WATER POLLUTION CONTROL RESEARCH SERIES • DAST-1
Complementary-Competitive Aspects
of Water Storage
U.S. DEPARTMENT OF THE INTERIOR • FEDERAL WATER POLLUTION CONTROL ADMINISTRATE
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WATER POLLUTION CONTROL RESEARCH SERIES
The Water Pollution Control Research Reports describe
the results and progress in the control and abatement of
pollution of our Nation's Waters. They provide a central
source of information on the research, development and
demonstration activities of the Federal Water Pollution
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in-house research and grants and contracts with Federal,
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Triplicate tear-out abstract cards are placed inside, the
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is provided on the card for the user's accession nunber and
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Water Pollution Control Research Reports will be distri-
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COMPLEMENTARY-COMPETITIVE ASPECTS OF WATER STORAGE
An Engineering-Economic Approach to Evaluate the Extent
and Magnitude of the Complementary and Competitive Aspects of
Water Storage for Water Quality Control
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
DEPARTMENT OF THE INTERIOR
by
Kenneth D. Kerri
Department of Civil Engineering
Sacramento State College
Sacramento, California
Program Number 16090DEA
December, 1969
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FWPCA Review Notice
This report has been reviewed by the Federal
Water Pollution Control Administration and
approved for publication. Approval does not
signify that the contents necessarily reflect
the views and policies of the Federal Water
Pollution Control Administration.
ii
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ABSTRACT
COMPLEMENTARY-COMPETITIVE ASPECTS OF WATER STORAGE
KEY WORDS; Allocation; Flow Augmentation; Marginal Analysis; Planning;
Reservoir Operation; Simulation; Temperature Control;
Water Pollution; Water Duality
f
Allocation of scarce water for flow augmentation to enhance water quality
and other beneficial uses conflicts with other water demands. An
analytical model is proposed that is capable of allocating water to
competing demands on the basis of economic efficiency. The value of
water is determined from the slopes of the benefit functions for water
uses and an algorithm, based on the theory of marginal analysis,
allocates water after considering the complementary and competitive
uses of available water. Operations strategies may be selected and
revised throughout the demand period regarding the amount of water to
remain in storage, or stored and then released for downstream uses or
downstream diversions. Results predict the frequency and magnitude
of shortages for each beneficial use of water.
Simulation of the hydrologic and economic systems of the proposed Holley
Reservoir in the Willamette Valley in Oregon was used to test the
effectiveness of the proposed analytical model and the results appear
very good. A daily streamflow model and a relationship between reservoir
operation and recreational attendance were developed to produce an
accurate simulation of the basin. Planners, designers, and operations
personnel are provided with a method of allocating water in proposed
and existing systems. This method indicates the value, extent and
magnitude of the complementary and competitive aspects of water storage
for water quality control.
This report was submitted in fulfillment of Project 16090 DEA between
the Federal Water Pollution Control Administration and the Sacramento
State College Foundation.
iii
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TABLE OF CONTENTS
Abstract
Figures
Tables
Section 1.
Section 2.
Section 3.
Section 4.
Section 5.
Section 6.
Section 7.
Section 8.
Section 9.
Section 10.
SUMMARY
Conclusions
Recommendations
INTRODUCTION
Statement of Problem
Scone and Objectives
ANALYTICAL MODEL
Algorithm
Applications of Analytical Model
SIMULATION MODEL
DESIGN OF EXPERIMENT AND SENSITIVITY ANALYSIS
Economic Analysis
Length of Simulation Run
Sensitivity of Benefit Functions
Interest Rates
Method of Steepest Ascent
Operating Rule Curves
RESULTS AND DISCUSSION
Results from Analytical Model
Discussion of Complementary and Competitive Aspects
Water Quality Response Surface
Feasibility of Flow Augmentation for Water Quality
Control
Comparison of Optimum Water equality Objectives with
Actual Standards
Summary
ACKNOWLEDGMENTS
REFERENCES
LIST OF PUBLICATIONS
APPENDICES
I. THEORY OF OPTIMUM ALLOCATION OF WATER
II. DAILY STREAMFLOW SIMULATION
III. RECREATION AND RESERVOIR OPERATION
IV. INPUT DATA
V. FLOW DIAGRAMS AND COMPUTER PROGRAMS
iii
vi
vii
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1
3
5
5
5
9
9
10
13
17
17
17
20
20
22
22
25
25
31
34
37
39
40
43
49
51
53
63
81
95
121
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FIGURES
ISSS.
1. Typical Benefit Function -^
2. Simplified Computer Logic for Hydrologic and Economic Simulation 14
Model
3. Location Map of Calapooia River Basin ^
4. Average Annual Net Benefits from Two-100 Year Simulation Runs 19
5. Initial Attempt and Optimum Operating Rule Curves 24
6« Illustration of Value of Complementary Factors 32
7. Average Annual Net Benefits and STandard Deviations, With and 33
Without Water Quality
8« Annual Losses Due to Water Shortages 35
9. Water Quality Net Benefit Response Surface 36
10. Typical Low Flow Hydrographs 38
vi
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TABLES
Page
1. Summary of Average Annual Net Benefits for 200 Years of 18
Simulation
2. Maximum Average Annual Net Benefit, Structural Input, and 21
Target Output for Different Interest Rates
3. Incremental Dollar Benefits from Uses of Water 27
4. Ranked Sgments of Benefit Functions 28
5. Establishment of Operational Priorities Based on Complementary 29
Uses
6. Frequency Densitv of Water Available for Allocation 30
vii
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SECTION 1
SUMMARY
CONCLUSIONS
1. An analytical model has been developed and tested that is capable
of indicating the extent and magnitude of the complementary and
competitive aspects of water storage for water quality control.
Techniques of marginal analysis are used to analyze the benefit
functions of water uses and allocate scarce water on the basis
of economic efficiency.
2. A daily streamflow simulator has been developed and tested which is
capable of generating daily nonhistoric flow sequences with
statistical properties and hydrographs similar to historical flows.
3. Reservoir recreation attendance has been analyzed and & definite
relationship was developed regarding the influence of reservoir
operation on recreational attendance for the area studied.
4. Results from the simulation of the hydrologic and economic systems
of the basin studied include a response surface showing the maximum
net benefit contours for water quality combinations of dissolved
oxygen concentrations of 4, 5, and 7 mg/1 and coliform bacteria
MPNs of 240, 1000, 2400, and 5000 per 100 ml. Associated costs
to achieve the water quality objectives are included. Optimum
objectives agree closely with the objectives of the Oregon State
Sanitary Authority.1 The minimum flow objective (6000 cfs) on the basis
of economic efficiency was higher than the State's objective (5500 cfs);
however, the State's appears to be more realistic in view of the
shortages associated with optimum conditions derived from economic
simulation models. Water quality management plans based on the State's
minimum flow objective would achieve fewer and less severe failures
to meet water quality objectives than a higher flow objective.
5. Flow augmentation, as shown by this research project, is an economic-
ally feasible means of achieving and maintaining water quality objectives,
The extent of flow augmentation is a function of the shape of the
hydrograph, the degree of treatment provided, the cost of alternative
means of waste treatment, and the value of complementary and competitive
beneficial uses of available water.
6. Reliability of flow augmentation is a function of other project
purposes and other facilities in the basin. Directly downstream of
a reservoir, annual demands should be met or almost met every year.
In a large, highly regulated system, with many reservoirs where
The name of this agency has since been changed to the "Oregon Department
of Environmental Quality".
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demands for the release of water for flow augmentation many occur
only during water short years, a new system may not be too reliable.
During water short years, if reservoir operations are based solely
on marginal benefit analysis, competing demands may provide greater
returns or may have priority in order to meet contractural commitments.
Even if water was legally appropriated for specific beneficial uses
on the basis of economic efficiency, sufficient water may not be
available to meet all of the appropriation demands during drought
periods.
7. Storage of water for temperature control accompanied by selective
withdrawal both compete with demands for flow augmentation to
meet other water quality objectives during certain periods of the
year. Frequency and magnitude of shortages in the minimum conser-
vation pool should be similar to shortages in downstream flows in
order to achieve maximum fishery enhancement benefits. Available
water for fisheries should be allocated between demands to meet
flow and also temperature target objectives. The sacrifice of either
objective for the other would cause considerable losses, even
though one of the objectives was achieved. Therefore, the several
demands for fisheries must all be met to some degree since they are
all necessary conditions for downstream fishery enhancement.
8. Small* frequent shortages will be encountered by water users and
occasional damages from floods will be encountered when economic
efficiency is the objective If structural inputs are sized, target
outputs are selected, and operational procedures are established on
the basis of economic simulation models or mathematical optimization
techniques.
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RECOMMENDATIONS
1. Techniques are needed to develop accurate benefit functions to
describe the economic losses incurred by water users when water
shortages occur and/or water of insufficient quality must be used.
2. The feasibility of dynamic allocations of water must be examined.
In the future the value of water associated with beneficial uses
will change as well as the demands for use. Increased leisure time
is expected to be accompanied with more recreational use of water.
Higher degrees of treatment will alter the value of water for water
quality control. A study of this problem should be attempted and
should consider trends in water uses, advances in waste treatment
technology,»and the influence of an increasing population and an
expanding economy on all affected water quality indicators. Current
projects should be capable of reallocating water in the future.
3. Institutions are needed that are capable of basin-wide regulation
of waste discharges and of land use if available water resources
are to be allocated in an optimal fashion.
4. Negative benefits from storage of water for water quality control
should be evaluated. Stored water is essentailly the wash water
from a basin. When stored water is released for water quality
control, the turbidity of downstream waters frequently increases
due to suspensions in the wash water and algal growths. If pro-
visions are not made for selective withdrawal, then downstream
temperatures could increase or the released water could be low in
dissolved oxygen. Existing water contact sports could be curtailed
when downstream temperatures are lowered for fishery enhancement.
5. Water quality benefits should be associated with water use benefit
functions, rather than to water quality per se as allowed in
Senate Document 97 (27). Application of Senate Document 97 allowing
benefits to be equal to the cost of external alternatives could
justify water quality objectives with excessively high associated
costs that might not receive sufficient evaluation.
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SECTION 2
INTRODUCTION
STATEMENT OF THE PROBLEM
When water is stored and subsequently released for water quality control,
two conflicting situations arise. Released water not only normally
improves downstream water quality, but also enhances those other down-
stream beneficial uses of water dependent upon water quality and higher
flows. Stored water improves reservoir recreation and fishing, provides
head for the production of hydroelectric power and furnishes a con-
servation pool for regulating the temperature of released water. When
water is released for water quality control, a competitive relationship
develops, not only between reservoir storage needs, but also between the
dcwnstream demands for water to be diverted for such purposes as irrigation.
If water is stored for water quality control, the extent and magnitude
of the complementary and competitive aspects should be known. An
associated problem during water short periods is how much water should
be released for what purposes, and when should it be released, as well
as how much should remain in storage. Reservoir storage space for the
regulation of potential floods frequently conflicts with reservoir
filling schedules essential for meeting water demands during low flow
periods.
SCOPE AND OBJECTIVES
The specific aim of this project was to investigate the complementary
and competitive aspects of water stored for water quality control. To
achieve this objective, a rational analytical model using marginal
analysis was developed. This model allows the extent and magnitude of
the complementary and competitive aspects to be quantified by a com-
parison with the probability density function- of the maximum reservoir
storage and expected reservoir inflow during a critical low flow period.
A simulation model of the hydrologic and economic systems of a test
basin verify the adequacy of the model.
Actual physical, hydrologic, and economic data to test the model were
obtained for the Calapooia River near the middle of the Willamette
River Basin in Northwestern Oregon. Potential project benefits from
the development of the proposed Holley Reservoir in addition to water
quality include flood control, irrigation, drainage, downstream fisheries,
reservoir sportfishing, and reservoir recreation, Other minor benefits
include downstream hydroelectric power generation and navigation which
were not included in this study because of their minimal influence in
relationship to the other potential project purposes.
Water quality benefits from flow augmentation were estimated on the basis
of the postponement of the construction of treatment facilities and the
avoidance of maintenance and operation costs of these facilities if the
target water quality flow objective was met. This procedure is in
accordance with standards for the measurement of water quality control
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benefits as outlined in Senate Document 97 (27). Currently most project
planners prefer to evaluate water quality benefits by determining the
direct effects of water quality on specific beneficial uses.
Inclusion of flow augmentation in any federal project currently must
be in accordance with Section 3 (b) of the Water Pollution Control
Act, as amended (33 U.S.C. 466 et seq.), which states that the storage
and release of water for flow augmentation shall not be provided as a
substitute for adequate treatment or other means of controlling the waste
at the source. FWPCA policy has been to interpret "adequate treatment"
to mean no less than the equivalent of secondary treatment.
The degree of treatment required to meet combinations of water quality
objectives for dissolved oxygen concentrations of 4, 5, and 7 mg/1 and
coliform bacteria MPNs of 240, 1000, 2400, and 5000 per 100 ml for
different minimum flow objectives was determined in two phases. Non-
linear programming was used to determine the minimum cost to remove or
treat an estimated sufficient amount of waste to achieve the water
quality objectives (16). The results were in terms of an allowable
discharge for each significant waste discharger(20 municipalities and
7 pulp mills) in the Basin. These results were inserted in an oxygen
sag model of the basin by Worley (28) and a coliform die-off model by
Kerri (17) and the response of the river system was checked to determine
whether the water quality objectives were met. The input data consisted
of field data collected during 1963 (4), and cost figures for the 1963-
1965 period (17).
Although the model used a minimum cost solution, the results from
current loadings would probably not be too different from the results
obtained by establishing a uniform effluent requirement. Current
Federal Water Pollution Control Administration policy stresses the
highest degree of treatment possible, which is consistent with the
approved Water Quality Standards for the Willamette River and Multnomah
Channel. Current approved standards require "at least 85% removal of
BOD and suspended solids plus effluent chlorination" (20). Provisions
are included to require a higher degree of treatment if necessary.
Industrial expansion and population growth will cause the 85% removal
requirement to be inadequate in the future. If the uniform effluent
requirement is accepted and enforced, then at some time in the future
all waste_ dischargers will have to increase their degree of treatment
to the 90 or 95% level of BOD and suspended solids removal. At this
point, the benefits from the alternative of releasing water for water
quality control will be extremely high. A review of previous enforcement
action indicates that, with the exception of the city of Portland and
the older pulp mills, the Oregon State Sanitary Authority successfully
concentrated its early activities along the lower, critical reaches
of the Willamette River and on the larger municipalities. This enforce-
ment is consistent with the results from minimum cost models.
A daily streamflow simulator was developed to simulate hydrologic
conditions in the basin (21). Originally, it was written in FORTRAN
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2
and then in DYNAMO. DYNAMO was found to be a superior computer language
than FORTRAN and a very effective research tool for this type of problem.
Consequently, the economic system and analysis section of the simulation
model were written in DYNAMO. Flow diagrams and copies of the programs
are contained in Appendix V.
This project model is not intended to be definitive of Holley Reservoir,
but is developed to accomplish the aims of this research project and in
order that it be useful for water resource projects of this general
nature. At the time (December 1969) this report was completed alter-
native cost and benefit functions for Holley Reservoir were being
developed and reviewed. The actual Holley data lend reality to the
investigation and make the results more clearly understood.
2
DYNAMO is a simulation language developed at MIT by J. W. Forrester
(6) to study problems in industrial dynamics.
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SECTION 3
ANALYTICAL MODEL3
To identify Che extent and magnitude of the complementary and competitive
aspects of water storage for water quality control, an algorithm is pro-
posed that incorporates the concepts of dynamic programming and marginal
analysis. In the process, available water is allocated to those
beneficial uses that produce the greatest return.
Hall, using techniques developed by Bellman (3), has used dynamic pro-
gramming as the optimizing procedure for selecting the capacity of an
aqueduct (7), the design of a multiple-purpose reservoir (8), and water
resources development (9). The proposed algorithm is an extension of
Hall's observation that the number of calculations could be "drastically
reduced" by developing a table of incremental benefits for each function
under consideration and selecting the largest remaining increment of
benefit for each additional increment of water (7). Beard (2) also has
indicated the feasibility of the proposed approach.
An allocation and incremental benefit table provides an excellent '
illustration of water demands and associated benefits. The proposed
model is dynamic from the standpoint that during low flow periods, at
the end of each time increment past and expected inflows, available
storage, and remaining demands are reviewed and allocations redistributed
if necessary to optimize output.
ALGORITHM
1. Identify the time span during which water must be released (low flow
period) from storage for beneficial uses. The time of maximum reservoir
level will vary from year to year, but the beginning of the demand
period can be approximated.
2. Develop benefit functions for beneficial uses creating demands
during the low flow period. The benefit functions will show the
losses resulting from failure to meet target outputs.
3. Determine the value of water for each segment of the benefit function
in dollars per acre-foot.
4, Rank the values of the segments in descending order.
Allocation of Water
5. Begin allocation of water by assuming an empty reservoir.
6,. Assume increasing volumes of water available for allocation. The
>
The theory and derivation of this model are contained in Appendix I,
Theory of Optimum Allocation of Water.
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initial increments may have to be stored before full advanatage
may be taken of the most valuable segments of the benefit functions.
The sequence of allocation of the segments of the benefit function
cannot be ignored because sometimes a low value increment may be
associated with minimal storage.
7. Assign priorities to water demands. The total benefit for all
possible uses of each increment must be estimated. Possible uses
include (1) storage, or storage and then release for either (2)
downstream use or (3) downstream diversion. Whichever of the three
possibilities that produces the greatest value receives the increment
of water under consideration. This step is repeated until all
demands are satisfied or the maximum possible volume of available
water has been allocated.
8. Estimate the extent and magnitude of the shortages for any beneficial
use from the probability or frequency density function of the
expected volumes of water available for storage or release. (Reservoir
storage plus expected inflow.)
9, Compare results from the algorithm with and without water quality
demands. The frequency and quantity of the shortages with and
without water quality as a project purpose will indicate the extent
and magnitude of the complementary and competitive aspects.
Verification of these results should be obtained from a simulation model
of the project under study. Simulation is essential because the
response of the basin can be observed using historical or simulated
flow sequences.
APPLICATION OF ANALYTICAL MODEL
Planners and designers will find the analytical model an excellent
screening tool. The model will be helpful not only in identifying the
extent and magnitude of the complementary and competitive aspects, but
it will be also applicable to estimating sizes of structural inputs,
target outputs, and operating procedures. The model will not be
particularly useful in determining flood storage and filling rates
because of the importance of flow sequences in determining these
factors. Simulation, combined with marginal analysis, is effective in
attacking this type of problem,
A very important use of the model should be in determining operational
procedures in simulation models and then applying the results to
actual facilities. If benefit functions in the simulation model are
prepared on the basis of percent target met and percent target benefit,
then varying target outputs and appropriately adjusting target benefits
will not change the priorities because the slopes of the benefit
function will remain the same (Figure 1). Figure 1 shows a typical
benefit function where economic losses are encountered whenever the
target output (thus the target benefit) is not met.
10
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100
w 5O
O
tt,
50
Target Output, %
Fig. 1. Typical Benefit Function
100
11
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Existing systems can be reviewed using the analytical model. Users
will have to recognize institutional constraints and delivery contracts.
During periods of extreme shortages, the model could be used to allocate
the water on the basis of economic efficiency. These results could be
compared with alternative means of meeting specific critical demands,
such as domestic needs.
In applying the model, either static or dynamic conditions may be
assumed. Static conditions consider the situation for the entire
critical period without regard for events within the period. Dynamic
conditions consider actual inflows, storage and releases on a daily,
weekly, or monthly basis within the critical period under consideration
and continually revise allocations for maximum economic efficiency.
This is consistent with the Bureau of Reclamation's procedure of meeting
contractual commitments and then maximizing hydroelectric power
production at their facilities (24).
12
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SECTION 4
SIMULATION MODEL4
To test the analytical model, a simulation model (Fig. 2) of the
hydrologic and economic systems of the Calapooia River Basin (Fig. 3)
was developed and tested. Daily increments were used to accurately
describe low flow conditions as well as estimating peak flood flows and
the routing of the flood hydrographs through the reservoir. Analyses
of 200 years of simulation runs (Section 5) indicated that similar
results could be obtained from 50-year runs in terms of the expected
annual net benefits.
In the hydrologic system, streamflows were generated at the proposed
reservoir site (designated upstream hydrology) and at a downstream
gaging station three miles above the confluence of the Calapooia
River with the Willamette River. Flows in the Willamette River were
simulated only during low flow periods at Salem, Oregon, the location
of the minimum flow objective station in the Willamette River. Con-
sideration was given to the regulated releases from the other 13
authorized reservoirs in the Willamette Basin System.
Reservoir operational procedures were developed on the basis of two
techniques. Releases of storage volumes during low flow periods were
allocated to downstream demands and reservoir needs on the basis of
results from the analytical model. The complementary and competitive
aspects were accounted for in allocating volumes of water for storage
and release. Flood control storage and filling schedules were derived
on the basis of applying the method of steepest ascent to the results
from the simulation model (Section 5).
Economic benefits from meeting water demands for beneficial uses were
calculated in the economic model on the basis of a percentage of the
target output which was successfully met. Benefit functions (Figure 1
and Appendix IV) attempted to estimate losses incurred by failures to
achieve the target output. Losses were measured by subtracting actual
benefits from target benefits, where actual benefits are determined from
the percent target output met. Project purposes included drainage,
flood regulation, irrigation, downstream anadromous fishery enhancement,
reservoir sport fishing, recreation, and water quality. Annual costs
associated with the project purposes are calculated on the basis of the
interest rate, life of facilities, and maintenance and operational costs.
A summary of the sources of input data is found in Appendix IV. For a
detailed description of the model, flow diagrams, and the computer
programs in FORTRAN and DYNAMO, see Appendix V. Good explanations of
the DYNAMO language may be found in the DYNAMO Users Manual (22) and in
a paper by Krasnow and Merckallio (18) . For applications of DYNAMO see
references 10 and 11.
interest rate may be tested in the model and rates between 3 and
5% were studied by this project.
13
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Hydrologic System
Economic
Upstream
Flow Generator
Holley Reservoir Level
Fish
Releases to meet
Water Demands, Flood
control needs, and
filling schedule
Downstream
Flow Generator
(Upstream Inflow
Considered)
Recreation
Recreation
Fish
_^
I
Calapooia River
Downstream Channel Level
Willamette
River Flow
Generator
Drainage j
- — S -- »J
Flood
Control
I
Willamette River
Flow at Salem
Water
Quality
$ H
Flood
Control 1
Benefits
Costs
Net Benefits
Figure 2. Simplified Computer Logic for Hydrologic and Economic
Simulation Model
14
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CORVAL
t_n
COLUMBIA RIVER
PORTLAND
WILLAMETTE
RIVER
HOLLEY RESERVOIR
CALAPOOIA BASIN
-XJ
^^
Fig. 3. Calapooia River Basin
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Performance of any proposed system of structural inputs, target outputs,
and operational procedures is evaluated by the economic analysis section
of the simulation model. Reservoir operation is measured in terms of how
close the reservoir came to being full each year, as well as its ability
to maintain the minimum conservation pool for temperature control. Spill
data and flood regulation ability are also recorded.
Various sized channels below the reservoir are evaluated in terms of
the channel's ability to contain reservoir releases and local inflow
durinc flood periods. Also considered are the flows in the channel
during the drainage season when the average channel level must be
below 30 percent of the channel capacity to receive full drainage benefits.
Irrigation capability is recorded on the basis of the percent irrigation
target met. Recreation and water quality are evaluated on a similar
basis,
For each project purpose, the economic analysis section records the
frequency and magnitude of the shortages for every simulation run.
Analysis of these results indicates how the system may be improved to
aleviate shortages or increase the maximum net benefits*
Shortage indices (1) for each project purpose also were calculated to
assist with the analysis of the project performance. Shortage indices
assume that losses from failures to meet target objectives can be
estimated on the basis of the square of the percent water shortage.
16
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SECTION 5
DESIGN OF EXPERIMENT AND SENSITIVITY ANALYSIS
This section describes the method of economic analysis, design of experi-
ment, sampling procedures, sensitivity analysis, and optimization
techniques used to search the average annual net benefit response sur-
face of the system being studied.
ECONOMIC ANALYSIS
Two types of economic analysis models are possible in simulation studies-
static and dynamic (13), In a static model, all capital facilities are
assumed to be installed at the start of the simulation period and the
demands (for water) remain constant throughout the time period under
consideration* A dynamic model is characterized by capital inputs and
levels of target outputs changing during the simulation period* Demands
may be increased annually or they may be held constant for a particular
demand period—-say the first fifteen years, and then the size of facilites
and the demand could be increased and held constant for another time or
demand period.
In planning studies which require estimation of future demands and
consideration of the facilities necessary to meet these demands a dynamic
model should be used. However, this is a research project whose objective
is to develop a model that will produce a rational analytical approach
to the evaluations of the magnitude and extent of the complementary and
competitive aspects of water storage and release for water quality
control. These aspects could become "clouded" if the growth rates used
in a dynamic model for the different demands and beneficial uses were
not realistic and similar to those that actually could be encountered
in the future. Also, in a dynamic model which discounts benefits to
the present, severe floods or droughts at the beginning or end of the
economic life of the project may have considerable influence on the
results. For these reasons, a static economic model was regarded as
the better approach to carry out the objectives of this research project,
LENGTH OF SIMULATION RUN
To determine the minimum acceptable length of simulation run while
searching the response surface and still expect to approach the population
mean annual net benefits, two 100-year simulation runs were compared.
The first 100 years used the regular random number generator while a
noise element was inserted In the random number generator for the second
100-year run, A noise element will vary the sequence of random numbers
generated, thus altering the hydrology by changing the random component
in the daily flow simulator and changing the times (years) of occurrence
of low flow demands in the Willamette River. Results of the runs are
summarized in Table 1 and are shown in Figure 4,
Examination of Table 1 reveals similar answers and 50 years appeared to
be a sufficient time period for a simulation run. The simulation runs
17
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lABIE 1. SUGARY OF AVERAGE ANNUAL NET BENEFITS
FOR 200 YEARS OF SIMULATION
AVERAGE ANNUAL NET BENEFITS, SlOOO
Year
0 - 50
51 - 100
0 -- ?00
Regular Run
1916
2053
Run With Noi.se
Element Included
1949
2032
1988
18
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2.0 -
200 YEAR AVERAGE
\A7
2l.8
V)
- 1 .6
X WITHOUT NOISE ELEMENT
200 YEAR AVERAGE
O
«
lit
<
1 .6
X WITH NOISE ELEMENT
20
40
60
80
YEARS
Fig. 4. Two-100 Year Simulation Runs
100
19
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were oroken down into four 50-year periods by separating the second 50
years in both the regular and noisp element runs, and the results
compared favorably with the 200-year average,
At optimum conditions, the noise element (change in hydrology) caused
a shift of 0.7 percent ($2009.7 vs. $1995,9) in the average annual net
benefits for a 50-year period. A longer simulation run at optimum
conditions will provide an in depth analysis of the system and better
indicate its response to adverse conditions.
SENSITIVITY OF BENEFIT FUNCTIONS
Sensitivity of benefit functions is reflected by the slope of a benefit
function (Fig. 1), A considerable change in the slope of any benefit
function would be required to shift the orders of most demand priorities
as determined by the analytical model, because many of the priority
values are weighted due to the complementary aspects of water use,
of target outputs does not change the priorities as long as
the benefit functions in the simulation model are described in terms of
the percent target output and percent target benefit, provided appro-
priate adjustments are made in the target benefit, Using this technique,
the slopes of the benefit functions remain constant. In this simulation
modt- 1 , the only exception was recreation which was a function of the
reservoir capacity,
INTEREST RATES
Although the maximum net benefits dropped considerably with increasing
interest rates, the structural inputs, target outputs, and operating
procedures at optimum conditions were surprisingly stable (Table 2).
Current (1969) high interest rates were not anticipated when this study
was undertaken. Unless otherwise noted, all results reported are for
an interest rate of 3-1/4/i.
20
-------
TABLE 2. MAXIMUM AVERAGE ANNUAL NET BENEFIT,
STRUCTURAL INPUT, AND TARGET OUTl'UT
FOR DIFFERENT INTEREST RATES
Interest
Rate
7.
3
4
5
SENSITIVITY
5
Reservoir
Capacity
1000 Ac-~ft.
140
138
138
140
Irrigation
Target
1000 Ac-ft.
84
84
82
34
Average Net
Benefit
$1000
2084.1
1780,2
1465.7
1453.8
21
-------
Under the sensitivity entry in Table 2 the optimum reservoir capacity
(target input) and irrigation target (target output) at a three percent
interest rate were used to find the average annual net benefit if the
interest rate increased to five percent. The change in average annual
net benefits was a decrease of less than 0.5 percent from the optimum
net benefits obtained by changing the inputs and outputs to adjust for
the increase in interest rates. The importance of these results is
that an apparent optimum technological mix exists for this particular
basin which is not significantly influenced by varying interest rates.
METHOD OF STEEPEST ASCENT
To find optimum structural inputs, target outputs, and operational
procedures, a form of the method of steepest ascent was used. Initially,
the methods used by Hufschmidt (12) were attempted. Results were
acceptable, but calculations did not produce new bases which were con-
verging on optimum conditions as rapidly as desired. A visual examination
of the results and application of the concepts of the method of steeoest
ascent proved to be the most efficient approach to converging on the
maximum net benefits.
OPERATING RULE CURVES
Considerable interest has developed recently in the field of reservoir
operation to optimize reservoir yields. James (14) economically derived
operating rules which maximized benefits. A stochastic linear programming
model was structured by* Loucks for defining reservoir operating policies
(19). Jaworski (15) and Young (29, 30) used dynamic programming to
develop operating rule curves. Young (31) presents a numerical flow
routing approach for assessing reservoir requirements for insuring that
releases equal or exceed those flows necessary for pollution control.
The approach used in this project to determine operating rule curves
considers flow sequences, costs of storage, and benefits from water,
including economic losses resulting from shortages.
During critical low flow periods, water was allocated, stored, and
released on the basis of the analytical model. Flood control storage
and filling schedules were developed using the previously described
modification of the method of steepest ascent.
Critical decision variables included the volume of flood control storage,
when filling should commence, and the rate of filling. Different
combinations of these Variables were tried using the concepts of the
method of steepest ascent in the search for the optimum operating
procedures during the flood season and reservoir filling period.
Another approach is to operate the reservoir during the flood and
filling seasons on the basis of the condition of the basin. A series of
rule curves based on the API (antecedent-precipitation index) or the
snow pack are other possible approaches which have application in
practice, but could not have been incorporated in the model due to the
method of simulating streamflows. For example, if the snow pack is
22
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significant, then capacity should be provided to contain a sudden runoff.
Operations decisions also should be aided by weather forecasts. These
other approaches are particularly helpful to action agencies whose
design criteria require the routing of historical records. If the
historical records include a late winter or early spring flood which
must be regulated, then it is extremely difficult to fill a reservoir
during dry years to meet low flow demands, without using the API or
a similar concept to operate a reservoir.
Figure 5 shows the first rule curve attempted and final optimum rule
curve, A total of 16 different curves were tested. Of particular
importance was the filling schedule. On October 1 (Day 1), the beginning
of the water year, the actual reservoir level was usually slightly above
the minimum conservation pool. Some water should be available for
fishery releases and to maintain the pool. The flood season usually
begins around November 15 (Day 45). Note that gradual filling of the
reservoir begins on December 15 (Day 75), before the most severe floods
usually occur. Gradual filling of the reservoir continues until the
summer demand period which starts around June 1 (Day 242),
Analysis of the final rule curve reveals that low flow demands produce
greater benefits than the reduction of damages due to occasional large
floods. Personnel with action agencies have indicated that it is
difficult to economically justify providing flood control storage for
large floods (26) ; however potential ioss of life is a constraint on
the reduction of flood control capacity.
23
-------
10O
INITIAL ATTEMPT
MINIMUM CONSERVATION POOL
OCT 1
60
120
180
DAY
240
300
360
Fig, 5* Operating Rule Curves
-------
SECTION 6
RESULTS AND DISCUSSION
Contained in this chapter is the insertion of actual data from the
proposed Holley Reservoir Project into the algorithm of the analytical
model. Results from the model are compared with results from the
simulation of the hydrologic and water resource related economic systems
of the basin. A discussion of the complementary and competitive aspects
of water storage for water quality control is based on interpretation
of results.
Optimum combinations of water quality objectives are illustrated by a
response surface showing the average annual net benefits for combinations
of dissolved oxygen concentrations of 4, 5, and 7 mg/1 and coliform
bacteria levels of 240, 1000, 2400, and 5000 per 100 ml. Flow augmentation
objectives should be selected on the basis of the shape of the low flow
hydrograph, the value of competing demands, and the costs of waste
treatment and water storage. Optimum water quality objectives determined
by the proposed analytical model agree closely with actual water quality
standards adopted by the Oregon State Sanitary Authority and approved
by the Federal Water Pollution Control Administration, A serious
shortcoming of mathematical optimization techniques is found in the
frequent, small water shortages that are encountered at optimum inputs,
target outputs, and operational procedures,
RESULTS FROM ANALYTICAL MODEL
To test and verify the proposed analytical model, the authorized U.S.
Army Corps of Engineers Holley Reservoir project was selected on the basis
of previous work in the area and the availability of data. Results are
not intended to be definitive of Holley, but will be useful for water
resource projects of this general nature. At the time (December 1969)
this report was completed, alternative cost and benefit functions for
Holley Reservoir were being developed and reviewed. Verification of
the proposed model was accomplished using the mathematical simulation
model of the hydrologic and water related economic systems in the
Calapooia River Basin. Details of the input data and benefit functions
are contained in Appendix IV, A description of the simulation model,
computer flow diagrams, and the actual programs are found in Appendix V,
Results of the application of the proposed analytical model to Holley
data are outlined in the following section, Ihe numbering of the steps
corresponds to the algorithm outlined in Section 3, Analytical Model,
Algorithm Procedures
1, Identify critical demand period.
Stored water must be released from Holley Reservoir to meet irrigation
demands and downstream fishery enhancement during the months of April,
and Hay. During June, July, August, and September, the dry season,
shortages may become acute because of demands to store water for
25
-------
temperature control, recreation, and reservoir sport fishing, as
well as additional releases for flow augmentation for water quality
control. Consequently June, July, August, and September were
identified as the critical time period.
2, Develop benefit functions. Results are outlined in Appendix IV.
3, The values of water for each segment of the benefit functions are
summarized in Table 3.
4. Rank the values of the segments of the benefit functions in
descending order as shown in Table 4.
5. Begin allocation of water by assuming an empty reservoir.
6. Assume increasing volumes of water available for allocation as shown
in Table 5. Note that priorities A and B are allocated to reservoir
storage in order to gain some control over the temperature of
released water to enhance the downstream fishery,
7. Assign priorities to water demands. The benefit for all possible
uses of each increment must be estimated. Possible uses include
(1) storage, or storage and then release for either (2) downstream
use or (3) downstream diversion. Incremental values are obtained
from Tables 3 and 4 and the benefits estimated for each of the
three possible types of uses. In priorities 1, 2, 5, and 6,
maximum benefits were obtained by storing a portion of the water
for temperature control for anadromous fish and releasing some of
the water to maintain a minimum flow and also to improve the DO
level to enhance the anadromous fishery.
8. Estimate the extent and magnitude of the shortages for any beneficial
use from the probability or frequency density function of the
expected volumes of water available for storage or release. (Reservoir
storage plus expected inflow.) See Table 4.
9, Examination of Table 5 allows a visual comparison of the extent and
magnitude of shortages with and without water quality as a project
purpr.se 4 If water quality was not a project purpose, then irrigation
priorities 3 and 6 should be inserted ahead of priorities 1 and 2,
Removal or omission of the water quality project purpose would
cause a loss In the anadromous fishery due to dissolved oxygen
deficiencies and loss of temperature control.
.10, Verification of the results using the algorithm are checked using the
mathematical simulation model of the basin. Results may be compared
in Table 4. Frequencies of shortages were closely estimated by
the algorithm as compared with results from simulation of the system.
Fewer shortages were expected by the algorithm because its estimates
are based on perfect knowledge, whereas in simulation and actual
practice, the exact sequence of future flows is not known.
20
-------
TABLE 3. INCREMENT AT, HOLLA* BENEFITS FROM USES OF WATER1
Irrigation
Fish
Recreation
Water Quality
Value2
$14,2 per ac-ft
31,0 per ac-ft
Reservoir Sport Fish
$ 0,80 per ac-ft
2,30 per ac-ft
6.00 per ac-ft
3.00 per ac-ft
0,80 per ac-ft
Anadromous Fish (Release)
Base Release, No Benefit
$50,90 per ac-ft
17.00 per ac-ft
4.20 per ac-ft
Anadromous Fish (Storage)
Base Storage, No Benefit
$24,80 per ac-ft
8,30 per ac-ft
2,10 per ac-ft
$ 7,70 per ac-ft
3,30 per ac-ft
2,80 per ac-ft
2,00 per ac-ft
1,85 per ac-ft
1,45 per ac-ft
$12,20 per ac-ft
8,20 per ac-ft
4.90 per ac-ft
Incremental Volume2
67,200 ac-ft
16,800 ac-ft
10,200 ac-ft
10,200 ac-ft
10,200 ac-ft
20,400 ac-ft
10,200 ac-ft
10,000 ac-ft
5,000 ac-ft
10,000 ac-ft
5,000 ac-ft
20,400 ac-ft
10,200 ac-ft
20,400 ac-ft
10,200 ac-ft
20,000 ac-ft
40,000 ac-ft
10,000 ac-ft
10,000 ac-ft
20,000 ac-ft
40,000 ac-ft
2,900 ac-ft
4,800 ac-ft
38,900 ac-ft
This table is a summary of benefit functions in Appendix IV,
The values and volumes associated with each benefit are ranked in
order of allocation, i.e., the first value results from the first
incremental volume allocated to the beneficial use.
27
-------
TABLE 4. RANKED SEGMENTS OF BENEFIT FUNCTIONS
Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Fish
Res.
6.0
3.0
2.3
0.8
Fish1
Anad.
16. 82
5.6
1.4
Irrig.
14.2
11,0
Recre-
ation
7.7
3.3
2.8
2.0+
1.85
1.5
Water
Qual.
12.2
8.2
4.9
r&s3
r
r
r
r
s
S
r&s
r
s
3
S
S
S
S
s
r&s
s
Vol.
Ac-ft.
15,200
59,100
2,900
14,900
4,800
20,000
10,200
30,400
38,900
40,000
20,400
10,000
10,200
10,000
20,000
40,000
15,200
10,200
Cum.
Vol.
15,200
74,300
77,200
92,100
96,900
116,900
127,100
157,500
196,400
236,400
256,800
266,800
277,000
287,000
307,000
347,000
362,200
372,400
1. Approximately one-third of volume is released (5000 ac-ft) and two-
thirds stored (10,200 ac-ft)
2. Computed as follows from TABLE 3
a ($50.90/ac-ft)(5000 ac-ft) + ($24.80/ac-ft)(10.200 ac-ft)
8 (15,200 ac-ft) 2*
*2 is used to average benefit between storage and release.
3. r, release; s, storage.
28
-------
TABLE 5. ESTABLISHMENT OF OPERATIONAL PRIORITIES
BASED ON COMPLEMENTARY USES
Pri-
ority
A
B
1
2
3
4
5
6
7
8
9
Volume
Ac.ft.
10,000s
10,000s
10,000r
6,100s
2,900r
4,500s
2,100r
59,100r
10,200s
5,000r
10,200s
5,000r
14,900r
10,200s
5,000r
16,600r
8,800s
10,000s
20,000s
40,000s
Cum.
Storage
Ac . f t .
10,000
20,000
26,100
30,600
40,800
51,000
61,200
61,200
70,000
80,000
100,000
140,000
Cum.
Release
Ac.ft.
10,000
12,900
15,000
74,100
79,100
84,100
99,000
104,000
120,600
Total
Increment
Benefit
$/Ac.ft.
8.5
5.0
2'7.0
25.6
14.2
12.1
11,4
11.1
5.7
4,9
2.8
2.0
1,8
1.5
Increment.
lienefits
$/Ac.ft.
s r
7.7
0.8
7.7
2.3
0 0
12.2
6.0
12.4 25.4
3.3
8.2
6.0
12.4 25.4
3.3
14.2
6.7
3.0
4.2 8.5
3,3
4.9
3.0
4.2 8.5
3.3
11,1
4.9
0.8
1.0 2.1
3.3
4.9
2,8
2.0
1.8
1.5
Uses
Recreation
Res. Sport Fish
Recreation
Res. Sport Fish
Anadrom.Fish
Water Quality^
Res. Sport Fir>h
Anadrom.Flsh
Recreation
Water Quality
Res. Sport Fish
Anadrom. Fish
Recreation
Irrigation
Water Quality
Res. Sport Fish
Anadrom.Fish
Recreation
Water Quality
Res, Sport Fish
Anadrom.Fish
Recreation
Irrigation
Water Quality
Res. Sport Fish
Anadrom.Fish
Recreation
Water Quality
Recreation
Recreation
Recreation
Recreat ion
s - Store
Release
2.
Water for irrigation, water quality, and anadromous fish must be stored
before it is released for downstream use; therefore, recreation will
benefit during the storage period. These benefits are assigned
directly to the recreation benefit to avoid double counting.
Not all of the releases for anadromous fish are applicable to water
quality. During some years, the minimum flow target in the Willamette
River is met independent of releases below the reservoir for down-
stream fishery enhancement *
29
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TABLE 6,. FREQUENCY DENSITY FUNCTION OF WATER
AVAILABLE FOR ALLOCATION
Available
Volume,
1000 ac-ft
125-130
120-135
135-140
140-145
145-150
150-155
155-160
160-165
165-170
170-175
Expected
Freq.
in 50 yrs
1
1
3
3
22
17
1
2
From
Priority
4
5
6
7
Table V
Cum.
Demand
119,900
135,100
150,000
165,200
Shortages
Ho. o£
Times
Expected
(algorithm)
0
1
5
47
No. of
Times
(Simulation
Run)
0
6
10
50
30
-------
To check the ability of the analytical model to properly establish pri-
orities, the most sensitive priorities in Table 5 were switched. The
difference between the marginal benefits of priorities 5 and 6 is
$0.3 per ac-ft. When priorities were established from Table 5 the
average annual net benefits were 1995.9 thousand dollars. Reversing
priorities five and six caused a decrease in average annual net benefits
to 1991.9 thousand dollars. Therefore results from a simulation with
reversed priorities verified the original order and the analytical model.
DISCUSSION OF COMPLEMENTARY AND COMPETITIVE ASPECTS
Complementary features of storing and releasing water can be visualized
by comparing the data in Tables 4 and 5 as shown in Figure 6. Note
that the benefits from available water are greater for the smaller
volumes because of the multiple uses whereas the competitive benefits
(each demand considered individually) are higher for higher volumes
because these uses were not combined with earlier demands that have
already been met. Marginal costs of storage also are provided for compar-
ison purposes.
To illustrate the contribution to the maximum net benefits, Figure 7
shows the increase in net benefits if water quality is a project purpose.
This contribution is measured by avoided treatment costs; however, other
beneficial uses also would suffer if adequate water quality in the
receiving waters was not maintained.
Particularly disturbing is the high standard deviation at maximum net
benefits and at other combinations of inputs and outputs. The standard
deviation is a measure of the stability of a particular design. The
lower the standard deviation, the greater the utility of the project
to the persons influenced by it in terms of a reduction in the uncertainty
of the response of the project. Dorfraan (5) has proposed that the cost
of uncertainty be subtracted from the expected net benefits. The cost of
uncertainty is a measure of the loss of utility suffered by water users
resulting from the losses they may encounter in the future due to water
shortages. If we measure the cost of uncertainty as
Cost of Uncertainty = v 0//2r (1)
where v is the normal deviate with probability a of being exceeded, a
is the specified probability that a fund to cover the costs of uncertainty
will be exhausted, a is the standard deviation of the annual net benefit
distribution, and r is the rate of interest. If v^ * 0.05 is 1.645 and
r is 3.25%, then the cost of uncertainty is 6.5a,
Examination of the results from the simulation model showed that a major
portion of the standard deviation was contributed by the flood control
benefits. In some years there were no flood threats and thus, no
flood benefits from the project, whereas in other years the project
reduced damages from very serious flood threats.
31
-------
u
20
u.
Ul
z
O
Z
«A
Z 10
O
u
Z
O
n
M. B. COMPETITIVE —
M . B. COMPLEMENTARY
MARGINAL COSTS
_L
_L
100 2OO
TOTAL VOLUME (103AC-FT)
Fig. 6. Illustration of Value of Complementary Factors
300
400
-------
tn m
O O
- - 15
M Z
*• o
si
E >
flu m
z
o
-I tt
< <
3 O
Z Z
z <
< »-
VI
UI
o •*
IX
10
OPTIMUM CONDITIONS;
W.Q.-6000 cfs, DO-5 mg/l
MPN lOOO/lOOml
MIN.RES. LEVEL =51000 AC-F1
WITHOUT W.Q.
>S WITH W.Q.
S WITHOUT W.Q.
120 14O 160
RESERVOIR CAPACITY (103AC-FT)
Fig. 7. Average Annual Net Benefits and Standard deviations,
With and Without Water Quality
33
-------
To examine the sources of losses, the losses from the inability to meet
water demands were examined. Losses were recorded every year for
recreation from the inability to keep the reservoir full during the
entire recreation season because of competitive demands. Shortages
also were recorded occasionally resulting from insufficient water to
meet water quality demands, storage for temperature control, releases
for minimum downstream fish flows, and irrigation demands. At maximum
net benefits the average annual loss was $133,600 with a standard
deviation of $166,000 with a minimum loss of $45,800 from recreation
losses only to a maximum of $489,500 for all uses. Increasing the
reservoir capacity from 140,000 ac.ft. to 160,000 ac.ft. reduced the
average annual loss to $89,500 and the standard deviation of the losses
from shortages to $71,100. The minimum annual loss was $31,100 and the
maximum was $346,200. The average annual net benefit dropped from
$1,995,900 to $1,914,800. Annual losses may be seen in Figure 8.
WATER QUALITY RESPONSE SURFACE
An important water quality management decision is the establishment
of water quality objectives or standards and a minimum target for flow
augmentation. Average annual net benefits for combinations of water
quality objectives of a dissolved oxygen concentration of 4, 5, and 7
mg/1 and coliform bacteria most probable numbers of 240,1000, 2400 and
5000 per 100 ml were determined by the simulation model. A minimum
flow objective of 6000 cfs at Salem, Oregon, produced the maximum net
benefit.6 To account for the associated costs to society for treat-
ment to achieve the water quality objective. The minimum level of
treatment for the objectives under consideration (DO » 4 mg/1 and MPN »
5000/100 ml) was selected as a base, and the additional annual cost of
treatment to each waste discharger was subtracted from the average
net benefits from the simulation model. Figure 9 shows the resulting
response surface.
Probably the greatest deficiency in the resulting water quality response
surface was the method of estimating water quality benefits. Measure-
ment of water quality benefits "by the most likely alternative" (27)
essentially insures the benefits exceed the costs. This approach also
favors higher water quality objectives due to the higher costs that
could be avoided by flow augmentation, These higher costs may not
reflect the true benefits to society from higher levels of water quality
which could create a better aquatic environment for fishing and swimming.
The shape of the response surface in Figure 9 is not similar to a
benefit response surface with benefits increasing as quality improves
6Normally one would expect the minimum flow augmentation target to vary
with water quality objectives, but 6000 cfs was the optimum target
in this situation because it is the flow target regulated by the
releases from thirteen other reservoirs.
34
-------
OPTIMUM
CONDITION
INCREASE RES.—
CAP. 20000 AC-FT
YEARS
Fig. 8. Annual Losses Due to Water Shortages
35
-------
5000
2400
O
o
z
o.
1000
24O
NET BENEFITS LESS ASSOCIATED COSTS
OF TREATMENT (103 $)
DISSOLVED OXYGEN (mg/I )
Fig. 9. Water Quality Benefit Response Surface
36
-------
for several reasons. Associated costs have a profound influence when
included in a response surface. These costs of treatment incurred by
each waste discharger in order to achieve and maintain the water quality
objectives in a basin at the optimum level of flow augmentation may
be extremely high in comparison with the benefits associated with high
levels of water quality. Other factors influencing the response
surface include the method of measuring benefits and actual benefits
associated with each level of water quality. Interest rates and
fixed and variable costs of waste treatment also are influential.
Theoretically one would expect the response surface of Figure 9 to
reveal an optimum combination of dissolved oxygen and coliform bacteria
by exhibiting a distinct peak somewhere on the response surface, but this
did not occur due to some of the reasons given above which influence
the response surface.
Examination of the response surface and a review of the data plotted
show that the optimum combination of water quality objectives would be a
dissolved oxygen concentration of 7 mg/1 and a coliform bacteria level
of 1000 per 100 ml. A drop in the dissolved oxygen objective to 5 mg/1
would cause the project benefits to drop 3 percent. Optimum water quality
objectives were selected at a dissolved oxygen concentration of 5 mg/1
and an MPN of 1000/100 ml because the drop in benefits would be slight
and the fact that the benefits were believed to be more accurate at this
level.
FEASIBILITY OF FLOW AUGMENTATION FOR WATER QUALITY CONTROL
Flow augmentation for water quality control is usually feasible when
low flow hydrographs are V-shaped (minimum flows occur during a short
time period) and its effectiveness is reduced when the hydrographs
become U-shaped, such as could be expected in basins with several
reservoirs and where flows are highly regulated. These different
shapes of hydrographs are shown in Fig. 10.
If in two identical basins all conditions were alike with the exception
of the shape of the hydrographs, then the optimum level of flow
augmentation could be considerably different. Comparison of the two
hydrographs in Figure 10 reveals that the volume of water (shaded area)
necessary to increase the minimum flow level is relatively small for
the V-shaped hydrograph in comparison with the U-shaped hydrograph.
If benefits are estimated on the basis of different levels of target
minimum flow, then the small volume of water in the V-shaped hydrograph
becomes very valuable because it is very effective in increasing
benefits.
The large volume of water required by the U-shaped hydrograph is not
very valuable on a dollar per ac-ft basis (determined from total
benefits) and this volume may not even be available for distribution
because of higher valued competitive demands. In this case, the cost
of additional waste treatment may be considerably less than the cost
of additional storage.
37
-------
FLOW AUG. TARGET
U-SHAPED HYDROGRAPH
FLOW AUG. TARGET
If
250
300
TIME, DAYS
V-SHAPED HYDROGRAPH
350
Fig. 10. Typical Low Flow Hvdropraphs
-------
When evaluating flow augmentation targets, the complementary and
competitive aspects must he carefully examined as previously outlined
in this chapter. The shape of the hydrograph is an important indicator
of the potential value and extent of flow augmentation; however, each
situation must be studied individually.
Selection of a minimum flow target is proposed in this report on the
basis of economic efficiency. When target outputs are selected on
this basis, shortages are usually greater and more frequent than allowed
by current design standards (23). A simulation model could be used to
indicate to water quality managers the loss in net benefits if a
reduction in shortages appears desirable.
COMPARISON OF OPTIMUM WATER QUALITY OBJECTIVES WITH ACTUAL STANDARDS
To compare optimum conditions obtained from the analytical model and
the simulation model, the Adopted Water Quality Standards, Willamette
River and Multnomah Channel, Oregon State Sanitary Authority, February,
1967, (20), will be reproduced in part below.
'The following standards are based on a minimum gauged river flow of
5,500 cfs at Salem.
!• ORGANISMS OF THE COLIFORM GROUP (MPN or equivalent Millipore
filter using a representative number of samples where associated
with fecal sources). Average less than 1,000 per 100 ml with
20 percent of the samples not to exceed 2400 per 100 ml.
2 • I>I S SOLVED OXYGEN
No wastes shall be discharged and no activities shall be conducted
which either alone or in combination with other wastes or activities
will cause in the waters of the Multnomah Channel or the
Willamette River:
a) (Multnomah Channel and main stem Willamette River from
mouth to the Willamette Falls at Oregon City, river mile
26.6.)
D.O. concentration to be less than 5 rag/1
b) (Main stem Willamette River from the Willamette Falls to
Newberg, river mile 50.)
D.O. concentration to be less than 7 mg/1
c) (Main stem Willamette River from Newberg to Salem, river
mile 85.)
D.O. concentration to be less than 90 percent of saturation.
d) (Main stem Willamette River from Salem to confluence of Coast
and Middle Forks, river mile 187.)
D.O. concentration to be less than 95 percent of saturation."
39
-------
Minimum Flow Target at Salem. A slight discrepancy exists between the
minimum flow of 5500 cfs used by the State Sanitary Authority (20)
and 6000 cfs objective used by the Corps (25). In routing 30 years
(1926 through 1955) of monthly historical flows through the authorized
Willamette River system the Corps failed to meet their objective of
6000 cfs six times. Minimum routed flows were 4580 cfs, 4600 cfs,
4600 cfs, 4840 cfs, 5400 cfs, and 5895 cfs.
Although the simulation model indicated 6000 cfs was the optimum flow
objective to maximize net benefits, the model failed to meet the
objective seven times in 50 years. Minimum flows were 4710 cfs, 4720
cfs, 4790 cfs, 4800 cfs, 4830 cfs, 5815 cfs, and 5830 cfs. The flow
objective of the State of Oregon appears more realistic in terms of
reducing the frequency and magnitude of damages resulting from failures
to meet water quality objectives caused by flows below the augmentation
target.
Organisms of the Coliform Group. The results from the simulation model
agree with the objective of the State.
Dissolved Oxygen. Dissolved oxygen profiles from Worley's (28)
simulation of the response of the Willamette River to possible waste
loadings indicate that the simulated results (16) would meet the State
Standards with the possible slight exception of the lower reaches of
the Newberg pool (part b).
Comparison of Degrees ofTreatment Required.
"At least 85% removal of BOD and suspended solids removal plus effluent
chlorination" (20) are required in the Willamette River Basin by the
Oregon State Sanitary Authority. Degrees of treatment used in the
simulation model were determined by nonlinear programming with the
objective being the minimum cost of waste treatment. Input data were
based on 1963 waste loadings and Willamette River responses during
1963 (4). If current or future waste loadings were used, the degrees
of treatment would probably be very similar to current requirements.
SUMMARY
Particularly disturbing is the inability of the optimal system (in
terms of economic efficiency) to provide additional water for flow
augmentation during critical flow periods. During periods of very
low flows, other water demands produce greater benefits than the release
of water for flow augmentation. This situation could be expected in
many basins with highly regulated flows, such as in the Willamette River
Basin.
In a basin where a single reservoir regulates the downstream flow, the
situation would not be as acute. Minimum flow objectives for fish
enhancement below the proposed Holley Reservoir in the Calapooia River
and the minimum conservation pool objective for temperature control
were consistently met, with a few minor shortages (6 in 50 years) at
optimum conditions. All of the shortages were only 5 percent or less
of the target value.
40
-------
Serious consideration should be given to the number and magnitude of
shortages in actual projects. Proponents of systems analysis (13)
claim this approach produces greater maximum net benefits than designs by
action agencies using conventional design standards. The difference
apparently stems from the fewer shortages allowed by current design
standards. Action agencies are expected by society to control floods
and meet irrigation contracts and power commitments. In view of the
loss in utility caused by shortages and floods which are probably not
accurately reflected by loss functions, current design standards are
considered superior in the opinion of the Project Director.
The question still remains—at what frequency and magnitude do shortages
become intolerable? This level varies with individuals and may be
examined by the use of indifference curves and the concepts of utility
resulting from a reduction in uncertainty (5). Subtracting the cost
of uncertainty caused by shortages is one approach to evaluating alternative
designs. A major contribution to this problem by systems analysis lies
in the fact that simulation models can provide society with incremental
costs and benefits associated with different designs and levels of
shortages. From this additional information, society can select the design
which offers a desired degree of security and sufficient returns from
project expenditures.
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SECTION 7
ACKNOWLEDGMENTS
Financial support for this research was provided by the Federal Water
Pollution Control Administration, Research Grant No. 16090DEA.
The Project Director is indebted to numerous individuals who contributed
to this project. Professors Fred Burgess and Emery Castle at Oregon
State University offered valuable insight to the complexity of the
problem when the research proposal was formulated. The simulation model
was an expansion of original work by Professor A. N. Halter at Oregon
State University.
Professor William R. Neuman, Sacramento State College, assisted with
a major portion of the project. Sacramento State College students
Kip Payne, Dan Hinrichs, John Apostolos, and David Isakion contributed
t o various phases of the project.
Miss Linda Smith and Mrs. Gloria Uhri typed many drafts and the final
copies of the papers and reports that were published from this project.
43
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SECTION 8
REFERENCES
1. Beard, L. R,, "Functional Evaluation of a rtater Resources System,"
paper presented at the International Conference on Water for Peace,
Washington, U, C«, May, 1967.
2. Beard, L. R., "Optimization Techniques for Hydrologic Engineering,"
paper presented at 47th Annual Meeting of American Geophysical
Union, Washington, D. C., April 22, 1966.
1. Bellman, R., Dynamic Programming, Princeton University Press, New
Jersey, 1957.
4. Burgess, F. J, and Worley, J, L,, unpublished data, Department of
Civil Engineering, Oregon State University, Corvallis, Oregon, 1964.
5. Dorfman, R,, "Basic Economic and Technological Concepts: A General
Statement," Design of Water-Resource Systems, Haass, A., e_£ al,
Harvard University Press, Cambridge, 1962, pp. 88-158,
6. Forrester, J, W., Industrial Dynamics, MIT Press, Cambridge, Mass,,
1961.
7. Hall, W. A,, "Aqueduct Capacity Under Optimum Benefit Policy,"
J. Irrigation and Drainage Division, ASCE, Vol. 87, No. IR3, Sept,
1961, pp. 1-12.
8, Hall, W, A., "Optimum Design of a Multiple-Purpose Reservoir,"
J. Hydraulics Division, ASCE, Vol. 90, No. HY 4, July, 1964,
p. 141-150.
9. Hall, W. A» and Buras, N., "The Dynamic Programming Approach to
Water Resources Development," J, of Geophysical Research, Vol. 66,
No. 2, Feb., 1961, p, 317-520.
10, Halter, A, ll»t and Dean, G. W*, "Simulation of California Range
Feedlot Operation," Giannini Foundation Research Report No. 282,
University of California at Berkeley, May, 1965,
11. Hamilton, 11, R,, e£ _al_, A Dynamic Model of the Economy of the
Susquehanna River Basin, Battelle Memorial Institute, Columbus,
Ohio, 1966.
12. Hufschmidt, M. M. , "Analysis by Simulation: Examination of Response
Surface," Design of Water-Resource Systems, Maass, A., et^ al,
Harvard Univ. Press, Cambridge, 1962, pp. 391-442.
13. Hufschmidt, M. M. and Fiering, M. B,, Simulation Techniques for
Design of Water-Resource Systems, Harvard Univ, Press, Cambridge, 1966.
-------
14. James, L. D., "Economic Derivation of Reservoir Operating Rules,"
J. Hydraulics Division. ASCE, Vol. 94, No. HY5, Sept., 1968,
pp. 1217-1230.
15. Jaworski, N. A., e_t al, Optimal Release Sequences for Water Quality
Control in Multiple-Reservoir Systems, Technical Publication, Joint
Research Project, Annapolis Science Center, FWPCA, April, 1968.
16. Kerri, K. D., "An Economic Approach to Water Quality Control,"
Journal Water Pollution Control Federation, Vol. 38, No. 12,
Dec., 1969, pp. 1883-1897.
17. Kerri, K. D., An Investigation of Alternative Means of Achieving
Water Quality Objectives, Department of Civil Engineering, Oregon
State Univ., Corvallis, Ore., 1965.
18. Krasnow, H. S, and Merckallo, R. A., "The Past, Present, and
Future of General Simulation Languages," Management Science,
Vol. 11, No. 2, Nov., 1964, pp. 236-267.
19. Loucks, D. P., "Computer Models for Reservoir Regulation,"
J. Sanitary Engineering Divisions, ASCE, Vol. 94, No. SA4, Aug.,
1968, pp. 657-669.
20. Oregon State Sanitary Authority, Water Quality Standards, Willamette
River and Multnomah Channel, Portland, Ore., 1967.
21. Payne, K., £££!_, "Daily Streatnflow Simulation," Hydraulics
Division. ASCE, Vol. 95, No, HY4, July, 1969, pp. 1163-1179.
22. Pugh, A. L, III, DYNAMO Users Manual, 2nd ed., MIT Press, Cambridge,
Mass., 1963.
23. Ray, R. C. and Walker, W. R., "Low-Flow Criteria for Stream
Standards," J. Sanitary Engineering Division, ASCE, Vol. 94, No.
SA3, June, 1968, pp. 507-520.
24. Sullivan, E, F, Personal communication.
25. U.S. Army Corps of Engineers, Report on Redistribution of Irrigation
and Other Water Resource Benefits, Portland. Ore. (Sept. 1959.
revised Nov. 1960).
26. Whipple, W. Jr., "Optimum Investiment in Structural Flood Control,"
J. Hydraulics Division. ASCE, Vol. 94, No. HY6, Nov., 1968,
pp. 1507-1515.
27. U.S. Congress, Senate, Policies, Standards and Procedures in the
Formulation, Evaluation^ and Review of Plans for Use and Development
of Water and Related Land Resources, Eighty-seventh Congress,
Second Session, 1962, Document No. 97.
46
-------
28. Worley, J. L., A System Analysis Method for Water Quality Management
by Flow Augmentation in a Complex River Basin, U.S. Public Health
Service, Region IX, Portland, Ore., 1963,
29. Young, G. K., "Finding Reservoir Operating Rules," J. Hydraulics
Division. ASCE, Vol. 93, No. HY6, Nov. 1967, pp. 297-321.
30, Young, G. K., "Reservoir Management: The Tradeoff between Low Flow
Regulation and Flood Control," Water Resources Research, Vol. 4,
No. 3, June, 1968, pp. 507-511.
31. Young, G. K., and Pisano, W. C., "Reservoir Analysis for Low
Flow Control," J. Sanitary Engineering Division, ASCE, Vol. 94,
No, SAC, Dec., 1968, pp. 1305-1307.
-------
SECTION 9
LIST OF PUBLICATIONS
1. Apostolos, John A., "Factors Influencing Recreation on Reservoirs,"
paper presented at the Pacific Southwest Conference of ASCE Student
Chapters, Reno, Nevada, 1967.
2. Hinrichs, D. J., "Comparison of Simulated and Historical Streamflows,"
paper presented at the Pacific Southwest Conference of ASCE Student
Chapters, San Diego, Calif., 1968.
3. Hinrichs, D. J., "Tolerable Shortages in Irrigation System Design,"
Paper presented at the Pacific Southwest Conference of ASCE Student
Chapters, San Francisco, Calif., 1969. Submitted to J. Irrigation
and Drainage, ASCE.
4. Kerri, K. D., "Allocation of Water for Flow Augmentation," paper
presented at the 1969 Water Pollution Control Federation Conference,
Dallas, Texas, October, 1969, Submitted to J, Water Pollution
Control Federation.
5. Kerri, K. D., "Application of Industrial Dynamics to Water Quality
Control," Industrial Dynamics Newsletter, MIT, May 1968.
6. Payne, Kip, Neuraan, W. R., and Kerri, K. D., "Daily Streamflow
Simulation," J. Hydraulics Division, ASCE, Vol. 95, No. HY4,
Proc. Paper 6665, July, 1969, pp. 1163-1179.
49
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SECTION 10
APPENDICES
I. Theory of Optimum Allocation of Water
II. Daily Streamflow Simulation
III. Recreation and Reservoir Operation
IV. Input Data
V, Flow Diagrams and Computer Programs
51
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APPENDIX I
THEORY OF OPTIMUM ALLOCATION OF WATER
Statement of the Problem
A technique is needed to aid planners, designers and operations personnel
determine the optimum allocation of scarce water. During periods of high
demands and low supplies of water, critical decisions must be made
regarding how much water should be released and for what purposes, as well
as how much should be stored for future releases or to be held to maintain
a minimum pool. Water quality frequently deteriorates to extremely
serious levels throughout water short periods. Frequently the only
method readily available to maintain a suitable water quality for aquatic
life and many other downstream beneficial uses is the release of stored
water for water quality coifrol.
ReJease of water for water quality control conflicts with demands for
municipal and industrial water supplies, irrigation, head for hydroelectric
power production, and reservoir fishing and recreational uses. Water stored
for future releases will complement these competing demands until released.
When released for water quality control, many downstream uses, including
aquatic life, will be complemented or will benefit. Proposed in this
report is an analytical model capable of identifying the extent and
magnitude of the complementary and competitive aspects of water storage
for water quality control.
Theory
Economists have used mathematical optimization techniques to study and
explain the actions of a rational entrepreneur in their literature known
as the "Theory of the Firm" (3). The entrepreneur's objective function
may be to (1) maximize output subject to a budget constraint (2) minimize
cost of production for a prescribed level of output or (3) maximize
profits.
These same concepts can be applied to a river basin. To optimize water
resources development or the economy within a basin or region, an
institution must be functioning that is capable of regulating or con-
trolling all pertinent actions within the system under consideration.
In the United States such an institution is rare, but there are trends
in this direction (4), Fortunately these optimization techniques can
be applied to programs or even a specific project with a basin by careful
definition of the system to be optimized.
To illustrate this flexible system concept, two examples will be briefly
outlined. One system could consist of a completed project with all
structural inputs (reservoir size and conveyance structures) fixed and
all target outputs already determined (crops planted, generators intalled
and municipalities connected to a distribution system). The critical
decision is the allocation of available water, Another system could be
-------
in the planning or design stages and neither the mangitude of the
structural inputs nor the target outputs have been established. In
either system, the operational decision is still the same—the allocation
of water to maximize the objective function or minimize costs. The main
difference is that the planning or design system has more decision
variables and fewer constraints than an existing system.
Derivation
Economists define production as "any activity intended to convert
resources of given forms and location into other resources of forms
and locations deemed more useful for purposes of further production or
consumption" (2). The term "location" is four dimensional, because
in water resource development water must be available where and when
needed. In any system the production or output is a function of an
input or set of inputs. This relationship is described by a production
function. In its simplest form the output, Y, is a function of an
input X.
Y - f(X).
To illustrate this concept, let Y (output) represent the production of
rice and X (input) represent water. If all other inputs, including
water quality, are constant, then the production function shown in
Figure 1 could result.
OUTPUT, Y
(Rice)
INPUT, X
(Water)
Simple Production Function
Fig. 1
Examination of Figure 1 reveals that points above the locus of points
describing the production function are physically impossible and all
points below the production function are inefficient.^- Figure 1 also
shows that excess water could result in a decrease in production.
(1)
•'•For a certain amount of water applied during the growing season, there
is a maximum output of rice when all other variables are held constant.
Also, if this volume of water is applied during the growing season
and the production of rice is less than the output indicated by the
production function, then the water was used inefficiently.
-------
This simple relationship can be expanded to be applicable to any water
resource system. Rearrange equation 1 to
Y - f(X) = 0. (2)
The production function for any water resource system is now written
in the implicit form and expanded to
H (YI,..,YS, KI( x2,..xn) = o. (3)
where Y represents outputs (] , 2,,,,s) resulting from sufficient water
of suitable quality being delivered when needed* X represents the n
input variables which include structural, nonstructural, and operational
input variables „
To simplify the notation, let Y . = X. (j = 1, 2,».n)
STJ J
-V
The production function may noiv* be rewritten as
F(Y,, Y2,.*.Y ) - 0
1 *• m
where m = n+s
To maximize the net benefits of a water resource system, the objective
function may be represented by the maximum net benefits,
m
" = L p.Y.
1=1 1 X
where PS+. = r (j = 1,2,... n).
The value p., normal Jy representes the price or value of the outputs,
Y, but in the implicit form used here, also represents the costs (r.)
of the inputs, X. In equation 4, the outputs contribute positive
values to the objective function, and inputs are negative terms.
The optimum combination of inputs and outputs is located on a response
surface described by the production function. Therefore, the objective
function is optimized subject to the production function contraint.
m
J = £ p^ + AF(YJP Y2,.f,,Yrn). (5)
The necessary or first-order conditions for maximization are
~ = Pi + AFi = 0 (i - 1, 2,...m) ' (6)
55
-------
where FI
and |i -FCY^Y^..^) -0. (7)
A. Roth Variables Outputs
To obtain a physical meaning for the nedessary conditions for maxi-
mization, select any two of the first m equations from equation 6 and
obtain
!i - II - "|!ii, (j,k- 1,2. ...m). (8)
Pk Fk 3Yj
The minus sign stems from the fact that if one output is increased,
the other must be decreased.
If both variables are outputs (j and k both < s) then equation 8
represents the relationship between all outputs of optimum conditons.
Therefore, at optimum conditions, the rate of product transformation
(RPT)2 for every pair of outputs (holding the levels of all other
outputs and inputs constant) must equal the ratio of their prices.
For example
MB.
In this example, at optimum conditions, if the inputs are held constant
and one output is decreased an increment and the unused inputs transformed
(applied) to increase another output an increment, then this rate of
product transformation is equal to the ratio of the prices or value of
the outputs,
This relationship can be visualized by examining equation 8. Assume
the value or price of output j is low in comparision with k. At
optimum conditions, a large increment of output j could be transformed
into a small increment of output k. The loss in net benefits from
reducing j would be equal to the increase in net benefits from increasing
k. This relationship will hold for all pairs of benefits at optimum
conditions and is sometimes referred to as "equating marginal benefits,"
B. One Variable an Input and the Other an Output
Assume that the j th variable is an input and the k th variable remains
an output.
2
The term rate of product transformation (RPT) is used because it is
more descriptive than the commonly used marginal rate of transformation
(MRT) and also because the use of marginal and rate in the same phrase
is redundant (3).
56
-------
Substitute p. » r,
J J""S
where s * number of outputs
and 3Y. » 3X.
J J~s
from Y . . - -X,.
s+j j
From equation 8 obtain
Pk j->
or r » PV. 3Yk (k = l,2,...s)
J-s k:>x (j = 8+1,. ..«).
J =•
Equation 10 states that at optimum conditions the value of the marginal
products (MP) of an input with respect to every output (p, jY^ ) must
be equated to its cost. Therefore :axV
j-s
MCj - MBk(MP)jk,
MC
The marginal product is the rate at which the Y, output can be increased
(or decreased) with respect to its inputs. Equation 11 states that
at optimum conditions the cost of an incremental input X must be equal
to the price or value of the resulting output Y, This relationship
is sometimes known as "equating marginal benefits to marginal costs*"
C. Boti'. Variables Inputs
If both variables .ire inputs, then equation 8 can be written in the form
. _ 5Xk-s (12)
whe re ( j , k = s + 1 , , « . n ) ,
The minus sign reappears because at maximum conditions if one input
is increased, then the other must be decreased. At optimum conditions,
equation 12 indicates that the rate of technical substitution (RTS)3
for every pair of inputs (holding the levels of all outputs and all
other inputs constant) must equal the ratio of their prices,
MC.
RTS, - — 1 . (13)
Kj 'Ic
The term rate of technical substitution (RTS) is used because it is
more descriptive than the commonly used marginal rate of substitution
(MRS) and also because the use of marginal and rate in the same phrase
is redundant (3) .
57
-------
This relationship can be visualized by examining equation 12. At
optimum conditions if all variables are held constant with the exception
of two inputs, then the reduction in coat resulting from decreasing
one input an increment must be equal to the cost of increasing or
substituting the other input. This relationship is sometimes known
as "equating marginal costs."
These conditions are the necessary or first-order conditions based on
the theory of maximization of differential calculus. They were
determined by setting the first partial derivatives equal to zero
(equations 6 and 7). Solving these equations produces either
maximum or minimum values for the response surface because the first
partial derivative describes the slope of the response surface. (Fig. 2)
(a) slope - 0
and
(c) Corner solution
(b) Slope • 0
and increasing (+)
Vector X, Y
Fig. 2. Two-dimensional response surface.
In Figure 2, the necessary or first-order conditions would not indicate
whether the results represented a maximum, such as (a), or a minimum,
such as (b) ,
To differentiate between maxima and minima on a response surface (or
points (a) and (b)) the sufficient or second-order conditions must be
determined. These conditions reflect the change of the slope of the
response surface. At maximum conditions the slope is decreasing (-),
whereas at minimum conditions, the slope is increasing (+). Therefore,
at maximum conditions the slope is decreasing or the sufficient or
second-order conditions are negative.
The second-order conditions for the maximum net benefits require that
the relevant bordered Hessian determinants alternate in sign:
21
>0
F. ...
mm
m
m
> 0.
(14)
Multiplying the first two columns of the first array and the first m
of the last by 1/X, and multiplying the last row of both arrays by X,
58
-------
F F F
11 12 1
F21 F22 F2
Fl F2
n
-' U
Fll
F
ml
Fl
Flm
F
mm
F
m
Fl
F
m
0
> 0.
(15)
Since A«0 from equation (6), the second order conditions require that
12
21 22
0
F.. . . . .
Fml • * ' "
F,
. . F,
mm
F
m
F
1
F
m
0
(16)
This derivation is based on the theory of maximization of differential
calculus and therefore also is subject to the limitations of the theory.
These shortcomings can be seen in Figure 2, The problem of differentiating
between maxima and minima can be overcome by checking the sufficient
conditions for maxima. Two other problems remain. When a maximum is
located, it is difficult to determine whether it is the global maximum
or possibly one of several local maxima. The other problem is that the
maximum may be a "corner solution" (Point (C) on Figure 2). Corner
solutions are found in economic problems because physical variables
must be positive and also because of other constraints, such as budget
or legal. Consequently, a solution may be at the maximum on a response
surface and not meet the necessary conditions,
Application
To apply the preceding derivation to the optimization of water resources
development equation 1> must be written in explicit mathematical terms,
n
iYl
'F(Y
1»
Y ,,,.Ym),
(5)
In equation (5) the objective is to maximize the net benefits ( £ )
subject to the production function constraint F(Y,,Y2..,,Y ). i-1
To accomplish this feat the price or value ol each of the outputs and
costs of each of the inputs would have to be expressed mathematically.
The price people are willing to pay for water depends on the amount
available or supply and the cost of inputs varies with the amount
needed or demanded. The magnitude of the inputs is a function of the
water handled and the size of the target outputs depends upon consumer
demand and the availability of sufficient water of suitable quality
when needed. Streamflow is a stochastic process, consequently uncertainty
is always involved regarding the allocation of volumes of water for
beneficial uses. Finally demands and prices change seasonally.
Obviously the task of expressing the situation in a water resource
system is formidable.
59
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To avoid some of these problems, researchers have developed simulation
techniques to describe a water resource system (1, 4, 6, 8, 9).
Simulation models attempt to generate stochastic process on high speed
computers similar to events that could occur in nature. The models
attempt to predict how proposed or existing systems might respond to
the stochastic processes. Various structural inputs, target outputs, and
operational procedures may be tested by the simulation model to approach
a region on the response surface of optimum conditions.
Common mathematical searching techniques include the method of steepest
ascent and other methods using incremental or marginal analysis
(gradient techniques). These methods essentially change the inputs,
outputs, or operational procedures by small increments, continuously
trying to improve the objective function. The approaches normally
will not locate an exact maximum (even if one existed) but produce a
combination of inputs, outputs, and operational procedures within the
limits of accuracy of the input data. A limitation of these searching
techniques, similar to a limitation of differential calculus, is that
it may be difficult to differentiate between local maxima and the
global maximum.
A major advantage of simulation models is their ability to generate
streamflows (stochastic processes) similar to what could occur in
the future, because the sequence of flows is of vital importance to
water users. In simulation models, it is easy to estimate the response
of the system to different inputs, outputs, and operational procedures
once a suitable simulation model has been developed and tested.
Early simulation models tended to use fixed operational procedures (7)
due to the complexities involved. Naturally this shortcoming was
recognized and numerous researchers delved into this area. Dynamic
programming was applied by many, not only to develop operational pro-
cedures, but also to size inputs and target outputs. The number of
computations using dynamic programming is high because of the iterative
procedure of tracing many possible sequences.
Simple, realistic procedures for practicing engineers have not evolved
because of the complexities of the complementary and competitive aspects
of water storage and the understanding of higher mathematics required
to comprehend and apply proposed techniques. The proposed Analytical
Model (Section 3) proposes a simple, straightforward technique capable
of identifying the extent and mangitude of the complementary and
competitive aspects of water storage for water quality control. The
model contains a step by step procedure for the allocation of scarce
water to various beneficial uses which is essentially a rational
searching procedure to identify the optimum conditions (Equations 9,11,
and 13).
60
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REFERENCES TO APPENDIX I
1. Dobbins, W. E., and Goodman, A. S., "Mathematical Model for Water
Pollution Control Studies," J. Sanitary Engineering Division,
ASCE, Vol. 92, No. SA6, Dec., 1966, pp. 1-19.
2. Dorftnan, R., "Basic Economic and Technologic Concepts: A General
Statement," Design of Water-Resource Systems, Maass, A., ejt_ £i,
Harvard Univ. Press, Cambridge, 1962, pp. 88-158,
3. Henderson, J. M. and Quandt, R. E., Microeconomic Theory, McGraw-
Hill, New York, 1958. " *~
4. Heubeck, A., e£ ai_, "Program for Water-Pollution Control in Maryland,"
J. Sanitary Engineering Division, ASCE, Vol. 94, No. SA2, April,
1968, pp. 283-293.
5. Ilufschmidt, M. M., and Fiering, M. B., Simulation Techniques for
Design of Water Resource Systems, Harvard Univ. Press, Cambridge,
1966.
6. Loucks, D. P., "Computer Models for Reservoir Regulation," J_._
Sanitary Engineering Division, ASCE, Vol. 94, No. SA4, Aug., 1968,
pp. 657-669.
7. Maass, A. et_ al^ Design of Water Resource Systems, Harvard Univ.
Press, Cambridge, 1962.
8. Shull, R., and Gloyna, E., Radioactivity Transport in Water-
Simulation of Sustained Releases to Selected River Environments,
CRWR26, Civil Engineering Dept., University of Texas at Austin,
1968.
9. Young, G. K., and Pisano, W. C,, "Operational Hydrology Using
Residuals," J. Hydraulics Division. ASCE, Vol. 94, No. HY4, July,
1968, pp. 909-923.
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APPENDIX li
DAILY STREAMFLOW SIMULATION
Reproduced from
Journal of the Hydraulics Division
Proceedings of the American Society of Civil Engineers
Volume 05, Number HY4, July, 1969
63
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6665 July, 1969 HY 4
Journal of the
HYDRAULICS DIVISION
Proceedings of the American Society of Civil Engineers
DAILY STREAMFLOW SIMULATION
By fclp Payne,1 W. R. Neuman,2 A. M. ASCE, and
K. D. Kerri,3 M. ASCE
INTRODUCTION
Dally streamflow simulation offers engineers an opportunity to study the
response of water resource systems to synthetic daily flow traces. The regu-
lation and routing of floods, and the release of water for water quality control
and fisheries during low flow periods, can be of special interest. The objective
herein is to develop a multiple-station daily streamflow generator capable of
simulating daily flow sequences with frequency characteristics similar to
those of the historical records. The hydrographs within each month are rear-
ranged to reduce the variability of the recorded flows. Flows are simulated
on the basis of the statistical parameters computed from the rearranged daily
flows. The adequacy of the technique is tested by comparing the frequency
distributions of the important statistical properties of the historical flows with
those of the simulated flows.
Other Flow Simulators.—Halter and Miller (8)4 developed a daily flow sim-
ulator using a linear regression model which generated 30 flows each month,
on the basis of the mean monthly flow and the standard error of the monthly
flow. The simulated hydrographs were not adequate because the serial cor-
relation between previous flows was not incorporated in the generator, with
the exception of recession curves. Flows followed a recession curve when a
generated flow exceeded an assumed high flow value. Some of the variation
between daily flows probably could have been reduced by using a variance
computed from the flows within a month and also based on a function of the
Note.—Discussion open until December 1,1969. To extend the closing date one month,
a written request must be filed with the Executive Secretary, ASCE. This paper is part
of the copyrighted Journal of the Hydraulics Division, Proceedings of the American So-
ciety of Civil Engineers, Vol. 95, No. HY4, July, 1969. Manuscript was submitted for
review for possible publication on August 23, 1968.
1Research Assoc., Sacramento State Coll., now Sanit. Engr., Los Angeles County
Sanitation District, Calif.
2 Assoc. Prof., Dept. of Civ. Engrg., Sacramento State Coll., Sacramento, Calif.
3Prof., Dept. of Civ. Engrg., Sacramento State Coll., Sacramento, Calif.
4Numerals in parentheses refer to corresponding items in the Appendix I.—
References.
1163
64
-------
1164 July, 1969 HY 4
simulated monthly mean. Examination of historical records reveals that
months with high flows usually exhibit a higher variation of flows within the
month than months with low flows.
Beard (2) has developed a daily streamflow simulator for a single station.
His model generates daily flows during the flood season using a second-order
Markov chain and the frequency characteristics of the daily flows within a
calendar month. Daily flows are adjusted to agree with the simulated monthly
flows. The proposed simulator is an extension of a monthly simulator de-
veloped by Beard (3), but differs from Beard's daily model in two respects:
(1) Historical hydrographs are rearranged; and (2) simulation of monthly flows
are not necessary. Operational monthly flow generators have been developed
and successfully tested by Thomas and Fiering (16), Harms and Campbell
(10), Beard (3), and Fiering (5). Additional streamflow simulation methods
have been proposed by Matalas (13), Quimpo (15) and Young and Pisano (19).
Yevdjevich (18) has reviewed simulation models.
Arrangement of Data.—Daily flows during certain seasons are apt to be
extremely variable. The variance computed for any particular day for a num-
ber of years is likely to be very high. If raw historical data for a season with
highly stochastic flows were analyzed, the means would be similar, the vari-
ances high, and the regression and correlation coefficients low. Attempts to
simulate flows from these statistical parameters would not produce hydro-
graphs with statistical properties similar to historical ones, because the
ascension and recession curves would not be simulated.
To preserve the ascension and recession curves of hydrographs, the his-
torical flows should be rearranged prior to analysis. The procedure for
rearrangement consists of the following steps:
1. Divide the annual flows into time spans of particular concern, depending
on the use of the simulator. Appropriate time spans could be months or
seasons.
2. Search the historical records of each time span and identify important
hydrologic events, such as peak flows, minimum flows, or trends. During a.
flood month, the magnitude and number of flood or peak flows and the time
between peaks are of extreme importance.
3. From an examination of important hydrologic events in each time span,
determine the expected day or days of occurrence. Consideration also must be
given to the expected time between events.
4. Rearrange the historical hydrographs around the peak or important ex-
pected day of the month. If a peak flow is expected on a certain day during a
time span, then all historical peak flows for the time span should be rear-
ranged around this day. As many of the ascension and recession curves of the
historical hydrograph as possible should be rearranged around the peak day.
The remaining segments of the hydrograph should be rearranged to preserve
as great a portion of the historical hydrograph as possible. The same pro-
cedure is applied to minimum flows or trends.
Some streams may exhibit flow characteristics from two populations during
a particular time span, such as a winter month with relatively steady, low flows
during ice or snow conditions and fluctuating high flows during periods of heavy
precipitation and runoff. Another possibility would be flows resulting from
two sources, such as ground water and snowmelt. If two populations are
65
-------
HY 4 STREAMFLOW SIMULATION H65
distinct, they should be separated, if possible, and the simulator can then be
programmed to generate flows from one population or the other, or both,
based on the probability and characteristics of each event.
Development of Daily Flow Simulator.—The rearranged historical flows for
each day usually are not normally distributed. The log-Pearson Type III
method is used to generate flows because it is the recommended technique
for determining flood flow frequencies (1,4). The step-by-step procedure for
developing a daily flow generator is outlined in the following section. Beard
has prepared detailed explanations of the analysis calculations (11), the syn-
thesis procedure (12) and he has also developed computer programs to per-
form these operations.
ANALYSIS SECTION
Convert all rearranged flows, Q, to corresponding natural logarithms, L.
Calculate mean, M, standard deviation, S, and skewer for each day from the
natural logs.
N / N \2
Z4 - (lLh )
/, = ! \k = l I
N- 1
N N N
(1)
(2)
„ =
in which N = the number of years of record; and 2 indicates the summation of
all values (h) for a particular day.
Calculate a k (Pearson Type III standard deviate) value for each daily flow
by subtracting the mean from the flow value and dividing by the standard
deviation.
(4)
Transform the k value to the normal standard deviate, X, using the skew
coefficient and the Pearson Type in function by the following approximation:
X" = I [(I kh + O"3 -1] + f
Treat these X values as variables and solve for the regression coefficients,
the standard deviations for the variables, and the correlation coefficients (R)
for each day.
66
-------
1166
July, 1969
HY4
(1)
(2)
(J)
(6)
in which X = logarithm of the daily streamf low transformed to a normal stan-
dard deviate; ft = regression coefficient; first subscript, i, represents the
day number; the second subscript, j, represents the station number; and the
superscript represents the independent variable number. A regression con-
stant does not appear in the normalized form of the regression equation.
Convert the regression coefficients to beta coefficients, B, in which
(1)
(1)
(7)
SIMULATOR SECTION
Simulation of flows begins with the generation of a random normal standard
deviate, RN (mean zero and variance unity) as in the following equation
(1) (2) (j + 1)
*i,i = Bitj Xt.ltj + Bitj *,,_,_! + Btlj Xitl + (1 - *»)<>.» (RN) (8)
in which ft = the multiple correlation coefficient.
Convert the normal standard deviates, X, to Pearson Type III deviates, k,
by the following approximation:
8
-
This approximation is not correct under certain circumstances and must
be checked with Fig. 1 to determine the value of k' in Eq. 10.
Calculate simulated flow, Q, in cubic feet per second.
In Q = M + —
(10)
or Q = exp [M + (fe'S/C)] in which C = a coefficient depending on the stream,
FIG. 1.—FLOW CHART FOR VALUES OF k'
67
-------
HY4
STREAMFLOW SIMULATION
1167
the rearranged flows, and whether k' is positive or negative. This term is
used to reduce any remaining excess variability in the simulated flows. A
trend component could be incorporated in Eq. 10 if one were detected in the
historical flows.
If today's simulated downstream flow is less than yesterday's simulated
upstream flow, appropriate adjustments can be made by considering travel
times and channel storage.
TEST BASIN
Description.—The proposed daily streamflow simulator was developed and
tested using the flow records for two gaging stations on the Calapooia River,
a tributary of the Willamette River in Oregon (Fig. 2). The headwaters of the
FIG. 2.—CALAPOOIA RIVER BASIN
Calapooia are located near the crest of the Cascade Mountains. Snow gen-
erally falls during the winter months and melts during the spring months. The
stream travels through a rather narrow canyon from the headwaters, and then
past a potential dam site at Holley, the upstream gaging station. Below Holley,
the river enters theWillametteValleyatBrownsville.lt then meanders across
the flat Willamette Valley, until the river reaches its confluence with the
Willamette River at Albany. The downstream gaging station is located three
miles above the mouth.
The Calapooia River, which is fed by snowmelt and runoff from rainfall,
could be described as a typical stream on the western slopes of the Cascade
Mountains in the Pacific Northwest. The flow is influenced by rainfall from
winter storms which can cause short duration floods. Sometimes, runoff from
a rain will be accompanied by high flows from melting snows. During early
spring, runoff is high due to melting snow. Flows gradually decrease through-
-------
1168
July, 1969
HY4
out the summer, and gradually increase during the fall as storm activity in-
creases. Peak flows of short duration are observed during the fall and spring
•when a rain storm passes over the basin.
Arrangement of Data.—Historical flows were rearranged in accordance with
the procedures outlined previously. Monthly time spans were selected because
these time periods appeared to group similar important hydrologic events.
Thus, the procedure for rearranging the historical flows depended on the
month under consideration. For a particular month, the days which exhibited
peak flows were recorded for each year of historical record. In the fall, the
months frequently displayed one peak near the end of the month. Winter
months usually had two or three peak flows, while spring months generally
had one peak early in the month. During the summer the flows gradually de-
creased throughout the month, because the stream was fed by snowmelt.
To rearrange the flows during a particular month, one or more days were
selected as the peak, and all historical flows were rearranged about it. For
example, the average peak day in November occurred on the 23rd, and most
FIG. 3.—TYPICAL JANUARY HISTORICAL HYDRO-GRAPH AND SAME HYDROGRAPH
REARRANGED ABOUT PEAK DAYS FOR ANALYSIS
Novembers experienced only one storm producing a significant peak. The flows
for every November of record were rearranged with the peak flow on the 23rd.
The flow sequences of the original hydrograph were maintained, as closely as
possible, with special priority given the ascension and recession curves. This
procedure was repeated for the spring.
Winter months having two significant peak flows, naturally had both the
highest and next to highest peak flows occurring around the fifteenth of the
month, on the average. This unrealistic event was eliminated by calculating
the average time between peak flows. For example, in January the average
time between peak flows was 11 days; therefore, the highest peaks were re-
arranged around the 20th day of the month and the next to highest peaks rear-
ranged around the ninth of the month. Fig. 3 shows a typical historical flow
and the resultant rearranged flow.
During the summer months, the flows gradually decreased throughout each
month, except when a few, scattered storms occurred. Since not many peak
-------
HY4
STREAMFLOW SIMULATION
1169
flows occurred, the summer flows were not rearranged.
Development of Daily Flow Simulator.—The rearranged historical flows
for each day were not normally distributed. In an attempt to transform the
rearranged flows to normal distributions, two transformations were examined.
Both a natural log and a normal standard deviate, based on a Pearson Type III
function transformation, were studied. A chi-squared goodness of fit test was
used to test for the normality of the transformed flows. The transformations
both apparently followed the nor maldistribution, atthe 5% level of significance.
Therefore, the use of the log-Pearson Type III method is justified.
A trend component was not incorporated into Eq. 10, because none was
detected in the historical flows. Summer flows were decreasing at the down-
H 1—H
-(—1—I—h
-I—h
00oooo°
II I I I I
S 10 3D SO 4O 9O «O 7O 10 tO M fi
FIG. 4.—PLOT OF MAXIMUM AND MINIMUM AVERAGE DAILY HISTORICAL FLOWS
ON LOG PROBABILITY PAPER, UPSTREAM STATION
stream station due to increased irrigation activity, butthe natural flows were
reconstructed (17).
Approximately once a year the simulated downstream flow was slightly
less than the previous day's upstream flow. On these occasions, the down-
stream flow was set equal to the upstream flow, because the travel time be-
tween the stations was one day.
Test of Model .—To test a flow simulator, twoquestions must be answered:
(1) What tests should be used; and (2) how is it decided whether or not the
statistical distributions of the Hows generated are close enough to historical
distributions? The tests used to examine the similarity between historical
70
-------
1170
July, 1969
HY4
and generated flows were comparisons of statistical parameters. These
parameters reflected important flow sequences, from the standpoint of
operating the water resource system and of the beneficial uses served by the
system. The daily flow generator was deemed sufficient, when plots of the
simulated data approximated those of the historical records. Important
parameters selected included the distribution of annual mean flow, maximum
TABLE 1.—FINAL C VALUES
Deviation, k'
(1)
Negative
Positive
Upstream
(2)
1.35
1.1
Downstream
(3)
1.45
1.2
§'"
HISTORICAL -
SIMULATED •
HISTORICAL
SIMULATED <
HISTORICAL
- SIMULATED
— HISTORICAL
— SlMULATID
FIG. 5.-TYPICAL JANUARY HISTORI- FIG. 6.-TYPICAL JULY HISTORICAL
CAL AND SIMULATED FLOWS AND SIMULATED FLOWS
and minimum daily flows, maximum three-day average flow, minimum seven-
day average flow, and minimum average summer flow (June, July, August,
and September). These properties were plotted on normal, log, and extremal
probability papers. All of them plotted closest to a straight line (Fig. 4) on
log-probability paper. Originally, the analysis of the generated flows revealed
that the distribution of the annual mean flow was successfully retained, but
71
-------
HY4
STREAMFLOW SIMULATION
1171
the .simulated maximum and minimum daily flows exhibited greater variation
than the historical flows, i.e., higher maximums and lower minimums. To
reduqe these variations, the coefficient C in Eq. 10 was introduced.
After an initial trial, the distribution of the simulated maximum flows cor-
responded closely to historical ones, but the simulated minimum flows re-
mained slightly low. To correct this situation, two different C values were
TABLE 2.-SUMMARY OF EXTREME VALUES OF HISTORICAL AND SIMULATED
FLOWS, UPSTREAM STATION, IN CUBIC FEET PER SECOND*
Run
(i)
i
2
3
4
5
6
7
8
9
10
Historical
Maximum
1-day
(2)
13,460
12,050
15,340
9,380C
15,600
12,490
10,250
14,490
18,670b
15,200
11,000
Maximum
3-day
(3)
10,460
8,820
10,760
6,230°
10,390
10,360
7,060
10,180
14,140b
11,660
8,830
Maximum
10-day
(4)
5,866
5,490
6,710
3,456C
5,941
5,850
5,169
5,849
7,585b
6,394
5,487
Minimum
1-day
(5)
18.7
15.0
16.4
14.0
10.9
12.7
18.3
8.2C
11.5
19.3
20.0b
Minimum
7-day
(6)
24.0
19.8
21.4
21.6
17.5
18.1
24.0
11.9C
15.7
24. 5b
24.0
Minimum
30- day
(7)
26.8
26.5
27. 3b
25.5
25.5
22.2
24.2
18.6°
22.4
23.9
22.8
Minimum
120-day
(8)
47.4
47.5
42.8
48. lb
43.5
47.1
39.1
34.2
44.9
41.5
32.5°
Annual
average
(9)
471.6
469.3
487.4
457.7
455.5
454.2°
497. 4b
480.6
478.7
468.4
465.8
a.V = 24 for all runs and historical record; Upstream (-*')
b Maximum.
c Minimum.
515
, (+i>) . Downstream (-*') , (+*') -.
TABLE 3.-SUMMARY OF EXTREME VALUES OF HISTORICAL AND SIMULATED
FLOWS, DOWNSTREAM STATION, IN CUBIC FEET PER SECONDa
Simulation
run
(1)
1
2
3
4
5
6
7
a
9
10
Historical
Maximum
1-day
(2)
27,400
34,990
29,800
28,800
42,130
44,lBQb
28,910
34,010
31,660
32,310
26,800°
Maximum
3-day
(3)
22,140
29,090
24,070
18,990°
33,210
36,84Cb
24.36C
26,760
29,930
26,660
21,970
Maximum
10-day
(4)
15,550
19,440
18,530
10,430°
17,870
2Q,940b
14,670
13,360
16,570
15,950
13,880
Minimum
1-day
(5)
21.8
17.6
18.8
18.7
11.2
5.6C
21.0
11.4
15.1
24. lb
11.0
Minimum
7-day
(6)
32. lb
27.3
26.0
27.9
23.0
23.0
29.1
15.3°
19.9
29.7
27.7
Minimum
30-day
(7)
34.3
34.6
35. lb
32.1
31.4
27.9
30.2
23.5°
28.7
29.9
26.5
Minimum
120-day
(8)
67. 2b
61.3
65.4
64.6
63.0
64.4
53.7
45.4
64.4
60.6
42.9°
Annual
average
(9)
982.3
986.6
1,015.0
949.5
941.6°
949.3
l,068.0b
1,019.3
1,000.3
978.3
949.4
24 for all runs and historical record; Upstream (-*') ^
-, (+6-) £-? i Downstream (-*') £1JL (+*•) *lf
1.1 1.45 1.2 '
selected for each station, and the value applied depended on whether the term
containing the deviation (k' in Eq. 10) was added to, or subtracted from, the
rearranged mean of the log of the historic flow. The final C values are shown
in Table 1.
Results.—Typical simulated and historical flows for the upstream and
72
-------
1172
July, 1969
HY4
downstream stations for a winter month and a summer month are shown in
Figs. 5 and 6. The generated flows at both stations appear similar to the
historical hydrographs with respect to smoothness between daily flows, ran-
domness in reductions and increases in the flow rate. Fig. 6 indicates the
ability of the simulator to generate a dry July. The relationships between the
daily means of the rearranged flows and typical historical and simulated wet
flows can be examined in Fig. 7.
MEAN OF REARRANGED
HISTORICAL HOW
SIMULATED FLOW
TYPICAL HISTORICAL
FLOW
* 30
13S
DATS
FIG. 7.-PLOT OF DAILY MEAN FOR REARRANGED FLOWS AND TYPICAL HYDRO-
GRAPHS FOR HISTORICAL AND SIMULATED WET FLOWS
*»•'••
ENVELOP OF 5 SO-YEAR
SIMULATED FLOWS
O 24-YEAR HISTORIC FLOW
I I I 1 J 1 1 L_
1 I 10 20 30 40 SO 60 70 10 VO 93 91
CUMULATIVE PROIARI1IY
FIG. 8.—DISTRIBUTIONS OF HISTORICAL AND SIMULATED MEAN ANNUAL FLOWS,
UPSTREAM STATION
Comparisons of the distributions of the parameters of the simulated flows
with the historical flows are shown in Figs. 9 through 14 and Tables 2 and 3.
Five 50-yr sequences were generated and compared with the 24 yr of historical
record. Figs. 8 and 9 show that the envelopes of the simulated annual mean
flows at both stations, agreed very closely with the historical annual mean
73
-------
HY4
STREAMFLOW SIMULATION
1173
V JO
T,
I
M.
I",
t- I
O 34-YEAI HltTOftlC
• NVEIOP Or 3 1O-VIAI
IIMULATID MOW!
10 30 40 50 60 70 M » 91
CUMULATIVE PRO1A1ILITT
FIG. 9.-DISTRIBUTIONS OF HISTORICAL AND SIMULATED MEAN ANNUAL FLOWS,
DOWNSTREAM STATION
£ I
>. 7
..••fS^i"***""
' o X
S..'
O 24-YIAR HIITOHIC FLOW
• iNvtLor or i-so TIA«
IIMU1ATID FLOWt
10 20 30 40 SO 60 70 10 90 *fl 91
FIG. 10.—DISTRIBUTIONS OF HISTORICAL AND SIMULATED MAXIMUM AVERAGE
THREE-DAY FLOWS, DOWNSTREAM STATION
-------
1174
July, 1969
HY4
flows. The maximum average days at both stations were distributed similar to
the historical maximum average daily flows. Figs. 10 and 11 indicate that the
historical maximum 3-day and 10-day average flows are contained within the
envelopes of the five 50-yr simulated values. The minimum one-day (Fig, 12),
£70
« -
• •
O 24 YEAH HISTORIC FLOW ~
Jo Jo J.
30 40 »0 60
CUMULATIVE FIOIABILITY
A A *o
FIG. 11.-DISTRIBUTIONS OF HISTORICAL AND SIMULATED MAXIMUM AVERAGE
TEN-DAY FLOWS, UPSTREAM STATION
••I- '
0 14-riAI H1STOIIC not,
• EN VI LOCI OF 5 50-YIAR
SIMULATED PLOWS
III - 1 - 1 - 1 - 1
10 30 30 40 SO 60 70 M 9O t9
CUMUL ATIV1 PROIA1I LI TV
FIG. 12.—DISTRIBUTIONS OF HISTORICAL AND SIMULATED MINIMUM AVERAGE
DAILY FLOWS, UPSTREAM STATION
7-day (Fig. 13), and 30-day historical flows for both stations were fairly well
contained within the five 50-yr simulated flows.
The distributions of the 120-day summer flows were slightly flatter (Fig.
14), indicating that the extremes were not as great as the historical, possibly
due to some loss of monthly correlation. However, correlation between spring
(March, April, May) and summer (June, July, August, September) runoff was
75
-------
HY4
STREAMFLOW SIMULATION
1175
greater for the simulated flows than the historical flows (ft = 0.412 versus
R = 0.162 for N = 25 and N = 29 respectively, for the upstream station), which
can be attributed, in part, to the rearrangement. Fig. 7 also illustrates the
ability of the simulator to retain monthly flow properties. If a significant loss
of monthly correlation was evident, a monthly simulator could be used to
generate monthly flows, and the generated daily flows could be adjusted ac-
• ENVELOP OF 9 90 TEAK
SIMULATED HOWS
O 14 TEA* HISTOBIC CLOW
10 3O 3O 40 90 M 70 (0 90 99
CUMULATIVE PIOIAIILITY
FIG. 13.—DISTRIBUTIONS OF HISTORICAL AND SIMULATED MINIMUM AVERAGE
SEVEN-DAY FLOWS, DOWNSTREAM STATION
I I I I I I I
• ENVELOP O* 9 90 TEA*
SIMULATED PLOWS
O 34 TEAt HISTORIC PLOW
I I I I I II |
0 10 » 40 90 «O 70 <0
CUMULATIVE PltOIAtlLITY
»
99 91
FIG. 14.—DISTRIBUTIONS OF HISTORICAL AND SIMULATED MINIMUM AVERAGE
120-DAY FLOWS, UPSTREAM STATION
cordingly. The same procedure could be extended to annual correlations (10).
Tables 2 and 3 reveal the numerical relationships between simulated and
historical maximum and minimum flows for both stations. Historical records
were available for 24 yr for both stations, and a simulation run was divided
into 24 yr periods. In most cases, the historical values were contained within
the range of the generated flows.
76
-------
1176
July, 1969
HY4
EXAMINATION OF DATA
A valid question is, what would have been the results if raw, historical
flows had been analyzed and simulated, instead of the rearranged flows? In
the test basin, the low flows were not rearranged; consequently, the simulated
minimum flows would be the same. Fig. 15 shows the difference in the sta-
tistical parameters of the raw and rearranged flows for January, a month with
highly stochastic flows.
Simulation of five 50-yr periods, using the results of the analysis of the raw
historical records and the final C coefficients, reproduce a distribution of
OL«
0.3
-OLA
i.o
J 10 15 20 25
DAYS
FIG. 15.—COMPARISON OF STATISTICAL PARAMETERS FOR RAW AND REAR-
RANGED HISTORICAL FLOWS FOR JANUARY, UPSTREAM STATION
annual flows very similar to Figs. 8 and 9. The maximum average daily flows
plotted considerably below the historical flows, but the slope was similar.
When the length of the time span for the maximum average flow increased (3
days and 10 days), the simulated flows approached the historical flows, but
the slope of the plotted flows became steeper. Therefore, to preserve the
distributions of the maximum flows when simulating the daily flows in the test
basin, it is necessary to rearrange the raw historical flows in a manner that
will preserve the ascension and recession curves of the hydrographs.
As in most simulation models, this one requires considerable time to pre-
77
-------
HY 4 STREAMFLOW SIMULATION 1177
pare the input data, this primarily involves the conversion of recorded daily
flows to a form for computer input. The rearranging of historical flows,
analysis of these flows, the flow simulation, and the analysis of the simulated
flows can be accomplished by computers. The selection of C coefficients to
adjust the simulated flows to historical flows, is a limitation of this approach.
Different people might select different C values from the same data. Other
problems common to most simulation models of this type include errors in
measuring observed flows and random sampling errors resulting from short
records of historical flows.
To reduce the variability of the daily flows, coefficient C was introduced
in Eq. 10. Consequently, this adjustment is not reflected to other stations or
subsequent time periods. If the simulated> normal standard deviate (Xitj, Eq.
8) was adjusted, then this regulation would be reflected in other stations and
later time periods. Adjustments in the simulated flows were applied in Eq. 10,
because this was the easiest location to alter the flows so that flows with
statistical distributions similar to historical flows could be produced.
Adverse, potential flow sequences are easily simulated by the proposed
model, If greater variability than historical flows are determined desirable
to investigate, the C value can be reduced. This procedure would allow the
study of the response of a design under consideration, to extremely high and
low flows. If the historical data were suspected of representing abnormally
wet or dry years, the simulated flows could be appropriately increased or
decreased and again the response of different plans or designs could be
scrutinized.
Daily streamflow generators have been written in FORTRAN and DYNAMO,
a simulation language (6), (7), (14). Most computers readily handle FORTRAN,
but the generator was more difficult to debug in comparison with DYNAMO.
DYNAMO is adaptable only to certain computers, and the program requires
considerable talent to be made operational on any computer. In contrast to
FORTRAN, the DYNAMO language was written for simulation, and programs
are very easy to debug because of the checking capabilities incorporated in the
DYNAMO program. FORTRAN compilers are too laconic for efficient debug-
ging for many programmers. DYNAMO'S limitations include an inability to
store large amounts of data and to use exogenous data. FORTRAN programs
apparently can handle larger or more complicated basins; however, DYNAMO
has been used in a study of the Susquehanna River Basin (9). The cost of sim-
ulation by either language seems to be a function of the computer on which they
are used, rather than any discernable differences in operating efficiencies.
The computer time to simulate and analyze the simulated flows for a 250-yr
period, required approximately 7-minutes on a Control Data Corp. (CDC) 6600
computer.
Other streams were not simulated by the proposed generator, because of
its empirical nature. The writers believe that most unregulated streams can
be simulated by the methods proposed. Recent developments in computer
technology that allow visualization of results, virtually permit engineers to
converse with computers, and C values (Eq. 10) can be quickly adjusted or
examined to the satisfaction of the user.
CONCLUSION
A daily multistation streamflow simulator has been proposed which is
78
-------
1178 July, 1969 HY 4
capable of generating both nonhistoric flow sequences with statistical proper-
ties and also hydrographs similar to historical flows. Planners, designers,
managers, and operations personnel have a tool which can help them analyze
the response of proposed and existing water-resources systems to potential,
nonhistorical now sequences of longer duration than historical records.
ACKNOWLEDGMENTS
Financial support for this research was provided by the Federal Water
Pollution Control Administration, Research Grant No. WP-01008, entitled,
"Complementary-Competitive Aspects of Water Storage."
APPENDIX l.-REFERENCES
\.A Uniform Technique for Determining Flood Flow Frequencies, Water Resources Council,
Washington, D.C., Dec., 1967.
2. Beard, L. R., "Simulation of Daily Streamflow," Proceedings, The International Hydrology
Symposium, Sept. 6-8, 1967, Fort Collins, Colo.. Vol. 1, Paper No. 78, June, 1967, Fort Collins,
pp.624-632.
3. Beard, L. R., "Use of Interrelated Records to Simulate Streamflow," Journal of the Hydraulics
Diwiion,ASCE,Vol.91,No. HY5, Proc. Paper 4463, Sept., 1965, pp. 13-22.
4. Benson, M. A., "Uniform Flood-Frequency Estimating Methods for Federal Agencies," Water
Resources Research, Vol. 4, No. 5, Oct., 1968, pp. 891-908.
5. Fiering, M. B., "A Multivariate Technique for Synthetic Hydrology," Journal of the Hydraulics
Division. ASCE, Vol. 90, No. HY5, Proc. Paper4027. Sept., 1964, pp. 43 60.
6. Forrester, J. W., Industrial Dynamics, MIT Press, Cambridge, Mass., 1961.
7. Halter, A. N., and Dean, G. W., "Simulation of a California Range Feedlot Operation," ,\o.
282, Giannini Foundation, University of California at Berkeley, May, 1965.
8. Halter, A. N., and Miller, S. F., "River Basin Planning: A Simulation Approach," Oregon State
Agricultural Experiment Station, Corvallis, Oregon, 1967.
9. Hamilton, H. R., et a). A Dynamic Model Of The Economy Of The Susquehanna River Basin,
Battelle Memorial Institute, Columbus, Ohio, 1966, pp. 1-26 and appendices.
10. Harms, A. A., and Campbell, T. H., "An Extension of the Thomas-Fiering Model for the
Sequential Generation of Streamflow," Water Researces Research, Vol. 3, No. 3, 1967. pp.
653-661.
11. Hydrologic Engineering Center, Monthly Streamflow Analysis, U.S. Army Corps of Engineers,
Sacramento, Calif., Sept., 1966, pp. 1-6.
12. Hydrologic Engineering Center, Monthl\ Streamflow Synthesis, U.S. Army Corps of Engi-
neers, Sacramento, Calif.. Sept., 1966, pp. 1-8.
13. Matalas, N. C., "Mathematical Assessment of Synthetic Hydrology," Water Resources
Research, Vol. 3, No. 4, 1967. pp. 931-945,
14. Pugh, A. L., Ill, Dynamo Users Manual, 2nd ed., MIT Press, Cambridge, Mass., 1963, pp.
1-57.
IS.Quimpo, R. G., "Stochastic Analysis of Daily River Flows," Journal of the Hydraulics Division,
ASCE, Vol.94, No. HY1, Proc. Paper 5719, Jan., 1968, pp. 43-57.
16. Thomas, H. A., Jr., and Fiering, M. B., "Mathematical Synthesis of Streamflow Sequences for
the Analysis of River Basins by Simulation," in Maass, A., et al. The Design of Water Resource
Systems. Harvard University Press, Cambridge, Mass., 1962, pp. 459-493.
17. U.S. Corps of Engineers, "Report on Redistribution of Irrigation and Other Water Resource
79
-------
HY4 STREAMFLOW SIMULATION 1179
Benefits, Willamette River Basin, Oregon," U.S. Corps of Engineers, Portland, Oregon,
Revised, Nov., 1960.
18. Yevdjevich, V. M., "Stochastic Problems in the Design of Reservoirs," Water Research,
Kneese, A. V., and Smith, S. C., eds., John Hopkins Press for Resources for the Future, Balti-
more, Md., 1966, pp. 375-411.
19. Young, G. K., and Pisano, William C., "Operational Hydrology Using Residuals," Journal of
the Hydraulics Division. ASCE, Vol. 94, No. HY4, Proc. Paper 6034, July, 1968, pp. 909-923.
APPENDIX II.-NOTATION
The following symbols are used in this paper:
B = Beta coefficient of regression equation;
b = regression coefficient;
C = dampening constant, depends on sign of k';
g = skew of natural logs of flow;
h = annual subscript for natural log of flow for a particular day;
i = time subscript (day);
j = station subscript;
k = difference between natural log of flow and mean divided by standard de-
viation (Pearson Type III standard deviate);
k' = adjusted k value depending on magnitude of skew, g;
L = natural logarithm of flow;
M = Mean of natural logs of flow;
N = number of years of record;
Q = rearranged natural flow;
R = multiple correlation coefficient;
RN = random normal standard deviate;
S = standard deviation of natural logs of flow;
X = normal standard deviate; and
^ = summation of all values for a particular day.
80
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APPENDIX III
RECREATION AND RESERVOIR OPERATION
Introduction
Water resource developers and recreation planners are confronted with
a conflict between the beneficial use of water impounded in reservoirs
for reservoir recreation or for release for downstream purposes, such
as water quality control and irrigation. To develop benefit functions
for recreation associated with a reservoir, the response of recreational
attendance caused by reservoir operation should be known,
Hufschtnidt and Firring (3) and the Outdoor Recreation Resources Review
Commission Study Report No. 10 (6) both stress the urgent need for
information revealing the response of recreational attendance to
reservoir fluctuations. I'llman (5) has indicated the need for statistical
analysis to demonstrate the influence of reservoir fluctuation on
recreation. This appendix reports findings of a study of Folsora,
Isabella, Millerton, Whiskeytown and Shasta Reservoirs in California.
Unfortunately, only Folsom Reservoir provided sufficient, accurate data
to report results with a degree of statistical confidence.
Numerous factors are known to contribute to the recreation attendance
of a reservoir in addition to fluctuations in the surface level.
Climate, topography, vegetative cover, water quality, and other environ-
mental influences also affect attendance. The type of recreation, the
proximity of population centers, and the availability of alternatives
are also important. Discussions of the factors that influence attend-
ance are available in work by others (1, 3, 5, 6).
Observations
Current opinion on the influence of reservoir operation on reservoir
attendance for recreational purposes is based apparently on personal
observations. The ORRRC Study Report 10 (6) states that "the fact
that at low stages an unsightly, often muddy and trash-littered shore-
line is exposed apparently does not appreciably decrease the number
of people who come to enjoy the water." The Report points out that
the quality of the recreational experience is decreased because of the
lowering of the surface Level.
The TVA (4) has observed that it is not clear the extent to which
surface fluctuations influence attendance. TVA notes that other
factors also influence recreation and that water skiers and boaters
appear not to be bothered too much by reservoir fluctuations.
Considerable insight regarding the influence of reservoir operation
on recreation can be obtained from examining data from Whiskeytown
Reservoir. During its first recreational season the surface only
fluctuated approximately one foot in order to maintain the optimum
81
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head on a hydroelectric power plant. Attendance was high early in
May when fishing season opened. It decreased and then increased when
the weather warmed in June and then continuously decreased during the
latter part of July and August. This latter decrease could have been
caused by the required drive in a hot car from population centers to
the reservoir, thus a reducation in the quality of the experience. An
increase in attendance was recorded during the Labor Day week end.
The reservoir surface level at Isabella increased during the spring
to a maximum during June and then continuously decreased during the
remainder of the recreational season. Monthly attendance figures
produced distribution curves similar to monthly Whiskeytown data and
probably for the sane reasons.
Observations on Shasta Lake indicate that attendance figures drop
after a year when the level is unusually low. Evidently people plan
to enjoy their summer vacation at Shasta and if the level is low, many
do not return the following year,
Folsom Reservoir
Folsom Reservoir is located approximately 20 miles east of Sacramento,
California, During the recreational season, from the third week end in
May through the third week end in September, the reservoir surface has
fluctuated from the maximum operating surface at elevation 466 (surface
area, 11,500 acres) to elevation 390 (surface area, 6,180 acres) during
the operating period from 1958 to 1965. In the spring the reservoir
fills and reaches a peak pool around the middle of June, The surface
then gradually recedes throughout the remainder of the recreation season,
Figure 1 depicts the level-duration diagram for Folsom Reservoir.
To furnisii an indication of the recreational environment at Folsom
Reservoir, the results of an evaluation by the California Department
of Parks and Recreation (1) is presented in Table I, The point system
employed was developed by the Department to estimate the value of
recreation benefits,
.Surface water quality samples during tne recreational season near
Granite Bay yielded ranges of temperature from 22 to 268C and dissolved
oxygen from 7 to 9 mg/1. The pH was usually slightly above 7 and the
water was clear (one turbidity reading of 987, light transmission) .
An indication of the magnitude of the use of the entire Folsom Lake
State Recreation Area is the fact that during fiscal 1965-66, 4,667,199
visitor-days were recorded in comparison with 1,817,000 visitor-days
at Yosemite National Park.
Accurate attendance counts, in terms of the number of automobiles,
are available for week ends during the recreation season at the Granite
Bay checking station. People use the Granite Bay area primarily for
82
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oo
470
460
450
•
^ 440
Z
2 430
420
LEVEL-DURATION DIAGRAM
FOLSOM LAKE
SEASONS OF 1958 - 1965
0 20 40
60
80
100
Ul
410
u
< 400
oe
«/> 390
PROPORTION OF TOTAL TIME SURFACE
WAS AT GIVEN LEVELS
% OF TOTAL TIME SURFACE
WAS ABOVE GIVEN LEVELS
FIGURE 1. LEVEL-DURATION DIAGRAM FOR FOLSOM RESERVOIR
-------
TABLE I. DESCRIPTION OF RECREATION ENVIRONMENT
AT FOLSOM RESERVOIR (1)
VALUE POINTS
Factor
Reservoir Operations
Location of Site
Variety and Quality of Recreation
Esthetic Qualities of Site
Total
DOLLAR EVALUATION
Basic Value Value Points
$ 0.50 70
Maximum
Points
20
30
30
20
100
Total
$ 1
Folsom
Reservoir
13
19.6
24.3
13
70 (rounded)
Value
.20
-------
launching boats and swimming. Good access is provided to all facilities.
The launch ramps are paved and well maintained and are satisfactory until
the pool drops below elevation 403. Well developed accommodations" are
maintained in the swimming area, with adequate parking and picnicking
space and modern comfort stations. Figure 2 shows the beach (slope
approx. 4.5%) and shade trees in the picnic area.
Attendance data in terms of automobile counts was converted to visitor-
days by multiplying the number of automobiles by four. The third week
end in May, June, July, August, and September and Labor Day week end
provided sample data for this investigation. The monthly week ends were
selected in an attempt to avoid any bias which might be created by
three or four-day week ends caused by Memorial Day or July Fourth.
Labor Day week end was included because it is always a three-day week
end and would allow the opportunity to observe attendance on a holiday.
To compare Labor Day with the other week ends, attendance figures
were multiplied by two-thirds.
Population changes in the area served by Folsom Reservoir were accounted
for by dividing attendance values by the population of Sacramento
County during the year they were recorded (Equation 1), This approach
transformed recorded values into dimensionless expressions of attendance
that would relate each year to a common base. Figure 3 illustrates
the relationship between adjusted attendance and the beach length,
measured from the high water line to the water surface.
Adjusted Attendance - Recorded Attendance (1)
County Population During Year Recorded
Variables considered influencing attendance at Folsom Reservoir in this
statistical analysis included reservoir operation, temperature, wind,
and time of year. Reservoir operation can be measured by a change in
reservoir surface level, surface area, or length of beach. This study
used the slope distance from the high water mark, which coincided with
the location of shade, picnic facilities, and comfort stations, to the
existing water line. This distance was considered the most accurate
description of the influence of reservoir operation on the recreational
experience at Granite Bay on Folsom Reservoir.
Regression analysis was performed on the data to determine if
statistically significant relationships (test hypothesis 3 • 0) and
correlations existed between attendance and the other measured variables.
Results of the analyses are summarized in Tables II and III (2). All
data were used to compute the results in the entire season row.
Simple regression analysis revealed that no statistically significant
relationship existed between wind and attendance at Folsom Reservoir
with the exception of Labor Day week end. The maximum wind recorded
during the study period was 25 mph and it is highly probable that
areas experiencing high winds could expect a significant reduction in
attendance during windy periods.
85
-------
co
CTJ
r(
Si
9
H-
n
o
^
fD
[U
n
-------
00
Ul
12
Q
z
Q I
ui *
14
May •
June X
July A
Aug. D
Labor D. O
S«pl. +
FOLSOM LAKE
GRANITE BAY
1958 - 1965
©
12
10 9 6
.•EACH LENGTH, 100 FEET
FIGURE 3. RELATIONSHIP BETWEEN ADJUSTED ATTENDANCE AND BE£CH LENGTH
-------
TABLE II
CORRELATION COEFFICIENTS
GRANITE BAY, FOLSOM LAKE, 1958-1965
Attendance vs. :
Surface
Month Elevation
iv-='y .5050
•tune -.H[].l|7
Julr --6393
••-u^ust .5539
Lnbor Day «38o5
September .3322
Entire
Season .7155
Maximum
Temperature
.7250
.75714
-M*59
.1395
-.5582
-.3651
.3009
Maximum
Wind
-.51*07
.1718
.6193
-.2298
-.7870
-.73U3
-.0823
88
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TABLE III
P TEST VALUES
GRANITE BAY, POLSOM LAKE, 1958-1965
Month
May
June
July
August
Labor Day
September
For the
with 1 and 6
For the
with 1 and 6
Entire
Season
For the
with 1 and i|6
For the
with 1 and 146
Adjusted Attendance vs. :
Surface Maximum
Elevation Temperature
2.05 6.65
1)4.95 8.08
IN 15 1.U9
2.66 0.12
1.02 2.72
0.7l4 0.92
5$ level of significance, the F value
degrees of freedom.
ifo level of significance, the F value
degrees of freedom.
148.26 U.58
5$ level of significance, the F value
degrees of freedom.
ifo level of significance, the F value
degrees of freedom.
Ma ximum
Wind
1.65
0.12
2.149
0.22
6,51
14.68
is 5.99
is 13.75
0.23
is 1+. 06
is 7.2U
89
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In general, temperatures in the seventies coincided with low attendance
figures and higher attendance figures were recorded when the temperatures
•A3re in the eighties. A significant relationship apparently exists
between temperature and attendance early in the recreational season.
Significant relationships also occurred at Seals Point, an area
frequented by families with small children, in May and at Granite Bay
in May and June, a swimming and boating area attractive to adults and
teenagers.
Multiple regression analysis did not yield any results not revealed
by si-rple regression analysis, consequently the results are not
reported.
Examination of the statistical analyses of attendance and reservoir
operation (expressed as length of beach) yields some interesting
results. TliC high, negative correlation coefficient in June could
indicate that perhaps there is an optimum length of beach. Examination
of Figure 3 shows that for the third week end in June (X), attendance
incrr.mpd if the beach length increased from zero, i.e., if the surface
elevition was below the maximum pool elevation.
A significant relationship existed between attendance and reservoir
operation (Figure 4) during the entire recreational season for the
entire period of record. This result would lead one to accept the
hypothesis that reservoir operation does influence attendance at Folsom
Reservoir. Inspection of the results for a particular time period
(such as the third week end in August) during the recreational season
reveals that the attendance was not influenced by reservoir operation.
Why are the results contradictory? Evidently people who attend Folsom
Reservoir are cognizant of the general seasonal trend in the operation
of the reservoir. Whether the level is especially high or low during
a particular month is evidently not too important to the visitors, but
the relevant factor is the relationship of the level to last month or
next month.
Why does attendance continually drop during the summer, similar to the
drop in surface level or when the length of beach increases? Folsom
Reservoir loses its attractiveness to swimmers during the summer
because of the increasing distances from shade and facilities to the
water. At low surface levels, the bathing area becomes muddy and
wasps and insects become pests.
Another factor that contributes to the reduction in attendance at
Folsom Reservoir is the availability of alternative opportunities.
During the late summer the lakes and reservoirs in the high Sierras
become more attractive due to better climatic conditions and the
State Fair during the Labor Day week end also attracts many persons.
This study started to be a quantitative investigation of the influence
of reservoir operation on reservoir recreational attendance.
-------
-------
Attendance at Folsom Reservoir apparently drops during the summer
because of a reduction in the quality of the recreational experience.
Evidently the average operating curve (Figure A) is an approximation
of the quality of the recreational experience. When the water level
increases, the quality of the recreational experience increases and
more visitors are attracted to the site. When the water level decreases,
marginal users cease to use the area and probably visit alternative
sites.
Use of Results
How can the results of this investigation be applied to the develop-
ment of benefit functions for recreation associated with a reservoir?
The writer proposes that for reservoirs similar to Folsom, the average
oper ition curve (length of beach) could be used to reflect the quality
of the recreational experience and the expected distribution of
attendance during the recreation season.
During periods of extreme drought, the benefits from recreation would
be reduced, If a decision had to be made between maintaining a pool
level for recreation or releasing water for downstream uses, an
indication of the anticipated change in attendance would be available.
However, it must be remembered that during periods of normal pool
levels, the attendance is not significantly influenced by reservoir
fluctuations.
The proposed approach would be most applicable for planning purposes.
Different operations studies could be simulated and different
operating curves would produce different attendance estimates and
thus, different recreation benefits. Sensitivity analysis could help
settle conflicts between recreational uses of stored water and releases
for downstream beneficial uses.
Conclusions
At Folsom Reservoir, seasonal attendance is influenced by the general
quality of the recreational experience. The average operating curve
or length of beach can be used to develop the expected seasonal
fluctuations in attendance. Evidently attendance during a particular
time period during the recreational season is not significantly
influenced by reservoir operation, but attendance is influenced by the
overall, seasonal pattern of fluctuations.
Extrapolation of these results to other reservoirs must be conducted
with due caution. For reservoirs offering similar recreational
experience and operational characteristics, the results should prove
helpful to recreation planners and reservoir operators.
92
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ACKNOWLEDGMENTS
Appreciation is extended to the many people who provided the data
analyzed herein and suggested helpful references.
Mr. John Apostolos helped with the analysis of the data and performed
the computer operations.
REFERENCES TO APPENDIX III
It A Method of Appraising User Derviced Recreation Benefits for
Proposed Water Projects, State of California, Department of Parks
and Recreation, Division of Beaches and Parks, Recreation Contract
Services Unit, Sacramento, California, 1966.
2, Apostolos, J. A., "Factors Influencing Recreation on Reservoirs,"
paper presented to the ASCE Student Paper Contest, Department of
Civil Engineering, Sacramento State College, Sacramento, California,
1967.
3. Hufschmidt, M. M. and Fiering, M. B., Simulation Techniques for
Design of Water Resource Systems, Harvard Univ. Press, Cambridge,
1966.
4. Outdoor Recreation for a Growing Nations; TVA's Experience with
Man-Made Reservoirs, Tennessee Valley Authority, Knoxville, Tenn.,
1961.
5. Ullman, Edward L., "The Effects of Reservoir Fluctuation on
Recreation," Appendix to the Meramec Basin, Vol. Ill, Chapter 5,
Washington University, St. Louis, Missouri, 1961.
6. Water for Recreation - Values and Opportunities, ORRRC Study
Report 10, Washington, D. C.t 1962.
-------
APPENDIX IV
INPUT DATA
Summary
I. Hydrology
A. Upstream Hydrology
B, Downstream Hydrology
C. Willamette River Hydrology
D. Evaporation
E. Flows Required in. Calapeoia River for Fishery Benefits
F. Irrigation Demands (Full Development)
G. Recreation Demands (Ultimate Development)
1. Recreation Attendance
2, Influence of Reservoir Operation on Recreation Attendance
H, Expected Summer Inflow to Reservoir
II. Economic Model
A, Drainage Benefits
1. Drainage Benefits
2. Drainage Benefit Function
3. Drainage Costs
B, Flood Control Benefits
1. Estimation of Peak Instantaneous Flows
2. Conversion of Flows to Flood Stages
3. Flood Damages (Calapooia Basin)
A. Flood Damages (Willamette River)
C. Irrigation Benefits
1. Target Benefit
2, Irrigation Benefit Function
3. Irrigation Costs
-------
I). Fishlife Enhancement Benefits
I. Sunmary of AnnuaL Benefits
2. Enhancement Costs
3. Fishery Benefit Functions
E. Water Quality Benefits
1. Procedure
2, Incremental Water Quality Benefits
3. Water Quality Benefit Function
4. Incremental Annual Associated Costs
5. Water Quality Values for the Analytical Model
F. Recreation Benefits
1. Visitation Value
2, Recreation Benefit Function
3. Cost Estimate
G. Reservoir Costs
1. Initial Reservoir Costs
2. Operation, Maintenance, and Repair
96
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INPUT DATA
TO BASIN MODEL
HYDROLOGIC AND ECONOMIC
The purpose of this Appendix is to identify the original sources of
input data used in the Calapooia River Basin Simulation Model and to
indicate the method and extent of modification and extrapolation.
I. Hydrology
A. Upstream Hydrology
(Flow at Holley, Oregon, proposed reservoir site.)
Daily flows were obtained from
1. U.S. Geological Survey Water-Supply Papers, Surface Water
Supply of the United States, Part 14, Pacific Slope Basins
in Oregon and Lower Columbia River Basin, U.S. Government
Printing Office, Washington, D. C. 1936 through 1960.
2. U.S. Geological Survey Surface Water Records of Oregon,
U.S. Geological Survey, Portland, Oregon. 1961 through 1964,
Flows were rearranged and analyzed according to procedures outlined in
Appendix II, Daily Streamflow Diaulation.
B. Downstream Hydrology
(Flow three miles above confluence of Calapooia with Willamette
River near Albany, Oregon.)
Daily flows were obtained from the same sources as the upstream
hydrology and were rearranged in a similar manner.
C. Willamette River Hydrology
(Generation of low flows at Salem, Oregon. U.S. Army Corps of
Engineers, "Willamette River Reservoir Regulation Study."
Portland, Oregon, 1959 (Unpublished).
In this study the Corps routed 30 years of monthly historical
flows (1926-1955) through the authorized 14 reservoir Willamette
Basin System, During six of the 30 years the target flow of
6000 cfs at Salem, Oregon was not achieved. These routed,
insufficient historical flows were drawn by distribution free
methods to simulate low flow conditions. Values were adjusted
when necessary to vary linearly on a daily basis and still
maintain the monthly average.
97
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SUMMARY OF ROUTED HISTORICAL MONTHLY LOW FLOW YEARS
Willamette River at Salem - W.R.
Release from proposed jtolley Reservoir - H.
Flow at Salem without release - F.S.
(used to simulate Willamette River low flows)
Year
1926
W.R.
H.
F.S.
1930
W.R.
H.
F.S.
1934
W.R.
H.
F.S.
1940
W.R.
H.
F.S.
1941
W.R.
H.
F.S.
1944
W.R.
H.
June
4600
100
4500
7278
100
7178
S500
100
5400
5640
100
5540
7161
100
7061
7173
100
July
4600
50
4550
6000
187
5813
4600
50
4550
4840
198
4642
4580
50
4530
5400
50
August
4600
50
4550
5895
211
5684
4726
50
4676
4873
193
4680
4647
50
4597
5400
396
Septenl
5731
65
5666
6624
51
6573
6683
50
6633
6175
140
6035
7661
191
7470
6758
54
F.S. 7073 5350 5004 6704
Water quality demands are composed of flows or volumes of water necessary
to increase simulated flows to target minimum flows in the Willamette River.
98
-------
D. Evaporation
Month ER, SFM/ACa Temp, °Fb
April 0.00300 50.8
May 0.00495 56.1
0.00595 60.9
0.00830 66.6
August 0.00690 65.9
September 0.00460 61.5
October 0.00190 53.2
a. U.S. Army Corps of Engineers, "Report on Redistribution of
Irrigation and Other Water Resource Benefits" Portland, Oregon,
Rev. No. 1960. Chart 4.
Evaporation fron Reservoirs in the Willamette Valley was con-
verted to ac-ft per day per acre of reservoir surface area. The
monthly averages p,iven in t'ie table were adjusted to vary linearly
on a daily basis and still preserve the monthly average.
b. U.S. Department of Commerce, Climatological Data, National
Summary. Mean monthly temperatures at Eugene, Oregon, were
available but not incorporated in this model.
Evaporation in the simulation model was treated as a function of surface
area and time of year. Considered in the evaporation rates were expected
water temperatures, wind velocities, humidity, and cloud cover.
1, Available Data
Pool Elevation, Storage,3 Surface Area,
ft. m.s.l. ac-ft Ac
694 186,000
685 160,000 2,850
660 97,000
645 1.720
590 500
a. Wilcox, B. E., Personal communication NPPEN-PL-9, dated
8 July 1966.
b. U.S. Army Corps of Engineers ."Preliminary Recreation Reconnaisance,
Calapooia River, Holley Uam Site, undated, Received 24 July 1965,
99
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2. Interpolated Input Data
Pool Elevation Storage, Surface Area
ft. m.s.l. ac-ft Ac
699 200,000 2,975
692 180,000 2,910
685 160,000 2,850
677 140,000 2,690
669 120,000 2,431
661 100,000 2,221
651 80,000 1,914
638 60,000 1,559
620 40,000 1,159
602 20,000 763
560 0 0
L. Flows Required in Calapooia River for Fishery Benefits3
i)ato Minimum Desirable Flows, cfs
Holley Dam to Brownsville Diversion
Brownsville Diversion to Willamette River
Sept. 1 to May 31 130b 130b
June 1 to June 15 250C 130d
June 16 to Aug. 31 250C 90e
Maximum Temperature of Water Released from Reservoir
October 1 - 55°F
Summer - 60°F
a. All data obtained from Mr. Kenneth Johnson, U.S. Array Corps
of Engineers during meeting on July 28, 1966, in Portland, Oregon.
b. Little or no irrigation releases for fish spawning.
c. High flows for fishery and irrigation.
d, Minimum flow for fishery.
e. Lower minimum flow for fishery in lower reach because fish have
moved upstream.
Simulation model used minimum flows in lower reach as fishery target
flow because irrigation releases provided sufficient flows to exceed
minimum flow target for fishery in upper reach.
100
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Irrigation Demands (Full Development)
Downstream irrigation demands were obtained from Halter and Miller's
work,3 Original data were provided by the Corps of Engineers from
estimates by the Bureau of Reclamation.
Downstream Irrigation
Month Demand, Ac-ft
2,100
5,400
June 14,000
July 24,800
August 21,300
September 2 ,300
Total Demand 69,900 Ac-ft
Demands were incorporated in the simulation model on a daily basis,
The daily demand varied linearly within 15 day periods on the basis
of a percentage of the target output.
a. Halter, A. N. and S. F. Miller, "River Basin Planning; A
Simulation Approach," Special Report 224, Agricultural
Experiment Station, Oregon State University, Corvallis,
Oregon, November, 1966, 117p.
G. Recreation Demands (Ultimate Demand)
1. Recreation Attendance
Recreation Potential for 685-foot Pool Elevation3
(Storage, 160,000 ac-ft; Surface Area, 2,850 acres)
Estimated Usage, Visitor-Days,
Without Project With Project
Time or Parks _
Present 5,000 NA
3 years after - 100,000
construction ,
100 years after 10,000 500,000D
construction
a. Wilcox, B, E., Personnel communication NPPEN-PL-9, dated
8 July 1966.
b, Expected attendance used in simulation model.
2. Influence of Reservoir Operation on Recreation Attendance
A definite reduction in visitor-days was shown in a study
reported in Appendix III. A statistical analysis of attendance
data and width of beach (distance from high water line to water surface
showed) that attendance drops as the distance to water increases
at the Granite Bay State Recreation Area on Folsom Lake, near
101
-------
1.2
.9
o
tv>
z
O .6
O
at
tt,
200
250
300
350
DAY
IRRIGATION DEMAND
-------
metropolitan Sacramento. These relationships were extended to
a potential recreation site at Holley in this simulation model.
The recreat.m season for both areas was assumed to be from the
day before Memorial Day (May 30) through September 15.
Comparison of Holley Reservoir and Folsom Reservoir Recreation,
potential and existing
Item Holley3 Folsomb
Slopes in recreation 3 to 20Z. Used 10% 3% at Granite
area on basis of U.S.G.S. Bay
topo map contours in
potential area.
Change in pool elevation Max. 685 Max. 470
during recreation season Mir. 645 Min« 390
Elev. 40 ft Elev. ~~80 ft
Anticipated Usage 500,000 persons within During Folsom Study.
1 hour's driving time Sacramento County
now. Estimate threefold Population
increase in next 50 years. 1955 - 374,300
1965 - 617,200
To approximate the Corps annual attendance estimate of 500,000
man-days (ultimate demand) 100 years after construction of the
dam,3 this simulation model assumed a daily attendance of 5000
visitors (actually the daily average for a week) when the
reservoir if full. Attendance drops linearly to zero as the
width of beach Increases to 1500 feet. The beach will never
reach this width; therefore, even if the reservoir is empty,
there will be some visitors.
a. U.S. Army Corps of Engineers, "Preliminary Recreation
Reconnaisance, Calapooia River, Holley Dam Site, Undated,
Received 24 July 1965.
b. Apostolos, John A., "Factors Influencing Recreation on
Reservoir," paper submitted to 1967 ASCE Student Content,
Reno, Nevada.
H. Expected Summer Inflow to Reservoir
To allocate available water during the flow periods the expected
flow during this time span should be considered. A prediction
equation was developed using regression analysis to estimate summer
inflow on the basis of spring flows.
Expected Summer Inflow, sfd - 8260 + (0.029)(Sum of three previous
months, sfd)
103
-------
The regression coefficient (0,029) indicates that the flow during the
three months before the low flow season does not exert a large
influence on the low flows and/or the spring flows are much larger
than the summer flows. To avoid over estimating expected flows which
could cause severe losses in benefits if the expected flows were not
available, safety factors from 0.8 to 1.0 were applied to the expected
flows with virtually no change in the average annual net benefit.
The value of 0.9 was the optimum safety factor.
II, Economic Model
A. Drainage Benefits
1, Drainage Benefits
Maximum Annual Drainage Benefits, Calapooia River, 1964 Dollars'
Channel Capacity,
cfs
5,000C
11,000
21,000
Maximum Annual Benefits
Dollars
0
200,000
500,000
a. Halter, A. N. and S. F. Miller, "River Basin Planning: A
Simulation Approach," Special Report 224, Agricultural
Experiment Station, Oregon State University, Corvallis,
Oregon, November, 1966, 117p,
b, Estimated by Corps of Engineers
c. Natural channel size.
Benefits from channel sizes other than values listed above
were assumed to vary linearly in the simulation model. Values
were not extrapolated beyond a channel capacity of 21,000 cfs
nor an annual benefit of $500,000,
2,^Drainage Benefit Function3
4-1
£ 100
a)
I 80
60
H 40
0)
60
C 2°
iH
£ 0
0 20 40 60 80 100
Average Channel Level, % Channel Capacity
104
-------
a. Halter, A. N. and S. F. Miller, "River Basin Planning:
A Simulation Approach, "Special Report 224, Agricultural
Experiment Station, Oregon State University, Corvallis,
Oregon, November, 1966, 117 p.
Crop production can be increased if drainage is provided soils
with poor drainability. Full drainage benefits can be achieved
if the average channel level during the drainage season (March,
April, May, and June) is below 30 percent of the channel
capacity, When the average channel level exceeds 30 percent
of the channel capacity the drainage benefit function is
reduced as shown above.
3. Drainage Costs
Costs of Improving or Increasing Channel Capacity3
Calapooia River, 1964 dollars
Channel Capacity, Total Construction Cost,b
cfs Dollars x 106
5,000C 0.1
11,000 1.6
21,000 8.0
Operation, maintenance and repair are estimated at 10 percent
of the authorized costs (life of 100 years assumed)3
a. Halter, A. N. and S. F, Miller, "River Basin Planning:
A Simulation Approach," Special Report 224, Agricultural
Experiment Station, Oregon State University, Corvallis,
Oregon, November, 1966. 117p.
b. Estimated by Corps of Engineers
c. Natural channel capacity. Some channel improvement will be
necessary to accommodate reservoir releases.
Costs listed above are solely for channel improvement and increase
in channel capacity. These improvements and increases in channel
capacity also will reduce flood losses. The costs of actually
draining the land are not included. The greater the channel
capacity and the lower the average channel level, the more
effective will be the drainage outlets.
B, Flood Control Benefits
1. Estimation of peak instantaneous flows.
Flood damages were estimated on the basis of peak instantaneous
flows. Peak flows were calculated from simulated average
daily flows. Regression analysis of historical data3 yielded
the following relationships.
105
-------
2.
Downstream Station. Albany
Inst. Peak, cfs » -846 + 1.209 (Ave. Daily Flow, cfs)
Correlation Coef., r - 0.954 and n * 24.
Upstream Station. Ilolley
Inst. Peak, cfs - 515 + 1.162 (Ave. Daily Flow, cfs)
Correlation Coef., r - a.967 and n - 24.
a. U.S. Geological Survey Water Supply Papers and Surface
Water Records of Oregon (See ref, 1 & 2, Section 1A of
this Appendix.)
In the simulation program, a table was prepared from the
regression equations and the peak flows were obtained from
the table on the basis of the simulated average daily flow.
Conversion of Flows to Flood Stages
Relationship between Channel Flow and Flood Stage at Shedda
Channel
Flow,
cfs
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
5,000
10.0
15.75
16.6
16.9
17.15
17.3
17.5
17.65
17.82
18.0
Flood Stage at Shedd, ft
Channel Capacity, cfs
11,000
10.0
14.0
15.75
16.35
16.6
16.75
16.9
17.05
17.15
17.25
21,000
10.0
11.0
14.0
15.1
15.75
16.15
16.35
16.5
16.6
16.7
a. Halter, A. N. and S. F. Miller, "River Basin Planning: A
Simulation Approach," Special Report 224, Agricultural
Experiment Station, Oregon State University, Corvallis,
Oregon, November, 1966, 117p.
Flood stage at Shedd is used because flood stages at the
downstream simulation station are influenced by backwater
resulting from flows in the Willamette River
106
-------
3.
Flood Damages (Calspooia Basin)
Flood Damages Based on Flood Stage at Shedd
Flood Stage
at Shedd, ft
10
11
12
13
14
15
16
17
18
20
Flow at Shedd,
Existing Channel
cfs
0
1,000
1,800
3,000
4,500
6,700
12,000
34,000
90,000
Damage,
Halter-Miller3
Dollars
0
2,200
16,000
133,000
550,000
1,000,000
Damage
Wilcoxb
Dollars
40,000
200,000
1,400,000
Damage
This Project
Dollars
0
0
2,200
5,500
16,000
40,000
200,000
1,400,000
4,400,000
a.
b.
Halter-Miller, Corps of Engineers estimates based on 1964
stage of development
Wilcox, B. E., Personal communication NPPEN-PL-9 dated
13 December 1966.
Data in Wilcox column taken from "Discharge-Damage Curve,
Willamette River Basin, Calapooia River, Zone B, Discharge
at Shedd, April 1, 1966. 1965 Prices and Development" The
curve contained the 1964 flood which had a discharge of 22,500
cfs and caused $780,000 in damages (values taken from plot
on curve).
The flood stage at Shedd is used to indicate flood damages
resulting from Calapooia River flows because the flood stage
at Albany is often influenced by backwater from the Willamette
River.
4. Flood Damages (Willamette River below confluence with
Calapooia River)
"Benefits creditable to Holley Reservoir for flood damage
reduction along the Willamette River are based on all 14
authorized Willamette Basin reservoirs being operated as a
system. Distribution of benefits to various reservoirs is
in proportion to each reservoir's contribution to reduction
of average annual flood damages. At 1965 prices and develop-
ment, these benefits would amount to approximately $610,000
annually for 90,000 acre-feet of flood control storage at
Uolley Reservoir," Wilcox, B. E., Personal communication
NPPEN-PL-9 dated 13 December 1966.
To incorporate average annual flood benefits for damage
reduction along the Willamette River was a problem, since
107
-------
only I of 14 reservoirs was being studied. Reductions in
flood damages should be recorded in the simulation model
when they occur, rather than on an annual basis. The
necessity of providing storage of 90,000 ac-ft for flood
control was questioned. A review of historical records
indicated that most severe floods on the Calapooia River
had a duration of three days (3 days of high flows). One
hundred ysars of reservoir inflows were simulated and yielded
the following results:
Rank Largest Mean Volume,
3-Day Flow, cfs Ac-ft
1 14,139 84,834
2 11,562 69,372
3 10,897 65,382
4 10,758 64,548
5 10,457 62,742
These results indicated that if no flows were released from
the reservoir during a severe flood, a flood storage capacity
of 60,000 ac-ft could hold most floods. Even under the worst
condition, the average release would be approximately 4100 cfs,
(neglecting any surcharge storage) which would be small in
comparison with the total flow in the Willamette River.
Consequently flood benefits from a reduction in flows in the
Willamette River were reduced proportionally, based on the
unavailability of storage available to contain a three-day
runoff of 60,000 acre feet. When Holley reservoir is
operated as an integral part of the Willamette Basin reservoir
system, it may be required to hold a major portion of flood
flows longer than three days.
To allow for a flood benefit from reduced flows in the
Willamette River, an annual flood benefit of $160,000 was
arbitrarily selected simply to be conservative. Since this
is a fixed, annual value, the size of the reservoir and other
target outputs would not change if another value was inserted,
only the maximum net benefits and benefit/cost ratio would
change.
Will. River Flood Benefit = $160,000/yr (Target Flood Storage 60.000 Ac-ft)
60,000 ac-ft + Insuf. Capacity
Insufficient Capacity, Ac-ft - 3 day Inflow - Available Flood
(zero or positive) Storage
C. Irrigation Benefits
1. Target Benefits
Irrigation Capability, acre3 53,400
Annual Net Benefits, $/acreb $10.35
Total Annual Net Benefits $552,690
108
-------
Benefits of $552,690 would result if the irrigation target output
of 69,900 ac-ft was met.
a. Provided Corps of Engineers by Bureau of Reclamation
b. Halter-Miller Report
In the simulation model, the target benefit was adjusted pro-
portionally on the basis of the target output for irrigation
water in ac-ft.
2. Irrigation Benefit Function
If sufficient water is not available to meet irrigation demands,
losses in net benefits result. The magnitudy of the dollar loss
is a function of the severity, duration, and time of the shortage,
The selection of a loss function for the simulation model was
a compromise between loss functions published in two different
references as shown in the following figure (Halter-Miller
report and Bower, Blair T. in "Design of Water Resource Systems,"
by Haass A,, et al, Harvard University Press, Cambridge, 1962,
pp. 263-298).
3. Irrigation Costs
Irrigation Capability, acre3 53,400
Construction Costs, $/acrea $ 17.44
Total Construction Cost $931,296
Operation, maintenance, and repair are estimated at 7.5 percent
of amortized costs.'3
a. Provided Corps of Engineers by Bureau of Reclamation.
b. Halter-Miller ileport
Costs above original irrigation target output of 69,900 ac-ft
were assumed to increase by the square of the ratio of the new
irrigation target to the original irrigation target. If the
irrigation target output was reduced, the costs were reduced
proportionally to the output.
109
-------
RRIGATION TA/RGET OUTMJT (%)
-60J-
IRRIGATION BENEFIT FUNCTION
110
-------
Fishlife enhancement Benefits
At the time this project's economic model was prepared, the data
below were obtained from Mr, Kenneth Johnson, U.S. Army Corps of
Engineers, an July 28, 1966.
Average Annual Projected Fishery Benefits. Dollars
A B B I) F
Reservoir Capacity,Ac-ft 186,000 201,000 186,000 160,000 97,000
Minimum Conservation 51,000 51,000 36,000 39,000 7.000
tool, Ac-ft
(For Temperature Contrrlj
Anadeomous Fish $334,000 $334,000 $334,000 $264,000 None
Reservoir Sport Fish $154,000 $160,000 $154,000 $145,000 $103,500
(Angler Use)
Downstream Sport Fish $ 90,000 $ 90,000 $ 90,000 $ 90,000 $ 30,000
(Angler Use)
Total Fishery Benefit $578,000 $584,000 $578,000 $499,200 $135,500
The identical benefits for plans A and C and different minimum conser-
vation pools represent the opinions of different agencies at this
time regarding the minimum conservation pool necessary to satisfy the
temperature control target of 60°F or lower during the summer and
55°F or lower after October 1. Plan A was selected as the basis for
preparing the economic model for this project. On December 7, 1967,
Mr. Johnson indicated that the minimum conservation pool would probably
be 51,000 ac-ft, Fishlife enhancement benefits were still being
reviewed at the time this report was prepared (Dec, 1969),
1. Summary of Annual Fishery Benefits
a. Reservoir Sport Fish - $154,000
(Angler use)
b. Anadromous Fish - 334,000
Downstream Sport Fish - 90,000
(Angler use)
Total Benefits $424,000
Release for minimum flow and storage for temperature control.
2. Enhancement Costs
An egg collection station below liolley has been proposed by
the Oregon State Game Commission
Total Construction Costs $800,000
Operation Maintenance, and Repair are estimated at 10% of
construction costs.
a. Estimated by the Corps of Engineers
111
-------
b. Halter-Miller report
3. Fishery Benefit Functions
a. Other Fishery Benefit Functions
The exact response of fish to low flows is not well defined
because of the influence of many other factors, such as water
quality (temperature, dissolved oxygen). Halter and Miller
used a benefit function based on minimum flows and related the
flows to a "percentage of mean-daily need met," where the
In percentage was the minimum for the year.
•H
U-l
M
-------
•H
*4-H
01
_
00
4-1
•H
U-l
C
"35
QJ 3 O-i
S3 C
d w
,C 10 3
tn o
•r-l U_| g
u< o o
Vi
?•? T3
b, Project Fishery Benefit Functions
(1) Anadromous Fish Enhancement
To achieve full anadromous fish benefits, both minimum flows
and temperature control must be achieved and~m"aintained,
Temperature control was based upon the ability of the reservoir
to maintain a minimum conservation pool of 51,000 ac-ft. In
an attempt to more accurately describe a benefit function
similar to field conditions, this project assumed the benefit
function shown below. The simulation model determined the
minimum annual percent flow target and percent conservation
pool target and used the minimum of the two values to estimate
the anadromous fishery benefit.
103
100
80
60
40
20
0
20
40
60
80
100
120
% Minimum Conservation Pool
Anadromous Fishery Benefit Functions
tn
(fi
-------
The deviation of the project benefit function from the one
provided by the Corps was Justified on the belief that the
percentage of the benefits does not drop from 50% to 0% at
the 40% target level, but is more gradual as reflected in
the project benefit function. If the target was exceeded,
a slight increase in benefits was allowed based on the
belief that fishery benefits do not cease to increase after
the target is met.
(2) Reservoir Sport Fish Enhancement
A benefit function for reservoir sport fishery was not
available. The simulation model used a benefit function
similar to the anadromous fishery function with some pertinent
modifications.
105 r-
100
80
60
40
20
0
Project
0
20
40
60
80
100
120
% Minimum Conservation Pool
Reservoir Sport Fishery Benefit Functions
When the minimum conservation pool level drops below 40%
of the target, a complete loss of the reservoir sport fishery
does not seem realistic. Some fishermen would be expected
to continue to attempt to catch fish.
E. Water Quality Benefits
1. Procedure
Previous work by Worley3 and Kerrib has established the response
of the Willamette River and its tributaries to various amounts of
waste discharge. For different combinations of water quality
objectives of DO of 4, 5, and 7 mg/1 and coliform group bacteria
MPN on 240, 1000, 2400, and 5000 per 100 ml Kerri used nonlinear
programming to find the minimum cost of achieving the water
quality objectives. Worley's computer program verified the
ability of the receiving water to achieve the DO objective and
Kerri's work verified the coliform objectives.
114
-------
Costs of achieving the water objectives are tabulated in terms
of initial treatment plant costs and annual maintenance and
operation costs for minimum flow levels in the Willamette River
of 4500, 5000, 5500, and 6000 cfa at Salem, Oregon.
Water quality benefits are measured in terms of reduced treatment
costs resulting from flows at Saletn above 4500 cfs, the minimum
excepted flow (based on the routing of 30 years of historical
flow) without the project under consideration. If a flow
target above 4500 cfs can be established, then higher incremental
degrees of waste treatment can be postponed by the release of
water for water quality control. If the target is not met,
then the annual benefit from avoided operation and maintenance
costs is reduced proportionally, assuming that downstream water
users must increase their operating costs or they incur some
damages from the decreased water quality.
Any combination of water quality objectives will require a
certain level of treatment by all waste dischargers in the basin.
Therefore, for any selected water quality objective in the
simulation model, the average annual net benefits should be
reduced by an appropriate increment to account for the associated
costs to the waste dischargers for their degree of treatment.
The associated costs are a function of the degree of treatment
required to meet water quality objectives at the minimum flow
objective under consideration.
a, Worley, J. L., "A System Analysis Method for Water Quality
Managing by Flow Augmentation in a Complex River Basin,"
U.S. Public Health Service, Region IX, Portland, Oregon (1963).
b. Kerri, Kenneth D., "An Investigation of Alternative Means of
Achieving Water Quality Objective," Ph.D. Thesis, Oregon
State University, 1965.
2, Incremental Water Quality Benefits for Q - 4500, 5000, and 6000
cfs are summarized in Table I.
3. Water Quality Benefit Function
Minimum flow in the Willamette River at Salem without this pro-
ject's contribution is estimated as 4500 cfs on the basis of a
Corps of Engineers' study which routed 30 years (1926-1955) of
monthly flows through the Willamette Basin reservoir system.
The minimum flow objective at Salem of the Corps is a flow of
6000 cfs. To determine the optimum target flow for water quality
control, various targets were tested in the simulation model.
As previously described, the degree of treatment to meet different
combinations of water quality objectives was determined for a
flow of 4500 cfs at Salem. The benefits from flows released for
water quality control are calculated on the basis of treatment
not required if the target flow is met. The treatment was
divided into facility costs and maintenance and operation costs.
115
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TABLE I. WATER QUALITY BENEFIT SUMMARY
INITIAL PLANT COSTS, $ x 106
ANNUAL OPERATION AND MAINT. COSTS, § x 103
Target DO Total Coliform
Flow, cfs mg/1 MPN per
Q - 6000 5000
4 0
0
5 .897
51.13
7 8.813
473.904
Q - 5000
4 .354
28.493
5 1.072
69.564
7 12.273
855.508
Q - 4500
4 .514
41.460
5 3.790
87.880
7 16.488
1182,305
2400
.005
10.935
.897
61.89
23.333
487.774
.325
33.951
1.572
91.892
27.503
863.226
.495
44.539
. 4.988
135.862
30.739
1104.023
Group Bacteria
100 ml
1000
.096
18.279
1.067
68.025
23.525
496.862
1.596
45,789
3.727
82.580
28.305
819.168
6.246
269.461
8.623
205.559
35.580
1152.254
240
8.798
1001.184
10.147
1042.481
30.481
1454.688
10.234
1052.643
11.353
1078.564
33.182
1637.365
12.410
1217.379
39.389
1265.221
38.471
2041.408
116
-------
The reduction in water quality benefits from a failure to meet
the target water quality flow objective results from increased
treatment costs by downstream water users. This reduction was
assumed to be a linear function of the difference between the
target flow for water quality and the minimum routed flow of 4500
cfs without the project as shown below.
100
o> TO
CQ 00
50 -
3 o e
Cf O
100
% Water Quality Flow Target Met
or
4500 cfs
W. Q. Target Flow
rt-
Water Quality Target Flow Met
Water Quality Benefit Function
Incremental Annual Associated Costs
Q - 6000 cfs at Salem; i - 3 1/8%; n - 20 years
To maximize net benefits in the simulation model, the optimum
low flow objective at Salem for all combinations of water quality
objectives is 6000 cfs.
Annual Incremental Treatment Costs,3
in One Thousand Dollars
Dissolved
Oxygen
mg/1
A
5
7
Total
5000
--
105
826
Coliform Group
MPN per
2400
56
158
877
Bacteria
100 ml
1000
88
186
888
240
1152
1245
1789
5.
Kerri, Kenneth D., "An Investigation of Alternative Means
of Achieving Water Quality Objectives," Ph.D. Thesis,
Oregon State University, 1965.
Water Quality Values for Analytical Model
To estimate expected values of water released for flow augmentation,
the low flow hydrographs were analyzed. For each hydrograph,
117
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volumes of water necessary to increase flows to specified levels
were calculated. Water quality benefits from higher flowa were
estimated and the value of the water in dollars per ac-ft was
calculated for each increment.
Results from the analysis of the low flow hydrographs indicated
that the V-shaped hydrographs consisted of three segments,
whereas the one U-shaped hydrograph was composed of two segments
similar to the second and third segments of the V-shaped hydro-
graphs. The value of the first segment of water released for water
quality control with the V-shaped hydrographs was approximately
$12 per ac-ft. Values for the second and third increments
were approximately $8 and $4 per ac-ft respectively.
F, Recreation Benefits
1. Visitation Value
"The Bureau of Outdoor Recreation has . . . concluded that
reasonable visitation values for estimating a monetary benefit
value would range between $0.75 and $1.00 per visitor-day. Full
development of recreation potential would be contingent upon
finding a non-Federal sponsor willing to share acquisition and
development costs and operate and maintain recreation facilities
as required by Public Law 89-72."a The simulation model used a
recreation value of $1.00 per visitor-day.
a. Wilcox, B. £., Personal Communication NPPEN-PL-9 dated
8 July 1966.
2. Recreation Benefit Function
Recreation attendance decreases as the distance from the high-
water line to the water surface increases. The value of a
visitor day was assumed to be $l/visitor-day.a
500C
O U "O
•H C I
sis25QC
t-i 0) -H
o u en
1500
1000
500
0
Distance from high-water line to water surface, ft
Recreation Benefit Function
118
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3. Cost Estimate
The estimated cost of initial and ultimate recreational development
is $1,870,000 exclusive of land costs3 as summarized in Table II.
G, Reservoir Costs
1. Initial Reservoir costs3
Total Maximum Estimated
Storage Fool Cost*
186,000 Ac-ft 694 ft m.s.l. $32,700,000
160,000 Ac-ft 685 ft m.s.l. $27,900,000
97,000 Ac-ft 660 ft m.s.l. $19,200,000
*Costs reflect all features of the project and include engineering,
supervision and administration, and interest during construction.
Downstream channel improvement costs totaling approximately
$3,000,000 are included in each of the above estimates.
2. Operation, Maintenance, and Repair"
Operation, maintenance, and repair costs were estimated at 7,5
percent of amortized costs.
a. Wilcox, B. E., Personal communication NPPEN-PL-9 dated
8 July 1966.
b. Halter-Miller Study
The simulation model estimated initial reservoir costs
using the above estimates, less $3,000,000. This data
plotted close to a straight line and the cost of reservoirs
of intermediate capacity were obtained by linear interpolation.
119
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TABLE II. TOTAL COST OF RECREATIONAL DEVELOPMENT1
Initial development cost
Future development cost
Total cost of development
ANNUAL COST - INITIAL DEVELOPMENT
M & 0
Replacement
Amortization
Total annual cost
ANNUAL COST - FUTURE DEVELOPMENT
M & 0
Replacement
Amortization
Total annual cost
$ 450,000
1.420.OOP
$ 1,870,000
23,400
8,700
14.800
46,900
82,600
34,100
56.900
$ 173,600
a. U.S. Army Corps of Engineers, "Preliminary Recreation Recon-
naissance, Calapooia River, Holley Dam Site," Undated.
Received 24 July 1965.
b. U.S. Army Corps of EnRineers, "Reconnaissance of Holley
and Thomas Creek Dam Sites with Bureau of Outdoor Recreation
Personnel," NPPEN-PP-3, 15 February 1965,
To fully investigate the complementary and competitive aspects of
water storage for water quality control, full recreation development
was assumed. Maintenance, operation, and replacement costs were
assumed to be twice amortization costs in the simulation model.
120
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APPENDIX V
FLOW DIAGRAMS OF COMPUTER PROGRAMS
by D. J. Hlnrichs
To simulate the hyclrologic conditions and economic response to potential
water resource systems in the Calapooia Basin, a daily flow simulator
was deemed essential. This simulator was developed and tested in FORTRAN
on a Control Data Corporation (CDC) 6600 computer.
DYNAMO appeared better suited to accomplish the aims of this research
project and consequently the hydrologic and water-related economic
systems of the Calapooia Basin were simulated, tested, and analyzed
by this program. Printout from the final simulation model revealed
the ability of potential designs to meet target outputs, identify critical
shortages, and report any excesses. The complementary and competitive
aspects of water storage for water quality control were easily identified
and analyzed from the results.
Contained in this appendix are flow diagrams which provide an explanation
of the DYNAMO and FORTRAN computer programs.
121
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SUMMARY OF DYNAMO PROGRAM
I. Hydrologic Simulation
A. Day, season, and year counters (DC 1-4, SK 1-4, YC 1-2)*
B. Upstream hydrology (UH 1-242)
C. Downstream hydrology (DH 1-258)
D. Generation of low flows only,
Willamette River Hydrology (WH 1-30)
E. Flows into the Willamette River (FW 1-8)
II. Reservoir Routing
A. Reservoir and channel level (RCL 1-12)
B. Reservoir releases (RR 1-243)
C. Routing Analysis (RA 1-11)
III. A. Drainage benefit (DB 1-12)
B. Flood loss (FL 1-18)
C. Flood benefit (FBC 1-16)
D. Irrigation return flow (IR 1-4)
E. Irrigation benefit (IB 1-9)
F. Fish benefits and costs (FB 1-28)
G. Water quality benefits (WQ 1-13)
H. Recreation benefits (RB 1-19)
I. Recreation costs (RC 1-4)
J. Structure sizes (SS 1-5)
K. Net benefits (NB 1-16)
L. Costs (C 1-13)
M. Capital recovery factors (CR 1-12)
* Location of each section given in parentheses.
122
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IV. Output Analysis
A. Maximum and minimum annual reservoir levels (E 1-41)
B. Flood loss distribution (E 42-63)
C. Irrigation (E 64-70)
D. Minimum channel flow and conservation pool (E 71-87)
E. Water quality (E 88-97)
F. Recreation attendance (equals recreation benefit)(E 98-107)
G. Sum of annual flows (FA 1-20)
H. Spill data (SP 1-6)
I. Maximum and minimum daily flows (DF 1-8)
J. Fish release (FR 1-5)
V. Economic Analysis and Shortage Indices
A. Drainage loss and shortage index (SI 1-10)
B. Channel shortage index (flood control)(SI 11-19)
C. Flood storage shortage index and Willamette River flood losses
(SI 20-28)
1. Channel storage
2. Reservoir storage
D. Irrigation loss and shortage idex (SI 29-36)
E. Fish loss and shortage index (SI 37-67)
F. Water quality loss and shortage index (SI 68-87
G. Recreation loss and shortage index (SI 88-99)
123
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DYNAMO FLOW DIAGRAM
I. llydrologic Simulation
A. Day. Season, and Year Counters
These counters are used to identify moments in time during the
simulation runs. Various demands occur on different days during
the year. Season counters were required in the hydrologic
simulation model to overcome space limitations in the table
functions of the DYNAMO program used in this project.
B. Upstream Hydrology
(Simulation of flow into reservoir)
JLog of flow «• historical mean + (K1) (standard deviation)!
1
1
Mean from
tables
/"
s_
|
0>K'>0>-i
1
Standard deviation
from tables
Pearson type III std. deviate
1.35
1
Pearson type III std, deviate
<
.0>Skew
IH
>0
0>K4±>0
g
L ,&
< (6
> + 1)3-1)
li
1.10
1 ( (l(x-J) + i)3 .
g O D
C. Downstream Hydrology
Downstream flows are generated using equations and flow diagrams
similar to the upstream flow, with the following changes:
1. Coefficient Ct
124
-------
a. If K'>0, change l.l to !.£
b. If K'<0, change 1.35 to 1.45
2> X' X1.J-B1,JX1-1'J + Bi.JXl,J-l + C1-R2>°'
D' Generation of LOW Flows Only. Willamettfe Riv«* Hydgolocv
(Flow augmentation not requested if Q is equal to or greater
than 6000 cfs)
I Flow in the Willamette River (0)1
|—< 66500
[SUMF - Sum of Spring Flows
day 151 to 2A1
SUMF
66500
ipOOOO > SUMF >
> 30000
|Q « 6000 cfsl
|Q - Table DRYL|
51000 > SUMF > 51000
1^0.0 > Random No. a. 0^0^! ^-0.5 > Random No. > -0.5^
i— ' , . L
JQ - Table DRYMlj JQ » Table DRYM2J |Q - Table DRYWlj |^.
1
|Q » Table DRYW2J <5.5>Random No.>0.5>
,„ \ —' , ' .
in - Table DRYW3J IP - bOQQ cfsl
Tables contain routed summer flows through authorized system,
less project flows in Willamette River for dry years based on
historical data from 1926 through 1955.
125
-------
E. Flows into the Willamette River
Total Flow in Willamette River - Simulated flow + Flow out
in Will, R, of channel
Flow Simulated
3 days in advance
to actuate reservoir
releases
II. Reservoir Routing
A. Reservoir and Channel Level
Reservoir level, ac-ft - (1/43560 ft2/ac) (Yesterday's flow in ft3
-Yesterday's flow out, ft3 - irrigation diversion flow, ft3
-Evaporation loss, ft^
Flow in from
Upstream
Hydrology
Flow out from I
Routine section!
Irrigation from
Routing section
Evaporation is
a function of
surface area
and time of year
Channel level - Previous channel level + Previous reservoir release +
simulated channel flow - previous inflow t6 reservoir + irrigation
return flow - flow out of channel.
126
-------
Reservoir Releases
|Flow out of the reservoir «)\\
Before DAY 240 After Go to next_page
(dry season)
(Reservoir Capacity - Reservoir Level) ;
IQ - inflow!
1
(channel capacity - channel flov)>0
i Q-ol
<0>(Spillway Capacity X.
-Rule curve release)>Q ^/^
IQ - Spillway Capacity!
IQ » Fish release!
•(Desirable Channel level
Q
"^s,^ -Rule Curve
« release that
maintains desirable
channel level**
q
Release) *>0 „
1
» release
determined
rule curve
-I
by
* Rule Curve Release - This is the release determined by reservoir rule
curve.
** Desirable Channel Level = Channel capacity - safety factor
Safety factor determined by marginal analysis to minimize flood
damage to channel and still maintain capacity in reservoir for flood
storage.
Flows from the reservoir during the dry season are released
on a priority basis determined by the analytical model and are
a function of the volume available to meet the remaining demand,
and the expected inflow during the remainder of the season.
Priority No. 1 stores water available above a dead storage level
of 20,000 ac-ft for temperature control for the downstream
fishery, plus additional water for water quality control. The
stored water also contributed to reservoir sport fish and
recreation benefits,
127
-------
Volume of water
after Priority No. 1
is met (Volume No, 1)
Reservoir level + Expected inflow
remainder of
dry season
- 60% minimum conservation pool
for temperature control
- 60% Volume for downstream
fish release
- Increments No. 1 & 2
Water quality demand in
excess of fish releases
If Volume No. 1 is negative, allocate expected available volume
of water proportionally between downstream fish release and
minimum conservation pool. The objective is to have the percent
target met for both the fish flow and reservoir level for temper-
ature control as high as possible to maximize anadromous fish
enhancement. Fishery releases will complement water quality
benefits.
If Volume No. 1 is positive, allocate Volume No. 1 to meet
remaining demands.
Priority No. 2 stores 80% of the remaining irrigation demand,
which is released on a daily basis according to varying demands
during the irrigation season.
Volume of water
remaining after priority
No. 2 is met (Volume No. 2)
Volume No. 1 - 80% of remaining
irrigation demand.
If Volume No. 2 is negative, allocate expected available volume
proportionally to irrigation demands during the remainder of
the irrigation season.
If Volume No. 2 is positive, allocate Volume No. 2 to meet
remaining demands.
Recreation and reservoir sport fisheries also benefit from
stored water.
Volume of water
remaining after
Priority No. 3 is met
(Volume No. 3)
Volume No, 2 - Remaining 40%
of conservation
pool
- Remaining 40% of fish demand
(reduced if water previously
_ allocated for water quality control)
128
-------
If Volume No. 3 is negative, allocate expected available volume
proportionally between downstream fish release and minimum
conservation pool.
If Volume No. 3 is positive, allocate Volume No. 3 to meet
remaining demands.
Priority No. 3 stores water for temperature control for the
downstream fishery and releases water for the downstream fishery.
Priority No. 3 stores the 20% of the remaining irrigation demand,
which is released on a daily basis according to varying demands
during the irrigation season.
Volume of water
remaining after - Volume No. 3 - 20% of remaining
Priority No. 4 is met irrigation demand
(Volume No. 4)
If Volume NO. 4 is negative, allocate the expected available
volume proportionally to irrigation demands during the remainder
of the irrigation season.
If Volume No. 4 is positive, allocate Volume No. 4 to meet
remaining demands.
Priority No. 5 stores 20% of the minimum conservation pool
volume for recreation and reservoir sport fish.
Volume of water
remaining after * Volume No. 4 - 20% minimum conser-
Priority No. 5 is met vation pool
(Volume No. 5)
If Volume No. 5 is negative, store the volume available (Volume
No. 4).
If Volume No. 5 is positive, allocate Volume No. 5 to meet
remaining demands.
Priority No. 6 stores water for third increment of water quality
demand, which is released on a daily basis according to varying
demands during the dry season.
Volume of water
remaining after - Volume No. 5 - Water quality demand,
Priority No. 6 is met Increment No. 3
(Volume No. 6) _______——
129
-------
If Volume No. 6 is negative, allocate expected available volume
proportionally to the water quality demand (third increment)
during the dry season.
If Volume No. 6 is positive, allocate Volume No. 6 to meet
remaining demands.
Priority No. 7 stores water for the fourth and final increment
of water quality demand, which is released on a daily basis.
Volume of water
remaining after
Priority No. 7 is met
(Volume No. 7)
- Volume No. 6 - Water quality demand,
Increment No. 4
If Volume 7 is negative, allocate expected available volume
proportionally to the final increment of water quality demand
during the dry season.
If Volume No. 7 is positive, store Volume No. 7 for recreation.
Water quality demand is divided into four increments on the basis
of the incremental value ($/ac-ft) of the released water's
contribution to the net benefits. The incremental value is a
function of the simulated Willamette River hydrograph. The more
water required to increase the minimum flow, the less the incre-
mental value. Each demand Increment is determined in a manner
similar to the procedure used for Generation of Low Flows,
Willamette River Hydrology Section. Whereas the tables in the
Willamette River Hydrology Section define the low flows, the tables
for water quality demand give the releases required to increase
these flows to attain the target flow for water quality control
(fourth increment will increase flow in the Willamette River to
6000 cfs if release demands are met). Since releases for the
downstream fishery complement low flow augmentation for water
quality, the water quality demand tables consider the amount
released for the fishery. In some cases the fish release will
fulfill the first two increments of water quality demand.
Routing Analysis
The day of the maximum reservoir level, days of maximum three-
day flow, and day of minimum reservoir level are found and
recorded in this section. Day of the maximum reservoir level
is found for the winter flood control (prior to day 182) and for
the entire year to aid the preparation of a filling schedule to
achieve maximum storage to meet summer demands. These procedures
simply compare today's level or flow with the maximum to date.
This is repeated for the time period under consideration.
130
-------
III. Economic Model
A.
Drainage Benefit - (% drainage target output met)
x (total annual benefit)
The %. target met is a function of the channel level. If the
average channel level is less than 30% of the channel capacity
during the drainage season (Spring), then 100% of the target
is met. As the average channel level increases from 30 to 60%,
the drainage benefit decreases from 100 to 40% of the target
benefit. If the average channel level increases from 60 to 100%,
then the drainage target benefit decreases from 40 to 0%
The total annual benefit is a function of the channel capacity.
As the channel capacity is increased from 5000 to 21000 cfs,
the total annual benefit (possible) increases from 0 to $500,000
as shown in the program.
B. Flood Loss
[Annual Flood Benefit!
Annual Flood loss potential at - Flood loss at Shedd with project
Shedd without project
[Without project!
|With project]
Flood loss « function of
Flood stage at Shedd
Flood stage1 at Shedd
from maximum instantaneous
flow1
Flood stage^ at Shedd
from maximum instantaneous
flow2
Instantaneous flow^ is
function of average daily
flow*
Instantaneous flow2 is
function of average daily
flow2
Average daily flow from
simulated downstream flow
in hydrology section
Average daily flow2 from
channel level in reservoir
routing section
Superscript 1 refers to conditions without the project.
Superscript 2 refers to conditions with the project.
131
-------
C. Flood Benefit
JAnnual Flood Control Benefit]
Flood loss
without project
Flood loss
with project
Adjusted Annual
Willamette River
flood benefit
From flood
loss section
Lowest flood storage
benefit to date
-| minimum |-
Reduction in benefit
if capacity not available
Sum of 3-day flow
0< - available storage < 0
Sufficient
[flood storage
I
[Insufficient
[flood storage)
No Reduction
in annual
benefit
Reduction «
6000
6000 + Insuff.
D, Irrigation Return Flow"
This section calculates the irrigation return flow which equals
15% of the irrigation release. Irrigation release is determined
in the routing section.
E. Irrigation Benefit
JAn
inual Irrigation Benefit
(% irrigation target benefit met)
x (total benefit)
Irrigation benefits depend on the ability of the system to meet
the target output. The irrigation loss function is determined
from percentage of the irrigation target output met.
132
-------
F. Fish Benefits and Costs
|An"
inual Fish Benefit » Annual Reservoir Sport Fishery Benefit
.. + Annual Anadromous Fishery Benefit
t
nnual Reservoir Sport
Fishery Benefit
(Proportion Demand Met)
($154000)
t Function of
Minimum reservoir level target
Annual Anadromous
Fishery Benefit
{(Proportion Demand Met) x ($424,OOQ)j
TFunction of Minimumr
Minimum proportion
channel level target
Minimum % reservoir level
target (for temperature
control)
Annual fish cost - (Initial fish cost) x (50-year capital recovery
factor
+ .10 for M & 0)
133
-------
G. Water Quality Benefit
Annual water
quality benefit
(Minimum proportion (water quality
water quality flow x benefit
objective mat) (annual M & 0
saving)
+(20-year capital
recovery factor)
x (Initial plant
cost saving)
Annual benefits are actually savings obtained from initial and
annual treatment costs (M & 0) not required due to anticipated
flow augmentation target. The minimum flow objective in the
Willamette River is 6000 cfs. A maximum flow augmentation release
of 1500 cfs would be required from the reservoir during the most
critical low flow periods. The minimum % water quality flow
objective met « (minimum flow, cfs - 4500 cfs) divided by
(water quality objective, cfs - 4500 cfs).
H. Recreation Benefit
Annual recreation benefit -
accumulated dally recreation
attendance @ $1 per person fron
day 240 to day 350 (Summer
recreation season)
The attendance is a function of reservoir level which is converted
to the distance from high water level to actual water surface.
I. Recreation costs
Annual recreation cost - (3)* x (initial cost)(50-year capital
___________ recovery factor
.
*M & 0 - 2 times amortized cost
J, Structure sizes
Structural inputs include channel capacity and reservoir capacity.
K. Net Benefits
Annual net benefits » the sum of annual benefits - the sum of
annual costs
The annual benefits were calculated in the previous sections.
134
-------
Most of the annual costs also were calculated in the previous
sections, while the remainder are calculated in the next
section.
The average annual net benefits are found by dividing cumulative
sum of net benefits by the number of years of concern.
A measure of the uncertainty associated with any proposed system
is the standard deviation of the net benefits and is calculated
as follows:
Standard
Deviation
Square
Root
Sum of squared
net benefits
Number
Sum of net
benefits squared
No. of years
of years - 1 I
L, Costs
Annual Ileservoir Cost - Initial reservoir cost amortized over
100 years
The initial reservoir cost is a function of reservoir capacity,
Initial irrigation cost
initial cost for 69,900 ac.ft
target output adjusted by new
irrigation target factor.
New irrigation target factor is
ratio of new target over 69,900
when target is below 69,900 and
ratio square when target is above
69,900
Annual cost for
69,900 ac.ft output
1.075* multiplied by the initial
irrigation cost
* Irrigation M & 0 » 7.5% of amoritized costs,
Drainage cost -1.1* multiplied by the initial cost amortized
over 100 years _____
The initial cost is a function of channel capacity
* M & 0 - 10% of amortized costs
135
-------
M. Capital Recovery Factors
F interest rate (1 + interest rate)'
* ' * " (1 + interest rate)" -1
where n - number of years. Capital recovery factors are
calculated for 20, 50, and 100 years.
IV. Output Analysis
A, Maximum and minimum annual reservoir levels
The annual maximum reservoir level is determined and counters
sum the number of times the reservoir level exceeds 90, 95, 98,
99.5, and 100 percent of the reservoir capacity on an annual
basis. The annual minimum reservoir level is also found. The
number of times the minimum reservoir level is 90, 98, 105, and
115 percent of the minimum conservation pool of 51,000 ac.ft
is determined.
The frequency of meeting 80, 90, and 100 percent of the drainage
target is counted in this section, too. The drainage target
is a function of the channel capacity as shown in the drainage
benefit section.
B. Flood Loss Distribution
The maximum annual instantaneous channel flows with and without
the project are calculated. Counters determine the number of
times that the flow exceeds 11,000, 16,000, 20,000, 21,000, and
25,000 cfs.
C. Irrigation
Counters in this section sum the number of times that 80, 90,
and 100 percent of the irrigation target is met.
D. Minimum Channel Flow and Conservation Pool
The percent minimum channel flow target is calculated, based on
minimum release flows and target flow for downstream fisheries.
The annual frequency of percent minimum flow exceeding 80, 90,
99.9, and 120 percent of the minimum target requirement is
determined. The number of times that the percent minimum
reservoir target level exceeds 80, 90, 99.9, and 120 percent
(necessary for reservoir fishery and for temperature control for
downstream fishery) is recorded also.
136
-------
E. Water Quality
This section counts the frequency of meeting 50, 80, 90, 100,
and 120 percent of the minimum water quality target flow of
6000 cfs in the Willamette River at Salem, Oregon.
F. Recreation Attendance
The number of times that the recreation attendance exceeds
450,000, 480,000, 500,000, 520,000, 550,000 people is determined
in this section. This equals the recreation benefit since the
value of recreation is assumed to be $1 per visitor-day.
G. Sum of Annual Flows
The simulated flows into the reservoir and in the channel are
summed and the maximum reservoir levels for each season are
recorded.
H. Spill Data
The annual volume spilled and the number of years when water
was spilled are calculated.
I, Maximum and Minimum Daily Flows
This section is used to calculate maximum and minimum flow into
the reservoir and channel.
J. Fish Release
This section sums the additional release of water for fish
above the actual inflow to the reservoir. This volume represents
the amount contributed by the reservoir to maintain minimum
fish flows.
V. Economic Analysis and Shortage Indices
A. Drainage Loss and jhortage Index
(Drainage shortage index - Proportion drainage shortage squared |
[drainage shortage (excess flow) / 0.3*1
average proportion channel level full
- 0.3
* If average channel flow during drainage season is less than 30%
of the channel capacity, then the drainage target is achieved.
137
-------
Dollar loss from drainage shortage
Benefit loss - annual total drainage benefit multiplied by portion
drainage benefit target not met
\l - proportion drainage target met]
B, Channel Shortage Index (flood control)
Jhannel shortage index - proportion channel shortage
squared
(if (-), no shortage, otherwise:)
Maximum Instantaneous flow
with no dollar loss
channel shortage - 1 - >Iaximum Instantaneous flow
Annual channel flood loss calculated in flood loss section of the
model (III - B).
C. Flood Storage Shortage Index and Willamette River Flood Losses
Flood storage shortage index « proportion reservoir storage!
shortage squared |
Insufficient storage
total 3-day inflow |
Willamette River flood loss
[flood lo.ss - Target flood benefit •» Actual flood benefit!
[$160.0001
Actual from flood
benefit calculation
in economic system
D. Irrigation Loss and Shortage Index and Losses
jshorta^e index •» proportion irrigation shortage squared!
' "~
|l - proportion target met)
. - ' • — ' _
[irrigation dollar loss - target benefit - actual benefit!
Actual benefit from irrigation benefit section
of the economic model.
138
-------
E. Fish Loss and Shortage Index
Downstream release shortage index - proportion downstream
release shortage squared
1 - total fish release
+ 130 std*
total fish demand
130 cfs release required due to
DYNAMO summation procedure.
Shortage index for reservoir
sport fish and temperature
control for anadromous fish
downstream
Proportion of shortage squared
(if (+) otherwise zero)
1 -
minimum reservoir level
minimum conservation pool|
Dollar loss for anadromous fish due to loss of reservoir temperature
control and insufficient channel flow.
j Loss
Target benefit
actual benefit|
|$A24.000|
(proportion target met)
(target benefit)
Dollar losses for anadromous fish (insufficient channel flow)*j
anadromous fish (temperature control in the reservoir)*, and
reservoir sport fish are calculated in the same manner as above.
* These values were calculated separately to test the ability
of the allocation procedure to distribute flows equitably.
F. Water Quality Loss and Shortage Index
[Shortage index • proportion shortage squared]
1 -
demand + flow shortage
demand
139
-------
The demand is from the routing section
Flow shortage - flow objective - actual minimum flow into
Willamette River
Dollar loss - (1 - proportion water quality met) (water quality
benefit)
G. Recreation Shortage Index
[Shortage index • proportion shortage squared |
- average reservoir level
reservoir capacity
(calculated for period from day 240
to day 350 only)
JDollar losa - $550,000 -accumulated recreation benefit]
140
-------
PRINT CARD
Many different print cards were used throughout this project. Every
section of the simulation model was tested on a daily basis for 730
days and all calculations by the computer were checked to be sure the
model was performing as intended. During searches for optimum conditions
only, the final results in terms of average annual net benefits and the
standard deviation were printed. At optimum conditions and other com-
binations of inputs, target outputs, and operational procedures of
interest, the performance of the design under consideration was analyzed
in detail at the end of each year. To give an indication of the infor-
mation collected, the symbols on a print card will be explained.
Column 1
YEARS - Number of years from beginning of simulation run.
SUM3 - Sum of inflows to reservoir during 3 months before low flow
demand period. Used with CURN to select a low flow hydro-
graph for Willamette River at Salem and to predict expected
summer inflow to reservoir.
CURN - Constant. A uniformly distributed random number from -1.0
to 1.0 that is generated once a year and is used with SUH3
to select a low flow hydrograph for the Willamette River at
Salem.
ASFR1 - Annual sum of slows into reservoir. (Upstream Simulation
Station).
ASFC2 - Annual sum of flows in channel. (Downstream simulation
station).
MXRLC - Maximum Reservoir Level Counter is the maximum reservoir
level for the year. It also is used to count the number of
times the reservoir exceeds specified levels.
RE900, RC950, RC980, and RC995 - Reservoir counters. They count the
number of years that the reservoir level exceed 90, 95, 98
and 99.5 percent capacity.
Column 2
RCCAP - Counts the number of years the reservoir capacity Is exceeded.
MIRLC - Minimum Reservoir Level Counter is the minimum reservoir
level for the year. It also is used to count the number of
times the reservoir exceeds specified levels.
RC115, RC105, RCCPL, RC098, RC090 - Reservoir counters. They count the
number of years that the minimum reservoir level exceeds 105,
conservation pool, 98 and 90% of the minimum conservation pool.
141
-------
PRCLV - Percent average channel level during drainage period. Used
to determine percent annual drainage target benefit achieved.
PDTM - Percent drainage target met.
ADBR - Annual drainage benefit received.
Column 3
DG100, DG90, DG80 - Counts number of years percent drainage target was
equal to or greater than 100, 90, and 80 percent.
MXACC - Maximum actual instantaneous flow in channel during year.
AFL01 - Annual flood benefit.
CAC11, CAC16
Column 4
CAC20, CCC21, CAC25 - Counts number of years actual instantaneous channel
flows exceeded 11, 16, 20, 21 (capacity), and 25,000 cfs.
CPCll, CPC16, CPC21, CPC25. Counts number of years flow potentially
will exceed 11, 16, 20, 21, and 25,000 cfs with project.
NIRGT - New irrigation target. Used to adjust irrigation demands,
costs, and benefits from a base target of 69,900 ac-ft.
TIRO - Total irrigation release out of reservoir, ac-ft.
Column 5
PITM - Percent irrigation target met.
ANIBH - Annual irrigation benefit.
IG100, IG90, IG80 - Counts number of years percent irrigation target
met is equal to greater than 100, 90, and 80 percent of
target.
MIPCF - Minimum percent channel flow for fishery enhancement.
Percentage is calculated on basis of minimum channel flow
and minimum target flow for fishery.
CG120, CG100, CG90, CG80 - Counts number of years minimum channel flow
was equal to or greater than 120, 100, 90, and 80 percent
of the minimum target flow.
142
-------
Column 6
MIPCP - Minimum percent conservation pool. Used to evaluate
temperature control objective.
PG120, PG100, PG90, PG8Q - Counts number of years minimum was equal
to or greater than 120, 100, 90, and 80 percent of the
minimum target conservation pool.
PFBRS - Percent fish benefit for reservoir sport fishery.
FIBRS - Annual fish benefit for reservoir sport fishery.
PFBAD - Percent fish benefit for anadromous fish.
FIBAD - Annual fish benefit for anadromous fish.
FB - Total annual fishery benefit, FIBRS + FIBAD
Column 7
MIFWR - Percent minimum flow target in Willamette River
PWQB - Percent water quality benefit.
WAQB - Annual water quality benefit.
MIPQW - Minimum percent water quality target
WG120, WG100, WG90, WG80, WG50 - Counts number of years water quality
exceeded 120, 100, 90, 80, and 50 percent of target output.
AREC - Accumulated daily recreation attendance for year.
Column 8
RCB - Annual recreation benefit.
RAC45, RAC48, RAC50, RAC52, RAC55 - Counts the number of years annual
recreation benefits exceeded 450, 480, 500, 520, and 550,000
dollars.
SP4 - Records volume of water spilled from reservoir during year,
ac-ft.
SPCTS - Counts the number of years water spilled from reservoir.
SUMBN - Sum of benefits during year.
SUMCT - Sum of costs during year.
143
-------
Column 9
NETBN - Annual net benefits.
SUNET - Sum of annual net benefits.
SSNET - Sum of squares of annual net benefits.
MADR - Maximum average daily flow into reservoir during year.
MNR - Minimum average daily flow into reservoir during year.
MADC - Maximum average daily flow into channel during year.
MNC - Minimum average daily flow in channel during year.
ERS12 - Difference between expected summer inflow to reservoir and
sum inflow to dam. Expected summer inflow to reservoir
used to allocate water during low flow period.
DAMRL - Day maximum reservoir level. Used in determining rule curve
during flood season.
DAM3D - Day of maximum 3 day flow into reservoir. Used to determine
maximum flood storage volume.
Column 10
MXLS1, MXLS2, MXLS3, MXLS4 - Maximum level of reservoir during season
1, 2, 3, and 4.
ADRF1 - Additional release for fish. Volume of water released to
meet minimum downstream fish demands above flows available
without project.
SIDR - Shortage index for drainage.
DRBL - Sum of drainage benefit losses.
SICH - Shortage index for channel. (Flood control).
FDLR2 - Sum of channel flood losses.
Column 11
WRFL - Sum of Willamette River flood losses from insufficient
reservoir storage.
SIIR - Shortage index for irrigation
IRL - Sum of irrigation losses.
SIFD - Shortage index for fish demand (downstream flows)
144
-------
SIFR
FADL
FADC
FADS
- Shortage index for reservoir sport fishery.
- Sum of anadromous fish losses from shortages in channel
(low flows) and reservoir (temperature control).
- Sum of anadromous fish losses from insufficient channel flows.
• Sum of anadromous fish losses from insufficient reservoir
storage to maintain temperature control.
SIWQ - Shortage index for water quality.
WQL - Sum of water quality losses.
Column 12
TWQRL - Total water quality release during year.
SIRL - Shortage index for recreation.
RECL - Sum of recreation losses.
AVENB - Average annual net benefit.
AWAR - Variance of annual net benefits.
DMR3S - Day of maximum reservoir level during third season.
FRS - Sum of reservoir sport fishery losses.
DAMIR - Day minimum reservoir level.
RLVA - Reservoir level. Used to determine reservoir level at end
of water year.
145
-------
*
RUN
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
1L
6R
C
41R
NOTE
NOTE
NOTE
1L
6R
C
41R
NOTE
NOTE
NOTE
1L
41R
NOTE
NOTE
NOTE
NOTE
12R
28A
7A
12A
51A
20A
20A
51 A
51A
51 A
53A
58A
36A
58A
G1753A-2«DYN»RESULT,45,55»C,0
0175BA
*****************#***#***************************************************
SACRAMENTO STATE COLLEGE
PROJECT — KERRI PROGRAMMER — HINRICHS
DYNAMO HYDROLOGIC SIMULATION AND ECONOMIC MODEL
DATE B/6/69
50 YEARS SECOND INCREMENT OF IRRIGATION
CALAPOOIA RIVER MODEL
MAXIMUM NET BENEFITS
CURN=-UND
HOLLEY K< + ) = KS/l.l,K(-> = KS/1.35
AL3ANY K(+> = KS/1»2, K(-) = KS/1.45
DAY COUNTER
DAY.K=DAY.J+(DT) (YRSIN.JK+0)
YRSIN.KL=PULSE<1,364,364)
UPSTREAM HYDROLOGY
RESERVOIR IN AT HOLLEY
RIN.KL=(FRIN1.K> <86400)
FRIN1•«=<1)EXP(LGRIN.K)
LGRIN»K=MRIN1»K+KR.K
KR.K=(KR1,K)(SRIN1«K)
KR1 •K = CLIP(KR2»K,KR3.K,KHilN.K,0)
KR2.K=KRIN.K/1 • 1
KR3.K=KRIN.K/1«35
MR IN1 • K = CLIP(ARM•K,ARMX.K,91,uAY•K)
ARMX.K=CLIP(BRM.K,6RMX.K,lb2,DAY.K)
BRMX»K=CLIP(CHM.K,DRM.K,273,DAY.K)
ARM,K=TABHL(ARMT,SEA«K»1,91,1)
BRM.K=TABHL
-------
ARMT*=3. 816/3. 755/3. 718/3. 757/3. 793/3. 803/3. 654/3.913/4. 023/4. 17C/
4.5S4/5.G49/4.S26/4. 334/4. 197/4. 162/4. 131/4. 233/4. 290/4. 444/4. 987/
5. 883/5, 50 1/5. 229/3. 036/4.805/4. 80 1/4. 677/4. 740/4. 860/4 ,669/5. 055/
5. 083/5, 009/4. 999/4. 949/4. 938/4. 914/4. 971/5. 038/5. 212/5, 383/5. 566/
5. 9 16/6. 491/6. 249/6. 051/5. 878/5. 650/5. 579/5. 672/6. 159/6. 952/7. 492/
7. 181/6. 7 16/6, 486/5. 91 0/5. 927/6. £03/6. 220/6. 296/6. 31 8/6.21 8/6. 126/
6. 042/6. 054/6, 063/6. 094/6. 298/6. 982/6. 70 1/6. 504/6. 31 3/6 ,204/6. OSS/
6.01 1/6 .022/6.039/6.14 1/6. 41 6/7. 022/7. 71 0/7. 413/7 .073/6. 807/6. 656/
6.476/6.357/6.284/6.349
bRMT* =6. 36 3/6. 2 17/6. 162/6. 1 45/6 .094/6 . 04S>/6 • 09 1 /6 « 404/6 » 947/6. 70 O/
6.541/6.352/6. 1 to7/6 . 047/D . 992/5. 983/6 . 1 3 1 /6 . 379/6 . 925/7.452/7 . 1 72/
6.9o7/6.716/6.504/o.399/6.263/6, 136/6.082/6. 1 5o/6. 133/6 . 383/6 .480/
6.3bG/6 .251/6. 172/6.270/6.454/7. 163/7.773/7.466/7. 1 59/6 • 977/6. 775/
6.589/6,356/6,31 1 /6 « 297/6 .52 1 /6 . 922/6 « 769/6 .544/6 .364/6 .276/6. 1 76/
6. 1 14/6. 062/6. 02 6/6 «O 17/6. 2 1G/6. 240/6. 177/6. 1 3 1 /6 . 345/6 . 578/6 . 505/
6.416/6.285/6.207/6. 1 48/6 .092/6 * 044/6 . 02S/6 • 053/6. 1 29/6 . 358/6 » 724/
7 • 27 1 /7 • 083/6. 8V4/6. 76 1/6 .634/6 .496/6 .397/6 .265/6 .190/6. 205/6. 182/
6. 24 V/6. 377/6. 594/6. 542
CRMT* =6. 4 33/6. 339/6. 235/6. 27 7/6. 354/6. 620/6. bo4/6. 690/6. 555/6. 446/
6. 374/6. 260/6. 15 1 /6 . 079/6 . 045/O . 065/6 . 223/6 • 437/6. 350/6.249/6. 12 I/
5. 9 90/5 ,886/5. 8 36/5 ,64 3/5. 856/5. 8 99/5. 972/5 .985/6. 044/5. 95 9/5. 896/
5.903/5.984/6.226/6.496/6.304/6. 1 70/6 . 07S/5 . 970/5 . 898/5 . 62 1 /5 . 792/
5. 84 4/5. 96 1/5. ti6 5/5. 7b9/5. 727/5. 662/5. 589/5. 555/5. 507/5. 457/5. 423/
5.395/5. J74/5. 349/5 .36 1/5. 420/5 .47 1/5 .460/5. 4O3/5. 328/5 .314/5 «252/
5. 22 1/5. 23 0/5.42 1/5. 752/0. 065/5.423/5. 323/5 .23 1/5. 1 40/5 . 056/4. 988/
4. 93 1/4. 903/5. O2o/ 5. 27 O/o. 1 1 9/5 . 023/4 • 953/4 . 892/4 .843/4 .779/4. 734/
4.71 1/4.61 1/4.840/4.762
DRMT* =4. 7 16/4. 65 2/4. 61 3/4 « 577/4 . 55o/4 • 529/4 « 489/4 * 473/4 . 439/4 .4 06/
4.368/4.325/4.309/4.290/4.255/4.236/4. 191/4. 167/4. 134/4. 1 1 1/4.C99/
4 .068/4,042/4 ,02 1/4.02 0/4, 035/4 .040/3 .976/3 .93 7/3 .91 7/3. 900/3.B92/
3.8J4/3.9ol /3. 386/3. 85 8/3. 85 9/3. 835/3. 8 10/3. 773/3. 736/3. 720/3. 702/
3. 682/3. 675/3. 679/3. 639/3, 626/3, 607/3, 569/3, 599/3. 622/3. 632/3. 675/
3. 64 fa/3. 7 GO/ j.6b 9/3. 636/3. 656/3. 64 2/3. 597/3. 64 9/3. 70 9/3. 623/3. 6 OO/
3. 67 1/3. 630/0. ab-3/3. 569/3. 542/3. 545/3. 605/3. 596/J. 628/3 « 623/3. 737/
3. 873/3. 646/3.70 9/3, 677/3, 722/3. 720/3. 656/3, 6ts4/3. 6 12/3. 59 1/3.660/
3. 74 9/3. 722/3. 695/3. 6to7
SRI Nil .K = CLIP< AH>S.K«ARSX.I<»91 , L>AY.K)
ARSX.K=CLIP(BRS.K«BRSX.K» 182»DAY,K)
6RSX.K=CLIP (Ci-cS.K.DRS,K»273»DAY,K )
ARS.K=TAoHL ( ARiT *5tA.K»l»91»l)
(oRST»SLA.K» 1 »91 » 1 )
ARST*=.680/.595/.500/. 54 0/.550/.554/.595/.674/.614/. 891/1 .OO9/1 .08
4/.974/,9O2/»85o/,9Ol/.921/l • 138/1 .236/1 .327/1 .326/1 .271/1 .209/1 . 1
45/1 .093/1 ,057/1 .069/1 .173/1.223/1,328/1.090/1 .183/1 .156/1.072/0.9
o3/. 804/.640/. 03 1/.845/.002/.902/. 92 i/. 932/1. 067/1. 039/0. 959/0. 978
/.991/.915/,961/1,001/1 . 045/O. 959/1 .013/0.984/1 .015/.951/1 .C37/.91
1/1 .035/1 . 157/1 . 108/.960/.057/.785/.733/.719/.724/.81 I/ .92 1 / .763/.
763/. 7 14/.o67/,64b/,6£9/.636/.736/,o09/, 699/1, 003/1 .127/1 .07Q/.977
/ . fc63/ . 746/ . 754/ .699V . 676/ . 670/ . 8 1 to
5RST*=.854/.756/.71 1 /.74t/,69fc>/. o9u/ . 7 1 £/ .772/ .907/. 63ti/ .770/ .673/
.600/.570/.575/.607/.740/.d42/.917/.902/.781/.742/.660/.fa09/.555/,
518/.466/.532/.730/.810/.764/.779/.657/.562/.539/.551/.736/.763/.7
26/.617/.037/.495/.497/.482/.479/.455/.536/.596/.750/.684/.615/.59
UH15
UH16
UH17
UH16
UH19
UH20
UH21
UH22
UH23
UH24
UH26
UH27
UH2d
UH29
UH30
UH31
UH32
UH33
UH34
UH35
UH36
UH37
UH38
JH39
UH40
UH41
UH42
UH43
UH44
UH45
UH46
UM47
UH4b
UH49
UH50
UH51
UH52
UH53
UH54
UH55
UH5b
UH57
UH58
UH59
UH60
IJH61
UH62
UH63
UH64
UH65
UHbb
UH67
UH68
UH69
147
-------
X4
X5
X6
C
XI
X2
X3
X4
X5
X6
C
XI
X2
X3
X4
X5
X6
20A
51A
51A
51A
58A
5SA
S8A
58A
C
XI
X2
X3
X4
X5
X6
X7
C
XI
X2
X3
X4
X5
X6
X7
C
XI
X2
X3
X4
X5
X6
X7
X8
C
XI
X2
X3
X4
8/.587/.570/.497/.467/.446/.b70/.662/.619/.633/.563/.b72/.608/.560
/.5b4/.470/.471/.457/.4bl/.447/.455/.514/.550/.636/.797/.622/.609/
.6u8/.584/.544/.544/.522/.487/.499/.470/.4fciC/.:364/.650/»720/.6B4
CRST*=.629/.567/.509/.474/.495/.5l8/.509/.475/.4fc>3/.442/.440/.422/
.412/.406/.426/.423/.461/.610/.582/.527/.475/.469/.474/.439/.432/*
439/.423/.431/.435/.546/.483/.445/.470/.513/.656/.763/.656/.577/.5
42/.523/»521/.505/.48S/.561/.60Q/.58&/.570/.549/.53b/.bl 1/.504/.49
2/«479/.463/.441/.428/.427/.497/.534/.536/.463/.398/.375/.365/«374
/.3a4/.42a/«576/.667/.597/.53S/.4a5/.439/.408/.389/.376/.371/«378/
.457/.b46//.459/.4G7/.377/.358/.338/.31b/*302/.304/.5bb/.551/.468
DRST*=.440/.396/.366/.329/.3lS/.324/.339/.330/.336/.361/.331/.316/
»298/.306/.317/»324/.26&/.27Q/.265/.260/.264/.2b2/.243/.238/.263/.
325/.430/.326/.2S5/.275/.277/.285/.27a/.£69/.29b/.274/.300/.308/.2
88/.261/.239/.227/.219/.222/.218/.231/.217/.221/.220/.237/.262/.31
1/.34U/.415/.335/.362/.365/.31Q/.332/.351/.272/.360/.569/.403/.381
/.450/.444/.369/.347/.31£/.293/.391/.448/.47£:/.443/.591/.719/.577/
.498/.417/.6C3/.601/.5OG/.555/.489/.437/.61 1 / • 71 7/ .607/ »572/ .484
GRlN2.K=GRINl.K/6
GRIN! •K=CLIP(ARG«KtARGX«K»91 »DAY»K)
ARGX.K=CLIP (BRG«K«BRGX.K» 182»DAY»K)
SRGX.K = C1_IP(CRG.K.DRG.K.273«DAY«K)
ARG.K=TABHL ( ARGT»S£A«K« 1 »91 » 1 )
BRG«K=TABHL(BRGT«SEA»K» 1 »91 « 1 )
CRG.K=TABHL(CRGT.SEA«Kt U91« 1)
DRG.K=TABHL(DRGT*SEA«Kt 1 »91 < 1 )
ARGT*=1 .622/1 .3S2/.9 1 7/ .^23/.46is/ .5£7/»309/ .335X.46 1 / .556/.3Q9/-.2
67/.323/»435/.432X.676/.o4b/l .271/1 . 1 7 1 / . 960/ . 346/- .465/- . 5 1 3/- .45
9/-.337/-.270/. 022/1 .019/1 . 24 1 / . 626/ . 6 1 1 / . 4 1 C/ . &76/ . 45 7/ . 137/.072/
-. 128/-« 151 /-.O64/-. 1 56/- »508/-» 206/- . 1 66/~ » 343/- . 427/- .669/- . 797/
-.703/-.633/-.646/-.81/-1 . 228/-. 399/-1 .332/-1 .367/-2. 1 7S/-2 . 1 28/- 1
.214/-1 .312/-1 .071/-.668/-.450/. 1 74/ . 027/. 05G/ .202/. 4 1 a/ . 29S/.564/
»373/-» 133/-»446/~.445/-.292/-.294/-.245/-.O64/.295/.443/.284/« 135
/-.476/-.219/-. 169/-.053/-. 158/.203/. 111/-. 1 43/- . 248/ .458
8RGT*=1 . 154/.671/.390/.354/.302/.483/.551/.lC7/-.456/-.448/-,320/-
.232/-.097/.037/.334/.4O8/.293/.077/.086/-.O93/-.210/-.31 1/-.406/-
.651/-.543/-.396/-.470/-.Oo2/.61 1 / . 537/. 233/ . 065/- .227/- . 325/-« 189
/-.449/-.028/-.517/-»680/-«826/-.792/-.662/-.077/-.Q25/. 141/.484/*
408/-.283/-.323/-.269/-.217/-.086/-.079/-.055/. 153/.332/-. 1O4/.489
/.280/.1 18/.1 l3/.207/-.612/-.393/-.493/-.387/-.696/-.7b2/-.513/-.5
C3/-.418/-.362/-.246/-.424/-.667/-.377/-.446/-.282/-.378/-.490/-.E
28/-.263/-.449/-.250/.034/. 109/-. 1 til /- • 1 9 I/ • 34 9/- .526/- . 6 1 7
CRGT*=-.487/-.599/~.754/-.573/-.690/-.750/-.607/-.890/-l .31 1/-1 .13
9/-.986/-1 .261/-.975/-.724/-.671/-.738/-.775/-.423/-.473/-.569/-.5
30/-.U46/-.010/. 108/.033/-.318/-.718/-1.000/-.924/.227/-.456/.079/
.476/.090/.109/.244/-.026/-.206/-.414/-.306/-. 1 70/- . 26 1 /- . S74/-.42
1/-.417/-.323/-.336/-.297/-.251/-.254/-.239/-.256/-.238/-.205/-. 19
8/-.288/-.196/.341/.396/.050/-.100/.289/.399/.292/.479/.418/.421/*
289/.223/.153/.147/.028/-.092/-. 121/-. 089/-. 020/. 1 24/ . 215/. 1 45/.00
4/-.241/-.266/-.332/-.451/-.418/-.420/-.174/-.239/2.41Q/1 .562/.96B
UH7Q
UH71
UH72
UH73
UH74
UH75
UH76
UH77
(JH7B
UH79
UH6Q
UH81
UHB2
UHB3
UH64
UHtib
UH66
UH67
UHSb
UH89
UH90
UH91
UH92
UH93
UH94
UH95
UH96
UH97
Uri9b
UH99
UH100
UH101
UH102
UH103
UH104
UH105
UH106
UH107
UH103
UH1C9
UH11C
UH111
UH112
UH113
UH114
UrillS
UHH6
DRGT*=.59b/.470/.384/.36o/.23u/-.073/. 10o/-. 1 oo/ .223/.
1/-.066/.U61/. 192/.412/. 1 60/. 081 / .047/ .066/ .295/ . 093/ . 121/. 138/.26
4/1 .070/2.400/1. 1 73/.587/.2B9/ .309/. 495/ . 04 1 / . 1 63/.3 1 O/- . 0 1 4/ .336/
.900/.454/. 165/-.013/-. 1 22/-. 084/-.070/-. C39/ . 1 1 O/-. 040/. 021 /-. 003
/.004/.608/.970/. 870/1 .22 1 /.747/«966/ 1 .254/ . 636/ . 879/ 1 «367/. 664/1*
148
-------
311/3.047/2.31 I/ 1.818/1. 33 1/2.009/1. 41 3/1. 52o/.69b/l. 01 1/1.542/1. 7
7o/i.9bB/l.i95/l • *64/1.37o/.6B=>/.77b/. 933/2. 04 I/ 1.777/1, 471 /1.356/
1 «5u5/l . 580/2. JbO/1 ,995/i .67b/l .462/1 .2b6
GRIN3.K=XRIN«K-GRIN2.K
GRIN4.K=1 + (GRIN4.K)
GRIN6.K=l/< (3) (GRIN2.K) )
KRN.K=(GRIN6.K> (GKlNboK-1 )
PKRN.K=-2/GRlNl .K
KRIN.K=SW ITCH(XRIN.K«KPN1 .K.GRIN1 •!<)
KRN2.K=KRN.K-PKRN.K
KRN3«K=CL IP (KRN.K.PKRivl.K. *KRI\2.K«0 )
KRN4 • K = CL I P ( KNixi . K , K + ( DRN2 •)<) CNL5ST1 .K)
DRN1 «K=1-DRIN.K
DRN2.K=< 1 )SQRT(DRN1.K)
B2RIN.K=CLIP(ARu.K.ARbX.K,9l . JAY.K)
ARBX.K = CLlP(BR6.K«BRbX.i<, 162»OAY.I<)
oR3X.K = CLlP(CRB.I< « DRo . K « 273 t DAY * K )
AR8.K=TABHL (ARdT»S£A.K« 1.91*1)
6RB.K=TABHL (BRBT»SEA»I<» 1 »91 « 1 }
CRB.K=TABHL (CRBT * SEA «K « 1 » 9 1 t 1 )
DR6.K = TAdHL (URbT «ScA.K t 1 »91 t 1 )
964/ . 934/ . 9o-/ . 9fa2/ • 95 7/
965/. 97 7/ « 9o4/ . 68£/
96
977/ . 995/« 9
3/.765/.617/.93C'/.e01/.820/.7<-9/«8b3/.661/.964/.964/.y59/.971/.989
/.9S4/.876/ .970/ . 9 ad/ . 944 / . 9 1 il/ * 974/ . 96 1 / « 970/ . 989/. 982/ * 978/ * 935/
.99o/.941/.909/.827/.fa5a/.9b3/.969/» v92/»993/.994/.983/.96b/.a64
6RBT*= .94£/.b74/.9oO/.860/«985/.973/ « 9s7/ . 64 O/ »77S/ . 976/ .9b6/ «940/
.944/.9aO/.946/.974/.906/.85b/.823/.927/.9b2/.967/.988/.9a4/.963-/.
97a/.978/.788/.92O/.9o2/.b25/.b81/.908/.966/.941/.817/.a67/.448/.7
68/.95a/.S97/.91 4/.v6l/.9b 1 / . 896/ • 92 ^/ • b04/ . 84 9/ »556/ • 982/. 954/ . 96
6/.99O/. vab/.976/.^79/.910/.86o/.67o/.906/.974/.9l3/«b27/.902/.939
/.989/.944/.990/.988/.993/.95b/.9b7/.961/.940/.a87/.912/.b04/«970/
•958/.960/.977/.942/.946/.912/.937/.8S1/.927/.376/.927/.831/.972
CRBT*=.974/.991/.974/.o9b/.903/.6ti6/.962/.967/.977/.967/.984/.962/
»956/.988/.9c^/.943/.906/.9U6/.991/.987/.976/.948/.967/.9a6/«954/.
965/.9oy/.923/.915/.779/.93v/.9'£l/.971/.935/.91b/.912/.963/.973/.9
yi / . 9ob/ . 9ci4/ . 94 v/ . 94o/ • o46/ « 9 1 4/. 9b8/ . 9o7/ • 91 1 / * 677
/.9a2/.969/.a41/.860/.983/.9b9/.993/.990/.990/.992/.993/.992/.98b/
.821/.b77/.978/.972/.992/.9^4/«996/.9b8/.990/.96b/.795/*900/.90e
DR3T*=.9b7/.997/.993/.989/.96o/.968/.976/.921/.965/.993/.997/«995/
•974/.974/.973/.992/.992/.y93/.996/.997/.969/.993/.992/.995/.963/,
v74/.916/.91d/.^l/.996/.991/.9«9/.93U/.939/.960/.967/.944/.979/.9
84/.99u/.991/.yyu/.99H/.993/.v=>9/.96b/.971/.991/.993/.984/.9ai/.aa
3/.921/.916/.971/.ai9/.990/.9o3/.844/.921/.Ci=9/.680/.806/.929/.937
/.668/.864/.869/.962/.928/.907/.820/.969/.929/.801/.784/.842/.919/
UH127
UHl2b
UH129
UH130
UM131
UH132
UH133
UH134
AR01 .!< = £ AMPLE ( UNDO 1 «K« 1 )
UND01 .K=( 1 ) NOISE
UH136
UH137
UH138
UH139
UH140
UH141
UH142
UH143
UH144
UH14b
UH146
UH147
OH148
UH149
UHlbO
Uhlb 1
UH1 bt:
UHlb3
UH154
UH155
UHlbb
UH157
Uhl58
UH159
UHloO
UH161
UH162
UH163
UH 1 64
UH165
UH166
UH167
UH168
UH169
UH170
UH171
UH172
UH173
UH174
UH17b
UH176
UH177
UH178
UM179
149
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33A
43A
33A
43A
33A
43A
33A
A3A
33A
43A
33A
43A
33A
43A
33A
43A
33A
43A
33A
43A
33A
1OA
10A
7A
51A
51A
51A
5SA
58A
58A
58A
C
X 1
X2
_ X3
X4
X5
X6
C
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X2
X3
X4
X5
X6
C
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X2
X3
X4
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X6
C
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X2
UND02.K=( 1 ) NO I SE
ARO3.K=SAMPLE(UNDO3.K« 1 >
UNDO3.K= ( 1 > NO I SE
AR04.K=SAMPLE
UND05.K=< 1 > NO I SE
AROb.K=SAMPLE(UNDO6.K« 1 )
UNDC6.K= ( 1 ) NO I SE
ARO7«i< = SAMPLE(UNDO7.l<» 1 )
UNDC7.K=< 1 ) NO I SE
AR08.K=SAMPLE(UNDO8.Kt 1 )
UNDO8.I<= ( 1 ) NO I SE
AR09«K=SAMPLE(UND09.K» 1 >
UND09.K=( 1 ) NO I SE
ARO10»K=SAMPLECUND10.K« 1 )
UND10.K=( 1 ) NO I SE
AR01 1 .K = £AMPl_E43/.949/.962/.941/.978/.964/«957/.a74/
.981/.886/.826/.685/.732/.967/.939/.984/.986/.988/.967/.932/.747
BRDT*=.888/»764/.96l/«739/.96^/«947/.916/.70o/.601/.956/.973/.864/
.892/.961/.894/.949/.821/.731/.677/.658/t964/.935/.977/.968/.928/*
957/»956/»622/»S46/.907/»66l/.776/.o24/«934/.8t;6/.668/.751/«201/«5
90/.912/»805/«835/«924/.90b/.803/»fabb/.646/«720/»309/.963/«91 0/»93
4/«981/»977/.953/»959/«b£a/'.7^0/»4oO/»820/«949/.o33/.C>o4/.ol3/«863
/.979/.S92/»960/.976/s9tsb/«91 7/ . 97b/ »923X «o64/ . 787/ . 83 1 / .646/ «942/
.917/.922/»95b/.ti87/»695/.b31/»879/.724/»859/.767/.859/»691/.945
CRDT*=.948/.982/.949/.801/.8ia/.430/.925/«936/.9bb/.935/.969/t9£5/
.914/.977/«97l/»a9O/.a21/.d21/«983/»974/«9b3/.u99/.934/«973/.910/t
93l/«920/.852/«836/«607/«obl/»c>48/.943/.874/.b3d/.b31/>927/.948/.9
64/.932/«991/»960/.914/.919/.dob/.97b/»96&/.9oO/.992/.983/.996/»99
4X.994/.993/»9d2/.97b/.969/.9uO/.899/«71=i/.ci35/.91e/.916/.b29/«770
/.963/.939/«707/«739/«96ri/.97ci/.986/'.9dO/.979/.98bX,990/«9a4/«977/
.674/.769/.9b6/e945/.9b4/.989/.992/»97b/»979/«932/.b32/.bl I/. 825
DRDT*=.974/.994/.987/.978/.971/.938/.953/.647/.931/.987/.994/.990/
.949/.949/.947X.984/«984/.987/«992/t993/«940/«9.d5/.984/«991/«92S/«
949/.843/.842/.983/.991/.9bl/.97S/.919/.8b3/.922/.936/.891/.9b9/.9
UH19G
UH191
UH192
UH193
UH194
UH19S
UH196
UH197
UH198
UH199
UH200
UH201
UH202
UH203
UH204
UH205
UH206
OH207
UH203
UH209
UH210
UH211
UH212
UH213
UH214
UH215
UH216
UH217
UH21B
UH219
UH220
UH223
UH224
UH225
UH226
UH227
UH228
UH229
OH230
UH231
UH232
UH233
150
-------
6a/«9ai/,9a2/.9fal/.985/.9tt7/.920/.
^.84ti/«S39/.943/.67l/.979/.92e/.7l2/.64«/.738/6a/.649/e63
/•4«6/.746/.790/.925/.862/.822/.672/.939/.863/.641/.615/.709/.e45/
•868/*947/.704/.732/.973/,76Q/.972/.904/.766/.867/.SOO/.905/.644
YRIN1.KL=XRIN.K
YRIN»K*=YR1N1»JK
NBST1.KL-NDST1.K
NASTI.K=NBSTI.JK
DOWNSTREAM HYDROLOGY
CHANNEL IN AT ALbANY
CIN.KLMFCIN2.K)<864OO)
FCIN2.K»CLIP(FCIN1.K»FRIN3»K»FCINI»K«FRIN3.K)
FCIN1•«*
6CMX.K=CLIP(CCM.K«DCM«K«273.DAY«K)
ACM.K=TABHL(ACMT.SEA.K*1.91« i)
3CM.K=TABHL(UCMT«SEA.K«1.91.1)
CCM«K=TASHL70/
6 .64 0/6. 634/6 .647/6. 644/6. 795/7. 09b/7. 606/7. 332/7. 130/6. 96 1/6.796/
6. 665/6»5oO/6. 6^4/6 .7 15/to. 942/7.3 j9/7.99SJ/b.463/8»244/7» 87 1/7.563/
7.368/7.204/7.090/7.122
BCMT*=7.OQO/6.943/6.865/6.742/6.6b3/6.774/6.953/7.221/7.523/7*757/
7.571/7.332/7,095/6.938/6.821/6.772/6.911/7.199/7.660/8.152/6.4 1 2/
8.Ob2/7.758/7.542/7.3b7/7.169/7.019/6.896/6.883/6.853/7.179/7 »299/
7.064/6.918/6.899/6.986/7.209/7.606/8.152/8.599/8.396/8.062/7.81i/
7.539/7.354/7.061/7.051/7.066/7.387/7.650/7.473/7.257/7.118/6.912/
6.733/6.6 10/6.582/6. 7i>4/6 .943/6. 92 1/6 .8 13/6.777/6.842/7.0 18/7»364/
7.235/7.u66/6.bo6/6.813/6.666/b.638/fc>»629/6.630/6.729/6.985/7. 284/
7.713/8.077/7.876/7.627/7.373/7.202/7.009/6.831/6.735/6.661/6,63 I/
6.706/6.992/7.292/7.096
CCMT* = 7.005/6.849/6,753/6.649/b.736/6.877/7.115/7.318/7.156/6.960/
6.848/6.756/6.628/6.512/6.429/6.349/6.480/6.687/6.925/6.794/6.§49/
6.480/6.316/6.228/6. 1 92/6. l64/t>. 2 1 3/6 .264/6.346/6.312/6.284/6.262/
6.244/6. 249/6. 394/6. 685/6. 9313/6. 746/6. 507/6. 389/6.296/6. 1V4/6.105/
6. 121/6.214/6.400/6.278/6.137/6.057/5.999/5.932/5.670/5.809/5.759/
5.730/5.702/o.669/s.622/5.62U/5.700/0.783/5.726/5.667/5.635/3 .561/
5.565/5.545/5.576/5.726/5.9o5/5.836/5.71S/5.625/S.536/5.469/5.404/
5.356/5.308/5.304/5.389/5.575/5.458/S.377/5.315/5.269/S.226/3.203/
5.179/5.258/5.285/5.178
DCMT*=5.128/5.101/5.066/5.025/4.993/4.986/4.9S9/4.939/4.925/4.685/
UH236
'UH237
UH23&
UH239
UH24Q
UH241
UH242
DM1
OH2
DH3
DH4
DH5
DH6
DH7
DH8
DH9
OHIO
DH1 1
DH12
DH13
DH14
QHlb
OH 16
OH 17
DH18
DH19
DM20
DM21
OM22
DH23
DH24
DH25
OH26
DH27
OH28
OM29
DH30
DH31
DH32
DH33
OH34
DH35
DH36
OH37
OH38
OH39
DH40
DH41
DH42
DH43
151
-------
XI 4 »8D 1/4. S26/4 .80 4/4. 79b/4. 783/4. 755/4. 727/4. o92/4.6D=/4. 624/4. 604/ urt44
X2 4.5BO/4.558/4.544/4.538/4.549/4*553/4*544/4.si 9/4.493/4*412/4»404/ jr!4b
X3 4.394/4.4OD/4.390/4.382/4«3b4/4.379/4.355/4.330/4.310/4.297/4.290/ Jh4o
X4 4. 272/4. 259/4. d's, 1/4.234/4.2 13/4. 195/4. 170/4. 1^1/4. 147/4.158/4. 141/ DH47
X5 4.118/4.087/4.030/3.980/3.944/3.898/3.828/3.7b9/3.793/3.800/3.842/ DH4d
X6 3.796/3.737/3.SO0/3.798/3.779/3.770/3.794/3.766/3.774/3»78b/3.676/ Dh4V
X7 3.908/3.927/4.UO9/3.934/3.919/3.883/3.694/3.940/3.886/3.853/3.600/ DH5Q
X8 3.932/3.945/3.945/3.913 DHbl
51A SCIN1 .K = CLIP(ACS.K»ACSX.I<«91 ,DAY.K> DHb2
S1A ACSX.K=CLlP DH53
51A 5CSX.K = CLlP(CCS.K,DCS.i<»273«UAY.K> DH54
58A ACS.K = TABHL(ACSTtS£A.I DH56
S8A CCS.K=TASHl_(CCSTtSEA.K« 1 i91 , 1 ) DH57
58A DCS.K=TABHL(DCSTtSEA.K»1»91,1) DHbd
C ACST*=.49G/.475/.512/«507/.486/.b72/.5ci:=>/.624/.6ba/.73:5/.630/l .022 DHb9
Xl /I . u78/.'991/.909/.b32/.d91/.965/l . 1 Ob/ 1 . 209/ 1 .2oo/l .3O6/1 .334/1 .c;9 DH6Q
X2 3/1.203/1•152/1 * 126/1.128/1.196/1.371/1.352/1.474/1.441/1.266/1«19 DH61
X3 1/1.171/1 .082/1 .041/1. 007/1 . 0 1 O/. 969/. 956/1 .109/1.043/1.013/1 .073/ DH62.
X4 1 . 148-/1 . 128/1 .099/1 .021/1 .039/1 . 141/1 . 168/1 .405/1 .197/1 .293/1 «347/ DH63
X5 1.205/1.19O/1.309/1.339/1.365/1«397/1.249/1»09o/1.O1D/•939/ • 926/•9 DH64
X6 14/.931/.964/.789/.774/.761/.740/.741/.713/.745/.803/.946/1.040/1• DH65
X7 U74/1.035/1.053/1.007/.961/.874/.b78/.b97/.o^2/.824 DH66
C BCST*=.921/.984/.871/.791/.6bo/.7oO/.627/.o22/.924/.9£>0/.937/.816/ DH67
XI .731/.692/.6o2/.72i;/.837/.930/.b91/.947/.94^/.90:b/.830/.799/.757/« Oribti
X2 723/«712/.719/.770/.840/.ot55/.823/.a69/.590/.494/.512/.5b6/.541/.6 QH69
X3 50/.761/.700/.609/.589/.606/.t)2a/.661/«654/.570/.7l4/.S07/.7ei/.70 DH70
X4 u/.66ti/.5b7/.535/ . o34/ • ^ 34/ . ^o9/ . o 1 3/ . 687/ . 621 / . 3U3/. 60 O/• 659/. 672 JH71
X5 /.649/.657/.61 3/ . 603/ . o65/ * o7v/ . 62 1 / . 648/ . 753/ . 769/ . 797/ . a78/ . 69 O/ LJH72
X6 .675/.676/.677/.669/.6o2/.6GO/.b67/.539/.571/.610/.805/.958/.S74 DH73
C CCST*=.780/.685/.599/.483/»49ii/.556/.640/.659/.6bti/.591/..564/.521/ DH74
Xl .481/.475/.509/.490/.592/.667/.751/.707/.652/.D04/.544/.476/.452/» 3H75
X2 460/.474/.527/.535/.466/.4t37/.532/.b2b/.551 / • 734/ . 922 / . 95 O/ . 847/.S DH76
X3 83/.61 U/.56C/.557/.520/.b72/.6c;4/.6c39/.699/.ol 7/.51 1 / . 6Q2/. 585/.54 OM77
.X4 0/.535/.527/.521/.345/.533/.542/.501/.596/.^U=/.442/.405/.386/.379 DH78
X5 /.382/.409/.442/.53o/.609/.56o/.499/.447/.39v/.366/.3o3/.337/«323/ Dh79
X6 .334/.367/.433/.3a4/.346/.331/.314/.30b/.297/.2ol/.463/.440/.472 uhBO
C DCST*-=.390/.357/.325/.327/«30o/.297/.30b/.304/.31 1 / . 3 1 3/ . 309/ . 3 1 O/ Drl&l
XI .302/.304/.319/.302/.294/.C&1/.273/.268/.262/.2&3/.253/.250/.272/. DH62
X2 323/.391/.406/.365/.334/.2fci7/.2o9/.2ti7/.293/.2fa9/.238/.298/.309/.2 DH33
X3 98/.287/.282/.276/.26&/.264/.264/.270/.281/.267/.263/.259/.257/.26 DHb4
X4 3/.304/.327/.330/.337/.319/.2b6/.2tol/.300/.2DO/.292/.300/.339/.453 LjH6b
X5 /.404/.329/.361/•37O/.345/»34u/.383/.362/.361/.473/.49o/•593/.560/ DHb&
X6 .556/.490/.442/.427/.349/.607/.527/.4a4/.452/.675/.bl2/.600/.490 DH67
2OA GCIN2.K=GCIN1.K/6 DH88
51A GCIN1 .K = CLIP< ACG . K t ACGX . l< « 9 1 ,u»AY«K) DHb9
51A ACGX.I< = CLIP(BCG.K,bCGX.I<. 182.DAY.K) UH90
51A ' faCGX.K = CLIP(CCG.K«DCG.i<»273,DAY.I<) DH91
58A ACG.K = TAbHL (ACGT»Sc.A.K» 1 «91 , 1 ) QH92
58A BCG«i< = TADHL(bCGT
-------
7/-.lu7/-,230/-.257/-.202/-.604/-i.013/-.20C/.174/-.410/-.593/-.6- ul-199
/V-.7i;4/-.:D56/-.;Dl3/-9:Db2/-.4b6/-.byb/-l . 173/-1.837/-1 .439/-1 ,494/ UH100
-1.126/-1 .044/~.'o32/-.:D65/-.b41/-.297/.07a/.0<:>l/.099/,227/.346/.06 DH101
d/-.070/-.088/-.266/-.343/-.389/-.497/-.367/-.049/.147/.229/.142/- OH 102
•106/~.431/-.4GG/-.419/-.242/-,092/.2Ga/.34b/»416/.6ai DH103
bCGT*=l•086/1.087/.644/.457/-.121/-.Ooa/-.03a/-.203/-.498/-.b64/-. DH104
396/-.29b/.03e/.26G/.b74/.647/.566/.22C/~.291/-.200/-.658/-.7S5/-. OH 105
625/-.647/-.447/-.22J/-.028/. 162/. 199/.591/.i:fc3/-.£42/-«263/-.276/ OH 106
• u6b~/.234/-,159/-.64o/-.966/-.653/-l .290/-1 .465/- « 969/- . 009/ . 323/ • OH1C7
535/.:j47/.19b/-.327/'-.48b/-.321/~»310/-»20a/-9157/.12 I/»22e/.452/ • OH 106
366/.593/»16v/.199/.469/,£83/-,156/-»5Ga/~.45S/-•519/-•719/-•605/- Chi 09
• 1J6/.lb7/.4y3/.736/.7^7/.325/-.239/-od58/-»498/-.421/-«41 1/-.399/ Uh 1 1 0
-*352/-« l86/-.12o/.122/-»230/-« 1 52/. 099/»308/-« 203/-« 240 DH 1 1 1
CCGT*=.036/.271/.3C6/« 1 12/-.OOS/-.1 la/-«197/~.156/-.173/-.413/-.3S DH1 12
3/-.444/-.659/-.41fc>/.059/.520/«767/*21C/-.26b'/-»2Ba/-.277/-.04a/-» Ohl 13
u91/-.026/-*043/-»123/-.166/«2a2/-.14a/-.61O/-•50o/.239X•770/*609/ DH1 14
.88a/.627/.273/«149/.071/-9153/0.019/.018/-»095/.1b4/»432/.08 1 /* 08 DH1 15
9/-« 1 18/-.009/-.006/»0=i3/-e 1 06/-« O40/ . Gb2/ « 1 1 6/. 276/• 29 1 / «335/, 053 DH1 16
/»624/.4= l/»o50/«50t)/.243/»37ti/e360/.526/«32b/.051/» 19b/.lo9/o094/ DH117
-«^.27/-»24'J/-«3i3/-«246/»» 19S/-.G41/ « 02S/- • O 1 9/- . 100/-«3bl/-.373/- DHllfc
.366/-.337/-.315/-»197/-.2Ui/i;. 132/1 .346/1 .721 CHI 19
DCGT*=.857X.4b3/«250/«141/«1C5/-«006/.090/•067/.093/«227/«448/ • 376 DH120
/»lJ^/-»l04/»C33/«2oa/8±>28/«360/»260/«£27/«23:3/« 1 69/«309/. 3£6/• 220 OH 121
/.6o3/l ,352/1 «o67/.93u/e679/«o57/.090/«079/.005/-,0&i/-«.l 13/-.037/ wH122
•15/»o31/-»03/-,Ol5/,06a/,12t>/»lll/»CbB/-,019/.214/,106/,0&l/,04b/ JH123
-.ubv/-»07e/«252/.t>o7/i.7o2/l»';tOb/1.4 1 to/« 934/. 4yb/. 9fa4/» 019/.998/1 » ujHl24
a29/l • 793/3 ,u 34/2 » 673/2.405/1 .736/1 »o93/l .461/1 . 477/. tioO/. 633/1 .10 UH125
2/1. ^47X1.561/2,046/1.052/1.037/1.147/1.231/1.471/2.091/1 .J70/1 »32 DH126
o/l.36-j/1.363/2.323/1. 90^/1.4 14/1.471 DH127
&CINo.< = XC I N.K-CaC IN2.K DH12ci
GCI,\4.K=l + (oCIN£.K ) (GCIN3.K) DH129
GCINb»K=(GCIN4.K) (GCIN4 «K) (GCIN4»K) DH130
GClN6.K=l/((3)(GCIN2.K)) DH131
KCN.K=(GCIN6.K) < GCIN5.K-1 ) DH132
PKCN.K=-2/GCINl,K DH133
KCIN.K = 5WITCH(XCIN,!<»KCN1.K«GCIM«K) DH134
KCN2,K=KCN,K-Pi
= TABHL(6CD2T*Sc.A.K* 1*91.1) DH146
= TABHL(CCb2T*S£A.K* 1*91*1) DH147
= TMoHl_(uC[j2T«Sc.A.K» 1*91*1) DHl4o
.772/.40a/.41d/.70a/.64^/.36o/.ob3/.a70/.6ia/.707/.64b/.691 UH149
/.247/.666/.749/.630/.37o/,6t>2/.467/1.018/.7b2/.5bl/.162/.696/.733 CHI 50
/.480/.642/.579/.3y4/.66b/.lo4/.927/.o22/.85G/.b3o/.826/.564/.594/ Dhlol
.7lb/.022/.&49/.706/.621/.7lO/.903/.20&/,994/.702/.612/.450/.94C/. DH152
153
-------
Xb
X7
c
XI
X2
X3
X4
Xb
X6
X7
C
XI
X2
X3
X4
X5
X6
X7
C
XI
X2
X3
X4
X5
X6
X7
bl A
51 A
51A
b8A
5SA
58A
. 58A
C
XI
X2
X3
X4
X5
X6
X7
C
XI
X2
X3
X4
591/.623/.B73/.76G/.9GJ/.9Gb/.764/.5bl/.9a4/.d40/.
b6/.389/.903/.827/.bd6/.640/.4o:D/.d94/.821/.941/«o76/.9id3/.743/.t>6
2
5CB2T*=.b~59/.762/.o95/.849/.724/.796/.634/.93:3/.=>28/.792/.976/.e23
/.774/.91b/.918/.716/.d26/.7:Dl/.532/.614/.7G3/.604/.6bl/.951/l.009
/I . u39/.943/»823/.£>3S/.6b4/. 162/•29b/•823/.9do/.902/•S76/•742/»652
/.591/.283/.937/.657/.894/«9t;u/.9G7/.d37/.a5^/.774/.471/.74e/.973/
1 .G63/.930/.7b7/»676/.b33/»:oby/.656/. 1 b 1 / »3fc>3/ . 73b/. fc>62/ .670/.368/
.b6o/.921/.9G4/.694/.&92/»291/«926/.b49/.7o1/•996/«822/•832/.684/.
b6d/.949/.b42/.638/.747/.7Ga/.784/.b2O/.79b/.761/.626/.487/.746/.3
38
CCB2T*=.716/.735/1.017/»69b/»533/»5^o/.47b/.516/•B86/•79 O/•824/•89
3/.635/.733/»9b2/»66G/.743/.b46/.780/«964/.9Gl/.742/.499/«667/.906
/«8b2/«501/»7o3/.600/.820/.743/.656/.922/«U4£./.b40/.494/«34b/»e04/
.7&3/.b42/«773/.d74/.893/.b63/.807/.D76/.941/.716/.773/.92e>/.975/»
834/.b7G/.9Ql/.969/.735/.9b2/.9bO/.713/.510/.235/.bd7/.766/.857/.i:i
bC/.bb6/.621/»825/.b40/.14G/«4&Q/.7tsy/l . G65/• btob/• 834/• 94b/• 9b/ • 964 / . *6 1 / » 86 9 / 1 «042/.666/«
826/.980/.974/1.U38/1 .039/1 * 0--7/ • 992/ . 996/ 1 . ^d 1 / . 9oO/ . 982/ . 996/ . 93
7/.999/1.004/.913/»748/•UoO/.b90/•871/•995/•98O/•o49/.953/1.016/.7
96/.ab3/.o39/.Ol6/.897/.602/.723/.8b'9/.602/.bl 7/. 384/. d 1 7/. 825/. 99
2/.b97/«664/.oll /.632/»6 1 o/ • 8 1 O/ • di 4/ • c33/ .303/.268
/•516/.361/.424/.615/.228/.<
C61/.399/
17b/.
[4b/.476/.415/
• 293/.183/* 132/.246/.297/»2o3/.G83/.737/-.GG2/.28i/. 1 89/. b45/• 038/
•139/.G54/.287/.61/-.G84/.4G7/.202/-.001/.233/.762/.339/.311/.245/
.418/.362/»lC9/.263/.09b/.067/.206/»454/-.OG^/.lb~i/.23b/.242/.307/
• 149/»o9=>/»G6b/. 1 3b/.38u/«ii96/.a77/. lGG/.lbG/.obb/»12V/.06o/.239/.
30b
bC53T*=.45G/»18fa/»11!/•lD2/.2bl/.lob/.343/-»G01/.471/.166/.C19/.18
3/. l89/.G83/.G54/»257/. 1 ub/. 1 7C/» 44b/. 372/. £i^9/.4 1 3/• 298/. G37/-. 02
7/-.068/.G46/.182/.48G/»3o9/.dG9/.7GG/.G6G/-»GlG/-.000/.&£2/»025/»
316/.331/.691/-.G04/»31G/.G4b/-«023/.lGl/-.G41/.166/»158/.486/.233
/•Gul/-.132/*G6b/.2b3/.328/.3-l/»4jQ/.237/.797/.o93/»£;36/«3O9/»260
DH176
DH177
OH176
JJH179
QrilBO
DMiai
DH182
DH183
DH164
DHloS
DHlb5
DH 1 b7
DH 1 od
OHlo9
DH1VO
UH193
/.3l7/.j92/.oi37/.142/.37^/.£b^/.284/,196/.161/.lb9/.211/.344/,444/ JH2C2
•143/.6b4 OH203
CCo3T*=. 29/ .253/ —• 02i)/»2bo/«4^3/.j73/«ssb/«477/. 1 17/» 19o/« 177/» 1 12 DHeiG4
.lbl/»494/.27v>/.393/.2u8/.271/.143/« G79/« 151/»474/.b02/.66G/.203/» DH206
22o/»163/.22o/.123/.112/.292/.184/»316/.G64/•312/.237/.07b/.018/»1 OH2C7
154
-------
X4
X-j
Xo
X7
C
XI
X2
Xj
XV
J1A
3lA
51A
OOM
30 A
XI
X2
X3
X4
Xa
Xo
C
XI
Xi.
X3
X4
Xs
Xo
C
XI
X2
X3
X4
X5
Xb
Xc
X3
X4
Xb
X6
Or,
6A
6H
6A
NOTE
NOTe
NOTii
6N
9/.3=7/,376/«199/,49*/.bbG/.5l7/»£G3/-.G73/.134/.170/.Q4e/.G80/-.l
02/.221/.364/. ^l/«39b/.469/-.Gl5/-.lGS/-.C26/.G6b/,29:5/.344/«679/
1.050 '
DC33T*=.327/«u29/.002/~.024/,o71/.i01/.l£6/.269/.027/'.146/.Q94/-.0
28/.058/.151/. 149/«ia2/-.006/-e054/-.C47/-.056/-«028/-.013/.042/-»
007/.222/»169/-.u21/-*039/«05S/.02b/« 1 8G/ . 036/ . 03C/» 154/-.C70/* 145
i_-H209
DH210
OH21 1
/-.C63/*632/»71 7/.789X * 903X-* 948/ * 93
7o2/ * 862/ • 636
UH237
987 /
99
OH242
037
966/ • 98
*= . 969/»
» 964 / »993/ • 9
747/ . 9&7/ « 9o3/ • 9-=- 1 / « 990/ . 9b4/ • 98
«92^/.c7C/.946/.969/.977/«9S4/.976
982/ . 9o7/ »9t>4/ «989/. 9o7/ • 993/.9B4/
63/.70s/.9b3/.762
949/ . 967/ . 970/ • 990/
L)H24b
DH246
DH249
DH2bO
63/ . ^LV/ . v93/ .9;> 7/ « 9957 • 997/ . 980/ . 9dO/ » 990/ -995/ . 993/ * 997/ . 995/ • 94
3/.&^/.9u6/»94b/.9lu/.969/.9a9/.926/.967/.9b6/.917/.749/.947/.621
/.t)78/.e83/.bb3/.9i6/.917/.66d/.5b3/.90b/.861/.914/.67£/.634/«857/
YCIN1 .,
-------
6N
6N
6N
6N
6N
6N
6N
6N
6N
NOTE
NOTE
NOTE
NOTE
C
6A
51A
51A
51A
52L
SIR
SIR
SIR
51A
58A
C
SI A
43A
33A
51A
58A
C
XI
58A
C
.XI
S1A
58A
C
XI
51A
58A
C
XI
51A
5SA
C
XI
6A
NOTE
NOTE
NOTE
20A
6A
12R
7A
SEA = U
YEARS=1
FRIN4=0
YRIN1=G
YCIN1=0
YCIN=1
YRIN=1
NAST1 =1
NBST1=0
GENERATION OF LOW FLOWS ONLY
WILLAMETTE RIVER HYDROLOGY
WRFOB=6000
WR.K=WRFOB WILL. RIVER FLOW OBJECTIVE
SUM1 .K=CLIP
UND.K=(2)NOISE
WIN4«K=CLIP (WNM1 »K » WNM2 »K « -0 • CO « CURN.K )
WNM1 «K=TABHL(DRYM1 .DAY.K.241 .373. 12)
DRYMl*=7061/7C61/7061/4530/4S30/456u/4597/4597/747u/74 70/7470/7470
WNM2»K=TABHL(DRYM2»DAY.K»241 » 373. 12)
DRYM2*=7l76/7l7b/717S/bol3/o813/57SO/S6d4/S664/ob73/6573/6573/6s73
WIN5.K = CLIPRYW1 . DAY. < .241 .373. 12)
DRYWl*=5400/540U/5400/455 0/455 0/46 10/4676/4676/0633/6633/6633/6633
WNW2 • K=CL I P C WNW3 • K . WN W4 • K « 0 • 0 » CURN • K)
WNW3.K=TA6HL ( DRYW2 . DA Y . K . 24 1 .373. 12 )
DRYW2*=5S40/S540/5S4 0/4642/4642/4660/4660/466' 0/6035/6 03S/6 035/6035
WNW4 . K = CL I P ( WNW5 . K » WNW6 . K . 0 . 5 . CORN . K )
WNW5«K=TABHL
-------
FWIN3.K=FWIN2. JK J~*J
FWIN4«KL=FWIN3.K ^
FWIN5«K=FWIN4»JK ^
Fv. o
INITIAL CONDITIONS FOR FLOWS INTO THE w/lLL. RIVtR
FWIN2=60CO
FWIN4=6000
SUM3=U
RESERVOIR AND CHANNEL LEVcL
EVAPORATION
RLVA«K=RLVA»J+CDT ) ( l/43b6u ) ( R I N . JK-RuUT . JK- I ixwoT . JK-EVAPu . Jls+0 + 0 )
CLVA.i< = CLVA « J+ (DT > (LROUT » JK + C IN. JK-k IN2« J.<+ I r
-------
c
51A
ISA
12A
5BA
C
XI
7A
12A
NOTE
NOTE
NOTE
10A
12A
51A
13A
6A
C
7A
14A
1L
SIR
SIR
13A
7A
6A
b2L
12A
6R
6R
Si A
SIR
NOTE
NOTE
.NOTE
5 1 A
18A
C
1L
6R
SIR
51A
58A
C
5 1 A
51 A
ISA
6A
1L
6R
SIR
S3A
C
6A
51 A
SPICA=4717E+06
RWOP 1 . K=CL I P ( RWOP A • K , 0 , RLV A . K , RWOPL • K )
RWOPA.<=(RLVA.K) (43560 )-K~R^GPL.K> (43560 >
RWOPL. K= (RCAP.K) (RWOPP.K)
RWOPP.K=TA3HL(WOPT»DAY.K, 1 »376, 15)
WOPT*=.90/.SO/.6C/,50/.40/.4G/»44/.54/«61/.6t}/.75/.77/»fc7/.91/,95/
.98/.98/.98/.98/.9b/.9a/.9o/.96/.95/.90/.90 RULE 16
ROT2.K=FIRL1»K+WQRL1 .K
ROUT2.K= (ROT2.K) (86400) FT. CU«/DAY
VOLUME AVAILABLE FOR DISTRIBUTION
VOL01 ,K=RLVA.K-CPO6.K+EXRSI • K-FD06 .<-WG.DOT »K+O (UNITS AC FT )
CP06.i<=( 0.6MMICVP.K)
EXRSI .K=CLIP(ERSI 1 »K»0»ERSI 1 «K»0)
ERSI 1 .K=(£XPFS.I<> (ERSI2.K) (2) CONV. SFD TO AC. FT.
EXPFS.K=EPFS FRACTION OF AVE. SUMMER FLOW
EPFS=0.90
ERSI2.K=EXSIF.K-SIFTD.K DIF. oETWEEN EXP. AND ACT.
EXS IF. K=826O+ (0.029) (SUM3«K)
SIFTD.K=SIFTD.J+(DT) (FR I NS • UK-TFRNS. JK >
FRINS.KL=CLIP(FRlNl »K,0,DAY.K,241)
TFRNS.KL=CLIP(SIFTD.K,0, 1 ,DAY.K)
FD06.I<=(0.6 ) (FIDMR.K) (2) 60 PERCENT FISH, CONV« CFS TO AC, FT»
FIDMR.K=FIDMD.K-FIRLS.K
FIDMD.K=12520 (SFD) (INCLUDES COMPL. FROM WATER QUALITY)
FIRLS.K=FIRLS.U+
WQR2.KL=WGR02.K
TWG01 .KL = CLlP(WGlR01.K,0,DAY.K,364)
WQR02.K=CLIP(WQRX2.K»0,DAY.K,241 )
WGRX2.K=TABHL(DL12«UAV.K,241 ,373, 12)
DL 12* =0/0/0/0/0/0/0/0/0/0/0/0 Q=50uO
WQD02.K=CLIP( WQD04»K» WQDC3 »K , SUMF «K , 5 1 000 )
WGD03.K = CLIP ( WQDU5«I<« WGD06.K,-0.0 »CURN»K >
WQD05.I<=(2) (DRM12.K-WGR03.K) CONV. SFD TO AC. FT.
DRM12.I< = 312 (SFD) G = SOOO
WGRo3.K = i/i/GR03.J+ ( DT ) (WGR4 »JI<— TWQ03»Oi< )
WGR4 .KL=WQR04.K
TWG03.KL=CLIP(WUR03.K,O,DAY.K,364>
WGR04.K=TABHL(DM12»DAY.K,241 ,373, 12)
DM12* = *j/G/0/13/13/0/0/U/u/w/0/G u = 5000
WQDo6.l< = 0 NO WATER QUALITY DEMAND
WQD04.K = CLIP( WGD06.K , WGDU7 • K , SUMF . i< «66bOC )
RR20
RR21
RR22
RR2j
RS24
RR2a
RR25
RR26
RR27
RR26
RR29
RR30
RR31
RR32
RR33
RR34
RR35
RR36
RR37
RR36
RR39
RR40.
RR41
RR42
RR43
RR44
RR4b
RR46
RR47
RR4d
RR49
RH50
RRbl
RRa2
RR^3
RRb4
RRb5
Kk56
RS57
RR5B
KR35
KR60
RR61
RR62
RR63
RR64
RR65
RR60
RR61
158
-------
WQuG7.K=CL IP ( WGDG8.K , t;;G.Du9«K, -G.b «CURN»K )
RR6o
18A
C
1L
6ri
SIR
58A
C
51A
1BA
6A
1L
6k
SIR
58A
C
b'lA
7A
12A
o6A
2uA
49A
20A
NOTE
NOTi-
NOTE
14A
12A
20A
6A
C
58A
C
NOTE
NOTE
NOTE
13A
56A
C
XI
51A
blA
46A
14A
NOTE
NOTE
9A
12A
14A
ISA
49A
*4A
SlA
7A
WQDvJ«3»K= ( 2 ) (DRW1 2«K-w/GRub»K)
DRW12=1872 (SFD) G=bOGO
WuR Jb.K=WGRG5» J+ < DT ) ( WGR6.JK-TWQG5.JK )
WGR6«KL=WQRG6«K
TWQ05«KL=CLIP(WQR05.l<»o »DAY.K»364 )
WGR06»K = TABHL. < DW 1 2 » DAY •!< «24 1 » 373 « 1 2 )
DW12*=G/0/O/72/72/ 12/u/o/u/LVw/O G=buCC
WGDG9.K = CL I P < WQD 1 0 •!< « WGDG6.K « G »0 « CURN»I< )
WQD1G.K=(2> (ORW21 .K-WGRG7.K) CONV. SFD TO AC, FT.
DRW21.K=G (SFD) G=5uOO
WGRG7.K=WQR07»J+(DT) (WQRb.JK — T»A/iiG7.JK)
WQR6. i t RDFF.K )
RDFF ,|<=|V|AX ( RurF 1 .!< » RDFF 2 .K ) Rc^UCi_J FISH FLOW FACTOR
RL/FFl .K = AVFR.K/FD06X.K
FD06X.K = SWlTCH(loG«rDu6.K,FD06.l<)
RDFF2.K=RLVA«K/M ICVP.K
IRRIGATION ALLOCATION AND ROUTING
VOL 02 .K = VOL01 »<+ ( -0.6 ) ( I txRNA.K )
IRRNA.K= ( IRR,\t3»i< ) (N IRTF.K >
N I RTF «1<=N 1 RGT »i
IRhJM l* = G/»001/.uC2/» O0270/.O0467/ .G0667/.G12/.ui2/.012/«Ulu67/.U02
/.001 /O/O
IRG1 »K = CLIP( Ik02.K»0,VOL01 «l<«^)
IR02»K = CLI P ( I uRN 1 »i< » I KKN2»i<« VoL02.i<»0>
IRRN2.<= < IRRN1 • K > ( AV I R • K ) ( 1 ) / < ( IRRNc.K ) (i-JlKTr . i^ ) ( u.d) )
AVIR«K = VOL02»K+(0«ti) ( IRKNA«I<)
NEXT INCREMENT f- OR HIS" AND lA/ATER QUALITY
VOL03.i< = VOL02.K-CPG4 .K-FD04.K
CP04.K=(G.4 ) (MICVP.K)
FD04.K = -WGDOT.K-t-(0.8) (FIDMR.K) 40 Pc.KCb.NT FISH, CONV. aFD TO AC FT
RMFF5»K= ( 0.4 ) (RMFF3.K )
FDG4X .K = SW I TCH ( 1 00 , FD04 * K • FD04 . K >
RMFF6.K= (RMFF5.K ) ( AVFR2 »K ) /FDO4X.K
AVFR2 . K = CL I P ( AXFR2 • K » 0 . AXFR2 • K • 0 )
AXFR2.K = FD04.K+VOLG3.K SECOND INCR. AVAIL. FISH RtLtASt. AC, FT.
Rk69
RR70
RR71
RR72
RR73
RR74
RR75
RR7b
RR77
RR7o
RR7y
RRt>0
RRb 1
KRb'2
Kko_,
Rko^
K[-<.O^J
kRbo
KRo7
Rhct^o
RRcl '-J
RR90
RR91
RR^2
KK93
KRV4
RR9b
RR96
RR97
RRVo
RR99
R R 1 00
t-
-------
51 A
51 A
7A
NOTE
NOTE
NOTE
14A
13A
51 A
51 A
46A
14A
NOTE
NOTE
NOTE
14A
NOTE
NOTE
NOTE
NOTE
7A
51 A
ISA
6A
C
1L
SIR
5 1R
58A
C
51A
51A
ISA
6A
. C
1L
SIR
5SR
C
6A
51 A
5 1 A
1 8A
6A
C
1L
51R
58R
C
51 A
ISA
6A
C
1L
51R
FRLS2.K=CLIP(RMFF5.K«RMFF6.K.VOL03.K,0> FISH REL. SECOND INCREMENT
FRLS3.K.=CLIP(FRLS4.K»0«VOLO2»K»0>
FRLS4.K = FRLS2.IOW0101 .!<
SECOUND INCREMENT FOR IRRIGATION
VOL04.K = VOL03.l<+<-0»2) ( IRRNA.K)
IRRN3.I<= (0.2) ( IRNM.K) (NIRGT.K) IRRIG. RELEASE IN AC-FT
IR03.K=CLIP ( IR04.K«0»VOL03.K.O)
IR04.K = CLIP( IRRN3.K* I RKN4 .i< » VOL04 « K t 0 )
IRRN4.i<= ( IRRN3.K ) ( AV I R2 . K ) ( 1 ) / < ( IRRNB.K) (0.2) (NIRTF.K) )
AVIR2.K=VOL04.I<+(0«2> ( IRRNA.K)
ADD AN INCREMENT OF STORAGE FOR RECREATION AND RESERVOIR SPORT FI
VOLG5.i< = VOL04.K + ( -0.2 ) (M ICVP.K)
RELEASE FOR THIRD INCREMENT OF WATER QUALITY
CONSIDER COMPLEMENT FROM FISH
VOL06.K=VOL05.K-RWQDT.K
RWQDT .K = CLIP(RWQD2.K«RWOD1 «I<»SUMF.K« 30 GOO )
RWQD1 .K=(2> (DRL3.K-RWG01 . K) CONVERTS SFD TO AC-FT
DRL3.K=LDR3
LDR3=33749 (SFD) Q=50OO
RWQ01 .K=RWQ01 .J+(DT) ( RWU02 • JK-TRWQ 1 . JK )
TRWQ1 .KL = CL IP(Rw/Q01 •!<» G «DAY.I<.364 )
R'wA/Q03. J+ ( DT ) ( RtoQ04 • JK-TRWQ3. JK )
TRWQ3.KL = CL IP(RlA/'Q03.K »0«DAY.K«364 )
RWQ04.KL = TA3HL ( DM3 »DAY.K»241 «373, 12)
DM3*=0/0/u/38o/360/35u/3 13/31J/0/0/0/0 Q=5000
RWQD6.K = C NO WATER QUALITY DEiviAND
KWQD4.K = CLI P(RWQD6.K»RWOD7.K.SuiViF.K»66500 )
RWQD7.K = CLIP (RWQD8.K«RWuD9.K»-0»5 tCUKN.K )
RWUuo.K= (2 ) (DRiA/31 .<-RWC*Ob.K ) CONV SFD TO AC-FT
DRU/31 .K = WDR31
WDR31=16992 (SFD) Q=5COO
Rv\/Q05.K = RWQ05. J+ ( DT ) (RWQO6. JK-TRWQ5. JK )
TRWQ5.KL=CL IP(RWQ05.K, 0«DAY.K,364 )
RWQ06.KL=TABHL (UW3 1 tDAY«K»241 »373» 12 >
Dto;31*=G/0/0/324/324/3^0/234/234/O/G/0/G Q=oOOO
RWQD9.K = CLI P ( Rw'QDO . K » RWQD6 • K » u .0«CURN.K )
RWQDG.K=(2) (DRW33.K-RWU07.K) CONV SFD TO AC-FT
DRW33.K=WDR33
WDR33=149o2 (SFD) Q=5000
RWQG7 .K=RWU07 • J+ ( DT ) ( RU/UG6 * JK-TRWQ7. JK >
TRWQ7.KL=CLIP(RiA/Q07.K»G«DAY.K«364)
RR1U
RR115
RR116
RR117
RR118
RR119
RR120
RR121
RR122
RR123-
RR124-
RR125-
RR126
RR127
RR128
RR129
RR130
RR131-
ftR132r
.RR.133
RR134;
RR13b;
RR136
RR137^
RR13b
RR13b
RKl4C:i
RR141;
RR142^
RR141-'
RR 1 4*'
RR14-:'
RR146
RN14"_
RR14E:'
RR14V
RR15("'
RR15:'
RR15i':
RRls-"'
RR15-"
RRlb:'"
RRlb(V
RR 1 2'"'
RR1=;'"'
IfiO
-------
3lA
51A
49A
:;44A
:;7A
.:NOTE
.;NOTt
:.NOTt
;7A
51A
13A
6A
;C
1L
SIR
SIR
5«iA
:C
:51A
•51A
;18A
:6A
:C
;1L
•SIS
RWQ06.KL = TABHL(DW33»DAY.i<»24i «373«12}
DW33*=0/0/0/266/266/250/230/230/0/0/0/0
WQ301•K=CLIP(WQ3U2.K»0»VCL05.K«0>
WQ3C2.I< = CLIP(WQ3G3.I<»WG304»K,VGL06.K,0)
RWQDX.!< = SW ITCH ( 10O«RWQGT.K»RWUDT.K)
WU304*K=
= 6000
:c
:1SA
•6A
-C
•1L
-51R
;C
• 51A
;51A
;16A
Ic
JSlA
IbA
;6A
*C
XV.QDC .!<= <2 ) (DRM42 •K-X'AOI 1 1 .K )
MOW42=9672 ( SFO ) G=6000
XWQ1 1 .K = XWQ1 1 . J+(DT)
TXWGO.KL=CL IP(XiA/'Ql 1«K«0»DAY»K«364. )
XWG1 'c. .KL = TABHi_ ( uM42 » DA Y . K » 24 1 »373 » 12 )
DM42* = v-'/0/u/97/97/ 1 wo/226/226/ 0/0/0/0
XWQD6.K = 0 NO \AiATER QUALITY DE.MAND
XWGD4 .K = CL IP(Xw/QD6«K»XWCiD7»K» SUMF.K « 6650C )
XWQD8.I<= (2 ) (DRW4 1 .K-XkvGOS .K. ) COislVcRT SFu
DRW41 .K=WDR41
WDR41=74dlb (SFD) Q=6OOO
XWQ05.K=XWQ05« J*< DT ) ( XWQu6 • JK-TXWQ5 . JIO
TXWQ5«KL=CL I P ( X'.VQO5 .K » 0 « DA Y .]< » 364 )
XWGo6.KL=TABHL
RR196
KK197
RR1 9c
RR 1 99
RR200
RR2C1
RR20c;
Q = 6000
RR206
RR207
RR20o
RR209
161
-------
ISA
6A
C
1L
SIR
58R
C
5 1 A
31 A
44A
7A
49A
NOTE
NOTE
NOTE
7A
8A
5 1 A
51 A
5 1 A
51A
51A
51A
51A
51 A
51 A
51 A
51A
51A
51 A
51 A
51 A
51 A
51A
.51A
51A
NOTE
NOTE
6N
6N
6N
6N
6iM
6N
6N
6N
6N
6N
6N
6N '
6N
6N
6N
6N
6N
XUifQU6.K = (2) ( AV*G4»K) /X*UDX«K
AVWQ4»K=XWQDT.K+VOL07.K
XWQDX.K=SWITCH( 1 00 » XWQDT »K * XWQOT »K )
RESERVOIR RELEASES FOR FISH AND WATER QUALITY
FIRL1 »K=FRLS1 .K+FRLS3.K
WURL1 «K = WQl 01 .K+WQ301 »K + WG401 . l<
WQlol •K=CLIP
WQ47.K=CLIP (XWQ06. JK i WQ48 .K , -O .5 < CURN • K )
WQ48.K=CLIP (XWQOa. JK t WG49.K« O.OtCUKN.K )
WQ49.K = CLIP (XWQ10. JK • 0 « Ci «b « CURN.K )
INITIAL CONDITIONS FOR RESERVOIR ROUTING
LROUT=0
ROUT=0
SIFTD=0
TFRNS=0
FIRLS=0
TRMFF=0
WQRO 1 =0
TWQ01 =0
WQRO3=0
T*'Qo3 = u
WQR05=0
TWG)C5 = 0
WQR07=0
TW/Q07 = 0
RWQ01 =0
TRWQ1 =0
RWQ03=0
a=6ooo
162
-------
6N RWQ07=0
6N TRWQ7 = O
6N FRINS=O
6IM RfviFF6 =
6N WQR2=0
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
ON
6N
6N
6N
6N
6N
RWQu2=0
nWG04=0
RWQ06=0
XWQO 1 =0
TXWQ1 =0
XWQ02=u
X W ^ C 3 = 0
TXW03-0
XV/C 4 = 0
XWGGb =u
TXWQb=0
XWQ06-C
Xl';.J07 = .-'
X W O 0 8 = (^
XWQ09=0
TXWC9-0
6N XW'Qi i =U
6N XWQ12 = 0
NOT£ ROUTING ANALYSIS
NOTE MXftL USED IN RA1 IS ucKINLD 1 1\ c.2
NOTE
51A DAMRL..K=CLIPOi»iKl_. Ji< » L A Y .K » ^^X^L « JK«HL1 » K) DAY MAX RES LEV FOR FLDS RA1
51A RL1 •K=CLIP(0»KLv'A.K«DAY«l<» 1<32> RA2
SIS DMRL.KL = CL I P ( 0 »uAMKL»i< »DAY»K«3b4) RA3
31A OAM3D.I< = CL I P (Ui-'i. D. J:< »u-AY»K»MX3u. Jl< »Fhi3uT.iv ) OAY OF ,"1AX 3UAY FLOW RA4
^l^ ,v,X3L. «Ki_ = CL I K ( o «i«iX3Dl . K »DAY »K . 364 ) RA5
36A MX3D1 .'<=,"''AX(FR3DT.<«XX3D. JK ) , RA6
S1R DW3D»KL=CLIP(0«OAM3D»K*DAY»K«364) RA7
51A DMR3S.K=CUIP(DMRL3« JK « DAY . x » WXkL . JK«RLVA»K) MX DAY RLVA 3 StASONS RA3
JK «DAY.K »RLVA«K«r'"iI NP;L« JK) RA1 0
_ .lK.K.DAY»l<»3fc4) RA11
NOTt
N°TL INITIAL CONDITIONS FOR ROUTINE ANALYSIS
DMRL3 =
163
-------
6N
NOTE
NOTE
NOTE
58A
C
42A
3L
SIR
51A
SIR
51 A
5SA
C
12A
51A
NOTE
NOTE
NOTE
S8A
C
56A
SIR
58A
C
51A
S8A
C
58A
56A
SIR
58A
C '
5BA
. 51 A
6A
C
NOTE
NOTE
NOTE
6N
6N
NOTE
NOTE
NOTE
8A
51 A
6A
C
6R
6A
19A
7A
7A
51A
DAMI=0
DRAINAGE BENEFIT CALCULATION
ATDRB.K=TABHLCATDBTtCCAP.K»50CG»21 000 « 2000)
ATDBT* =0/66667/133333/200000/260000/32000 0/380 00 0X440 00 0/500 000
PRCLV.K=ACLVA.K/< (CCAP.K) (86400) ) PROP CHANNEL FULL
ACLVA.K=ACLVA.J+ < DT > ( I/DOR. J) < RCLVA • JK-CLV AO .JK > AVE CHANNEL LEVEL
RCLVA.KL=CLIP(CLVAA.K,0,DAY.K»151 >
CLVAA.K=CLIP(0»CLVA.K»DAY.K»273)
CLVAO.KL=CLIP
DDR.K=CLlP( 1 « 122»DAY.K.273>
PRDTM .K = TABHL(PDTMT»PRCLV.K» 0* 1 »0« 1 )
PDTMT*=l/l/l/l/.8/.6/.4/.3/.2/« 1/0
ANDRt3.K= (PRDTM.K) ( ATDRBtK)
ADBR.K=CLlP(ANDRB.KtO«DAY»K*364)
FLOOD LOSS
TRC lS.K=TA6HL(CODIT»FClN2.KtG»4500GtbOOO)
COD IT *= 1 9/5 199/1 1 244/1 72o 9/^33 34/2 93 7 9/3s 424/4 1 469/4 7b 14/:o3559
MTIN«K=MAX(MIN.JK.T«CIS«K)
MlN.KL=CLlP(OtMTIN.K»DAY»K»364)
FLDLP.K=TABHL(FLDLT«FLDSH»K, 10« 18t 1 ) FLOOD LOSS POTENTIAL
FLDLT*=0/O/2200/5500/16uOO/4UgOO/2UOOOO/14E5/44E5
FDLPR.K=CLIP(FLQLP»K«0»DAY.Kt364) FLOOD LOSS POTENTIAL (ANN.)
FLDSH.K=TABHL
-------
51A FADJT.K=CLIP(0,FADJ1.K.DAY.K, 162)
TARGET FLOOD STORA&w
— ^ — • i •—• » i '*[-xT w r^ i w ix V 1 wJ *r ^ cr ~ f
6A TGFDS.K = TFDS TAo,i;--r d-, ™-> ,-™,,», ^DCU,
C TFDS=60000
50A WLFB3.K=(WLFd2.K) < TGFQS . K ) / < TGFDS .K+FAU JT »i< ) FBC14
54A WLFB1 .K = MlN(WLFB4.JK»WLFb3.l<) F'Cl'
SIR WLFB4.KL=CLIP<160000.WLFB1.K,DAY.K,364) FBC16
6N WLFB4=160000
NOTE
NOTE IRRIGATION RETURN FLOWS
NOTE
12R IRRIN.KL=(PERRF)(IROUT.JK) IR1
C PERRF=.15 PERCENT RETURN OF IRR. FLOW IR2
7A IR05.K=IR01.K+IR03.K AC. FT. I«3
12R IROUT.KL=(IR05.K)(43560) jR4
NOTE
NOTE IRRIGATION BENEFIT CALCULATION
NOTE
12A ANIB.K=(NIRTF.K) (552690) ANNUAL TARGcT btNtF IT 11,1
1L TIROT.K = TIROT.. J+(DT) ( IROUT. JK-ACIRO. JK) IB2
SIR ACIRO.KL=CLIP(TIROT.K,0»DAY.K,364) IB3
20A TIRO.K = TIROT»I1 ICL»K ) Fbl
SIR MICL1.KL=CLIP(MICL5.K,20,DAY.K,2) • FB2
20A Piv]ICL.K = CLVAS.K/RMFFl .K FbJ
20A PMIRL.K=RLVA.K/MICVP.!< FB4
6A MICVP .K=iV| INPL |ViINlMUivi CONSER. PCOL CAisfNOT BE ZERO FbD
C MINPL=51000 Ft>b
54A MIRL.K=MIN(MIRL1 . JK , P,«11 RL .K ) Fc37
SIR MIRL1.KL=CLIP(20,MIRL.K,OAY.K,364) -FbB
54A MlCRL.K = MlN(MICLS.K»i'v1IRL.K) Fd*
51A MICR3.K=CLIP(MICR1.K,0»PAY.K,364) FB10
54A MICR1.K=MIN
-------
ISA
SIA
NOTE
NOTE
NOTE
6N
6N
6N
NOTE
NOTE
NOTE
54A
SIR
26A
6A
C
SIA
SIA
ISA
6A
C
6A
C
SIA
NOTE
NOTE
NOTE
6N
NOTE
NOTE
NOTE
58A
C
58A
7A
20A
6A
C
53A
C
6A
51A
SIA
6R
1L
SIR
12A
6A
C
51A
NOTE
NOTE
NOTE
C
6A
FCST.K=< INFC1.K) (CRF50.K+.10) FISH COST
AFCST.K=CLIP(FCST.K.O,DAY.K,364> ANN. FISH COST
INITIAL CONDITIONS FOR FISH BtNEF I T CALC«
MICL1=2
MICR2=2
MIRL1=2
WATER QUALITY BENEFITS
MIFWR.K=MIN(MIFW1 . JK»PMIFW.K)
MIFWl .! / ( WQOB J.K-4500 + 0 >
WQOBJ.K=WQBJ WATER QUALITY OBJECTIVES
WQBJ=6000
MIPWQ.K=CLIP < INPLC.K)
WQBN.K=WQB WATER QUALITY BENEFIT
WQB=244600 Q6000 05 M1000
INPLC.K=INPC
INPC=7.56E6 Q6000 D5 M1000
AWAQB.K=CLIP(WAQB.KtO«DAY.K,364) ANN. WATER QUAL . BENE.
INITIAL CONDITIONS FOR WATER QUALITY BENEFITS
MIFWl =2
RECREATION BENEFITS
PLELV.K = TABHL(PLEV «RLVA.K«G»2uOOGO»2000G>
PLEV*= 560/6 O2/62G/638/6S 1/66 1/669/67 7/665/69^/099
MXPL.K=TABHL(PLEV»RCAP.K«G«2GGOOO»2QGOO > MAX POOL ELEV
PLDRP.K=MXPL.K-PLELV.K
LNBCH.K=PLDRP.K/SLP.K
SLP.K=SLOPE SLOPE OF THE BEACH
SLOPE = G. 1O
ATND1 .K=TABHL< ATTND «LNBCH . K , C « ISOOt 15 GO)
ATTND*=5000/G
ATND.K=ATND1 .K DAILY ATTEND. ADJ» bY RECREATION GRO. FAC.
RATD1 .K=CLIPCATND.K.O.DAY.K.24C)
RATD2.K=CLIP(OiRATDl .K«DAY.K,3SO)
RATD3.KL=RATD2.K
AREC.K=AREC.J+(DT) (RATD3. JK-RATD4. JIO ACCUM DAILY REC ATTEND
R ATD4 . KL = CL IP ( AREC • K » 0 . D A Y . K « 364 )
RECB.K= ( AREC.K) ( VALRC.K)
VALRC.K=VALR
VALR=1 VALUE OF RECREATION
RCB.K=CLIP(RECB.K,0«DAY.K,364)
CALCULATION OF RECREATION COSTS
INREC=187E4 TOTAL INITIAL REC. COSTS
INRC1 .K=INREC
FB27
FB28
WQ1
WQ2
WQ3
WQ4
WQ5
WU6
WQ7
WQ8
WQ9
WQ10
WQ1 1
WG12
WQ13
RBI
Rb2
RB3
RB4
RB5
RB6
Ro7
RBB
RB9
RdlO
Rbll
RB12
Rbl3
RB14
RBI 5
RB16
RB17
RSI"
RBI 9
RC1
RC2
166
-------
13A
51A
NOTE
NOTE
NOTE
6A
12A
C
6A
C
NOTE
NOTE
NOTE
6N
6N
6N
6N
6N
NOTE
NOTE
NOTE
10A
10A
7A
6R
12R
1L
1L
20A
49A
7A
20A
49A
7A
7A
44A
30A
NOTE
NOTE
NOTE
6N
6N
6N
6N
NOTE
NOTE
NOTE
58A
C
13A
SlA
13A
SIA
13A
C
RCST.K=(3) ( INRC1 .K) SUM NET BENt.
SSNET .K=SSNET. J+ ( DT) ( NETB2. JK+0 > SUM N£T oEN. SU«
AVENB.I< = SUNET«K/NOYRS«I< AVE NET oENtFITS
NOYRS.K=SWITCH< 1 . A JYRS • K » A JYRi . K )
AJYRS.K=YEARS.K-1
AVVAR.K=SSQNT.K/NMNS1 .K AVE VARIANCE OF NB
NMNS1 .K = SWITCH( 1 .YMNS1 .K.YMNSl .K)
YMNS1 .K=Y£ARS.K-2
SSQNT.K=SSNET.K-SUMX2.K
SUMX2.I<= (SUNET.K) ( SUNET .K ) /NO YRS «l<
AVSTD.I<= ( 1 )SQRT( AVVAR.K ) AVE STD Dt-V OF NcT otNt
INITIAL CONDITIONS
SUNET=0
SSNET=0
NETB1=0
NETB2=0
COSTS
IRCST.K=TABHL< I RC »RCAP , 50000 » 225000 t 2SuOO ) INITIAL RES COSTS
IRC#= 12E6/lb467E3/163E5/ 1 9tO/£i30=)ot^/27(j7t4/3i;
-------
51A
58A
C
13A
51A
NOTE
NOTE
NOTE
C
6A
7A
29A
2SA
50A
29A
28A
50A
29A
28A
50A
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
S6A
SIR
51A
SIR
12A
1L
SIR
12A
1L
SIR
12A
1L
SIR
12A
1L
51R
1L
54A
SIR
51A
SIR
12A
1L
SIR
12A
1L
SIR
12A
1L
AIRCT.K=CLIP( IRRCT.K.O.DAY.K.364)
IDRC.K = TABH|_< IDRCl»CCAP.K»lGGu«21000«500G)
IDRC1*=0/12500G/16E5/4E6/&E6
DRCST.K=( 1. 1 ) ( IDRC.IO (CRFOO.K)
ADRCT.K=CLlP(DRCST«KtO»OAY.K*364)
CAPITAL RECOVERY FACTORS
INTR=0.0325 INTEREST RATE
I NT! «K=INTR
INT2.K=1+INT1.K
INT3.K= (20>LOGN( INT2.K)
INT4.K=(1)EXP(INT3.K)
CRF20.K=< INT1.K) ( INT4.K)/< INT4.K-1 )
INT5.K=<50 >LOGN< INT2.K)
INT6.K=( 1 )EXP< INT5.K)
CRF50.I<=( INT1 .K) ( INT6.K )/( INT6.K-1 >
INT7.K=( 100>LOGN< INT2.K)
INT8.K=( 1 )EXP( INT7.K)
CRFOO.I<=( INT1 .K) < INT8.K)/( INT8.K-1 )
ANALYSIS OF STATIC ECONOMIC MODEL
MAXIMUM AND MINIMUM ANNUAL RESERVOIR LEVELS
MXRLV.K*MAXCRLVA.KtMXRL« JK >
MXRL.KL=CLIP(OtMXRLV»K»DAY»K.364)
MXRLC. K=CLIP(MXRLV.K«0»DAY.K,364)
RG900.KL=CLIP( 1 « 0 * MXRLC «K » R9CO »K )
R900.K=(0«90> (RCAP.K)
RC900.K=RC900.J+(DT) (RG900. JK+0) NO. TIMES
RG950.KL=CLIP( 1 « 0 tMXRLC «K t R95u »K )
R950.K=(0.95) (RCAP.K)
RC9SO.K=RC950.J+(DT) (RG950* JK+0) NO. TIMES
RG980.KL=CLIP( 1 « 0 » MXRLC * K « R980 • l<>
R980.K=(0.98) { RCAP.K)
RC980.K=RC980. J+(DT) (RG980. JK+0) NO. TIMES
RG995.KL=CLIP( 1 « 0 t MXRLC . K « R995 .K )
R995.K=< 0.995) (RCAP.K)
RC995.K=RC995. J+(DT) (RG995. JK+0) NO. TIMES
RGCAP.KL=CLIP( 1 « 0 » MXRLC »K » RCAP .K )
ANN. IRRIG. COSTS
INITIAL DRAIN COSTS
ANN. DRAIN COSTS
N=20YEARS
CRF FOR N=20
N=bOYEARS
CRF FOR N = i50
N=100YEARS
CRF FOR N=100YEARS
MAX. RES. LEVEL
MAX. RES. COUNTER
GREATER THAN 0.90 RCAP
GREATcR THAN .95 RCAP
GREATER THAN .98 RCAP
GREATER THAN .993 kCAP
RCCAP.K=RCCAP. J+(DT ) (RGCAP. JK+0 ) NO. TIMES GRtATER THAN RES. CAP
M IRLV.K=MIN (RLVA.K»MINRL. JK )
MINRL.KL=CLIP(RCAP.i
-------
SIR
12A
1L
51R
1L
51A
SIR
1L
SIR
1L
SIR
1L
NOTE
NOTE
NOTE
51A
SIR
1L
SIR
1L
SIR
1L
51R
1L
SIR
1L
51A
51R
1L
SIR
1L
SIR
1L
SIR
1L
SIR
1L
NOTE
NOTE
NOTE
51A
SIR
1L
SIR
1L
SIR
1L
NOTE
NOTE
NOTE
SIA
SIR
1L
SIR
IL
RG090.KL=CLIP< 1 « 0 » M I RLC »K » R090 •!< )
R090.l<=(0.90) CMICVP)
RC090. K=RCG9G. J+CDT) CRGU9G.JK+G) NO. TIMES ^Ki^ATER THAN .90 KiICVP
RGCPL.KL = CLIPC 1 * 0 « M IRLC .K«M I CVP .K )
rp /~* f~* D i is* — • o f* /"* I~M i i / r^ -i- \ / i "i /•"*"• r^i i »-- ii". * ni^- -i- • • .1 —
HCCKL .K-KCCPL. J+ C DT ) (RGCPL. JK+G ) NO. TIMES GREATER THAN CONS. PL
PDTM.K=CLIP(PRDTM.K.G,DAY.K,364)
PD1GO.KL = CLIP( 1 »0,PDTM.K. 1.0) DRAINAGE TARGET COuNT-W
DG100.K = DG100. J+CDT) CPDluO.JK + G) NO. TIME'S EujAL TO 1.0
PD90.KL=CLIP< 1 »0«PDT,M.K.0.9)
DG90.K=DG90. J+CDT ) CPD90.JK+0)
PD80.KL=CLIP( 1 *0«PDTM.K«U»6)
DGBO.K-DG80. J+CDT ) CPD80. JK+0 )
FLOOD LOSS DISTRIBUTION MAXIMUM ACTUAL AND POTENTIAL FLOWS
MXACC.K=CLIPCMTIN.K«G«DAY.K»364) MAX. ACTuAL INST.CHAN. FLGw
CAG1 1 .KL=CLIPC 1 .O.MXACC.K* 1 lOoG)
CAC1 1 .K = CAC1 1 .J+CDT) (CAG1 1 .JK + 0) NO. TIDIES ACTUALLY ABOVt llGGGCFi
CGC21 .KL=CLIP( 1 »0«iViXACC.K«210uO)
CCC21 »K = CCC21 . J+ ( DT ) C CGC21 . JK + 0 ) NO. TIMES ACT. AcOVL 2100GCFS
CAG16.KL=CLIP< 1 tOiMXACC.K. 160uO)
CAC16.K=CAC16. J+CDT) (CAG16. JK+0)
CAG20.KL=CLIP( 1 , 0, MX ACC.K« 20000 )
CAC20.K=CAC20. J+CDT) CCAG20. JK+0)
CAG25.KL=CLIPC 1 « 0 » MXACC »K t 2bOuO >
CAC25.K=CAC2b. J+CDT) CCAG2b.JK+0)
MXPCC.I< = CLIP
CPC20.K=CPC 20. J+CDT ) CCPG20. JK+0)
IRRIGATION TARGET
PITM.K = CLIPC,
E4G
£41
£42
£4-i
£44
t4o
£40
£47
£46
£49
EbO
ESI
£32
c.b3
Lb4
Ebb
Ea6
Eb7
£30
E3S-
E6G
£61
£62
£63
£64
t65
£66
£67
E6b
£69
E7L,
£71
t_72
£73
£74
£73
169
-------
SIR
1L
SIR
1L
SIR
1L
SIR
1L
SIR
1L
SIR
1L
NOTE
NOTE
NOTE
SIR
1L
51R
1L
SIR
1L
SIR
1L
SIR
1L
NOTE
NOTE
NOTE
SIR
1L
SIR
1L
SIR
1L
SIR
1L
SIR
1L
NOTE
NOTE
NOTE
6N
6N
6N
6N
6N
6N
6N
6N-
6N
6N
6N
6N
6N
6N
PCF9.KI_ = CLIPC 1 «0»MIPCF.K»0«9)
CG90.K=CG90.J+(DT) (PCF9.JK+0)
PCF8.KL=CLIP( 1 «0»MlPCF.K«Oi8)
CG80.K=CG80.J+(DT > (PCF8. JK+0)
PCP12.KL=CLIP< 1 «0«MIPCP.K,1 .2) POOL TA
PG120.K=PG120.J+(DT) (PCP12.JK+0) NO. TIM
PCP10.KL=CLIP< 1 «0,MIPCP.K«»999>
PG 1 00 • K = PG 1 00 • J-K DT ) < PCP 1 0 • JK+0 )
PCP9.KL=CLIP< 1 tO»M!PCP.K»0»9)
PG90.K=PG90.J+ (PCP8.JK+0)
WATER QUALITY TARGET
PW120.KL=CLIP( 1 *0«MIPWG.K» 1 .2) W.Q. TA
WG120.K=WG120. J+(DT) (PW120.JK+O) NO.
PW100.KL=CLIP< 1 »0«MIPWQ.K..999)
WG100.K=WG100.J+
WG50.K = WG50.J+(DT) (PWSO.JK-fO)
RECREATION ATTENDANCE=REC » BEN. IF VALR=1
RAG45.KL=CLIP( 1 i 0 « RGB . K » 450000 )
RAC45.K=RAC45. J+(DT) (RAG45.JK+OJ NO. TIMES Gft .
RAG48.KL=CLIP( 1 « 0 « RGB . K «4800OO )
RAC48.K=RAC48» J+(DT) ( RAG46 • JK+0 >
RAG50.KL=CL IP( 1 « 0 » RGB .K « 500000 )
RACSO.K=RAC50.J+(DT) ( RAG50 . JK+0 )
RAG52.KL=CLIP( 1 « 0 »RCB.K * 5200OO )
RAC52«K = RAC52. J-f(DT) (RAG52.JK+0)
RAG55.KL=CLIP( 1 « 0 « RCB.K » 550 000 )
RAC55.K = RAC55.J-f (DT) (RAG55.JK + G)
INITIAL CONDITIONS FOR ECON. ANALYSIS
MXRL=0
RG900=0
RC900=O
RG950=0
RC950=0
RG980=0
RC980=0
RG995=0
RC995=0
RGCAP=0
RCCAP=0
MINRL=RECAP
RC09O=0
RG090=0
:T COUNTER
GR. THAN 1.2
JGc.T COUNTbR
TIMES GR. THAN 1.2
THAN 450000
E76
E77
£78
E79
E80
£81
E82
E83
£84
E85
E86
£87
£68
E89
£90
£91
£92
£93
£94
£95
£96
£97
£98
£99
£100
£101
£102
£103
£104
£105
£106
£107
170
-------
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6M
£>M
OIM
6N
6l\|
6N
6N
6N
6i^
GN
6N
6N
RC098=O
RG098=0
RG105=0
RC105=0
RG1 15=0
HC1 15=0
RGCPL=0
RCCPL=0
PD1 00=0
DG100=0
PD90=0
DG90=0
PD80=0
DG80 = 0
CAG1 1 =0
CAC1 1=0
CGC21=0
CCC21=0
CAG16=0
CAC16=0
CAG20=C
CAC20=C
CAG2b=0
CAC25=0
CPG1 1=0
CPC1 1=0
CPG21=0
CPC21=C
CPG25=0
CPC25=0
CPG16=0
CPC16=0
CPG20=0
CPC2O=0
PI 1OO = U
IG1 00=0
PI90=0
IG90=0
PISO = 0
1G6C=0
PCF12=0
CG120=0
PCF10=0
CG100=0
PCF9=0
CG90=0
PCF8=0
CG80=0
PCP12=0
PG120=0
PCP10=0
PG 100=0
PCP9=0
PG90=0
PCP8=0
171
-------
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
NOTE
NOTE
NOTE
NOTE
6R
1L
51 A
6R
6R
1L
51. A
6R
56A
51R
51 A
56A
51R
51 A
56A
SIR
51 A
56A
SIR
51 A
NOTE
NOTE
NOTE
6N-
6N
6N
6N
6N
6N
6N
PG80=0
PW120=0
WG 120=0
PW100=0
WG1 00=0
PW90=U
WG90=0
PW80=0
WGBO=u
PW50=0
WG5G=U
RAG45 = 0
RAC45=C
RAG48 = G
RAC48=0
RAG50 = 0
RAC50=0
RAG52=0
RAC52=0
RAG55=G
RAC55=0
SUM OF ANNUAL FLOWS
SFR1 1 ,KL=FRIN1 .K
SFR12.K=SFS12. J+ (DT ) ( SFR 1 1 • JK-A 1FR1 • JK )
ASFR1 «K = CL I P(SFR 12.K«G «DAY »l<«364 ) ANN. SUM
A1FR1 .KL=ASFR1 .K
SFC21 .KL=FCIN2.I<
SFC22.K = SFC22. J+(DT) (SFC21 . JK-A 1 FC2 « Jl<>
ASFC2.K=CLIP(SFC22.K*0 tDAY«K,364)
A1FC2.KL=ASFC2»K
MXLS1 »K=MAX (MXFL1 • JK tFXLl »K ) MAX SEASON
MXFL1 .KL=CLIF(O.MXLS1 .K«QAY.Ki364 )
FXL1 •K=CLlP(O.RLVA«KtDAY.Kt92)
MXLS2.K = iMAX(MXFL2. JKiFXL2.:<) MAX SEASON2
MXFL2.KL = CLIP(0»MXLS2.K
-------
6N
6N
6N
NOTE
NOTE
NOTE
21A
51R
1L
SIR
51R
1L
NOTE
NOTE
NOTE
6N
6N
6N
6N
6N
NOTE
NOTE
NOTE
56A
SIR
56A
SIR
54A
SIR
54 A
ilR
&N
6N
6M
6N
NOTE
NOTE
NOTE
51R
7A
51A
1L
SIR
NOTE
NOTE
NOTE
NOTE
NOTE
NOTE
1L
ISA
5lA
20A
MXFL2=0
MXFL3=0
I/XFL4 = 0
SPILL DATA
SP2.K=( 1/43560) ( ROUTs . K-|V| I NXX . K)
SP3.KL = CLIP (SP2.K,G«SP2«I<«0)
SP4.K=SP4. J+(DT> (SP3. JK-SP5.JK)
SP5.KL = CLIP
f'NR 1 . KL = CL I P ( 1 0 u u i MNR . K , D A Y . \< , 364 )
i.-NC . K =M I N ( HNC 1 . JK « FC I N2 . !<)
MNC 1 ,KL = CL IP ( 1 GOO ,l-'(NC.!4 )
SHORTAGE INDEX
DRAINAGE SHORTAGE I.MJ^X
SIDR.K=SIDR.J+(UT ) (SlORl . JK+0)
SIDR1 .!<= (PDSH.K) (P05H.K )
POSH. K = CL I P (PDRSH •!< « U » OAY •!< ,364)
PDRSH.K=DRSH1 .K/0.3
VOL. SPILL AC. FT<
NO. YEARS SPILL
SP1
SP2
SP3
SP4
SP5
MAX. AVE. uAlLY RL.S •
lAX.AVE.DAILY CHAN.
lli\« AVti. OAILY R£S.
|v,Ii\ AVt_ DAILY CHAN
-OF1
DF2
DF3
DF4
DFb
OF6
DF7
DF&
I- ISH
FR1
FRi
FR3
FK4
7A
DRSH1 .K = CLIP(DRSH.K»0»DRSH.I<«0
DRSH.K=PRCLV.K-0,3
Sits
173
-------
1L
12R
51A
7A
NOTE
NOTE
NOTE
20A
7A
56A
SIR
1L
12R
51A
SR
1L
NOTE
NOTE
NOTE
1L
12R
51 A
56A
SIR
2CA
7R
51 A
1L
NOTE
NOTE
1L
12R
51A
51A
7A
1L
7R
51A
NOTE
NOTE
NOTE
1L
12R
51A
51 A
40A
1L
12R
51 A
51 A
7A
1L
SIR
7A
51 A
DRBL.K=DRbL.J+(OT> (DRBL1 • JK + G)
DRBL1.KL=(ATDRo.K)(PDTNM.K)
PDTNM.K=CL1P(PDTN1.KtGtDAY•K»364)
PDTN1 .K=l ,0-PRDTN'i.K
CHANNEL SHORTAGE INDEX
CHR.K = MIOFL .K/MTIN.K
CHR1.K=1-CHR.K
CHRM.K=MAX(CHR2.JK»CHR1. K)
CHR2.KL=CLlP(u»CHRM.K«DAY»K«364)
SICH.K=SICH.J+(JT)(SICH1.JK+G)
SI CHI .KL=(PCHS.I< ) (PCHS.K)
PCHS.K=CLIP
WRFL.K = WRFL.J+(DT ) ( W I RFL • JK-f 0 ) W»
IRRIGATION SHORTAGE INDEX
LOSS
FLOOD
LOSS
R. FLOOD £ LOSS
SIIR«K=SIIR«J+(DT)(SIIR1.JK+O)
SI IR1 .KL=(PIRS.!<) (PIRS.K)
PIRS«K=CLIP(PI RSI .K»0«DAY»K«364)
PIRS1.K = CLIP
PFSD1.K=CLIP
PFSR2.K=1-MIRL.K
FADL.K=FADL.J+(DT)(FADL1.JK+0) FISH ANAD
FADL1 .!
-------
1L
al«
12A
blA
7A
S3 A
1L
SIR
12A
51 A
7A
S3A
1L
12R
51A
51A
7A
MOTS
NOTE
NOTE
1L
12R
51A
49A
40A
49A
56A
7A
51R
1L
51R
7A
51R
1L
SIR
6R
1L
12R
ilA
7A
NOTE
NOTt
NOTt
3L
SIR
51R
SlA
= U
1L
27A
1L
SIR
7A
FISH $
FADC.K=FADC.J+(UT)(rAJC1.JK+0) ANAu. 5
FADC1.KL=CLIP(FADC2.K,0,DAY.K,364)
FADC2.K= (PACL.K) ( AuFu.K )
PACL.K=CLIP(PACL1.K,O,PACL1.K,0)
PACL1.K=1-PACT.K
PACT.i< = TABHL(PFIbl ,MICLS.K,0, 1.2,0.2)
FAOS»K=FADS•J+(DT>(FAUS1•JK+u) ANAj. $ LC
FADS1 .KL = CLIP(FADS2.I<»0,DAY.K,364 )
FAOS2.K=(PASL.K)(ADFu.K)
PASL.K=CLIP(PASL1.K,0,PASL1,K,0)
PASL1 .K=1-PAST.I<
PAST .1< = TA6HL (PF I L31 t M IRL.K, 0 , 1 .2,0.2)
FRS«i< = FRS. J+(DT> (FRS1 • JK + u) RtlS SPORT
FRS1 .iI71
SI 72
SI73
o!7o
SI 77
SI7o
SI7S-
S lot;
i I >^ 1
S I o4
S I 03
olb6
olo?
i> I oci
i 109
SI 90
SI91
oI92
o 193
o I 96
o I •* 7
175
-------
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
,6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N
6N.
6N
NOTE
NOTE
NOTE
PRINT
XI
ADRF1=0
ADRF2=0
TAFR=0
SIDR=0
DRBL=0
DRBL1=0
CHR2=0
SICH=0
SICH1 =0
FDLR1=0
FDLR2=0
SIFS=0
SIFS1=0
PRS2=0
WIRFL=0
WRFL=0
SIFD=0
SIFD1=0
SIFR=0
SIFR1=0
FADL=0
FADL1 =0
FADC=0
FADC1=0
FADS=0
FADS1=C
FRS = 0
FRS1 =0
S I WG=0
SIWG1=0
WQDD1 =C
TFTMD=0
SFTMD=0
WQRL2=0
AWQRL=0
WQL = 0
WQL1 =0
ARLVA=0
TARLV=0
ARLV=0
SIRL=U
SIRL1 =0
RECL=0
RECL1 =0
FTMD=0
TWQRL=0
SI IR=0
SI IR1 =0
IRL = 0
IRL1=J
NEW PRINT CARD FOR 50 YEAR SIMULATION 7/17/6b
1 > YEARS »SUM3»CURI\.ASFR1 i ASFC2 « T':XRLC t RC90 0 . RC9:
P«MIRLC«RCllStRC105»RCCPi_
-------
X2 *DG8O»MXACC»FLDLP»MCLVA«FDLAR» AFLO1 **-ACU * CA^ 1 6/4 ) CAC2G »CCC21 »CAC2
X3 5.CPC 1 1 ,CPC16,CPC20»CPC21 » CPC2b «N I KGT t T I RO/b ) R 11>i » AMI bH i IGlOOt IGVQ
X4 » IGSO tMIPCF«CGiaG»CGluO.CG90»CG8G/6},
-------
DYNAMO HYDROLOGIC SIMULATION AND ANALYSIS
The primary purpose of the hydrologic simulator was to develop flows
for a period of time greater than the number of years of historical
records. This hydrologic simulator is identical to the one outlined
in the previous DYNAMO program, except for the two additions. The
maximum and minimum avaerage monthly historical flows for the downstream
station are added to the input data (minimum downstream - minimum
upstream). These additions are used later in the flow analysis section.
Before the hydrologic simulator could be used in the previous DYNAMO
program, the simulated flows had to be analyzed and compared to the
istorical records by use of important parameters. These parameters,
found for both stations for each year simulated, were as followsi
1. Annual sum of flows
2. Maximum daily flow
3, Minimum daily flow
4. Maximum instantaneous flow
5. Maximum consecutive 3-day flow
6. Minimum consecutive 7-day flow
7. Minimum consecutive 120-day flow
8, Frequency of flows occurring below the average monthly historical
minimum
9. Frequency of simulated flows occurring above the absolute
maximum historical flow
10, Frequency of simulated flows greater than:
a) maximum average daily flow
b) maximum instantaneous flow
c) monthly average maximum flow
11. Maximum average simulated flow for each season
12. Minimum average simulated flow for each season
The Willamette River hydrology section is identical to the one used in
the previously outlined DYNAMO program. Following this is an analysis
section which determines the number of years that the sum of the spring
inflow is less than 66,500, 51,000, and 30,000 acre feet. This is done
to aid in water quality design decisions.
178
-------
EXPLANATION OF FORTRAN HYDROLOGIC SIMULATION AND ANALYSIS
A flow diagram for the FORTRAN hydrologic simulator would be identical
to the flow diagram for the DYNAMO hydrologic simulator. The FORTRAN
flow analysis section is similar to the DYNAMO flow analysis except
some additional hydrologic parameters are measured. The yearly para-
meters found are (for both upstream and downstream stations):
1, Yearly mean flow
2. Yearly standard deviation
3. Largest daily flow
4. Maximum average three-consecutive day flow
5. Maximum average ten-consecutive day flow
6. Minimum daily flow
7. Minimum average seven-consecutive day flow
8. Minimum average thirty-consecutive day flow
9. Minimum average 120-consecutive day flow
179
-------
JC«350000.803278«KIP
RETURN. TO
SACRAMENTO STATE COLLEGE
RUN(S<
KERRIi
EXIT.
DMP.
i
163B4C)
PROGRAM KERRI4C I NPUT i OUTPUT » TAPE6=OUTPUT >
DIMENSION AX (367) , SXC367) «GXC367) »DX<365> »S(4)
EB(9»365) »AS (3i365 ) »SS<3«365 > tGS(3»36£) « AL(3»365)
NO ( 3 ) \ XC < 3 » 366 ) . Q < 3 • 367 )
S (3«366 ) »G(3i367) , PC (6 » 366 ) »PP<6»365) (E(3«367) »F(3
DAC365 J..,N(3) , A(4i5)
QX( 1OO »2«366 ) »GKC2»366)
NYX( 100 )
BIG (2* 1 00) «SMALL(2» 100) «SUM3(2) »£Ui"135<2t ICO ) «SUM7(
SUM7S<2« 100) ,SU10(E) »SU105<2i ICO) «£U3G(2) i£U30S(2,
5120(2) »S120S(2» 10G) «AR( 100) »SXI<(2» 1 00 ) *SX2(2« ICO)
DIMENSION
DIMENSION
D Ir'iENS ION
DIMENSION
DIMENSION
DIMENSION
DIMENSION
DIMENSION
DIMENSION
I 5OM5-0
CAY = 1.
ICO)
NY = 50
•LP = NY
C
C
25
C
C
C
JC =0
JA =0
CX =0
LX=0
N(1) = 19
N(2) = 47
N C 3) = 50
NSIM=0
READ STATMtNT FOR THE HYDROLOGY PLOTTER
READ 250*NXX«NlHtNlAtNZZ
FORMAT (4A1 )
DO 10 L=1»NS
LA=L+1
LXR=LX
READS STATISTICAL ANALYSIS AN^ SMOOTHES
DO 97 M=2»366
READ 7 »NO ( L ) « AX ( M ) * SX ( v| } » GX ( i-1 )
TO CARD 10
180
-------
7 FORMAT (15,10X.6F7.3)
AX'CM) = AX(M) #.43429
SXCM) = SX(M) * .43429
97 CONTINUE
DO 6 M=2«366
READ 7» NO (L ) «DX C.:-l). (b(L2) »L2=1 * LA)
DO 6 L2=liLA
LX=LXR+L2
6 35=B(L2)
AX(1)=AX(366)
AX(367)=AX<2)
SX(1)=SX(366)
SXC367)=SX(2)
GX( 1 )=GX(366)
GXC367)=GX(2)
DO 10 M=2i366
ASCL»M-1 > = ( .S4#AX(M) + .08#< AXC;#3X{M)+.25#(SX(M-1 )*SXCi-l )+£X(fvi+l } *3X C,.',+
SS(L«M-1) = SQRTFCSST) * 2.3C26
GS ( L * M- 1 5 = . 3*GX (r/;) 4- . l 5* ( GX ( M- 1 > +GX (;.-i+ 1 > )
AL(L»iVl-l >=SQRTF( 1 .-OX CM-1 > )
u, CONTINUE;
LPA=LP+2
C
C SIMULATION SECTION CARDS 101 TO 334
C
101 IF (CX)IS,15,16
15 DO 30 L=1,NS
3C XCCLi1)=C.
CX =1 .
16 JA = JA + 1
DO 35 M=l«365
LX = 0
RAN = CAY
CAY =0.
DO 65 I = 1*12
66 CAY = CAY + RG£N( 1 . }
CAY = CAY - 6.
DO 35 L=1«NS
LB=L-1
IFC2-L32C1»2G1«£02
232 XC C L t M+ 1 ) =E3 ( LX + 2 «1^, ) ^XC ( L »f-'i ) +AL ( L »<•',) wCAY
GO TO 203
201 XC ( L » M+1 ) =B3 < LX + 2 »i-'i) *XC C L » M ) + Ai_ ( L » ^ ) *«,AN
2C3 CONTINUE
LX=LX+2
IF (L-l) 37.37*33
3c DO 3 L2=l»LB
LX = LX4-1
XCCL.M+1 )=XC(L«.-i + l )+65(LX»iv|)*XC(L2»M+l )
3 CONTINUE
37 IF(GS(L«M) )32-»321 »~ii'.
321 GT = XC(L»Ni+l )
GO TO 337
GST=GS(L«M)*»165667
181
-------
QTT=GST*(XC(L«M+i)-<
QT=
PLIM=-2«/GS(L*M>
IF(GS(L.M)>333*337*335
333 IF(QT-PLIM)337,337*334
334 QT=PLIM
GC TO 337
335 IF(QT-PLIM>334«337«337
337 IF(L-2) 14,13*13
13 IF ( QT ) 1100*1101*1101
1100 Q (L»i^ ) =EXPF (AS(L,M) + ( (QT#SS(L*M) 5/1»45) )
GO TO 336
1 1 u 1 G ( L , iVi) =EXPF ( AS ( L , M ) + ( < GT#SS < L , M ) > /1 • 2 ) )
GC TO 336
14 IF C QT ) 1102,1103,1103
1102 a(L,M)= EXPF(AS(L » M) + ( (QT#SS < L * M) )/1•35 ) )
GO TO 336
1103 Q < L , M ) =EXPF ( AS <\- « M ) + ( ( QT#SS ( L , M ))/!.!))
336 IF (M-365)35»27«27
27 XCCL*15=XC(L,366)
35 CONTINUE
IYK = JA - 2
IF (IYR) 16, 16, 42
42 DO 43 L=1,N5
DO 43 r-1= 1*365
43 QX ( I YR * L , M } =Q ( L , ,v, )
IF(IYR-NY) 101,602,602
C
C HYDROLOGY PLOTTER TO CA«L 450
C
602 -IFCKILLPT) 600,600,601
600 C A =15•
DO 251 !<= 1 , 1 00
NYX(K)=NXX
251 CONTINUE
DO 45o M=1,365
HOL=G(1*M)
AL5 = Q(2,;'.:5
CA=CA+1•
I F ( Q ( 1 » M ) -Q ( 2 * ;•-••) ) 460 , 460 , 46 1
461 UU=HOL
GO TO 462
460 UU=AL3
462 IFCUU-10C.>463«463»464
464 CONTINUE
466 IF(UU-10000.)467,467,468
46o IF(UU-1CJOOO.)469,463,479
463 HH=HOL+»5
AA = ALo+ « 5
,\i A = A A
GC TO 470
465 HH=HCL/10.+.5
AA=ALE/10.+.5
182
-------
NA = AA
GO TO 470
457 HH = KCL/100.-f .5
NH = HH
AA = Aub/l00 « + .b
NA = AA
GC TC 470
469 HH=HOL/1000.+,2
NH = HH
AA = ALd/l CCO « + .5
NA = AA
GO TO 470
470 IF(NH-1 } 42 0,421 ,422
42u NH=NK+1
421 NH=NH+1
422 IF(NA-1)423,424»425
423 NA=NA+1
424 NA = NA-fl
425 LH=NH-1
LA=NA-1
IF(CA-15.)471,472,472
472 CA=0
WRITE (6,473)
473 FORMAT(25HYEAR DAY HOLLEY ALBANY . ,49X,1H.,49X,1H. )
471 IF(NA-NH)4SO,4S1,482
431 WRITE (6,490) I YR , ,v,, Q ( 1 , M ) , Q ( 2 * M ) , ( NYX ( I > , I = 1 , Lri ) , NZZ
490 FOR,',AT ( I3,2X, 13, 2F3.0 , 1H. , 100A1 )
GO TO 449
480 NI-P = NH-NIA
NCP=NIP-1
IF(NOP)451,451,452
452 '.VR I TE (6,490) I YR , M , Q ( 1 , I'M ) , G ( 2 » M ) , ( N YX ( I ) t I = 1 , LA ) * N I A , (i\YX C I ) , I = 1 ,
11MOP) ,NIH
GC TO 449
451 WRITE (6,490) I YR , M , Q ( 1 , M ) » Q ( 2 , f-l) , ( NYX ( I ) , I = 1 , LA ) , N I A , i\ I H,
GO TO 449
432 NIP=NA-NH
NOP=NIP-1
Ir (MOP )493,493,433
433 WRITE (6,490) I YF<,M,Q( 1 « M ) , G < 2 , M ) » ( NYX ( I ) « I = 1 »Ln) ,NIH, ( ,-;YX ( I ) , 1 = 1 «
1NCP) ,NI A
GO TO 449
493 WR I Tt£ (6,490) I YR , M , Q ( 1 , !••' ) , Q ( 2 i M ) , ( N YX < I ) t I = 1 , LH ) , i\j I r., N I *
GC TO 449
479 WRITii (6,4955 I YR , M , Q ( 1 1 '15 » O ( 2 »;-i)
495 FOR.MAT( 13,2X, I2,2F3. 0 « ISH.RANGc. EXC^^Jli, )
GO TO 449
449 CONTINUE
450 CONTINUE
/"
C 5EGINNING OF ANALYSIS SECTION
C
DO 17 L=1,NS
DO 166 J=l,365
G(L,367-J)=G(L«366-J)
183
-------
166 CONTINUE
17 CONTINUE
NY5=NY-1
AN=NYo
5N=AN-1«
CN =( AN+1•)/(AN-l •)
DO 11 L=1»NS
11 Q(L,367)=Q(L»366)
IF(AAU)12»12«5
12 AAU=1.
NYC = 0
5C4 LX = 0
DO 51 L=1,NS
LXR=LX
DO 52 M=1,366
S(L»M>=0
G(L,M)=0
DC 52 L2=l,L
LX=LXR+L2
52 PC(LX,M)=0.
DO 51 M=l,365
DOS L2=l»L
LX=LXR+L2
a pp(LX,,vi) =0.
51 CONTINUE
1F(IBOMB)505*505,5
5C5 GO TO 101
5 LX=0
NYC=NYC+1
DO £2 L=1«NS
22 GCL,1)=Q(L,367J
DC 53 L=l,NS
LXR=LX
DO 54 M=1,366
IFCIJOM3)511,511,512
512 G ( L < :••'• ) =QX ( NYC , L , ."••; )
Q < L , i"i > = ( Q ( L , M ) -E < L , ."':) ) /F ( L , >i)
FQ=.5*GK(L,M)#Q(L «M) + 1 .
G (L»M )=6./GK(L,iv. )*(SIGNF ( ASSF ( FG )**• 33333 , Fu )- 1 . )
GO TO 513
511 Q(L,M)=LOGF(Q(L,M ) }
QX(NYC»L»M)=Q(L»M) '
513 S(L,M)=S(L,M)+Q(L,M)
G C L , M ) =G (L , f 1) +Q ( L , ,'-•; ) *Q ( L , ,<•.) *Q (L , r-;)
DO 54 L2=l«L
LX=LXR+L2
54 PC ( LX tM ) =PC ( LX , r'l > -f-Q ( L , M ) *Q ( L2 , i'\ )
DO 18 M=l,365
DO18 L2=l,L
LX=LXR+L2
1 £ PP ( LX , M ) =PP ( LX , r/( ) +Q ( L , ,M > *t ( L2 • M+ 1 >
I F ( I tiOMB ) 5 1 4 , 5 14 , 53
514 Q(L,367)=EXPF(Q(L,366))
53 CONTINUE
IF(NY-NYC)56»56,55
184
-------
55 IFC I50M3J520, 520.5
520 GO TO 101
56 LX=0
DO £6 L=l »N£
LXR = LX
30 25 i/i = 1.366
E ( L . M ) =S ( L , K ) / ( AN+ 1 . )
DO 23 L2=l .L
LX=LXR+L2
GT = G ( L » M ) -E ( L . ;••; ) * ( 3 . #PC ( LX » M } -E • *E ( L » i"'i ) *S ( L . "-, ) }
23 PC(LX.M) = PC(LX» M )-:=! / < F ( L * M ) *PC ( LX « i«i ) }
DO 25 M= 1 . 365 *
DC 25 l_2=l .L
LX=LXR+L2
25 PP ( LX . M ) =PP ( LX » ."i ) -£ ( L . M ) #£ ( L2 » M+ 1 )
26 CONTINUE:
IF < loOMB )500 .50 J . 501
50C I50,MB = 1
WRITE (6.502)
502 FORMAT (26HPROP1ZRT I ES OF LOG OF FLOWS . 1 OX » 26r!,v,EAiM i,TANJARD LJ^VIATI
IN SKEVJ//)
DO 503 L=l .NS
DO 503 M=2,366
r-'C=:;-i
'A'R I TE (6.1) N ( L ) . .-1C . E ( L . i-i ). F < L ..'!). GK ( L » ;-i )
5C3 CONTINUE
NYC = 0
GO TO b04
5T1 '.vRITE(5.506 )
5c6 FORMAT (60KPROPERT I£G OF LOG KCk.v.AL OLVIAT££ STATION DAY RoQuARLD
1ETAS//)
C
C START OF f-.'ATRIX INVERSION
KX = ( - 1 )
DO 50 ;<=i ,NS
KA = K + 1
KAA = K + 2
,
-------
61 Ad , U)=PCCKX»M>
DO 41 1 = a*XA
KX = KX + 1'
41 A
DO 48 J = IDA* KAA
46 ACID.U) = A(ID.U) / ACID,ID)
DO 62I=IDA,KA
DO 62 J=ftKAA
62 AC I ,U)=A(I,J) - AC I .ID)-*A < ID.J)
B(KA) = ACKA.KAA) / A(KA.KA)
I = K
73 IA = I + 1
Ed ) = A(I .KAA)
DO 71 U= IA«KA
71 3(1) = 8 CI )-B(J)*A(I,U)
1 = 1-1
IF (1)77*77,73
77 D=3C2)#PP(KX+1 «i"i-l )
5(2) = E(2) * FCK,|V;-1) / F(K,M)
IF (K-l>79.79*80
60 DO SI U=3tKA
KX = KXR + U
D = D + 6(U) * PC ,U =1 * KA)
1 FORMAT C 15, I7,3X,8F7.3)
57 CONTINUE
50 CONTINUE
C
C THIS IS THE FLOW TESTING SECTION TO CARD 130
C
6C1 MX=0
NSIM=NSIM+1
UA =0
UO = UO + 1
I AC=1
ND=365
i^El =0
,v,El 0 = 0
i iSl=0
MS3C=0
:••' S 1 2 C = 0
C TC INITIALIZE IXAX AND K IN VARIABLES
C
186
-------
DC 401 IYR=1»NY
DO 4C1 L=l,NS
SXK(L,IYR)=0
SX2(L, IYR)=G
BIG(L, IYR)=C
SUM3B *C < L »M)
S5=Q(L«M)-5IG(LtIYR)
IF(Sb)1C7«107»108
103 5IG(L» I YR)=Q(L »:••'. )
M51=M
1-^7 Siv;L = G(L «:".) -SMALL (L« IYR)
IF(SML)111.111»109
111 SMALLCL»IYR)=Q(L»M)
MS1=M
109 IF(M-3) 136, 113. 1 13
1 1 3 SUM3 ( L ) = ( Q ( L »'-; ) +O ( L t
-------
SU10(L)=SU10(L)/1Q.
IF(SU1C(L)-SU10B(L»IYR))127,127«128
123 SU10B(L« IYR )=SU1 0(L>
MB10=M-9
127 CONTINUE
IF(M-30) 136 , 130,130
130 M = M+1
DO 131 I<=1 ,30
JO=M-K
SU30(L)=SU30(L)+Q(Li JO)
131 CONTINUE
M=M-1
SU30(L)=SU30(L)/3C»
IF(SU30(L)-SU30S(L»IYR}}132»133»133
132 SU30S(L,IYR)=SU30(L)
MS3C=M-29
133 CONTINUE
IF(M-120)138»135»135
135 M=M+1
DO 136 K=l,120
JO=M-K
136 S120(L)=S120(L>+Q/120.
IFCS12CCL)-S120S(Lt IYR) ) 137 % 133« 138
137 S120S(L»IYR)=S12C(L)
MS120=M-119
133 CONTINUE
5X2 SX2(L,IYR)
148 FORMAT(23HTHE YEARLY STD DEV IS «Fl0.1)
WRITE (6.140) 3IG(LtIYR).ME1
140 FORMAT ( 16HLARGE3T ONE DAY «F6.-0»16H DAY BEGINNING ,I5/)
WRITE (6,141) SUM3BCL,IYR), MS3
141 FORMAT(25HLARGEST MEAN THREE DAYS ,F6»0«16H CAY BEGINNING ,I5/)
WRITE (6,142) SU10B'(L» IYR) »MB10
142 FCRMAT(23HLARGEST MEAN TEN DAYS ,F6.Q»16H DAY SdGINNING ,I5/)
WRITE (6,143) SMALL(L,IYR)«MSI
143 FORMAT < 16HSMALLEST ONE DAY,F6.0,16H DAY cEGlNNlNG , IS/-)
WRITE (6,144) SUM7S(L,IYR),MS7
144 FORMAT(25HSMALLEST MEAN SEVEN DAYS »F7.1«16h DAY utoINNlNG ,I5/)
WRITE (6*146) SU30S(L,IYR)IMS30
146 FORMAT(26HSMALLEST MEAN THIRTY CAYS ,F7»1,16H DAY BEGINNING ,IS/)
WRITE (6»147) S120S(L,IYR),MS120
147 FORMAT(23HSMALLEST MEAN 120 DAYS ,F7.1,16H ^AY oEGINNlNG ,IS/)
303 CONTINUE
C
C TO RANK MAX AND MIN VARIA5LES
C
188
-------
loo
17C
132
15C
171
139
151
172
190
152
173
183
153
174
154
154
175
185
155
176
186
156
177
137
157
178
DO 180 L=l,NS
WRITE (6.168) N(L)
FORMAT(//14HTHE STATION IS.I5//)
CONTINUE
DO 161 K=1,NY
GO TO ( 170, 171 , 172, 173, 174, 175, 176, 177, 17«, 17-?)
AR=SUM3B (L.K)
IF(1-K)193, 189, 189
CONTINUE
WRITE (6.151)
FORMAT<23HLARGEST MEAN THREE ^AYS/)
GO TO 198
AR(iO=SU10B CL.K)
IF(1-K)193,190,190
CONTINUE
WRITE (6.152)
FORMAT (21HLARGEST MEAN TEN DAYS/)
GO TO 198
AR(!O=SMALL(L«;<)
IF(1-K)193,183,1£3
CONTINUE
•; 198, Io5, 185
CONTINUE
.vRITE (6. 155 )
FORMAT(25HSMALLEST MEAN THIRTY
GO TO 193
AR(K) =S120S(L,,<)
IF{1-K)198,186.186
CONTINUE
.,v'RITE(6» 156)
FORMAT(22HSMALLEST MEAN
GO TO 198
AR(K) =SXK(L,I<)
IF(1-K)198,187,187
CCNT I NUE
WRITE(6,157)
FORMAT{11HYEARLY MEAN/)
GO TO 198
AR(K)=SX2(L,<)
IAC
ONE UAY/)
SEVEN
120 DAYS/)
189
-------
IF( 1-K) 198« 138* iae
138 CONTINUE
WRITE (6» 158)
15S FORMAT ( 14HYEARLY STD DEV/)
196 CONTINUE
181 CONTINUE
1011 CONTINUE
DO 1010 1=1 .NY
DO 1020 I<=1 .NY
IF (ARC I )-ARCK> > 1003. 1004 < 1004
1004 CONTINUE
1020 CONTINUE
IFCMX-NY > 1003* 1008* 1006
IOCS CONTINUE
WRITE (6. 1005) I . ARC I )
1C 05 FORMAT ( I5»F1C» I/)
AR(I)=0
1003 CONTINUE
1010 CONTINUE
GO TO 1011
1006 IAC=IAC+1
MX=0
GO TO 169
179 CONTINUE
IAC=1
ISO CONTINUE
I50MB=0»
AAU=0»
CX = 0.
JO-0.
I F ( NP-NS I M ) 92 . 92 . 1 0 1
92 END FILE 6
END
190
-------
BIBLIOGRAPHIC: Kerri, K. D., Comple-
mentary Competitive Aspects of Water
Storage, FWPCA Publication No. DAST-1,
1969.
ACCESSION NO:
KEY WORDS:
Allocation
Flow Augmentation
Marginal Analysis
ABSTRACT: Allocation of scarce water
for flow augmentation to enhance water
quality and other beneficial uses con-
flicts with other water demands. An
analytical model is proposed that is Planning
capable of allocating water to compet-
ing demands on the basis of economic Reservoir
efficiency. The value of water is deter- Operation
mined oa the basis of the slopes of the
benefit functions for water uses and an Simulation
algorithm based on the theory of marginal
analysis allocates water after consider-
BIBLIOGRAPHIC: Kerri, K. n. , Comple-
mentary Competitive Aspects of Water
Storage, FWPCA Publication No. DAST-1,
1969.
ACCESSION NO:
KEY WORDS:
Allocation
Flow Augmentation
ABSTRACT: Allocation of scarce water
for flow augmentation to enhance water
quality and other beneficial uses con- Marginal Analysis
flicts with other water demands. An
analytical model is proposed that is Planning
capable of allocating water to compet-
ing demands on the basis of economic Reservoir
efficiency. The value of water is deter- Operation
mined on the basis of the slopes of the
benefit functions for water uses and an Simulation
algorithm based on the theory of marginal
analysis allocates water after consider-
BIBLIOGRAPHIC: Kerri, K. D., Comple-
mentary Competitive Asoects of Water
Storage, FWPCA Publication No. DAST-1,
1969.
ACCESSION NO:
KEY WORDS:
Allocation
Flow Augmentation
ABSTRACT: Allocation of scarce water
for flow augmentation to enhance water
quality and other beneficial uses con-
flicts with other water demands. An
analytical model is proposed that is
capable of allocating water to compet-
ing demands on the basis of economic
efficiency. The value of water is deter-
mined on the basis of the slopes of the
benefit functions for water uses and an Simulation
algorithm based on the theory of marginal
analysis allocates water after consider-
Marginal Analysis
Planning
Reservoir
Operation
-------
ing the complementary and competitive
uses of available water. Results
indicate the frequency and magnitude of
any shortages for each beneficial use of
water. A daily streamflow simulation
model and a relationship between
reservoir operation and recreational
attendance were developed to produce an
accurate simulation model of the basin
studied.
This report was submitted in fulfillment
of project 16090 DFA between the Federal
Water Pollution Control Administration
and the Sacramento State College
Foundation.
Temperature
Control
Water Pollution
Water Quality
ing the complementary and competitive
uses of available water. Results
indicate the frequency and magnitude of
any shortages for each beneficial use of
water. A daily streamflow simulation
model and a relationship between
reservoir operation and recreational
attendance were developed to produce an
accurate simulation model of the basin
studied.
This report was submitted in fulfillment
of project 16090DEA between the Federal
Water Pollution Control Administration
and the Sacramento State College
Foundation.
Temperature
Control
Water Pollution
Water Quality
ing the complementary and competitive
uses of available water. Results
indicate the frequency and magnitude of
any shortages for each beneficial use of
water. A daily streamflow simulation
model and a relationship between
reservoir operation and recreational
attendance were developed to produce an
accurate simulation model of the basin
studied.
This report was submitted in fulfillment
of project 16090DEA between the Federal
Water Pollution Control Administration
and the Sacramento State College
Foundation.
Temperature
Control
Water Pollution
Water Quality
------- |