U.S. ENVIRONMENTAL PROTECTION AGENCY
       Annapolis Field Office
      Annapolis Science Center
     Annapolis, Maryland  21401
         TECHNICAL PAPERS
            Volume 21

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                            Table of Contents


                               Volume 21


11           A Steady State Segmented Estuary Model
12          Simulation of Chloride Concentrations in the
            Potomac Estuary - March 1968
13          Optimal  Release Sequences for Water Quality
            Control  in Multiple-Reservoir Systems - 1968

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                            PUBLICATIONS

                U.S.  ENVIRONMENTAL PROTECTION AGENCY
                             REGION III
                       ANNAPOLIS FIELD OFFICE*


                              VOLUME 1
                          Technical  Reports


 5         A Technical  Assessment of Current Water Quality
           Conditions and Factors Affecting Water Quality in
           the Upper Potomac Estuary

 6         Sanitary Bacteriology of  the Upper Potomac Estuary

 7         The Potomac Estuary Mathematical Model

 9         Nutrients in the Potomac  River Basin

11         Optimal  Release Sequences for Water Quality Control
           in Multiple Reservoir Systems


                              VOLUME 2
                          Technical  Reports


13         Mine Drainage in the North Branch Potomac River Basin

15         Nutrients in the Upper Potomac River Basin

17         Upper Potomac River Basin Water Quality Assessment


                              VOLUME  3
                          Technical  Reports


19         Potomac-Piscataway Dye Release and Wastewater
           Assimilation Studies

21         LNEPLT

23         XYPLOT

25         PLOT3D


     * Formerly CB-SRBP, U.S. Department of Health, Education,
       and Welfare; CFS-FWPCA, and CTSL-FWQA,  Middle Atlantic
       Region, U.S. Department of the Interior

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                             VOLUME 3   (continued)

                         Technical Reports


27         Water Quality and Wastewater Loadings - Upper Potomac
           Estuary during 1969


                             VOLUME 4
                         Technical Reports


29         Step Backward Regression

31         Relative Contributions of Nutrients to the Potomac
           River Basin from Various Sources

33         Mathematical Model Studies of Water Quality in the
           Potomac Estuary

35         Water Resource - Water Supply Study of the Potomac
           Estuary

                             VOLUME 5
                         Technical Reports


37         Nutrient Transport and Dissolved Oxygen Budget
           Studies in the Potomac Estuary

39         Preliminary Analyses of the Wastewater and Assimilation
           Capacities of the Anacostia Tidal River System

41         Current Water Quality Conditions and Investigations
           in the Upper Potomac River Tidal System

43         Physical Data of the Potomac River Tidal System
           Including Mathematical Model Segmentation

45         Nutrient Management in the Potomac Estuary


                             VOLUME 6

                         Technical Reports


47         Chesapeake Bay Nutrient Input Study

49         Heavy Metals Analyses of  Bottom  Sediment in the
           Potomac River Estuary

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                                  VOLUME  6  (continued)

                              Technical  Reports

     51          A System of Mathematical Models for Water Quality
                Management

     52         Numerical Method for Groundwater Hydraulics

     53         Upper Potomac Estuary Eutrophication Control
                Requirements

     54         AUT0-QUAL Modelling System

Supplement      AUT0-QUAL Modelling System:  Modification for
   to 54        Non-Point Source Loadings

                                  VOLUME  7
                              Technical  Reports

     55         Water Quality Conditions in the Chesapeake Bay System

     56         Nutrient Enrichment and Control Requirements in the
                Upper Chesapeake Bay

     57         The Potomac River Estuary in the Washington
                Metropolitan Area - A History of its Water Quality
                Problems and their Solution

                                  VOLUME  8
                              Technical  Reports

     58         Application of AUT0-QUAL Modelling System to the
                Patuxent River Basin

     59         Distribution of Metals in Baltimore Harbor Sediments

     60         Summary and Conclusions  - Nutrient Transport and
                Accountability in the Lower Susquehanna River Basin

                                  VOLUME  9

                                 Data Reports

                Water Quality Survey, James River and Selected
                Tributaries - October 1969

                Water Quality Survey in  the North Branch Potomac River
                between Cumberland and Luke, Maryland - August 1967

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                            VOLUME 9  (continued)

                           Data Reports


           Investigation of Water Quality in Chesapeake Bay and
           Tributaries at Aberdeen Proving Ground, Department
           of the Army, Aberdeen, Maryland - October-December 1967

           Biological Survey of the Upper Potomac River and
           Selected Tributaries - 1966-1968

           Water Quality Survey of the Eastern Shore Chesapeake
           Bay, Wicomico River, Pocomoke River, Nanticoke River,
           Marshall Creek, Bunting Branch, and Chincoteague Bay -
           Summer 1967

           Head of Bay Study - Water Quality Survey of Northeast
           River, Elk River, C & D Canal, Bohemia River, Sassafras
           River and Upper Chesapeake Bay - Summer 1968 - Head ot
           Bay Tributaries

           Water Quality Survey of the Potomac Estuary - 1967

           Water Quality Survey of the Potomac Estuary - 1968

           Wastewater Treatment Plant Nutrient Survey - 1966-1967

           Cooperative Bacteriological Study - Upper Chesapeake Bay
           Dredging Spoil Disposal - Cruise Report No. 11

                            VOLUME 10
                           Data Reports

 9         Water Quality Survey of the Potomac Estuary - 1965-1966

10         Water Quality Survey of the Annapolis  Metro Area - 1967

11         Nutrient  Data on Sediment Samples of the Potomac Estuary
           1966-1968

12         1969  Head  of the Bay Tributaries

13         Water Quality Survey of the Chesapeake Bay in the
           Vicinity  of Sandy Point - 1968

14         Water Quality Survey of the Chesapeake Bay in the
           Vicinity  of Sandy Point - 1969

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                             VOLUME 10(continued)

                           Data Reports

15         Water Quality Survey of the Patuxent River -  1967

16         Water Quality Survey of the Patuxent River -  1968

17         Water Quality Survey of the Patuxent River -  1969

18         Water Quality of the Potomac Estuary Transects,
           Intensive and Southeast Water Laboratory Cooperative
           Study - 1969

19         Water Quality Survey of the Potomac Estuary Phosphate
           Tracer Study - 1969

                             VOLUME 11
                            Data Reports

20         Water Quality of the Potomac Estuary Transport Study
           1969-1970

21         Water Quality Survey of the Piscataway Creek Watershed
           1968-1970

22         Water Quality Survey of the Chesapeake Bay in the
           Vicinity of Sandy Point - 1970

23         Water Quality Survey of the Head of the Chesapeake Bay
           Maryland Tributaries - 1970-1971

24         Water Quality Survey of the Upper Chesapeake Bay
           1969-1971

25         Water Quality of the Potomac Estuary Consolidated
           Survey - 1970

26         Water Quality of the Potomac Estuary Dissolved Oxygen
           Budget Studies - 1970

27         Potomac Estuary Wastewater Treatment Plants Survey
           1970

28         Water Quality Survey of the Potomac Estuary Embayments
           and Transects - 1970

29         Water Quality of the Upper Potomac Estuary Enforcement
           Survey - 1970

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   30


   31


   32
   33
   34
Appendix
  to 1
Appendix
  to 2
    3


    4
                  VOLUME 11  (continued)
                 Data Reports

Hater Quality of the Potomac Estuary - Gilbert Swamp
and Allen's Fresh and Gunston Cove - 1970

Survey Results of the Chesapeake Bay Input Study -
1969-1970

Upper Chesapeake Bay Water Quality Studies - Bush River,
Spesutie Narrows and Swan Creek, C & D Canal, Chester
River, Severn River, Gunpowder, Middle and Bird Rivers -
1968-1971

Special Water Quality Surveys of the Potomac River Basin
Anacostia Estuary, Wicomico .River, St. Clement and
Breton Bays, Occoquan Bay - 1970-1971

Water Quality Survey of the Patuxent River - 1970

                  VOLUME 12

               Working Documents

Biological Survey of the Susquehanna River and its
Tributaries between Danville, Pennsylvania and
Conowingo, Maryland

Tabulation of Bottom Organisms Observed at Sampling
Stations during the Biological Survey between Danville,
Pennsylvania and Conowingo, Maryland - November 1966

Biological Survey of the Susquehanna River and its
Tributaries between Cooperstown, New York and
Northumberland, Pennsylvnaia - January 1967

Tabulation of Bottom Organisms Observed at Sampling
Stations during the Biological Survey between Cooperstown,
New York and Northumberland, Pennsylvania - November 1966

                  VOLUME 13
               Working Documents

Water Quality and Pollution Control Study, Mine Drainage
Chesapeake Bay-Delaware River Basins - July 1967

Biological Survey of Rock Creek (from Rockville, Maryland
to the  Potomac River)  October 1966

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                             VOLUME   13   (continued)

                          Working  Documents

 5         Summary of Water Quality  and  Waste  Outfalls,  Rock  Creek
           in Montgomery County, Maryland and  the  District of
           Columbia - December 1966

 6         Water Pollution Survey  -  Back River 1965  -  February  1967

 7         Efficiency Study of the District  of Columbia  Water
           Pollution Control  Plant - February  1967

                             VOLUME   14

                          Working  Documents

 8         Water Quality and Pollution Control  Study - Susquehanna
           River Basin from Northumberland to  West Pittson
           (Including the Lackawanna River Basin)  March 1967

 9         Water Quality and Pollution Control  Study,  Juniata
           River Basin - March 1967

10         Water Quality and Pollution Control  Study,  Rappahannock
           River Basin - March 1967

11         Water Quality and Pollution Control  Study,  Susquehanna
           River Basin from Lake Otsego, New York, to  Lake Lackawanna
           River Confluence, Pennsylvania -  April  1967

                             VOLUME  15
                          Working  Documents

12         Water Quality and Pollution Control  Study,  York River
           Basin - April 1967

13         Water Quality and Pollution Control  Study,  West Branch,
           Susquehanna River Basin - April 1967

14         Water Quality and Pollution Control  Study,  James River
           Basin - June 1967 .

15         Water Quality and Pollution Control  Study,  Patuxent  River
           Basin - May 1967

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                             VOLUME 16

                          Working Documents

16         Water Quality and Pollution Control  Study,  Susquehanna
           River Basin from Northumberland, Pennsylvania,  to
           Havre de Grace, Maryland - July 1967

17         Water Quality and Pollution Control  Study,  Potomac
           River Basin - June 1967

18         Immediate Water Pollution Control  Needs, Central  Western
           Shore of Chesapeake Bay Area (Magothy, Severn,  South,  and
           West River Drainage Areas)  July 1967

19         Immediate Water Pollution Control  Needs, Northwest
           Chesapeake Bay Area (Patapsco to Susquehanna Drainage
           Basins in Maryland) August 1967

20         Immediate Water Pollution Control  Needs - The Eastern
           Shore of Delaware, Maryland and Virginia -  September 1967

                             VOLUME 17
                           Working Documents

21         Biological Surveys of the Upper James River Basin
           Covington, Clifton Forge, Big Island, Lynchburg, and
           Piney River Areas - January 1968

22         Biological Survey of Antietam Creek and some of its
           Tributaries from Waynesboro, Pennsylvania to Antietam,
           Maryland - Potomac River Basin - February 1968

23         Biological Survey of the Monocacy River and Tributaries
           from Gettysburg, Pennsylvania, to Maryland Rt. 28 Bridge
           Potomac River Basin - January 1968

24         Water Quality Survey of Chesapeake Bay in the Vicinity of
           Annapolis, Maryland - Summer 1967

25         Mine Drainage Pollution of the North Branch of Potomac
           River - Interim Report - August 1968

26         Water Quality Survey in the Shenandoah River of the
           Potomac River Basin - June 1967

27         Water Quality Survey in the James and Maury Rivers
           Glasgow,  Virginia - September 1967

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                             VOLUME  17  (continued)

                           Working Documents

28         Selected Biological  Surveys in the James River Basin,
           Gillie Creek in the  Richmond Area, Appomattox River
           in the Petersburg Area, Bailey Creek from Fort Lee
           to Hopewell  - April  1968

                             VOLUME  18
                           Working Documents

29         Biological  Survey of the Upper and Middle Patuxent
           River and some of its Tributaries - from Maryland
           Route 97 Bridge near Roxbury Mills to the Maryland
           Route 4 Bridge near Wayson's Corner, Maryland -
           Chesapeake Drainage Basin - June 1968

30         Rock Creek Watershed - A Water Quality Study Report
           March 1969

31         The Patuxent River - Water Quality Management -
           Technical Evaluation - September 1969

                             VOLUME 19
                          Working Documents

           Tabulation, Community and Source Facility 'Water Data
           Maryland Portion, Chesapeake Drainage Area - October 1964

           Waste Disposal Practices at Federal Installations
           Patuxent River Basin - October 1964

           Waste Disposal Practices at Federal Installations
           Potomac River Basin below Washington, D.C.- November 1964

           Waste Disposal Practices at Federal Installations
           Chesapeake Bay Area of Maryland Excluding Potomac
           and Patuxent River Basins - January 1965

           The Potomac Estuary - Statistics and Projections -
           February 1968

           Patuxent River - Cross Sections and Mass Travel
           Velocities - July 1968

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                            VOLUME  19 (continued)

                         Working Documents

          Wastewater Inventory - Potomac River Basin -
          December 1968

          Wastewater Inventory - Upper Potomac River Basin -
          October 1968

                            VOLUME 20
                         Technical Papers

 1         A Digital Technique for Calculating and Plotting
          Dissolved Oxygen Deficits

 2         A River-Mile  Indexing System for Computer Application
          in  Storing and Retrieving Data      (unavailable)

 3         Oxygen  Relationships in Streams, Methodology to be
          Applied when  Determining the Capacity of a Stream to
          Assimilate Organic Wastes - October 1964

 4         Estimating Diffusion Characteristics of Tidal Waters -
          May 1965

 5         Use of  Rhodamine B Dye as a Tracer in Streams of the
          Susquehanna River Basin - April 1965

 6         An  In-Situ Benthic Respirometer - December 1965

 7         A Study of Tidal Dispersion in the Potomac River
          February  1966

 8         A Mathematical Model for the Potomac River - what it
          has done  and  what it can do - December 1966

 9         A Discussion  and Tabulation of Diffusion Coefficients
          for Tidal Waters Computed as a Function of Velocity
          February  1967

10         Evaluation of Coliform  Contribution by Pleasure Boats
          July 1966

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                            VOLUME  21

                         Technical Papers

11         A Steady State Segmented Estuary Model

12        Simulation of Chloride Concentrations in the
          Potomac Estuary - March 1968

13        Optimal Release Sequences for Water Quality
          Control in Multiple-Reservoir Systems - 1968

                            VOLUME  22
                         Technical  Papers

          Summary Report - Pollution of Back River - January 1964

          Summary of Water Quality - Potomac River Basin in
          Maryland - October 1965

          The Role of Mathematical  Models in the Potomac River
          Basin Water Quality Management Program - December 1967

          Use of Mathematical Models as Aids to Decision Making
          in Water Quality Control  - February 1968

          Piscataway Creek Watershed - A Water Quality Study
          Report - August 1968

                            VOLUME  23
                        Ocean Dumping Surveys

          Environmental Survey of an Interim Ocean Dumpsite,
          Middle Atlantic Bight - September 1973

          Environmental Survey of Two Interim  Dumpsites,
          Middle Atlantic Bight - January 1974

          Environmental Survey of Two Interim Dumpsites
          Middle Atlantic Bight - Supplemental Report -
          October 1974

          Effects of Ocean Disposal Activities on Mid-
          continental Shelf Environment off Delaware
          and Maryland - January 1975

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                            VOLUME 24

                           1976 Annual
               Current Nutrient Assessment - Upper Potomac Estuary
               Current Assessment Paper No.  1

               Evaluation of Western Branch Wastewater Treatment
               Plant Expansion - Phases I and  II

               Situation Report - Potomac River

               Sediment Studies in Back River  Estuary, Baltimore,
               Maryland

Technical      Distribution of Metals in Elizabeth River Sediments
Report 61

Technical      A Water Quality Modelling Study of the Delaware
Report 62      Estuary

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                         TABLL 0^ CONTENTS

                                                             Page

      ACKNOWLEDGMENTS

  I.  INTRODUCTION .............. 	     1-1

 II.  GENERAL APPROACH TO THE PROBLLM" .	    II - 1

III.  DETAILED DERIVATION	   Ill - 1

 IV.  MATHEMATICAL TECHNIQUE EMPLOYED IN THE
      MODEL FOR MATRIX III VERSION ............    IV - 1

  V.  PREPARATION OF THE COMPUTER PROGRAM  .......     V - 1

 VI.  INPUT DATA PREPARATION AND PROGRAM CASE
      CONTROL	    VI - 1

VII.  BIBLIOGRAPHY ...........  n .......   VII - 1

      APPENDIX   I - FLO1,-/ DIAGRAMS

      APPENDIX  II - IBM 3oO FORTRAN PROGRAM

      APPENDIX III - SAMPLE INPUTS

      APPENDIX  IV - TYPICAL PROGRAM CASE SOLUTIONS

          A.  Sample Input and Output Data for Case 1 with
              Control IMAT=1, INDEX (l)=l.  Output aA"1.

          B.  Sample Input and Output Data for Case 2 with
              Control IHAT=1, INDEX (2)=1.  Output  LctA-1.

          C.  Sample Input and Output Data for Case 3 with
              Control IMAT=1, INDEX (l) and INDEX (2).  Both =
              1.   Outraut aA~l and LaA~l.

          D.  Sample Input and Output Data for Case 1| with
              Control II-1AT=2, INDEX (3)=1.  Output aB"1.

          E.  Sample Input and Output Data for Case 5 with
              Control IMAT=2, INDEX (10=1.  Output FaB"1.

          F.  Sample Input and Output Data, for Case 6 with
              Control IMAT=2, INDEX (3) and INDEX
              Output aB~l and

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                   TABLE OF CONTENTS (Continued)

          G.  Sample Input and Output Data for Case 7 with
              Control IMAT=3, INDEX (5)=1.  Output air1 A"1.

          H.  Sample Input and Output Data for Case 8 with
              Control IMAT=3, INDEX (6)=1.  Output VD times
              aB-l A-l.

          I.  Sample Input and Output Data for Case 9 with
              Control IMAT=3, INDEX (?)=!.  Output L (ultimate
              BOD Vector) times Output Matrix in II. above.

          J.  Sample Input and Output Data for Case 10 with
              Control IMAT=3, INDEX (8)=1.  Output = Dissolved
              Oxygen at Saturation plus output from E. above
              minus Output from I. above.

          K.  Sample Input and Output Data for Case 11 with
              Control IMAT=3, INDEX (l) through INDEX (8)=1.
              All cases above, i.e., A to  J.
                          LIST OF FIGURES

Figure

  1       Estuary Segments

  2       Advection Into and Out of Segment K

  3       Program Deck Structure

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                        ACKNOWLEDGMENTS







        Special appreciation and acknowledgment are expressed to




Mr, Emanuel Mehr, Research Scientist, New York University, for




allowing us to employ his tridiagonal matrix inversion routine.




This routine is exceedingly fast and allows rapid inversion of




the tridiagonal matrix utilized in the model.  His guidance and




encouragement was a great contribution during the course of




certain phases of this work.




        Grateful acknowledgment is made to Mr. Richard L. O'Connell




of the Central Pacific River Basins Comprehensive Project, FWPCA,




for the assistance he gave in understanding the model and setting




up the program while he was Director of the Chesapeake Field Sta-




tion; to Mr, John M. Jeglic of the Re-entry Systems Department of




General Electric for the many programming ideas which were taken




directly from his time-dependent version of the model; and to Dr.




Robert Thomann of the Delaware Estuary Comprehensive Study Project,




both for the basic trieory on which the program is based and for




his detailed, patient explanations of ito

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                                                          I - 1






I.  INTRODUCTION




        The "oxygen sap" equation developed in 1925 "by Streeter




and Phelps1 has found widespread use in the analysis of a partic-




ular type of stream pollution problems.  This mathematical model




may be applied where the pollutant of concern is biologically




degradable organic material which brings about a depression of




the natural dissolved oxygen (DO) content of a stream.




        The "oxygen sag" formula, however, is not applicable to




tidal bodies of water, primarily because of the over-riding impor-




tance of turbulent diffusion in estuaries which is not normally




taken into consideration in streams.  In fresh water streams "plug




flow," in effect, is assumed, and this is not an unreasonable




assumption in most cases.  Although longitudinal diffusion does in




fact occur in streams due to horizontal and vertical velocity




gradients, the longitudinal exchange which this brings about




involves similar material; viz., the material that is "diffused"




upstream is very nearly the same with respect to age, concentra-




tion, etc., as that which is "diffused" downstream.  The net result




is usually negligible in the analysis of stream pollution problems.




Furthermore, advection, or transport downstream by the stream,




produces a transfer of waterborne material which greatly exceeds




the transfer brought about by diffusion.  In estuaries, however,




because of their relatively large cross-section and small net flow




downstream, the advective transport is often quite small compared




to the transfer of materials by turbulent diffusion.  For this




reason, the latter effect must be considered.

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                                                          1-2







        In I960, 35 years after the development of the "oxygen




sag" formula for streams, O'Connor2 devised a similar mathematical




model for estuaries which added to Streeter and Phelp's formula a




term to account for longitudinal diffusion.  As witu the original




stream sag formula, the O'Connor model is given as a differential




equation which may be integrated to give a solution for the dis-




solved oxygen as a continuous function of distance along the




longitudinal axis of the tidal estuary.




        In 1963 Thomarm3 developed a computational procedure based




upon the principles of systems analysis which incorporated tne




terms of the O'Connor model for estua,ries.  This method of compu-




tation employs an incremental or segmented approach where average




conditions in a finite number of connected segments are determined




rather than a continuous function solution.  The degree of resolu-




tion possible in the solution is directly related to the number




of segments chosen.  This approach simplifies the mathematics in-




volved and allows much greater flexibility in its use.  The models




previously cited apply to tne one dimensional steady state case;




whereas, with the segmented approach, a second or third dimension




may be added, and the time dependent situation may also be investi-




gated.  Also, any pollutant for which the relationships affecting




its behavior can be expressed mathematically can be incorporated




into the segmented model.




        The model has been described previously by Thomann3, and




solutions to the one-dimensional time-dependent model have been

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                                                          1-3






programmed, for both the digital and analog computer '.   Applica-




tions of the model and methods of estimating required parameters




also have been presented6'7'8'9.   The purpose of this paper is to




describe in detail the theory of the "Thomann Model" as  applicable




to the one-dimensional steady-state case of organic pollution of




an estuary and to document a digital computer program developed




to solve this case.

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                                                          II - 1






II.  GENERAL APPROACH TO THE PROBLEM




         A first step in the application of the model is to divide




 the estuary into a satisfactory number of segments.   A mass balance




 for the pollutant is written for each segment.  The  results from




 these balance a series of equations equal in number  to the number




 of segments.  The only unknowns in these equations are the mean




 steady-state concentrations of the pollutant in each segment.




 Thus, a series of n equations with n unknowns is obtained where




 n is the number of segments.  By combining terms, this series of




 equations may be expressed in matrix notation as:




                              AC = L




 where A is a collection of known terms such as flow, diffusion




 constants, deoxygenation constants, and segment volumes in com-




 binations having units of cubic foot/day.  C is a vector matrix




 of unknown concentration of pollutants in pounds/cubic foot.   The




 product of A and C is L, a vector of pollutant loads added directly




 to each segment expressed as pounds/day.  The terms  of the vector




 L have been referred to as forcing functions by Thomanri.




         The matrix of unknown concentrations, C, may be solved by




 inverting A, since:




                             C = LA""1




 where A  , the "unit loading matrix," is the inverse of A.   C may




 then be obtained by performing the matrix multiplication of L




 times A   as indicated.

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                                                         II - 2




        This is an extremely convenient arrangement since, once


having solved for A  , it can be multiplied by any distribution


of loads along the estuary as described by the vector L.  Further-


more, because of the nature of A  , it is possible to determine


easily what part of the resulting pollutant concentration in any


one segment is due to a given discharge in any other segment.


The unit loading matrix is essentially a table having n rovs and


n columns, the elements of which have the units Ibs/cfs per lb/


day discharged.  Thus, A,   , the element in the fourth row and
                        4 5 I

seventh column of the A   matrix, would give the numerical value


for the concentration in segment U resulting from a discharge of


one pound per day in segment 7-  By multiplying the element,


A,   , by the actual load applied to segment 7 the concentration
 ^4 I

in segment k resulting from that discharge will be obtained.  If


the estuary being studied has been modeled using correctly verified


parameters, it will be possible to reproduce known pollutant dis-


tributions from known input loads.  The verification step must be


carried out with satisfactory results if the model is to be useful


for predicting altered loading conditions expected in the future.


That  is to say, the computer model is no substitute for the great


quantity of engineering field and office work required for any


sound, scientific discussion.


        Once a verified unit loading matrix is obtained, the pollu-


tant  distribution resulting from any loading pattern may be obtained.

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                                                         II - 3






In the analysis of oxygen conditions, it is necessary as a first




step to multiply the unit loading matrix by the particular ulti-




mate oxygen demand (UOD) loading conditions being studied.  Having




the UOD distribution among the segments, a mass balance may then




be written for each segment incorporating the terms which affect




the oxygen distribution, namely, advection, diffusion, deoxygena-




tion, and reaeration.  When applicable, terms describing uptake




by benthal loads and the net effect of photosynthesis and respira-




tion can also be included.  Just as in the case of the pollutant




distribution, these mass balances around each of n segments results




in a series of n equations in n unknowns which are the DO concen-




trations being sought.  Through the use of matrices, it is possible




then to obtain a series of linear expressions for the DO in any




segment as a function of the discharged loads, benthal uptake and




photosynthetic effects in all other segments.

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                                                          Ill - 1
III.  DETAILED DERIVATION




          Having divided the estuary into n sections, a mass balance




  is written for the oxygen in the k   section (Figure l).   Assume




  the concentration of oxygen in each section is uniform and equal




  to C ,  the mean concentration in the section.
Section k-1
c
k-1
Section k
c
k
Section k+1
c
k+1
           Flow 0
Flow Q.
                              Figure 1
          Oxygen can be gained or lost by several ways  in Section k.




              1.   Advection into Section k from Section k-1 and




  out of Section k to Section k+1.




              2.   Diffusion into or out of Sections  k-1 and k+1.




              3-   Reaeration of Section k from the atmosphere.




              h.   Use of oxygen in  Section k by oxygen  consuming




  waste (UOD).




              5.   Production of oxygen in Section k  by  photosynthesis,




              6.   Other mechanisms  (benthol deposits, immediate




  oxygen demands,  etc.).

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                                                         Ill - 2
Advection
        In the system  pictured below,
                        a
                                k
              k-1
                  k+1
                             Figure 2
the C's represent mean  concentrations in each segment of length, L.




        If it is assumed  that  the concentration gradient through




any two adjacent sections is  approximated satisfactorily by a




straight line, then the concentration at a boundary, a, between




the two segments can  be shown  geometrically to be:
                      p  _

                      a ~
which can be written  as:
\ Ck-! + Lk_! Ck



    Lk + Lk-l
                         C.    L.        C.  L.

                          k-1   k-1       k  k
                   O  ~~  'T- ~~"  v.-j.--.j^i---.  -f-
                    a   L.  .  +  L.    L,  n  + L,
                          k-1     k     k-1     k
or by letting

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                                                        Ill - 3






the concentration at the boundary may be expressed as:






           Ca = W Ck-l + (1 ~ 5k-l,k} Ck




        The amount of material advected across boundary "a" is




then given by:






           Ak-l,k = Qk-l,k [5k-l,k Ck-l + (1 - ^k-l,!* k]





where ,      is defined as above.
       K _L , J_




        For the case of boundary"b" the concentration gradient



is rising and has a sign opposite to that passing boundary "a."



In this case it can be shown that       will be defined as:
                                   K ,K ' X
or
                       Lk
                    Lk + Lk+l



        For a falling gradient, then, C is defined by the ratio



of the downstream segment length to the sum of the upstream and



downstream lengths; whereas, for a rising gradient, 5 is defined



by 1 minus this quantity or the ratio of the upstream length to



the sum of the upstream and downstream lengths.



        The above procedure may be used to find  subject to the

                        rp

restrictions that >1 - .

-------

-------
                                                        Ill - k






        Following this derivation, the advection from Section k-1



to k becomes:






           \-l,k = \-l,k C?k-l,k Ck-l + (1 - W> Ck]          10



        In a similar manner, the advection out of Section k into



Section k+1 is:






           Ak,k+l = \,k+l [5k,k+l Ck + (1 ~ ^k+l' Ck+l]          n





Diffusion



        The rate of diffusion from one section to another can be



assumed to be proportional to the difference in concentration



betveen the sections or:





           D.  n .  = E.  ., .  (C,  , - C, )                              12
            k-l,k    k-l,k   k-1    k





           Di  T ^i  = E!  i u.-,  (ci ^ - c, )                              !3
            k,k+l    k,k+l   k+1    k



where E is an exchange factor related to the classical diffusion



factor (K) by:



                  -  Kk,k+l \,k+l                                   ,

           \,k+l   0.5 (Lk + Lk+]_)




        This expression for E can be derived by assuming that



diffusion proceeds according to Fick's first law, i.e.,




           H . -K                                                 15





where H is the time rate of transfer of substance per unit area,


 M
p, and K is the coefficient of diffusion for the system shown

L T

below:

-------

-------
                        'k-1
                                                         III  -  5
                       L.
and
                        k-1
           i =    k-l  " Ck

           3X   1/2L   .  + 1/2L.
                    k-1        k
                     "k-1
           N = K





        D, the total time rate of transfer of substance across



the boundary between Se/gnent k-i and K which has a cross-sectional



area A is fjiven by:
           D = All



               AK
                        - Ck)
                                                                    16
                                                                     17
18




19
or
where
           E,
                      (r
                      [
                          KA
                    1/
        If E is taken as positive, the direction of the  diffusion



will be fixed by the relative magnitude of C    , C  , and C
                                                                    20

-------

-------
                                                        Ill - 6





Re aeration



        The rate of reaeration (r ) into Section k may be expressed
                                 K-


as being proportional to the difference in the actual oxygen



concentration and the oxygen saturation value C
                                               s c



           R.  = r. V, (C   - C, )                                      22
            k    k k  sc    k




BOD



        The rate of utilization of oxygen by the UOD present is
expressed as:
              = \ \(t) Lk(t)                                      23
vhere d (t) = the decay coefficient (k ) in Section k at time t.
       K.                              1


L. (t) = the UOD in Section k at time t.
 K
Other Sources and Sinks
        The effect of algae, benthal deposits, COE, and any other



sources or sinks of oxygen in Section k will be expressed as S (t).
                                                              k


Later it may be desirable to separate these effects and treat them



separately; but for the present, in order to keep the analysis



tractable, they will be considered together.



        If an equation is now written for all the sources and sinks



of oxygen in Section k, the following differential equation for the



mass rate of change in Section k is obtained.

-------

-------
                                                        Ill  - 7
               l = Qk_1>k [5k_lfk Ck-1 H. (1 - ^    )  Ck]
             at

                 - Vk+1 U k,k+l Ck + (1 - ^+l}  Ck+l]


                 + Ek-l,k (Ck-l - V + Ek,k+l (Ck+l  - Ck}


                 + rk \ [Csc(t) - Ck] - \ dk(t)  Lk(t)
or rearranging:


           -vk5i H- Qk_l5k Sk_l5k cR_1 + Qk_ljk (i - 5k_1>k)  c
              Q-Ti
                                                              k
           -Qk,k+l ?k,k+l ck - Qk+l (1 - ^k,k+l}  ck+l               25
           +Ek-l,k ck-l " Ek-l,k ck + Ek,k+l ck+l ~ Ek,k+l ck
           - Vk Ck + -rk\Csc(t)  + Vk(t)  Lk(t)  + \Sk(t)

Factoring out C ' s and multiplying  through by -1:
               K.

           ~ CQk-i,k sk-i,k + Ek-i,k]  ck-i- f\ It  + \-i,k (1  - ?k-i,

                           " Ek-i,k -  Ek,k+i  - rk \ ck             26
             Ck-l [-\,k+l (1 - ?k,k+l}  + Ek,k+l]  = rk\Csc(t)
           - vkdk(t) Lk(t) - sk(t)
Letting

           ak-l,k = -[Qk-l,k Sk-l,k + Ek-l,k]                        2T

                  = [-\-l,k (1 - **-!,*)  +  \,k+l  Sk,k+l  +  Ek-l,k   28
                                                                    29

-------

-------
                                                         Ill  - 8
the mass balance equation reduces to:
           ak-l,k Ck-l + \,k Ck +  ak,k+l Ck+l  =




           -rkVkCsc(t) + Vk(t) Lk(t) + Sk(t)  \                    3



        If steady state conditions  are assumed:




           T~= 0                                                    31
           dt



           C  (t) = C                                                32
            sc       sc



           dk(t) = dk                                                33




           L(t) = L                                                 3k
therefore:
           Sk(t) = Sk                                                35
               = [Qk,k+l ?k,k+l = Qk-l,k
                          rk \]                                     36
and
a,  . .  C.  , + a, ,  C.  + a, , _^n - r, V. C   + V.  d.  L.  +  S,  V.  = P,    37
 k-l,k  k-1    kk  k    k,k+l     kksc     kTck     kk     k




        Assuming appropriate boundary conditions,  i.e.,  C   and



C    and writing mass balance equations  for each section,  we



obtain an equation of the following  type:

-------

-------
                                                        Ill - 9
allCl



a!2Cl
                   a!2C2 = Pl
a22C2
                           a23C3
           a23C2 + a33C3
                                                 38
           a  ..   C  . + a   C
            n-l,n n-1    n,n n
              = P
or in a matrix notation
        !2
 a21   a22   E23
       &32   a33
                    n,n-l
                 n
0
0
0
a
n-l,n
a
nn







Cl
C2
C3


C
n
=
=





Pl
P2
P3


P
n
                                                 39
           A C = F
             C = F A
                    -1
                                                 ho



                                                 hi
        The system can thus be solved for all values of C by finding



the inverse of the matrix A.  Matrix inversion, although time-



consuming by hand, can be accomplished easily by high speed digital



computers.

-------

-------
                                                          IV - 1




IV.  MATHEMATICAL TECHNIQUE EMPLOYED IN THE MODEL FOR MATRIX

     INVERSION


         The matrix of coefficients we are dealing with in the


 program is of a particular type.  The system of equations is tri-



 diagonal since the matrix of unknowns is tridiagonal, i.e., each


 element is zero except the main diagonal and its adjacent diagonals,


         The solution to such a system is conveniently handled on


 the computer by solving for the inverse employing a tridiagonal


 technique.


         This may be illustrated by an example:
            C    q    0    0






            0    P,   C3   q,


            0    0    p    C;




         Now define an S sequence recursively by:
                                                                     US



                                                                     kh
             0    0
             3    3
U5

-------

-------
                                                          IV - 2
           s  = c  - -^-

            k    k     bk-l

           II    II



           I!    II
                     Pn_
           s  =       n
            n    n      b
                         n
        In terms of this sequence, define the  sequence  K by:



           K  = b




                     pl kl

           K2 = b2 ~ ~S~
           t*    II
           II    II
           It    T?
           K. = b. -     -                                           50
            i    i     si_1
           II    IT
                     p  , k
           v  - -K     n-1  n-1

           Kn = bn - ~S	
                        n-1



        The solution to the set of equations  can now be written



down by means of a backward sweep as  follows:



NOTE:  We illustrate by means of a hxh.   The  generalization is



       obvious.

-------

-------
                                                         IV - 3
                                                                    53
                K2-
                Kl -
                                                                    55
                     1

        The above procedure is well known.  In order to prove this,

we note that the forward sweep corresponds to taking the i-th row,
                  -C.
multiplying it by 	, and adding it to the 14-i-th row as i advances

from 1 to n.  This procedure triangularizes the matrix, i.e., it

is reduced to:
sl ql  
0 S2 ci2 0
0 0 S3 q3
0 0 0 S]




Xl
X2
X3
X*
=



Kl
K2
K3
Klt
                                                                    56
        The backward sweep is now clear.  Obviously now X  is

determined since X>  is known, etc.

-------

-------
                                                          V - 1







V.  PREPARATION OF THE COMPUTER PROGRAM




        The program was vritten in Fortran IV and originally run




on the IBM 709^ at the National Bureau of Standards in Washington,




D. C.  The more recent version presented here vas run on the IBM




360 system at the U. S. Geological Computer Center, Washington,




D. C.  Though Fortran programs will run on any installation that




maintains a Fortran compiler, it usually requires a number of




changes to be made when switching from one system to another.




Generally, these changes require an understanding of the installa-




tion's job control language, together with the particular level




of the compiler.




        In developing the program and in the choice of mnemonics,




an effort was made to make the program as compatible as possible




with the time dependent model previously programmed by Jeglic.4




        The complete program deck structure is shown in Figure 3.




The entire package consists of one main program and eight sub-




routines.  The main program calls these various sub-routines as




they are needed and controls the actual operating features and




cycling.  The sub-routine POLYB reads in coefficients and the




powers of polynoraian equations when the vectors for reaeration,




decay, and dissolved oxygen are to be generated rather than read




in as input data.  The sub-routine PRELIM reads in various vector




quantities and prepares the coefficients of the matrix and other




required vectors.  Sub-routine PRECAL loads the calculated matrix




elements in their proper positions and returns control to the

-------

-------
                                        Subroutine FINAL
                                   Subroutine PRTMAT
                               Subroutine  SCAVEC
                           Subroutine INVERT
                      Subroutine  PRECAL
                  Subroutine  POLYB
             Subroutine  PRELIM
         Program  MAIN
     // FORT SYSIN DD
  //EXEC FORTHCLB
JOB CARD
                          FIGURE   3.
    PROGRAM     DECK    STRUCTURE

-------

-------
                                      /Subroutine  FINAL
                                   Subroutine  PRTMAT
                               Subroutine SCAVEC
                          Subroutine INVERT
                      Subroutine PRECAL
                 Subroutine  POLYB
             Subroutine PRELIM
         Program MAIN
     // FORT SYSIN DD
   //EXEC FORTHCLB
JOB CARD
                          FIGURE  3.



    PROGRAM    DECK   STRUCTURE

-------

-------
                                                          V - 2


main program, which then calls the matrix inversion program.

This sub-routine then inverts the tridiagonal matrix.  The sub-

routine SCAVEC performs the calculations on the inverted matrix

that have been specified in tne control card,  PRTMAT is a general

sub-routine used to print the inverted matrix ana could be used

to print any matrix with five elements printed per row per page.

Sub-routine FINAL is used only when both the A and B matrix

inversions have been specified for a single case of input data,,

        PRECFH is employed to adjust the vectors witn proper

dimensions when it is more convenient to enter tne vectors in

units other than tnose employed in the actual calculations.  Tnis

allows the analyst to enter a conversion constant into the program

when the source data set up is Jn other units.

        As shown in "Figure 3, the first card of the program deck

is the job control card.  The card format lor this card at tne

UoSoG-So Computer Center where the program was run is as follows:


                        JOB CONTROL CARD

 Card
Columns	Re quired Inf ormat i on	

 1-2       //

 3           Center Code:  For use in conjunction with the job or
             program number to identify the center originating or
             assigning the job or program numDer,

 ^ - 5       Federal Agency code

 6 - 8       User Registration Code:  Individual users registration
             code.  To be assigned by Computer Center Division.

-------

-------
                                                          V - 3


                  JOB CONTROL CARD (Continued)

 Card
Columns 	Required Information	

 9-10    User's ID:  This is structly a user's ID to uniquely
           identify submissions of data to the Computing Center.
           The only caution to be observed by the user is when
           two sets of data for the same program are submitted
           simultaneously, then different alphanumeric characters
           should be punched in columns 9-10.

11         Blank column

12-lit      JOB (e.g., the word JOB)

15         Blank column

16         (   (left parenthesis)

17 - 20    Program Number:  Four digit numeric job or program
           number assigned by the Computer Center Division at
           each field center and Washington, D. C.  When a new
           number is assigned at any field center, the attached
           Program Registration Form should be completed in
           dxiplicate and transmitted to the Computer Operations
           Branch, Washington, D. C.

21         ,   (comma)

22 - 25    User assigned auxiliary account number.  Four alpha-
           numeric characters chosen by the user according to any
           method he chooses.  Accounting data will be sequenced
           and subtotaled by this number for user information.

26         ,   (comma)

27 - 30    Estimated execution time in minutes.  Requires four
           numeric digits.

31         ,   (comma)

32 - 35    Estimated lines of print expressed in thousands of
           lines.   Requires four numeric digits (e.g., 0001 =
           1000 lines of print).

36         ,   (comma)

-------

-------
                                                          v - U


                  JOB CONTROL CARD (Continued)

 Card
Columns	Required Information	

37 - ^0    Estimated number of cards to be punched.  Requires
   *        four numeric digits and is an exact number (e.g.,
           0100 = 100 cards).

Hi         ,   (comma)

U2         Reserved for future use - must be 1.

^3         ,   (comma)

kh         Reserved for future use - must be 1.

^5         ,   (comma)

h6         Type run.

                C = Compile only
                T = Test of program
                P = Production use of program
                D = Data conversion required to convert from
                    prior systems

^7         )   (right parenthesis)

U8         ,   (comma)

^9         '    (single quote)

50 - 70    Programmer or user's name.  May be from 1 to 20
           characters, with or without imbedded blanks.   Must
           be followed by one single quote (')  This field is
           required and cannot exceed 20 characters.

           If the user requires additional information in the
           JOB card,  the following rules apply:  (e.g.,  MSGLEVEL
           1 or other comments).

           A - Place  a comma immediately following the trailing
               quote  after name field.

           B - Punch  any alphanumeric character into column 72  -
               Do Not Use this column for any other purpose.

-------

-------
                                                          V - 5
           C - Punch // in columns 1 and 2 of a second card.

           D - Columns 3-15 MUST BE BLANK.

           E - If MSGLEVEL = 1 is desired, it must be punched in
               columns 16 - 25 and followed by one or more blanks
               prior to any other comments.

           F - If comments only are desired,  leave column 16
               blank and start the comment in column 17.

           G - Column 72 of the second card MUST BE BLANK.


        The second card in the program source deck is the EXEC

statement card.  The EXEC statement indicates the beginning of

a job step and describes that job step.   For  the program here,

the EXEC statement should appear as:

        Columns No.  1  2  3  	

                     //bEXECbFORTHCLG

           (b = blank)

        The third card in the program contains the following:

        Columns No.  1  2  3  ^  5  ....  	
                     //FORT  .   SYSINbDDb*

           (b = blank)

        The statement specifies the location  of the source module(s)

or the object module(s) to the control program.

-------

-------
                                                         VI - 1



VI.  INPUT DATA PREPARATION AND PROGRAM CASE CONTROL


     A.  General


         The model contains the feature of running any number of


cases during a production run.  The original run would consist


of placing the FORTRAN source program before the data deck.  Sub-


sequent computer runs would use the binary deck (called the object


program) in front of the data.


        Appendix III shows a typical data deck structure.  The first


card in the deck contains the number of cases to be run.  This

        *
variable  is identified by the name HCASES.   The first three


columns on the card are used to enter the value.  It is possible


to run 999 cases on an individual computer run.


        The format for this card is:
            CARD COLUMNS _1  2  3  4  5  .

                                8
        Note that for the sample shown, the program would operate


on 8 data sets before termination.   In entering data for the num-


ber of cases, the value should always be right justified.   If, for


example, the 8 were inadvertently entered in column 2,  the program


would try to operate on 80 sets of information rather than the 8


desired.


        The second card in the data deck is the date card.   This


should be given as the date the computer run will be made.   Its
*
   The word "variable" is not used in the normal mathematical sense.

-------

-------
                                                         VI - 2


main use is to quickly identify the computer run since, in most

simulation modeling, input information will "be adjusted upon

analysis of initial output, and at a later time the analyst may

want to refer to prior runs.

        The numeric values and special symbols normally used to

write the date may be entered as:

                  5/1T/67  (Starting in column 1)
              or 05/17/67  (Starting in column l)

        The date may be entered in columns 1 to 2k on the card,

but for use of identification, it would be convenient to establish

a definite entry technique as shown above.

        The third card in the data deck should contain the name

of the user.  Again 2h columns are employed, and the entry may

appear in any of the card columns 1 through 2k.

        The fourth card in the data deck is the title card.  This

card is employed to identify the first set of data the program

will operate on.  Note in Appendix III that each subsequent set of

input data contains a title card.  Card columns 1 through 22 are

employed.  The data may be numeric or alphabetic.

        The title card and its subsequent set of data may be

considered as a separate subdivision from the entire data deck.

In practice, the title card and its associated input data is a

subset of the input deck; therefore, the following discussion

will outline the subset structure.

-------

-------

    .5 .   " .' nine lint In p u 1

         J.  ^eneral Description  of Xa'T.elisl  Jrrout Witu Rule

         Tuc Panelist input "iio.le  was c^o^ei;  ii, o/ver  to nvoi

 .. taiX  iK;ce;-:nry to code  input uata into r  definite  format F.tru

 .uf-e.   lluaer ^A^ELl^? options, trie uat-i to  GO entered into tLc

 oni^jtor is ion.tje^ i;j Tnencry ^iti'
         Lero nane^.  is  tlje  i.arc of the list  of variables whose

varies  are soecifieu by V. ,  W. .  T.ic i.air,e  of the liAI'LLIBT ~;L.y  u

frcn  r;..K' to r- ix  characters  in  ifn^tri.

         Tr: order to u.uacrstnna t-io daLo c.-iitr:/ for  a  vrr'able

a^oOcL.tec -.vith  a '.ANKMGT, t;if following p-cntr:1.!  ro-[u: i 2- -.<-;/: t:i
                  ]^ac ^ iAJ'-jLioT Lorlnr-i vili.  ..n a;:.rc^r3ai;d {":}  ii;
                  colani:i  L\  "ollc-;;cd L ;; the  :.:'>":,;.!..".  na."-, ;\;;o
                  foLlo;:e:l  uy a1- least one u'rin-i.
                  Blankn ir.ay not, be  iEbeded  "be Tore or  afi.er the  r"
                  Hign.  (Ex.  A -  5.0,  is illegal and  1-3 ho aid  be
                  puiichcc.  an:  A^^.Q,,.1

-------

-------
                                                 VI  - h
    g.   Blanks may be embedded between data values after
        the first value of vectors or arrays as shown
        below:

              (1=1.2,1.3,1.5     2.2,2.3,2.5,)

    h.   Exponential notation may be used for large or
        small values, i.e., 2.153E5 and 2.15^E-2 denote
        215300 and 0.02151*.

    i.   If the decimal point is omitted, it is assumed
        to be at the extreme right.

    j.   No decimal point may be used in the entries of
        variables typed integer.

    k.   When an array name appears without subscripts,
        all elements in the array must be present.

    1.   To enter the same value in several elements of
        an array, the data card may be set up as follows:

              If X is dimensioned as X (10); then

              X-1.U,2.H,6.3,5*6,.2,7.1,8.5,

2.  Description of Namelist and Variables Used in This
    Program

    a.   WAMELIST CF

        This namelist deals with the problem controls and
        conversion factors.

        NSECTS (integer)   - Number of estuarine segments

        IMAT (integer)     - Program Control for A and/
                             or B matrix

        INDEX (i)(integer) - Printing Option Control

        ITP (i)(integer)   - Control value variable
                             employed by polynomial sub-
                             routine and temperature
                             conversion control

        CFQ (real)         - Advection conversion constant
                             employed in sub-routine PRECFM

-------

-------
                                                         VI - 5


                CFLEN (real)  - Length conversion constant
                                employed in sub-routine PRECFM

                CFK (real)    - Diffusion conversion constant
                                employed in sub-routine PRECFM

                CFL (real)    - UOD conversion constant employed
                                in sub-routine PRECFM

                CFAREA (real) - Area conversion constant employed
                                in sub-routine PRECFM

                CFVOL (real)  - Volume conversion constant
                                employed in sub-routine PRECFM

                CFP (real)    - Dissolved oxygen sink and source
                                conversion constant employed in
                                sub-routine PRECFM

        The above CF namelist is developed for each data set.

        INDEX controls the printing of information with regard

to a particular state of IMAT.  In the event that IMAT would

equal 1, two sets of information may be optionally printed, i.e.,

ALPHA x A"1 or ALPHA x VECTOR (L) x A"1.  If IMAT would equal 2,

then the index would optionally be used to print ALPHA x B   or

ALPHA x F x B"1.  In the third state, i.e., IMAT = 3, the INDEX

option allows printing of ALPHA x A~ , ALPHA x L x A~ , ALPHA x

B"1, ALPHA x F x B'1, ALPHA x A"1 x B"1, VD A"1}*"1, LVD A'1 B"1,

and D.O. Sat. + ALPHA x F x B"1 - LVD A""1 B"1.  IMAT and the index

values will be discussed in greater detail later in this section.

        A large number of possible combinations of output may be

obtained.  A typical output is shown in Appendix III, and each

case shown here has been verified.  Case K in the Appendix shows

the results for IMAT = 3 and all INDEXES 1 through 8 set equal

to 1.

-------

-------
                                                         VI - 6


        The ITP variable is entered on the card, following the

INDEX control card.  Two values should always be given for this

variable.  If ITP (2) is set equal to 1, the polynomial sub-

routine is called.  This sub-routine, discussed in Section V,

generates the reaeration, dissolved oxygen at saturation, and

the decay vector.  If ITP (l) is set equal to 1, the temperature

vector may be given in degrees Fahrenheit and is converted in

the sub-routine to degrees Centigrade.

        The conversion constants CFQ, CFLLiI, CFK, CFL, CFAREA,

CFVOL, and CFP are entered in succeeding cards.  These constants

are employed to convert tneir corresponding vectors to the proper

units so that the actual vector input data may be entered in any

units providing the corresponding conversion factor is given.

In the event that the original input vectors are already in the

proper units, the corresponding conversion factor would be set

equal to 1.

            b.  NAMELIST RIVER

                This namelist contains the parameters which

describe the geometry of the river and the waste loadings to

the system.

                Q (i)(real) - Qi_^ j_, net flow of the estuary
                              between segments i-1 and i, ex-
                              pressed in cubic feet per second.
                              All boundaries, including the flow
                              into the first and the flow out of
                              the last segment, must be specified.

-------

-------
                                         VI - T
LENGTH (i)(real) -
VOL (i)(real)
AREA (i)(real)
DIFFCO (i)(real) -
L (i)(real)
P (i
  _}_, length of the estuary seg-
ments.  Since a length above the
uppermost segment and below the
lowermost segment is required
(see equations 9 and 19) n + 2
lengths must be specified.  The
input must be in feet.  If other
units are to be used, the proper
conversion factor CFLEN (Namelist
CF)  must be used.

V-j_,  volume of section i in cubic
feet.  All sections must be spec-
ified.  If units other than cubic
feet are used, a suitable conver-
sion factor must be specified
(CFVOL in namelist CF).

^i-1 i' cross-sectioned area of
the  interface between segments
i-1  and i, in square feet.  All
interfaces, including the first
and last, must be defined.  Con-
version factor CFAREA may be used.

KJ__J j_, longitudinal dispersion
coefficient between segments i-1
and  i in square miles per day.
All  segment boundaries, including
the  first and last, must be spec-
ified.  Conversion factor CFK is
available if different units are
used.

LJ_ ,  ultimate oxygen demand being
discharged to segment i in pounds
per  day.  All segments must be
defined.  Conversion factor CFL
may  be used if desired.

Pi,  other sources or sinks of
oxygen in segment i, in pounds
per  day.  All segments must be
defined even if all values are
zero or meaningless.  Conversion
factor CFP is available.

-------

-------
                                                         VI -
            c.  NAMELIST RIVTO

                This namelist is used if one wishes to specify

definite values for the ultimate oxygen demand decay rate, the

reaeration rate and the saturation value of oxygen in each segment.

                DISOXS (i)(real) - C  , the saturation value of dis-
                                   solved oxygen in segment i.  All
                                   segments must be defined.  The
                                   values must be entered in mg/1.

                REAERK (i)(real) - r^, the reaeration coefficient
                                   for segment i in units of I/day.
                                   All segments must be defined.

                DECAYK (i)(real) - dj_, the ultimate oxygen demand
                                   decay rate in segment i also with
                                   units of I/day.  All segments
                                   must be defined.

            d.  NAMELIST R R

                This namelist is used if one wishes to generate the

values of the ultimate oxygen demand decay rate, the reaeration rate

and the saturation value of oxygen from the river temperature using

polynomials.

                T P (i)(real)    - The temperature of the water in
                                   segment i.  The temperature may
                                   be given in degrees Centigrade if
                                   ITP (2) in namelist CF is set
                                   equal to 0 or in degrees Fahren-
                                   heit if ITP (2) in namelist CF is
                                   set equal to 1.

                K D (Integer)    - The order of the polynomial which
                                   is being used to describe the
                                   decay rate.

                C D (j)(real)    - Polynomial coefficient of the jth
                                   term in the polynomial which is
                                   being used to describe the decay
                                   rate.  C D must be defined for all
                                   values of j < K D + 1.

-------

-------
                                                         VI - 9


                K R (integer)    - The order of the polynomial which
                                   is being used to describe the
                                   reaeration rate.

                C R (j)Creal)    - Polynomial coefficient of the jth
                                   term in the polynomial which is
                                   being used to describe the reaera-
                                   tion rate.  C R must be defined
                                   for all values of j  <_ K R + 1.

                K C (integer)    - The order of the polynomial which
                                   is being used to describe the
                                   dissolved oxygen saturation value.

                C C (j)(real)    - Polynomial coefficient of the jth
                                   term in the polynomial which is
                                   being used to describe the dis-
                                   solved oxygen saturation value.
                                   C C must be defined for all values
                                   of j <_ K C + 1.

        In order to understand the arrangement of the various NAME-

LISTS in the input data structure, the following explanation should

prove helpful:

        Consider the following:

                1.  CF Namelist (Always First and Present)

                2.  RIVER Namelist

                3.  RIVTO Namelist

                U.  R R Namelist

        1.  CF is always first and present.

        Now, if ITP (2) = 0, NAMELIST R R is second, NAMELIST RIVER

is third, and RIVTO is not required.

        If ITP (2) = 1, RIVER is second, RIVTO is third, arid RR

is not required.

-------

-------
                                                          VII - 1
VII.  BIBLIOGRAPHY
  1.  Gtreeter, K.  W. ,  and. Phelps ,  E.  B. ,  "A Study of the Pollution
      and Natural Purification of the  Ohio River - III,  Factors
      Concerned in the  Paenoraena of Oxidation and Reaeration,"
      Public Health Bulletin No. lh6,  U.  S.  Public Health Service,
      February 1925.

  2.  O'Connor, Donald  J., "Oxygen  Balance of An Estuary," Journal
      of the Sanitary Engineering Division,  American Society of
      Civil Engineers,  Proceedings  Paper  2U'f2, Vol.  86,  No.  SA3,
      May I960.

  3.  Thomann, Robert V.,  "Mathematical Model for Dissolved Oxygen,"
      Journal of the Sanitary Engineering Division,  American Society
      of Civil Engineers,  Proceedings  Paper  368-0, Vol.  89, No. SA5,
      October 1963.

  h.  Jeglic, John M. ,  "Mathematical Simulation of the Estuarine
      Behavior," Digital  Computer Technology and Programming Anal-
      ysis Memo. No. 1032, Rev.  A,  General Electric  Re-Entry Systems
      Department, Philadelphia,  Pennsylvania, July 1967-

  5.  "Program for Analog Computer  Simulation of Dye Diffusion in
      the Potomac River,"  Final  Report by:  Electronic Associates,
      Incorporated, Washington Computation Center to the Chesapeake
      Field Station, Chesapeake  Bay-Susquehanna River Basins Project,
      Federal Water Pollution Control  Administration, Annapolis,
      Maryland, in completion of Contract  RO-3-2131-65,  October 1965.

  6.  Hetling, Leo J.,  and O'Connell,  Richard L. , "A Study of Tidal
      Dispersion in the Potomac  River," Water Resources  Research,
      Vol. 2, No. k, Fourth Quarter, 1966.

  T.  Hetling, Leo J.,  and O'Connell,  Richard L., "An Oxygen Balance
      for the Potomac Estuary,"  CB-SRBP Technical Paper  No.  13,
      Federal Water Pollution Control  Administration, Middle Atlantic
      Region, Charlottesville, Virginia (in  press).

  8.  Hetling, Leo  J.,  "Simulation  of  Chloride Concentrations in
      the Potomac Estuary," CB-SRBP Technical Paper  No.  12,  Federal
      Water Pollution Control Administration, Middle Atlantic Region,
      Charlottesville,  Virginia  (in press).

  9.  Hall, Charles W., and Hetling, Leo J.,  "Use of Mathematical
      Models as Aids to Decision Making in Water Quality Control,"
      Presented at  the  Sixty-third  National  Meeting  of the American
      Institute of Chemical Engineers, St. Louis,  Missouri,
      February 19,  1968.

-------

-------
APPENDIX   I






      PROGRAM




   FLOW DIAGRAMS

-------

-------
FALSE
YSTEM CALL
MED (0)
N .


                                                                          SYSTEM
                                                                          CALL  TIMEIN
                                                             NUMBER  OF
                                                                CASES
                                                              (NCASES)
                                                              DATE  OF
                                                                THIS
                                                                RUN
                                        ICTN = ICTN t I
                                                            NAME OF  THE
                                                              PROGRAM
                                                                USER
                                                                TITLE
   TITLE
   DATE
   PAGE
  NSECTS
   IMAT
  INDEXES
CFO,CFLEN
 CFK, CFL,
  CFAREA
CFVIJIL, CFP
 SUBROUTINE  POLYB  1
POLYNOMIAL  DATA IS READ
IN  TO COMPUTE  THE  VEC-
TORS  REAERATION,  DECAY,
DISSOLVED  OXYGEN   SATUR-
ATION
   GENERAL
   PROJECT
   HEADING
                                                               TITLE
                                                                DATE
                                                                USER
      REWIND  BINARY  TAPES
NSECTS, ITP (2)
     IMAT
INDEXES  (1-8)
                                                             CFQ,  CFLEN,
                                                              CFK,CFL,
                                                               CFAREA
                                                             CFVOL, CFP
                                                     COLUMNS  1-3
                                                     NCASES  999
                                                     COLUMNS  1-24
                                                     (ALPHANUMERIC)
                                                     COLUMNS  1-24
                                                     (ALPHANUMERIC)
                                                                            COLUMNS  1-72
                                                                            (ALPHANUMERIC)
                                                     INITIAL  OUTPUT  PAGE
                                                     FOR EACH  CASE  RUN
                                                     NSECTS - NUMBER  OF
                                                              ESTUARINE
                                                              SECTIONS
                                                     IMAT   - MATRIX OPTION
                                                     INDEX(I-B)PRINTING  CONTROL
                                                              OPTIONS
                                                     ITP(I)  -TEMPERATURE
                                                              INPUT  OPTIONS
                                                     ITP(2) -CONTROL
                                                              POLYNOMIAL
                                                              SUBROUTINE
                                                            FLOW  CHART NUMBERJ   | I  | OF
                                                            PROGRAM NAME:  MAIN
                                                                U S  DEPARTMENT  OF  THE  INTERIOR
                                                            FEDERAL  WATER POLLUTION  CONTROL  ADMINISTRATION
                                                                       MIDDLE  ATLANTIC  REGION
                                                                      CHARLOTTESVILLE,  VIRGINIA

-------

-------
                    NAMELIST/RR /
(KR.KD, KC, CR, CD, cc, TP  j
                                                         POLYNOMIAL  EQUATIONS,
                                                                REAERATION:   cr, = ^>;  crKT,
                                                                                   K=0
                                                                              Co, = ^>]  CDT
DISSOLVED          __     K
OXYGEN        Cc  = ^  CcKTK
SATURATION         ^TT   K
                                                              POLYNOMIAL  OUTPUT
                                                                   DATA  PAGE
                                                                I             '
                                                                 WRITE
          J = 2, MO

    CD, = Co, +CD, x TPiJ"
          0 = 2, MC

    Cc, = Cc, + Cc,  X


   30
                                                                 WRITE
      TITLE

     DATRUN

      IPAGE
                                                                  FLOW  CHART  NUMBER)   | 2 | OF |I  [I

                                                                  PROGRAM NAME! SUBROUTINE   POLYB
                                                                      U S. DEPARTMENT OF  THE  INTERIOR

                                                                   FEDERAL  WATER POLLUTION CONTROL  ADMINISTRATION
                                                                            MIDDLE  ATLANTIC  REGION
                                                                            CHARLOTTESVILLE,  VIRGINIA

-------

-------
   RATIOL(I)= (1.0 -0.5*
   TURBEX(I)/ADVECQO)>


10
[  1, IMAX
AFTSEC(I)' ADVECQ(I)
ADVECOU)- 86400.*ADVECO(I)
ADJLUM ALENTH(I) + AL,ENTHd+l>
TURBEXd) - ((DIFFCO(n*(AREA(l)/AOJL(I)))CONST)


20

IMAX - IMAX - 1
    AKK = TURBEXd -l)/ADVECQ(l -I)
       AJJ = TURBEXdl/ADVECQd)
         All = (ALENTH(I-I>/
       (ALENTHII-D +ALENTH(I)l)
                                                        TRUE
                                                   RATIOLU)"  \
                                                  I 0- AJJ + .01
                                                             1  J
                                                                                                                  FALSE
                                       RATIOL(t)  All
                                                70
I - I, ISPEC
 AUPPER(I) = (ADVECQd + I)*
    (1.0 -RATIOLU+ 1)1) -
       TURBEXd +1)
IOO
I 'I, NSECTS   .,

                                                                 1=2, NSECTS
 /    ISPEC =
A   NSECTS - I    /
    BOTTUMd- I) =
  (-I.O((ADVECO(I)
RATIOL(I) +  TURBEX(I))))
(RATIOL(IMAX) =05
     ASTORE(J) = (-1 0* ADVECO(I)*
   (lO-RATIOL(D)  +ADVECO(I+D*
 RATIOLII tl) + TURBEXd) + TURBEXd -HI)
                                              CONTINUED
                                            ON FLOW CHART
                                                NUMBER
                                                                                          FLOW CHART  NUMBERJ   |3TOF I '  I '
                                                                                          PROGRAM  NAME: SUBROUTINE   PRELIM
                                                                                              U S  DEPARTMENT  OF  THE  INTERIOR
                                                                                           FEDERAL WATER POLLUTION CONTROL  ADMINISTRATION
                                                                                                     MIDDLE  ATLANTIC  REGION
                                                                                                    CHARLOTTESVILLE,  VIRGINIA

-------

-------
    CONTINUED
FROM FLOW CHART
     NUMBER
                                                                                 IDISOXS, 1*1, NSECTSI
                                                                                 IVOLUME.I-I, NSECTSI
                        J.TPIJ), UL80DIJ)
                          DOSKSR(J),
                            ISEC, I,
                           OIFFCOU),
                           AFTSEC(I)
  ISEC
         ISEC + I

         I +1
  750
                             I = I
                             J" I
                            ISEC =0
HEADING
^^^^


TITLE
DATRUN
IPAGE
                                                                        IPAGE  IPAGE + I
    J.REAERKIJ),
DECAYK(J), DISOXS(J)
 ISEC,I,RATIOL(I),
    TURBEX(I),
    ADVECQ(l),
                                                       TO 760
                                                 CONTINUED
                                               ON FLOW CHART
                                                  NUMBER
                                                     (5)
                               
                                                          FLOW CHART NUMBER]  |4J OF  \ I \ I

                                                          PROGRAM  NAMErSUBROUTINE   PRELIM
                                                                                     U. S  DEPARTMENT OF  THE  INTERIOR

                                                                                 FEDERAL  WATER POLLUTION CONTROL  ADMINISTRATION
                                                                                            MIOOLe  ATLANTIC  REGION
                                                                                           CMARLOTTESVILLE, VIRSINI*

-------

-------
                                                           CONTINUED
                                                        FROM FLOW CHART
                                                            NUMBER
                       TRUE
IPASE = IPAGE + I
    TITLE,
   DATRUN,
    IPAGE
 WRITE
WRITE


I, I, ADIAG(I),
I, J.AUPPEWW,
J, I,BOTTUM(U
_ 	 -^

^^ IF ^^^ FALSE / 1=1+1
^-L .^^ \ J = J + i
                            810
                                                                    FLOW CHART NUMBER |  |sj OF [ I  | I

                                                                    PROGRAM  NAME:SUBROUTINE   PRELIM
                                                                        U S  DEPARTMENT  OF  THE INTERIOR
                                                                     FEDERAL WATER POLLUTION CONTROL AOMINI STRflTION
                                                                              MIDDLE  ATLANTIC  REGION
                                                                             CHARLOTTESVILLE,  VIRGINIA

-------

-------
                                       ENTER
                                           J-l, NSECTS
                              DOSKSRtJ)  CFP # DOSKSR(J)
                              VOLUME(J)'CFVOL#VOLUME(J)
                               ULBOD(J) - CFL # ULBOD(J)
(MAX-NSECTS
                                                                              K  I, IMAX
                                                                ADVECO(K)  CFO # ADVECO(K)
                                                                OIFFCO(K) * CFK # DIFFCO(K)
                                                                AREA(K) ' CFAREA * AREA(K)
                                                                        FLOW CHART  NUMBER | I | I | OF | I |
                                                                        PROGRAM NAME: SUBROUTINE  PRECFM
                                                 l, ISPEC
                                                AMATRXII + I, I) * BOTTUM(I)
                                                AMATRX(I,I + I)  AUPPER(I)
I  I, NSECTS
                                                                       FLOW CHART NUMBER)  |6|oF|l|l

                                                                       PROGRAM  NAME:SUBROUTINE PRECAL
                                                                            U S  DEPARTMENT  OF  THE  INTERIOR
                                                                        FEDERAL WATER POLLUTION CONTROL  ADMINISTRATION
                                                                                  MIDDLE  ATLANTIC  REGION
                                                                                 CHARLOTTESVILLE,  VIRGINIA

-------

-------
180=1,  NSECTS
                                                  I "I, NSECTS
                                                  VECTOR
AMATF
= ALF
AMATF
3

X(I,J)
HAW
X(I,J)



ALPHA=
1 66+4



J= 1, NSECTS
SUMVEC(J) = 00
2
[ OCA'1
                                                                   FLOW CHART NUMBER[   | 7 | OF | I { I

                                                                   PROGRAM NAME:SUBROUTINE SCAVEC
                                                                      U S DEPARTMENT  OF  THE INTERIOR
                                                                   FEDERAL WATER POLLUTION  CONTROL A DM I N I STRATI ON
                                                                            MIDDLE  ATLANTIC  REGION
                                                                            CHARLOTTESVI LLE, VIRGINIA

-------

-------
                                    -( REWIND
(DISOXSd), 1 = 1, NSECTS)
                                                          (ULBOD(I), 1 = I, NSECTS)
                                                                                       KAMATRXd.J), 1 = 1, NSECTS),
                                                                                              J = I, NS'ECTS)
UBMATRXU.J), 1=1, NSECTS),
       J = l, NSECTS)
, , . V A V A 	 V A
DO 1: 1= , NSECTS
,,(VOLUME(I), 1 = 1, NSECTS) (DECAYK(I), I = 1, DO |- J* , NSECTS
0 NSECTS) CCTN(I,J) = 00
DOI IK= .NSECTS
	 + CCTN(I,J)=CCTN(I,J) +
BMATRX(r,IK)#
AMATRX(IK.J)
1
1=1, NSECTS
1 = 1, NSECTS , j.|, NSECTS
\-LUME (=I>* . FALSE^
-------

-------

1 = 1, NSECTS
0(1) =
AMATRXIt, I)


                                                    I - I, MA
                                                    II <
                           *< MA = NSECTS - I
B(K) ' 00
7



AMATRXII, K) 
X(I)


X(LL) =(T(LD-
OA(LL)*
XILL+ I))/S(LL)
E t




QA(I) = AMATRX(I,H)
AMATRXdl, I)
2
DO 7. K = 1, NSECTS
B(K)= 1.0
S(l)  0(1}
T(D- BID
I  1, NSECTS


K" 1, NSECTS
B(K)  0 0
3
I ' 1, MA
LL  NSECTS - I
J = I - 1


S(D- Dd)-PA(J)*
OA(J)/S(J)
Till" 8(I)-PA(J)*
T(J)/S(J)
4



                                                                                                     X(NSECTS)-
                                                                                                     T(NSECTS)/
                                                                                                      S( NSECTS)
                                                                              FLOW CHART NUMBER |  |9JOF |l j
                                                                              PROGRAM  NAME: SUBROUTINE  INVERT
PAUSED





^^xNSE




CTS^/
TRUE





f

1

(
WRITE:
I, AMATRX(l.J)
J = LL, KCTN



I HEAD(I),
I'LL,
KCTN
_ ^^
                                                                              FLOW CHART  NUMBER | 1  | 0 | OF j I | I

                                                                              PROGRAM NAME:SUBROUTINE PRTMAT
                                                                                  U 5  DEPARTMENT  OF THE  INTERIOR
                                                                               FEDERAL WATER POLLUTION CONTROL  ADMINISTRATION
                                                                                        MIDDLE  ATLANTIC REGION
                                                                                       CMARLOTTESVILLE, VIRGINIA

-------

-------
  APPENDIX   II




   IBM 360  VERSION I




FORTRAN PROGRAM LISTING

-------

-------
ISM 0002
ISN 0003
ISN 0004

ISN 0005
ISN 0006
ISN 0007
             C
             C
             C
             C
             C
             C
             C
             C
             C
 PROGRAM MAIN
 MIDDLE  ATLANTIC REGION - IBM 360 VERSION I
 STEADY  STATE SEGMENTED ESTUARY MODEL
 FOR FURTHER INFOf- NATION CONTACT
       PROJECT ENGINEER- OR. L.HETLING
       SYSTEMS ANALYST-PROGRAMMER- R.E.BUNCF
 STORAGE ALLOCATION-MAIN PROGRAM
 DOUBLE  PRECISION DATRUNJ4),USER(4)tTITLE!12)
 COMMON/DATUSE/DATRUN,USER,IPAGE
 COMMON/CONTRL/TITLE,NCASESfNSECTS,IMAT,INDEXI8),KK,ISPEC,IMAX,ITP(
12},CFQ,CFLEN,CFKfCFL,CFAREA,CFVOL,CFP
 COMMON/AWORKS/KCON(3),CVAL(30),TP(40),TP1(4P)
 COMMON/8WORKS/ABLOCK(3600),CCTNI 1600)
 NAMELIST/CF/NSECTS.IMAT.INDEX,ITP,CFQ,CFLEN,CFK,CFL.CFAREA,CFV9L,C
1FP











ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN



ISN
ISN
ISN
I-SN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN











0008
0009
0010
0011
0012
0013
0014
0015
0016



0017
0018
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
0029
C
C
C
C
C
C
C
C
C
C
C









C
C
C














CONTROL INFORMATION

TITLE-72ALPHANUMERIC CHARACTERS
NCASES - NUMBER OF RUNS FOR PRODUCTION CONTROL CARD
DATRUN - DATE FOR THE COMPUTER RUN CONTROL CARD
USER - NAME OF THE PROGRAM USER CONTROL CARD
TITLE - INFORMATION FOR THE HEADING CONTROL CARD

DATA INPUT-CONTROL INFORMATION AND HEADING OUTPUT DATA

CALL TIMEIN
ICTN=l
READ (5,100) NCASES
READ (5,150) (DATRUNU ),!=!, 4)
READ (5,150) (USER(I),I=1,4)
6 READ (5,200) ( TITLE U ) , I = I , 1 2)
WRITE (6,250)
WRITE (6, 300) (TITLF( I ) , I = 1 , 1 2 ) , ( DATRUNC I ) , I = 1 ,4) , ( USER( I ) ,
READ (5,CF)

INITIALIZE CORE

DO 10 J=l,3
10 KCON
-------

-------
ISN 0030
ISN 0031
ISN 0032
ISN 0034
ISN 0035
ISN 0036
ISN 0037
ISN 0038
ISN 0039
ISN 0041
ISN 0043
ISN 0044
ISN 0045
ISN 0047
ISN 0048
ISN 0049
ISN 0050
ISN 0051
ISN 0052
ISN 0053
ISN 0054
ISN 0055
ISN 0056

ISN 0057
ISN 0058
ISN 0059
ISN 0060
ISN 0061
ISN 0062
ISN 0063
ISN 0064
ISN 0065
ISN 0066
 40
 50
 60

 70

 80

100
150
200
250
    WRITE (6,550) INDEX(5),INDEX(6),INDEX(7),INPEX(8)
    WRITE (6,650) CFQ,CFLEN,CFK,CFL,CFAREA,CFVOLtCFP
    IFUTP(2).EQ.l) CALL POLYB
    CALL PRELIM
    CALL PRECAL
    CALL INVERT
    CALL SCAVEC
IF (IMAT.EQ.3) GO TO 60
IF (ICTN.EQ.NCASES) GO TO  80
ICTN=ICTN-H
GO TO 6
IF (KK.EQ.2) GO TO 70
GO TO 40
CALL FINAL
GO TO 50
REWIND
REWIND
FORMAT
FORMAT
FORMAT
FORMAT
           2
           4
           ( 13)
           (4A6)
           (12A6)
           <1HI///////////////44X,49(1H*)/44X,49H
                                                /53X,36HSTEADY  STATE  SEGMENTED FSTUARV
                                         .12A6/16X18HDATE  Op  RUN
   1 ALTANTIC REGION
   2 MODEL/44X,49(1H*)//////////1
300 FORMAT <1HO,15X18HPROBLEM TITLE
   1,4A6/16X8HENGINEER,7X,3H*   ,4A6)
350 FORMAT U2,1 2, 812,21 2)
400 FORMAT (1H1,12A6,2X,4A6 , 2X5HPAGE  ,I2///)
450 FORMAT (1H ,26X20HPROGRAM CASE CONTROLf/i18X30HNUMBFR OF FSTUAPINf
   1 SECTIONS= .I2//18X34HMATRIX CASE  BEING  CONS IDEPFP=I MAT = 112/2lX?3H
   2WHERE= IMAT=l  A MATRIX/28X16HIMAT=?   B  MATPIX/28X22HIMAT=3  A ANH
   3 B MATRIX//18X38HPRINTING INDEX OPTIONS    IF  INDEX(N ) = 1/21X23HFOR
   4THIS CASE lNOEXm = ,I2,2X,22HALPHA  A  MATRIX  INVERSE)
500 FORMAT (1H ,34X,9HINDEX<2)=,12,2X24HALPHA  A  MATRIX  INVERSE  L/35X,9
   1HINDEX(3)=,I2,2X,22HALPHA R  MATRIX  INVERSE/35X,9HINDEX<4)=,I 2,?X,2
   24HALPHA B MATRIX INVERSE F)
550 FORMAT <1H ,34X,9HINOEXC5) = ,I 2,2X24HALPHA  B  A  MATRIX  INVEPSF/35X,9
   1HINDEX(6)=,I2,2X,70HALPHA B  A MATRIX  INVERSE  TIMES  ELEMENTS VO(I)
   2FORMES ON MATRIX COLLJMNS/3SX ,9H I NDEX ( 7) =  12, 2X , 3 1HALPHA  9  A MATRIX
   3 INVERSE VOL /35X,9HINDEX(8)=,I 2,2X,69HDISOXS  + ALPHA  B  MATRIX
   4INVERSE F - ALPHA B A  MATRIX INVERSE  VOL   ///)
600 FORMAT I1H ,18X68HTHE  CONTROL VALUE ITP  ALLOWS  COMPUTATION  BY POLY
   1NOMIAL APPROXIMATION/19X66HFOR THE  VECTORS  *  REAERAT I ON,DECAY,AND
   2DISSOLVED OXYGEN SATURATION//35X55HIF  ITP(2)  IS  SET  EQUAL  TO  I THF
   3POLYNOMIALS ARE EMPLOYED/35X51HIF  ITP1)  IS  SET  EQUAL TO 1  TFMPEHA
   4TURE DATA MAY 8E/35X61HENTEREO IN  DEGREES  FAHRENHEIT  FOR  THF  PDLVNJ
  50MIAL CQMPUTATIONS//35X22HFOR THIS  CASE ITP(Z1)=,I2/49X,7HITP(2.=,I
   62)
650 FORMAT (1H ,////I8X42HCONVFRSION  FACTORS  USED  ON  INPUT VARIABLFS/2
   19X,8HCFQ    =,F6.2/29X,8HCFLEN  =,F6.2/29X,PHCFK     =,F6.2/29X,8HT
   2FL    =, F6.2/29X.8HCFAREA =,F6.2/29X,8HCFVOL   =,F6.2/29X,8HCFP
   3 =,F6.2//)
    CALL TIMEDIO)
    STOP
    END

-------

-------
ISN 0002
ISN 0003
ISN 0004

ISN 0005
ISN 0006
ISN 0007
ISN 0008
ISN 0009
ISN 0010
ISN 0011
ISN 0012
ISN 0013
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0020
ISN 0021
ISN 0022
ISN 0023
ISN 0024
ISN 0025
ISM 0026
ISN 0027
ISN 0028
ISN 0029
ISN 0030
ISN 0031
ISN 0033
ISN 0034
ISN 0035
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
   SUBROUTINE PQLYB

   STORAGE ALLOCATION

   DOUBLE PRECISION DATRUNJ 4) , USER< 4) , TITLF < 12 )
   COMMON/CONTRL/TITLE,NCASES,NSECTS,IMAT,TNDEX(8),KK,ISPFC,IMAX,
  lITPf 2),BC{7)
   COVIMON/DATUSE/DATRUN,USFR,IPAGE
   COyMON/AWORKS/Kp,KD,KC,CR(n),CO( 10)tCC(10),Tp(40),TPl(41)
   COMMON/BWORKS/AMATRX(40,40) ,RPAERK(40),AOVECC(40),DPSKSR(
-------

-------
ISN 0036
ISN 0037
ISN 0038
ISN 0039
ISN 0040
ISN 0041

ISN 0042

ISN 0043

ISN 0044
ISN 0045
ISN 0046
    WRITE (6,150) KR,(CR(I),1=1,MR)
    WRITE (6,200) KD,(CD(I),I=1,MO)
    WRITE (6,250) KC,(CC(I),1=1,MC)
    WRITE (6,300) ( I,REAERK(I),DECAYK(I),DISOXSm,TP< I),I = 1,I
100 FORMAT (1H1,12A6,2X,4A6,2X5HPAGE  ,I2///)
150 FORMAT (1H ,18X55HPOLYNOMIAL  POWER  AND  COEFFICIENTS  FOR  REAEPATIQN
   I VALUES//27X3HKR=,I?,16X2HCD/(40X,E15.8))
200 FORMAT <1HO,18X50HPOLYNOMIAL  POWER  AND  COEFFICIENTS  FPR  DECAY VALU
   1ES//27X3HKD=,I2,16X2HCD/(40X,E15,8))
250 FORMAT (1HO,18X65HPOLYNOMIAL  POWER  AND  COEFFICIENTS  FOR  DISSOLVE0
   10XYGEN SATURATION//27X3HKC=,I2,16X2HCC/(40X,E15.8))
300 FORMAT (1H ,///l8X45HCOMPUTEO VALUES  FROM  THE  POLYNOMIAL EQUATIONS
   1//18X2H I,7X10HREAERATION,12X5HDECAY,3X14HD.O.SAT(JRATION,6XI!HTEMP
   2ERATURE/18X19H              VALUES,11X6HVALUES,11X6HVALUES,11X6HVAL
   3UES//I18XI2,4XE13.6,4XE13.6,4XE13.6,4XE13.6))
    RETURN
    END

-------

-------
ISN 0002
ISN 0003
ISN 0004
ISN 0005
             C
             c
             C
ISN
ISN
0006
0007
ISN 0008
ISN 0009
ISN 0010
ISN 0011
ISN 0012
ISN 0013
ISN 0014
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0020
ISN 0021
ISN 0022
ISN 0024
ISN 0025
ISN 0026
ISN 0027
ISN 0028
ISN 0029
ISN 0030
I.SN 0031
ISN 0032
ISN 0033
ISN 0034
ISN 0035
ISN 0036
ISN 0037
ISN 0038
ISN 0039
ISN 0040
ISN 0042
             C
             C
             C
             c
             c
             c
   SUBROUTINE PRELIM

   STORAGE ALLOCATION

   DOUBLE PRECISION DATRUNC4),USER(4),TITLE(12)
   COMMON/DATUSE/DATRUN,USER, I PAGE
   COMMDN/CONTRL/TITLE,NCASES,NSECTS,I MAT,INDEX(P),KK,ISPFC,IAX,
  1ITPI2),BC(7)
   COMMON/AWQRKS/KR,Kn,KC,CRUO),CD(lQ) ,CC(10),TP40),TP1(40)
   COMMON/BWORKS/AMATRX<40,40),REAERK(40),ADVECO(40 ) ,DOSKSRl40),
  10(40),ALENTH(40) , AFTSEC<40) , AOJL ( 40 ) , TUP FX{ 40 ) , R AT IOL< 40) ,V'FCTnR{
  240),AWASTE(1000),ASTORE(40) ,AD IAG(40),PDIAGI40),AUPPER(401 . OTTUM(
  340),DISOXSl40),ULBOa<40),VOLUME(40),DECAYK(40),VDl40),UVT<40),ARCA
  4(40),SUMER(40).CFINAL<40),SUMVEC(40),CCTNf1600)
   DIMENSION QJ40),L(40),P(40),LENGTH(40), VHH40)
   REAL L,LENGTH
   EQUIVALENCE (Q,ADVECO,(ULBOO,L),(OOSK^R,P),(ALFNTH,LENGTH),(VOLUM
  IE,VOL)

   NAMELIST FOR INPUT DATA

   NAMELIST/RIVER/Q,L,P,VOLtAREA,niFFCQ,LENGTH
   NAMELIST/RIVTO/DISOXS,REAERK,r)ECAYK
   NAMELIST/GOGO/TP1
   IF  (ITP(2).EQ.l) GO TO  5
   READ 15,GOGO)
   DO 4 I=1,NSECTS
 4 TP(I)=TP1(I)
 5 CONTINUE
   READ (5,RIVER)
   CALL PRECFM
   IF(ITP(2J.EQ.1) GO TO 10
   READ (5,RIVTO)
10 IMAX = NSECTS + 2
   CONST= 2.*15280.0**2)
   DO 20 1=1,IMAX
20 ALENTH(I)=ALENTHtI)*5280.
   IMAX=IMAX - 1
   DO 30 1=1,IMAX
   AFTSECtI)=ADVECO(I)
   AOVECQ(I) = 36400.*ADVFCQ(I)
   ADJL(I)   = ALENTH(I) -  ALENTH(I-H)
30 TURBEX(I) = ((OIFFCO(I )* ( AR EA{ I)/AOJL ( I ) ) )*CON'ST)

   PREPARATION OF  THE RATIOL  VALUES

   RATIOLf!)=(!.0-0.5*TURPEX(1)/ADVECQ<1))  
   1 = 2
40 AKK=TURBEX(I-1)/ADVECQ(I-1)
   AJJ=TURBEX(I)/ADVECQ(I)
   AII = IALENTH( I-1 ) /
-------

-------
rsN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0043
0045
0046
0047
0049
0050
0051
0052
0053
ISN 0054
ISN 0055
ISN 0056
ISN 0057
ISN 0058
ISN 0059
ISN 0060
ISN 0061
ISN 0063
ISN 0064
ISN 0065
ISN 0066
ISN 0068
ISN 0069
ISN 0070
ISN 0071
ISN 0073
ISN 0074
ISN 0075
ISN 0076
ISN 0077
ISN 0078
ISN 0079
ISN 0080
ISN 0081
ISN 0082
ISN 0083
ISN 0084
ISN 0085
ISN 0086
ISN 0087
ISN 0088
ISN 0089
ISN 0091
ISN 0092
             C
             c
             C
             c
             c
             c
 50 IF(RATIOL(I).GE.AII) GO TO 60
    RATIOL(I)=AII
 60 CONTINUE
    IFII.6Q.IMAX) GO TO 80
    1 = 1*1
    GO TO 40
 70 RATIOUI) = 1.0-AJJ+.01
    GO TO 50
 80 RATIOL(IMAX)=0.5

    PREPARATION OF THE DIAGONAL MATRIX ELEMENTS

    DO 90 1=2,NSECTS
 90 BOTTUNII-1)=(-1.0*< (ADVECQ( 1 )*RATIOL (I )+TURBEX( I)) ))
    ISPEC = NSECTS - 1
    DO 100 I=ltISPEC
100 AUPPER , I SEC, VOLUME ( J ) , ALENTH ( I )
               IF( ISEC.EQ. NSECTS) GC TO 560
               GO TO 550
           560 ISEC=ISEC+1

-------

-------
ISN 0093
WRITE (6,503)  ISFC,ALFNTHJISEC)



ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN

ISN
ISN
ISN
ISN



ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN

ISN
ISN
ISN
ISN




ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN



0094
0095
0096
0097
0098
0099
0100
0101
0102
0103

0104
0106
0107
0108



0109
0110
0111
0112
0113
0114
0115
0116
0117
0118

0119
0121
0122
0123




0124
0126
0128
0129
0130
0131
0132
0133
0134
0136
0137
0138
0139
C
C HYDRAULIC-LOAD OUTPUT - DESIGNED AS UNIT
C
IPAGF=IPAGE + I
WRITE (6,1) (TITLF( I).I = 1,12) .(OATRUNU ),I=1,4), IPAO
WRITE (6,600)
1 = 1
J = l
ISFC=0
WRITE (6,601) ISFC, I,DIFFCOm,AFTSFC(I )
650 ISEC=ISEC+1
1 = 1 + 1
WRITE (6,602) J , TP< J ) , UL B00( J ) ,OOSKSR(J) , I S FC , I , DIFFCO< I), APTSEC( I
1)
IF( J.EQ.NSECTS) GO TO 660
J=J + 1
GO TO 650
660 CONTINUE
C
C COMPUTED SYSTEM PARAMETERS
C
IPAGE=IPAGE+1
WRITE (6,1) (TITLFU ),! = !, 12) ,(DATRIJN( I ),! = !, 4), IPAGE
WRITE (6,700)
1 = 1
J=l
ISEC=0
WRITE (6,701) ISEC, I , R AT IOL ( I ) , TURBEX( I ),AOVFCQ( I)
750 ISEC=ISEC+1
1=1 + 1
WRITE (6,70?) J,REAERK( J) , DEC AYK  J ) , D I SPXS ( J ) , I ST , I , R AT IOL ( T ) , TIP
1BEX( I) ,AOVEC3(I )
IF( J.EQ.NSECTS) GO TO 760
J = J + 1
G?0 TO 750
760 CONTINUE
C
C MATRIX FLtMENT OUTPUT DATA
C
C
IF( IMAT.EQ.l) GC, TO 800
IF< IMAT.EU.2) GO TQ 830
800 I PAGE= IPAGE+ 1
WRITE 16,1) (TITLE! I I ,1=1 ,12),( DATRUNI I ), 1=1,4) , IPAGF
WRITE (6,901)
1 = 1
J = 2
810 WRITE (6,802) I , I , A DI AG ( I ) , I , J , AUPPER ( I ) , J , I , POT TOM ( I )
(F( J.EQ.NSECTS) GO TO 820
1 = 1 + 1
J = J + l
GO TO 810
820 WRITE (6,805) J,J,ADIAG(J)

-------

-------
ISN 0140
ISN 0142
ISN 0143
ISN 0144
ISN 0145
ISN 0146
ISN 0147
ISN 0148
ISN 0150
ISN 0151
ISN 0152
ISN 0153
ISN 0154
ISN 0155
ISN 0156
ISN 0157
ISN 0158
ISN 0159
ISN 0160
ISN 0161

ISN 0162
ISN 0163
ISN 0164

ISN 0165
ISN 0166

ISN 0167


ISN 0168

ISN 0169
ISN 0170
ISN 0171
ISN 0172
830
840
850
  1
500
IFUMAT.NE.3) GO TO 850
IPAGE=IPAGE-H
WRITE (6,1)  (TITLE(I),I=1,12),(DATRUNU),!=!,4),IPAGE
WRITE (6,803)
1 = 1
J = 2
WRITE (6,804) IfI,BOIAGlI),I,J,AUPPER(I),J,I,BOTTUM(I)
IF(J.EQ.NSECTS) GO TO 850
1 = 1*1
GO TO 840
WRITE C6,806)  J,JTBDIAG(J)
FORMAT ( lHl,12A6,2X4A6,2X5Ht>AGE
FORMAT (1HO,42X39HG E 0  M F. T R
                                      I2///)
                                     I C
1
502
503
600
       (1H
       (1H
       ( 1H
                             AREA
                     LENGTH/13X86HNUMBER
                            CU.FT.)
               ,10XI2,2X1H-,2XI2,11XF10.
               , 10X12,2X1H-,2X12,11XF10
               ,53X12,34XFll.ll
               .29X53HH YDRAULIC
                                  T
                                    K
N P U T
 SECTION
                                                       DAT
                    A///11X89H
                          VOLU
               (SO.FT)
         (FT.)//)
0, 13X12,34XFH.1)
0,13XI2,I4XF13.6,7XF11.I)
          A 0  INPUT  D
                          p
             0/lX,108HNUMBrP
                    NUMBER
   1INTERFACE
   2ME
   3   NUMBER
501 FORMAT (1H
    FORMAT
    FORMAT
    FORMAT (1H , 29X53HH YDRAULIC   AND   LO
   1A T A///1X.103HSECTION        T               J
   2            INTERFACE
   3      (DEC C)       (LBS/DAY)           (LBS/DAY)
   4      (SQ.MI/DAY)         (CU.FT/SEC)//)
601 FORMAT (1H ,63X12,3H -  ,I 2,6XE13.6,6XE13.6)
602 FORMAT ( 1H ,2XI 2,6XF8.3,6XF13.6,6XE I 3.6,7X12,3H -  ,I 2,6XE13.6,6XF1
   13.6)
700 FORMAT (1H .43X49HC OMPUTEO   SYSTFM  PARAMETER
   1S//5X7HSECTION,9X1HR,IOX1HD,10X10HSATURATION,9X9HINTERFACF,13X2HXI
   2,12XIHE,15XIHQ/5X6HNUMBER,7X6H
-------

-------
ISN
ISN
ISN
0002
0003
0004
ISN 0005
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0006
0007
0008
0009
0010
0011
0012
0014
0016
0017
0018
0019
0020
0021
0022
  SUBROUTINE PRECAL
  DOUBLE PRECISION DATRUN(4),USE(4),TITLF{1?)
  COMMCN/CONTRL/TITLE.NCASFS.NSEfTS,IMAT,INDFX(2),BC(7)
  COMMON/8WORKS/AMATRX(40,40).REAcRKf ^0),ADVFCC(40),OPSKSR(40>,DJFFC
 10(40) ,ALENTH(40) , AFTSEC ( 40 )  AD JL ( 40 ) , Tin ^ EX ( 40 ) , R AT I OL ( 40 ) , VECTOR (
 240)tAWASTE(1000),ASTORE(<0) ,Ar)14G(40) .^^li^J^Ol.AIJPPFRt^O) , BOTTj^J
 340),DISOXS(40)fULBOD(40).VOLUME(40),DE^AV(40),VD(40),UVDl40),APA
 M40),SUMERUO),CFINALUO),SUMveC<40) ,CCTN( 1600)
  DO 6 I=1,NSECTS
  DO 6 J=1,NSECTS
6 AMATRXdt J)=0.0
  DO 1 I=1,ISPEC
  AMATRX (1+1,1)  = BOTTUM(I)
1 AMATRX (1,1+1)  = AUPPER(I)
  IF(IMAT.EQ.Z) GO TO 3
  IF(KK.EQ.l) GO  TO 3
  00 2 I=1,NSECTS
2 AMATRX(I,I)=ADIAG(I)
  RETURN
3 DO 4 I=1,NSECTS
4 AMATRXtI,I)=80IAG(I)
  RETURN
  END

-------

-------
ISN
ISN
ISN
ISN
0002
0003
0004
0005
ISN 0006
ISN 0007
ISN 0008
ISN 0009

ISN 0010
ISN 0012
ISN 0013
ISN 0014
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0043
ISN 0044
ISN 0045
             C
             C
             C



ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN






0020
0022
0024
0026
0027
0029
0030
0031
0032
0034
0035
0037
0039
0040
0042



C
C
C















C
C
C
                                                                               IMA*,
             C
             C
             C
   SUBROUTINE  SCAVEC
   DOUBLE PRECISION OATRIJN ( 4 ) , USER ( 4 ) , TI TL E ( 1 2 J
   COMMON/DATUSE/DATRUN,USER,IPAGF
   COMMON /CONTRL/TITLE|NCASESNS EC TS, I'lAT , I NTEX ( o ) , K< , I
  1IT0(2) ,BC<7)
   COMMQN/P,hlQBKS/AMATI'X(40,40),PEAERK(40),ADVFC1(40),DnS><,SR(40),njFFr.
  10(40) ,ALFNTH(40) , AFT SEC (40) , AOJL( 40) ,TUCREX(40) , RATIOL (40) ,V?CT1J(
  240),AWASTE(1000),ASTPRE(40),ATIAG(40),RDIAG(^0),AUPPE':M40),Rr'TTUM(
  340) ,0150X5(40) ,ULRnO( 40) .VOLUME (43) , DEC AVK< 40) ,Vr)( 40), UVOf 40) ,AOC-
  4(40) , SUME(40) ,CF IN Ail 40) ,SUMVEC<40) ,CCTN1600)
   DIMENSION Q( tO) ,L(40) , (40) , LENGTH) 40) , VOL (40)
   REAL  L.LFNGTH
   EQUIVALENCE  ( 0 , ADVECO ) , I ULBQO , L ) , i OOSK ^R , P ) , ( A I. ENTH , L FNGTH )
  IE, VOL)
   IF (KK.NF.l) GO  TO  1
   WRITE (4) UAMATRXU ,JJ ,I=1,NSECT5) ,J=1 ,NS=CTS)
 1 READ  (2>  (VECTOP(I) ,I=1,NSECTS)
   00 2  J=1,NSECTS
 2 SUMVECU) =  0.0

   CONSTANT  ALPHA  TIMES  MATRIX INVERSE

   ALPHA =  1.6F+4
   DO 3  I=1,NSECTS
   DO 3  J=1,NSECTS
 3 AMATRX1I,J)= ALPHA  *  AMATRX(I,J)

   PRINTING  OPTION  ALPHA  INVERSE

   IF I  IMAT.EQ.3)  GO  TO  6
 4 IF UNDEX< D.EQ.l)  GO  TO  R
 5 If (INOEXO).EQ.l)  GO  TO  9
   GO TO 11
 6 IF (KK.EQ.O) GO  TO  7
   GO TO 4
 7 WRITE (4) (AMATRX(I,J) ,I = 1,NSFCTS) ,J=1,NSECTS)
   GO TO 4
 8 IF (  KK.EQ.O)  CALL  PRTMAT
   GO TO 5
 9 IF UMAT.EQ.2)  CALL PRTMAT
   IjF (IMAT.EQ.3)  GO TO  10
   GO TO 11
10 IF JKK.EQ.l) CALL PRTMAT
11 CONTINUE

   ALPHA TIMES  MATRIX  INVERSE  TIMES VECTOR

   DO 12 I=1,NSECTS
   DO 12 J=1,NSECTS
12 SUMVEC(I) =  SUMVEC(I)  + VECTOR! J ) *AMATRX ( I , J )

   PRINTING  OPTION  ALPHA  * MATRIX INVERSE  *  VECTOR

-------

-------
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0046
0048
0050
0051
0053
0054
0056
0058
0059
0060
0061
0062
0063
0064
0065
0066
0067
0068
0069
0071
0972
0073
ISN 0074

ISN 0075
ISN 0076
ISN 0077
   IF ,(OATRUN< I),! = l,4) ,
   WRITE (6,51)
   WRITE (6,53) II ,SUMVEC(I ),!=!,NSECTS)
   GO TO 13
17 IPAGE=IPAGE+l
   WRITE (6,50) (TITLEII)tl=l,l?) ,
-------

-------
ISN 0002
ISN 0003
ISN 0004
ISN 0005

ISN 0006
ISN 0007
ISN 0008
ISN 0009
ISN 0010
ISN 0011
ISN 0012
ISN 0013
ISN 0014
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0020
ISN 0021
ISN 0022
ISN 0023
ISN 0024
ISN 0025
ISN 0026
ISN 0027
ISN 0028
ISN 0030
ISN 0031
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
  SUBROUTINE FINAL
  DOUBLE PRECISION DATRUN(4),USER(4),TITLEC 12)
  COMMON/DATUSE/DATRUN,USER,IPAGE
  COMMON/CONTRL/TITLE,NCASES,NSECTS,IMAT,INDEX<8),KK,ISPEC.IMAX,
 1ITP(2),BCI7)
  COMMON/BWORKS/AMATRX(40,40),BMATRX(40,401,01SOXSC40),ULBOD(40),VOL
 1UME(40),DECAYK(40>,VDf40),UVD(40),AREA!40),SUMERI40),CFINAL(40),SU
 2MVEC(40),CCTN(40t40)
  DIMENSION L(40),VOL(40)
  REAL L
  EQUIVALENCE (ULBOD,L),(VOLUME,VOL)
  REWIND 2
  REWIND 4

  READ IN BINARY MATRIX DATA ALPHA  A-INVFPSE  AND
  B-INVERSE MATRIX, READ IN VECTORS  ULBQD,DISOXS
  ,VOLUME AND DECAYK
  READ
  READ
  READ
  READ
  READ
  READ
  READ
(4)
(4)
(2)
(2)
(2)
(21
(2)
( (AMATRX(I,J) ,I=1,NSFCTS),J=1,NSECTS)
((BMATRXU,J),I=l,NSECTS),J=1,NSECTS)
(ULBODU ),I=1,NSECTS)

(DlSOXSCI)tI=1,NSECTS)
(VOLUME*I),I=1,NSECTS)
(DECAYKU),I=1,NSECTS)
ISN 0032
ISN 0033
ISN 0034
  COMPUTE THE PRODUCT MATRIX WHICH  IS  EQUAL  TO  THE
  ALPHA A INVERSE MATRIX TIMES B  INVERSE  MATHIX.
  PRINT OUT PRODUCT RESULTS ON INDPSI5) OPTION

  DO 1 I=1,NSECTS
  00 1 J=1,NSECTS
  CCTNfI,J)=0.0
  DO  I IK=1,NSECTS
1 CCTNd ,J)=CCTN(I, J)--BMATRX{ I,IK)*AM4TRX(IK,J)
  DO 3 I=1,NSECTS
  DO 3 J=1,NSECTS
  BMATRXlI,J)=AMATRX(I,J)
3 AMATRX(I,J)=CCTN(IJ)
  IF( INDEX(5).EQ.1) CALL PRTMAT

  COMPUTE THE VOLUME-DECAYK VECTOR  PRODUCT  AS VO

  DO 2 I=1,NSECTS
2 VD(I)=VOLUME(I)*DFCAYK(I)

  FORM SPECIAL MATRIX-EACH ELEMENT  OF  VO  VFCTP"
  IS MULTIPLIED  TIMES COLUMN OF AMATRX,PRIOR TO
  THIS THE AMATPX IS SAVED IN BMATRX.

  DO 4 J=1,NSECTS
  DO 4 I=1,NSECTS
4 AMATRX(I,J)=VO(J)*AMATRX(I,J)

-------

-------
ISN 0035
ISN 0037
ISN 0038
ISN 0039
ISN 0040
ISN 0041
ISN 0042
ISN 0044
ISN 0045
ISN 0046
ISN 0047
ISN 0048
ISN 0049
ISN 0050
ISN 0052
ISN 0053
ISN 0054
ISN 0055
ISN 0056
ISN 0057
ISN 0058
ISN 0059
ISN 0060
ISN 0061
ISN 0062
             C
             C
             C
             C
             C
             C
             C
             C
             C
             C
    IFfINDEX(6).EQ.l) CALL PRTMAT

    FORM THE ULBOD VOLUME DECAY VECTOR + AREA VECTOR

    DO 5 I=1,NSECTS
  5 UVDCI)=ULBOD(I)

    FORM THE ALPHA A INVERSE 8 INVERSE ULBOD VOLUMF DFCAYK PRODUCT

    DO 6 I=1,NSECTS
    DO 6 J=1,NSECTS
  6 SUMERU ) = SUMER(I)+UVD( J)*AMATRXU , J )
    IF(INDEXm.EQ.l) GO TO 7
    GO TO 8
  7 WRITE 16,100) JTITLE(I),I = l,12)f (DATRUNU) ,1 = 1,4), IPAGE
    WRITE (6,150) ( I,SUMERU),I = 1,NSECTS)


    OISOXS + ALPHA B INVERSE F - ALPHA A B INVERSF L V D A

  8 CONTINUE
    DO 11 I=1,NSECTS
 11 CFINAL(I)= DISOXSU) + SUMVECU) - SUMFP(I)
    IF 
-------

-------
ISN 0002
ISN 0003
ISN 0004
ISN 0005

ISN 0006
ISN 0007
ISN 0008
ISN 0009
ISN 0010
ISN 0011
ISN 0012
ISN 0013
ISN 0014
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0020
fSN 0021
ISN 0022
ISN 0023
ISN 0024
ISN 0025
ISN 0026
ISN 0027
ISN 0028
ISN 0029
ISN 0030
ISN 0031
ISN 0032
ISN 0033
  SUBROUTINE INVERT
  DOUBLE PRECISION DATPUNt4),USPC(4),TITLF(1?)
  COMMON /DATUSE/OATR.UM, USER, I PAGF
 1ITP12) ,BC(7)
  COMMON/BWDRKS/AMATPX<40,40),AWASTE2000}
  DIMENSION PA(50), D(50),QAC50) ,S(50) , T<50,P(50) , X(SO)
  DO 1 I =1,NSECTS
  DU) = AMATRXU ,1 )
  MA = NSECTS - 1
  00 2 1=1,MA
  11=1+1
  QA(I)=AMATRX(I,II )
 ! PA(I)=AMATRX(II,I )
  DO 3 K =1,NSECTS
 t B(K)=0.0
  DO 7 K =1,NSECTS
  B(K)=1.0
  DO 4 I =2,NSECTS
  J = I-1
  S(I)=D(I)-PA(J)*QA(J)/S(J)
4 T(I)=B(I)-PA(J)*T(J)/S(J)
  X(NSECTS) = TINSECTS)/S(NSECTS)
  DO 5 I=1MA
  LL = NSECTS - I
5 X(LL) = mLL)-QA(LL)*X(LL+l) )/S(LL)
  DO 6 I=1,NSECTS
6 AMATRXd,K) = X(I J
7 B(K)=0.0
  RETURN
  END

-------

-------
ISN 0002
ISN 0003
ISN 0004
ISN 0005

ISN 0006
ISN 0007
ISN 0008
ISN 0009
ISN 0010
ISN 0011
ISN 0013
ISN 0014
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0020
ISN 0021
ISN 0022
ISN 0023
ISN 0024
ISN 0026
ISN 0027
ISN 0029
ISN 0030
ISN 0031
ISN 0032
ISN 0033
                                         ( 12 )
                                                     1 5 .
   SUBROUTINE
   DOUBLE PRECISION DATPUNf 4) , US ER ( 4 ) , T I Tl
   COMMON/DATUSE/DATRUN,USE,IPAGE
   CO"4MCN/CONTRL/TITLE,NCASES, N SECTS, FIAT, I NOF x ( t ) , 
-------

-------
ISN 0002
ISN 0003
ISN 0004

ISN 0005

ISN 0006
ISN 0007
ISN 0008

ISN 0009
ISN 0010
ISN 0011
ISN 0012
ISN 0013
ISN 001*
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0020
ISN 0021
ISN0022
  SUBROUTINE  PRFCFM
  DOUBLE  PRECISION DATRUN(4),USER(4),TITLF(1?1
  COMMON/CONTRL/TITLE,NCASES,NSECTS,IMAT,INDEX(S),KK,TSPeC,I WAX,
 1ITP(2),CFQ,CFLEN,CFK,CFL,CFAREA,CFVOL,CFP
  COMMON/BWORKS/AA(1640),ADVECQC40),DOSKSP(40),PIFFCO(40),ALENTH
 1,BB(480),ULBOD(40),VOLUME(40),ABl120),AREA(^0),AC(1720)
  DIMENSION 0(40),L(40),P{40),LENGTH(40),VOL(40)
  REAL  L,LENGTH
  EQUIVALENCE  (Q,ADVECQ),(ULBODtL),(OOSKSR,P),(ALENTH,LENGTH),(VOLUM
 IE,VOL)
  DO 1  J=I,NSECTS
  OOSKSR(J)=CFP *OOSKSR(J)
  VOLUME(J)=CFVOL*VOLUME(J)
.  ULBOO(J) =CFL*ULBOO(J)
  IMAX=NSECTS+1
  DO 2  K=I,IMAX
  ADVECQ(K)=CFQ*ADVECQ(K)
  DIFFCO(K)=CFK*DIFFCO(K)
!  AREA(K)=CFAREA*AREA(K)
  IMAX=IMAX-H
  DO 3  I=1,IMAX
>  ALENTH{I)=CFLEN*ALENTH(I)
  RETURN
  END

-------

-------
APPENDIX   III
    3AMPLL INPUTS

-------

-------
  7
 11/1/67
NAPE TF THE  PRCGRA!" USER   RONALD  BUNCE
N/.wf CF TFE  ff.SFLARY BEING IMESTIGATEC
 $CF
 f*SrCTS=14,
 f w/\T=:^,
 IM:F->=J!* i ,
 ITP=?C,
 (. F C == 1  
 CFlfEH=l. ,
 CFK=1. ,
 C F L= 1 . ,
 CFVC1=1. ,
 rFt- = l.,
 $rKD
 ifcsc
 JflHLA=13F^,A*1325C,1210C,lAOOC, 13C5C, 12100,12680, 14200,4*14400,
 C I FFCG=C.O,C.1?,C. 14, 0.15,0.16, 0.16,0.17,0.1 8, C.I 9, 0.20, 2*0.2 1,3*0.23,
 lFN61H=C.3,15*l.r,
 |E^r)
 $HIVTG
 P ISO>S=6a7.92,3*7.77,5*7.63,
 CECAYK=6*C.46,3C.49,5*C.52,

-------

-------
C.*Sr M'l"R  rf  ?  N'APF  CF ESTi/AKY" HflKG INVESTIGATED
 $Cf
 ITF=2*( ,
 CFC=1.
 CFLEN=I.,
 CFK=l.t
 CFI=].,
 CFAIUA^J .
 r.FVOL=l.,
 I;F-P=I. ,
 IGCGC
             , ] 3*1300,
 VI. L=l^r 6,^*701 6,64E6,7^t6,69E6,64E6,676,75t:6,3*76t6,
                   , 12100, 14OC,13C5C,1210C,1268Cjr 14200,
 t;fFFCC=C.C,0.12tr.l4,0.15,0.16,0.16,0.17,0.18,0.19f0.20,2*0.2130.23f
 I fcNGH-1=C.3,l5l.Cf
 $RIV70
 I-ISOXS=^*7.92
 REAF.P!< = 14O.C
 DEC A YK=6*G. 46, 3*C. 49,5*0.52,

-------

-------
     APPENDIX   IV
TYPICAL PROGRAM CASE SOLUTIONS

-------

-------
SECTION  A -SAMPLE
   INPUT  a  OUTPUT
          I MAT * I
        INDEX(I) l

-------

-------
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-------

-------
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-------

-------
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-------

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-------
             SIMULATION OF CHLORIDE CONCENTRATIONS

                     IN THE POTOMAC ESTUARY


                               BY
                                      *
                        Leo J.  Hetling
*
   Now employed as Director of Research Unit, Environmental
   Health Services, New York State Department of Health,  Qh
   Holland Avenue, Albany, New York.

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-------
                          TABLE OF CONTENTS







   I.  INTRODUCTION	   1-1




  II.  THE POTOMAC ESTUARY	II - 1




 III.  PRESENT AND FUTURE WATER SUPPLY REQUIREMENTS .... Ill - 1




  IV.  THE SEGMENTED ESTUARY MODEL	IV - 1




       The Pumping Problem	IV - 2




   V.  EVALUATION OF MODEL PARAMETERS	   V-l




       Segmentation 	   V-l




       Segment Volumes  	   V-l




       Net River Flow	   V-3




       Boundary Conditions	   V-l;




       External Sources of Chlorides  	   V - 6




       Turbulent Exchange Factor  	   V - 6




       Proportionality Factor	   V - 10




  VI.  VERIFICATION RESULTS	VI - 1




 VII.  SIMULATION	VII - 1




VIII.  DISCUSSION OF RESULTS	VIII - 1




       Validity of the Model arid Parametric Analyses  . .   .VIII - 1




       Simulation Results	VIII - 3




  IX.  CONCLUSION	IX - 1




   X.  BIBLIOGRAPHY	   X - 1

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                           LIST OF TABLES
Number                                                       Page

  1    Present and Proposed Major Waste Water
         Discharges to the Upper Potomac Estuary 	    II - 2
  2    Present Sources of Water Supply
         Washington Metropolitan Area  	  Ill - 2
  3    Monthly Distribution of Annual Water Usage  ....   Ill - 3
       Projected Water DemandWashington
         Metropolitan Area	Ill - h
  5    Potomac Estuary Chloride ModelPhysical
         Parameters	     V - 2
  6    Potomac Estuary Chloride ModelInterface
         Parameter	    V - 9
  7    Hydrologic Conditions Simulated 	   VII - 2

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-------
                          LIST OF FIGURES

Number

   1    Study Area Map

   2    Washington Metropolitan Area Water Supply Needs

   3    The Pumping Problem

   h    1930-1965-1966 Potomac River Hydrographs

   5    1965 Chlorides at Great Falls

   6    Relationship Between Chlorides and River Flow at Great Falls

   7    Assumed 1965 Lower Boundary Conditions

   8    Assumed 1930 Lower Boundary Conditions

   9    Potomac Estuary Chloride Model - 1965 Chlorides at
          Possum Point

  10    Potomac Estuary Chloride Model - 1965 Chlorides at
          Maryland Point

  11    Potomac Estuary Chloride Model - 1965 Chlorides
          October 8, 1965

  12    Potomac Estuary Chloride Model - 1930 Chlorides at
          Indian Head

  13    Potomac Estuary Chloride Model - 1930 River Flows
          2010 V/ater UseWaste Discharge Out of Basin

  lit    Potomac Estuary Chloride Model - 1966 River Flows 
          2010 Water Use

  15    Potomac Estuary Chloride Model - 1930 River Flows
          2010 Water UseParametric Analysis I

  16    Potomac Estuary Chloride Model - 1930 River Flows
          2010 Water UseParametric Analysis II

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                                                          I - 1






I.   INTRODUCTION




        A significant water resource problem in the Potomac River




Basin is the provision of an adequate water supply to meet the




projected needs of the rapidly growing Washington Metropolitan




Area.  The conventional approach to this problem would be the




construction of upstream reservoirs to supply the required water.




However, rapid changes in technology and state of our social-




economic outlook are forcing planners to look at an ever-enlarging




matrix of solutions to water resource problems.1  In this case,




conflicting interests are exerting significant pressure against




the construction of these reservoirs.2




        Use of the upper Potomac Estuary as a water supply source




has been proposed as an alternative to the upstream reservoirs.




This proposal has been discarded previously because waste water




treatment technology was lacking [it is projected that the rate




of waste water being discharged to the upper Estuary will increase




from its present rate of 2JO million gallons per day (rapd) to




over 800 mgd by the year 2010.], and because of uncertainty con-




cerning the possibility of salinity (chloride) intrusion from




the Chesapeake Bay if large withdrawals of fresh water from the




upper Estuary were made.  Advances in the technology of waste




water treatment are rapidly eliminating the first objection, except




for the buildup of chlorides and total dissolved solids.  The




purpose of this paper is to present the results of a simulation

-------
                                                          1-2






model of chloride concentrations in the upper Estuary.  It is




hoped that these simulation results will prove useful to water




resource planners in tnis critical area.

-------
                                                          II - 1






II.  THE POTOMAC ESTUARY




         The Potomac River is the second largest river in the




 Middle Atlantic states.  Its tidal section begins in the Washing-




 ton, D. C., Metropolitan Area at Little Falls and extends Il6




 miles southeastward to the Chesapeake Bay (Figure l).  The Estuary




 is several hundred feet in width at the head and broadens to nearly




 six miles at its mouth.  A channel with a minimum depth of 2k feet




 is maintained in the Estuary up to Washington, D. C.  Except for




 the channel and depths up to 80 feet just below Chain Bridge, the




 Estuary is relatively shallow.




         The Estuary is bounded by the large metropolitan areas of




 Washington, D. C., and Arlington and Alexandria, Virginia, in its




 upper part and by forest and farmland in the lower portion.




         Several waste water treatment plants presently discharge




 treated waste to the Estuary, and several more are projected in




 the future.  These are shown in Figure 1.  Additional information



 on these plants is given in Table 1.

-------

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II - 2




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                                                          Ill - 1






III.  PRESENT AND FUTURE WATER SUPPLY REQUIREMENTS




          The present status of the major water supply systems in




  the Washington Metropolitan Region is given in Table 2.   It can




  be seen from this table that presently 72 per cent of the area's




  water needs are supplied by the Potomac River.




          In estimating future water supply demands, the data pre-




  sented in Volume 5 of the Corps of Engineers 1962 Potomac River




  Basin Report3 was used.  The report's conclusion that in the




  future only 92 mgd would be available from sources other than




  the Potomac River was also accepted.   A more recent report*4 indi-




  cates that this is a conservative assumption, and that local




  sources other than the Potomac will provide a safe yield of 110




  mgd in 1985 and 150 mgd in 2010.




          Although more recent, possibly more exacting, demand data




  could be developed, they should not change the major conclusions




  of the simulations.




          Because of the time-dependent nature of the system, it




  was necessary to estimate the distribution of the annual demands




  by month.  An analysis of the I960 to 1965 records of the Corps




  of Engineers Washington Aqueduct  Division gave the distribution




  of filtered water pumped to the District of Columbia shown in




  Table 3.




          Using the above monthly distributions and the base data




  from the Corps of Engineers report, the water demands on the




  Potomac River shown in Table h were developed.  These data,

-------
                                                        Ill - 2


shown graphically in Figure 2, clearly indicate the need for the

development of additional supplies.
                            TABLE 2

                PRESENT SOURCES OF WATER SUPPLY

                  WASHINGTON METROPOLITAN AREA
         Water System
 Use
_(mgd)
District of Columbia

Arlington County

City of Falls Church - Fairfax
  County Water Authority

Fairfax County Water Authority

Fairfax City

Washington Suburban Sanitary
  Commission

Washington Suburban Sanitary
  Commission

Rockville City

Alexandria Water Company

Other Miscellaneous Small
  Systems

                      Sub-total

                      Sub-total
Potomac River

Potomac River


Potomac River

Wells

Goose Creek


Patuxent River


Potomac River

Potomac River

Occoquan Creek
                                Potomac River
                                Other Sources
                                                            20
                                                            11
   30


    9
 230

   90
                      Total All Systems
  320

-------

-------
                                                     Ill - 3
                         TABLE 3




        MONTHLY DISTRIBUTION OF ANNUAL WATER USAGE




                     Mean
Month
January
February
March
April
May
June
July
August
September
October
November
December
Average
Monthly
Use*
11+8.5
1U8.2
1U8.8
15^.1
168.9
189.7
206.1
20>t.7
183.9
161.9
153.2
150.6
168.2
Mean Monthly Use
Average Annual Use
0.883
0.881
0.885
0.916
l.OOU
1.128
1.225
1.21?
1.093
0.962
0.911
0.895
1.000
Mean value of filtered water pumped from I960 to 1965,

-------

-------
                                                  Ill - k
                      TABLE h




PROJECTED WATER DEMANDWASHINGTON METROPOLITAN AREA
         1985
2010
Month
January
February
March
April
May
June
July
August
September
October
November
December
Average
Annual
Gross
Demand
(mgd)
513
512
51^
532
583
655
712
707
635
559
529
520
581
Available
from Other
Sources
(mgd)
92
92
92
92
92
92
92
92
92
92
92
92
92
Net Demand
from
Potomac
River
(mgd)
k21
kzo
h22
kho
1*91
563
620
615
5^3
^67
J+37
1+28
^89
Gross
Demand
(mgd)
907
905
909
91*!
1,031
1,158
1,258
1,250
1,123
988
936
919
1,027
Available
from Other
Sources
(mgd)
92
92
92
92
92
92
92
92
92
92
92
92
92
Net Demand
from
Potomac
River
(mgd)
815
813
817
8U9
939
1,066
1,166
1,158
1,031
896
Qhk
827
935

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-------
                                                          IV - 1






IV.  THE SEGMENTED ESTUARY MODEL




         The mathematical model employed in the simulation study




 was a modification of the model developed by Thornann.5  This model




 consists of a system of "n" equations, each describing a mass




 balance of the material being studied for each of the "n" segments




 of an estuary.  For an estuary where good vertical and lateral




 mixing may be assumed, these segments are selected along the




 longitudinal axis of the estuary.




         The mass "balance over each of the segments includes terms




 describing changes in chloride concentration caused by advection,




 dispersion, and, in the case of the segment to which sewage was




 added, a chloride source.  A mass  balance constructed for the




 "i"th segment takes the form:
                                        - C-)  C.]
                 dt
              + J.
                 1




 where




         V.  = volume of "i"th segment,  cubic feet (cf)




         C.  = mean  chloride concentration in "i"th segment (ib/cf)




         Q.  = net waterflow across the  upstream boundary of the




              "i"th segment (cf/day)

-------

-------
                                                         IV - 2
        .  = a dimensionless proportionality factor used to



             estimate concentration at upper boundary of the



             "i"th segment



        E.  = turbulent exchange factor for upstream boundary of
             the "i"th segment (cf/day)



        J. = rate of chloride addition from external source
         i


             (Ib/day)



        t  = time (days)





        Since for this study 28 estuary segments were employed,



a like number of expressions similar to Equation 1 were obtained.



This system of 28 linear first order, non-homogeneous, ordinary



differential equations may be solved simultaneously by numerical



methods using a digital computer or by programming the equations



on a relatively large analog computer.6'7'8  In either case, all



terms of the equations must be known in order to simulate the



chloride concentration of each segment.





The Pumping Problem



        In simulating the future use of the upper estuary as a



source of water, it was necessary to modify the above basic model



in order to account for the transfer of relatively large quanti-



ties of water (and its chloride content) from the uppermost sec-



tion of the estuary through the city's water supply system and



back into section six of the estuary as sewage.  This transfer



is shown schematically in Figure 3.

-------

-------
                                                         IV - 3





        To handle this transfer theoretically would mean an



extension of the above model into the second dimension.   However,



a simpler approach was sought and found to be adequately accurate.



The simpler approach taken consists of the following sequence of



operations:



        1.  Integrate over a period of time, A t (normally 1 day),



            ignoring the transfers, J  and J .



        2.  Stop the integrations.



        3.  Modify the concentration in segments one and six



            according to the effect of Jn  and J,.
                                        1       b


        U.  Resume the integration over the next time period of



            time, A t, again ignoring the  flow exchanges and



            continue in this manner.





        A detailed description of the modified simulation model



and the computer program has been published.6  Although  the



computer program has the capability of distributing the  pumped



flow to different segments, it was assumed that all wastes were



discharged into segment 6.  It is projected that over 70 per cent



of the waste water will be discharged to this segment.   It did not



appear that the additional precision in the final results justi-



fied the additional office and computer time that would  have been



required to spacially redistribute the effluent.

-------

-------
                                                          V - 1
V.  EVALUATION OF MODEL PARAMETERS




Segmentation




        The size of the segments selected represents a compro-




mise betveen accuracy and computational efficiency.  In this




case the segments were made small (approximately two miles in




length) in the upper critical portion of the estuary and rela-




tively large (six miles in length) near the mouth.  The final




segmentation chosen is shown in Figure 1.






Segment Volumes (V.)




        The segment volumes were determined from the latest




(1965) U. S. Coast and Geodetic Survey navigation charts for




the Potomac Estuary which give soundings at mean low water.




The water volumes determined by planimetering these charts were




increased by an appropriate amount to give estimates of mean




tide level volumes.  Ho corrections were made for the small




deviations of the mean tidal elevations from the long term mean




values upon which the volume calculations were based.  The seg-




ment volumes used are given in Table 5.

-------

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                                                       V - 2


                         TABLE 5


   POTOMAC ESTUARY CHLORIDE MODEL - PHYSICAL PARAMETERS
                                                       *
                                                 Volume
Segment
1
2
3
1+
5
6
7
8
9
10
11
12
13
Ik
15
16
17
18
19
20
21
22
23
2k
25
26
27
28
Length
(Miles)
2.69
2.09
1.75
1.31
1.87
2.11
2.57
2.19
2.M*
2.06
2.25
3-95
2.9k
2.93
It. Ul
14.26
It. 1*2
^.57
5.36
5.20
5.69
6.00
6.00
6.00
5. HO
8.60
6.00
11.00
(Cubic Feet)
x 10?
25
21*
33
im
1+5
52
76
66
79
65
92
252
170
250
330
U5
520
535
620
525
650
I,l6o
1,593
1,957
1,620
2,165
3,055
5,655
Mean Tide Level

-------

-------
                                                          V - 3






Net River Flow (Q.)




        The term "Q." refers to the net flow into the "i"th seg-




ment from the adjacent upstream segment, i.e., the net flow across




the i-l,i or upstream boundary of the "i"th segment.




        In a dye diffusion study of the estuary,9 it was found




upon examination that the inflows to the estuary, except for the




gaged Potomac River flow and the District of Columbia waste dis-




charge, were approximately balanced by losses due to evaporation.




Therefore, in order to reduce the number of flow input functions,




Q  was taken as the gaged Potomac River flow reported for the




U. S. Geological Survey gaging station (Leiter Gage) at Washing-




ton, D. C.; Q  through Q,- were taken as the gaged River flow




minus the quantity of water pumped for water supply purposes;




and Q  through Q  were set equal to Q,- plus the sum of all the




waste water discharges.  In the simulation studies, this was




assumed to be equal to 90 per cent of the water pumped.




        The net tidal flow into and out of each segment was




assumed to be zero over a complete tidal cycle.  No considera-




tion was given to the small changes in tidal elevation and,




therefore, tidal flow which occur on succeeding days during a




lunar tidal cycle.




        Hydrographs showing the 1930, 1965, and 1966 River flows




used are given in Figure k.

-------

-------
                                                          V - U






Boundary Conditions (C  and C   )




        In order to solve the system of differential equations,




the time variation in chloride concentrations at the upper and




lower boundary must be known.




        At Great Falls approximately ten miles above the upper




boundary, there is a National Water Quality Network Station of




the Federal Water Pollution Control Administration.  Chlorides




are measured at this station at weekly intervals.  Since there




are no known sources of chlorides between the station and the




upper boundary of the model, these values were used in the veri-




fication studies.  The values measured at this station for 1965




are shown in Figure 5-  Upper boundary conditions for 1966 were




determined in a similar manner.




        No measurements of the chloride concentration of the




incoming River flow were made in 1930.  In order to construct




a 1930 upper boundary, a regression of the log River flow on




the log chloride concentration using the 1957 to 19^5 data




collected at Great Falls Water Quality Network Station was run.




This regression gave the following equation.




             Log Cl = 3.65^ - 0.712 Log Q




        A graph showing this equation is shown in Figure 6.




Daily chloride values for 1930 were calculated using the 1930




gaged flows and Equation 2.

-------

-------
                                                          V - 5






        Obtaining boundary conditions at the lower boundary




proved more difficult.  There were no regular measurements of




chlorides made at the mouth of the Potomac Estuary.  A search




of all known sources of data produced the following salinity




measurements.




        1.  Daily surface water salinity measurements were taken




by the U. S. Coast and Geodetic Survey at Fort McHenry, Baltimore,




from 191^ to the present, and at Solomons, Maryland, since 195^-10




        2.  In an atlas of salinity and temperature by Stroup and




Lynn,11 graphical summaries of the distributions of salinity in




Chesapeake Bay measured on various cruises from 1952 to 196l are




given.  Seasonal averages for the period 19^ to 196l are also




given.




        3.  In conjunction with some oyster studies, sporadic




salinity measurements were taken approximately seven miles up




from the mouth of the Potomac,12 at Bean's Pier in Smith Creek




and at Jones Shore approximately four miles above Point Lookout.




        h.  Salinity measurements were taken at the mouth of the




Potomac River by Chesapeake Bay Institute in conjunction with a




Potomac River nutrient study.






        All of the above measurements taken in 1965 are plotted




in Figure 9-  Using all of the data shown in Figure 9 the solid




line labeled "assumed 1965 boundary conditions" was drawn.




Similarly, the 1963 "to 1966 boundary conditions were determined.

-------

-------
                                                          V - 6

For 1930 only (the year of the worst drought on record), the
measurements for Baltimore Harbor were available.  Using these
values and judgment obtained from the study of the 1963 to 1966
records, the solid line marked "assumed 1930 boundary conditions"
was drawn as shown in Figure 8.  The resultant salinities were
then converted to chloride concentrations using the classical
relationship:
             S = 0.03 + 1.805 Cl
where
        S  = Salinity in parts per thousand
        Cl = Chloride concentration in parts per thousand

External Sources of Chlorides (J.)
        Since there are no major chloride producing industries
either present or planned in the Washington Metropolitan Area,
the only external source of chlorides considered in the simula-
tion is that which is added to the waste water by people.  Fair
and Geyerltf report that wastes from the human body contain from
5 to 9 grams of chloride a day.  In all of the simulation studies
made, the higher value of 9 grams per capita per day was used.
Turbulent Exchange Factor (E.)
        The turbulent exchange factor "E" is calculated for each
segment boundary from the expression:
                                K.  A.
             E. (cf/day) =
                                     Ji-l'

-------
                                                          V - 7





where the "i" subscript refers to the boundary between segments



i-1 and i, "K" is the longitudinal dispersion coefficient (analo-



gous to the classical Fickian diffusion coefficient, expressed in



areal units per day), "A" is the cross-sectional area of the



boundary plane, and "L" is the segment length.



        The above expression is based on Pick's first law of



diffusion, i.e.,




             N. (ib/sf/day) = K f^-
              1                 Q.X



where "N" is the rate of mass transfer of substance per unit area



across a boundary where the spatial gradient of the substance is



"dC/dx" ("C" is in Ibs/cf) and "K" is defined as above.



        If the mean concentration in two adjacent segments is



assumed to occur at their midpoints, and the gradient between



these midpoints is linear, it can be shown by geometry that:



                     c    - r
             dC       i-l    i
             dx ~ 0.5 (\_x + L)




        Substituting Equation 5 into Equation k gives:



                                K(C    - C. )

             N. (Ibs/sf/day) =

        Multiplying Equation 6 by the cross-sectional area across



which the turbulent exchange takes place yields the mass flow
rate "V -."
                                .

             T-,  C-IT.  /,  \    1  1
             D. (Ibs/day) =
                            A. K. (C. .,  - C. )
              .               o.3 (L. , + L. )
                                   1 ""* X    1

-------

-------
                                                          V - 8
        Substituting Equation 3 into Equation 7 yields:




             D. = E. (C. .  - C. )
              i    i   i-l    i



which is the expression used in Equation 1 to describe the mass



flow of substance across a boundary due to turbulent exchange.



        The "E" term, or more specifically "K," was the  unknown



parameter which the verification study was designed to evaluate.



The "K" term as used herein is defined as the coefficient of longi-



tudinal dispersion.  This term applied to net longitudinal mass



transport resulting not only from turbulent diffusion but also



from velocity and concentration variations in a cross-section.



The latter effect has been shown to be of greater significance



in estuary type flows.15  It has been assumed that dispersion is



analogous to Fickian diffusion with the diffusion coefficient



replaced by a dispersion coefficient.



        The values of "K" for the upper 12 boundaries were obtained



from a large-scale dye diffusion study described elsewhere.9  For



the lower 17 boundaries, initial values of "K" were first assumed



on an empirical basis.16  These values were then adjusted to obtain



good agreement of the model output with the salinity concentrations



observed in the estuary.



        A list of the values which gave the best matching between



observed and computed values is given in Table 6.  These values



were used in the simulation studies which follow.

-------

-------
                                                    v - 9
                      TABLE 6




POTOMAC ESTUARY CHLORIDE MODEL - INTERFACE PARAMETER
Interface
0-1
1-2
2-3
3-1+
4-5
5-6
6-7
7-8
8-9
9-10
10-11
11-12
12-13
13-1*1
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
22-23
23-24
24-25
25-26
26-27
27-28
28-29
Area (A. )
(Sd. Ft*)
4,610
30,000
214,300
29,000
34,300
32,700
47,600
49,900
43,600
59,000
66,500
84,900
111,000
130,000
171,000
117,000
221,000
220,000
243,000
193,000
217,000
2145,000
490,000
576,000
509,000
604,000
753,000
1,160,000
1,700,000
Longitudinal
Dispersion
Coefficient
(K )
(Sq_. Mi /day)
0.00
0.05
0.10
0.15
0.20
0.25
0.35
O.H5
0.55
0.65
0.75
0.90
1.20
1.50
1.95
2.80
3.90
5.30
6.00
6.00
6.00
6.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
Turbulent
Exchange
Factor (E. )
(Cu. Ft /day)
x 108
0.000
0.033
0.067
0.150
0.228
0.217
0.376
0.498
0.546
0.900
1.222
1.301
2.041
3-508
4.797
3.990
10.486
13.696
15.505
11.580
12.625
13.279
43.120
50.688
47.149
45-559
54.463
72.056
81.600

-------

-------
                                                         V - 10

Proportionality Factor (.)
        The proportionality factor "5" is used in the first two
terms of Equation 1 that describe tbe advective movement into and
out of a segment.  This mass movement across the i-l,i boundary
due to advection may be expressed simply as the product of the
net advective flow "Q." and the concentration at the boundary.
However, since only the average concentration of the adjacent
segments is considered in the model, the concentration at the
boundary must be calculated.  It can be shown by geometry that,
for the case of a linear gradient between the midpoints of two
adjacent segments, the concentration at the boundary is given by
the first two terms in brackets in Equation 1 where:
                      L.
                   1-1    i
Equation 9 gives a satisfactory first approximation for the pro-
portioning factor applicable to the i-l,i boundary.  To assure a
realistic solution, however, the following relationship must be
observed:
To simplify computations where "Q" was changed frequently,  the
inequality given by Equation 10 was treated as an equality.  So
long as the proportionality factor "" remains within the lower
limit defined by Equation 10 and the upper limit of unity,  the
solutions obtained by the model are relatively insensitive to
the value chosen for "."


-------

-------
                                                          VI - 1







VI.  VERIFICATION RESULTS




         Various sources of chloride data were used in the verifi-




 cation of the model.  The most significant were the data provided




 by the D. C. Department of Sanitary Engineering and by the Virginia




 Electric and Power Company's Possum Point Power Station.  The D. C.




 Department of Sanitary Engineering made bi-weekly sampling runs




 down the Estuary and also obtained daily values at Woodrow Wilson




 Bridge (12 miles downstream from Chain Bridge), while the Virginia




 Electric and Power Company runs daily chloride analyses at Possum




 Point (approximately UO miles downstream from Chain Bridge).




         As stated previously, knowing values of the river inflow




 and the boundary conditions, the values of "K" were adjusted to




 obtain good agreement of the model output with observed chloride




 concentrations.  The final results of these adjustments are shown




 in Figures 9, 10, and 11 for 1965.  Similar results were obtained




 for 1963 and 196^ using the same "K" values.




         In attempting to reproduce the 1930 conditions, only the




 results of one set of 11 grab samples could be found.17  These




 data and the computed 1930 conditions are shown in Figure 12.

-------

-------
                                                          VII - 1







VII.   SIMULATION




          With the values of "K" obtained in the verification stud-




  ies, it was possible to simulate the effects of future diversions




  into and out of the Estuary system on chloride concentration.  In




  order to investigate the question posed in the introduction and




  to examine the sensitivity of the results to the assumption made




  in formulating the model, the simulations shovn in Table 7 were




  made.  The results of these simulations are shown in Figures 13




  to 16.

-------

-------
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                                                                                       VII  - 2

-------

-------
                                                          VIII - 1







VIII.  DISCUSSION OF RESULTS




   Validity ofthe Model and Parametric Analyses




           The mathematical model utilized in this study is actually




   a numerical approximation of the partial differential equation




   which describes the temporal and spatial relationships of a con-




   servative substance in an estuary.  Two problems arise in its use




   here.




           1.  The model does not completely explain the integrated




   mechanisms which control the hydrograph of an estuary.




           2.  The lower portion of the estuary is highly stratified,




   and the assumption of vertical homogeneity is not actually valid.




           The validity of both of the above statements is strongest




   near the mouth and weakest in the upper estuary.  From an engineer-




   ing and planning standpoint, it was assumed for this study that




   since the model matched historical data with reasonable accuracy,




   it has sufficient integrity to predict future effects as long as




   the simulated conditions are reasonably similar to the verified




   conditions.




           For example, recent studies indicate that the exchange




   coefficient is not a fixed physical parameter which depends only




   on tidal velocity and geometry, but that it is a time-varying




   parameter which depends on density currents set up by chemical




   concentration (salinity) gradients.  Therefore, it must be real-




   ized that if there are drastic changes in salinity within the

-------

-------
                                                       VIII - 2







system caused by diversions, the results of the model must "be




interpreted with caution.




        The most significant case in the simulation study where




this (drastic salinity changes) occurred was the one where the




waste effluents were pumped out of the system and the chloride




concentration rose rapidly to levels never experienced in the




system during the verification studies.  In this case since the




higher chlorides would probably cause an increase in "K" and,




therefore, an increase in the rate at which the chlorides were




diffused into the upper segments of the estuary, this effect




would not change the obvious conclusions of this result.




        Another way in which the simulated condition varied sig-




nificantly from the verified condition is in the direction of




river flow in the upper segments.  Such a change might also




affect the values of "K."




        The effect of an increased turbulent exchange factor




which might be caused by the changes in the tidal and flow regimes




forced on the system in simulations were investigated by varying




the value of "K" in the upper eight segments.  The results of




this study are shown in Figure 15-  From Figure 15 it was con-




cluded that the effect of such changes, should they occur, would




not change the study conclusions.




        The effect of an error in the assumption of a. per capita




chloride contribution of 9 gm/day to the system was also checked.




This rate of chloride addition was doubled, with the results shown

-------

-------
                                                       VIII - 3






in Figure 15.  This shows that major errors in this estimate




would have only a small effect on the results.




        The effects of a large consumptive withdrawal for a short




period (e.g., as might be caused by a major conflagration) was




also investigated, and the water withdrawal rate was increased




by 50 per cent for the last 15 days of October.  None of this




increase was returned to the estuary.  This had the effect of




increasing consumptive use by a factor of six.  The results of




this simulator, also shown in Figure l6, indicate that such an




action would only increase the chloride concentration from 6l




to 6k mg/1.




        In order to check the possible cumulative effect of all




the above conditions, a final simulation run was made witn all




of the above conditions imposed.  This run, also shown in Figure




16, showed an increase in the maximum chloride concentration by




25 per cent should this occur.






Simulation Results




        The simulation results shown in Figure 13 indicate that




if the water of the upper estuary is used as a water supply source,




and the waste water is transferred out of the upper estuary,




salinity intrusion will become a significant problem.  In such




a case, provision for desalting equipment must be made.   How-




ever, if the present plans to discharge waste to the upper estuary




are carried out, the results shown in Figures 15 and l6 show that

-------

-------
                                                       VIII - k






it can be used as a source of water supply without a significant




problem of chloride buildup occurring.




        Even in the extreme event of the water use rate doubling




during a critical period, the chloride concentration of the




upper estuary did not approach the Public Health Service Standard




for drinking water of 250 mg/1.

-------

-------
                                                          IX - 1






IX.  CONCLUSIONS




         1.  The results of computations of the temporal and spa-




 tial variation in chlorides in the Potomac Estuary using the




 segmented estuary model developed by Thomann are in reasonable




 agreement with observed data.




         2.  Simulation results using this  model indicate that




 if the Washington Metropolitan Area used the upper Potomac  Estu-




 ary as an auxiliary source of  water, the chlorides in the system




 would not even begin to approach the Public Health Service  limits;




 and thus, desalting equipment  would not be required.

-------

-------
                                                           X - 1
 X.  BIBLIOGRAPHY
 1.  Davis, Robert K., "The Range of Choice in Water Resource
     Management:   A Study of the Potomac Estuary," Resources for
     the Future,  Inc., Washington, D.  C. (in press).

 2.  Fox, Irving  K., "The Potomac PuzzleIs There a Reasonable
     Solution?" Atlantic Naturalist, April-June 1962.

 3.  U.S. Army Corps  of Engineers, "Potomac River Basin Study,"
     Water Supply and Water Quality Control, Vol 5 > Prepared by
     Division of  Water Supply and Pollution Control, U.  S.  Public
     Health Service, Charlottesville,  Virginia, 1962.

 h.  Hazen, Richard, et al, "Future Water Supply,  Metropolitan
     Washington Region, Report No. 1,  Requirements and Sources,"
     Metropolitan Washington Council of Governments, Washington,
     D. C., 1967.

 5.  Thomann, Robert V., "Mathematical Model for Dissolved  Oxygen,"
     Journal of the Sanitary Engineering Division, American Society
     of Civil Engineers, Vol. 8^, No.  SA5, Proceedings Paper 3680,
     Oct. 1963, pp. 1-30.

 6.  Jeglic, John M.,  "Mathematical Simulation of the Estuarine
     Chloride Distribution," Digital Computer Technology and Pro-
     gramming Analysis Memo No. 1033,  General Electric Re-Entry
     Systems Department, Philadelphia, Pa., Feb. 196?.

 7.  Hetling, Leo J.,  and Bunce, Ronald E., "A Digital Computer
     Program for  the Steady-State Segmented Estuary Model," (in
     press).

 8.  Jeglic, John M.,  "Mathematical Simulation of the Estuarine
     Behavior," Digital Computer Technology and Programming Analysis
     Memo No. 1032, Rev, A, General Electric Re-Entry Systems
     Department,  Philadelphia, Pa., July 1967-

 9.  Hetling, Leo J.,  and O'Connell, R.  L., "A Study of Tidal Dis-
     persion in the Potomac River," Water Resources Research, Vol.
     2, No. k, Fourth  Quarter 1966, pp.  825-8U1.

10.  U. S. Department  of Commerce, "Surface Water Temperature and
     Salinity, Atlantic Coast, North and South America," Coast
     and Geodetic Survey Publication 31-1, U. S. Government Print-
     ing Office,  Washington, D. C., 1965.

-------

-------
                                                           X - 2
11.  Stroup, E.  D., and Lynn, R.  J., "Atlas of Salinity and Tem-
     perature Distributions in Chesapeake Bay 1952-1961 and
     Seasonal Averages 19^9-1961," Chesapeake Bay Institute,
     Graphical Summary Report 2,  Johns Hopkins University,
     Baltimore,  Md., Feb.  1963.

12.  Dunnington, Elgin, Private Communication, Research Biologist,
     Chesapeake  Biological Laboratory, Natural Resources Institute,
     University  of Maryland.

13.  Whaley, R.  C., Carpenter, J. H., and Baker, R.  L., "Data
     Summary Potomac River Nutrient Cruises 1965-1966," Chesapeake
     Bay Institute, Special Report 11, Johns Hopkins University,
     Baltimore,  Md., Aug.  1966.

Ik.  Fair, Gordon M., and Geyer,  John C., "Water Supply and Waste
     Water Disposal," John Wiley and Sons, Inc., New York,  195^-

15.  Holley, E.  R., Jr., and Harleman, D. F., "Dispersion of
     Estuary-Type Flows," M.I.T.  Hydrodynamics Laboratory Report
     No. 7^, Cambridge, Mass., Jan. 1965-

16.  Hetling, Leo J., and O'Connell, Richard L., "Estimating
     Diffusion Characteristics in Tidal Waters," Water  and Sewage
     Works, Vol. 112, No.  10, Oct. 1965.

17.  Durford, C. N., "Water Quality and Hydrology in the Fort
     Belvoir Area, Virginia, 195^-1955," Geological  Survey Water
     Supply Paper 1586-A,  U. S. Government Printing  Office,
     Washington, D. C., 1961.

-------

-------
             LEGEND

               MAJOR  WASTE  TREATMENT  PLANT

             	ESTUARY  SEGMENT

A               GAGING  STATION
               POTOMAC  RIVER at  WASHINGTON. D.C

            A  DISTRICT OF COLUMBIA

            0  ARLINGTON  COUNTY

            C  ALEXANDRIA  SANITARY AUTHORITY

            D  FAIRFAX  COUNTY - WESTGATE  PLANT

            E  FAIRPOC  COUNTY - LITTLE  HUNTING CREEK PLANT

            F  FAIRFAX  COUNTY - OOGUE  CREEK PLANT
                                                 JC
                                                                                   .OCATtON MAP
POTOMAC
R   STUDY   AREA
             SCALE   M  MLES
                                                                                             FIGURE  I

-------

-------
Q
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in
oc
LJ

I
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_
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a
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or
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o


I
                                                                              8
                                                8
                                                
-------

-------
                        THE  PUMPING  PROBLEM
                                = -Q PUMP  C|
E 7.8
                                 Q PUMP
                            Q IN - Q PUMP
                                                WATER




                                                 AND




                                                SEWER




                                                SYSTEM
                              J6 = 0.9 Q PUMP C| + P
O.I Q  PUMP
                                                        CONSUMPTIVE USE
                                  0.9 Q PUMPED
                                 Q IN -  O.I  Q PUMP
                                                                FIGURE  3

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                                                                                       \
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                            5
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                                     (P) MO1J M3AIM
                                                                                                 FIGURE   4

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                                                                         FIGURE   5

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                                                                                     FIGURE  6

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                                                      FIGURE    7

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                                  TAHLB OF CGSKSSffiS
         PRSFAC2	
         LIST OF TABUS	       yll
         LIST OF FIG833S   .....                                        ,..,
                                    >**o*'. ..   nil
         LIST OF APPJDIGSS  
                            *"*<>*'...	     x
    y     Chatty
    5
    }        I.   IOTBOOTCTIQ3 . .	             l
    I       II.   WIST OF LITSamJSE	             5

                                                    .	     5
                                           MKHCES FOB 1HALIS58   ....    16
                       Descriprti-78 Analysis	              lg
                      Statistical Modl3	    17
                      Kiirar Flow SlasLLatIai	    19
                             asia Ekaa^iaent .	    21
                              B^alaticn ifedala	    21
    '*                   Trsatat B^jmiraasmt*	    23
                         Cas* Stm47? Th Potoc Estaasy	    25
         III.   FLOW HSLSAS1 HODSL	       .              27
                   THE HlOBiai ....                                      ~7
     I                                   	
*   '             QEMSSII, APISSSA.CH  .	    29
    t-1             Q7J4T T'T*y 'HTYOusr/ saTa
                                               	    29
                                               	    30
                                               	     31
                      P^aleal  Pa^raatftara	^  ^	     33
                      H@srrair Qoali-ty	     33
                  ciscai?rr?s  BISAGCS  .......                        34
                  mmL GB^TIO^S	o	              35

                          EsooaAacaG SOLDTIOK	    36
                                    AM) CX3SPOTSR PROGRAMONQ	    41
                                                                          V-
                                        iv

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                  TASLE OF CONTENTS (continued)
IV.   PATUXENT AND POTOMAC RIVER BASBI SYSTEMS ,  ....... .    45
         THE PATUXENT SYSTEM ...... ....... . .  .  . .    45
         THE POTOMiC SYSTEM  ..................    4b
            Source of Data .....,..........    46   
            Description of Basin .......,....,,.    4?   ^
 V.   DETELOEtSHT AND INTERPRETATION OF TABLEAUX AND THE                <
      FORMATION C? H3SEKVOIH HELSAS2 PATTETOB. .........    52
         DEVELOHHEMT AND BirERPREEATlON OF TABLEAUX  ......    52
            Development of Tableaux  ..............    54
                                                                   rs   *
            Incremental Flow Tableaux  .............    DO
            Dynamic Prograaaning Tableaux , ...........    6?   ^
         FLOW JRSLS4SE PATTERNS ............ .....    68
         WATER QUALITY CCJITP.OL CQN3IDERATIOJE IN
         EESEHVDIR DESIGN  ............ .....  . .    70
VI.   SEJSmVTTY ASALTBES ............ . ......    73
         BIOCHEMICAL AND HOSICAL PABAMETEESS . ......  ...    73
            Reaeratiem .....................    ?4    4
            Deasraticm and Minimum BOD Concentrations ..... .    75
         D3SIGN PARAMETERS ......... ..... .....    77
            Temperature  .......... ........  .     77
                                                                         K
            BCD-DO Concentrations ia the Reservoirs  ......    78
            Waste^ater Leadings  ........  ........    79    *
            CO Concentration in the Wastewater Effluents ....    81
         SOCIO-2CCBJGUIC PARAMETERS . . ...... .......    82
            Water Quality Objectives ..............    82
            Imposed Was tester Loadings  ............    82

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                    TABLS 0? COSTBHS (continued)

gharrtar

  VII.   FOBTHEa DSVSLOHCaTS OF THS FLOW HSLEASE MODEL	   86

            LEAST-COST SGL3TIG3S	   a6

            CC2IPARISON 0? QPTIMIZATiaf PAB4MSTa3S	   88

            OTHER POSSIBLE SAXES QUALITX MSASUBaCSCS	   90

            LDJMOE TO SBrsa FLCST siMiLarics MODELS .......   92

               Use of Yield Curves	   92
               Hivsr Flos Simulation Modals	   94

            LIHKAGS TO SSXniHT AMD RITES BASIS QOALItT -
            SDflJLiTICW 1HQDBLS	   95

            IU-STKSAM IMPCOJfEMEaflS	   95

 VIII.   D3SCDSSIOH OF BS5DLTS	   99

                    POSUBLAIIONS	   99

                       S CCSi'CSFZS AND AMfTATIOJS	100

            US2 0? OPTIMAL ESLiaSE SSQ02HCES	104

            OSS OF WJiTEH QUALITY ISlMGaiSNT MODELS WITHIN THS
            FSASS'fQRX OF CUHHSST TECaKOLCGIGAL AND BSTITU-
            TIOSAL PMCJTICES	105

   IX.   Smai&EI ADD COtfCLTBIOSiS	110


    nd!^

    A		    115

    B    	, . .	    137

    C    ........ 	    157

    D	    188

    E	  .	    200
BIBLICGHAPHT
225

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LIST OF TABLES
1
2

3
4
5
6
7
8
9
10
11

12
13
U

15
16

17

18
19

20

Inventory of the Potcaaae Hirer Basin 	
Inventory of Flow Release Model for the Potomac
River Baain 	  	
Reservoir Data - Potomac River Basin 	
Incremental Flow Tableau - Nodes 570, 562, and 494 . .
Inereaieatal Flow Tableau - Nodes 462 and 458 	
Incresaental Flc-r Tableau - Node 460 	
Incremental Flow Tableau - Node 436 	
9ynaadc Prograaaiug Tableau - Node 560 	
Pynaaic Programming Tableau - Node 460 	 	
r>ynasdc Programing Tableau - Node 456 	
Dynaaaio Prxsgrawsingr TabTL^a^ (Churchill K^
Forrolation) - Node 456 	 	 . f .......
Flow Eanga Data - Upper Potosae River Baain 	
Example of an Orxtiaal Release Sequence 	
Optimization Criteria of the Flow Release Model -
Version II 	

Stream Flow Eata for Flow Release Model - Potcwac
River Baain 	
Surface Watar Supply and Waatewatar Inventory -
Potomac Hivar Basin 	 ..
Cost of Field Studies 	
Card Foraats for Verification Link and Flow
Relsass Model 	
Array Notation for Verification Link and Flow
Release Model 	
47

48
51
57
58
59
60
61
62
63

64
65
69

87
123

150

153
156

160

168
      vii

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                           LIST OF JTGDHBS
                                 .                                 Page

 1     Factors Affactiag Streaa Dissolved Oxygen
       In a Non-Tidal Syataw ..................    15

 2     A Schematic Raprsaantatioa of Proposed Rearvoir Systa
       - Poteaae River Basin ..................    71

 3     Simplified Flow Chart for Flow Raleaae Jfcxil   ......    44

 4     Potoasac filvsr Baaia Map Showli^; Proposad Reservoirs  ...    50

 5     Soheaatic of Upper Potcaaac Hivr Basin Flow Relcaaa
       ikxlal ..........................    53

 6     Reservoir Release Sequences for Various Flows  at
       th Eat'oary .......................    71

 7     Ccaapariaon of Reservoir Release Sequences with
       Varying Biochemical and Physical Paraaeters for
       1500 cfs at the Estttary .................    76

 8     Ccasparison of Saseryoir Relaaae Sequences with
       Varying Engineering Design Parameters for 15CO cfs
       at the Estuary  .....................    80

 9     Coarparison of Reservoir Release Sequences with
       Varying Social-Econoadc Parameters for 1500 cfa
       at the EstTiary  .....................    83

10     Ccmpariaon of Reservoir Releaaa Sequences for
       Various Optiaiissatian Paraaetars for 1500 cfs at
       the Estuary .......................    89

11     West Branch of Conococheagua Cresi, Site No. 5,
       Uniform Use Bate Tarsus Storage .............    93

12     Linkage for Eivr Basin Sater Quality Sisalatian  ....    97

13     Nomograph for Heaeratioa Batas, O'Cozmor and Dobbins   .  .  119

H     Kcjaograph for laaeration Rates, T7A ...........  120

15     Ncaograph for E^eratiooa Rates, OSCS  ..........  121

16     Ccapatad Tssrpratures , DO and BOD Profiles and
       Streaaa Survey Data for the North Branch Potomac
       Riyar ...... . ...................  122

!7     Depth and Haa^ratica Variations, North Branch
       Potcsac River ......................  128
                                 viii

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LIST OF FIGURES (Continued)

           Title
                                                                 Page
18    CcBput*d Phosphate Profiles and Stream Survey Data
      for the Pattucent River Basin  ..............

19    Velocity Versus Flow and Depth Versus Flow for the
      Pattucent River at Hardesty, Md ..............   133 ^

20    Lower Potosaac and Monocacy Rivar  ., ..........   139
                                                                      *
21    Lower-Middle Potoaac and Antietaa Creek   ........   140 

22    Lower-iiain Stem Shenandoah Hivwr  ............   141 <

23    North Fork Shanandoah Hiver ...............   142
                                                                      t
24    South Fork Shenandoah Rivar ...............   143

25    North, Middle and South Rivers of South Fork                    t
      Shenandoah River  ............. . ......   144

26    Upper-Middle Potomac River and Lower Conococh*ague              *
      and Opaquon Creelcs  ............ . ......   145

27    Upper Conocheagu* and Opequon Creeks  ..........   14^ <

28    Upper-Main Stesn and South Branch Potoaoac River   .....   147

29    North Branch Potoaac River  . ..............   148

30    Over-all Potoaac River Basin System ...........   149

31    Forsats for Data Cards  .................   174  '

32    Typical Data Compilation for Verification Link   .....   175 <

33    Typical Data Compilation for Flow Release Model  .....   176

34    Patuxent River Basin  ..................   177
                                ix

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                          LIST OF APPENDICES
Appendix:
   A     SOME CdMEHTS ON MODEL VERIFICATION
            REAEHATIGN CQEFFICI2HT	
    B
    D
    E
               Calculated Pro* Observed Reaoration Rates
               Predictive Foranlatiana	
               Gaseous Tracer Techniques	
               Comparison of Methods	
            USE OP PREDICTIVE FORMJLATIGKS	
            CROSS-SECTION DATA	,
            BOD J4ECHANISMS AM) FACTORS . .  . ,
            A PREDICTIVE MODEL FOR PHOSPHATES
            TIME OF TRAVEL	,
            A PROCEDURE FOR VERIFICATION OF THE QUALITY
            FORMOLATIQSS	
                                                          115
                                                          115
                                                          115
                                                          116
                                                          117
                                                          117
                                                          118
                                                          125
                                                          127
                                                          129
                                                          131

                                                          134
               Defining the Physical Systea	
               Establishing Stareaan Channel Characteristics .  .
               Basin Partitioning and Parameter Determinations
               Verification of Quality Formulations	
MODEL DATA FOR THE POTOMAC RIVER BASIN.
   COST OF DATA	
         COMPUTER PROCSAM DOCDMSSTATIOM AND USAGE WITH
         SAMPLE PROBLai	
            DATA FOaflUS AND TYPICAL DECK CCMPUTATIOHS
            PROGBAM USAGE WITH SAMPLE PROBLEM  ....
            SAMPLE OF IHFOT DATA FOR FLOW RELEASE MODEL
            PATUXESrr RIVER BASIN
VERIFICATION LBK COMPUTER PROGRAM  ....
OPTBIAL FLOW RELEASE MODEL COMR3TER PROGRAM
134
135
135
137
156

157
157
157
158

178
188
200

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                             CHAPT3S I





                            HffBOWTCTIO*



     To better control,  protect,  and sausage the water quality of our



rivers, water resources  engineers have directed increased attention to



development of analytical techniques for determination of procedures and



policies by which optical operation and sanagenent of entire river basins



nay be realized.   Analytical approaches to the design and soanagaaent of



water resources systems  have as their fundaaental objective the pro-



vision of water at a pre-eet quality for the least cost.  The analyses



also include investigation of alternatives, determination of inadequacy



probabilities, and establishment  of optiaal operational procedures.



     There are essentially three  methods for controlling water quality



within a given river basin:



     1.  Regulation of the total  waste lead.  This approach requires



         establishment of specifications for the degree of treatment of



         wastewatrs to  he effaeted prior to discharge, or, in the case



         of soae  industrial processes, for certain in-plant modifica-



         tions or process changes.



     2.  Regulation of river flow, either by reservoirs, pumping from



         well fields, or by poxped storage, in order to provide appro-



         priate dilution of waste loads when required.



     3.  Installation of in-streaa treatment devices which either pro-



         vide an  integral jaeana for removal of pollutants or which act



         to enhance the  rate of natural removal of pollutants; stream



         aarators, for example, function in the latter capacity.

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     The esginaariag approach to analysis and solution of water quality



control problisss is graatly influsBced by the degree of river basin de-



velopment.  Two general types of situations which are encountered in



the regulation of flow far  Quality control ara:
For a river basin  ia ^Jsieh ths rosarvoir systasa ia fully



developed, tha problem ia  oz of determining that flow release



sequence wiiieh will provicla best quality for a giran proba-



bility of iuadaq-oaey.   Other  watar reqtiireaeuts say or say not



be included ia tiia approach.



       and
     2.



         For a basia ia which flo regulation posaibilities are either



         limited or cooeadatent, but  for ^tiieii reservoir development is



         proposed, tha problaa beccaaes  ona of j^ijsijig decisions regarding



         both design aad operation.   Not only oast storage requirements



         for Quality control be deterjaiaed, but also a flew release



         sequence to asset the prescribed quality control criteria for a



         givan probability of inade
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              2.  investigate various physical, biochemical, engineering design,
                  and socio-econcsaie parameters which say influence the optixaal
                  flow rslaaae sequencej
              3.  dsaaonstrata the response sensitivity of the method to these
                  parameters in an actual basin; and
              4  investigate the significance of various definitions of optimal
                  such as Tjest" quality, miniswa flow, and least-cost on the
                  reservoir release sssquenees.
              Chapter II presents a brief review of the literature pertaining to
         formulations and relationships for description of water quality trans-
         formations and for detgraining flow regulation and wastewater treatment
         requirements.  Included in the review are models which have been pro-
         posed or are currently being used in the area of water pollution control
II       for least-cost solutions for wastewater treataent, flow regulation,
c
         estuary analysis, and generation of synthetic hydrology.
              Chapter III is devoted primarily to development of the flow release
                                                                                   1
         model.  The basic concepts of the Bodel and the development of the
                                                                                   i
         descriptive paragon are presented.  A brief description of the Patuxent
         and Potomac River Basin Systaas which ware used as test basins for
         the model are presented in Chapter IV.
              In CMptar V, the developsjent and interpretation of the incremental- ,
         flow and the dynaadc-prcgraasming "tableaux are explained.  Formulation of
         flow release patterns is presented in the latter part of Chapter V.

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     Chapter VI is davoted to a sensitivity analysis of certain physical,
biocb.ead.eal, engineering dasiga, aad socio-econottie paraaeters.
     Variooa adaptations of the flow release aodal, including' that pro-
viding for leaat-cost solution, are presented  in Chapter VII.  A coa-
parison is usad* of the reservoir release sequence aa developed using
various optimization parameters.  Other possible sjodel  expansions are
proposed, including river basis water quality  simulation with linkage
to estuarina isodela.
     In Chapter VIII, the results of the flow  release model are dis-
cussed.  The summary and conclusions of the study are presented in
Chapter IX.
     Seme typical problssas and possible solutions encountered in model
verification are presented in Appendix A.  A proposed aodel for predicting
phosphate concentration in flowing streaas is  also presented therein.
     Detailed schematics of the Potomac Hiver  Basin showing wastewater
discharges, daas, water iataJcas, etc. are exhibited in Appendix B,
along with the basic inventory and stream flow data used in the flow
release aodal.
     Data foraats, array notation and a brief  description of the use of
the verification link and flow release jaodel are contained in Appendix C.
The ecsaputer prograas for the verification lini and flow release model
are given in Appendices D and E, respectively.

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                             CHAPTER II


                        RFHEW OF LITERATURE

     Before one can attempt to evaluate the effects of wastewater dis-

charge o? flow regulation on water quality in a stream, it Is necessary

to understand the relationships between the geophysical character-

istics of the drainage area and the biochemical and physical environ-

ment of the stream.  The first part of this chapter presents the

historical development of the relationships between dissolved ozygen (IX)),

biochemical oxygen demand (BOD), stream flow, temperature, velocity,

depth, and certain other parameters which say affect water quality.  The

basic quality parameters considered in this study are DO, BOD,^and

temperature.  The latter part of the chapter presents various models

which are currently being used for determining treatment requirements

and flow regulation policies.
     The first quantitative description of deooygenation and reaeration

relationships in streams was presented in the classical studies of

Streeter and Phelpeflj in 1925.  These authors noted that the net rate

of change (**) in the ojtygftn deficit (D) in a streaa at any tiae was

equal to the algebraic SUB of the opposing rates  of deozygenation and

reaeration.  This is expressed mathematically as:
                     dj>  -  K.L - KJD                  ----- (2-1)
                     dt      -1     d

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in which



         X,  =  Bate coefficient for deoxygsaation,  reflects  tha



                availability of organic catter and tha activity of



                the organisffis pr-33 ?nt



         L   =  Oxygen daasd of the organic matter, in sg/1



         jC,  a  Rats ccttjfficiesxt for raaeration,  reflects tha degree



                of turbulence a_ad the transfer-efficiency at  the air-



                watsr interface



         D   *  Dissolved oxygen deficit of tha water in sag/1



The expression given by otreet^r and Pb.alps ia  a  linear differential



equation of the first order.  Tha first tena, JLL, ezpresaea  the rate



of oxygen utilization or daaeration resulting from oxidation  of organic



weste isatter.  The tern 1C D is tha rate of reaeration,  which  is a



function of the difference bwlryaen the dissolved  oxygan concentration



at any time and the concentration corresponding to a condition of ozygen



saturation^



     Streeter and Phal3>s f-orther stated that "The rats  of biochejnical



oxidation of organic natter is proportional to. the remining  concen-



tration sf the uno:ddi3ad substance^ measured ia  terns  of oxidiaa-



bility."  This can be erpr.?s3ad jrathscsatically as a  first order reaction



*ith tha intc-gratad fou"ia
         L,     L 
          t      a
in which
         L     ^a initial concentration of oxidisabla organic i3
                Sis cone snt/rat ion of oxidizable organic zmttar at
                                 days

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     Ih iatsgratsd form of th Strsater-Phelpa linear differential



equation for -rr defines tha dissolved coygaa deficit, &., at any tia



in teras SL, 3L, L , and tha initial dafleit, D , &3
          JL.      i                            a
                I.L
                                                                   (2-3)
     In thair studies of the Ohio Hivsr, Strater aad Phelps also in-



vestigated tha effect of taarp^ratxira on t&e dsoa^snation aad tha



r-3aeration coefficients aad formulatad appropriate empirical relation-



ships.   Tha basic forssolation for the effect of teaperatures on the



deoxygenatlon rats coefficisat is
         S

         K
                                                           (2-4)
       f                                      f

where T  and T are t-s?o Icoown tearperatoires, K and K are the corresponding



values of the deoxygeaation coefficient, and 6 is the thermal coefficient,



a constant for the reaction.



     Tha reaction rate constant for reaeration was determined ezperl-



-nentally for the Ohio River, and was found to vary with flow and depth



according to the relationship
   vhich
V



H



C
                 H
               Yalocity of flow in feet/sec



               Maan rivar depth in feet



               Eiapirical eorstaat



             n  Empirical
                                                                    (2-5)

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     The original formulation proposed by Streeter and Phelps has been




expanded over the years.  However, tha dissolved oxygen and BOD formu-



lations, temperature corrections , and reaaration formulation have held



true with slight saodif ications .





     In 1939, Fair[2] simplified tha use of the oxygen sag relation-



ship developed by Streeter and Phelpa.  Fair introduced a new constant



called the Self -Purification Factor, "f".





                K

                                                         ----- (2-6)
     By setting 4r = 0 in Equation 2-1, one then obtains




                Z?

        L   -   ~D                                     ----- (2-7)
By solving for the critical deficit, D , and incorporating the Mf" factor



                      -JL


                       -*                                ----- (2-8)
where D  is the maximum dissolved oxygen deficit at the critical
       c


deficit point, in Bg/1.



     To further facilitate the use of the oxygen sag equation, Fair



developed a noBograa and a table of Mf w values for various types of



streaas.  The use of this equation eliminates the need for determining




a separate reaaration coefficient.  However, it aust be recognized that



the formulation is basad on the assxunptions that the reach is homogen-



eous.  The uss of this self -purification factor ia quits popular today,



priaarily for rough a valuation or approximation.




     In 1948, Thomas [3 3 expanded the oxygan sag relationship to in-



clude a third terra, K~.  The factor K  was used to reflect the

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ccsrpcaiticn of the waate and receiving water and th relative quies-


cence of the straaai at tb point of interest.


     The equation developed by Thorns ha* the form
            Vl
     t  -               k           - e        + D  e     ---- (2-9),
in which 1C, is a constant of proportionality reflecting the ccoposition  ,


of the waata and recairhjg streaa, and the quiescence of the stream,


     Thessaa indieatad that the tiaa-veraga value of K~ is zero, with


fluctuations occurring witb cbangan in taperturef flow, and channel


conditions.  The ranga of valaee of K- given by Thonaa was -0.36 and


+0.36.  Thcjaaa also davalcpad a noKcgrass for the solution of the ex-


pandad equation.


     Another variation of the oxygen aag equation for establishing


coygan relationsaipa in streaxv waa proposed by Vela U, 5, 6, 7] .  This


vmriatiso, called the "Qaygen Budget," is an accownting stepwiae method


for deteraining oxygea balance.


     On the asset side of the accounting ledger, 7elz includes dis-


solved oxygen present in the stream, that provided by reparation, and


that contributed by photcaynthetio activity.  On the liability side of


the ledgar, Vela includes exertion of the BOD, demand of sludge deposits,


biological extraction, etc.  The DO deficit is calculated for a given


rach and stream flow by sunming the sources and sinks of oxygen and


applying proper conversion factors.


     In 1951, Thonaa[dj simplified the oxygen sag relationship and


=*da it sore ajaecabla to stre** stapling data.  An approximate

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                                  J.U
  iution to the basic  linear differential equation proposed by Streeter



- d Phelps was developed.  The equation for the appraxiiaate solution or



rtep-jnethod" of Thomas  is
        n     Y+  ~2     +  0  -2D                        ..... (2-10)
        t      t                    *




 '. which I. is the oxygen uptake in the reach, ng/1 or #/day, and all
         *


.-tv.*r terms are as previously defined.   The principal advantage of the



*-.ep method is that only 5-day  BOD analyses need to be determined.



7.-.e time -consuming deoxygenation coefficient (K..) and ultimate BOD (L )



trotlyses are not required.



     Thomas developed ncnograae to reduce the number of calculations



required to determjin* the necaasary coefficients and constants.  Once



 pproxiaate values of K., and  Kp are obtained from statistical analysis



:y interpolation and extrapolation of observed streaai survey data, the



^;-^tion can then be used to  determine  the oxygen balance in the stream



tt different streeja conditions, loadings or teaperatures .



     In  order to more realistically represent the BOD reaction in the



istreaa,  Thomas proposed  using a second -order f emulation rather than



the first-order forawlation of  Streeter and Phelps.  This can easily be



incorporated into the step  method and the nomograas are also available


:^r its  solution.



     The step method as  originally proposed by Thonaas does not in-



^luae any benthic or photosynthetic components; however, these can be



^aiiy  added to th equation.   Th approximate solution is accurate



'-' *.r.e change in deficit is kapt to less than 3 mg/1 within a saction.



     In  considering the  stabilisation of organic aattar in a natural



        O'Connor [9] distinguishes between factors that affect th

-------
                                 11





 -.-erall removal of oxygen-utiliziiig material and those that affect



 .-f  direct oxidation of organic material.   The total rate of removal is



         by the coefficient  "K ", while the rate of oxidation is



         by the coefficient  "Kd".  The coefficients "Kd" and "K "



-..iv  be quite different from that determined in the standard laboratory



    :*-it  "K,".  This is primarily due to the difference in physical



- ;  :hes&ical characteristics  of the laboratory and stream environments.



    The  relationship for the oxygen balance in the stream as proposed



:v O'Connor is
               K.L     f  -K t    -ILt  1         -K_t

        n    -  =&-*    Ler-e^J+De^    ---- (2-11)
        t      X~X                           a
 .  above equation, which is similar to the  formulation developed by



 ":~cz&3, also provides for factors like biological extraction and sludge



 :e7c,sit3 as proposed by Velz.



     A tine-dependent dissolved osygen sag relationship, developed by



 -ilO], incorporates non-uniform stream channel cross sections and



        variations of BGD and BO in the mstewmters   Li obtained the



     rirg equation for the oxygen sag


                                                     (Kp-IL )t

                -K0t    | C  - F( ?  ) + f(  v    x A " ~  ^  J-
        Dt    :  -
                                                        	 (2-12)
        t(x)  =    ^-^ is the tias of travel  from outfall to point x



        V    *  Velocity of stream fiery



        c    =  Saturation value of  IX)



        F\0  =  CO of stream at waste outfall



             =  BOD of stream at waste  outfall



             =  Variable time element indicating the net effect of time



               of day and travel time  downstream.

-------
                                    11


  v.erall removal  of oxygen-utilizing material and those that affect

  j-.e direct  oxidation of organic material.  The total rate of removal  is

  Pi-dressed by the coefficient "K ", \>rhile the rate of oxidation is

  Ascribed by the coefficient "Kd".  The coefficients "Kd" and "Kr"

  v> Y be quite different fron that determined in the standard laboratory

   :? iftit "K,".   This is priffiairlly due to the difference in physical

  ..- ^heaucal characteristics of ths laboratory and stream environments,

       The relationship for the oxygen balance in the stream as proposed

  vy O'Connor is

                  K,LQ    f  -K t    -JUt 1        -K-t
          D4   =   ^"t    Ler-e*J+De*    	(2-11)
          T        O~ T                         ^


  ?:.e above equation, which is similar to the fonaulation developed by

  ~:.cc&3t al^c provides for factors like biological ejctraction and sludge

  -eposits as proposed by Vela.

       A time-dependent dissolved oxygen sag relationship, developed by

  1-t'IC], incorporates non-^miforai stream channel cross sections and

   spcrai variation of BOD and DO in the wastevater*   Li obtained the

  p-.Li jirlr^r equation for the oxygen sag

.,                                               C      (K -IL)t    -
 M                 -Xt     C  -F(?) + f\)  jiLe          dx
m        =e2Ls                    vu
                                                          	 (2-12)


      *   t(x) =    ^-^  is  the time of travel from outfall to point x

          V    =   Velocity of stream flow

          c    =   Saturation value of DO

          ?(|) =   DO of streasn at waste outfall

          '() =   BOD of stream at waate outfall

           5 -   Variable time element indicating the net effect of time

                  cf day and travel time downstream.

-------
                                 12
     Tha non-untfora channel aspect  investigated by Li is important.

Hoirevsr, modern high-speed computers permit the incorporation of many

gaiall streams  in  the baaic formulation, thus reducing the significance

of tha non-uniform channel solution given by Li.  The temporal fluctu-

ations in an effluent can be significant in some areas, especially for

industrial waste  discharges,

     Fraiikelfll,12]  expanded the femulations of Li and developed a

dynamic ojcygen sag analysis which alao incorporates photosynthetic

effecta.  A colifonn and detergent xaodel was also advanced by Frankel.

     Expanded  BOD and DO formulations which include the effects of sedi-

xentation, absorption, additions of BOD along the stretch of a stream,

removal of oxygen by benthal demand or plant respiration, and the addi-

tion of oxygan by photosynthesis have been developed by Dobbins {13,14].

The equation for  the dissolved oxygen profile as proposed by Dobbins

is given belosr:
          r    _jl    r   -(K^
          LLa * K.  + K J    Le
                                      e-Kpt
                                    D    *
                                     a
TD-
                                      n
                                      J
        D^      Denotes the net  rate of oxygen reiooval by benthal

               dazaand and the effects of plants

        LA   *   Bate of addition of BOD along the reach

    otner tanns in the equation are similar to those in the previous

-------
            Dobbins  also investigated the effect of longitudinal dispersion on

       BOD and DO profiles,  and concluded that the effect is negligible in

       jaost fresh-water streaa*.

            In field surveys of the Truekee River, O'Connell, ejt ej,. 115,16],

       measured the  effects  of benthic algae and other attached plants.  A

       modified form of the  oxygen relationship which includes the net oxygen

       change caused by aquatic plants was used successfully for predicting

       daily aiininrena DO concentrations In the Truckee River,  the DO concen-

       trations were calculated using the following expression:
              -^k      -K-t   -IC^t      (-0 f)\       ~^0^           V +
                       e2  --- (2-14)
I      where (P-H)  is the net contribution (photosynthesis minus  respiration)

|      and all other terns  are as  previously defined.
i
|           O'Coanell and ThOMs concluded that the oxygen produced by the

 j      algae and other attached plants generally has little  net effect on the
 %
 t      oxygen balance of a  streaa. However, nighttime  respiration may add a
 r
       large oxygen demand.
            In a study of the Jterrioack Hiver,  Caapfl?]  developed an oxygen

       balance formation which iacluded the addition of BOD fron bottom

       deposits, removal  of BOS by settling,  CO production by photosynthesis,

       and the effects of longitudinal  mixing by  tides.   Caxp reported that

       the amount of DO supplied by photosynthetic activity  in the Merriaack

       River is considerably  higher than  that by  atmospheric reaeration,  and

       that  BOD reaaoval by sattlizig is  greater  than that by  oxidation.

-------
     A general  form which  describes  the  temporal and spatial distribu-




tion of either  a  conservative  or a non-conservative substance in a one-



dinensional  stream haa been  described by 0'Connor[l8J as follows:
                      *   (Q(xt)  c)
in which  c  is the  concentration  of a  substance  of interest,  A is  the




cross-sectional area of the stream, Q is the  flow rate,  and  S represents




the appropriate sources and sinks.  The above formulation accounts for




variations in the fresh-water flow  and cross-sectional  area,  various




sources and sinks  of oxygen, natural  and artificial  reaeration, the




pbotosynthetic contribution, bacterial and algal  respiration, carbona-




tious  and nitrogenous oxidation, and  benthie  deposits.




    Thus,  the formulation for oxygen balance in  a stream originally pro-




posed  by  Streeter  and Phelps has evolved gradually into  the  more  elab-




orate  relationship given by O'Connor.  A schematic summary of factors




vhich  affect the dissolved oxygen  content  of  a  stream  is shown in



Figure 1.

-------


_
C
^1
c
<
Q
Q
<
(/














r
)
r
i

'
i
>
>

fc


o:
V) O
Z ce
< ^!
fE 2
^*^
^ I
o 
i f




_J
<
O
3
m

5
o
X
O

UJ
cc

^
C
c
*
c
i
<




f
c
h
U
-i
i-
^
>
U
f
1
u
0
3
G
Q
O
ir
Q.
i

I
I
<
t
1
t
t
\
>
J
>
t





= 1
c> 1
E t li
i -- *
^ 1-
^ o
2 <
)
^ ui2
_, zz
o  X 8 < 
no *  LJ rS
^ ^ m
CO
/
So
^^
Z ODflC
u auj
O ?<
> Hy
s
o









-J UJ
 H9
V f/\ ^
0 
^ k
o3
z<
 I
^ r;
cr h;
"-*- CO
Q





4 






E TRANSPORT
DVECTIV
<




  Ld
  I-
  co
  >
  to
  <
  Q

  f-

  Z
  O
  z
  z
  Ld
  o

  I

  Q
  U
 O
 (O
 to

 Q
 U
 CCL
 h-
 CO


 O
 Z

 f-
 u
 UJ
 u_
 U.
 CO
 cc
 o
 f-
 u
Figure  1

-------
                                  16





     One of the major challenges facing the water resource engineer



today is the selection and implementation of a quality algorithm or



zodel which is best  suited for a particular application.  Judgments



r.ave to be made regarding  the significance of various parameters in



a particular situation. For example,  an untreated waste discharge



zay currently be  resulting in deposition of a sludge bed in a particu-



lar section of streaaa; if  the waste is treated, will the sludge bed



b a significant  parameter in the BQD and DO formulations?



     Another problem associated with the implementations of a quality



algorithm is the  lack of systematically collected data.  One of the



Dost important contributions of the systematic approach to water



resource problems has been to point out the ned for well -planned



field studies 
     This section presents  a review of the current literature on



rathenstieal methods  and moclls ccsraaonly used in water resources for



analysis and control  of pollution.  For ease of presentation, the de-



velopments have been  grouped into four categories.  These are:



     1.  descriptive  analysis;



     2.  statistical  models;



     3.  river flow simulation; and




     ~>  basin management models,,
     - 'Descriptive analysis provides for mathematical representation



?: a process or processes by algorithms such as the "oxygen sag" rela-



--^r-3.aip.  The analysis is non-statistical and non-optimal seeking.

-------
                                      17
  Tills type  of  analysis is used  'prinaxaly to dsaronstrats cause and effect



  relationships of various pa:r>ii~atr8   A descriptive algorithm may be



  an integral part of another type of analysis, as  discussed later in




  this chapter,



       The computer programming  of the "cxrgen budget" by Gannon and




  3o7mfl9] and  the dynamic "c/zygen e.-ig" eodel 33 developed by Frankelfllj




  *:<-. example  of descriptive aralysi* /c-r nen-tidal v/aidrs,,  ThoBJaxtn's[20j




;  segmented  and 0? Connor 'a (213 estuary models- are t^o ex^jirplea of descrip-



l  live analysis for esiuarizse waters,




| Si.*Lti5tIctl Kfodals



       Interpretation of obaarvsa  data c^j.; r.fuen ba asasxtrably iarprovsd



? by u-e  of  statistical modejus,  Gry,vcli.i(2] ^j?ga>st-3 a three-step apprcach



 ,, to th2  use of statistical models:



       1,  selection of a aodel  to represent the physical situation;



       2.  mathamatieal treatrra-at  of tha jaodal to oo~'riir, information



           about ths varicua ccapon'Sntci^ and,,



       3.  use  of the model to ^aka deoLsicas reg-a.rd.ing the physical
        Various'  .statistical uica^^s  have D:.-?:: oS *d fc-r ;~/r vdictlzig water pol-



    it:on control needs.  In 1950,  LeBc-sq^et and T-sivcglu[2,3^24] used a



    irpie regression analysis tc relate di-solved o^ygea  deficit to stream




    .cw   This relatioriship provides  s. sicrpJlifiad approach to calculation




    ,  ."-rr^33lb]e B03 leadings for  &  gL7-;=:,hod for detarainLcg  5*.1D .I,k..i.clnathod '>ra3

-------
                                   18
      by the Virginia State Water Central Beard for aatiiaation of th
 assisdlatiGn capacity of the Chickalsosiiay Biv*r[26].  Okmn, gfc.il* t27J,
 also reported tha -asa of j^tipLa-rsgression teahaiguwi for analysis of
 non-tidal watars.  Wolxsaa and &ayarl28J, arid sora raoeatly Durum and
 Langbain[293, hava attempted regressive analysis la the Potcanac
 Satuary.
      Bacsas* regression axxJels ar aot valid cniiaida of tha ranga  of tha
 original data, tfeair tL33 for flow nsg^alatlon for a systaa of nailtlple-
 resorvoira la rather Halted*  Jbrtiier, aftar aaalysiag various regres-
 aicai squatiesas used far datenaiuisg pollution cozrtrol naads, Thomas [8]
 has  snggatM that this tacimiqua is Bre suitabla for data reduction
 for  us a ia tha Streetar aad Phalpa formLation than it is for davelop-
 swnt of a prsgdietive zaodal.
      ThoJoasDO] davsloped a queueing aodel saploying porobability
 theory  and fiaite l^r^oy chains for pollation transport in streams.
 Tha  object of the jsodel ^aa to predict tha quantity and quality of
 watar at givan control points for aoy pattara of flow, temparatura,  solar
 radiaticm, cbaanal eaafiguraticea, daa location, and pattarn or type  of
 pollution.  The sxdal includes a stochastic forssulation of hydrology
 with lag-oaa serial correlation bsfij^sen floie; pollataata with both
 la^-ona serial correlation and a dacay sachaaiaa.  The aodal is lim-
 ited to a a 133510 3=7i of stream rsaohss.  Although may of the para-
 eters for self -purification in tha 023^^0 budget are not included, tha
 2dal rapres^nta tha first attasrot to Incorporata t-so interdapeadaat
 atochuatic paraisrtars, a'fcra-aai flew -and ^rastswatar.
      LosacLs[31,32] d7lopacL a jaathamatical cdal to predict tha prob-
 aoiiity diatribtitian of tha aiBisiua dissolved o^ygan coaeantration

-------
                                   19





which occurs downstream from any waste-water treatment facility..  The



model has utility for determination of stream standards and treatment



requirements that maximize net benefits, for a given economic benefit



loss function.



     Wastler[33J studied interactions of tides, solar radiation, river



flow, and waste loads in the Potomac Estuary isith the aid of spectral



analysis, including the computation of cross -spectra.  The cross -spectra



were used to gain quantitative information on the response of a change



in DO as a function of a change in BOD.  Spectral and cross -spectrum



analysis was used very successfully as a statistical tool in the Potomac



River and csore recently in the Delaware River Estuarine Studies [34],



Rive
     The use of stream flow simulation to evaluate a given wastewater



treatment policy or for design and operation of a system of dams in



water resources management, inaies maximum use of information available



from a given hydrologic record.



     A model for synthetically extending a given historical, hydrolog-



ical record has been advanced largely through the efforts of Thomas



and Fiering [37, 48] .  The siodel, a lag -one Aiarkov process, asay be repre-



sented by the equation






           *  v. + 0 (Xj. - ix) + ti+1  0(1 - p2)^       ----- (2-16)





"-n which



     Xi+i  =  The flow in the i+1 interval, a linear function of X.




     X1    =  The flow in the "i"th interval



     t .  .,  =  The standardised random deviate

-------
                                 20

            u.   Population ciean
            cr   Population standard deviation
            0   Regression coefficient for th* values of flows in
                 the i+1 and "^'th interval
            p *  Correlation coefficient between flows in successive
                 tiae periods.
     The Markov model as given above was expanded to simulate the stream
flows in an entire river basin by FieriBgC37J.  The aodel uses principal
components to maintain first and second moments, serial, and spatial
correlation for all streaa gaging stations in the basin.
     MatalasD9] has proposed a xaore sophisticated simulation niodel
which jaaintaias the third acwent, and spatial and serial correlation
more effectively.  Other developments in flow generation have been
provided by ChowRO}, Beard[41], Crawfordf42}, and AST AssociatesI43],
and, more recently, on the "regional" basis by the United States Geo-
logical Survey[44l.
     Simulation is currently being iised quite extensively in the United
States in water resource planning and evaluation.  The Harvard Water
Resources Group[363 has designed a simulation model for the Lehigh
River to aid in identification of the particular combination of flow-
regulating structures, treatment plants, and other hydraulic works
"'hich raost nearly achieves the objectives of the Delaware Comprehensive
-"Ian.
     Simulation was also used by the United States Corps of Engineers
p-nd lately by Davis of Resources for the Future [45] in the study of
tae proposed reservoir system in the Potomac River Basin.  Stream flow
simulation is also currently being used by the Chesapeake Field Station

-------
                                 21






of the Federal Water Pollution Control Administration for evaluating




water quality needs in the James, Potomac, and Patuxent River Basins.
     Management models are algorithms which may incorporate some of the



techniques mentioned above, plus some type of decision-making mech-



anism.  -Most of the past river basin developments in water resources



:.av9 been primarily devoted to water quantity, and not directly towards



srater quality manageffient.  In water pollution control activities there



have been two general types of decision models:  (l) wastewater-



treatment requirement models, and (2) flow-regulation models.  Included



in the ensuing review of these two types of models is a case study of



the Potomac Estuary in which three alternatives have been considered.





A .  Flow
     Thomas and Watermey0r[46], and acre recently Young (47 ], have sxun-



narized the research on that aspect of flow regulation relating to the



probabilistic characteristics of storage systems and dynamic decision



-aking.  Thomas describes the flow regulation problem as one of choosing:



     1.  the optimal operative policies;



     2.  the optimal level of development; and,



     2.  the optimal reservoir capacities.



     The optimal conditions are defined in economic terms as the expected



r.et benefits of the reservoir system.



     Dor fmanUS j  has studied the relationships between design and opera -



t.on decisions.  A mathematical model  for analyzing a hypothetical



-/stem involving two dams for the development of an irrigation and hy-



'- -"^electric project has been proposed.   Dorfman obtained an optimal



       deduced froa operating considerations,

-------
                                 22





     Thomas  and Watermeyer[46],  utilizing linear programming, proposed



B model  for  the reservoir operation problfte,  The model optimizes the



operating policy and the levels  of development and, by sampling, the



reservoir capacity.   It has the  further advantage over the Dorfman



,-r.odel that the stream flow is treated as a stochastic variable.  The



irodel, limited to a  single reservoir, has no mechanism for incorpor-



ftting quality considerations.



     Hall [49]  has applied dynastic prograjaoiDg for allocating water for



various  purposes such as hydroelectric power generation, consumptive



us, and water quality control.   The model proposed by Hall is limited



to the economic considerations involved in the design of a single reser-



voir. However, the  application  of dynamic programming for designing



cultiple-purpose water projects  was shown.



     In  order to evaluate the need for, and the value of, storage for



 juality control according to United States Public Law 660, WorleyfSOj



 las developed a general rivr basin model capable of determining and



  lusting flows necessary to maintain a minimum allowable dissolved



       concentration in a stream.  The model was not an optimum-seeking



      ; that  is, there was no mechanism incorporated that would provide



  or the best operation of a reservoir system.



     The model does  have the advantage that reservoir quality is taken



  it.0 consideration.   Another advantage of the Worley model is that for



  j' 6'iven flow rate, the effect  of the physical parameters of the basin



    -"-orpcrated into the quality determinations.  There are no economic



               in the model.



               hag developed two Monte Carlo techniques for finding



            annual operating policies for single reservoirs such that

-------
                                  23





 the econocdc loss as  s function of draft rate is  minimized.   Hydrologic



 simulation and a forward -looking dynamic progrwnaiing  algorithm is  used



 in the solution.  The techniques ere limited to three reservoirs.   No



 cons ideret ion is given to the water  quality in the system.





 B .   Treatent
      Various  methods  for forxnule.tion of water pollution control policies



      regard to treatment requirements have been developed.   In recent



years,  considerable effort has been directed  toward  the problems in-



 volved  in finding the miniatim cost  of iraste treatment to meet  a set of



 stream  quality standards.  Thomann  and Sobel{51] have presented some



 of the  first  formulations of  this problem in  their studies  of  the



^Delaware  Estuary.



      Deininger[523 has investigated alternative means for determining



 vaste treatment policies.  Least-cost linear  programing, chance-



 constrained,  and  integer-programs aiodels were formulated to determine



 optimal solutions.



      Sobel[53J has also  proposed a  linear programming solution, and a



 Birred integer formulation for the water quality improvement problem.



 The maximization of the  benefit-cost  ratio in water  resources  planning



 aas been transformed  into a linear  programming  problem  by Sobel.



      Thoaann[543 has utilized the results of  the steady-state  segmented



 estuary model  and a linear programming formulation to determine a least-



 cost  water pollution  control policy for the Delaware Estuary.



      In order  to overcome non-linear  cost functions, Kerri[55]  has



      a  dissolved oxygen  cost matrix to transform the least-cost formu-



        into &  linear programming problem.  Liebman[56]  has  used dynamic

-------
..^ramming for determining iraste treatment requirements for problems


giving non-linear cost functions.


   While the least-cost solutions are of great interest in water re-

jorces planning and management, there are some inherent technical


-jficulties in the use of this technique:


   1.  Except for scene industrial waste treatment facilities, there


       is a poor relationship between effectiveness of treatment


       and cost of the waste treatment facility.


   2.  It is difficult to estimate with any accuracy the cost of a

i;
       proposed wastewater treatment plant.

 $
 "I 3.  The least-cost solutions are sensitive to physical parameters
 V

 ^.     of the stream and to DO constraints .


^example, in the Delaware Estuary, Thomann[57J reported that, for
;f
::ien flow conditions, if the reaeration coefficient was overestijnated
" >%$.
TlOO percent the least-qost solution increased about 350 percent.

t  *
          , although contrary to engineering judgment, was easily


        by Thomann.  The allocation of treatment cost was also
 anged quite drastically.  A significant change in treatment cost al-

 f
 xatioa was also reported by Liebnian[56] in Ms studies of the

 t'
 H&mette River when the DO constraint was changed by 0.1 mg/1.


   In the opinion of the author, the least-cost solutions have  indi-


 tted two things :


   1.  the great sensitivity of the solution to the physical


i       parameters in the stream; and


   2.  the ability to adequately describe and predict the water


       quality in a stream by the descriptive formulations is


       greatly exceeded by the accuracy maintained in the

       optimization processes .

-------
                                     25
    C.  Case Study. The FfftflMfi
         The water quality problem in the Potcaac River Basin are unique
    in that the quality in the estuary is not greatly affected by upstream
    wastevater dischargee.  This independence, a result of the geological
    "fall-line" above Washington, B.C., siagpllfies the quality investiga-
    tion for the efltttaxy.
         A large municipal wartwat*r lod fron th Waahington, D.C,,
    area is causing a eerloua quality problaa in th eatuary.  The deteri-
    oration ia not only do* to low diaaolvad oocygaa but also to high
    nutrient levels, resulting in large al^al populations.
         Three nethods for alleviating water quality problew in the estu-
    ary are as follows:
         1.  a high decree of wastewater treataent including nutrient
             removal;
         2.  flow regulation froa upstream reservoirs to provide dilution
"?'
 t            of wastewater; and,
;-;
         3.  diversion of the wastewater farther down the estuary.
    In studying the various alternatives, Hetling[58J, using the segmented
    estuary model, investigated all possible solutions and combinations
    of solutions.  By ranking the alternatives, least-cost solutions were
    obtained to Beet the various levels of water quality constraints.
         Davis [59,60), using a sampling strategy consisting of systemat-
    ically sampling the trade-off relationships among the various altern-
    atives, also developed a method for cost minimization in the Potomac
    Eatuary.  In later studies, Davis used river flow simulation to
    evaluate the various alternatives.

-------
                                26
     The Potcamc Estuary is an ideal caae atudy in that there are
thr* alternative adUrtlom, two baaio quality conaiderations, coet
data available, and the quality for a given condition can be predicted
by the segmented iaatbamtical nodal.

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                           CHAPTER III





                       FLOW RELEASE MODEL
     The problem pursued in this study is as follows:  given a basin



with a developed and/or proposed reservoir system, develop a method for



formulating reservoir op*rating policies for quality control in some



optimal manner.  An optimal release sequence for the initial phase of



this study is defined as providing the "best" quality of water for a



given flow rate at a point in the system while maintaining a minimum



preset dissolved oxygen level in all reaches of the basin above this



point.  The "best" quality of water is further defined as the minimum



DO deficit for a given level of BOD.  The method for determining the



optimal release sequence should also incorporate:



     1.  Physical and biochemical parameters of the stream for



         a given section:



         a.  Flow



         b.  Temperature



         c .  Velocity



         d.  Depth



         e.  Biological activity



     2.  Wastewater discharge parameters:



         a.  Rate of discharge



         b.  Concentration and characteristics of the pollutants



             in the wastewater



         c.  Treatment policy
                                  27

-------
                                  28
     3.  Eagtilated aad unregulated streaa flow parameters:
         a.  Beaervoir 
-------
                                  29
GEERAL
     Various methods  for solving the proposed problem have been investi
gated, such as linear programming, application of influence lines, and
dynamic prograaaning .  Due to tha nature of the stream flow network in
the basin, the use of dynamic programming to obtain an optimal solution
was found to be an ideal approach.  The general approach to the flow
regulation problem has been divided into four phases:
     1.  the adaption of existing foraulations to describe the appro-
         priate water quality parameters in the river basin;
     2.  development  of a paragon which describes the physical basin
         and is readily adaptable to computer programming;
     3.  utilisation  of the dynamic programming optimization
         technique; and,
     4.  overall algorithm formulation and computer programming of
         the model.
     Quality considerations in the formulation have been limited to
temperature, DO, and BOD, with the main parameter being DO.  As illus-
trated in Figure 1, there are isany factors which influence dissolved
oxygen in a river.  Control of flow directly affects advective transport
of oxygen and reaeration.  Temperature, advective transport of waste
loads, and biological activity are indirectly affected by change in
flow.
     In order to make the problem sore manageable initially, only the
direct effects have been included in the study.  However, provisions are
made in the forKulationa to add the indirect effects at a later time.

-------
                                  30
     The basic water quality algorithm which has been used in the present



-,vork is Thomas's modification [8] of the Streeter-Phelpa equation.  The



.integrated form of the equation may be written as





         D(l)  =  Y * P  + D(0) * P2                      ----- (3-1)





where




         Y     =  LQ (1 - e ~Klt), oxygen sink



         P       e "^ 2  '2', reaeration parameter



         D(l)  =  Dissolved oxygen deficit at lower node



         D(0)  =  Dissolved oxygen deficit at upper node



The advantages of this formulation over others are:



     1.  the formulation can easily incorporate other than first order



         reactions ;



     2.  solutions for the integrated forms exist for all ranges of



         reaeration and deaeration coefficients; and



     3.  if the oxygen deficit is kept to less than three nsg/1



         indirect effects can be readily added or subtracted to the



         oxygen sink (Y) in the reach.



     In solving the algorithm, four states are carried forward.  These



-.re DO, BOD, temperature, and the deaeration coefficient.  The fifth



state, which is flow, is used to calculate the reaeration coefficient



and the time of travel.
     As indicated in Figure 1, there are three main sources of dis-



       oxygen.  Reaeration is usually the most important factor in the



 Dissolved oxygen budget.  Various formulations are available for



     ing the reaeration coefficient to the depth, slope, velocity, and

-------
                                  31

longitudinal diffusion in the stream channel.  In this study, the re-
aeration formulations employed have been the non-isotrophic relation-
ship developed by 0'Connorf6l]:
J/2
and the Churchill formulation 163]:
                                                                 (3-2)
         K2  *
                 5.026   V
                          .0.969
 Hl.673
                                              (3-3)
where D,  is the coefficient of diffusion of oxygen in water and all
other terms are as previously defined.
     Other formulations, such as those of Dobbinsf13,14], Streeter and
?helps[l], and Kren]cel[63], can easily be substituted into the system.
The effects of the different formulations for the reaeration coefficient
on the verification of the system are discussed In Appendix A.
Teispera,ture
     Since the reaeration and deaeration coefficients are temperature
dependent it has been necessary to incorporate a aechnniaa for adding
and subtracting various temperature sources end sinlca.  Various types
~f stream temperature models, as stnanarised by Zellerf64], have been
'investigated.  To maintain siatplicity, the exponential dscay tenpera-
ture model of Duttveiler{65] has been incorporated into the overall
algorithm.  The formulation is given below:
  +   [TsQ  - To] e"
                                                                 (3-4)

-------
                               32
where
         
-------
                                  33
     A third order polynaaLel for determining the solubility of dis-
solved oxygen in water at a given temperature (T) has been incorporated
into the model.  The polynomial coefficients have been those developed by
ti*TVA[67j, yielding
         Sat DO  *  14.652 - 0.41022T + 0.0079910T2
                           - 0.000077779T-
(3-6)
where "Sat DO" represents the saturation concentration of dissolved
oxygen at temperature (T).
     In the above dissolved oxygen, reaeration, and temperature formu-
lations, physical parameters of the etreaa such as width, W, velocity, V,
and depth, D, are required for various ranges of flow, Q.  Leopold and
Maddox[63J have carried oat extensive study of the changes in velocity,
depth, and width for a ehaag* ia flow rate at a given stream cross
section.  The characteristic relationships developed by these investi-
gators for the mean values for these parameters are:
         D   -   aQb       '                            ----- (3-7)
         V   -   cQd                                   ----- (3-8)
         W   -   eQf                                   ----- (3-9)
rbere a,c,e and b,d,f are characteristic coefficients and exponents for
correlation with Q.  Operational problems involving the use of these
formulations are discussed in Appendix A.
     To provide for possible BOD, DO,  and temperature variations with
     from unregulated and regulated stream sources,  a linear relation-
     has been assumed and incorporated into the flow release zoodel.

-------
                                  34





     Extensive review of stream survey data for the unpolluted, un-



regulated reaches of the Potomac River Basin revaalad that the linear



assumption was a fair approximation for DO, BOD, and temperature.



However, a recent study by Churchill and Nicholas[83] indicated that



the linear assumption for a regulated system was an oversisrplification.



Therefore, in the developing of the optimal solutions as presented in



Chapters V and VI, the \rater quality of all regulated and unregulated



sources was assumed to be constant (a preset  level) for all ranges



of flow.






            PARAGON
     In order to formulate a general flow release model, it has been



necessary to develop a descriptive paragon which can be used for data



storage and retrieval, -which adequately describes the branching of a



physical basin and relates it to waste discharge points, impoundments,



hydrologic conditions, etc., and which is easy to program on the eom-



pater.  Various types of descriptive rivar basin systems were investi-



gated such as the Stcret Systeja[69J, the method used by Worley{50],



and the numbering systesi of the FsfTPCA stream flow simulation modelf70],



A simplified method similar to that of an arroTr-and-line diagram[71]



of a critical path network was adapted,



     For a given segjaeat of streaia the following restrictions are to



be maintained:



     1.  stream flow in aegaent; remains constant;



     2.  all tributaries, waste discharges, or water intakes are



         indexed at the upper node of ths segment;



     3.  the relationships asong velocity, width, depth, and with



         flow in the segment regain constant;

-------
                                             35






                4.  only one wastewater discharge, tributary, or intake is  allowed



                    per node (if two or saore above entities are close together, a



                    greater number of shorter segments are established); and,




                5.  the nuaerical valua of tha upper noda should be greater than



                    the loirer noda (not absolutely necessary; however, it sim-



                    plifies some of the coding and sorting procedures).




                To aid in tha computation procedures and yet maintain flexibility



           in data analysis, storage and retrieval, the stream nodes, wastewater



           discharges, and stream flow additions have been indexed as given in



I          Appendix C.  Tha ability to add or subtract any waste source, stream



           flow, or add more sections to tha system is maintained if the numbering



           of nodes is in units of 2 or greater.

                All xeathexatical operations are at the upper noda of a given reach,



           For nodes at which there is an addition of flow due to a waste load  or



           confluence with another tributary,  a zaass balance is made with respect



           to flow, pounds of BOD, and pounds  of dissolved oxygen deficit.  The



           deaeration coefficient is prorated  according to tha pounds of BOD of



           tha respective caatributions.   The  temperature of the combined system



           is prorated according to the flow values of the two components.




                The isass balance of BOD and the prorating of the deaeration  co-



           efficient treats tha system linearly and does not take into consider-



           ation any antagonistic or synergistic actions or reactions.  The



           treattaent of this entire aystam non-linsarly is beyond the scope  of



           this study.

-------
H[	

     The solution to the multiple-reservoir release problem is very

amenable to dynaaic programming technique.  The complex problem can

readily be decomposed, called staging, into a series of saaaller

problems.  The technique* relies upon decision-waking at each stage

rather than trying to solve the entire N-etage optimization problem

s intuit anaous ly.

     There are two general approaches to the reservoir problem:

     1.  starting at mouth of the basin, proceeding upstream, and

         treating the regulated confluence points as diverging

         branches; or

     2.  starting at the uppermost point of the basin, proceeding

         dcsmstraaffl, and treating the regulated confluence point

         as converging branches.

Since SOU, DO, deaeration, and temperature are flow dependent, the

problem is significantly simplified by the latter approach.

     The overall schematic of the proposed reservoir system for the

Potomac River Basin shown in Figure 2 typifies this converging

structure.  The reservoirs (triangles) are the controlling mechanisms,

and the regulated confluences (squares) are the decision points or

the stages.  In the Potoaae system, the converging branches structure

results in a 13-rultistage optimization problam.

     A general solution to a jsultistage converging dynamic programming

problem has been structured by Nembauser{72j.  Bepresented below,
    ~*For a complete discussion of the dynaicic prograiraning technique,
u Neohauser[723.

-------
NODE
588
570
568
492
458
434
428
420
393
398
402
356
156
244
56
PROJECT
MOUNT STORM
BLOOMINGTON
SAVAGE H
ROYAL GLEN
TOWN CR.
TONOLOWAY CR.
LICKING CR. ^^
N. MOUNTAIN ^X
W. BRANCH
BACK CR.
CHAMBERSBURG
WINCHESTER
BROCKS GAP
STAUNTON
S\X BRIDGE

                                       LEGEND
                                       / \ RESERVOIR
                      I     
CONFLUENCE  POINT

ESTUARY
         A  SCHEMATIC  REPRESENTATION
                      OF
PROPOSED  RESERVOIR SYSTEM - POTOMAC RIVER  BASIN
                                                        Figure 2

-------
                                38
stage of a regulated river system is characterized by six factors:

                                  1  (D)
igulated system(M)
   Xm
igTilated systea(N)
(t)
Xo
                                                  Regulated system(O)
                                  |W
   1.  An input state (Xm), flow from a regulated system (M), the
       dependent states being BOD, DO, daaeration, and temperature.
   2.  An input state (Xn), flow from a regulated system (N), the
       dependent states being BQD-, DO', deaeration, and temperature.
   3.  An output state (Xo), flow from the combined regulated
       systems (M) and (N), the values of the dependent states being
       a function of a combination of (Xm) and (Xn).
   4.  A decision variable (D), dictates combination of (Xm) and
       (Xn) for a given state of (Xo).
   5.  A stage return (r), for a given (Xo), the best water quality
       measured in terms of miniaium dissolved ozygen deficit (DOD
       for a given BOD state).
   6.  A stage transformation (t), couples (Xm) and (Xn) linearly,
       as for the dependant states described earlier in the section
       on nodal operations.
   The flow release problem ia different from the problems structured
'y Nemhauser in three respects:
    1.  each stage consists of two input states;

-------
                                          39





             2.   flow release optimization is required for all output states



                 in order to provide for regulation for quality control down-



                 stream if needed;  and



             3.   the stage return is a dual-valued function.



        The latter requires a minimization decision procedure for two dependent



        states.   In the decision process, the object is, for  a given flow



        state, Xo, and within a given BOD grid,  to determine  that combination



        of Xn and Xm which will yield the minimum DOD.  Combinations of Xm and



        Xn with  greater DOD are deleted.


; I
<:           For a given stage or decision point, the range of Xo is dependent



        on the regulation capabilities of Xm and Xn.  For example, if the


: 

$|      regulation capability of Xm is from 100  to 300 cfs and of Xn, from



        200 to 500 cfa, the range of Xo would be from 300 (200 + 100) to 800



        (300 + 500) cfs.  To reduce the infinite number of input and output



        states,  reservoir releases  are made in discrete increments.  In the



        above example, if a 20 cfs  increase is employed, there would be



        26 states (800/20 - 300/20 + l) of Xo.  The number of feasible solutions



        per Xo is mainly a function of the BOD grid size.



             The number of combinations of Xm and Xn which will equal a given



        Xo state is dependent on the value of Xo and the number of feasible



        solutions per states of Xm and Xn.  The  maximum number of combinations



        will be  near the mean of the Xo range with a decreasing number towards



        the extremes of the range.



             For each state of Xo,  starting with the minimum  and progressing



        to the maxiimim regulation capability, the optimization algorithm,  which



        is an efficient enumeration process, consists of the  following steps:

-------
                                          40






             1.   calculate all dependent  variables  for all combinations  of



                 ftrf and Xn which equal the given Xo state;



             2.   sort and rank upward all feasible  solutions  according to value



                 of BOD parameter;



             3.   determine BOD grid size  by subtracting minimum BOD value from



                 the maximum,  comparing BOD difference to various  input  grids,



                 and selecting proper BOD increment size;




             4.   for the given Xo and BOD values within the first  increment




                 range, select the  combination of Xm and Xn which  has the



                 in'i'n'tpniTn DOD;




             5.   increment to  the next BOD state and repeat step 4 until all



                 feasible solutions are exhausted.



             With the converging branches approach  the flow regulation needs of



        reaches  downstream from the decision point  under investigation are un-



        known.  Therefore, for a given stage, a range of feasible  solutions for




        all states of Xo must  be carried  downstream.



             In the initial development of the flow release model, the dual-



I        value return function  is not cumulative. The optimization process for



        all output states for  a given s~tage is expressed mathematically  as



        follows:






                 F (Xo(k,p))  *  Min [DOD(k,p)   I BOD(k,p) (   Xo(k,p)



                                       =  Xm(i) +  Xn(J)]       	 (3-10)




        where



                 F (Xo(k,p))  =  Optical  operation  or return measured by the



                                 minimum  DOD for a  given BOD and flow state

-------
                                   a






     Xo(k,p)  -  States of output Xo, k = 1,2,	(M+N)




                                      P  1,2,	P



     Xm(i)    =  States of input Xm,  i = 1,2,	M



     Xn(j)    =  States of input Xn,  J - 1,2,	N



         as measured in



     P        -  Maximum number of increments in BOD grid



     M        =  teuciBum number of input states for Xm



     N        =  Maximum number of input states for Xn



     BOD(k,p) =  State of the first dependent variable for a given Xo



                 state and DOD value



     DOD(k,p) =  State of the second dependent variable for a given Xo



                 and BOD state.



This enumeration process makes maximum use of the natural assimilation



capacity of the stream, and yet maintains the principle of optimality.



If an accumulation stage return is substituted for the DOD parameter,



such as a total cost parameter, the optimization procedure can easily



be modified to include a minimum of cost; this is presented in



Chapter VII.





OVERALL ALGORITHM AND COMPUTES PROGRAMING



     The quality and descriptive formulations adopted in the flow re-



lease model are general in nature and applicable to moat river basins.



The following assumptions are made in the overall formulation:



     1.  there is complete lateral mixing in the stream;



     2.  all flows are steady-state with no longitudinal diffusion;



     3.  the wastewater discharges are uniform in quality and quantity



         for a given time period;

-------
                                 42

     4*  all saajor iarpewndaenta are in the headwaters of the basin.  If
         two or more are in series they are treated as one unit; and
     5,  the quality formulation as presented earlier adequately
         described the process in the stream.
The first three assumptions could possibly be eliminated if temporal
aspects were incorporated into the jaodel.  However, other technical
limitations make these refinements impractical at the present tiae.
     In the overall ccvputer prograa for the flow release model,
the description paragon mathematically links the water quality formu-
lations, nultistaging process and optimization procedure to the stream
network of the river basin.  The paragon also selects stream flow
routing patterns and sequences the Bultiataging process in the
dynamic programing technique.
     The basic computational steps of the flow release model are given
below.
     1.  Read in and display input data.
     2.  Determine minimum and maximum stream flow ranges for each
         node in the basin.  Required in the stream flow routing and
         multistaging process.
     3.  Route the unregulated stream flcrws to regulated sections of
         the basin.
     4.  Starting at uppermost decision point, route the stream flows
         and davelop optimal solutions for each stage of the con-
         verging branch systems.  (In Chapter V, a more detailed
         description of the routing, staging, and optimization process
         is presented along with an example problem for tha upper
         Potomac Basin.)

-------
                                  43


     5.   Print out all flow routing data and optimal solutions for

         each stage.

     A simplified flow chart* of the release model is given in

Figure 3.  The formulations have been programmed in FORTRAN IV,

?-ir.set E.  Complete listings of the variables and computer programs

r.rfe given in Appendices Ct D, and S.

     The input data formats are flexible to allow for various input

options  depending on refinements needed in the calculations (see

Appendix C for data input formats and a compilation of data deciks).

     The output of the computer program is a series of incremental

flow and dynamic programming tableaux.  The incremental flow tab-

leaux contain all pertinent information required for the optimization

process, while the dynamic programming tableaux consist of the results

of the process for the given decision point.  The interpretation of

the tableaux, development of optimal reservoir release sequence,

and analysis of results are presented in Chapters V and VI.

     A computer program employing the same formulations as in the

''-w release model was written to aid in verifying the concepts of

1 he model.  The program is also used to tebulate all input data.

: -o in coefficient modification, and display of specific quality

 "ofiles.  A listing of the program is given in Appendix E.
     *Since flow charting capabilities via the computer are now
 "andard subroutines at most computing centers, a detailed flow
 *" be readily obtained and therefore was not included in the
 Assentation.

-------
44





















































SIMPLIFIED FLOW CHART FOR FLOW RELEASE MODEL
RCAD IN DATA
1

WASTE NODES
1

M 0 A MUM

J


CO SECTIONS
1
1
J3ELCCT UPPERM 5T REGULATED ftES*VO(R
1


I

( |"

1 ' '
1
C^NO /" "N

IS VES
CONTINUE TO CALCULATE STREAM QUAL-
,T,  CHtCK,0 CON5TT. '""'"" r*"-U"
1


1
MO /^ "Xl
"J (NODE  CONFLUENCE or REGULATED TB )
H
INCREMENT FLOW U  ' 	 ^/ FLOW c MAXIMUM FLOW J
H


[NO
I /^ ^\


J..



1

PROGRAMMING ROUTINE
1
	 \KT FLOW ACCOWNO TO TABLEAU K 	 ^STORE DYNAMIC PflOGHAMMINO TABLEAU ON
( VALUES 1 { TAPE 2

                                   Figure

-------
                              CHAPTER IV






               PATUXENT AND POTOMAC RIVER BASIN SYSTEMS



     Most of the emphases in the river baa in models reviewed in



Chapter II have been focused on the consequence of a feasible solu-



tion.  Little attention has been given to physical and biochemical



parameters that dictated a given solution.  The lack of good field



data has been the major factor limiting a comprehensive sensitivity



analysis of the formulations.



     To fully evaluate the flow release model and to analyze some of



the controlling parameters, the formulations have been applied to two



river basins in the present study,  the Patuxent and the Potojnac, in



the Middle Atlantic Region.  A brief description of the two river



basin systems is presented in this  chapter.





THE
     The Patuxent River Basin,  which has two existing reservoirs in



series and a drainage area of 930 square miles,  has been used for a



pilot study in the testing of the quality formulations and developing



methods for data analyses.  There are six major  sources of wastewater



and two water intakes in the non-tidal portion of the basin.   See



Appendix C for a further description, including  a schematic of the



basin.




     Although small in scope, the pilot study of the Patuxent River



revealed the following:



     1.  large amounts of data  are required to describe the physical




         and biological systems of a river basin;
                                      45

-------
ii
                                            46

               2.  a systematic method of data analysis and reduction is
                   needed to implement the flow release model; and
               3.  a procedure for the adjustment of the various coefficients
                   is required for model verification.
          See Appendix A for a detailed description of a procedure for verifi-
          cation of the quality formulations.

          THE POTCMA.C SJZ
     The final testing and analyses of the flow release model were
done on the non-tidal portion of the Potonac River Basin, which has
15 proposed reservoirs and a drainage area of over 10,000 square miles,
     The Potomac River, being located in the political center of our
nation, has been studied almost continuously by various agencies
since the early 1940'a.  The availability of data, proposed reser-
voir development, and current water quality problems have been
decided assets in testing the formulation in the flow release
model.
Source of Data
     The data required for the field testing have been obtained from
numerous sources, including:
     1.  Chesape3ce Field Station, FWPCA, U.S. Department of the
         Interior;
     2.  Department of Water Resources, State of Maryland;
     3.  Department of Health, State of Jtfaryland;
     4.  State Water Control Board, Commonwealth of Virginia;

-------
                                  47


    5.  Division of Sanitary Engineering, Coaaonwealth of

        Pennsylvania;

    6.  Division of Water Basoarcea, State of West Virginia;

    7.  U. S. Geological Surrey;  and

    8.  U. S. Aray Corps of Engineers.

Data also have been extracted from various technical and non-technical

reports on aany diverse topic* concerning the Fotcwic Basin.  Of the

approximately 450 reports written  concerning the Potonac, the aajor

sources of data are references [73] through [79].
    The non-tidal portion of the Potoaac Elver Basin, which contains

oost of the typical water quality problene, provided diverse con-

ditions for testing the flow release model.  Soae of the pertinent

data describing the basin is given in Table 1.



                            Table 1


             INVZNTQKr OF TSE POTOMiC EIVEH BASIN

             Entity                             QffliTVtlliT

    Square Miles of Drainage Area                  11,500

    I960 Population -
        (Exclttding Washington, D.C.)            1,000,000

    Strean Miles -
        (Above River Mile 116.0)                    2,750*

    Wastewater Dischargee to Streams                  173

    Surface Water Intakes                              74


         *Does not include minor tributaries

-------
                                  48


     For the model development and evaluation phase of this study, only

the streaa reaches receiving significant waatewater discharges or

those subject to flow regulation hare been incorporated into the

system.  (See Table 2.)  Included in the waatewater inventory are all

dischargee with a flair equal to or greater than 0.5 jagd, or a popu-

lation equivalent equal to or greater than 1,000.


                                Table 2
                    INVENTORY 07 FLOW RELEASE MODEL
                      FOR TBS POTOMLC HITCH BASIN
            Wastewater Dischargee

                 Organic                                64

                 Tberael                                 8

            Stream Flow Addition Point*

                 Regulated                              14

                 Unregulated                            11

                 Increment*                             56

            Surface Water Supplies                      26

            Strea* Segaesta                            307

            Streaa Mile*                               694

            Eriating Intpoundeiita                        2

            Proposed Isspoundaents                       14



     The wasterater diachargea included in the raodal represent over

 90 percent of the total BOD load to the stream, and all Bajor water

-------
                                  49

supply intake* in tfc* son-tidal portico of the Potoaac Baa IB have
*P,'J i included.
     Figure 4 is a gnr?a aap of the Potoaae Hiver Bavin, inoludlng
the proposed rM*rvoir syrtaai.  In Tabl 3 *r prMot*d data on 14
proposed ittpoundaanta for tl Fotcnao ayt.  Appandlx B oontaina
detailed st^oawft'tioa of th individual atraa* raohM, showing water
Intakes, ^-ststewmter discharg**, low le-ral daaa, gging stations,
stream segments, and reaerroira.  Basin data used in the flow release
model are also presented in Appendix B,                           ;

-------
Figure t

-------
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1

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-------
                                 AND DiTSRFSSCATICN OF TABLEAUX
                   AMD THE FOEMATIO! 0? BSS2RTOIH B2LSASS PATTSH8S
                The most  current  data available hsvw been used for testing the
           various quality algorithms in the  computer runs of the flow release
           model for the  Potcaac  Biver Basin.  Although it has not been the main
           purpose of  this study  to obtain a  completely verified  modal of the
           entire Potomac Basin,  a great deal of effort, especially  in the  North
f          Branch sub-tasin, has  been spent in data analysis so that the develop-
          ment, interpretation,  and sensitivity analysis reported are a true
|          indication  of  natural  streaa  conditions.
\               The first part of this chapter is  devoted to the  development and
'I
f          interpretation of the  Inoraaantal  Flow  Tableaux (IFT)  and the resulting
|          Dynaadc Pregraaaaing Tableaux  (DPT).   In the latter part of  this
J|          chapter, the foraation of the release sequences for rater quality
 |          control froM aailtiple-reservoir systeaas from the tableaux ia
K          presented.
                For ease of presentation, the development and interpretation of
          the tableaux are llaitad to the upper portion of Potoaac River Basin.
          (See  Figure  5.)  Tha entire watershed is included in the foraation of
          general  release  patterns for various flow requirements at the estuary.
          Appendix B includes detailed schematics of the various sub-basins and
          a  listing of the input data,

-------
.EGEND
    " *""
    RESERVOIR
 Q NODE
    DECISION  POINT
                   s~\
                   U62V-
                  SCHEMATIC  OF
         UPPER  POTOMAC  RIVER  BASIN
             FLOW  RELEASE  MODEL
                                                           Figure 5

-------
                                  54
            of Tableaux
     A simplified flew chart of the satire model including the develop-

ment of the tableaux within tb* general basin paragon is  presented in

Figure 3.   An itemized description of the basic computational steps of

the model  specifically relating the formation of the various  tableaux

to the paragon of the  upper portion of the Potoaac River  Basin is  given

below.  The pertinent  nodes and reaches are shown in Figure 5.

     1. For reach 1 containing the Blocanington Project (node 570),

        set the reservoir release rate to the minimum discharge

        value.

     2. Route flow from reservoir and resulting water quality to  first

        decision point (node 560) incorporating into the system

        changes in quality or quantity resulting from any downstream

        waste loads,  unregulated tributaries, water intakes, etc.

        During the routing process, the water quality is monitored at

        prescribed increments of distance to determine if the DO  con-

        straint is being met.  If the constraint is violated , the

        release rate  is increased by a fixed flow increment  and the

        routing process is repeated.

     3. Continue routing process froa the reservoir by increasing the

        discharge rate by the fixed flow increment until the maximum

        release rate  froa the impoundment ia obtained, thereby com-

        pleting the development of the IFT for reach 1.   The tableaux

        for reach 1 are indexed* by node 570.  (See Table 4.)
     *In the model, the IFT for a given reach is indexed by the first
node upstream fraza the decision point.

-------
                              55






4.  For reach 2 containing Savage II project (node 566), repeat



    the operations similar to those for the Bloomington Reservoir



    in steps 1, 2, and 3.  The IFT for this reach is indexed by



    node 562.  (See Table 4.)



5.  Utilizing the converging branch system of dynamic programming



    and the enumeration process, develop for the first decision



    point from the IFT's of nodes 570 and 562 the optimal flow




    release sequences from the Bloomington and Savage II Reser-



    voirs.  The end product of the enumeration process is a DFT



    which contains a listing of all feasible solutions for all



    flow states within the minimum and maximum flow regulation



    capabilities of reaches 1 and 2.  (See Table 8 for a DFT for



    node 560.)



6.  Similar to the operations in step 2, in reach 3 route all



    feasible solutions of the above decision point to the next



    downstream decision point (node 460).  The IFT for reach 3 is



    indexed by node 494.  (See Table 4.)



7.  For reach 4 containing the Royal Glen Project (node 492),



    repeat the operations similar to those for the Bloomington



    Reservoir in steps 1, 2, and 3.  The IFT for this reach is



    indexed by node 462.  (See Table 5.)





-------
                                56
     9.  Similar to the operations la step 2, route in reach 5  all
         feasible solutions of th* above decision point to the next
         downstream decisioa point (node 456).  The IFF for reach 5 ia
         indexed by node 460.  (See Tabl 6.)
    10,  For reach 6 containing the Town Creek Project (node 458),
         repeat the operations similar to those for the Bloomington
         Reservoir ia steps 1, 2, and 3.  The IFT for this reach is in-
         dexed by node 453.  (See Table 5.)
    11.  As daeeribed in step 5, develop for the third decision point
         (node 456) all optiaal release sequences from the Town Creek
         Project and the feasible solutions in reach 5 front IFT's of
         nodes 453 and 460, respectively.  (See Table 10 for DPT for
         nod* 456.)
    12.  For the final reach of the tipper portion of the Potomac River
         Basin, the tezsdnal IFT ia developed by routing all feasible
         solutions from the above decision point to node 436.  (See
         Table 7.)
     In ouaaary the following aggregation of tableaux has been computed
for the sodas belsur:
         Jbaeremeatal Flow Tableaux
             Nodes
Dynamic Programming
     Tableaux
             570-
             562.

             462-
560	3

         ___   C

         _____7
                        7
         IFT

-------
                                   57



                                 Table k

                         INCREMENTAL FLOW TABLEAU

                                 NODE 570
Flow
(cfs)
31.20
51.20
71.20
91.20
111.20
131.20
151.20
171.20
191.20
211.20
231.20
BOD
(mg/1)
2.1k
2. 78
2.81
2.83
2.85
2.86
2.87
2.87
2.88
2.89
2.89
DO Deficit
(ng/1)
0.33
0.61*
0.93
1.18
1.1*0
1.59
1.76
1.91
2.05
2.17
2.27
Sat DO
(rag/1)
8.51
8.53
8.57
8.62
8.66
8.70
8.7^
8.78
8.82
8.85
8.88
Temp
(c)
22.95
22.78
22.55
22.29
22. Ok
21.79
21.56
21.3l
21. lU
20.95
20.77
 61.80
 81.80
101.80
1.81*
1.87
1.89
NODE 562

   0.35
   0.1*5
8.56
8.61
8.67
                                                    22.65
                                                    22.33
                                                    21.99
^3.33
263.33
283.33
303.33
323.33
3^3.33
363.33
383.33
1*.30
l*.i6
l*.0l*
3.93
3.83
3. 7l*
3.167
3.59
               NODE l*9l*

                  0.86
                  0.87
                  0.88
                  0.89
                  0.90
                  0.91
                  0.92
                  0.93
                     8.50
                     8.50
                     8.50
                     8.50
                     8.50
                     8.50
                     8.50
                     8.50
               23.00
               23.00
               23.00
               23.00
               23.00
               23.00
               23.00
               23.00

-------
                                  58



                               Table 5

                       IHCRS4EHTAL  FLOW TABLEAU

                               NODE 462
Flow
(cfs)
31 . 10
101.10
121.10
11*1.10
i6i.lO
181.10
201.10
221.10
2U1.10
261.10
281.10
301.10
321.10
31*1.10
361.10
331.10
1+01.10
1*21.10
Ml. 10
1*61.10
i.81.10
501.10
521.10
51*1.10
561.10
BOD
(mg/1)
0.73
0.79
0.81*
0.89
0.93
0.96
0.99
1.02
1.05
1.07
1.09
1.11
1.13
1.15
1.16
1.18
1.19
1.21
1.22
1.23
1.25
1.26
1.27
1.28
1.29
DOD
(mg/1)
0.10
0.09
0.09
0.09
0.09
0.09
0.10
0.10
0.10
0.10
0.11
0.11
0.11
0.12
0.12
0.12
0.13
0.13
0.13
0.14
0.14
0.14
0.15
0.15
0.15
Sat DO
(fflg/1)
8.53
8.53
8.52
8.52
8.52
8.51
8.51
8.51
8.51
8.51
8.51
8.51
8.51
8.51
8.51
8.51
8.51
8.51
8.50
8.50
8.50
8.50
8.50
8.50
8.50
Temp
(c)
22.78
22.82
22.85
22.87
22.89
22.90
22.91
22.92
22.93
22.93
22.94
22.94
22.94
22.95
22.95
22.95
22.96
22.96
22.96
22.96
22.96
22.96
22.97
22.97
22.97
  5.00
 25.00
 -o.OO
 65.00
 55.00
--5.00
 ,80
 .86
 ,88
 .90
 .90
1.91
NODE 458

   0.01
   0.05
   0.11
   0.18
   0.2U
   0.29
8.50
8.51
8.53
8.55
8.58
8.60
23.00
22.95
22.82
22.67
22.53
22.40

-------
           59
        Table 6




IHCKEMBHTAL FLOW TABLEAU




        BODE 1*60
Flow
(cfs)
32l*.l*2
341*. 1*2
361*. 1*2
381*. 1*2
404.42
, - 1 | -.
24.1*2
Hi* 1*. 1*2
u64.1*2
481*. 1*2
504.1*2
521*. 1*2
544.42
564.22
581*. 1*2
604.1*2
624.1*2
644.1*2
664.1*2
684.1*2
-rf\\, ] 
04.42 t
^24.42
"*)ili 1.0
, 44 , i|^
"64.1*2
"84.42
504.1*2
=21*. 1*2
SP"* u , ii2
564.1*2
364.1*2
904.42
524.42
-i.4 ).o
- ^ . ^c
BOD
(aw/1)
3.19
3.07
2.97
2.88
2.79
2.72
2.66
2.60
2.55
2.50
2.1*6
2.1*2
2.38
2.35
2.32
2.29
2.27
2.21*
2.22
2.20
2.18
2.17
2.15
2.13
2.12
2.13
2.13
2.11*
2.11*
2.11*
2.15
2.15
DOD
(n/i
0.1*1
0.1*0
0.39
0.39
0.38
0.38
0.37
0.37
0.36
0.36
0.35
0.35
0.35
0.3k
0.3k
0.3k
0.33
0.33
0.33
0.33
0.33
0.32
0.32
0.32
0.32
0.33
0.35
0.36
0.37
0.38
0.39
0.1*0
                           Sat DO
                                            Temp
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99

-------
          60
        Table 7




INCBJ04ENTAL FLOW TABLEAU




        NODE 1*36
Flov
(cfs)
386. U2
1*06.1*2
1*26.1*2
1*1*6.1*2
1*66.1*2
1*86.1*2
506.1+2
526.1*2
51+6.1+2
566.1*2
586.1*2
6o6.1*2
626.1*2
6l*6.U2
666.1*2
686.1*2
706 . 1*2
726.1*2
71*6.1*2
766.1*2
786.1*2
806.1*2
826.1*2
81*6.1*2
866.1*2
886.1+2
906.1+2
926.1+2
91*6.1+2
966.1*2
986.1+2
1006.1*2
1026.1*2
101+6.1+2
1066.1+2
1086.1+2
1106.1+2
BOD
(ntt/1)
1.15
1.16
1.18
1.17
1.16
1.16
1.15
1.15
1.15
1.15
1.15
1.15
1.15
1.15
1.15
1.15
1.15
1.15
1.15
1.15
1.16
1.16
1.16
1.16
1.1?
1.16
1.17
1.17
1.18
1.19
1.19
1.20
1.21
1.21
1.22
1.22
1.23
DOD
(mg/1)
0.11
0.12
0.12
0.12
0.12
0.12
0.13
0.13
0.13
0.13
0.13
0.11+
O.lU
0.11+
0.11+
O.lU
O.ll*
0.15
0.15
0.15
0.15
0.15
0.16
0.16.
0.16
0.16
0.16
0.16
0.17
0.17
0.17
0.17
0.18
0.18
0.18
0.18
0.19
Sat DO
(mg/D
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
8.50
Temp
(c)
23.00
23.00
23.00
23.00
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.99
22.98
22.98
22.98
22.98
22.98
22.98
22.98
22.98
22.98
22.98
22.98
22.98
22.98
22.98

-------
            61









          Table 8




DYNAMIC PROGRAMMING TABLEAU



          NODE 560
"otal Flow
(cfs)
93.00
113.00
133.00
153.00
173.00
193.00
213.00
233.00
253.00
273.00
293.00
313.00
333.00
Flow at 562
(cfs)
61.80
81.80
101.80
101.80
101.80
101.80
101.80
101.80
101.80
101.80
101.80
101.80
101 . 80
Flow at 570
(cfs)
31.20
31.20
31.20
51.20
71.20
91.20
111.20
131.20
151.20
171-20
191.20
211.20
231.20
BOD
(mg/1)
2.1U
2.11
2.09
2.19
2.27
2.33
2.39
2.13
2.U7
2.51
2.5^
2.56
2.58
DOD
(mg/1)
0.3^
0.1*2
0.1*9
0.57
0.70
0.8U
0.99
1.13
1.27
1.1*0
1.52
1.61*
1.71*

-------
            62
          Table 9




DYNAMIC PROGRAMMING TABLEAU




          NODE UbO
"... Flow
, 12
...,1*2
..1*2
 ,.1*2
.::. 1(2
-jl*. 1*2
.'.I*.l2
 o!. .1*2
-31*. 1*2
.3". 1*2
1^.1*2
--4.1i2
:cl*.l*2
;-:4.1*2
:3U 1*2
2u.l*2
"4,1*2
-.61*. 1*2
4.42
'U.U2
24 1*2
"'1.1*2
a. 1*2
""4.1*2
:^.1*2
J4 U2
-'4, 1*2
-'34 . 1*2
 3 L 1 2
'^.1*2
-1..U2
""-.i*2
Flow at 1+62
(cfs)
81.10
101.10
121.10
lUl.10
161.10
181,10
201.10
221.10
21*1.10
261.10
281.10
301.10
321.10
31*1.10
361.10
381.10
1*01.10
U21.10
1*1*1.10
1*61.10
1*81.10
501.10
521.10
5U1.10
561,10
561.10
561.10
561.10
561.10
561.10
561.10
561.10
Flow at 1*9H
(cfs)
21^3.33
21*3.33
21*3,33
21*3.33
21*3.33
21*3.33
21*3,33
2U3.33
21*3.33
2U3.33
2U3.33
21*3,33
21*3.33
2U3.33
21*3.33
21*3.33
21*3.33
21*3.33
21*3,33
21*3.33
2U3.33
21*3,33
21*3,33
2U3.33
21*3,33
263.33
283.33
303,33
323.33
3U3.33
363-33
383.33
BOD
(mg/1)
3.U1
3.27
3.15
3.05
2 ,,96
2.88
2.80
2,7l*
2.68
2.63 '
2.58
2,5^
2.50
2.1*6
2.1*3
2.1*0
2.37
2.3**
2,32
2.29
2.27
2.25
2.23
2.22
2.20
2 21
2.21
2.22
2.22
2.22
2.22
2.23
DOD
(mg/1)
0.67
0.63
0.50
0.58
0.55
0.53
0.51
0.50
0.1*8
0.1*7
0.1*6
0.1*1*
0.1*3
0.1*3
0.1*2
0,1*1
0.1*0
0,1*0
0.39
0.39
0.38
0.38
0.37
0,37
0,36
0.38
0,1*0
0,1*1
0.1*3
O.UU
0,1*6
0.1*7

-------
?
                                     Table  10




                           DYNAMIC PROGRAMMING TABLEAU




                                     NODE 1*56
Total Flow
(cfs)
329. !*2
3^9. 1*2
369.1*2
389. k2
'(09.1*2
1*29.1*2
UQ.1*2
Uo9.1*2
1*89.1*2
509. 1*2
529.1*2
5^9.1*2
569.1*2
589.1*2
609.U2
629.1*2
ol-9.1*2
069.1*2
639. 1*2
709.1*2
729.1*2
7l*9.U2
769.1*2
739.1*2
309.1*2
o29.1*2
31*9.1*2
i69.1*2
659.1*2
909.1*2
929.1*2
^9.1*2
X<9.1*2
V89.1*2
1C09.U2
-'29.1*2
"-9.42
Flow at 1*58
(cfs)
5.00
25.00
1*5.00
1*5.00
1*5-00
1*5.00
1*5.00
1*5.00
1*5.00
1*5.00
1*5-00
1*5.00
1*5.00
1*5.00
1*5.00
1*5.00
1*5.00
1*5.00
1*5.00
1*5-00
1*5.00
1*5.00
1*5.00
1*5.00
1*5. OC
1*5.00
1*5.00
65.00
85.00
105.00
105.00
105.00
105.00
105.00
105.00
105.00
105.00
Flow at 1*60
(cfs)
32U.1*2
32l*.l*2
321*. 1*2
31*1*. 1*2
361*. 1*2
381*. 1*2
l*0l*.l*2
1*2U. 1*2
1*1* I*. 1*2
U6U.1*2
1*81*. 1*2
501*. 1*2
521*. 1*2
5l*l*. 1*2
561*. 1*2
581*. 1*2
6oU.l*2
621*. 1*2
61*1*. U2
66U. 1*2
681*. h2
701*. 1*2
72U. 1*2
71*1*. 1*2
761*. 1*2
78U. 1*2
801*. 1*2
8Ql*.l*2
80U.1+2
80i*.l*2
821*. 1*2
81*1*. 1*2
86U.U2
88U. 1*2
90U.1*2
92l*.l*2
9l*l*.1*2
BOD
(mg/1)
3.17
3.10
3.0l*
2.9l*
2.85
2.77
2.70
2.61*
2.59
2.51*
2.1*9
2.1*5
2.1*1
2.38
2.35
2.32
2.29
2.27
2.2U
2.22
2.18
2.18
2.17
2.15
2.13
2.12
2.11
2.10
2.10
2.10
2.10
2.11
2.11
2.12
2.12
2.12
2.12
DOD
(fflg/1)
0.1*0
0.38
0.37
0.37
0.36
0.36
0.35
0.35
0.35
0.31*
0.31*
0.31*
0.33
0.33
0.33
0.33
0.32
0.32
0.32
0.32
0.32
0.31
0.31
0.31
0.31
0.31
0.31
0.31
0.31
0.32
0.33
0.31*
0,35
0.36
0.37
0.38
0.39
                                                                                          I

-------
                                             Table 11

                                   DYNAMIC PROGRAMMING TABLEAU
                                   (Churchill's  K  Formulation)

                                             NODE 1*56
i
Total Flow
(cfs)
31*9.1*2
369.1+2
389.1*2
1*09 . 1*2
1+29 . 1*2
1*1*9.1*2
1*69.1*2
1*89.1*2
509.1*2
529.1*2
5!*9.1*2
569.1*2
589.1*2
609.1*2
629.1*2
61*9. U2
669.1*2
689. 1*2
709 . 1*2
729.1*2
71*9.^2
769.1*2
789 . 1*2
809 . 1*2
829.1*2
81*9.1*2
869.1*2
889.1*2
909.1*2
929.1*2
91*9.1*2
969.1*2
989.1*2
1009.1*2
1029.1*2
101*9.1*2
Flov at 1*58
(cfs)
5.00
25.00
1*5.00
65.00
65.00
65.00
65.00
65.00
65.00
65.00
65.00
65.00
65.00
65.00
65.00
65.00
1*5.00
1*5.00
1*5.00
1*5-00
1*5.00
1*5.00
1*5-00
1*5-00
1*5.00
1*5.00
1*5-00
65.00
85.00
105.00
105.00
105.00
105-00
105-00
105.00
105.00
Flow at 1*60
(cfs)
31*1*. 1*2
3l*U. 1*2
31*1*. 1*2
3U1*. 1*2
361*. 1*2
381*. 1*2
1*01*. 1*2
1*21*. 1*2
1*1*1;. 1*2
1*6U. 1*2
1*81*. 1*2
501*. 1*2
52U.U2
51*1*. 1*2
' 561*. 1*2
581*. 1*2
62U. 1*2
61*1*. 1*2
661*. 1*2
681*. 1*2
701*. 1*2
72l+.l*2
7l+ 1*. 1*2
761*. 1*2
781*. 1*2
80U.U2
82l*.l*2
821*. 1*2
821*. 1*2
821*. 1*2
81*1*. 1*2
861*. 1*2
881*. 1*2
90l*.l*2
921*. 1*2
91*1*. 1*2
BOD
(mg/1)
3.13
3.06
3.00
2.95
2.86
2.79
2.72
2.66
2.60
2.55
2.51
2.1*7
2.1*3
2.1*0
2.36
2.3l*
2.29
2.27
2.25
2.23
2.21
2.19
2.17
2.16
2.11*
2.13
2.11
2.11
2.11
2.10
2.11
2.11
2.12
2.12
2.12
2.12
DOD
(mg/1
0.62
0.59
0.57
0.55
0.51*
0.53
0.52
0.51
0.50
0.50
0.1*9
0.1*8
0.1*7
0.1*7
0.1*6
0.1*5
0.1*5
0.1*1*
0.1*1*
0.1*3
0.1*3
0.1*2
0.1*2
0.1*1
0.1*1
0.1*1
0.1*0
0.1*0
0.1*0
o.Uo
0.1*1
0.1*2
0.1*1*
0.1*5
0.1*6
0.1*7

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                           65






                      Table 12



                   FLOW BAittS MIA



              Upper Potome Hirer Basin

i
f

~
EL

I
1
1
&
,
:
r

1
i

Node
#**
570
566***
562
560
494
,92***
462
.,60
.53***
456
06

Mtniana Flow*
(cfs)
&.20
61.80
61.80
93.00
143.33
40.00
81.10
224.42
5.00
229.42
286.42

* minima flow for this study coopated as 7-day
recurrence interval of once in ten years.
** aarLnani flow eouals nlniani flow -plus reiralatd
y\t
Maxioun Flow
(cfs)
231.20
101.80
101.80
333.00
393.33
520.00
561.09
944.42
105.00
1049.42
1106.42

low flow with
Lon capacity.
denotes reeerroir sites.


-------
     Partial  listing of the taole&ux for conditions typical for the




m-.T-th of July are given in Tables k through 10,   A reduced form of the




minimum-maximum flow range listing for the above nodes is presented in




>.blp 12.



 n< r i' m e; < t a 1 F i ow Tab 1 qaiix.




     .As an integral part of the model output, the IFT's are used for




enveloping the release patterns and are also very useful for establishing




crie effects of flcrw regulation on the various water quality parameters.




In IFT-s for  nodes 570, 5fo2, U62, and U50, the effects of increasing




reservoir release rates vassuming the quality in the impoundment remains




tinstant with flow) are clearly demonstrated.  In these reaches, the




vater quality is primarily controlled by the conditions in the im-




prandment and the stream reaeration capacity.




     For the  reservoir at nodes 570 and 568, the BOB was assumed t<-> be




:..0 tng/1 and  CO concentration 5.0 mg/1, and c',0 mg/1 of BOD and 8.0 mg/1




DC-, respectively,.  With the quality remaining constant with flow, the




IFT for this  node clearly demonstrates how the increase flew rates




lessen the recovery of initial DO deficits.  Similar response is shown




for the reservoir at node 5&S, although in this case the response is not




so drastic because of the longer stream reach*




     The effects of the i?astewater loads it. reach 3 the quality con-




straints, and flow augmentation can be readily seen in IFT's for




nodes ^9^ an0.  In the downstream end of reach 3, as indexed by




toe IFT for node ^9**, the flow range is from lU3 to 383 cfs.  (See




Table 12.) However, due to large wasted-rater loads in reach 3? a mini-




mum of 2U3 cfs is required to meet the DO quality constraint of U.O mg/1.




This results  in a feasible range of flow from 2^3 to 383 cfs instead

-------
                                  67


 of the maximum regulatable range of 143 to 383 cfa,  A similar reduction

it also imposed on downstream nodes affected by the releass range in

reach 3e

                    Tableaux
     As  can be seen in the DPT's for nodes 560, 460, and 456 in

    ci*  8,  9, and 10, respectively, the tableaux contains for each flew

o+.ste an optimal combination of tha two contributing tributaries or

reaches,  The tableaux also contains the flow contributions of the

I^T's indexed by the first upstream node and the numerical values of

TH? two return variables, BOD and DOD0  Not included in the partial

Us ting  are two remaining state variables, temperature and deoxy-

j*"nation rate,.  Appendix C includes a complete display of computer

-.-pa4-,  of  the flow release model for the Patuxent Basin.

     Tb tnd&xlng as described above and a listing of irj rdsvan-

naximuni flow ranges for each node as given in Table 12 provides a

simple  linkage* between the DPT's and IFT's.  This linkage is nees-

^firy in developing the reservoir release sequences which is discussed

in the  next two sections of this chapter,

     Since there are no iua,jor waste sources above th^ first decision

point (node 560), the jaajor factor controlling the optiniz&tion prcceas

!* the  water quality in the proposed reservoir sits0  In the dynamic

programming optimisation routine for nods 560, 33 fe^sifcle sclution=

          investigated usi^g a flow grid of 20 cfs.  With the selecV.on
     ^Linkage in this study is defined as providing a mechanism,
       manual or via the computer, for data transmission between
T"'? output of a series of calculations and/or decisions ar,d the
     red input for a succeeding series of calculations ar^l/or
-"visions.

-------

                                  68





of the minisBBB BOD increment of 0,5 Bg/1, the zncnber of feasible solu-



tions wa? reduced to thirteen,,  Since the BOD range was never greater



than Oo5 fflg/1 per flow statft, only on feasible solution was  retained



pw flew artate,  Hence, th* optimal solution for th given flow state



i that combination which yields the miniania DO deficit,



     For tha s^esnd decision point (ned 4^0), tha release pattern is



from ths predcaainantly better quality of reach 4.  Tha 200 feasible



solutions were reduced optimally to 32, corresponding to the  maber of



flow states ,  Similar to nod 560, thars is only oa solution per



flew stato



     The DPT of tha third decision pcint (ncsda 456) is sad of  1ST 'a



cf nodes 458 and 460, which are quit* different in quality*  At thia



~.'Aef the 192 feasible soltrtions wer r*diaced to 37 optiaal solutions 0



/LS presented in Table 10, there is a slight vacillation in relaas



pattern as the flow state is increased.  The vacillation is even



asre prcsusmeed fear this nod* -when the Churchill rsaeration is  used,



a.n can b& e&sn in Table 11,  This v&eillatiam is due to the following'



       :  (l) a coarse Bf?D grdf (2) the water quality in tha res ear-



     at nod 458^ and (3) ths POD ret-am pazsraeter,.  In Chapter VI,



      and ether factors will bs dis crossed in greater detail,,




     REL2&SE
     From ths Ifl'a and DET's, it is possible to deterudne two typea



cf qptimnl reservoir release ssqueaees:  (l) "best1 water quality for



* given flow requirejoierrfe , or (2) minimum release rates for a given



watsr quality req'airsiQent   Assuming that all reservoirs in the upper



F"3Jt of the Pofecaac Basin are operational, ths development of a



release pattern is best illustrated by an exaamle.  USTT.CT +>,*

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' I
                                           69





        test  runs and tableaux for July, the  optimal release sequences given



        in Table 13 would be required to provide the best water quality (mini-



        mam DOD for a given BOD state)  for a  flow target of 706 cfs at node 436.





                                       Table  13



                       EXAMPLE OF AN OPTIMAL RELEASE SEQUENCE
Point
Terminal
3rd Decision
2nd Decision
1st Decision
Node
436
456
460
560
Total Flow
(cfs)
706
649
644
193
IFT
Node

458*
462*
562*
Flew
(cfs)

45
401
102
Node
i 
460
494
570*
IFT
Flow
(cfs)

604
243
91
             *XFT's  downstream from reservoirs





             The above release sequences  for the decision points have been



        developed in reverse order from which the tableaux were formed  That



        is, by starting with the terminal node 436, proceeding upstream, and



        diverging at each decision point, the flow requirements for each con-



        tributing IFT of  each stage have  been datsrmined as indicated in Table 13.



             From the above  Table  13, Table  12, and by subtracting the flow con-



        tributions of the unregulated drainage areas, the following reservoir



        operating scheme  has been  derived for the imposed conditions:



             1.   Reservoir at node 570, a release rate of 91 cfs.



             2.   Reservoir at node 568, a release rate of 102 cfs.



             3.   Reservoir at node 492, a release rate of 360 cfs,



             4.   Reservoir at node 458, a release rate of 45 cfs.

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                                  70





Since the reservoir at code 568 is drawn to its "3xlmm capacity,  the



draw down of the reservoir at node 270 ia necessary to s&et quality



constraints in reach 3.



     It ia also possible to develop a flow release pattern which is



dictated by desired quality at a decision point.  For example,  at



node 456 a total of 529 cfs or greater would be required to maintain



a BOD level of 2.5 ffig/1 or loss.  A release pattern can be obtained



to maintain the BOD objective similar to the sequence developed for



a given flow rate at node 436.





WATER QUALITY CONTROL CQtSIDSBAIIOtB IS HESERVOIH DESIGN



     As indicated in the previous section, the flow pattern may vary



for a given decision point, depending on the total flow.  While it is



not feasible to construct a reservoir to meet these vacillations, the



existence of a trend in release patterns is as important as are abso-



lute release sequences.



     In studies at the Chesapeake Field Station, Hetling[79] determined



effects of flow regulation and waste treatment on the water quality in



the Potowic Estuary.  Using a DO objective of 4.0 B^g/1, 91, 92, and



93 percent removal of the 5-day BOD is required for 2000, 1500, and



1000 cfs of flow, respectively.  The optiaal flow release sequences



for the proposed reservoir system to meet the three flow targets are



shown in Figure 6.



     These release patterns have been developed employing the following



conditions:



     1.  Wastewater loadings and water supply usage as given in



         Appendix B.

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                                                      71
I

                                                   t -|__J_L !  '
                                                   t..L 4-U
                                                   I ..I. 1 j-j-l

                                                        rt  f
                                                                                                   Figure  6

-------
                                  72





     2.  Water quality of all streaa flow addition points (including



         reservoirs) regains constant with flow.  BOD and DO are



         assxuaed to be 2.0 and 8.0 mg/1, respectively.



     3.  O'Connor's Kg formulation is used to determine reaaration



         rate.



     4.  Steady-state temperature for entire river system is 23  C.



     5.  Base flow and regulation capacity of the reservoirs are as



         indicated in Figure 6,



     6.  DO constraint is 4.0 sag/1 in all reaches.



The above have been used also as standard test conditions for the sensi-



tivity analysis in conjunction with 1500 cfs requirement in the



estuary.



     For the preceding conditions, it can be seen that the Savage II



and Brocks Gap Reservoirs at nodes 104 a&d 56*8 are at their maximum



release rate for all three target flows at the estuary while the



Tonoloway Creek and Six Bridge Reservoirs at nodes 56 and 434 are at



their base flow rates.  The two reservoirs which are at their maximum



rates are of primary importance in the optimal flow release pattern.



The Staunton, Winchester, Chaabersburg, Back Creek, and West Branch



Reservoirs at nodes 244, 356, 393, 398, and 402, respectively, are .



utilized to their capacity at 1500 and 2000 cfs target, indicating a



secondary importance in the release pattern.



     In the entire Potomac River Basin affected by the proposed reser-



voir system, the North Branch is the only section of the Potonac that



requires additional flow regulation to meet the 4.0 Eg/1 DO objective.



This is reflected in the constant release rates from Savage II and



Bloomington Reservoirs for all targets and levels at the estuary.

-------

                             CHAPTER VI





                        SENSITIVITY ANALYSES



     In thla chapter the spatial sensitivity of the reservoir release



patterns are related to changes in (l) biochemical and physical,



(2) design,  and (3) socio-economic parameters.   Comparisons of the



various release sequences in response to a change in a given parameter are



made to the  standard test run which was described in the previous chapter



and is presented in Figure 6.  The biochemical  and physical parameters



investigated were time of travel, reaeration, minimum BOD concentrations



and deaeration; the design parameters were stream temperature, BuD-DO



concentrations in the proposed reservoirs, wastewater loadings, and DO



concentration in the wastewater effluent; and the socio-economic.param-



eters were water quality objectives and imposed waste loadings.





BIOCHEMICAL  AffD PHYSICAL PARAMETERS



     The three basic biochemical and physical parameters required in



t'o quality  formulations are (l) time of travel, (2) reaeration rate,



and (3) deaeration rate.  Problems in determining these parameters



and suggested steps in simplifying the verification of the quality formu-



lations are  given in Appendix A.



     Based on verification studies in the North Branch of the Potomac



River and in the Patuxent Basin, the most important parameter appears



*o be time of travel.  An example of the important!-? -^ travel time is



given in Appendix A,  where a 65 percent over-estioatier; in time of travel



         in  a 3QO percent error in calculating  the assimilative capacity

-------
                                  74





of tha North Branch.  Not only is tbe travel time an integral part of



the water quality formulations, "but also a constituent parameter in



the predictive reaeration formulations and used in calculating the



deaeration rate of the stream.  Therefore, any analysis of the sensi-



tivity of the flow release pattern to this parameter would also reflect



changes in the temperature profile, reaeration rates, etc., and would



not yield any definitive information.  Also, with the use of tracers



the time of travel measurement is becoming more exact and less costly.



Reaeration.



     Of the remaining two parameters, the reaeration rate appears to



be next in importance.  Even with good information on deaeration rates



and times of travel, considerable engineering judgment is required in



the selection and use of the reaeration formulations.  In Table 15 and



in Figures 13, 14, and 15, it can readily be seen that even with the



same velocity and depth data, more than a threefold difference in re-



aeration rates can be observed depending on which formulation is used.



     A test run has been made using the Churchill K2 formulation and



with all the remaining parameters being the same as in the standard



test conditions.  When the release pattern is compared to the standard



test run (O'Connor's Kp formulation), differences in the release rates-.



from four reservoirs are observed.  (See Figure 7.)  Three of these



changes are minor, 20 cfs, with the remaining being more significant,



60 cfs.



     The small number of changes in the entire release pattern is pri-



marily due to the location of the waatewater loads in the Potomac Basin.



In only one section of tha basin, reach 3 in the North Branch watershed,



flow augmentation is required to meet the DO quality objective.  The

-------
                                  75





constraining section of this area (River Mile 305-310) is in waters



ranging from 6 to 12 feet in depth.  As can be seen in Figure 16, the



two computed DO profiles are essentially the same at this critical reach,



hence there is only a slight difference in the flow requirements.  How-



ever, if the constraining reach had been downstream about 10 miles,



the change in release pattern would have been significant.



Deaeration and Minimum BOD Concentrations



     The deaeration rates of the wastewaters used in the standard test



runs were either determined as outlined in Appendix A or obtained from



previous water quality studies.  For all stream flow addition points, a



deaeration rate of 0.1 (base 10 at 20C) was assumed.



     An additional computer run was made using the standard test con-



ditions, except that the deaeration rate of all wastewaters was set at



0.15 (base 10 at 20C).  The reservoir release sequence to maintain



1500 cfs at the estuary was very similar to the standard test run.  See



Figure 7 for comparison to standard test run.



     The insensitivity is primarily due to the small changes in the



overall stream deaeration rates.  In setting all values at 0,15, some


                                                                                I1',!
wastewater rates are increased while others are decreased, with an               ji;


                                                                                *''*
overall slight increase of less than 0.02 for the entire basin.                  ill



     Of equal importance is the assumption of a minimum equilibrium             : jjj



level for BOD between the waters of the stream and the stream bed.        ,      \v.\

                                                                                Jill

Field studies conducted by the Chesapeake Field Station and by others           jiji



indicate that there is a background BOD of 1.0 to 3.0 mg/1 with a               |; !

                                                                                1:1"

corresponding DO level of about 80 to 90 percent of saturation in long          ! |;



reaches of the Potomac containing no point-source pollution.  With the           |, {

                                                                                .! i';
                                                                                 i I' *
first-order BOD decay equation used in the model, the resulting BOD              j M

-------
f
                                                                             Figure 7

-------
                                  77






.Oncentrations approach 0.0,  and the DO values are near saturation in



j;ese reaches.  As  can be  seen in Table 7 for Node 436 (River Mile 238.0),



,ve BOD  is about  1.0 mg/1  with the DO near saturation.  Since there is



-j3 aiajor point-source  of pollution between Node 436 and the estuary,



 i.e BOD  approaches  0.0 mg/1 and the DO remains near saturation for the



ncceeding downstream  reaches.



    Under standard test conditions, a computer run was made in which



je dynamic equilibrium was limited to a minimum level of 2.0 mg/1.  In



-.ne run, whenever the  BOD  dropped below 2.0 mg/1, it was reset to



: 0 ng/1.



    Major changes  occurred in the release rates from Six Bridge and



oyal Glen Reservoirs  when compared to standard test runs.  The limiting



::" the BOD to 2.0 mg/1 causes all the reservoirs in the lower portion



:f the basin to draw down  first.  (See Figure 7.)  If the existence of



ZTWO.C  equilibrium level  can be firmly established for various flow



Auditions and temperatures,  the effect of this equilibrium could be sig-



nificant for developing release rates for water quality control in the
   The effects of four engineering  design parameters  have been investi



ftted in this study; these are  (1) temperature,  (2) BOD-DO levels in the



>-3ervoir, (3) wastewater loadings, and  (4) DO concentrations  in the



n^tewater effluents.
    In the flow-release model, the temperature  algorithm exponentially



    s an increase or decrease in temperature to a steady-state temp-



     .  For the standard test run a steady -state temperature  of 23C

-------
f
                                   78





bas  been used,  with the temperatures of the waters from the reservoirs



being taken as  20C.



     The steady-state temperature was determined from a statistical



analysis of the temperature data by months.  The value of 23C is an



average of all  the mean temperatures for the month of July for all water



quality stations in the Potomac Basin.



     To test the effect of temperature on the release rates, a computer



run  was made with the temperaturea set at 28C,  with other parameters



being the same  as for standard test conditions,   As can be seen in



Figure 8, only  a slight change, 20 cfs, occurred in the release sequence



from four reservoirs.



     With an increase in temperature, tha deaeration and the reaeration



rates both increase.  Therefore, there is only a small net change in the



maximum DO deficit which is attributed to the differences in reaction



constants.  The major effect of temperature is on the DO saturation



concentration.   This effect is most pronounced in the North Branch area



which receives  wastewater high in BOD and large  volumes of cooling water,



as can be seen  in Figure 16 and where flow regulation is required to



meet the DO quality constraints.



BQD-DQ Concgn^raJ^ons in the Reservoixs



     A computer run was made to investigate the  effect of water quality



in the reservoirs on the flow release pattern.  In this run the BOD and



DO were set at  3.0 and 5.0 mg/1, respectively, as compared to 2.0 and



8.0 rag/1 for the standard test run,



     The optimal reservoir release sequence to meet the 1500 cfs flow



requirement is  almost similar to that for the standard test run, except



-cr the Royal Glen project  (See Figure 8.)  The small sensitivity of

-------
                                  79

the release sequence to a change, in reservoir quality in the Potomac is
primarily due to the location of the proposed upstream impoundments.
     The distance of moat iapoundaents froa the decision points is
ample to allow significant recovery of initial DO deficit isrposed in
the reservoirs.  The extant of the recovery can be readily seen when
the IFt's are ezaadned in detail.  (See Tables 4, 5, and 6.)  Similar
recoveries restated for the runs whan the BOD and DO were 3.0 mg/1 and
5.0 ng/1, respectively.
Wastewat**r
     To test the sensitivity of the release sequence to changes in
waste loadings, the current BOP loadings before treatment were doubled
for all discharges.  The release pattern developed for the doubled
loading for which the minjwaa treatment was set at 85 percent removal
of BOD is presented in figure S.
     then ccnrpared to the standard test run, release rates from five
reservoirs are changed for a doubled waste load, with Royal Glen having
the greatest change of about 120 cfs.  The increase in release rates
froa North Mountain, Licking Creek, and Town Creek follows naturally
since there are no waste loads in these sub-basins.
     The doubling of waste load resulted in flow requirements above the
base flow in the North Fork and stem of the Shenandoah River.  However,
due to quality difference* at the confluence point with the Potonaac
River, the release rates frc two reservoirs in the Shenandoah sub-basin
are at their nadjsux to meet the 1500 cfs requirements for the estuary
as determined optiaally using the flow release model.

-------

Figure

-------
                                 81






   One of the parameters often overlooked or minimized is the DO  con-


-r.tration in the wastewater effluents.  The effects of low DO waste-


a-,er discharges are most pronounced in reaches where the ratio of


*stejmter to stream flow is greater than 0.5, such as the North Branch.


^ Figure 16, the large drops in the DO at River Mile 338 and 312 are


 result of cooling water and wastewater discharges which are low in


fjsolved oxygen and/or have a high immediate dissolved oxygen demand.


   In the model, the concentration of BOD in thermal discharges is


K*. equal to that of intake water plus any BOD added by the industrial


 f:ility.  The DO and heat content can be set at any prescribed level


  inprt data.  For the standard test runs, the DO of the large waste


cjcharges, including cooling water, was assumed to be 0.0 iag/1.


   To meet a 4.0 ag/1 DO requirement in the North Branch for the BOD


iing used in the standard test, approximately 193 cfs is required                      ; I


 '- :ode 560.  If the BOD loading is doubled with the waste volume held


  	, the flow requirement is about 213 cfs.  Howevar, if the DO


 *Jie cooling water is set at 2.0 Eg/1 instead of 0.0 ffig/1, the flow


^-reaent is about 173 cfs.  This is a 20 cfs decrease in flow require-


   ?jen with the BOD loading being doubled.  Although not shown in


        the effect of a 2.0 mg/1 change in DO in the effluent can

     m
         than the effect of doubling the waste loads, as illustrated


  ^ for-the North Branch sub-basin, indicating the importance of this


         i design.

-------
                                   82






QCIO-ECQNCaCC PARAMETERS



     To determine the effect of selected socio-economic parameters on



the release sequences, ccmput-ar runs hare "been made for an increased




wit*r quality objective to 4.5 rog/i  of DO and for imposed BOD loadings



it two different .reaches   The remaining parameters hav been held




 cnstant as stated for the standard  test runs,
     The effect of selecting a given water quality objective can be



 -*idily observed when the sequences  for the doubled BOD loadings in



 Figures 8 fe.na 9 are compared.  In  Figure 8, the JX) constraint was at



 
-------
                                   83
1
                           -f- -H
                         rn:tx[
                          ! Li LU
                                                                  Figure 9

-------
    As  also can be seen in Figure 9, the release sequence is sensitive



to the imposed loadings at node 448, especially in the upstream portion



of the basin.  The release rates from four upstream reservoirs are



changed  with the greatest change being at the North Mountain Reservoir,



^bout  60 cfs.  However, the release sequence is not sensitive to the



laposed  load at node 2&L; in fact, the release rates are similar to



r,no5e  for the standard test run.



    In  summary, it has been demonstrated for 1500 cfs flow target at



-.he estuary, the spatial reservoir release sequences are sensitive to



Changes  in reaeration rates, stream temperature, wastewater loading,



etc,,  when cosrpared to standard test run.  The greatest changes in



release  rates, as shown in Figures 7 to 9, were in the Blooadngton,



royal  Glen, Town Creek, Licking Creek, and North Mountain Reservoirs,



all of which have an effect on the pollution problem originating in



the North Branch.  The insensitivity of the release sequences from the



>vest Branch, Back Creek, Chaabersburg, Staunton, Brocks Gap, Winchester,



and Six  Bridge Reservoirs is mainly due to two causes (l) relatively




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I
                                     85




        The grouping of the parasaetara as presented in  Figures  71  &,  and


    9 gives the engineer a great insight as to which parameter in a partic-


    ular group may have the greatest effect on a given solution. The


    insight Is even more meaningful whan coupled to the  ability  to  predict


    i given parameter in the future is considered.  For  example, of the


    :hysical and biochemical parameters, velocity and the reaeration rates


    for a given flow and temperature condition should remain fairly constant

S.
    in the future while the deaeration rates are very dependent  on  the


    future wastewater characteristics.  Fortunately,in the Potomac  system


    .he deaeration rates appear to have the least effect on  the  optimal


    .low release patterns and thereby minimizing any possible change in the


    release sequence due to any future changes in wastewater characteristics,


    Tr.e above example demonstrates how with the use of the flow  release


    sodel effective planning can be realized even when all parameters  cannot


    : accurately predicted.

-------
                            CHAPTER VII





           FURTHER DICVKLOPSffiHTS OF THS FLOW RELEASE MODEL



     An expanded version of the flow release model (Version II), which



incorporates the cost of reservoir construction and operation, is pre-



sented in this chapter.  Least-cost solutions are compared to those in



Chapters V and VI, which were primarily concerned with water quality.



Other possible expansions of the model, such as minimizing the deficit



miles, inclusion of nutrient considerations, etc., are also proposed



in this chapter.



     Methods for overcoming the deterministic flow system are pre-



sented in the latter part of this chapter.  Linkage to water quality,



stream flow, and estuary model is also presented.





           SOLUTIONS
     Froa the interpretation of DPT's in Chapter V and the sensitivity



analysis in Chapter VI, it can be generally concluded that the second



return variable, DOD, is not too significant in the optimization pro-



cedure.  This is especially true in the Potomac Basin or when the



waste loads are not overlapping, when reservoir quality is similar,



or when the DO quality constraint is high.  Based on this finding,  the



model has been expanded to incorporate the cost of reservoir construc-



tion and operation.



     The cost of reservoir storage for a given release rate was sub-



stituted for the DOD parameter as the second return variable in the



optimization algorithm.  To provide for non-linear cost data, the cost
                                 86

-------
                                  87






information is read in discrete units amenable to the  flow-increment



grid.  This is explained  in greater detail later in this  chapter.



    For the  least-cost solution,  the problem is expressed mathe-



matically as:



    Fo(Xo(k,p))      Jttn  [Cost(k,p)  BQD(k,p) | Xo(k,p)  -



                                Xa(i) + Xn(j)]        	(7-1)



There



    Cost(k,p)        State of the second dependent variable for



                      a given Xo and BOD state



    Fo(Xo(k,p))      Miniwoa cost of flow regulation  for a given  flow



                      and BOD state; other variables as defined  in



                      Chapter III.



Since the cost state is additive,  an accounting  mechanism is also  in-



corporated  into the aodel.



    With Version II of the flow release model,  it  is  possible to  obtain



a flow release sequence for the optiaization  criteria  listed in  Table 14.





                              Table 14




                 OFTDHZATIQM CRITERIA OF THS FLOW

Optimization
_ Index
I
II
III
IV
V
First Return
Variable
BOD
	
BOD
	
BOD
Second Beturn
Variable
DOD
DOD
COST
COST
	 j_i-___m
Reaarks
Standard test runs
Use large BOD grid
Least-cost solutions
Use large BOD grid
Read in gll cost
                                              data as zeros

-------
                                  88

Version II also has greater flexibility in choice of reaeration pre
diction formulations, temperature coefficients and BOD algorithm
parameters.  See Appendices C, D, and E.
     Using Version II of the flow release model, a series of computer
runs were made to determine the effect of various optimization param-
eters.  As can be seen in Figure 10, release sequences are greatly
affected by the choice of the optimization criterion.
     In the DO deficit and BOD optimization procedure (Optimization
Index l) as discussed in Chapter V, only one solution was normally
retained per flow increment even when a BOD grid as small as 0.5 mg/1
was employed.  The retaining of one solution per flow increment is
essentially reducing the optimization to a single return variable.
(Optimization Index II.)
     With a smaller BOD grid, more solutions could be retained in up-
stream reaches of the Potomac.  However, these additional feasible
solutions would be eliminated at the lower decision points due to lo-
cation of wastewater loadings, assumed reservoir quality, and smooth
response surfaces of the BOD and DO profiles.
     Similar to the above optimization parameters, the least-coet/BOD
(Index III) and least-cost (Index IV) methods yield identical release
sequences for the prepared reservoir system of the Potomac River Basin.
The release sequences for least-BOD optimization parameter (Index V)
is also given in Figure 10.
     While the release sequences are very dependent on the choice of
the optimization criteria, the effect on the water quality entering

-------
                                          89
I,
M
                                                                             Figure  10

-------
                                  90
the estuary is ndnliaal.  Excluding the runs using a dynamic equilibrium
BOP level and imposed BOD loads , the BOD and DO concentrations for
1500 cfa at the estuary vary only about 0.5 mg/1.  Since the greatest
difference in water quality ia in the upstream tributaries of the
Potomac, the release sequences for the various optimisation criteria
are more indicative of upstream conditions and reservoir cost for least-
cost solution than they are of conditions in the main stream.
     A detailed study on the cost of alternative systems for DO manage-
ment in the Potomac Estuary has been made by Davis [3] .  The effect of
developing optimal release patterns for the non-tidal portion of basin
on the various alternatives as presented by Davis is beyond the scope
of this study.

              : WAiEa QUAITY
     In the above flow release model, primary emphasis is given to the
water quality at the decision points.  While the constraints guarantee
an acceptable water quality in the reach, the entire optimization pro-
cedure is based on the quality of the two contributing streams at the
decision point.
     With judicial use of the quality constraint and well-defined
quality algorithms, one can obtain sufficient information for develop-
ment of a flow release pattern; however, the solution is nonencompassing
in regards to the number of stream miles at a given quality level.
Three possible measurements indicative of water quality in the entire
reach are as follows:

-------
                                  91
     1.   Number of streaa miles at a prescribed water quality level,



         e.g.,  at or above a DO of 6.0 Eg/1 or at or above a BOD of



         3.0 sngA.



     2.   Number of Eg/l-mil3 of the waatattttor constituatrtT profilea,



         e.g.,  the area undar tha BOD or DOD quality profiles.



     3.   Siailar to Muaiber 2, ^rith the area calculation being pro-



         rated  according to a predetermined scale, based on the



         degree of the deterioration of the water quality.



     Before any of the above EieasTaresients can be applied realistically



in flow  regulation, it is necessary to assess wastewater treatment



requirements in a similar Esannr.  A method for financing waste treat-



ment facilities using tha constituent profile has bsen advanced by



the State of Ohio[80].



     Another water quality parameter which is receiving much attention



today and which is quit indicative of streaa conditions is that of



nutrient level.  High concentrations of nutrients, ssainly phosphates



and nitrates, usually result in algal bloods, which nay res-alt in



further  deterioration in water quality.  An exponential-loss modal for



predicting the  concentration of phosphates in flowing streasas was de-



veloped  as part of this study and is currently being tested at tha



^esapeaks Field Station.  If it is poaaiblo to express the loss in



Phosphates jDathssjatically, the phosphate level could be used as the



      return variable, instead of the DOD paraaetar.  See Appendix A



    a description of tha phosphate siodel.

-------
I
'%
                                  92






TJgKAGE TO HIVSE IffXET SIJUJLATION MQD5IS



     The  flow release model optimizes in space, i.e., within the



physical  dimensions of  the basin.  The solutions are developed for



independent time units  such as months, seasons, etc.  Since the solu-



tions are independent,  it is hydrologically possible that reservoir



storage required for a  given time unit zaay not be sufficient to



operate optimally.   The deteralnistie tableaux can be transformed



into statistical solutions with the us a of yield curves and validated



Tith linkage to river flew a inflation jaodels.



Uaq of Yield Ciirvea



     Yield curves similar to that for the West Branch project can be



developed for 313. given reservoir sites by routing historical or syn-



thetically generated stream flows through the impoundments.  (See



Figure 11.)



     Thirty-six years of historical data ware routed through the pro-



posed reservoir site on West Branch of the Conococheague Creek for



rarious reservoir sizes and yield targets using the Hirer Basin Simu-



lation Prograa[8l].  The probability of deficiency in months for each



routing and storage capacity iras determined for a prescribed uniform



use rate.



     The  probability of failure can be introduced into the flow release



         sisrply by  developing such curves for each proposed site.  The



       and raaytgftfln flow regulation ranges (required input for the



     raleasa model) can be obtained from these curves for a probability



 D- failure.  For esaapla, for a maxisiura of 50,000 acre-feet of storage



 * A'eat Branch site, the flow range is from a jninimua of 20 cfs to a



       of 120 cfs  for 1 percent probability of failure.

-------
       93
   2jO        30        40
-SIQAAGE. r JQO.O-_ACM._ii_
                                        Figure 11

-------
                                 94

    Using the typical reservoir cost-storage curves as developed by
   Corps of Engineers[731, it is possible to transform the Figure 11
    a uniform use rate (BUB) versus storage cost relatiocsnip for
the various probabilities of deficiency.  This traaaforsaation is re-
quired in the least-coat solutions.
3jvpr Flow S
    In a basin as large as the Poteaaac, there are great differences
in rainfall patterns, ground water, terrain, etc.  These differences
introduce a joint probability of deficiency for each decision point.
    The probability of failure in the flow release sequence developed
in conjunction with the yield curves can be further evaluated by using
option B of Hirer Basin Simulation Program [81].
    The operation patterns as developed from the flow release model  are
raad in as input controls in the simulation model.  The option B
Trograa attempts to maintain the prescribed releases for each reser-
rair for each time unit.
    A more sophisticated model for river flow simulation has been
'TOloped by the Corps of Engineers and greatly expanded by Resources
'or the Future[82].  The simulation program has the advantage of incor-
porating an operating policy (release rules) that is consistent  with
'ct multiple purpose uses served by the proposed reservoirs.  The
       rules accomplish the objectives of rnai.Trtaitd-ng  reservoir pools
   reaeration and flood control, as well as meeting downstream  flow
            for water supply, quality control, etc.
        feature of beiag able to prescribe preference  release patterns
   the various control points (or decision points) makes the simula-
   1 program very aaesabl to the solutions generated by flow release

-------
                                       95
             Fron the ITT'a and DFT's as  described in Chapter V, it is



     possible to determine optimal release patterns.  Further, from the



     tableaux, it  is also possible to determine for each decision point                 jj i



     the next best level of operation.  Thus,  fron the flow release modal,



     one can not only determine the specific release sequence needed to



     operate the system optimally, but also determine the next best



     operational pattern in case there is  insufficient storage to meet



     the optimal release sequence.



         By using the output data of the  flow release model as input



     date for the  river flow simulation program, a linkage in determining



     flow requirements including the probability of failure can be real-                 ,



     ized.  This linkage also can be used  to statistically evaluate the



     significance  of various physical,biochemical, design, and socio-



     economic parameters in regard to failure  frequencies.





     T TW5TA^T? tn^\ TJHu^FTTA en** AUT) TJTT!R?D TtAQ"Tiff f\fTAT T^f^f   C! ^TUTTT AfTT/TTM VjBTYTYEPTC!
     MA!A^M*^UA 1 tJ JEaji u^^Jr^^ .fl-MSr Jj^^ w ifttL X^0tD J^ Si vUJ^^^^UuX. i, * () AgfiJw^^MvX JLv~ri jTm_ft.ir CM^J



         In the application of the Tboaaann steady-state, Thoaana time-



     dependent, or the O'Connor estuarine  models, boundary conditions of



        r,BQD, DO, and temperature are required.  The final tableaux front



         release  program contain these states, and also costs for regu-



     lation, optimally determined for each incremental flow state.  By



          the results of the tableaux aa  input for the estuary jcodela



            can be obtained.



         A complete s isolation program would  be required to completely



             a water quality control prograa  for an entire river basin,



              its estuary.  The following considerations should be in-



     :av?orated in such a basin model.
AT..

-------
                                  96

     1.  A mechanism for streaa flow generation.
     2.  A mechanism for stream temperature generation.
     3.  A model for determining the optimal  reservoir release
         sequences conditional on the status  of the reservoirs.
     4.  A routing of stream flows according  to optimal release
         sequences while maintaining given prescribed conditions  in
         the individual reservoirs.
     5.  A routing of the water quality in non-tidal portion of the
         basin to develop the boundary conditions  at the estuary.
     6.  A routing of the water quality in the  estuary.
The simulation could be either steady-state or  time-dependent.
     Algorithms for many of the above steps currently exist.  Since the
overall program would be enormous, it probably  would have to be accom-
plished in various links.  A proposed flow chart showing the linkage
of the various algorithms is presented in Figure 12.
     Boundary conditions for the upper stream terminal points and im-
posed wastewater loads would be read in as input data.  The upper
boundary conditions of the  estuary model would  be  generated from the
upstream portion by the verification link.
     The development of an  overall basin water  quality simulation model
is the next logical step in evaluating any proposed water quality
           prograa.

-------
97
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                                           Figure  12
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-------
                                  98
     In the flow release model, it has been assumed that there are no
in-stream Impoundments capable of flow regulation.  The imposition of
in-stream impoundments adds additional decision points in the flow
regulation system.  Further, in these impoundments the quality
formulations as given in Chapter III are invalid.
     One possible solution is to develop the release patterns in
reaches bounded by the up-etreaa reservoirs and in-stream impoundments.
The problem would be to (l) maintain a prescribed quality in the reach,
and (2) to optimize the water quality entering the in-stream impound-
ments.  For the lower reaches, assumptions would have to be made on
the water quality leaving the in-stream impoundments.  Models for pre-
dicting water quality from impoundments are currently being developed
by Churchill and Nicholas [S3] and Symons e. aJL. [&4K
     Another possible solution IB to expand the flow release model to
include the in-etream impoundment decision points.  The structuring of
the problem would be very similar to that of the converging branch net-
vork proposed by Nemhauser[72] and more recently by Meier and Beightler[85]
     In expanding the model, it would be necessary not only to add an
algorithm for optimization at the in-stream impoundments, but also to
incorporate quality foraulatioBS through the impoundments.  The quality
formulation and coefficients will probably be specific for a given im-
poundment, thus it is probable that additional input data will also be
required.  Since the quality formulations are not fully developed and it
is possible to develop the release patterns in the bounded sections, a
^odei which incorporates in-stream impoundments would not yield any
additional beneficial use at the present time.

-------
                             CHAPTER VIII






                         DISCUSSION OF RESULTS




     The adequacy and. the compatability of the water quality formulations



with the optimization criteria,and. optimization concepts and adaptation



are discussed in this chapter.  Specific and general uses of tha optimal



release sequence are discussed in the latter part of this chapter.






QUALITY
     In Chapter VI, the spatial sensitivity of the reservoir release



patterns to various biochemical and physical, design, and socio-economic



parameters is presented.  From the release sequences presented in



Chapter VI and the quality profiles shown in Figure 16, it appears



(1) that the release patterns are sensitive to changes in quality param-



eters such as reaeration, velocity, temperature, etc. in the reaches



receiving large volumes of wastewater, demonstrating the need for well



verified quality formulations; and (2) that in relatively unpolluted



reaches, the quality formulations, especially the BOD algorithm, used



in this study were not adequate.



     Two possible solutions to the inadequacy problem are (l) the



inclusion of all sources and siaks of oxygen in the formulation, as



reviewed in Chapter II, or (2) the assumption of a minimum dynamic



equilibrium BOD level by reaches,  A major factor as to which approach



is taisn in selecting a given formulation should be the compatability



of the quality algorithms with the optimization criteria, including



the indicators or measurements of overall water quality in the basin.
                                    99

-------
                                  100





     For the optimization criteria of BOD and DOD concentrations at tin



decision points, the fcrsnulation should include all sources and sinis.



If a ainisam dyaaaic equilibrium level for BOD ia used, the optimiza-



tion criteria should be coupled to more encompassing indicators of



water quality, such as the area under the constituent profiles as sug-



gested in Chapter VII.  The ability to take either approach with only



slight Eodification in the algorithm as presented in the previous



chapter and as discussed in the next section of this chapter taalces the



flow release isodsl developed in this study a very flexible and power-



ful planning tool.





           K CONCEPTS AND AIAPTATIOKS
     As described in Chapter III, the optimization procedure used in



this study was an eraoaeration process.  In conjunction "with the descri;



tive paragon and the converging branches multistage system of dynamic



programming, the enumeration process was very effective in developing



the optimal flow release patterns for the proposed reservoirs in the



Potossac Basin.



     With the converging concept, the number of feasible solutions re-




tained for each stage or decision point was a function of the numerical



range of the first return variable (BOD), the distribution of the




values of BOD within this range, and the size of the flow increment.



Since a uniforn flow increment 7/as used for a given test run, the



number of solutions retained par flew state was mainly dependent on



the range and to a lesser extent on the distribution of BOD at each




decision point.

-------
                                 101



    In the optimization procedure, the range  of first  return variable

controls the size of tha BOD increment per  flow state.   The selection              .  ;, j

of one of five possible increment siaes depending on tha range provides

for jaaxiaaaaa variation in water quality without a corresponding loas in

sensitivity vhen the ranges of BOD are small.

    Daring the enumeration process, only one  feasible  solution is

retained per BOD increment.  If a large BOD grid is  used or if the range

of BCD ia very small, only one feasible solution is  retained per flow

increment.

    For most of the test runs excluding  the least-cost solutions in

the Potomac Basin, the range of BOD per flow state was  usually less than

;.5 nsg/l.  For the stages with a BOD range  greater than 0.5 Eg/1 (the

airujnum increment used in the tast runs), sore than  one solution was

retained per flow state.  Eowavsr, in succeeding downstream decision

points the range of the BOB values converged and the addition of

feasible solutions were eliminated in the enumeration process.

    Upon close examination of the optimal  solutions  for many of the

stages, it was observed for a given flow  state that when the release

pattern yielded the Bri.niiaqi BOD it usually  yielded the  minimum DO

"-eficit.  While the two mini mans do not neesssarily hava to occur simul-

taneously, this observation indicates that  the second return variable

     ia not significant in tha optimization process.   This observa-
                                                                                      !j
  n led to the development of the leaat-cost  solutions as  presented

  Chapter VII,

    The ability to control the number of feasible solutions  which are

  ried forward in the converging concept zaakes  ths enumeration process

  Ascribed above a very powerful optimization procedure.  Moreover,

-------
                                   102
^;
- eliminates  the need for either a complete enumeration of all



feasible solutions or some other complex or time consuming optimization



:rocess  such as  steepest descent.



    The enumeration process can be used with both non-cumulative and



relative  return variables.  The need for continuous and smooth



rr,urn functions is completely eliminated.



    In  general, the optimization technique used in this study is



iirple yet  very  flexible.  Maximum use is made of water quality ranges



r. each  decision point; and, therefore, the optimization procedure can



 4 considered  forward looking.  Also, with the proper use of the input



;"r grids and  increments, a balance between the accuracy of water



 jlity  predictive formulations and optimization capabilities can be



 oily realized.



    One of the  disadvantages of the dynamic programming technique such



  torployed by Liebmanf$6] in comparison to linear programming is the



 -i of  sensitivity analysis associated with the dual variables in the



 '-srlex  solution.  The enumeration process and resulting IFT's and



   s developed  for this study overcome this disadvantage.



    ?or all decision points in the converging branch system, it is pos-



   - to investigate the sensitivity of various controlling parameters



   *o determine the effect of selecting a sub-optimal solution in any



  '"ieular  reach on the overall release sequence pattern.  These added



     *es of the  model produce a mechanism for possible "trade-off"



   "--I the  system.



     ""'2 optimal reservoir release sequence as presented in Figures 7



   '-*-  10  has been developed for 1500 cfs of flow at the Potomac



     ~J> While  the "principle of optissality"[723 is ciaintained for

-------
                                  103
all upstream decision points or stages, the optimal solution for the



estuary may not always provide the "best" solution for a particular local



situation.   The preference of a sub-optimal solution can occur when the



quality difference at decision points is small  and the reaches below it



receive an  insignificant amount of biodegradable wastewater.



    An example of this condition for the standard test run is at the



decision point for node 460.  The optimal solution requires a total of



about  200 cfs from the Blocaaington and Savage Reservoirs, with about



120 cfs froa Boyal Glen impoundment.  If the 60 cfs above the base flow



Royal  Glen  were to be released froa Bloemington, the minimum DO level



in the North Branch would be increased by 0.5 Eg/1 to 4.5 mg/1.  The



additional  release from Royal Glen contributes very little towards in-



creasing the DO level in the South Branch, since its minimum DO level



is greater  than 5.0 wg/1.



    The release of the additional 60 cfs from Blooaington will in-



crease the  BOD and DO deficit at node 460 to about 0.5 Bg/1.  However,



this small  increase will be greatly attenuated in reaches below



node 460.   This can readily be seen when the BOD and DOD concentration



of the standard test runs for nodes 460 and 436 in Tables 6 and 7 are



compared.



    If a return variable acre indicative of overall water quality as



suggested in the previous section were employed, the additional &0 cfs



f flow would be frooa Blooaington instead of Royal Glen.  In lieu of



^ing  another measureaent of water quality, local situations can be



        simply by maMng a series of computer ruaa of the flow



       model at different treatment levels.  For decision points at



      the quality difference is minimal and there are not any critical

-------
                                  104

reaches below it, a trade-off between reservoirs can readily be made
when the release rates are established from the IFF's and DPT's.
     This type of a trade-off can also be made when economic consider-
ations are incorporated into the optimization procedure as in the least-
cost solutions.  The development and use of release sequences including
least-cost solutions for flow regulation and wastewater treatment are
discussed in the next section.
USE OF OPTIMAL flffi
                            SEQUENCES
     As listed in Chapter VI, five flow release sequences  can be
developed, depending on the type of parameter employed in  the optimiza-
tion routine.  The reservoir release rates, which are usually developed
for monthly units of time, are also a function of temperature, treat-
ment levels, reservoir conditions, etc.  If monthly variations of the
above are significant, the release rates have to be determined for
each individual month.
     Jrom the individual IfT's, one can also determine the minimum
flow requirements to maintain a given water quality objective.  By
comparing a series of tableaux at various treatment levels, the effect
of wastewater treatment policies or flow regulation requirements can
be readily observed.  A similar approach 'can be taken in studying the
effect of various water quality objectives.
     Another valuable use of the output of the flow release model is
its ability to investigate alternative methods and use trade-offs.
For example, at node 494, the total cost of reservoir storage for
water quality control in North Branch from Bloomington and Savage II
win be about $10,000,000  for a DO objective of 4.0 mg/1. If the

-------
:;a':it.y constraint is raised to 4.5 ing/1 the cost of storage is increased


;. ,'.v.-OUt $16,000,000.

    1 ne additional 60 cfs of flow needed at node 460 to meet the re-

. ;;re;nent at the estuary can be obtained from Royal Glen at a cost of

i-iut $2,600,000.  If additional wastewater treatment in North Branch

-n result in an increase of the minimum DO level to 4.5 Eg/1 for less

r.in $3,400,000 ($6,000,000 minus $2,600,000) a more economical solution

 ,-r\ l>.  obtained by the trade-off.

    Least-cost solutions for various combinations of flow regulation

  i w&stewater treatment levels can be readily added to the flow

rdase model.  This additional feature is not needed in the Potomac

-53 in as most of the waste loads are not overlapping and trade-offs

 in be  readily made outside of the model as illustrated in the above

-ticaple.  If the need arises for the inclusion of the additional stages

 :r -ach waste discharge, consideration should also be given to the

.."Corporation of other measurements of water quality as return

 riibles.
^c C5 WATER QUALITY MANAGEMENT MODELS WITHIN THE FRAMEWORK OF CURRENT
^rcoGicAL AND INSTITUTIONAL PPACTICSS
    The model as developed in this study represents the first

 "?npt  t-o determine an optimal flow regulation scheme for an entire

 :-'?r basin based on water quality considerations.  One of the signifi-

 "* findings of the study is that most of the optimal solutions for

 : 7:>sed reservoir syste.Tis in the Potomac Basin are predicated on BOD

  - LOO  ron-entration differentials of less than 0.5 mg/1.  That is,

 "" selection of the optimal solution for a given flow state is from

  ^M nation of release sequences which has a resulting BOD and DOD

             differentials of less than 0.5 mg/1.

-------
                                  106
    While it is possible mathematically to define an optimal solution



meaning either best quality of water for a given flow state, or minimal



fj-w or storage requirement  for a  given quality objective), the reduction



in storage requirement  or the increase in water quality level based on



-oece eolutiona for the proposed Potomac reservoir system appears to



; vsftli.  The location of proposed reservoirs, low incidence of over-




,--ping of pollution loads,  and the small difference in quality of the




'.we contributing tributaries at the decision point tend to make the



:;al1ty problems in the various sub-basin areas somewhat independent of



<.-ie another.  Moreover, least-cost waste treatment solutions as re-



viewed in Chapter  II would appear  to have limited use In the non-tidal



portion of the Potomac  Basin.



    While it has  been  clearly demonstrated that the reservoir release



patterns are sensitive  to various  biochemical,  physical, design, and



":-': "-economic parameters, the magnitudes of the release rates appear



 > be dictated by  quality constraints in the critical reaches, and/or



  ^.ner non-quality needs such as water supply in the various sub-



 v'.-ri.  Once the  quality constraints are satisfied in the critical



''Vhes by either  flow  regulation  or-waste treatsaent, the effects of



 r "'^sed treatment or  regulation  on water quality at the decision



-'l^t are minimal. This  effect will ba further reduced when the full




'':>-- of the 1965 Water  Quality Act is felt.



     ..^tensive stream surveys have been conducted, primarily for forjiru-




 ^"v verification, in 1967 by the Chesapeake  Field Station,  For .30



 '-*""n sampled around-the-clock, considerable diurnal, variations in



    -i-ia DO deficit have been observed.  The mean standard deviations of



  :  "nd DO deficit were  2.06  and 8.15 asg/1, respectively.  While it can

-------
                                        107
        argued  that  mean values represent a net  balance without utilizing



       1 rr? -dependent  formulations, the BOD and  DO ranges used in the <"ptiT.i-



        -ilcn were  greatly exceeded by the diurnal fluctuations.



           With  time-dependent quality formulations  including all sour?es



       ." ;  inks  cf oxygen, a more sensitive model could be realised,  ilov-




        '  , will the  additional cost of data collection, analysis, and



        - '^rprel.si't-Joa  increase the significance  of an optimal solution within




       ;  '" .-*,!. rreirt-  institutional practices cf the  water resources planning
           Based  on expenditures for the Potomac  data presented in Appendix




         v:ll. cost  approximately $600,000 to  obtain sufficient information




       ; c ,1 'o.Tr.e-~dependeti.t model.  Assuming aboxit equal expenditures f?r an



\       .,=: ineeriag evaluation of the data, the total cost could easily exceed




       !-l,.?00,000.



           For compstability purposes, the time-dependent quality fo.rrnuia~



       ' --ri? should  be  coupled to new "yardsticks" for overall basin quality.



          .  *ne /n^rhodr-logy is developed .and  rjeces^ar"/ d^t.a r ^liec-t.ed f-"...7



        -.'.Ting the monet.'"V value cf a given water quality and anan:trty 1-?<



            g!V*n fail-ire rs-fe, t-ne pr^^ent \rster quality control mcdsl-5



        ;..r^T to b^  adequate.



           r'nr ar4 ovsz-e.ll water resource iiianagement. model, thR problem car. b'-



        j-essed as  .ujai'imizing the benefit-cost ratio.   Benefits per water




          . -e iise  per ; tJr-?ain reach would be  s. function of quality, quant j ' v,



          "'ii.liir-^ rs.te.   Such a concept could be  easily incorporated into



           . ar;iov.'or'lc cj  the /low release model as  presented in the preview

-------
                                  108


     Even with overall optimal planning models, will the instittrtiorsal

arrangements be adequate to act to implement the optimal sclutions?

A opf-opriations of funds for water resource planning by the U. 3.

'"ongre;s have not always been dictated by monetary considerations.

     Haveaian[90] in an analysis of Federal expenditures in ten

         states concluded the following:
     1.  "Although projects with the highest benefit-cost
          ratios tend to be chosen before projects with low
          ratios, no consistent or persistent pattern is
          manifested" and

     2.  "A somewhat stronger and more consistent motive seems
          to be present in both force of aid to low income and
          depressed areas and the drive to exploit development
          potential in areas of substantial opportunities to
          productive resources investments."

This appears to be the case in the Potomac River Basin.  From the

initial studies in the 1940's up to the present, the major construction

-"Taviti.es have been in the Appalachia Region.  This region is cur-

T-rotly defined as a socially and economically "depressed" area.

     While at the Chesapeake Field Station, the writer also had the

            to study and field test other water resources management

         In the opinion of the author, the most urgent research need?           j

 '  the area of water quality managejneirt are as follows j                         j

     1.  Inexpensive methods for easily obtaining large quantities

         of field information such as cross-sectioning, tiais-of-

         travel5 chemical parameters, etc.;

     2.  More precise and readily adaptable water quality formulations

         especially for low BOD stream reaches and in low level

         impoundments ;

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                         109






Continued development of methods  for  projecting industrial



water supply requirements and resulting wastewater loadings ;



Methodology and necessary information for assessi'ing,  by



individual water user, the monetary value of given water



quality and quantity level for  a  given failure rate;  and



3ocio-econo.ii.ic: significance of  optimal river basin plajtrnjjg




within the framework of current institutional pr-actJce-s.



operational viewpoint, the research areas delineated  above



->f the ne^rt barriers to overcome  in effective rlvsr baa^n
                                                                              I'.'l

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                           CHAPTER IX






                    SUMMAJOf AND CONCLUSIONS




    Tl.is st-udy has  been  concerned with the development and field




 e:-'i:if of a method  for determining optimal flow release sequences




.,,: Tf^ter quality control from multiple reservoir systsms,   It has




.:?> oeen the intent of this study to investigate, using gn actual




-::&? basin, the sensitivity of  the release sequence to changes in




various physical and biochemical,  design,  and socio-economic




:era~eters.




    The flow release problem was  structured  as  a converging "branch,




-licistage dynamic programming decision system.   An optimal flow




-eiease model has been developed with the  decision-making procedure




at each stage (the confluence of two regulated streams) being an




efficient enumeration process.   Using both single and dual return




"ittables, the model has  five options for  determining optimal release




flour sequences for a given flow  state at a decision point.   These are'




 i  minimum DO deficit for a given BOD state; (2) a minimum DO




"fiflcit; (3) least-cost of reservoir storage  for a given BOD state;




 -  least-cost of reservoir storage; and (5)  a minimum BOD.




    Predictive algorithms for temperature, BOD, and DO have been




 cooperated in the  flow  release model. Ability to vary stream




 aj.ocity and depth with flow has also been Incorporated into the




 ^1,




    A general descriptive mathematical paragon  capable of repre-




 fi- *irig the stream flow system of a river  and its network of
                               110

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                                  Ill





tributaries including its hydraulic characteristics and location of all



impoundments,  waste discharges,  water intakes,  etc., has been developed.



In the flow release model, the paragon provides the required mathe-



matical linkage for both the quality formulations and converging branch



multistage decision system to the physical features of the basin.



     Optimal reservoir-release sequences  from the proposed impound-              \



aents in the Potomac River Basin have been developed for the control



of water quality at mile point 116,,0 (the start of the Potomac estuary).



In developing  the various optimal release sequences, a minimum preset



dissolved oxygen level had to be met in all regulated systems



     The sensitivity of  the release sequences developed by the flew



release model  to various physical and biochemical, design, and socio-



economic parameters has  been investigated for the proposed reservoir



system in the  Potomac River Basin.  Comparisons have been made to a



standard test  run for a  flow target of 1500 cfs at the Potomac



estuary.  The  conclusions of the sensitivity analysis and comparisons



are;



     1.  Verification of the predictive quality formulations is



         essential.  This requires well-established time of travel



         coefficients, which appear to be the most sensitive of the



         physical and bioch.ead.cal parameters  investigated.  A method



         Including a specially designed mathematical model has been



         developed to aid in verifying the predictive quality formu-



         lations .



     2.  Of the remaining physical and biochemical parameters,  the



         reaeration coefficient  was the most  difficult to define and



         appears  also to hava a  great  effect  on the release patterns.

-------
                             112





3.  Changing the quality of the water in the reservoir from 800



    to 5.0 Hg/1 and 2.0 nsg/l to 3.0 iag/1 for DO and BOD, respec-



    tively, had only a small effect on the release pattern.



4.  The release rates and spatial sequence can be affected by changes



    in waste loadings, atreaa temperatures, water quality objec-



    tives, DO concentrations in waste effluents, etc.



5.  The location of wastewater discharges, impoundments, etc., and



    the orientation and gecscorphology of the river basin play very



    important roles in determining release sequences.  Therefore,



    no general conclusion can be saade as to which parameter has the



    greatest effect unless specific conditions are stipulated.



6.  The choice of the optimization criterion has a great effect on



    the release sequence for a given flow rate at the estuary;



    however, the resulting release pattern has only a minimal effect



    on water quality entering the estuary,



7.  When dual return variables (DO deficit and BOD) were used in



    the optimization routine, the second return variable, DOD, was



    significant only for some of the upstream decision points, thus



    indicating a need for only one return state indicative of water



    quality.



8.  The predictive algorithms used in the model for BOD and DO for



    relatively unpolluted reaches appear to "be inadequate.  The



    imposition of a dynamic-equilibrium for BOD overcomes some of



    the shortcomings; howevar, the effects of the imposition on



    the release sequence are significant,



9.  Even with better predictive fonmlations, the use of concen-



    trations, BOD and DOD, as return variables at the decision

-------
                                113





       points  are next encompassing indicators of water quality



       conditions in the contributing reaches.



  10.   A need  exists for a new indicator of water quality,  such as



       the area under the constituent profile of a pollutant.  The



       employment of this indicator for the first return variable,



       with cost of reservoir storage being the second return vari-



       able , would provide for a more meaningful approach in



       forming optimal release patterns for water quality control.



  11.   One of  the most difficult aspects of implementing the flow re-



       lease model is the obtaining of adequate, systematically col-



       lected  field data.  There is a definite need for better,



       faster,  and less costly methods for collecting and analyzing



       field data.



   A method for overconing -the deterministic nature of release rates



>QB reservoirs  has been suggested.   Included in the method are the use



- yield curves  and linkage to river flow simulation models.



   In  summary,  the optimal flow release model with the efficient enun-



^ttion  process  which was designed to make mftTlnum use of the ranges of



* return variables and to provide the cosrpatability between the



"*Hty  formulations and the optimization criteria has utility for:



   1.   developing an optimal flow release sequence from multiple-



       reservoir sites to maintain a given water quality objective,



       flow requirements, or for the least-cost of reservoir storage;



   2.   determining flow regulation needs to meet a given water quality



       objective for a particular stream reach in the basin;



   3.   investigating the sensitivity of the release sequence to



       various  parameters;

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                                1U
 '4
 ^

 %

 *.



I
<&
 3

   4.  demonstrating the effects  of flow regulation on water quality;


   5.  providing a mechanisa for  "trade-off"  between flow regulation


       cost and wastewater treatment coats; and


   6.  locating sites  for  possible industrial plants which would allow


       mflyimnia flexibility with minimum effects on flow requirements.


   A river basin model for simulating water quality is proposed in the


latter part of the study.  The simulation model, a logical next step,


Kwld include linkage to synthetic  hydrology, river flow routing, optimal


flow release, non-tidal  quality routing, and estuarine models.


   The model developed in  this study has been used to determine optimal


reservoir release sequences  for water quality control under various con-


iitions in the Potomac River Basin.  The small  ranges of BOD and DO


:ficit concentration differentials for a given flow state in the op-


timization procedure has been  one of the most significant findings of


~e application phase of the study.  This finding indicates that the


ulutions of water quality problems in most of  the sub-basin are inde-


;*-dent of one another,  thus optimal reservoir  release sequences based


T- quality control or even least-cost wastewater treatment solutions


*ve limited significance unless a  new measure  of overall basin quality


* utilized.


    Future developments in  modeling should not only include better


 -*iity formulation and  measure of  water quality, but also include better


**.r.ods for quantizing the monetary value of water per stream reach per


"- =ased on quality, quantity, and failure rate.  To avoid unnecessary


'"         and redundancies, there also exists a need for a balance


           competency, data  collection, benefit analysis, and project

-------
                            APPENDIX A




               SOME COMMENTS  ON  MODEL VERIFICATION




   in the dissolved oxygen  and BOD formulations, the three moot dit'fi-




..:  and costly parameters  to evaluate  are the deaeration coefficient,




 ..eration coefficient,  and time-of-travel.   Some of the pro clems which




 '  i'f-en encountered in the  study, possible solutions and a delineation




 .reas in which more field  data and research are needed to fully cope




 :.-.  tne problems are presented  in  this appendix.  A proposed model for




-dieting phosphates in flowing streams is  also presented.




   A fully detailed analysis of each  of the problems is beyond the




 - of this study, however,  the author is  of the opinion that the




 ".icular problems presented in this appendix are basic in model




 ification.




 CATION COEFFICIENT
   Tne tnree methods currently  being  used for determining reaeration




 '-s in a given stream reach  are as  follows:




   1.  calculated from observed data;



      prediction formulations,  either empirical or theoretical; and




   3.  gaseous tracer technique.




   -ach of the methods has merit, depending  on the situation, available




  "ces, and projected use.  For the  flow release model,  a method was




   ~-'i which could be used to determine the  reaeration rate for all




 ""'? of the basin for various  ranges of stream flow.




 ~-ii-e'"" from Observed Reaeration Rates



   -'- establishing the reaeration rates from observed field data,



                                                                                       H
    ~.urveys are required for a  minimum of two different  stream flows




      aeaeration rates and  time-of-travel well established.   One of

-------
                                  116
tr.e major disadvantages of this method is the great dependence of the




reaeration calculation on the accuracy of the measured deaeration rate




ir:d time-of-travel, and the ability to identify and quantize other




r..'
-------
                                  117
    In the past decade a  considerable  aaiouat of research effort has been

s.-xerted in developing various  formulations  for computing the reaeration

coefficient baaed on the physical  properties  of the streaa channel.   Using

various gas transfer theories, predictive formulations have been proposed

cy O'Connor and Dobbins[86], Krenkel  and Orlob[63j, and more recently by

Dobbins[13,1^].  The formulations  relate the  reaeration rate to the

physical parameters of the stream,  such as  velocity,  depth, slope, longi-

tudinal diffusion, etc.

    A statistical approach was taken by Churchill  et.al.[63] of the

Tennessee Valley Authority (TVA) in investigating various formulations

for determining the reaeration rates  in the Tennessee Valley.  In their

studies, they concluded that a simple equation relating the reaeration               ,
                                                                                    11
rate to velocity and depth was adequate to  describe the process, and

that parameters such as slope and  roughness are automatically included

:n the formulation.  A similar approach vas taken by  Langbein and Durum[87]

:f the U. S. Geological Survey (USGS) in which the  reaeration rate was

-sterained to be primarily a function of velocity and depth.

2jjeous Tracer Techniques

    A method for accurately evaluating atmospheric reaeration rate  using

11 radio-active gas tracer  has been  developed  by Tsivoglou et.al. [86].

"e technique arid the theoretical concepts  have been  developed in a

-moratory with limited field testings.  Until the  method is  more fully

 :"-^eds its value is rather limited,  and the  need for a complete evalua-

 -^n of predictive formulations remains.


-^HAgn of Methods

    ~o gain insight as to which predictive formulation in general most

--'lately describes the reaeration process for various streams, a

-------
;l
I!
   f*;.
                                           11.8
 .,-.; lion -'<.i.  s-^en nade for four different  stream reaches.   A complet.t




 j, uat ion  is  beyond the scope of this study;  however,  aue to the sensi-




.  sty  of the  flow release model to the reaeration parameter, the lircir.cn




 iiariwua  IB  sufficient to illustrate the variations.




   The basic  data cf tne four reaches and  the  reaeration rates calcu-




.>-:\  by the various methods are presented in  Table 15=   As  can be seen




,  '. fii:,le 3$, excxuding the tracer technique, no  one method adequately




 r.;D and temperature profiles for the  North Branch of




  l'<*tornac Kiver are presented in Figure 16.  The DO profiles were c-nu--




 e>i  using- the TVA ana O'Connor reaeration  formulations.  The effect j; ^'t'^'M^v be necessary'' to ad.juat the  reaeratiun  coefficients to




    '-i;c:r. &imiir to trie values computed fron  oLservea data,  Tne aaju;>t-




    rtr: be upplie.'i to o/er-aii forr.u Lations or  to one  of the constituent




    vters  6'jch as velocity or depth.

-------
119
                                    Figure 13

-------
121
                                    Figure 15

-------
                                       120
r~
                                                                               Figure  14
!:*
|! '
i> i

-------

-------
                                             122
    COMPUTED  TEMPERATURE,  D.Q.  AND  B.QD.   PROFILES   &   STREAM  SURVEY  DATA
                                            for HM
                       NORTH BRANCH POTOMAC RIVER.     AUGUST  I - 8. 1966
                           LEGENO  OBSERVED  DATA
T                              MAXIMUM
                              AVERAGE
    K
                    LEGEND FOR D.OL PROFILES
                    	O'CONNOR'S K2 WITH I.O DEPTH FACTOR
                    	 O'CONNOR'S K2 WITH 1.2 DEPTH fCTOR
                    	CHURCHILL'S K- WITH UO DEPTH FACTOR
if 30
I
                                            313      3K)
                                            RIVER  WILES
                                                            305
                                                                             295
                                                                                               Figure  16

-------
123










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rt
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O O O O



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ft* ^T rr* *%. > i 
" 

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-------
         Of the  formulations  investigated, in the pilot study of the Patuxent



     -'isin, the TVA  relationship appeared to describe the reaeration process



     .---.,t.  However,  it  was  still necessary to adjust the coefficient  to make



         computed 00 profiles  similar to '-he observed profile.



         Various methods  for  adjusting the TVA formulation were investigated



     .'Burning  the constants  and exponents of the TVA formulation to be  valid,



     viid  establishing the  time-of-travel by dye studies, the only parameter



     . ,1' to adjust  was  the  depth,  Further, after examining the cross-section



     "fi-'-'i from the I'atuxent  Basin, the rectangular transformation appeared to



     ,-j",a a too  low mean  stream depth.  (See next section.)



         A series of computer runs was made in which trie mean depth was



     .:,creasec linearly  by a depth-factor until the computed profiles  compared



      ..'..rably to the observed data.  The depth-factor was then used in veri-



     fying observed  data from  other independent stream surveys, and the calcu-



     .a*,ed profiles  were very  similar to the observed profiles,,  A similar



      .r :,"-oach  was used for the Potomac Basin.



         AF, can  be  seen in  Figure 16, the DO profile computed using the



      '.Archill formulation with no depth-factor appears to match the observed



      *'s.  With  a depth-factor of 1.2, tne DO profile computed using the



        "T.r.or  formulation  also appears to be satisfactory-  The choice  as to
K..

     -".- formulation to  use  is dictated primarily by which formulation in



        ra'i best describes  the reaeration process for the entire basin,



         prior to the use of  any factor, it is necessary to analyze the field



          '..-arefuliy  ana  delineate, manually or, if sufficient data is avail-



       -- ::y spectral analysis, any periodicity in the survey data.  For



       1 -"'.-le,  a. tremendous diurnal DO fluctuation was observed in the lower
                                                                                         ilfc

-------
reaches of the North Branch, as also can be seen in Figure 16,  Average

!  \alue? were used for model verification.

     More research effort is required to either develop a more general

;orraulation and/or methods for systematically adjusting the known methods.

CK,.:S-SECTION DATA

     As indicated in the previous sections, most of the formulations  for

predicting the reaeration process in streams are dependent upon a depth-

of-stream parameter.  The depth of a stream cross-section i's usually

j* fined as area/top width.  Implicit in this definition is a rectangular

transformation of the stream cross-section.

     From over ICO cross-sections of the Patuxent and Potomac Rivers,  it

~-;ears that the stream is consistently more parabolic than rectanscu]-ar.

'.no problem is, "what is the depth of a non-rectangular section?"   Further-

"ore, the velocity of the stream is usually greater in the deeper part.s

..'" the cross-section,

     Tnree methods for cross-section transformation, excluding inspection,

  :'': riven below:

     Rectangular transformation


                   if~u       V

     f-'oments of depth proportional to discharge

          depth = I q. * d * v * d = I. q*d
                    E D * d * v       Q

     '-Vnents of depth proportional to area

      assuming v.  =



          depth = v*Z! q>*d*d  - T. ^*ar: = I u

-------
                                 126
                                                                                    I
      -  /:idth  of  -in  increment of the cross-section




    .    avor?;>-rt> Jcptu of an increment of t.re cross-section




    ;  --  rr.eari velocity of an increment, of the cross-section




    ,  -  iischarfie of an increment of the cross-section




    ''  =  total  wiath  of cross-section




    .",'  -  f'otaJ  discharge of cross-section




    A  =  total  area of cross-section




    A  <"onparison  of  the three transformations was made for a  limited




,:;'; or  of cross-sections in the coastal area of the Patuxent Basin  and




  cr-* ream portions  of the Potomac Basin.  From cross-sectioning data




  . ;-R  "atuxent Pasin, the mean depths as computed by net hoc III  were




 : i3  to 25  percent greater than method I; while in the Potoaac  Basin,




>tr>o2  III  yielded a  mean depth about 10 to 15 percent greater than




-".:.oct  I,   At LFSGS gaging stations, method II and III were both about 10




  ."it greater than  method I.




    ':tn the limited number of cross-sections with velocity measurements,




   ''; 5',ical comparison cannot >e made; however, results tend to indi-




  '' ""r.^t a rectangular transformation does not yield a representative




    :erth, especially in coastal streams such as the Patuxent,   More-




    ;"  the area  transformation is similar to the discharge transfoma-




      xislderabie saving in field work can ce realized.




      '"r.'.r probler,  : r. interpreting cross-section data is the variability




      ;  a-or;p;  the longitudinal profile ar;c tne possibility of bias on




     ''  ''' the field personnel in selecting cress-section points.  For




       "^ocT-aphicaiiy homogeneous reach of stream channel in  the Patuxent




     ' '",.'. rfivers, the distribution of depth i-.as been four,, to ce  normal.
 i

-------
                                  127
See Figure 17 for variations  in  depth in the North Branch of the Potomac.




 'Connor[9] also reported a normal  distribution of depth in his studies




-; lae Wabash Clarion,  and Codorus  Basins.




    Assuming a normal  distribution,  it is  possible to determine statis-




.tcfjily the number  of cross-sections  needed to assure a given probability




:-.at the measured mean  value  will represent the true mean.  While it is




-. jssible to determine the number of cross-sections required, the reaera-




ric.Ti rate, which is a function of depth to  a power, may not be normally




,-stributed and statistically less  significant,




    In a ten-mile  reach of the  North Branch of the Potomac River below




 :y;-er, the reaeration  rate was  calculated  from fifty-two cross-section




Tints using the O'Connor and Dobbins formulations.  As also can be seen




.n -"igure 17, the reaeration  rate for this  reach has a skewed distribution,




    While the point calculations introduce an additional bias in the




velocity term, the  pronounced skewness in the reaeration rate for the




each is indicative of  some of the  problems in data interpretation.  Some




.: tne variability  in the predictive formulations may be due to the inter-




pretation of the cross-section data and the aggregation of sections for




  ~iven stream reach.   Incorporated in the  suggested research effort in




"-'e reaeration study should be comprehensive field testing, including a




 :-'ailed analysis of cross-section  transformations.




^_MLCHANISMS AKD  FACTORS




     sing a first  order reaction,  the calculated BOD concentrations for




 -""", relatively unpolluted stretches of the Potomac River tend to ap-




 r '-*?:> 0.0 mg/1 of  BOL, with  resulting DO values near 100 percent of




  -'^ration.  Field  BOD  measurements in these reaches normally range from




   to 3.0 mg/1, with DO levels  about 80 to 90 percent of saturation.

-------
(rfO
                  128
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  i
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                                 129





Similar observations were made by Hall [89] In his work on tha Jazae* River,



 sister basin to the Potomac.



    It appears that various not-readily-quantifiable sources and sink*



 f oxygen such as bank loads, nitrification, scouring, etc. result in a



iynamic-equilibrium level for BOD of about 2.0 ag/1.  Associated with



iis 2.0 rag/1 of BOD dynamic-equilibrium is a depressed DO level of about



30 to 90 percent of saturation..



    Two methods for coping with this problem are (1) inclusion of all



icurces and sinks of oxygen in the quality algorithm, or (2) the setting



:f a minimum value for the BOD dynamic -equilibrium level.  Since techno-



logical developments at the present time are either not adequate or too



 :ostly to completely quantify all sources and sinks, the latter approach



 x* been used in the quality algorithms,



    In the verification link and flow release models, whenever the BOD



 sncentration decays below a prescribed level (read in as input data),



 ' is reset to the prescribed level after the oxygen uptake for the given



    on has been computed.  BOD and DO profiles obtained from computer



    of the verification link appear to be similar to observed profiles



         from field data.



            ynDEL FOR PHOS PRATES
   -"
        As indicated in Chapter VI, high concentrations of nutrients and



       ^suiting algal blooas are becoming an increasing problea in water



       lty management .  One method for reducing the algal problem is to



            a phosphate concentration in the streaa> below the ainijnum



             lialts for an algal blooa.



        Studies in the Eatuxeut River Basin indicate a large portion of



              costing froai waste treatment plants are being lost to plants,

-------
                                                 130
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-------
                               131
ear: oed, etc.  In analyzing data  from  the  Patuxent, it appears that




 loss of phosphates can be mathematically  approximated by a first order




:--_on similar to that of a biologically  degradable waste.  An algorithm




 rcx'ehinc the loss of phosphates  based on  the first order reaction is




.idea in the verification link, and  provisions are made for inclusion




 , tne flow release model.




  fomputed and observed profiles  for three studies are presented in




.re 16'.  The loss rate appears to be a function of temperature and




.-, with values ranging from 0.1 to 0.2.




  More field studies are required, to determine how stationary the loss




pnosphates is throughout an annual cycle.   If the loss rate is predict-




e. ihe model could be used to determine  phosphate treatment requirements




  .r incorporate into the flow release  model as indicated in Chapter VII.




- :F TRAVEL
  "f all the parameters required in  the  model,  the most basic and sig-




 irit is the travel time.  As  indicated  in Appendix B, the cost of the




 -""-travel studies range  from about $50 to $100 per mile.  Preliminary




 -"i indicate that gaging  station data in conjunction with limited dye




 -?s can reduce this  cost  considerably.




  ;-3 presented in Chapter  III, the velocity at  a given cross-section




  e expressed mathematically as:




  elocity = CC X (Flow)DD




 "^ gaging stations in the Potomac Basin, the value of exponent




  ~"^.~ep from  .300 to .500 with constant "CC" fluctuating more, depend-




    - OW* 




   f- quality relationship being time dependent requires the time-of-




    -tveen two points rather  than the velocity at a given point.  By

-------
                                132





? suiting  (l)  that time-of-travel and flow can be expressed similarly to the



,-iiocity  at a cross-sect ion, and (2) that exponents are equal, a  consider-



ate .amount of effort and money can be saved. .



    For  a 7.8 mile of geographically homogeneous reach of the Patuxeiit



;:v;",000, If the general relationships can be firmly established, con-



1-Arable expenditures of money can be saved in some of the field



      required in model verification.

-------

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     Based on the experience in the Patuxent Basin,  a  method for



  -olementing the flow release model has been developed  according to the



 fallowing format.



     1.  Define the physical system including  an inventory of all



         wastewater discharges and water  intakes.      



     2.  Establish the stream channel characteristics.



     3.  Partition the river basin and determine all parameters,



         constants, etc.



     4.  Verify the physical and quality  formulations.



     The above format provides for a systematic  development of the



 data, thus reducing the chance for error;  it can  also be used to indl-



 -ate data voids.



 Defining the Phsical S
     A detailed inventory of vastewater discharges, water intakes,



iams, and other topographic features is necessary to define the



-;ystem.  Included in the data requirements are wastewater quality and



i'-antity, water withdrawals, stream flow quality and quantity, river



~il^ indexing, drainage area, etc.  Knowledge of the basin area and



engineering judgment are essential for definition of the system.



                           Chax'scteristics
     For ell stream flow gaging stations, data required to establish



velocity-flow and depth-flow relationship can be obtained from the



-:"il.ed States Geological Survey.  The data are obtained each time a                 i



5 * at ion is rated by the Survey.



     Depth relationships for additional points can be obtained by



 ~oss-sectioning the stream at two different stream flows.  Similarly,

-------
                                         135
--*,-

a greater number of sections can be rated and more velocity relation-



ships  established.   A method of relating time -of -travel to velocity



and statistical analysis of cross -sect ion data is given in this



appendix.



BBS in  Partitioning  a/ifl Parameter DetermjjTations



      Partitioning  of the baa in and the determination of various



parameters, constants, etc., are two of the most important steps for



implementation of the model.  To expedite the study, the following



procedure has been  established for a given reach of stream.



      1.  Plot the  longitudinal profile of the stream.



      2.  Section the reach into segments according to instructions



          given in  the section on the descriptive paragon.



      3.  Partition similar segments, according to channel



          characteristics .



      4.  By segments, plot the drainage area profile.



      5.  By segments, plot the base stream flow (such as 7 -day



          low flow  with a recurrence interval once in 10 years ) .



      6.  From time -of -travel data, plot by segments a velocity



          profile for the base flow.



      7.  From cross -section data, plot by segments a depth profile



          for the base flow.



      8.  Number the nodes and evaluate the constants and exponents



          for each  segment.



           n of Quality Formulations
              Good stream survey data are vital to validation of the quality



                       By plotting the isopleths of the quality data, diurnal



         -'Actuations can be observed arid quantized.  These plots are also

-------
                                   136
useful In reducing the survey data to steady-state conditions and in




checking the tiree-of-travel determinations.




      Having reduced the data and plotted the stream quality profiles,




t.he coefficients of the formulations have to be adjusted until the cal-




culated and observed profiles are similar.  The procedure given below




has been developed for the verification process.




      1.  Check and correct if necessary the calculated depth and




          velocity profiles.




      2.  Compare the calculated temperature profiles with the field




          data, and if necessary adjust the temperature coefficient.




      3.  From existing quality data and isopleth plots determine




          the deaeration coefficients for the various stream reaches.




      lj.  Compare the calculated BOD profiles with the survey data, .




          and where necessary adjust the deaeration coefficient.




      5.  Whenever necessary the depth-factor constants for each




          segment are adjusted so that calculated and observed DO




          profiles are similar.




      Due to the dependence of the parameters and coefficients upon




those in the preceding step, the order of development and verification




as given in the above procedure is important.  For example, both  the




"OD and DO quality formulations are temperature dependent.   Therefore,




it is a necessity to have a well defined temperature algorithm before




sne attempts to verify the BOD and DO formulations.
M
   t

-------
                               APPENDIX B




                 MODEL DATA FOR THE POTOMAC RIVER BASIN






     Reduced  listings  of the Potomac River Basin basic data, used in the




flow  release  model are exhibited in this appendix.  Since numerous computer




runs  have been made under various conditions, it is not feasible to include




all of  the input data.  The various data inputs are linked by the descrip-




tive  paragon  as described in Chapter III.




     Detailed schematics of individual stream reaches of the Basin, showing




all major waste discharges, water intakes, gaging stations, impoundments,




etc., are displayed in Figures 20 through 29.  An overall general schematic




of the  Potomac River Basin system is presented in Figure 30.




     For 81 nodes, including the ih proposed reservoirs, stream flows were




accrued as summarized in Table l6.  In stream reaches below a terminal




source  where  there are no major tributaries, the incremental flow based




on the  increase in drainage area has been introduced into the system at




add points.  Unregulated tributaries not receiving any significant waste




-cads or used for water supply have been indexed similar to add points.




     In the non-tidal portion of the Basin, there are over 200 surface-water




supplies and  waste-water discharges.  For this study all surface-water




supplies with an intake rate greater than 0.5 mgd and all waste-water




i-scharges with a flow greater than 0.5 mgd or population equivalent of




-.000 or greater were included in the model.  The surface-water supplies




-".i waste-vater discharges used in this study are presented in Table 17.




     Current  waste treatment levels have been used except in the North




-"'inch  area.   For the North Branch area, in order to stay within the




"'-V"-uiation capacity of the impoundments, the treatment levels for Vest






                                   137

-------
                                  1 ?H
    i.oa  jh.jp atid taper Compaiiy end Celanese Corpor  tion hi./e been  .   f




   and  9$ percent, respectively.  For discharges currently eaterin^ ;




s,:>te:i:  above  the proposed impoundments and for  the South River of v    _c




.  I,,  oLfcp.flndoab. Biv^r,  the waste loads have been routed  MS shown iij t-




 . iHIled  schematics.




     The  b&sit: data  for the 1^ proposed reservoirs  are  presented in




. -v/ie   "?.  Not included are the Seneca Project  which has been removed




,..->;2  the  recommended  plan and the Stony Creek Project which  is in setieo




,.;la  the  Blocaaington  impoundment.  Since there  are no significaxit or^nio




. ,otri loads between the impoundments, and Stony Creek is small when ccii^v




   Bloomngton,  the omission of Stony Creek due to model limitations  is




i 't, tjn significant.

-------
                       139
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             140
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                             141
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                                      143
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                                                                 144
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                                 146
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                                148
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-------
           149
STOHV  CREEK
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                                               SAVAGE RIVER
     OVERALL POTOMAC  RIVER BASIN SYSTEM
                                                              Figure

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t- t~ t~ ;~co c)

















OQ
S-t

-i>
^~3

"
r*i

r'
;T"!

<1>
1-J
o
^

-J-
J

i -5
vf
>
1

Pi
c>
c^
>1)
^ J
t
r >
V * ;*-l
'.; TC
j>
?; <, j r-
-^ f*( vH
.-;.' V V
.^1 >"
r,^ ,n*j
i3 a1 "H
n v^
T' > C
CO Ctf r-<
'-o r.o
O >>
a, >> 01
'M '
Tii -.' ?
W .p, i;
V' 5 IT
-P i  i j
O '. ^ *-
SU \ K
.!/ U .,J
t- * +
V. ^

-------
"4V
                                      Table 17

                   SURFACE WATER SUPPLY & WASTE WATER INVENTOR

                                 Potomac River Basin
Name
ct of Columbia
ct of Columbia
gtr>n Suburban
ary Commission
lie, Maryland
Typ_e
2
5

5
5
Node
2
10

11
12
Flow
(cfa)
2.20
167.00

5.50
2.20
Receiving;
Potomac River
Potomac River

Potomac River
Potomac River
        kv
             Electric and
            Company
        oaiae Electric and
      Power Company
      'rederick, Maryland
      Frederick, Maryland
      anp Detrickj, Maryland
      .'nap De trick, Maryland
      .  S. Steel Company
        ?. Gteel Company
      '-Itown Board Company
      otcmac Edison Company
      .-romac Edison Conrpany
      Winchester , Virginia
      "irssbarg, Virginia
      "V-dstock, Virginia
         Jackson, Virginia
- Knr
                 Virginia
      .. ') valley Packers
       .--ir^.h'^ffi Poultry
      -^ervllle, Virginia
      - i?idvay, Virginia
      : :.adway, Virginia
      ~:-r'o Royal, Virginia
      --frican Viscose Conipany
      '- Virginia, Inc,
      ;~erican Viscose Company
      -"gi-nia Oak Tannery
      _-""'!% Virginia
      '^aandoah, Virginia
      r?r'indoah, Virginia
3
         '' und Company
        ''""ies, Virgicia
        'i:-"_ is Metal Company
        ^esboro v Virginia
        ."np ton  Shenandoah. Company
        '-- .  Ihipont Company
        -. Dupont Company
                                 17   355-00
Potomac River
5
5
2
2
5
5
3
2
3
5
5
2
2
2
2
2
2
5
2
5
2
2
2
5
2
2.
P
^
2
2
2
P
2
2
C-
3
18
32
36
40
42
72
74
76
100
102
108
116
126
136
1^0
3_4p
iJs'u
1^6
1.50
152
158
160
162
164
178
180
198
202
2QL
205
216
?l6
226
228
229
230
355.00
1.10
3.80
0.65
0.8o
0.72
0.^2
1.00
10.64
10.6^
2.80
0.30
o.i4
0.11
0,35
0.18
0.71
1,00
0.13
0.10
0,85
13.45
0.10
13.50
0.28
0.28
0.71
0.50
0,18
7.86
0.09

-------
                          Table I,7  ..Continued )


                                          Flow
                                  Node   (cfs)
v. j . Dupont Company
jT..ix:nton, Virginia
>rona Sanitary District,
.'irginia
American Safety Razor
,~ -mpany
\::erican Safety Razor
Jompaoy
VMgewater, Virginia
I" /con , Virginia
-.rrisonburg, Virginia
-perstownj, Maryland
' -':gerstown Electric
i '-. gerstown Electric
j --irchild Aircraft Company
 Vrt.b American Cement
' ^mosny
v Ar'ierl*. an Cement
r^ny
)  "ne.-.bor.,- _ Pennsylvania
' .:/3-ginia
i '- 'isburg;, w*-st
j ..%inia
1 -v-'rf.ta M & M Company
. - ..l'^?f-:r> West Virginia
 LX- orrt Company
R
2

2

2

5
2
2
2
2
3
5
2

3

c
k.

2

2
"*
2
.c'
232
250

254

2C6

2?3
266
o*l^
278
296
298
302
y

310

512
3-'"-

326

o ,A
o.'"
3.^
-iou
>r !
1U.UO G :-J.f.. 3-k. S:i, -.
330 M.H.S F-v. ^--r ' :

0,19 M.R,,';. Fk :V>-.T.- v;

0 50 " ? 3 Hi; r.b -v - "'--. .1-

0 SO Jj1 R *3 ^"'' ">'* """ "

0..26 K.P.i". i'k o'3.>^,-j .'..;,
0.16 ff-P,S "k , ^h-"!"a;i'! ')

5.7^1 Acti?4;am C'r^ek
0..33 An'tietam Cr-->el-;
0,33 Antietarr Crc-eit
0 50 Arjti;1':^ Cr-"-.'X

7 A^ ja-irv'-- n^ .">-.,_,-,
' *~* .j '! --Ii. -ft.

3.12 Antielaui Creek
1.20 Ant; ?iam Creek

O.lU Potomac River

2,00 >pe''?.       "" '"*
 "sc  Ed if on Company      3     "'?     "-  '--       r'"''-  ':"
 ."i  and  "? Coxappny      ?       ~r       '>   iO       '.".

 -..;^r* ar-d  Company       2     jyC       0. -.2       '<.  ?-"
 --3b\re, Pennsylvania  2     v-v       0  "^       w. Sr
 -.va-stle., Pennsylvania  2     ,H-;^       0,1}       C-:5r.rj
 -'":r-Vir^.-.  Pennsylvania 2     kG'-*       3  00       Co^of
 ^:';.'" $'. TK Hilc-ctric       '-i     4-i>>       ?  '~0       C'-1";-":,
 '".  o"iArs E^^ctii'       5     '+0'.1       ?  ;>C       ."j"'/"'
   -"^..'.r"   Mfifvi&po      3     -+12       *",' -*>       F^'- ~-'"'.
      '^r--". Virgin.!?       ?
     *-.}  '"7est Virginia  2
                                                       .-   --   r-;r-,v                         jl
  -'V'.- a no  C'->mC'Vr_y       >     ' v~-       "   -"*       '   H'   .,,--.-,.-                      b

   "oisr^. West Virginia  .?
  ~? '* an<-  "-mpp-ny       ~i     -'-&'"       0.20
                            S     --.'i."       2  ">"

-------
Dlat,e Glass
Piste Glass
Maryland
;.iO" Company
so,i C-.'5Kpany
gf i i^ld >r'umpe" >xv
gfield Cosapacy
sn,, Maryland
rporation
rporation
rporatioa
rporation
Maryland
allistlca
sfcx'ag Camps cy
t Virginia
ac River
S. o - 1  n
ia Pulp and
ar
"\
c
s
5
3
5
S
2
3
"^
?
?
 '
2

?.

2

~\
500
502
506
5] u.
316
513
550
522
32^
526
5-?8
5^9
530
532
x; )S
un

sL^.

5*8

c. :,,-!
i?
,'\
-;
0
0
\
2
0
?
53
58
r*
C
0
0
o
i

^u



?9
00
2'b
C^'}
69
V-, ~*
.bO
- ',' ''
.18
80
. 00
. CO
,60
-28
07
,?5
00

;. %

^O
O *^ 3

~ ^ 0
,j B, P:,!:J;?,:,C :-..
" Br , tx:-cc~U':
j' .Jr. F-. -.--, A-  -i'- -^i"-;-'
TJ; ' T' /
?" "I r . /- - ^..i*: ::'--  "!
I"1 , *i T ^ . ; *" " "-',?- "" -  -- tj" '-
??. 8r, Pot->-!~. i' f-i A^
N, nr, ":i. -;?-, ':- - - ?
fi 3r> Fooo'oa-. "r"..
I"-. B:: r^t'^-.B.- oi -'i
T-' Sr . F ^cc-na-"' 7?-- '-\;
"" 1 P-V Pf .-T ^~* -4 "- "' ^ ,,' -j
?!  Si ,> '-?v"V -'""-'7Li. " ^1.% ;-'
7T IH -* "^fN^~ f ' i1^! "> "j ^j ^ - '
]- 7 -O 1. - V. f^'>f.^)p Iv* .. A
J., ;':r , "-*" ~:.i-'- ::.; ;

'^ ' t"> .^ - -^ t ^ ,- ." -

y. Br- Pot'-rrac F.ive

-' ?.: ?vi -:-,.- :" T
 ? sa p t cvn,
 "; ^gheay
 ser Fi.ol
  ., -j "- {  "j^^"";
'?r  Virginia
^aper <  '
?t  Vi:
" 2per Compa o:/
,3t  Virginia  Pulp  and

...t  Virginua  JH.\.:p  and

-------
                                         156
                                                                                               I
Wf
A',
$
           As ir^.l -at.ed, 3-. Appendix A, a l?..rg-r  ame"iit ->f *"ield  w-rlr

         '.^ing -i~--3.-n atr? w^t** tr^^Hiemt rvrvsys  ic-- required r-o ijn

         '"low release model.  Irs  order t : determine the (ir.-~t, of co

         nsces-3;ary  information reo.ulr^'l t>: implement the mocJfel, cost

        '.re.s have been kepi, on -soiise of ths major field activities at tte

             ke Fi^-id S tat Jon.

           A S'jcBms.ry  of the coat  data is givKi  in  Table 18.


                                     Table 18
       Tlant Survey
                                  per Fdle

                                  per s set-ion
                                  per  24-h
                                    survey
                                  per
                                                              Cost
$  50 -  $  100

$   4 -  $   10



$2000 -  $3000

$  25 -  $   50
           The-
                        The wsate
                                             *_ i^Tsr- si  time p'.n ..a a 33

                                             plant and stream survey

                                             ", P"
                                                        n?t :T per 
-------
                           APPENDIX C




 COMPUTER PROGRAM DOCUMENTATION AliD USAGE WITH SAMPLE  PROBLEM





^



 :ie computer programs  for  the verification link and  flow release




 have been coded jn FORTRAN  IV Subset E,  The same algorithms, nota-




 end data inputs are common  to both programs




:ror easy reading and understanding of the programs ,  symbols for the




 les are usually abbreviations of the algorithm parameters,,  Allow -




 have been made for possible expansion of the model  concepts, inclua-




nnut formats 




iu the verification link,  all calculations are made  in the  concentra-




,,.:ae (rng/l), while in  the  f.ov release model, the .Tiode is pcuna5/<;ay .




:-.? cf concentration in the verification link aids in displaying of




trious profiles.  For  example, the computed BOD profile is  listed




:'!./ HOD values, which  simplifies comparison to field data,




  " vS-'tZ JtliD TOPICAL paCK CtWL'T.A 1 ^T^S




  'i.led listings of the ten-;: rut formats ana array notation are




 ". in Tables 19 anc  20,  respectively   A? ?an be seen in  Figure




 . i*.put formats are fixed fie. :-   Card for.-r.at 6. wr::ch current-,-




   '..ai, has been designed  for t ^r-.Me expansion of  the BOD,  DO end




 '-'-.re formulations and to a.;-vw for greater flexibility in the
        ,-ia* n d"cK  compi iat icr.s for t.ne verification  link  ana ,';".x




         are  r.sriuyed  in ri^urf-  v'  an"  33, reo_r.-.-cci ve ,y   ?'or




         ctt ~, or, ,  ;.-":  '.^raer ^. *" .r'.r-. . .>i\ . or.  " a~ foi^^^3




         all levels  of  waste" tr^^tr.^nt tor pciven  flov module;




         all f-ow  r-ets  fcr a FI vu:; waste ws :er module; and,

-------
                                  35S
         3..  all waste water sets for a  typical  computation.


    If many waste water sets are included for compilation,  each waste


  :-ii;> ji.uat contain name number of flow eet:i.


    Jince there are no data sorting routines designed  into  program, all


 mats must be placed in proper sequence.  Consequently,  Format 5, which


  ^r,ed to link the various modes, must be ranked upward by  J(N) parameter.


  -'^M USAGE WITIi SAMPLE PROBLEM
    To illustrate the data inputs and computer outputs  formed for the


  ,-iT'ication link and flow release model, a sample set of  data for the


 -.:.uxent River Basin is presented in this appendix.


    For demonstration purposes, regulation capability not currently


  -rinse has been introduced in the Little Patuxent River.   Cost  con-


 ..-.orations are not included in the sample problem*  A schematic  of the


 nuxent River Basin model is given in Figure 34^


    In the flow release model, the distance increment,  flow increment,


   test grid, and BOD increments are read as input data,  with  the  latter


   .^t required in the verification link^  The latter three parameters


   -roiled the number of feasible solutions with first,  the  frequency


   :.'iinber of water quality monitoring points in the basin.


    ''or the sample problem, a flow increment of 5 cfs has been used ,  In


    "tomac Basin, a 20 cfs increment appeared to be adequate.  To prevent
j
    -'.itional problems, the regulation range must be a multiple of the


    "ncrement or vice versa-.  This also applies to the  reservoir cost.


                        !

                        /
       ailcw for maximum flexibility at a decision uoiac  (or stage),                 ||

                                                                                     I
     -  increment is selected by the computer according to BOD range  for              f


     "'" state under investigation.  As can be seen in the Patuxent                   'f

-------
'.asm data,  if  the  BOD range is between 1,0 and 0.0 rig/1, an Incre-




' 0 .' m/i  is .--elected;  between 2.0 and 0.0 m.Q.'l, 0 '* my,/1 ; between




 U,u ing/1,  0.6 m^/1;  etc.   ir. the Potomac Basin, as Indicated




 , the BOD  range was usually about 0.5 zng/1 or less.




r the temperature  model the decay coefficient appears to vary




-iccording  to season and stream.   Verification studies of Potomac




uxent have  indicated  a coefficient rans;e of 0,2 to O.BO, with a




 value  of  about 0  3.

-------
                                    160
                                 Table  19

       CARD FORMATS  FOR VERIFICATION LINK AMD FLOW RELEASE MODEL

                       iMaJ n rarair.et.er Oarc] (f>i->.  I!

  ;'-y_mbo L     ___               jescription  _______ _
; 3TALN         Nuraoer of stream sections                              1-3

" .":7ALW         Kirnber of water intakes  and waste water
               discharge                                              o-1

  :TALR         Ii umber of streamflov add points

 """           lumber of reservoirs

L"". KIT:         First  node of basin or terminal  node of data                       :;
               sets                                                   c*\-i'.rj         )'
                                                                                    \,
                                                                                    I
:"'<'            Number of data sets                                   26- JO
                                                                                    ;j
                                                                                    i!
 '."1            Jiuir.cer of flew sets per  data set                      31-35         j

;:-;M.dOI}         dumber of treataent levels  per data set              36-'tO         i!

ITiOD          Index  for vaste vater BOD loading                    ^1-^5
                  1.   in pounds /day                                                 |<:
                  2.   in rag/1
                                                                                    i
 r'TYPE         Index  for optimization                                U6-50         ':
                  .1.   BOD-DCD routine                                               i
                  2.   BOD-COST routine                                              ;i
                                                                                    "i
                                                                                     i
 VI!"1          Index  for reaeration formulation                      51-^5          >
                  i.   O'Connor                                                      ,|
                  2.   Churchill                                                     !l
                  3.   U.S.G.S.                                                       i1

 ----- A          Flow increment from reservoirs in cfs                5" oC         I,1

                                                                                    !i
               Minifnura SOD removal level of all  vaste waters        6l-o5         .|

    FIRST)     Piver  mileage of first node                           66-70         ,;

               Fi stance increr^-nr. o^ POD-DO quality                                1
               formulations in rr.iles                                 71-75

               'iininiuin phospr;:ru5 re.crvaL  level  of all vaste
               waters                                                7 fa- 80

-------
                                 lol
...rr.nol
"yrnbol
         Table 19 (Continued)

 Five  Waste Treatment Levels  (No   2)

	Description	
             First mininai  BOD removal level of all waste
             vatera

             Second minimal BOD removal level of all waste
             vaters

             Third ninimal  BOD removal level of all waste
             waters

             Fourth minimal bCD re-oval level of all wastp
             waters

             Fifth minicial  301- removal level of ail vaste
             waters
Dynamic Programming  7'ar-a - Gr..d Increment  (lie.  .;.

                       Description
             BCT grid  increment, for Te-;t 1 grid

             BOD grid  increment vror Test 2 grij

             B^D grid  increment fcr Test 3 prid

             bOL grid  increment for Test k grid

             LCD (.trio  increment r'rr Test -j K-I
                                                          Field
                                                    1-iO
                                                   11-20
                                                   21-30
                                                   1 > ,- ^
                                                   '-J.~ /C
                                                   Field
                                                    1-10
             Dynamic  Programming i>sta - Test Grid  (No

                                jjes c r i "c 11 on
              Decor.c  F.'CD test, .rrid pii

              Tnird ti.'-'^ test yr,r<. --.-;
                                                    ied
                     ^>v ;..  -ea \. KJ

-------
                    Regulated terainal strean flew source

                    Unregulated terminal stream flow source
                                  162
                         Table 19 (Continued)

              Physical Data of Stream by Section  (No-  5)

 : Vmbol ___ __ __ _ __ De:;cript. ion __ ____ ___ ___ _____ JUL^iiL

 '.ri)           Lower node of section                                 1-5

 ' ." ,'           Upper node of section                                 6-10

. .\i(N)         River mile distance at upper node                    11-20

.REA(lO       Trainaee of basin at upper node                      21-30

.'' .' }           Constant of depth-flow relationship for  section     31-^*0

:i,"'^'           Exponent of deptn-flov relationship for  section     ^1-50

  N ,'           Constant of velocity-flow relationship for
              section

.!'./           Exponent of velocity-flow relationship for
              section

. ryFE(N)       Index of upner node

                1.   Node where there is a physical
                    discontinuity

                2.   Confluence of two tributaries

                3,   Waste water discnarxe

                ^ .   Water intaKe
                                                                                   .,
                                                                                   I

-------
; -:';. AYT(N)
JiiCAYP(H)




TiiOS(M)
iX730D(N)
                         Table 19  (Continued)




              Continuation of Card 5  -  Optional  (No.  6)




              	pcacr ipt. urn	 __
Lover node of section                                1-5




Upper node of section                                6-10




Slope cf section (ft/ft)                            11-20




Depth factor of section                             21-25




DO constraint of section                            26-30




Temperature decay coefficient of section            31-35




Steady-state temperature of section                 36-Uo




Phosphorus decay coefficient of section             1*1-1*5




Dynamic-equilibrium level of phosphorus             1+6-50




Photosynthesis DO contribution (future use)         51-55




BOD contribution of sludge deposits (future use)    56-60




BOD loss due to extraction (future use)             6l-b5




Dynamic-equilibrium level of BOD                    66-70

-------
                                   164
Symbol
NRES(W)
NRN(N)
MRES(N)
IRES(N)
ACREFT(N)
i
WQ ACFT(N)
TCOST(N)
WQ COST(N)
AVRESQ(N)
INRESQ(N)
Table 19 (Continued)
Reservoir Information (No. 7)
Description
Reservoir Number
Node of reservoir
Number of cost cards
Flow increment for cost increment
Total storage of reservoir in acre-feet
Total storage for water quality control in acre-
feet
Total cost of reservoir
Cost of storage for water quality control
Average stream flow at reservoir
Increase in dependable flow by reservoir
Field
'1-5
6-10
11-15
16-20
21-30
31-UO
Ul-50
51-60
61-70
71-80
                                                                               I
  Symbol
          Reservoir Cost (No. 8)

         	Description
Field
NRES(N)

CARD

COST
Reservoir number

Number of cost card

Reservoir cost for given flow increments
(fields of six)
 1-1*

 5-8


 9-80

-------
  Symbol
WTYPE(K)
Wr3CD(N)


WT)G(N)

WTEMP(N)

WPHOS(N)
           Table 19 (Continued)

    Waste Water Discharge Data (No. 9)
        (including water intakes)

                  Description	
Discharge or intake flow
  (For units see WTYPE(N) index)

Deaeration rate (base 10 at 20C)

BOD loading - untreated
  (Fcr units see ITBOD - Card 1)

DO content of waste discharge in mg/1

Temperature of waste discharge in C

Phosphorus content of waste discharge in mg/1

Percent BOD removal 'by treatment facility
                                                    Field
                                                     5-10
Node of discharge or intake

Index of discharge or intake

  1.  Biological waste water discharge in cfs

  2.  Biological vaste water discharge in mgd

  3.  Thermal waste water discharge in mgd

  U.  Conservative vaste water discharge in ingd

  5.  Surface water supply intake in mgd
                                                    11-20


                                                    21-30

                                                    31-^0


                                                    Ul-50

                                                    51-60

                                                    bl-70

                                                    71-80

-------
f  I
                          Table 19 (Continued)

                   Secondary Parameter Card (No, 10)

  Symbol	Description	Field

 ;.-;            Index of steady-state temperature                     1-5
                 1.   Uniform basin temperature
                 2.   Temperature by sections from Card 6

7TSXP1         Uniform basin steady-state temperature in C          6-10

IT3            Index of DO constraint                              11-15
                 1.   Uniform basin DO constraint
                 2.   DO constraint by sections from Card 6

    Tl         Uniform DO constraint in mg/1                       16-20

               Index of depth factor                               21-25
                 1,   Uniform basin depth factor
                 2.   Depth factor by sections from Card 6

               Uniform depth factor                                26-30

:75            Index of temperature decay coefficient              31-35
                 1.   Uniform basin decay coefficient
                 2.   Decay coefficient by sections from Card 6

I.'ITEMP         Uniform temperature decay coefficient               36-Uo

17'j            Index of phosphorus decay coefficient               ^1-^*5
                 1.   Uniform basin decay coefficient
                 2.   Decay coefficient by sections from Card 6

I'.-IPKOS         Uniform phosphorus decay coefficient (base  10)       ^6-5C

-~"            Index of dynamic-equilibrium of phosphorus          51-55
                 1.   Uniform basin equilibrium level
                 2.   Equilibrium level by sections from Card 6

-'FHOS         Uniform dynamic-equilibrium level of phosphorus
               in mg/1                                             56-bO

-~'-'            Index of dynamic-equilibrium level of BOD           61-65
                 1.   Uniform basin equilibrium level
                 2.   Equilibrium level by sections from Card 6

-" -oS          Uniform dynamic-equilibrium level of BOD in mg/1    66-70
                                                                                         f
                                                                                         fe

-------
MAXQ(N)

=BOD(N)

?DO(K)

;?KOS(N)
?T2MP(N)

??TMP(N)

 ~ 0 (N )

-r3:-D(K)

??hOS(H)
                         Table 19 (Continued)

             Data at Streamflov Addition Points  (No.  11}

             	    	Description	
Node of addition point

Index of addition point
  0.  Increment flow addition
      (not a terminal source)
  1.  Unregulated terminal source
  2.  Regulated tenoinal source

Minimum flov at addition point in  cfs

Maximum flov at addition point in  cfs

BOD of addition point in mg/1

DO of addition point in mg/1

Phosphorus content of addition point in  mg/1

Deaeration rate of BOD of addition point (base
10 at 20C)

Temperature of addition point

Slope of temperature-flow relationship

Slope of DO-flow relationship

Slope of ZOD-flov relationship

Slope of phosphorus-flow relationship
                                                     Field
                                                                    1-U

                                                                    5-8
 9-15

16-21

22-27

28-32

33-38


39-^5

J46-51

52-57

53-63

5fe-68

69-75

-------
                               Table ?0

     ARRAY NOTATION FOR VERIFICATION LINK AND FLOW RELEASE MODEL
               *  Constant for the log-log depth versus  flow relation-
                  ship for a given section

               =  Acre-feet of storage in a given reservoir

               =  Average flow of stream at given reservoir site

               =  Exponent for the log-log depth versus  flow relation-
                  ship for a given section

               =  BOD at node in mg/I

               =  Constant for the log-log velocity versus flow
                  relationship for a given section

               =  Dissolved oxygen constraint for a given section in
                  mg/1

  *.:ZA(N)        -  Drainage area at upper node of section in square miles

               =  Exponent for the log-log velocity versus flow
                  relationship for a given section

               =  Decay rate for phosphorus (base 10) for a given
                  section

               =  Decay rate for temperature (base e) for a given
                  section

               =  Difference between steady-state and computed tempera-
                  tures at a given point
               =  Average water depth in feet for a given section
?
               =  Distance in miles of given node from confluence of
                  basin

               =  Distance in miles of given point from confluence of
                  basin

               =  Dissolved oxygen concentration at given point in mg/1

               =  Dissolved oxygen deficit at given point in ng/1

               =  Depth factor for giver, section

               =  For expansion to include extraction in tne i'OD model
                  (Future use)

-------
 5)
 ZS(N)
 -OD(JJ)
.COW(JJ)
.:EMP(JJ)


-------
                                 170
5COST(JJ)

BDOD(JJ)
NK(JJ)


HS(JJ)
NBSS(H)

HRJ(M)

HTEMP(N)

NRH(JJ)

HTYPEOO

OBOD(S)


OCOST(S)


ODOD(S)


OFLOW(S)
OTSXP(S)
       Table 20 (Continued)

Huaber of cards vhich contain cost data for a given
rirroir site

Temperature of given grid unit in the incremental
flov tableau

Counter-part to MBOD(JJ) in dynaaic programming
solution

Similar to HCOST(JJ)

Counter-part to MDOD(JJ) in dynamic programming
solution

Counter-part to M7LOW(JJ) in dynamic programming
solution
                        - *
Counter-part to MK(JJ) in dynamic programming
solution

Section number for given upper node

Index of upper node of a given section (data input)

Humiber of given reservoir site

Bode of given reservoir site

Steady-state temperature of a given section

Reservoir number for a given node

Index type of upper node (reassemble by program)

BOD in mg/1 of feasible solution from dynamic
programming tableau

Reservoir cost of a feasible solution in the dynamic
programing tableau

DO deficit of a feasible solution in the dynamic
programming tableau

Plow in cfs of a feasible solution in the dynamic
programing tableau

Deoxygenation coefficient of feasible solution in the
dynamic programming tableau (baa* 10)

Temperature in degrees centigrade of feasible solution
in the dynamic programming tableau

-------
                                  171
                          Table 20  (Continued)
OXFLOW(S)



OYFLOW(S)



rfiOS(T)

PHOTOS (I?)



??HOS(N)



=30D(N)

?:OST(NRA,ICR)


?DO(N)

 iAIR(jj)



 :730D(N)
  Flov in cfs from M-arrays of feasible  solution  in  the
   dynamic programming tableau

=  Flov in cfs from N-arrays of feasible  solution  in  the
   dynamic programming tableau

=  Phosphorus in mg/1 at a given point

=  For expansion to include photosynthesis  in BOD  model
   (Future use)

=  Steady-state limiting value of phosphorus for a given
   section

-  BOD in mg/1 at a given stream flow addition  point

=  Cost data for a given reservoir  for  a  given  release 
   rate

=  DO in given reservoir at a given flow

=  Average reaeration coefficient for a given section
   (base 10)

=  Slope of BOD versus flow relationship  for stream flow
   addition point

-  Slope of DO versus flow relationship for stream flow
   addition point

=  Flow in cfs for a given node

=  Slope of phosphorus versus flow  relationship at a
   stream flov addition point

=  Slope of temperature versus flow relationship at a
   stream flow addition point

=  Node of given stream flow addition point

-  Deoxygenation coefficient in I/days  at a stream flow
   addition point (base 10)

=  Maximum flow rate in cfs at a given  stream flow
   addition point

=  Minimum flow rate in cfs at a given  stream flow
   addition point

-------
                                  172
                          Table 20 (Continued)
RPHOS(N)


RTEMP(H)


RTYPE(N)

SATDO(T)



SBOD(JJ)

SDELL(JJ)


SDOD(JJ)

SEDBOD(N)


SFLOW(JJ)

SK(JJ)

SLDBOD(N)


SLOPE(N)

SQCOST()


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SSDOD(T)

SSTEMP(T)

STEMP(JJ)

SX?LOW(X)


SYFLOW(Y)
  Phosphorus in rag/1 at a given  stream  flow  addition
   point

*  Temperature in degrees centigrade  at  a  given stream
   flow addition point

=  Index of a stream flow addition node

*  Dissolved oxygen saturation concentration  in mg/1 for
   a given point

*  BOD in #/days at a given node

  Difference between steady-state and calculated
   temperature at a given node

  DO deficit in #/days at a given node

  For expansion to include sedimentation  in  the model
   (Future use)

  Flow in cfs at a given node

  Deaeration coefficient at a given  node  (base 10)

=  For expansion to include sludge deposit in the BOD
   nodel (Future use)

  Slope of stream in ft/ft for a given  section

  Cost storage in given reservoir for water  quality
   control

  BOD in jC/daya at a given point

  DO deficit in f/days at a given point

  Temperature in degrees centigrade  at given point

*  Temperature in degrees centigrade  at given node

  Flow in cfs for given solution in  the dynamic
   programming routine, M-arrays

=  Flow in cfs for a given solution in the dynamic
   programming routine, N-arrays
                    otal  coat  of a given reservoir

-------
                   173
          Tabl 20 (Continued)
TDIS(H)

TBCP(T)


TRET(N)

TTQfP(N)


VEL(JJ)


WBOD(H)


WDO(H)

WFLOW(H)
WJ(N)

WK(N)


WPHOS(N)

WQACFT(Y)
VTEMP(N)
 WYPE(H)
*  Distance in miles fro the confluence for given node

  Steady-state teaperature in degrees centigrade for a
   given point

  For expansion of reservoir site data

  Steady-state temperature in degrees centigrade for a
   given section

  Average velocity for section in ft/sec indexed by
   upper node

*  Untreated BOD in I/day or rag/1 of a waste load for a
   given node

  DO in mg/1 in the vast* load for given node

  Flov in cfs for a given node

  Average width in feet for section indexed by upper
   node
                                            Jt
  Node of waste water discharge

  Deaeration coefficient of waste load in I/days (base
   10)

  Phosphorus in mg/1 in waste load for given node

*  Reservoir storage in acre-feet for water quality
   control

  Percent removal of BOD of given waste load

-  Minion* BOD treataent level

  ?easprature in degrees centigrade of waste load for
   given node

  Index of waste load for a given node

  Flow in ragd of waste load for a given node

-------
                       174
            FORMATS   FOR  DATA  CARDS
                VIA IN PARAMETER
                                      TTnrmTtTnTtTrrr
          _   	 OESllG
          TEST 4     i  TEST 51
       DYWvllC
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 -^	\-
 WASTE_WArER_rj|ISCHARGE DATA
                                                       tofPHOslNl     IWREMIN)
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WKINll      iWBOD(N)|      IWDOfN)
         ATIA Al.BTREAM__FLOW_JADDlLTiON
                                  RTEMPIN)! RFTEMHNf Rf DliD(N) JRFSOD(N)

                                                r^'i^MMjH"n'T!7
                                                                 Figure 31

-------
                                175
                                                  TEHMINATJON CARD
 DATA   SET
REPEATED N-TIMES"
      DATA  SUBSET
'REPEATED N-TIMES
-A
                                               CARD(S) 11
                       GAUD 10
                                         CARD(S) 9
                    OPTIONAL
                                     CARD(S)  6
                                  CARD(S)
                                CARD 2
                             CARD 1
                         VERIFICATION LINK?
                          COMPUTER PROGRAM
                          SOURCE or BINARY)
                  TYPICAL  DATA  COMPILATION
                               FOR
                      VERIFICATION    LINK
                                                                Figure 32

-------
                              176
                                                 TERMINATION CARD
  DATA  SET     	
REPEATED N- TIMES
                           DATA SUBSET
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         CAJUXS) 11
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                                        CARD(S)  9
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             COMPUTER PROGRAM
             (SOURCE or BINARY)
         _y
                                                 LJ/
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                                                               Figure  33

-------
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                         BIBLIOGRAPHY
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elz, C. J., "Stream Recovery," WSW, Vol. 100, No. 12,  pp. 1*95-501
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'Connor, D. J., "Oxygen Relationships in Streams:  Robert A. Taft
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rankel, R. J., "Water Quality Management:  An Engineering and
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rankel, R. J., "Water Quality Management:  Engineering Economic
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                             225

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  *O    Davis, pas s i m.                                                            'i

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                                                                              ?
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                                                                             It":
                                                                             f,

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                                                                                I
                                 231
89.  Hall, Charles, Sanitary Engineer,  Federal Water Pollution Control
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                       KEY TO ABBSEVIAIIOiB


ASCE     American Society of Civil Engineers

ASCE-BX  American Society of Civil Engineers, Hydrology Division

ASCE-SA  American Society of Civil Engineers, Sanitary Division

JWPCF    Journal of Water Pollution Control Federation

SIW      Sewage and Industrial Waste

SWJ      Sewage Works Journal

WRR      Water Resources Research

WSW      Water and Sewage Works

                                                                              I
                                                                             I

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