-------
                                  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

I«S VES
CONTINUE TO CALCULATE STREAM QUAL-
,T, » CHtCK,»0 CON5T««T. '""'"" 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.  Chesape»3ce 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 Intpound»eiita                        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 g«n»r?a aap of the Potoaae Hiver Bavin, inoludlng
the proposed rM*rvoir syrtaai.  In Tabl« 3 *r« prM«ot*d data on 14
proposed ittpoundaanta for tl» Fotcnao ay»t««.  Appandlx B oontaina
detailed st^oawft'tioa of th« individual atraa* r«aohM, showing water
Intakes, ^-ststewmter discharg**, low le-ral daaa, g«ging 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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-------
                                 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
2.1»3
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
-------
                           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 nee«s-

•^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 sit€»s0  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 stat»o



     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 gr±df (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 +>,«*
-------
' 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.
-------
                                  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.
-------
                                                      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 20°C) 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 20°C).  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 23°C
-------
f
                                   78





bas  been used,  with the temperatures of the waters from the reservoirs



being taken as  20°C.



     The steady-state temperature was determined from a statistical



analysis of the temperature data by months.  The value of 23°C 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 28°C,  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



-------
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-mil«3 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 Esann«r.  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
                                                           ir
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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

rd»ase 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 ;
-------
                         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
-------
                           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
-------
                                  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;
-------
                                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.

2jj»eous 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.


-^£HAg°n 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 <••!"




 '••'---section  transformation and a depth-factor  is also  shown.  This vnll




  • c.,ered.  in  dcitcti] in the next two sections  of the appendix.




  :---^'-i- ^ ci: vii FORMULATIONS




    ;-t:f<;re any one: of the prediction formulas can l,e used basin-wide,




   '-•• • >j; ^'t'^'M^v be necessary'' to ad.juat the  reaeratiun  coefficients to




    '-i;c:r. &imii»r 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 f»CTOR
                    	CHURCHILL'S K- WITH UO DEPTH FACTOR
if 30
I
                                            313      3K)
                                            RIVER  WILES
                                                            305
                                                                             295
                                                                                               Figure  16
-------
123










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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.
-------
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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 cci«i^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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-------
           149
STOHV  CREEK
               -<	1586]—	(580
                                               SAVAGE RIVER
     OVERALL POTOMAC  RIVER BASIN SYSTEM
                                                              Figure
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-------
"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™, -.
3»30 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 20°C)

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)

??T£MP(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 20°C)

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
r«i«rroir 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(»)


SSBOD(T)

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

«  ?easp«rature 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
                	CARD5_L	I      	
                 DATA OF "STREAM!BY SECT i ONsT
                      MOP CARD
                     5IQPI1IQNAL
CQNJJJUAIiQ
           coNSTtN) xcarwt. TTEMPIN; DECWWN) PPHOSIN
                :SERVDIR  INFORMATION
                      i_CAR'D  8  !	:
                    RESERvQlR COST
		
 —-^	\-
 WASTE_WA£rER_rj|ISCHARGE DATA
                                                       tofPHOslNl     IWREMIN)
                                                     'RA7TJVA'/K7r~rT i i t~r~r frx~
WKINll      iWBOD(N)|      IWDOfN)
         ATIA Al.BTREAM__FLOW_JADDlLTiON
                                  RTEMPIN)! RFTEMHNf Rf DliD(N) JRFSOD(N)

                                                r^'i^MMj«H"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
                      'REPEATED  N- TIMES'
         CAJUXS) 11
       CARD 10
                                        CARD(S)  9
        OMIT  IF  OPTYPE = 2
CARD(S) 8
                                 CARD(S) 7
             OPTIONAL
                              CARD(S) 6
                          CARD(S) 5
                        CARD
                      CARD 3
                    CARD 2
                  CARD 1
               FLOW RELEASE
             COMPUTER PROGRAM
             (SOURCE or BINARY)
         _y
                                                 LJ/
                TYPICAL  DATA  COMPILATION
                             FOR
                  FLOW   RELEASE    MODEL
                                                               Figure  33
-------
                                               177
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-------
                                  228
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-------
                                   230
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     Branching Multistage Water Resources Systems," WRR,  Vol.  3, No.  2
     (December 1967) .

86.  O'Connor, D. J., and Dobbins, W. E. , "The Mechanism  of Reaeration
     in Natural Streams," ASCE-SA, Vol. 82, No.  SA6 (1956).

87.  Langbein, W. B., and Durum, W.  H., "The Aeration Capacity of
     Streams," U. S.  Geological Survey Circular 5^2, U.  S.  Department of
     the Interior, Washington, D. C. (1967).

     Tsivoglou, E. C., O'Connell, R. L. , Walter, C.  M. ,  Godsil,  P.  J.,
     and Logs don, G.  3., "Tracer Measurements of Atmospheric Reaeration  -
     I. Laboratory Studies ,"JV?CF, Vol. 37, No.  11  (October 1965).
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89.  Hall, Charles, Sanitary Engineer,  Federal Water Pollution Control
     Administration, U.  S.  Department  of the  Interior,  Chesapeake Field
     Station, Annapolis, Maryland,  private communications.

90.  Haveman, R.  H., Water Resource Investment and the  Public Interest,
     Vanderbilt University Press, Nashville,  Tennessee
                       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

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