DOCUMENTATION REPORT
FWQA DYNAMIC ESTUARY MODEL
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DOCUMEHTATION REPORT
FWQA DYNAMIC ESTUARY MODEL
by
Kenneth D. Feigner1
Howard S. Harris2
^Sanitary Engineer, Systems Analysis and Economics Branch, Federal
Water Quality Administration, U. S. Department of the Interior,
Washington, D.C.
2Ch1ef, Planning Branch, California-Nevada Basins Office, Federal
Water Quality Administration, U. S. Department of the Interior,
Alameda, California
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PREFACE
The purpose of this document is to present the necessary theory,
background, and guidelines for applying the FWQA dynamic estuary model
to an arbitrary estuary. The discussion reflects FWQA experience in
applying the model to the San Francisco and San Diego Bay estuaries.
The model has been utilized to simulate a wide variety of hydraulic
and water quality conditions In these two systems, and has, through
the course of its development, testing, and use, undergone significant
change. New features continue to be incorporated as the model is
utilized and applied to new systems and to new problems. It is
anticipated that supplemental renorts describing new applications and
new model features will be prepared when warranted.
The preparation, review, and publication of this documentation
report has largely been a joint and cooperative effort between the
California-Nevada Basins Office (Alameda, California) of the FWQA
Southwest Region and the Systems Analysis and Economics Branch of
the FWQA Headquarters Office. Water Resources Engineers, Inc. of
Walnut Creek, California who, under contract, developed the model,
has continued to develop new model features and has provided insight
and guidance on the use o’ the model over the past several years.
It was primarily through the efforts and foresight of James C.
McCarty, current Deputy Director of the Southwest Region, who served
as project officer for the development contracts, that the model was
carried to a successful completion. Dr. Howard S. Harris, California-
Nevada Basins Office, also provided valuable insight and suggestions
during all phases of the development, testing, and use of the model
and has contributed significantly to the writing and editing of this
document.
The principal author of this report is Kenneth D. Feigner, currently
on the FWQA headquarters staff, who was responsible for implementing
the model studies during assignment to the FWQA Central Pacific Basins
Office in Alameda.
Other contributors to this report from the FWQA Alameda Office
Include David R. Minard, who conducted the prototype tracer studies
for model verification and contributed to the writing of this report,
William M. Thurston, who contributed to the writing of the user’s
manual, Marie Cleveland who prepared the figures, and Karen S. Relephord
who typed preliminary drafts 0 f the report.
Additional contributions from FWQA headquarters staff include
the adaptation of the model components to the IBM 360 System by
William S. Gillam III and the typing of the Intermediate and final
drafts of this report by Mrs. Ida Weiner.
I
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The preliminary draft of this report was distributed to selected
FWQA employees for review and coninent. Constructive coimnents and
suggestions were received from Mr. R. J. Callaway of the National
Coastal Pollution Research Program at the Pacific Northwest Water
Laboratory in Corvallis, Oregon, from Messrs. J. J. Troyan and David R.
Minard 0 f the California-Nevada Basins Office in Alameda, California,
from Dr. Norbert A. Jaworskl and Mr. Leo J. Clark of the Chesapeake
Technical Support Laboratory in Annapolis, Maryland, from Mr. Edwin L.
Johnson, Chief of the Systems Analysis and Economics Branch, FWQA,
Headquarters, and Mr. William P. Somers of the Systems Analysis and
Economics Branch, FWQA, Headquarters.
Each suggestion was considered and, where possible, was incorporated
into this final version of the report. The authors are grateful for all
coninents received and for the resulting improved document.
Kenneth D. Feigner
Howard S. Harris, Ph.D.
July 1970
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TABLE OF CONTENTS
PART I. THEORY AND APPLICATION
t PITRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
HYD ULIC MODEL THEORY ........ .••••••••••••••••••• •••••••• 2
HYDRAULICMODELAPPLICATION................ 7
NetworkConfigurat ionandSize........................ 7
Channel Parameters . . . . . . . . . . . 9
Junction Parameters .....•.•••••s s ••• •••S•S••••t •t• 12
NetworkNumberingSystem.............................. 14
Tidal Input •.. .s..•e••q•e •••e•••e•• ••••es• 14
Accretions and Depletions.... ... . . . . . . . . . . . . . . . . . . . . . . . 15
Inflows ••*.*.•••••.ø••••st •• 15
Exportati ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5
WaterUseWithinBasln........................... 15
Evaporat ionandPrecipitatiofl.s................. 16
Model Execution .... ..• . . .. ••• •••SeS•st••••••• e•t• 16
QUALITY MODEL THEORY •. • .... ......•...••.••.•••.• . 17
Advection . . . . . . . . . . . . . . . . . . . . . . . . . . . . •....... . 19
Eddy Diffusion ..... .. . 19
CombinedlransferEquation............................ 20
Longitudinal Dispersion . . . . . . ... . .. . . . .. .. .. . . . . . 20
Finite Difference Form of Transport Equation ..... 20
Diffusion Coefficient ................................, 21
Degradation and Mass Transfer ... ....... 22
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QUALITY MODEL THEORY (continued)
Import and Export .. •*...s••e 24
Suninary of Finite Difference Formulations ............ 25
Solution Technique 27
QUALITY MODEL APPLICATION . . . . . . . . . . . . . . . . . . . . • . . . • . . . . . . . . 28
Input Requirements .. . 29
Time Interval • .. . .• s•ø•e•••••’*S•e•t 29
Inflows . . . . . . . • . . . . • a . a . a . . • . . . • . . • . . . . . . . . . . . . . 29
Waste Discharges • .4s*SSs*, • •. a.... a... 29
Diversions . . . . . . . . . . . . . . . . . . . . . . . . 29
Boundary Conditions . . . . . . . . . . • . . . . a a a . . a a a • • • • • 29
Starting Conditions a........ a a. a .• a a•.• as... a a a 30
Special Considerations •.. ...........•........ 30
Precipitationand Evaporation •.......... ........ 30
Agricultural Use .... .s•• 5.s•s•sS•••at’••t 31
PART II. MODEL TESTING, VERIFICATION, AND CASE STUDIES
INTRODUCTION .................. .. .e .st . 5 5 5* . 50 5** a 34
SANFRANCISCOBAY—DELTASYSTEM........................... 34
HydraulicModel Verification.......... 35
QualityModel Verification .......................... 37
Salinity Incursionand Repulsion ............... 37
TracerRe leaseS imulat ion...... ... ... . ...... ... 50
SAN DIEGO BAY a.. .... ..S•.S .t• 5tSS••e•S 5*•t••••••••SISess• 65
Hydraulic Verification 5 5 55 ••••• . . . ........... ..... 65
Quality Verification 65
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LINEAR ESTUARY AND SENSITIVITY STUDIES ......... .... 75
Hy rau1ic Model •.S.• . .• . . . .• .• . ..• .• .e. .•• .S.. ...... .. 75
Time Interval and Network Scale .................. 75
Manning II I! Values . . 75
Quality Model . . . . . . . * . . . . . . . . . . * . . . . . . . . . . . . . . . . . . . . . . 76
Time Interval and Network Scale .................. 76
Diffusion Coefficient • • • ......,. . . . . . . 81
Solution Technique for Advective Transport ....... 81
DISCUSSIONOFDISCREPANCIES................................ 93
OTHER APPLICATIONS •...s.................................... 94
PART III. USER 1 S MANUAL
I NTRODIJCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
HYD ULIC PROGRAM (DYNHYD) . . . . . . . 97
FlowDiagramandProgramLogic........................ 97
Input Requirements . . . . . . . . . . . . 111
OutputOptions and Control ............................. 113
Sign Convention •..............s....................... 115
Interpretat lonofOutput........ . ...... .. 115
Potential Implementation Difficulties ................. 116
Execution Time ................ ... ..................... 118
Description and Format of Program Inputs (DYNHYD)....P. 119
Variables Internal to Program DYNHYD .................. 123
Variables Internal to Subroutine HYDEX ................ 125
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QUALITY PROGRAM (DYNQUA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Flow Diagram and Program Logic ........................ 129
Input Data Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Control Parameters •. .. ................... . .s .. . . 142
Waste Load Data •.. .. . .•••••• ••••••••••• . .. .. ... 142
Initial Conditions •......• . . . . . . . . . . . . . . . . . . . . . . 144
Boundary Condtions 145
OutputOptions and Control ... . ........ 147
InterpretationofOutput............ . ... . .. . .••••’’ • 148
Potential Implementation Difficulties ............. .. 149
Execution Time ••••••••••••••••tS•s••••S••• ••• 149
Description and Format of Program Inputs (DYNQUA) .... 150
Variables Internal to Program DYNQUA ................. 166
Variables Internal to Subroutine QUALEX .............. 169
Variables Internal to Subroutine ZONES •.............. 169
REGRESSIONANALYSISPROGRMI(REGAN) •,,•• . ., . . . . .. . ....... 172
Description and Format of Program Inputs(REGAN) ..... 172
DATAPREPARATIONPROGRAM(DATAP) .......................... 174
Description and Format of Program Inputs(DAT P) •.... 175
ILLUSTRATIVE EXAMPLE ..e ..•• .•s•*e•ss*•••• ...........• .•. .. 176
REFERENCES •.•....•..•................•.•.............••... 180
APPENDIX - Program Listings and Sample Output
Program DYNIIYD Listing ...•. . . .S•est•sss•e•ts ••e•••s• ..... 183
Subroutine HYDEX Listing • * • • ... • • • a a . .•..,,, • • • • • • • . • . •1S 189
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Sample Job Control Language for Program DYNHYD ............ 193
Output from DYNHYD .....• . . . ..S.S•S•S•SSS.•. ..•.•SS•S••SS.S 194
Output from HYDEX .................................. 201
Program DYNQUA Listing . .... ...... •...... ....... .... ....... 204
Subroutine QUALEX Listing . . . . . . . . . . . . . . . . . . . . . •. . . . . . . . . . . 214
Subroutine ZONES Listing . . . 21 5
Subroutine PUNCH Listing . . . . . . . . . . . . . . . . . •....... . . •1•SSS• 217
Sample Job Control Language for Program DYNQUA 219
Output from DYNQUA .............,...,............,...•..... 220
Output from QUALEX 228
Output from ZONES . . . . . 230
Program REGAN Listing •. . .S . .••e•••••e•••tIt•••••S•••• •••t 239
Output from REGAN ....................•.................••. 241
Program DATAP Listing . . . . . . . . . . . . . . 243
Output from DATAP ..............................•.••,•.,,.. 246
LIST OF FIGURES
FIGURE IITLE PAGE
SAN FRANCISCO BAY AND DELTA 8
2 SUISUN BAY NETWORK 10
3 TYPICAL CHANNEL AND JUNCTION ELEMENTS 13
4 TIDAL INPUTS AT SEAWARD BOUNDARY -- SAN FRANCISCO BAY— 36
DELTA
5 COMPARISON OF MODEL AND TIDE TABLE PREDICTIONS OF 38
TIDAL STAGE -- JULY 1955
VII
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FIGURE TITLE PAGE
6 COMPARISON OF MODEL AND TIDE TABLE PREDICTIONS OF 39
TIDAL STAGE -- SEPTEflBER 1955
7 SPECIFIED BOUNDARY CONDITIONS -- JULY AND SEPTEMBER 41
1955 CHLORIDE IN SAN FRANCISCO BAY-DELTA
8 SAN FRANCISCO BAY-DELTA COMPARISON STATIONS 42
9 JULY 1955 CHLORIDE CONCENTRATION HISTORIES -- SAN PABLO 43
AND SLJISUN BAY STATIONS
10 JULY 1955 CHLORIDE CONCENTRATION HISTORIES - - SACRAMENTO 44
RIVER STATIONS
11 JULY 1955 CHLORIDE CONCENTRATION HISTORIES - - SAN JOAQIJIN 45
RIVER STATIONS
12 SEPTEMBER 1955 CHLORIDE CONCENTRATION HISTORIES -- SAN 46
PABLO AND SUISUN BAY STATIONS
13 SEPTEMBER 1955 CHLORIDE CONCENTRATION HISTORIES -- 47
SACRAMENTO RIVER STATIONS
14 SEPTEMBER 1955 CHLORIDE CONCENTRATION HISTORIES -- 48
SAN JOAQUIN RIVER STATIONS
15 EFFECT OF INITIAL CONDITIONS ON MODEL PREDICTIONS -- 51
JULY 1955 CHLORIDE
16 EFFECT OF INITIAL CONDITIONS ON MODEL PREDICTIONS - - 52
SEPTEMBER 1955 CHLORIDE
17 STUDY AREA WITH TRACER SAMPLING STATIONS -- SAN FRANCISCO 54
BAY-DELTA
18 OBSERVED AND COMPUTED MAXI JM AND MINIMUM TRACER 56
CONCENTRATIONS AT ANTIOCH BRIDE
19 TRACER CONCENTRATION HISTORIES AT SELECTED STATIONS 57
IN SIJISUN BAY
20 TRACER CONCENTRATION HISTORIES AT SELECTED STATIONS 58
IN SUISUN BAY
21 TRACER CONCENTRAT1ON HISTORIES AT SELECTED STATIONS 59
IN WESTERN DELTA
22 TRACER CONCENTRATIONS IN SHIP CHANNEL -- BENICIA TO 60
COLLINSVILLE
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FIGURE TITLE PAGE
23 ILLUSTRATION OF COMPARISON DIFFICULTIES DUE TO 62
NONCORRESPONDENCE OF OBSERVATION AND PREDICTION POINTS
24 EFFECT OF SPECIFIED TRACER LOSS RATE ON MODEL 64
PREDICTIONS -- SAN FRANCISCO BAY-DELTA
25 STUDY AREA WITH TRACER SAMPLING STATIONS -- SAN 66
DIEGO BAY
26 COMPARISON OF MODEL AND TIDE PREDICTIONS OF TIDAL 67
STAGE -- SAN DIEGO BAY
27 TRACER CONCENTRATION HISTORIES -- SAN DIEGO BAY 69
28 TRACER CONCENTRATION HISTORIES -- SAN DIEGO BAY 70
29 TRACER CONCENTRATION HISTORIES -- SAN DIEGO BAY 71
30 TRACER CONCENTRATION HISTORIES -- SAN DIEGO BAY 72
31 EFFECT OF SPECIFIED TRACER LOSS RATE ON MODEL 73
PREDICTIONS -- SAN DIEGO BAY
32 EFFECT OF SPECIFIED TRACER LOSS RATE ON MODEL 74
PREDICTIONS -- SAN DIEGO BAY
33 EFFECT OF INCREASED CHANNEL RESISTANCE ON COMPUTED 77
TIDAL STAGE AND PHASE
34 EFFECT OF TIME INTERVAL ON INTRUSION IN A SIMPLE 78
LINEAR CHANNEL
35 EFFECT OF TIME INTERVAL ON DISPERSION FROM POINT 79
SOURCE -- SAN FRANCISCO BAY-DELTA
36 EFFECT OF TIME INTERVAL ON DISPERSION FROM POINT 80
SOURCE -- SAN FRANCISCO BAY-DELTA
37 EFFECT OF TIME INTERVAL ON DISPERSION OF CONSERVATIVE 82
TRACER FROM POINT SOURCE -- SAN DIEGO BAY
38 EFFECT OF TIME INTERVAL ON DISPERSION OF CONSERVATIVE 83
TRACER FROM POINT SOURCE -- SAN DIEGO BAY
39 TYPICAL CHANNEL ELEMENT AND CONCENTRATION GRADIENT 87
40 COMPARISON OF SOLUTION TECHNIQUES 90
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FIGURE TITLE PAGE
41 COMPARISON OF SOLUTION TECHNIQUES -- JULY 1955 CHLORIDE 91
42 COMPARISON OF SOLUTION TECHNIQUES -- JULY 1955 CHLORIDE 92
43 SIMPLIFIED FLOW DIAGRAM -- PROGRAM DYNHYD 98
44 SAMPLE DATA DECK MAKEUP -- PROGRAM DYNHYD 127
45 SAMPLE JOB DECK MAKEUP -- PROGRAM DYNHYD 128
46 SIMPLIFIED FLOW DIAGRAM -- PROGRAM DYNQIJA 130
47 APPLICATION OF RESTART FACTORS 146
48 SAMPLE DATA DECK MAKEUP -- PROGRAM DYNQUA 170
49 SAMPLE JOB DECK MAKEUP —- PROGRAM DYNQIJA 171
50 SAMPLE DATA DECK MAKEUP -- PROGRAM DATAP 177
LIST OF TABLES
TABLE TITLE PAGE
1 SUIfIARY OF COEFFICIENTS FOR DEFINING REAERATION RATE 24
2 NET FLOWS IN DELTA CHANNELS 37
3 EFFECT OF DIFFUSION CONSTANT, C 4 , ON MODEL PREDICTIONS -- 84
SAN FRANCISCO BAY
4 EFFECT OF DIFFUSION CONSTANT, C 4 , ON MODEL PREDICTIONS -- 85
SAN DIEGO BAY
5 COMPARISON OF ADVECTION METHODS 88
•6 EXECUTION TIMES FOR HYDRAULIC MODEL 118
7 EXECUTION TIMES FOR QUALITY MODEL 150
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PART I. THEORY AND APPLICATION
INTRODUCTION
The dynamic estuary model described herein was originally
developed by Water Resources Engineers, Inc., of Walnut Creek, Cali-
fornia, under contract to the Division of Water Supply and Pollution
Control of the Public Health Service [ 1]. Additional development
for the Federal Water Pollution Control Administration (FWPCA) [ 2]
and for the State of California [ 3] was also completed by that firm.
Development and refinements have also been completed by the Federal Water
Quality Administration (FWQA) for utilization in specific studies
[ 4,5]. Limited comparisons between model and prototype behavior
have been presented in the previously cited references and elsewhere
[ 6,7].
Although the model was developed specifically for the San Fran-
cisco Bay-Delta estuary, experience by Water Resources Engineers and
FWQA has demonstrated its applicability to other estuaries. The
model represents the two-dimensional flow and dispersion characteris-
tics of an estuary and can be applied to any estuary wherein vertical
stratification Is either absent or is limited to relatively small
areas within the estuary. This would include estuaries such as San
Francisco Bay in which stratification is limited to the area near
the mouth or to other areas only during specific periods of the year
such as during peak freshwater outflow. If appropriate boundary
conditions can be specified the model can be applied to particular
problem areas without modeling the entire estuary. However the
problems associated with specifying appropriate boundary conditions
under such applications can be formidable, and to avoid such problems
it may be necessary to extend the modeled area to boundaries with
relatively constant (or at least predictable) flow and quality char-
acterl stics.
The model can accomodate a range of time and space scales as
may best suit the nature of the problems and the physical character-
istics of a particular estuary. In applications described herein
predictions for tidal flow and stage were computed at frequencies
on the order of 1/2 to 5 minutes on the time scale and at Intervals
on the order of a few hundred to severaT thousand feet on the space
scale. Predictions of quality levels are computed on the same space
scale as for the hydraulic parameters but on an expanded time scale
of the order of 15 ml nutes to one hour. The model Is thus truly
dynamic in character; it predicts fluctuating tidal flows and computes
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tidally varying concentrations of constituents, in contrast to a non-
tidal model based on the net flow through the estuary such as that
developed for the Delaware Estuary [ 8).
The model can acconnodate both conservative and non-conservative
constituents including the interrelationship between biochemical oxygen
demand (SOD) and dissolved oxygen (DO).
The model consists of two separate, but compatible components;
namely, a hydraulic program (DYNHYD), and a quality program (DYNQIJA).
A third program, a harmonic regression analysis (REGAN) Is utilized to
reduce the input requirements for specifying the tidal conditions im-
posed on the system. A hydraulic extract program (HYDEX) in the form
of a subroutine of the hydraulic program, sumarizes the hydraulic
output and prepares the appropriate hydraulic input to the quality
program. Similarly a quality extract program (OUALEX) is incorporated
as a subroutine of the quality program to sumarize the output from
the quality program. A final program (DATAP) has been developed to
prepare many of the basic data Inputs to the hydraulic program.
HYDRAULIC MODEL THEORY
The hydraulic behavior of estuaries and other coastal waters is
usually Influenced significantly by the ocean tides, by the freshwater
Inflow to the system, and by the shape of the estuary and inflowing
river system. While Coriolls and wind forces may be significant in
certain estuaries they are not represented In the model described
herein. In modeling the hydraulic behavior of an estuary the problem
Is essentially one of solving the equations describing the propagation
of a long wave through a shallow water system. In open channels in
which the flow Is predominately one-dimensional the hydraulic behavior
can be described by the one-dimensional form of the equations of motion
and continuity (9). The equation of motion takes the form:
.= -u! -KJuJu -9 (1)
where:
u = velocity along x-axis, positive in the direction of Increas-
Ing x
x distance along x-axls
H = water surface elevation
g acceleration of gravity
K frictional resistance coefficient
t time
The equation of continuity can be expressed as:
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(2)
b x
where:
b = mean channel width
A = cross sectional area of the channel
The assumptions on which equations (1) and (2) are based include:
1. Acceleration normal to the x-axis is negligible
2. Coriolis and wind forces are negligible
3. The channel is straight
4. The channel cross-section is uniform throughout its length
5. The wave length is at least twice the channel depth
6. The bottom of the channel is level
The term on the left hand side of the equation (1) is the local accel-
eration (time rate of change of velocity). The terms on the right
side of the equality sign represent, respectively, the rate of momentum
change by mass transfer, the frictional resistance, and the gravita-
tional driving force or potential difference between the ends of the
channel element. The absolute value sign in the frictional resistance
term assures that the resistance always opposes the direction of flow.
The left hand side of equation (2) Is the time rate of change of
the water surface elevation while the right hand side represents the
change in storage over the channel length per unit width of channel.
As presented, equations (1) and (2) both apply to a channel. For
a system represented by a network of channels these equations could
be solved for each channel in the network and boundary conditions
matched at the connecting junctions. To minimize computational require-
ments, the elevation of the fluctuating water surface (and the corre-
sponding change in volume) of the system is associated with the junctions
while flow (velocity and discharge) is associated with the channel
elements of the network. This approach permits the application of
equation (1) to the channel elements and equation (2) to the junctions
of the network.
In finite difference form, the equation of motion becomes:
AU 1 — U 1
. —Ui .. . - KIU 1 I Uj -g (3)
where i refers to the channel under consideration, Li Is the mean
velocity, and x is the channel length.
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Similarly the equation of continutiy becomes:
zQ
if
where the subscript n denotes the junction under consideration. The
term EQ is the algebraic flow rate into the junction, both from the
channels entering the junction and from external sources (waste dis-
charges, Inflows, diversions, etc.). The term A* is the surface area
of the junction.
The roughness coefficient K in equation (3) can be evaluated by
Manning’s equation, which can be written as:
22
2.208 R 4 /3
where:
2 Energy gradient
dx
n Manning’s roughness coefficient
U mean velocity In channel
R hydraulic radius
Application of Manning’s equation is normally restricted to conditions
of steady uniform flow. For a tidally influenced estuary, few, if any,
of the channels experience steady flow. However, over relatively short
time Intervals the flow can be considered steady. In fact steady,
uniform flow Is implicit in the assumptions listed previously for
application of equations (3) and (4).
The relationship between frictional resistance and the slope of
the energy gradeline can be expressed as:
KIUIIJ = g (6)
Substituting equation (5) into (6) results in the definition of K:
K = g
2.208 R 413
The determination of the velocity gradient term, hU,/xj, In
equatIon (3) presents certain computational difficulties in that the
computed velocity In each channel element is constant for the entire
length of the channel, hence there Is no velocity gradient predicted
within a given channel. Although a velocity gradient could be estab-
lished by utilizing the predicted velocities In the next adjacent
4
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upstream and downstream channel elements, such a technique is not
completely appropriate in that in networks with branching channels
there may be several 1 upstream” and Hdownstream t channels, each ‘ 1 rith
a different orientation.
To avoid this difficulty MJ /x 1 in equation (3) is computed by
utilizing the continuity equation (2) as suggested by Lai [ 10 ). From
equation (2):
b iH_ _u A_A (8)
or
_ ub H u (9)
a A x
In finite difference form equation (9) becomes:
- tJj b AH 1 U. AA (10)
X 1 A.At x.
Even in this form AtJ /x is not tractable in that equation (1) applies
to a channel element an the two terms AH/t.t and AI\j/x in equation
(10) are not computed for channels. Since fluctuations in water sur-
face elevation are associated with junctions in equation (10) is
computed as the average of the changes in elevation during the time
step at the junctions at both ends of the channel. Similarly the
cross—sectional area gradient t A /x 1 is obtained by computing an area
at both ends of the channel based on the predicted water surface eleva-
tions at those junctions.
The numerical integration of equations (3) and (4) was programmed
for solution using a modified Runge-Kutta procedure. Equation (3) is
first solved for each channel in the network with a time interval equal
to one-half the full time interval At. Similarly Equation (4) is
solved for each junction for the half-time interval. These half-step
results (velocities, flows, areas, and heads) then serve as the basis
for solving the equations using the full time interval. . step by
step solution of equations (3) and (4) proceeds as follows:
(1) The mean velocity for each channel is predicted for the
middle of the next time interval using the values of channel
velocities and cross—sectional areas and the junction heads
at the beginning of the time interval.
(2) The flow in each channel at the middle of the next time in-
terval is computed based on the above velocity and the cross-
sectional area at the beginning of the interval.
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(3) The head at each junction at the middle of the next time
interval is predicted based on the above predicted flows.
(4) The cross-sectional area of each channel is adjusted to the
middle of the next time interval based on the above predicted
heads.
(5) The mean velocity for each channel is predicted for the end
of the next time interval using the values of channel veloci-
ties and cross-sectional areas and junction heads at the
middle of the interval.
(6) Steps (2), (3) and (4) are repeated for the end of the time
interval. Computation proceeds through a specified number
of t time intervals.
The solution will converge, for a given set of boundary conditions, to
a dynamic equilibrium condition wherein the velocities and flows in
each channel and the heads at each junction repeat themselves at in-
tervals equal to the period of the tide imposed at the seaward boundary
of the system.
Selection of the time interval t to be used in the program is
based primarily on a computational stability criterion. Generally, the
solution wifl be stable if the following relationship between the time
interval t, the channel length x 1 , the tidal velocity U 1 , and the
celerity of a shallow water wave, a, is maintained.
xj (a 1 •t Uj) t (11)
The celerity of a shallow water wave, a, for a given channel can be
roughly determined from the relationship:
= ,‘ y- (12)
where g = acceleration of gravity
y = maximum mean channel depth
Ideally x and it should be made as large as possible, consistent with
the degree of detail and precision required in the solution. For many
of the channels of the San Francisco Bay Delta the maximum channel
length was fixed, I.e., x could not exceed the actual length of the
channel. Thus, in a sense, the shortest channel modeled dictates the
maximum time interval which can be used. However, it Is apparent
from equation (12) that a relationship such as equation (ii) cannot
be considered precise In that the wave celerity varies with the
depth of the water, which of course, fluctuates with the tide. Even
If, for a given tidal condition, the maximum wave celerity is used
in the relationship there is no assurance that for some other tidal
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condition (or higher inflow condition) the same maximum mean channel
depth would result. The same is true of the maximum mean tidal velocity
U. The maximum mean tidal velocity is dependent on the Imposed tidal
condition and on the freshwater inflow to the system. There is the
additional problem of even estimating the maximum mean tidal velocity
in a channel. In the absence of adequate field measurements of channel
velocities for each and every channel in the network the best that can
be done is an estimate based on “typical” channel velocities in the
system. In spite of these difficulties, however, equation 11 does
serve as a very useful guide for selecting the time interval and the
lengths of the channel elements in the network.
HYDRAULiC MODEL APPLICATION
The mathematical model, as described herein was developed originally
for and limited to the system of interconnected channels of the Sacra-
mento-San Joaquin Delta [ 1]. It was later determined that the one
dimensional equations of flow and continuity used to simulate the
hydraulic characteristics of these channels could also be successfully
applied to wide, shallow embayments such as Suisun, San Pablo, and San
Francisco Bays [ 2]. While this discussion is intended as a guide for
applying the dynamic estuary model to any well-mixed estuary it will
be expedient to illustrate certain points in the discussion with experi-
ence gained with the San Francisco Bay system.
The San Francisco Bay system represents extremes In physical con-
figuration and hydraulic environment, i.e., the wide, shallow embayments
of San Francisco, San Pablo, and Suisun Bays and the well defined system
of relatively narrow interconnected channels of the Delta. The system
Is illustrated in Figure 1. The entire system is tidally influenced as
evidenced by the periodic fluctuation of water surface elevation at
essentially every point in the system. During periods of low freshwater
inflow to the Delta the hydraulic behavior of the entire system is largely
tidal In nature, i.e., significant fluctuations of water surface eleva-
tions and flow reversal in channels between flood and ebb tides. During
periods of high freshwater inflow to the Delta the tidal effect is less
pronounced near where major rivers enter the Delta.
While the model has not been applied by FWQA to this complex
hydraulic regime in its entirety it has been applied to the system
beginning at the seaward entrance to San Pablo Bay (near Point Orient)
and Including essentially all upstream waters which are subject to
tidal action. The network for this system totals some 830 junctions
and 1050 channels.
Network Configuration and Size
There is a great deal of flexibility allowed In laying out the
network of interconnected channels and junctions to represent a
particular system. The choice of the boundary locations should include
7
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FIGURE 1.
SAN FRANCISCO BAY AND DELTA
6
S
S
O4 I. d
S
5. ! LS .
S
S
S
S
8
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considerations of both hydraulic and quality factors. To minimize
difficulties with boundary conditions the network should ideally
extend to the ocean at the downstream boundary and to or beyond the
limits of tidal effects on Inflowing streams so that the Inflow can be
considered steady. Such a network eliminates problems associated with
dynamic boundary conditions such as changing salinity or other quality
conditions which could be present if an inland point is chosen for the
seaward boundary. Other considerations which could influence the
location of the network boundaries, the overall size, and the scale of
network elements include the location of specific points where quality
predictions are required, the location of existing or planned sampling
stations and the availability of data for verification, the degree of
network detail desired, and the computer time required for solution.
If the model will be utilized to study the impact of anticipated
physical changes in an estuary, e.g., the construction of a jetty, a salt
water barrier, a ship channel, etc., the network should be laid Out so
that it can easily accomodate these changes. The network should
initially be representative of existing conditions in order to demon-
strate the modePs capability to reproduce prototype behavior.
Channel elements are normally oriented in directions which minimize
the variation in depth between junctions. This generally Implies that
the network elements which represent the dredged or naturally scoured
deep-water channels of a bay are oriented parallel to these main channels
of flow. For the wide, shallow portions of a bay where the principal
direction of the flow is not well defined by channelization, the net-
work can be laid out In a grid pattern with the orientation of any
particular channel element being relatively unimportant. For applica-
tion to Sulsun and San Pablo Bays the shallow areas were characterized
by a rectangular grid network.
For a system of well defined channels, such as In the Delta, the
model network essentially follows the prototype configuration, i.e.,
If a significant channel exists in the prototype it Is represented by
a channel element or series of elements in the model network. Because
the desired network scale ma.y dictate channel element lengths a pro-
totype channel may have to be divided into a series of channel elements
In the model network. The channels of the network are connected by
nodes or “junctions’. These network junctions thus not only exist for
all real junctions in the prototype but also must connect all channel
elements In the network. Figure 2 illustrates the network used for
Sulsun Bay and depicts the channel element orientation following the
main tidal flow through Carqulnez Strait and along the southern shore-
line, the rectangular grid network of the embayments, and the well
defined channels of Sulsun and Montezuma Sloughs. The network extends
to or slightly beyond the mean lower low water line (MLIV).
Channel Parameters
The parameters associated with the channels of the network are
length, width, cross-sectional area, frictional resistance coefficient
9
-------
L
b
LEGEND 1
• TIDE GAGE
C4
C,
0
C,
• M,I s Londing
CA NEZ
Eckley “?
Chico o
FIGURE 2. SUISUN BAY NETWORK
0
-------
(Manning’s “n”), velocity (or flow rate) and hydraulic radius. The
network channel lengths (distance between junctions) are governed by
the computational stability criteria discussed previously and by the
actual length between real junctions in the prototype. Typical channel
lengths in the Delta vary between 3000 feet and 5000 feet while in the
Bays from 3000 feet to 7000 feet.
There is no apparent restriction on the width of the network
channels although con,non sense would dictate that the width of a channel
not be so wide that the mean velocity prediction for the channel would
mask important velocity patterns. For example, for wide channels with
one portion much deeper than the other, the channel might best be
broken into two parallel channels, one deep and relatively narrow, and
the other wide and shallow. Such refinements in the model network,
however, should be consistent with the detail (velocity or flow patterns,
head fluctuations, etc.) desired. For representing well defined channels
such as in the Delta, the network channel widths are merely the mean
bank to bank widths. In the case of the Delta these widths approach
4000 feet. For the enba mient portions of the San Franciso Bay system
the rectangular grid network channels typically have widths of 3000 to
5000 feet. For such embayments a complete overlap of channels may exist,
i.e., for a square grid all channels have the same width as length.
It Is within this overlapping grid network that the two—dimensional
flow patterns are represented.
The cross-sectional area of a channel is dependent on the width
of the channel and on the head or water surface elevations at the ends
(junctions). Since the head fluctuates with time the cross-sectional
area is continually changing within the model. For computational pur-
poses an initial cross-sectional area is assigned to a channel which
Is determined from the heads initially assigned to the junctions at
both ends of the channel. As the heads fluctuate a corresponding
adjustment is made for the channel cross-sectional area.
The network channels can be assigned “typical’ Manning roughness
coefficients which are normally associated with naturai channels. The
coefficients assigned to channels of the San Francisco Bay network
vary between 0.018 and 0.050 with the smaller coefficients normally
associated with San Pablo and Sulsun Ba)s and the larger coefficients
with the channels of the Delta.
An initial estimate of mean channel velocity Is required for each
simulation run. For an Initial hydraulic simulation with the model
the mean velocity estimates can be taken as zero. For hydraulic simu-
lations In which only minor changes from some previous hydraulic
solution are desired It would be desirable to utilize the mean channel
velocities from that previous solution as starting estimates for the
new solution. Depending on the significance of the differences in the
two hydraulic runs the required computational time to converge to a
steadystate solution may be significantly reduced by such a procedure.
11
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In applications by FWQA the channel element widths have generally
been greater than 10 times the channel depths. For this reason the
hydraulic radius for each channel is assumed equivalent to the mean
depth 0 f the channel.
Channel widths and lengths can usually be scaled from navigation
charts published by the Coast and Geodetic Survey. Depths at mean
lower low water (MLLW) can be read directly from these charts and it
Is usually possible to establish the cross-sectional area from these
soundings. The depths have to be adjusted to a datum selected for
the model, and for certain channels near the periphery of the network
the depths may have to be increased somewhat above those indicated on
the charts in order to adequately represent the volume of the system.
Since there is no provision for allowing a junction to run dry” the
network is normally extended only to the 1411W line. There is also no
provision for increasing or decreasing the surface area of the system
as the tide rises and falls. In areas of tidal flats it is therefore
necessary to increase the depths of the peripheral channels to ade-
quately represent the volume of the system at higher tidal stages.
Junction Parameters
The parameters associated with the junctions of the network are
surface area, volume, head, and any accretion or depletion from the
system.
For junctions In those portions of the network with well defined
channels the surface area of a junction is generally taken as the sum
of the surface areas of each half-channel entering the junction. For
the embayments the surface areas can be determined by laying out a
polygon network similar to that of the Thiessen polygon method frequently
used for estimating the area of Influence of a rain gauge on a watershed.
The area for each junction can be computed based on the dimensions of
the polygon surrounding it or, for complex polygons, by planimetering.
FIgure 3 illustrates a typical two-dimensional space as it might be
represented by a system of junctions and connecting channels. Channel
widths and junction surface areas are Indicated in 3(b) and 3(c)
respectively.
Junction volumes are computed by multiplying the surface area of
the junction by a depth which represents the mean depth of the half-
channels (weighted according to surface area) entering the junction.
The junction volume varies with time as the head at the junction varies.
The head at each junction represents the elevation of the water
surface above a horizontal datum. The selection of the datum is arbi-
trary, and In fact can be changed from one solution to another. Normally
however, the same datum Is used for all solutions sInce ft Is usually
advantageous to utilize the solution from one run as starting conditions
for subsequent runs. This procedure minimizes the number of Iterations
12
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FIGURE 3.
TYPICAL CHANNEL AND JUNCTION ELEMENTS
(a)
(b)
Cc)
13
-------
required to converge to a steady state solution, particularly when there
is a great deal of hydraulic similarity between the runs. In studies on
the San Francisco Bay system [ 4) It was found that when starting condi-
tions were selected from a previous hydraulic solution which was Identical
to the desired hydraulic condition except for the location of the Master
Drain, the computer time for reaching a steady state solution was from
one-third to one-half less than for hydraulic solutions which utilized
starting conditions from runs with less similar hydraulic characteristics.
Any accretion or depletion from the system is handled through the
addition to, or removal from, the junction voltm es. For computational
purposes an accretion is assigned a negative value and a depletion is
assigned a positive value. At every junction in the network the net
accretion or depletion is specified. Inflows, waste water discharges
and precipitation are treated identically as accretions and diversions,
exportatlons, consumptive use, and evaporation are treated as depletions.
Network Numbering System
For computational procedures it is necessary that the junctions of
the network be numbered consecutively beginning with one The assign-
ment of numbers to the network can be based on any arbitrary considera-
tion. A separate but similar numbering system for the channels is also
necessary. Each junction may have from one to five channels entering
It. A channel must have a junction at each end; thus dead-end sloughs
such as occur in the Delta must end with a junction. Associated with
each junction number are from one to five channel numbers; and associated
with each channel number are two junction numbers. For the Bay-Delta
system the network Is numbered (both channels and junctions) beginning
at the downstream boundary and proceeding generally upstream.
Tidal Input
The tidal condition imposed at the seaward boundary of the model
must be characteristic of the conditions under consideration. For
simulation of an historic condition the tide chosen should be represen-
tative of the tidal conditions which existed during the period In
question. For comparison between alternate waste water disposal plans,
a less specific tidal condition would be selected, e.g., a tide repre-
senting a mean annual tidal condition. The desired tidal Input could
be obtained from prototype tidal stage recorders if such were available
at the boundary. In the absence of such data It may be necessary to
rely on the predictions presented Ift Tide Tables published annually by
the Coast and Geodetic Survey for a point(s) on the model boundary.
These projections yield the tidal elevations in feet for the four
extreme stages of the tide (higher high, lower low, lower high, and
higher low) and the time of occurrence of these four stages. The
tidal elevations are then referenced to the datum selected for the
model and a harmonic regression analysis performed for obtaining the
curve of best fit as defined by a rplationsblp of the form:
“4.
-------
Y=A 1 +A 2 Sjn(wt)+A 3 Sin (2wt)+A 4 Sin(3wt)+
A 5 Cos (wt) + A 6 Cos (2 wt) + A 7 Cos (3 wt) (13)
The harmonic analysis program yields the coefficients Al, A2 .....,
which, along with the period of the tide, are used in the hydraulic
program to define the tidal fluctuation at the lower boundary.
Accretions and Depletions
There is no distinction, within the hydraulic model, between the
various water uses, as only the net accretion or loss at a junction is
utilized. In fact accretions and losses are assigned a common variable
name (QIN) and are distinguished by assigning a negative sign to the
accretions to the system. If more than one diversion and/or waste
discharge exist in close proximity in the prototype they can be combined
into a single net depletion or accretion at a single junction in the
model without significantly affecting the hydraulic solution. However,
to assure the appropriate quality impact it may be desirable to separate
individual waste discharges from diversions and assign them to different
junctions.
For studies on the San Francisco Bay system the various hydraulic
inputs handled as accretions or depletions at junctions included:
1. Inflows . Inflows include the perennial streams entering the
system and can include seasonal streams and storm runoff in
studies covering periods when these freshwater sources are
significant. Significant groundwater sources can also be
included as inflows. Streamfiow data are available for
historic periods from published U. S. Geological Survey Water
Supply Papers for specific basins. These data are generally
in the form of mean daily flow for the entire water year with
monthly sunluaries. Synthetically generated hydrologic inputs
could also be utilized.
2. Exportations . Exportations include all waters diverted from
the basin within the confines of the model network. If
diversions are made for exportation from points between the
stream gaging station and the model boundary the inflow should
be adjusted accordingly. losses to groundwater can also be
included if identifiable.
3. Water Use Within Basin . Waste waters discharged to an estuary
resulting from municipal, industrial, agricultural, or other
use are handled in one of three ways within the model. The
method chosen in any given case Is dependent on the specific
use of the water and on its origin.
15
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(a) In cases wherein a diversion is made from within the area
modeled with subsequent return to the system of all or
part of the diversion at a different quality level or at
a different location, the diversion and the return are
assigned to different junctions. Waters transferred from
one point in the estuary to another can be handled in
this manner also.
(b) Waste waters discharged to the system but for which the
water source originated from outside the modeled area
are treated as an accretion to the system, i.e., no
diversion is made from the system but a waste discharge
is added.
(c) Diversions and return flows can be combined into a net
diversion which equals the consumptive loss if such a
procedure has no significant effect on the hydraulic or
quality characteristics of the system. Cooling water
diversions and returns could be included in this category.
4. Evaporation and Precipitation . The net evaporative loss or
accretion due to precipitation can be included as a hydraulic
Input. If climatological conditions are relatively uniform over
the entire estuary, a net evaporation or precipitation rate could
be applied to the entire water surface area of the estuary to de-
termine the net loss or accretion to the system. This loss or
accretion could then be distributed over the system at selected
points or could be distributed over every junction if desired.
For an estuary such as the San Francisco Bay-Delta wherein
climatological conditions vary markedly over the system a some-
what more complex approach can be utilized. In that system
several evaporation and precipitation gauging stations have been
established by the U. S. Weather Bureau. The area of influence
of each of these stations was determined by constructing Thiessen
polygons for the entire area covered by the model. The net
evaporation or precipitation rate for each polygon was applied
to the surface area of each junction within the polygon to
determine the evaporation or precipitation component of the
“net” diversion or discharge at each junction.
Model Execution
During the execution of the program the predicted channel velocities,
flows, and cross-sectional areas and the predicted water surface eleva-
tions at each junction for each time interval are recorded on magnetic
tape or disk. In addition, output in printed form can be obtained at
selected time intervals (such as hourly) for a specified nui er of
junctions In the network. The written output includes the elevation of
the water surface at each junction as well as the velocity and flow in
16
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each of the channels entering the junction. As the solution approaches
an equilibrium condition the predicted head for any given junction will
repeat itself at an interval equal to the period of the tide specified
at the seaward boundary of the system. Although a condition of equilib-
rium is that the predicted heads repeat themselves at the proper interval,
this alone is not necessarily a sufficient test for equilibrium as a
relatively minor change in head during a time interval can represent
a significant flow change. This is particularly true for junctions with
large surface areas where even a change of 0.01 foot in the water surface
elevation can represent a significant quantity of water. A more reliable
test for equilibrium of the hydraulic solution is comparison of the net
flows computed in the program against those computed from the program
inputs. The net flow past a point in the system can be computed by
algebraically sunining all inflows, diversions, returns, exportations,
etc. which are used as inputs for the run, with the stipulation that
the sunration include all such depletions and accretions to the system
upstream from a plane cutting completely through the network at the
point. As the hydraulic solution approaches equilibrium the combined
net flow through the channels cut by the plane will approach the com-
puted value.
In its present state the model component for computing net flows
is run as a subroutine of the hydraulic program. The subroutine utilizes
as input the tape or disk written in the hydraulic program. Normally
the predicted velocities, flows, and heads for each time interval over
the last full tidal cycle of the hydraulic solution are utilized for
computing the net flows in that they should be the most representative
of the equilibrium solution. For purposes of extracting, the full tidal
cycle is divided into a whole number of equal intervals each of which is
some whole multiple of the basic time interval used in the hydraulic
program. As will be discussed in a later section the interval at which
the hydraulic parameters (velocity, flows, and heads) are extracted is
usually dictated by the choice of the time interval used in the quality
program. The extracted hydraulic parameters are stored on tape for
subsequent input to the quality program. rn addition a printout of the
net flows is obtained for each of the channels in the network.
QUALITY MODEL THEORY
A constituent introduced Into the waters of an estuary is trans-
ferred from one point to another by two basic transport mechanisms,
advection and diffusion. A portion of the constituent may be removed
from the system along with the water extracted for municipal, industrial,
or agricultural purposes or for exportation. The concentration of a
constituent is also affected by waste water discharges, by biological
or chemical decay, and by mass transfer between the water surface and
the atmosphere.
17
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Transport by advection Is primarily a hydraulic mechanism and
moves the constituent In the direction of flow. Transport by diffusion
on the other hand is primarily dependent on the concentration gradient
between two points and can take place in a direction opposite the flow.
Longitudinal dispersion of a constituent which in the prototype results
from the non-uniform velocity distribution at a cross—section, is not
specifically represented since the predicted channel velocity In the
model is the mean velocity across the flow section.
The water quality component of the mathematical model is very
closely tied to the hydraulic component discussed previously. The
solution of the quality program is based on the dynamic steady-state
hydraulic condition predicted in the hydraulic program. As was dis-
cussed previously, the hydraulic parameters (velocities, flows, heads)
for each time Interval are normally stored on tape or disk and form the
basis for the hydraulic inputs Into the quality program. Whereas the
time interval In the hydraulic program is relatively small (50 to 300
seconds) the time interval used in the quality program is much larger
(900 to 3600 seconds). The average flows and heads for the larger
time interval are determined In a separate hydraulic extract subroutine.
These condensed parameters for the full tidal cycle are stored on tape
or disk for Input Into the quality program and thus can form the hydraulic
basis for any number of quality runs. The quality solution proceeds
over a full tidal cycle at which point the hydraulic Input tape Is
rewound and used again as the basis for the succeeding cycle.
Five constituents can be handled simultaneously including both con-
servative and non—conservative constituents and including the inter-
relationship between biochemical oxygen demand (BOD) and dissolved
oxygen (DO).
The model can be used to predict the dynamic steady-state concen-
trations at every junction in the network resulting from a specified
set of boundary conditions (tidal conditions, inflows, waste discharges,
diversions, exportations, etc.).
The rate of buildup of a constituent can also be computed by the
model. For example, in the verification studies discussed in Part II
the rate of salinity incursion In the San Francisco Bay system during
two historic periods was simulated.
The model is extremely flexible and can easily accomodate changes
in the physical configuration of the prototype or in the operation of
the water resource system. For any proposed physical or operational
change In the system, the hydraulic program can first be used to predict
the changes In hydraulic behavior of the system and then the quality
program can be used to predict the effect of these changes on quality.
18
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Advecti on
Advection or advective transport is the transport of a particular
mass of a constituent at a rate equivalent to the velocity of the volume
of water with which the constituent is associated. This can be expressed
as:
TaUc (14)
where Ta is the advective transport through a unit area in a unit time,
u is the velocity of the water, and c is the concentration of the con-
stituent in the water. The time rate of change of concentration,
ac/at, in a given element, i, of the system is dependent on the mean
velocity in the element, Uj, and on the concentration gradient through
the element. This relationship can be expressed as:
(15)
ax
Each of the terms of equations (14) and (15) are functions of space
and time.
y Diffusion
Whenever a concentration gradient is established In water, a
mechanism Is established for the transfer of the constituent from the
regions of high concentration to those of a lower concentration. For
a quiescent body of water, this transport (molecular diffusion) is
extremely slow. The transfer rate is greatly increased in a non-quiescent
or turbulent body of water as a result of eddy currents. The term eddy
or turbulent diffusion is frequently used to describe this transport
process in a turbulent body of water. This process may be expressed
as:
(16)
ax
where T, is the turbulent transport by diffusion through a unit area
In a unit time, K. j Is a coefficient which describes the rate of transfer,
and ac/ax Is the concentration gradient of the constituent under con-
sideration. For a given element of the system In which the diffusion
coefficient Icj can be assumed constant, the time rate of change of
the constituent ac/at Is dependent on the second derivative of c with
respect to x, as follows:
acl ,Kda 2 c (17)
at
19
-------
As with equations (14) and (15) the direct solution of equations
(16) or (17) Is normally possible only for relatively simple cases.
Combined Transfer Equation
The processes of advective transport and eddy diffusion act as
independent phenomena. Combining equations (15) and (17) the net rate
of change of concentration Is:
ac 2 c (18)
= U 1 — +
Equation (18) can be applied to an element of the system If the follow-
ing assumptions are not violated:
1) the element is completely mixed vertically,
2) the velocity U is the mean velocity in the cross-section,
3) the flow and transport within the element are unidirectional
(one-dimensional flow), and
4) the mean velocity U and K,j are constant throughout the length
of the element within the computational time Increment.
Longitudinal Dispersion
Although the flow of a channel can be represented by a mean
velocity, in actuality the velocity varies from point to point In the
cross-section. Thus, in a given channel, a certain portion of the
flow advances at a rate higher than the mean velocity and a certain
portion advances at a lower rate. The mechanism through which liquid
particles (and any associated constituent) undergo relative displace-
ment due solely to the difference in velocities along adjacent stream-
lines is termed longitudinal dispersion. Since the velocity in equa-
tion (18) Is assumed to be the mean velocity at the cross-section
this dispersion phenomenon Is not specifically represented. Although
the numerical solution technique utilized does result, coincidently,
in the longitudinal dispersion of a constituent this coincidental
transfer is only partially controlled and Is not a true representation
of the longitudinal dispersion process. This phenomenon will be dis-
cussed in more detail in subsequent sections.
Finite Difference Form of Transport Equation
For the network of channels and junctions which characterizes
a system It is convenient to express total transport by equations (14)
and (16).
TtTa+TdUic+Kd (19)
where Tt Is the total transport per unit area per unit time. Applied
to a discrete channel, equation (19), in finite difference form be-
comes:
20
-------
M A U 1 c* + KdAl c
(20)
where 11 is the mass of pollutant transported, A 1 is the cross-sectional
area of the channel I under consideration, Is the mean velocity in
the channel during the time Interval t, c is the difference in con-
centrations at each end of the channel, and Xj is the channel length.
The concentration c* is a representative concentration of the water
advected and is dependent on the concentration gradient that exists
over the channel length and on the direction of flow in the channel.
The computational procedure for advective transport results in
longitudinal dispersion since the constituent is moved from one junction
to another during a single time interval while the water itself typi-
cally moves a portion of the channel length. This phenomenon has been
termed ‘induced advective dIspersion” [ 1] or “numerical mixing” [ 7]
and is controlled through the specification of the concentration c
In equation 20.
Diffusion Coefficient
It has been demonstrated [ 11] that the diffusion coefficient Kd
Is dependent upon the rate of energy dissipation in the system and
on the scale of the phenomenon, This can be expressed as:
K j C 1 E 1 / 3 Le 4 1/ 3 (21)
where E is the rate of energy dissipation per unit mass, 1 e Is the
statistical mean size of eddies participating in the mixing process,
and C1 Is a function of relative channel roughness. For water flowing
at a uniform depth at a steady mean velocity U, the rate of energy
dissipation In foot pounds per pound of water per foot of channel
length Is equal to the slope of the energy grade line. The reciprocal
of the mean channel velocity, 1/U, defines the time interval over which
the energy loss occurs, The mass of each pound of water Is 1/9.
The rate of energy dissipation per unit mass In a channel can there-
fore be represented by:
r_dH/dX _u gdH
l/g 1/U 1 — (22)
The mean eddy size Le can be related to a dimension of the channel
such as the width or depth. Utilizing the depth y as a measure of scale
and defining the slope of the energy line by Manning’s equation,
equation (21) becomes:
Kd = c 3 u 1 y 819 (23)
21
-------
where 4/3 1/3
C 12 9
(1.486) / (24)
and L
C 2 ze (25)
y
For computational purposes it is convenient to replace the channel
depth with the hydraulic radius and simplify equation (23) to
C 4 IUIR (26)
where K has dimensions length squared over time. The absolute value
sign is Included to Indicate that the transport by eddy diffusion Is
independent of the direction of flow in the channel and depends only
on the sign of the concentration gradient as indicated in equatIon (20).
For early studies with the model (1) C 4 was taken as 0.042. Sub-
sequent FWQA studies utilizing C 4 values ranging between zero and 5.0
indicated that transport by diffusion in the model is relatively
insignificant when compared to transport by advection. For studies
on the San Francisco Bay system, C 4 was taken as 0.025.
Degradation and _ Miss Transfer
The concentration of a non-conservative pollutant, such as a
municipal or industrial organic waste can be biochemically converted
or stabilized to matter which is stable. The rate at which the organic
matter is stabilized Is directly proportional to the amount of unstabil-
Ized material remaining and Is expressed mathematically as:
dL —K 1 1 (27)
where I is the concentration of pollutant at time t as measured by the
biochemical oxygen demand (BOO), and K 1 Is the reaction rate with
dimensions 1/time. Equation (27) can be integrated to yield the
relationship defining the concentration at any time:
it i,,e-k 1t (28)
where L 0 Is the concentratlaii at time zero and e Is the base of the
Naperian logarithms. Expressed in finite difference form and applied
to the ss of unstabUized material remaining in a junction S of the
model network, equatIon (28) becomes:
Nj —K 1 5 L Vj (29)
22
-------
where Mj is the total mass remaining at the end of the time step, L
is the concentration of the unstabtlized material at the beginning öf
the time interval, Vj is the volume of the junction, and
= e l t (30)
which is dimensionless.
The dissolved oxygen in a body of water is depleted by an amount
equivalent to the BOD exerted. The oxygen in the system Is naturally
replenished through the process of mass transfer at the surface. This
rate can be expressed as:
(31)
dt 2
where D is the saturation deficit and K 2 is the reaeratlon coefficient,
with dimensions 1/time, describing the rate of the reaction. The
saturation deficit D Is the difference between the saturation concen-
tration and the actual concentration. The overall effect of reaeration
and decay on the saturation deficit is:
dD (32)
. K 1 L -
Although equatIon (32) can be lnteqrated to yield a single expression
defining the saturation deficit at any time It was more convenient
for computational purposes to separate the reaeratlon and decay effects.
Equation (29) defines the mass of BOD exerted during each time Interval
which is equivalent to the mass of oxygen depleted during the time
interval. The deficit of any time. t, is obtained by integrating
equation (31):
D( eK t (33)
where D 0 is the deficit at time zero. Equation 33 was expressed in
finite difference form and applied to the saturation deficit existing
at a junction in the network, such that:
Oj -K D Y (34)
where Oj Is the mass of oxygen replenished, Dj is the saturation
deficit concentration existing at the junction, Vj Is the volisne of
the junction, and
K 2 j 1.0 — eK2 ftt (35)
which is dimensionless.
23
-------
The reaeration coefficient K 2 is highly dependent on the degree
of fluid turbulence existing in the system. This is con non1y related
to the velocity and depth of the fluid in the general form:
K 2 =CUy (36)
where C is a constant, U is the velocity of the fluid, y is the depth
0 f the fluid, and a and b are exponents. There is not universal agree-
ment on the most suitable values for C and the two exponents. These
parameters are determined empirically and therefore may be biased
toward an investigator*s selection of experiments. A sunm ary of these
parameters found In three investIgations [ 1) is presented In Table 1
for K 2 expressed as day 1 , U In feet per second, and y in feet.
TABLE 1. SUI’V4ARY OF COEFFICIENTS FOR DEFINING REAERATION RATE
Investigator
C
a
b
O’Connor and
Dobbins
12.9
1/2
-3/2
Churchill et
al
11.5
1
-5/3
Krenkel and
Orlob
2.5
1
-l
It Is not apparent which of three resulting expressions would
best represent the reaeration rates in any particular estuary. In many
estuaries photosynthetic production of oxygen and respiration by algal
populations may play significant roles in the oxygen balance of the
system. These phenomena have not as yet been sufficiently defined,
functionally such that they could be Incorporated into the mathematical
model. Because of these and other factors, no attempt has been made
to relate K 2 to any hydraulic or biological parameters within the model
although it would not be difficult to do so.
Import and Export
The total mass of constituent present in the system may be changed
by one or more of four principle mechanIsms: 1) by introduction as a
part of the inflow to the system (whether it be a river inflow, tidal
Inflow, or a waste discharge), 2) by removal from the system In water
diverted or exported, 3) loss from the system by decay, or 4) addition
through reaerat lon. Within the system the distribution and fate of the
constituent is governed by the functional relationships presented pre-
viously.
24
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The mass of constituent Introduced at each junction in the system
during each time interval is equivalent to:
= c At (37)
where Is the total mass of constituent added to the system Q is
the inflow to the system at junction j, c is the concentration o the
constituent In the inflow, and At is the time interval. Equation (37)
is also used to compute the total mass of constituent lost from each
junction. For a diversion, however, the concentration c is taken as
the concentration existing in the system at junction j whereas, for an
inflow, the concentration must be specified. It should be pointed out
that Qj in equation (37) does not affect the hydraulics of the system
but is used merely as a basis for either adding or removing the appro-
priate mass of constituent during each time interval. Since the effect
of any waste discharge or diversion in the hydraulic model Is automati-
cally carried over to the quality model (through its effect on the
junction volume) it is imperative that Qj (and c fora discharge) be
specified In the quality model to assure the appropriate rate of with-
drawal of mass from (or discharge to) the system.
Summary of Finite Difference Formulations
The basic formulations governing the distribution and fate of a
constituent in the quality model can be sun narized as follows:
a. Advection (and longitudinal dispersion)
AMa Aj Uj C At (38)
b. Eddy Diffusion
AMd = K 4 jA 1 Ad (39)
x l
c. Degradation — Decay
AMb (1.0- k ) L V 3 At (40)
d. Reaeratlon
AM 0 = K 2 j D Vj At (41)
e. Import Export
AMe Qj Cj At (42)
where:
AMa the mass advected from the junction at the upstream end of
channel I to the downstream 5unction
25
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A 1 cross-sectional area of channel I during time step at
tJ. mean velocity in channel I
concentration of the advected water
At — time step
the mass of constituent transferred by diffusion from the
junction of higher concentration to that of lower concen-
tration, through channel I
Kd — the diffusion coefficient in channel i during the time
step at
AC 1
___ the concentration gradient over channel I which has
length x 1
a the mass of constituent lost through decay or degradation
during time step at
K 1 j — a dimensionless factor, computed from equation (30), which
specifies the loss per time step at junction S
concentration of non-conservative constituent existing at
junction 5 during time step at
V 5 volume of junction 5 during time step at
a the mass of oxygen added to junction 5 by reaeration during
time step at
k 4 • a dimensionless factor, computed from equation (35), whIch
specifies the fraction of the existing saturation deficit
that is replenished each time step
• the dissolved oxygen saturation deficit occurring during
the time step At
AMe the mass of constituent removed from the system in the
diversion Q at junction 5 during time step at, or the
mass of comtltuent added to the system in the waste
discharge Qj at Junction 3
Cj — the concentration existing at junction 5 if Q is a diver-
sion or the concentration !p!cJfl. If is I waste
discharge
26
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Equations (38) and (39) represent the individual components of the com-
bined transport formulation presented as equation (20) previously.
For convenience these components are treated separately in the program.
Solution Technique
Conservation of mass within the model Is maintained at the network
junctions. Equations (38) through (42) descrIbe the transfers of mass
between junctions and the loss or addition of mass at a junction.
Specified for each junction is an initial volume an an initial concen-
tration which determines the associated total mass of constituent
initially present within each junction. Also specified Is the net
discharge (and associated constituent concentration) or withdrawal at
each junction.
A quality constituent is distributed in the system in a stepwise
procedure as follows:
1. HydraulIc parameters are read from the input tape (which was
generated in the hydraulic solution). These include:
a) the head (water surface elevation) at each junction
at the start of the time step
b) the flows between junctions during the time step
2. Transfers of constituent are made between junctions based on:
a) advection -- The mass transferred is equal to the
product of the flow and a representative
concentration.
b) diffusion -- The mass transferred is proportional to
the concentration gradient between the
junctions.
The solution proceeds from one channel element to another
with advective transfers made from the upstream junction
to the downstream junction (as determined from the direction
of flow during the time step) and diffusive transfers made
from the junction of higher concentration to the other. The
net mass transfer through each channel Is removed from the
appropriate junction and Imedlately added to the junction
at the other end of the channel to maintain a mass balance.
The solution proceeds through all channel elements before
passing to step 3.
3. If the constituent is non-conservative the mass in each junction
is decayed by applying a decay coefficient. If the constituent
Is dissolved oxygen a reaeration coefficient is applied. These
adjustments are made at all junctions before passing to step 4.
27
-------
4. ContrIbutions of constituent from net inflows are added to
each junction.
5. Withdrawals of constituent by diversions at each junction are
made. Steps 4 and 5 are completed for all junctions before
passing to step 6.
6. The water surface elevation at each junction for the beginning
of the next time step is read from the hydraulic input tape
and the volume of each junction is adjusted to that elevation.
7. The new total mass in each junction is divided by the new
volume to determine the new concentration.
8. The new flows between junctions are read from the hydraulic
input tape.
9. Steps 2 through 8 are repeated a specified number of times.
In steps 2 through 5 above there is no adjustment during the time step,
of the existing concentration at each junction, I.e., all losses,
additions, and transfers are applied to the existing mass at each
junction and not to the concentration. It Is only after all adjust-
ments of the total mass have been made during a time step that a new
concentration Is computed (step 7).
The representative concentration used in the advective transport
equation (38) is determined from a weighted average of the concentra-
tions existing at the junctions at both ends of the channel In which
the transfer Is being made. A discussion of the selection of the
weights used in model studies for the San Francisco and San Diego Bay
systems Is Included tn a later section.
The quality solution can start at any desired point on the tidal
cycle. At the completion of each tidal cycle the hydraulic Input tape
Is rewound and used again.
QUALITY MODEL APPLICATION
Because the water quality program utilizes the identical network
developed for the hydraul Ic program, no additional “modeling” effort
is required to represent the physical parameters of the prototype.
Application of the quality program to a particular system therefore
consists primarily of defining the various rate coefficients for
diffusion, decay, and reaeratlon and of specifying the various inputs
required. Under certain conditions it may be necessary to Incorporate
other factors Into the qua1ity program, e.g., the effects on quality
of evaporation or of agricultural use. Provisions are Included in the
quality program to handle these phenomena In a special way.
28
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Input Requirements
While many of the Inputs required for the qua1ity model present
no particular difficulty others may require very careful selection and
consideration for certain types of problems.
Time Interval . The structure of the model is such that the coinpu—
tatlonal time interval can be varied from run to run. There are certain
restrictions on the quality time interval, however. Namely, 1) that
it be some whole multiple of the time interval in the hydraulic program,
2) that it be such that the period of the tide used In the hydraulic
solution is some whole multiple of It, and 3) that it be such that the
quality solution remains stable. As an example, for a hydraulic solu-
tion utilizing a 100-second time interval and a tide with a 25.0 hour
period the quality program could utilize a 1/4, 1/2, or 1 hour time
Interval (among others) provided the solution remains stable. On the
other hand, for a hydraulic solution utilizing the same 100-second
time interval but with a 24,5 hour tide a one hour time interval for
the quality solution could not be used since the 24.5 hour period
cannot be divided into a whole number of one-hour intervals.
Experience with the quality program in simulating several historical
conditions indicates that a one-half hour time interval Is more than
adequate to describe the quality fluctuations due to the tidal motion
in the San Francisco Bay and Delta system.
Inflows . One of the principal sources of many constituents is the
freshwater inflow to the system. The flow of each of the streams enter-
ing the system must be specified along with the concentration of the
constituent (s) under consideration.
Waste Discharges . For computational purposes there is no
distinction within the model between a waste water discharge and an
inflow. The contribution of constituent to the system from each is
normally Identified by specifying a flow and associated concentration.
Because of certain problems associated with some agricultural waste
waters special provisions were Incorporated to handle these wastes.
This special problem Is discussed in more detail in a later section.
Diversions . The quality of any diversion for exportation, or for
local use, is the concentration existing at the point of the diversion
during each time Interval. Water leaving the system at the seaward
boundary also leaves at the concentration existing at the boundary.
Boundary Conditions . Of the various inputs to the quality program
one of the most significant is the specified quality condition at the
seaward boundary of the network. If the situation permits, the model
should extend to the sea, a sump of known concentrations; otherwise,
the problem Is one of estimating the appropriate concentration — tidal
stage relationship. This problem Is illustrated in the various case
studies presented in Part II.
29
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Starting Conditions . Similar to the problem of establishing the
boundary concentration is the problem of initial concentrations at all
junctions. For certain studies these concentrations are defined by the
problem, i.e., the concentrations are historical concentrations or those
resulting from a previous study. If the problem is to determine the
dynamic steady state concentrations resulting from given inputs, it is
desirable to minimize computation time by selecting as starting concen-
trations the estimated final concentrations. If the starting concen-
trations are too low, such that insufficient mass is present in the
System, the additional mass must be added through the various specified
inputs, 1 4 e.,, waste discharges, inflows, or the flooding tide. Similarly
if the starting concentrations are too high, the excess mass must be
flushed from the system. A similar problem is that of starting with an
Improper distribution of consituent In the system.
To reduce the computation time required to achieve a steady state
quality solution, provision was made to increment the mass of constituent
in selected areas of the model. This feature was used either to adjust
the final solution from one quality solution to serve as the starting
conditions for a similar quality solution based on a different hydraulic
condition, or, to adjust the concentrations in the system after running
the program for a specified number of tidal cycles and evaluating the
results. Thus, if the concentrations in one area were Increasing while
those in another were decreasing, a factor greater than unity uld be
applied to the concentrations existing in the first area and a factor
less than unity to those in the latter area. The relationship utilized
was such that:
C ia C j f (43)
where Cia is the adjusted concentration at junction j after applying
the factor f to the existing concentration cj. Equation (43) can be
applied to up to ten specified groups of consecutively numbered junctions
for each constituent. A solution Is evaluated after a short simulation,
the factors applied, and the solution continued for a specified period.
This process can be repeated any number of times until the steady state
solution Is achieved. Even with limited experience in evaluating the
results and applying the factors the average computation time to reach
a steady state solution can be cut significantly.
Special Considerations
Additional factors which can significantly affect the quality of
the waters of an estuary Include evaporation, precipitation, and
agricultural use.
Precipitation and Evaporation . The dilutional effect of precipi-
tation which falls directly on the water surface is relatively Insig-
nificant. However the Increase in freshwater flow through the system
due to precipitation may result In a more effective hydraulic barrier
against Incursion of seawater Into the estuary with significant Improve-
30
-------
ment in mineral quality. The reduction in flow caused by evaporation
has the opposite effect.
The importance of evaporation and precipitation as they affect
water quality can perhaps best be evaluated by considering the magnitude
of the contribution of each to the overall hydrology of the system.
Evaporation and precipitation, as considered here, is that quantity
of water either lost from or added to the water surface of the estuary.
Evaporation in this sense does not include evapotranspiration from
adjacent lands nor does precipitation Include local runoff as these
factors can be Included as separate inputs. For the San Francisco
Bay system, in a month such as July, when precipitation is normally
zero, evaporation from the channels of the Delta alone totals approxi-
mately 29,500 acre-feet. For a winter month such as January, the net
precipitation (precipitation minus evaporation) which falls directly
on the Delta channels normally totals 8,660 acre-feet. It Is obvious
that for conditions of low controlled Delta outflow (1500 cfs or 92,000
acre-feet per month), these contributions are not Insignificant. The net
outflow is further decreased by evaporation from Sulsun Bay of 21,400
acre-feet and 46,300 acre-feet from San Pablo Bay during a month such
as July.
Although It would be possible to include the effects of precipita-
tion on water quality by treating it as an Inflow with zero concentra-
tion, another treatment proved more convenient. Advantage is taken
of the fact that the hydraulics of the system are not altered or
affected by any input into the quality program. In the hydraulic
program, precipitation is included as an inflow to each junction but It
Is not Included as inflow in the quality program. The result is to add
water but nat constituent. In the same way, evaporation Is included In
the hydraulic solution but not in the quality solution. Hence, water
Is removed but not constituent.
Agricultural Use . In one sense evapotranspiratlon from adjacent
agricultural lands is Identical to evaporation from the water surface
of the system, I.e., they both account for a consumptive loss of water
from the system. From the quality standpoint, however, their effects
are somewhat different. When water is lost from the surface of a
channel or bay by evaporation the effect on quality is lniiiediate, that
Is, water is removed but the constituent remains In the channel resulting
In an Increase In concentration of the constituent.
Water used consumptively by agriculture, however, is first diverted
from a channel to a tract (either through direct diversion or by seepage)
and with it is diverted associated constituents. The diversion (or
seepage from a channel) per se does not directly affect the quality of
the remaining water. As the water is used consumptively, the salts or
other constituents accumulate in the soil or are returned to the
channel In the drainage water. If the buildup of salts is allowed to
continue, the soil will eventually become unsuitable for the raising
of crops. The soil salt buildup may be controlled through the applica-
tion of water In excess of plant needs and by percolation of this excess
31
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water through the root zone of the plant. The resulting leachate will
contain, in addition to the original salt content, those salts formerly
present in the water lost through evapotranspiration and any salts
dissolved from the soil.
Where surface irrigation is practiced salt accumulation can nor-
mally be controlled through the normal irrigation practice with the
excess water (leachate) either percolating down to the ground water
or being collected in drainage tile and returned to the channels.
For tracts irrigated by subsurface methods (such as practiced in
the Delta of the San Francisco Bay system) water reaches the root zone
by capillary movement upward from the water table. The salts which
move upward with the irrigation water into the root zone remain there
when the water is removed by evapotranspiration. Thus salts tend to
accumulate in the soil during the irrigation season. In the late fall
or winter leaching of these salts is accomplished by precipitation
and the application of excess quantities of water to the land and the
accumulated salts are returned to the channels. On a long term basis
there is an approximate salt balance maintained, i.e., the salt diverted
to a tract equals the salt removed. For certain tracts leaching may
be necessary every year, while for others small quantities of salts may
be allowed to build up for several years before leaching is required.
On a short term basis (such as a month), there may be a net increase
of salts on a tract (during months of the Irrigation season) or a
net decrease (during months leaching is carried out). The quality of
the water in the channels is not improved merely because more salts are
removed than returned during a certain month as the concentration of
salts in the drainage water is invariably as high or higher than that
in the applied water. During months when leaching is carried out, the
concentration of salts in the drainage water may be very much higher
than that applied, resulting in a significant increase in concentration
In the channels.
For the San Francisco Bay system data were available to relate the
total mass of a particular constituent returned in agricultural drainage
in a given time period to the total applied In that period, as follows:
Qdcd=mQa ca+b (44)
where:
= flow rate of drainage, cfs
Cd concentration In drainage flow
Qa = flow rate of applied water, cfs
Ca concentration In applied water
m = return factor
b = return constant (mass units)
32
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The Delta agricultural tracts were grouped into study units and
the various terms in equation (44) determIned on a monthly basis.
Depending on the constants m and b, a constituent can either be stored
on a tract, removed at the same rate applied, or removed at a rate
exceeding the rate applied.
33
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PART II. MODEL TESTING, VERIFICATION, AND CASE STUDIES
I NTRODUCT ION
Regardless of the theory on which a model such as the one described
herein is based the real test of Its utility lies in its capability to
adequately reproduce prototype behavior. The difficulties associated
with simulating the hydraulic and water quality behavior of a complex
estuartal system are many and complex. As discussed heretofore many
simplifying assumptions are necessary to apply the governing equations
to an estuary. Oiscretizlng the system and numerical solution of the
equations Involve additional simplifications which can affect the pre-
dicted distribution of a constituent.
In addition to these problems associated with the model structure
there can also be significant difficulties associated with the quality
and quantity of prototype data for verification. Data to sufficiently
define the entire hydraulic regime and the distribution of quality
constituents throughout the system are rarely, If ever, available.
Extr i care must therefore be exercised in selecting test cases for
verification. Prototype behavior continuously changes as governed by
changing hydrologic, tidal, and other conditions. Although there is
nothing Inherent in the model structure to preclude the Inclusion of
such factors as variable inputs, the Inadequacy of data on prototype
behavior in most cases would not justify such a refinement.
Numerous studies for testing and verifying the hydraulic and water
quality models have been conducted both by Water Resources Engineers,
Inc. ( f) and FI A. Certain studies were conducted with an Idealized
linear estuary to determine the sensitivity of model behavior to various
model parameters. Md ltionally model behavior has been tested by FWQA
on the San Francisco and San Diego Bay systems.
SAN FRANCISCO BAY-DELTA SYSTEM
Verification of the hydraulic and water quality models was obtained
by comparing predicted hydraulic and quality conditions with those
observed In the prototype. The ability to simulate tidal characteris-
tics such as stage, phase, and flow was tuwesttgated together with
Its ability to adequately represent such quality considerations as
salinity Incursion, repulsion, and the dispersion of a pollutant fro, a
34
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point source. Numerous verification studies on the San Francisco Bay
system were made by WRE prior to FWQA acceptance of the models; the
results of these studies are not included here. This discussion is
limited to additional studies by FWQA.
Hydraulic Model Verification
The extent to which the hydraulic model can be verified is largely
dependent on the availability of measurements of prototype behavior.
For the system under consideration there are extensive records available
from many permanently Installed tidal stage recorders throughout the
Bay-Delta system. There have also been limited investigations by various
local, State, and Federal agencies for determining specific hydraulic
characteristics such as tidal flows in certain channels or flow splits
between key channels of the Delta. Other sources of information on the
hydraulic behavior of the Bay and Delta are the Tide Tables and Current
Tables published annually by the Coast and Geodetic Survey.
The historical periods suitable for verification purposes are
limited to those periods where hydraulic and quality data are both
adequate. In particular the periods of July 1955 and September 1955
were selected to demonstrate the model’s ability to simulate salinity
incursion (July) as well as salinity repulsion (September). Although
a part of the required historical input data for the hydraulic model
(river flows, tidal conditions, exportatlons) were available on a daily
basis, other data were available only on a monthly basis (agricultural
consumptive use and evaporation). Thus mean monthly hydraulic condi-
tions were used for the two months In question.
Tidal conditions for the two months were obtained from actual tidal
records maintained by the Coast and Geodetic Survey for the Golden Gate
station. The mean tide for each of the two months was computed on the
basis of averaging each of the four stages of the tide (higher high,
lower low, lower high, and higher low). Similarly the average durations
of rise and fall were computed for each of the four stages. The daily
recorded tide during the period in question which most closely approxi-
mated this “mean” tide was chosen as the actual input tide. This tide
was then projected to the model boundary at the entrance to San Pablo
Bay (Point Orient) using the Tide Tables. The tides imposed at the
model boundary for the July and September 1955 hydraulic runs are
Illustrated In Figure 4.
Municipal and industrial diversions and waste water returns for
the two months in question were obtained from published data [ 12, 13,
14, 15]. Streamflows, exportations, and agricultural diversions and
return flows were obtained from publications of the California State
Department of Water Resources [ 16, 17]. Precipitation and evaporation
data from U. S. Weather Bureau publications and from a published re-
port of the U. S. Army Corps of Engineers [ 18] were used for determining
the net evaporation loss from the system for the two months. A suninary
of the hydraulic inputs to the system indicated levels of net Delta
35
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‘U
L
LU
‘it
FIGURE 4.
3
2
0
—I
—2
—3
3
2
I
0
—I
—2
—3
TIDAL INPUTS AT SEAWARD BOUNDARY--SAN FRANCISCO BAY-DELTA
July, 1955 Input Tide ( Point Orient)
DATUM
0 3 6 9 2 ‘8 2’ 24 27
TIME — HOURS
September) 1955
Input Tide (Point Orient)
0 3 6 9
TIME —HOURS
2 ‘5 18
27
36
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outflow (past Ctiipps Island) of 1570 cfs for July 1955 and 5540 cfs for
September 1955.
Results of the 1955 July and September runs indicated excellent
agreement between model predictions and prototype data. To illustrate
the model behavior the results of the July 1955 and September 1955 runs
for several stations are presented in Figures 5 and 6.
In addition to the tidal stage and phase comparisons, it was
possible to r ake comparisons between net flows in certain Dclta channels
as predicted in the model with prototype net flows as predicted by
relationships developed by the California Deoartment of Water R-
sources [ 19]. These comparisons are sun ariz d in Table 2.
TABLE 2. NET FLOWS IN DELTA CHANNELS
July
1955
Sept. 1955
DWR
FWQA
DWR
FWQA
Prediction*
Model
Prediction*
Model
(cfs)
(cfs)
(cfs)
(cfs)
Sac. River @ Sac.
8990**
8990**
9841**
9841**
Sutter Slough
1550
1539
1750
1811
Steamboat Slough
820
670
1000
795
Delta Cross-Channel
2950
2916
3100
3177
Georgiana Slough
1850
1561
1950
1755
*Empjrical relationship **Specified
Quality Model Verification
Three separate studies were made with the quality program for pur-
poses of additional verification. Two of these involved simulation of
quality changes during historic periods (July 1955 and September 1955).
The third study involved the simulation of a continuous tracer release
from a point source.
Salinity Incursion and Repulsion . The projected increase in
export and consumptive use of waters normally flowing to the Bay-Delta
system has raised questions about the adequacy of the proposed minimum
flows. The relationship between Delta outflow and salinity levels in
the western Delta and the historical significance of salinity incursion
made it essential that the model adequately represent this phenomenon.
Historical periods of seawater incursion (July 1955)and repulsion
(September 1955) were selected for simulation.
37
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• Modsi P, dic$ion
• Proto$ 1 01 ITidTobIt)
.
•
I I I I I I I
) 3 6 9 12 15 18 21 24 27 30
ANTi OCH
• e .
.0
• • f•
I I I I I I I i_ I
o 3 6 9 12 IS 18 21 24 27 30
FIGURE 5.
COMPARISON OF MODEL AND TIDE TABLE PREDICTIONS OF TIDAL STA(E--
JULY 1955
38
4
2
a
e
CROCKETT
S _•
4.
—2
4
S
•e
BE NIC IA
. S
I I
I I
4
2
0
—2
—4
4
2
0
—2
-4
I-
w
U-
IiJ
0
4
U)
0
3 6
9 12
IS
i8 21 24 2730
C OLLI NS Vi LIE
2 .
.
-
.
.‘
0.
—
2
.
•&.
V
0
I I
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I I
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I I P 1
1518 21242730
-4
1 -
LU
LU
U-
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4
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4.
2-
C
I®..
• S
S
.
S
S
.
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4.
2
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w
I 1 I I I L
MOSSDALE BRIDGE
• S S
-2
—4
o 6 9 2 151821242730
HOURS
— .
I I I I I I I
I
o 3 6 9 2 iS 18 2’ 24 27 30
HOURS
-------
I—
w
w
U-
U i
I.-
U)
FIGURE 6. COMPARISON OF MODEL AND TIDE TABLE PREDICTIONS OF TIDAL STAGE--
SEPTEMBER 1955
Key:
P.lodel
®Proto’ype (Tide Table)
4
2
I).
CROCKETT
.
—2
—4
I I I I I I I I
o 3 6 9 2 15 18 21 24 27 30
CO LU N S VI L L E
4
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Ui
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03
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—2
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BENICIA
4-
G
2 - . .0.
0 5 . —
-2-
• S
w
—4
I I I I I • I I I
0 3 6 9 i2 5 18 21 24 2730
ANTIOCH
4.
2 -
: L±’:::®, ,
o 3 6 9 2 ‘5 18 21 24 27 30
MOSSDALE BRIDGE
4-
• . 5 0’ •
0 — S • —
—2
—4
I I I I I I I I I
.
CLARKSBURG
. .
—2
—4
I I I I I I I I J__ J
0 36 9 ‘2 IS 8 21 24 27 30
HOURS
5 6 9 Il iS 8 2’ 24 27 30
HOURS
39
-------
Chloride concentration was chosen as the quality constituent to
represent salinity. Since data were available for only about 30 model
junctions for the initial day of each simulation, initial concentrations
were estimated for the remaining 800 junctions. In general the avail-
able chloride data represented concentrations at slack water following
higher high water. Since slack water does not occur at the same
instant in time throughout the system it was necessary to adjust these
data to values which might have occurred simultaneously. These start-
ing concentrations are extremely important in both simulations as they
determine the mass of chloride in the system at the start of the run.
For both the July and September 1955 runs sufficient data were
available to establish the maximum chloride concentrations at the
seaward boundary. Other data [ 15] indicated the chloride fluctuation
over the full tidal cycle. For both runs the simulation was completed
in three steps: 1) a short initial run to assure proper starting
conditions, 2) a longer run with a given set of boundary conditions
representing the first part of the month, and 3) a final run with a
different set of boundary conditions representing the last part of the
month. This segmentation of each run was desirable since the prototype
chloride level at the boundary increased during July 1955 and decreased
during September 1955. This segmented approach made it possible to
make appropriate changes in concentrations of other inputs, such as the
inflowing streams. Initial chloride concentrations at the boundary
for July and September 1955 are illustrated in Figure 7. After the
first 27 days of the July simulation, the curve representing the
boundary input was incremented upward by 2250 mg/l, while the September
boundary concentrations were incremented downward 890 mg/I after the
first 15 days.
Chloride concentrations in the tributary streams were obtained
from published data (16). Similarly, chloride concentrations in munici-
pal and industrial waste water discharges were available [ 12, 13, 14,
15]. Data for total dissolved solids (TDS) levels in the agricultural
drainage water were converted to chloride concentrations using appro-
priate TDS/chloride ratios [ 17].
Comparisons of model predictions and prototype behavior, at stations
indicated in Figure 8, are illustrated in Figures 9 to 11 for the July
1955 simulatIon and in Figures 12 to 14 for the September 1955 chloride
simulation. The model results are the maximum concentrations predicted
for each day while the prototype concentrations were measured at slack
water following the higher high stage of the tide, except as noted.
The agreement between model predictions and prototype observations
is apparent. In several instances poor initial concentrations contrib-
uted to a slight discrepancy throughout the month. It is obvious from
these figures that the prototype concentrations fluctuate considerably
at most stations. This is caused in part by the continual change in
tidal conditions over the lunar month. The difference between any two
40
-------
I ‘
/
/
DAT1/A /
%
/
/ Tidal Iflout
‘5
/
/ JuIy, 1955
/
/
9 12 l 18 21 24 27
HOURS
16000
000
F
o000 —
/
/
/ I /
‘I
20000
I*000
I$000
1000
FIGURE 7. SPECIFIED BOUNDARY CONDITIONS—-JULY AND SEPTEMBER 1955 CHLORIDE
IN SAN FRANCISCO BAY—DELTA
41
0 3 6
E
I J
0
a:
0
-J
z
()
E
a:
0
-J
C-,
4—
0
Lj
2.0
w
10
• I-
U)
0
4
—. 10 1—
— 2.0
—3.0
4-
a,
a,
U-
I d
w
4
F-
U)
-J
4
0
I-
HOURS
-------
1. Point Orient
2. Crockett
3. Benicia
4. Port Chicago
5. O&A Perry
6. Coflinsville
7. 3- i1e Si. (Sac.R.)
8. Rio Vista
9. Isleton
10. A.ntioch
1.1. 3— i1e Si. (San Joaquin R.)
12. San Ardreas Landing
13. Mossda] e Bridge
FIGURE 8. SAN FRANCISCO BAY-DELTA--COMPARISON STATIONS
Sl S.4*s
U
STATIONS
0 ..d
U
U
N....
U
U
S....., C..,
42
-------
20000 -
10000 LI> “ ‘ lp
0
BENICIA
I I I I
0 10 20 30 40
Prototype
A
I aodes
FIGURE 9.
JULY 1955 CHLORIDE CONCENTRATION HiSTORIES - SAN PABLO
IND SUISUN BAY STATIONS
CROCK ETT
20000 -
10000
E
U i
0
-J
I
C-;
0 tO 20 30 40
PORT CtIICAGO
10000
1000-
WOO I I >
I I
o 10 20 30 40
DAYS
2000
0
$0.0
05A FERRY
0
0 10 20 30 40
DAYS
43
-------
000 COLLINSvILLE 100 3 .$ILE SLOUGH
(SAC.R.)
5000 500
400C 400
3000
300
2000
I000
0 $0 20 30 40 0 FO 20 30 40
U i
0
0
—3
300 RIO VISTA ISLETON
200- $00-
$00 50
0
a 0 20 30 40 0 $0 20 30 40
DAYS DAYS
£ Prototy
Mode4
FIGURE 10. JULY 1955 CHLORIDE CONCENTRATION HISTORIES -- SACRAMENTO
RIVER STATIONS
44
-------
3000 ANTIOCH 12000 - 3 MILE SLOUGH
I SAN JOAQUIN R,)
10000
2000 - $00
1000- 600-
400
I I 0 -
200
0 tO 20 30 40 0 10 20 30 40
E
0
0
-J
X SAN ANDREAS LOG. °° MOSSDALE BRIDGE
U
500
4.OO 200-
300
200 100
to: b, .____ —— -—— ——— —:r1 0
0 10 20 30 40 0 SO 20 30 40
DAYS DAYS
Prototype
Model
FIGURE 11. JULY 1955 CHLORIDE CONCENTRATION HISTORIES —- SAN JOAQUIN
RIVER STATIONS
45
-------
30000 CROCKETT 30000 SENICIA
20000 - 20000
- -p ..pL
10000 10000 -
* • i _______________________________________
0 0 20 50 40 0 10 20 50 40
E
‘ I i
a
0
-I
IS000 PORT CHICAGO 44000 0 5A FERRY
2000
0000
l000C
000 -
4000-
2000
o I I - 0 I I
0 10 20 30 40 0 0 20 30 40
DAYS DAYS
£ Pro$otppt
Uod I
FIGURE 12. SEPTEMBER 1955 CHLORIDE CONCENTRATION HISTORIES -- SAN PABLO
AND SUISUN BAY STATIONS
46
-------
6000 COLLINSVILLE 1500 3 MILE SLOUGH
( SAC.R.)
5000
4000 1000
3000
2000 500
1000
o 1 — 0
0 10 20 30 40 0 10 20 30 40
0
oo RIO VISTA 150 1SLETON
200 100
100- 50 .
t , 0 - - . r .
0 0 10 20 30 40 0 10 20 30 40
DAYS DAYS
Prototype
Model
FIGURE 13. SEPTEMBER 1955 CHLORIDE CONCENTRATION HISTORIES -- SACRAMENTO
RIVER STATIONS
47
-------
60 00- ANTIOCH 00 SAN ANDREAS LDG.
5000
200
3000
2000 100
1000
I i __ j I LH tH H
0 tO 30 40 0 10 20 30 40
£
U4
0
0
300 MOSSDALE BRIDGE
$00 3 MILE SLOUGH
(SAN JOAQUIN R.)
( -I
500
400 200 H
300
ZOO tOO
I00
_____________________________ I I I
0
0 tO tO 10 40 0 tO 20 30 40
DAYS DAYS
£ Pr6to p
Model
FIGURE 14. SEPTEMBER 1955 CHLORIDE CONCENTRATION HISTORIES -- SAN
JOAQUIN RIVER STATIONS
48
-------
consecutive maximum concentrations at a given point is significantly
dependent on the difference in tidal excursions on the days the samples
were taken. Thus even though the overall trend is upward during July,
there are short-term downward trends at many stations. Because the
model uses a constant average tidal condition the model predictions
do not follow these irregular trends. The changes in concentration
predicted by the model generally follow smooth curves.
The most apparent discrepancies between model predictions and
prototype behavior are at Antioch, Rio Vista, and Port Chicago for
the July simulation and at Three-mile S1ough (San Joaquin River), Rio
Vista, San Andreas Landing, and Port Chicago for the September run.
With the exception of the Antioch and Port Chicago stations the model
predictions are somewhat higher than prototype observations. It is
noteworthy that the discrepancies (with the exception of Port Chicago)
occur at stations which are near the salinity front where the salinity
gradient is very steep. A slight horizontal displacement of the grad-
ient can result in a significant change in concentration at such points.
It is at such stations that comparison between model predictions and
prototype observations is difficult in that the prototype observations
fluctuate in accordance with differences in tidal excursion distances
from day to day and any given observation may or may not be indicative
of the general trend at the point. There is also the problem of correl-
ating the actual sampling points in the prototype with junctions in the
model network. Since the model network was generally dictated by
geometric considerations (or, as previously discussed, by the computa-
tional stability criterion) the junction locations do not necessarily
coincide with sampling stations in the prototype. In addition a
sampling station may be located at a particular point because it is
convenient for sample collection. Samples collected at such a point
usually won t be representative of the entire cross-section at that
point. The model prediction for a point, on the other hand, represents
the mean concentration of the completely mixed volume of the network
junction.
The underlying cause of the discrepancies at the Port Chicago
station is not known with any certainty. Improper initial conditions
for much of Susuin Bay may be responsible. For example, it can be noted
in the July comparison that the model predictions decreased during the
initial ten days and then increased through the remainder of the month,
a phenomenon that could result from an improper initial chloride
distribution in the embayment portions of Suisun Bay.
For studies such as these, wherein historic conditions are being
simulated, the specification of starting concentrations for the initial
day of the simulation can present significant problems. For the July
and September runs prototype observations were available for only a
very limited number of stations in the system and for a specific tidal
stage (generally at higher high slack water). From these extremely
limited data the initial chloride distribution for the entire system
was estimated. Since only a small area of the estuary is at higher
49
-------
high slack water at any instant it was necessary to adjust the slack
water observations at most stations to the tidal phase which would
exist at that point at the start of the simulation. The problem was
thus one of estimating the initial conditions for the entire system
such that the higher high slack water concentrations predicted by the
model during the initial day of the simulation matched the observed
prototype concentrations for the initial day of the period. Even if
this criterion is satisfied there is no real assurance that the starting
concentrations are correct since there are large areas for which no
comparison is possible. Although the Initial conditions specified in
areas far removed from the comparison stations have little effect on
the model predictions for the initial day of the simulation they may
have significant effects later. This is illustrated in Figures 15 and 16
wherein the July and September 1955 chloride simulations are compared
for two different sets of starting concentrations. For both the July
and September runs the starting concentrations originally specified
(labeled model #1) were adjusted and the simulation repeated (labeled
#2). Generally the adjustments were confined to areas near stations
at which the above criterion was not met (i.e., where the predicted
maximum concentration for the first day of the simulation did not match
the observed prototype value). Other adjustments were made in the em-
bayment portions of Suisun Bay and in areas of the Delta wherein no
prototype data were available since It was in such areas that the
original chloride distribution was specified with the least confidence.
The adjustments were relatively minor and the resulting chloride dis-
tribution was considered as probable as the original.
Significant differences in model predictions at several stations
are noted for both months. For the July runs the predictions for the
rerun more closely match prototype behavior (with the exception of the
Autioch station). The rerun for September resulted in improvements at
some stations but inferior predictions at others. The predictions
could probably be further improved at many stations with additional
refinement of the initial conditions.
In light of the many problems associated with comparisons of
model and prototype behavior discussed above, the July 1955 and Septem-
ber 1955 chloride runs were considered satisfactory verification of
the model’s ability to simulate salinity Incursion and repulsion.
Tracer Release Simulation . In the fall of 1966 the (then) FWPCA
Central Pacific Basins Project conducted a field study of the dispersion
characteristics of Sulsun Bay and the western Delta. Primary purposes
were to investigate the fate of agricultural waste water consituents
which might be discharged near the Antloch Bridge by the proposed San
Joaquin Valley Drain and to develop data for model verification purposes.
The study was designed to determine both the rate of increase in tracer
concentration at various locations within the study area resulting from
discharge of tracer over an extended period, and the concentration which
would be attained at steady state. The California Department of Water
Resources cooperated In this study.
50
-------
3 MILE SLOUGH RIO.VISTA
SAC. N.)
400
— 200
300
200
100 —
100
II oL1 I
0
0 (0 20 30 40 0 10 20 30 40
ANTIOCH SAN ANDREAS LDG.
a.
E 200( 400
I i i
1000 300
200
—
l00
U
0 I I I
0 10 20 30 40
DAYS
3 MILE SLOUGH
(SAN JOAQUIN N.)
•00 Model
Model
600
— ProIoty e
400
200 . ._, . . . . . . . . ..P I
0
0 10 20 30 40
DAYS
FIGURE 15. EFFECT OF INITIAL CONDITIONS ON MODEL PREDICTIONS --
JULY 1955 CHLORIDE
51
-------
PORT CHICAGO
0 &A FERRY
-L I
o 10 20 30 40
ANTIOCH
I I _I
o 10 20 30 40
COLL.INSVILLE
IN
5000
6000
4000
2000
0
400 -
300
200
I00
I I I I
0 10 20 30 40
3 MILE SLOUGH
(SAN JOAQUIN RJ
0 JO 20 30 40
D ÀY S
*1
Model
Model
Proto tyoe
I 4 1
0 tO 20 3O 40
DAYS
FIGURE 16. EFFECT OF INITIAL CONDITIONS ON MODEL PREDICTIONS --
SEPTEMBER 1955 CHLORIDE
10000
5000
‘ 1 •
— —
E
U
a
0
-J
C)
4000
3000
2000
1000
0
4000
3000
1000
52
-------
Experience with the mathematical model and the Corps of Engineers
Bay Model indicated a minimum of three weeks release was necessary to
build up tracer concentrations to the point where they could be extrap-
olated to steady state concentrations. The release period was scheduled
from HHWS on September 20, 1966 at 2232 POT to HHWS on October 12 at
0420 POT, a total of 21 days, 5 hours, and 48 minutes. Using an 18
barrel supply, the discharge rate would be 56.1 nil/mm.
The tracer was released at the Antioch Bridge pier from 55 gallon
drums equipped with constant flow rate devices. When used with air-
tight, rigid wall drums, these devices maintain a balance between
atmospheric pressure and the negative pressure within the drum such
as to produce a constant flow rate despite the changing depth of liquid
in the drum. By using two 55 gallon drums it was possible to maintain
an almost uninterrupted flow while replenishing the dye supply from the
manufacturer’s plastic barrels. The discharge point was about three
feet below the water surface at mean lower low tide. The actual flow
rate was monitored on both daily and instantaneous bases. An estimate
of the daily rate was made from the frequency with which the 55 gallon
discharge drum was filled. The daily rate of discharge was approximately
constant at an average of 0.85 barrels a day. Measurements of instan-
taneous flow rates with a graduated cylinder indicated a diurnal
fluctuation of up to 50 percent above or below the average flow rate.
During the first 18 days and 10 hours of the study, a total of
15.5 drums of dye, at 250 lbs. apiece, was discharged. This averaged
55.9 ml/min for the period, as compared with the 56.1 ml/min flow rate
calculated prior to the test. On the 19th day of the release a com-
plete stoppage of undetermined cause occurred, which lasted 10 hours
before being detected. For the remainder of the release period, or
2 days and 11 hours, an average rate of 50.1 ml/min was maintained.
This represented an additional 2.9 barrels, making a total of 17.4
barrels of dye discharged to the system.
Tracer concentrations were observed in the principal channels at
slack water using G. K. Turner Model III Fluorometers mounted in two
boats. Continuous records were obtained from Fluorometers at the
Antioch Bridge and the Contra Costa Canal Pumping Plant intake. After
the discharge of tracer was stopped on the 21st day, measurement of
tracer concentration continued with lesser sampling frequency for about
five weeks, at which time the observed concentrations were little above
background. The study area in which the movement of tracer was moni-
tored is shown in Figure 17.
If the rate of tracer injection, tidal dispersion characteristics,
net advective flow, length of the tidal excursions and system geometry
were all constant, the concentrations measured at the same stage of the
tide at a given station would produce a smooth cumulative concentration
history. This result is obtained with the usual mathematical or physi-
cal model. In the prototype study, however, only the dye injection
rate, the geometry of the system, and the distance from the release
53
-------
LEGEND
Som.uinq Stot on
.
VALLEJO
RIO vi$T*•
CM
MARTINEZ
P0 IN?
PITTSBURGH
ANT I CC H
Tracer Discharge Point CAIAL
at Antloch Bridge
FIGURE 17. STUDY AREA WITH TRACER SAMPLING STATIONS -- SAN FRANCISCO BAY — DELTA
-------
point to the observation station were constant. The hydrodynamics and
hence the dispersion processes at each station were continually changing
in response to variable tidal excursion distances, fluctuations in
fresh water inflow, and progressive transitions in tidal stages. The
result was somewhat unordered station histories and longitudinal pro-
files. The section of the study area in which the most erratic station
concentration histories occurred lay within an average excursion
distance up and downstream from the release point at the Antioch Bridge.
Beyond an excursion distance the observed station histories more closely
approach the idealized concentration histories.
The Continuous, point discharge of dye resulted in local areas of
high concentration near the release point at slack water. The areal
extent was such that high concentrations were observed frequently at
the intake of the Fluorometer mounted on the Antioch Bridge, at a
distance of about 200 feet. However, after the next running of the
tide the dispersion of this patch of high concentration was such that
no tracer peak was observed at the next slack. Such peaks apparently
do not survive the dispersion effects during the tidal excursions but
instead reinforce a single cumulative peak. The longitudinal profiles
show slight irregularities superimposed on this cumulative peak but
It was not possible to identify these as the result of specific slack
periods.
The observed concentrations near the release point at the Antioch
Bridge are presented in Figure 18. High concentrations associated with
the spread of tracer at slack water have been excluded. Also shown
are the concentrations computed by the mathematical model as will be
discussed subsequently. The erratic variations in prototype concentra-
tion should be noted. As would be expected concentrations tend to
increase during the period that tracer was discharged but decrease
rapidly after the tracer was stopped on the 21st day. The maximum
concentrations on the 17th day were observed between IH and HL tides,
which corresponds to the shortest excursion during the release period.
The concentration histories for several locations in Suisun Bay
and the western Delta beyond a tidal excursion distance from the re-
lease point are presented in Figures 19 to 21. Concentration profiles
along the ship channel in Suisun Bay on the 19th and 20th days of the
tracer release period are presented in Figure 22. Included on these
figures are the concentrations predicted by the mathematical model as
discussed below.
The mathematical model was used to predict the concentration
histories resulting from the introduction of a tracer under the
conditions experienced in the prototype study discussed above. The
model was applied consecutively as follows:
55
-------
100-
eo -
60
40
20 -
0
DAYS
40
‘(-
Observed Mèpiimum
40 - Computed Minimum
20 - —
S. ---
0 I I I 1 D b _ I ) . —
0 5 10 IS 20 25 3o 35 40
DAYS
FIGURE 18.
OBSERVED AND COMPUTED MAXIMUM AND MINIMUM TRACER CONCENTRATIONS
AT ANTIOCH BRIDGE
56
Observed Moximun • .
Computed Maximun —
I I I • I
z
0
a.
U)
I-
a
U)
z
0
1-
I-
z
‘Ii
( .1
z
0
U
ia
>
I-
4.
-J
“a
0 5 10 15 20 25 30 35
-------
BUOY H5H
I B. ni ci o
10 - -
5—
z 1 T TT I
o I
0 4 S It 1 5 20 24 2 5 32 31 40
DAYS
I,
BuOY “14”
(Roe Is.)
I0 -
0
—-------
— — I.
— A
0 — — .—
—— A
— —
., £ I
O 4 S 2 6 20 24 25 32 36 40
DAYS
0 Observed o LLWS
A Observed ol IIHWS
- Computsd for LLWS
CornOuted for HI4WS
FIGURE 9.
TRACER CONCENTRATiON HISTORIES AT SELECTED STATIONS
IN SUISUN BAY
I-
SI
4.
I -
0
0
I-
4
z
w
U
z
0
U
57
-------
15
I0
BUOY ‘22” 0
(UCAvO 1 )
0
— — — — — —
— — —
5- ‘ U4 0 4L
—
—
p I I .AI I I I
0 4 12 IS 20 24 26 32 36 40
DAYS
20
• 13
0 -
5
0 4 6 12 IS 20 24 26 32 36
DAYS
o Observed c i LLWS
.a Observed at HHWS
Computed for LIWS
Ccmpute for HHWS
FIGURE 20. TRACER CONCENTRATION HISTORIES AT SELECTED STATIONS
IN SUISUN BAY
40
0
S
a
(Chippi Is)
BUOY “25”
z
0
I-
I-
z
I-,
z
0
I
0
0
0
0
0
0
0
— - — -
LN — — 0 “
4 LH
0
I I I I I
58
-------
30
o0
0
0
A 0
A
LH
•
o
0
B uQY “S C
(CoIF,nsvjlle)
0
AA,
i
I
I
I
4
5
12
15
20
24
25 32 36
40
.
LIGHT li5•I
It &i’ t Yorit Slough I
.
0
0
0
1 .A
0
0 0
.A
.
—
A
LH A
—
—
0
A
—
4
5
12
I I
20
24
21 32 36
-
—
——— BUOY”25”
A (Son Joochim RI
‘
‘
/
.
A ¶4
¶4
-
¶4
A
-
.
‘
A
A
-
0 0
i __ j
OL
0 S 2 6 20 24 2* 32 36 40
DAYS
0 Obs•rvod at LLWS
A Obs.rvld *t HHWS
CoMOuted for LLWS
- CoII puted to’ HH*S
FIGURE 21. TRACER CONCENTRATION HiSTORIES AT SELECTED STATIONS
IN WESTERN DELTA
0
0
0
0
0
I0
0
40
30
20
C
0
C D
4-
a,
0.
4-
a
0
z
0
4
I-
z
U i
0
z
0
C-)
10
I ’
40
30
to
I0
59
-------
z
0
I—
I,-
z
V
0
V
20
I,
I0•
5.
0
0 4 8 2 16 20 24 28 32 36
DISTANCE,1000 YARDS
FIGURE 22. TRACER CONCENTRATION IN SHIP CHANNEL -- BENICIA TO COLLINSYILLE
60
C
0
m
0
b
‘I
I
‘I
¼
¼
b
/
-
F
A A
.--.
e-. -a
I I
Observed at LLWS 1 l9thond 20th days
_____ ObsCryCd t HHWS ,I9th day
Computed to ’ LLWS 1 2Oth doy
Computed for HHWSZOth doy
I I
-------
1. Ten days of tracer addition with mean September hydraulic
conditions.
2. Eleven more days of tracer addition with mean October
hydraulic conditions.
3. Twenty-one more days with mean October hydraulic conditions
without addition of tracer.
Hydraulic input was based primarily upon measured inflow to the Delta,
estimated Delta consumptive use, and typical municipal and industrial
waste discharge rates. A tracer loss rate of 3.4 percent per day was
assumed based upon a previous study under estuarine conditions [ 20].
The predicted tracer concentrations together with the prototype
observations were presented in Figures 18 to 22. The prototype
concentrations were observed at slack water following the higher high
and lower low tidal stages except as noted in the figures. The back-
ground fluorescence, determined prior to the tracer release, was sub-
tracted from observed prototype concentrations.
The model predictions presented are the maximums and minimums
over the tidal cycle and do not necessarily correspond to slack water
conditions since, at points within a tidal excursion up and downstream
from the re1eas point, the maximum and minimum concentrations do not
necessarily occur at slack water.
Figures 18 through 21 indicate generally good agreement between
model predictions and prototype observations. At most stations good
agreement was obtained for both higher high water slack (HHWS) and
lower low water slack (LLWS) conditions. Figure 22 indicates the
model prediction of the longitudinal distributions of tracer in the
main channel of the system closely matches that observed in the proto-
type with agreement generally improving with distance from the release
point. This is expected since the concentration gradients are generally
most pronounced near the release point and the observed slack water
concentrations at a station are strongly influenced by the varying
tidal excursion distances from day-to-day. At stations farther removed
from the release point where concentration gradients are relatively
flat the tidal effects are much less pronounced.
In some instances the prototype observation stations do not coin-
cide with model prediction points (network nodes). In such cases the
network node nearest to the prototype observation station was used.
In areas with pronounced concentration gradients the model predictions
at such stations may be consistently biased either upward or downward.
This problem is illustrated in Figure 23 which indicates the position
of a prototype station (Buoy 22) relative to the three nearest network
nodes and compares the model predictions for the three nodes with the
prototype observations.
61
-------
FIGURE 23.
S
a
a
Q.
a
0.
z
0
I ,..
I .-
z
w
z
0
U
15
ILLUSTRATION OF COMPARISON DIFFICULTIES DUE TO NONCORRESPONDENCE
OF OBSERVATION AND PREDICTION POINTS
SAMPLING STATION
BUOY “22”
REDICT%ON POINT
o PrototyDe LL.WS
P,o4ot ,oe HI4WS
Compufed for LLWS
- Corn puf d for 14HWS
10
I I
4
.
£LN
A
5 10 IS 20 25 30 35 40
DAYS
62
-------
As indicated earlier two different hydraulic conditions were
utilized for the model simulation. Although the measured inflows
and pumped exportations remained relatively constant throughout the
study period, other hydraulic losses such as evaporation and agri-
cultural consumptive use were undoubtedly decreasing through the period.
The net outflow from the system would correspondingly increase under
such circumstances and increase the rate of flushing from the system.
This would not be reflected in the model predictions since the hydraulic
conditions utilized by the model remained constant throughout the last
eleven days of the tracer release period and the entire twenty-one
days of the washout period (following the tracer shutoff).
The effect of the hydraulic conditions on the model predictions
can be noted in Figures 18 through 21. The net outflow (past Chipps
Island) was increased approximately fifteen percent (from 5540 cfs)
following the initial ten days of the release. There is little apparent
effect at the stations in Suisun Bay but at stations in the western
Delta the rate of buildup of tracer during the initial ten days of the
release period is significantly different than that during the next
eleven days. This may indicate the effects are attributable more
to the balance of flows between the Sacramento and San Joaquin Rivers
for the two parts of the simulation than to the combined net increase
in outlow. The stations not apparently affected are in Suisin Bay,
downstream from the confluence of the two rivers.
Most of the increase in outflow resulted from a 51 percent increase
in the net downstream flow of the San Joaquin River (from 1372 cfs)
with only a minor increase (two percent) in the net downstream flow in
the Sacramento River. The stations most affected are Buoy 25 on the
San Joaquin River, Buoy SC at the confluence of the two rivers, and
the station near the release point at Antioch Bridge on the San Joaquirt.
Another factor which may affect the comparison is the tracer loss
rate utilized for the simulation. As indicated previously the loss
rate specified (3.4 percent per day) was determined from data gathered
in a tracer study on the Potomac River in which a mass balance was
maintained over a period of 20 days following the release. For that
determination all tracer not detectable was assumed to contribute to the
loss rate computed. This included tracer at a concentration below the
lower limit of the detection instrument; therefore the computed rate
was undoubtedly somewhat above the actual loss rate.
Limited laboratory studies by FWQA indicated an overall loss factor
between one and two percent per day. This is consistent with estimates
obtained from earlier experimental work with Rhodamine WT dye conducted
by the Chesapeake Bay Institute [ 2fl.
The significance of the tracer loss rate specified for the model
simulation is illustrated in Figure 24. The model simulation was
conducted with two different decay rates, as indicated. Generally the
utilization of the lower loss rate (1.7 percent per day) resulted in
63
-------
‘U
25
20
15 -
JO.
5
0
0 3
0 Observed at LLWS
HHWS
LLWS
HHWS
£ Observed 01
— omeuted to’
(Omouted for
FIGURE 24.
EFFECT OF SPECIFIED TRACER LOSS RATE ON MODEL PREDICTIONS --
SAN FRANCISCO BAY-DELTA
64
BUOY “SC”
(COLUNSVILLE)
0
0
0
0
0
— -.& ..
0
A
0
AA
LH O
C
0
0
a.
z
0
I-
I-
z
Iii
‘I
z
0
U
3.4 per cent
per day
I I I I
10 IS 20 2 5 30 35 40
TIME, DAYS
0 S 10 IS 20
DAY $
25 30 35 40
-------
predictions above those observed in the prototype, particularly during
the washout period of the Study. Because of the aforementioned un-
certair.ty of the prototype hydraulics during the latter part of the
study it is difficult to evaluate whether such discrepancies are due
more to the loss rate specified, the hydraulics of the system, or to
the model structure. A discussion of the significance of other para-
meters (which are associated more with the model structure or general
behavior rather than with a particular constituent or study) affecting
model predictions is included in a later section.
In view of the many factors affecting and complicating a compari-
son of this type the agreement between model predictions and prototype
behavior for this study is considered very good.
SAN DIEGO BAY
The dynamic estuary model was applied to San Diego Bay by FWOA
as part of the Vessel Pollution Study of San Diego Bay, California [ 5].
The model was utilized in this study to predict coliform distributions
resulting from the U. S. Naval Fleet anchored in San Diego Bay. The
Bay is illustrated in Figure 25.
San Diego Bay was characterized by a two-dimensional network of
112 junctions (nodes) connected by 170 channel elements (links). The
entire Bay was modeled including the channel 1 1/2 miles seaward of
Ballast Point.
Hydraulic Verification
The ability of the model to simulate the hydraulic behavior of
San Diego Bay was demonstrated by comparing the tidal stages at points
within the Bay predicted by the model with those predicted using U. S.
Coast and Geodetic Survey Tide Tables. For this study the tide imnosed
at the seaward boundary (Point Loma) was representative of a mean annual
tidal condition in the Bay. Other significant hydraulic inputs included
evaporation (78 cfs), which was distributed uniformly over the Bay, a
diversion to the salt ponds in the South Bay (2.6 cfs), and a cooling
water diversion and return (646 cfs). A Manning’s roughness coefficient
(n) of 0.018 was assumed for the entire Bay. The solution for dynamic
equilibrium was obtained using a time step of 50 seconds.
The comparison of predictions at two points is presented in
Figure 26 together with the specified tide imposed at Point Loma.
Quality Verification
Few existing data were available on the distribution or dispersion
of a water quality constituent through San Diego Bay. To help define
the dispersion characteristics of the Bay and to provide data for use
65
-------
North lslo.id
Selloit Pdnt
-o
-1
SAN DIEGO
9 1090
TA D l
I
T racer
ReIö s.
LEGEND
o • somIie roars
4$_s
i.qe ssqm• ti used for
model verificoflon
FIGURE 25. STUDY AREA WITH TRACER SAMPLING STATIONS
SAN DIEGO BAY
66
S
0
‘.4
0
I”
z
-------
3
a
0
— I
—2
—3
0
a
0
—I
—2
—3
0
• Model
O Tide Tobles
MOdil Dotum = MSL
FIGURE 26. COMPARISON OF MODEL AND TIDE PREDICTIONS OF TIDAL
STAGE -- SAN DIEGO BAY
61
.
I
S
.
•
S
.
S
1
II
I
20
I
24
2 1
0
4-
a,
a,
U-
0
UJ
-t
4
U) 2
3
0
Broadway
S
.
.
S
.
S
.
.
c .
•
.
-
I
S
S
S
S
V
•
.Q .
-
.
.
‘p
.
I I
I
I_________
I
0
4 I
2
II
20
24
2 1
I
NotiOnol City
SO.
5
I
0
S
S
•
S
I
.
S
.
I
S
S
•®e
.
-
S
-
S
0
I
I
I
I
I
0
4 S 12
H OUR S
6 20 24 ZS
-------
in verification of the mathematical model, a 15-day continuous release
of Rhodamine WT Solution was made from the end of Pier 3 in the U. S.
Naval Station as indicated in Figure 25. Histories of the buildup and
subsequent decline of dye concentration at various points in the Bay
were prepared from these data. This tracer release was then simulated
with the mathematical model and a comparison made between the model
predictions and the field observations (Figures 27 to 30). For this
simulation the dye was treated as non-conservative with a loss rate of
3.4 percent per day, similar to that rate determined by a study of
the Potomac River estuary [ 201. Background concentration specified
at Point Loma corresponded to field observations. The prototype data
illustrated in these figures indicate significant fluctuation in con-
centration from one sampling time to the next beyond what would be
expected from the long-term change in concentration. This is due in
part to the continuously chanqing hydraulic conditions in the Bay re-
sulting from wind induced currents and changes in tidal conditions.
In areas with pronounced gradients, the concentration at any point is
strongly influenced by tidal excursions, and variation in excursion
yields erratic station histories. However, the mathematical model used
a recurring mean tidal condition with identical tidal excursion distances
for every tidal cycle. Thus, no attempt was made to simulate these
day to day fluctuations of the prototype but only the mean change in
concentration. In addition the prototype concentrations are represen-
tative of only a relatively small volume of water at the sampling point.
The model predictions on the other hand represent the mean concentration
of the volume of water represented by a network junction, which might
typically have a surface area one-half mile square. Other factors
perhaps introducing difficulties into the simulation are the uncertainty
of the loss or decay rate of the dye in the prototype, the level (and
origin) of background concentration, and the question of whether the
Bay is indeed vertically unstratified.
The effect of the dye loss rate specified for the simulation of
the San Diego Bay tracer study is illustrated for selected stations
in Figures 31 and 32. The dye was treated as a conservative constituent
(zero loss rate) and was decayed at the rates of 1.7 percent per day
and 3.4 percent per day, as indicated. It can be noted that the model
predictions utilizing a 1.7 percent per day loss rate follow the pro-
totype observations more closely than did the comparable rate for the
San Francisco Bay study. Because there are a very limited number of
significant hydraulic inputs to San Diego Bay as compared to San Fran-
cisco Bay there is much less uncertainty in the hydraulic conditions
specified for the San Diego Bay simulation. The comparisons of the
two dye loss rates may therefore be somewhat more meaningful for the
San Diego Bay study than for the San Francisco Bay system. Wherein
the 3.4 percent rate resulted in the most favorable comparison for the
San Francisco Bay study the comparison for San Diego Bay does not
indicate conclusively which rate gives the better comparison.
68
-------
7.0
6.0 -
5.0 -
4.0 -
3.0 -
ao
1.0 -
0 ID
15 20 25 30 35 40 45 50 55
DAYS
4 Prototype
- Prototype
Model IL
— — Model NH
LL Slack
NH Slock
Slack
S [ c
FIGURE 27. TRACER CONCENTRATION HISTORIES -- SAN DIEGO BAY
69
C
0
0
cn
a
a-
L
0
( ii
0
RANGE 0 Section I
(StatIon 0- I )
0
I I I
00
00
,-
I-
i ..
0 0
z
U. ’
I . ’
a
U
60
-------
à Prototype
0 PrOtOtype
— Model LL
—— ModsI HH
FIGURE 28.
TRACER CONCENTRATION HISTORIES - SAN DIEGO BAY
70
C
0
I - .
0.
U)
0
0
a
U
z
0
U
t j
0
0 AYS
IL Slocli
HH Slock
Stock
SI oc k
-------
I :o1oly ,
O PrOtOlyDS
— I odeI LI.
——Model 14K
FIGURE 29. TRACER CONCENTRATION HISTORIES -- SAN DIEGO BAY
C
0
0
4-
I ..
0
0
U
z
0
U
lsJ
>
0 5 10 IS 20 25 )0 )5 40 45 50 55
0 5 JO 15 20 25 50 55 40 45 50 55
DAYS
LL Slock
NH Slick
Slock
Sloc
71
-------
4.0
3.0 -
2.0
1.0
5.0 -
-
0 5 JO Is
3.0 -
2.0•0
zo 25 30 35 40 45 50 55
RANGE 4S Section 3
(Sfdtlon 4S—3)
Q
I I I I
0 5 10 IS 20 25 30 35 40 45 50
DAYS
1.0 -
A Prototype
0 Prototype
—Mod.I LL
——Modil HH
LL Stock
HH Slack
Slack
Slack
FIGURE 30. TRACER CONCENTRATION HISTORIES -- SAN DIEGO BAY
N.
N.
iiiO
0
RANGE 4N—SeCt iofl 2
(Statron 4N-2)
E l
I _ a I I I I -
C
0
0.
0
a-
z
0
U
IAJ
0
0
0
A
/
NI
I ..
0
N.
N.
I-
3
I I
72
-------
C
0
a,
U)
4-
I-
a
a-
L)
2
0
L)
w
0
F-
7.0
6.0
5.0
4.0
3.0
2.0 -
10 -
0-
o 40 50
DAYS
A PrOtOtype LLSlack
• Prototype liii Slack
Model U. Slack
—— Model HH Slock
FIGURE 31. EFFECT OF SPECIFIED TRACER LOSS RATE ON MODEL PREDICTIONS --
SAN DIEGO BAY
RANGE 0— Section 1
Conservo tive
L7 /o per Day
3 .4°/s per Day
A
I i .
I . .
0
S
20 30
73
-------
5.0
C
0
0.
4-
a-
C)
z
0
C)
w
C-)
4
I .-
£ Protof D• LI Slack
• PrototVpe HH Slack
— Modal LL Slack
— — Model HH Stbck
FIGURE 32. EFFECT OF SPECIFIED TRACER LOSS RATE ON MODEL.
PREDICTIONS -- SM DIE$O BAY
4 O
2.0
1.0
0 5 10 15 20 25 30 35 40 45 50
DAYS
74
-------
The results of both hydraulic and quality simulations lead to the
conclusion that the model is adequate to represent dispersion phenomena
in San Diego Bay and permit comparison of various water quality manage-
ment plans.
LINEAR ESTUARY AND SENSITIVITY STUDIES
In addition to the verification runs discussed previously, several
studies were conducted on the San Francisco and San Diego Bay systems
and on an idealized linear estuary to determine the sensitivity of the
hydraulic model to parameters such as time interval, network scale,
and Manning “n” values and of the quality model to such parameters as
time interval, network scale, diffusion coefficient, and the solution
technique for advective transport.
Hydraulic Model
Time Interval and Network Scale . The time interval used in the
hydraulic solution and the lengths assigned to channel elements of the
network must satisfy the stability criterion discussed in Part I.
While the time and space scales can be selected with a certain degree of
flexibility the range of choice may be limited by the geometry of the
prototype and/or the degree of detail desired. To minimize computation
time the time interval should be as large as possible; however, the
stability criterion dictates a sacrifice in network detail (i.e., in-
creasing element lengths) as the time interval is increased. Studies
on an idealized linear estuary indicate that, for a given network, time
intervals below the allowable maximum have little affect on the pre-
dicted hydraulic behavior of the system. Similarly, for a given time
interval, increasing the lengths of the channel elements (modeling the
idealized estuary with fewer elements) has little effect on the predicted
channel velocities and junction heads. It must be kept in mind, however,
that this analysis was conducted on an idealized system with no branch-
ing channels such as occur in real systems. In real systems there is
obviously a restriction on the maximum channel lengths since they may
be dictated by the geometry of the system.
Manning “n’ Values . The network configuration characterizing
the San Francisco Bay system was originally developed as three separate
networks, one for the Delta area, another for Suisun Bay, and a third
for San Pablo Bay. Each was tested independently before the three were
linked into a single network. The initial hydraulic verification run
on the combined network indicated several discrepancies between model
predictions and prototype behavior, particularly in the area of the
confluence of the Sacramento and San Joaquin givers in the western
Delta. The predicted tidal range at stations in this area significantly
exceeded the tidal range experienced in the prototype. It was not
possible to determine the exact cause of the discrepancies but additional
studies indicated the hydraulic solution to be rather insensitive to
75
-------
changes in the model network layout but quite sensitive to changes in
channel roughness coefficients.
The model structure does not account for energy losses due to
changes in momentum at junctions. At major junctions, such as at the
confluence of the Sacramento and San Joaquin Rivers, where the streams
meet at essentially a right angle, it is possible to compensate for the
momentum energy loss through increased friction losses. For the case
in question the roughness coefficients in the channels entering such
junctions were increased with significant results as illustrated in
Figure 33. Typically the values of the Manning coefficients were
increased from values around 0.025 up to values of 0.050 at the extreme.
Quality riodel
The effects of varying the quality time step, the network scale,
the dispersion coefficient, and the method of advective transport can
be evaluated separately; howeve” the effects may or may not be independ-
ent and the net combined effect may be difficult to predict from inde-
pendent sensitivity analyses on the various parameters. While it is
possible that a single criterion which would define the optimum combina-
tion of time interval, network scale, diffusion coefficient, and method
of advective transport exists for the quality program, no such relation-
ship has yet been developed. Because the criterion would also have to
be compatible with the hydraulic stability criterion discussed previously,
the definition of such a relationship is not likely to be simple.
Time Interval and Network Scale . Because the quality program util-
izes the identical network used in the hydraulic solution it is not
possible to independently alter the network scale. A new hydraulic
solution must be obtained for each different network layout desired.
In studies utilizing the idealized linear estuary wherein the number of
network nodes and channels .o model the system was decreased approximate-
ly two-thirds, the quality predictions for simulated salinity incursion
were not significantly affected although a slight increase in incursion
was noted.
Studies to evaluate the effect of the quality time step have been
conducted on the San Francisco and San Diego Bay systems and on the
linear estuary. Figure 34 illustrates the effect on the concentration
profile at both high and low tide, of varying the time step for the
linear estuary. This study indicates increasing upstream dispersion
with decreasing time steps.
The predicted rate of transport from a point source was evaluated
for the San Francisco Bay system utilizing time steps of one-quarter
and one-half hour. Comparison of model predictions with prototype
observations is presented in Figures 35 and 36. During the initial
period of the release the maximum concentration at a station results
from utilizing the smaller time step. The constituent is moved the
same distance (from one junction to another) regardless of the time step;
76
-------
4 )
4)
LL
U i
C)
C l ,
FIGURE 33.
EFFECT OF INCREASED CHANNEL RESISTANCE ON COMPUTED
TIDAL STAGE AND PHASE
0 3 6 9 12 18 21 24 27
HOURS
77
-------
30
Tide
-J
0
0
0
z
2
I- .
4
1-•
z
Mi
4-)
2
0
4-)
20
10
t 1 -: 15 m*nuses
—— tit; 3Ominutes
— . 4 t 50minubu
3 4 5 6 7 8
RELATIVE DISTANCE
FIGURE 34. EFFECT OF TIME INTERVAL ON INTRUSION IN A SIMPLE LINEAR CHANNEL
9
10
ti
-------
FIGURE 35.
25
20
O Observed
A Obseryed
Computed
— — — Computed
0$ LLWS
ot HHWS
for 1 1W S
for HHWS
BUOY “22
(MC AVOY
‘5
0 -
S
C
0
*
0
S.
0 5 10 5 20 25 30 35 40
z
0
I-
4
I .-
z
4-)
z
0
C-,
DAYS
EFFECT OF TIME INTERVAL ON DISPERSION FROM POINT SOURCE --
SAN FRANCISCO BAY-DELTA
79
-------
25
C
0
Q
0
A.
2
0
I-
I-
2
U
z
0
U
FIGURE 36.
20 -
$5
I0
5
A
Observed at LLWS
£ Observed at HHWS
— Computed for LLWS
Corn Duf•d for IIHWS
EFFECT OF TIME INTERVAL ON DISPERSION FROM POINT SOURCE --
SAN FRANCiSCO BAY-DELTA
80
0
BUOY SC
(Co Iii nsvi He)
0
-0
0
5
I I I t I
tO $5 20 25 30
35 40
0 5 10 * 15 20 25 30 35 40
DAYS
-------
therefore the tracer fronth will progress most rapidly from the release
point utilizing the smaller time step. On the other hand the total mass
of constituent transferred between two junctions during each time step
is greater for the larger time interval, which can result in a more
rapid buildup at a station. This is reflected in Figures 35 and 36
wherein the curves for the one-half hour interval start out below those
for the quarter hour interval for most stations but rise more ranidly
and eventually cross the quarter-hour curves. There are of course,
other complicating factors which affect the shape of the curves, includ-
ing the transfer of constituent by diffusion and the method utilized
to specify the concentration in the advective transport term. These
factors will be discussed subsequently.
The predicted rate of dispersion from a point source was evaluated
on the San Diego Bay system utilizing time steps of one-eighths one-
quarter, and one-half hours as illustrated in Figures 37 and 38 For
this comparison, the tracer was treated as conservative hence no
comparison with prototype observations is included. As for the San
Francisco Bay system the maximum concentrations ‘ere obtained utilizing
a one-half hour time step even though the concentrations for that
time step started out below those for the two smaller steps at most
stations. Because of other complicating factors it is again not
possible to separate out the effect due solely to the tine step.
Diffusion Coefficient . As discussed previously the nuality model
predictions are rather insensitive to the magnitude of the diffusion
coefficient used in the solution. This is illustrated in Tables 3 and
4 which show the effect of increasing the constant used for calculating
the diffusion coefficient (C 4 in eq. 26, p. 22) by a factor of 100
(0.025 to 2.5) for, respectively, the San Francisco Eay and San Diego
Bay systems. As can be noted most of the differences are less than
ten percent in both systems, with larger differences mostly associated
with low concentrations where a small change in concentration represents
a significant percent change. Roundofferror also can influence such
small numbers significantly.
At first glance there is no apparent consistency in the changes
noted in the Tables. However if the location of each station is con-
sidered it can be noted that the higher constant yields higher maximum
concentrations at stations far removed from the release point and in
lower maximum concentrations at stations near the release point. Such
a phenomenon is expected since the higher diffusion coefficient should
result in more rapid transport of a constituent away from the release
point resulting in a lower concentration peak but with higher surrounding
concentrations. The lower diffusion constant should yield a higher
peak concentration at or near the release point but with a rapid dropoff
with distance from the peak.
Solution Technique for Advective Transport . Equation 38 presented
previously defines the mass transfer in a general channel element. This
can also be expressed as:
81
-------
7
T IS
I I _ __I I I
5 10 15 20 25 30 35 40 45
O 5 10 IS 20 25 30 35 — 40 45
Compvt•d Mailmum
—— — ComDvted Minimaim
DAYS
FIGURE 37.
EFFECT OF TIME INTERVAL ON DISPERSION OF CONSERVATIVE TRACER
FROM POINT SOURCE - SAN DIEGO BAY
82
6
T: 30 mm.
RANGE 39 -Section 4
/
4
0
U)
S
0
a-
3
2
7.5
30
5
7 -5
mm.
mm.
01
0
2
0
I—
I-
z
w
U
z
0
U
5
4-
15mm
7.Smi,
3
2
T: 30mm
T: IS mm
7 7 .5m m.
RANGE 2N.-Sethon 3
I I _ J_ _ I I I I I I
AT 15mm
.T: 7.5mm.
-------
4
RANGE 4N-Sect on 2
-I
LST 30 mi. .
T: 15mm
7.5 m in.
0 5 tO
6-
RANGE4S-
iS
20
25
30
35
40
45
-
IS mm.
Section 3
5-
4.
3-
I
I
2-
I
I
I
I
I
I
1
5 to iS 20 25 30 35 40 45
DAYS
Comoutld Mo*imum
———Comouted Minimum
,
/
1=
IS mm.
:
7 5 mm.
:
30 mm
30 mm.
: 1.5 mitt
FIGURE 38.
EFFECT OF TIME INTERVAL ON DISPERSION OF CONSERVATIVE TRACER
FROM POINT SOURCE -- SAN DIEGO BAY
83
3-.
T: IS mm
2-
0
L
— T;3Omifl.
0
1.
U,
0.
I d ,
4-
0
2
0
a:
I-
2
w
2
0
U
-------
*All concentrations predicted utilizing one-half hour time step and 3.4 percent per day
dye loss rate.
Station
Buoy hhl4H
(Roe Is..)
TABLE
3.
Mm.
Max.
EFFECT OF DIFFUSION CONSTANT, C 4 ,
ON MODEL
PREDICTIONS--SAN FRANCISCO BAY
21
10
Conc.,
Days
ppb
Pe, T
Change
0
+ 8
16
Conc.,
Days
ppb*
Percent
Change
+10
+18
Conc.,
0.025
Days
ppb*
Percent
C 4 — 0.025
.1
1.2
C 4 — 2.5
.1
1.3
C 4 —
2.5
7.8
C 4 =2.5
2.9
8.7
+16
+12
C 4 — 0.025
1.0
4.5
C 4 — 2.5
1.1
5•3
Buoy “22”
(McAvoy)
Mm.
Max.
.2
3.9
.2
4.1
0
+ 5
1.7
10.1
2.1
10.8
+24
+ 7
3.8
14.1
4.4
14.5
+16
+ 3
Buoy ‘25”
(Chipps Is)
Mm.
Max.
.9
7.1
1.1
7.3
+22
+ 3
3.8
15.7
4.5
16.2
+18
+ 3
6.9
19.7
7.8
19.6
+13
- 1
Buoy “SC:
(Col iinsvi lle)
Light “5”
(New York Si.)
Mm.
Max.
Mm.
Max.
4.3
17.0
3.8
40.5
4.5
16.8
4.1
39.3
+ 5
- 1
+ 8
— 3
10.2
20.8
10.0
53.5
11.0
20.9
10.6
50.6
+ 8
+ 1
+6
- 5
14.4
24.1
13.8
56.3
14.7
23.5
14.5
52.5
+ 2
- 2
+ 5
- 7
Buoy “25”
(San Joaquin
R.)
Mm.
Max.
5.3
39.8
5.7
39.3
+ 7
- 1
6.5
43.9
7.3
42.3
+12
- 4
6.8
44.5
7.4
42.1
+ 9
- 5
-------
TABLE 4. EFFECT OF DIFFUSION CONSTANT, C 4 , ON MODEL PREDICTIONS-—SAN DIEGO BAY
6 1/2 Days 14 1/2 Days 22 _ D ys
Conc., ppb* Percent Conc., ppb* Percent Conc., ppb* Percent
0.025 C 4 = 2.5 Change C 4 = 0.025 C 4 = 2.5 Change C O25 C 4 = 2.5 Change
Range 4N Mm. .5 .5 0 .5 .5 0 .5 .6 +20
Section 2 Max. .7 .8 +14 1.6 1.8 +13 2.4 2.6 + 8
Range 2N Mm. .7 .8 +14 1.7 1.9 +12 2.5 2.6 + 4
Section 3 Max. 1.6 1.7 + 6 3.4 3.6 + 6 3.6 3. 6 0
Range 0 Mm. .9 1.0 +11 2.2 2.4 + 9 3.0 3.1 + 3
Section 1 Max. 7.0 6.1 -13 10.9 9.7 —11 6.3 5.7 -9
U,
Range iS Mm. 1.3 1.4 + 8 3.1 3.3 + 6 3.7 3.6 - 3
Section 2 Max. 6.7 6.0 -10 10.5 9.5 -10 6.3 5.7 -10
Range 3S Mm. 1.4 1.3 - 7 4.2 4.1 - 2 5.7 5.3 - 7
Section 4 Max. 3.0 2.8 -7 6.9 6 ,4 -7 6.5 5.9 -9
Range 4S Mm. .8 .8 0 2.6 2.6 0 4.5 4.4 -2
Section 3 Max. 1.7 1.7 0 5.0 4.8 — 4 6.0 5.6 - 7
*A11 concentrations predicted utilizing one-half hour time step and zero loss rate
-------
1 a C t t (45)
where
1 a = advected mass
Q = flow in channel
c = representative concentration
time step
This equation can be applied to a typical channel element, as shown in
Figure 39, which connects two junctions “a” and “h”. A junction volume
is defined by the volumes of the half-channels enterina the junction and
the concentration existing at the junction exists uniformly thrnughout
the volume (as per the assumption of complete mixing at junctions). For
computational purposes, however, it is convenient to consider the con-
centrations at junctions as point concentrations connected by linear
gradients as indicated in Figure 39. During a given time step t the
actual fluid displacement along a channel is equivalent to UAt which is
frequently much shorter than the actual channel length X. The transfer
of a quality constituent, however, is from one junction to another (the
full channel length) regardless of the magnitude of the fluid displace-
ment. A certain mass of constituent is therefore advanced ahead of the
fluid. This “numerical mixing 1 ’ can lead to inaccuracies in the solution,
especially in regions of steep concentration gradients. The ratio of
the fluid displacement Wit to the channel lenath X is a crude measure
of the degree to which this “induced disperscn” may affect the solution.
Obviously, when the ratio as defined in equation 46,
• = u t (46)
x
is at, or near, unity the numerical mixing problem is minimized. In a
given channel in a dynamic tidal system • will approach zero near the
occurrence of slack water and normally only approaches unity during
periods of maximum tidal velocity. Numerical mixing can therefore be
significant over much of the tidal cycle. The magnitude of the problem
is largely dependent on the specification of c in equation 45 which
determines the mass of constituent transferred. The concentration c
is determined by an arbitrary function of ca and cb:
C = f(ca,cb) (47)
In its simplest form c is taken as the concentration existing at the
upstream junction. Thus, if Q is in the direction shown in Figure 39
then C Ca. Experience with this approach on the San Francisco Bay
system Indicated excessive numerical mixing (excessive dispersion).
Four other functional relationships have been investigated and evaluated
as stnnarlzed in Table 5. Each technique was evaluated for degree of
numerical mixing, accuracy of solution, and computational stability, as
indicated. 86
-------
U’ ”
2X
Co
Concintration Gradi.nt
3C 0 — Cb
4
C.—Cb
2
CD
FIGURE 39.
TYPICAL CHANNEL ELEMENT AND CONCENTRATION GRADIENT
-------
TABLE 5. COMPARISON OF ADVECTION METHODS
Method Definition of c Nun erica Mixing Accuracy Stability
UPSTREAM C Ca High Poor Excellent
SIMPLE AVERAGE c Ca + Cb Low Good Very Poor
2
QUARTER POINT 3 Ca + Cb Moderate Good Acceptable
4
PROPORTIONAL c Ca + Cb + , (Ca - Cb ) Low Good Poor
(TWO-WAY) 2 2 -
PROPORTIONAL c Ca + Cb + . (Ca Cb) , If Ca>cb Moderate Moderate Good
(ONE-WAY) 2 2
C Ca , if Ca< Cb
Note:
$ U t
Ca Cb are as indicated in Figure 39
-------
Computational instability may occur whenever significantly more
mass is removed from a junction than is added during a time step (or
series of time steps) resulting in a sharp drop in the concentration
at one junction and a sharp increase at an adjacent one. The instabil-
ity does not normally correct itself and the concentration gradient
becomes very steep resulting in a zero or negative concentration at one
junction and an extremely high concentration at an adjoining junction.
This instability is prevented from continuing by a trap in the program
which terminates execution whenever the concentration at any junction
exceeds a specified value.
Figure 40 illustrates the results of testing four of the five
techniques on the San Francisco Bay system. Identical hydrologic and
quality boundary conditions were specified in all cases. No comparison
is included for the Simple Average method listed in Table 5 because it
was so unstable that a solution could not be obtained for the problem
studied. The Figure depicts the predicted salinity gradient through
the main channel of the system after approximately thirty tidal cycles.
The starting concentrations at all stations were identical for each
method; therefore the total mass of chloride in the system is the same
in each case.
The Proportional Two-way and Quarter-point methods produce the
most pronounced gradients through the system (typifies the least numeri-
cal mixing). The significance of the numerical mixing problem is
illustrated in Figures 41 and 42 by comparing the three most stable
solution techniques with observed prototype behavior at several stations
in the system. The most significant differences are noted at stations
near the salinity front (Antioch, Isleton, Collinsvi11e, and O&A Ferry)
with only minor differences in the fresh water (as typified by Mossdale
Bridge) and saline (as typified by Benicia) portions of the estuary.
Slight differences in the concentrations for the initial day of the
month are apparent at some stations; however this is due to the solution
techniques and not to differences in starting conditions. The concen-
trations plotted for time zero are the maximums computed during the first
24 hours of the simulation and are not the initial concentrations speci-
fied as input. The effect of starting concentrations was illustrated
earlier.
The results of these and other studies indicated that the Quarter-
point and Proportional Two-way methods most adequately represent proto-
type behavior. However, instability problems with the latter method
are significant and therefore, the Quarter-point method has been used
exclusively in FWQA studies.
89
-------
SAN PABLOBAY
+ SUISUN BAY
DELTA j
-J
32,000
U i
0
8,000
0
-J
C-)
4,000
0
FIGURE 40. COMPARISON OF SOLUTION TECHNiQUES
20,000
36,000
PROPORTIONAL METHOD (2-WAY)
UPSTREAM METHOD
PROPORTIONAL METHOD (I-WAY)
3/4 POINT METHOD
0
0
z
U,
w
-J
-J
>
U)
0
a.
—
0
C.) C.)
I.-
z
U i
0
z
0
a-
I.-
z
0
0.
Ui
0
z
0 .
I —
U)
0
0
C-)
N
U)
z
I-
C D
0
U)
>
0
C,
2
—I
C D
9
C l)
U)
C l )
CD
0
0
2
C !)
2
0
I-
U)
-J
U)
C-,
D
U)
—J
0
0 20 40 60 80
DISTANCE IN MILES FROM GOLDEN GATE
95
-------
OÔA FERRY
COLLINSVILLE
6000
4000 -
2000
a
I I I
0 10 20 30 40
w DAYS
0
0
-j
I
U
5000 BEN ICIA
10000
0 (0 20 30 40
DAYS
6000
‘000
2000
£
A—A
u- I
0 (0 20 30 40
DAYS
Prototype ( HH Slack)
Quarter Point Method (Maiimum)
Upstream Method ( Mo imum I
One Way Proportional Method IMo imum)
FIGURE 41. COMPARISON OF SOLUTION TECHNIQUES -- JULY 1955 CHLORIDE
E
I I I
91
-------
400 ISL
300
zoo
I 00 -
-
300 k4OSSDALE BRIDGE
200
A
400
0 40 -- 30 40
DAYS
I I
0 ID 20 30 40
DAYS
ANTIOCH
3004
2000 -
P000
• -S
AA
I I I I I
0 40 20 30 40
DAYS
Prototype H H Stock I
Quarter Point Method (Mozimum)
Upstream Method (Mozimu.m)
One Way Proportional Method (Mozimurn)
FIGURE 42.
COMPARISON OF SOLUTION TECHNIQUES -- JULY 1955 CHLORIDE
a.
E
u -I
0
C
-J
x
‘a
92
-------
DiSCUSSION OF DISCREPANCIES
Flodel predictions and the prototype observations differ somewhat
in a number of instances for both San Francisco and San Diego Bays.
These discrepancies result to a great extent from the type of compari-
son made. Several sources of these differences should be noted.
1. The model concentration is the average for a reach perhaps
3000 to 5000 feet in length which includes the prototype
sampling location. The prototype sampling station is
typically near one shore and is not necessarily representa-
tive of the cross-section, much less an extensive reach.
2. The model used a mean tide repetitively while the prototype
tide was continuously changing. In areas with significant
concentration gradients the tidal excursion on the day of
sampling significantly influences the concentration observed.
3. The number of model junctions for which initial concentrations
are known is a trivial fraction of the total number of junctions
requiring initial concentrations. Vast areas of San Pablo
and Suisun Bays and the Delta are without any sampling stations
whatsoever and it is not possible to check estimates of initial
starting conditions. Similar deficiencies exist for the San
Diego Bay system. The effect of improper starting conditions
is apparent over extensive areas and concentrations at the
prediction points may be significantly affected.
4. The hydraulic conditions in the model are defined exactly
while flow conditions in the prototype are largely unknown
at any time. The use in the model of the best available
estimates may nevertheless result in overall hydraulics
which differ from the actual (but unknown) prototype values.
Certain of the difficulties above could probably be corrected if
warranted. For instance if a11 daily flows and other input parameters
are known the use of the actual tide for the day might be justified.
Clearly the quality of information available about the prototype in
either of the two systems does not now justify such operation.
The agreement between the model predictions and prototype opera-
tion to the extent that it is known Is very good. It is clearly im-
possible at present to determine what proportion of discrepancies, if
any, can be attributed to the model structure. In both systems
historical prototype behavior was successfully matched without relying
on any empirically derived dispersion coefficient or other factor to
obtain satisfactory agreement. Since predictions do not depend on an
empirically derived factor (which may be valid over a narrow flow range)
reliable comparison between future alternative water quality management
schemes can be made even though the future hydraulics of the system may
be significantly different than any utlizied to evaluate model behavior.
93
-------
OTHER APPLICATIONS
In applications to the San Francisco and San Diego Bay systems
the model has been uti1ized to predict the distribution of constituents
which were treated as conservative (e.g., salinity, total nitrogen,
tracer, etc.) and those treated as nonconservative (e.g., SOD, DO,
coliform, tracer, etc.).
The mechanism for handling nonconservative constituents in the
model has been extensively tested for both San Francisco and San Diego
Bays and is believed to adequately represent the decay of independent
constituents as well as the gross relationship between BOD and DO;
however, due to a general lack of prototype data for verification,
no intensive effort has been made to evaluate the efficacy of the
model in this regard. Obvious shortcomings of the model, as presented
herein, include: 1) the reaeration and deoxygenation rates are assumed
constant, both spatially and with time, 2) temperature effects are not
included, 3) algal photosynthetic and respiration effects are not
included, and 4) benthlc demands are not included.
Each of the above can be included in the model if warranted. In
the simplest form the reaeratlon rate can be adjusted with changing
tidal velocities and depths with time. A temperature distribution
could also be specified and the reaeration and deoxygenation rates
varied with temperature. Algal photosynthetic and respiration rates
as well as benthic demands could also be specified spatially for a
system.
In a more sophisticated approach the above effects can be an
integral part of the model structure. Temperature could be included
as one of the quality constituents and could thus be used to adjust
temperature dependent parameters both spatially and with time. Algal
populations can likewise be treated as a separate constituent with
associated production and respiration rates for dissolved oxygen.
The major problem in such applications lies in determining the sig-
nificant parameters which affect the predictions and in defining the
functional relationships between the various parameters.
Efforts to include the heat budget into the model structure for
the purpose of predicting the time varying temperature distribution
In an estuary have been completed by the FWQA Pacific Northwest Water
Laboratory at Corvallis. This significant modeling approach will be
further tested by the Northwest Regional Office in applications to the
tidal portion of the Columbia River [ 22).
Another significant effort has been completed by the FWQA
California-Pacific Basins Office in Alameda by including the effects
on the dissolved oxygen budget of mechanisms such as photosynthesis
and respiration by algal populations, the decay of the algal mass, and
the benthic demand, in addition to the usual decay and reaeration mechan-
isms. Through the predictions of chlorophyll levels (and associated
94
-------
algal mass) the contributions to the total oxygen demand of both the
carbonaceous and nitrogenous demands of the algal mass are included.
This approach has been utilized to simulate the diurnal fluctuation
of DO in the Klamath River in Oregon.
Five additional FWQA efforts currently (1970) underway are the
application of the model to Boston Harbor by the New England Basins
Office in Needham Heights, to the Yaquina Bay Estuary by the Pacific
Northwest Water Laboratory, to the Potomac River Estuary through a
joint effort by the Chesapeake Technical Support Laboratory in
Annapolis and the FWQA Headquarters Office, to the Rappahannock River
Estuary by the Middle Atlantic Regiona1 Office, and to Port Royal
Sound, South Carolina by the National Field Investigations Office in
Cincinnati.
In the application to the Rappahannock Estuary the model was
refined to include a time varying reaeration rate (computed by a
relationship of the form of equation 36 on page 24) and a spatially
varied benthic oxygen demand in the dissolved oxygen budget.
The Chesapeake Technical Support Laboratory has also included
these two features in applications to the Potomac and additionally
has included the nitrogenous demand as well as algal photosynthesis
and respiration in the dissolved oxygen budget. That office also
successfully included a second (or higher) order decay relationship
to simulate phosphorus distributions in the estuary. It is anticipated
that reports will be forthcoming on these applications as the new model
features are refined and verified.
95
-------
PART III - USER’S MANUAL
I NTRODUCTION
The programs comprising the FWQA dynamic estuary model have been
tested and run under a wide variety of hydraulic and water quality con-
ditions and, while it is impossible to state they are completely
“bug-free”, there are no known difficulties. The basic model structure
and logic has, for the most part, remained as developed by the con-
tractor. The most basic changes incorporated by FWQA Include the revised
method of computing the velocity gradient au/ax in the hydraulic program
and the implementation of the so-called quarter-point version of the
quality model. The contractor concurrently incorporated the same
changes In computing au/ax and has also tested and used the quarter-
point version for many studies. Many additional features have been
added to the model by FWQA as the needs arose. Output routines in
particular were revised to provide much more flexibility in the type
and quantity of output obtained.
Other features were Incorporated to meet specific needs of the
studies of the San Francisco Bay system, e.g. the special method of
handling agricultural water use. Auxiliary routines (QUALEX, ZONES,
and DATAP) were added to cut down input data preparation requirements
and to reduce the necessary interpretation and suninary of quality
outputs.
Part III of this report is Intended to serve as a user’s manual
for implementing the programs comprising the model. The discussion
will reflect certain problems and pitfalls which may arise under certain
conditions or for certain types of studies.
Basic program logic, In the form of simplified flow diagrams and
a brief discussion, will be presented for each program. Input data
formats and deck arrangement will be included along with current program
listings for reference.
The model has been executed on various computer hardware systems,
including IBM 7094, CDC 6600, and IBM 360/65. The listings and dis-
cussions presented herein are as adapted to the IBM 360/65 system.
96
-------
HYDRAULIC PROGRAM (DYNHYD)
The sequence of required steps to implement the hydraulic program
varies from run to run depending on the availability and adequacy of
previously completed runs. A discussion of program logic, input require-
ments, output options, and potential Implementation difficulties will
be presented, followed by a detailed description of program variables,
Input card formats, etc.
Flow Diaq _ ram and Program Logic
The simplified flow diagram in Figure 43 presents the sequence of
steps and significant decision points for program DYNHYD and subroutine
HYDEX. The number assigned to each step is for reference only and does
not appear in the program. It should be relatively easy, however, to
identify each step with a particular sequence of statements in the
program listing.
The initial step involves reading alphanumeric data to identify
the printout and the parameters for defining the size of the network
(number of junctions and channels), the ntanber of cycles (time steps)
to be completed, the printout frequency, the number of junctions for
which detailed printout Is to be obtained, the time interval to be
used in the numerical solution, the starting point on the specified
input tide, and a decision variable which specifies whether a hydraulic
sumary of the run Is to be completed, i.e., whether or not subroutine
HYDEX is to be called.
The alphanumeric data to identify the run is printed as part of
the heading for the output (step 2) imedIately after which additional
control parameters are read (step 3) which define the cycle number at
which printed output is to begin, the cycle number at which storage
of data on tape or disk is to begin, and the frequency (in cycles) at
which restart capability is desired. These and the previously discussed
control parameters are printed as part of the output heading (step 4).
Steps 5 and 6 involve reading a separate card for each junction
In the network and checking to detennine if the cards are in sequence.
If a card Is missing or if the cards are not In numerical order the
job is aborted. Included on each card Is the junction number, the
initial head at the junction, the surface area of the junction, the
inflow or withdrawal, and the numbers of the channels entering the
junction. After all junction cards have been read the data are printed
(step 7).
Steps 8 and 9 involve reading a separate card for each channel in
the network and checking to assure that no card is missing and that
all cards are in numerical sequence. Each card contains the channel
number, the physical characteristics of the channel (length, width,
cross-sectional area, hydraulic radius, and Manning’s n), the initial
97
-------
[ EAD CONTROL DATA j 1
PRINT OUTPUT HEADING1 2
[ READ OUTPUT CONTROL DATAI 3
INT CONTROL PARA ETERS]4
READ JUNCTION DATA
SET Yr(J)=Y(J)
AFE 6 __________
CARDS IN NO
SEQUENCE BORT
7 —
YES
PRINT JUNCTION DATA 7
AD CHANNEL DATA 8
RE 9
CARDS IN NO
SEQUENCE ABORT
7
YES
PRINT CHANNEL DATA I 10
1 READ JUNCTION NUMBERS FOR PRINTOUTI 11
kA1 AND PRINT TIDAL COEFFICIENTS J 12
a..
FIGURE 43. SIMPLIFIED FLOW DIAGRAM — PROGRAM D’tI*WD
98
-------
TAPE 10
AND SYSTEM DATA) 14
INITIALIZE COMPUTATION PAFSA ETERS 15
COMPUTE CHANNEL
FRICTION COEFFICIENTS 16
TO
AL CONDITION >
TAPE 10
COMPUTE
AND WRI
285 ICYG1, NCYCI 20
[ INC MENT ELAPSED TI 1 21
4,
ICOMPUTE
HALF—STEP VELOCITIES A
ND
FLOWS
4 ,
Si
23
COMPUTE
HALF—STEP HEAD
‘
COMPUTE HALF—STEP u — t i IUNAL ANLAS
AND FULL STEP VELOC IT ES AND FLOWS
24
FIGURE 43.
(Cont.)
UNCTARE ALL
ON AND CHAN
S COMPATIBLE
CARD YES
I WRITE
LCONT ROL
I
SWITCH JUNCTION NUM8ERS (IF NECESSARY)
FOR SIGN CONVENTION 17
NO ABORT1
-I______
CHANNEL FLOW$
TETAPE 10 J 19
YES
99
-------
ICOMPUTE FULL—STEP HEADS
] 25
27
STORE
PARANETERS ON
TAPE 10
7
NO
29
THIS A PRINT
CYCLE
7
NO YES
Is 32
THIS THE LAST
C YCLE
7
NO
33
DOES
VELOCITY IN ANY
CHANNEL
EXCEED 20 FPS
I
NO
C
3
COMPUTE FULL—STEP CROSS—SECTIONAL AREA 26
YES
‘I
WRITE 28
TAPE
10
YES
SET NEXT PRINT
CYCLE 1
[ PRINT RESULTS FOR
SPEC FlED CHANNELS
30
31
YES
+
CALL DUPJF 1
ABORT j
FIGURE 43 (Cont.)
100
-------
CALL
SUBROUT INE
HYDEX
YES
FIGURE 43 (Cont.)
PR I NT
C
IS
HIS THE LAST
YES
PUNCH DECK
CYCLE
,
NO
FOR RESTARTING
IS
36
THIS
A
SPECIFIED RESTAR
CYCLE
SPECIFY NEXT
RESTART CYCLE
37
35
1 38
NO
L
WRITE TAPE 3 FOR RESTART
f
[ REWIND TAPE 3
s ’s
RESTART PARAr ETERS
285 I
1 END OF MAIN LOOPj 41
¶1’
RINT RESTART DATA
42
40
Q [ 9 J45
RETURN FROM HYDEX j
CALL HYDEX 1 44
101
-------
I REWIND TAPES
L AND INITIALIZE
3 & 10
VARIABLES
1
L READ I NDEPENDENT
CONTROL DATA
I
READ SYSTEM DATA
FROM TAPE 10
]
COM UTE NSTART,
NSTOP 1
‘I
PRINT HEADING AND
CONTROL PARA ETERS
J OCITY
- , HANNEL = 0 ___,,,P
COIPUTE X—SECT I ONAL AREAS BY
DIVIDING FLOW BY VELOCITY AND
INITIALIZE AVE. X—SECTIONAL AREA
FIGURE 43 (Cont.)
102
P
46
47
48
49
50
t
[ READ HYD.CYCLE NO.FROM TAPE 10 J
51
EQUAL
IS 52
CYCLE No.
LESS LESS THAN, EQUAL
TO, OR GREATER THAN DESIRE
STARTING CYCLE (NSTART)
7
GREATER
( )
[ KFLAG=KFLAG+1 I 56
INITIALIZE:
NET FLOW
EXTRACT FLOW
EXTRACT VEL.
MAX. VEL.
MIN. VEL.
YES
53
55
3
KFLAG = 0
KFLAG2= 0
54
59
IN I I I AL I ZE:
AVE. HEAD
MIN. HEAD AND CYCLE NO.
MAX. HEAD AND CYCLE NO.
-------
58
‘ COMPUTE CHANNEL CROSS—I
I SECTIONAL AREA OF THATI
[ CHANNEL FROM HEADS ]
<( 60
DOES
FLAG EQ.UAL
EQUAL
ACCUMULATE:
NET FLOW
EXTRACT FLOW
EXTRACT VELOCITY
CHECK FOR:
MIN. VELOCITY
MAX. VELOCITY
MIN. X—SECTIONAL
AREA
MAX. X—SECT tONAL
AREA
ii ’
CHECK FOR:
MIN. HEAD
MAX. HEAD
ACCUMULATE AVE.
HEAD
64
THIS THE
END OF A QUALIT
TIME
FIGURE 43
103
= KFLAG2 + 1 I 65
1
INITIALIZE MIN. & MAX.
X—SECTIONAL AREAS j 61
62
63
V
No
(Cont,)
-------
I COMPUTE EXTRACT FLOW AND J 66
VELOCITY FOR QUALITY IlivE STE
E QU AL
FLAG2 EQUAL
OR EXCEED 1 EXTRACT FLOW MAX ] 68
INITIALIZE MIN AND
EXCEED
ICHECK FOR MIN AND l
LMAX EXTRACT FLOW J69
STORE EXTRACT FLOW
AND VELOC ITY Ot\J TAPE 3 70
REINiTIALIZE EXTRACT
FLOW AND VELOCITY 71
IS 72
THIS THE END YES
OF TIDAL CYCLE
_______ ____ T
7
NO
I WRITE CYCLE NO. AND
IJUNC. HEADS Ot’J TAPE 3
JRITE = URITE + NODYN 74
( )
FIGURE 43 (Cont.)
104
-------
FIGURE 43 (Cont.)
COMPUTE
¶
NET FLOW, AVE.
X—SECT ION,
AND
HYD.
RADIUS IN EACH
CHANNEL
It
OMPUTE
TIDAL RANGE AND
AVE. HEAD
f
75
76
77
78
STORE NET FLOWS AND SYSTEM
PARA? TERS ON TAPE 3
t
PRINT HYDRAULIC SUMMARY
i
I
REWIND TAPE 3
79
ICOMPUTE NO. OF QUALITY TI 1E
(STEPS PER TIDAL CYCLE
II !
tREAD THROUGH TAPE AND
[ PRINT SELECTED DATA
80
81
P
]
____I:
RETURN
82
105
-------
mean channel velocity, and the numbers of the two junctions at the
ends of the channeL These data are then printed (step 10).
The list of junctions for which detailed printout is desired is
read as step 11. The program is dimensioned to allow up to 50 such
junction numbers.
The tidal coefficients and the period of the desired tide are read
and imeediately listed (step 12). The coefficients are computed in the
separate program REGAN.
Step 13 involves checking the compatibility of the two separate
numbering systems, i.e., that for the junctions and that for the chan-
nels. This assures that for each junction all of the entering channels
are Identified and for each channel the junction numbers at both ends
are properly Identified. Thus If a junction is listed as being
connected to a given channel then that channel should also be listed
as being connected to the junction. The run will abort If any discrep-
andes are found.
The control parameters and the junction and channel data are
stored on tape 10 (step 14). This record can be maintained either as
a permanent record 0 f the run (on tape or disk) or as a temporary
record available only during execution (scratch tape or disk).
Step 15 initializes various computation parameters such as the
elapsed time and the restart interval and also converts the starting
time and the tidal period from hours to seconds.
The friction coefficient for each channel is computed (step 16)
and a check is made to determine which of the two junction numbers at
each end of the channel is the smallest (step 17). The two numbers
are Interchanged whenever the second number Is smaller than the first
i.e. whenever NJUNC(N,2) is smaller than NJUNC(N,l). This switch is
necessary for the sign convention utilized for specifying the direction
of flow in a channel. After completion of step 17, NJUNC(N,1) will
always be smaller than NJUNC(N,2).
Normally the initial junction heads and channel velocities and
flows need not be stored on tape 10 (steps 18 and 19). Only if the
run Is a continuation of a previous run is it desirable to record the
initial conditions (in effect the initial conditions become cycle zero).
The main computation loop begins at step 20. After incrementing
the elapsed time (step 21), the velocity In each channel is projected
to the middle of the time step utilizing the equation of motion dis-
cussed in Part I. This projection (step 22) is completed Independently
for each channel in the network during each time step. The half-step
velocities are utilized to compute the half-step flows (product of the
velocity and cross-sectional area) and these in turn are used to adjust
106
-------
the junction heads for the half time step (step 23). This Is accom-
plished by computing the net flow into (or out of) a junction from all
sources and adjusting the volume (head) accordingly. These new junction
heads are then used to adjust the channel cross-sectional areas to the
half time step and also to project the channel velocities (and flows)
to the end of the full time step (step 24). The head at each junction
is then computed for the full time step (step 25) and the cross-sectional
area of each channel adjusted (step 26) by the product 0 f its width
and the average change In head at both ends of the channel (channel
widths are assumed constant).
The junction heads and channel velocities and flows are stored on
tape 10 if the cycle number is equal to or greater than a specified
value (steps 27 and 28). A check is then made to determine whether the
predictions for the current cycle are to be printed (step 29). If the
current cycle is a print cycle the next print cycle is set (step 30)
and printout is obtained for the specified junctions (step 31). If
the current cycle is not a specified print cycle printout will still
be obtained if the cycle is the last cycle of the run (step 32), i.e.,
printout Is always obtained for the last computation cycle.
The computed velocities in each channel are checked for reasonable-
ness (step 33). If the absolute value of the velocity In any channel
exceeds 20 feet per second (indicating computational instability) the
run is aborted. A core dump is obtained for certain junction and
channel parameters to aid In determining the cause of the instability.
Prior to recycling to the start of the main computation loop a
check Is made to determine whether the current cycle is the last compu-
tation cycle (step 34). If It is the last cycle the current junction
and channel parameters are punched into a deck with a format which
can be used as an input deck in the event it is necessary or desirable
to extend the run (step 35). Prior to the last computation cycle a
check Is made to determine whether the current cycle is a specified
restart cycle (step 36). At each specified restart cycle (prior to
the final computation cycle) the current junction and channel para-
meters are stored on tape 3 (step 38). The tape Is then rewound
(step 39) and If computations proceed to the next restart cycle the
tape Is updated with the current parameters. After each write coninand
pertinent restart parameters are printed to provide information for
restarting (step 40). Following the completion of the specified number
of computation cycles for the main loop (step 41) the final status of
the run is printed for all junctions and channels (step 42). A check
Is then made as to whether subroutine HYDEX Is to be called (step 43).
Except for certain test runs subroutine HYDEX would normally be called
to suninarize the run.
The Initial step (step 46) in the subroutine Is to rewind both
the hydraulic tape (tape 10) and the extract tape (tape 3). Up to
this point in overall execution tape 3 has been utilized as a restart
device in the event of premature termination of execution. Under such
107
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condt lons subroutine HYDEX would never be called and tape 3 would
have on it the necessary data for restarting the run from the cycle
at which the tape had last been written. If execution is not termi-
nated prematurely and subroutine HYDEX is called then the ending
hydraulic conditions have already been punched Into a restart deck and
the record on tape 3 is no longer needed. Thus the rewind conriand In
subroutine HYDEX readies the tape for its new use as the storage device
for the extracted hydraulic parameters (which is used as Input to the
quality program). Tape 3 thus serves a dual purpose during execution
of the hydraulic program.
In addition to the system information stored on tape 10 two addi-
tional cards of alphanumeric Input are read in subroutine HYDEX which
are printed as part of the heading of the output. Also the time inter-
val which will be utilized in the quality solution is specified
(step 47) as some whole multiple of the time Interval used in the
hydraulic solution (NODYPI). For example if the hydraulic time step
Is 100 seconds and the desired quality time step is one-half hour
(1800 seconds) NODYN would be specified as 18. Following the specifca-
tion of the independent control data the system data stored on tape 10
during execution of the hydraulic program is read (step 48).
The hydraulic suninary provided by subroutine HYDEX Is for a
complete tidal cycle; therefore it Is necessary to compute the cycle
numbers In the hydraulic solution at which the last full tidal cycle
began and ended (step 49). In some cases the data on tape 10 may
have been limited to exactly one tidal cycle. In others more than
a full tidal cycle may have been stored on the tape. Because the
hydraulic solution converges to a dynamic steady state condition
the predictions only over the last full tidal cycle should be used
for the suninary as they are the most representative of a steady state
condition.
A heading for the output from the subroutine Is provided to
Identify the run (step 50).
Following the initial read coninand for tape 10 In which the system
data were read (step 48) the tape is positioned at the start of the
continuous record of predictions for each hydraulic cycle (time step).
At step 51, whIch starts the main computation loop In subroutine HYDEX,
the value for the first cycle number stored on tape 10 Is read, along
with the values of hydraulic parameters predicted for that time step.
A check Is then made to determine whether the cycle read is less than,
equal to, or greater than the cycle number computed previously which
specifies the desired starting point on the tape (NSTART). If the
number Is less than NSTART the next cycle and associated hydraulic
parameters are read from tape 10 (step 51) and the check at step 52
made again. This continues until the cycle read equals NSTART at
which point the sumary begins (step 53). Several separate sunmiarles
are initialized in this step Including the mean or net flow In each
108
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channel over the entire tidal cycle, the mean velocity and flow in each
channel during the initial quality time step, and the minimum and maxi-
mum velocities in each channel over the full tidal cycle. For the net
flow computation the values for each cycle (time step) are accumulated
over the entire tidal cycle and the accumulated total divided by the
total number of time steps comprising the tidal cycle. Similarly the
means for the initial quality time step are computed by accumulating
the values for each individual hydraulic cycle over the full quality
time step and the accumulated total divided by the number of hydraulic
cycles per quality cycle (NODYN).
If the hydraulic solution has, in fact, reached a dynamic steady
state condition the values predicted for the hydraulic parameters at
the initial cycle (NSTART) will be Identical to those predicted for
the final time step of the tidal cycle (NSTOP). Normally however, the
solution will not have reached true steady state and slight differences
between the starting and ending points on the tidal cycle will exist.
Rather than use one set of values or the other in computing the averages
over the tidal cycle, both are used, but each is assigned a weight of
one-half to average out the difference.
To initialize the determination of the minimum and maximum values
for the velocity in each channel each is initially assumed equal to
the velocities existing for the initial cycle. At each successive cycle
these values will then be compared to the current values and updated
as required.
Two internal counters are initialized (step 54) which will be
utilized later to flag the beginning of other special suninaries. The
determination of the minimum and maximum heads at each junction is
Initialized (step 55) by equating both to the head at the initial
cycle. Following the completion of the initial cycle (step 55) control
passes to step 73 where the initial cycle number (NSTART) and the heads
at each junction for that cycle are stored on tape 3. The cycle number
at which the next quality time step begins Is determined (step 74)
and control passes back to step 51 to read the parameters for the
next hydraulic time step. Steps 53 through 55 will be completed only
once, i.e., for the initial time step (NSTART). For all subsequent
cycles control passes to step 56 where the computations initialized
in steps 53 through 55 are continued.
At the start of each cycle (except the initial one) the counter
KFLAG is incremented by one (step 56).
Included in the sunuiary of the hydraulic run is the determination
of the mean, maximum and minimum cross-sectional areas of each channel
over the full tidal cycle. The values for the cross-sectional area
were not stored on tape 10 for each time step; however they can be
regenerated at this point by dividing the channel flow by the velocity.
To avoid the problem associated with division by zero a check for
zero velocity Is made (step 57). For any channel in which the velocity
109
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is zero the cross-sectional area Is computed from the heads existing at
both ends of the channel (step 58). OtherwIse the channel cross-sectional
area Is computed by dividing the flow by the velocity (step 59). In both
cases the cross-sectional area for each channel Is added to the total
accumulated previously which will be used to determine the average over
the full tidal cycle.
A check Is made (step 60) to determine if KFLAG Is equal to or
exceeds one. KFLAG will equal one only the first time through this
step, indicating that the computations for determining the minimum
and maxImum cross-sectional areas need to be initialized (step 61).
For all subsequent cycles step 61 will be bypassed.
The flow In each channel is added to the accumulated totals for
the net tidal cycle flow (QNET) and to the extract flow (QEXT) for
the quality time step. The velocity in each channel is similarly
added to the accumulated total for the extract velocity (VEXT) for the
quality time step. The maximum and minimum values previously established
for the channel velocities and cross-sectional areas are checked against
the current values and are updated as necessary. These accumulations
and comparisons are represented as step 62 in the flow diagram.
Step 63 involves a similar accumulation for determining the
average head over the tidal cycle and a comparison and updating of the
minimum and maximum heads established previously.
Following the above computations for each hydraulic cycle read
from tape 10 a check is made (step 64) to determine whether the end
of a quality time step has been reached (occurs each NODYN cycles).
If not the next cycle is read from tape 10 (step 51) and the above
sequence repeated. At the completion of each NODYN hydraulic cycles
KFLAG2 is incremented by one (step 65) and the extract flow (QEXT)
and velocity (VEXT) for the quality time step are determined (step 66)
by dividing the accumulated totals for each by the number of hydraulic
time steps (f400YN). Following the initial quality time step KFLAG2
will equal one (step 67) which triggers the Initialization of the
computations for determining the minimum and maximum values of the
extracted flows (QEXT). For all subsequent cycles the previously
established minimum and maximum values for QEXT are compared to the
current values and updated as required. The values for the extracted
channel flows and velocities are then stored on tape 3 (step 70) for
later input to the quality program. The accumulated totals for the
extract flows and velocities are then reinitialized (step 71) for the
next quality time step.
After completing the extract for each quality time step a check
Is made to determine if the last cycle on tape 10 (NSTOP) has been
reached. If not the current value of the hydraulic cycle number and
the head at each junction Is stored on tape 3 to mark the start of a
110
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new quality time step (step 73). The cycle number identifying the start
of the subsequent quality time step is computed (step 74), followed by
the next reading of tape 10 (step 51).
When computations for the last cycle (NSTOP) have been completed
the net flow (QNET) and the average cross-sectional area (ARAVE) in
each channel are computed by dividing the accumulated totals for these
parameters by the total number of hydraulic time steps in the full tidal
cycle (step 75). The mean channel depth (hydraulic radius) is computed
by dividing the average cross-sectional area by the channel width as
part of step 75.
The tidal range at each junction is computed as the difference
between the maximum and minimum heads and the average head at each
junction is computed by dividing the accumulated total for the parameter
by the total number of time steps (step 76).
The net flow in each channel and pertinent system parameters are
stored on tape 3 (step 77). These parameters are stored at the end of
tape 3 rather than the beginning to avoid the necessity of having to
read over these data each time the tape is read during execution øf the
quality program. Hydraulic parameters for only a single tidal cycle
are stored on tape 3; hence for quality simulations of greater duration
than one tidal cycle the tape must be rewound and the values used again.
This repeated use of the hydraulic parameters is continued as necessary
to complete a specified number of cycles.
A printed sunrary of the net flows and the minimum and maximum
velocities and flows in each channel is obtained along with the mini-
mum, maximum, and average channel cross-sectional areas (step 78). A
similar suninary of the heads at each junction is also provided.
Tape 3 is then rewound (step 79) and the number of quality time
steps comprising a full tidal cycle is computed (step 80). Tape 3 is
then read completely through (step 81) and each hydraulic cycle number
which had been stored on the tape Is printed along with the correspond-
ing head at junction number one and the extracted flow in channels
number one and two. This list of data provides a convenient check on
the data stored on the tape.
At the completion of subroutine HYDEX control returns to the main
program (step 82) and the execution terminates (step 45).
input Requirements
The Input requirements for the hydraulic program can vary tremen-
dously from run to run depending on the uniqueness of the conditions to
be simulated. The data requirements for the initial application of the
111
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model to a new system are considerable. The system must be represented
by a network and the physical parameters of each channel and junction
element determined. The most demanding of these Inputs are the channel
cross-sectional areas and the junction heads. The specified junction
heads establish the water surface elevation throughout the network and
it is Imperative that the cross-sectional areas assigned to each channel
correspond to those heads. The heads throughout the system are refer-
enced to a conron, horizontal datum. Channel depths can usually be
obtained with sufficient accuracy from the soundings printed on naviga-
tion charts published by the Coast and Geodetic Survey. Unfortunately,
however, these soundings are normally representative of a mean low water
condition at the point of the sounding and are not referenced to a
comon datum. It is therefore necessary to establish the relationship
between low water at each point In the system and the horizontal datum
selected for the model. Such relationships may be available for certain
points in the system, such as at tidal stage recorders or at other points
where tidal predictions are made. River bed profiles may also be avail-
able from which such relationships could be determined. Once the re-
lationships between the junction heads and channel cross-sectional areas
have been properly established for a given system they should never have
to be reestablished because the model program maintains the proper re-
lationship at all times during execution. It is usually most expeditious
to specify a constant value for each of the junction heads (assumes a
horizontal water surface) In preparing the data for the first time and
then adjust the channel depths (and cross-sectional areas) accordingly.
While It might be desirable, In order to save computation time, to
specify the initial heads at each junction in such a manner that the
water surface profile Is more representative of one which actually
occurs In the prototype, such an effort is probably not warranted.
Unless extensive tide data are available to establish the water surface
elevation at many points in the system for a given instant in time a
great deal of interpolation between points will be required. It Is
doubtful whether the execution time saved by such a procedure warrants
the additional effort Involved.
A similar argument holds for the specification of the initial
velocity in each channel. Normally data in sufficient quantity will
not be available to establish a detailed velocity pattern for the entire
system at a given instant in time. Therefore a constant initial velocity
(such as zero) Is assumed throughout the system. Thus for the initial
run on a new system the total mass of water might initially be assumed
to be at rest with a horizontal water surface. As the solution pro-
gresses it will converge to the appropriate dynamic steady state condi-
tion wherein the head at each junction and the velocity and flow in
each channel are repeated with a frequency equal to the period of the
specified tide.
For all runs subsequent to the initial run the input data require-
ments are greatly reduced. Many of the physical parameters such as
channel lengths and widths and the surface area of each junction remain
constant during execution and therefore do not vary between runs.
112
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Similarly the network layout and numbering systems generally remain
constant. Only if physical changes in the prototype (real or proposed)
are to be modeled is it necessary to change the model network. Even
then the changes normally affect only a small fraction of the total
number of junction and channel elements.
The initial junction heads and channel velocities can be obtained
directly from the restart deck punched at the end of any previous
hydraulic run. Although the specified tidal conditions for the two
runs may not be identical it is usually possible to choose the starting
point on the new tide to correspond closely to the ending tidal eleva-
tions on the previous tide. Care must be exercised to assure that the
tidal phase as well as elevation is matched at the boundary so that
the ending conditions from the previous run are appropriate throughout
the system e.g. if the ending elevation at the boundary is at a certain
level and rising, the starting point on the new tide should be as close
as possible to that elevation and on a rising portion of the curve.
If this can be accomplished the ending channel velocities from the
previous run should also provide excellent starting conditions for the
new run.
Other than the control data, which will be unique for each run,
the only inputs that may need to be respecified from run to run are the
tidal condition imposed at the boundary and the specified accretion or
depletion at each junction in the system. Frequently, however, only a
small number of these inputs need be changed. For example when evaluat-
ing and comparing various waste disposal schemes in an estuary the tidal
conditions and basic hydrologic inputs may remain the same for all runs
with only the key waste discharge inputs changing (either in location
or in quantity) from run to run. For those cases wherein different
tidal conditions and/or different hydrologic inputs are to be specified
the two auxillary programs REGAN and DATAP are available to aid in the
preparation of these data.
Output Options and Control
Three forms of output can be obtained from the hydraulic program:
(1) printed output which provides a written record of the status of
the run and a suninary at the end of the run, (2) a permanent record
of the run on tape (one or two tapes) and (3) punched output in the
form of a restart deck.
Printed output is controlled by three separate parameters, NPRT,
NOPRI, and IPRT. NPRT specifies the interval (in time steps) between
printouts. Generally output at half-hourly intervals is sufficient to
define the dynamic character of the predictions over the tidal cycle.
For a given time interval, DELI, (for example 100 seconds) the specified
number of time steps between printout, NPRT, (for example 18) defines
the print interval (one-half hour). NOPRT defines the number of junctions
for which printout is to be obtained. For each of the NOPRT junctions
the head predicted during the time step is printed along with the velocity
113
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and flow in each of the channels entering that junction. Output of this
form is illustrated on pages 196 through 198 in the Appendix. The
control parameter IPRT defines the initial cycle number for which print-
out is to be obtained. Printout is obtained beginning at cycle number
IPRT and at each NPRT cycles thereafter. Printout is automatically
obtained for the last cycle of the run regardless of whether it coincides
with a normal print cycle. In many cases computations must proceed for
three or four tidal cycles before the solution converges to a steady
state condition. In such cases printed output can be limited to only
the last complete tidal cycle by the appropriate specification of IPRT.
IPRT can also be specified to assure that printout begins at a conveni-
ent reference point on the time scale (such as precisely on the hour or
half-hour) regardless of the starting point on the input tides (as
specified by TZERO).
There is no specific control over printout obtained from subroutine
HYDEX. If the subroutine is called a printout of the hydraulic suninary
is provided. An example of the output obtained from HYDEX is provided
on pages 201 through 203 in the Appendix.
Although it is not necessary to maintain a permanent record of the
hydraulic run (tape 10) it is necessary that the predictions for every
time step over a complete tidal cycle be stored on tape 10 durIng execu-
tion In order that the hydraulic extract tape (tape 3) can be prepared.
If a permanent record of the run is not desired tape 10 can be specified
as either a scratch tape or disk. A permanent record of the extracted
tape (tape 3) must be established (either or magnetic tape, disk pack,
or data cell) to provide the required hydraulic input to the quality
program.
It may be desirable to also establish tape 10 as a permanent (or
semi-permanent) record of the run for any of three reasons: 1) If
tape 10 is treated as a scratch device and execution is prematurely
terminated for any reason (such as time estimate, lines of output, etc.)
the entire run might have to be repeated in order to create the extract
tape, 2) if any record on the extract tape is damaged or destroyed the
entire tape can be re-created from the hydraulic record (using subrou-
tine HYDEX as a separate program), and 3) if it Is desired to utilize
a quality time step other than that for which the hydraulic extract
tape was originally created the hydrualic record can be re-extracted
utilizing a different time step (again using subroutine HYDEX as a
separate program). Whether or not the record on tape 10 should be main-
tained as a permanent record depends on the relative cost of re-creating
the run and the purchase and storage cost for magnetic tape, disk pack,
or data cell. Such a comparison will vary from system to system and Is
largely dependent on the size of the network (number of junctions and
channels). For large systems which require significant execution time
a permanent record on tape 10 might eliminate the necessity of a costly
rerun.
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The length (in hydraulic cycles) of the record stored on tape 10
is controlled by the input variable IWRTE. The record begins at cycle
IWRTE and continues for every cycle thereafter. If the specified
duration of a run exceeds one full tidal cycle IWRTE can equal the cycle
at which the last full tidal cycle begins.
The ending junction heads and the final channel velocities and
cross-sectional areas computed in the run are punched into a deck which
can be used to extend the run or which can be used as the starting con-
ditions for a different hydraulic run.
Sign Convention
Two different sign conventions are utilized in the model. One
is utilized to describe flow into or out of a junction and the other to
define the direction of flow in a channel. When referring to a junction
any flow entering the junction is assigned a negative value and any flow
leaving the junction a positive value. This convention holds regardless
of whether the flow is from an external source e.g. an inflow or waste
discharge or from an internal source, i.e., from an adjacent junction.
When considering a channel element the flow (and velocity) is
assigned a negative value whenever the flow is from the end with the
higher of the two junction numbers to the end with the lower of the two
numbers and is assigned a positive value when the flow is in the opposite
direction. These sign conventions can be illustrated by observing the
sample output on pages 196 through 201 in the Appendix. For example on
page 197 the printout for junction number 16 indicates a negative flow
in channel 17 and positive flows in channels 18, 19, and 21. Since these
flows are in reference to junction 16 these signs indicate that the
flow in channel 17 is entering junction 16 and the flows in the remain-
ing channels are leaving the junction. It should be pointed out that
the signs associated with the velocities and flows listed for channels
17, 18, 19, and 21 on page 197 have been converted to the sign convention
for the junctions strictly for convenience in Interpreting the output.
The signs should not be interpreted to indicate a negative or positive
flow in terms of the sign convention used for the channels. For example
on page 200 it can be noted that channel number 17 connects junctions
15 and 16. Since the printout on page 197 indIcated the flow in channel
17 was flowing into junction 16 It Is obvious that the flow direction
is from junction 15 toward junction 16. Thus, using the channel sign
convention, the flow is positive. The negative sign printed on page 197
merely allows the flow direction in channel 17 to be determined without
the need to determine the junction numbers at each end.
Interpretation of Output
At the conclusion of each hydraulic run it is important that a
determination be made as to whether the run reached a steady state
condition. It is difficult to estimate a priori how long a solution
must be continued to produce the required full tidal cycle of predictions
115
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representative of a steady state condition. If good starting conditions
are available the solution may converge after a few hours (simulated time)
such that the total simulated time only slightly exceeds the tidal period.
With poorer starting conditions the solution may have to be continued
for three or more full tidal cycles in order that the last full tidal
cycle of the run be at steady state.
As a hydraulic solution progresses the heads predicted for each time
step over the tidal cycle converge to unique values for each junction in
the network. The predicted channel flows also converge to unique values
which are repeated each tidal cycle. Precise repetition of these para-
meters is not required; however, the degree of precision required is
difficult to define and may vary between systems. For example if a
system is represented by a relatively course network (such that the
junction surface areas are large) a small variation in head (e.g. 0.01
feet) can represent a significant volume (which in turn can represent
a significant change in flow). It can thus be erroneous to conclude a
solution is at steady state solely on the basis of comparing the pre-
dicted heads at those junctions for which printout is obtained. A more
reliable test is to determine whether the net tidal cycle flow (the average
over the entire tidal cycle) has converged to a predetermined value in
selected channels. The combined steady state net flow through all the
channels cut by a plane which passes completely through the network is
equal to the algebraic summation of all the inflows, waste water dis-
charges, diversions, exports, etc. assigned to those junctions on the
upstream side of the plane.
The importance of the determination for a steady state hydraulic
solution lies not so much with a necessity to accurately define the
net flow but with the fact that the ultimate distribution of a quality
constituent can be quite dependent on the net seaward (or landward)
flow. When comparing alternative waste disposal schemes or when deter-
mining the freshwater outflow required to prevent salinity incursion
it is important that the model prediction has converged to the specified
net flow in order that proper conclusions be drawn.
Potential Implementation Difficulties
The difficulties associated with implementing the hydraulic pro-
gram generally fall into one of two categories, i.e., either 1) the
solution becomes unstable, or 2) execution terminates prematurely. A
third problem, involving storage limitations on magnetic tape, may arise
for large networks or on certain computer systems. As will be discussed
later in this section, this problem can be prevented (once discovered)
by certain programming changes and should not be of a recurring nature.
Execution of the hydraulic program is terminated if the velocity
in any channel exceeds twenty feet per second, indicating an unstable
(diverging) solution. This problem genera1ly arises most frequently
during the initial applications of the model to a new system. It can
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arise, however, even after many successful previous applications, par-
ticularly if the hydraulic conditions are significantly different from
any previously considered.
An unstable solution usually results from one or more of the
following conditions: 1) one or more inputs have been improperly
specified (keypunching error, etc.), 2) the stability criterion is
violated for a certain channel (indicating the channel length should
be increased or the time step decreased), 3) a junction surface area is
not properly represented (occurs frequently at dead end channels), or
4) a junction volume is not properly represented (occurs either at dead
end channels or in areas such as tide flats where the depth at low tide
may be zero). Under such conditions unrealistic hydraulic gradients can
be created which result in excessive velocities. If execution is termi-
nated for this reason a core dump is obtained which gives the values of
the junction heads, channel cross-sectional areas, and channel flows.
These values can be helpful in determining the cause of the instability.
The instability can usually be eliminated at dead end channels by
increasing the surface area of the end junction somewhat above that
indicated on published maps or charts to eliminate wave reflection
caused by the abrupt channel ending. There may be little, if any,
wave reflections In the prototype since a real channel rarely ends as
abruptly as represented by the model network.
Similarly in areas such as tide flats where the depth at low tide
may reach zero the instability can normally be corrected by increasing
the depths 0 f the peripheral channels slightly. As prograniiied the model
does not adjust the water surface area of a junction as the water rises
and falls. There is also no provision for allowing a junction to
‘run dry” (reach zero depth). The model network parameters in these
areas may be specified to compensate for these shortcomings however.
The channel depths and the surface area assigned to the junctions are
representative of the mean tide level such that at low tide the junction
volumes are slightly over-represented and at high tide under-represented.
Premature termination of program execution due to improper estimates
of execution time or lines of output can result in costly reruns unless
built-in restart options are exercised. The specification of the fre-
quency with which restart capability is desired is not difficult; however,
in the event it becomes necessary to restart a run (or extend a previous
run) It is very important that execution begin precisely at the point the
previous execution was terminated. This requires the proper specification
of the initial time, TZERO. At the completion of each update on tape 3
and also after punching the restart deck at the end of a run the value of
TZERO for restarting is printed. It is printed to seven places beyond
the decimal point to provide the necessary accuracy for restarting the
computations at the point they were discontinued.
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It Is possible to execute the hydraulic program utilizing a scratch
disk rather than ri agnetic tape for unit 10 since the records stored on
this unit are used only during execution of subroutine HYDEX to generate
a permanent record of extracted hydraulic parameters on magnetic tape
or disk (unit 3) for input to the quality program. Creating a permanent
record for unit 10 (on tape or disk) does, however, provide a backup
record which can be used to re-create the extract tape without re-running
the entire hydraulic run. Such a permanent record can also be utilized
to extract the hydraulic parameters with different time steps (which
may be desirable during the early application and testing of the quality
model).
For systems represented by a network with a large number of junctions
and channels the length of the record to be stored on tape 10 may exceed
the maximum limit for a magnetic tape, i.e., the tape may be completely
filled. For such cases it may be necessary to reprogram the hydraulic
program and the extract subroutine to acconinodate two tapes rather than
one. The reprograming effort is largely tied with specification of the
starting and stopping points on each tape.
Execution Time
Typical execution times for the hydraulic program are sumarized
In Table 6. The execution time is dependent on the computer used (and
on the accounting procedure utilized), the size of the network, the time
step utilized, the duration of the run, and the amount of output specified.
TABLE 6. EXECUTION TIMES FOR HYDRAULIC MODEL
Size of Network
Junctions Channels
Time
Step
(seconds)
Length of
Run
(hours)
Execution
Time
(Minutes)
Computer
Used
112
170
50
37.5
5
CDC 6600
112
170
50
50
8
COC 6600
112
170
50
25
8
IBM 360/65
247
306
75
12.5
4
COC 6600
247
306
75
12.5
7
IBM 360/65
247
306
75
25.0
13
IBM 360/65
830
1050
100
12.5
8
CDC 6600
830
1050
100
25
12
CDC 6600
830
1050
100
37.5
15
CDC 6600
830
1050
100
49
23
CDC 6600
118
-------
Description and Format of Program Inputs (DYNHYD )
In the following description defining the format of the input data
deck required to execute program DYNHYD the symbol:
* denotes that a series of cards as described may be required.
a denotes that the card or series of cards may not be required.
R indicates “right hand justified,” i.e., any quantity so
described must appear as far as possible to the right of
its data field.
• indicates a decimal point must appear in the field.
R. indicates that the value is right hand justified but may
have a decimal point to override the progranm ed decimal
point.
• indicates the continuation of the same format on a card.
indicates the start of a new card.
Card Column Name Description
1-80 ALPHA(I) Alphanumeric identifier -- printed
as first line of output (up to 80
characters). I = 1,20 with A4 format.
2 1-80 ALPHA(I) Alphanumeric identifier -- printed
as second line of output (up to 80
characters). I = 21,40 with A4 format.
3 l—5R NJ Total number of junctions in system.
6-1OR NC Total number of channels in system.
ll-l5R NCYC Total number of time steps (cycles)
to be completed.
l6-20R NPRT Number of time steps between printouts.
Normally specified to give output at
one-half or hourly frequencies.
21—25R NOPRT Number of junctions for which output
is printed.
119
-------
Card Column Name Description
26-35R. DELI Time interval, in seconds, used in
solution.
36-45R. IZERO Time, in hours, at which computations
begin. Allows starting point to be
anywhere on tidal cycle.
46-50R NETFLW Option parameter. If NETFLW is
specified as any non-zero integer
Subroutine HYDEX is called to compute
net flows and sun!narize hydraulic
parameters. If NETFLW is specified
as zero Subroutine HYDEX is not called.
4 l-5R IPRT Printed output begins at this cycle
number and at each NPRT cycles there-
after.
6-1OR IWRTE Hydraulic parameters are stored on
magnetic tape or disk beginning at
this cycle number.
ll-15R KPNCHI Punch interval for restarting. Mag-
netic tape is written at this cycle
and at each KPNCHI cycles thereafter.
*5 l-5R J Junction number (read as dumy
variable JJ to check card sequence).
6-15R. Y(J) Initial head specified at junction J,
in feet.
16-25R. AREAS(J) Surface area of junction J, in
square feet.
26-35R. QIN(J) Specified inflow or withdrawal at
junction J, in cfs. Inflows must be
assigned negative values, withdrawals
positive.
36-40R NCHAN(J ,l) Channel number of any one of the
channels entering junction J.
120
-------
Card Column Name Description
41-45R. NCHAN(J,2) Channel number of a second channel
(if it exists) entering junction J
If only a single channel element
enters the junction NCHAN(J,2) and
the remaining NCHAN values must be
assigned a zero value. If exactly
two channels enter the junction
NCHAN(J,3) and the remaining NCHAN
values must be assigned a zero
value, etc.
S
a
56-60R NCHAN(J,5) Channel number of the fifth channel
(if it exists) entering junction J.
If less than five channels enter
the junction (NCNAN(J,5) must be
assigned a zero value.
.. S.
Card 5 is repeated for each junction
in the network (NJ cards).
*6 )-5R N Channel number (read as dumy
variable NN to check card sequence).
6-13k. CLEN(N) Length of channel N, in feet.
14-21k. B(N) Width of channel N, in feet.
22-29k. AREA(N) Initial cross-sectional area of
channel N, in square feet. Must
correspond to the initial heads
specified at the junctions at the
ends of the channel.
30-37R. R(N) Hydraulic radius of channel N, in
feet. Taken as the channel depth.
38-45R. CN(N) Manning t s roughness coefficient,
dimensioni ess.
46-53R. V(N) Initial mean velocity in channel
N, in fps.
121
-------
Card Column Name Description
54-58R NJUNC(N,l) The junction number at one end of
channel N.
59—63R NJtJNC(N,2) The junction number at the other
end of channel N.
Card 6 is repeated for each channel
in the network (NC cards).
*7 l-5R JPRT(l) Numbers of those junctions for
6-bR JPRT(2) which printout is desired. There
ll-15R JPRT(3) will be NOPRT different junction
numbers, fourteen to a card. The
numbers need not be in sequence.
S
Card 7 is repeated as many times
as necessary to include all junction
numbers for which printout is
desired.
8 l-5R NK Number of coefficients used to
specify the tidal input
9 1- 1OR. PERIOD Period of the input tide, in hours.
1l-20R. A(l) Coefficients for tidal input at
21—30R. A(2) specified junction(s). Obtained
• from regression analysis program,
REGAN.
S
71-80R. A(7)
10 1-80 ALPHA(I) Alphanumeric identifier--printed
as part of heading for printout
resulting from HYDEX. I = 41,60
with A4 format.
11 1-80 ALPHA(I) Alphanumeric identifier--printed
as part of heading for printout
resulting from HYDEX. I 61,80
with A4 format.
12 I-5R NODYN Number of hydraulic time steps per
quality time step. Defines the
quality time step as the product
of NODYN and DELT.
122
-------
NOTE:. Cards 10, 11, and 12 are read by Subroutine HYDEX but immediately
follow the previous data cards.
Variables Internal to Program DYNHYD
Variable Description
OELT2 Half time step
W 2ir * PERIOD
G Acceleration of gravity
KWRITE Cycle number at which tape for restarting
is written. KWRITE is updated throughout
run.
I Total elapsed time, in seconds. T is
initidily set equal to TZERO and is
incremented by DELI at the start of
each time step.
T2 Total elapsed time, in seconds, for
half-step computations. T2 always lags
I by DELT2.
MS Number of Sine (and Cosine) terms in rela-
tionship defining tidal input.
NL Lowest number of the two junction numbers,
NJUNC(N,l) or NJLJNC(N,2) at the ends of
a channel.
NH Highest number of the two junction numbers,
NJUNC(N,l) or NJUNC(N,2),at the ends of
a channel.
KEEP Temporary variable to store NJUNC(N,l)
while NJUNC(N,1) and NJUNC(N,2) are
interchanged. The two are interchanged
whenever NJUNC(N,l) is a larger number
than 1IJUNC(N,2). Following the inter-
change NJUNC(N,l) is always the smaller
of the two numbers.
NCYCC Counter for the number of hydraulic cycles
(time steps) completed.
AKT Friction coefficient during full-step
computations.
123
-------
Variable Description
AKT2 Friction coefficient during half-step
computations.
YT(J) Head at junction J during half-step.
AREAT(N) Cross—sectional area of channel N during
half—step.
VT(N) Velocity in channel N during half-step.
Q(N) Flow in channel N.
DVDX Defines the velocity gradient U/ x in a
channel.
SUMQ The net inflow or outflow at a junction
from all sources.
TIME Total elapsed time, converted to hours.
VEL Velocity, in feet per second, converted
to sign convention used for hydraulic
printout.
FLOW Discharge, in cfs, converted to sign
convention used for hydraulic printout.
TZERO2 Both are used temporarily to compute the
KTZERO appropriate value for TZERO in case of
restarting.
Tape 3 Tape 3 is the hydraulic extract tape
created to serve as input to the quality
program. Tape 3 also serves as a restart
device in the event of premature termina-
tion of execution.
Tape 5 Tape 5 indicates card input.
Tape 6 Tape 6 indicates printed output.
Tape 8 Tape 8 indicates punched output.
Tape 10 Tape 10 used as a temporary (or permanent
if desired) record of the entire hydraulic
solution. Pertinent hydraulic parameters
are stored on tape 10 for each time step
and for every junction and channel in the
system *
124
-------
Variables Internal to Subroutine HYDEX
Variable Description
NSTOP The last cycle completed in the hydraulic run.
NSTART The last cycle number of the hydraulic run at
which the last full tidal cycle began. The
total number of cycles (time steps) in the
full tidal cycle equals NSTOP - NSTART.
DELTQ Time interval in hours, to be used in quality
run and on which hydraulic parameters are to
be suninarized. DELTQ = (DELT * NODYN)/3600.
JRITE The cycle number from the hydraulic run at
which the hydraulic extract tape (Tape 3)
is written. JRITE is initially set equal to
NSTART and is then incremented by NODYN at
the completion of each write corrinand.
ICYCTF Cycle number from the transient flow (hydraulic)
program which was stored on tape 10.
YNEW(J) A new name for the head at junction J to
differentiate it from the head at the same
junction at another time step.
QNET(N) The mean or net flow in channel N over the
full tidal cycle. QNET(N) is used to accum-
ulate the entire flow in channel N over the
full tidal cycle. This total Is then divided
by the number of hydraulic time steps compris-
ing the tidal cycle to compute the net flow.
QEXT(N) The mean flow in channel N over each quality
time step.
VEXT(N) The mean velocity in channel N over each
quality time step.
VMIN(N) The minimum velocity in channel N over the
entire tidal cycle. If flow reversal occurs
in channel N, VMIN(N) will be the maximum
negative velocity.
VMAX(N) The maximum velocity in channel N over the
entire tidal cycle. If flow reversal occurs
in channel N, VMAX(N) will be the maximum
positive velocity.
125
-------
Variable Oescrjptlon
KFLAG A flag which marks the beginning of the
computations for determining the minimum
and maximum cross-sectional areas in each
channel.
KFLAG2 A flag which marks the beginning of the
computations for determining the minimum and
maximum values of QEXT(N).
YAVE(J) The mean head at junction J over the full
tidal cycle.
YMIN(J) The minimum head at junction J over the
full tidal cycle.
NMIN(J) The hydraulic cycle number at which the
minimum head at junction J occurs.
YMAX(J) The maximum head at junction J over the full
tidal cycle.
NMAX(J) The hydraulic cycle number at which the
maximum head at junction J occurs.
ARAVflN) The mean cross-sectional area of channel N
over the full tidal cycle.
ARNIN(s) The minimum cross-sectional area of channel
N over the full tidal cycle.
ARMAX(p() The maximum cross-sectional area of channel
N over the full tidal cycle.
QEXMIN(N) The minimum of all the QEXT(N) values for
channel N.
QEXMAX(N) The maximum of all the QEXT(N) values for
channel N.
RANGE (J) The tidal range at junction J, I.e., RANGE(J)
YIIAX(J) - YMIN(J).
126
-------
I Junction data cards (Nd cards)
Data for HYDEX (3 cards)
Tidal Coefficients (i card )
List of junctions for output (1-4 cards)
\
- .4
Channel data cards (NC cards)
Control cards (4 cards)
H
FIGURE 44. SA iPLE DATA DECK MAKEUP — PROGRAM DYNHYD
-------
Job Control Cards
Perjoheral Hardware Control
FIGURE 45.
SAMPLE JOB DECK MAKEUP —— PR RAM DYNHYD
-------
QUALITY PROGRAM (DYNQUA)
As with the hydraulic program the requirements for implementing
the quality program can vary tremendously from run to run. Although
certain provisions have been incorporated in the model to aid in
implementing various types of quality studies the input data requirements
may still be significant. These provisions and other features of the
model will be discussed briefly in the following section. Following
the discussion of the program logic a more thorough discussion of the
input requirements, output options, special features, and potential
implementation difficulties will be presented. Detailed descriptions
and formats of the input variables and a description of program variables
will also be included along with illustrations of the data deck and
overall job deck. The program listing for the quality program is included
in the Appendix along with a sample of the output from the program.
Flow Dj gram and Program Logic
The quality program has been changed significantly since the
development by the contractor. In addition to the previously discussed
changes in the method utilized for advective transport several routines
have been incorporated to handle special quality problems (such as
agricultural water use), to decrease computation time to attain steady
state conditions, or to provide more flexibility in the types and
quantities of output obtained. In general it is possible to bypass
these special routines with specification of appropriate control para-
meters. It might also be appropriate, in certain cases, to remove them
from the program entirely; however, it is suggested that this latter
alternative not be exercised until a user is intimately familiar with
the program as the effect on other portions of the program may not
always be apparent.
The discussion of the program logic will generally follow the
simplified flow diagram presented in Figure 46. The numbers adjacent
to each step are for reference only and do not refer to numbers within
the program.
The network size (number of junctions and channels), the starting
and stopping point on the hydraulic extract tape, and the quality time
step are specified as the initial step of the quality program. The
hydraulic extract tape (tape 3) is then read completely through to
obtain the geometric and physical data for the system (step 2). The
tape Is then rewound to ready it for reading the hydraulic parameters
for each time step stored at the beginning of the tape. The starting
point on the tape Is specified along with the length of the run, the
output options, and other control parameters (step 3). These parameters
are printed as part of the heading to identify the run (step 4).
The number of quality constituents to be considered, their charac-
ten stics (conservative, non-conservative, decay coefficients, etc.),
and an alphanumeric Identifier for each constituent are specified
(step 5). The upper concentration limit for each constituent (above
129
-------
READ INITIAL CONTROL DATA
J1
READ
‘I ,
SYSTEM DATA FROM HYD. EXTRACT TAPE
[ AD CONTROL DATA
FOR QUALITY
RUN
PRINT OUTPUT
HEADING
AND CONTROL
PARA ETERS
4
‘I
3
READ CONSTITUENT CH
ARACTERISTICS 1
READ
l
CONCENTRATION LIMITS
1 6
I PRINT CONSTITUENT CHARACTERISTICS
APPLY 8
w::TE WATER RETU
YES
LPRINT
NETWORK
AND HYD. PARAPWETERS
READ
INITIAL
CONDITIONS AND WASTE
LOAD
DATA FOR
ALL CONSTITUENTS
INITIAL
< CONDfTIONS ,__.>
YES
17
READ WASTE WATER
RETURN FACTORS
10
11
I
READ JUNCT I ON NUMBERS AND
FACTORS
FOR ADJUSTING
INITIAL
CONDITIONS
FIGURE 46
SIMPLIFIED FLOW DIAGRAM — PROGRAM DYNQUA
NO
13
130
-------
APPLY FACTORS
P
TO INITIAL CONCENTRATIONS 14
15
f
L
READ AND PRINT
CONCENTRAT IONS
BOUNDARY
FOR ALL
CO(JST ITUENTS
p
READ JUNCTION NUMBERS FOR PRINTOUT I
PRINT WASTE WATER RETUF J FACTORS
16
17
18
INITIALIZE
COUNTERS
AND
COMPUTATION
PARMETERS
1
SWITCH
NUMBERS IF
JUNCTION
NECESSARY
19
20
COMPUTE INITIAL MASS OF EACH
CONSTITUENT IN EACH JUNCTION
COMPUTE DIFFUSION CONSTANT
25
FIGUF€ 46.(Cont.)
PRINT
INITiAL
CONDITIONS AND
WASTE
LOAD
DATA
FOR
ALL CONSTITUENTS
I CALCULATE VEAN VOL U E OF EACH JUNCT I ON
4
I 21
READ TAPE TO ESTABLISH
INITIAL JUNCTION HEADS
22
23
ADJUST ? AN JUNCTION
VOLUI’ ES TO INITIAL HEADS
24
131
-------
I COMPUTE VOLUPVE OF INFL(Yii—OUTFLOW
DURING A FULL IRE STEP
NIT IAL COND1
1 D C 536 ICYC = INCYC, NQCYC
READ VELOCITIES AND FLOWS FROM
TAPE 3 FOR CURRENT TIP& STEP
32
THIS THE END OF
NO
DETERMINE FLO* DIRECT (ON AND
COMPUTE QUARTER—POINT
CONCENTRAT JON FOR EACH
CONST ITUENT
1!
I
MAKE CONST ITIENT TRANSFERS
L
(ADVECT ION AND DIFFUSION)
FIGUIE 46 (Cont.)
26
YES
NO
1
WRITE TAPE 10
28
I
FLAG CYCLE
I NCREPENT
NUMBER AND
COUNTER 29
I J30
I
] 31
YES
+
REWIND TAPE 3 33
READ JUNCT I ON HEADS FOR CURRENT I I PC STEP
1
34
35
36
132
-------
NO
D
IS 37
CONST ITUENT
< NCONSERVAT I VE
IS 39
CONST TUENT
4
AD JUST MASS FOR WASTE
DISCHARGE OR INFLOW
REMOVE MASS IN DIVERSIONS
APPLY WASTE WATER RETURN FACTORS
1
NO
YE S
YES
‘I !
REDUCE OXYGEN
MASS BY AMOUNT BOD
WAS DECAYED
) APPLY REAERATION COEFF. J
j42
j 44
COMPUTE NEW JUNCTION VOLUMES
FOR CURRENT I I ME STEP
COMPUTE NEW CONCENTRATION
FOR EACH CONSTITUENT
FIGURE 46 (Cant.)
45
46
I I
38
40
41
133
-------
47
NO
YES
49
YES
SET CONG. AND MASS
EQUAL TO ZERO
50
NO
53
54
IS
CONC . ABOVE
SPECIFIED LIMIT AT
ANY JUNCTION
9
IS THIS
THE BEGINNING OF
THE LAST TIDAL CYCLE OF
RUN
NO
1 INITIALIZE COUNTER
AND REWIND TAPE 10
57
FIGURE 46 (Cont..)
134
-------
IS “ - 58
THIS A ‘•—‘-.
SPECIFIED SU ARY
TIDAL CYCLE
YES
IS
THIS THE
INITIAL POINT ON
THE TIDAL CYCLE
WRITE QUALITY DATA FOR
CYCLE ON TAPE 10
FIGURE 46 (Cont,)
REINITIALIZE
COUNTER AND SET
NEXT WRITE
65
NO
59
YES
61
135
-------
DATA FOR A
FULL TIDAL CYCLE
BEEN STORED ON
TAPE 10
PRINT DATA FOR
SELECTED LJUNCT I ONS
INCRE ENT PRINT COUNTER
AND SET NEXT PRINT CYCLE
75
REINITIALIZE COUNTEI
AND SET NEXT PRINT
CYCLE
FIGURE 46 (Gon±.)
67
68
NO
71
136
-------
76
SUBROUTINE QUALEX
[ PRINT SUMMARY HEADING J
79
u
80 I
AND QUALITY
10
READ CYCLE NUMBER
DATE FROM TAPE
81
IS THE
TIDAL CYCLE
IT IAL INT T P0 INT ON TH
NO
ACCUMULATE TOTAL FOR AVE. CONC.
FOR MIN. AND MAX. 1
TO THIS POINT ]
CHECK
CONC.
INITIALIZE COMPUTATIONS FOR1 82
MIN.,, MAX., AND AVERAGE
CONCENT RAT IONS
YES
84
FIGURE 46 (Cont)
YES
77
91
0
137
-------
85
YES
COMPUTE AVE. T i DAL CYCLE
CONC. AT EACH JUNCTION
86
87
YES
NO
CALL ZONES
TO SUMMARIZE DATA
IN SPECIFIED MANNER
89
90
FIGUFE 46 (Cont.)
38
-------
which execution is terminated) is specified (step 6) and the constituent
characteristics are printed to identify the run (step 7).
If waste water return factors are to be applied (step 8) the speci-
fied diversion and return flow junctions and the factors to be applied
are read (step 9). A sumary of the network and hydraulic parameters
is printed to provide a reference for the inputs which had been specified
for the hydraulic run on which the quality run is based (step 10).
The quality waste loads (flows and concentrations for each constit-
uent) are read along with the initial concentrations of each constituent
at each junction (step 11). If the initial concentrations for any con-
stituent are to be adjusted (step 12) the multiplication factors are
read (step 13) and applied to specified groups of junctions (step 14).
The adjusted concentrations and a summary of the specified waste loads
are printed for reference (step 15).
The seaward boundary concentrations for each constituent for each
time step over a tidal cycle are read and printed (step 16). If the
concentration of a particular constituent does not vary over the tidal
cycle a constant value can be specified. The list of junction numbers
for which quality predictions within a tidal cycle are to be printed
is read (step 17). The waste water return factors which had been read
previously are printed at this point (step 18) and the various counters,
flags, and computation parameters are Initialized (step 19). The
junction numbers assigned to each channel are interchanged, if necessary,
to assure compatibility with the sign convention established in the
hydraulic run (step 20).
The mean volume of each junction is computed, based on the mean
depth computed in the hydraulic run (step 21). Tape 3 is then positioned
at the hydraulic cycle number at which the quality run is to begin and
the junction heads are read (step 22). The mean junction volumes are
then adjusted to the new heads (step 23) to establish the volume of the
system at the start of the quality run.
The total initial mass of each constituent is computed for each
junction (step 24) and the diffusion constant is computed for each
channel (step 25). The total volume of inflow (or withdrawal) at each
junction during a quality time step is computed (step 26) prior to
entering the main computation loop.
A check is made to determine if the initial conditions are to be
written on tape 10 (step 27) for suninarizing the predictions over the
first tidal cycle. If so the values are stored on tape 10 (step 28),
the cycle number is flagged and a counter Is incremented which records
the number of times the tape is written (step 29).
Step 30 begins the main computation loop which is executed for
each time step. Tape 3, which had been properly positioned prior to
entering the main loop Is read to establish the initial channel velocities
139
-------
and flows in each channel (step 31). A check is made (step 32) each
time the tape is read to determine if the end of the tidal cycle has
been reached. If so, the tidal cycle will he repeated by rewinding
tape 3 (step 33) and reading the junction heads for the start of the
next time step (step 34). If the end of the tidal cycle has not been
reached the heads for the next time step are read as the next record on
the tape.
Transfers of quality constituents are made from junction to junction
based on the flow in the connecting channel and on the concentration
gradient between the junctions. The flow direction in each channel
is determined and the concentration at the quarter point (from the up-
stream end) of the channel is computed (step 35). The mass of constit-
uent to be transferred in each channel both by advection and diffusion,
is then computed and the transfers made (step 36).
For each non-conservative constituent the mass existing at each
junction is decayed by applying the specified decay coefficient (steps
37 and 38). If a constituent is dissolved oxygen (step 39) its mass
at each junction is reduced by the amount the associated BOO was decayed
(step 40) and the specified oxygen reaeration coefficient applied to the
saturation deficit existing (step 41).
At each junction where an inflow or a waste discharge exists
constituent is added to the system (at the concentration specified for
the input) and at junctions where diversions exist constituent is re-
moved at the concentration existing at the junction (steps 42 and 43).
The waste water return factors are then applied to the specified
junctions (step 44).
The new concentrations at each junction are then computed by first
adjusting the junction volumes to the start of the next time step
(step 45) and then dividing the mass of each constituent by the new
volume (step 46).
If the predicted concentration at any junction is below zero
(step 47) the concentration and the mass are set equivalent to zero
(step 51). A statement pointing out the correction is either printed
(step 50) or not depending on the control option specified (step 48)
and on whether computations have proceeded to the last tidal cycle of
the run (step 49). GuIdelines for printing or suppressinq these print
statements are included in a later section.
To prevent supersaturation of dissolved oxygen the predicted con-
centration Is set equivalent to the specified saturation concentration
if the saturation concentration is exceeded (steps 52 and 53) and a
statement to that effect is printed (step 54).
The predicted concentrations are also checked against the specified
upper limits for each constituent and the run is aborted if any limit is
exceeded (step 55).
140
-------
A summary (minimum, maximum, and average concentrations over the
full tidal cycle) of the predictions for the last full tidal cycle is
always provided. Therefore at the start of the last tidal cycle
(step 56) tape 10 is rewound and the counter for writing the tare is
reinitialized to zero (step 57). The counter is then incremented to
unity (step 59), the cycle number (time step) flaqged (step 61), and
the predictions stored on tape 10 (step 65). For all time steps other
than that markina the start of the last tidal cycle a check is made to
determine whether the predictions for the time step are to he included
in a summary or not (step 58). If so, the counter recordinq the number
of times tape 10 is written is incremented (step 59) and a check made
(step 60) to determine whether the counter has a value equal to unity
(indicating the start of the record on tape 10) or greater than unity
(indicating the continuation of the record on the tape). For the initial
record the time step number is flagged (step 61) and the tape is written
(step 65). For time steps beyond that of the initial record a check is
made to determine whether the end point of the full tidal cycle of data
has been reached (step 62). The number of the time step marking the
end of the record on tape 10 is also flagged (step 63), the counter is
reinitialized to zero and the time step number marking the start of the
next summary is set (step 64) before the tape is written (step 65).
When the last computation cycle of the run is reached (step 66)
the final predictions are stored on tape 9 (step 67). The record on
tape 9 can be used to extend the run at a later time, if necessary.
Restart capability is also provided each time the summary is obtained
(step 69). Tape 9 is rewound (step 68) at the completion of each update
so that only the most recent predictions are retained.
Printout is automatically obtained for each time step of the last
full cycle of the run (steps 70 and 71). For other print cycles
(step 72) the print counter is incremented and the next print cycle
set (step 73). Printout continues at the specified print interval until
a full tidal cycle of printout is obtained (as determined at step 74)
at which point the print counter is reinitialized and the next print
cycle (usually several tidal cycles later) established (step 75).
At the completion of storing a full tidal cycle of data on tape i
(step 76) subroutine QUALEX is called (step 77) to summarize the data.
Following the summary, control returns to the end of the main computation
loop (step 78) and execution proceeds for the specified number of cycles.
A heading to identify the summary is provided each time subroutine
QUALEX is called (step 79). A cycle number (and its associated data)
is read from tape 10 (step 80) and, for the initial time step on the
tape (as determined at step 81) the romputations for the minimum, maxi-
mum, and average concentrations for each constituent are initialized
(step 82). The data for the next time step is then read from tape 10
(step 80) and the new concentrations for eac constituent are added
to the accumulated totals for determining the average (step 83).
141
-------
The previously established values for the minimum and maximum concen-
trations are checked against the new concentrations at each junction
and are updated if necessary (step 84). Following the last cycle on
tape 10 (as determined at step 85) the averacie concentration over the
full tidal cycle is computed (step 86). The results of the suninary are
printed (step 87) and depending on the specified control option (step 88)
subroutine ZONES is either called (step 89) or not (step 90) before
returning to the main program (step 90). Prior to nroaram termination
subroutine PUNCH is called (step 91) to punch the restart record stored
previously on tape 9. A discussion of subroutine ZONES is included
in a later section.
Input Data Requirements
As the quality model has been refined and developed by FWQA the
input data requirements to execute the program have increased. Generally,
the additional inputs are required to provide additional flexibility in
the types of problems that can be modeled or studied, to better control
the types and quantities of output obtained, or to reduce the required
execution time to attain steady state predictions.
For discussion purposes the inputs will be broken into four cate-
gories: control parameters, waste load data, initial conditions, and
boundary conditions.
Control parameters . The control parameters are required to specify
the number and types of quality constituents, the length of the run,
the type and frequency of printout, the time step to he utilized, the
starting point on the tidal cycle, etc. The specification of these
parameters is generally straightforward and does not present a problem.
A more complete description of these parameters (variable names, format,
etc.) is included in a later section.
Waste Load Data . Although not always the most difficult to specify,
the waste loads to the system are the most basic inputs to any quality
simulation. These inputs include the specification of the concentration
of each constituent considered In each hydraulic inflow to the system,
e.g., streamflows, storm runoff, waste water discharges from any source,
etc. It Is through these inputs that the appropriate mass of each
constituent is added to the system during the time period considered.
For inflows and wastewater discharges it is necessary to specify both
the hydraulic and quality inputs, i.e., flow and concentration, in order
to define the rate of addition of quality constituent. For diversions
it is necessary to specify only the flow since the constituent is re-
moved at the concentration existing (computed) at the diversion point.
For convenience the hydraulic component at each junction will normally
be the same as specified in the hydraulic run (except as noted below).
The hydraulic behavior of the system for each quality time step has been
fixed in the hydraulic program and is not affected by the inflows or
waste discharges specified In the quality program. Thus if a diversion
142
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existed in the hydraulic solution it is necessary to re-specify that
diversion in the quality solution in order that the appropriate mass
of constituent be removed, otherwise water ri1l be removed but not
constituent. Similarly if an inflow or waste discharge existed in the
hydraulic solution it is necessary to specify both the flow rate and
the concentration in order to add the appronriate mass of constituent
during each time step. If either component is not specified water will
be added but not constituent. As was discussed previously in Part I,
this feature of the quality model allows the effects of evaporation and
precipitation to be included in the cuality predictions.
This feature makes it convenient to add constituent at any desired
point in the system regardless of whether a hydraulic inflow exists at
the point. For simulating a release of dye or other tracer constituent
wherein a very small quantity of tracer (but with high concentration)
is released any convenient flow rate and concentration can be specified
such that the appropriate mass is added each time step. Because of the
programed output formats it may be necessary to scale the inputs such
that the desired units are obtained e.g. parts per million or parts per
billion.
For certain water uses the concentration of the waste water return
is dependent on the quality of the water diverted or on other factors
such as described previously in Part I for agricultural water use. The
model can treat such diversions and waste water returns in a special way.
If water is diverted from the system for a specific use and all or part
of the diversion is subsequently returned at the same or a different
concentration it is possible to relate the total mass of constituent
returned to that diverted as indicated previously by enuation 44.
QdCd = aCa + b (44)
The junction from which the water is diverted is paired with the junction
at which the waste water is returned. For convenience such pairs of
diversions and waste water returns are grouped into units, two pairs to
a unit. The same return factor m and constant h are applied to both
pairs within a unit. In certain cases, wherein it is desired to relate
a single return to a single diversion, a unit will have only a single
pair; however, the program logic requires that appropriate dunry junction
numbers be included to fill out the unit. This can easily be accomplished
by selecting any two junctions which have no assigned inflows or with-
drawals as the duniny junctions to be included. The entire routine for
applying the waste water return factors can be bypassed by specifyinn
the number of units (NUNITS) as zero.
One additional input required for each constituent which is to be
treated as non-conservative is the decay rate (or reaeration rate)
constant to be applied. The desired rate is expressed for a time base
of one day (e.g. 023 per day, base e). Because the model uses a smaller
time step (such as one-half hour) the rate is converted to the appro-
priate time base by an expression of the form:
143
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D = e t
where z t is equal to the quality time step used (in days), K is the
decay (or reaeration) rate per day, e is the base of the natural
logarithms, and 0 is the decay factor or reaeration rate applied to the
mass at each junction during each time step. The conversion is internal
to the program; therefore the required input must be for a time base
of one day and for logarithm base e.
Initial Conditions . For certain studies (for example prediction
of steady state distributions) the initial or starting concentrations
for a run may be relatively unimportant in that they do not affect the
final quality predictions. For other studies (such as studies to
determine the rate of salinity buildup or flushino) the starting con-
centrations significantly affect the final distribution and therefore
must be carefully specified.
For verification runs in which historic quality conditions are
simulated for a specific time period the initial quality distribution
may be very critical and can be quite troublesome to specify unless
adequate historic data are available. The importance of the starting
concentrations in such runs and the difficulties associated with speci-
fying them were discussed previously in Part I I.
Although the initial concentrations do not affect the final steady
state distribution predicted for a given set of hydraulic and quality
inputs, the execution time required to achieve the steady state con-
dition can be significantly affected. Obviously the closer the initial
concentrations are to the steady state concentrations the shorter will
be the required execution time. It is, of course, difficult to estimate
a priori the steady state distribution of any particular constituent
resulting from a given set of hydraulic and water quality inputs. It
is possible to utilize steady state predictions from previous quality
runs as the starting concentrations for new runs. A special feature
of the model allows the adjustment of such initial concentrations within
the program by applying a multiplication factor to the concentrations
read from the input deck. The utilization of this feature can also
reduce significantly the required execution time to attain steady state
conditions. For example a run might typically be continued for fifteen
tidal cycles and then examined to determine whether the predictions
have converged to a steady state condition. If not, the predictions are
extrapolated to an estimated steady state condition and multiplication
factors computed which, when applied to the ending concentrations of
the fifteen tidal cycle run, would result in the estimated steady state
conditions. These factors are applied to the concentrations existing at
each junction in a specified group of consecutively numbered junctions.
The ending concentrations from the previous run are normally punched
in a restart deck which is used to restart the run. The mulitplication
factors are applied to the concentrations after they are read from the
deck; therefore, no manual adjustment of the concentrations in the deck
144
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is required. This restart procedure is illustrated in Figure 47 showing,
in (a) a restart multiplication factor greater than unity, and, in (h)
a factor less than unity. Extrapolations such as illustrated should be
determined for several locations throughout the system. rn many cases
the solution may have reached a steady state condition in one area while
the concentrations in another area are increasing and those in yet
another area decreasing. Separate factors are prepared for each of
the latter two areas and applied to the appropriate sequences of junction
numbers to increment the concentrations. In the event the factors over-
adjust the concentrations the solution will converge to the steady state
solution from the other direction, as illustrated in Figure 47(b).
Boundary Conditions . Frequently one of the most troublesome inputs
is the specification of the quality conditions at the seaward boundary.
Ideally the model boundary would be the ocean, a source and sink of
known concentration. At upstream locations in an estuary the concentra-
tions of most constituents vary with the flooding and ebbing of the
tide and may also be a function of both the freshwater flow through
the estuary and the waste loads on the system. Because each of these
(tides, freshwater flow, and waste loads) is time dependent an estuary
rarely approaches a steady state quality condition. The problem of
specifying the boundary thus is one of estimating the tidal cycle varia-
tion of a constituent at the boundary location for a given freshwater
flow through the system. In effect the boundary concentration specifies
the concentration of the tidal flow entering the system on each flood
tide. For simulation of historic conditions sufficient data must
be available to establish the appropriate boundary conditions. For runs
predicting future conditions or for comparing alternative waste disposal
schemes it is necessary to estimate the quality levels which will result
at the boundary for the specified set of hydraulic, tidal, and waste
load conditions, i.e., the final results need to be known before the
boundary can be specified. This dilema can perhaps best be circumvented
by the proper location of the boundary and by determining (through trial
runs) the sensitivity of upstream predictions to the specified boundary
conditions. Generally the effect of the boundary on upstream predictions
decreases as the distance from the boundary increases. The model boundary
should thus be located well downstream from any area of concern in the
system and the specified boundary condition should be such that it not
significantly bias the predictions in the areas of concern.
For certain constituents with little or no concentration gradient
through the system the boundary can properly be snecified as a constant
value. For constituents (such as salinity) with a significant gradient
through the system the concentration in the water entering through
the seaward boundary will vary with the tidal phase. In such cases the
boundary condition is defined by specifying a concentration for each
quality time step over the full tidal cycle.
145
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(a)
I 1
1 I I
I I I
I I I
I I
I
5 10
IS 20 25
30 35 40
45 50 53
60 65
70
75 80
S Model
— MeOel without foctors
M nu l e*tr000lQtiofl
FIGURE 47. APPLICATION OF RESTART FACTORS
z
0
I-
a
I-
z
w
C-)
z
0
C - )
t
(b)
a — — _ — — —
S I C iS 20 25 30 35 40 43 50 55 10 65
ELAPSED TIME, IPI TIDAL CYCLES
146
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Output Options and Control
A great deal of flexibility exists for specifying the type and
quantity of printed output from the quality model. Two basic types
of output are available: 1) predictions at specified junctions and
at specified time steps to define the intratidal variation of a
particular constituent, and 2) a summary in the form of the minimum,
maximum, and average concentrations predicted at every junction in
the system over a full tidal cycle. Output of both types is obtained
only for selected tidal cycles through the run with output of the first
type typically obtained at hourly (or once ever.y two hours) intervals
within the tidal cycle.
In addition to the printed output the quality predictions are
stored on tape or disk at periodic intervals through the run to provide
restart capability in the event execution terminates prematurely. If
the run terminates normally the ending conditions are stored and are
normally punched into a restart deck that can be used to extend the run.
Printout of the intratidal variation of the quality predictions
is controlled through the specification of the four inDut parameters,
IPRT, NQPRT, NEXTPR, and INTBIG. IPRT defines the initial print cycle
in the quality run and NQPRT defines the print interval, in cycles
(time steps). Printout which begins at cycle IPRT continues at the
specified interval, NQPRT, for one complete tidal cycle and is then
terminated. Printout begins again at cycle FIEXTPR and is obtained
each NQPRT cycles for a complete tidal cycle and is then again terminated.
NEXTPR is then incremented by INTBIG to define the starting point for
the third print sequence which again continues for a full tidal cycle.
NEXTPR is incremented by INTBIG again, etc., etc. Generally IPRT is
specified to obtain printout for the initial tidal cycle of a run to
provide a check on the starting concentrations. Execution can then
continue without output for as long as desired, as specified by NEXTPR.
Printout for a full tidal cycle is then obtained at equal intervals
for the remainder of the run as defined by INTBIG, i.e., INTBIG defines
the interval between each print sequence.
Printout of the quality sumary for a full tidal cycle is controlled
through the specification of the three input parameters IWRITE, NEXTWR,
and IWRINT. IWRITE is the quality cycle number at which the initial
sumary begins, NEXTWR is the quality cycle number at which the second
suninary begins, and IWRINT is the interval (in quality cycles) between
all subsequent sumaries.
Output can also include the sumary of the quality predictions
in any special manner desired, as programed into subroutine ZONES.
For example if it is desired to compute the mean constituent concentra-
tion in a certain zone or embayment of the system the junction numbers
comprising the zone are programed into the subroutine. Subroutine
ZONES is thus unique for each system and can include as many special
features as desired. Subroutine ZONES can be bypassed with the proper
specification of the control variable KZOP.
147
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An option is also provided to suppress the printout of the state-
ment generated whenever the concentration drops below zero (depletion
correction). For runs such as the simulation of a prototype dye re-
lease, wherein the initial concentrations at every junction in the
network may he zero, many such depletion corrections will occur and
it is desirable to sunpress the printed statement. During the initial
time steps of such a simulation a quality gradient beqins to form with
the maximum concentration existirn’ at the discharae point of the dye.
As the solution progresses the dye continues to build up and snread to
adjacent junctions. At any given tire there are several junctions which
lie just beyond the plume of dye, i.e., which remain at zero concentra-
tion but which are imediately adjacent to a junction which received
dye. In such cases there is an apparent concentration gradient between
the junctions and, when the flo%z direction is from the junction with zero
concentration to the junction with an above-zero concentration, the
program will compute an above-zero concentration at the ouarter-noint
and remove mass from the u strear junction, creating a ne’iative concen-
tration. The neqative concentration is corrected (i.e., assigned a
zero value) and, unless suppressed, a statement of the correction iill
he printed. As the peripheral edge of the dye spreads more and more
junctions are affected. Printout of the depletion correction can be
suppressed in such runs by the proper specification of the control
variable KOCOP.
For runs in which dissolved oxygen is one of the constituents
considered the printout of the depletion correction statement should
not be suppressed as the occurence of a negative concentration of
dissolved oxygen may indicate anaerobic conditions. Care should he
exercised in interpreting depletion corrections however, because the
depletion may be caused by a slinhtly unstable solution technique and
may not be an indication that the dissolved oxygen has been biochemically
depleted.
Interpretation of Output
Output from subroutine ( UALEX and ZONES can significantly reduce
the manual effort required in the interpretation of model predictions.
For example in determinina hether a solution has reached steady state
throughout the system it is only necessary to compare the maximum
(the minimum or average could also be used) concentrations listed for
representative junctions for the last tidal cycle of the run with those
listed for the same junctions for the previous tidal cycle sumarized
(usually five to ten tidal cycles earlier). If the change in concentra-
tion at each junction is within acceptable limits the solution can be
considered at steady state. For the San Francisco Bay system a solution
was generally considered at steady state if the concentration change
at each junction over the last ten tidal cycles of the run did not
exceed three percent. If the change in concentration at any junction
is greater than the acceptable limit the concentration can be extrapo-
lated to steady state and an appropriate restart factor determined as
discussed In an earlier section.
148
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In cases wherein model predictions are being compared to prototype
data it may be necessary to refer bdck to the hydraulic solution to
assure that the comparisons are for the proper tidal phase, e.g., if
slack water concentrations are bein’j compared it is necessary to deter-
mine that the model prediction is representative of slack water. The
ouality printout defining the intratidal variation includes the tidal
stage for each junction so that the velocity data associated with that
tidal staoe can be determined from the hydraulic run (provided printout
was provided for the junctions in question).
Potential Implementation Difficul ties
In its present form several of the variables used in the nuality
program share comon storage locations (as specified in the EOUIVPLFNCE
statement) to reduce overall storage requirements. If rrograrn logic is
altered or if DIMENSION changes are made the programed EQUIVALENCE
statement may also require modification.
For quality studies wherein the hydraulic or waste load conditions
change during the period of study it may be desirable to break the qual-
ity solution into two or more parts with a different hydraulic solution
utilized for each part. In such cases the transition from one part to
the next can introduce difficulties, particularly if different tidal
conditions are utilized for the two parts. At the end of each run the
ending concentrations of each constituent are stored on tape or are
punched into a restart deck. It is thus the concentration and not
the total mass which is carried over if the run is extended. It is
therefore important that the volume of the system at the start of a
continuation run be the same as the volume existing at the end of the
previous run. If a run is extended utilizing the same hydraulic solu-
tion the restart point on the tide will be identical to the previous
stopping point (as specified by NRSTRT and NTAG), assuring the proper
starting mass of each constituent in the system. If the extension of a
run is based on a different hydraulic solution it is important that
the starting point on the new tide be as close as possible to the ending
point on the previous tide (both tidal stage and phase) so that the
starting volume (and hence the initial mass of each constituent) is
appropriate.
Execution Time
The time required to execute the quality program is dependent on
the computer used (and the accounting procedure utilized), the size
of the network, the number of constituents included in the simulation,
the time step utilized, the overall length of the simulation, and the
amount of printout specified. When considering the overall cost to
execute the quality program it is necessary to realize that the quality
program cannot be executed without a proper hydraulic input, i.e., the
hydraulic program must first be solved to create the necessary hydraulic
input. Typical execution times for the quality program are sumarized
149
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in Table 7. A CDC 6600 computer was utilized for the solutions in each
case. Experience indicates comparable execution times on an IBfl 3 0/€5
would be approximately two to three times greater than those indicated.
Inconsistencies apparent in the execution tines may be attributable to
the difference in the amount of output obtained for each run.
TABLE 7. EXECUTION TIflES FOR QUALITY ‘0DEL
Size of
Junctions
Systeni
Channels
Time Step
Utilized
(r inutes)
Number of
Constituents
Lenpth of
Run
(days)
Execution
Time
(minutes)
112
170
15
3
20
5
112
170
15
1
20
3
112
170
7.5
1
20
7
C30
10 O
30
1
28
14
830
1050
15
2
10
10
830
1050
30
3
15
8
830
1050
30
3
20
10
Description and Format of Program Inputs (DYNQUA )
The symbols and format used in the follo ’ing description of the
input data deck for DYNQUA are identical to those used for program
DYNHYD on page 119.
Card Columns flame Description
1 l-5R NJ Total number of junctions in system.
Identical to NJ in program OYNflYD.
6-bR NC Total number of channels in system.
Identical to NC in program DYNI4YD.
1-15R NSTART Cycle number from hydraulic solution
which is the initial cycle on the
hydraulic extract input tape 3.
Identical to NSTART in Subroutine
HYDEX.
150
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Card Column Name
16-20R NSTOP Cycle number from hydraulic
solution which is the final
cycle on the hydraulic extract
tape 3. Identical to NSTOP
in Subroutine HYDEX.
21-25R NODYN Number of hydraulic time steps
per cuality time step. Identi-
cal to NODYN in Subroutine HYDEX.
2 l—5R NRSTRT Cycle number on input tape 3
(hydraulic extract tape) at
which auality run is to begin
(NSTART . NRSTRT $ NSTOP).
6-bR INCYC Initial quality cycle number.
For first run of a series INCYC
should equal 1. For continuation
or restart runs INCYC should
equal x+l where x eQuals the
numt er of cycles completed pre-
viously.
ll-15R NQCYC Total number of auality cycles
to be completed. NOCYC must
include all cycles previously
completed, i.e., NOCYC equals
INCYC plus the additional cycles
to be completed in the current
run.
16-20R KZOP Control option for callinci Sub-
routine ZONES. ZOP must equal
1 to call ZONES or 2 to bypass
ZONES.
21-25R KDCOP Control option for printout of
depletion correction message.
KDCOP must enual 1 for print-
out or 2 to delete printout of
depletion correction message.
26-30R NTAG Counter which is reset to zero
at the completion of each full
tidal cycle. NIAG varies be’-
tween zero and NSPEC where
NSPEC is the number of quality
cycles ner tidal cycle.
151
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Card Column Name Description
31-40R. CDIFFK Constant for computinq diffusion
coefficient.
3 l-5R IPRT Initial print cycle (IPRT must
be > INCYC). Printout begins
for the first time at cycle !PRT
and continues for one full tidal
cycle at intervals of NOPRT
cycles (time steps).
6-1OR NQPRT Number of ouality cycles (time
steps) between printouts. NOPRT
normally is such that printout
is obtained at hourly or two-hour
intervals.
l1-15R NEXTPR Quality cycle number at which
printout begins for second time
and continues at NOPRT intervals
for a full tidal cycle.
16-20R INTBIG Interval, in nuality cycles (time
steps), between the start of print-
outs over a full tidal cycle.
NEXTPR is increased by INTPI( at
the completion of each full tidal
cycle of output.
21-25R IWRITE Cycle number at which storage
of quality data on tape or disk
begins for the first time. Data
for each time step over a full
tidal cycle is passed to Subroutine
QUALEX.
26-30R NEXTWR Cycle number at which storage
of quality data on tape or disk
begins for the second time.
3l-35R IWRINT Interval, in auality cycles
(time steps), between the storage
of data on tape or disk. NEXTWR
is increased by IWRINT at the com-
pletion of storing data for a full
tidal cycle. Quality sumaries
are obtained at IWRINT intervals.
152
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Card Column Name Pescription
4 1-ge ALPHA(1) Alphanumeric identifier for
quality run--printed as heading
for output (1=41 ,6P with M
format).
5 1-80 ALPHP.(I) Alphanumeric identifier for
quality run-—printed as headinq
for output (I= 1,8O with A4
form t)
6 l-5R NUflCON Number of quality constituents
considered in the run
(1 NUMCON 5).
7 1-5R NCONDK(I) Nurnlcr (1 through 5) of the first
nonconservative constituent, e.g.,
if the first two constituents are
conservative and the third noncon-
servative then !ICOrIDK(1)3. If
none of the N(JMCON constituents are
treated as nonconservative NCONDK(1)
must be set equal to zero.
6-bR NCONOX(l) Number of the constituent which
is dissolved oxygen and which
is associated with the noncon
servative constituent (BOO) assigned
to NCONDK(1). If dissolved oxygen
is not being considered rlCONOX(l)
must be set equal to zero.
1l-15R NCONDK(2) Number of the second nonconser-
vative constituent considered.
If only one (or none) of the
constituents being considered
is nonconservative NCONDK(2)
must equal zero.
16-20R NCOFIOX(2) Number of the constituent (if
any) associated with the con-
stituent assigned to NCONDK(2).
21-25R NCONDK(3) Number of the third nonconser-
vative constituent. NCONDK(3)
must equal zero if two or fewer
nonconservative constituents are
considered.
153
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Card Column Name flescrirtion
26-3OF NCONOX(3) Number of the constituent (if
any) associated with the con-
stituent assigned to NCONDK(3).
4 1-45R NCONDK(5) Number of the fifth nonconserva-
tive constituent. NCONDK(5)
must equal zero if four or fewer
nonconservative constituents are
considered.
46—50R NCONOX(5) Number of the constituent (if
any) associated with the constit-
uent assigned to ICONDV(5).
*7a 1-bR. DECAY(l) Decay coefficient (base e, r’er
day) applied to the nonconserva-
tive constituent assigned to
NCONDK(l), i.e., to the first
nonconservative constituent.
ll-20R. REOXK(l) Reoxygenation coefficient (base
e, per day) applied to the DO
constituent (if any) assigned to
NCOfIOX(l).
2l-30R. CSAT(l) Dissolved oxygen saturation
concentration, in rrg/l, for the
DO constituent assianed to
fZCONOX(l).
1-1OR. DECAY(2) Decay coefficient (base e, per
day) applied to second noncon-
servative constituent.
ll-20R. REOXK(2) Reoxygenation coefficient (base
e, per day) applied to the DO
constituent (if any) assigned
to P4CONOX(2).
21-30R. CSAT(2) DO saturation concentration,
in mall, for DO constituent
assigned to NCONOX(2).
154
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Card Column Hame Description
1-10R. DECAY(5) Decay coefficient applied to
fifth nonconservative constituent.
1l-20R. REOXK(5) Reoxygenation coefficient anplied
to the DO constituent (if any)
assigned to NCONOX(5).
21-30R. CSAT(5) DO saturation concentration for
constituent assigned to
1 CON0X(5).
*8 1-80 ALPHA(1) Alphanumeric identifier, one card
for each constituent (1=121,
NALPHA where NALPHP. = NUMCON*20).
9 1-bR. cLWIT(1) Concentration limit for first
constituent. Run is aborted if
concentration exceeds CLIMIT.
ll-20R. CLD1IT(2) Concentration limit for second
constituent.
41-50R. CLIMIT(5) Concentration limit for fifth
constituent.
10 1-5R NUNITS The number of units for which
waste water return factors are
applied. A unit consists of two
junctions at which diversions
occur and two junctions at which
the waste water from those diver-
sions is returned. The same re-
turn factor is applied to both
junctions in each pair,
*lOa 1-3R JDIV1(l) The junction numt-’er of the first
diversion in unit 1.
1 55
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Card Column Name Descrt on
4-7P JDIV2(1) The junction number of the second
diversion in unit 1.
9-hR JRET1(l) The junction nuifter of the first
return flow in unit 1. JRET1(l)
is raired :ith JDrV1(l).
12-15R JRET2(l) The junction nunTher of the
second return flo in unit 1.
JRET2(l) is pair d pith
JDIV2(l).
l( —2flP. RETFAC(1,1) Return factor for unit 1 and
constituent 1
21--23R. CONST(l,1) Constant applied to junction
in unit 1 for constituent 1.
29-33P. PETFAC(1 ,2) Return factor for unit 1 and
constituent 2.
34_L11R. CONST(l,2) Constant for unit 1 and constit-
uent 2.
6P-72P. PETFP.C(1 . ) F:eturn factor for unit 1 and
constituent 5.
73- flP• CO IST(1 ,5) Constant for unit 1 and con-
stituent 5.
1-3fl J IV1(2) Junction number of the first
:vor iri in unit 2.
4-7R JDIV2(2) Junction num!”er of the second
diversion in unit 2.
8-hR JRET1(2) Junction number of first return
flow in unit 2.
12- 1ER JRET2(2) Junction number of second return
flow in unit 2.
156
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Card Column Name Description
16-20R. RETFAC(2,l) Return factor for unIt 2 and
constituent 1.
21-28R. CONST(2,l) Constant for unit 2 and constit-
uent 1.
• .
.
68-72R. RETFAC(2,5) Return factor for unit 2 and
constituent 5.
73-80R. CONST(2,5) Constant for unit 2 and constit-
uent 5.
Card lOa Is repeated NUNITS times,
i.e., one card per unit. If
NUNITS eauals zero, no cards in
this series are reciulred.
*11 l-5R J Junction number. Read as dumy
variable JJ to check card sequence.
6-15R. QINWQ(J) Flow rate of waste water discharge
or diversion at junction J, in
cfs. QINWQ(J) nust be negative
for a waste water discharge and
positive for a diversion.
16—25R. C(J,1) Initial concentration assigned to
junction J for the first constit-
uent.
26-35R. CSPEC(J,l) The specified concentration of
the first constituent in the waste
water discharge QINWQ(J) at junction
J. If QINWQ(J) is zero or Is
positive (indicating a withdrawal)
CSPEC(J,l) will be Ignored.
36-45R. C(J,2) Initial concentration assigned
to junction J for the second
constituent (if more than one
constituent is considered).
157
-------
Card CoIumn Name Descrip ion
46-55R. CSPEC(J,2) The stecified concentration of
the second constituent in the
waste water discharqe Tfl iQ(J)
at junction J.
58-65R. C(J,3) Initial concentration assicined to
junction J for the third constit-
uent. (If more than two constit-
uents are considered).
6f-75R. CSPEC(J,3) The specified concentration of
the third constituent in the
waste water discharge QIH 1Q(J)
at junction J.
.... .... ....
Card 11 is repeated NJ times,
i.e., one card for each junction
in the nettiorl.
*lla l-5R J Junction number. Cards in this
series are required only if
more than three constituents
are being considered slmu1tan-
eously. These cards must also
be in senuence, beainning
with junction 1.
6-15R. C(J,4) Initial concentration assigned
to junction J for the fourth
constituent.
6-25R. CSPEC(J,4) The specified concentration of
the fourth constituent in the
waste water discharge QINWQ(J)
of junction J.
26-35R. C(J,5) Initial concentration assigned
to junction J for the fifth
constituent.
36-45R. CSPEC(J5) The specified concentration of
the fifth constituent in the
waste water discharge f?INWO(J)
at junction J.
ests S... S...
158
-------
Card Colurin ? Iame Description
Card ha is repeated !IJ times,
i.e., one card per junction.
12 1-5R 1r,ROUP(1) The number of groups (up to 10)
of junction numhers for which
it is desired to increnent the
initial concentrations of the
first constituent which were prev-
iously read as input. There is
no limit (up to NJ) to the number
of junctions cornprisin a group
but the numbers nust be consecu-
tive.
*128 l—5R. FACTR(l,1) u1tiplication factor to he
applied to the initial concen-
tration of the first constituent
at those junctions in the first
group. This card will not be
required if HrP.OUP(l)=O.
f .— IOR NJSTRT(l,l) The first (lowest) junction num-
ber in the sequence of junctions
comprising the first qroup for
the first constituent.
11—15R NJSTOP( 1,1) The final (highest) junction
number in the sequence of
junctions comprisina the first
groun for the first constituent.
16—20R. FACTR(1,2) 1 4 ultiplication factor to be
applied to the initial concen-
tration of the first constituent
at those junctions in the second
group (if more than one group is
specified).
21-25R NJSTRT(l,2) The first junction number in the
sequence of junctions comprising
the second group for the first
constituent.
26—30R NJSTOP(1,2) The final junction number in
the sequence of junctions coin—
prising the second group for
the first constituent.
159
-------
Card Column Nar’e Description
61-65R. FACTR(l,5) t’ultiplication factor to he
applied to the initial concen-
tration of the first constituent
at those junctions in the fifth
group (if more than four groups
are specified).
66—7gR !JJSTRT(l,5) The first junction number in
the fifth group for the first
constituent.
71—75R JSTOP(1,5) The final junction number in
the fifth group for the first
constituent.
l-5R. FACTR(l,C) ultiplication factor to be
anplied to the initial concen-
tration of the first constituent
at those junctions in the sixth
group. This card is required
only if more than five groups
were specified, i.e.,
NGROUP(l) > .
6—bR !IJSTRT(l,6) The first junction number in
the sixth group for the first
constituent.
ll-15R NJSTOP(l,6) The final junction number in
the sixth groun for the first
COn ti tu?rlt.
S
61—65R. FACTR(l,lO) Multiplication factor to be
applied to initial concentra-
tions of the first constituent
at those junctions in the tenth
group.
160
-------
Card Column Name Descrintion
66-70R NJSTRT(l,lO) The first junction number in
the tenth group for the first
constituer.t.
71-75R NJSTOP(l,10) The final junction number in the
tenth group for the first con-
sti tuent.
13a 1-5P. NGROUP(2) The number of arouns (up to 10)
of junction numbers for which
it is desired to increment the
initial concentrations of the
second constituent. This card
t il1 not he required if
MU 1CON = 1.
If NGP.OUP(2) = 0 no additional
cards in this series are re-
ouired. If F R0UP(2)>0 one or
two additional cards are re-
quired followinq card 13a with
values for FACTR, JSTRT, and
iJSTPP for up to five c roups
on the first of these cards
and values for the sixth through
tenth groups (if needed) on the
second card. The format is
identical to cards *12a
14a 1-5R NGROUP(3) The number of groups (up to 10)
of junction numbers for which
it is desired to increment the
initial concentrations of the
third constituent. This card
is not required if NUMCON . . 2.
If 1GflOUP(3)=0 no additional
cards in this series are re-
quired. If ‘IGROUP(3) >0 one
or two additional cards are
required following card 14a
with values for FACTR, NJSTRT,
and ¶ JSTOP for the groups
desired for the third constitu-
ent. The format is identical
to cards *12a
161
-------
Card Column Name Description
15a l-5R GROUP(4) The numt;er of qrouns of junction
numbers for 4iich it is desired
to increnent the initial concen-
trations of the fourth constit-
uent. This card is not renuired
if M1COti 3.
If UCROEJP(4)=O no additional
cards in this series are rnnuired.
If ROUP(4) >‘ one or two addi-
tional cards are required follow-
in card l5 to specify the
values for FACTR, JSTRT, and
ik STOP for the grouDs desired
for the fourth constituent. The
fonnat is identical to cards
*1’)
.
1€a l-5R NCROUP(5) The nunl’er of aroups of junction
numbers for ‘hich It is desired
to increrent the initial concen-
trations of the fifth constituent.
This card is not required if
NUF1C( ! 4.
If N(R0UP(5)=fl no additional
cards in this series are required.
If i( RO ’P(5) >‘l one or two addi-
tional cards are renuired follow-
inn card lfa to specify the values
for FACTfl, !JSTRT, ?nd NJSTOP for
the groups desired for the fifth
constituent. The forn at is
identical to cards *12a
17 l-5R KBOP(l) Control option for specifying
concentration of first constit-
uent at toundary. If boundary
concentration is constant over
full tidal cycle KBOP(l)=l, if
variable over tidal cycle
KBOP(1 )=2.
6-bR KBOP(2) Control option for specifying
concentration of second constit-
uent at boundary. KBOP(2)=l for
constant boundary, or 2 for
variable boundary.
162
-------
Card Column Name Description
21-25R Control tion for specifvinq
concentration of fifth constit-
uent at boundary. KBOP(5)=l
for constant boundary, or 2 for
variable boundary.
l-5R NSPEC The number of nuality time steps
per tidal cycle.
*19 i-v ,r. CIN(l,l) The boundary concentration speci-
fied for the first constituent
for the initial tine step. If
KBOP(l)=l then CIN(l,l) is the
constant boundary concentration
and no additional specification
is required for the first constit-
uent.
ll-20R. CIN(l,2) The boundary concentration speci-
fied for the first constituert
for the second time sten if
KBOP(1 )=2.
61-70R CIN(1,7) The boundary concentration speci-
fied for the first constituent
for the seventh time step.
SS••
Card 19 is repeated as necessary
to specify all NSPEC boundary
concentrations for the first
constituent.
1 3
-------
Card Column Name Description
*20a 1- lOR. C!M(2,l) The boundary concentration speci—
fled for the second constituent
for the first time step. If
KBOP(2)=1 then CIN(2,1) is the
constant boundary concentration
and no additional specification
is required for the second con-
sti tuent.
S
S
.
Card 2 0 a is repeated as necessary
to specify all NSPEC boundary
concentrations for the second
constituent. if NUMCON=1 the
card series 20a is not required.
SSS •
*2 la llOR. CIN(3,l) The boundary concentration speci-
fied for the third constituent
for the initial time step. if
KBOP(3)=1 no additional specifica-
tion is required for the third
constituent. If MUttON s 2 this
card series is not required.
5 0
5••5 • St O
Card 21a Is repeated as necessary
to specify all NSPEC boundary
concentrations for the third con-
sti tuent.
*22a 1- bR. CIN(4,b) The boundary concentration speci-
fied for the fourth constituent
for the initial time step. If
KBOP(4)=l no additional specifica-
tion Is required for the foUrth
constituent. If NUMCON 3 this
card series is not required.
164
-------
Card Column Name Description
. S
Card 22a is repeated as necessary
to specify all SPEC boundary con-
centrations for the fourth con-
sti tuent.
.... S...
*23a 1-bR CIN(5,1) The boundary concentration speci- .
fied for the fifth constituent
for the initial time step. If
KBOP(5)=l no additional specifica-
tion is required for the fifth
constituent. If NUMCON 4 this
card series is not renuired.
Card 23a is repeated as necessary
to specify all NSPEC boundary con-
centrations for the fifth constit-
uent.
24 l-5R NOPRT The total number of junctions
for which printout is desired.
*25 1-5R JPRT(l) Junction number for which printout
is desired.
6-bR JPRT(2) Junction number for which printout
is desired.
165
-------
Card. Column Name Description
6f-7 0R JPRT(14) Junction nuniber fer ‘hich printout
is desired.
Card 25 is repeated as necessary
to specify all junctions (up to 50)
for whic’- printout is desired
(fourteen junction numFers per
card).
Variables Internal to Program DYNQUA
Variable Description
Tape 3 Hydraulic extract tape which was created by
subroutine I-!YDEX in the hydraulic run and
which serves as the basic hydraulic input
to the quality program.
Tape 5 Indicates card input.
Tape 6 Indicates orinted output.
Tape 9 Indicates punc!’ed output.
Tape 10 Scratch tape or disk used to store ouality
predictions during program execution. Data
stored on unit 10 are sumarized in sub-
routine IUALEX and ZONE:S.
K Defines the number of ciuality time steps
comprising a full tidal cycle (also equals
ISPEC).
ICYCTF Cycle number, read from tape 3, from the
transient flow (hydraulic) program.
YNEtI(J) A new name for the head at junction J to
differentiate it from the head at the same
junction at another time step.
166
-------
Variable
escription
Q ( ! )
‘/ (
Or [ T( 1)
ALPHP ( I)
DELT
Cu(1!)
i (N)
fl(M)
CL F N C N)
Y (j)
APE/\S(J)
flIfl(J)
!CHAN(J ‘K)
AREA(h)
TJJL’NC(N ,J)
These variables have been
viously fcr the hydraulic
They are stored on tane 3
DYTUA.
defined rre-
rrogram DYNHYr.
for input to
DFLT l
DEL 1(12
The cuality time ster, in hours.
The print interval , in hours.
I1DECAY (K)
The coefficient, ‘ hicb t ben anplied to
0D, defines the °D exerted, or
equivalently, the nass of ox’men utilized.
Defines the total nurher of PLPHP.(I)
values reciuired.
A flaq which is set enual to one when-
ever a full tidal cycle of cuality data
has been stored on tape lf’. Uhen this
occurs subroutine UALEX is called and
KDONE is reinitialized to zero.
The initial quality cycle number of the
data stored on tape if’, i.e., the start
of a full tidal cycle of nuality data.
The final ouaiitv cycle number of the
data stored on tare in, i.e., the end
of a full tidal cycle of cuality data.
Tine step for nuality solution, in seconds.
A counter used to determine when a full
tidal cycle of printout has been obtained,
A courter used to determine when a full
tidal cycle of quality data has hcen
stored on tape 10.
W’LPIIA
KDCNE
lIAR K2
DELTQ
MCOUr T
KOU NTT
167
-------
Variable
TE P
AVOL(J)
VOL(J)
C i S (J K)
LIFFK(’ )
vouun(J)
I CYC
CO! C
jtD!¼IASS
DI 1\SS
I- URS
KDAYS
V’ L FL:
Fi\CTOP
Pescri nti on
Cycle nun er t!hiCh n rks the end of the
record on tarne 3 and sinnals a EWI ’
coTT mand.
The rean volure of junction i in cubic
feet.
Volume of junction J, in cubic feet.
ass of constituent r at junction 3.
jiffusion coefficient in c! annel P.
The volume of the diversion or waste
water discharae QJq(j) durin each time
step.
Cycle number (iteration) durino x cution
of euality pregrar.
uv iber of ciuality cycles (tire stens)
comnieted at any instant during execution.
Flow volume in a civor channel durirci a
full time step.
Factor used to determine cuarter-noint
concentration fer advective transrort.
i 1 uality gradient existino in a given
channel.
The concentration used in the advective
trans ort ecuation.
The mass of a niven constituent advected
from one junction to anothr r.
The mass of a njven constituent transferred
from one junction to another by diffusion.
Total elapsed hours f prototyne simulation.
Total elapsed da ’s of prototyne simulation.
168
-------
Variahle.s Internal_to cubroutine U1 LEX
VariaHe Description
ICYCfl Cycle nu er fron rp ljt prooran y’ ich
stored on t e l .
CX(J,K) The concentration of constituent at
junction 3. Pead as CX(3 ?) fro!11 t r e lt
to differentiate fror f (J,Y) in the
callinn rro9ranh.
C1W [ (J,K) The av rage concentration nf co stitti nt I’
at junction J cni rutcd ever a full tidal
cyci e.
CrIN(J,K) The minimum concentration of constituent V
at junction J over a full tidal cycle.
cr / x(J,v) The maximum concentration of constituent K
at junction J over a full tidal cycle.
Variables Internal to uhroutine ZONES
TVUL1 The total ji ean volumes of zones l,2 ....(
TVeL2 The zones are unique for each estuary
studied.
TVOLf
TYOLT The :nean volure of the total estuary.
SJ .T Total surface area of the estuary.
TL sCt(I) Total ii ass of constituent I in zones
TLBSC2(I) 1. 2 , at moan tide.
TL sCc(r)
TLPSCT(1) ass of constituent. I in total estuary
at mean tide.
169
-------
FIGURE 48. SAMPLE DATA DECK MAKEUP——PROGRAM DYNQUA
*needed only if NUMCON >3
-------
FiGURE 49.
SAMPLE JOB DECK MAKEUP — PROGRAM DYNQUA
-J
JOB Card
-------
Variable Pescrirtie.n
CAVE1(I) Thc riean concentration of constituent I
CAVE2(1) in zones 1. 2 , ( at mean tide.
CAVE 5(1)
CAVFT(1) The nean concentration of constituent I
in total estuary at mean tide.
RE!RESS1P MU\LYSIS PPPGRAM (r EGP.9)
The required bound1ary input for the hydraulic rroçirar includes
the specification of the water surface. elevation at the model boundary
for each time step in the solution. This is accorrlished t y specifying
the period of the tide plus the seven coefficients P through I\7 in
the relationship:
V = A + A 2 Sin (wt) + A 3 Sin (2 t . t) + A in (3 tat) +
Cos (wt) + A€ Cos (2 wt) + A 7 Cos (3 at)
which appeared before as equation 13.
The coefficients are deternined by a least squares regression
analysis (RFGAfl) on a specified numl’er of enually spaced data points
over the desired tidal cycle. ! oririally points on a ore_half or one
hour basis are adequate for the analysis.
Description and Format of Proyam Inruts (P F’W )
Card Columns Descr iption
1 l-3R 1 (0 Recycle option. 1(0 1 to read
ne -i data set.
4-CR 111 Total numher of points specified
over tidal cycle.
7-9R NJ Number of coefficients in trig-
onorletric enuation.
10-12R I4AXIT “aximum number of Iterations
reauired in the analysis (normally
less than 8).
172
-------
Card Column t ane Descri ion
l_2M . DELTA Maximum value of residual allo ed
(fl.OflOl is typically used). Will
not be exceeded unless the number
of iterations exceeds flAXTT.
25 3CR. PERIOD The period 0 f the tide, in hours.
37 / 9R• ALAG Variable available to shift time
scale on specified inputs (normally
enuals zero).
49- )R. 1 LAG Variable available to shift phase
angle in trigonometric relationship
(noniially epuals zero).
2* l- . 1(1) Time, in hours, of first specified
data point on input tide.
9—1ER. Y(l) Elevation, in feet, of first
specified data point on inout tide
(referenced to model datum .
17-24R. 1(2) Tine, in hours, of second specified
data point on input tide.
25-32R. Y(2) Elevation, in feet, of second
specified data point on input tide.
49-5€R. T(4) Time, in hours, of fourth specified
data point on input tide.
57-€4P . ‘((4) Elevation, in feet, of fourth
specified data point on input
tide.
l—8R. 1(5) Time, in hours, of fifth specified
data point on input tide.
9—16R. v(5)
Card 2 is repeated as required to
include all !I values of T(I) and
v(i).
173
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DATA PREPARATION PROGRAM (DATAP)
The data preparation program was developed to reduce the input
data requirements for the hydraulic model. For the San Francisco Ray-
Delta system the program computed agri cul tural cons umpti ye use,
evaporation, precipitation, and soil moisture depletion or accretion.
The program combines these various components into a net accretion or
depletion at each junction in the network and punches the input data
deck for the hydraulic program.
The program developed for the San Francisco Bay system is quite
specific and lacks general applicability to other estuarial systems.
The program presented herein is a generalized version with provisions
for computing monthly evaporation and precipitation and combining
them with a specified inflow or withdrawal to obtain a net accretion
or depletion at each junction.
Input requirements for the program include the surface area of
each junction, any specified inflow or withdrawal at each junction,
monthly evaporation, and monthly precipitation. Evaporation and pre-
ci pitatlon rates are assumed to be uniform over the entire system;
however if rates vary significantly over the system it may be desirable
to divide the system into sub-areas and apply different rates to each.
Such a refinement would require certain programing changes and would
increase input requirements considerably. For most systems mean evapor-
ation end precipitation rates computed from available records from all
pertinent gauging stations in the basin would suffice.
Additional Input requirements include the head (water surface
elevation) at each junction and the channel numbers (up to five) of
the channels entering each junction.
Normally the basic input deck for DATAP is the deck resulting
from a previous hydraulic solution in which the solution reached
steady state. The final junction heads from such a run are thus used
as the initial heads in the deck prepared In DATAP. The surface areas
and the numbers of all channels entering each junction are also read
from that deck. The values for the net inflow or withdrawal (QIN)
at each junction are also read from the deck but they will not normally
be appropriate for the current run and are therefore rei ni ti all zed
to zero Imedlately after they are read. For those junctions where
zero Is not the desired value for QIN the appropriate value is speci-
fied on a separate input card.
Output from DATAP Includes a listing of the values for evaporation,
precipitation, and the specified Inflow or withdrawal. Two decks are
punched--one has only the junction numbers and the values of QIN which
were specified at each junction (not including evaporation and precip-
itation), and the other Is in the appropriate format for input to the
hydraulic program DYNHYD. The initial deck can be used as the basis
of the required Input deck for the quality program, requiring only the
Initial concentrations and the specified waste water discharge concen-
trati ons for each cons ti tuent considered.
174
-------
Description and Format of Program Inputs (DATAP)
Card Columns Name Description
1-80 ALPHA(I) Alphanumeric identifier which is
printed as first line of heading for
output (1=120 with A4 format).
2 1-80 ALPHA(I) Alphanumeric identifier which is
printed as second line of heading
for output (1=21,40 with A4 format).
3 1-5R NJ Total number of junctions in system.
6-bR MONTH The number of the month being con-
sidered, e.g., 7 for July.
*4 l-5R J Junction number. Read as dummy
variable JJ to check card sequence.
6-15R. Y(J) The head at junction J, in feet.
Should be equal to the desired start-
Ing head at junction J for the planned
hydraulic solution.
16-25R. ASUR(J) The surface area of junction J, In
square feet.
26-35R. QIN(J) The inflow or withdrawal at junction J,
in cfs. Read as dummy variable at
this point.
36-40R NCHAN(J,1) Channel number of one of the channels
entering junction J.
41-45R NthAN(J,2) Channel number of a second channel
entering junction J.
• .
•
.
S
56-60R NCHAN(J,5) Channel number of a fifth channel
entering junction J.
5 l-5R EVAP Evaporation, In inches.
6— bR PRECIP Precipitation, in inches.
175
-------
Card Column Name Description
6 l—5R NJREAD The number of junctions for which it is
desired to specify a hydraulic input
(other than precipitation or evapora-
tion).
*7 l—5R J Number of a junction at which a
hydraulic input is to be specified.
6—15R. QIN(J) The hydraulic input specified at
junction J. QIN(J) is negative
for a discharge and positive for a
withdrawal.
S... •SeS S...
Card 7 is repeated as necessary to
specify all hydraulic inputs.
ILLUSTRATIVE EXAMPLE
Following the program listings in the Appendix are partial output
listings which resulted from execution of each program. Also following
the listings of the two main programs (DYNIIYD and DYNQUA) are listinçs
of job control language (JCi) which was utilized for the sequence of runs.
To facilitate interpretation of the output this discussion presents a
brief description of the sample problem and the required inputs. This
discussion should supplement the previous discussions on prooram
input and output.
The illustrative problem utilized the San Diego Bay network which
consists of 112 nodes (junctions) with 170 connecting links (channels).
The hypothetical problem presented is the simulation of the dynamic
steady state distribution of conservative and non-conservative con-
stituents from a point source. Four different constituents are
considered, 1) a conservative tracer, 2) a non—conservative tracer,
3) a waste load with an associated biochemical oxygen demand (BOD),
and 4) dissolved oxygen (DO), which is linked to constituent 3.
A mean annual tidal condition was selected for the simulation.
The tidal coefficients required to specify the desired tide in the
hydraulic program were determined by program REGAN. Page 241 of the
Appendix is a partial list of the required inputs to REGAN. As can be
noted the tidal period associated with the desired tide was adjusted
to the nearest half-hour (25.C hours) for convenience. The tidal
elevations (with respect to the datum selected for the model simulation)
were specified for each half-hour over the 25.0 hour tidal period
176
-------
Inflow & Diversion Data (I — NJ cards)
Central Parameter (1 card )
Evap. — precip. card
Junction Data (Nd cards)
I Control Parameter (1 card)
. -
Alphanumeric Identifier (2 cards)
j
i i
\
FIGURE 50• SAMPLE DATA DECK MAKEUP — PROGRAM DATAP
-------
(51 points). These values were determined from a graphical plot of the
desired tide similar to those presented on page 36. The number of
terms in the regression equation was specified as seven.
Output from REGAN (page 242) includes the seven coefficients (which
later became Input to program DYNHYD) along with a comparison of the
tidal elevations computed by the regression coefficients with those
specified for each half-hour over the tidal cycle (listed as observed).
The data preparation program DATAP was used to facilitate prepara-
tion of the input deck for program DYNHYD. Output from DATAP Is listed
on pages 246 through 248. The program computes evaporation (or precipi-
tation) from each junction in the network based on the total evaporation
(or precipitation) specified for the month. In this example evaporation
totaling 4.8 inches for the month of September was specified. The
program combines the evaporation withdrawal rate with any other with-
drawal or accretion specified (as listed under QIN on pages 246 and 247).
This net accretion or depletion is punched in the appropriate format
for direct Input to program DYNHYD as listed on page 248.
Output from program DYNHYD is presented on pages 194 through 203.
For this example the hydraulic simulation was limited to exactly one
full tidal cycle. For the specified time step of 50 seconds
(DELI 50.0) this requires 1800 cycles (NCYC = 1800) to complete
the full 25-hour tidal cycle. Output was specified at hourly intervals
which is equivalent to 72 time steps (NPRT = 72). The printout was to
begin at cyicle 72 (IPRT = 72). Computation began at the beginning
of the tidal cycle (TZERO = 0.0) which was arbitrarily assigned through
the inputs to the regression program REGAN. Because the hydraulic
extract subroutine HYDEX requires the computed hydraulic parameters
to be stored on unit 10 for each time step over a complete tidal cycle
It was necessary that the initial conditions (corresponding to time
0,0 hours) be stored on unit 10 in addition to the results of all 1800
cycles. Thus the binary tape (unit 10) was written from cycle 0 to
cycle 1800 as indicated on page 194 (IWRITE = 0). Restart capability
after 900 cycles was specified (KPNCHI = 900).
Output from subroutine HYt)EX is presented on pages 201 through 203.
The desired time step for the quality simulation was one-half hour;
therefore the hydraulic parameters were suninarized each 36 cycles
(NODYt4 = 36) begInning at cycle 0. The hydraulic cycle associated
with the start of each half-hour time period for Input to the quality
program Is listed on page 203.
Output from program DYNQIJA Is presented on pages 220 through 238,
The quality simulation was started at the point on the tidal cycle
corresponding to time 0.0 hours in the hydraulic run (NRSTRT = 0).
For a simulation of this type wherein the steady state distribution
Is desired the starting point on the tidal cycle can be arbitrary.
For other runs, such as simulation of prototype quality conditions
178
-------
for specific historic periods it may be desirable or even necesssary to
begin the simulation at a specific tidal phase. Under such circumstances
the quality simulation can begin at any one of the hydraulic cycles
which marks the beginning of each quality time step as listed in the
output from subroutine HYDEX on page 203. The duration of the quality
run was specified as 600 cycles (NQCYC 600) and, since the run was
not a continuation of a previous run, the initial cycle was specified
as unity (INQCYC = 1). The 600 quality time steps (one-half hour each)
are equivalent to 12 full tidal cycles (12 days and 12 hours). Output
was specified at two hour intervals (NPRT = 4) beginning at cycle 50
(IPRT = 50). A quality sumary was also specified for the tidal cycle
beginning at time step 50 (IWRITE = 50).
For this demonstration run the input deck was prepared with initial
junction concentrations equal to 1.0 mg/i for constituent number one
rather than the desired 0.5 mg/i at all junctions. The initial concen-
trations were adjusted to 0.5 mg/i by applying a 0.5 multiplication
factor to each junction as indicated on page 222. The initial concen-
trations listed on page 223 for each junction are the adjusted concentra-
tions.
The point source for tracer and BOO release was specified at junction
52. An arbitrary discharge was specified (18.8 cfs) along with tracer
(1190 mg/I), 800 (300 mg/i), and DO (2.0 mg/i) concentrations as
indicated on page 223. In addition to the 0.5 mg/i initial concentrations
for the first two constituents (both tracer) the initial BOO and DO
concentrations were specified as 2.0 and 5.0 mg/i (constituents 3 and
4 respectively).
Another model feature utilized in this example problem was the
waste water return factors for selected junctions. As can be noted
on page 223 there was a significant diversion (646 cfs) at junction 93
which was cooling water for a power plant. This diversion was returned
undiminished in quantity at junction 96. Any constituent diverted with
the cooling water should thus be returned undiminshed in quantity
(except for decay which would normally be negligible because of the
short detention time in the cooling system). This return is accomplished
in the model by pairing junction 96 with junction 93 and specifying a
return coefficient of 1.00 for each constituent as indicated on page
225 . Two other junctions were also paired (97 and 98) to satisfy
program logic; however those junctions have no effect on the solution
because neither had a diversion or a return flow assigned.
The effect of the point discharge at junction 52 is evident in
the output on pages 226 through 238. The predicted maximum tracer and
BOO concentrations occur at the release point (junction 52) while the
minimum DO concentration (maximum sag below saturation) occurs nearby.
179
-------
RE FERENCES
1. Water Resources Engineers, Inc., June 1965. A Water Quality Model
of the Sacramento-San Joaquln Delta, Report to the U. S. Public
Health Service, Region IX.
2. Water Resources Engineers, Inc., March 1966. A Hydraulic Water
Quality Model of Suisun and San Pablo Bays, Report to the Federal
Water Pollution Control Administration, Southwest Region.
3. State of California Water Resources Control Board, March 1969.
Final Report - Abridged Preliminary Edition - San Francisco Bay -
Delta Water Quality Control Program.
4. Federal Water Pollution Control Administration, Janury 1967.
San Joaquin Master Drain - Effects on Water Quality of San Fran-
cisco Bay and Delta.
5. Federal Water Pollution Control Administration, June 1969.
Vessel Pollution Study, San Diego Bay, California.
6 Shubinski, R. P., J. C. McCarty and M. R. Lindorf, September 1965.
Computer Simulation of Estuarial Networks, Journal Hydraulics
Division, ASCE.
7. Orlob, G. T., R. P. Shubinski and K. D. Feigner, August 1967.
Mathematical Modeling of Water Quality In Estuarlal Systems,
Proceedings of the National Symposium of Estuarine Pollution,
Stanford University.
8. Jeglic, John M., Decenter 1966. DECS III, Mathematical Simulation
of the Estuarine Behavior. Prepared for the Federal Water Pollution
Control Administration, Delaware Estuary Study.
9. Dronkers, J. J., 1964. Tidal Computations in Rivers and Coastal
Waters, North-Holland Publishing Company - Amsterdam.
10. Lal, Chintu, May 1966. Discussion - Computer Simulation of Estuarial
Networks, Journal of the Hydraulics Division, ASCE.
11. Orlob, G. 1., 1958. Eddy Diffusion in Open Channel Flow, Contribution
No. 19, Water Resources Center, University of California.
12. State of California, San Francisco Bay and Central Valley Regional
Water Quality Control Boards, 1960-1965. Published and unpublished
data on waste discharge.
13. CalIfornia State Department of Water Resources, 1958, 1963. Recla-
matIon of Water from Sewage and Industrial Wastes in California.
Bulletin No. 68.
180
-------
14. California State Department of Water Resources, 1966. Quality
and Use of Waste Water.
15. University of California, Sanitary Engineering Research Laboratory,
1960-1965. A Comprehensive Study of San Francisco Bay. Annual
Reports.
16. California State Department of Water Resources, 1957. Report of
Sacramento-San Joaquin Water Supervision for 1955. Bulletin
No. 23-55.
17. California State Department of Water Resources, 1956. Investiga-
tion of the Sacramento—San Joaquin Delta. Quantity and Quality
of Waters Applied to and Drained from the Delta Lowlands. Report
No. 4.
18. U. S. Department of Agriculture, Agricultural Research Service,
1959. Estimated Evaporation and Evapotranspiration Losses Under
Various Proposed Barrier Plans of the San Francisco Bay System,
California. Prepared for U. S. Army Engineer District, San
Francisco, California.
19. California State Department of Water Resources, 1962. Salinity
Incursion and Water Resources, Delta Water Facilities. Bulletin
No. 76, Appendix A.
20. Hetling, L. J., and R. 1. O’Connell, A Study of Tidal Dispersion
in the Potomac River, CB-SRBP Technical Paper Mo. 7, Federal Water
Pollution Control Administration, Region III.
21. Personal Coimiunication with Donald W. Pritchard, Chesapeake Bay
Insti tute.
22. Callaway, R. J.,, K. V. Byran, and G. R. Ditsworth, November 1969.
Mathematical Model of the Columbia River From the Pacific Ocean
to Bonneville Dam, Part I, Federal Water Quality Administration,
Corvallis, Oregon.
181
-------
APPENDIX
PROGRAM LISTINGS AND SAMPLE OUTPUT
-------
PROGRAM DYNHYD
C FEDERAL WATER QUALITY ADMINISTRATION 10
C DYNAMIC FLOW IN A TWO—DIMENSIONAL SYSTEM 20
C EXPLICIT SOLUTION 30
40
c******************************* ** ** 41
C 42
C THE PROGRAM LOGIC IN THIS DECK WAS DEVELOPED FOR THE NETWORKS 43
C REPRESENTING THE SAN FRANCISCO BAY—DELIA AND SAN DIEGO BAY 44
C SYSTEMS WHEREIN A SINGLE TIDAL CONDITION IS SPECIFIED SIMUL— 45
C TANEOUSLY AT TWO NODESINUMBERED 1 AND 2) AT THE SEAWARD BOUNDARY. 46
C APPLICATION TO OTHER SYSTEMS MAY REQuIRE PROGRAM MODIFICATION. 47
C 48
49
50
DIMENSION ALPHA(80),Y(840),YT(840),AREAS(840) ,QIN(840), 60
* NCHAN(840,5),CLEN(1300),B(1300),AREA(1300),AREAT(1 300 ), 70
* CN(1300),V(1300),VT(13OO),Q(130O),R(1300),AK(1300) A( 7), 80
* NJUNC(1300,2),JPRT(50) 90
COMMON ALPHA,Y ,YT,AREA,Q,AREAS,QIN,V,8,CLEM,R,CN,OELT, 100
* NCHAN,NJUNC,JPRT,NJ,NC,NCYC,NPRT,NOPRT,PERIOD,NCYCC 110
REWIND 10 120
REWIND 3 130
140
C****************** 150
C READ, PRINT, AND CHECK DATA 160
170
180
C**** GENERAL CONTROL DATA 190
200
REAO(5,100 )(ALPHA(I), 11,40) 210
100 FORMAT(20A4) 220
READ(5,1O5)NJ,t9C,NCYC,NPRT,NOPRT,DELT,TZER0, T W 230
105 FORMAT (5I5,2F10.0,I5) 240
WRITE(6,110)(AIPHA(I),I1,40) 250
110 FORMAT (1H1/// 260
* 1H 20A4,1OX,37H FEDERAL WATER QUALITY ADMINISTRATIDN/ 270
* 1H 20A4,1OX,41H DYNAMIC FLOW IN A TWO—DIMENSIONAL SYSTEM////) 280
READ(5,530) IPRT,IWRTE,KPNCHI 290
530 FORMAT(315) 300
WRITE(6,115) NJ,NC,NCYC,NPRT,DEIT,TZERO,IWRTE,NCYC,KPNCH1, IPRT 310
115 FORMAT(132H JUNCTIONS CHANNELS CYCLES OUTPUT INTERVAL TIME 320
* INTERVAL INITIAL TIME WRITE BINARY TAPE RESTART INTERVAL 330
*START PRINT/I 340
* 1H 16,3111,71-4 CYCLES,F11.0,5H SEC.,F12.3,14H HRS. CYCLES 14,4H T 350
*0 14,18,19 11 CYCLES CYCLE 14//lI) 360
370
C**** JUNCTION DATA 380
390
DO 119 J1,NJ 400
READC 5,120) ,JJ,Y(J) ,AREAS(J),QIN(J), (NCHAN( J,K),K=1,5) 410
120 FORMAT(15,3F10.0,5I5) 420
YT(J) = Y(J) 430
IF(JJ—J)116,119ir116 440
116 WRITEI6,117) JJ,J 450
117 FORMAT(4OHOJUNCTION DATA CARD OUT OF SEQUENCE. JJ= 14,4H,J 14) 460
CALL EXIT 470
119 CONTINUE 480
183
-------
WRITE(6,124) 490
124 FORMAT (111 ,25X,2111** JUNCTION DATA **///) 500
121 WRITE(6,125)1J,Y(J),AREAS(J),QIN(J ),(NCHAN( J,K),K=1,5),J=1,NJ) 510
125 FORMAT (86H JUNCTION INITIAL HEAD SURFACE AREA INPUT-OUTPUT 520
* CHANNELS ENTERING JUNCTION//(lH ,I6,F15.4,F17.0,F11.2,112, 530
* 416)) 540
550
C**** CHANNEL DATA 560
570
DO 129 P4=1,NC 580
READ(5,130) NN,CLEN(N),B(N),AREA(N),R(N),CN(N),V(N), 590
* (NJUNC (N,K),K=1,2) 600
130 FORMAT(15,2F8.0,F9.0,F7.0,2F8.0,215) 610
RIM) = AREA(N) / 6(N) 620
IF(NN—N)126,129,126 630
126 WKITE(6,127) NN,N 640
127 FORNAT (39HOCHANNEL DATA CARD OUT OF SEQUENCE. NN= 14,4H,N= 14) 650
CALL EXIT 660
129 CONTINUE 610
WRJTEI6,128) 680
128 FORMAT (1111//I 690
* 111 ,25X,20H** CHANNEL DATA **/I/I 100
131 WRITE(6,135)(N,CLEN(N),B(N),AREA(N),CN(N),V(N) ,R(N), 710
*INJUNCtN,K),K=1,2),N1,NC) 720
135 FORMAT( 9TH CHANNEL LENGTH WIDTh AREA MANNING VELOCIT 730
*Y HYD RADIUS JUNCTIONS AT ENDS/I 740
*(1H 15,F11.0,F8.O,F10.1,F9.3,F10.5,F13.1 , 123,16),) 750
760
C**** DATA FOR PRINT LIST 770
780
READ(5,137)(JPRT1I),I 1,NOPRT) 790
131 FDRM*TU415 ) 800
810
C**** Fo BtJJNO RY tONDIT IONS 820
830
READ(5, 137 )Nt( 840
REAQ(5,177)PERIOD, (A(I),I=1,NK). 850
177 FORMAT(8F10.0) 860
WR ITE(6,179)PERIOD,A(1) 870
119 FORMATI1HIF/F4011 ** SPECIFIED TIDAL CHARACTERISTICS **// 880
* 16H TIDAL PERIOD F5.2,6H HOURS! 890
* 1911 MEAN TIDE LEVEL = F10.6,5H FEET! 900
* 7411 HARMONIC COEFFICIENTS FOR SINE TERMS * COEFFICIENTS FOR 910
* COSINE TERMS/) 920
NS*NK/2+ 1 930
DO 449 I=2,NS 940
K =I—1 950
WRITE(6,448)K,A(I),A(NS+I1) 960
448 FORMAT( IH 12,4H*W*T,F20.6,15X,F17.6) 970
449 CONTINUE 980
NSNS—1 990
1000
C**** COMPATIBILITY CHECK 1010
1020
NEXIT 0 1030
DO 150 N =1,NC 1040
DO 150 1*1,2 1050
J=NJUNCIN,I) 1060
DO 140 K=1,5 1070
IF(N—NCHAN(J,K)) 140,150 ,140 1080
140 CONTINUE 1090
NEXIT =NEXIT+1 1100
184
-------
WRITE(6,145) N,J 1110
145 FORMAT(3OHOCOMPATIB IIITY CHECK. CHANNEL 14,11H, JUNCTION 14) 1120
1130
150 CONTINUE 1140
DO 110 J=1,NJ 1150
DO 165 K=1,5 1160
IF(NCHAPj(J,K))17 0,17 0,155 1170
155 N=NCHANLJ,K) 1180
D C 160 1=1,2 1190
IF(J—NJUNC(N,I)) 160,165,16o 1200
160 CONTINUE 1210
NEXIT=NEXIT+1 1220
WRITE(6,145) N, J 1230
165 CONTINUE 1240
110 CONTINUE 1250
IF(NEXIT)176,176, 175 1260
175 CALL. EXIT 1270
176 CONTINUE 1280
1290
C**** STORE CONTROL AND SYSTEM DATA ON TAPE 10 1300
1310
WRITE(10) (ALPHA(j),I=1,40),NJ,NC,DELT,(CN(N),R(N),B(N), 1320
* CLEN(N),N=1,NCJ 1330
WRITE(1O) (Y(J),AREAS(J),QIN(J),(NCHAN(J,K),K=1,5),J=1,NJ), 1340
* (AREA(N),V(N),(NJUNC(N,I),I=1,2),N=1,NC) 1350
1360
1370
C********************************************’************************** 1380
C INITIALIZATION 1390
C******** *************************************************************** 1400
1410
OELT2 = DELT/2.0 1420
TZERO = TZERO*3600. 1430
PERIOD = PERIOD*3600. 1440
W = 6.2832/PERIOD 1450
KWRITE = KPNCHI 1460
0 = 32.1739 1470
1480
C*****CHANNEL CONSTANTS 1490
1500
00 190 N=1,NC 1510
AK(N) = 0 * (CN(N)**2/2.208196) 1520
IF(NJUNC(N,1 )—NJUNC(N,2 1 )190,190,185 1530
185 KEEP=NJUNC(N,1) 1540
NJUNC(N,1)=NJUNC(N,2) 1550
NJUNC(N,2)=KEEP 1560
190 CONTINUE 1570
1580
1590
1600
C MAIN LOOP 1610
C******************************************************* 1620
1630
1640
IF(IWRTE)298,298,301 1650
298 00 300 N=1,NC 1660
Q(N) = AREA(N) * V(N) 1670
300 CONTINUE 1680
WRITE(10) IWRTE,(Y(J),J1,NJ),(V(N),O(N),N1,NC) 1690
301 T = IZERO 1700
00 285 ICYC=1,NCYC 1710
NCYCC ICYC 1720
185
-------
12 = T + OELT2 1130
T =T+DELT 1740
1750
C*********HALF—STEP VELOCITIES 1760
1770
DO 204 Ni.tit 1780
NL=NJUNC(N,1) 1790
NH=NJUNC(P4,2) 1800
R(N) AREA(N) / 8(N) 1810
AK.T = AK(N) I (R(N **1.333333) 1820
DVDX = (1.O/R(N))*(((V(NH)—YT(M-4)+Y(NL)—YTINL))/DFLT)+ 1830
* (V(N)FCLEN(N))*(Y(MU—Y NL))) 1840
VT(N) =V(N)+DELT2*((V(N)* OVDX) —AI(T *V(N)*ABS (V(N ) 1850
* —(G/CLEN(N))*(Y(NH)—YINL))) 1860
204 0(N)=VT(N)*AREA(N) 1870
1880
C*********HALF—STEP HEADS 1890
1900
‘(Til) = AU) 1910
DO 450 I=1,NS 1920
F l = FLOATU) 1930
YT(1) YT(1) + A(t+L)*5 1P4(FI*W*T2)+A(NS+1+1)*COS(Ff*W*T2) 1940
450 CONTINUE 1950
YT(2) = YT(1 ) 1960
DO 225 J =3,NJ 1970
SUM O =QIN(J) 1980
DO 220 Krl,5 1990
1FINCHAN(J,K))225,225,205 2000
205 N-NCHAN(J,K) 2010
1F (J-NJUNC N,1))215,210,215 2020
210 SUMQ SUMQ+Q(N) 2030
GO 10 220 2040
215 SUMQ=SUMQ—Q(N) 2050
220 CONTINUE 2060
225 ‘ (1(J) = Y(J) — ((DELT/AREAS(JU*0.5)*SUM O 2070
2080
C****S****HALF—STEP AREAS ——— FULL—STEP VELOCITIES 2090
2100
DO 230 N=1,NC 2110
NL=NJUNC(N,1) 2120
NH=NJUNC(N,2) 2130
AREAT(N)=AREA IN)+O.5*B(N)*(YT(NH)—Y(Ml)+YT(NL)—Y(NL )) 2140
R(N) = AREATIN) I 8(N) 2150
AKT2 = AK(N) I (R(N)**1.333333) 2160
DVDX = (I.0/RIN))*(((YT(NH)—YU*4)+YT(NL)—Y (N1))/DEIT) + 2170
* (VT(N)/CIEN(N)) * (YT(NH)—YT(P41))) 2180
V(N)=V(N)+DEIT*((VT(N)*DVDX) —Ak12 *VT(N)*ABS (VT(N)) 2190
* -(G1CLEN(N)) * (YT(NH) YT(NLJ)) 2200
230 Q N)=V(N)*AREAT(N) 2210
2220
C*********FULL—STEP HEADS 2230
2240
V (1) = AU) 2250
DO 451 I=1,NS 2260
F! FLOAT*I) 2270
V (1) V (1) + A(I+1)*SIN(FI*w*T )+A(PIS+1+I)*COS(FI*W*T ) 2280
451 CONTINUE 2290
‘(12) ‘((1) 2300
00 255 J =3,NJ 2310
SU$Q=QIN(J) 2320
00 250 I(=1,5 2330
IF(NCHAN(J,K))255,255,235 2340
186
-------
235 N=NCHAN(J,K)
IF( J—NJUNC(N,1) )245,240,245
240 SUMQ=SUMQ+Q(N)
GO TO 250
245 SUMQzSUMQ—QIN)
250 CONTINUE
255 Y(J) = Y(J) — (DELT/AREAS(J))*SUMO
C*********FULL—STEP WIDTHS AND AREAS
00 256 N=1,NC
NL=NJUNC(N,l)
NH=NJUNC tN,2)
256 AREA(N) AREAT(N)+O.5*8(N)*(Y(NH)—YT(NH) .Y(NL)—YT(NL))
C**** WRITE BINARY TAPE FOR WATER QUALITY PROGRAM
IF( ICYC—IWRTE)259,252,252
252 WRITE( 10) ICYC,(Y(J),J—1,NJ),(V IN),0(N),N—1,NC)
IF(ICYC — IPRT)2 60,261,260
IF(ICYC — NCYC)263,261?263
IPRT= IPRI+NPRT
CONT INUE
C**** SELECTIVE PRINT ROUTINE
TIME = 1/3600.0
WRITE(6,302) ICYC,TIME
302 FORt4AT(LH1///
* 27H SYSTEM STATUS
* 54H JUNCTION
* 54H NUMBER
00 340 I=1,NOPRT
JJPRT( I)
WRITE(6,305) J,Y(J)
305 FORMAT(1HOI5,F13.4)
00 335 K1,5
IF(NCHANIJ,K) )335,335,310
310 N=NCHAN(J,K)
jF(J—NJUNC(N,1) )320,315,320
315 VEL=V(N)
FLOW Q( N)
GO TO 325
320 VEL=—V(N)
FLOW=—Q( N)
325 WRITE(6,330) N,VEL,FLOW
330 FORMAT (1H 128,F14.5,F12.1)
335 CONTINUE
340 CONTINUE
C**** CHECK VELOCITIES AND RECYCLE
263 DO 275 N1,NC
IF(ABS (V(N))— 20.0)2 5,265,265
265 WRITE(6,270) ICYC,N
C****** *** *****************************************.*..*****s,*** .***
C HYDRAULIC OUTPUT
r**s*** *** ***ss*******ss**s**a******s**s***sssss**ss**s***a***s*********
259
260
261
262
2350
2360
2370
2380
2390
2400
2410
2420
2430
2440
2450
2460
2470
2480
2490
2500
2510
2520
2530
2540
2550
2560
2570
2580
2590
2600
2610
2620
2630
2640
2650
2660
2670
2680
2690
2700
2710
2720
2730
2740
2750
2760
2770
2780
2790
2800
2810
2820
2830
2840
2850
2860
2870
2880
2890
2900
2910
2920
2930
2940
2950
2960
AFTER
CYCLE 14,F12.2,6H HrIPRSI/
HEAD
CHANNEL
VELOCITY
FLOW/
(F l)
NUMBER
(FPS)
(CFS))
187
-------
270 FORMATI34HOVELOCITY EXCEEDS 20 FPS IN CYCLE 13,10K, CHANNEL 13, 2970
*23K, EXECUTION TERMINATED.) 2980
WRjTEd6,271)(J,Y(J),YT(J),AREA(J),Q(J),J 1,NJ) 2990
L=NJ+1 3000
WRITE (6,272)(J,AREA(J),Q(J),JL,NC) 3010
271 FORMAT (52H NO. VT AREA OFF 3020
* ( 15,F13.6,F13.6,F15.1,F14.2)) 3030
272 FORMA1(I5,26X,F154,F14.2) 3040
CALL EXIT 3050
275 CONTINUE 3060
3070
C***** WRITE TAPE FOR RESTARTING 3080
3090
279 IFIICYC — NCYC)278,405,405 3100
278 IF(ICYC — KWRITE)285,277,277 3110
277 KWRITE * KWRITE + KPNCMI 3120
WRITE43) ICYC,(Y(J),YT (J),J 1,NJ), (V(N),AREA(N),N1,NC) 3130
REWIND 3 3140
GO TO 415 3150
3160
C***** PUNCH RESTART DECK 3170
3180
405 WRITE(8,406)(J,Y(JI,AREAS( JI,QIN(J),(NCHAN( J,K),K*1,5) ,J=1,NJ) 3190
406 FORMAT ( 15,F1O.4,F10.0,F1O.2 ,515) 3200
413 WRITE(8,414)(N,CLEN(N),8(N),AREA(P4),RIN),CN(N) ,V(N), 3210
* INJUNCIN,K),K 1,2),N*1,NC) 3220
414 FORMAT( 15,2F8,O,F9,1,F7.2,F8.3,F8.5,215) 3230
415 TZERO2 I / PERIOD 3240
KTZERO • TZERO2 3250
TZERO2 (1/3600.) — FLOAT (KTZERO) *(PERIOO/3600.) 3260
WR ITE(6,281) ICYC,TZERO2 3270
281 FO*MAT(1H II//48H RESTART DECK TAPE WAS LAST WRITTEN AFTER CYCLE 14 3280
5,26*4 IZERO FOR RESTARTING F10.7) 3290
285 CONTINUE 3300
3310
C***** PRINT RESTART DATA 3320
3330
Cs JUNCTION DATA 3340
3350
400 WRITE 6,402) 3360
402 FORMAT I1H1/FF 3370
* 32K JUNCTION DATA FOR RESTART DECK//I) 3380
WRITE(6,404) (J,Y(J),AREAS( J),QIN(J), (NcHAN(J,K),K1,5),J1,NJ) 3390
404 FORMAT 486K JUNCTION INITIAL HEAD SURFACE AREA INPUT—OUTPUT 3400
* CHANNELS ENTERING JUNCTION/RhI4 ,Ib,F15.4,F11.0,F11.2,112, 3410
* 416)) 3420
3430
Cs CHANNEL DATA 3440
3450
‘,09 WRITE(6,410) 3460
410 FORMAT (1H1/// 3470
* 31K CHANNEL DATA FOR RESTART DECK//I) 3480
WR ITE(6,412) (N,CLEN4N),8 1N),AREA(N),CN(N),V(N),R(N), 3490
*(NJUNC(N,K),K 1,2 ),N 1,NC) 3500
412 FORMATI 9 TH CHANNEL LENGTH WIDTh AREA MANNING VELOCIT 3510
*y HYD RADIUS JUNCTIONS AT ENDS// 3520
SIlK IS,F1l.0,F8.O,F1O.1,F9.3,F10.5,F13.2, 123,16)) 3530
wR)TE(6,299) IWRTE,NCYCC 3540
299 FORMAT(32*4OTAPE 10 WAS WRITTEN FROM CYCLF 16,10*4 TO CYCLE 16/i) 3550
3560
188
-------
C**** EXIT 3570
3580
WRITE(6,422) NCYCC 3590
422 FORt4AT(42HOEND OF TWO—DIMENSIONAL EXPLICIT PROGRAM. 14,8H CYCLES.) 3600
424 IF(NETFLW)426,428,426 3610
426 CALL HYDEX 3620
428 CALL EXIT 3630
END 3640
SUBROUTINE HYDEX 3650
3660
C FEDERAL WATER QUALITY ADMZNZSTRATZON 3670
C NET FLOW PROGRAM 3680
3690
DIMENSION YAVE(840) 3700
DIMENSION VMIN(1300),VMAX(1300),ARMIN(1300),ARF4AX(130 0), 3710
* QEXMIN(1300),QEXMAX(13 00),YMIN(840)?YMAX(84 0),RANGE(84 0), 3720
* ARAVE(13O0),NMIN(80O),Nt4AX(800 3730
DIMENSION A1PHA(8O),Y(840),AREAS(840),QjN(840 ,NCHAN(840,5), 3740
* V(1300),Q(1300),AREA(1300),B(1300),CLEN(13 00),R(13 00), 3750
* CN(1300),NJUNC(1300,2),JPRT(50),YNEW(840),QNET(1300), 3760
* QEXT(1300),VEXT(1300),YT(840) 3770
COMMON ALPHA,Y ,YT ,AREA,Q,AREAS,QIN,V,B,CLEN,R,CP4,DELT, 3780
* NCHAN,NJUNC,JPRT,NJ,NC,NCYC,NPRT,NOPRt,PERIOD,NCYCC 3790
REWIND 10 3800
REWIND 3 3810
DO 78 N=1,NC 3820
ARAVE(N) 0.0 3830
78 CONTINUE 3840
3850
C**** READ INDEPENDENT CONTROL DATA 3860
3870
READ(5,103) ALPHA(l),l=41,80) 3880
103 FORMAT (20A4) 3890
REAO(5,80) NODYN 3900
80 FORMAT(5 15) 3910
3920
C**** READ SYSTEM INFORMATION FROM DYNAMIC FLOW PROGRAM 3930
3940
READ(1O) (ALPHA (I),I t,40),NJ,NC,DELT,(CN(NI,R(N),B(N), 3950
* CLEN(N),N 1,NC) 3960
READ(10) (Y(J),AREAS(J),QIN(J),(N AN(J,K),K1,5),J1,NJ), 3970
* (AREA(N),V(N),(NJUNC(N,I),I=I,2)N=1,NC) 3980
NSTOP NCYCC 3990
NSTART NCYCC - (PERIOD / DELI) 4000
WRITE(6,I05)(ALPHA(I),I 1,80) 4010
105 FORMAT (1H1/// 4020
* 1M 20A4,1OX,37H FEDERAL WATER QUALITY ADMINISTRATIDN/ 4030
* 1H 20A4,1OX,32H NET FLOWS AND HYDRAULIC SUMMARY! 4040
* 1K 20*4/1K 20*4/1/!) 4050
DELTQ DELT*FL0AT (NODYN)/3600.0 4060
189
-------
WRITE(6,351) NSTART,NSTOP,DELT,NODYN,DELTQ 4070
351 FORMAT (88H *******s FROM HYDRAULICS PROGRAM ******** HYDRAULIC 4080
* CYCLES PER TIME INTERVAL IN! 4090
*8TH START CYCLE STOP CYCLE TIME INTERVAL QUALITY CYCLE 4100
* QUALITY PROGRAM/I 4110
*j )4 I7,I14,F11.O,9H SECONDS,1OX, 16,12x,F9.2,iH HOURS/////) 4120
4130
C**** EXTRACT HYDRAULICS TAPE AND COMPUTE NET FLOWS 4140
4150
200 JRITE = NSTART 4160
202 READ( 10) ICYCTF,(YNEW(J),J=1,NJ),(V(N),Q(N) ,N=1,NC) 4170
203 IF(ICYCTF — NSTART)202,204,208 4180
204 DO 206 N=1,NC 4190
ONET(N) = 0.5*0(N) 4200
QEXTIN) = 0.5*0(N) 4210
VEXT(P4) = 0.5*V(N) 4220
VMIN(N) V(N) 4230
VNAX(N) = VIN) 4240
206 CONTINUE 4250
KFLAG = 0 4260
KFLAG2 0 4270
DO 207 Jal,NJ 4280
YAVE(J) 0.0 4290
YMIN(J) YNEW(J) 4300
NMIN(J) ICVCTF 4310
YNAX(J) YNEW(J) 4320
NMAX(J) ICVCTF 4330
207 CONTINUE 4340
GO TO 218 4350
208 KFLAG KFIAG + 1 4360
DO 154 N1,NC 4370
IF(V(N))152,150,152 4380
150 M L. a NJUNC(N,j) 4390
NH = NJUNC(N,2) 4400
AREA(N) AREA(N) +((B(N)/2.) * (YNEW(NH)—y(Mi) + YNEW(NL)—Y(NL))) 4410
ARAVE(N) ARAVE(N) + AREA(N) 4420
GO TO 154 4430
152 AREA(N) = 0(N) I VIM) 4440
ARAVE(N) = ARAVE(N) + AREA(N) 4450
154 CONTINUE 4460
IF(KFLAG — 1)157,155,157 4470
155 00 156 N=1,NC 4480
ARMININ) = AREA(N) 4490
ARMAX(N) = AREA(N) 4500
156 CONTINUE 4510
157 CONTINUE 4520
DO 210 N=1,NC 4530
QNET (N) ONETIN) + 0(N) 4540
QEXT(N) QEXT(N) + 0(N) 4550
VEXTIN) VEXT(P4) + V(N) 4560
IF(V(N) — VMAX(N))16O,158,158 4570
158 VMAX(N) * VIM) 4580
GO TO 164 4590
160 IF(V(N) — VMIN(N))162,162,164 4600
162 VMINIP4) a VIM) 4610
164 CONTINUE 4620
IF(AREA(N) — ARMAX(N))168,166, 166 4630
166 ARMAX (P4) - AREA(N) 4640
60 10 172 4650
168 IF(AREA(N) — ARNI$(N))17 0,17 0,172 4660
170 ARMIN(N) AREA(N) 4670
172 CONTINUE 4680
210 CONTINUE 4690
90
-------
00 180 J 1,NJ 4700
IF(YNEW(J) — YMAX(J) )176, 174,174 4710
174 YMAXIJ) = YNEW(J) 4720
NMAX(J) = ICYCTF 4730
GO TO 179 4740
176 IF(YNEW(J) — YMIN(J)) 178,178, )79 4750
178 VMIN(J) = YNEW(J) 4760
NMINIJ) = ICYCTF 4770
179 CONTINUE 4780
180 CONTINUE 4190
00 211 J=1,NJ 4800
v(J) = YNEW(J) 4810
YAVE(J) = YAVE(J) + YNEW(J) 4820
211 CONTINUE 4830
IF(ICYCIF — JRITE)213,212,213 4840
213 GO TO 202 4850
212 KFIAG2 = KFLAG2 + 1. 4860
00 214 N=1,NC 4870
QEXTIN) = QEXT(N1 — 0.5*0(N) 4880
QEXT(N) = OEXT(N)/FLOAT (NOOYN) 4890
VEXT(N) = VEXT(N) — O.5*V(N) 4900
VEXT(N) = VEXT(N)/FLOAT (NODYN) 4910
214 CONTINUE 4920
IF(KFIAG2 — 1)183,215,183 4930
215 00 181 N =1,MC 4940
QEXMIN(N) = QEXT(N) 4950
QEXMAX(N) = OEXT(N) 4960
181 CONTINUE 4970
GO TO 188 4980
183 DO 187 N=1,NC 4990
IF(QEXT(N) — QEXMAXtN))184,182,182 5000
182 QEXMAX(N) = OEXT(N) 5010
GO TO 187 5020
184 IF(OEXT(N) — QEXMIN(N))186,186,187 5030
186 OEXMIN(N) = QEXT(N) 5040
187 CONTINUE 5050
188 CONTINUE 5060
WRITE( 3) IQEXTIN) ,VEXT (N),N1,NC) 5070
00 216 N=1,NC 5080
QEXTCN) 0.5*0(N) 5090
VEXT(N) = O.5*V(N) 5100
216 CONTINUE 5110
IF( ICYCTF—NSTOP)218,220,220 5120
218 WRITE(3) ICYCTF,(YNEW(J),J1,NJ) 5130
JRITE = JRITE + NODYN 5140
GO 10 202 5150
220 DO 222 N=1,NC 5160
QNET(N) = QNET(N) — 0.5*0(N) 5170
QNET(N) = QNET(N)/FLOAT (NSTOP—NSTART) 5180
ARAVE(N) = ARAVE(N) /FLOAT (NSTOP—NSTART) 5190
R(N) = ARAVE(N) / 8(N) 5200
222 CONTINUE 5210
5220
00 260 J=1,NJ 5230
RANGE(J) = YMAX(J) — YMIN(.J) 5240
YAVE(J) = YAVE(J) / FLOAT (NSTOP — NSTART) 5250
260 CONTINUE 5260
5270
REWIND 3.0 5280
WRITE(3)( ONET(N),N1,NC) 5290
WRITE(3) (A1PHA(I),I1,40),NJ,NC,DELT,( (, ’ 5300
* CLEN(N),N1,NC) 5310
191
-------
WRITE(3) (yAVE(J),AREAS(J),QIN(J),(NCHAN(J,K),K 1,5),J=1,NJ), 5320
* (ARAVE(N), (NJUNC(N,I),I=1,2),N 1,NC) 5330
WRITE(6,224HN,QNET(N),QEXMIN(N),QEXMAX(N),VMIN(N), 5340
* VMAX(N),ARNIPI(N),ARNAX(N),ARAVE(N),N=1,NC) 5350
224 FORMAT( 11911 * * * * * FLOW * * * * * 5360
* * * VELOCITY * * * * a CROSS—SECTIONAL AREA * * */ 5370
a 1181$ CHANNEL NET FLOW MIN. MAX. 5380
* 14 1N. MAX. MIN. MAX. AVE./ 5390
* 11911 NUMBER (CFS) (CFS) (CFS) 5400
* (FPS) (FPS) (SQ. FT) (SQ. FT) (SQ. FT)// 5410
* (111 15,F15.2,2F16.2,2F13.3,F16.1,F13.1,F12.1)) 5420
REWIND 3 5430
WRITE(6,262)(J,YMIN(J),NMIN(J),YMAX(J),NMAX(J),YAVE(J),RANGF(J), 5440
* J=1,NJ) 5450
262 FORMAT( 1H1//// 5460
* 98 1$ JUNCTION MINIMUM HEAD OCCURS AT MAXIMUM HEAD OCCU 5470
*RS AT AVERAGE HEAD TIDAL RANGE/ 5480
* 94H NUMBER (Fl) CYCLE (Fl) CV 5490
*CLE (FT) (FT)// 5500
a (1H I6,F15.2,113,F16.2,113,F16.2,F15.2)) 5510
C**** CHECK DATA ON BINARY IAPE 5520
K=( NSTOP—NSTART)/NQDYN 5530
WRITE(6,242) 5540
242 FORMAT(IH1/// 5550
* 5311 **** OUTPUT FOR CHECKING DATA ON EXTRACTED TAPE ****/// 5560
a 4911 HYDRAULIC HEAD AT *FLOW IN CHANNEL*/ 5570
* 4911 CYCLE JUNCTION NO.1 NO.1 NO.2/I) 5580
00 234 1 1,K 5590
READ(3) ICYCTF, (YNEW(J),J.1,NJ) 5600
READ(3) (QEXT(N),VEXT(N),N*1,NC) 5610
WRITE(6,232) )CYCTF, YNEW(1),QEXT(1),OEXT(2) 5620
232 FDRMAT(17,5X,F10.2,6X,F11.2,F12.2) 5630
234 CONTINUE 5640
REWIND 3 5650
WRITE(6,240) 5660
240 FORMAT(25HOEND OF NET FLOW PROGRAM.) 5670
RETURN 5680
END 5690
192
-------
SAMPLE JOB CONTROL LANGUAGE FOR PROGRAM DYPFYD
/1118012F7 JOB (807200,10902,0015,0014,0350,1,1, ,61) ,‘FEIGNER’, X
// CLASS B,MSGLEVEL=1
/*SETUP 002033/9R
1/ EXEC FORTGCLG,TIME=15,REGION.FORT=252K,REGION.GO=252K
//FORT.SVSIN DO *
********** INSERT SOURCE DECK HERE **********
1*
//GO.FTO3FOO1 DO UNIT=2400,DCB=(RECFM=VBS,LRECL=504,BLKSIZE=5040), X
II DISP=(NEW,KEEP),LABEL=(,,,IN),DSNAME=SDBHX, X
ii VOL=SER=002033
//GOIFT1OFOO1 DO UNjT=SYSDK,DCR=(RECFM VB5,LRECL=5O4,BLKSIZE 504O), X
II DISP=(NEW,DELETE),SPACE=(CYL,(30,30),RLSE),DSN=SDBHY
//GO.SVSIN DO *
********** INSERT DAIA HERE **********
1*
193
-------
SAN DIEGO BAY HYDRAULICS WITH MEAN ANNUAL TIDE(25.0 HOUR PERIOD) FEDERAL WATER QUALITY ADMINISTRATION
DEMONSTRATION RUN FOR DOCUPIENTATION REPORT 05-27—70 DYNAMIC FLOW IN A TWO—DIMENSIONAL SYSTEM
JUNCTIONS CHANNELS CYCLES OUTPUT INTERVAL TIME INTERVAL INITIAL TIME WRITE BINARY TAPE RESTART INTERVAL START PRINT
112 170 J8 00 72 CYCLES 50 , SEC. 0.0 HRSe CYCLES 0 TO 1800 900 CYCLES CYCLE 72
** JUNCTION DATA **
- JUNCTION INITIAL HEAD SURFACE AREA INPUT—OUTPUT CHANNELS ENTERING JUNCTION
1 2.6020 5500000. 0.80 1 2 0 0 0
2 2.6020 3125000. 0.50 2 0 0 0 0
3 2.6020 10500000. 1.60 1 3 0 0 0
4 2.6020 11454545. 1.80 3 4 0 0 0
5 2.6362 7827273. 1.20 4 5 6 0 0
6 2.6578 5781818. 0.90 5 8 9 0 0
7 2.6489 3436363. 0.50 6 7 0 0 0
8 2.6620 3627273. 0.60 7 9 10 0 0
9 2.6754 5645455. 0.90 $ 11 0 0 0
10 2.6842 3163636. 0.50 10 13 14 0 0
11 2.6934 6763636. 1.00 11 12 13 0 0
12 2.6868 2345454. 0.40 14 15 0 0 0
13 2.6875 4581818. 0.70 15 16 0 0 0
14 2.6876 2127273. 0.30 16 0 0 0 0
15 2.7176 7009091. 1.10 12 17 0 0 0
16 2.7421 6163636. 1.00 17 18 19 21 0
17 2.7428 2918182. 0.50 19 20 0 0 0
• • S S S • • • .
• S S S • . S •
• S S S S 5 • S
101 3.0173 3900000. 0.60 149 151 0 0 0
102 3.0257 545455. 0.10 152 153 0 0 0
103 3.0329 1309091. 0.20 153 0 0 0 0
104 2.8995 1281818. 0.20 154 155 156 0 0
105 2.9110 1390909. 0.20 156 157 0 0 0
106 2.9167 13 0909. 0.20 158 0 0 0 0
107 2.9330 2727273. 0.40 159 160 0 0 0
108 2.9413 2563636. 0.40 160 161 162 0 0
109 2.9485 2836364. 0.40 162 163 164 0 0
110 2.9527 2945455. 0.50 164 165 0 0 0
111 —3.0000 3125000. 0.50 170 0 0 0 0
112 —3.0000 3125000. 0.50 170 0 0 0 0
-------
** CHANNEL DATA **
CHANNEL. LENGTH WIDTH AREA MANNING VELOCITY HYD RADIUS JUNCTIONS AT ENDS
1 2500. 4400. l’t3178.0 0.015 —0.01362 32.5 1 3
2 2500. 2500. 88334.4 0.015 0.0 35.3 1 2
3 2500. 4200. 128258.9 0.015 —0.01492 30.5 3 4
4 2500. 1700. 90875.9 0.015 —0.61698 53.5 4 5
5 2500. 2400. 106882.4 0.015 —0.40138 44.5 5 6
6 2500. 1500. 60946.8 0.015 —0.21437 40.6 5 7
7 2500. 1500. 57966.3 0.015 —0.22431 38.6 7 8
8 2500. 2350. 107046.5 0.015 —0.32512 45.6 6 9
• • • S S S S S S
• S S S S S • . .
• S • S S . S S
159 2100. 2050. 65441.5 0.015 —0.04254 31.9 50 107
160 2500. 1200. 19108.0 0.015 —0.12633 15.9 107 108
161 2100. 2400. 83593.9 0.015 —0.01236 34.8 52 108
162 2100. 1300. 20711.6 0.015 —0.14923 15.9 108 109
163 2100. 1200. 40721.9 0.015 0.02578 33.9 54 109
164 2100. 1600. 25503.9 0.015 —0.06425 15.9 109 110
165 2100. 1100. 32932.6 0.015 0.03693 29.9 56 110
01 166 1950. 1300. 44126.1 0.015 —0.03365 33.9 56 58
167 2100. 1450. 23123.7 0.015 —0.05357 15.9 58 60
168 1950. 1800. 57512.6 0.015 0.01527 32.0 59 60
1650. 1500. 25422.7 0.015 —0.08194 16.9 57 59
170 2500. 2500. 75000.0 0.015 0.0 30.0 111 112
** SPECIFIED TiDAL CHARACTERISTICS **
TIDAL PERIOD = 25.00 HOURS
MEAN TIDE LEVEL = 0.067964 FEET
HARMONIC COEFFICIENTS FOR SINE TERMS * COEFFICIENTS FOR COSINE TERMS
1*W*T —0.878729 0.768662
2*W*T 0.559115 1.740088
3*W*T —0.082364 0.025251
-------
SYSTEM STATUS AFTER CYCLE 360 5.00 HOURS
JUNCTION HEAD CHANNEL VELOCITY FLOW
NUMBER (F l) NUMBER (FPS) CCFS)
1 —1.5814
1 —1.05205 —131253.6
2 0.0 0.0
2 —1.5814
2 0.0 0.0
5 —1.6143
4 1.50025 125545.7
5 —0.95528 —92317.5
6 —0.57167 —31193.6
9 —1.6329
8 0.77239 74881.1
11 —0.79320 —73418.3
16 —1.6644
17 1.04434 111964.3
18 —0.79004 —80046.6
19 —0.04226 —1436.5
21 —0.42027 —28895.9
24 —1.6695
25 0.04464 363.9
30 —1.6867
32 0.19185 11024.3
33 0.51705 31645.1
36 —0.60075 —37688.8
37 —0.31784 —4059.5
36 —1.6984
39 0.40146 31655.4
42 0.26754 11331.1
46 —0.21834 —13805.5
47 —0,60991 —27666.4
42 —1.7289
53 0.97169 74113.5
56 —0.88453 —59005.5
57 —0.08175 —4685.5
59 —0.59315 —9211.7
48 —1.7566
69 0.85169 64969.4
72 —0.77792 —62971.1
74 —0.25872 —5088.4
157 0.20972 5077.3
158 —0.01088 —370.3
-------
SYSTEM STATUS AFTER CYCLE 864 12.00 HOURS
JUNCTION HEAD CHANNEL VELOCITY FLOW
NUMBER IFT) NUMBER (FPS) (CFS)
1 0.6878
1 0.71947 96904.7
2 0.0 0.0
2 0.6878
2 0.0 0.0
5 0.6975
4 —1.05566 —92421.3
5 0.65898 67311.1
6 0.40538 23520.4
9 0.7026
8 —0.53111 —54367.7
11 0.54316 53227.0
16 0.7104
17 —0.72240 —81852.1
18 0.52701 56377.4
19 0.03040 1119.4
21 0.31577 23120.9
• S S S S
• S • S
• • S S
48 0.7278
69 —0.54945 —45220.1
72 0.49548 43284.7
74 0.22295 5349.9
157 —0.17187 —4882.5
158 0.00736 273.5
RESTART DECK TAPE WAS LAST WRITTEN AFTER CYCLE 900 hERO FOR RESTARTING = 12.5000000
-------
SYSTEM STATUS AFTER CYCLE 1800 25.00 HOURS
JUNCTION HEAD CHANNEL VELOCITY FLOW
NUMBER (FT) NUMBER (FPS) (CFS)
1 2.6020
1 0.02045 2926.1
2 0.0 0.0
2 2.6020
2 0.0 0.0
5 2.6541
4 —0.03194 —2900.3
5 0.01047 1118.6
6 0.02898 1766.6
9 2.6790
8 —0.01429 —1528.9
11 0.01479 1514.6
16 2.7207
17 ‘-0.02336 —2767.4
18 0.00429 479.2
19 0.00052 20.3
21 0.02916 2245.6
• I I S
• I S •
• S S •
48 2.8257
69 —0.09257 —8089.4
72 0.07610 7060.4
74 0.03733 1033.2
157 —0.00166 —53.2
158 0.00023 9.1
RESTART DECIc TAPE WAS LAST WRITTEN AFTER CYCLE 1800 TZERO FOR RESflRTING = 0.0
-------
JUNCTION DATA FOR RESTART DECK
JUNCTION INITIAL HEAD SURFACE AREA INPUT—OUTPUT CHANNELS ENTERING JUNCTION
1 2.6020 5500000. 0.80 1 2 0 0 0
2 2.6020 3125000. 0.50 2 0 0 0 0
3 2.6163 10500000. 1.60 1 3 0 0 0
4 2.6322 11454545. 1.80 3 4 0 0 0
5 2.6541 7827273. 1.20 4 5 6 0 0
6 2.6678 5781818. 0.90 5 8 9 0 0
7 2.6622 3436363. 0.50 6 7 0 0 0
8 2.6705 3627273. 0.60 7 9 10 0 0
9 2.6790 5645455. 0.90 8 11 0 0 0
10 2.6846 3163636. 0.50 10 13 14 0 0
ii 2.6904 6763636. 1.00 11 12 13 0 0
12 2.6868 2345454. 0.40 14 15 0 0 0
13 2.6874 4581818. 0.70 15 16 0 0 0
14 2.6875 2127273. 0.30 16 0 0 0 0
15 2.7054 7009091. 1.10 12 17 0 0 0
16 2.7207 6163636. 1.00 17 18 19 21 0
17 2.7212 2918182. 0.50 19 20 0 0 0
• • • S S S S • S
• • S • • S • • S
• S • S • I S S S
89 2.8799 7200000. 1.10 133 134 136 137 0
90 2.8773 6300000. 1.00 131 134 135 138 0
91 2.8774 6872727. 1.10 132 135 139 0 0
92 2.8825 5481818. 0.80 136 140 0 0 0
93 2.8830 5427273. 646.80 140 141 0 0 0
94 2.8824 6790909. 1.00 137 141 142 143 0
95 2.8800 5972727. 0.90 138 139 142 144 0
96 2.8878 6572727. —645.00 145 147 0 0 0
97 2.8852 6272727. 1.00 143 145 146 148 0
98 2.8837 6245455. 1.00 144 146 149 0 0
99 2.8878 2645455. 3.00 147 150 152 0 0
100 2.8865 4118182. 0.60 148 150 151 0 0
101 2.8853 3900000. 0.60 149 151 0 0 0
102 2.8900 545455. 0.10 152 153 0 0 0
103 2.8939 1309091. 0.20 153 0 0 0 0
104 2.8160 1281818. 0.20 154 155 156 0 0
105 2.8226 1390909. 0.20 156 157 0 0 0
106 2.8259 1390909. 0.20 158 0 0 0 0
107 2.8353 2727273. 0.40 159 160 0 0 0
108 2.8402 2563636. 0.40 160 161 162 0 0
109 2.8444 2836364. 0.40 162 163 164 0 0
110 2.8468 2945455. 0.50 164 165 0 0 0
111 —3.0137 3125000. 0.50 170 0 0 0 0
112 —3.0137 3125000. 0.50 170 0 0 0 0
-------
CHANNEL DATA FOR RESTART DECK
CHANNEL LENGTH WIDTH AREA NANP4ING VELOCITY HYD RADIUS JUNCTIONS AT ENDS
1 2500. 4400. 143103.9 0.015 0.02045 32.52 1 3
2 2500. 2500. 88227.6 0.015 0.0 35.29 1 2
3 2500. 4200. 128245.1 0.015 0.02274 30.53 3 4
4 2500. 1700. 90811.3 0.015 0.03194 53.42 4 5
5 2500. 2400. 106809.0 0.015 0.01047 44.50 5 6
6 2500. 1500. 60963.7 0.015 0.02898 40.64 5 7
7 2500. 1500. 57976.0 0.015 0.03035 38.65 7 8
8 2500. 2350. 106955.6 0.015 0.01429 45.51 6 9
9 2350. 2200. 91293.1 0.015 —0.00464 41.50 6 8
10 2500. 1250. 52073.4 0.015 0,02549 41.66 8 10
11 2500. 2300. 102398.8 0.015 0.01479 44.52 9 11
12 2500. 2800. 121978.3 0.015 0.02287 43.56 11 15
13 2350. 2350. 111688.4 0.015 0.01159 47.53 10 11
14 2100. 650. 12122.3 0.015 0.00203 18.65 10 12
15 2100. 1650. 34110.1 0.015 0.00053 20.67 12 13
16 2100. 2100. 39220.3 0.015 0.00015 18.68 13 14
17 2500. 2600. 118475,4 0.015 0.02336 45.57 15 16
18 2500. 2400. 111769.3 0.015 0.00429 46.57 16 19
19 2500. 1200. 39241.9 0.015 0.00052 32.70 16 17
• S S S S S • I I
• S I I I S • S I
I S S I S I S I S
160 2500. 1200. 18982.2 0.015 0.03765 15.82 107 108
161 2100. 2400. 83246.6 0.015 —0.00253 34.69 52 108
162 2100. 1300. 20571.3 0.015 0.02363 15.82 108 109
163 2100. 1200. 40590.1 0.015 0.00734 33.82 54 109
164 2100. 1600. 25329.2 0.015 0.03015 15.83 109 110
165 2100. 1100. 32809.0 0.015 —0.02262 29.83 56 110
166 1950. 1300. 43980.0 0.015 0.01188 33.83 56 58
167 2100. 1450. 22960.2 0.015 0.02221 15.83 58 60
168 1950. 1800. 57309.5 0.015 —0.00858 31.84 59 60
169 1650. 1500. 25253.2 0.015 0.02633 16.84 57 59
170 2500. 2500. 74775.0 0.015 0.0 29.91 111 112
TAPE 10 WAS WRITTEN FROM CYCLE 0 TO CYCLE 1800
ND OF TWO—DIMENSIONAL EXPLICIT PRUb AM. 1800 CYCLES.
-------
SAN DIEGO BAY HYDRAULICS WITH MEAN ANNUAL TIDE( 25.0 HOUR PFR!OD)
DEMONSTRATION RUN FOR DOCUMENTATION REPORT 05—27—70
EXTRACT HYDRAULIC RUN AFTER 50.0 HOURS USING 0.50 HOUR TIME STEP
THIS EXTRACT COMPLETED AS PART OF HYDRAULIC RUN ON 05—27—70
FEDFRAL WATER QUALITY ADMINISTRATION
NET FLOWS Af”fl HYDRAULIC SUMMARY
******** FROM HYDRAULICS PROGRAM ***** **
START CYCLE STOP CYCLE TIME INTERVAL
HYDRAULIC CYCLFS PER
C)UALITY CYCLE
TIME INTERVAL IN
QUALITY PROGRAM
0 1800
50. SECONDS
36
0.50 HOURS
* ****
MIN.
(CFS)
FLOW * * * * *
MAX.
(CFS)
* * VELOCITY * *
* * * CROSS—SECTIONAL AREA
.
S
S
S
.
CHANNEL
N T FLOW
WIN.
MAX.
WIN.
MAX.
AVE.
NUMBER
(CFS)
(FPS)
(FPS)
(SQ. Fl)
(SQ. Fl)
(SD. FT)
1
—340.56
—200798.00
150913.44
—1.562
1.214
119837.8
143589.2
131968.9
2
0.0
0.0
0.0
0.0
0.0
75086.5
88334.1
81966.1
3
—343.78
—197372.00
145223.81
—1.725
1.343
105939.5
129192.0
117558.3
4
2 5
—364.31
—663.24
—193546.56
—143164.25
145244.94
107340.31
—2.283
—1.453
1.750
1.117
81776.9
93956.4
91245.8
107329.6
86481.5
100634.9
6
295.56
—47683.69
35828.89
—0.856
0.662
52893.1
61254.5
57076.0
7
294.57
—46485.11
34911.03
—0.881
0.682
49885.8
58269.9
54076.0
8
—504,91
—115814.19
86392.50
-1.172
0.896
94324.6
107483.1
100881.4
9
—160.06
—25317.88
19395.25
—0.302
0.237
79488.6
91802.0
85619.3
10
134.28
—70522.94
53329.72
—1.478
1.148
45309.8
52296.4
48808.9
11
—506.21
—113799.31
84861.25
—1.205
0.922
89996.9
102913.3
96428.4
12
—374.62
—177460.81
133002.56
—1.579
1.216
106801.3
122522.7
114661.0
13
132.22
—66111.81
49994.91
—0.637
0.495
99002.4
112198.0
105579.4
14
1.34
—3273.50
2590.66
—0.546
0.402
8598,6
12209.8
10423.3
15
0.96
—2426.37
1919.84
—0.151
0.125
25152.6
34379.4
29787.2
16
0.30
—769.53
608.78
—0.043
0.039
27817.0
39632.0
33718.2
160
547.07
—8247.88
7201.46
—0.540
0.523
12172.3
19103.8
15658.0
161
—158.31
—2237.70
1478.21
—0.030
0.020
69681.3
83585.3
76638.9
162
391.38
—9409.29
7865.35
—0.568
0.528
13182.6
20707.0
16964.3
163
108.90
—1088.35
1517.21
—0.031
0.043
33764.9
40717.6
37255.3
164
503.24
—6706.56
5871.29
—0.331
0.320
16223.8
25498.1
20884.0
165
—506.29
—4927.70
5462.61
—0.177
0.186
26546.3
32928.5
29749.2
166
157.71
—5953.93
4637.16
—0.151
0.122
36574.7
44121.3
40361.9
167
159.49
—5237.50
4093.89
—0.287
0.246
14695.5
23118.3
18924.9
168
—162.10
—3303.18
4194.99
—0.067
0.081
47044.3
57505.8
52295.7
169
631.85
—6910.03
6293.24
—0.334
0.337
16701.8
25417.1
21077.7
170
0.0
0.0
0.0
0.0
0.0
74887.5
74999.9
74936.6
S
S
S
.
S
S
S
S
S
S
S
.
S
S
S
S
I
S
-------
JUNCTION MINIMUM HEAD OCCURS AT MAXIMUM HEAD OCCURS AT AVERAGE HEAD TIDAL RANGE
NUMBER (F l) CYCLE (Fl) CYCLE (FT) (El)
1 —2.69 520 2.60 0 0.07 5.29
2 —2.69 520 2.60 0 0.07 5.29
3 —2.70 521 2.78 3 0.07 5.48
4 —2.71 522 2.86 3 0.07 5.57
5 —2.72 524 2.83 5 0.07 5.56
6 —2.73 525 2.85 7 0.07 5.58
7 —2.73 525 2.86 6 0.07 5.59
8 —2.73 526 2.86 7 0.07 5.59
9 —2.74 526 2.86 8 0.07 5.60
10 —2.74 527 2.85 8 0.07 5.59
11 —2.74 527 2.86 9 0.07 5.61
12 —2.74 527 2.82 15 0.07 5,56
13 —2.74 527 2.87 15 0.07 5.61
14 —2.75 528 2.89 15 0.07 5.63
15 —2.75 528 2.85 10 0.07 5.60
16 —2.76 530 2.82 11 0.07 5.59
17 —2.16 530 2.86 14 0.07 5.62
18 —2.76 530 2.89 14 0.07 5.65
19 —2.77 531 2.82 13 0.07 5.59
20 —2.71 530 2.82 12 0.07 5.59
21 —2.77 531 2.82 13 0.07 5.59
22 —2.77 531 2.79 15 0.07 5.56
23 —2.77 531 2.81 20 0.07 5,58
• • I I I I
• • I • I • S
• I I I I S S
95 —2.89 552 3.01 0 0.07 5.90
96 —2.91 557 3.02 0 0.07 5.93
97 —2.90 555 3.02 0 0.07 5.92
98 —2.90 554 3.01 0 0.07 5.91
99 —2.91 557 3.02 0 0.07 5.93
100 —2.91 556 3.02 0 0.07 5.92
101 —2.90 555 3.02 0 0.07 5.92
102 —2.92 560 3.03 0 0.07 5.95
103 —2.94 566 3.03 0 0.07 5.98
104 —2.82 540 2.90 0 0.01 5.72
105 —2.83 541 2.91 0 0.07 5.74
106 —2.83 541 2.92 0 0.07 5.75
107 —2.84 543 2.93 0 0.07 5.77
108 —2.84 544 2.94 0 0.07 5.78
109 —2.85 545 2.95 0 0.07 5.80
110 —2.85 545 2.95 0 0.07 5.80
111 —3.01 1800 —3.00 0 —3.01 0.01
112 —3.01 1800 —3.00 0 —3.01 0.01
-------
**** OUTPUT FOR CHECKING DATA ON EXTRACTED TAPE ****
HYDRAULIC HEAD AT *FLOW IN CHANNEL*
CYCLE JUNCTION NO.1 NO.1 NO.2
o 2.60 —71820.00 0.0
36 2.54 —93625.56 0.0
72 2.35 —76629.88 0.0
108 2.05 —71167.63 0.0
144 1.64 —84553.56 0.0
180 1.16 —134856.06 0.0
216 0.61 —178309.88 0.0
252 0.04 —200798.00 0.0
288 —0.53 —188441.63 0.0
324 —1.08 —151712.81 0.0
• • S I
• S • I
• S S S
936 1.25 52801.16 0.0
972 1.37 15694.23 0.0
1008 1.39 —28763.05 0.0
1044 1.30 —67205.00 0.0
1080 1.12 —90490.31 0.0
1116 0.86 —97496.31 0.0
1152 0.54 —94650.75 0.0
1188 0.20 —89584.31 0.0
1224 —0.14 —84433.75 0.0
1260 —0.44 —76900.19 0.0
1296 —0.68 —61057.69 0.0
1332 —0.84 —33219.55 0.0
1368 —0.89 5898.60 0.0
1404 —0.83 50700.91 0.0
1440 —0.66 90866.88 0.0
1476 —0.39 117790.13 0.0
1512 —0.04 129040.50 0.0
1548 0.38 128225.88 0.0
1584 0.83 122350.75 0.0
1620 1.28 115867.88 0.0
1656 1.71 107984.56 0.0
1692 2.08 93238.63 0.0
1728 2.36 66040.13 0.0
1764 2.54 26010.03 0.0
END OF NET FLOW PROGRAM.
-------
PROGRAM OYNOUA
C FEDERAL WATER QUALITY ADMINISTRATION 10
C DYNAMIC WATER QUALITY MODEL 20
c QUARTER—POINT VERSION 30
C 40
50
C 60
C THE PROGRAM LOGIC IN ThIS DECK WAS DEVELOPED FOR THE NETWORKS 70
C REPRESENTING THE SAN FRANCISCO BAY—DELTA AND THE SAN DIEGO BAY 80
C SYSTEMS WHEREIN A SINGLE QUALITY CONDITION IS SPECIFIED 90
C SWULTA EOUSLY AT TWO NODES(NUMBEREI) 1 AND 2) AT THE SEAWARD 100
C BOUNDARY. APPLICATION TO OTHER SYSTEMS MAY REQUIRE PROGRAM 110
C MODIFICATION. -SUBROUTINE ZONES IS SPECIFIC TO THE SAN DIEGO 120
C BAY NETWORK. 130
C 140
150
C 160
DIMENSION DECAY(5),REOXKI5),NCONDK(5),NCONOX(5),CSAT(5h0DECAY(5), 170
* NGRO$JP(1O),FACTR(5,1O),NJSTRT(5,1O),NJSTOP(5,10),KBOP(5) 180
DIMENSION JOIV I(20),JD IV2(20),JRET I(20),JRET2(20),RETFAC (20,5), 190
* CONST(20,5),AVDI(840),CAVE(840,5) 200
DIMENSION YNEbII84O),VOLQIN(84O),C 840,5),CSPEC(840,5),0NETU300), 210
* CIN(5,840),VDL(840),ASUR(840),QINWO(840hCMASS(840,51, 220
a DIFFK(1300),AIPHA(220),CLIMITt5),JPRT(50) 230
DIMENSION Y(840),AREAS(840),QIN(840 ),NCHAN(840,5) ,V( 1300) ,Q( 1300), 240
* AREA(13001,B(1300),CLEN(1300),R(1300),CN(1300),NJUNC(1 300 , 2 ) 250
COMMON ALPHA,NSPEC,DELTQ,NUMCON,NALPHA,NJ,ASUR,MARK1,MARK2,K DONE, 260
a KZOP,CAVE,AVOL 270
EQUIVALENCE (AREAS,ASUR),(QIN,QINWQ,VOLQIN),(CN,DIFFK), 280
a (CMASS,NCHAN) 1 (YNEW,AREA),(AVOL,QNET) 290
300
CONTROL OPTIONS 310
320
c***** KDCOP = 1,2 PRINT DEPLETION CORRECTIONS, OR NOT 330
C***** KBOP(M) = 1,2 SEAWARD BOUNDARY CONCENTRATION FOR CONSTITUENT M 340
C IS CONSTANT, OR VARIABLE OVER TIDAL CYCLE 350
C*** * KLOP 1,2 QUALITY EXTRACT CALLS ZONES ROUTINE, OR NOT 360
370
REWIND 3 380
REWIND 9 390
REWIND 10 400
410
C**** READ SYSTEM INFORMATION FROM DYNAMIC FLOW PROGRAM 420
430
READ(5,80) NJ,NC,NSTART,NSTOP,NODYN 440
80 FOR$AT(7 15) 450
K = (NSTOP—NSTART)/NODYN 460
DO 86 I 1,K 470
READ( 3) ICYCTF, (YNEW( j) ,J=1,NJ) 480
READ 3) (Q(N),VIN),N1,NC) 490
86 CONTINUE 500
READ 3) (QNET(N),N1,NC) 510
REA O(3) (AIPHA(I),I=1,40),NJ,NC,DEIT,(CN(N),R(N),B(N), 520
* CLEN(N),N=1,NC) 530
READ(3) (Y(J),AREAS(J),QIN(J),(NCHAN(J,K),K1,5) ,J1,NJ) , 540
* IAREA(N), (NJUNC(N,I ,Il,2),N1,NC) 550
REWIND 3 560
570
204
-------
C**** READ INDEPENDENT CONTROL DATA 580
590
READ(5,84) NRSTRT,INCYC,NQCYC,KzOP ,KDCOP,NTAG,CDIFFK 600
84 FORMAT(615,F10.0) 610
READ(5,80) IPRT,NQPRT,NEXTPR,INTBIG,IWRITE,NEXTWR,IWRINT 620
READ(5,103)(ALPHA(I),I=’+1,8 0) 630
103 FORMAT(20A4) 640
WRITE(6,105) (ALPHA(I ),I=1,80) 650
105 FORMAT(IH I//// 660
* 1H 20A4,14X,37H FEDERAL WATER QUALITY ADMINISTRATI(Th / 670
* 1H 20A4,14X,28H DYNAMIC WATER QUALITY MODEI/ 680
* 1H 20A4/1H 20A4//I/) 690
DELT01 DELT*FLOAT (NODYN)/3600.O 700
DELTQ2=DELTQL*FLOAT (NOPRT) 710
WRITE(6,106) NSTART,NSTOP,DELT 720
106 FORMAT(42H ******** FROM HYDRAULICS PROGRAM ********/ 730
* 42H START CYCLE STOP CYCLE TIME INTERVAL/I 740
* IH 17,I14,F12.O,9H SECONDS/////) 750
WR ITE(6,1 07)NRSTRT,INCYC,NQCYC,INTBIG,DEIT Q2,DELTQ1,CDIFFK 760
107 FORMAT(117H STARTING CYCLE INITIAL QUALITY TOTAL QUALITY * 770
*** OUTPUT INTERVALS *** TIME INTERVAL IN CONSTANT FUR/ 780
* 122H ON HYD. EXTRACT TAPE CYCLE CYCLES 790
* CYCLES HOURS QUALITY PROGRAM DIFFUSION COEFFICIENT 800
810
* 113,1 18,116, I13,F14.2,F17.3,6H HOURS,F17.3////) 820
WRITE(6,109) IPRT,IWRITE 830
109 FORMAT(31H PRINTOUT IS TO BEGIN AT CYCLE 14 1/ 840
* 49H QUALITY TAPE FOR EXTRACTING IS TO BEGIN AT CYCLEI5////) 850
860
C***** READ AND PRINT QUALITY COEFICIENIS 870
880
DID = DELTQ1 / 24. 890
READ(5,112) NUNCON 900
READ(5,40) tNCONDK(K),NCONOX(K),K=1,NIJMCON) 910
40 FORMAT( 1015) 920
DO 44 K=1,NUMCON 930
IF(NCDNDK(K))46,46,41 940
41 REAO(5,42) DECAY(K),REOXK(K),CSAT(K) 950
42 FORMAT(3F10.0) 960
DECAY(K) = EXP(—DECAY(K) * DTD) 970
REOXK(K) EXP(—REOXK(K) * DTD) 980
REOXK(K) = 1.0 — REOXK(K) 990
ODECAY(K) = 1.0 — DECAYCK) 1000
44 CONTINUE 1010
46 CONTINUE 1020
NAIPHA = 120+ NUMCON * 20 1030
REA D(5,1 03) (ALPHA(I),I=121,NALPHA) 1040
READ( 5,110) (CLIMIT(K),K=1 ,NUMCON) 1050
110 FORMAT(5F10.0) 1060
1070
WRITE(6,120) NUMCON 1080
120 FORMAT(1110J5,42H CONSTITUENTS BEING CONSIDERED IN ThIS RUN//) 1090
WRITE(6,122) (ALPHA(I),I=121,NALPHA) 1100
122 FORMAT(1H020A4) 1110
IF(NC ONDK(1))48,48,51 1120
48 WRITE(6,50) 1130
50 FORMAT(IHOI/ 1140
* 53 )10*11 CONSTITUENTS TREATED AS CONSERVATIVE IN THIS RUN//) 1150
GO TO 60 1160
51 DO 59 K=1,NUHCON 1170
IF(NCONDK(K))60,60,52 1180
52 IF(NCONOX(K))57,57,54 1190
205
-------
54 WRITE(6,56)NCONDK(K),DECAY(K),NCONOX(K) ,REOXK(K) ,CSAT(K) 1200
56 FORMAT(iHO//17HOCONSTJTUENT NO. I1,33H IS BUD WITH DECAY COEFFICIE 1210
*NT = FIO7,44H THE ASSOCIATED OXYGEN IS CONSTITUENT NO. Il/3 1H W 1220
*ITH REAERATION COEFFICIENT = F15.9,32H AND SATURATION CONCENTRATID 1230
= F10.2) 1240
GO TO 1250
57 WRITE(6,58) NCONDK(K),DECAY(K) 1260
58 FORMAT(1HO/ 1270
* 17HOCONSTITUENT NO. I1,59H IS TREATED AS A NON—CONSERVATIVE 1280
* WITH DECAY COEFFICIENT = F10.7,451-I BUT IS NOT PAIRED WITH ANY 0TH 1290
*ER CONSTITUENT) 1300
59 CONTINUE 1310
60 CONTINUE 1320
1330
C***** READ WASTE WATER RETURN FACTORS 1340
1350
READ(5,1i2) NUNITS 1360
112 FORMAT(15) 1370
IF(NUNITS) 118,118,114 1380
114 00 117 I=I,NUNITS 1390
READ(5,1 16) JDIV I(I),JDIV2(I),JRET I(J),JRET2(J), 1400
* IRETFAC lI,M),CONST(I,M),M=1,NUMCON) 1410
116 F0RMATU3,3I4,5U 5.O,E8.2)) 1420
117 CONTINUE 1430
118 CONTINUE 1440
1450
C****S PRINT NETWORK AND HYDRAULIC PARAMETERS 1460
1470
IF(NJ — NC)72,72,70 1480
70 Ni = NC 1490
N2 = NJ 1500
GO TO 74 1510
72 NI NJ 1520
N2 = NC 1530
74 WRITE(6, 196) (N,CL.EN(N),B(N),AREA(N),CNUd) ,QNET(N), 1540
* R(N),(NJUNC(N,(),K=i,2),P4,QIN(N),Y(N),(NCHAN(N,I ),I=1,5),N=1,NI) 1550
Ni = Ni + 1 1560
IF(NJ — NC)76,79,78 1570
78 WRITE(6,i95) (J,QIN(J),Y(J), (NCHAN(J,K),K=1,5),J=N1,N2) 1580
GO TO 79 1590
76 WRITE(6, 194) (N,CLEN(N),B(N),AREA(N) ,CN(N),ONET(N), 1600
* R(N),( NJUNC(N,K) ,K=1,2),N=Ni,N2) 1610
194 FORMAT(I5,2F8.O,F9,O,F8.3,F12.2,F1O.1,19,16 ) 1620
195 FORMAT(82x,I5,F9.1,F7.2,I7,415) 1630
196 FORMAT(1H1////42X,48H ***** SUMMARY OF HYDRAULIC INPUTS ** 1640
****//86H ** JUNCTION HEAD AND HYD. RADIUS AND X—SECTIONAI AREA OF 1650
*CHANNELS ARE AT MEAN TIDE **/// 1660
* i32H***************************** CHANNEL DATA ******** 1670
************** JUNCTION DATA **** 1680
1690
* 132H CHAN. LENGTH WIDTH AREA MANNING NET FLOW HYD. 1700
*RADIUS JUNC. AT ENDS JUNC. INFLOW HEAD CHANNELS ENTERING 1710
* JUNCTION// 1720
* ( 15,2F8.0,F9.0,F8.3,F12.2,F1O.1,I9,I6,7X, 15,F9.1,F7.2,17,415)) 1730
79 CONTINUE 1740
1750
C****s READ INiTIAL QUALITY CONDITIONS 1760
1770
IF(NtJMCON — 3)126,124,124 1780
124 NFIRST = 3 1790
GO TO 128 1800
126 NFJRST = IIUMCON 1810
206
-------
128 DO 206 J=1,NJ 1820
READ(5,200) JJ, OINW O(J),(C(,J,K),CSPFC(J,K),K=1,NF IRST) 1830
200 FQRMAT( 15,7F IO.O) 1840
IF(JJ — J)202,206,202 1850
202 WRITE(6,204) jj, 1860
204 FORMAT(31HODATA CARD OUT OF SEQUENCE. JJ= 14,3H,J= 14) 1870
CALL EXIT 1880
206 CONTINUE 1890
IF(NUMCON — 3)212,212,207 1900
207 NFIRST = NFIRST + 1 1910
DO 210 J=1,NJ 1920
READ( 5,200) JJ, (C(J,K),CSPEC(J,K),KNFIRST,NUMCON) 1930
IF(JJ — J)208,210,208 1940
208 WRITE(6,204) JJ,J 1950
CALL EXIT 1960
210 CONTINUE 1970
212 CONTINUE 1980
1990
C** ** READ AND APPLY FACTORS TO ADJUST INITIAL CONCENTRATIONS 2000
2010
DO 222 I=1,NUMCON 2020
READ(5,112) NGROUP (j) 2030
IF(NGROUP (11)222,222,218 2040
216 FORMAT(52H0N0 MULTIPLICATION FACTOR APPLIED TO CONSTITUENT NO.12/) 2050
218 NG = NGROUP (I) 2060
READ(5,220) (FACTR( I,K),NJSTRT (I,K),NJSTOP(I,K),K=1,NG) 2070
220 FORMAT F5.O,2 15,F5.0,215,F5.0,2 15,F5.O,215,F5.0,2 15) 2080
222 CONTINUE ?090
WRITE(6,224) 2100
224 FORMAT(70H1*****MULTIPLICATION FACTORS APPLIED TO OPTAIN STARTING 2110
*CONCENTRATIONS/f 2120
* 51H CONSTITUENT GROUP FACTOR JUNCTION NUMBERS) 2130
00 230 1=1,NUMCON 2140
IF(NGROUP (1)1230,230,226 2150
226 NC = NOROUP (I) 2160
WRITE(6,228)I ,(K,FACTR(I,K),NJSTRT (I,k),NJSTOP(1,K),K=1,NG) 2170
228 FDRMATUH //18,111,F11.2,112,2H —,14/ 2180
* (119,F11.2,112,2H —, 14)) 2190
230 CONTINUE 2200
DO 232 I=1,NUMCON 2210
IF(NGROUP (11)231,231,232 2220
231 WRITE(6,216)I 2230
232 CONTINUE 2240
DO 238 M=1,NUMCON 2250
IF(NGROUP (P4)1238,238,233 2260
233 NC NOROUP (P4) 2270
DO 236 K=1,NG 2280
NJ1 = NJSTRT (M,K) 2290
NJ2 = NJSTOP(M,K) 2300
00 234 J=NJ1,NJ2 2310
C(J,M) = C(J,M) * FACTR(M,K) 2320
234 CONTINUE 2330
236 CONTINUE 2340
238 CONTINUE 2350
2360
C***** PRINT INITIAL DUALITY CONDITIONS 2370
2380
WRITEtb,241) 2390
207
-------
241 FDRMAT(1H1//// 2400
* 120H*********************************************** WATER 2410
*QIJAL ITT DATA ***********************************************/ 2420
* 120H * FIRST CONSTITUENT * SECOND CONSTITUENT 2430
* * THIRD CONSTITUENT * FOURTH CONSTITUENT * FIFTH CONSTITUENT */ 2440
* 1181 1 INITIAL INFLOW INITIAL INFLOW 2450
* INITIAL INFLOW INITIAL INFLOW INITIAL INFLOW/ 2460
* 119H JUNC. INFLOW CO lIC. CONC. CONC. COlIC. 2470
* CONC. COlIC. CONC. COlIC. COlIC. CONC./l) 2480
DO 283 J=1,NJ 2490
WRITE(6,282) J,QINWQIJ),(C(J,K),CSPEC(J,K),K=1,NLJt ICON) 2500
282 FORNAT( 14,F10.1,F12.2,2F10.2,F11.2,3F10.2,F11.2,2F1 0.2) 2510
283 CONTINUE 2520
2530
C***** READ AND PRINT BOUNDARY CONCENTRATIONS 2540
2550
READI 5,80) (KBQP(M),M=1 ,NUNCON) 2560
READ(5,112) NSPEC 2570
00 187 $ 1,NUl4CON 2580
I KBOP($) 2590
GO TO(185,183),L 2600
183 R€AD(5,184)(CIN(N,I),I 1,NSpEC) 2610
184 FORMAT(7F10.O) 2620
GO TO 187 2630
185 READ(5,184) CIN(M,1) 2640
00 186 I 2,NSPEC 2650
CIN(M,I) CIN(N,1) 2660
186 CONTINUE 2670
187 CONTINUE 2680
2690
2700
00 190 Nzl,NUMCON 2710
WRITE(6,188) M,(CIN(N,I),I 1,NSPEC) 2720
188 FORMAT(55HOSPECIFIED C—FACTORS AT JUNCTION 1 FOR CONSTITUENT Nfl. 1 2730
*1/, 2740
* CIH 7F12.3)) 2750
190 CONTINUE 2760
2770
C***** READ LIST OF JUNCTIONS FOR PRINTOUT 2780
2790
READ(5,112) NOPRT 2800
READ(5,192) (JPRT(I ),I 1,NOPRT) 2810
192 FORNAT( 1415) 2820
2830
C***** PRINT WASTE WATER RETURN FACTORS 2840
2850
IF(NUNITS.GT.0)GO TO 197 2860
WRITE(6,81) 2870
81 FORMAT(38110N0 WASTE WATER RETURN FACTORS APPLIED//) 2880
GO TO 353 2890
197 WRITEE6,198) 2900
198 FORMATI 1 1 11/I/I 2910
* 1321 1**********************************t*******s** TABLE 0 2920
*F WASTE WATER RETURN FACTORS ********************************* 2930
2940
4 ’ 3711 JUNCTIONS USED JUNCTIONS USED/ 2950
* 13211 FOR DIVERSIONS FOR RET. FLOWS 1ST. CONSTITUENT 2960
* 2ND. CONSTITUENT 3RD. CONSTITUENT 4Th. CONSTITUENT 5TH. CO 2970
*NSTITUENT/ 2980
* 13211 UNIT NO. 1 NO. 2 NO. 1 NO. 2 COEFF. CONST. 2990
* COEFF. CONST. COEFF. CONST. COEFF. CONST. COEFF. 3000
* CONST.//) 3010
208
-------
DO 352 I=1,NUNITS 3020
WRITE(6,35 0) I,JDIV1(I),J 0 1v2(I),JRET1(I),JRET2(I), 3030
* (RETFAC (I,M),CONST(I,M),p41,NUMcON) 3040
350 FORMAT( I 3 , 18, 17,I1O, 17,F9.2,E12.?,4(F7.2,E12.2)) 3050
352 CONTINUE 3060
353 CONTINUE 3070
3080
C**** INITIALIZATION 3090
3100
KOONE = 0 3110
MARK1 = 0 3120
MARK2 = 0 3130
DELTO=DELT*FLOAT (NODYN) 3140
NCOUNT = 0 3150
KOUNTT = 0 3160
NTEMP = NSTOP — NODYN 3170
DO 358 N=1,NC 3180
IF(NJUNC(N,1)—N,JIJNC(N,2))358,358,357 3190
357 KEEP=NJUNC(N,1) 3200
NJUNC(N,1)=NJIJNC(N,2) 3210
NJUNC(N,2)=KEEP 3220
358 CONTINUE 3230
3240
C***** CALCULATE MEAN JUNCTION VOLUMES 3250
3260
359 DO 373 J1,NJ 3270
AVOL(J) = 0.0 3280
ASUM = 0.0 3290
DSUM = 0.0 3300
DO 371 K1,5 3310
IF (NCHAN(J,K)) 372,372,370 3320
370 N = NCHAN(J,K) 3330
ABAR = CLEN(N)*B(N) 3340
ASUM ASUM + ABAR 3350
DSUM = OSUM + ABAR*R(N) 3360
371 CONTINUE 3370
372 DBAR = DSUM/ASUM 3380
AVcL(.J) ASUR(J) * OBAR 3390
373 CONTINUE 3400
3410
C***** CORRECT VOLUMES FOR INITIAL STARTING CONDITIONS 3420
3430
774 READ(3) ICYCTF,(YNEW(J),J=1,NJ) 3440
IF( ICYCTF—NRSTRT)775,776,776 3450
775 READ(3) (Q(N),V(N) ,N=1,NC) 3460
GO TO 774 3470
776 DO 780 J=1,NJ 3480
VOL(J) =AVOI(J) + ASUR(J)*(YNEW(J)—YLJ)) 3490
Y(J) = YNEW(J) 3500
780 CONTINUE 3510
3520
C***** CALCULATE INITIAL MASS 3530
3540
DO 378 J=1,NJ 3550
DO 377 K=1,NUMCON 3560
CMASS(J,K)= C(J,K) * VOL(J) 3570
377 CONTINUE 3580
378 CONTINUE 3590
3600
C**** EDDY DIFFUSION CONSTANT 3610
3620
00 385 N=1,NC 3630
209
-------
385 DIFFK(N)=CDIFFK*R(N)*DELTQ/CLEN(N) 3640
3650
C***** COMPUTE VOLUMES OF INFLOW—OUTFLOW 3660
3670
DO 388 J=1,NJ 3680
VOLQIN(J) QIP4WQ(,J) * DELTQ 3690
388 CONTINUE 3700
3710
C***** STORE INITIAL CONDITIONS TO EXTRACT FIRST TIDAL CYCLE 3720
3730
IF(IWRITE.GE.IP4CYC)GO TO 34 3740
WRITE(10) IWRITE,((C(J,K),K=1,NUMCON),.J=1,NJ) 3750
MARK 1 = IWRITE 3760
KOUNTT = KOUNTT + 1 3770
34 CONTINUE 3780
3790
C MAIN QUALITY LOOP 3800
C*********************************************************************** 3810
DO 536 ICYC=INCYC,NQCYC 3820
NQCYCC = ICYC 3830
3840
C*****READ SYSTEM CONDITIONS 3850
3860
READ(3) (Q(NhV(N) ,N=1,NC) 3870
IF (ICYCTF—NTEMP) 790,794,794 3880
790 READ(3) ICYCTF,(YNEW(J),J=1,NJ) 3890
GO TO 407 3900
794 REWIND 3 3910
READ(3) ICYCTF,(YNEW(J),J=1,NJ) 3920
407 CONTINUE 3930
3940
C***** DETERMINE FLOW DIRECTION AND COMPUTE 1/4 POINT CONCENTRATION 3950
3960
DO 416 N=1,NC 3970
VOLFLW = 0(N) * DELTQ 3980
Nt = NJUNC(N,1) 3990
NH = NJUNC(N,2) 4000
IF(N.GT.2) GO TO 406 4010
!F(Q(N))402,404,4 04 4020
402 FACTOR = 0.0 4030
GO TO 412 4040
404 FACTOR = 1.0 4050
GO TO 412 4060
406 IF(Q(N))408,410,410 4070
408 FACTOR = 0.25 4080
GO TO 412 4090
410 FACTOR = 0.75 4100
4110
412 DO 414 K=1,NUMCON 4120
OGRAD = C(NL,K) — C(NH,K) 4130
CONC C(NH,K) + FACTOR * OGRAD 4140
4150
C***** ADVECTION AND DIFFUSION 4160
4170
ADNASS = CONC * VOLFIW 4180
DIMASS = DIFFK(N) * ABS (Q(N)) * QGRAD 4190
CMASS(M1,K) CMASS(NH,K) + ADMASS + DIMASS 4200
CMASS(NL,K) = CMASS(NL,K) — ADNASS — DIMASS 4210
414 CONTINUE 4220
416 CONTINUE 4230
4240
C**** DECAY AND MASS TRANSFER 4250
4260
210
-------
IF(NCONOK(].))424,424,417 4270
417 00 422 K=1,NUMCON 4280
IF(NCONDK(K))424,424,41 8 4290
418 NCON NCONDK(K) 4300
NC ONO = NCONOX(K) 4310
00 420 J=3,NJ 4320
CMASS(J,NCcW4)=CMASS(J,NCON) * DECAY(K) 4330
IF(NCONO)420,420,419 4340
419 CMASS(J,NCONO) = CMASS(J,NCONO) — C(J,NCON) * VOLIJ) DDECAY(K) 4350
* + REOXK(K) * VOL(.i) * (CSAT(K) — C(J,NC ONfl)) 4360
‘+20 CONTINUE 4370
422 CONTINUE 4380
424 CONTINUE 4390
4400
C***** WASTE DISCHARGES AND DIVERSIONS 4410
4420
DO 434 J=3,NJ 4430
IF(VOL OIN(J))430,434,432 4440
430 00 431 K=1,NUMCON 4450
CMASS(J,K)=CMASS(J,K) — CSPEC(J,K) * VOLOIN(.J) 4460
431 CONTINUE 4470
GO TO 434 4480
432 00 4 K=1,NUMCON 4490
CMASS(J,K)=CMASS(J,K) — C(.J,K) * VOLOIN(J) 4500
433 CONTINUE 4510
434 CONTINUE 4520
4530
C***** APPLY WASTE WATER RETURN FACTORS 4540
4550
IF(NUNITS)442,442,436 4560
436 00 440 I=1,NUNITS 4570
JD1 = JDIV1(I) 4580
J 02 = JDIV2(I) 4590
JR1 = JRET1(I) 4600
JR2 = JRET2(I) 4610
DO 438 M1,NUMCON 4620
CMASS(JR1,M)=CMASS(JR1,M)+(C(JD1,M)*VOIQIN(JD1)*RETFAC (I,M))+ 4630
* CONST(I,M) 4640
CMASS(JR2,M)=CMASS(JR2,M)+(C(JD2,M)*VOLOIN(J02)*RETFAC (I,M))+ 4650
* CONST(I,M) 4660
438 CONTINUE 4670
440 CONTINUE 4680
442 CONTINUE 4690
4700
C***** CORRECT JUNCTION VOLUME AND FIND NEW CONCENTRATION FACTOR 4710
4720
NTAG = NTAG + 1 4730
1F(NTAG — NSPEC)428,426,426 4740
426 NTAG = 0 4750
428 DO 429 K=1,NUMCON 4760
C(1,K) = CIN(K,NTAG+1) 4770
C(2,K) = C(1,K) 4780
429 CONTINUE 4790
00 446 J=3,NJ 4800
VOL(J) = VO1(J) + ASUR(J) * (YNEW(J) — y(J)) 4810
00 444 K=1,NUMCON 4820
C(J,K) CMASS(J,K) / VOL(J) 4830
444 CONTINUE 4840
446 CONTINUE 4850
4860
C***** PREVENT NEGATIVE CONCENTRATION AND SUPERSATURATION 4870
4880
211
-------
00 466 J=1,NJ 4890
Y J) = YNEW(J) 4900
DO 464 K=1,NUMCON 4910
IF(C(J,K))451,464,464 4920
451 GO TO(452,462),KDCOP 4930
452 IFUICYC+ NSPEC + 1) — NQCYC)462,458,458 4940
458 WRITEt6,460) J, ICYC,K,C(J,K) 4950
460 FDRMAT(39H DEPLETION CORRECTION MADE AT JUNCTION 13,7H CYCLE 14, 4960
* 21H FOR CONSTITUENT NO. 11,12K. CONC. WAS F10.2) 4970
462 C(j,K) = 0 O 4980
CMASS(J,K)= 0.0 4990
464 CONTINUE 5000
466 CONTINUE 5010
IF(NCONDK(1 ) )479,479,470 5020
470 DO 476 Kz1,NUMCON 5030
IF(NCONDK(K))476,476,471 5040
471 IF(NCONOX(K))476,476,472 5050
472 NCON = NCONOX(K) 5060
DO 475 J=1,NJ 5070
IF(C(J,NCON) — CSAT(Kfl475,475,473 5080
473 WRITE(6,474) NCON,J,ICYC,C(J,NCON) 5090
474 FORMAT(36HOSUPERSATURATION OF CONSTITUENT NO. 11,23K PREVENTED AT 5100
*JUNCTION 14,Th CYCLE 14,10K CONC. WAS F10,2//) 5110
C(J,NCON = CSAT(K) 5120
CMASS(J,NCON) = C(J,NCONI * VOL(J) 5130
475 CONTINUE 5140
476 CONTINUE 5150
419 CONTINUE 5160
5170
C***** CHECK CONCENTRATIONS AGAINST SPECIFIED LIMITS 5180
5190
00 482 J=1,NJ 5200
00 480 K 1,NUMC0N 5210
IFtC(J,K — CLIM IT(K))480,480,477 5220
477 WRITE(6,478) K,CL1MIT K),J,ICYC 5230
478 FDRMAT(34HOCONCENTRATIDN OF CONSTITUENT NO. 11,8K EXCEEDS,F1.1, 5240
* 13K IN JUNCTION 13,14K DURING CYCLE 15,25H. EXECUTION TERMINATE 5250
*0.) 5260
WRITE(6,481) ((C(L,M),M1,NUMCDN),L1,NJ) 5270
481 FDRMATI1H 8E16.8) 5280
CALL EXIT 5290
480 CONTINUE 5300
482 CONTINUE 5310
5320
C***** WRITE BINARY TAPE FOR EXTRACTING 5330
5340
IF( (ICYC+NSPEC)—NQCYC)486,484,490 5350
484 KOUNTT = 0 5360
REWIND 10 5370
GO TO 490 5380
486 IF(ICYC.LT.IWRITEJGO TO 500 5390
490 KOUNTI = KOUNTT +1 5400
IF(KOUNTT.GT.1)GO TO 494 5410
MARK1 = ICYC 5420
494 ZF(KDU$TT.LT.(NSPEC+1))GO TO 498 5430
MARK2 ICYC 5440
KOUNTT 0 5450
KOONE * 1 5460
IWRITE NEXTWR 5470
NEXTWR P4EXTWR + IWRINT 5480
498 WRITE(10) ICYC,((C(J,K),Km1,NUMCON),J1,NJ) 5490
500 CONTINUE 5500
5510
212
-------
C***** STORE OR UPDATE FOR RESTARTING
IF(ICYC.EQNQCYC)GO TO 5 Z
IF(KODNE.EQ.O) GO 10 520
512 WRITE(9) (ALPHA(I),I=1,80)
WRITE(9) (V0LQIN(J),(C(J,K),C5PEC(J,K),K=1,NUMCON),J 1,NJ)
WRITE(6,518) ICYC,ICYCTF,NTAG
518 FORMAT(1HI//147H RESTART DECK TAPE WAS LAST WRITTEN AFTER CYCLEI5/
* 50H HYDRAULIC CYCLE ON EXTRACT TAPE FOR RESTARTING = 15/
* BH NTAG = 13/ /I)
REWIND 9
520 CONTINUE
C***** PRINT QUALITY OUTPUT OVER TIDAL CYCLE
IF((ICYC + NSPEC + 1) — NQCVC)522,528,528
522 IF(ICYC — IPRT)535,524,524
524 IPRT = IPRT +NQPRT
NCOUNT NCOUNT + 1
IF(NCOUNT — ((NSPEC / NQPRT) 4- 1))528,526,526
526 NCOUNT = 0
ZPRT = N€XTPR
NEXTPR = NEXTPR + INTBIG
528 HOURS = DELTQ * FLOAT (ICYC) / 3600.0
KDAYS HOURS / 23.99999
HOURS = HOURS — FLOAT (24 * KDAYS)
WRITE(6,530) ICYC,KDAYS,HOURS
530 FOR AT( 1H1////
* 35H SYSTEM STATUS AFTER QUALITY CYCLE 14, 112,6H DAYS,
* F6.2,6H HOURSI/
* 109H
* CONCENTRATION FACTORS
* ].09H JUNCTION
*1. 3RD. CONSTIT.
* 105H NUMBER
* (MGL ) (MGL)
DO 534 I =1,NOPRT
J=JPRT( I)
WRITE(6,532) J,Y(J),(C(J,K),K=1,NUMCON)
532 FORMAT(1H0 15,F12.4,F20.2,4F17.2)
534 CONTINUE
535 IF(KDONE.EQ.1) CALL 0UALEX
536 CONTINUE
C***** EXIT
REWIND 3
REWIND 9
CALL PUNCH
WRITE(6,542) NQCYCC
542 FORMAT(2OHOEND OF QUALITY RUN.,15,9H CYCLES.)
CALL EXIT
END
5520
S530
5540
5550
5560
5570
5580
5590
5600
5610
5620
5630
5640
5650
5660
5670
5680
5690
5700
5710
5720
5730
5740
5750
5760
5770
5780
5790
5800
5810
5820
5830
5840
5850
5860
5870
5880
5890
5900
5910
5920
5930
5940
5950
5960
5970
5980
5990
6000
6010
6020
6030
6040
************************** /
HEAD 1ST. CONSTIT. 2ND. CONSTI
4TH. CONSTIT. 5TH. CONSTIT./
(FT) (MGL) (MGL)
(HG L) I)
213
-------
SUBROUTINE QUALEX 6050
DIMENSION CX( 840,5), CMIN( 840,5),CMAX( 840,5), 6060
* CAVE( 840,5),AVOL( 840), ASUR( 840),ALPHA(220 6070
COMMON ALPHA,NSPEC ,DEITQ,NUMCUN,NALPHA,NJ, ASUR, MARK1 , MARK2, KOOME, 6080
* KZDP,CAVE,AVOL 6090
6100
REWIND 10 6110
6120
ca** * PRINT SUMMARY HEADING 6130
6140
HOURS1 = DELTO FLOAT (MARK1 ) / 3600.0 6150
HOURS2 = HOURSI + (FLOAT (NSPEC)*DELTO/3600.) 6160
KDAYS2 = HOURS2 / 24.0 6180
HOURS1 = HOURSI — FLOAT (24 * KDAYS1) 6190
HOURS2 = HOURS2 — FLOAT (24 * KDAYS2) 6200
WRITE(6,111) MARK1,KOAYS I,HOURSI,MARK2,KDAYS2,HOURS2 6210
111 FORMAT(1HU/,/72H****s**a*********#******* QUALITY SUMMARY * 6220
6230
a 55H SUMMARY STARTS AT SUMMARY ENDS AT! 6240
* 6 4 - I CYCLE,15,2H (,13,5f4 DAYS,F5.1,7H HDURS),12H CYCLE, 6250
* 15,241 (,13,5H DAYS,FS.1,7H HOIJRS)///i/) 6260
112 WRITE(6,113) CALpHA(I),r=121,NAL.pI-tA) 6210
113 FORMAT(1H020A41 6280
6290
C**** EXTRACT QUALITY TAPE 6300
6310
114 REAO(1O ) ICYCO,HCX(J,K),K=1,NUMCON),J1,NJ) 6320
IF(ICYCQ — MARK1)114,115,118 6330
115 DO 117 J=1,NJ 6340
DO 11.6 K=1,NUMCON 6350
CAVE(J,K) = 0.5 *CX (J,K) 6360
CMIN(J,K) =CX(J,K) 6370
CMAX(J,K) =CX(J,K) 6380
116 CONTINUE 6390
117 CONTINUE 6400
GO TO 114 6410
118 00 124 J=1,NJ 6420
00 122 K=1,NUMCON 6430
CAVE(J,K) = CAVE(J,K) +CX(J,K) 6440
IF(CMIN(J,K) -CX(J,K) )120,119,119 6450
119 CMIN(J,K) =CX(J,K) 6460
GO TO 122 6470
120 IF(CMAX(J,K) —CX(J,K))121,121,122 6480
121 CMAX(J,K) =CXIJ,K) 6490
122 CONTINUE 6500
124 CONTINUE 6510
IFIICYCO— 44ARK2)114,126,126 6520
126 00 130 J=1,NJ 6530
00 128 K=1,NIJMCON 6540
CAVE(J,K) = CAVE(J,K) — 0.5 *CX(J,K) 6550
CAVE(J,K) = CAVE(J,K) / FLOAT (MARK2 — MARKI) 6560
128 CONTINUE 6570
130 CONTINUE 6580
WRITE(6,131) 6590
131 FORMAT(1H U/I 6600
* 132H 5* CONSTITUENT NO. 1 * * ** CONSTITUENT NO. 2 ** 6610
* ** CONSTITUENT NO. 3 ** ** CONSTITUENT NO. 4 ** ** CONSTITUENT 6620
* NO. 5 *5/ 6630
* I31HJUNC. MIN. MAX. AVE. I’UN. MAX. AVE. 6640
* MIN. MAX. AVE. MIN. MAX. AVE. MIN. MAX. 6650
* AVE.//) 6660
00 133 J=1,NJ 6670
214
-------
WRITE(6,132) J,(CMIN(J,K),CMAX(J,K),CAVE(J,K),K=1,NUMCON) 6680
132 FORMAT( 14,3X,(IX,3F8.2, IX,3F8.2,IX,3F8.2, 1X,3F8.2, 1X,3F8.2)) 6690
133 CONTINUE 6700
6710
C***** COMPUTE AVERAGE CONCENTRATIONS IN SPECIFIED ZONES 6720
6730
GO TO(140,150),KZOP 6740
140 CALL ZONES 6750
150 CONTINUE 6760
6770
C***** PREPARE FOR NEXT EXTRACT AND RETURN 6780
6790
REWIND 10 6800
KDONE = 0 6810
RETURN 6820
END 6830
SUBROUTINE ZONES 6840
C 6850
C********* ***************** *********** ** * 6860
C 6870
C THIS SUBROUTINE IS SPECIFIC TO THE SAN DIEGO BAY NETWORK 6880
C 6890
6900
C 6910
DIMENSION CAVE( 840,5),TLBSC1(5),TLBSC2(5),TLBSCB(5),T1BSC4(5), 6920
* TLBSC5(5),TLBSCo(5),TLBSCT(5),AVOL( 840),ASURt 840),ALPHA(220), 6930
* CAVE1(5),CAVE2(5),CAVE3(5),CAVE4(5),CAVE5(5},CAVE 6 CS), ’IETtS) 6940
COMMON ALPHA,NSPEC,DELTQ,NUMCON,NALPHA,NJ,ASUR,MARKl,MARK2,k00 , 6950
* KZOP,CAVE,AVOL 6960
6970
C***** INITIALIZATION 6980
6990
TVGL1 = 0.0 7000
P 1012 = 0.0 7010
TVOL3 = 0.0 7020
TVOL4 = 0.0 7030
TVOLS = 0.0 7040
TVOL6 = 0.0 7050
TVOLT = 0.0 7060
SAT = 0.0 7070
7080
C***** COMPUTE ZONE VOLUMES 7090
7100
DO 96 J=1,NJ 7110
IF(J.LE.4.OR.J.GT.110)G0 TO 96 7120
TVOLT = TVOLT +AVOL(J) 7130
IF(J.LE.9)GO TO 88 7140
IF(J.LE.34)GO TO 86 7150
IF(J.LE.58) GO TO 84 7160
IF(J.LE.103)GO 10 78 7170
215
-------
IF(J.LE..106)GO TO 90 7180
GO TO 82 7190
78 TVOI1 = TVOL1 +AVOL(J) 7200
GO TO 96 7210
82 TVOI2 = TVOL2 #AVO1(J 7220
GO TO 96 7230
84 TVOL3 = TVOL3 +AVOL(J) 7240
GO 10 96 7250
86 TVOI4 = IVOL4 +AVOLt.i) 7260
GO TO 96 7270
88 TVOL5 = TVOL5 +AV (J) 7280
GD 10 96 7290
90 TVOI6 = TVOL6 +AVOI(J) 7300
96 CONTINUE 7310
7320
C***** COMPUTE TOTAL MASS IN EACH ZONE 7330
7340
DO 134 I=1,NUHCON 7350
TIBSC1(I) = 0.0 7360
TLBSC2(I) 0.0 7370
TLBSC3(1) = 0.0 7380
TLBSC4(I) = 0.0 7390
TLBSC5(I) = 0.0 7400
TIBSC6(I) = 0.0 7410
TLBSCT(I) = 0.0 7420
134 CONTINUE 7430
DO 156 J=1,NJ 1440
1F(J.LE.4.OR.J.GT.110) GO TO 156 7450
00 154 I=1,NUMCON 7460
TLBSCT(I) = TLBSCT(I) + CAVE(J,I) *AVOLIJ) 7470
IF(J.LE.9)G0 TO 146 7480
!F(J.LE.34) GO 10 144 7490
IFIJ.LE.58) GO 10 142 7500
IF(J.LE.103) GO TO 136 7510
IF(J.LE.106) GO TO 148 7520
GO TO 140 7530
136 TLBSCI(I) = TLSSCI(I) + CAVE(J,I) *AVOI(J) 7540
GO TO 154 7550
140 TLBSC2(1) = TLBSC2UJ + CAVEtJ,1J *AVOL(J1 7560
GO TO 154 7570
142 TLBSC3(I) = TIBSC3II) + CAVE(J,I) *AVOL(,J) 7580
GO TO 154 7590
144 TLBSC4(I) = TLBSC4(I) + CAVE(J,I) *AVOL(J) 7600
GO TO 154 7610
146 TLBSC5( 1) = TLBSC5(I) + CAVE(J,I) *AVOL(J) 7620
GO TO 154 7630
148 TIBSC6tI) = TLBSC6(I) + CAVE(J,I) *AVOI(j) 7640
154 CONTINUE 7650
156 CONTINUE 7660
7670
C***** CCI4PUTE MEAN CONCENTRATION IN EACH ZONE 7680
7690
DO 158 I=1,NUMCON 7700
CAVELU) TL.BSCI(I) /TVOL I 7710
CAVE2(I) = TLBSC2(I) / 1V012 7120
CAVE3(I) = TLBSC3(I) / 1V013 7730
CAVE4(I) = TLB5C4U) / TVDL4 7740
CAVE5(I) = TL85C5(I) I TVOL5 7750
CAVE6(I) TLBSC6(I) / TVOL6 7760
CAVETI 1) = TLBSCT(I) / TVOLT 7770
158 CONTINUE 7780
1790
2 6
-------
C***** PRINT ZONE CONCENTRATIONS 7800
7810
00 162 1=1,NUMCON 7820
WRITE(6,16 0)I,cAvE1(I),J, CAvE2(I),I,CA VE3(1)IcA VE4(I)l 7830
* CAVE5(I),I,CAVE6(I),J,CAVET(I) 7840
160 FORMAT(1H /1/i 7850
* 41HAVERAGE CONCENTRATION OF CONSTITUENT NO. I1,16H IN ZONE Nfl. 1 7860
* =,F10.].,6H MG/L.// 7870
* 41HAVERAGE CONCENTRATION OF CONSTITUENT NO. 11,16 1 - I IN ZONE Nfl. 2 7880
* =,F10.I,6H MG/L.// 7890
* 41HAVERAGE CONCENTRATION OF CONSTITUENT NO. I1,16H IN ZONE Nfl. 3 7900
* =,F10.1,6H MG/L.// 7910
* 41HAVERAGE CONCENTRATION OF CONSTITUENT NO. 11,16H IN ZONE NO. 4 7920
* =,F1O,1,bH MG/L.// 7930
* 41HAVERAGE CONCENTRATION OF CONSTiTUENT NO. I1,16H IN ZONE NO. 5 7940
* =,F1O.1,6H MG/L.// 7950
* 41HAVERAGE CONCENTRATION OF CONSTITUENT NO. I1,16H IN ZONE Nfl. 6 7960
* =,F1O.1,bH MG/L.// 7970
* 41HAVERAGE CONCENTRATION OF CONSTITUENT NO. 11,151-i IN TOTAL BAY 7980
*=,F1O.1,bH MG/L.//) 7990
162 CONTINUE 8000
8010
C***** PRINT ZONE VOLUMES 8020
8030
WRITE(6,214) TVOLL,TVOL2,TVOL3,TVOL4,TVOI5,TVOL6,TVCLT 8040
214 FORMAT(281 -IOMEAN VOLUME OF ZONE NO. 1 =,E16.9,12H CUBIC FEET.// 8050
* 28H MEAN VOLUME OF ZONE NO. 2 ,E16,9,12H CUBIC FEET.// 8060
* 28H MEAN VOLUME OF ZONE NO. 3 ,E16.9,12H CUBIC FEET.// 8070
* 28H MEAN VOLUME OF ZONE NO. 4 =,E16.9,12H CUBIC FEET.I/ 8080
* 28H MEAN VOLUME OF ZONE NO. 5 =,E16.9,12H CUBIC FEET,// 8090
* 28H MEAN VOLUME OF ZONE NO. 6 =,E16.9,12H CUBIC FEETS// 8100
* 27 1 -I MEAN VOLUME OF TOTAL BAY =,E16.9,12H CUBIC FEET.//) 8110
8120
C***** COMPUTE AND PRINT TOTAL SURFACE AREA OF SYSTEM 8130
8140
DO 290 J=5,11O 8150
SAT = SAT + ASUR(J) 8160
290 CONTINUE 8170
SAT = SAT / 43560. 8180
WRITE(6,292) SAT 8190
292 FORMAT(1H ///55HTOTAL SURFACE AREA OF SAN DIEGO BAY(TO BALLAST P01 8200
*NT = F9.2,bH ACRES//) 8210
238 CONTINUE 8220
RETURN 8230
END 8240
SUBROUTINE PUNCH 8250
DIMENSION ALPHA(220),CP(840,5),CSP(840,5),VQ(840),ASUR(840), 8260
* CAVE(840,5),AVOL(840) 8270
COMMON AIPHA,NSPEC,DELTO,NUMCON,NALPHA,NJ,ASUR,MARK1,MARK2,KOONE, 8280
* KZOP,CAVE,AVOL 8290
REWIND 9 8300
READ(9) (AIPHA(I),I=1,80) 8310
217
-------
READ(9) (V0(J), (CP(J,K) ,CSP(J,K),K=1,NUMCON),J1,NJ) 8320
WRITE(8,100} (ALPHA(I),I=1,80) 8330
100 FORMAT(20A4) 8340
IF(NUMCON.LT.3) GO TO 514 8350
NFIRST = 3 8360
GO TO 515 8370
514 NFIRST = NtJMC ON 8380
515 00 556 J=1,NJ 8390
QWQ = VQ(J) / DELTQ 8400
WRITE(8,555) J,0WQ,(CP(J,K),CSP(J,K ,K1,NF1RST) 8410
555 FORMtSLT( I5,F10.1,6F10.2 8420
556 CONTINUE 8430
FF(NUMCON.LE.3) GO TO 517 8440
NFIRST = NFIRST + 1 8450
00 558 J=1,NJ 8460
b4RITE(8,557) J,(CPtJ,K),CSP(J,K),KNFIRST,NUMCON) 8470
557 FORMATCIS,6F10.2) 8480
558 CONTINUE 8490
517 CONTINUE 8500
REWIND 9 8510
RETURN 8520
END 8530
218
-------
SAMPLE JOB CONTROL LANGUAGE FOR PROGRAM DYPIOUA
//118012J1 JOB (BO 72 OO,IO 9 O2,0Oj5,oOo3,o3oo,1,),, 1,,.FEIGpIfR., X
ii CLASS=C,MSGL EVEL1
/*SETUP 002033/9
Ii EXEC FORTGCLG,TI$E15,REGION.FORTZ300K,REGJON.GO_330K
//FORT.SYSIN DD *
********** INSERT SOURCE DECK HERE **********
1*
//GO.FTO3FOO1 DO UNIT=240O,OCB RECFMV8S,LRECLB5 ,BLKSIZEB5O4O), X
II DISP=(OLD,KEEP),LABELz(,,,IN),DSp 5D X, X
// VOL=SER 0O2O33
//G0.FTO9FOO1 DO UNIT=2314,DCB5(RECFM*VBS,LRECLZ5O4,BLKSIZE 04O), X
// DISP=(NEW,KEEP),SPACEZ(TRK,(20,2 0),RLSE), X
1/ DSN=SYS2.0148,P(JPICH ,VOLLSER.TEMPAA
//GO.FT1OFOO1 DO UNIT=SYSDK,DC B(RECFMIVBS,LRECLIISO4,BLKSIZE.5040), X
// DISP (NEW,DELETE),SPACE*(CYL,3),DS.NAME SDB1O
//GO.SYSIN DO *
********** INSERT DATA HERE **********
1*
219
-------
SAN DIEGO SAY HYDRAULICS WITH MEAN ANNUAL TIDEI25.O HOUR PERIOD) FEDERAL WATER QUALITY ADMINISTRATION
DEMONSTRATION RUN FOR DOCUMENTATION REPORT 05—27—70 DYNAMIC WATER QUALITY MODEL
QUALITY DEMONSTRATION RUN FOR DOCUMENTATION REPORT
DYE RELEASE — BOO — DO
ss*as*s* FROM HYDRAULICS PROGRAM ****S***
START CYCLE STOP CYCLE TIME INTERVAL
0 1 500 50. SECONDS
STARTING CYCLE INITIAL QUALITY TOTAL QUALITY $** OUTPUT INTERVALS ss* TIME INTERVAL IN CONSTANT FOR
ON HYD. EXTRACT TAPE CYCLE CYCLES CYCLES HOURS QUALITY PROGRAM DIFFUSION COEFFICIENTS
0 1 600 500 2.00 0.500 HOURS 2.500
PRINTOUT IS TO BEGIN AT CYCLE 50
QUALITY TAPE FOR EXTRACTING IS TO BEGIN AT CYCLE 50
4 CONSTITUENTS BEING CONSIDERED IN THIS RUN
FIRST CONSTITUENT IS DYE TREATED AS A CONSERVATIVE
SECOND CONSTITUENT IS DYE WITH DECAY 0.034 PER DAYIBASE E)
THIRD CONSTITUENT IS BOO WITH 0.20 PER DAY DECAY RATE(BASE F)
FOURTH CONSTITUENT IS DISSOLVED OXYGEN WITH REOX. RATE 0.25 PER DAYIBASE E)
CONSTITUENT NO. 2 15 TREATED AS A NON—CONSERVATIVE WITH DECAY COEFFICIENT a 0.9992919 BUT IS NOT PAIRED WITH ANY OTHER CONSTITUENT
CONSTITUENT NO. 3 IS BOD WITH DECAY COEFFICIENT • 0.9958420 THE ASSOCIATED OXYGEN IS CONSTITUENT NO. 4
WITH REAFRATION CO€FFICIENT • 0.005194783 AND SATURATION CONCENTRATION • 8.40
-------
SUMMARY OF HYDRAULIC INPUTS
** JUNCTION HEAD AND HYD. RADIUS AND X—SECTIONAL AREA OF CHANNELS ARE AT MEAN TIDE **
**************************** CHANNEL DATA *****************************
CHAN. LENGTH WIDTH AREA MANNING NET FLOW HYD. RADiUS JUNC. AT ENDS
JUNC. INFLOW HEAD
JUNCTION DATA
CHANNELS ENTERING JUNCTION
.
S
S
S
S
S
S
S
S
S
.
S
S
S
.
S
S
S
S
.
S
1
2500.
4400.
131969.
0.015
—340.56
30.0
1
3
1
0.8
0.07
1
2
0
0
0
2
2500.
2500.
81966.
0.015
0.0
32.8
1
2
2
0.5
0.07
2
0
0
0
0
3
2500.
4200.
117558.
0.015
—343.78
28.0
3
4
3
1.6
0.07
1
3
0
0
0
4
2500.
1100.
86482.
0.015
—364.31
50.9
4
5
4
1.8
0.07
3
4
0
0
0
5
2500.
2400.
100635.
0.015
—663.24
41.9
5
6
5
1.2
0.07
4
5
6
0
0
6
2500.
1500.
57076.
0.015
295.56
38.1
5
7
6
0.9
0.07
5
8
9
0
0
7
2500.
1500.
54076.
0.015
294.57
36.1
7
8
7
0.5
0.07
6
7
0
0
0
8
2500.
2350.
100881.
0.015
—504.91
42.9
6
9
8
0.6
0.07
7
9
10
0
0
9
2350.
2200.
85619.
0.015
—160.06
38.9
6
8
9
0.9
0.07
8
11
0
0
0
10
2500.
1250.
48809.
0.015
134.28
39.0
8
10
10
0.5
0.07
10
13
14
0
0
S
S
S
S
S
•
S
S
S
S
S
S
•
•
S
.
•
•
S
S
•
S
S
I
•
•
S
•
•
S
—
91
92
2500.
1800.
1900.
2100.
24804.
29511.
0.015
0.015
508.48
494.58
13.1
14.1
68
54
71
55
91
92
1.1
0.8
0.07
0.07
132
136
135
140
139
0
0
0
0
0
93
1800.
2500.
35144.
0.015
366.91
14.1
55
69
93
646.8
0.07
140
141
0
0
0
94
2500.
2500.
35144.
0.015
330.21
14.1
69
70
94
1.0
0.07
137
141
142
143
0
95
2500.
2500.
33895.
0.015
281.28
13.6
70
71
95
0.9
0.07
138
139
142
144
0
06
2250.
1650.
47936.
0.015
—3158.50
29,1
54
56
96
—645.0
0.07
145
147
0
0
0
91
2300.
2000.
28111.
0.015
621.96
14.1
55
57
97
1.0
0.07
143
145
146
148
0
98
2500.
2100.
29517.
0.015
449.41
14.1
69
72
98
1.0
0.07
144
146
149
0
0
99
2500.
2500.
35144.
0.015
560.41
14.1
70
73
99
3.0
0.07
147
150
152
0
0
100
2500.
1950.
27407.
0,O 5
794.97
14.1
71
74
100
0.6
0.07
148
150
151
0
0
101
1850.
1700.
23891.
0.015
214.26
16.1
56
57
101
0.6
0.07
149
151
0
0
0
102
1900.
1400.
19671.
0.015
207.92
14.1
57
72
102
0.1
0.07
152
153
0
0
0
103
2500.
2500.
36394.
0.015
—1026.20
14.6
72
73
103
0.2
0.07
153
0
0
0
0
104
2500.
2500.
33894.
0.015
—782.64
13.6
73
74
104
0.2
0.07
154
155
156
0
0
105
2100.
1100.
31949.
0.015
—3020.90
29.0
56
59
105
0.2
0.07
156
157
0
0
0
106
2800.
1700.
23890.
0.015
—1472.36
14.1
59
72
106
0.2
0.07
158
0
0
0
0
107
2500.
2400.
40937.
0.015
—750.20
17.1
59
75
107
0.4
0.07
159
160
0
0
0
108
2500.
2450.
34441.
0.015
217.91
14.1
72
76
108
0.4
0.07
160
161
162
0
0
109
2500.
2500.
35144.
0.015
323.56
14.1
73
77
109
0.4
0.07
162
163
164
0
0
110
2700.
850.
11511.
0.015
17.91
13.5
74
78
110
0.5
0.07
164
165
0
0
0
111
2400.
2300.
32331.
0.015
—523.44
14.1
75
76
111
0.5
—3.01
170
0
0
0
0
112
2500.
2600.
36551.
0.015
—341.88
14.1
76
77
112
0.5
—3.01
170
0
0
0
0
113
1800.
2350.
30685.
0.015
108.69
13.1
77
78
114
2900.
2650.
39905.
0.015
—217.53
15.1
75
79
115
2800.
2000.
26112.
0.015
43.23
13.1
76
79
116
2450.
2250.
32753.
0.015
—120.54
14.6
77
80
117
2100.
1300.
16965.
0.015
179.78
13.1.
78
81
-------
118 2800. 2500. 351’t5. 0.015 492.61 14.1 79 80
119 1850. 2400. 31339. 0.015 141.06 13.1 80 81.
120 2400. 2700. 40659. 0.015 —657.64 15.1 79 82
ut 2400. 2400. 32539. 0.015 237.48 13.6 80 83
122 2500. 1150. 1.5580. 0.013 274.25 13.5 81 84
123 2500. 2500. 27647. 0.013 —581,94 11.1 82 83
• • • S S • S S
• S S S • S S • S
• S S • S S S
159 2100. 2050. 59560. 0.015 544 43 29.1 50 107
160 2500.. 1200. 15658. 0 ,015 547.07 13.0 1.07 108
161 2100. 2400. 76639. 0,015 —158.31 31.9 52 108
1.62 2100. 1300. 16964. 0.015 391.38 13.0 108 109
163 2100. 1200. 37255. 0.015 108.90 31.0 54 109
164 2100. 1600. 20884. 0.015 503.24 13.1 109 110
165 2100. 1100. 29749. 0.015 —506.29 27,0 56 110
1.66 1950e 1300. 40362. 0.01.5 157.71 31.0 56 58
167 2100. 1450. 1.8925. 0.01.5 159.49 13.1. 58 60
168 1950. 1800. 52296. 0.015 —162.10 29.1 59 60
169 1650. 1500. 21078. 0.01.3 631.85 14.1 57 59
170 2500. 2500. 74937. 0.01.5 0.0 30.0 111 112
*****MULTJPLICATION FACTORS APPLIED TO OBTAIN STARTING CONCENTRATIONS
CONSTITUENT GROUP FACTOR JUNCTION NUMBERS
1 1 0.50 1 — 1.10
NO MULTIPLICATION FACTOR APPLIED TO CONSTITUENT NO. 2
NO MULTIPLICATION FACTOR APPLIED TO CONSTITUENT NO. 3
NO MULTIPLICATION FACTOR APPLIED TO CONSTITUENT NO. 4
-------
********************************************** WATER QUALiTY DATA
* FIRST CONSTITUENT * SECOND CONSTITUENT * THIRD CONSTITUENT * FOURTH CONSTITUENT * FIFTH CONSTITUENT *
INITIAL INFLOW INITIAL INFLOW INITIAL INFLOW INITIAL INFLOW INITIAL INFLOW
JUNC. INFLOW CONC. CONC. CONC. CONC. CONC. CONC. CONC. CONC. CONC. CONC.
1 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
2 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
3 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
4 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
5 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
6 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
7 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
8 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
9 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
10 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
• . S • . S
• S S • S S S
• S S • S S S
52 —18.8 0.50 1190.00 0.50 1190.00 2.00 300.00 5.00 2.00
53 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
54 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
55 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
56 0.0 0,50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
57 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
• S S S S S S S
• • • S S S S I
• S S S S S S S
92 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
93 646.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
94 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
95 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
96 —646.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
97 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
98 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
99 2.6 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
100 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
101 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
102 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
103 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
104 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
105 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
106 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
107 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00
108 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
109 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
110 0.0 0.50 0.0 0.50 0.0 2.00 0.0 5.00 0.0
111 0.0 1.00 0.0 0,50 0.0 2.00 0.0 5.00 0.0
112 0.0 1.00 0.0 0.50 0.0 2.00 0.0 5.00 0.0
-------
SPECIFIED C—FACTORS AT JUNCTION 1 FOR CONSTITUENT NO. I
N)
N)
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0,500
0.500
0.500
0.500
0 • 500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
O • 500
0,500
0,500
O • 500
0,500
0.500 0.500 0.500
0.500
0.500
0.500
0.500
0.500 0.500 0.500
0.500
0.500
0.500
0.500
0.500 0.500 0.500
0.500
0.500
0.500
0.500
0.500 0.500 0.500
0.500
0.500
0.500
0.500
0.500 0.500 0.500
0.500
0.500
0.500
0.500
0.500 0.500 0.500
0.500
0.500
0.500
0.500
0.500 0.500 0.500
0.500
0.500
0.500
0.500
0.500
SPECIFIED C—FACTORS AT JUNCTION 1 FOR
CONSTITUENT
NO.
2
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
SPECIFIED C—FACTORS AT JUNCTION 1 FOR
CONSTITUENT
NO.
3
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
SPECIFIED C—FACTORS AT JUNCTION 1 FOR
CONSTITUENT
NO.
4
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.bOO
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
2,000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2 • 000
2.000
2.000
2.000
2.000
2.000
2.000
2 • 000
2.000
2.000
2.000
7.500
7.500
7.500
7.500
7.500
7,500
7.500
7.500
7.500
7.500
7.500
7.500
7,500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
7.500
-------
TABL€ OF WASTE WATER RETURN FACTORS
JUNCTIONS USED JUNCT3ONS USED
FOR DIVERSIONS FOR RET. FLOWS 1ST. CONSTITUENT 2ND. CONSTITUENT 3RD. CONSTITUENT 4TH. CONSTITUENT 5TH. CONSTITUENT
UNIT NO. 1 NO. 2 NO. 1 NO. 2 COEFF. CONST. COEFF. CONST. COEFF. CONST. COEFF. CONSI. COEFF. CONST.
1 93 98 96 97 1.00 0.0 1.00 0.0 1.00 0.0 1.00 0.0
U’
-------
SYSTEM STATUS AFTER QUALITY CYCLE 50 1 DAYS, 1.00 HOURS
********SS**************** CONCENTRAT ION FACTORS ***************i**********
JUNCTION HEAD 1ST. CONSTIT. 2ND. CONSTIT. 3RD. CONSTIT. 4TH. CONSTIT. 5TH. CONSTIT.
NUNBER IFT) 4NG L) ( ) NGL) (MGI.) CMGL)
1. 2.6020 0.50 0.90 2.00 7.90
2 2.6020 0.50 0.50 2.00 7.90
3 2.6020 0.50 0.50 1.98 7.49
4 2.6020 0.50 0.50 1.97 7.49
3 2.6362 0.50 0.50 1.96 7.50
6 2.6578 0.50 0.50 1.94 7.56
30 2.7855 0.50 0,48 1.62 5.46
33 2.8113 0.30 0.48 1.62 5.45
44 2.8849 0.50 0.49 1.62 5.44
52 2.9410 2.38 2.35 2.07 5.41
70 2.9570 1.05 1.02 1.74 5.40
75 2.9698 0.81 0.78 1.68 5.41
80 2.9789 0.53 0.51 1.62 5.41
90 3.0039 0.50 0.48 1.61 5.40
106 2.9167 0.58 0.56 1.64 5.43
112 —3.0000 1.00 0.48 1.62 5,45
-------
SYSTEM STATUS AFTER QUALITY CYCLE .98 2 DAYS, 1.00 HOURS
************************** CONCENTRATION FACTORS **************************
JUNCTION HEAD 1ST. CONSTIT. 2ND. CONSTIT. 3RD. CONSTIT. 4TH. CONSTIT. 5TH. CONSTIT.
NUMBER (FT) (MGI) (MGI) (MGI) (MGI) (MGI)
1 2.3613 0.50 0.50 2.00 7.50
2 2.3613 0.50 0.50 2.00 7.50
3 2.3691 0.50 0.50 1.99 7.49
4 2.3775 0.50 0.50 1.98 7.49
5 2.3892 0.50 0.50 1.98 7.50
6 2.3968 0.50 0.50 1.95 7.53
30 2.4398 0.50 0.47 1.33 5.84
35 2.4482 0.50 0.46 1.33 5.83
44 2.4712 0.52 0.49 1.33 5.83
52 2.4881 3.24 3.14 1.93 5.76
70 2.4933 1.76 1.67 1.57 5.76
75 2.4974 1.00 0.95 1.42 5.80
80 2.5004 0.63 0.59 1.35 5.81
90 2.5085 0.51 0.48 1.32 5.80
106 2.4808 0.80 0.75 1.38 5.82
112 —3.01.32 1.00 0.47 1.33 5.84
RESTART DECK TAPE WAS LAST WRITTEN AFTER CYCLE 100
HYDRAULIC CYCLE ON EXTRACT 1APE FOR RESTARTING 0
NTAG 0
-------
************************ QUALITY SUMMARY ********s****** a
SUMMARY STARTS AT SUMMARY ENDS AT
CYCLE 50 (*** DAYS***** HOURS) CYCLE 100 ( 2 DAYS 2.0 HOURS)
FIRST CONSTITUENT IS DYE TREATED AS A CONSERVATIVE
SECOND CONSTITUENT IS DYE WITH DECAY 0.034 PER DAY(BASE E)
THIRD CONSTITUENT IS 800 WITH 0.20 PER DAY DECAY RATE(BASE E)
FOURTH CONSTITUENT IS DISSOLVED OXYGEN WITH REOX. RATE 0.25 PER DAY(BASE E)
** CONSTITUENT NO. 1 ** ** CONSTITUENT NO. 2 ** ** CONSTITUENT NO. 3 ** ** CONSTITUENT NO. 4 ** ** CONSTITUENT NO. 5 **
JUP4C. NIN. MAX. AVE. MIN. MAX. AVE. MIN. MAX. AVE. MIN. MAX. AVE. MIN. MAX. AVE.
1 0.50 0.50 0.50 0.50 0.50 0.50 2.00 2.00 2.00 7.50 7.50 7.50
2 0.50 0.50 0.50 0.50 0.50 0.50 2.00 2.00 2.00 7.50 7.50 7.50
3 0.50 0.50 0.50 0.48 0.50 0.50 1.58 2.05 1.90 6.38 7.66 7.34
4 0.50 0.50 0.50 0.48 0.50 0.49 1.53 2.03 1.84 5.96 7.63 7.20
5 0.50 0.50 0.50 0.48 0.50 0.49 1.52 2.02 1.79 5.65 7.67 7.02
6 0.50 0.50 0.50 0.47 0.50 0.49 1.48 2.01 1.72 5.43 7.70 6.79
7 0.50 0.50 0.50 0.48 0.50 0.49 1.52 1.93 1.72 5.79 7.47 6.86
8 0,50 0.50 0.50 0.47 0.49 0.48 1.45 1.85 1.63 5.41 7.43 6.54
9 0.50 0.50 0.50 0.47 0.50 0.48 1.41 1.90 1.63 5.44 7.50 6.50
10 0.50 0.50 0.50 0,47 0.49 0.48 1.39 1.77 1.57 5.40 7.27 6.28
11 0.50 0.50 0.50 0.47 0.49 0.48 1.37 1.77 1.55 5.43 7.29 6.16
12 0.50 0.50 0.50 0.47 0.48 0.48 1.37 1.65 1.48 5.65 6.29 5.82
13 0.50 0.50 0.50 0.47 0.48 0.47 1.33 1.63 1.47 5.47 5.91 5.68
14 0.50 0.50 0.50 0.47 0.48 0.47 1.32 1.62 1.47 5.45 5.87 5.66
15 0.50 0.50 0.50 0.47 0.49 0.48 1.37 1.72 1.51 5.48 7.06 5.96
16 0.50 0.50 0.50 0.47 0.49 0.48 1.36 1.69 1.49 5.51 6.83 5.82
17 0.50 0.50 0.50 0.47 0.48 0.47 1.33 1.63 1.47 5.48 5.91 5.67
18 0.50 0.50 0.50 0.47 0.48 0.47 1.32 1.62 1.47 5.45 5.85 5.66
19 0.50 0.50 0.50 0.47 0.48 0.47 1.35 1.65 1.47 5.50 6.46 5.72
20 0.50 0.50 0.50 0.47 0,48 0.47 1.35 1.65 1.47 5.54 6.37 5.72
21 0.50 0.50 0.50 0.47 0.48 0.47 1.34 1.63 1.47 5.50 6.04 5.66
22 0.50 0.50 0.50 0.47 0.48 0.47 1.32 1.62 1.46 5.48 5.89 5.65
23 0.50 0.50 0.50 0.47 0.48 0.47 1.32 1.62 1.46 5.44 5.85 5.65
24 0.50 0.50 0.50 0.46 0.48 0.47 1.32 1.62 1.46 5.44 5.85 5.65
25 0.50 0.50 0.50 0.46 0.48 0.47 1.31 1.62 1.46 5.44 5.84 5.65
26 0.50 0.50 0.50 0.46 0.48 0.47 1.31 1.62 1.46 5.44 5.84 5.65
27 0.50 0.51 0.50 0.47 0.49 0.48 1.34 1.63 1.47 5.49 6.11 5.67
28 0.50 0.50 0.50 0.47 0.48 0.47 1.32 1.62 1.46 5.47 5.89 5.65
-------
• • • • . • . S S
• S S S S I S S S • I I
• S • • S S S I S S S S S
34 0.50 0.50 0.50 0.46 0.48 0.47 1.31 1.62 1.46 5.44 5.84 5.65
35 0.49 0.68 0.53 0.46 0.65 0.50 1.32 1.62 1.47 5 45 5.85 5.65
36 0.50 0.62 0.52 0.47 0.60 0.50 1.32 1.62 1.47 5.44 5.84 5.65
37 0.50 0.64 0.53 0.47 0.62 0.50 1.32 1.62 1.47 5.44 5.84 5.65
38 0.50 1.20 0.64 0.48 1.16 0.61 1.32 1.67 1.49 5.44 5.84 5.64
39 0.48 1.29 0.62 0.46 1.25 0.59 1.31 1.69 1.49 5.44 5.84 5.64
40 0.50 2.41 0.86 0.48 2.35 0.82 1.32 1.95 1.54 5.44 5.84 5.63
41 0.49 1.29 0.68 0.46 1.25 0.64 1.31 1.70 1.50 5.44 5.84 5.64
42 0.44 2.84 1.07 0.41 2.77 1.03 1.32 2.05 1.59 5.44 5.84 5.63
43 0,50 2.46 0.93 0.48 2.40 0.90 1.32 1.97 1.56 5.44 5.84 5.63
44 0.45 3.20 1.29 0.43 3.13 1.24 1.32 2.16 1.63 5.44 5.84 5.62
45 0.49 3.32 1.51 0.47 3.25 1.46 1.32 2.20 1.68 5.43 5.84 5.61
46 0.51 2.39 1.28 0.49 2.32 1.23 1.32 1.91 1.62 5.43 5.84 5.61
47 0.61 2.41 1.63 0.59 2.32 1.57 1.42 1.80 1.69 5.42 5.81 5.59
48 0.46 3.33 1.77 0.45 3.23 1.71 1.33 2.15 1.74 5.43 5.83 5.60
49 0.58 2.43 1.63 0.56 2.33 1.56 1.41 1.88 1.69 5.41 5.81 5.59
50 0.32 3.57 2.14 0.31 3.48 2.07 1.32 2.16 1.82 5.43 5.82 5.59
51 0.54 2.73 1.73 0.52 2.63 1.66 1.44 1.86 1.71 5.41 5.79 5.59
52 1.73 4.74 3.39 1.69 4.64 3.32 1.83 2.38 2.12 5.41 5.77 5.58
53 0.91 4.06 2.48 0.87 3.95 2.41 1.59 2.13 1.89 5.39 5.75 5.58
54 0.41 4,03 2.08 0.38 3.92 2.02 1.48 2.18 1.81 5.39 5.74 5.59
55 0.84 3.81 2.11 0.81 3.70 2.05 1.57 2.14 1.81 5.38 5.74 5.59
56 0.62 2.81 1.37 0.60 2.72 1.32 1.46 1.98 1.65 5.40 5.77 5.61
57 0.53 2.94 1.43 0.50 2.84 1.38 1.49 1.99 1.66 5.38 5.76 5.60
58 0.78 1.78 1.11 0.75 1.71 1.07 1.47 1.81 1.59 5.41 5.79 5.62
r... 59 0.52 1.86 0.92 0.49 1.78 0.89 1.41 1.81 1.55 5.41 5.78 5.62
60 0.64 1.00 0.77 0.61 0.94 0.74 1.41 1.67 1.52 5.42 5.81 5.62
61 0.60 1.99 1.17 0.57 1.92 1.12 1.41 1.80 1.60 5.42 5.81 5.61
62 0.70 1.58 1.21 0.67 1.51 1.15 1.49 1.66 1.60 5.42 5.79 5.61
63 0.56 0.91 0.70 0.54 0.86 0.67 1.39 1.63 1.50 5.43 5.81 5.63
64 0.50 0.56 0.52 0.48 0.53 0.49 1.32 1.62 1.46 5.43 5.83 5.64
65 0.70 2.39 1.51 0.67 2.29 1.45 1.55 1.81 1.67 5.40 5.76 5.59
66 0.79 3.08 1.89 0.76 2.96 1.83 1.57 1.94 1.76 5.39 5.75 5.59
67 0.68 2.36 1.33 0.66 2.26 1.27 1.52 1.79 1.63 5.40 5.75 5.60
68 0.64 1.77 1.03 0.61 1.68 0.99 1.47 1.69 1.56 5.40 5.77 5.61
69 0.55 2.90 1.44 0.52 2.79 1.39 1.50 1.93 1.66 5.39 5.75 5.60
70 0.52 1.88 0.95 0.50 1.79 0.91 1.43 1.74 1.55 5.40 5.77 5.61
11 0.52 1.32 0.76 0.50 3.25 0.72 1.41 1.65 1.51 5.41 5.79 5.62
72 0.53 2.01 0.96 0.50 1.93 0.92 1.41 1.80 1.55 5.40 5.77 5.61
73 0.49 1.20 0.67 0.47 1.13 0.63 1.38 1.66 1,49 5.41 5.79 5.62
74 0.50 0.88 0.59 0.48 0.82 0.56 1.37 1.62 1.47 5.41 5.80 5.62
75 0.53 1.08 0.68 0.50 1.02 0.65 1,39 1,68 1.49 5.41 5.80 5.6
76 0.51 1.25 0.69 0.48 1.19 0.66 1.38 1.69 1.50 5.40 5.79 5.6
77 0.50 0.88 0.57 0.47 0.83 0.54 1.37 1.64 1.47 5.41 5.81 5.6
78 0.49 0.70 0.53 0.47 0.66 0.51 1.34 1.62 1.46 5.41 5.81 5.62
79 0.48 0.82 0.56 0.46 0.77 0.53 1.37 1.64 1.47 5.41 5.81 5.6.
80 0.49 0.66 0.52 0.47 0.62 0.50 1.33 1.62 1.46 5.41 5.81 5.6
81 0.50 0.58 0.51 0.47 0.55 0.48 1.32 1.61 1.46 5.41 5.82 5.62
82 0.49 0.63 0.52 0.47 0.59 0.49 1.33 1.62 1.46 5.41 5.81 5.6
83 0.49 0.55 0.50 0.47 0.52 0.48 1.31 1.61 1.45 5.40 5.81 5.61
84 0.49 0.53 0.50 0.47 0,49 0.47 1.30 1.61 1.45 5.40 5.82 5.61
85 0.49 0.55 0.50 0.47 0.52 0.48 1.31 1.61 1.45 5.40 5.81 5.61
86 0.49 0.51 0.50 0.46 0.48 0.47 1.29 1.61 1.45 5.39 5.81 5.61
-------
.
S
9
S
S •
0.Z9 o.o
S
S S
S
0.49 0. 6
•
S
I
0.48
.
S
I
0.47
S
S
S S
1.29 1.61
•
I
i.Zs
•
I
5. 9
S
•
S
5.81
•
I
S
5.60
96
0.48 0.49
0.49 0.45
0.47
0.47
1.27 1.60
1.44
5.35
5.78
5.58
97
0.48 0.49
0.49 0.45
0.47
0.47
1.28 1.60
1.44
5.36
5.79
5.58
98
0.49 0.49
0.49 0.45
0.48
0.47
1.28 1.60
1.44
5.37
5.80
5.59
99
0.48 0.49
0.49 0.45
0.47
0.46
1.27 1.59
1.44
5.35
5.77
5.57
100
0.48 0.49
0.49 0.45
0.47
0.46
1,27 1.60
1.44
5.35
5.78
5.57
101
0.48 0.49
0.49 0.45
0.47
0.47
1,28 1.60
1.44
5.36
5.78
5.58
102
0.48 0.49
0.49 0.45
0.47
0.46
1.27 1.59
1.44
5.35
5.77
5.57
103
0.48 0.49
0.49 0.45
0.47
0.46
1.27 1.59
1.43
5.34
5.76
5.56
104
0.33 2.99
1.31 0.31
2.93
1.27
1.31 2.11
1.64
5•43
5.84
5.62
105
0.49 3.10
1.66 0.47
3.02
1.61
1.34 2.12
1.71
5.42
5.83
5.61
106
0.52 0.80
0.65 0.50
0.75
0,62
1.37 1.64
1.49
5.43
5.82
5.64
107
0.76 2.40
1.47 0.73
2.30
1.41
1.51 1.74
1.66
5.41
5.77
5.60
108
1.00 2.32
1.41 0.97
2.22
1.35
1.53 1.80
1.65
5.41
5.76
5.60
109
0.92 1.82
1.19 0.88
1.74
1.14
1.52 1.73
1.60
5.41
5.78
5.61
110
0.60 1.19
0.92 0.58
1.12
0.88
1.44 1.65
1.54
5.42
5.80
5.62
111
1.00 1.00
1.00 0.47
0.48
0.47
1.32 1.62
1.47
5.45
5.86
5.66
112
1.00 1.00
1.00 0.47
0.48
0.47
1.32 1.62
1.47
5.45
5.86
5.66
AVERAGE
CONCENTRATION OF
CONSTITUENT NO, 1 IN ZONE
NO. 1
0.7 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 1 IN ZONE
NO. 2
1.3 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. I IN ZONE
NO. 3
1.3 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 1 IN ZONE
NO. 4
=
0.5 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 1 IN ZONE
NO. 5
0.5 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 1 IN ZONE
NO. 6
=
1.1 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 1 IN TOTAL
BAY
0.8 MG/L.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 2 IN ZONE
NO. 1
0.7 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 2 IN ZONE
NO. 2
=
1.2 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 2 IN ZONE
NO. 3
1.2 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 2 IN ZONE
NO. 4
0.5 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 2 IN ZONE
NO. 5
=
0.5 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 2 IN ZONE
NO. 6
1.0 MG/I.
AVERAGE
CONCENTRATION OF
CONSTITUENT NO. 2 IN TOTAL BAY •
0.8 MG/L.
-------
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 3 IN
ZONE
NO. I
1.5
MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 3 IN
ZONE
NO. 2
1.6
MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 3 IN
ZONE
NO. 3
=
1.6
MG/L.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 3 IN
ZONE
NO. 4
=
1.5
MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 3 IN
ZONE
NO. 5
=
17
MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 3 IN
ZONE
NO. 6
=
1.6
MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 3 IN
TOTAL
BAY =
1.6
MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
4 IN
ZONE
NO. 1
5.6
MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
4 IN
ZONE
NO. 2
=
5.6
MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
4 IN
ZONE
NO. 3
=
5.6
MG/I.
‘a
AVERAGE
AVERAGE
CONCENTRATION
CONCENTRATION
OF
OF
CONSTITUENT
CONSTITUENT
4 IN
4 IN
ZONE
ZONE
NO. 4
NO. 5
=
=
5.8
6.8
MG/I.
MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
4 IN
ZONE
NO. 6
=
5.6
MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
4 IN
TOTAL BAY
2
5.8
MG/I.
NO.
NO.
NO.
NO.
NO.
NO.
NO.
MEAN
MEA N
MEAN
MEAN
MEAN
MEAN
VOLUME
VOLUME
VOLUME
VOLUME
VOLUME
VOLUME
OF ZONE
OF ZONE
OF ZONE
OF ZONE
OF ZONE
OF ZONE
NO. 1
NO. 2
NO. 3
NO. 4
NO. 5
NO. 6
O.250401050E
= O.224610608E
O.280840986E
= O.300359552E
= O.108537216E
2 O.804166400E
10 CUBIC
09 CUBIC
10 CUBIC
10 CUBIC
10 CUBIC
08 CUBIC
FEET.
FEET.
FEET.
FEET.
FEET.
FEET.
MEAN VOLUME OF TOTAL BAY = O.970626253E 10 CUBIC FEET.
TOTAL SURFACE AREA OF SAN DIEGO BAY(TO BALLAST POINT = 10714.41 ACRES
-------
SYSTEM STATUS AFTER QUALITY CYCLE 550 11 DAYS, 11.00 HOURS
CONCENTRATION FACTORS
JUNCTION HEAD 1ST. CONSTIT. 2ND. CONSTIT. 3RD. CONSTIT. 4TH. CONSul. 5TH. CONSTIT.
NUMBER (Fl) (MGI) (MGI) (MGL (MGI) (MGL)
1
2.6020
0.50
0.50
2.00
7.50
2
2.6020
0.50
0.50
2.00
7.50
3
2.6020
0.50
0.50
1.98
7.50
4
2.6020
0.50
0.50
1.97
7.49
5
2.6362
0.50
o.so
1.97
7.49
6
2.6578
0.50
0.50
1.97
7.47
30
2.7855
0.94
0.68
0.30
7.76
35
2.8113
1.10
0.80
0.27
7.76
44
2.8849
2.02
1 ,54
0.30
7.69
52
2.9410
6.99
6.07
1.12
7.42
70
2.9570
6.43
5.37
0.85
7.31
75
2.9698
4.35
3.50
0.55
7.42
80
2.9789
4.00
3.14
0.46
7.41
90
3.0039
2.07
1.56
0.28
7.48
106
2.9167
4.09
3.24
0.49
7.52
112
—3.0000
-------
SYSTt-; STATUS AFTER
J1Jl\ CTJ(lF
NL1kR ER
HEAD
( FT )
DUALITY CYCLE 599 12 flAYS, ]i.50 HOURS
C.11FCFNTRAT I 11f’ FACTORS
ST. C [ NSTIT. ? ( P. CIINSTI T. 38 e C1)r ’ST IT.
MOL ) C MOL ) ( MOL
4T -I. CDNSTIT. 5TH. Cfl ’STIT.
fr (; ) ( (; 1.
1
2.5409
0.50
0.50
2.00
7.5()
2
2.5409
0.50
0.50
2.00
7. O
3
?.553()
0.50
0.50
1.98
7.49
4
2.5 62
0.50
0.50
1.97
7•49
5
?.5H45
0.50
0.5()
1.97
7.49
6
2.5961
0.50
0.50
1.98
7.47
30
2.66 1
1.06
0.75
0.26
I.H
35
2.6(64
1.25
0. 9
0.24
(.84
44
2.f134
2.26
1.69
0.28
7.78
57
2.7407
7.33
6.28
1.08
7.51
70
2.7487
6.81
5.61
0.82
7.47
(5
2.7553
4.69
3.71
0.5?
7.54
80
2.760()
4.35
3.36
0.43
7.53
90
2.7728
2.31
1.7()
0.25
7.62
1(:6
2.7289
4.48
3.49
0.47
7.61
11?
—3.0135
1.00
0.33
0.16
7.94
RESTART DECK 1.APE WAS LAST RRITTEN AFTER CYCLE 60()
HYDRAULIC CYCLE ON EXTRACT TAPE FOR RESTARTING =
NTAG = 0
0
-------
SYSTEM STATUS AFTER
OLJALJTY CYCLE 600 12 DAYS, 17.ou I-4FJIIPS
‘ * ‘ ‘ ‘ C nr’ c Er ITMA I I (‘N F AC TIIR S
1ST. CCiNSTIT. 2ND. CLINSTIT. 3RD. CUNSTIT.
( frGI_ ) ( NCL ) C MCI)
* c * :c * * ,
4TH. CIINSTIT. 5TH. CIJNSTIT.
C Mi;L ) ( MGL )
JUNCTION
NUMBER
HEAI)
(I T)
I
2.6020
0.50
0.50
2.00
7.5()
2
2.602C)
0.50
0•5()
2,0’)
7.50
3
2.6020
0.50
o.so
.
7.50
4
2.6020
0.50
0,50
1.97
7.49
5
2.6362
0.50
0.50
1.97
7.
6
2.6578
0.50
0.50
i.Th
7.47
30
2.7855
1.05
0.74
0.27
7.83
35
2.8113
1.23
0.87
0.24
7.84
44
2.1
2.22
1.66
0.27
7.77
52
2.9411
7.31
6.27
1.09
7.49
70
2.95(()
6.f 1
5.61
(.R
7.38
75
).U69%
4.70
3,7
0.5,
7.49
81)
2.9789
4.36
: .37
0.43
7.48
90
.U039
2.33
1.1?
0.25
(.55
106
2.9167
4.46
3.48
0.46
7.60
112
—3.0000
1.00
0.33
0.1.6
7.94
-------
************************ DUAL ITY SUMMARY ***************‘ * *
SUMMARY STARTS AT SUMMARY ENDS AT
CYCLE 550 (*** DAYS** ** HOURS) CYCLE ADO ( 12 DAYS 17.0 140(185)
FIRST CONSTITUENT IS DYE TREATED AS A CONSERVATIVE
SECOND CONSTITUENT IS DYE WITH DECAY 0.034 PER DAY(RASE F)
THIRD CONSTITUENT IS BOO WITh 0.20 PER DAY DECAY RATE(BASF F)
FOURTH CONSTITUENT IS DISSOLVED OXYr,EN WITH REOX. RATE 0.75 PER I)AY(RASE F)
** CONSTITUENT NO. 1 ** * CONSTITUENT NO. 2 ** ** CONSTITUENT Nfl. 3 4* 4* CONSTITUENT Nfl. 4 *4 *4 CIINSTI TIJENT Nfl. 5 *4
JUNC. WIN. MAX. AVE. WIN. MAX. AVE. Mjt’ ‘AX. AVE. MINI. MAX. AVE. WIN. NAX. AVF.
‘ 1 0.50 0.50 0.50 0.50 0.50 0.50 2.00 2.00 2.O() 7.50 7.5() 7.50
2 0.50 0.50 0.50 0.50 0.50 0.50 2.00 2.00 2.00 7.50 7.50 7.50
3 0.49 0.54 0.50 0.46 0.50 0.49 1.09 2.12 1.84 7.41 7.52 7.48
4 0.49 0.59 0.51 0.46 0.50 0.49 0.78 2.09 1.7? 7.43 7.60 7.4Q
5 0.49 0.69 0.53 0.46 0.52 0.49 0.50 2.10 1.57 7.43 7.70 7.51
6 0.48 0.89 0.57 0.45 0.63 0.50 0.22 2.12 1.35 7.44 7.8() 7.54
7 0.50 0.68 0.54 0.46 0.51 0.48 0.58 1.92 1.41 7.44 7.67 7.52
8 0.50 0.90 0.59 0.45 0.63 0.50 0.21 1.83 1.13 7.44 7.80 7.57
9 0.48 1.08 0.63 0.46 0.77 0.52 0.21 1.94 1.09 7.44 7.81 7.59
10 0.50 1.09 0.65 0.46 0.78 0.52 0.20 1.66 0.90 7.45 7.81 7.62
11 0.50 1.28 0.73 0.46 0.93 0.57 0.20 1.67 0.79 7.44 7.81 7.65
12 0.55 0.67 0.62 0.40 0.49 0.46 0.39 0.74 0.50 7.64 7.79 7.74
13 0.56 0.59 0.57 0.39 0.41 0.40 0.29 0.35 0.31 7.78 7.85 7.83
14 0.52 0.54 0.53 0.36 0.37 0.36 0.22 0.26 0.24 7.81 7.91 7.88
15 0.51 1.41 0.83 0.45 1.03 0.62 0.22 1.44 0.60 7.47 7.83 7.69
16 0.51 1.55 0.93 0.45 1.14 0.69 0.22 1.25 0.46 7.49 7.84 7.73
17 0.66 0.78 0.74 0.47 0.54 0.52 0.25 0.33 0.27 7.77 7.86 7.82
18 0.58 0.62 0.60 0.40 0.42 0.41 0.20 0.23 0.21 7.81 7.90 7.86
19 0.54 1.86 1.11 0.44 1.39 0.81 0.22 0.91 0.35 7.57 7.84 7.76
20 0.57 1.33 0.97 0.46 0.97 0.70 0.23 0.83 0.35 7.60 7.84 7.77
21 0.71 1.45 1.15 0.53 1.06 0.83 0.22 0.50 0.27 7.69 7.84 7.80
22 0.78 1.07 0.95 0.54 0.77 0.67 0.20 0.32 0.23 7.75 7.87 7.83
23 0.71 0.84 0.77 0.49 0.58 0.53 0.18 0.22 0.20 7.80 7.89 7.86
24 0.59 0.63 0.60 0.40 0.42 0.41 0.17 0.21 0.1w 7.82 7.91 7.87
25 0.75 0.88 0.81 0.52 0.61 0.56 0.19 0.22 0.20 7.79 7.89 7.84
26 0.63 0.70 0.66 0.43 0.47 0.45 0.17 0.21 0.19 7.80 7.90 7.85
27 0.63 2.14 1.32 0.48 1.63 0.97 0.22 0.58 0.29 7.67 7.84 7.78
28 0.91 1.63 1.30 0.66 1.20 0.94 0.22 0.32 0.24 7.75 7.85 7.80
-------
• S • S • • • . S S •
• S S S S S • . . S • S
• S S p 5 • . S S • S I S
34 1.04 1.21 1.12 0.74 0.85 °.79 ( .20 n.?: 0.71 7.76 7.86 7.81
35 1.1(1 3.72 2.08 0.P ( 1 2. $ 1.5$ 0.23 fl4 0.30 7•84 7•74
36 1.41 3.45 2.09 1.06 2.74 1.58 0.23 0.45 .29 7•(’f) 7.84 7.74
37 1.59 3.30 2.32 1.19 ?.f ’2 1.77 0.74 0.44 ( ( 7 7 7.A 7.7?
38 1.68 5.57 2.94 1.26 4.62 2.31 fl 5 ()74 7•46 • i 7.67
39 1.41 5.94 2.79 1.04 4.95 2.18 0.73 o.7 0.37 7•4h 7 (43 7.69
40 1.73 1.R1 3.67 1.3() 6.70 2.95 0.25 1.14 7 . c 7.81 7.63
41 1.63 5.52 3.13 i. 4.59 2.67 0.?’. ( 1 4 0•4j 7.4M 1. 2 7.’,6
42 1.79 8.25 4.26 1.35 7.12 3.48 0.25 ].? fl.57 7.3 ‘•
43 2.07 7.61 4.00 1.59 6.53 3.74 0.7K 1.1? .53 7 37 7.78 7.60
44 2.02 8.76 4.86 1.54 7S’3 4.01 0.77 i s o . ,#, 7.31 7 ,7M 7.55
45 2.45 8.92 5.54 1.90 7.78 4.60 0.31 1.39 ( ‘.75 7,30 7.76 7.50
46 2.46 7,78 5.54 1.91 6.64 4. 8 ( 1. 2 1.11 (‘.1? 7.36 7.74 7.48
47 4.30 7.85 6.66 3.50 6,64 5,57 0•53 ]•05 0.M7 7.30 7.61 7.’.0
48 2.96 8.49 6.10 7.33 7.38 5.11 0.37 1.31 0. 3 7.31 7.69 7.46
49 4.46 7.69 6.68 3.64 6.55 5.58 0.56 1.0 t fl.87 7.37
50 3.61 8.60 6.80 2.86 7.43 5•75 fl•47 3.30 95 1.42
51 4.97 7.81 6.82 4.0$ 6.60 5 .7o 0.61 3.0g . 7.31 7.53 7.38
5? 5.95 9.59 8.11 4.98 8.39 7.03 (1•#3 1.5? 1.75 7.3 7.51 7.39
53 5.78 8. $ 7.45 4.7j 7.78 6.33 fl•4 , 1.35 1.6 7.31 7.44 7. 7
54 3.72 8.74 6.42 2.87 7.57 5. 0.39 1.32 ‘. 7.3 7. 7.42
55 4.98 8.56 6.70 4.00 .?7 5. 3 ( (.59 1.78 0.9? 7.30 7.44 7.40
56 3.55 7.45 5.27 2.76 6.29 4.31 0. .1 1(13 ( 1 ,7 7.35 7.52 7.46
57 3.87 7.48 5.57 3.01 6.33 4.57 0.43 ].05 0.71 7 . ? 7.49 7•’3
58 4.24 5.89 4.87 3.36 4.82 3.93 0.44 0.75 0.59 7,30 7. • ‘“
59 3.07 G.09 4.46 7.35 4.99 3.55 0.35 0.78 0.5? 7.38 7.54 7.48
6(7 3.93 4.59 4.24 3.08 3.61 3.34 0.45 0.’ 3 (1,48 7.45 7.55 7.50
61 3.89 6.96 ‘v.30 3.15 5.88 4.34 0.50 0.96 (1.67 7.39 7.63 7.50
62 5.42 6.5(1 6.09 4.47 5.37 5.03 0.68 0.82 (1.76 7.36 7.51 7.41
63 4.63 5.18 4.91 3.67 4.11 3,90 0.52 0.58 0.55 7 .4 7.55 7.5(1
64 3.07 3.56 3.27 2.32 7.68 2.48 0.34 0.38 0. 7 57 7.67 7.43
65 5.99 7.46 6.60 4.88 6.31 5, ( ’5 0.70 1.01 0.84 7.31 7.46 7.36
66 5.46 8.01 6.90 4.42 6.80 5.78 I. , 1.11 0. 1 7.30 7.42 7.37
67 5.49 7.37 6.46 ‘s.43 6.15 5.33 0.63 0.96 7.30 7.4? 7.37
6$ 5.81 6.90 6.33 4.70 5.67 5.17 ((.66 0,84 0.74 7.30 7.4? 7.37
69 4.46 7.69 6.07 3.52 (.49 5.00 0.49 1.06 (1.76 7 ,30 7.45 7.’.0
70 4.54 6.81 5.71 3.57 5.61 4.6? 0.49 0. 5 (1.66 7.31 7 45 7.40
71 5.04 6.45 5.75 5.22 6.62 0.54 (1.74 0.64 7.31 7.44 7.39
72 3.58 6.58 5.07 2.77 5.43 4.08 (1.40 0.84 0.59 7.33 7.49 7.44
73 3.50 5.98 4.83 7.69 4.81 3.8? 0.38 0.4 14 0. 2 7,34 7.50 7.44
74 4.37 5.84 5.13 3.40 4.64 4.05 0.46 0.6? (1.54 7.34 7.47 7.42
75 2.64 4.70 3.68 2.00 .72 2.87 0.31 0.55 (1.42 7.47 7.56 7.51
76 7.72 5.50 4.15 2.06 4.41 3.26 ( ‘.3? 0.64 0.46 7.37 7.54 7.48
77 2.76 5.28 4.05 2.08 4.37 3.14 (1.31 0.57 (1.43 7.37 7.54 7.48
78 3.36 5.19 4.27 2.55 4.06 3.31 0.35 0.54 0.44 7.37 7.5? 7.46
79 1.65 4.79 3.06 1.70 3.34 7.34 (1,73 0.48 0.34 7.43 7.58 7.53
80 2.06 4.36 3.21 1.53 1.37 7.45 0.76 0.46 0.35 7.41 7.57 7.51
81 3.00 4.58 3.77 2.26 3.53 7.89 0.32 (1•4(’ 0.38 7.40 7.54 7.48
82 1.28 3.56 2.45 0.97 2.72 1.84 0.21 0.39 0.29 7.45 7.60 7.54
83 1.52 3.65 2.56 1.11 2.77 1.92 0.?? 0.38 0.29 7.43 7.59 7.53
84 2.40 3.96 3.21 1.79 3.00 2.42 0.28 0.60 0.33 7.41 7.56 7.50
85 1.07 3.04 1.97 0.76 2.2(4 1.46 0.19 0.34 0.25 7.47 7.61 7.55
86 1.32 3.10 2.05 0.95 2.31 1.51 0.21 0.33 0.25 7.43 7.60 7.54
87 1.74 3.49 7.63 1.27 2.62 1.96 0.26 0.35 0.29 7.39 7.58 7.51
(38 1.18 2.10 1.51 0.85 1.54 1.09 0.19 0.26 0.22 7.49 7.67 7.55
-------
S
S
S
95
S
S
0.71
S
S
1.81
e
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1.20
.
.
S
0.49
S
S
l.?1
S
I
0.85
P
•
0.17
5
S
0.74
5
•
(1.20
0.17
I
S
7.46
7.41
I
S
7.6 1
7.60
S
S
7.54
7.51
96
0.79
0.91
0.85
0.55
0.63
0.59
0.16
0.19
0.17
7.43
7.61
7.51
97
0.71
1.04
0.83
0.49
0.73
0.58
0.16
0.18
7.45
7.63
7.52
98
0.73
1.32
0.97
0.51
0.94
0.68
0.17
0.21
0.18
0.17
7.39
7.58
7.49
99
0.68
0.79
0.73
0.47
0.54
0.5(1
7.40
7.59
7.49
100
0.67
0.83
0.73
0.46
0.56
0.50
0.15
0.18
0.19
0.17
7.41
7.60
7.50
101
0.67
0.95
0.78
0.46
0.65
0.54
0.16
7.39
7.58
7.48
102
0.54
0.77
0.68
0.37
0.53
0.47
0.15
0.18
0.16
7.37
7.56
7.66
103
0.59
0.68
0.63
0.40
0.46
0.43
0.15
0.68
7.3?
7.77
7.53
104
2.13
8.33
5.05
1.62
7.23
4.17
0.28
0.38
1.29
(1.80
7.31
7.69
7.48
105
3.09
8.58
5.88
2.44
7.41
4.91
0.47
7.5?
7.61
7.57
106
4.00
4.49
4.23
3.11
3.50
3.31
0.44
0.84
7.35
7.46
7.38
107
6.17
7.42
6.66
5.11
6.22
5.54
0.75
0.96
0.95
0.83
7.33
7.42
7.38
108
6.26
7.32
6.64
5.14
6.11
5.50
0.74
0.85
0.76
7.37
7.43
7.39
109
5.67
6.90
6.30
4.61
5.68
5.17
0.68
7.34
7.46
7.42
110
4.97
6.22
5.71
3.99
5.02
4.62
0.58
0.72
0.18
7.85
7.94
7.90
111
1.00
1.00
1.00
0.33
0.34
0.33
0.16
0.1(1
7.85
7.94
7.90
112
1.00
1.00
1.00
0.33
0.34
0.33
0.16
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 1 IN
ZONE
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 1 IN
ZONE
80. 2
6.3 Mc,/L.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. I IN
ZONE
Nfl. 3
4.5 MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 1 IN
ZONE
Nfl. 4
1.1 MG/L.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 1 IN
ZONE
NO. 5
0.6 4G/L.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
Nfl. 1 IN
ZONE
811. 6
=
4.9 MG/L.
AVERAGE
CONCEN1RA1 ION
OF
CONSTITUENT
Nfl. 1 IN
TOTAL
86?
=
2.9 Mr,/L.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
Nfl. 2 IN
lONE
8(1. 1
•
2.9 MG/L.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
Nfl. 2 IN
ZONE
Nfl. 2 =
.? NG/L.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
NO. 2 IN
ZONE
Nfl. 3 =
.7 MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITUENT
Nfl. 2 IN
ZONE
Nfl. 4
0.8 MG/I.
AVERAGE
CONCENTRATION
OF
CONSTITuENT
Nfl. 2 18
ZI:INE
80. s =
0.5 ‘c,/L.
AVERAGE
AVERAGE
CONCENTRATION
CONCENTRATION
OF
OF
CONSTITUENT
CONSTITUENT
NO. 2 18
Nfl. 2 IN’
ZONE
TOTAL
Nfl. 6 •
RAY
3.9 MG/I.
2.3 MGIL.
-------
NO. IN 7(Jt E Nfl. 1
AVERAGE
AVERAGE
AVERAGE
AVERAGE
AVERAGE
AVERAGE
AVERAGE
CUNCENTRAT ION
CONCENTRATION
CONCENTRAT ION
CLINCENTRAT iON
CONCENTRATION
CIINCENTRAT ION
CUr ’CEETRAT ION
4 IN ZONE Nfl. 1 =
4 II ” ZONE MO. 2 =
4 IN ZONE N f l. 3
4 IN ZONE Nfl. 4 =
4 IN ZONE Nfl. 5 =
4 IN ZONE N f l. 6 =
4 IF TOTAL RAY =
7.5 MG/L.
7.4 MC,/L.
7.6 NC/I.
7.R NC,/L.
7.5 M(/I.
•1.5 MG/I.
AVERAGE
AVERAGE
AVERAGE
AVERAGE
AVERAGE
AVERAGE
AVERAGE
C(JMCENT RAT ION
CUECEN1 RAT ION
CONCENTRATION
CONCENTRATION
CONCE NI RAT ION
CONCEN1 RAT ION
CI)NCENTRAT ION
OF CONSTITUENT
OF CONSTITUENT
OF CONSTITUENT
OF CONSTITUENT
(IF CONSTITUENT
OF C()f ’STITUE#T
OF CONSTITUENT
NO.
NO.
M n.
NO.
NO.
NO.
3 iN ZONE NO. 2
3 IN ZONE F’fl. 3
3 IN Z(JF’E Nfl. 4 =
3 IN ZONE NO. 5 =
3 IN ZONE Nfl. 6
3 IN TIJIAL RAY
0.4 MG/I.
U.N MG/I.
0.6 MG/I.
0•4 MG/I.
1.3 MG/I.
0.6 MG/I.
0.6 MG/I.
OF CONSTITUENT NO.
(iF CON!TITUENT NO.
OF CONSTITUENT NO.
OF CONSTITUENT Nfl.
OF CONSTITUENT Nfl.
OF CONSTITUENT NO.
(iF CONSTITUENT NO.
7.6 hC,/I.
MEAN
VOLUME
OF
lINE
NO. 1
= fl.25040t050€
10
CUFIC
HEFT.
MEAN
VOLUME
OF
ZONE
NO. 2
U.22461060NF
09
CUFIC
FEFT.
MEAN
VOLUME
OF
ZONE
NI’. 3
fl.2BOH4UVRAF
10
f,IFIC
E FT.
MEAN
VUIUMF
(IF
ZONE
En. 4
0.30035Q55?F
10
C(IPIC
REFT.
MEAN
VOLUME
(IF
ZONE
NO. S
(l.108537?IAF
10
CUBIC
FEFT.
MEAN
VOLUME
OF
ZONE
NO. 6
= O.RO4 lAA400F
OR
CUBIC
FfFT.
MEAN
VOLUMI
(IF
TIJIAL
BAY
O.970626?53F
1(1
CUBIC
FEFT.
TOTAL
SURFACE
AREA OF SAN
UIEGO MAY(T1) BALLAST
POINT = 107 )4.41 ACRRS
FM) OF filiAL ITY RUN. 600 CYCLES.
-------
PROGRAM REGAN
C FEDERAL WATER QUALITY ADMINISTRATION 10
C 20
CURVE FITTING BY LEAST SQUARES *** Y(T) A(1)+ A2*SIN(WT)+ A3*SIN(2WT)+ 30
C A4*S!N(3WT)÷ A5*COS(WT)+ A6*COS(2W1)+ A7*COS(3WT) 40
C 141= NO. OF POINTS NJ= NO. OF TERMS 50
C 60
DIMENSION Y(100), T(100), A(20), X(20), SXX (20,20), SXV(20) 70
1 READ (5,10) KO,N1,NJ,MAXIT,DEITA,PERIOD,ALAG,BLAG 80
10 FORMAT (413, 4F12.6 ) 90
READ(5,20J (T(I),Y(II,I=1,N1) 100
20 FORMAT (8F8.3 ) 110
W = 2.*3.14159 /PERIOD 120
WRITE (6,11) NI,NJ,PER1OD,W,AIAG,BLAG 130
11 FORMAT I 14H1NO. OF POINTS , 14 / 14H NO. OF TERMS , 14 / 7H PERIO 140
1D , F8.3 , 5X, 6H OMEGA , F10.4 / 5H ALAG , Fl0.4, 5H BLAG ,F1O.4) 150
WRITE (6,21) 160
21 FORMAT ( 29H0 140. TIME VALUE ) 170
WRITE (6,22) (I,T(I),Y(I),I=1,NI) 180
22 FORMAT ( 14, 2F12.3 ) 190
DO 27 I=1,NI 200
21 1(I) = TI!) + ALAG 210
C 220
ccc * * * NORMAl.. EQUATIONS 230
C 240
DO 30 J =1,NJ 250
DO 26 K=1,NJ 260
26 SXX(K,J) = 0. 270
A(J) = 0. 280
30 SXY(J) = 0. 290
NJ2 = NJ/2 + 1 300
DO 50 I = 1,NI 310
DO 49 .1 =1,NJ 320
FJ I = FLOAT(J—1) 330
FJ3 = FLOAT I .i—N.J2 ) 340
IF ( J.LE.NJ2 ) GO TO 48 350
XI .. )) = COS(FJ3*W*T(I)+ BLAG ) 360
GO TO 49 370
48 X(J) = SIN(FJ I*W*T(I)+ BLAG ) 380
IF( J.E0.1 ) X (J) = 1. 390
49 SXY(J) = SXY(J) + X(.J) * Y(I) 400
DO 45 J = 1,NJ 410
0045K = 1, NJ 420
45 SXX(K,J) = SXX(K,J) + X(K) * XI . )) 430
50 CONTINUE 440
WRITE (6,59) 450
59 FORMAT I 42H0 J SIGMA XY(J) SIGMA XX(K,J), K=1,NJ ) 460
D C 60 J = 1,NJ 470
60 WRITE (6,62) J,SXYIJ),(SXX(K,J),K=1,NJ) 480
62 FORMAT I 14, SF14.6 ) 490
C 500
CCC * * * * NORMAL EQUATION SOLUTION 510
IT = 0 530
105 IT = IT + 1 540
DEIMAX = o. 550
DC 115 K j j 560
SUM = 0. 570
239
-------
DO 110 J1,NJ 580
IF (J.EQ.K) GO TO 11.0 590
SUM = SUM — A(J)*SXX(K,J) 600
110 CONTINUE 610
SUN = (SUM+SXY(K))/SXX(K,K) 620
DEL = ABS(SUM—A(K)) 630
IF (DEI.GT.OELNAX I OELMAx DEL 640
115 A(KP = SUM 650
IF ( IT.GE.MAxIT ) GO TO 1.50 660
IF (DELMAX.GT.DELTA I GD 10 105 670
150 WRITE(6, 158) I1,DELMAX 680
158 FORMAT (12HOITERATIONS ,14,5X, 13HMAX, RESIDUAL , F12.6 ) 690
WRITE (6,160) (A(K),K=I,NJ) 700
160 FORMAT I 28HOCOEFFICIENTS A(J) J=1,PIJ / 8F14.6 ) 710
WRITE (6,168) 720
RES = 0. 730
DO 170 1 = 1,NI 740
SUM=0. 750
DO 167 J =2,NJ 760
FJ1 FLOAT I J—1 } 770
FJ3 = FLOAT C J—NJ2 ) 780
IF I J.LE.NJ2 ) GO TO 166 790
SUM = SUM + AIJ) *COS(FJ3*w.TII) + BLAG ) 800
GO 10 167 810
166 SUM SUM + AIJI *SJN(FJ1*w$T(I) + BIAG ) 820
167 CONTINUE 830
SUM - SUM + AU) 840
01FF a SUM — VU) 850
RES — RES + ABS(DIFF) 860
170 WRiTE (6,169) T(Z),YI1),SUM,DIFF 870
168 FORMAT I 46H0 TIME OBSERVED COMPUTED 01FF 1 680
169 FORMAT C 4F12.4 ) 890
WRITE (6,171.) RES 900
171 FORMAT I 6HOTOTAL , 30X, F12.,4 ) 910
IF I KD.EQ.1 ) 60 10 1 920
1943 STOP 930
END 940
240
-------
NO. OF POINTS 51
NO. OF TERMS 7
PERIOD 25.000 OMEGA 0.2513
ALAG 0.0 SLAG 0.0
NO. TIME VALUE
1 0.0 2.600
2 0.500 2.540
3 1.000 2.350
4 1.500 2.050
5 2.000 1,640
6 2.500 1.160
7 3.000 0,610
8 3.500 0.040
9 4.000 —0,530
10 4.500 —1.080
11 5.000 —1.580
12 5,500 —2.010
13 6.000 —2.340
14 6.500 —2.570
15 1.000 —2.680
16 7.500 —2.670
17 8.000 —2.550
18 8.500 —2.320
19 9.000 —1.990
20 9.500 —1.590
21 10.000 —1.140
22 10.500 —0.650
23 11.000 —0.170
24 11.500 0.290
25 12.000 0.690
26 12.500 1.010
27 13.000 1.250
28 13.500 1.370
29 14.000 1.390
30 14.500 1.300
31 15.000 1.120
32 15.500 0.860
33 16.000 0.540
34 16,500 0.200
35 17.000 —0.140
36 17.500 —0.440
• • •
• S
• S S
48 23.500 2.080
49 24.000 2.360
50 24.500 2.540
51 25.000 2.600
J SIGMA *Y(J) SIGMA XX(K,J), K=1,NJ
1 6.000006 51.000000 —0.000021 —0.000024 —0.000037 0.999934 0.999937 0.999909
2 —21.968155 —0.000021 24.999908 0.000001 —0.000009 —0.000017 0.000006 0.000019
-------
3 13.977745 —0.000024 0.000001 24.999847 —0.000007 —0.000027 —0.000018 0.000030
4 —2.039213 —0.000037 —0.000009 —0.000007 24.999847 —0.000045 —0.000054 —0.000028
5 21.818253 0.99993’. —0.000017 —0.000027 —0.000045 25.999802 0.999936 0.999915
6 46.103821 0.999937 0 ,000006 —0.000018 —0.000054 0.999936 25.999817 0.999927
7 3.233039 0.999909 0.000019 0.000030 —0.000028 0.999915 0.999927 25.999832
ITERATIONS 5 MAX. RESIDUAL 0.000000
COEFFICIENTs A J) J 1,NJ
0.067964 —0.878729 0.559115 —0.082364 0.768662 1.740088 0.025251
TIME OBSERVED COMPUTED DIFF
0.0 2.6000 2.6020 0.0020
0.5000 2.5400 2.5381 —0.0019
1.0000 2.3500 2.3502 0.0002
1.5000 2.0500 2.0466 —0.0034
2.0000 1.6400 1.6421 0.0021
2.5000 1.1600 1.1567 —0.0033
3.0000 0.6100 0.6145 0.0045
3.5000 0.0400 0.0422 0.0022
• • • S
• . • S
• S • S
11.5000 0.2900 0.2856 0.0044
12.0000 0.6900 0.6878 —0.0022
12.5000 1.0100 1.0141 0.0041
13.0000 1.2500 1.2468 —0.0032
13.5000 1.3700 1.3742 0.0042
14.0000 1.3900 1.3917 0.0017
14.5000 1.3000 1.3028 0.0028
15.0000 1.1200 1.1182 —0.0018
15.5000 0.8600 0.8560 —0.0040
16.0000 0.5400 0.5400 0.0000
16.5000 0.2000 0.1984 —0.0016
17.0000 —0.1400 —0.1386 0.0014
17.5000 —0.4400 —0.4409 —0.0009
18.0000 —0.6800 —0.6810 —0.0010
18.5000 —0.8400 —0.8358 0.0042
19.0000 —0.8900 —0.8889 0.0011
19.5000 —0.8300 —0.8316 —0.0016
20.0000 —0.6600 —0.6640 —0.0040
20.5000 —0.4000 —0.3946 0.0054
21.0000 —0.0400 —0.0398 0.0002
21.5000 0.3800 0.3773 —0.0027
22.0000 0,8300 0.8284 —0.0016
22.5000 1.2800 1.2828 0.0028
23.0000 1.7100 1.7089 —0.0011
23.5000 2.0800 2.0771 —0.0029
24.0000 2.3600 2.3613 0.0013
24.5000 2.5400 2.5409 0.0009
25.0000 2.6000 2.6020 0.0020
TOTAL 0.1116
-------
PROGRAM DATAP
C FEDERAL WATER QUALITY ADMINISTRATION 10
C DATA PREPARATION PROGRAM 30
C PROGRAM DATAP 40
C 50
C 60
DIMENSION QIN( 840),ASUR( 840),Y( 840),QINEV( 840),QINPR( 840), 70
* NCHAN( 840,5),ALPHA(40) 80
C 90
C***** READ INPUT DATA 100
C 110
READ 5,1OO) (ALPHA(I),I 1,40) 120
100 FORMAT(20A4) 130
C 140
READ(5,102) NJ,MONTI-4 150
102 FORMAT(315) 160
C 170
DO 108 J=1,NJ 180
READ(5,233)JJ,Y(J),ASUR(J),QIN(J),CNCHANtJ,K),K=1,5) 190
QIN(J) = 0.0 200
IF(JJ — J)104,108,104 210
104 WRITE(6,106) JJ,J 220
106 FORMAT( 33 1 -40 DATA CARD OUT OF SEOUENCE JJ = 15,411 J= 15) 230
CALL EXIT 240
108 CONTINUE 250
C 260
WRITE(6,110) (AIPHA(I ),I=1,40) 270
110 FDRMAT(1H1////1H 20A4,1OX,37H FEDERAL WATER QUALITY ADMINISTRATION 280
*/ IH 20A4,1OX,25H DATA PREPARATION PROGRAM////) 290,
READ(5,17O) EVAP,PRECIP 300
170 FORMAT(2F10.O) 310
C 320
WRITE(6,172) MONTH,EVAP,PRECIP 330
172 FORMAT(9HOMONTH = 13/I 340
* 15H EVAPORATION = F8.2,7H INCHES/I 350
* 1714 PRECIPITATION = F8.2,714 INCHES/I) 360
C 370
C***** DETERMINE NUMBER OF DAYS IN MONTH BEING CONSIDERED 380
C 390
IF(MONTH.NE.2)GO TO 178 400
DAYS = 28. 410
GO TO 184 420
178 IF(MONTH.EQ.4.OR.MONTH.EQ.6.OR.MONTH.EO.9sOR.M0NN.E0.1 1)G0 TO 180 430
DAYS = 31. 440
GO TO 184 450
180 DAYS = 30. 460
184 CONTINUE 470
C 480
C***** CONVERT EVAP AND PRECIP TO FEET PER SECOND 490
C 500
CONYRT = (1./t12.* 3600. * 24. * DAYS)) 510
EVAP = EVAP * CONVRT 520
PRECIP = PRECIP * CONVRT 530
C 540
C***** COMPUTE EVAP AND PRECIP AT EACH JUNCTION 550
C 560
DO 188 j=1,NJ 570
QINEV(J) = ASUR(J) * EVAP 580
243
-------
OINPR (J) ASUR(J) * PRECIP 590
188 CONTINUE 600
C 610
C READ HYDRAULIC INPUTS AT SPECIFIED JUNCTIONS 620
C 630
REAO(5,102) NJREAO 640
DO 222 I=1,NJREAD 650
READ(5,220) J,QIN(J) 660
220 FORMAT(15,F10.O) 670
222 CONTINUE 680
C 690
C***** PRINT SEPARATE HYDRAULIC INPUTS 700
C 710
WRITE(6,223)(J,QINEV(.J) ,OINPR (J) ,QIN(J),Ja1,NJ) 720
223 FORMAT(IH1//// 730
* 5014 JUNCTION EVAPORATION PRECIPITATION DIN! 740
* 51H CFS) (CFS) (CFS)// 750
* (I7,f17.1,F17.1,F1o.1)) 760
C 770
WRITE( 8,224HJ,QIN(J),J=1,NJ) 780
224 FORMAT(I5,FjO.1) 790
C 800
C***** COMPUTE NET WITHDRAWAL OR DISCHARGE AT AT EACH JUNCTION 810
C 820
DO 228 Jal,NJ 830
OIN(J) a OIN(J) + QINEV(J) — QINPR (J) 840
228 CONTINUE 850
C 860
C****S LIST PREPARED INPUT DECK 870
C 880
WRITE(6,229) 890
229 FORMAT(1H1//// 900
* 4914 ***** LISTING OF INPUT DECK PREPARED IN THIS RUN!!! 910
* 6614 JUNC. HEAD SURFACE INPUT— CHANNELS ENTERING 920
*JIJNC./ 930
* 3814 AREA OUTPUT! 940
* 31H (F l) (SQ.FT) (CFS)//) 950
C 960
DO 232 J=1,p4J 970
WRITE (6,230)J,Y (JJ,ASUR(Jp,QIN(J), (NCHAN(J,K),K=1,5) 980
230 FORMAT(15,FjO.4,F14.1,F10.j, 18,4 15) 990
232 CONTINUE 1000
C 1010
C***** PUNCH INPUT DECK FOR HYDRAULIC RUN 1020
C 1030
00 234 Jal,NJ 1040
1050
233 FORMAT(]5,F10.4,F1o.1,f1o.1,5 15) 1060
234 CONTINUE 1070
C 1080
C***** COMPUTE TOTAL EVAP AND PRECIP FROM ENTIRE SYSTEM 1090
C 1100
QEYT a 0.0 1110
OPRT OeO 1120
QNET a 0.0 1130
DO 302 Jal,NJ 1140
QEVT a OEVT + QINEV(J) 1150
QPRT a OPRT + QINPR (J) 1160
OMIT • ONET + OIN(J) 1170
302 CONTINUE 1180
244
-------
WRITE(6,322) QNET,QEVT,QPRT it o
322 FORMAT(27HONET OUTFLOW FROM SYSTEM = F1O.1,6H CFS/ 1200
* 33H TOTAL EVAPORATION FROM SYSTEM = F1O.1,4H CFS/ 1210
* 33ff TOTAL PRECIPiTATION ON SYSTEM = FIO.l,4H CFS////) 1220
C 1230
WRITE(6,324) 1240
324 FORMAT( 11ff END OF RUN) 1250
C 1260
CALL EXIT 1270
END 1280
245
-------
PREPARE INPUT DECK FOR HYDRAULIC RUN FOR SAN DIEGO BAY FEDERAL WATER QUALITY ADMINISTRATION
MEAN SEPTEMBER CONDITIONS DATA PREPARATION PROGRAM
Mth ITH. 9
EVAPORATION • 4,80 INCHES
PRECIPITATION • 0.0 INCHES
JUNCTION EVAPORATION PRECIPITATION OIN
(CFS) (CFS) (CFS}
1 0.8 0.0 0.0
2 0.5 0.0 0.0
3 1.6 0.0 0.0
4 1.8 0.0 0.0
5 1.2 0.0 0.0
6 0.9 0.0 0.0
7 0.5 0.0 0.0
8 0.6 0.0 0.0
9 0.9 0.0 0.0
10 0.5 0.0 0.0
11 1.0 0.0 0.0
•
• • •
• • •
46 0.7 0.0 0.0
47 0.6 0.0 0.0
48 0.9 0.0 0.0
49 0.8 0.0 0.0
50 0.9 0.0 0.0
51 0.8 0.0 0.0
52 0.7 0.0 0.0
53 0.6 0.0 0.0
54 0.6 0.0 0.0
-------
55 0.7 0.0 0.0
56 0.4 0.0 0.0
57 0.5 0.0 0.0
58 0.3 0.0 0.0
59 0.6 0.0 0.0
60 0.4 0.0 0.0
61 0.4 0.0 0.0
62 0.4 0.0 0.0
63 0.5 0.0 0.0
64 0.3 0.0 0.0
65 0.8 0.0 0.0
66 0.7 0.0 0.0
67 0.8 0.0 0.0
68 1.0 0.0 0.0
69 0.8 0.0 0.0
70 1.0 0.0 0.0
71 0.7 0.0 0.0
72 0.9 0.0 0.0
73 1.0 0.0 0.0
74 0.8 0.0 0.0
75 1.2 0.0 0.0
76 0.9 0.0 0.0
77 0.9 0.0 0.0
78 0.4 0.0 0.0
79 1.3 0.0 0.0
80 0.9 0.0 0.0
81 0.5 0.0 0.0
82 1.2 0.0 0.0
83 0.9 0.0 0.0
84 0.6 0.0 0.0
85 1.2 0.0 0.0
86 0.9 0.0 0.0
87 0.5 0.0 0.0
88 0.7 0.0 0.0
89 1.1 0.0 0.0
90 1.0 0.0 0.0
91 1.1 0.0 0.0
92 0.8 0.0 0.0
93 0.8 0.0 646.0
94 1.0 0.0 0.0
95 0.9 0.0 0.0
96 1.0 0.0 —646.0
97 1.0 0.0 0.0
98 1.0 0.0 0.0
99 0.4 0.0 2.6
100 0.6 0.0 0.0
101 0.6 0.0 0.0
102 0.1 0.0 0.0
103 0.2 0.0 0.0
104 0.2 0.0 0.0
105 0.2 0.0 0.0
106 0.2 0.0 0.0
107 0.4 0.0 0.0
108 0.4 0.0 0.0
109 0.4 0.0 0.0
110 0.5 0.0 0.0
111 0.5 0.0 0.0
112 0.5 0.0 0.0
-------
***** LISTING OF INPUT DECK PREPARED IN ThIS RUN
SURFACE
AREA
ISO. FT
INPUT—
OUTPUT
(C PS)
JUNC. HEAD
PT)
CHANNELS ENTERING JUP4C.
1 2 0 0 0
2 0 0 0 0
1 3 0 0 0
3 4 0 0 0
4 5 6 0 0
5 8 9 0 0
6 7 0 0 0
7 9 10 0 0
8 11 0 0 0
10 13 14 0 0
11 12 13 0 0
2
2.6020
3125000.0
0.5
3
2.6020
10500000.0
1.6
4
2.6020
11434545.0
1.8
5
2.6362
7827273.0
1.2
6
2.6578
5781818.0
0.9
7
2.6489
3436363.0
0.5
8
2.6620
3627273.0
0.6
9
2.6754
5645455.0
0.9
10
2.6842
3163636.0
0.5
11
2.6934
6763636.0
1.0
.
I
I
I
I
S
I
I
I
I
I
I
93
3.0133
5427273.0
646.8
94
3.0123
6790909.0
1.0
95
3.0084
5972727.0
0.9
96
3.0218
6572727.0
—6450
97
3.0171
6272727.0
1.0
98
3.0146
6245455.0
1.0
99
3.0218
2645455.0
3.0
100
3.0194
4118182.0
0.6
101
3.0173
3900000.0
0.6
102
3.0257
545455.0
0.1
103
3.0329
1309091.0
0.2
104
2.8995
1281818.0
0.2
105
2.9110
1390909.0
0.2
106
2.9167
1390909.0
0.2
107
2.9330
2727273.0
0.4
108
2.9413
2563636.0
0.4
109
2.9485
2836364.0
0.4
110
2.9527
2945455.0
0.5
111
—3.0000
3125000.0
0.5
112
—3.0000
3125000.0
0.5
I
I
I
140
137
138
145
143
144
147
148
149
152
153
154
156
158
159
160
162
164
170
170
*
I
I
I
i
I
S
I
141
141
139
147
145
146
150
150
151
153
0
155
157
0
160
161
163
165
0
0
I
I
S
0
142
142
0
146
149
152
151
0
0
0
156
0
0
0
162
164
0
0
0
I
S
I
0
143
144
0
148
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
S
I
I
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
NET OUTFLOW FROM SYSTEM
TOTAL EVAPORATION FROM SYSTEM
TOTAL PRECIPITATION ON SYSTEM
80.3 CFS
77.7 CFS
0.0 CFS
tND OF RUN
------- |