Technical Paper Number II
A STEADY STATE
SEGMENTED ESTUARY MODEL
by
Ronald E. Bunce
Leo J. Hetling
U. S. DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
MIDDLE ATLANTIC REGION
CHARLOTTESVILLE, VIRGINIA
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hr'
Page
ACKNOWLEDGMENT'S
I. 1'ITRODUCTION . .................. I - 1
II. GENERAL APPROACH TO THL ^POBLE' . , II - 1
III. DETAILED DERIVATION ............... Ill - 1
....... IV - 1
V, PREPARATION OF Tin, COMPUTER PROGRAM ....... V - 1
VI. INPUT DATA PREPARATION AND PROGRAM CASE
CONTROL .... ,..,..,. , VI - 1
VII. EIELJOOPA^EY „.,,,.,,,,, ....... VII - 1
APPENDIX I - ^LGT,.; DIAGRAM::
APPENDIX II - Ib!.T 3oO FORTRAN PROGRAM
APPENDIX III - CAMPLE TNnuTG
APPENDIX IV - TYPICAL PROGRAM CASE SOLUTIONS
A.
C. Ga,raple Input r->nd Output Data for Case 3 with
Control If[AT=l, IMDI.'X (l) and I:IDLX (2). Both =
1. Outnut aA"1 and LaA"1,
K. Sample Input arid Output Data for Case 5 with
Control IMAT=2, IIIDLX (10=1. Output Pair1.
F. Sample Input and Output Data for Case 6 witn
Control IHAT=2, II^X (3) and INDEX
Output ai3~l and Fal)~J-o
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TABLE OF CONTENTS (Continued)
G. Sample Input and Output Data for Case 7 with
Control IMAT=3, INDEX (5)=1. Output air1 A"1.
H. Sample Input and Output Data for Case 8 with
Control IMAT=3, INDEX (6)=1. Output VD times
aB-1 A"1.
I. Sample Input and Output Data for Case 9 with
Control IMAT=3, INDEX (?)=!. Output L (ultimate
B01) Vector) times Output Matrix in Ii. above.
J. Sample Input and Output Data for Case 10 with
Control IFIAT=3, INDEX (8)=1. Output = Dissolved
Oxygen at Saturation plus output from E. above
minus Output from I, above.
K. Sample Input and Output Data for Case 11 with
Control IMAT=3, INDEX (l) turough INDEX (b')=l.
All cases above, i.e., A to J.
LIST OF FIGURES
Figure
1 Estuary Segments
2 Advection Into and Out of Sepmerit K
3 Program Deck Structure
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ACKNOWLEDGMENTS
Special appreciation ana acknowledgment are expressed, to
Mr, Emanuel Mehr, Research Scientist, New York University, for
allowing us to employ his tridiagonal matrix inversion routine.
This routine is exceedingly fast and allows rapid inversion of
the tridiagonal matrix utilized in the model,, His guidance and
encouragement was a great contribution during tne course of
certain phases of this work.
Grateful acknowledgment is made to Mr, Richard L, O'Connell
of the Central Pacific River Basins Comprehensive Project, FWPCA,
for the assistance he gave in understanding the model and setting
up the program while he was Director of the Chesapeake Field Sta-
tion; to Mr. John M. Jeglic of the He-entry Systems Department of
General Electric for the many programming ideas which were taken
directly from his time-dependent version of the model; and to Dr.
Robert Tnomann of the Delaware Estuary Cornprenensive Study Project,
both for the basic trieory on wni en tne prog,ram is baseu and for
his detailed, patient, explanations of it
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I. INTRODUCTION
The "oxygen sag" equation developed in 1925 by Streeter
and Phelps1 has found widespread use in the analysis of a partic-
ular type of stream pollution problems. This mathematical model
may be applied where the pollutant of concern is "biologically
degradable organic material which brings about a depression of
the natural dissolved oxygen (DO) content of a stream.
The "oxygen sag" formula, however, is not applicable to
tidal bodies of water, primarily "because of the over-riding impor-
tance of turbulent diffusion in estuaries whicn is not normally
taken into consideration in streams. In fresh water streams "plug
flow," in effect, is assumed, and this is not an unreasonable
assumption in most cases. Although longitudinal diffusion does in
fact occur in streams due to horizontal and vertical velocity
gradients, the longitudinal exchange which this brings about
involves similar material; viz,, the material tiiat is "diffused"
upstream is very nearly the same with respect to age, concentra-
tion, etc., as that which is "diffused" downstream. The net result
is usually negligible in the analysis of stream pollution problems.
Furthermore, advection, or transport downstream by the stream,
produces a transfer of waterborne material which greatly exceeds
the transfer brought about by diffusion. In estuaries, however,
because of their relatively large cross-section and small net flow
downstream, the advective transport is often quite small compared
to tne transfer of materials by turbulent diffusion. For tnis
reason, the latter effect must be considered.
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1-2
In I960, 35 years after the development of the ''oxygen
sag" formula for streams, O'Connor2 devised a similar mathematical
model for estuaries which added to Strceter and Phelp's formula a
term to account for longitudinal diffusion. As witn tne original
stream sag formula, tne O'Connor model is given as a differential
equation which may ue integrated to give a solution for the dis-
solved oxygen as a continuous function of distance along the
longitudinal axis of tne tidal estuary.
In 1963 Thomarm developed a computational procedure based
upon the principles of systems analysis which incorporated tne
terras of tne O'Connor model for estuaries. This method of compu-
tation employs an incremental or segmented approach where average
conditions in a finite number of connected segments are determined
rather than a continuous function solution. The degree of resolu-
tion possible in the solution is directly related to the number
of segments chosen. This approach si^nlifies the mathematics in-
volved and allows much greater flexibility in its use. The models
previously citea apply to tne one dimensional steady state case;
whereas, with the segmented approach, a second or tnird dimension
may be added, and the time dependent situation may also be investi-
gated. Also, any pollutant for which tne relationships affecting
its behavior can be expressed mathematically can be incorporated
into the segmented model.
Trie model has been described previously by Thomann3, and
solutions to the one-dimensional time-dependent model have been
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1-3
programmed for both the digital and analog computer '. Applica-
tions of the model and methods of estimating required, parameters
also have been presented6'7'8'9. The purpose of this paper is to
describe in detail the theory of the "Thomann Model" as applicable
to the one-dimensional steady-state case of organic pollution of
an estuary and to document a digital computer program developed
to solve this case.
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II - 1
II. GENERAL APPROACH TO THE PROBLEM
A first step in tne application of the model is to divide
the estuary into a satisfactory number of segments. A mass balance
for the pollutant is written for each segment. The results from
these balance a series of equations equal in number to the number
of segments. The only unknowns in these equations are the mean
steady-state concentrations of the pollutant in each segment.
Thus, a series of n equations with ri unknowns is obtained where
n is the number of segments. By combining terms, this series of
equations may be expressed in matrix notation as:
AC = L
where A is a collection of known terms such as flow, diffusion
constants, deoxygenation constants, and segment volumes in com-
binations having units of cubic foot/day. C is a vector matrix
of unknown concentration of pollutants in pounds/cubic foot. The
product of A and C is L, a vector of pollutant loads added directly
to each segment expressed as pounds/day. Tne terms of the vector
L have been referred to as forcing functions by Thomann.
The matrix of unknown concentrations, C, may be solved by
inverting A, since:
C = LA"1
_n
where A , the "unit loading matrix," is the inverse of A. C may
then be obtained by performing the matrix multiplication of L
times A as indicated.
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II - 2
This is an extremely convenient arrangement since, once
having solved for A , it can be multiplied by any distribution
of loads along the estuary as described by tne vector L. Further-
_^
more, because of the nature of A , it is possible to determine
easily what part of the resulting pollutant concentration in any
one segment is due to a given discharge in any other segment.
The unit loading matrix is essentially a table having n rows and
n columns, the elements of which have the units Ibs/cfs per lb/
day discharged. Tnus, A, , the element in the fourth row and
^ 5 I
_j
seventh column of the A matrix, would give the numerical value
for the concentration in segment h resulting from a discharge of
one pound per day in segment 7- By multiplying the element,
A, , by the actual load applied to segment 7» tne concentration
^» I
in segment H resulting from tnat discharge will be obtained. If
tne estuary being studied has been modeled using correctly verified
parameters, it will be possible to reproduce known pollutant dis-
tributions from known input loads. The verification step must be
carried out with satisfactory results if the model is to be useful
for predicting altered loading conditions expected in the future.
That is to say, the computer model is no substitute for the great
quantity of engineering field and office work required for any
sound, scientific discussion.
Once a verified unit loadinp- matrix is obtained, the pollu-
tant distribution resulting from any loading pattern may be obtained,
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II - 3
In the analysis of oxygen conditions, it is necessary as a first
step to multiply the unit loading matrix by the particular ulti-
mate oxygen demand (UOD) loading conditions being studied. Having
the UOD distribution among the segments, a mass balance may then
be written for each segment incorporating the terms which affect
the oxygen distribution, namely, advection, diffusion, deoxygena-
tion, and reaeration. When applicable, terms describing uptake
by benthal loads and the net effect of photosynthesis and respira-
tion can also be included. Just as in the case of the pollutant
distribution, these mass balances around each of n segments results
in a series of n equations in n unknowns which are the DO concen-
trations being sought. Through the use of matrices, it is possible
then to obtain a series of linear expressions for the DO in any
segment as a function of the discharged loads, benthal uptake and
photosynthetic effects in all otner segments.
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Ill - 1
III. DETAILED DERIVATION
Having divided the estuary into n sections, a mass balance
is written for the oxygen in the k section (Figure l). Assume
the concentration of oxygen in each section is uniform and equal
to C , the mean concentration in the section.
Section k-1
Ck-l
Section k
Ck
Section k+1
Ck+l
Flow Q
k-l,k
Flow Q,
Figure 1
Oxygen can be pained or lost by several ways in Section k.
1. Advection into Section k from Section k-1 and
out of Section k to Section k+1.
2. Diffusion into or out of Sections k-1 and k+1.
3. Reaeration of Section k from the atmosphere.
k. Use of oxygen in Section k by oxygen consuming
waste (UOD).
5. Production of oxygen in Section k by photosynthesis,
6, Other mechanisms (benthol deposits, immediate
oxygen demands, etc.).
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Ill - 2
Advection
In the system pictured below,
k-1
k-1
k+1
Figure
the C's represent mean concentrations in each segment of length, L.
If it is assumed that the concentration gradient through
any two adjacent sections is approximated satisfactorily by a
straight line, then tne concentration at a boundary, a, between
the two segments can be shown geometrically to be:
C =
a
L, C, + L. n C.
K. k-1 k-1 k
L.
k + Lk-l
which can be written as:
C, . L. .
k-1 _k-l
C. L.
k k
a L + L. L, . + L.
k-1 k k-1 k
or by letting
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Ill - 3
the concentration at the boundary may be expressed as:
Ca = ^k-l,k Ck-l
The amount of material advected across boundary "a" is
then given by:
An , , = Q, , , [ C, , , C. , + (1 - L n , ) C, ]
k-l,k 'k-l,k LS>k-l,k k-1 ^k-1,1 k
where £, . , is defined as above.
k-1,1
For the case of boundary"b" the concentration gradient
is rising and has a sign opposite to that passing boundary "a.1
In this case it can be shown that £, ._ will be defined as:
k,k+l
-! -Vl
~~ _L ~~ _
Lk+l
or
Lk
Lk
For a falling gradient, then, £, is defined by the ratio
of the downstream segment length to the sum of the upstream and
downstream lengths; whereas, for a rising gradient, 5 is defined
by 1 minus this quantity or the ratio of the upstream length to
the sum of the upstream and downstream lengths.
The above procedure may be used to find 5 subject to the
restrictions that
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Ill - h
Following this derivation, the advection from Section k-1
to k becomes:
Vi,k =
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and
III - 5
'k-l
k-l
P - P
k-l k
3X ~ 1/2L
N = K
(Ck-l " Ck}
/2 (I +
D, the total time rate of transfer of substance across
the boundary between Segment k-l and K which has a cross-sectional
area A is fjiven by:
D = AIT
K (C
k-l
1/2(L
k-l
or
16
17
18
19
where
KA
k-l,k 1/2 (L + L, )
K— _L K.
If E is taken as positive, the direction of the diffusion
will be fixed by tne relative magnitude of C 5 C 5 and C
K—l K
20
21
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Ill - 6
Reaeration
The rate of reaeration (r ) into Section k may be expressed
as being proportional to the difference in the actual oxygen
concentration and the oxygen saturation value C
J - sc
R = rn V, (C - C, ) 22
k k k sc k
BOD
The rate of utilization of oxygen by the UOD present is
expressed as:
B. - V, d. (t) L. (t) 23
k k k k
where d (t) = the decay coefficient (k., ) in Section k at time t.
L (t) = the UOD in Section k at time t.
Other Sources and Sinks
The effect of algae, benthal deposits, COE, and any other
sources or sinks of oxygen in Section k will be expressed as S (t).
.K
Later it may be desirable to separate these effects and treat them
separately; but for the present, in order to keep the analysis
tractable, they will be considered together.
If an equation is now written for all the sources and sinks
of oxygen in Section k, the following differential equation for the
mass rate of change in Section k is obtained.
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Ill - T
Ek-i,k (ck-i - ck} + Ek,k+i (ck+i - CK)
rk \ [Csc(t) - Ck] - \ dk(t) Lk(t)
or rearranging:
at
_ljk
Ck - \+l (1 - ^k+l) Ck+l
+Ek-l,k Ck-l ~ Ek-l,k Ck + Ek,k+l Ck+l ~ Ek,k+l Ck
- Vk Ck + -rk\Csc(t) + \dk(t) Lk(t) + Vk(t)
Factoring out C Ts and multiplying through by -1:
K
- [\-i,k 5k-i,k + \-i,k] ck-i- tvk ~ - Qk_ljk (i - Ck_lj
\-i,k - Ek,k+i - rk \ ck 26
- Ck-l [-\,k+l (1 - 5k,k+l} + Kk,k+l] = rk\Csc(t)
Letting
- \dk(t) Lk(t) - sk(t)
ak-l,k = -[Qk-l,k 5k-l,k + Ek-l,k]
Qk,k+l Sk,k+l + Ek-l,k 28
Ek,k+l + rk\ - \ t]
ak,k+l = [Qk,k+l ( I - 5k,k-l} - E
k,k+l
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Ill - 8
the mass balance equation reduces to:
£L _, _ L-, _ • 9, , w, ' cL n _ L/n -,
k-l,k k-1 k,k k k,k+l k+1
-rk\Csc(t) +Vk(t) Lk(t) +Sk(t) \ 30
If steady state conditions are assumed:
TT= ° 31
dt
C (t) = C 32
sc sc
dk(t) = dk 33
Lk(t) = Lk 3^
Sk(t) = Sk 35
therefore:
= [Qk,k+l Ck,k+l = Qk-l,k (1 ~ Ck-l,k} + \-l,k
and
a, n . C. -. + a, , C, + a. , _ul - r. V. C + V, d. L. + S. V_ = P. 37
k-l,k k-1 kk k k,k+l kksc kTik kk k
Assuming appropriate boundary conditions, i.e., Cn and
C and writing mass balance equations for each section, we
obtain an equation of the following type:
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Ill - 9
allC
a!2C2 Pl
n <*~) n oo o "• f} •?) ^ o ^
12 1 dd. d d$ j c
a23°2 + a33°3 + &3hCh = Pl
38
a , C . + a C
n-l,n n-1 n,n n
or in a matrix notation
a
21
a
!2
&
33
n,n-l
= P
n
0
0
0
a
n-l,n
a
nn
Cl =
C2
S
•
C
n
PX
P2
P3
•
P
n
39
A C = F
C = F A
-1
hi
The system can thus be solved for all values of C by finding
the inverse of the matrix A. Matrix inversion, although time-
consuming by hand, can be accomplished easily by high speed digital
computers.
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IV - 1
IV. MATHEMATICAL TECHNIQUE EMPLOYED IN THE MODEL FOR MATRIX
INVERSION
The matrix of coefficients we are dealing with in the
program is of a particular type. The system of equations is tri-
diagonal since the matrix of unknowns is tridiagonal, i.e., each
element is zero except the main diagonal and its adjacent diagonals,
The solution to such a system is conveniently handled on
the computer by solving for the inverse employing a tridiagonal
technique.
This may be illustrated by an example:
P
X
Now define an S sequence recursively by:
Sl = Cl
IT tl
II II
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IV - 2
Pi, i
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IV - 3
X3 =
K3 -
53
Kl -
55
"1
The above procedure is well known. In order to prove this,
we note that the forward sweep corresponds to taking the i-th row,
-C.
multiplying it by , and adding it to the ifi-th row as i advances
from 1 to n. This procedure triangularizes the matrix, i.e., it
is reduced to:
S 00
1 1
0 S2 q? 0
0 0 S q
0 0 0 SJ(
,
X,
1
X2
X3
\
.,„,._ _ ^
K
1
K2
K3
KU
|
The backward sweep is now clear. Obviously now X is
determined since Xi is known, etc.
56
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V - 1
V. PREPARATION OF THE COMPUTER PROGRAM
The program was written in Fortran IV and originally run
on the IBM 709^ at the National Bureau of Standards in Washington,
D. C. The more recent version presented here was run on the IBM
360 system at the U. S. Geological Computer Center, Washington,
D. C. Though Fortran programs will run on any installation that
maintains a Fortran compiler, it usually requires a number of
changes to "be made when switching from one system to another.
Generally, these changes require an understanding of the installa-
tion's job control language, together with the particular level
of the compiler.
In developing the program and in the choice of mnemonics,
an effort was made to make the program as compatible as possible
with the time dependent model previously programmed by Jeglic.*4
The complete program deck structure is shown in Figure 3.
The entire package consists of one main program and eight sub-
routines. The main program calls these various sub-routines as
they are needed and controls the actual operating features and
cyclings The sub-routine POLYB reads in coefficients and the
powers of polynomian equations when the vectors for reaeration,
decay, and dissolved oxygen are to be generated rather than read
in as input data. The sub-routine PRELIM reads in various vector
quantities and prepares the coefficients of the matrix and other
required vectors. Sub-routine PRECAL loads the calculated matrix
elements in their proper positions and returns control to the
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Subroutine FINAL
Subroutine PRTMAT
Subroutine SCAVEC
Subroutine INVERT
Subroutine PRECAL
Subroutine POLYB
Subroutine PRELIM
Program MAIN
// FORT.SYSIN DD *
//EXEC FORTHCLB
JOB CARD
FIGURE 3.
PROGRAM DECK STRUCTURE
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V - 2
main program, which then calls the matrix inversion program.
This sub-routine then inverts the tridiagonal matrix. The sub-
routine SCAVEC performs the calculations on the inverted matrix
that have been specified in tne control card. PRTMAT is a general
sub-routine used to print the inverted matrix and could be used
to print any matrix with five elements printed per row per page.
Sub-routine FINAL is used only when both the A and B matrix
inversions have been specified for a single case of input data,,
PRECFN is employed to adjust the vectors with proper
dimensions when it is more convenient to enter the vectors in
units other than those employed in the actual calculations. This
allows the analyst to enter a conversion constant into the program
when the source data set up is in other units.
As shown in Figure 3, the first card of the program deck
is the job control card. Tne card format for this card at tne
UoScGoS. Computer Center where the program was run is as follows:
JOB CONTROL CARD
Card
Columns Required In formation
1-2 //
3 Center Code: For use in conjunction with the job or
program number to identify the center originating or
assigning the job or program number.
U - 5 Federal Agency code
6-8 User Registration Code: Individual users registration
code, To be assigned by Computer Center Division.
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V - 3
JOB CONTROL CARD (Continued)
Card
Columns Required Information
9-10 User's ID: This is structly a user's ID to uniquely
identify submissions of data to the Computing Center.
The only caution to be observed by the user is when
two sets of data for the same program are submitted
simultaneously, then different alphanumeric characters
should be punched in columns 9-10.
11 Blank column
12-lU JOB (e.g., the word JOB)
15 Blank column
16 ( (left parenthesis)
IT - 20 Program Number: Four digit numeric job or program
number assigned by the Computer Center Division at
each field center and Washington, D. C. When a new
number is assigned at any field center, the attached
Program Registration Form should be completed in
duplicate and transmitted to the Computer Operations
Branch, Washington, D. C.
21 , (comma)
22 - 25 User assigned auxiliary account number. Four alpha-
numeric characters chosen by the user according to any
method he chooses. Accounting data will be sequenced
and subtotaled by this number for user information.
26 , (comma)
27 - 30 Estimated execution time in minutes. Requires four
numeric digits.
31 , (comma)
32 - 35 Estimated lines of print expressed in thousands of
lines. Requires four numeric digits (e.g., 0001 =
1000 lines of print).
36 , (comma)
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V -
JOB CONTROL CARD (Continued)
Card
Columns __ Required Information ___
37 - kO Estimated number of cards to be punched. Requires
" four numeric digits and is an exact number (e.g.,
0100 = 100 cards).
hi , (comma)
k2 Reserved for future use - must be 1.
k3 , (comma)
kh Reserved for future use - must be 1.
1*5 , (comma)
H6 Type run.
C = Compile only
T = Test of program
P = Production use of program
D = Data conversion required to convert from
prior systems
hj ) (right parenthesis)
U8 , (comma)
k9 ' (single quote)
50 - 70 Programmer or user's name. May be from 1 to 20
characters , with or without imbedded blanks . Must
be followed by one single quote ( ' ) . This field is
required and cannot exceed 20 characters.
If the user requires additional information in the
JOB card, the following rules apply: (e.g., MSGLEVEL
1 or other comments).
A - Place a comma immediately following the trailing
quote after name field.
B - Punch any alphanumeric character into column 72 -
Do Not Use this column for any other purpose.
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V - 5
C - Punch // in columns ] and 2 of a second card.
D - Columns 3-15 MUST BE BLANK.
E - If MSGLEVEL = 1 is desired, it must be punched in
columns l6 - 25 and followed by one or more blanks
prior to any other comments.
F - If comments only are desired, leave column l6
blank and start the comment in column 17-
n - Column 72 of the second card MUST BE BLANK.
The second card in the program source deck is the EXEC
statement card.,, The EXEC statement indicates the beginning of
a job step and describes that job step. For the program here,
the EXEC statement should appear as:
Columns No. 1 2 3
/ / b E X E C b F 0 R T K C L G
(b = blank)
The third card in the prop-ram contains the following:
Columns No, 1 2 3 h 5 . , „,,.......
//FORT.BYBINbDDb*
(b = blank)
The statement specifies the location of the source module(s)
or the object module(s) to the control program.
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VI - 1
VI. INPUT DATA PREPARATION AND PROGRAM CASE CONTROL
A. General
The model contains the feature of running any number of
cases during a production run. The original run would consist
of placing the FORTRAN source program before the data deck. Sub-
sequent computer runs would use the binary deck (called the object
program) in front of the data.
Appendix III shows a typical data deck structure. The first
card in the deck contains the number of cases to be run. This
*
variable is identified by the name NCASES. The first three
columns on the card are used to enter the value. It is possible
to run 999 cases on an individual computer run.
The format for this card is:
CARD COLUMNS 123^5. . . .
8
Note that for the sample shown, the program would operate
on 8 data sets before termination. In entering data for the num-
ber of cases, the value should always be right justified. If, for
example, the 8 were inadvertently entered in column 2, the program
would try to operate on 80 sets of information rather than the 8
desired.
The second card in the data deck is the date card. This
should be given as the date the computer run will be made. Its
*
The word "variable" is not used in the normal mathematical sense.
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VI - 2
main use is to quickly identify the computer run since, in most
simulation modeling, input information will "be adjusted upon
analysis of initial output, and at a later time the analyst may
want to refer to prior runs.
The numeric values and special symbols normally used to
write the date may be entered as:
5/1T/6T (Starting in column 1)
or 05/17/67 (Starting in column l)
The date may "be entered in columns 1 to 2k on the card,
but for use of identification, it would be convenient to establish
a definite entry technique as shown above.
The third card in the data deck should contain the name
of the user. Again 2h columns are employed, and the entry may-
appear in any of the card columns 1 through 24.
The fourth card in the data deck is the title card. This
card is employed to identify the first set of data the program
will operate on. Note in Appendix III that each subsequent set of
input data contains a title card. Card columns 1 through 22 are
employed. The data may be numeric or alphabetic.
The title card and its subsequent set of data may be
considered as a separate subdivision from the entire data deck.
In practice, the title card and its associated input data is a
subset of the input deck; therefore, the following discussion
will outline the subset structure.
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;.:. Panelist Input
j. General Description of ICar.c-list L:;r,ut Wit- Rule;-;
"he r-arnelist input node W:JK choker: in c--c.er to a/oio u.c
U'_"LaiI necessary to code ir.pat utta Into a definite fori-i".'.. r.truc-
:.are. Uiiacr .;A;'"h'LlRC options, i,ne cie.ty tc bo eritcrca into ti*e
coriputo1' is loiiucu. iu mcircry rfit'.jou1. Lhc.- -jc-e of vXi:liciL ]if:^:.
Trie general f(jrri of f.:,o "tf^"i.LI£'^ L5tat^^v;:^^ ir,:
-/JTi^lFT/n-me1Y1, V,, V,,,..., V JnwcjV^ ,. ^,,,. . . ^ ^
L&rc nane. is the rare- of the list of variables whose
names are soecificu i;y V. , T.-,r. . The c,arr,e of tiie iiAi'l.LIhT1 nc.y >.e
frof' oiiu- to six characters Ir. jenp;tn.
Tr order to understand th;; iJatu c-ntr,/ for a V.M-J-iole
aGoOcLi,,tad "vlth a hA^T'.fCT, l;^o fcllo.vinn 2>-:rtJit:i
nus t :>o s;..ti bficti:
M . G:i3r coJ unnr 2-7? cf thu data nar.'s '. ...v ;>; 11^20.
e. All entries arc .oeparated by coir"iiui; tat last
cn'ory inur,t also be followec uy a cor;-;;;.
f. Blanks n.ay not be inbeded he fore nr P.f^cr tivo
Kign. (Ex. A = 5-0, is illegal and ishould be
punches as : A=lj. 0,)
-------
-------
VI - It
g. Blanks may be embedded between data values after
the first value of vectors or arrays as shown
below:
(7=1.2,1.3,1.5 2.2,2.3,2.5,)
h. Exponential notation may be used for large or
small values, i.e., 2.153E5 and 2.15^E-2 denote
215300 and 0.0215H.
i. If the decimal point is omitted, it is assumed
to be at the extreme rifdit.
j. No decimal point may be used in the entries of
variables typed integer.
k. V/heri an array name appears without subscripts,
all elements in the array must be present.
1. To enter the same value in several elements of
an array, the data card may be set up as follows:
If X is dimensioned as X (10); then
X-l.It,2.U,6.3,5*6,.2,7-1,8.5,
Description of Handlist and Variables Used in This
Program
a. NAMELIST CF
This namelist deals with the problem controls and
conversion factors.
HSECTS (integer) - Number of estuarine segments
IMAT (integer) - Program Control for A and/
or B matrix
INDEX (i) (integer) - Printinp; Option Control
ITP (i)(integer) - Control value variable
employed by polynomial sub-
routine and temperature
conversion control
CFQ (real) - Advection conversion constant
employed in sub-routine PRECFM
-------
-------
VI - 5
CFLEN (real) - Length conversion constant
employed in sub-routine PRECFM
CFK (real) - Diffusion conversion constant
employed in sub-routine PRECFM
CFL (real) - UOD conversion constant employed
in sub-routine PRECFM
CFAREA (real) - Area conversion constant employed
in sub-routine PRECFM
CFVOL (real) - Volume conversion constant
employed in sub-routine PRECFM
CFP (real) - Dissolved oxygen sink and source
conversion constant employed in
sub-routine PRECFM
The above CF namelist is developed for each data set.
INDEX controls the printing of information with regard
to a particular state of IMAT. In the event that IMAT vould
equal 1, two sets of information may be optionally printed, i.e.,
ALPHA x A"1 or ALPHA x VECTOR (L) x A"1. If IMAT would equal 2,
then the index would optionally be used to print ALPHA x B or
ALPHA x F x B"1. In the third state, i.e., IMAT = 3, the INDEX
option allows printing of ALPHA x A~ , ALPHA x L x A~ , ALPHA x
B"1, ALPHA x F x B"1, ALPHA x A"1 x B"1, VD A~1B"1, LVD A""1 B"1,
and D.O. Sat. + ALPHA x F x B~ - LVD A"1 B"1. IMAT and the index
values will be discussed in greater detail later in this section.
A large number of possible combinations of output may be
obtained. A typical output is shown in Appendix III, and each
case shown here has been verified. Case K in the Appendix shows
the results for IMAT = 3 and all INDEXES 1 through 8 set equal
to 1.
-------
-------
vi - 6
The ITF variable is entered on the card following the
INDEX control card. Two values should always be /riven for this
variable. If ITP (2) is set equal to 1, the polynomial sub-
routine is called. Ttiis sub-routine, discussed in Section V,
generates the reaeration, dissolved oxygen at saturation, and
the decay vector. If ITP (l) is set equal to 1, the temperature
vector may be Driven in decrees Fahrenheit and is converted in
the sub-routine to degrees Centigrade.
The conversion constants CFQ, CFL^iJ, CFK, CFL, CFARUA,
CFVOL, and CFP are entered in succeeding cards. These constants
are employed to convert tneir corresponding vectors to the proper
units so that the actual vector input data may be entered in any
units providing the corresponding conversion factor is given.
In the event that the original input vectors are already in the
proper units, the corresponding conversion factor would be set
equal to 1.
b. NAMKLIST FIVER
This namelist contains the parameters which
describe tne geometry of the river and tne waste loadings to
the system.
Q (i)(real) - Oj__]_ j_, net flow of the estuary
between segments i-1 and i, ex-
pressed in cubic feet per second.
All boundaries, including toe flow
into the first and the flow out of
the Itist segment, must be specified.
-------
-------
VI - T
LENGTH (i)(real) -
VOL (i)(real)
AREA
rea
1)
DIFFCO (i)(real) -
Df the estuary seg-
ments. Since a length above the
uppermost segment and below the
lowermost segment is required
(see equations 9 and 19), n + 2
lengths must be specified. The
input must be in feet. If other
units are to be used, the proper
conversion factor CFLEN (Namelist
CF) must be used.
Vj, volume of section i in cubic
feet. All sections must be spec-
ified, If units other than cubic
feet are used, a suitable conver-
sion factor must be specified
(CFVOL in namelist CF).
AJL i i' cross-sectioned area of
the interface between segments
i-1 and i, in square feet. All
interfaces, including the first
and last, must be defined. Con-
version factor CFARKA may be used.
KJ__J j_, longitudinal dispersion
coefficient between segments i-1
and i in square rules per day.
All segment boundaries, including
the first and last, must be spec-
ified, Conversion factor CFK is
available if different units are
used.
L.£ , ultimate oxygen demand being
discharged to segment i in pounds
per day. All segments must be
defined. Conversion factor CFL
may be used if desired.
P
PJ_, other sources or sinks of
oxygen in segment i , in pounds
per day. All segments must be
defined even if all values are
zero or meaningless. Conversion
factor CFP is available.
-------
-------
VI - 8
c. NAMELIST RIVTO
This namelist is used if one wishes to specify
definite values for the ultimate oxygen demand decay rate, the
reaeration rate and the saturation value of oxygen in each segment.
DISOXS (i)(real) - C , the saturation value of dis-
o C-
solved oxygen in segment i. All
segments must be defined. The
values must be entered in mg/1.
REAERK (i)(real) - rj_, the reaeration coefficient
for segment i in units of I/day.
All segments must be defined.
DECAYK (i)(real) - dj_, the ultimate oxygen demand
decay rate in segment i also with
units of I/day. All segments
must be defined.
d. NAMELIST R R
This namelist is used if one wishes to generate the
values of the ultimate oxygen demand decay rate, the reaeration rate
and the saturation value of oxygen from the river temperature using
polynomials.
T P (i)(real) - The temperature of the water in
segment i. The temperature may
be given in degrees Centigrade if
ITP (2) in namelist CF is set
equal to 0 or in degrees Fahren-
heit if ITP (2) in namelist CF is
set equal to 1.
K D (Integer) - The order of the polynomial which
is being used to describe the
decay rate.
C D (j)(real) - Polynomial coefficient of the jth
term in the polynomial which is
being used to describe the decay
rate. C D must be defined for all
values of j < K D + 1.
-------
-------
VI - 9
K R (integer) - The order of the polynomial which
is being used to describe the
reaeration rate.
C R (jKreal) - Polynomial coefficient of the jth
term in the polynomial which is
being used to describe the reaera-
tion rate. C R must be defined
for all values of j <_ K R + 1.
K C (integer) - The order of the polynomial which
is being used to describe the
dissolved oxygen saturation value.
C C (j)(real)
Polynomial coefficient of the jth
terra in the polynomial which is
being used to describe the dis-
solved oxygen saturation value.
C C must bo defined for all values
of j <^ K C + 1.
In order to understand the arrangement of trie various NAME-
LISTS in the input data structure, the following explanation should
prove helpful:
Consider the following:
1. CF Namelist (Always First and Present)
2. RIVER Nanelist
3. RIVTO Namelist
U. R R Namelist
1. CF is always first and present.
Now, if ITP (2) = 0, li/YMELIST R R is second, NAMELIST RIVER
is third, and RIVTO is not required.
If ITP (2) = 1, RIVER is second, RIVTO is third, and RR
is not required.
-------
-------
VII - I
VII. BIBLIOGRAPHY
Gtreetor, II. W. , and Pnelps, L. B. , "A Study of the Pollution
and Natural Purification of the Ohio River - III, Factors
Concerned in the Puenoinena of Oxidation and Reaeration,"
Public Health Bulletin No. 1^6, U. S. Public Health Service,
February 1925-
O'Connor, Donald J., "Oxygen Balance of An Estuary," Journal
of the Sanitary EngineeringDivision, American Society of
Civil Engineers, Proceedings Paper 2U'(2, \fol. 86, No. SA3,
May I960.
Thomann, Robert V., "Mathematical Model for Dissolved Oxygen,"
Journal of the Sanitary Engineering Division, American Society
of Civil Engineers, Proceedings Paper 3680, Vol. 89, Ko. SA5,
October 1963.
Jeglic, Jonn M. , "Mathematical Simulation of the Estuarine
Behavior," Digital Computer Technology and Programming Anal-
ysis Memo. No. 1032, Rev. A, General Electric Re-Entry Systems
Department, Philadelphia, Pennsylvania, July 1967.
"Program for Analog Computer Simulation of Dye Diffusion in
the Potomac River," Final Report by: Electronic Associates,
Incorporated, Washington Computation Center to the Chesapeake
Field Station, Chesapeake Bay-Susquehanna River Basins Project,
Federal Water Pollution Control Administration, Annapolis,
Maryland, in completion of Contract RO-3-2131-65, October 1965.
Hetling, Leo J., and O'Connell, Richard L., "A Study of Tidal
Dispersion in the Potomac River," Water R e s o ur c e s Re s e arch,
Vol. 2, No. U, Fourth Quarter, 1966.
Hetling, Leo J., and O'Connell, Richard L., "An Oxygen Balance
for the Potomac Estuary," CB-SRBP Technical Paper No. 13,
Federal Water Pollution Control Administration, Middle Atlantic
Region, Charlottesville, Virginia (in press).
Hetling, Leo J., "Simulation of Chloride Concentrations in
the Potomac Estuary," CB-SRBP Technical Paper No. 12, Federal
Water Pollution Control Administration, Middle Atlantic Region,
Charlottesville, Virginia (in press).
Hall, Charles W., and Hetling, Leo J., "Use of Mathematical
Models as Aids to Decision Making in Water Quality Control,"
Presented at the Sixty-third National Meeting of the American
Institute of Chemical Engineers, St. Louis, Missouri,
February 19, 1968.
-------
-------
APPENDIX I
PROGRAM
FLOW DIAGRAMS
-------
-------
(SUBROUTINE SCAVEC 5 )
t
(SUBROUTINE INVERT 4
WRITE
TITLE
DATE
PAGE
NSECTS
IMAT
INDEXES
CFQ, CFLEN
CFK, CFL,
C FARE A
CFVIJIL , CFP
ATION
d CALL
t°)
;.CTN =
\
READ
/ NUMBER OF
CASES
| INCASES)
READ
/ DATE OF
THIS
| RUN
CTN 1 1 J
/ NAME OF THE
PROGRAM
| USER
READ
| TITLE
6
OLYB i) WR'TEl
' GEN
4 IS READ PRO
THE VEC- HE;S
N, DECAY,
EN SATUR-
y
1
:RAL
JECT
DING
SYSTEM
CALL TIMEIN
COLUMNS 1-3
NCASES "= 999
COLUMNS 1-34
(ALPHANUMERIC)
COLUMNS 1-24
(ALPHANUMERIC)
COLUMNS 1-72
(ALPHANUMERIC)
INITIAL OUTPUT PAGE
FOR EACH CASE RUN
TITLE
DATE
USER.
l__
READ
NSECTS, ITP(Z)
IMAT
INDEXES (1-8)
CFQ, CFLEN,
CFK, CFL,
CFAREA
CFVOL , CFP
NSECTS - NUMBER OF
ESTUARINE
SECTIONS
IMAT - MATRIX OPTION
INDEX(I-8)PRINTING CONTROL
OPTIONS
ITP(I) -TEMPERATURE
INPUT OPTIONS
ITP(2) -CONTROL
POLYNOMIAL
SUBROUTINE
FLOW CHART NUMBER) | I | OF | I | I
PROGRAM NAME: MAIN
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
MIDDLE ATLANTIC REGION
CHARLOTTESVILLE, VIRGINIA
-------
-------
5,
J = 2 , MR
Cr, iCr^CrjXTP,'1"1
0
CD,
J =
= Co,
2, MD
+ CD, X
TP,"
POLYNOMIAL EQUATIONS
REAERATION: Cr
20 "
i
J = 2, MC
Cc, = Cc, + Cc, X TP^"1
Cr,
Cd,
Cc,
= Cr, t Cr,
= Cc, 4- Cc,
Cr^T,
K = 0
DECAY: CD, = "^ co^Tf
DISSOLVED . i K
OXYGEN Cc = ^>\ CckT,K
SATURATION j^7^
POLYNOMIAL OUTPUT
DATA PAGE
I
WRITE
FLOW CHART NUMBERJ | 2 | QF | I | |
PROGRAM NAME:SUBROUTINE POLYB
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
MIDDLE ATLANTIC REGION
CH ARLOTTESVILLE , VIRGINIA
-------
-------
READ
GOGO
FALSE
TRUE
READ
RIVER
SUBROUTINE PRECFM
RATIOL(I) HI 0 -0 5*
TURBEXtD/ADVECQd))
1 = I, IMAX
AFTSECdl'ADVECOd)
ADVECQ(I)- 864OO.*ADVECQ(I>
ADJLd)'ALENTH(I) + ALENTHd + l)
TURBEX(I) = ((PI FFCOdlt (ARE A(I)/ADJL(I)1)« CONST)
30
AKK = TURBEX(I-I)/ADVECQ(I-I)
AJJ = TURBEXdl/ADVECOd)
AH HALENTHd-l)/
(ALENTH(I-I) + ALENTH(I»)
TRUE
RATIOLd) *
I 0-AJJ + .01
FALSE
RATIOLd) = All
I - I, ISPEC
AUPPER(I) = (ADVECOd+l)*
(10 -RATIOLd + l))) -
TURBEX(I + I)
IOO
I «l, NSECTS . .
/
\
1 -Z, NSECTS
ISPEC =
NSECTS
\
y
BOTTUMII- I) =
(-I.O*((ADVECOd)»
RATIOLd) + TURBEXd))))
TRUE
(RATIOL(IMAX) * 0 5
ASTORE(I) = (-1 0*ADVECO(I> *
(10- RATIOL(D) + ADVECOU+ I)*
RATIOLd + I) + TURBEXd) + TURBEXd til)
CONTINUED
ON FLOW CHART
NUMBER
©
FLOW CHART NUMBER] | 3J OF | I | I
PROGRAM NAME:SUBROUTINE PRELIM
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
MIDDLE ATLANTIC REGION
CHARLOTTESVILLE, VIRGINIA
-------
-------
CONTINUED
FROM FLOW CHART
NUMBER
I = I, NSECTS
ADIAG(I) -
ASTORE(I) +
DECAYK(I)*
VOLUME(I)
ULBOD(I),
I = I, NSECTS
120
DOSKSR(I),
I«l, NSECTS
WRITE
750
IOISOXS, I "I, NSECTSl
IVOLUME,!*!, NSECTSI
• DECAYK.IM, NSECTSI
WRITE
WRITE
HEADINS
^.S^
TtTLE
OATRUN
IPAGE
^/^
', IPAGE = IPAGE + I
TITLE
DATRUN
I PACE
IPAGE = IPAGE + I
J,TP(J), ULBOD(J)
OOSKSR(J),
ISEC, I,
DIFFCO(I),
AFTSEC(I)
IF \FALSE
J = NSECTS
ISEC,I,
RATIOL(I),
TURBEX(I)
ADVECQU)
TITLE
DATRUN
IPAGE
IPAGE » IPAGE + I
J.REAERK(J),
DECAVK(J), DISOXS(J)
ISEC,I,RATIOL(I),
TURBEX(I),
ADVECQ(I),
ISEC = ISEC +
I = Itl
CONTINUED
ON FLOW CHART
NUMBER
FLOW CHART NUMBER] |4| OF | I | I
PROGRAM NAMErSUBROUTINE PRELIM
U S. DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
MIDDLE ATLANTIC REGION
CHARLOTTESVILLE, VIRGINIA
-------
-------
CONTINUED
FROM FLOW CHART
NUMBER
(4)
FALSE
IPA6E = (PAGE t I
830
TITLE,
DATRUN,
I PAGE
WRITE
I = I
J = 2
IPAGE = IPAGE + I
TITLE,
DATRUN,
IPAGE
WRITE
I * I
J = 2
\
y
HEADING
WRITE,
1,1, ADIAG(I),
I, J.AUPPERU),
J, I.BOTTUMd)
^- -^
^^ IF ^^^ FALSE / 1=1+1
^- _s^ \ J = J + I
TRUE
I, I.BDIAGd),
I,J.AUPPERU)
J,I.BOTTUMd)
FLOW CHART NUMBERJ |5|OF|l]l
PROGRAM NAME-SUBROUTINE PRELIM
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
MIDDLE ATLANTIC REGION
CHARLOTTESVILLE, VIRGINIA
-------
-------
ENTER
i'J -I, NSECTS...
DOSKSR(J) ' CFP # DOSKSR(J)
VOLUMEt J) • CFVOL* VOLUME(J)
ULBOO(J) ' CFL * ULBOO(J)
*
-------
-------
I8J-I, NSECTS
AMATRX(I,J)
= ALPHA*
AMATRX(I,J)
3
ALPHA=
1 6E + 4
J=l, NSECTS
SUMVEC(J) = 0.0
2
_A-I
I = I, NSECTS
VECTOR
FLOW CHART NUMBER] |7| OF jI|I
PROGRAM NAMEISUBROUTINE SCAVEC
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
MIDDLE ATLANTIC REGION
CHARLOTTESVILLE, VIRGINIA
-------
-------
(DISOXS(I), 1 = 1, NSECTS)
(ULBOD(I), 1 = I, NSECTS)
KAMATRXd.J), 1=1, NSECTS),
0=1, NSECTS)
((BMATRXU.J), 1=1, NSECTS),
J = I, NSECTS)
(VOLUME(I), 1 = 1, NSECTS)
(DECAYKU), I.I,
NSECTS)
DO I: 1 = 1, NSECTS
DO I J'l, NSECTS
CCTN(I,J) = O.O
DO I- IK=I, NSECTS
CCTNU.J) =CCTN(I,J)-I-
BMATRX(I,IK)#
AMATRX(IK.J)
= 1, NSECTS
1 = 1, NSECTS
. J=l, NSECTS
BMATRXU.J) = AMATRX(I.J)
AMATRX(I.J) = CCTN(I.J)
FLOW CHART NUMBERJ |e| OF | I | I
PROGRAM NAME:SU8ROUTINE FINAL
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
MIDDLE ATLANTIC RFGION
CHARLOTTESVILLE, VIRGINIA
-------
-------
ENTER
t=l, NSECTS
D(I) *
AMATRX(I.I)
I = I, MA
II • I + l
*< MA = NSECTS - I
8(K) • 00
7
'
AMATRXd, K) •
X(I)
6
X(LL) =(T(LD-
QAILD*
XILL+ I))/S(LL)
5
K' 1, NSECTS
OA(I)'=AMATRX(I,II)
AMATRXIII, I)
2
1 DO 7. K = 1, NSECTS
B(K) = 1.0
S(l) • D(l)
I • 1, NSECTS
3
I • 1, MA
LL • NSECTS - I
J • I - 1
QA(J)/S(J)
Till" B(I)-PA(J)*
T(J)/S(J)
4
X(NSECTS).
T(NSECTS)/
S(NSECTS)
FLOW CHART NUMBER | |9\OF | I |
PROGRAM NAME: SUBROUTINE INVERT
^^\ySE
i
:TS^-^
TRUE
/
4
FLOW CHART NUMBER] I | 0 | OF | I | I
PROGRAM NAME:SUBROUTINE PRTMAT
U S DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
MIDDLE ATLANTIC REGION
CHARLOTTESVILLE. VIRGINIA
-------
-------
APPENDIX II
IBM 360 VERSION I
FORTRAN PROGRAM LISTING
-------
-------
ISN 0002
ISN 0003
ISN 0004
ISN 0005
ISN 0006
ISN 0007
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0008
0009
0010
0011
0012
0013
0014
0015
0016
0017
0018
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
0029
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
PROGRAM MAIN
MIDDLE ATLANTIC REGION - IBM 360 VERSION I
STEADY STATE SEGMENTED ESTUARY MODEL
FOR FURTHER INFORMATION CONTACT
PROJECT ENGINEER- OR. L.HETLING
SYSTEMS ANALYST-PROGRAMMER- R.F.BUNCF
STORAGE ALLOCATION-MAIN PROGRAM
DOUBLE PRECISION DATRUNJ4),USER(4)fTITLE(12)
COMMON/DATUSE/DATRUN,USER,IPAGE
COMMON/CONTRL/TITLE,NCASES,NSECTS,IMAT,INDEX(8),KK,ISPEC,IMAX,ITP(
12),CFQ,CFLEN,CFK,CFL,CFAREA,CFVOL,CFP
COMMON/AWORKS/KCON(3),CVAL(30),TP(40),TP1(40)
COMMON/BWORKS/ABLOCK(3600),CCTN(1600)
NAMELIST/CF/NSECTS,IMAT,INDEX,ITP,CFQ,CFLEN,CFK,CFL,CFAREA,CFVOL,C
1FP
CONTROL INFORMATION
TITLE-72ALPHANUMERIC CHARACTERS
NCASES - NUMBER OF RUNS FOR PRODUCTION
DATRUN - DATE FOR THE COMPUTER RUN
USER - NAME OF THE PROGRAM USER
TITLE - INFORMATION FOR THF HEADING
CONTROL CARO 1.COL1-3
CONTROL CARD 2.COL1-24
CONTROL CARD 2,COLl-24
CONTROL CARO 3.COL1-72
DATA INPUT-CONTROL INFORMATION AND HEADING OUTPUT DATA
CALL TIMEIN
ICTN=1
READ (5,100)
READ (5,150)
READ (5,150)
READ (5,200)
NCASES
(DATRUNH ), 1=1,4)
(USFR(I),I=1,4)
(TITLE(I),I=l,l2)
WRITE (6,250)
WRITE(6,300)(TITLF(I),I=1,12),(DATRUN(I),I=1,4),
-------
-------
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0030
0031
0032
0034
0035
0036
0037
0038
0039
0041
0043
0044
0045
0047
0048
0049
0050
0051
0052
0053
0054
0055
40
50
60
70
80
100
150
200
250
WRITE (6,550
WRITE (6,650
IFUTP(2).EQ
CALL PRELIM
CALL PRECAL
CALL INVERT
CALL SCAVEC
KK=KK+1
IF (IMAT.EQ.
IF (ICTN.EQ.
ICTN=ICTN+1
GO TO 6
IF (KK.EQ.2)
GO TO 40
CALL FINAL
GO TO 50
REWIND 2
REWIND 4
FORMAT (13)
FORMAT (4A6)
FORMAT ( 12A6
FORMAT (1H1/
ISN 0056
ISN 0057
ISN 0058
ISN 0059
ISN 0060
ISN 0061
ISN 0062
ISN 0063
ISN 0064
ISN 0065
ISN 0066
INDEX(5»,INOEX(6),INQEX(7),
CFQ,CFLEN,CFK,CFL,CFAREA,CFVOL,CFP
L) CALL POLYB
3) GO TO 60
NCASES) GO TO
GO TO 70
80
<1H1///////////////44X,49(1H*)/44X,49H
MI DDL?
1 ALTANTIC REGION /53X,36HSTEADY STATE SEGMENTED
2 MODEL/44X,49(1H*)//////////)
300 FORMAT
-------
-------
ISN 0002
ISN 0003
ISN 0004
ISN 0005
ISN 0006
ISN 0007
ISN 0008
ISN 0009
ISN 0010
ISN
ISN
0011
0012
ISN 0013
ISN 0015
ISN 0016
ISN 0017
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISfl
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0018
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
0029
0030
0031
0033
0034
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
SUBROUTINE PQLYB
STORAGE ALLOCATION
DOUBLE PRECISION DATRUNJ4),USER(4),TITLF(12)
COMMON/CONTRL/TITLE,NCASES,NSECTS,IMAT,INDEX(8),i * TP(I)**(J-1)
CD(J) * TP(!)**(J-l)
*
TO
CC(J) *
CR(l)
CD(1)
CCd)
40
TP(I)**(J-ll
ISN 0035
PREPARE OUTPUT CONTROL PAGE
40 WRITE (6,100)
-------
-------
ISN 0036
ISN 0037
ISN 0038
ISN 0039
ISN 0040
ISN 0041
ISN 0042
ISN 0043
ISN 0044
ISN 0045
ISN 0046
WRITE (6,150) KR,(CR(I)tI=l,MR)
WRITE (6,200) KO,(CD(I),!=!,MO)
WRITE (6,250) KC,ICC(I),1=1,MC)
WRITE (6,300) (I,REAERK(I),OECAYK(I),OISOXS(I),TP(I),1=1,NSFCTS)
100 FORMAT (1H1,12A6,2X,4A6,2X5HPARE ,I2///)
150 FORMAT (1H ,18X55HPOLYNOMIAL POWER AND COEFFICTFNTS FOR REAfPATIQN
1 VALUES//27X3HKR=,I?,16X2HCD/(40X,E15.8M
200 FORMAT (1HO,18X50HPOLYNOMIAL POWER AND COEFFICIENTS FOR DECAY VALU
1ES//27X3HKD=,I2,16X2HCD/(40X,E15,8))
250 FORMAT (1HO,18X65HPOLYNOMIAL POWER ANO COEFFICIENTS FOR OIS<:nLVFn
10XYGEN SATURATION//27X3HKC=,12,16X2HCC/(40X,E15.8))
300 FORMAT (1H ,///18X45HCOMPUTED VALUES FROM THE POLYNOMIAL EQUATIONS
1//18X2H I,7X10HREAERATION,12X5HDECAY,3X14HD.O.SAT(JRATION,6X1IHTEMP
2ERATURE/18X19H VALUES,11X6HVALUFS,11X6HVALUES,11X6HV4L
3UES//(18XI2,4XE13.6,4XE13.6,4XE13.6,4XE13.6))
RETURN
END
-------
-------
ISN 0002
ISN 0003
ISN 0004
ISN 0005
ISN
ISN
0006
0007
ISN 0008
ISN 0009
ISN 0010
ISN 0035
ISN 0036
ISN 0037
ISN 0038
ISN 0039
ISN 0040
ISN 0042
C
C
C
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
I.SN
ISN
ISN
ISN
0011
0012
0013
0014
0016
0017
0018
0019
0020
0021
0022
0024
0025
0026
0027
0028
0029
0030
0031
0032
0033
0034
C
C
C
C
C
C
SUBROUTINE PRELIM
STORAGE ALLOCATION
DOUBLE PRECISION DATRUN(4) ,USER ( 4) , TTTL E ( 12 )
COMMON/DATUSE/DATRUN,USER,IPAGE
COMMON/CONTRL/TITLE,NCASES,NSECTStIMAT,INDFX(8) , KK , I SPFC , I M AX ,
HTPm ,BC(7)
COMMON/AWORKS/KR,KO,KC,CR( 10 ) ,CD( 10 ) ,CC ( 10 ) ,TP( 40 ) ,TP1( 40)
COMMON/BWORKS/AMATRX(40,40) ,RE AERK( 40 N ADVECQ(40 ) ,DOSKSR( 40) ,
10(40) ,ALENTH(40) ,AFTSEC(40) , AD JL ( 40 ) , TUR RFX( 40 ) ,RATIOL(401 , VECTOR (
240), A WASTE 1 1000) ,ASTORE(40> , ADI AG f 40) , RDI AGI 40) , AUPPER { 40) . ROTTUM (
340) ,DISOXSI40),ULBOO<40) , VOLUME (40) t OEC AYK ( 40 ) , VD( 40 ) ,UVT(40) ,ARCA
4(40) ,SUMER(40) ,CFINAL ( 40 ) , SUMVEC ( 40 ) ,CCTN(1600)
DIMENSION Q140) ,L(40),P(40) ,LENGTH(40) ,VnL(40)
REAL L, LENGTH
EQUIVALENCE ( Q, ADVECC) , ( ULBOO,L ) , ( DDSK^R ,P ) , ( AL FN'TH, L FNGTH ) , ( VOLUM
IE t VOL)
NAMELIST FOR INPUT DATA
NAN|ELIST/RIVER/Q,L»P»VOLt AREA, niFFCO, LENGTH
NAMEHST/RIVTO/DISQXS,REAERK,OFCAYK
NAMELIST/GOGO/TP1
IF UTP(2).EQ.l) GO TO 5
READ (5,GOGO)
DO 4 I=1,NSECTS
4 TP( I)=TP1( I)
5 CONTINUE
READ (5, RIVER)
CALL PRECFM
IFUTPI 2).E0.1) GO TC 10
READ (5tRIVTO)
10 IMAX - NSECTS + 2
CONST= 2.*(5280.0**2)
DO 20 1=1, IMAX
20 ALENTH(I)=ALENTH(I)*5280.
IMAX=IMAX - 1
DO 30 1=1, IMAX
AFTSECl I)=AOVECO(I )
ADVECQ(I) = 86400. *ADVECQ(I )
ADJL(I) = ALENTHU) * ALENTH(I + 1)
30 TURBEX(I)=( (DIFFCO(I)*(AREA( I)/AOJL( I) ) )*CDNST)
PREPARATION OF THE RATIOL VALUES
R ATI OL(1)=< 1.0-0. 5*TURREX(1)/ADVECQ< 1) ) •
1 = 2
40 AKK = TURBEX(I-1)/ADVECQU-1)
AJJ=TURBEX( I )/ADVECQ(I)
AII = (ALENTH( I- 1 ) /{ ALENTH( 1-1 ) +ALENTH ( I ) ) )
IF(AKK.GE.AJJ) GO TO 70
RATIQtt I )=(1.0 - (0.5#(AKK * AJJ)))
-------
-------
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0043
0045
0046
0047
0049
0050
0051
0052
0053
ISN 0054
ISN 0055
ISN 0056
ISN 0057
ISN 0058
ISN 0059
ISN 0060
ISN 0061
ISN 0063
ISN 0064
ISN 0065
ISN 0066
ISN 0068
ISN 0069
ISN 0070
ISN 0071
ISN 0073
ISN 0074
ISN 0075
ISN 0076
ISN 0077
ISN 0078
ISN 0079
ISN 0080
ISN 0081
ISN 0082
ISN 0083
ISN 0084
ISN 0085
ISN 0086
ISN 0087
ISN 0088
ISN 0089
ISN 0091
ISN 0092
C
c
C
c
c
c
50 IF(RATIOHI).GE.AII) GO TO 60
RATIOL(I)=AII
60 CONTINUE
IFd.EQ.IMAX> GO TO 80
1 = 1*1
GO TO 40
70 RATtOL(n = 1.0-AJJ*.01
GO TO 50
80 RATIOL(INAXI=0.5
PREPARATION OF THE DIAGONAL MATRIX ELEMENTS
DO 90 I=2»NSECTS
90 BdTTUN«-ll=<-1.0*«ADVECQ
-------
-------
ISN 0093
WRITE (6,503) ISFC,ALFMTHJiseo
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0094
0095
0096
0097
0098
0099
0100
0101
0102
0103
0104
0106
0107
0108
C
C HYTRAULIC-LOAD
C
It>AGF=IPAGE +
WRITE (6,1) (T
WRITE <*,600)
1 = 1
J = l
ISFC=0
WRITE (6,601)
650 ISEC=ISEC+1
1 = 1+1
WRITE (6,602)
1)
IF( J.EQ.NSECTS
J = J + 1
GO TO 650
660 CONTINUE
C
OUTPUT - OESIGNFO AS UNIT
I
ITLF(I),I = 1,12) , JOATRUNC I ) , I = 1 , 4) , I P ACf-
ISFC, I ,DIFFCQ( I ) , AFTSFC( I )
J,TP
-------
-------
ISN 0140
ISN 0142
ISN 0143
ISN 0144
ISN 0145
ISN 0146
ISN 0147
ISN 0148
ISN 0150
ISN 0151
ISN 0152
ISN 0153
ISN 0154
ISN 0155
ISN 0156
ISN 0157
ISN 0158
ISN 0159
ISN 0160
ISN 0161
ISN 0162
ISN 0163
ISN 0164
ISN 0165
ISN 0166
ISN 0167
ISN 0168
ISN 0169
ISN 0170
ISN 0171
ISN 0172
IFUMAT.NE.3) GO TO 850
830 IPAGE=IPAGE+1
WRITE (6,1) (TITLE( I ) , I = 1,12),(DATRUN(I ),!=!,4),IPAGE
WRITE (6,803)
1 = 1
J = 2
840 WRITE (6,804) I,I,BDIAGlI),I,J,AUPPER(I),J,I,BQTTUM(I)
IF(J.EQ.NSECTS) GO TO 850
J=J+1
GO TO 840
850 WRITE (6,806) J,J,BDIAG(J)
1 FORMAT ( IH1,12A6,2X4A6,2X5H<>AGE ,I2///
500 FORMAT (1H0.42X39HG E
II NTERFACE
2ME
^ NUMBER
I C
I
N P U T
SECTION
DAT A///11X89H
VOLU
(SO.FT)
(FT,
0 M E T R
AREA
LENGTH/13X86HNUMBER
(CU.FT.)
501 FORMAT (IH , 10X12,2X1H-,2X12,11XF10.0,13X12,34XF11.1)
502 FORMAT (IH ,10X12 , 2X1H-,2X12,11XF10.0,13X12,14XF13.6,7XF11.1)
503 FORMAT (IH ,53X12,34XF11.1)
,29X53HH Y D R A U
600 FORMAT (IH
1A T A///1X.103HSECTION
2 INTERFACE
3 (DEG C)
4 (SO.MI/DAY)
LIC AND LOA
T J
K •
(LBS/DAY) (LBS/DAY)
(CU.FT/SEC)//)
1 f M P U T 0
c>
0/lX,108HNUMBi?P
NUMBER
601 FORMAT (IH ,63X12,3H - ,I2,6XEl3.6,6XE13.6)
602 FORMAT (IH ,2X12,6XF8.3,6XF13.6,6XE13.6,7X12,3H - ,I 2,6XE13.6,6XE1
13.6)
700 FORMAT (IH ,43X49HC OMPUTED SYSTEM PARAMETER
IS//5X7HS6CTION,9X1HR,IOX1HD,10X10HSATURATION,9X9HINTERFACF,13X2HXI
2tl2XlHE,l5XlHQ/5X6HNUMBER,7X6H(/DAY),6X6H(/DAY),8XIOHD.O.(MG/L),lO
3X6HNUMBER,24X12H(CU.FT./DAY),5X12H(CU.FT./OAY)///)
701 FORMAT (IH ,62XI2»3H - ,12,8XE13.6,2XF13.6,4XE13.6)
702 FORMAT (IH ,6X12.8XF7.3,5XF7.3, 9XF7.3,11X12,3H - ,12,8XE13.6,2XE1
13.6,4XE13.6)
801 FORMAT (IH ,43X45HO IAGONAL MATRIX ELEMENT S//6
13X8HA-MATRIX//16X22HMAIN DIAGONAL ELEMENTS,19X23HUPPER DIAGONAL EL
2EMENTS,18X23HLOWER DIAGONAL ELEMENTS///)
802 FORMAT ( IH ,14X2HA(,I 2,IH,,I 2,2H)=1XE15.8,16X2HA(,I 2,IH,,I2t2H) = ,I
1XE15.8,16X2HA(,I2,1H,,I2,2H)=,1XE15.8)
803 FORMAT (IH .43X45HO IAGONAL MATRIX FLEMENT S//6
13X8HB-MATRIX//16X22HMAIN DIAGONAL ELEMENTS,19X23HUPPER DIAGONAL FL
2EMENTS,18X23HLOWER DIAGONAL ELEMENTS///)
804 FORMAT (IH ,14X2HB(,I 2,IH,,I 2,2H)=IXE15.8,16X2HBI,I 2,IH,,I 2,2H)=,I
1XE15.8,16X2HB(,I2,1H,,I2,2H)=,1XE15.8)
805 FORMATdH , 14X2HA f , I 2, IH, , 12, 2H) = 1XE15. 8 )
806 FORMAT(1H ,14X2HB<,I 2,1H»,I 2,2H)=1XE15.8)
RETURN
END
-------
-------
ISN 0002
ISN 0003
ISN 0004
ISN 0005
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
JSN
IS>N
ISN
0006
0007
0008
0009
0010
0011
0012
0014
0016
0017
0018
0019
0020
0021
0022
SUBROUTINE PRECAL
DOUBLE PRECISION DATRUN( 4) , USE» ( 4) , TITL F ( 1? )
CO^MCN/CONTRL/TITLEf NCASFSf NSEf TS, IMAT,INDEX(8),KK,ISDPCfIMAX,
IIT»(2) ,BC(7)
COMMON/BWORKS/AMATRX(40f40) .REAERKI^O) , ADVEC Qi 40 ) , HPSK SR ( 40 ) , D IFFC
10(40) ,ALENTH140) , AFTSEC t 40 ) t A3JL ( 40 ) , TU'-J ^EX { 40 ) , R AT IGL ( 40) , VECTOR (
240),AWASTE(1000)?ASTORE(40) , ADI AG ( 40 ) , ^n I a^l 40 ) f AIJPPFR { 40 ) ,eOT~<"UM{
340),DISOXS(40),ULBOD(40) .VOLUME (40) ,D?rivK(40),VO(40) ,UVO(40) ,
4(40) ,SUMER(40),CFINAL(40)»SUMVEC(40) ,CCTN( 1600)
DO 6 I=1,NSECTS
DO 6 J=1,NSECTS
AMATRXJIt J)=0.0
DO 1 I=1,ISPEC
AMATRX (1*1,1) = BOTTUM(I)
AMATRX (1,1+1) = AUPPER(I)
IF(IMAT.EQ.2) GO TO 3
IF(KK.EQ.l) GO TO 3
00 2 I=1,NSECTS
AMATRX(I,I)=ADIAG(I)
RETURN
DO 4 I=l,NSECTb
RETURN
END
-------
-------
ISN
ISN
ISN
ISN
0002
0003
0004
0005
ISN 0006
ISN 0007
ISN 0008
ISN 0009
ISN 0010
ISN 0012
ISN 0013
ISN 0014
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0043
ISN 0044
ISN 0045
C
C
C
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0020
0022
0024
0026
0027
0029
0030
0031
0032
0034
0035
0037
0039
0040
0042
C
C
C
C
C
C
SUBROUTINE SCAVEC
DOUBLE PRECISION DATRIJN ( 4 ) , USER I 4 ) , T I TL F ( 1 2 )
CCHMON/DATUSE/DATPUN.USERiIPAGF
COMMON /CONTRL/TITLE,NCASES,NS EC TS,rUT,T NT
1ITP(2) ,BC(7)
, P ) , < A|_ ENTH , L FNGTH 5 ,
C
C
C
10(40),ALFNTH(40),AFTSEC(40),ADJL(40),TU<:fiEX(40),RATIOL<4P)
240), AWASTE( 1000) , AS TORE (40) • AT 1 AG ( 40 ) , BO I AG( u 0 ) , AUPPF* ( 40)
340 ),OISOXS(40),ULRn 0(40), VnLU^F(40),0'5'"AVK(40),
4(40),S'JMErU40),CFINAL(40),SUMVEC(40),CCTN|«1600)
DIMENSION Q(tO) ,L<40) , 0(40) ,LENGTH( 40) , VOL (40)
REAL L, LENGTH
EQUIVALENCE ( 0 , ADVECC ) , ( ULBOO , L ) , i TOSK
IE, VOL)
IF (KK.NF.l) GO TO I
WRITE (4) UAMATRXU tJ» »I=1,NSECTS) ,J = 1 ,NS?CTS)
I READ (2) (VECTOFU) ,I = 1,NSECTS)
00 2 J=1,NSECTS
2 SUMVECU) = 0.0
CONSTANT ALPHA TIMES MATRIX INVERSE
ALPHA = 1.6F+4
DO 3 I=1,NSECTS
00 3 J=l,NSECTS
3 AMATRX(I,J)= ALPHA * AMATRX(I,J)
PRINTING OPTION ALPHA INVERSE
IF I IMAT.EQ.3) GO TO 6
4 IF (INDEX! 1) .EQ.l) GO TO 8
5 IF (INOEX(3).EQ.l) GO TO 9
GO TO 11
6 IF (KK.EQ.O) GO TO 7
GO TO 4
7 WRITE (4) ((AMATRX(1,J) ,I = 1,NSECTS) ,J=ltNSECTS)
GO TO 4
8 IF ( KK.EQ.O) CALL PRTMAT
GO TO 5
9 IF UMAT.EQ.2) CALL PRTMAT
I(F (IMAT.EQ.3) GO TO 10
GO TO 11
10 IF (KK.EQ.l) CALL PRTMAT
11 CONTINUE
ALPHA TIMES MATRIX INVERSE TIMES VECTOR
DO 12 I=1,NSECTS
00 12 J=1,NSECTS
12 SUMVEC(I) = SUMVECU) + VECTORf J ) *AMATRX ( I , J )
PRINTING OPTION ALPHA * MATRIX INVERSE * VECTOR
fyFCTrP(
, RPTTUM(
-------
-------
ISN 0046
ISN 0048
ISN 0050
ISN 0051
ISN 0053
ISN 0054
ISN 0056
ISN 0058
ISN 0059
ISN 0060
ISN 0061
ISN 0062
ISN 0063
ISN 0064
ISN 0065
ISN 0066
ISN 0067
ISN 0068
ISN 0069
ISN 0071
ISN 0972
ISN 0073
ISN 0074
ISN 0075
ISN 0076
ISN 0077
IF
-------
-------
ISN
ISN
ISN
ISN
0002
0003
000*
0005
ISN 0006
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN-
ISN
ISN
ISN
0007
0008
0009
0010
0011
0012
0013
001*
0015
0016
0017
0018
0019
0020
0021
0022
0023
002*
0025
0026
0027
0028
0030
0031
ISN 0032
ISN 0033
ISN 003*
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
SUBROUTINE FINAL
DOUBLE PRECISION DATRUN(*),USER(*),TITLE(12)
COMMON/DATUSE/DATRUN.USERf I PAGE
COMMON/CONTRL/TITLE»NCASES,NSECTS,IMAT,INDEX(8),KK,ISPEC,I MAX,
IITP(2),BCI7)
COMMON/BWORKS/AMATRX(*0,*0),BMATRX(*0,*OI,OISOXS(*0),ULBOD<*0),VOL
IUME(AO),DECAYKI *0}rVD(*0),UVDUO),AREAl*0) , SUMERUO) ,CF INAL (*0) ,SU
2MVEC(*0),CCTN(*0,*0)
DIMENSION L(*0),VOL(*0)
REAL L
EQUIVALENCE (ULBOD,L),(VOLUME,VOL)
REWIND 2
REWIND *
READ IN BINARY MATRIX DATA ALPHA A-INVFPSF AND
B-INVERSE MATRIX, READ IN VECTORS ULBOD,DISOXS
fVOLUME AND DECAYK
READ
READ
READ
READ
READ
READ
(*)
(*>
(2)
(2)
(2)
(2)
( UMATRX
-------
-------
ISN 0035
ISN 0037
ISN 0038
ISN 0039
ISN 0040
ISN 0041
ISN 0042
ISN 0044
ISN 0045
ISN 0046
ISN 0047
ISN 0048
ISN 0049
ISN 0050
ISN 0052
ISN 0053
ISN 0054
ISN 0055
ISN 0056
ISN 0057
ISN 0058
ISN 0059
ISN 0060
ISN 0061
ISN 0062
C
C
C
C
C
C
C
C
C
C
IF! INOEXI61.EQ.1) CALL PRTMAT
FORM THE ULBOD VOLUME DECAY VECTOR + AREA VFCTOR
DO 5 I=1,NSECTS
5 UVDII)=ULBOD(I)
FORM THE ALPHA A INVERSE B INVERSE ULBOD VOLUMF DFCAYK PRODUCT
DO 6 I=1,NSECTS
DO 6 J=1,NSECTS
6 SUMER!I) = SOMERU)HIVD( J)*AMATRX(I,J)
IF(INDEXm.EQ.l) GO TO 7
GO TO 8
7 WRITE (6,100) (TITLEU),I = 1,12),(DATRUN( I) 11 = 1,4),IPAGE
WRITE (6»150)
-------
-------
ISN 0002
ISN 0003
ISN 0004
ISN 0005
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
fSN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0006
0007
0008
0009
0010
0011
0012
0013
0014
0015
0016
0017
0018
0019
0020
0021
0022
0023
0024
0025
0026
0027
0028
0029
0030
0031
0032
0033
SUBROUTINE INVERT
DOUBLE PRECISION DATPUNl4),USER(4),TITLF ( 1 ?}
COMMON/DATUSE/DATR.UN, USER, I PAGF
COMMON/COM TRL/ TITLE ,NCASESrNSECTS,IMATfI\3?X(A),k'K,lSi;'F<",T^\v,
1ITP12),BC(7)
CONMON/BWORKS/AMATPX(40,40),AWASTE<2000 )
DIMENSION PA(50), D(50),QA(50),S(50),T(50),P(50) , V{SO)
DO I I =1,NS6CTS
1 DU J = AMATRXU ,1)
MA = NSECTS - 1
00 2 1=1,MA
11=1+1
QA(I)=AMATRX(I,11)
2 PA(I)=AMATRX(IItI)
DO 3 K =1,NSECTS
3 B(K)=0.0
00 7 K =1,NSECTS
B«K)=1.0
s
-------
-------
ISN
ISM
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
ISN
0002
0003
0004
0005
0006
0007
0008
0009
0010
0011
0013
0014
0015
0016
0017
0018
0019
0020
0021
0022
0023
0024
0026
0027
0029
0030
0031
0032
0033
SUBROUTINE °RTMAT
DO'JBLE PRECISION DATPUN ( 4 ) , USER ( 4 ) , T I TL r ( 12 )
COMMON/DATUSE/DATRUN,USE",I PAGE
CT«IMCN/CONTRL/TITLE,NCASES,NJSECTS, I MAT, I^nr> (
1ITPJ2),BC«7)
COMMON/BWORKS/AMATRXt40,40),AWASTEI?000)
DIMENSION IHEAD(50)
50 FORMAT(1H1,12A6,2X,4A6,2X5HPAGE ,!?///)
51 FORMAT (IH ,8X6HI J,7X I?,17X12,17XI? , 17*I 2
52 FORMAT (IH ,7X12,6XE 15.P ,4XE 15.S,4XF1S.E,4X£ 1
IF (NSECTS.LE.5) GO TO 1
KCTN = 5
GO TO 2
I KCTN = NSFCTS
2 LL = 1
3 DO 4 I=LL,KCTN
4 IHEAD(I)=I
IPAGE=IPAGE+1
WRITE (6,50) (TITLE(I) ,1 = 1,12) ,(OATR(JN( I) ,1=1,4)
WRITE (6,51) (IHEADH),I=LL,KCTN)
DO 6 I=1,NSECTS
6 WRITE (6,52) I, (AMATRX(I,J),J = LL,KCTN)
IF (KCTN.EQ.NSECTS) GO TO 5
KCTN = KCTN + 5
IF (KCTN.GT.NSECTS) KCTN = NSECTS
LL = LL + 5
GO TO 3
5 CONTINUE
RETURN
END
, 1 7 X [ ? )
5 . B , 4X
1 ', .
-------
-------
1SN 0002
ISN 0003
ISN 0004
ISN 0005
ISN 0006
ISN 0007
ISN 0008
ISN 0009
ISN 0010
ISN 0011
ISN 0012
ISN 0013
ISN 0014
ISN 0015
ISN 0016
ISN 0017
ISN 0018
ISN 0019
ISN 0020
ISN 0021
ISN»0022
1
SUBROUTINE PRECFM
DOUBLE PRECISION DATRUN(4),USFRl4),TITLF(1?)
COMMON/CONTRL/TmE,NCASES,NSECTS,IMAT,INnFXm,KK, I SPEC, I'.'AX,
HTP{2)fCFQ,CFLEN,CFK,CFL,CFAREA,CFVOL,CFP
COMMON/BWORKS/AA(1640), ADVECQC40),DOSKSP(40) .PIFFCCMAn) ,ALENTM<401
1,BB(480),UL80D(40),VOLUME(40)»A8(120),AREA(*0>,AC(1720)
DIMENSION Q140),L(40),P<40),LENGTH140),VOL(40)
REAL L,LENGTH
EQUIVALENCE (Q,ADVECQ),(ULBOD,L),(OOSKSR,P),(ALENTH,LENGTH),(VOLUM
IE,VOL)
DO 1 J=I,NSECTS
DOSKSR(J)=CFP *DOSKSR(J)
VOLUME(J)=CFVOL*VOLUME(J)
ULBOO(J) =CFL*ULBOO(J)
IMAX=NSECTS-H
DO 2 K=I,IMAX
AOVECQ(K)=CFQ*AOVECQ(K)
DIFFCO(K)=CFK*DIFFCO(K)
AREAIK)=CFAREA*AREA(K)
IMAX=IMAX-H
DO 3 I=1,IMAX
ALENTH11)=CFLEN*ALENTH(I)
RETURN
END
-------
-------
APPENDIX III
SAMPLE INPUTS
-------
-------
2
11/1/67
KAK TF TFP PRCGRAK USER RONALD BUNCF
N'/««e CF THE ESTLAPY BEING INVESTIGATED
$CF
IM. f >=r* t,
^ fTP=2*C,
CF! F.N=l. ,
CFK=1.,
C F I = 1 . ,
V
r.F !- = !.,
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L=f 3fCC,^l6CC,*-J«C.Ct672»2?50C»7*C.Ot
AI^L A=13F^,A*1325C,1210C,1AOOC, 13C5C, 12100t1268C, 14200,4*14400,
C IFFCO=C.O,C.12»C. 14,0. 15 ,C. 16, 0.16, C.I 7, 0.18,0.19, 0.20, 2»0.2 1,3*0.23,
riSO>S=6»7.92,3*?.77,5*7.63,
CECAYK=6*C.46,3*C.4Q,5*C.52,
$F.\C
-------
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c.*sr M>R A ? \A.n CF ESTUARY" BCING INVESTIGATED
$Cf
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C=1245,1245, ] 3*130C,
l=63COC,PlrCC,:!*C.C,fc72,14?OC,7*C.C,
P=-9rO,»/-5C,- b50,-57C,-640»-685,-695,7*-700,
Vt L=10r 6,4*7rL6,64E6,7At6,69E6,64E6,67£6,75F6,3*76t6,
, 12100, 14fiOC, 13050, 1210C,1268Ci 14200,
i: I FFCC=C. C, 0. 12, C. 14 ,0.1 5, 0.16, 0.16, 0.17, 0.18,0. 19,0. 20, 2»0.21t 3*0.23,
I. tNGTH=C.3,15*l.C,
$RIVTO
! ISOXS=^*7.92,3*7.77,5*7.63,
«EAEPK=14»O.C4,
C EC A YK=6*0. 46, 3*C. 49,5»0.52,
-------
-------
APPENDIX IV
CYPICAL PROGRAM CASE SOLUTIONS
-------
-------
SECTION A -SAMPLE
INPUT 8 OUTPUT
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