DOCUMENTATION REPORT FWQA DYNAMIC ESTUARY MODEL cc ------- 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 ------- 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 ------- 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 Ii ------- 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 iii ------- 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 iv ------- 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 V ------- 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 vi ------- 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 ------- 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 v ii I ------- 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 i x ------- 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 x ------- 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 ------- 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: 2 ------- (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. 3 ------- 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 ------- 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. 5 ------- (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 6 ------- 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 ------- FIGURE 1. SAN FRANCISCO BAY AND DELTA 6 S S O4 I. d S 5. ! LS . S S S S 8 ------- 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 ------- 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 ------- 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 ------- (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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- ‘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 ------- 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 ------- • 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 3 6 I I 9 ‘2 I I P 1 1518 21242730 -4 1 - LU LU U- IL l 4 U) 4. 2- C I®.. • S S . S S . •—. 4. 2 -4 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 2-.® I — Ui Ui L i i U) . •G S • E I I I I I I I I I I 03 6 9 2 151821 242730 0 —2 —4 4 2 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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. 114 ------- 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 ------- 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 116 ------- 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. 117 ------- 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 ------- 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 ------- 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 ------- 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 ------- (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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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 ------- 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.?’. 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(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 • 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 ------- |