-------
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.
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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
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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.
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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;
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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.
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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
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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;
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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;
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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.)
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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.
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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
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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
-------
.
1
i
c
•H
«
H O «
& <^
H W «3
r-i
o ,0 *-^
ca
a} 3
rH *
< CO
•H W
r-l O
O O
Js JH H
«> -P-5*
cfl D"
3= U
a -p o
43 ra O
O O rH
EH O-«J
O *r4 "
^ H H .
« O (
MS
a a ..
f-l rH O O
o w o *«;j
eo 0
<1> 4*
O C! I
-P M O
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£-1 -P O
to -*c
•3
o
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oo o^>
\i)M>
-
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vD-=>--* ro
H <-H
w
oovo o
ir\
'1-1
o ro on co QO
- t- H
t-
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lf\
rH
IA t*- t-
CO CO r-\
-T-q' t—
r-( lAVD ITvCO 1-4 H
PO\ID lf^ f-l H VO
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if\
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r-4 cuco
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a a o
-------
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:
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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.
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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.
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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
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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..
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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.
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97
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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.
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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,
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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
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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
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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.
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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
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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
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108
Even with overall optimal planning models, will the instittrtiorsal
arrangements be adequate to act to implement the optimal sclutions?
A opf-opriations of funds for water resource planning by the U. 3.
•'"ongre;s« have not always been dictated by monetary considerations.
Haveaian[90] in an analysis of Federal expenditures in ten
states concluded the following:
1. "Although projects with the highest benefit-cost
ratios tend to be chosen before projects with low
ratios, no consistent or persistent pattern is
manifested" and
2. "A somewhat stronger and more consistent motive seems
to be present in both force of aid to low income and
depressed areas and the drive to exploit development
potential in areas of substantial opportunities to
productive resources investments."
This appears to be the case in the Potomac River Basin. From the
initial studies in the 1940's up to the present, the major construction
-•"Taviti.es have been in the Appalachia Region. This region is cur-
T-rotly defined as a socially and economically "depressed" area.
While at the Chesapeake Field Station, the writer also had the
to study and field test other water resources management
In the opinion of the author, the most urgent research need? j
' the area of water quality managejneirt are as follows j j
1. Inexpensive methods for easily obtaining large quantities
of field information such as cross-sectioning, tiais-of-
travel5 chemical parameters, etc.;
2. More precise and readily adaptable water quality formulations
especially for low BOD stream reaches and in low level
impoundments ;
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109
Continued development of methods for projecting industrial
water supply requirements and resulting wastewater loadings ;
Methodology and necessary information for assessi'ing, by
individual water user, the monetary value of given water
quality and quantity level for a given failure rate; and
3ocio-econo.ii.ic: significance of optimal river basin plajtrnjjg
within the framework of current institutional pr-actJce-s.
operational viewpoint, the research areas delineated above
->f the ne^rt barriers to overcome in effective rlvsr baa^n
I'.'l
-------
CHAPTER IX
SUMMAJOf AND CONCLUSIONS
Tl.is st-udy has been concerned with the development and field
e:-'i:if of a method for determining optimal flow release sequences
.,,:• Tf^ter quality control from multiple reservoir systsms, It has
.:?••> oeen the intent of this study to investigate, using gn actual
-:•:&? basin, the sensitivity of the release sequence to changes in
various physical and biochemical, design, and socio-economic
:era~eters.
The flow release problem was structured as a converging "branch,
-•licistage dynamic programming decision system. An optimal flow
-eiease model has been developed with the decision-making procedure
at each stage (the confluence of two regulated streams) being an
efficient enumeration process. Using both single and dual return
"ittables, the model has five options for determining optimal release
flour sequences for a given flow state at a decision point. These are'
i minimum DO deficit for a given BOD state; (2) a minimum DO
"fiflcit; (3) least-cost of reservoir storage for a given BOD state;
- least-cost of reservoir storage; and (5) a minimum BOD.
Predictive algorithms for temperature, BOD, and DO have been
cooperated in the flow release model. Ability to vary stream
aj.ocity and depth with flow has also been Incorporated into the
••^1,
A general descriptive mathematical paragon capable of repre-
fi- *irig the stream flow system of a river and its network of
110
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Ill
tributaries including its hydraulic characteristics and location of all
impoundments, waste discharges, water intakes, etc., has been developed.
In the flow release model, the paragon provides the required mathe-
matical linkage for both the quality formulations and converging branch
multistage decision system to the physical features of the basin.
Optimal reservoir-release sequences from the proposed impound- \
aents in the Potomac River Basin have been developed for the control
of water quality at mile point 116,,0 (the start of the Potomac estuary).
In developing the various optimal release sequences, a minimum preset
dissolved oxygen level had to be met in all regulated systems„
The sensitivity of the release sequences developed by the flew
release model to various physical and biochemical, design, and socio-
economic parameters has been investigated for the proposed reservoir
system in the Potomac River Basin. Comparisons have been made to a
standard test run for a flow target of 1500 cfs at the Potomac
estuary. The conclusions of the sensitivity analysis and comparisons
are;
1. Verification of the predictive quality formulations is
essential. This requires well-established time of travel
coefficients, which appear to be the most sensitive of the
physical and bioch.ead.cal parameters investigated. A method
Including a specially designed mathematical model has been
developed to aid in verifying the predictive quality formu-
lations .
2. Of the remaining physical and biochemical parameters, the
reaeration coefficient was the most difficult to define and
appears also to hava a great effect on the release patterns.
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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
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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
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•£*•.
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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
-------
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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
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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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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
ODO<]
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140
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141
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142
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-------
144
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if
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-------
148
CO 9NIHS1NU
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Figure 29
-------
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?
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•-;
0
0
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0
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53
58
r*
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2'b
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69
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? 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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-------
178
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