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133
APPENDIX B
AUT0QD - PROGRAM DESCRIPTION/OPERATING INSTRUCTIONS
GENERAL
AUT0QD and AUT0SS are very similar in their construction and
their method of use. Only the main differences in operating procedure
will be discussed. The reader should read the AUT0SS operating instruc-
tions first. The main differences in the operation of the models lie
in the entering of computational data.
AUT0QD is written in the same language as AUT0SS and requires
the same input/output devices. Machine storage requirement is 115K.
Typical running time is 0.15 second (compute time) per day of simu-
lation for a 150 section network. These times will vary depending on
the computer used, the network used, the constituents being modelled,
and the integration step.
PROGRAM LOGIC:
AUT0QD is also controlled by "program control cards". Their format
is the same as in AUT0SS. The program control cards and their respective
functions are:
Program Control Card Function
(Cols. 1 thru 4)
DATA Same as AUT0SS
FL0W Same as AUT0SS
CB0D Directs the program to read in
the input CB0D values and then
compute CB0D for the specified
period. Data cards follow
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134
Program Control Card Function
(Cols. 1 thru 4)
NB0D Directs the program to read the
input NBjDD values and compute
NB0D for the specified period.
Data cards follow.
D0 Directs the program to read input
CB0D, NB00 and 00 values and then
compute CB0D, NB0D and D0 for the
specified period. This; is differ-
ent from AUT0SS, because CB0D and
NB0D are done simultaneously with
D0. Data cards follow.
HALT Same as AUT0SS
Any 4-letter word The program assumes this is the
except the above name of a conservative parameter.
Input values are read, and the
concentrations are computed for
the specified period.
DATA DESCRIPTION
The data for AUT0QD have the same characteristics as the data for
AUTjBSS. The physical and network data is identical for both programs.
The computational data is the same except additional information is
needed for time keeping:
1. Beginning and Ending data of period (day-month-year), e.g.
(1-10-1971).
2. Print period (days): This number specifies the number of days
between quality print outs. If a period consists of 50 days
and the solution is to be printed every 5 days, the print
period would be 5. If the print period is omitted the program
will assign a value of 1 day.
-------
135
3. Integration time step (hours): This is the integration step
used in the program. It must be less than or equal to 24
and an even divisor of 24. If no value is entered the program
will compute its own time step. (See model development, AUT0QD
solution.)
The meaning of initial concentrations changes slightly in AUT0QD
In AUT0QD they are considered as starting concentrations. Since
continuous simulation can be done with AUT0QD the starting concentra-
tions are updated every integration step (time step). Concentrations
at the end of one period become the starting concentrations for next
period.
ENTERING DATA
Data is entered under the direction of a program control card,
except the run title and network data. As in AUTJ9SS variables are
zeroed or set to default values before data is entered or computed.
I. Run title card
Same as AUT0SS
II. Network card
Same as AUT0SS
III. Entering physical data
Same as AUT0SS
IV. Entering computational data
A. Flows
1. The program control card FL0W precedes the data
cards.
-------
136
2. Immediately after the program control card Is the timing
card which specifies the dates of the flow period to be
entered:
Beginning month number: cols. 1- 2 (right hand justify,
(1-12) no decimal point)
Beginning day number : cols. 4- 5 (right hand justify,
no decimal point)
Beginning year : cols. 7-10
Ending month number : cols. 16-17 (right hand justify,
no decimal point)
Ending day number : cols. 19-20 (right hand justify,
no decimal point
Ending year : cols. 22-25
3. Next are the data cards in the following format:
River mile of data point: cols. 11-20 (include a decimal
point)
Inflow (cfs) : cols. 21-30 (include a decimal
point)
Diversion (cfs) : cols. 31-40 (include a decimal
point)
4. After the data cards a card with ST0P punched in the first
4 columns is placed in the deck.
B. CB0D
1. The program control card CB0D precedes the data cards.
2. Immediately after the program control card is a card
which specifies the dates of the period, the print
interval, and the integration step (optional):
-------
137
Beginning month number
Beginning day number
Beginning year
Ending month number
Ending day number
Ending year
Print interval
(optional)
Integration step
(optional)
cols. 1- 2 (right hand justify,
no decimal point)
cols. 4- 5 (right hand justify,
no decimal point)
cols. 7-10 (right hand justify,
no decimal point)
cols. 16-17 (right hand justify,
no decimal point)
cols. 19-20 (right hand justify,
no decimal point)
cols. 22-25
cols. 31-35 (right hand justify,
no decimal point)
»
cols. 41-50 (include a decimal
point)
3. Next are the data cards in the following format:
(Note: If it is desired to fix (establish a boundary
condition) the concentration of a point, the word
FIXED is punched in the first 5 columns of that data
card; otherwise, these columns are left blank.)
River mile of data point: cols. 11-20 (include a decimal
point)
Inflow at data point
cols. 21-30 (include a decimal
point)
Inflow concentration at : cols. 31-40 (include a decimal
data point point)
Fixed concentration at
data point (if FIXED
option is chosen)
cols. 41-50 (include a decimal
point)
4. After all data cards are entered, a card with ST0P punched
in the first 4 columns is placed in the deck.
-------
138
C. NB0D
1. The program control card NB0D precedes the data cards.
2. The rest of the cards have the same format as CB0D.
D. Conservative constituents
1. The program control card with the constituent name on it
precedes the data cards.
2. The rest of the cards have the same format as for CB0D.
E. D0
1. The program control card 00 precedes the data cards.
2. The next card is the same as CB0D.
3. Next are the data cards in the following format:
River mile of data point
Inflow at data point
CB0D inflow concentration
NB0D inflow concentration
00 inflow concentration
CB0D fixed concentration
(if desired)
NB0D fixed concentration
(if desired)
D0 fixed concentration
(if desired)
cols. 11-20 (include a decimal
point)
cols. 21-30 (include a decimal
point)
cols. 31-37 (include a decimal
point)
cols. 38-44 (include a decimal
point)
cols. 45-51 (include a decimal
point)
cols. 52-58 (include a decimal
point)
cols. 59-65 (include a decimal
point)
cols. 66-72 (include a decimal
point)
4. After all data cards are entered a card with ST0P punched in the
first 4 columns is placed in the deck.
-------
139
After all the data has been entered the HALT program control card is
placed in the deck.
OUTPUT DESCRIPTION
The output for AUT0QD is also controlled by the program control
cards and is referenced to river miles as well as to channels or junctions.
The first items printed are a title and listing of the general net-
work data. Included here is the run title, mile of upstream and downstream
end, mile of fall line, and the number of sections.
Each time physical data is entered, it is printed out under the
heading "Estuary/Stream Data".
When a flow condition is entered two groups of information are
printed. Under the heading "Depth or Velocity Dependent Variables for the
Flow Period Month, Day, Year thru Month, Day, Year", the following are
printed:
1. Cross-sectional Areas
2. Channel Depths
3. Channel Velocities
4. Junction Volumes
5. Computed Reaeration Rates (if the compute option is used)
Under the heading "Flow Conditions for the Period Month, Day, Year,
thru Month, Day, Year" the inflows, diversions and channel flows are
printed. The same sign convention is used as in AUT0SS.
When a constituent control card is encountered, two other groups are
printed. Under the heading (Constituent Name) "Input Concentrations for
Month, Day, Year thru Month, Day, Year: the input concentrations for the
-------
140
period are printed. The solutions are printed under the heading of
the run title and (Constituent Name) "Concentrations for the Period
(Month, Day, Year) thru (Month, Day, Year)" at interval specified.
In addition to the regular output, error messages may be printed.
These are the same as AUT0SS except there are no zero divisor messages.
DATA CODES FOR PHYSICAL DATA
Same as AUT0SS
RUNNING TIPS
The same general rules apply to AUT0QD as in AUT0SS; however,
there are some differences due to the different types of solutions.
1. DATA should be the first control card for the same reasons
as for AUT0SS
2. FL0W is the second control card. The dates entered under
the FL0W card have no computational significance; they are
for the user's reference. A flow condition will continue
to be used in the program until it is replaced.
3. CB0D and/or NB0D are run simultaneously with D0. They can
be run separately if desired, however, they will have no
effect on the DjJ budget if they are.
4. The starting (initial) concentrations for a constituent
are updated every integration step.
A general example of control card setup is given below (see the end
of this appendix for a specific example problem)
-------
141
PROBLEM STATEMENT
Given flow condition 1, which represents flow from 1/01/72 to
2/01/72, and flow condition 2, which represents flow from 2/02/72 to
3/01/72. Run TDS with 4 downstream boundary conditions (1/01/72-
1/15/72, 1/16/72-2/01/7?, 2-02/72-2/15/72, 2-16/72-3/01/72) print out
values every 2 days. Run CB0D, NB0D and D0 with 4 different input
conditions (same dates as TDS) print solutions every day, and let the
program compute the time step.
The arrangement of the control cards would be:
DATA - enter physical data
- (1/01/72 - 2/01/72)
=«*=
o
•J3
•»—
•o
o
o
(1/01/72 - 1/15/72) Print interval = 2
(1/01/72 - 1/15/72) Print interval = 1
(1/16/72 - 2/01/72) Print interval = 2
(1/16/72-2/01/72) Print interval = 1
(2/02/72 - 3/01/72)
§ TDS - (2/02/72 - 2/15/72) Print interval = 2
E j
'•5 < D0 (2/02/72 - 2/15/72) Print interval = 1
(2/01/72 - 3/01/72) Print interval = 2
(3/16/72 - 3/01/72) Print interval = 1
-------
142
AUT0QD VARIABLE GLOSSARY
Variable
A (N)
Definition
CBDIN(J)
CBPD(J)
CIN(J)
CS(J)
DELT
DELT2
DELTD
OKI(J)
DK2(J)
D0S(J)
EVAP(J)
IDAYB
I DA YE
IM0B
IYRB
cross-sectional area of channel N
flow equation coefficients at
channel N
surface area of junction J
concentration at junction J,
can be any parameter
CB0D input concentration at
junction J
CB0D concentration at junction J
input concentration at junction J
can be any parameter
conservative constituent concen-
tration
timestep (sec.)
half timestep (sec.)
timestep (hrs.)
CB0D decay rate at junction J
NB0D decay rate at junction J
oxygen saturation concentration
at junction J
net evaporation minus rainfall
at junction J
beginning day
ending day
beginning month
beginning year
-------
143
IYRB
IYRE
K2FL
LALPHA(K)
MFS(K.I)
NBEG
NC
NDAYS
NEND
NFS(K)
NJ
N0JFX
NPRT
NQCYC
NRD
NSES
NWR
0XIN(J)
0XY(J)
PH0T0(J)
Q(N)
QIN(J)
Q0UT(J)
beginning year
ending year
flag to tell if reaeration rates
are to be computed
run title
Ith fixed parameter at Kth fixed
junction
period beginning day number
number of channels
number of days in a period
period ending day number
K fixed junction number
number of junctions
number of fixed junctions
print interval
number of timesteps per day
card reader unit number
number of sections
line printer unit number
D0 input concentrations at
junction J
D0 concentration at junction J
photosynthesis minus respiration
rate at junction J
flow in channel N
inflow at junction J
diversion at junction J
-------
144
REAIR(J)
RMC(N)
RMDUN
RNFR
RMJ(J)
RMUP
SEDKT(J)
TEMP(J)
V(N)
VJBL(J)
WIDTH(N)
XCMAS(J)
XLEN
XMASS(J)
XMIL
XNDIN(J)
XNNAS(J)
XN0D(J)
X0MAS(J)
Z(N)
reaeration coefficient at
junction J
river mile of channel N
downstream river mile
river mile of fall line
river mile of junction J
upstream river mile
sediment uptake rate at
junction J
water temperature at junction J
velocity in channel N
volume of junction J
width of channel N
CB0D mass in junction J
channel length in feet
constituent mass in junction J
channel length in miles
NB0D input concentration at
junction J
NB0D mass in junction J
NB0D concentration at junction J
D0 mass in junction J
dispersion coefficient in channel N
-------
145
SUBROUTINE DESCRIPTIONS
Following is a brief description of each subroutine of AUT0QD
MAIN BRANCH
Same as AUT0SS
SETUP
Same as AUT0SS
NETDAT
Same as AUT0SS
FL0WS
Same as AUT0SS, except the dates of the period are also read in
FL0CMP
Same as AUT0SS
VAULIN
The dates of the quality period, the print interval and time step
(optional) are read. In addition, the quality inputs are read
and assigned to the proper junction. D0 is not considered here.
If more than one input is read in for a junction, they are combined
according to their respective inflows and concentrations. Junctions
may also be fixed. Conservative constituents, CB0D and NB0D, may
be entered here.
VALCMP
The quality equations are integrated over the period specified in
VAULIN. The concentrations are printed at the specified intervals
(print interval).
-------
146
CDERIV
The quality derivatives are evaluated. This routine Is called
from VALCMP.
VD0IN
The period dates, print Interval and time step are read, as in
VALCMP. The input CB0D, NB0D and D0 concentrations are read.
The D0 title for this quality output is printed.
VD0CP
The CB0D, NB0D and D0 equations are integrated over the period
specified in VD0IN, and the solutions are printed at the specified
interval.
PDERIV
The CB0D, NB0D and D0 derivatives are evaluated.
JKFND
Same as AUT0SS
SERIAL
Converts a date (month, day, year) into a corresponding day
number.
TABU
Same as AUT0SS
INTER
Same as AUTflSS
CALEN
Converts a day number into a corresponding (month, day, year).
0UTG0
Same as AUT0SS
-------
147
PROGRAM LISTING
Following is a listing of program AUT0QD:
-------
MAIN PROGRAM
148
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SUBROUTINE SETUP
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SUBROUTINE VALCMP (Con't.)
171
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SUBROUTINE VALCMP (Con't.)
172
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SUBROUTINE CDERIV
173
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SUBROUTINE VD0IN
174
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SUBROUTINE VD0IN (Con't.)
175
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SUBROUTINE VD0IN (Con't.)
176
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SUBROUTINE VD0IN (Con't.)
177
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SUBROUTINE VD0CP
178
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SUBROUTINE VD0CP (Con't.)
179
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SUBROUTINE VD0CP (Con't.)
180
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181
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AUTgQD EXAMPLE PROBLEM
The stream/estuary system used in the AUT0SS example is used for this
example. The input data is the same except for the flow at mile 100.0
(River Flow) and the TDS (Total Dissolved Solids) boundary condition
at mile 0.0.
PROBLEM STATEMENT
Using the steady state values obtained in the AUT0SS example problem
(5000 cfs at mile 100.0), as initial values, run the same constituents
(TDS, CB0D, NB0D, D0) for a continuous 20 day period (January 1-20, 1973)
using the following inflows and downstream TDS boundary conditions:
Jan. 1- 5 Flow Q mile 100.0 = 6000 cfs
TDS @ mile 0.0 = 18000 ppm
Jan. 6-10 Flow @ mile 100.0 = 8000 cfs
TDS @ mile 0.0 = 15000 ppm
Jan. 11-15 Flow 9 mile 100.0 = 6000 cfs
TDS @ mile 0.0 = 18000 ppm
Jan. 16-20 Flow @ mile 100.0 = 5000 cfs
TDS @ mile 0.0 = 20000 ppm
CB0D, NB0D and D0 inflow concentrations will remain the same for the
entire period. Have the program compute its own time step and print
out qualities every day.
The data deck for this example is as follows:
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-------
266
APPENDIX C
APPLICATION, CALIBRATION. VERIFICATION, AND SENSITIVITY
In the past much effort was spent in the planning effort
evaluating alternative water qaulity management schemes. It was
this type of analysis that stimulated the use and growth of mathe-
matical techniques. Little or no effort was spent determining the
reliability of the individual models in predicting absolutes.
It was then considered that the ability of a model to reproduce
nature was secondary to its ability to predict differences between
alternatives consistently. Considering the defined problems of that
time, it was certainly proper to take that viewpoint.
Since that time, water quality standards have been introduced.
These standards are absolutes in terms of defined quantities of
that may be present in the receiving waters. Plans and proposals must
now be weighed not only against each other but ultimately against the
"standards". Plans which will not allow the receiving water quality
to be at or above standards must be rejected as infeasible on the
basis of standards.
The introduction of water quality standards, and the civil and
criminal penalties for their violation, adds a new dimension to
mathematical modelling for water quality planning. The model user
must now be concerned with the accuracy of a technique as well as
its consistency.
-------
267
MODEL CALIBRATION:
There are constants and coefficients of functions inherent
in the AUT0-QUAL set that can not be directly determined or
measured. For example, there are no methods for making direct
field measurements of dispersion coefficients (E). The reader may
recognize these quantites as being:
1. Dispersion coefficients (E)
2. CBOD decay rate (Kc)
3. NBOD decay rate (KN)
4. Reaeration rate (K2).
While techniques exist for the determination of KC and KN, the
wide range of values obtained in the tests of the replicate
samples preclude considering KC and KN as "knowns". Similarly,
field measurements for the determination of the reaeration rate
(Kg) show a wide range of values. The Dobbin's - O'Connor formula
is currently the most common function used, and as such it is
considered to be the standard form.
Dispersion is probably the most obvious calibration coefficient
in the above group. The elimination of tidal effects in the flow
computations demands that some mechanism be incorporated in the
model to represent the smearing of the quality profiles by the
tides (See Model Development).
Those inputs to the model that can be directly measured
or determined with good reliability are considered as knowns.
Since the calibration process consists of matching a predicted
profile (or profiles) to an observed profile by means of adjusting
-------
268
the calibration constants. Any errors in the knowns will be
incorporated into the calibration constants.
The primary knowns and their sources are:
1. Flow - from streamflow gages operated by State or
Federal agencies or direct field measurements.
2. A-], Ap. A- - from stage/discharge records maintained
by State or Federal agencies or direct field
measurements.
3. A- (in estuaries) - nautical charts or field measurements.
4. widths - charts, maps or direct measurements.
5. Q . (amount and location) - diversion records.
6. Q. (amount and location) - waste water records or direct
measurement (direct measurement is preferable)
7. Water temperature - direct field measurements or existing
records.
8. Tidal velocities - current tables or direct measurements.
9. Sediment uptake of oxygen rate - direct measurements or
existing records.
10. Photosynthesis-Respiration rate - direct field measurements
or existing records.
Where field measurements are indicated, they must be made at the
same times as the observed profiles. To do otherwise is to assume
that those inputs are in fact constant. The above list may, of course,
be tailored to the particuliar constituents under considerartion.
SENSITIVITY:
The following figures illustrate the sensitivity of the AUT0-QUAL
set to normal variations in the magnitudes of the important varibles.
The reader should study the figures and experiment with his own systems
to get a better feeling for the effects of the different factors.
-------
269
AUT0SS was generally used to compute the sensitivity
profiles. The effects are identical in AUT0QD. Figure C16 shows
the convergence of the AUT0QD solution, over time, to the AUT0SS
solution. Since natural streamflow and waste sources are rarely
constant for the period of time required for a body of water
to reach a steady state condition in water quality, AUT0QD should
be used in the calibration process. The calibration coefficients can
then be transferred to AUT0SS for the planning runs.
-------
FIGURE Cl
SCHEMATIC DIAGRAM OF ESTUARY/STREAM
USED IN SENSITIVITY ANALYSES
270
icr^;
i ^O
I xd
-------
271
The following data values were assigned to the example
stream/estuary system:
Mile of upstream end 150.0
Mile of downstream end
Mile of fall line
Number of sections
PHYSICAL DATA;
Ar>
Miles 0.0 thru 48.0
@ mile 50.0
§ mile 150.0
0.0
50.0
150
A,=0.0
A,1 =0.040
A=0.025
Miles 0.0 thru 48.0
0 mile 50.0
Miles 50.0 thru 150.0
A=0.0
A3;
@ mile 0.0
@ mile 50.0
Miles 50.1 thru 150.0
Widths;
@ mile 0.0
@ mile 50.0
Miles 50.0 thru 150.0
Tidal Velocities;
@ mile 0.0
3 mile 25.0
@ mile 50.0
Miles 50.1 thru 150.0
Dispersion Coefficients;
@ mile 0.0
@ mile 10.0
@ mile 20.0
@ mile 30.0
A=20.0
Width=21200.0 ft.
Width=l000.0 ft.
Width=l000.0 ft.
V.=1.2 fps
V^=0.8 fps
V:>0.6 fps
V^=0.0 fps
E=5000.0 ft£/ sec
E=4300.0 f
E=3500.0 ftp/ sec
E=2200.0 ft /sec
-------
272
(a mile 40.0 E=1200.0 ft?/sec
@ mile 50.0 E=400.0 ft«/sec
@ mile 55.0 E=100.0 ftf/sec
Miles 55.0 thru 150.0 E=100.0 ftVsec
When point values are specified, the program will interpolate
linearly between the points for intermediate values.
These values will remain the same for all the runs on the
example stream/estuary, except where changes are specified. The
other inputs are specified for each run.
-------
ui
u
O
u
FIGURE C2
EXAMPLE RUN WITH ONLY CBOD INPUTS
(AUT0SS)
273
10.0-
9.0-
8.0-
7.O-
6.0-
5.0-
4.0-
3.0-
2.0-
1.0-
DISSOLVED OXYGEN
FIRST STAGE BOO (CBOD)
10 20 30 40
50 60 70 80 90 IOO 110 120 130 140 ISO
RIVER MILE
INPUT DATA:
TEMPERATURES:
@ mile 0.0 T=28.0°C
g mile 25.0 T=25.0°C
& mile 75.0 T=20.0°C
Miles 75.0 thru 150.0 T=20.0°C
CBOD DECAY RATE = 0.23(l/day)
NBOD DECAY RATE = 0.1 03(1 /day)
SEDIMENT UPTAKE;
COMPUTED REAERATION RATES
COMPUTED OXYGEN SATURATION
CONCENTRATIONS
INFLOW DATA:
@ mile 150.0
2000.0 cfs * «!• «-°e)20.0p|m CBOD »
PHOTOSYNTHESIS-RESPIRATION RATES ? O.Oppm DO
Miles 0.0 thru 30.0 P-R =-0.2(gr.02/mp/day)
@ mile 35.0 P-R =-1.0(gr.O«/m /day) ml'e 45.0
@ mile 50.0 P-R = 0.0(gr.b,/m,/day) 200-° cfs PSO.Oppn
Miles 50.0 thru 150.0 P-R = O.Ofgr.O^/m /day) O.Oppm DO
-------
FIGURE C3
EXAMPLE RUN WITH CBOD AND NBOD INPUTS
(AUT0SS)
274
Q.
a
u
o
u
10.0
9.0-
8.0
7.0
6.0
5.0
4.0
3.0-
?,.0-
1.0-
— DISSOLVED OXYGEN
FIRST STAGE BOD (C BOD)
— SECOND STAGE BOD (N BOD)
.*x
v
% ..
j» • •
1 * 1
/V"L
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
RIVER MILE
SAME INPUT DATA AS FIGURE C2 WITH THE FOLLOWING INFLOWS:
& mile 150.0
2000.0 cfs @4.0ppm CBOD & 2.0ppm NBOD & 9.0ppm DO
@ mile 145.0
150.0 cfs eiOO.Oppm CBOD & 50.0ppm NBOD & O.Oppm DO
@ mile 65.0
50.0 cfs @12Q.Oppm CBOD & GO.Oppm NBOD & O.Oppm DO
mile 45.0
200.0 cfs @50.0ppm CBOD & SO.Oppm NBOD & O.Oppm DO
-------
FIGURE C4
BASE CONDITION FOR SENSITIVITY RUNS
(AUT0SS)
275
&
O.
I
UJ
u
I
10.0
9.0
8.0
7.0
6.O-i
5.0
4.0
3.0
2XH
1.0
DISSOLVED OXYGEN
FIRST STAGE BOD (C BOD)
SECOND STAGE BOD (N BOD)
A A
/:-.xx.^ j
/ : • •' \
' : '• •' i
/ .-' — :
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
RIVER MILE
INPUT DATA:
TEMPERATURE * 20.0°C
CBOD DECAY RATE = 0.30(l/day)
NBOD DECAY RATE = 0.10(1/day)
SEDIMENT UPTAKE =0.0 (gr.02/m2/day)
(P-R> = 0.0 (gr.02/m2/day)
REAERATION RATE = 0.30(l/day)
COMPUTED OXYGEN SATURATION CONCENTRATIONS
OTHER INPUT DATA IS THE SAME AS FIGURE C2
INFLOW DATA:
SAME AS FIGURE C3
-------
FIGURE C5
276
2
Q.
O.
10.0-
9.0-
8.0-
7,0-
6.0-
5.0-
4.0-
3.0-
2.0-
1.0-
EFFECT OF CBOD DECAY RATE (KC)
(AUTJDSS)
Kc = 0.lO( '/day)
Kc = 030('/day)
Kc = O.SCX'/day)
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 ISO
RIVER MILE
INPUT AND INFL0W DATA IS THE SAME AS FOR FIGURE C4,
EXCEPT THE CBJDD DECAY RATE HAS BEEN VARIED
-------
FIGURE C6
EFFECT OF NBflD DECAY RATE (Kp)
(AUT0SS)
277
a
a
10.0-
9.0-
8JO-
7.0-
6.O-
5.0-
4JO-
3.0-
2.0-
1.0-
Kn = 0.10 ('/day)
Kn= 0.20 ('/day)
O 10 20 30 40 SO 6O 70 80 90 IOO IIO I2O 130 I4O ISO
RIVER MILE
INPUT AND INFL0W DATA IS THE SAME AS FOR FIGURE C4,
EXCEPT THE NB0D DECAY RATE HAS BEEN VARIED
-------
FIGURE C7
EFFECT OF REAERATION RATE (K2)
(AUT0SS)
278
a
a
10.0-
9,0
8.0-
7.0»
6.0-
5.0-
4.0-
3.0-
2.0-
K2=0.2{'/doy)
K2= 0.3 (^day)
K2=0.4('/day)
10 20 30 40 50 60 70 80 90 100 110 120 130 (40 150
RIVER MILE
INPUT AND INFL0W DATA IS THE SAME AS FOR FIGURE C4»
EXCEPT THE REAERATION RATE HAS BEEN VARIED
-------
FIGURE C8
EFFECT OF SEDIMENT UPTAKE
(AUT0SS)
279
a.
a
10.0-
9.0
7.0-
6.0-
5.0-
4.0-
3.0-
2.0-
1.0
•S«diiMf)t = 0.0 (gr O2/m2/doy)
S«dim«nf = 1.0 (gr O2/m2/doy)
S«dim«nf = 2.0(gr O2/m2/day)
10 20 30 40 SO 60 70 80 90 100 110 120 I3O 140 ISO
RIVER MILE
INPUT AND INFLOW DATA IS THE SAME AS FOR FIGURE C5,
EXCEPT THE SEDIMENT UPTAKE HAS BEEN VARIED
-------
FIGURE C9
EFFECT OF PHOTOSYNTHESIS - RESPIRATION RATE
(AUT0SS)
280
a
a
O
a
lO.O-i
9.0
8.0-
7.0-
6.0-
5.0-
4.0-
3.0-
2.0-
1.0-
CP-R) = -l.Otgr 02/roVday)
-(P-R) =0.0{gr O2/m2/doy)
.-(p-R) = * l.0(gr 02/m2/day)
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 !50
RIVER MILE
INPUT AND INFL0W DATA IS THE SAME AS FOR FIGURE C4,
EXCEPT THE PHOTOSYNTHESIS-RESPIRATION RATE HAS BEEN VARIED
-------
FIGURE CIO
EFFECT OF TEMPERATURE
(AUT0SS)
281
11.0-
IO.O-
9.O
Q.
a
o
o
ao-
7.0-
6.0-
5.0-
4JO-
3.0-
2.0-
1.0-
0
T=IO.O*C
•T=20.0*C
•T = 30.0*C
10 20 30 40 50 60 70 80 90 IOO 110 120 130 I4O ISO
RIVER MILE
INPUT AND INFLJDW DATA IS THE SAME AS FOR FIGURE C4,
EXCEPT THE STREAM TEMPERATURE HAS BEEN VARIED
Note:
D.0. Saturation Concentrations
10°C = 11.4 ppm
20°C = 9.08 ppm
30°C = 7.52 ppm
-------
FIGURE Cll
EFFECT OF DISPERSION COEFFICIENT
(AUT0SS)
282
a
a
O
o
10 -
9 -
8 -
7 -
6 -
5 -
4 -
3 -
O w
I -
0 -
E='/2Eo
E = Eo
E = 2Eo
i i i i i i i I i i I r i I I
10 20 30 40 50 60 70 80 90 100 110 120 130 140 ISO
RIVER MILE
INPUT AND INFL0W DATA IS THE SAME AS FOR FIGURE C4,
EXCEPT THE DISPERSION COEFFICIENTS (E) HAVE BEEN
VARIED. E0 ARE THE DISPERSION COEFFICIENTS SPECIFIED
IN FIGURE C4.
-------
FIGURE C12
EFFECT OF DISPERSION COEFFICIENT
(AUT0SS)
283
P
a
a.
20 30 40
RIVER MILE
INPUT AND INFL0W DATA IS THE SAME AS FOR FIGURE C4,
EXCEPT SALINITY IS BEING RUN WITH THE DOWNSTREAM END
FIXED AT 15000 ppm. THE DISPERSION COEFFICIENTS ARE
VARIED AS SHOWN WHERE E_ ARE THE DISPERSION COEFFICIENTS
SPECIFIED IN FIGURE C4. ONLY THE ESTUARY PORTION IS
SHOWN BECAUSE THE SALINITY CONCENTRATIONS WERE NEGLIGIBLE
IN THE FREE FLOWING SECTION.
-------
284
To demonstrate the use of AUT0QD a run was made on the same
hypothetical stream/estuary that was used for the AUT0SS examples.
A hypothetical hydrograph and downstream boundry condition (salinity
concentration^ were chosen for this example (see Figure CIS). Notice
that the hydrograph and the downstream concentration are represented
in a stairstep fashion.
The same general input data used in AUT0SS has been used for
AUT0QD. A steady state solution (AUT0SS) for the 2000.0 cfs flow
condition was used for starting concentrations. A time step of 1
hour was specified for the run. Figures C14 & C15 show the results
of the model run, only the estuary portion was shown because the "
salinity concentrations were negligible in the free flowing portion.
-------
FIGURE CIS
28D
9000-
ui
I
"o
Q.
a
o
•
o
UJ
16000
14000
IZOOO
10000
8000
6000
4000
20OO-
I I
JANUARY 1-31
FEBRUARY 1-28
-------
P
a.
Q.
Z
FIGURE C14
AUT0QD RUN RESULTS - SELECTED POINTS
286
MILE 0.0 - FIXED BOUNDRY CONDITION
JANUARY 1-31
DAY
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FIGURE CIS
AUT0QD RUN RESULTS - SELECTED DATES
287
P
a
a
0 -i
.JAN. I
,JAN. 10
,JAN. 15
JAN. 20
JAN. 25
JAN. 30
10
40
5O
RIVER MILE
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288
Figure C16 shows a comparison of the AUT0SS steady state
solution and the AUT0QD solution as it approaches steady state.
A condition with a total fresh water inflow of 2300.0 cfs
(2000.0 cfs river flow and 300.0 cfs total for inputs 1, 2 & 3),
and the downstream concentration fixed at 15000.0 pprn, was chosen
for this example. The starting concentrations for AUT0QD were
purposely chosen not to coinicide with the AUT0SS steady state to
better see the two solutions converge. The inputs for these runs
are the same as for Figure C4.
-------
FIGURE C16
COMPARISON OF AUT0SS AND AUT0QD
WHEN RUN UNTIL STEADY STATE
289
(ONVSnOHl M3d SlUVd) AilNHVS
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290
For the next set of runs a uniform, free flowing stream
was selected. The charateristies of this stream are defined as
follows:
T— ' ~ • ' •—' "—• —I
I i
i l
i '
mile 100.0 mile 0.0
Mile of downstream end 0.0
Mile of upstream end 100.0
Mile of fall line 0.0
Number of sections 100
PHYSICAL DATA;
A^ 0.04
A2= 0.60
Width = 1000.0 ft.
CBOD decay rate = 0.6@20.0°C (I/day)
DO Saturation = 10.0 ppm
Reaeration rate = 0.4@20.0°C (I/day)
All other physical data assumes their respective default
values.
INFLOWS;
@ mile 100.0 1000.0 cfs at 10.0 ppm CBOD &
10.0 ppm DO
All runs have these values as inputs, except for the stated
variations.
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291
By using a uniform stream it is possible to make comparisons
between the model solution and an analytical solution. For these
comparisons the integrated forms of the Streeter-Phelps DO sag
equation are used [23];
„ r
c
D .
c KA
x^=
where;
D = dissolved oxygen deficit (ppm) (saturation concentration
minus stream concentration)
I* in stream BOD (ppm) at X=0, for this application L =10.0
0 ppm at river mile 100.0 (X=0) °
KD= deoxygenation rate (I/day), corresponds to CBOD decay rate
K.= reaeration rate (I/day)
X-= distance to location of maximum deficit (miles)
U = stream velocity (miles/day)
DC= maximun DO deficit (ppm)
These equations are resticted to the case where the initial deficit
(@ X=0) is zero, which is the condition specified in the runs.
(DO saturation = 10.0)
-------
FIGURE C17
EFFECT OF A!
(AUT0SS)
292
2
Q.
Q.
9 H
8 H
7 H
6 H
3 H
2 H
o
A, = 0.02
A, =0.04
A, = 0.06
O Streeter — Phelps Equation - Computed Sag
Point.
T
10
20 30
1
40
50
I "
60
I
70
I
80
90 100
RIVER MILE
-------
FIGURE CIS
EFFECT OF A2
(AUT0SS)
o.
a.
O
o
10
9 -
8 -
7 -
6 -
5 -
4 -
3 -
2 -
O
A2 = 0.4
A2=0.6
A2 = 0.8
Streeter —Phelps Equation — Computed Sag
Point.
I i^ III1 i I I l
0 10 20 30 40 50 60 70 80 90 100
RIVER MILE
-------
FIGURE C19
EFFECT OF Ai WITH COMPUTED REAERATION RATES
294
(AUT0SS)
5
a
a
O
0
10-
9-
8-
7-
6-
5-
4-
3-
2 -
1 -
•
n-
^****^^;- •••-.. .••'']
NX"^
X^ts//
xd
A- n r\?
| — \J.\JC.
A f\ f\ A
M | — U.VJ*f
A ,= 0.06
O Streeter — Phelps Equation — Computed Sag
Point.
0 10 20 30 40 50 60 70 80 90 !00
RIVER MILE
Ai HAS BEEN VARIED AND REAERATION RATES
HAVE BEEN COMPUTED RATHER THAN SPECIFIED
AT 0.4 (Vday).
-------
FIGURE C20
EFFECT OF A2 WITH COMPUTED REAERATION RATES
(AUT0SS)
295
10
a.
Q.
O
O
9-
8-
7-
6-
5
4-
3-
2-
I-
0
O
A2 = 0.4
A2=0.6
A2=0.8
Str««t«r — Phdps Equation — Computed Sag
Point.
10 20 30 40 50 60 70 80 90 100
RIVER MILE
A2 HAS BEEN VARIED AND REAERATION RATES
HAVE BEEN COMPUTED RATHER THAN SPECIFIED
AT 0.4 (Vday)
-------
FIGURE C21
EFFECT OF INCOMING LOAD
(AUT0SS)
296
c>
ci
4.0
30 -
20 -
1.0 -
0
O
L0 = I2.5ppm (+25<%)
LQ = 10.0 ppm
— — — • LQ = 7.5 ppm (-25<#»)
Q STREETER-PHELPS EQUATION-COMPUTED SAG POINT
i
10
20 30
I 1 I
40 50 60
RIVER MILES
I
70
I
80
1
90
100
THE INCOMING CB0D CONCENTRATIONS
AT MILE 10Q.O (LQ) HAVE BEEN VARIED.
-------
FIGURE C22
EFFECT OF FLOW RATE
297
50 -
40 -
30 -
20 -
10 -
0 -
LEGEND
•••• QlOO = 1250cf» (+25«7b)
QIOO = lOOOcfs
Q|00 = 750cfs (-25*%)
STREETER-PHELPS EQUATION-COMPUTED SAG POINT
i I r r i i i i i i
10 20 30 40 50 60 70 80 90 100
RIVER MILES
THE INFLOW AT MILE 100.0 (Q100) HAS BEEN VARIED-
-------
FIGURE C23
EFFECT OF NETWORK SIZE
298
£L
a
o
0
10
9 -
8 -
7 -
6 -
5 -
4 -
3 -
10 SECTIONS (L= 10 MILES)
50 SECTIONS (L- 2 MILES)
100 SECTIONS (L=l MILE)
200 SECTIONS (L= V2 MILE)
Str««t«r - Phelps Analytical Solution
I -
0
r
10
i
20
30
r
40
SO
I
60
I
70
I
80
I
90
100
RIVER MILE
THE SAME INPUT DATA HAS BEEN USED
AND THE NETWORK SIZE HAS BEEN VARIED.
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299
MODEL VERIFICATION:
As stated under Model Calibration, errors in the known quantities
will be absorbed by the calibration coefficients. The model verification
process should indicate the amount of such errors and give a measure
of their effect on the model's prediction of other conditions.
The verification procedure requires that the same amount of
information that is required by the calibration step be collected
and used as input to the model (AUT0QD). The computed or predicted
quality profiles are then compared to the observed profiles.
The two sets of profiles should be in close agreement. If they
do not agree within the normal range of laboratory errors, some
investigation should be made into the nature of the problems. All of
the major inputs to the model should be checked for errors under
bothethe calibration conditions and the verification conditions.
In most cases the source of the errors will be found in the
input data. The use^s knowledge of the prototype system and the model's
sesitivities will be the most valuable guides.
In some cases it may be desirable to recalibrate the coefficients
using both observed data sets. The user must be cautioned, however,
that in such cases he will not have a verified model, and another
verification period must be monitored, predicted and compared.
Common sense Indicates that extreme conditions, such as periods
of heavy algal blooms, drought conditions, or winter temperatures should
not be used for either the calibration or verification steps. The
various rates and functional forms incorporated in the AUT0-QUAL
set are not generally adequate to describe extreme conditions.
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300
REFERENCES
1. Crim5 Robert L., "A System of Mathematical Models for Water
Quality Management," Technical Report 51, U. S. Environmental
Protection Agency, Region III, Annapolis Field Office,,
January 1972.
2,.3, 4. ST0RET, CPSF and AUT0MAP are components of the Water Quality
Information System operated by the Monitoring and Data Support
Division of the Office of Air and Water Programs, U. S.
Environmental Protection Agency, Washington, D. C.
5. Streeter, H. W. and E. B. Phelps, "A Study of the Pollution and
Natural Purification of the Ohio River, Part III, Factors
Concerned in the Phenomena of Oxidation and Reaeration/ U. S,
Public Health Service, Public Health Bulletin 145, 1925.
6. Henderson, F. M., "Open Channel Flow." Macmillan Company,
New York, p. 69, 1966,
7. Hansen, A. G., "Fluid Mechanics," John Wiley and Sons, New York,
p. 121, 1967.
8. Thomann, Rovert V., "Systems Analysis and Water Quality
Management," Environmental Research and Applications, Inc.,
. New.-York, p.- 129, 1971.
9. "Effects of Polluting Discharges on the Thames Estuary," Water
Pollution Research, Technical Paper No. 11, Dept. of Scientific
and Industrial Research, Her Majesty's Stationery Office,
London, p. 216, 1964.
10. See Reference # 5.
11. See p. 96 of Reference # 8.
12. See p. 221 of Reference # 9.
13. See pp. 218-219 of Reference # 9.
14. See p. 219 of Reference # 9.
15. Hyer, P. V., C. S. Fang, E. P. Ruzecki, and W. J. Hargis, Jr.,
"Hydrography and Hydrodynamics of Virginia Estuaries, Part II,
Studies of the Distribution of Salinity and Dissolved Oxygen
in the Upper York System," Special Report in Applied Marine
Science and Ocean Engineering Number 13, Virginia Institute
of Marine Science, Gloucester Point, Virginia, p. 41, August 1971.
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301
16. O'Connor, D. J. and W. E. Dobbins, "Mechanism of Reaeration
in Natural Streams," Transcript American Society of Civil
Engineers, Vol. 123, 1958.
17. See p. 8 of Reference # 8.
18. Tsivoglou, E. C., "Tracer Measurement of Stream Reaeration,"
Federal Water Pollution Control Administration, U. S. Department
of the Interior, Washington, D. C., June 1967.
19. Tsivoglou, E. C. and J. R. Wallace, "Characterization of Stream
Reaeration Capacity," Project No. 16050 EOT, Office of Research
and Monitoring, U. S. Environmental Protection Agency,
Washington, D. C., October 1972.
20. O'Connell and Weeks, "An In-Situ Benthie Respirometer," CB-SRBP
Technical Paper No. 6, Federal Water Pollution Control Admin.,
Middle Atlantic Region, U. S. Department of the Interior,
Washington, D. C.
21. McCalla, T. R., "Introduction to Numerical.Methods andJF0RTRAN"
Programming," John Wiley and Sons, New York, pp. 180-185, 1967.
22. See pp. 310-313 of Reference # 21.
23. "Simplified Mathematical Modeling of Water Quality," Hydroscience,
Inc., Environmental Protection Agency, p. 72, March 1971.
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