50
38
67
TABLE 2
Maximum snowmelt runoff (mm/day) at a point having a duration of at least 3
days as calculated from snow surveys.
1976 1977 1978 1979 1980
1981 1982
Bensbyn open field
B
B
- small field with
bushes
- forested area
Porsttn open field
P
- forested area
13
17
8
25
10
24
22
9
24
10
40 15
38 13
21 8
20
21 11
15
15
10
12
9
30 15
20 13
15 11
— -
222
-------
fluxes to the base of the snow cover, can be assumed to occur during at least
three consecutive 12 h periods.
As can be found from Table 2 the maximum observed daily melt from the
open field in Bensbyn is 40 mm/day, but the median value is only 15 mm/day.
For the forested area the maximum observed value is 21 mm/day and the median
value 10 mm/day.
Snowmelt Intensities from Observations of Runoff from an Asphalted Surface
The runoff from a 25 m long and 8 m wide asphalted study plot having a
slope of 2% has been measured with a resolution in time of 1-10 minutes during
the snownelt periods in Lulea the years 1979, 1980, 1981 and 1982. For
periods of intense snowmelt over one hour or more the runoff corresponds to
the melt flux to the base of the snowpack, and also to the surface melt when
the reduction of the total liquid holding capacity of the snowpack is
subtracted. In Table 3 maximum observed runoff over 1 h, 12 h, 24 h and
maximum weekly runoff is given. The four highest independent 1-h values of
runoff for the different years are given in Table 4. The corresponding 12 h
runoff values are given in Table 5. Consecutive days have only been included,
if the runoff ceased during the nights in between daytime hours.
The runoff over 12 h is observed to be very close to the runoff over 24
h. A very intense melt flux is about 15 mm/12 h, but in 1981 a melt exceeding
20 mm/12 h was observed at two occasions. The highest observed hourly runoff,
i.e. approximately the melt flux to the base of the snow cover, is 4.1 mm.
However, only at two occasions runoff of higher intensity than 3 mm/h has been
observed .
Observations in Downtown Lulea
In 1980 snow surveys and runoff measurements were carried out and radia-
tion measurements were taken in downtown Lulea. The degree-day coefficient
from a small park surrounded by streets with heavy traffic was found to be 8.5
mm/ C day and for a larger park 7 mm/ C-day. The runoff was distributed over
the daytime hours. During the measurement period the maximum 12 h melt was 30
mm. However, for an early warm period when no measurements were made, the 12
h melt from the two parks was using the degree-day approach estimated to 40
and 50 mm respectively.
Degree-Day Coefficient
From the snow surveys in Bensbyn Research Basin and at PorsOn an average
degree-day coefficient for each year and each site was determined. The calcu-
lated coefficients "are shown in Table 6. The median value for "open field" is
4.8 mm/°C day and for "forest" 1.8 mm/0C day. The maximum degree-day coeffic-
ients were found for 1979. The "open field" coefficients were 8 and 12 mm/ C
day, but the "forest" coefficients did not exceed the median value very much.
The refreezing-degree-day method was used on Bensbyn-data for the snow-
melt period of 1981 and 1982. The degree-day coefficient was then found to be
2.8 mm/°C day for both years for the open field, and 1.4 and 1.5 for the two
223
-------
TABLE 3
Mafcimun observed snowmelt induced runoff (mm) from a 25 m long asphalted study
plot having a slope of 2%.
1 - h v al ue
12-h value
24-h value
weekly runoff
1979
3.3
16.9
17.7
84
1980
2.5
14.6
14.7
75
1981
4.1
21.3
23.2
90
1982
2.0
9.6
11.3
50
TABLE 4
The four highest observed independent hourly runoff values due to snownelt
(mm) for different years from a 25 m long asphalted study plot having a slope
of 2% in Lulea and date when the runoff was observed.
1979
1980
1981
1982
3.
2.
4.
2.
3
5
1
0
1
(25/4)
(15/4)
(18/4)
(17/4)
2.
2.
3.
1.
9
1
0
8
2
(28/4)
(13/4)
(17/4)
(1/4)
2.7
1.9
2.7
1.4
3
(23/4)
(12/4)
(17/4)
(26/3)
2.
1.
2.
1.
6
9
1
4
4
(24/4)
(1 6/4 )
(19/4)
(21/4)
224
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TABLE 5
The four highest observed independent 12-h runoff values (mm) for different
years from a 25 m long asphalted study plot in Lulea and date when the runoff
was observed .
1979
1980
1981
1982
16.
14.
22.
9.
9
6
3
6
1
(23/4)
(15/4)
(11/4)
(1/4)
16.
12.
21.
8.
0
4
4
5
2
(28/4)
(1
(1
(1
4/4)
8/4)
7/4)
15.
10.
10.
8.
6
6
1
0
3
(25/4)
(13/4)
(14/4)
(26/3)
4
-
10.2 (7/4)
8.9 (15/4)
7.4 (16/4)
TABLE 6
Degree-day coefficient (mm/°c day) estimated from snow surveys for entire melt
periods using 0 C equilibrium temperature.
1975
Bensbyn open
field
B - an all field
with bushes
B - forested
area
Person open
field 4.0
P - forested
area 2. 1
1976
2.8
2.3
1.8
2.9
1.8
1977
5.9
3.7
2.2
6.5
2.2
1978
7
6
2.1
10
2.2
1979
8
6
2.2
12
2.5
1981
4.8
4.8
1.8
3.7
1.8
1 981 1 982
3.1 3.9
- -
1.5 1.6
-
225
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years for the forested area.
When refreezing is accounted for the degree-day coefficient has more
physical significance than when it is not accounted for. The coefficient is
reduced and is more constant, which enables better forecasts.
The runoff data for 1981 from the asphalted study plot at WREL was used
by WesterstrSm (1982) for determining the degree-day coefficient using differ-
ent temperature index. He separated "early" and "late" melt. When the daily
mean temperature was used as the temperature index the degree-day coefficient
for early melt was found as 1.7 mm/ C day and for late melt (after about 25
accumulated degree-days) as 6.5. When only the part of the day having air
temperatures above freezing was included in the temperature index (which then
corresponds to for example number of degree hours above freezing) , the degree-
day coefficients for early and late melt were found to be 1.5 and 4.4 mm/°C-
day respectively. The "late" melt period using this temperature index could
not be considered to have started until after about 45 accumulated degree-days
( C-days).
SNOWMELT INDUCED RUNOFF
Infiltration
When a snowpack has been saturated above its irredicuble liquid content
and meltwater reaches the base of the snow cover, the melt-water can, depend-
ing on the conditions of the soil, either infiltrate into the soil or run
along the ground. The soil beneath a melting snowpack is usually frozen.
Even if the ground has not been asphalted, the infiltration capacity of the
soil is reduced. In the early phase of a melt period all the meltwater can
usually infiltrate into the soil. Then the soil moisture is gradually
increased. Also seme of the meltwater refreezes, when it penetrates into the
frozen soil. The infiltration capacity of the soil is reduced. In the late.
phase of a long melt period the infiltration may cease completely. Since the
total melt amounts to large quantities, it may also be that the ground water
level rises almost to the ground surface.
Tne theory of imfiltration is not treated in this paper. It is only
noted that there is a relation between negative soil temperature and the
amount of liquid water in the frozen soil. If the moisture content of the
soil is high when the soil freezes in the autumn, and if the ground is cooled
down and very frozen before it is covered by an insulating snow cover, the ice
content of the soil will be large and the infiltration capacity reduced very
much. Then only a small amount of meltwater can be introduced into the soil
before runoff takes place along the surface.
A measure of the infiltration capacity of the frozen soil can be obtained
by measuring how much the water equivalents of a snow cover is reduced before
any runoff is observed in nearby small perennial streams. Such observations
have been made in Bensbyn Research Basin. The observed reduction of the snow
cover for consecutive years is shown in Table 7. After the runoff has started
the daily runoff corresponds almost to the daily mel± found from the snow
large open field, which constitutes 30% of the 1.6 km catchment, is meadow
226
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TABLE 7
Reduction of the water equivalents of the snow cover 4- rain precipitation (mm)
during different snowmelt periods up to the time when runoff was first
ob serv ed .
1977 1978 1979 1980 1981 1982
Bensbyn - open field
Bensbyn - forested areas
70
70
90 90
50
100
100
10
10
grass. There is a sandy layer of some 10-30 cm above a silty soil.
Runoff from Bensbyn
The Bensbyn Research Basin can be divided into two parts. The upper
part, about 1.1 km , of the catchment is covered with dense coniferous forest.
The lower part, about 0.5 km~, is flat and is mainly a large meadow. Across
the meadow there are two small ditches. Two small rivulets, which are dry
most of the year, meet at the edge of the meadow. The discharge is measured a
few hundred metres below the confluence.
Maximum observed runoff from Bensbyn for different years is given in
Table 8. For daily runoff only one of consecutive days of high discharge has
been included .
From Table 8 it is seen that the maximun daily runoff every year during
the period 1977-1982 has been at least 6 mm. The three highest daily runoff
values without contribution from rainfall are 18, 12 and 11 mm. The corres-
ponding highest 1-h runoff values are 0.75, 0.5H and 0.53 mm/h. The largest
weekly runoff corresponds to 9 mm/day.
The very highest runoff from Bensbyn has, however, been observed as a
consequence of rainfall just after the snowmelt period in 1982. A daily
runoff of 26 mm and an hourly peak value of 1.3 mm/h were observed.
The runoff given in Table 8 is referred to the area of the entire catch-
ment. However, the snowmelt starts earlier from the open area than from the
forest. Many years the snow in the open field has disappeared completely
before runoff commences from the forested areas. The snowmelt induced runoff
fron the separate areas is therefore higher than the average value for the
whole catchment as given in Table 8.
'IXiring 1978, 1980 and 1981 the maximun discharge in the small stream was
not observed until the open field was free frcm snow. For these three years
it was possible to separate the runoff from the forest and the meadow. The
maximun daily runoff for the two areas and the three years is given in Table
9.
227
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TABLE 8
The three highest observed runoff values (mm) for different time intervals
from Bensbyn Research Basin and date when the runoff was observed.
1-h
val ue
daily
r uno f f
weekly
runoff
1977
0.80X
(16/5)
0.75
(5/5)
0.58X
(13/4)
17.8
(5/5)
16.2X
(16/5)
11. 9X
(13/5)
8.1
(13-19/5)
1978
0.34
(16/5)
0.32
(17/5)
0.30
(18/5)
7.3
(17/5)
6.0
(19/5)
4.4
(15/5)
40
(15-21/5)
1979
-
-
-
12.2
(4/5)
9.7
(2/5)
9.7
(30/4)
63
(30/4-6/5)
1980
0.32
(23/4)
0.29
(1/5)
0.28
(4/5)
6.0
(1/5)
5.6
(4/5)
5. 1
(23/4)
36
(30/4-1/6)
1981
0.54
(13/5)
0.53
(12/5)
0.53
(14/5)
11. 1
(14/5)
10.3
(12/5)
8.0
(10/5)
68
(11-17/5)
1982
1.28Z
(29/5)
0.391
(9/5)
0.34
(25/4)
26. Oz
(29/5)
7.81
(9/5)
6.0
(25/4)
43
(4-10/5)
x) during the period 12-14 May the rain precipitation was 12 mm.
z) during the previous day the rain precipitation was 60 mm.
i) during the previous day the rain precipitation was 9 mm.
TABLE 9
Maximum snowmelt induced daily runoff (mm) fron the forested area and the open
field of the Bensbyn Research Basin for the years 1978, 1980 and 1981.
Bensbyn - open field
Bensbyn - forested area
1978
10.4
10.8
1980
8.6
5.7
1981
19.9
23.0
228
-------
It should be noted that the design runoff values for stream flow
generated from farming areas suggested in Swedish handbooks is 13 mm/day.
Runoff from WREL Study Plots
In a previous chapter runoff data from an asphalted study plot at WREL
was presented. Now this data will be compared with the runoff from two study
plots with grassed and gravelled surfaces. The area of these two study plots
is for the asphalted surface 8 x 25 m and the slope is 2%. The three plots
are next to each other. The grassed surface is shaded by a house towards the
evening, so the melt rate at the grassed surface may in late afternoon be
reduced compared to the melt rate at the asphalted surface.
The most intense observed runoff for different years is given in Table 10
and as runoff over 12 h in Table 11. All of these runoff values were exclu-
sively due to snowmelt.
The maximum weekly runoff varied between values corresponding to 7-14
mm/day for the asphalted surface, 3-11 for the gravelled surface and 1-8 for
the grassed surface. In 1980 the maximum weekly runoff corresponded to 11
mm/day' from the asphalted as well as for the gravelled surface. No data
exists for that year for the grassed surface.but usually the runoff from the
surface covered with grass is very close to the runoff from the surface
covered with gravel.
The runoff from the surface covered with gravel may be as high as from
the asphalted surface as was found in 1980, when all the three daily maximum
runoff values were equal. All the meltwater ran along the ground. Usually,
however, the runoff from the grassed and gravelled surfaces is about half the
melt value found as the runoff from the asphalted surface. When plotting
accumulated runoff versus accumulated degree-days Westerstrbm (1982) found the
("runoff"-) degree-day coefficient for grass and gravel to be about half of
the degree-day coefficient for snovmelt.
Runoff Observations in Downtown Lulea
During the snovmelt of 1980 some few measurements of the runoff from a
6500 m peak, where the snow had been removed from the gravelled paths, were
made. The maximum observed runoff corresponded to 2.3 mm/h, when the area of
the gravelled paths was excluded. This peak value is in agreement with the
data from the WREL study plots.
Rain During the Snowmelt Period
Rain on snow has only a minor effect on the melting process, but it has
the effect that it increases the degree of liquid saturation of a snow cover.
If the snow is wet when the rain starts to fall, all the rain precipitation
reaches the bottom of the snow cover. In the late phase of a snownelt period
all the rain precipitation may run off as overland flow.
When a thick snow cover is completely gone, the infiltration capacity of
the soil is still very much reduced. Most of the rain precipitation on this
229
-------
TABLE 10
The three yearly highest observed hourly runoff
sloping study plots, WREL. Date of observation
asphalt
gravel
grass
1979
3-3 (25/4)
2.9 (28/4)
2.7 (23/4)
2.4 (28/4)
1.6 (25/4)
0.9 (29/4)
-
-
-
1980
2.5 (15/4)
2. 1 (13/4)
1.9 (12/4)
2.2 (15/4)
2.1 (13/4)
2.0 (12/4)
-
-
-
TABLE 11
values (mm) from 25 long, 2%
is given within brackets.
1981
4.1 (18/4)
3.0 (11/4)
2.7 (17/4)
1.9 (18/4)
2.6 (20/4)
1.6 (11/4)
1.8 (18/4)
1.6 (20/4)
1.2 (11/4)
The three yearly highest observed 12-h runoff values (mm) from
sloping study plots, WREL, Lulea. Date of observation is
brackets .
asphalt
gravel
grass
1979
16.9 (23/4)
16.0 (28/4)
15.6 (25/4)
12.7 (28/4)
8.2 (25/4)
4.9 (29/4)
-
-
_
1981
14.6 (15/4)
12.4 (14/4)
10.6 (13/4)
14.2 (15/4)
12.4 (14/4)
10.6 (13/4)
-
-
_
1981
22.3 (11/4)
21.4 (18/4)
10.1 (14/4)
11.0 (18/4)
10.1 (11/4)
5.8 (19/4)
11.6 (18/4)
8.5 (11/4)
6.7 (20/4)
1982
2.0 (17/4)
1.8 (1/4)
1.4 (26/3)
1.2 (17/4)
0.8 (18/4)
0.7 (16/4)
0.2 (17/4)
0.1 (23/4)
0.1 (18/4)
25m long , 2%
given within
1982
9.6 (1/4)
8.5 (17/4)
8.0 (26/3)
4.4 (16/4)
37 (18/4)
3.4 (16/4)
1.0 (17/4)
0.7 (23/4)
0.5 (18/4)
230
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wet soil, which still is frozen at sane depth below the ground, may except for
evaporation losses run off as overland flow.
The runoff from the Bensbyn Research Basin was observed to be high during
the period 12-17 May 1977. By that time the open field was snow free. From
energy balance computations based on measurements of radiation balance, wind-,
temperature-, and humidity profiles and controlled by snow surveys, the total
snowmelt from the forested areas was for the period calculated to be 47 mm
with reference to the area of the whole catchment. The rain precipitation was
12 mm. The observed total runoff of 56 mm almost matched the sun of the total
melt and the rain precipitation.
The peak runoff from Bensbyn during the snowmelt period of 1982 was
observed on 9 May. At that time the open field was free from snow. The melt
rate in the forest was during 8-10 May about 7-8 mm/day, which with the total
area as reference corresponds to 5 mm/day. The rain precipitation was 6 mm on
8 May and 3 mm the day after. The mean runoff of 9-10 May was almost 7
mm/day, which should be compared to the mean melt rate and precipitation, 9.5
mm/day. Most of the rain ran off rather fast.
The highest discharge ever in the small Bensbyn stream was recorded on 29
May 1982. Tne open field had been snow free for one month, and the last snow
in the forest had melted two weeks earlier. During the night between 28 and
29 May there fell 61 mm of rain. At 9 o'clock in the evening of 28 May the
low discharge of 21 I/sec in the stream began to increase. A peak value of
570 I/sec was observed at 4 o'clock the following afternoon. By noon 31 May
the discharge had decreased to 80 I/sec. The total runoff during the two days
29-30 May only corresponded to 38 mm.
From the above rather brief analysis of the combined snowmelt-rain runoff
it can be concluded that rain on snow or rain directly on frozen soils can
give rise to fast runoff from normally permeable surfaces.
SUMMARY OF THE MEASUREMENTS
The melt rate of 2 year return period was from precipitation and temper-
ature observations estimated to 20 mm/12 h for open areas in southern Sweden
and to 30 in northern Sweden. The values for 10 year recurrence interval were
30 mm for southern and 40 for northern Sweden.
From snow surveys over 7 years around Lulea the median value of maximum
daily melt was found to be 15 mm for open fields and 10 mm for dense forest.
The corresponding maximum observed values were 40 and 21 mm/day, respectively.
The degree-day" coefficient for forested areas is about 4 mm/°C-day. The
degree-day coefficient for open areas may vary between 2-10 mm/ C-day. By
accounting for refreezing of the liquid water held by the snowpack and apply-
ing a refreezing-degree-day approach, a rather constant degree-day coeffic-
ient, 3-4 mm/ C-day, can be used, which enables more accurate forecasts.
The hourly maximun runoff observed from a small impermeable study plot at
231
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WREL is 4.1 mm/h. However, only twice a melt flux exceeding 3 mtn/h has been
observed. Most of the melt flux reaches the bottom of a snow cover over a 12
h period. The 12 h runoff is very close to the total daily runoff. The
maximun observed runoff over 12 h is 22 mm.
In the late phase of a melt period the infiltration capacity of normally
permeable soils may be almost completely reduced. Overland flow can take
place also from surfaces covered with grass or gravel. In the Bensbyn
Research Basin runoff from an open field is usually not observed until on the
average 70 mm of meltwater has infiltrated into the soil, and runoff from the
forest not until about 40 mm has infiltrated. Thereafter the runoff corres-
ponds almost to the melt rate. The values given above vary from year to year
and depend on the soil conditions by the time of the first snow cover in early
winter .
Tne maximun observed daily runoff from the open field in the Bensbyn
Research Basin corresponds to 23 mm and that from the forested area to 16 mm.
From an analysis of the diurnal discharge fluctuations in the Bensbyn stream
Bengtsson (1982 c) suggests that half of the daily runoff is contributed to
groundwater .
The measurements of runoff from the WREL study plots show that in the
late phase of a melt period the runoff from packed grassed and gravelled
surfaces may be very close to the runoff from asphalted surfaces.
The maximun observed runoff from the study plots covered with grass and
gravel is 2.4 mm/h, which is in agreement with measurements from a city park
in downtown Lulea. The maximun observed daily runoff from the study plot with
gravel is 14 mm, but almost all the meltwater ran off during a 12 h period.
The total weekly runoff for that period was 80 mm.
When rain falls on snow or just after a snownelt period almost all of the
rain may run off as overland flow also on surfaces covered with grass or
gravel .
SOME RULES OF THUMB FOR ENGINEERS
There are no design criteria for snownelt. From the experience gained at
WREL the following very rough rules of thumb are suggested for Swedish
conditions.
A design melt rate of 1 year return period is for open areas in Sweden 20
mm/12 h and for a shorter interval 3 mm/h. For urban areas a value of at
least 30 mm/12 h is suggested. For forested areas the value should be 10
mm/12 h. Rain during the snownelt should be added to the melt. The melt is
linearly distributed over 12 h.
If there is much rain in the autumn and if the soil temperature is low
before a snow cover is formed, overland flow can be expected to take place
from all surfaces in the late snowmelt period. If the soil is packed hard,
the runoff may correspond to the melt rate.
232
-------
2.00 r mm
100 ,.
SO -
10 15 ZO
Figure 1 Observed accumulated snownelt 1976 (solid line) from the open field
in Bensbyn Research Basin and the measured radiation balance as
corresponding to melt (dashed line).
233
-------
15
20 hours
Figure 2 Snownelt intensity (solid line) from measured at WREL, 24 April 1979
and observed runoff from a snow plate (dashed line).
7 13 19 1 7 13 19 I 7 13 19 1 hour*
Figure 3 Runoff 16-18 April 1981 frcm the short asphalted surface study plot
at WREL Water Resources Engineering, Lulea.
234
-------
mm
140
20 " 30
march
april
Figure 5 Water equivalents of the snow cover in the open field in Bensbyn
Research Basin 1982.
mm
14Q.-
80
20
20 30 5
mars april
30 5 15
may
Figure 6 Water equivalents of the snow cover in the forest in Bensbyn
Research Basin 1982.
235
-------
REFERENCES
Bengtsson, L. (1976), "Snownelt estimated for energy budget studies", Nordic
Hydrology 7, PP. 3-18.
Bengtsson, L. (1981), "Snownelt generated runoff in urban areas", Proc. Second
Int. Conf. Urban Storm Drainage, pp. 444-451, Urbana, Illinois.
Bengtsson, L. (1982 a), "Percolation of meltwater through a snowpack" , Cold
Regions Science and Technology, 6, pp. 73-81.
Bengtsson, L. (1982 b) , "The importance of refreezing on the diurnal snowmelt
cycle", Nordic Hydrology, 13, pp. 1-12.
Bengtsson, L. (1982 c) , "Ground and meltwater in the snovmelt induced runoff" ,
Hydrological Sciences Journal 27, pp. 147-158.
Bengtsson, L. , A. Johnsson, P. A. Malmquist, E. S3rner, J. HSllgren (1980),
"Snow management in urban areas", Swedish Council of Building Research,
Report R27, 1980.
Colbeck, S. C. (1978), "The physical aspects of water flow through snow", Adv.
Hydrosci. 11, pp. 165-206.
Gray, D. M. and D. H. Male (1981), Handbook of Snow, Pergammon Press, Toronto.
Kuusisto, E. (1980), "On the values and variability of degree-day melting
factor in Finland", Nordic Hydrology 11, pp. 235-242.
Westerstrom, G. (1982), "Estimating snowcover runoff by the degree-day
approach", Nordic Hydrologic Conf., Forde, Norway, WREL, Ser. A, No. 107,
TULEA, 1982: 29.
The work described in this paper was? not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
236
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AN ADVANCEMENT IN HYDRAULIC MODELING
OF POROUS PAVEMENT FACILITIES
Gary F. Goforth
Espey, Huston & Associates, Inc.
Austin, Texas
ACKNOWLEDGEMENTS
The study addressed in this paper was part of a comprehensive investi-
gation of operational characteristics of porous and conventional paving systems
conducted by Espey, Huston & Associates, Inc. and the City of Austin, Texas. The
project was executed in fulfillment of Grant No. R806338-01-Z with the City of
Austin, under the sponsorship of the U.S. Environmental Protection Agency. A report
documenting the entire project will be completed during the summer of 1983.
INTRODUCTION
The liabilities of urban development to indigenous water resources are
generally accepted to be manifested in stormwater runoff peaks and event volumes of
greater magnitude than in the predeveloped state, often occurring in association with
a degradation of receiving water quality. The increase in impervious areas such as
roofs, streets, and parking lots in urban areas reduces the infiltration capacity of
urban watersheds and produces a corresponding increase in runoff rates and volumes.
Stormwater runoff from developed areas has been recognized as a source of contami-
nant loading to surface and ground water bodies. Impervious areas generally have
limited assimilative properties and in some cases tend to yield contaminants that are
not amenable to control and removal using standard treatment procedures(l). Storm-
water flows transport contaminants which have accumulated on the watershed during
dry weather, however, the total mass transported is a function of the contaminant
accumulation rate, the number of antecedent dry days, the intensity of the rainfall,
the velocity and volume of surface flow and other physical properties of the
catchment. Heavy metals, exhaust products, oils and other hydrocarbons from
automobiles and machinery, suspended solids from dust and dirt accumulation and
airborne pollutants washed out during precipitation events are typical contaminants
present in urban stormwater runoff(4).
Stormwater management generally consists of collecting and transporting
overland runoff in a conveyance system of storm sewers and possibly channels which
are tributary to a nearby stream or lake. Although local flooding problems may be
solved by this system, the shorter time of concentration and higher peak flows which
are generated may tend to create more severe flood problems downstream. The
increase in flow velocities in the improved channels creates a high erosion and scour
potential, thus exacerbating the problem of pollutant transport to receiving bodies of
water.
237
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POROUS PAVEMENTS
A porous pavement facility is an innovative solution to the problem of
stormwater drainage from parking and other low density traffic areas in the urban
landscape. This type of pavement uses the natural infiltration capacity of the soil to
absorb rainfall and local runoff after accumulation in a porous base, consisting of sand
or large diameter open graded gravel. If infiltration into the soil is undesirable or not
practical, lateral drainage to a sump or channel may be provided. Porous pavement
systems can be designed to minimize changes in the runoff quantity and quality
characteristics of a watershed during and after development. A cross-section of a
typical porous pavement facility is presented in Fig. 1.
In regular applications for highway and airport runway construction, a
commonly used porous pavement surface has been referred to as plant mix seal coat,
open graded mix, gap graded mix, popcorn mix, or porous friction course(2). This
material consists of an open graded asphalt and concrete mixture with a high
percentage by weight of aggregate larger than a number four seive, laid to a thickness
of /i to 1 inch. The resultant paving has a coarse surface texture and a high void ratio
resulting in temporary storage of surface water while maintaining the coefficient of
friction between a vehicle tire and pavement at values comparable to the coefficient
under dry conditions. The open graded asphalt mixture underlain by a gravel base
course with appreciable storage capacity is the most frequently used type of porous
pavement. The whole system may be isolated from the natural ground by an
impermeable membrane such as a polyethylene liner, in which case some type of
artificial drainage would be needed; or, the porous pavement system may be allowed to
drain into the natural ground at all points of contact. The latter arrangement does not
preclude the use of artificial drains, as in the case of highly impervious natural ground.
Where storage is provided, flow control devices can be incorporated to regulate the
release rate, e.g., to prevent discharge during a predetermined period after a storm
event.
By design, several inches of rainfall and runoff can be stored within a
porous pavement system prior to discharge. The pavement can be designed to retain
all of the runoff with no drainage from the site, to retain a sufficient volume of runoff
to reduce the after-development hydrologic conditions to predevelopment conditions,
or to delay runoff from the site, thus attenuating peak discharges and reducing the
impact of associated pollutant transport. Any combination of these properties can be
incorporated into an overall project drainage design to satisfy municipal or watershed
drainage management criteria.
Pollutant removal mechanisms in a porous pavement system have not been
fully documented. The relatively slow hydrodynamics may allow some settling of
suspended matter. Adsorption to and absorption in the base media may also be
realized. Although transport of soluble constituents into the ground via infiltration
removes them from the porous pavement system, subsequent groundwater transport to
receiving waters may result.
SIMULATION OF STORMWATER HYDRAULICS
Prediction of hydraulic characteristics is a valuable tool for assessing the
performance of stormwater runoff control strategies. Stormwater hydraulic
238
-------
Collection Drain
L length of pavement
W width of pavement
D depth of base layer
Sb slope of base layer
ir rainfall intensity
is infiltration rate
dD depth of water in base layer
Qs surface discharge
Qb collection drain discharge
Fig. 1.. CROSS SECTION OF TYPICAL POROUS PAVEMENT FACILITY
239
-------
characteristics of porous and nonporous pavement study sites were evaluated using a
revised version of the computer model PORPAV, initially developed for incorporation
into the EPA Storm Water Management Model (SWMM)(3). PORPAV is a two-
dimensional dynamic water budget analysis of a pavement facility. The utilization of
PORPAV allows a comprehensive analysis of flow and storage in porous and nonporous
pavement facilities, facilitating comparisons of the hydraulic response of alternative
pavement designs. The computational scheme of PORPAV is described below.
The rate of inflow to the pavement facility from rainfall and, if present,
any contributing area is compared to the permeability of the porous pavement for each
time interval. For porous systems in general, the permeability is much greater than
the inflow rate and all of the water moves into the pavement control volume. For
nonporous pavements the permeability is generally less than the inflow rate and
limited portion of the inflow moves into the pavement. The excess is stored on the
surface of the pavement for subsequent computation of surface runoff from the
facility.
The inflow into the pavement control volume is added to the existing
storage and then compared to the permeability of the base. If the base permeability is
greater than the stored volume in the pavement, all of the flow is transferred into the
base control volume. This is true for most porous pavement systems operating
according to design. In those instances where the base permeability is less than the
inflow volume, the inflow into the base is computed as the vertical seepage into the
base, at a rate limited by the smaller of the pavement or base permeabilities. The
lateral outflow from the pavement top layer volume is assumed to be negligible as
compared to the vertical flux. The difference between the flow into the pavement and
the transport to the base layer is stored in the pavement control volume.
The inflow to the base control volume is added to the existing base
volume. The revised PORPAV includes a routing procedure to account for the vertical
transport of water within the layers, simulating the vertical movement of the wetting
front as it passes through the pavement system. In essence, volumes of water, defined
by the permeability of the layer and the length of the computational time step, are
routed through the depth of the layer. PORPAV allows the option of utilizing single or
multiple collection drains for discharge from the base layer. An expression for
estimating the horizontal discharge from the porous pavement base was developed to
reflect the nonsteady flow regime in the porous media. Darcy's Law was employed as
the governing flow equation(S),
Qb = KbA dh/dx
where Q, is the average horizontal discharge;
K^ is the permeability of the base media;
A is the cross-sectional area of flow; and,
dh/dx is the energy gradient.
The energy gradient was approximated by
dh/dx = H/L
where H is the total elevation potential, equal to d^ + LS^j
djj is the depth of water in the base layer;
240
-------
L is the normal length of the base layer; and,
S, is the slope of the base layer.
The cross-sectional area of flow was approximated as
A = wd/2
where w is the width of the layer.
This yields
Qb = &W V2 + {Kbw)
or on a unit area basis,
% = Cldb + C2db2
where c, = K,S, /2L; and,
When there is no impermeable seal present to restrict flow, some
horizontal discharge will occur to the adjacent soil. However, this horizontal flux is
generally negligible when compared to the vertical component leaving the layer via
infiltration because of the much smaller cross-sectional area of flow. Also, the
moisture content of the surrounding soil increases during the storm event, thereby
reducing the hydraulic energy gradient between the porous media and the soil. In a
narrow, high-wall trench without an impermeable seal or a drain pipe, the horizontal
flux to the soil during the initial period of the storm, before the hydraulic gradient
between the base and the soil diminishes, may be of the same order of magnitude as
the infiltration flux. By neglecting the horizontal flux when there is no impervious
seal present this assumption represents a conservative case with regard to the
effective storage of the porous pavement system.
PORPAV incorporates Horton's equation to describe the variable rate of
infiltration during and subsequent to a precipitation event. This was expressed as
,. . \ -kt
ls = lt + (lo - af} e
where i is the infiltration rate at time t;
i is the infiltration capacity (minimum rate) of the soil;
i is the initial infiltration rate;
k is the first-order decay coefficient; and,
t is the elapsed time.
The initial infiltration rate is dependent on the initial moisture condition
of the soil. The difference between the initial and minimum infiltration rates can
result in significantly greater vertical transport calculated during the storm event. If
a constant infiltration rate is preferred, the initial rate may be replaced by the
infiltration capacity (minimum rate) of the soil. If the bottom is sealed with an
impermeable membrane, no flow is discharged to the natural ground. The difference
241
-------
between the inflow to the base layer and the outflows (vertical and lateral) from the
base is stored in the base control volume.
All stored volumes within each layer are compared to maximum void
volumes. If the storage volume in the base is exceeded, the excess is stored in the
pavement; if the storage volume in the pavement is exceeded, the excess is addded to
the surface storage on the pavement, if any exists. Surface runoff is then computed as
broad channel flow from the pavement using Manning's equation.
Provisions were added to PORPAV to calculate the theoretical detention
time provided by a pavement facility. This duration was calculated as the elapsed
time between the center of mass of the inflow hydrograph and the center of mass of
the discharge hydrograph. Additionally, average and cumulative inflow, peak and
cumulative discharge and other discharge hydrograph characteristics are compiled for
each simulation.
DESCRIPTION OF THE MONITORING SURVEYS
An extensive monitoring program was initiated to document hydraulic
characteristics of several pavement systems. A monitoring network of three parking
lots was selected, representing a variety of pavement surfaces. The following text
discusses the physical characteristics and sampling procedures for each of the study
lots.
Porous Asphalt Lot
A plan drawing of the porous asphalt study lot is presented in Fig. 2. The
porous asphalt lot consisted of three layers of stone and asphalt constructed on an
impervious limestone bedrock base. The lowest layer was made up of a stone base
course with rocks ranging from 1.5 to 2.5 in (3.0-6.5 cm) in diameter. This base ranged
in depth from approximately 4 in (10 cm) on the upslope end to 42 in (107 cm) on the
low end and provided a void space of approximately 40 percent of its volume for water
retention. The second layer averaged 2 in (5 cm) in depth and consisted of a stone top
course (filter course) with material ranging from 0.4 to 0.6 in (1.0-1.5 cm) in diameter.
This intermediate layer was selected to provide a uniform surface for the application
of the porous asphalt. The final layer consisted of 2.5-in (6.4 cm) of porous asphalt
mix with 5.5 to 6.0 percent asphalt content.
The original design called for runoff to be monitored within a collection
basin located at the downslope corner of the lot. A 6-mil polyethylene impermeable
liner was installed along the above-grade downslope width and side to prevent seepage.
However, this seal leaked and the base discharge did not flow into the monitoring
barrel. Small trenches and berms were constructed along the periphery of the lot to
ensure all runoff was captured. However, these trenches were not lined and,
consequently, some percolation and erosion inevitably occurred. A 90-degree V-notch
weir was installed below the lot in order to measure the discharge rates. Visual stage
readings at this weir by the field crew were used as a basis for the runoff calculations.
242
-------
Fig. 2.
POROUS ASPHALT
JJUT
>-.
•OUECTICH .>
BIT ^
4 DEEP --""
ENTRANCE
RftMP ,
'SENCH^
I c.^.rn;'
.MUM
FLO* /
/ J!0'
', \ ' \ i \ "Ji 1
' : '
5 . n,.1 , ' ± \
* !^~~; 7 ; I
30TEI ' ; \ • 1
/It • GRAVEL TRENCH U0r h [
'. S 51 i ,
-< \ " '. \ \
\ N ,' '
^ \ 1 f*l ItNTW. »« • 1
! '""*" ^ i j
"LOW i i i " - ^ t
;;';/ '; '1
2' DEEP ^_^_ — ' [
-j-, . Q AUSTIN MIMCIPftl. AIRFO"
"•*-&• J • 3HAVEL TRENCH LOT
H
1
s
cmi.p»8
'o»e»
NiaawTE
243
-------
Gravel Trench Lot
A plan drawing of the gravel trench lot is presented in Fig. 3. The study
area consisted of a conventional asphalt lot with a 4-ft (1.2-m) wide and 3-ft (0.9-m)
deep drainage trench at the downslope end. The trench was lined with a 6-mil
polyethylene impermeable membrane and filled with 1.5 to 2.5 in (3.8-6.4 cm)
diameter crushed stone, cleaned and washed. This base was topped with approximately
1 ft (30 cm) of smaller than 1-inch (2.5-cm) diameter gravel. The trench was
subsequently flushed with several volumes of water to rinse out construction fines.
Stormwater flows within the drainage trench were monitored within a 55-gallon
(208-1) barrel. A 4-in (10-cm) diameter pipe was used as the discharge control. All
discharges were calculated based on readings of the water level within the barrel by
the field crew.
Conventional Asphalt Lot
A plan drawing of the conventional asphalt lot monitored in the Austin
study is presented in Fig. 4. Runoff discharge estimates were estimated from water
levels ina3x3xl.5ft (0.9 x 0.9 x 0.5 m) 90-degree V-notch box weir.
SPRINKLER-GENERATED RUNOFF EVENTS
Sprinkler-induced "storms" provided the ability to control the intensity,
duration and timing of the inflows at the study sites. Impact-type sprinklers, supplied
by the City of Austin Parks and Recreation Department, were used during the tests
with the City's fire hydrants used as the source of water. Field observations indicated
a spectrum of spray droplet sizes, ranging from fine mist at the periphery of the spray
stream to large droplets in the center. A similar range of drop sizes were observed
during natural storm events. The number of sprinkler heads were varied for each
induced storm and care was taken in placement of the heads to provide uniform
coverage of the lot. A schematic of the sprinkler application is presented in Fig. 5.
Equivalent rainfall estimates were obtained by placing eight wedge type rain gages on
wooden stands around the test lot. During the tests, readings of the rain gages were
made at regular intervals (every 15 to 30 minutes) and at the conclusion of the event.
Once the individual rainfall totals were compiled, the values were averaged to provide
an approximation of the total event volume.
The gravel trench lot was too large for sprinkler coverage, so 2000-gallon
(7600-1) capacity rear-end-dispensing water trucks provided by the City of Austin were
used. The trucks drove slowly across the upper end of the lot releasing water at
approximately 300 gallons per minute (19 1/s). Different event intensities were
obtained by varying the number of trucks used, trips made, and number of trucks
releasing at one time.
RESULTS OF THE MONITORING SURVEYS
Hydraulic performance results obtained in the stormwater surveys are
discussed below. A summary of hydraulic characteristics of the pavements during
each runoff event is presented in Table 1.
244
-------
FIREHOSE-
FIRE
HYDRANT
Fig.5. Schematic of Sprinkler Application
245
-------
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Porous Asphalt Lot
A maximum intensity of 1.67 in/hr (3.5 cm/hr) was achieved with no
resulting surface runoff at the porous asphalt lot. As presented in Table 1, the total
discharge volume, the time to peak flow and the peak discharge rates were similar for
each event although the inflow varied from 0.94 in (2.4 cm) to 1.53 in (3.8 cm) and the
nominal intensity varied from 0.94 in/hr (Z.4 cm/hr) to 1.67 in/hr (4.2 cm/hr).
Observed base runoff ranged from 37 to 73 percent of recorded sprinkler inflow.
Runoff ratios less than unity were attributed to wetting of the base media, storage
within the base layer and percolation along the trenches.
Gravel Trench Lot
Table 1 includes a summary of the sprinkler events monitored at the
gravel trench lot. The application rates were not varied enough to produce
significantly different discharge characteristics. Observed runoff ranged from 64 to
77 percent of recorded inflow, with an average of 72 percent for the three events.
Observations made during storm events indicated the small diameter surface gravel
was impeding the vertical flux of water, i.e., runoff was flowing across the top of the
trench.
Conventional Asphalt Lot
A sprinkler-generated runoff event and a natural precipitation event were
monitored at the conventional asphalt study lot, and the results are summarized in
Table 1. Estimated runoff volumes ranged from 71 to 118 percent of recorded rainfall.
The runoff ratio greater than unity was attributed to rainfall measurement error.
STORMWATER SIMULATION RESULTS
Stormwater hydraulics for each pavement type were simulated with
PORPAV. PORPAV was calibrated for each lot using the initial set of observed runoff
data. The remaining events were subsequently simulated as verification. A list of
PORPAV input data is presented in Table 2. Pavement characteristics such as
pavement length, width and depth were obtained from onsite or construction measure-
ments. Other parameters such as the Manning's roughness coefficient, volume of dead
storage on the pavement and pavement porosity were estimated. Records of observed
inflow were input to PORPAV. Calibration of the model was initialized by varying
values of the estimated parameters to reproduce the observed runoff volume.
Generally this was accomplished by adjusting the base void volume (the product of
depth and porosity) for the pervious lots and the volume of surface storage for the
impervious lots. The second objective was to reproduce the observed peak runoff rate.
Variations in runoff rates were effected by varying the estimates of average surface
slope and the roughness coefficient. For the porous asphalt and gravel trench lot the
coefficient of permeability for the base layer was varied to reproduce the observed
peak base discharge rate. Results of the simulations are discussed below. A
comparison of simulated and observed hydraulic characteristics is summarized in
Table 3.
247
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TABLE Z
INPUT DATA FOR PORPAV SIMULATIONS
Element
Rainfall rate
Pavement surface
Pavement base
Natural soil
Parameter
Magnitude
Length
Width
Slope
Area
Permeability
Depth
Porosity
Initial dead storage
Manning's n coefficient
of roughness
Permeability
Depth
Porosity
Initial and dead storage
Collection drain capacity
Initial and final infiltration
rate
Unit
in/hr
ft
ft
ft/ft
ft2
in/hr
in
ft3/ft3
in
f«1/6/s
in/hr
in
«3/f,3
in
in/hr
in/hr
. -1
Horton's infiltration decay
coefficient
hr
248
-------
TABLE 3
SIMULATION RESULTS
POROUS ASPHALT LOT
POROUS ASPHALT LOT -
Observed
Simulated
Deviation
POROUS ASPHALT LOT -
Observed
Simulated
Deviation
GRAVEL TRENCH LOT -
Observed
Simulated
Deviation
GRAVEL TRENCH LOT -
Observed
Simulated
Deviation
GRAVEL TRENCH LOT -
Observed
Simulated
Deviation
Peak Flow
(cfs)
- STORM 1
O.Z7
0.273
+0.003
- STORM 2
O.Z4
0.514
+0.274
STORM 1
0.44
0.497'
+0.057
STORM 2
0.58
0.487
-0.093
STORM 3
1.67
0.472
-1.198
Time to Peak
(rain)
58
50
-8
53
55
+2
60
90
+30
66
70
+4
55
60
-^5
Runoff Volume
(cubic feet)
745
745
0
721
1,409
+688
1,960
2,107
-147
1,693
1,650
-43
1861
1,448
-413
Detention Time
(min)
42
28
-14
42
25
-17
29
24
-5
24
24
0
19
23
+4
CONVENTIONAL ASPHALT LOT - STORM 1
Observed
Simulated
Deviation
0.34
0.297
-0.543
53
50
-3
368
269
-99
1
5
+4
CONVENTIONAL ASPHALT LOT - STORM I
Observed
Simulated
Deviation
0.22
0.257
+0.037
7
10
+3
138
140
+2
5
8
+3
1 cfs = 28.32 Ips
1 ft3 = 28.32 1
249
-------
Porous Asphalt Lot
The discharge hydrograph for the calibrated data set, presented in
Fig. 6a, accurately resembles the observed one, but is advanced about fifteen minutes,
as is reflected in the difference in detention times. The calibrated coefficients of
dead storage and base permeability were held constant during the simulation of the
remaining event. Observed and simulated discharge hydrographs for the final event
are displayed in Fig. 6b. The significant overestimation of peak discharge rate and
volume probably resulted from an incorrect sprinkler inflow measurement (used as
input to PORPAV) or an inconsistent hydraulic response, possibly increased base
storage or percolation.
Gravel Trench Lot
Three artificial rainfall events were simulated for the gravel trench lot.
For each case the runoff from the conventional asphalt lot was simulated with
PORPAV and subsequently used as input to the gravel trench simulation, hence,
characteristics for both facilities had to be determined. A summary of simulation
results is presented in Table 3. Coefficients of base permeability and dead storage on
the asphalt lot and in the gravel trench were determined by calibrating PORPAV with
the initial runoff event data. The calibration hydrograph is presented in Fig. 7a.
Runoff characteristics were reproduced quite well for the second event, as displayed
in Fig. 7b. Incorporating the same physical characteristics of the asphalt and gravel
trench for the final event simulation yielded a less satisfactory comparison, presented
in Fig. 7c. The major discrepencies in the two hydrographs of the third event occur
during the periods of water release from the water trucks, possibly an artifact of
utilizing a constant inflow rate during this period in the simulation.
Asphalt Lot
Simulation results for the conventional asphalt lot are compared with
recorded values in Table 3. The second event was used to calibrate PORPAV and was
accurately simulated, as shown in Fig. 8a. The simulated hydrograph for the second
event is compared to observed results in Fig. 8b. The simulation did not reproduce the
peak discharge rate, possibly a result of a short, intense burst of rain which was
undetected in the rainfall data. Both simulations depicted the very rapid detention
times associated with the asphalt lot events.
CONCLUSIONS
The revised PORPAV satisfactorily simulated sprinkler-generated storm-
water hydraulics of both porous and nonporous pavement facilities. Sprinkler
application rates ranged from 0.4 to 1.7 inches per hour. The favorable simulation
results obtained hi this study suggest that PORPAV can be used to assess the relative
hydraulic performance of pavement facilities available for urban runoff control. The
option of using a drain pipe for the base layer discharge has not been evaluated. A
future study should be conducted at an existing pavement facility utilizing a collection
drain system to assess the ability of PORPAV to simulate such a control strategy.
250
-------
g
f/l
cfi
251
-------
2* '-if) 99 30 tac 12$ me ie<» i%» ze«
ELPPSED TCME (minufss)
FT5. / cLsiMULPTED VS. OBSERVED HYDftOGROPHS FOR 3/5/S2.
9 29 U0 59 89 199. 129 149 169 189 299
ELPPSED TIME
-------
OO
i«0i 39SHHOSIO
253
-------
REFERENCES
1. Biggers, D. J., J. P. Hartigan, Jr. and H. A. Bonuccelli, Urban Best Management
Practices (BMP's): Transition from Single-Purpose to Multipurpose Stormwater
Management. Conference Paper, International Symposium on Urban Storm
Runoff, Univ. of Kentucky, Lexington, Kentucky - July 28-31, 1980.
2. Diniz, E. V. Porous Pavement Phase I - Design and Operational Criteria,
EPA-600/2-80-135, May 1980.
3. . Storm Water Management Model Supplement to the User's Manual, EPA
Project No. CR-805664, March 1981.
4. Heaney, J. P., W. C. Huber, M. A. Medina, Jr., M. P. Murphy, S. J. Nix and S. M.
Hasan. Nationwide Evaluation of Combined Sewer Overflows and Urban
Stormwater Discharges, Volume II: Cost Assessment and Impacts, EPA-600/
2-77-064, March 1977.
5. Israelson, O. W. and V. E. Hansen, Irrigation Principles and Practices, 3rd
Edition, John Wiley and Sons, Inc., New York, N.Y., 1962.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
254
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PLANNING AND IMPLEMENTATION OF REGIONAL STORMWATER
MANAGEMENT FACILITIES IN MONTGOMERY COUNTY, MARYLAND
JANUARY 1983
John M. Crouse, P.E.,1 Vincent H. Berg, P.E.,2 and Linda J.D. Mitchell3
I. INTRODUCTION
Montgomery County, Maryland, is located to the north and the west of
Washington, D.C. The County is geologically located just above the fall
line between the Piedmont Plateau and the Coastal Plain. The County is
characterized by gently rolling topography with steep slopes adjacent to
the major stream valleys. Most of the major streams originate in the
County and drain into the Potomac River. The watersheds generally range in
size from 20 square miles to approximately 130 square miles. The County
contains approximately 500 square miles.
Being adjacent to the Nation's Capital, the County has experienced a
major growth in population and development over the last 30 years. The
population in 1950 was approximately 160,000 and today it is approximately
600,000. The majority of the population is concentrated along the major
transportation corridors extending out like spokes of a wheel from Washing-
ton, D.C. These corridors do not follow watershed boundaries, but extend
across several watersheds as they radiate out from the District of Columbia.
Each year, approximately 2,000 to 2,500 acres are converted from rural
to urban land use to house the population increase and satisfy demographic
changes. As a result of this urban growth, it is estimated that approxi-
mately 200 miles of the County's 1,015 miles of streams have suffered
deterioration in the form of increased flooding, accelerated channel ero-
sion, and reduced water quality. An additional eight miles are estimated
to be affected each year.
Project Manager, Water Resources Section, Greenhorne & O'Mara,
Incorporated, Riverdale, Maryland.
Senior Environmental Engineer, Water Resources Section, Department of
Environmental Protection, Montgomery County, Maryland.
Former Project Engineer, Water Resources Section, Greenhorne & O'Mara,
Incorporated, Riverdale, Maryland.
255
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II. STORMWATER MANAGEMENT (SWM) PROGRAM DEVELOPMENT
Stormwater management was first required as an outgrowth of sediment
control requirements. In July 1961, the State Attorney General interpreted
the powers and duties of the State Water Pollution Control Commission to
include regulation of sedimentation resulting from land development activi-
ties as an industrial pollutant.
Throughout the late 1960's and early 1970's local jurisdictions and
the State General Assembly adopted legislation requiring sediment control
during land development operations. In 1971, the Maryland Attorney General
made another landmark interpretation which said that the state and local
jurisdictions, under sediment control powers, could require the control of
runoff after development in a manner to prevent off-site erosion.
In July 1971, the Montgomery Soil Conservation District (MSCD) adopted
its first stormwater management policy. This policy required the detention
of stormwater runoff from the two-year storm event on each development
site. The release rate could be no greater than the runoff that would have
left the site prior to development. To achieve these criteria, the major-
ity of the developers used on-site stormwater detention ponds as the
simplest and least expensive means of compliance. However, where the site,
due to size, topography, or the value of the land, did not lend itself to a
surface impoundment, other means have been used, such as rooftop detention,
underground vaults and pipes, infiltration pits, surface storage on parking
lots and pervious parking lots.
The action of the MSCD in requiring on-site detention facilities in
conjunction with new development was a significant step forward in achiev-
ing better control of storm runoff. Requiring developers to plan for
stormwater detention recognizes the public responsibility to regulate the
allowable peak runoff associated with land development. However, reliance
on only this approach to achieve the stormwater management objectives is
viewed as only a partial solution for the following reasons:
1. In many instances, individual development proposals have site con-
ditions which preclude the installation of truly effective on-site
controls. However, until recently, no mechanism existed to permit
a developer to contribute, as an alternative solution, to a more
strategically located facility that could provide a much higher
level of stormwater control and which is more cost effective.
2. In some instances, greater stormwater control is desirable at
particular locations then can be required under existing MSCD
criteria.
3. While certain types of control structures are effective in meeting
present MSCD requirements for on-site controls, they may be highly
undesirable from other standpoints such as public safety or
aesthetics.
256
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4. By themselves, present on-site control requirements are incapable
of handling runoff volume and velocities accompanying storms of
greater intensity than the two-year frequency storm.
5. No reliable mechanism for insuring perpetual maintenance of pri-
vate, on-site facilities exists. Therefore, many facilities fail
to function as designed due to a lack of maintenance.
In addition to the above considerations, a review of stormwater man-
agement plans for on-site facilities, reviewed and approved by the MSCD
during the 12-month period from October 1, 1978, through September 30,
1979, indicated that 78 developments on 1,584 acres would expend over $3.5
million to provide on-site stormwater management.
III. CURRENT PROGRAM DIRECTION
In recognition of the growing problems created by uncontrolled urban
storm runoff and the limitations of the ongoing program of on-site deten-
tion of the two-year frequency storm, the County embarked upon an aggres-
sive program to provide stormwater management protection on a watershed
basis. In May 1973, the stormwater management program was established
within the Montgomery County Department of Environmental Protection (DEP)
to develop and implement a County-wide stormwater management program. The
program consists of two major thrusts, first, the implementation of
remedial projects, and, second, the development of preventive stormwater
management projects on a watershed basis.
A. Remedial Projects
The remedial focus of the County SWM program includes projects to
correct existing problems caused by uncontrolled runoff from previously
developed areas. These projects are designed to help stabilize conditions
in critical deteriorating stream reaches.
B. Preventive Programs - On a Watershed Basis
While the remedial efforts serve to control or eliminate existing
problems, they do little to fulfill the need for comprehensive, long-range
stormwater management. Experience has taught us that controls for storm
runoff never realize the optimum potential until we consider the watershed
as a whole and evaluate the effects that proposed land use changes will
have on the quantity of storm flows throughout the watershed. In an effort
to fulfill this need, Montgomery County has embarked upon an ambitious pro-
gram of planning stormwater mangement on a watershed basis.
In 1973, the County Council authorized funds for consultant studies of
three major watersheds within the County. Several common conclusions
emerged from the three studies:
1. Control of runoff should be accomplished near the source either on
each development site, or near the site where several individual
developments could share one facility.
257
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2. The level of control should be expanded to include not only the
2-year storm, but also the 10-year storm, and, where appropriate,
up to the 100-year storm.
3. Needs for non-point source pollution control should be evaluated
and appropriate controls implemented.
These studies also indicated that stormwater management controls (pri-
marily detention impoundments) were most effective when located in or near
the headwaters. Conversely, detention structures placed on tributary sub-
watersheds near the mouth of the watershed had little benefit and could
actually reinforce peak flows due to timing of the release of the detention
structure to coincide with the peak flow of the main stream. For this rea-
son it has become evident that the watershed must be considered as a whole
when planning an effective program.
As a result, the on-site stormwater management program has undergone
several changes. The major change is to allow a developer the option of
contributing towards the costs of a central (public) facility when an on-
site facility is deemed less appropriate than a central facility. This
approach allows the developer more flexibility in designing his proposed
development and enhances the County's ability to pool resources from
several developments for a more cost-effective solution, while providing
the County with the flexibility in selecting the best sites for central
stormwater management facilities.
IV. STORMWATER MANAGEMENT ORDINANCE
The culmination of these long years spent in developing the County's
SWM program came on March 3, 1980, with the signing of the new County Code
amendment, which became effective on June 2, 1980. The Ordinance assigned
to Department of Environmental Protection (DEP) the responsibility of coor-
dinating SWM in the County.
A. Legislative Intent
1. All developers are intended to be held responsible for the impacts
of storm runoff created by their development. This has been
accomplished by requiring the installation of on-site detention on
all new development or, in the event the on-site requirement is
waived, through the payment of a "contribution" or fee not greater
than the cost of on-site SWM.
2. The contribution structure is such that lighter-density develop-
ment is rewarded. The Ordinance provides for the collection of
SWM fees based on typical impervious areas and storage quantities
required for excess runoff rates, which are proportionately lower
for less dense development. In fact, construction of single-
family residences on lots of two acres or more are completely
exempt from the provisions of the Ordinance.
258
-------
3. The planning and building of small, on-site structures is discour-
aged. Many of these on-site detention structures have proven to
be relatively expensive to build, and most take up usable land
area. Most of these structures have been transferred to Home-
owners Associations basically uninterested and incapable of proper
maintenance, and consequently they have not received the required
maintenance.
4. The Ordinance provides for DEP to develop operational plans for
centralized SWM structures to be placed in strategic locations.
It also provides for County participation to assist developers of
strategic sites to design and build regional structures with
greater than required storm runoff controls.
5. To assure fulfillment of SWM controls within a watershed with the
onset of development in a given watershed, a program for construc-
tion of public SWM facilities has also been implemented through
the Capital Improvement Program (CIP).
6. The Ordinance provides for the coordination of proposals for
potential and needed central SWM sites to be incorporated into
updated versions of master planning documents.
B. Regional Stormwater Management
The new legislation, while encouraging SWM on all developments, relies
heavily on the use of centralized SWM facilities, each of which serves a
number of developments and possibly provides multi-use opportunities for
the community. The SWM legislation has had a marked effect on reducing the
number of small on-site SWM structures. Under the County's stormwater
management ordinance small on-site structures can be waived, and larger
centralized SWM structures can be built, either through the County's CIP
Program or through developer-constructed SWM projects with County partici-
pation. This combination system of regional and on-site SWM structures is
most effective when SWM facilities are strategically placed in watersheds
which will have the greatest benefit for the environment as well as the
community.
When development pressure is increasing within a major subwatershed
the Department of Environmental Protection can conduct a detailed study of
a subwatershed utilizing CIP funds under the Preliminary Stormwater Manage-
ment Investigation Project. The major purpose of these studies is to
determine the stategic location of regional stormwater management facili-
ties and to develop a detailed operational plan for the subwatershed. The
subwatershed studies will generally be for areas of two to four square
miles.
To date, five of these studies have been completed and two additional
studies are now being conducted. The Cabin Branch study is typical of
these preliminary stormwater management studies.
259
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V. CASE STUDY - CABIN BRANCH
A. Introduction
Cabin Branch is a tributary of Great Seneca Creek in the Potomac River
basin. Cabin Branch is located on the north side of Gaithersburg, the
second largest city in Montgomery County. The location of the study area
is shown on Figure 1. The drainage area of the studied portion of Cabin
Branch is approximately 4-1/4 square miles.
The Gaithersburg area has been and is expected to be an area of high
growth in the County. The effects of such growth have been partially con-
trolled by sediment control and required on-site stormwater management
facilities.
The Montgomery County Department of Environmental Protection con-
tracted with the consulting firm of Greenhorne & O'Mara, Incorporated, to
perform a preliminary investigation of stormwater management, flood con-
trol, and erosion control requirements for the existing and projected
conditions of the Upper Cabin Branch watershed. The purpose of the study
was to determine the larger-scale effects of on-site SWM facilities on the
receiving stream, to evaluate and locate regional SWM facilities, and to
evaluate the impact of multiplefrequency control on stream discharges.
MINCI«IOR*riCO.
Figure 1. Vicinity Map
260
-------
Excerpts of the report on the investigation presented in this paper
illustrate the process of analyzing watersheds and locating regional storm-
water management facilities.
B. Data Acquisition
Extensive data from such County agencies as the Office of Planning and
Capital Programming and Department of Transportation along with information
from the Montgomery Soil Conservation District, the Maryland-National Capi-
tal Park and Planning Commission, the Washington Suburban Sanitary Commis-
sion, and the Federal Emergency Management Agency was assembled. This
information included proposed capital improvements, bridge and culvert
crossings, hydrologic soil groups, existing stormwater management facili-
ties, master plans, flood plain delineation, and utility locations. Other
data such as aerial photography taken at various periods, tax maps, topo-
graphic maps, and historical sites atlases proved valuable in developing
predeveloped land use (used as baseline data), existing land use, and pro-
jected land use mapping. The information obtained from these data sources
was checked with the field conditions, and modifications or additions to
the data were made where necessary.
C. Methodology
1. Hydrology model
The hydrologic analysis of the watershed was accomplished by utilizing
the Soil Conservation Service Technical Release Number 20 Computer Model.
The hydrologic condition of the soils was taken from the SCS Soil Survey
for Montgomery County. Cover conditions were determined for predeveloped
(circa 1942),.existing, and projected land use conditions through the data
acquisition process previously described.
The Cabin Branch study area was approximately one percent developed in
the early 1940's, consisting mostly of farmhouses and farmsteads. Approxi-
mately seventy percent of the area was in cultivation, approximately twenty
percent was forested, and the rest of the watershed was pasture or open
space.
Currently, the watershed is undergoing rapid residential development,
generally of high density. Approximately fifty percent of the study area
is now developed. About twenty-five percent is still in cultivation. Much
of the stream valley of Cabin Branch contains open space.
Approximately eighty percent of the study area is projected to be
ultimately developed. The remainder is zoned to be park land, golf course,
and other open space. The area in the vicinity of the airpark is planned
to be developed as commercial/light industrial sites. The extreme north-
east corner of the study area will be developed as single-family
residential.
261
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2. Subarea delineation criteria
In order to provide stream flow estimates at several points along
Cabin Branch, the watershed was divided into subareas according to runoff
flow paths and velocities and points of discharge into the stream. Drain-
age area divides were first drawn between direct tributaries to Cabin
Branch which were shown on the USGS 7 1/2-minute quadrangles- as perennial
streams. If forks or tributaries of the direct tributaries were also indi-
cated as perennial streams, the subdivides between them were then delineat-
ed. If very dissimilar land uses were encompassed in a subarea, then the
area was further subdivided. Discharge points used in other studies and
such landmarks as major road crossings were also used to separate the dif-
ferent subareas, as well as major existing SWM facilities or potential
sites for facilities. No subarea was to be greater than fifteen percent of
the study area.
The final analysis for Cabin Branch was performed using eighteen basic
drainage subareas as shown on Figure 2. These subareas were further subdi-
vided as necessary to account for additional road crossings and significant
SWM facilities in existence. A schematic diagram of the study area hydro-
logy is shown in Figure 3.
3. Key point selection
Seven sites of interest called key points were located along the main
stem of the study stream to serve as convenient points at which to compare
the predeveloped, existing, and projected discharges. Easily recoverable
locations such as road crossings and confluences of the main stem and major
tributaries were designated as key points as well as other strategic loca-
tions such as areas where land use has undergone or will undergo signifi-
cant change.
4. Existing SWM facility screening criteria
Data on the existing SWM facilities were compiled from the previously
mentioned data files and field reconnaissance. An extensive amount of
information was available because the watershed has undergone urbanization
since the inception of the sediment control and SWM regulations and the
requirement for submission of plans and computations. Screening criteria
were developed to remove from the investigation certain SWM facilities that
were believed to have little impact for the scale of the investigation.
Dry and wet ponds were considered in the hydrologic analysis. Other
SWM measures (such as rooftop detention, gravel trenches, and seepage pits)
found in the watershed were not of sufficient size to achieve significant
stormwater management.
It is interesting to note that the two SWM ponds in subarea 10 are in
a subdivision currently under construction and the ponds are being built
under the County's participation program. Wet and dry ponds were consider-
ed not significant and were excluded from the hydrologic analysis of the
262
-------
3) Sutwren Number
Kcu Point
Are* = 2,7/3 Ac.
L
Limif of
Figure 2. Drainage Areas and Subareas
263
-------
CABIN BRANCH
PACUJTV oocc «ND DRAINAGE
*m*CAcnn) OK SUBAREA
ftoum coot
OK CULVBUT CROSSING
/WJALV^eO POK HYDHOLO9IC
Figure 3. Schematic Diagram of Hydrology
watershed if the pond drainage area was less than five percent of the sub-
area in which the facility was located and less than five-tenths percent of
the entire study area. If the drainage areas for the ponds which were
screened out by these criteria summed to more than five percent of the sub-
area in which the ponds were located or to more than one percent of the
total study area, the largest excluded structure was reincluded. An
excluded facility may be assumed to have little impact on the watershed as
a whole but does provide some protection against erosion and flooding in
the immediate downstream vicinity. Eighteen ponds in the Cabin Branch
study area were determined to be significant; eight smaller ponds were
dropped from consideration.
5. Peak discharge determination
Estimates of the peak discharges in the watershed for the 2-, 10-, and
100-year storms for predeveloped, existing, and projected conditions were
produced using the SCS TR-20 computer model with the input data previously
described and rainfall from the U.S. Weather Bureau Technical Paper Number
40. The peak discharges are summarized in Table 1 for key points along the
stream.
264
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Table 1. Peak Discharges at Key Points
Key 2-Year 10-Year 100-Year
Point* Predev. Ex. Proj. Predev. Ex. Proj. Predev. Ex. Proj.
A 154 219 326 495 609 763 955 1110 1297
B 210 304 364 654 811 905 1246 1455 1586
C 331 626 837 1030 1542 1906 1976 2683 3205
D 420 720 923 1252 1666 2184 2479 3221 3910
E 440 718 866 1209 1786 2246 2619 3616 4320
F 482 771 920 1281 1916 2373 2774 3819 4506
G 500 793 941 1313 1918 2343 2837 3661 4230
*Key Point locations are as follows:
A - downstream of subareas, 1,2, and 3, in headwaters
B - downstream of subareas, 1,2,3, and 4, north of Montgomery County
Airpark, near Green Farm
C - downstream of subareas, 1-9, at Snouffers School Road
D - downstream of subareas, 1-12, at Goshen Road
E - downstream of subareas, 1-16
F - downstream limit of subarea 17, at Montgomery Village Avenue
G - downstream limit of study area
6. Runoff increase criteria
To determine sites where SWM basins may be most beneficial, the per-
cent change in discharge from existing to projected conditions was examined
for each key point. Subareas with relatively high increases in discharge
were considered for SWM facility sites.
7. Site considerations
The percent increase analysis indicated that key points A and C should
be explored for SWM sites. A significant increase in peak discharge from
existing to projected conditions was also shown at key point D, but no fea-
sible basin sites were apparent in that area. Five sites were analyzed:
site 1 was located at key point A; sites 2, 3, and 5 were situated upstream
of key point C on tributaries to Cabin Branch; and site 4 was at a location
for which a preliminary design had been completed for another study.
Potential sites were evaluated in terms of the downstream land uses,
the timing of the peak discharge relative to the times of downstream peaks,
and the natural storage available at the site without unduly infringing on
the surrounding land uses. Soils in the immediate vicinity of the sites
were examined for suitability as embankment material and for reservoir
lining.
Factors other than land use, soil type, hydrologic response, and
hydrologic performance serve an important role in SWM facility location
study. Acquisition of property, construction cost, and utility conflicts
are three such factors with potentially high impacts. The impacts of these
factors for the five proposed sites were evalutated and are indicated in
Table 2.
265
-------
Table 2. SWM Site Considerations
Factor
Area Property Owners
Construction Cost
Project Area
Access Right-of-Way
Utilities
Specifics
Comments
Site 1
MNCP&PC Hadley Farms Dairy, Inc. Favorable
and First Citizens Development
Corp. et al
$111,300
11.18 acres (MNCP&PC); 2.68 acres
(Hadley); 1.47 acres (First Citiz
0.35 acres (MNCP&PC);
1.29 acres (First Citiz.)
8-inch, 10-inch and 12-inch
sanitary sewers (1450 L.F.)
Site 2
Area Property Owners H.J. Bobys, et al
Construction Cost
Project Area
Access Right-of-Way
Utilities
Area Property Owners
Construction Cost
Project Area
Access Right-of-Way
Utilities
$92,000
11.03 acres
0.35 acre
Apparently none
Site 3
Montgomery County Airpark, Inc.
and A.W. & E. Stang
$83,000
11.49 acres (MCA); 0.80 acres
Stang
0.41 acres (Stang)
Apparently none
Site 4
Area Property Owners C.J. and I.B. Savage
Construction Cost unknown
Project Area
Access Right-of-Way
Utilities
Area Property Owners
Construction Cost
Project Area
Access Right-of-Way
Utilities
Moderate
.)
Requires relocation
or protective measures
unknown
unknown
10-inch sanitary sewer
Site 5
MNCP&PC, J.E. Richardson Trus.,
and Montgomery Co. Revenue Auth.
$93,800
8.46 acres (MNCP&PC); 3.22 acres
(Richardson); 1.30 acres (MCRA)
0.06 acre (J.E. Richardson Trus.)
8-inch sanitary sewer (1920 L.F.)
Favorable if developed
by owner
Moderate
Very favorable
Favorable if developed
by owner
Moderate
Very favorable
Favorable if developed
by owner
Pond privately pro-
posed
Requires relocation
or protective measures
Favorable if developed
by owner
Moderate
Requires relocation
or protective measures
266
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8. Proposed pond development
Preliminary designs for sites 1 and 2 were based on providing reduc-
tion of the 2-, 10-, and 100-year storms from the projected peak levels to
approximately the lesser of predeveloped or existing levels. The basin at
site 3 was sized based on the intents of the potential developer of the
area as discussed with the engineer retained by the developer. Site 4 was
based on file data as obtained from the Montgomery Soil Conservation Dis-
trict. Site 5 design was based on providing 2- and 100-year control to the
predeveloped conditions and control to near-predeveloped conditions for the
10-year storm.
Storage requirements at a site were estimated by the methodology pres-
ented in the SCS Technical Release number 55, "Urban Hydrology for Small
Watersheds." Initial peak discharge reduction was typically accomplished
with a low flow orifice/riser/barrel arrangement, with computations based
on the Maryland SCS publication, "Standards and Specifications for Soil
Erosion and Sediment Control in Developing Areas." The size and location
of the outlet works were adjusted as necessary to attain the desired goals
based on the initial design as suggested by the above references.
9. Scenario development and testing
Upon obtaining satisfactory peak discharge reductions for the individ-
ual sites by utilizing the TR 20 program, the watershed hydrology model for
the projected land use conditions was modified to reflect the individual
and combinations of individual proposed sites. Ten scenarios were develop-
ed to determine the effects of the five proposed SWM sites. The scenarios
and the sites comprising the scenarios were:
Scenario
Scenario
Scenario
Scenario
Scenario
Scenario
Scenario
Scenario
Scenario
1
2
3
4
5
6
7
8
9
- SWM
- SWM
- SWM
- SWM
- SWM
- SWM
- SWM
- SWM
- SWM
Site
Site
Site
Site
Site
Sites
Sites
Sites
Sites
1
2
3
4
5
1
1
2
1
Only
Only
Only
Only
Only
and
and
and
, 2,
2
3
3
and
Scenario 10 - SWM Sites 1, 3, and 5
The discharge values at the key points for the projected land uses are
shown in Table 3 for scenarios 1 to 5. Table 4 presents the percent change
in estimated peak discharges from predeveloped, existing, and projected
conditions to the proposed conditions at key points for selected scenarios.
The more desirable scenarios produce a smaller percent change in discharges
for a greater number of key points.
267
-------
Table 3. Key Point Discharges for Scenarios 1 to 5
Key Point Existing Structures Only
Predev.
Two-year storm
A
B
C
D
E
F
6
154
210
331
420
440
482
500
Ex.
219
304
626
720
718
771
793
Ten-year storm
A
B
C
D
E
F
G
495
654
1030
1252
1209
1281
1313
One hundred-year storm
A
B
C
D
E
F
G
326
364
837
923
866
920
941
609
811
1542
1666
1786
1916
1918
763
905
1906
2184
2246
2373
2343
955 1110 1297
1246 1455 1586
1976 2683 3205
2479 3221 3910
2619 3616 4320
2774 3819 4506
2837 3661 4230
Proposed Land Use Conditions,
with SWM Scenario Number:
1
Basin
1 only
2
Basin
2 only
155**
185
701
786
763
821
844
321
357
778
860
818
870
890
507** 755
599 889
1501 1696
1682 1908
1822 1989
1945 2093
1954 2078
963** 1287
1180 1560
2496 2907
3213 3544
3582 3916
3747 4004
3626 3800
3
Basin
3 only
321
357
716
807
782
832
853
755
889
1666
1907
1991
2086
2074
1287
1560
2935
3573
3953
4042
3840
4
Basin
4 only
321
357
823
905
807
857
878
755
889
1875
2130
2060
2167
2148
1287
1560
3151
3814
4174
4301
4046
5
Basin
5 only
321
357
596
704
714
766
789
755
889
1451
1670
1790
1897
1900
1287
1650
2593
3245
3565
3703
3557
*At key points above the proposed SWM sites, the listed peak discharges
with and without the proposed SWM may differ slightly due to the use of a
larger time increment in modeling the proposed SWM Scenarios.
**0utflow from proposed SWM Basin 1.
268
-------
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269
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D. Conclusions and Recommendation
1. Conclusions
a. From predeveloped to existing conditions, discharges at key
points in the Cabin Branch watershed have increased as much as
89 percent for the 2-year frequency, 50 percent for the 10-
year frequency, and 38 percent for the 100-year frequency.
b. From existing to projected conditions, discharges have been
estimated to increase as much as 34 percent, 31 percent, and
21 percent for the same frequencies.
c. The largest percent increases generally occur in the upper
portion of the watershed.
d. The Snouffers School Road and Goshen Road crossings of the
main stem have a significant impact on the peak of the more
frequent discharges.
e. Proposed stormwater management facilities located in the upper
portion of the watershed generally reduce the peak discharges
throughout the main stem to the downstream limit of the study.
f. Scenario 7 provides control of the 2-, 10-, and 100-year
frequency discharges to existing conditions from the proposed
facilities to the watershed outfall and hydraulically out-
performs the other scenarios.
g. Scenario 5 provides more control for the 2-year frequency than
Scenario 1. The control is approximately equal for the 10-
and 100-year frequencies. However, Scenario 1 protects an
additional reach of about one-half mile of Cabin Branch as
compared to Scenario 5.
h. Scenario 10 provides control to a point about half-way between
existing conditions and predeveloped conditions for 2-, 10-
and 100-year frequencies for key points downstream of key
point A.
i. Discharge control to at least the existing conditions is
desirable for Cabin Branch to prevent higher velocities and
erosion potential.
2. Recommendation
It is recommended that three SWM facilities be designed and con-
structed in the Cabin Branch watershed. The facilities would be located at
sites 1, 3, and 5. Such a combination of facilities would control the 2-,
10-, and 100-year discharges to a point about half-way between existing and
predeveloped conditions for all key points downstream of key point A.
270
-------
If for any reason only one SWM facility can be constructed in Cabin
Branch, the facility should be located at site 1.
E. Epilog
The development process is dynamic and the implementation of a
comprehensive stormwater management system must be flexible. The Cabin
Branch study recommended construction of three regional facilities and one
regional facility was being designed while the study was being conducted.
To date two regional SWM facilities have been constructed (10A & Site 3),
Site 5 is about to be designed as a County CIP project and Site 1 is being
planned as on-site controls.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
271
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STORM SEWER OPTIMUM DESIGN
DONG HOANG M-Sc.P-E.
INTRODUCTION.
One of the main challenge the engineer is facing is to insure
that the design is technically sound and competitive in terms
of costs. In other words, the optimization of a design is one of
his major concerns.The optimization is becoming urgent and cri-
tical in the today world where the resources are scarce.
This paper presents the highlights of a computer model called
the STORM SEWER OPTIMUM DESIGN whose objectives are to provide
the least expensive design.
To evaluate the water runoff for storm sewer design the rational
formula < Q=CiA ) was the most often used.
In order to use the formula a set of rainfall intensity—duration
-frequency < IDF ) curves relating the rainfall intensity to the
time and return period should be developed.
The IDF curves are constructed based on the extreme values of
the partial duration series and the rainfall record length*con-
sequently they yield conservative values/in term of peak dis-
charge rate/ when compared to the actual storms.
The IDF curves shape corresponds to the immediate peak situation
which unlikely happens in reality. The shape of the IDF curves
has also the effect of reducing the flow. As matter of fact/more
water is absorbed by the infiltration when the overland water is
flowing at peak over a soil whose infiltration potential is re-
latively high at the beginning of the rain.
Besides, the runoff coefficient*C» is too simplistic to reflect a
very complicated situation.
In general/the method of evaluating the overland flow with the
rational formula is too simple to reasonably represent the real
s i tuat ion.
272
-------
Finally, the design process, including the cost computation, is la-
borious to the extent that it discourages the effort to explore
all the situations in order to arrive to the optimum design.
Considering all the above facts,the ideal design method should:
1. be capable of making use of the real rainfall instead of eva-
luating it from the IDF curves
2. combine the engineering and economic aspects simultaneously
3. use method of computation which results in realistic estima-
tion of the overland flow and the pipe flow
4. be capable of exploring all the situations quickly to arrive
to the optimum design.
The STORM SEWER DESIGN OPTIMIZATION is developed according to
the four points exposed above.
The model is composed of 2 parts. l.PART ONE : HYDROGRAPH COMPU-
TATION 2. PART TWO : DESIGN.
PART ONE : HYDROGRAPH COMPUTATION
Once the sewer system is laid out, it is necessary to compute
the runoff from each subcatchment tributary to the correspon-
ding sewer line.The runoff is computed for each rainfall in-
crement in the form of hydrograph based on the infiltration,
the imperviousness condition,the ground slope,the Manning's
coefficient of the subcatchment and the? shape, slope, length,
Manning's coefficient of the gutter conveying the runoff to
the manhole.
In the case of designing the extension of an existing sewer sys-
tem the model computes the combined hydrographs which are gene-
rated by the combination of the hydrographs of the upstream
basins and the hydrographs of the area whose seu»er system is to
be designed.
Another task performed by the model is to create the node and
line numbers system.
PART TWO : DESIGN
Using the hydrographs just created, the second part of the model
will compute the design-flows.
273
-------
Given the ground profile,t he minimum cover-, the maximum invert
elevations, the underground constraints, the minimum pipe size S<
slope.- the sewer construction elements prices, the design objec-
tives are to find out the opt; muni s 3 ope, the pipe size, the- pipe
class &( bedding types corresponding to the least sewer cost to
carry the design flow. The model makes sure that the design
flow at the current time step is the greatest design flow.
The design process of a line consists of varying the slope by a
constant amount corresponding to the fixed drop increment a num-
ber of times consistent with the drop availab 1e. The drop avail-
able is the difference between the downstream invert elevation
of the line (if a minimum slope is passed through its upstream
invert) and its maximum allowable downstream invert elevation.
For each slope a diameter is calculated to carry the design
flow .Corresponding to the computed diameter/two immediate
surrounding commmercial pipe diameters are selected.With each
commercial pipe selected recompute the slope to carry the design
flow. This slope should create the downstream invert elevation
falling in between two values: one is the upper limit (if speci-
fied), the other is the maximum allowable downstream invert ele-
vation. If this condition is not met/ using the slope which makes
the downstream invert elevation match with the maximum allowable
one. Under either cireumstances, onee the commercial pipe diameter
and the corresponding slope to carry the design flow are found*
without conflicting the underground constraints»the construction
cost of the line is computed. By comparison the cost correspon-
ding to two commercial pipe diameters>the selection of the com-
mercial pipe diameter corresponding to the least cost can be
mad e.
The same process is repeated with a different slope which is
equal to the previous slope plus the slope increment corres-
ponding to the drop increment. The least cost between the pre-
vious and the actual and the associated, elements are saved.
After varying the slopes a number of times/the optimum slope
and diameter can be found to carry the design flow without
conflicting the underground constraints.
The model use the Manning formula for design. For a time step/ the
model computes the flow out and the flow stored in the line by
solving for the depth such that the change in the storage is
equal to the difference in the flow in and flow out. The Newton-
Raphson technique is again used to find the water depth and
flow.
The model computes the transition width/the earth load/ the traf-
fic load/ if any/ to figure outvthe type of pipe and the type of
bedding. Comp1ying with the design procedure in force/and the
unit prices list/the model computes the sewer construction cost.
274
-------
Once the design is done, it is advisable to check the behaviour
of the system using the SWMM model, or any similar model with
the same storm used for design.Flows adjustment factors are
provided to adjust the design flows and consequent1y,the slope
and pipe diameter, in any desired proportion to the maximum
flows generated by the checking model (SWMM or any similar
mode Is).
MODEL APPLICATION
The basin served by the sewer system to be designed covers an
area of 87.72 Ac with the imperviousness factor equal to 397.,
and the average ground slope of O. O15. The Manning's factor*
surface storage and Morton' coefficients are as follows:
Manning factor Surface storage
Imper- Per-
vious vious
area area
Horton coefficients
Imper-
vious
area
IN
Per-
vious
area
IN
Max imum
rate
IN/HR
Infi1trati on
Minimum Decay
rate rate
IN/HR I/SEC
Max imum
allowed
IN
O13
. 025
. O62
184
3. OO
. 52 . 00115 12. 00
The total length of the system is 67OO Ft.Other informations
concerning the sewer system can be found in the output listings*
The rainfall used for design is from the 1O—year recurrency IDF
curves of the City of Portland.Rainfal1 intensities are recorded
for every 5-minutes-Only the first 1O rainfall steps are used
for design. The rainfall is labelled: 1OIDF6-OO-5. It stands for
1O year recurrency storm*6 hours duration*immediate peak & 5
minutes interval.
For comparision purpose (with the rational method) synthetic
rainfall is used instead of real rainfall. The output listings
are self explanatory.
THE OPTIMUM DESIGN METHOD VERSUS THE RATIONAL METHOD
To avoid spending time to find the slopes to be used in the
storm sewer design with the Rational Method*the optimum slopes
system created by the Optimum Design Method is used.
*See Figure 1, Tables 1-3.
275
-------
By doing this/a significant amount of
design time with the Rational Method.
time is saved from the
In reality.it is impossible that the optimum slopes system can
be found in the practice of the Rational Method because the
design process/inc1uding the cost computation/is laborious to
the extent that it discourages the effort of exhausting all
the situation to reach the optimum design.
LEGEND
JK32O - MANMCX.C NUMKft • J1OZO
Km - scvuoi Lint Nuuae* • 2020
K>,t - BHANO4 OAOCft • IO. M1CAAACHY
Figure 1. Storm Sewer System
276
-------
Table 2. Elemental Quantity of the Sewer System
DIAMETER LENGTH
CLASS I CLASS 3 CLASS II CLASS III CLASS IV CLASS V
(FT) (FT) (FT) (FT) (FT)
8
IO
12
15
18
24
27
30
36
200.
750.
O.
O
O
O.
O
O.
O
0.
0
O
O
0
O.
O
0
0
0.
O.
4OO
&5O
O
O
0
O
0
O.
0.
750.
75O.
aoo.
O.
O.
0.
0
0
0
0
0
250
150
200.
1 5OO
3OO
0
0
O
0
O
O
O
0.
O
PAVEMENT PAVEMENT EXCAVATION DACKFILL
BASE CBANOLAH
VD2 Y03 VD3 VD3
3043
2? 4 52
BEDD1NC
D-c A
V03 V03
FOUNDATION
STADIL1ZATION
VD3
MANHOLE
3FT-SECTN
EA
The C—factor of the Rational Formula associated with the combi-
ned area is a weighted factor between 2 constituant areas (right
& left) with 2 associated imperviousness factors.Examp1e:the
area served by manhole 3036 is equal to 1. 52 Ac = 83 •«- . 69
The C-factor of area 1. 52 Ac is:
. 83X. 35
69X. 4O
-=. 37
1. 5;
For comparisi on purpose,the sewer system characteristics desig-
ned by the Rational Method and the Optimum Design Method are
checked by the SWMM model with the same rainfall 1OIDF6-OO-5
used for design.
CONCLUSION
1. The Optimum Design Method, based on the principle of the
least sewer construction cost, produces the optimum sewer
system characteristics which is never realized in the prac-
tice of storm sewer design with the Rational Method
2. The Optimum Design Method can make the sewer system fully
used. Meanwh i le» even using the optimum slopes system/ the Ra-
tional Method yields a sewer system which is over designed
about 67X (average percentage of flow occupancy is 33%)
278
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Table 1. Sewer System Characteristics and Sewer Cost
LINE
NUMBER
DO36
2O36
1036
2034
1034
2032
1032
5O3O
403O
3O3O
SO3O
103O
4O24
3O24
2O24
1O24
3028
2028
1O28
3038
2O38
1O38
2O26
1O26
2O22
1O22
302O
2020
1O2O
PIPE PIPE
DIAMETER SLOPE
(INI (FT/FT)
IO O OO264
12 0 OO933
15 O. OO391
12. O. 002OO
15 O. OO4O9
18 O. O0817
IB. O. 01271
12 O. OO536
15 O. OO572
15 O. Ol 1O1
15 O. O1927
18. O. OO93O
24. O. OO872
27 O. OO678
30 O. OO339
3O O. OO633
10 0. OI480
12 O. O1972
13. O. O1332
8. 0. O1482
IO O O1424
12. O. Oil 36
18. O. OI488
18. O. 02786
3O. O. O1339
36. O. OO776
3O. O. O1373
3O. O. O1372
3O. 0. O17OO
INVERT PIPE TRENCH DESIGN VELOCITY
ELEVATION LENCTH WIDTH FLOW FLOW-FULL
(FT) (FTI (FT) (CFS) (FPS)
14821 3OO 00 2.5 1 13 206
146.34 2OO OO 25 3 44 4.38
145. 16 2OO OO 2. 5 4 97 4 05
BRANCH NUMBER 36 COST - 2O963
144. 5O 25O. OO 2. 5 I. 59 2. O3
143.07 35000 2.5 4.13 3.37
BRANCH NUMBER 34 COST - 221OO
141.43 2OO.OO 2.9 9. 5O 5.37
138.26 250. OO 2.9 11.84 6. 7O
BRANCH NUMBER 32 COST - 21O94.
149.93 20O OO 2.5 2 61 3.32
148. 78 2OO OO 2. 5 4 89 3. 98
146 O3 25O. OO 2. 3 6. 7B 5 52
142.18 2OO OO 2.5 8.97 7.31
140.28 200.00 2.9 IO. 24 5.79
BRANCH NUMBER 3O COST - 38O23.
136.93 ISO. OO 3.3 21.13 6.72
135. 59 2OO OO 3. 8 25. 3O 6. 41
133. 97 3OO. OO 4. 1 3O. 12 6. 13
132.71 2OO.OO 4.1 32.63 6 64
BRANCH NUMBER 24 COST - 66270
151.04 2OO.OO 23 2 67 4.89
146. 11 23O OO 2 3 5. OO 6. 37
143.41 20O.OO 25 7 31 6 12
BRANCH NUMBER 28 COST - 2O796
149.04 2OO.OO 23 1.47 4.21
143.48 25O. OO 25 2.61 4.79
142.64 23O OO 25 3. 8O 4.83
BRANCH NUMBER 38 COST - 21O14
139.66 2OO.OO 29 12.81 7.23
134. Of 2OO.OO 2.9 17.33 9.92
BRANCH NUMBER 26 COST - 17233.
128. 69 3OO. OO 4. 1 47. 46 9. 67
126. 36 3OO. OO 4. 7 38. 73 8. 31
BRANCH NUMBER 22 COST - 33491.
122. 24 3OO. OO 4.1 48. O9 9. 79
119. O9 2OO.OO 41 31.43 IO. 48
113.69 2OO.OO 41 33.48 IO. 89
BRANCH NUMBER 2O COST - 36O81
PIPE TYPE OF SEUER
CLASS BEDDING COST
2 C 7656
II 0 6424
II n 6883
III B 9113
III B 12987
III B 9233.
IV B 11839
I I B 63O5
II B 6856
II B 8371
III B 7181.
Ill B 9110
IV B IOO43.
IV B 15O66
IV B 24623
IV B 16539
2 C 5368
III B 8137
III B 7271
2 C 3305.
2 C 73O2
III B S4O7
III B 8318.
Ill B 8913.
IV B 24313.
IV B 28976.
IV B 23487.
IV B 16O78.
IV B 16316.
SEWER SYSTEM TOTAL COST -
277
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FROM
NODE NUMBER LINE
TO
NODE NUMBER NUMBER
Table 3. Comparison
PIPE DIAMETER
-------
3. The Optimum Design Method can use the real rainfall for
design
4. The Optimum Design Method which calculates the costs of the
sewer lines*sewer branches and the sewer system as a whole
makes the Cost-Benefit Analysis of alternative routes easy
and effective
5. The Optimum Design Method Which computes and lists the ele-
mental quantities regarding the sewer construction makes the
preparation work for bidding accurate and fast
6. The Optimum Design Method is a very effective tool for plan-
ning as well
7. The Optimum Design Method with 2 incorporated features :
1. the automatic way to number manholes and sewer lines 2. the
capability to design the extension of an existing sewer sys-
tem/makes the preparation work less extensive and the storm
sewer design more flexible
B. The Optimum Design Method is very fast and effective. It can
be handled by people whose engineering knowledge is not nec-
cessarily as high as the knowledge of the people who use the
Rational Method for storm sewer design.
The work described in this paper was not funded by the U.S. Environmental
Protection Agency. The contents do not necessarily reflect the views of the
Agency and no official endorsement should be inferred.
280
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ATTENDEES
USERS GROUP MEETING
January 27-28, 1983
Thomas Barnwell, Jr.
EPA
Athens, GA
Kenneth G. Eggert
Simons, Li & Associates
Fort Collins, CO
Lars Bengtsson
McM as t er Uni ver s i ty
Hamilton, Ontario
Vincent Berg
Montgomery County
Rockville, MD
Patrick Beron
Ecole Polytechnique
Montreal, Quebec
John Capece
University of Florida
Gainesvi lie
Raymond A. Ferrara
Princeton University
Princeton, NJ
David Firmage
Colby College
Waterville, ME
Efi Foufoula
University of Florida
Gainesville
Yvonne Froscher
Miller & Miller
Orlando, FL
Ivan Chou
ESE, Inc.
Gainesville, FL
John M. Grouse
Greenhorne & O'Mara
Riverdale, MD
Robert Frost
University of Florida
Gainesvi lie
Gary Goforth
Espey, Huston and Associates
Austin, TX
Robert Dickinson
University of Florida
Gainesvi lie
Hoang Dong
City of Portland
Portland, OR
Debbie Dunnam
University of Florida
Gainesville
Philip Gronstal
Dallas Water Utilities
Dallas, TX
Brendon M. Harley
Camp, Dresser & McKee
Waltham, MA
Bruce W. Harrington
Maryland Water Resources
Administration, Annapolis, MD
David Dwornik
University of Florida
Gainesville
James P. Heaney
University of Florida
Gainesville
281
-------
Michael Helfrick
Montgomery County Environmental
Protection, Rockville, MD
Wayne C. Huber
University of Florida
Gainesville
Maine Hutchison
Oklahoma Water
Resources Board
Cheri Porter
Miller & Miller
Orlando, FL
Mark Robinson
McMaster University
Hamilton, Ontario
Ian Simmers
Free University
Amsterdam
William James
McMaster University
Hamilton, Ontario
Peter Jaffe
Princeton University
Princeton, NJ
Terrie Lee
University of Florida
Gainesville
Khlifa Maalel
University of Florida
Gainesville
Stanley I. Mast
Howard, Needles, Tammen and
Bergendoff, New York, NY
Ed McBean
University of Waterloo
Waterloo, Ontario
Janusz Niemczynowicz
Lund Institute of Technology
Lund, Sweden
Alexander Padva
Environmental Quality Lab
Port Charlotte, FL
Charles Simon
Nat'l Council for Air & Stream
Improvement, Gainesville, FL
Gary Trott
Wiedeman & Singleton Engineers
Atlanta, GA
William F. Walker
Environmental Engineer
Concord, MA
Flora Wang
Louisiana State University
Baton Rouge, LA
Roger K. Wells
HMM Associates
Raleigh, NC
Stanley Wong
Maryland Water Resources
Administration, Annapolis, MD
Grace Wood
Dames & Moore
Washington, DC
Jy S. Wu
University of North Carolina
Charlotte, NC
282
*U.S. GOVERNMENT PRINTING OFFICE 1963 - 659-095/0745
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