-------
VII '(4)
Revision No. 0
2 and vgs s 5, and estimates a stream flow ratio 7Q10/avg QS =
0.005, for this condition near the lower bound for effl uent-dom-
inated streams.
The conditions under which the design stream flow is greater than
zero are listed in more detail in Table 4-9. Results for several additional
intermediate effluent dilution ratios (7Q10/QE = 0.2 and 0.5) are also
presented. A comparison of results for an effluent ratio of 1.0 presented
here as an upper bound, and previously (Table 4-4 and Figure 4-1) as a .
lower bound will indicate that results are similar but not exactly the
same. Ihe differences are due to different assumed values for 7Q10/QS and
the range of coefficients of variations used as inputs for the PDM-PS
model. • .
For the case where the design stream flow is zero, 7Q10 is zero and
there appears to be a problem since 7Q10/Q5" and 7Q10/DT are both zero.
However, what actually matters is "OT and "QF. Thus, in order to
evaluate these cases, the use of the actual "DT, TJE" and a small
7Q10 suffices since the computation depends only on QSVTjF and 7Q10 cancels
i
out {Equation D-14). Finally, the use of a small 7Q10/OTT correctly indicates
that the WLA is. done with QS = 0 (Equation D-15). Thus, no problems arise. .
Screening analysis results indicate that in the case of effluent-
dominated streams, a 30-day permit averaging-period provides adequate protec-
tion for pollutants with the acute-to-chronic ratios summarized below:
4-26
-------
VII (4)
Revision No. 0
When
30-Day Permit Average
Acute-to-Chronic . Is Adequate for
Ratio , Acute Protection
3 or more Al ways
2 to 3 Effluent variability is
relatively high, but
less than VCE - 1.1
4-27
-------
-------
VII (A)
Revision Wo..-0
APPENDIX A
Statistical Properties of Log-Normal Distributions
-------
•\
-------
VII (5)
Revision No. 0
. . CHAPTER 5 . - •
. . . USES AND LIMITATIONS
The probabilistic dilution model has been demonstrated to be useful in
selecting the appropriate averaging period for discharge permits. The method
is easily adaptable to situations which vary widely in terms of stream and
effluent characteristics, data availability, and'policy-level assumptions •
used in the analysis. Although the example in Chapter 3 of how to use
the method is based on the typical WLA assumptions of 7Q10 as the design-flow
and chronic criteria as the effluent limit, the method is easily adjusted to
accommodate other assumptions.
The method is intended to apply to pollutants for which the regulatory
concern is at the point of complete mixing and for which the toxicity can be
evaluated in terms of the total pollutant concentration. The method has been
applied to a range of stream and effluent characteristics which typify the
characteristics of streams and effluents in the United States. The'results
of this application are useful as a screening tool, by which the appropriate
averaging period for many field situations can be readily identified.
However, pollutants whose toxicity is a function of pH, temperature, and
hardness require site-specific evaluations incorporating these parameters.,
There are also several limitations on'the use of the method. .One of
the technical limitations is that the level of chronic protection is based on.
» ' •.'•-'";•
state-specified design flow, e.g., 7Q10, 7Q2, etc., which may be overprotec-
tive or underprotectiye for many site-specific conditions. The EPA is
presently considering the issue of allowable duration and frequency of
5-1
-------
.VII (5)
Revision No. 0
exposure to acute as well as chronic toxicity. Users of this manual are
advised to refer to Part A, Stream .Design Flow, of Book VI, Selecting Design
Conditions, when considering the choice of an appropriate, chronic exposure
event. Book VI is currently under peer review and will be issued by the
Office of Water Regulations and Standards once the peer review process is
completed. ' ,'•-.-'
Modifications are required to compute the probability distribution of
30-day average-concentrations, as-required for chronic criteria compliance;
these would have to be investigated and verified in the field. .
The major shortcoming, of the log-normal probabilistic dilution model
is Its misrepresentation of the lowest stream flows, thus tending to overesti-
mate the probability of high stream concentrations. The use of a seasonally
segmented approach could be investigated.
The effect of serial correlation on. the return period specification
would also need to be investigated, particularly with regard to the duration
of criteria violations. For example, a knowledge of the return period for
n-day successive violations could be compared'to the time scales of the
criteria themselves. This would provide a direct link to the toxicity data.
At a less sophisticated level of analysis, the tendency of criteria
violations to cluster on successive days could be investigated to provide a
basis for modifications to the method.
For pollutants whose toxicity is a function of such secondary vari-
ables as pH, temperature and hardness, probabilistic methods are essential in
that it is not possible to rationally choose "critical" or "sufficiently
5-2
-------
VII (5) :
Revision Wo. 0
protective" values for these variables. Arbitrary choices cannot be defended
in terms of the probability of criteria violations. Methods for analyzing
these situations could be developed, following the logic of probabilistic
dilution and incorporating the additional random variations of the variable..
..The application of this method to dissolved oxygen has indicated that
the probabilistic method provides a useful approach to the problem of
DO deficit. However this work has only been a first step. Probabilistic.
methods can be further developed to assess the effects of DO fluctuations on
fishery resources and to provide a more rational approach to advanced waste
treatment decisions.
5-3
-------
"'.I
-------
VII (6)
Revision No. 0
CHAPTER 6 .
. . ' . ': . REFERENCES .
1.. DIToro, D. M.t Probability Model of Stream Quality Due to Runoff. J.
Environmental Engineering, American Society of Chemical Engineers, Vol
110, No. 3, June 1984, p. 607-628.
2. DIToro, D. M. and,Fitzpatrick, J. J., Verification Analysis of the
• Probabilistic Dilution Model., report prepared for EPA Contract No.
68-01-6275, U. S.,Environmental.Protection Agency, Washington, O.C.,
1982.
3. Driscoll & Associates, Combined Sewer Overflow Analysis Handbook for
Use in 201 Facility Planning, report prepared for EPA Contract No.
68-01-6148, U. S; Environmental Protection Agency, Washington, D.C.
(1981). ' • . _ ' ,
4. Hazen and Sawyer, Review of Performance of Secondary Municipal
, Treatment Works. Draft Final Report for Contract 68-01-6275, Work
; Assignment No. 5, U. S. Environmental Protection Agency, Washington,
D^C., December 1982.
5. Niku, Shroeder, and Samaniego, Performance of Activated Sludge Process
and Reliability Related Design. JWPCF, Vol. 51, No. 12, December 1979.
.6. Niku, et al., Performance of Activated Sludge Processes: Reliability.
Stability and Variability. EPA 600/52-81-227, December 1981.
6-1
-------
VII (6)
Revision No. 0
7. Haugh, et al., Performance of Trickling Filter Plants: 'Reliability
Stability and Variability, EPA 600/52-81-228, December 1981.
• * _»
8. H/droscience, Inc., Simplified Mathematical Modeling of Water Quality. "'
for U.'S. Environmental Protection Agency, March 1971.
6-2
-------
VII (A)
Revision No. 0
. This appendix is intended to present a brief, simplified review of
the statistical properties of log-normal distributions which characterize
the important variables in the water quality analysis procedures used for
this'-report. It is designed to help the user without a formal background
in statistics to appreciate the physical significance of the statistical
properties employed. It is not the intent of this appendix to present a
theoretical discussion or to provide technical support for developing
relationships or equations used in the development of the methods employed.
A-l, , General Considerations '
The factors which influence the concentration of ,a pollutant in a
receiving water body are subject to a significant degree of variability.
This variability results in fluctuations in the resulting stream concen-
tration, which is compared with target concentrations such" as criteria
or standards, and which provides a basis for decisions on treatment ..
requirements. The approach adopted in this report for examining the
effects-of different averaging periods on treatment plant discharges uses
the concept "how much — how often" as a basis for such decisions. It is,
therefore, essential that statistical aspects be incorporated into the
methodology even though they may add complexity.
The standard statistical parameters of a population of values for
a random variable which are used as a concise means of describing central
tendency and spread are: . .
Mean: ( nx pr x) the arithmetic average, x" defines the
average of the available (usually limited) data set;
A-l
-------
Variance:
Standard
Deviation:
VII (A)
Revision No. 0
MX denotes the true mean of the total population of
variable x. Twill be an increasingly better approx-
imation of MX as the size of the sample (the number
of data points) increases.
(«Tx) *>y definition, the average of the square of the
differences between individual values of x and the
mean (x"). The greater the variation in the data, the
higher the variance:
2 (xi-x)2 + (xe-lT)2 +
— - - '
N
(.ox) another measure of the spread of a population of
'random variables; by definitioni the square root of
the variance:
Coefficient of , "
Variation: ( vx) is defined as the ratio of the standard
deviation ( ox) to the mean ( Mx):
vx = ax/. MX
It is the principal measure of variation used in
the analyses described in this report. The
coefficient of variation is a dimension!ess
quantity and is thus freed from any dependence on
A-2
-------
VII (A)
Revision No. 0
•_ .• < the specific dimensions used to describe the
variable (e.g., flow rate, concentrations, etc.).
High coefficients of variation reflect greater
variability in the random variable x.
Median: (~) This is the value in a data set for which
half the values are greater .and half are lesser.
Mode: The "most probable value" -- more of the individual
/ • • .. ^
. . data points are at this value (or are within this
^interval) than at other values,or ranges. On a
frequency histogram, this is the highest point on
• / ' •
; . the graph. The mode has no real significance in
the calculations in the methodology employed.
Comparing the statistical properties of different data sets pro-
vides a convenient, concise way of recognizing similarities and differ-
ences. This could not be accomplished simply by "looking at the data"
where reasonably large data sets are involved. These statistical proper-
ties convey ho information concerning frequency, or"the probability at ' '
which any particular value or range of values in the total popul ation.will
, • ' ,- t •
occur. . This essential item of information is provided by a knowledge of
the type of distribution, technically, the probability distribution
function (PDF).
A-2. Probability Distributions ^ -
There are several different" patterns which characterize the distri-
bution of individual values in a large population of variable events.
r /••'":'•-.'•'-•' A-3 . •,
-------
VII (A)
Revision No. 0
Most analysts are familiar with the normal distribution, in which a
histogram of the frequency of occurrence of various values describes
the familiar bell-shaped curve (Figure A-l(a)). When the cumulative
frequency! is plotted'on probability paper, a straight line is generated
as in Figure A-l(b)*
, "L
Many variables, particularly those which are important in water
' • *.
quality applications, have been shown by a rapidly accumulating body of
data to be represented by or adequately approximated by a log-normal
distribution. A log-normal distribution has a skewed frequency histogram
(Figure A-l(c)) which indicates an asymmetrical distribution of values
about an axis defining the central tendency of the data set. There is a
constraining limit to lower values (sometimes zero) and a relatively small
number of rather large values but ho upper constraint. Point source
effluent concentrations [1,2], and pollutant concentrations in combined
sewer overflows and separate storm runoff [3,4], are parameters which are
usually well characterized by log-normal distributions. In general, daily
stream flows are satisfactorily approximated by log-normal distributions
E5,6]. Scattered data from a number of unpublished sources suggest that
receiving water concentrations are also log-normally distributed. Stream
flows and concentrations are currently being examined from this perspec-
tive. A log-normal distribution appears as a straight line on log/proba-
bility paper (using cumulative frequency) as shown in Figure A-l(d). In
this report natural (base "e") logs are used throughout.
Cumulative frequency is the relative frequency (or probability) of
values being less than or equal to a specific value.
A-4
-------
Vll (A)
Revision No. 0
tu
<
UJ
u.
O
UJ
O
e>
<
CG)
MAGNITUDE OF VALUE (X)
NORMAL
I '10 50 9O
PROBABILITY .
% LESS THAN OR EQUAL
99
O
I-
a:
UJ
en
ca
O
a.
O
.
ox
u.^E
o-r
UJ
a
MAG-NITUDE OF VALUE (X)
LOG-NORMAL
I IO 5O 9O 9.9
PROBABILITY
% LESS THAN OR EQUAL
Figure A-1 - Probability distribution. .
A-5
-------
.VII (A)
Revision No. 0
A-3. Relationship Between Distributions .
There are circumstances when two different types of distribution
can begin to look similar — so that either one will provide a reasonably
good approximation of the probability distribution of a particular data
set. For example, as the coefficient of variation becomes smaller and
smaller, approaching .zero, log-normal distributions begin to look more and
more like a normal distribution. Figure A-2 shows a series of histograms
for log-normally distributed populations, all having (arithmetic) pop-
ulation means of 100, but with different coefficients of variation (v )
as shown. As discussed above, smaller values of v approach a normal
distribution.
, ., •
A-4. Properties of Log-Normal Distributions - •
• Figure A-3 summarizes the pertinent statistical relationships for
log-normal probability distributions. The mathematical formulas shown
are based on statistical theory, and permit back-and-forth conversions
between arithetic properties (in which concentrations,.flows, and loads
are reported) and the log of the'variable (In which probability and frequency
characteristics are defined).
Normalized plots of probability versus the magnitude of a variable
expressed as a multiple of the mean are presented in Figure A-4 for
log-normal distributions. These plots present a family of curves reflecting
the effect of coefficient of variation on probability of .occurrence of
events of specific magnitude. These, plots can be used directly in the
A-6
-------
VII (A)
Revision Mo. 0
o
z
UJ
ID
o
UJ
or
u.
MEDIAN 7
MEAN /xx
COEFFICIENT OF
VARIATION
Z>x=,'0.25
UJ
•3
a
UJ
or
u.
o
•z.
UJ
13.
O
UJ
cc.
u.
X
, I
COEFFICIENT OF ;
VARIATION
COEFFICIENT OF
VARIATION
l/ = 2.5
. . -•• • • . • ;X • •.--• - •
RANDOM VARIABLE . .
Figure A-2 - Effect, of coefficient of variation on frequency, distribution.
A-7
-------
Frequency
Arithmetic Space
—Mode
— Median x
Mean P.
X
x is a random variable
Definition or' Terms
•x Random Variable .•
u... -. - Mean
cr Variance
/\
VII (A)
Revision No. 0
Log Space
Natural Logs (base e)
Pr
o"x Standard Deviation ......... o^
vx Coefficient of Variation ... (not used)
x ..' Median
Relationships Between Statistical Properties
In Arithmetic and Log Space
°x
x « exp [nlnx]
>/exp (
lnxj
Tnx s ln
Figure A-3 - Pertinent relationships for log-normal distribution.
• A-8 .
-------
VII (A) •
Revision No. 0
10
UJ
2
UJ
X
u.
o
UJ
_J
a.
»-
_j
o
1.0
COEFFICIENT
OF ..
VARIATION,
O.I
0.1 0.51 2 5 10 2O
iOcr ' ——
i t
50 70 90 98 99.8 99.99
UJ
X
Hv
UJ
_J
a.
COEFFICIENT OF
VARIATION,
1.0
O.8
O.I 0.5 I 2 5 10 20 50 7O 90 98 99.8 99.99
PERCENT LESS THAN OR EQUAL TO
Figure A-4 - Cumulative log-normal distribution-
A-9
-------
VII (A) .
Revision No. 0
analysis methodology and permit direct determination of frequency for
events of any specified magnitude with a known or estimated coefficient of
variation.
A-5. Standard Normal Tables .
For normal (or log-normal) distributions, probabilities can be
defined in terms of the magnitude of a value, normalized by the standard
deviation. 'This technique is used in the calculations of the probability
of exceeding specified receiving water concentrations in this analysis.
Standard normal tables can be obtained from any statistics textbook [8,9].
Table A-l presents the standard normal table to provide a convenient source
for the analyses used,jn this report. Table A-l lists the probability for
the interval betw.een 0 and the ;value of Z listed. Thus, it represents the
probability that a value will be less than or equal to the selected value
of Z.
A-10
-------
TABLE A-l - Probabilities for the standard normal distribution.
Each entry in the table indicates the proportion of the total area under the
normal curve to the left of a perpendicular raised at a distance of Z
standard deviation units.
Example: 88.69 percent of the area under a normal curve lies to the left
of a point 1.21 standard deviation units to the right of the mean. . -
Z
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2-4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
0.00
0.5000
0.5398
. 0.5793
0.6179
0.6554
0.6915
0.7257
0.7580
0.7881
0.8159
0.8413
0.8643
0.8849
0.9032
0.9192
0.9332
0.9452
0.9554
0.9641
0.9713
0.9772
0.9821
0.9861
0.9893
0.9918
0.9938
0.9953
0.9965
0.9974
0.9981
0.9986
0.9990
0.3993
0.9995
0.9997
0.9998
0.9998
0.9999
0.9999
1.0000
0.01
0.5040
0.5438
0.5832
0.6217
. 0.6591
.0.6950
0.7291
0.7612
0.7910
0.8186
0.8438
0.8665
0.8869
0.9049
0.9207
0.9345
0.9463
0.9564
0.9649
0.9719
0.9778
0.9826
0.9864
0.9896
0.9920
0.9940
0.9955
0.9966
0.9975
0.9982
0.9987
0.9991
0.9993
0.9995
0.9997
0.9998
0.9998
0.9999
0.9999
1.0000
0.02
0.5080
0.5478
0.5871
0.6255
0.6628
0.6985
0.7324
0.7642
0.7939
0.8212
0.8461
0.8686
0.8883
0.9066
0.9222
0.9357
0.9474
0.9573
0.9655.
0.9726
0.9783
0.9830
0.9868
0.9898
0.9922
0.9941
0.9956
0.9967
0.9975
0.9982
0.9987
0.9991
0.9994
0.9995
0.9997
0.9998
0.9999
0.9999
0.9999
1.0000
0.03
0.5120
0.5517
0.5910
0.6293
0.6664
0.7019
0.7357
0.7673
0.7967
0.8238
0.8485
0.8708
0.8907
0.9082
0.9236
0.9370
0.9484
0.9582
0.9664
0.9732
0.9788
0.9834
0.9871
0.9901
0.9925
0.9943
0.9957
0.9968
0.9977
, 0.9983
0.9988
0.9991
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
'0.9999
l.OCOO
0.04
0.5160
0.5557
0.5948
0.6331
0.6700
0.7054
0.7389
0.7704
0.7995
0.8264
0.8508
0.8729
0,8925
0.9099
0.9251'
0.9382
0.9495
0.9591
0.9671
0.9738
0.9793
0.9838
0.9875
0.9904
0.9927
0.9945
O.S949
0.9969
0.9977
0.9984
0.9988
0.9992
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
0.9999
l.OOQO
0.05
0.5199
0.5596
0.5987
0.6368
0.6736
0.7088
0.7422
0.7734
0.8023
0.8289
0.8531
0.8749
0.8944
0.9115
0.9265
0.9394
0.9505
0.9599
0.9678
0.9744
0.9798
0.9842
0.9878
0.9906
0.9929
0.9946
0.9960
0.9970
0.9978
0.9984
0.9989
0.9992
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
0.9999
1.0000
0.06
0.5239
0.5636
0.6026
0.6406
0.6772
0,7123
0.7454
0.7764
0.8051
0.8315'
0.8554
0.8770
0.8962
0".9131
0.9279
0.9406
0.9515
0.9608
0.9686
0.9750
0.9803
0.9846
0.9881
0.9909
0.9931
0.9948
0.9961
0.9971
0.9979
0.9985
0.9989
0.9992
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
0.9999
l.OCOO
0.07
0.5279
0.5675
0.6064
0.6443
0.6808
0.7157
-0.7486
0.7794
0.8078
0.8340
0.8577
0.8790
0.8980
0.9147
0.9292
0.9418
0.9525
0.9616
0^9693
0.9756
0.9808
0.9850
0.9884
0.9911
0.9932
0.9949
0.9962
0.9972
0.9979
0.9985
0.9989
0.9992
0.9995
0.9996
6.99.97
0.9998
0.9999
0.9999
1.0000
1.0000
0.08
0.5319
^0.5714
0.6103
, 0.6480
5 0.6844
0.7190
0.7518
0.7823
0.8106
0.8365
0.8599
0.8810
0.8997
0.9162
0.9306
0.9429
0.9535
0.9625
0.9699
0:9761-
0.9812
0.9854
0.9887
0.9913
0.9934
0.9951
0.9963
0.9973
0.9980
0.9986
0.9990
0.9993
0.9995
0.9996
0.9998
0.9998
0.9999
0.9999
1.0000
1.0000
0.09
0."5359
0.5753
0.6141
0.6517
0.6879
0.7224
0.7549
0.7852
0.8133
0.8389
0.8621
0.8830
0.9015
0.9177
0.9319 ,
0.9441
0.9545
0.9633
0.9706
0.9767
0.9817
0.9857
0.9890
0.9916
0.9936
0.9952
0.9964
0.9974
0.9981
0.9986
0.9990
0.9993
0.9995
0.9997
0.9998
0.9993
0.9999
0.9999
1.0000
1.0000
A-ll
-------
VII (A)
Revision No. 0
A-6. References
1. Niku, et al ./'Performance of Activated Sludge-Processes and Reli-
ability Based Design." Journal WPCF, Vol. 51, No. 12, (December,
1979).- •
2. McCarty, et al ., "Reliability of Advanced Wastewater Treatment."
3. EPA Water Planning Division, "Preliminary Results of the Nationwide
Urban Runoff Program," (March 1982).
4. Mancini, J. L., "Methpds for Developing Wet Weather Water Quality
Criteria." Progress Report, June 1981; EPA ORD Grant No. R806828010,
Cincinnati.
5. Chow, V.T. "Handbook of Applied Hydrology." Mc-Graw Hill, New York
(1964). ' -
6. Linsley, et al., "Hydrology for'Engineers." Mc-Graw Hill, 2nd
Edition, (1975). ,
7. Hydroscience, In., "A Statistical Method for'the Assessment of
Urban Stormwater." USEPA, EPA 440/3-79-023, (May 1979).
8. Benjamin, J. R. and C. A. Cornell, "Probability, Statistics and
Decision for Civil Engineers." McGraw-Hill, New York, (1970).
9. Johnson, R. R., "Elementary Statistics." Duxbury Press, North
Scituate, Massachusetts, (1980).
A-12
-------
VII (B)
Rev'fsfon No. 0
APPENDIX B , .
Field Validation of Log-Normal Distribution
and Related Assumptions .
-------
-------
VII (BJ
.Revision No. 0
This appendix presents a discussion of several technical issues and
assumptions which are necessary to the use of the probabilistic dilution .
model to guide selection of permit averaging periods. This discussion is
organized in two sections: the first provides a justification for the use
of the probabilistic dilution model in the method; the second, provides a
discussion of several key assumptions.
, • - • «•* i
B-l. Use of the Log-Normal Distribution
• A relatively simple and straightforward analysis is made possible
by the'assumption that each of the input, variables is log-normally dis-
tributed and independent. The appropriateness of these assumptions and
-.their implications are discussed below.
A basic feature of any random time series of numerical values
is its probability distribution function, which specifies the distribution
of values and their frequency of occurrence. More detailed characteriza-
tions which account for seasonal trends and day-to-day correlations are
also possible, but at minimum the univariate probability density function
is required. An examination onflow data from a number of streams indi-
cates that the data can be reasonably well represented by a log-normal
distribution. Figure B-l summarizes an examination of the adequacy of a
log-normal distribution for daily flows of 60 streams with long periods of
record. The actually observed 10th and 1st percentile low flows are
.compared with the flow estimated by a log-normal distribution. The major
important discrepancy occurs at the lowest flows where the predicted
distribution is lower than thai actually observed. The most likely cause
B-l
-------
VII (B)
Revision No. 0
UJ
.J
UJ
o
a:
UJ
CL
ID
H
O
UI
«*•
o
UJ
UJ
o
or
13
l-
O
= 10 PERCENTILE
10'
10'
10'
-I s t titiMt? t.titntri i tfttttri ; tit
10
!0°
!0
I0
LOG NORMAL APPROXIMATION (cfs )
«= i PERCENTIL£
10 !0W 10' ^lO*1 10"
LOG NORMAL APPROXIMATION (cfs)
Figure B-l: Evaluations of log-normal distribution for stream flows.
'8-2
-------
VII (B)
Revision No. o
the prince of a base strea™ f,ow whi
which does
Log probabiHty plots of treataent
are .,,«,t«tid in Figure B 2 f
in sane cases.
p,ant efHuent fl
,3
Uted do»stream
r: rr
for upstrea™ and eff,uent f,ow
concentrations I
T 9"
as .„ as
PercentiUs
f
B-3
-------
in
m
°l
*
o
=
c
2 •*-
•»* ta
" T"
*-« >
»—« 03
£» £C
§;
it ;
ZL
3
a
8
Q
o
21
I -
SSI
01
p-
B
9
a-
a
a
en
or
»
-H
CT
a
HN
a
a
cu
in
•rl
' .'P
H
li
r ;
—a
B"
CO
o
tu
..Si
ri
a
a
9
v-
GO
O
(T
tn
a
tu
(1/6UJ) 009
(I /6tu) QOO iN3nidJ3
I
w
c
o
1^
v> o
i- O
(O 0)
ja >
o c
s_ c
. a. o
CM
I
CO
B-4
-------
o.
u»
>
^
- ,
'
' •(
Q • *"
**
• • . *
• ' ' •
: j
• ' • ; -
* . . •
a*
* . • a
a «
°: - '.
D • B
* * - • a
• *
' * »•
•
*t ' "
»•
f * • "
•s :
i ** i
utti » » i mm f t* f suit tit
«l •* C
> 0 O C
•1 »-• *H • T-
(I/fin) no
,
•
*i
> c
•« *•
• . • : - ' ;. •'• . ;
: •
• '* «
•: J
' : ' •
• *
, **
• •
' •
' *
.
":.
•
.
•• .
'-. • • = •
' - -
* • • ' *
• > •
i • .'•••' !
UTt i ( f nitti i i \ inn f i ",
01 -* o
> O 0 C
•< »-< •,_!.•.,.
-.
0
o»
i
x™'
^ :
o 3
m
<
CD
O
cc
«4
>
^ '
"•• i
M
O
^
•|
l
4J
C
03
"a..
+j
i
^
c
• , •
; "
• . ^
* • •»
*
- • . *
1 « • - " **
• - . ' 'a
• •• '
• _
• . '•
5 . . ' •
• ^
• •
. ' ;^ . " * «
:: -
mi»i « i Wto « « t Vntt iii "
> «< «« 0
> o o c
1 A
> c
• «
' : ' • - :
. ' 4
* ' 4
e , ' «
*
. •
.... ,
• ' a
*
* ' " ^
•
*
•
* , ^
* . ~
•• •
1. j
itiil f 1 l mtt« i i f bllM ill
» ei >• a
3 O 0 C
! • • j
. r
o •£•
°* - 'U
*^ M- 4->
• ^- ^
.1 • .2 >•
Si II
03 j
03" i
' « |
2 c
>
(I/On)
(I/fin) jo
B-5
-------
*
TABLE B-l - Comparison of
* *
Median
Location
North Buffalo Creek, NC
Jackson River, VA
Haw River, NC
Pigeon River, NC
Mississippi River, MN
VII
: Revi
(B)
sion No, £ - '
observed and computed downstream concentrations^2) .
(50th Percentile) Concentrations
Model . Observed
Variable- Prediction Quantile
BOD (rag/1) 9.7 10.0
COD (mg/1) 51.0 59.0
TSS (rag/1) 16.0 15.0
BOD (rag/1)' 6.0 5.3
TSS (mg/1) 15.8 13.6
Color (PCU) 110.0 100.0
BOD (mg/1) 2.0 1.7
COD (mg/1) 23.8 22.0
BOD (mg/1) 3.7 3.8
COD (mg/1) 85.0 78.0
"NHs (mg/1) 1.0 1.1
»
Confidence
Limit of
Observed
Qjjantile
8.5 - 11. 0
47.0 - 66.0
12.0 - 22.0
4.2 - 5.0
10.0 - 17.0
90.0 - 130.0
1.5 - 1.7 .
19.0 - 26.0
3.0 - 5.1
65.0 - 87.0 •
1.0 - 1.2
95th Percent! le Concentrations
North Buffalo Creek, NC
Jackson River, VA
Haw River, NC
Pigeon River, NC
BOD (mg/1) 31.0 22.0
COD (mg/1) 120.0 97.0
TSS (mg/1) 15.8 13.6
BOD (mg/1) 18.1 15.6
TSS (mg/1) 41.6 32.0
Color (PCU) 324.0 330.0.
BOD (mg/1) 4.5 4.7
COD (mg/1) 43.0 46.0
BOD (mg/1) 8.7 7.6
COD (mg/1) 186.0 229.0
20.0 - 33.0
82.0 - 129.0
10.0 - 17.0
13.0 - 20.0
30.0 - 40.0 !
300.0 - 410.0
3.2 - 5.6
33.0 - 53.0
6.4- 9.4
188.0 - 233.0
Mississippi River, MN
(mg/1)
3.5
4.3
3.2 - 5.0
B-6
-------
.VII (B)
Revision No". 0
distribution of quantiles, are also listed. In all but one case, the ""
computed quantiles are within the confidence limits. '
Thus, there is no statistical evidence to reject the computed quan-
tiles as not being the true quantiles of the observed concentration distribu-
tion. This is strong statistical evidence that indeed the log-normal
probabilistic dilution model is representative of actually observed down-
stream concentration distributions for the 95th percentile at least.
The 11 data sets used in the verification analysis were examined
for cross correlations between effluent, flows and concentrations. The
observed ranges in correlation coefficients have no significant impact on
the computation. -Correlations between stream flow and effluent load for
a point source are not expected. Upstream concentrations are not employed
in the comparison of permit averaging period effects, so that any correla-
tion between stream flow and concentration is not relevant to this analysis.
Modifications to the probabilistic dilution model computations are avail-
able for use in situations .where cross correlations must be considered ,[!].
The influence of, possible deviations from the assumed log-normality
of the upstream and effluent flows and concentrations upon more extreme
quantiles is unknown at present due to lack of larger data sets that encompass
these extreme quantiles. However, the quality of the alternatives to and the '
simplicity of this model argue strongly for its use in the present context of
describing comparative differences in water quality impacts.
B-7
-------
VII (B)
Revision No. 0
B-3. Appropriateness of Assumptions - « .
., ' '
We have chosen to ignore the' seasonal and day-to-day correlation
••'.'.• '••-.-
structure of both'stream flow and effluent behavior in order to simplify
the characterization of each variable. TTie consequences of this simpli-'
fication are discussed below in more detail, but it should be pointed out
that trends and correlations do not invalidate the use of the log-normal
probability distribution function to characterize the frequency of occur-
»,'...
rence of flows and concentrations. Trends and day-to-day correlations
affect the time sequences with which certain values occur, but not their
long term frequency of occurrence. This is judged to be an acceptable
penalty to be endured when compared to the simplification achieved. If a
•more refined, site specific analysis is required, then a seasonal breakdown
of the data, with the appropriate means and standard deviations for each time
period, can be generated and the analysis performed as described below.
The consequence of a possible serial correlation can be approxi-
mately quantified as follows. If, in fact, the serial correlation is such
that 10 consecutive daily violations always occur when one violation
occurs, then the proper percent! le to consider is not 0.0274 (10 years)
but rather 0.274 (1 year return period). The degree to which the 10 year
return period concentration is overestimated can be estimated by comparing
the ratio of the 10 year to the 1 year stream concentrations which are .
computed without regard to serial correlation.
The ratio of the 10 -year return period concentration to that for
B-8
-------
VII (B)
Revision No. 0
some other return period can be computed for log-normally distributed
random concentrations by: •
x
where
EXP[(Z10yr - Zxyr)
lnc = log standard deviation of stream concentrations (C)
\
yr> C10.yr = z score and concentration corresponding to a
10 year return period
Zx yr, Cx yr = Z score and concentration corresponding to an
x year return period • ' . .
Table B-2 summarizes results for' a range of values for coefficient
of variation of stream concentrations. Clustering tendencies of 5 and 10
are examined as approximations of the degree of serial correlation which
might exist. If clusters of 10 occur, the comparison is between 10 and 1
year return periods as discussed above; for clusters of 5S the comparison
is between 10 and 2 year return periods. On the basis of this analysis,
the water quality effects presented in Chapter 4 for various permit
averaging periods may overstate the 10 year stream concentrations by
approximately a factor of 1.5 to 2.0. •
Until stream and effluent data can be analyzed to define the serial
correlation structure and the methodology modified to incorporate it,, the
results presented in Table B-2 should be interpreted to indicate with the
following possibilities:
B-9
-------
.VII (B)
Revision No. 0
TABLE B-2-- Approximate overestimation of 10 year return period stream
concentration by ignoring serial correlation.
Variability of
Stream Concentration
Coefficient
of Variation
(*c)
0.5
1.0
1.5
2.0
Log
Sigma .
( °lnc)
0.4724
0.8326 .
1.0857
1.2686
Ratio of Stream Concentration
At Indicated Average Return Periods
10 Year
. to 1 Year
(CIQ/CI)
1.4
1.8
2.1
2.4
10 Year
to 2 Year
(Clo/C2)
'1.25
1.50
1.65
1.80
Cl,2
= EXP
lncl
(10 year Return Period) = 3.456
"Li (lyear Return Period) = 2.778
7-2 (2 year Return Period) =2.
996
B-10
-------
VII (B)
Revision No. 0
o Stream concentrations indicated by the methodology used in the
report to recur on average for 1 day every 10 years would, if.
they actually never occur except in clusters of 5 to 10 days,
have return periods of 50 to 100 years.
o Conversely, for the same clustering assumptions, the stream
concentrations that occur at 10-year intervals should be; 50 to
, 70% (1/2 to 1/1.5) of the 10-year concentrations projected by
. the report methodology.
B-4. References
1. DiToro, D.M., "Probability Model of Stream Quality Due to Runoff."
J. Environmental Engr. ASCE, Vol. 110, #3, June 1984 p. 6.07-628.
2. DiTqro, D.M. and Fitzpatrick, J.J., "Verification Analysis of the
Probabilistic Dilution Model" Report prepared for EPA Contract No.
68-01-6275, U.S. Environmental Protection Agency, Washington, D.C.,
(1982), . ,
B-ll
-------
-------
VII (C)
Revision Ndi 0
APPENDIX C
Characteristic Values for Input Parameters
-------
••1
-------
VII (C)
Revision No, 0
The results reported here represent an attempt to .develop character- •
istic values and ranges for stream flow and effluent variability. These
values and ranges have been extracted from the results of published
analyses, and are used in Chapter 4 to evaluate the influence'of the
permit averaging period on typical receiving water conditions. These
' ' ' • ' ' !' ' •
values are provided for, effluent flows (Section 1),, effluent coneentra- . -
tions (Section<2), and stream flow (Section 3).
C-l. Treatment'Plant Effluent Flows
• s ' ' • ' '
. ' A recent study [1] analyzed several years of performance data from
approximately 400 secondary treatment plants in 8 different process ,
categories. Average plant effluent flows ranged from .0.002 to 82 MGD. .
Table C-l summarizes the coefficient of variation of treatment plant
effluent flows. .
• i i . • . • ' .
C-2. Treatment Plant Effluent Concentrations "'
Data on the variability of effluent BOD5 and total suspended
solids (TSS) from municipal biological treatment plants are available •from
several sources. . Niku, et al. £2] provide analysis results for 37 acti-
vated sludge plants which show the coefficient of variation of effluent
BOD5 concentrations to range between 0.34 and 1.11 for individual
plants. The median of the individual plant.values was 0.635. The EPA
research report [3] on which the foregoing was based reported a mean
coefficient of variation for 43 activated sludge plants using a variety of
processes. Daily effluent concentrations were found to be well represented
C-l
-------
VII (C)
Revision No. £
TABLE C-l - Coefficient of variation of daily effluent flows, vgE.
• n
Process Category
Trickling Filter
Rock
Trickling Filter
Plastic
Conventional Activated
Sludge
Contact Stabilization
Activated Sludge
Extended Aeration
Activated Sludge
Rotating Biological
Contact
Oxidation Ditch-
Stabilization Pond
Number of
Plants
64
17
66
57
28
27
28
37
Range
Individual
0.06-
0.16 -
0,04 -
0.06 -
0.11 -
• 0-12 -
0.09 -
. 0.00,-
For Median of -
Plants All Plants
0.97 0.27
0.88 0.38
1.04 . 0.24
1.35 0.34
1.32 0.34
1.19 0.31
1.16 • 0.31
0.83 0.31
C-2
-------
VII (C)
Revision No. 0
by a log-normal distribution. The mean of all plants analyzed had co-
efficients of variation of 0.7 for BQD5 and 0.84 for TSS.
Two recent studies have extended the analysis of effluent concentra-
tion variability, and, report coefficients of variation of BOD5 and TSS
for 7-and 30-day averages as well as for daily values. Results reported
by Hazen and Sawyer [1] provide the .basis for the summary presented.in
Table C-2 as well as the two other sources cited in the table. An analysis
of the performance of 11 trickling filter plants by Haugh, et al. [4] produced
the results summarized by Table C-3.
Based on available data, a single'representative value for coeffi-
cient of variation of effluent concentrations cannot be defined. The most
Appropriate characteristic value will be influenced by process category,
effluent concentration averaging period, .and the pollutant in question
(e.g., BOD, TSS, etc.), as well as individual plant differences. The
computations in this report are performed using a range of values esti-
mated, to encompass most of the conditions of interest.
C-3. Stream Flow ; ' , • ,. '
Figure C-l provides a basis for estimating the coefficient of
variation of daily stream flows on the basis of the ratio of 7Q10 to -
average (7JS) stream flow. These flow values are usual!/ readily avail-
able. The relationship shown is .derived from a set of flow measurements and
statistics, which has been developed for a sample of 130 streams in various "•'
areas of the country [5] and is summarized in Table C-4, along with addi-
tional details on the location of the stream gages used. The ranges
C-3
-------
of
J
rf—*-*1 O
On- •>
"— » «/> C
*-«**" °
— • QJ 4J
s» cc n
•r-
ra
u-
o
•«J
c
a
•r-
O
51
u-
o
u
ra
•5
cu
s
1
to
0
ra
&n
0
u-
a>
a.
4->.
c°"
ra
a.
c
fll
rj£
^^
ra
CD
t_ .
>* *""^
f*
•° S
"c *-
8 ?!
Si"
" 2
0 E
« ^- O
»*^ S™
In **~
§ LU
J ^
1
CM
O
LU
<:
^•^
>^.
cr
E
^_*
(—
[ <
C
cu
3
LU
ro •
a (/>
4— 1 O»
o o >
* CO «£
-r^ ^"
c o
cu ••->,•
•r- 4-) ra CO
O ro O O>
•f- .r- 1 >
<4- ro
CU > V)
o >>
^
O
ca
4->
0 0 >
* CO «C
4-3 C
•r- 4-> ra to
o ra a o>
.^- .r- I >
<>- ro
cu > to
o >, cu
0 ,->3
ra ra
c
S
c- to
-Q <4- C
S O ra
S3^ ^
—
t"
o
o*
ra
0
to
/»!
cu
o
o.
a.
in
CM
o
v
0
CO
• 0
0
in
CD
CO
in
CM
CM
•
0
o
CO
o
o •
CO
o
vo
CM
to
^
o
o
az
c_
a;
4-J
P>_
uZ
a>
c
r"~
^£
U
'l—
.0
o
in
0
in
to
o
•*
i-H
O
co
•
o
in
CO
0
0
o
in
O
o
•
i—4
*£
• o
•r™
CO
^O
^•"
n.
&.
4-*
»^^
Lu
C31
C
^^
^^
u
1—
'• "-'
in
o
O
. to
0
in
03
O
CO
•— I
o
9
o
. in
m
d
in
to
p
CO
•
*— i
VO
to
•o
(U
4^
ra
o
^c
ra
c
o
4J CJ>
c -o
(U 3
> 1 —
c to
o
o
0
VO
o
to
0
o
o
03
co
«— 4
o
0
• o
o
m
0
0
VO
C3*
VO
CM
f— 4
• in
c
o
j_> cj
ra C7>
N T3
•«- 3
^ co
ro -a
4J CU
C/) 4J
ro
4J >
0 ••-
ra 4->
4-9 U
C «=C
o
C_3
0
CO
C3
m
0
in
VO
o
03
a\
in
^
o
0
to
e'
0
o
o
CM
•^
CO
CM
•—
ra CO
Ig
"O ra
O) >
"O •!—
C 4->
cu u
4J «=C
X
LU •
in
co
o
0
m
o
o
0
CM
m
l-H
m
CO ^
o
in
C3
O
VO
0
O
O
1— 1
CM
t^«
ro
(J
cn
o
*o
•i- C_
ca cu
•M
O) (J
C ra
•r™ ), y
4-> C
-Q
0 §
o
c_
r~- oj
CM ro
CM
C
3
0
.c
to
CO 3
r™"
ra
"O
1
c
0
N
,H.
.^K
ra
4-5
OO
-
,
*"
.c
ra
01
c
•o
•r-
•p
ra
4- i—
o a.
c c
O ra
•r- '^
4-> T3
rO CO
^
CU 4—
0 0
•a c
t- ra
ra QJ
^3 ^^
ra
CO
II
LU
o
in
1J-
to
ra
23 '
C-4
-------
VII (C)
Revision No. 0
Table C-2 (Cont.)
Chemical Precipitation/Settling*
Pollutant Coefficient, of Variation
,Cr .99
£u . .60
M6 ' «57
Mn .84
Nl . .81
Zn .84
Tss . .66
Pharmaceutical. Industry2
Coefficient of Variation
Plant Number BOD (n)TSS"
12015
- 12072
12026 • '
12036
12097
12098
12117
12160
12161
12186
12187
12136
12248
12257
12294
12307
1.01
.97
.95
.74
1.08
1.37
.70
.92
.55
.71
.21
1.02
.58
.64
.93
1.55
»•• '
' 46
392
44
366
222
24
39
. 34
249
54
12
110
50
56
56
39
.85
.63
.49
1.12
1.21
1.52
.81 .
1.11
.99
.50
.26
1.16
.55
.92
1.25
1.34
195
395
53
364. >
249
25
51 '
32
355
54
12
111
52
56 •
50
'38
14'of 10-18-83 memorandum .from H. Kahn to:E
t0 Data and Analys1s of the Combined".
2From preliminary descriptive statistics generated on pharmaceu-
tical data by SRI International, 11-12-82.
C-5
-------
VII (C)
.: Revision No. J3
TABLE C-3 - Effluent concentration variability for trickling filters
(from reference 4). .
,
Mean for 11 plants (mg/1)
Coefficient of Variation (median of
individual plant values):
Daily Values
7-Day Averages .
30-Day Averages
BOD5
29.6
•
0.39
0.35
0.31
TSS
29.3
0.55
0.31
0.26
shown reflect the bulk of the data in the sample of stream records which
were used. However, a relatively small percentage of streams will have
coefficients of variation which fall outside the indicated ranges. The
statistical analysis was performed for the entire period of record.
Results in some-cases may be distorted, if flow regulation works were
installed on the stream sometime during the period of record.
C.4. References ,
1 . Hazen a*Hl Sawyer, "Review of Performance of Secondary Municipal
Treatment Works." Draft Final Report for Contract 68-01-6275, Work
Assignment No. 5, U.S. Environmental Protection Agency, Washington,
D.C., (December 1982).
2. Niku, Shroeder, and Samaniego, "Performance of Activated Sludge
Process and Reliability Related Design." JWPCF, Vol. 51, No. 12,
(December 1979). • J
3. Niku, et al., "Performance of Activated Sludge Processes: Reliability;
Stability and Variability." EPA 600/52-81-227, (December 1981). i
4. Haugh, etal. "Performance of Trickling Filter Plants: Reliability,
Stability and Variability." EPA 600/52-81-228. (December 1981). .'- r
5. Driscoll & Associates, "Combined Sewer Overflow Analysis Handbook
, for Use in 201 Facility Planning." Report prepared for EPA Contract
No. 68-01-6148, U.S. Environmental Protection Agency, Washington, I
D.C. (1981). 4
C-6 . I
-------
VII (C)
Revision No* 0
o
r-
O
u.
UJ
-------
ol
« *
3.
CJ 4-
*•— ' t/J
•— *>
4—4 CO
'-
* .
CO
0
•JM*
•*•>
CO
r
(U
5 * ^J
U
re
t_
*tj
j::
o
5
o
r"~
^4—
•
CU
I—
•4J
CO
O
*
^>
§
ys
3
«O
1
*s3*
i
o
UJ
CO
J2
3
O ^"^
r- CM
ft )^^
E *-.
re co
cu <«-
r- u
,
c
re
• h
c
o
•r—
4_d
re
u
2
CO
CT
re
CIS
2 CM
Or or
r-. t-4
sU
M
CD-
CM
CD-
CD
i— i
r-.
c"o-
lo-
re CM
Qj >•— i
•* 5.
^— ^ .
&.
re
zs
£_
O
^J*
S
CO
*f™
0£
CO
re
4_5
CO
•
£
to
C3 CO
=D re1
in co cr> o r*.
en co in vo
CM t-4 i—4 t-4
.
. CO VO «*• CO
to O VO *— 4
O O O O CD
VO CO V-.' CM r-<
^- in i— i o cr>
•-I CM •— i. CM *-4
«3- co ^* vo r-»
CO O CO «-4 .— 1
o o o o o
CM »— 4 CD en
O i— 4 CO CM
l-H O 1-4 O O
^" ^J ^? ^O CO
CO vo co vo r*.
O i-l
en CM o en co
** ^ ° "* "2
o co !••» CM «a*
LO i-» m ft o
CM f-4 «S- •— I
1— 1
UJ
• LU
•2: A re
CO 2='
LU A, —
^*^ CHr^* "^ 'A
re *f— 21 c
A CO > 3
JZ^tf >> « 0
CO CO CO E 4J
re 3 c re co
OTO 4-> JZ "—
.re c -r- e_ £_ 4->
> CO 0
•r- .OJ-r— > CO
r^ re /^^ •!<— >p—
co 01 a.
J= ^ CO
co co re c_ •
re 3 i- co t_
CDT3 J= 4-> CO
re c o co
r— co re >•> •
. o en 1-4
in o co o CM
r^ vo in en co
o en •— i <3* i— i
I-H »— i in en en
t— 4 i-H '.-
^ •
«c t_ -f-
-1— -^ CO "4— t-
Q£ O > 4J CO
O -r- CO >.
re t_ ce co •>-
3 CO 3 O£.
<— O^
co 4-> re • jc
re co o t- u
2: . . .
21
A ""3
co >- 2:
C712T
•a •
.,- A CO
i— i— CQ i— re
o c; T- >
CO 3= t-
A «,— QJ
* • r^T\ vx ^
• • re re •!-
• • LU O O£
c.
c- co
CO -^ >
> CO -r—
.,- t- C CO 0£.
C£. CO > C_J ^i
cn-r- -i- o
3 o; as r— re
re r— co
^3 O O -i- C
CO T- •»- ^tf CO
C 4-> CO CO J^
•i- e o 4-» o
"•• .M g^ - as o z
!— 1— >- >- -D
o o 2: 2: 2:
c o o o o
O O 0 O 0
o m in in o
CM CM CO VO r*.
I^^HIJ^
co en in co CM
1—41—4 t— I
^r vo vo vo vo.
O O O O ir-4
co in r^ i-^ ^^
CD co 1—4 en P**.
in co CM en in
en vo O ^j" r^
O O t— 4 i— 1 1— 1
vo co CM en r*-
r»» co in t— i <— t
O i— 1 i— 4 r-4 CM
o «=f «a- en t-«
• CM co r-» «a- 1-4
CM VO CO CM CO
r-» CM vo o co
i—4 CM CM CM t-4
vo •— 4 vo i** ^r
CM -sj- VO r-4 —4
CM CO
>- >- UJ
-a 2: 2: a
A A *"* A
* to o c
CO r— f— • O
•— re •!- t- en
•r— U. > CO C
«-r~ ^.^ ,— •
•*£ t- O £=
t_ o re 4J ^=
re Or— re •»-
U_ 0 0 = 3
C_ '
CO
•r—
C£ 3£
c. -a
c at co
re > c_
4-> -i- C_5
•f— r— O£
g r— • >x Q|
re t- -s«i co c
cc ^^ c co i—
t- t_ 3
• C_ CO 0 >»
CQ > CO -C C
re > i — re
2:03 2: 3 ca
••3 >- >- «C uj
2: 2: Z 0_ £2
0 O O O O
O CD O O O
LO in o in in
co o LO en t-4
en CM co «a- co
CO «=1- -3- -3- «3-
—^——
-------
o|
o
.;:
VI
>
.
T
c .
a
•
LU
CQ
^C
1 —
0
i— I CM
o- o*
^^ «™l
o
cr
. ' '
o •—
p— CM
ii i— i
(O CO
« en to co
«3- co r^ CM in
P^ CO CM CM in
CO i— 1 •— 1 •— I CM
. O O O 0 O
»-4-p>. in 1-4 in
CO P-- -!S- •— I CM
O O O O CD
en co in to en
CO P"^ <3" to * "5f CM i-r4
£^Sc?
••2; •> •> «
re *••• en re
r— *» p— C «r»
r— re ai -i— +J
•O co ex t- E
re re s cv r—
3 i— i O OO Q
N>
0)
> -K: o
•r- .r- c_ o en
as os t_ re
re re T- ea 4->
c cnos c
co °a re
re -i- c: o .c
. £Z G Q. O a
.3 C7) U 4->
cr c o 4- +J
CO O -C -I- 01
<^i=<3c%i3
2= 2= z: CL 2
o o o o o
o o o o o "
in in m o in
o 1—4, en .co in
O i— 1 CM •!!• in
in in in in un
fl— 4
C
CMO 0
i— i •— i • -: CM
• - :
CM en co
r-* O O O O
CO O CO CO CM
p** co en p** co -
. O O i— i «— I
to to co i-i en
O CO i— 4 P»> O
*- ' O O O O
«3- to P-»
CM CO r-l
i-4 O O O O.
CM in in co «—<
co p^» p**> vo co
«* co co o -=r
o en to co to
in co i— 1 1— i in
><
o en •
0 3 £•
-— «S * **** i— •
si c co •!—
« O C >
* >•> •*-> ••- >>
re -!-> C 4-> t_'
8S&£-£
i.
CO <1> OJ -i£
Q. > O) t_ O)
re -T~ c. o or
+j QS o • e_
nj • as O
Q- j_> (1) t_
C OJ O C
• re 3
CO 3.J3 0 0-
-t-> re to a)
• «3 £_ 3 a.
2= 0- 0 1— 0
Q O Q > cC
s s s 5: ^
o o o o o
O 0 O O O
o o o o o
to »-i i — r--.in
co en en •— * I-H
in in in to to
'.t»j ^j-
p
VO r"-<
C3 O 0
f"H ^^ d^
en to 'S-
CO i-l
to -« 1-1
to o co
o o o
0 «d-
in 1-4
000
to co r^.
to CM to
en co in
CO CO i-H
"— i CO P^
0 «q- CO
^H r-( CM
a
«<:
O ^ ' A
tn. « ^_
•r- CO p—
C CO >
O CO >,
co re tu
3 c x
o. s 5
a; , «.
0) . (U
3 as
re as
u i —
§
o o o
C3 O 0
o o in
in i — co
«?!• m to
to to to
i— 1 CO »-4 CO
•* r-< CO
CO CO «?T CO
, — < 0 — • 0 0
CM CM O CM OV
CO «fl- i— 1 in r-H
i— 1 i— 1 i— i CO i—t
to rv, to •— t if
CO CM <* O «3-
o o o o o
i— 1 to CM ^~
in co •=!• co
•-H O i-i O O
o CM en r-i p^
r**» to to co r*^
tO CO CM CM O
i-H O O i— 1 i-H
«-< «3- in r~» o
f— < to «— i in co
^" to ^1" to
CM
•-§
A
en o
S- cC < 0 2=
CO •
, A A A \>*
CD re a) a> 2
c t. c T- re
i— so co re
!— ' O O =
LU a. ca «c i—
£_
ai
^
c^
c
Q
C '
t. i- 3 ^£
^J ^J 1^ 't^
> > j_j OJ C-
.,_.,_ co £_ aj
OS OS -^- C_3 >
O C -iS -i-
co c o -^ -i:
j^ re c co o
o > «s3" to .in
co to en en
.rt •
O r- < «^ >— »
•— t co co en
O CM 1-1 O
CO to CO CO
«;r r»» CM in
O CM CM CM
in co CM CM
»«• co in o
I— 1 i— 1 f-H
to en o i— «
en in ,-1 -3-
I-H CM i— 1
^* en p>» co
- CM CM to en
r-l i— 1
2= 2: 0
t_ .C «
«a o o o
C CO 2= _
CD c. re
r— . oj «-a
•a -M o s
cz *j ja s
v
£_
a-
£- -r-
«- >
<1> -r- -0
t- > as .re
QJ T— O
> OS GJ «_
•f— F— CO
as c i—
•t— V- 4->
' Q.JK: > co
aj -a c t_
aj re -i— -P-
Q >- _I Ix.
0 O O 0
o o o o
O O O 0
in o in in
cr> •— i co CM
en i—i co in
O i— 4 r— * i— I
C-9
-------
°J
^s
e
•— . * m
•-* ">
*-H m
•
*
6
•
•
T*
4J
C
O
0
^r
i
CJ
UJ
1
CO
«-f
O
rH CM
,o* o*
o
rH
0 |0*
cr
^
o *—*
r- CM
U. HH
ta vt
CO 4-
t- o
tr
CM
o-
rH
O
rH
O*
-
lo-
.,- _>
c_
•r-
CO
4J
I <
co
,'
O
CO
CD CO
co o
CD
j—
0 0 O
• • • C?
rH in CO
CO
in rH ^f
o o co o
^O ^3* ^M ^^
O CO O rH
rH co CM in
CO rH in
in o o
o o o o
rH VO «*• CO
vo CD in I-H
O O rH O O
vo o o r>. co
r^ CM CM I-H cn
co o in en co
rH oo «* oo cn
rH
co cn co CM o
r-. CM «a- PO I-H
CO CO VO rH i— 1
s'
,,-J ^J
« —1 U. U.
C
s v> o •<-> jz
§t~* ta cn
in o ••-
8r5l]SS
£.
cu
> f
•r~
Q£
CO CO
CO CO
cn , t_
t- r— J«J ^£ O
CO 3 CO CO
> S CO CO £-
•r- O C_ C_ CO
oi o o cj j->
(O
3 CO rtJ 3
O r- CO 3 -S£
r— •»-> ex: o
co -I— ta o r—
>i— I 3= -^ CD
^C ^C i i t
Co CD LL. LL. LL.
. O O 0, 0 O
0 O 0 0 O
in o CD I-H m
r-» vo co r». CM
o I-H co cn CD
CM CM CM CM CO
CM
O '
co CM P>. I-H r»»
rH in rH «* CM
. -..
* ^* *3j" LO CO GO
*T O rH CM f-*
^O CO CM ^ O
CO CO GO CAJ O^
. -*
oo rH m vo vo
m i— i CM in I-H
«*• O rH i-H rH
o r^ co m CM
o m o co rH
vo o CM vo co
en I-H co o vo
CM CO O CM CM
<-H rH CM rH
i*- m cn r^ o
co co co CM r*.
m vo «a- •53- vo
co «a- «=»• r«~ in
•in CM I-H «a- oo
_.s
_J U_ •>
— J CO
« 3 Q.
A M cn co ta
4J r-* S~ *r- <•*
t- r- 3 > CJ
O CO t^> JJ
'D.4-> CO VI CO
3 I/I r- CO C
co 3
CO CO -i-
> t_ - cc
•r- O
Q£ J£ t- CO
t_ CO CO CO
in CO CO > -M
.Si -M (_ >r- 4->
t. g o cn co r— ta
• O) -r— 03 O J* CO
•r- > CO O
0 C- C_
.C 0. C. O >>
,0 ITS CO CO
§N^
t_
££^£,2
j^ 1 I C/} t
CD ^C ^ 21 <
OO O O 0
O O O O O
o o m o o
CM CM CM ««• VO
en rH CM co in
CO ^* ^" ^" ^"
oo
VO O
CM
CMrH
O OO
vo PO «a-
CM rH P>
co com
^
o oo
,0 00-
CM f^-
CO rH
o oo
CM O rH
m vo CM
cb coin
o cn CM
CM CM «T
in cnco
co
CO S
y
co •
•> s o
CO-r-
co u
CO >>
C. CO C
(_}•!— ITS
|SJ -^x •
CO C O.
CO 0
CO «r^
t. > Wl O
O 3 ^ O
0 Q.
t. •••- t_
• CO
•t— CO
rv t
-^ C_3
O C
CO O t-
t_ C^f CO
O C C- >
'O ^2 'O
<- J= U. CO
(0 J* CQ
• en o >%
3 3 t_ •
CO CQ O. _1
^C ^* ^* ~~
0- 3 3 O
o o o o
0 0 0 O
o in o in
in co in cri
CM in vo o
O O O rH
CO
o
••••
-------
OJ
ta
. •!•—
>
CO
J
c
0
LU
_J
CQ
^
1—
S CM
o- o-
0
o-
3'
o ^->
r— CM
U_ r-l
113 VI
, CO
*os
CD ,
2
•S
CO
CD 0}
C0.cn
.CD
VO CO O CO
«*• «3- CM
CO
O O rH O O
I-H en rH ' in en
co, vo co en o
1-4,1-4 rH CO
CO
1—4 rH i-H CO O
O O rH O O
CO CO OO
ro. vo CM o
O O CM O O
• « « e
O C7» CO CM VO
LO -sj- en I-H co
rH
en LO o O ro,
en en CM LO rH
r-l CM rH
ro. cn o co i-H
CO LO O CVJ CO
LO «3- CO rH •
3: «=c
0 3» .
A A ^X
Z CO C • 3
O to O
•r- +J > «
« c. e 3 t_
Jtt 0. O. CO
C- t- 10 «JS
ro co ,:>> c. +j
^ *4J 10 cj C' .
^ScDC^cS
t- t- CD -1£
Ol .CD
> > O) -i- O!
•r- -r- >, Oi £_
as as -r- cj
a: to
en en = «_
c: c «C
0 0 > 3 >
O O O O O
• o o o o .0
LO LO O LO LO
vo ro. o .vo co
^i- LO ro, co i— i
I— 1 rH rH rH CM
co
o
1—4 CO VO LO
CM «* r-l rH
• -
O O O O O
•4* VO O 00 CO
O CM CM CM rH
CO rH CO r-l CM
CO CO CO
O CM O CO O
O O O O O
LO I— 1 ** rH
o o o o o
CO VO LO CO rH
CM «d- CM «* «3-
en «^ ^f co co
co fs. co ro. en
en en co co vo
en CM vo en CM
rH CM CM CO
s: -SS.
rH' A *— i
— ®
S O C r3 CO
O O •!- 1
" c en to •'m
>» 3 c t. >
O) O -i— CO -to
i — -M -U r— i—
J— iwi C r-— CD
•gssss
^<:
co e~ CD
CO CO t.
c. > c. cj
CJ -r- CJ
a; > ji +j
CD -r- CO 3
C -r- OS CO C '
OS S_ r- .
•M IO CO CJ .-O
tO »r™ r— 35
+•> S 4-> r-r
CO JJ r— C31
.C • 'r- (O 'r-
3 — I — I U_ CQ
3C 3C 3= Z Z
oo-S55
o o o o o
o o o o o
LO O O LO LO
^S- O «3- CM fo.
CM ^f CM LO LO
.CM CM CO CO CO
OO CO
•a- co
- f
LO rH
.00
rH CO
CTl rH
rH CO
CO
CM O
0 0
'•
,cn I-H
O'O
CO CO
CO «5T
CO CO
ro. LO
rH 1—4
O CM
VO CM
1—
CD "ZZ.
r- 1—
•r- ^
>. to
c to
C IO
•^ °
S in
£3
£_
CD
>
£
to
t— CO
CD c
> 0
as oo
to -^
•r- C3
r^ ^
O -•
CJ LU
1— 1—
o o
o o
O LO
CM CM
VO *^ CO ^* OO
CO CM r-4 i-H CM
LO co vo CM en
«3- CM rH 0 0
CTI'CO LO rH •*
t^ ^^ OO »^^ OO
CM rH
LO
co en ro. o CM
rH O O O O
.•^ CM rH O O
-
LO LO rH CO «*
OO fo. VO CM CO
«=}• co en I-H vo
O en ro LO to
rH
en co co I-H rH
(o, CM CM CM CO
CM LO rH CM
^^ t*^
CX3
»»-4 <_t
3—i2 «
S a- en>— i
•O ' ' • « 3 .
C JJ OS J2 '•>
(O CD t- CD'
r— C CD 03 r-
f— t» c "o en *
tO fO -i— OJ (O
> CO CD CD
•1- .1- > t_
a; as -r- cj en
OS C
CD ^^ £- -r-
.-Jf ^ c -S "o
-C i— -i— CD O
3 co a. o _i
3 S 3 3 S
0 O. O O 0
o o o o o
LO O LO LO LO
ro. vo «* vo «^-
CM «!j- vo oo i— i .
O O O O rH
^.
o .
l/> «5 <=> 1—
to its O O *-
CD i — en e_ to
,ifc iE £ S S
. •
CO .
OS C. SU Jbi
t- cj en CD
CD CO > C CD '
r- T- as ess cj
re os '
00 ^4 t- S-
• CD U O) (O
en c -a
•i— •!— r— -c— CO
CQ a. co as cj
SSSSH-
o o o o o
O O O O CD
O LO LO LO O
co LO en vo o
CM LO LO VO CO
rH rH rH rH rH
r. 11
-------
3
IO
at
*
T*
c
a
CJ
LU
«J
CD
*^C
1—
I.
3
0 "^
i— CM
1 f hurt
U"* rT;
E "«*.
•1—.
0£
CO
+J
1 *
s
c/3
CD CO
co cn
3D (13
CO
r^r-
CM CM
fH LO
O O
cn vo
P-. VO
CM i-H
co en
0 ^H
0 0
#
CO
O LO
o o
•*f CO
CM 10
CM CM
P*1* r~i
1— <
f«H r^
P-. i— i
CO ^T
i-H
A
CO
OJ
[ "CJ
5 *j"
CO
A
C t/)
CO T-
> ^"^
C£ CO
CO
c
O CO
c- c
5-
03^
*•
0 0
0 0
o to
cn CM
•—i CM
^"
o
o cn cn co
CM CO CM
• " -"
•3- CO LO CO
O «* CM O «3-
LO en en en en
to o I-H
CO LO .-H O
cn co T-H co
o o o o co
VO CO
cn co co vo
O «—< r-H O CM
10
CM O CM «=J- O
O «3- 'S- CO VO
^" LO cn *^* *™H
i-> *y to vo vo
co LO cn •— < vo
cn P^ vo vo »!r
CO CM CM
3
*™^ _^T
' *s 4-> SO
CJ 3 t- C rtJ
S5 CO
> T- CO
•r- o; t-
Q£ O
-U
^ o t. ^:
CO CO ^ 4->
(B OC > CO C_
CO -r- CO J^
i— U_ c «- .O
r-* - CO CD CO CQ
Z |E I-H eC w
O O O O O
O O O O O
O IO LO f- LO
., co to co r*-*»_ vo
en co •— i •— i o
CM CO ^3- -sf «3-
LO
o
cn «*• »-H CM
CO CO LO CM
"
co r^ CM I-H
1— t 1— < l-H O O
(— * P^ o cn ^°
i-l O IO CM LO
i— 1 i-H i-H CO LO
O O O •— < VO
CO CO ^H O O
o o o o o
r>. co
i— I O LO O '
r-4 r-l O O O
*sj* co co vo en
«3- CO CM I-H O
vo vo i— i r-. cn •
VO LO «3- LO *3-
-
co vo LO co en
P** ^* CM P^* ^"
CM i-H «3- LO CO
I-H
3
A .^J ^^
C ^""^ ^T ^C ^"^
0 S i-«
"cn co" « «jT'
e to c ns i—
•i- o •<- c: -> o 3
t_ c to i— t_
cSc^^
c^
CO
•r"" "^^ £••
o; co co
CJ U > «_
0£ >
c e £ _c S
O t- Ifl
4J O t- ••- J=
n3 -C -• -J ^ <: «c
O O O O 0
o o o o o
LO O O LO O
CM *3r r~» LO — i _1
A r\ I-H I— 1
, to «~l * 'O **
J3 CO IO i —
•r- J= CO •— .
C J-J C -u O)
C t- t_ c 3
= s<5<£li
c_
CJ C.
> CO
C-r- >
CO OC T-
> A^
•I- WJ
*^ r** CO CT ^^
CO C O CO
CO CO •!- -i- CO
£_ CO «3 i— t-
O J^ r- ^- O
03 Q. .i—
t. ^tf g ^J
» LO
CM o <— « «a- «a-
O i-H O -^ «3-
vo o «a-
«S- CO CM «*• CM,
•— t CO i-H LO CO
LO •— 1 CM P«- CM
O -C O - CO > CO
v- Ol •-- t_
oc t_ o; >, Or-
o -i- c- j= -u
•»~ o; nj o 4-J
j^* ^C? ^ * ^3
O C C T3 4->
« re 3 c co
•— 3 O CO 4->
sa co ea 3 t/5
1— 1— Q < C£.
O O 0 O O
o o o o o
CD CD LO O LO
LO CD «— « LO P»»
co r~> CM LO p^.
CO CO CO ^f •— «
CM
•— 1
-1
r-1? .
-------
'
T
•*->
w
o
c_>
u
LU
—1
<=Q
2
.
• 3'
' O •*"-*
«— CM
1 I !_(
<5 co
c. u
_i_\ ^~- .-•
oo
c
Q
o
•p—
^rt
O
o
— 1
CT
(O
C3
-
<
01
i — 11 Osl
O
P-I
cr 1 cr
cr
CM
o-
v— t
o
i-H
r*.
20-
Icy
iv"'
<0 C\P
» t— i o «3-
' P*» en ^j* en en
^ .«3- CM «S* •— I
O o r^ CM in
en o CM en «s-
vo o «a- in CM
f—4
in o vo co vo
in CM en co in
CO I-H f-4
• «c
3 " cr
c fa O) IB a)
»-H CJ — 1 2: OO
•
/C*
£_
-C
•f~ *f™ Cu &_
£ OS QJ OJ
O > >
t. 4J T- T-
>,r- {_ OS OS
-^ O QJ '
c/> .f— > >> ^
•r^ f^ trt
^£ JX Q^ r»« rtj
t. C « C
O O C 3 -H ^f
CM 00
O CO
CM CM
o r^^
in «*
O CM
co «a-
i— i
3 3
M A
1 :
p*™" ^^
r— ' (XJ
•SOS
£_
di
>
OS'
- s
*"^
C- 3
.Z
•p- O)
OS £=
fO -^
Q. t.
is oo
< «C
3 3'
O O
o o •
in o
CO «5l-
i-H CM
O C3
i en co co r^ in
. co in «* o I-H
CO OO CO CO i-H
CO PH i-H r-4 O
CO 00 O O CO
oo CM co en o
i-H p-4 i— t CO
in co «*> en I-H
o «3- CM I-H o
CM O O O O
o in o o o
CO CM I-H CM O
r^^ r^ en in r**
co, co *^* r** o
i— i
^- i— 1 O «— I «3-
^f ;^r co vo CM
CM l-H pH
VO O CM CO O
CM CO CM T-H O
co co vo CM in
CM
a
I-H Q
A ^
Q co "
i— i cj> aj
C OS C a. * •>
<- OO 19 3 t_
t- -COO)
•p- C «O i — Q.
3 -P- C •— O
.<^r?^'^5
^, c
t- d) OJ
S. U
£_•!-
> > -i- O OS
•r- -r- OS
OS OS C . in CM co I-H
«a- cc en I-H in
O i-l CM CO CO
CO
1—4
»3- VO CO i-H CM
CM p-4 CO CO CM
in ^ vo in ^^
O VO r-4 O i-H
in 1-4 en CM r^
in co o r*» en
rH i— 4 i— 4
•'•*
p-« co »sr en co
O CO i-H O CO
CO CM
co co in o co
O i—4 ^ CO 00
CM
in r^ r^, oo CM
co CM en o -H
co I-H co ^*
in I-H o CM in
vo ^ en I-H r*^
,co CM vo in
I-H m CM in P*.
vo *3- en CM oo
CO CO i—4 CM
OS
o
,- «
f^
0 • eC
• « oo c o
co a; o o
(/T NX
:, — c. o -i- o ,
O (O <** QJ (X3
CO — 1 (O = O-
• s~
p— 3 >
•1- C_ -r- O) •!-
OS « P*. m CM vo
i—4 in «3"CM CM
O O i-H CM CM
1—1 • '
' in
VO CM CM i-H «tf- O
in CM i— 4 vo "ff vo
p-4 CO i-4 CM P*. CO
o o o o o o
I-H I-H oo vo o CM'
CO pi CM CM .-4 CM
O OO i-H O •— 4 CM
000000
VO VO O CM
co oo 1— i co in «a-'
O I-H O O O I-H
vo oo ob vo en CM
co I-H o in co vo
CO I-H O f«
P-^ in oo ^* co co
en co I-H p^. p^ co
CM VO CO i-H O «*•
en CM in o co CM
in P-I.CM P«. co «^-
p-4 i— 1 r-H VO i-H
1-H
i
t_ •
o os es •
0 0 OS
. "OS OS O
JZ O O f » .
^3 * * fl3 * ^3
S • >> * • £
O • fl.» ^ O —
i— . • r«. {J £J >PH.
Jd QJ *f— t_ fO ^O
0- 2 Q CQ _J H-
• .
cu o t_
>
•i-
OS • +J -r-
_ 4J OS
13 eo co
•i— C- -r—
4-> U Ol 0) O
. C OJ > r— C
t— IB > *p- 4-> *r—
'03 OO .f— QS J-> i—
> * OS -I— r—
•p- • fl3 _l i— i
OS SI C 3
CO OJ 4-> SX £_ £_
- •— « j= o o
>>•!-> i — = U_ U-
£- +J (O
f3 «p- 3 * * •
S -J p— OO OO LU
es as es os os ' es'-
f-^ ^^ <"» CO ^"^ fj>
CO O O O C3 O
O 0 O O 0 O
o in in -o in in
i-H CM CO CM i-4 CM
r**» co o r-H
-------
-------
VII (0)
Revision No. 0
APPENDIX D '
Computer Program for the
Probabilistic Dilution Model - Point Source
. (PDM-PS) . "-
-------
-------
VII(D)
Revision No. 0
This appendix describes a computer program (PDM-PS) which performs
the computations of the Probabilistic Dilution Model for Point .Source
discharges using numerical methods based on quadratures. The program is
written in BASIC for the HP-85 and the IBM-PC, and should be readily applicable
to other personal computers with perhaps minor modifications to reflect
individual machine characteristics.
The program is structured around a slightly different input format -
than that used for the manual calculation using the moments approximation.
A series of normalizations (ratios) of certain of the input data items is
used to provide a computation framework that provides a more generalized
perspective. , .
The appendix is organized as follows. Section 1 describes the
basis for the formulation and normalization of the input data, as .used in
the program. Section 2 provides an annotated description of the CRT and
printer functions, as well as the nature-of the user's response. Figures
D-l and D-2 provide the results of running the PDM-PS through the example
described in Section 3.2 of this report. Finally, Figure D-3 provides a
Tisting of the PDM-PS program for entry into a personal computer.
Drl• Formulation and Normalization • .
The analysis can be made more useful in a general way if the
normalization described below is applied to reduce certain of the.inputs
;to readily recognized ratios, and to express results (stream concentra-'
tions) as a multiple or fraction of the target stream concentration (CL). .
D-l
-------
VII (D)
Revision No. 0
The explicit assumptions in the normalization scheme that is used
. . „ , . .
are that:
o The stream target concentration (CL) is produced when the
discharge flow is the mean effluent flow (TJE"), the discharge
pollutant concentration is equal to the permit effluent limit
(EL), and the stream flow is equal to the design value (here
designated 7Q10 - though any other basis may be used for desig-
nating the numerical value of stream design flow, e.g., 30Q5, '
30Q10, etc.).
o The'reduction factor (R = "CF/EL) determines the mean effluent •
concentration of the pollutant being evaluated. It could be
selected arbitrarily; however, as applied in this manual for
evaluating the permit averaging period, the value selected will
be dictated by the variability of effluent concentrations and
the permit averaging period.
In the usual case, where the stream target concentration (CL) is set at
the chronic toxicity level, the multiples .of the, target - in which stream
concentrations are expressed (CO/CL) - correspond with the acute toxicity
level. The basis for the normalization scheme adopted is as follows.
The downstream concentration, CO, is given by the dilution equation:
" - *'
co = QTTir*CE. ^
• '' " ' .
For a chronic criteria concentration, CL, the effluent limit concentration,
D-2
-------
vii (d)
Revision No. 0
EL, is computed using QS = 7Q10 and an average effluent flow, TJF:
'- CL = EWSTO (D-2)
where STO . (p.3)
However, the choice of permit averaging period forces a reduction of
"CF of magnitude, R, so that permit violations occur only 5 percent
or 1 percent of the time. Thus the actual long term average, effluent
concentration is:
?F = R EL = R CL/0STD . . (D-4)
The problem is to compute the probability that the downstream
\ ' . , .
concentration exceeds a multiple, 3, of the chronic concentration, CL. In
particular, if the acute criteria concentration is selected", then p is the
acute to chronic criteria ratio for the pollutant being regulated. Hence
It is necessary to compute:
Pr [CO > PCL] = Pr [CO > p
-------
VII (D)
Revision No. 0
and CE/CITis the normalized effluent concentration. The probability
distribution of this random variable no longer depends upon the mean
effluent concentration, but only on the coefficient of variation, VCE.
This is easily seen from the following representation of a log-normal
random variable:
InCE = InCE + Zo-lnCE (D-7)
t *^^ ' • '
where CE is the median,
-------
VII (D)
Revision No. 0
Note that QS/QE is log-normally distributed since both QS and QE are
assumed to be log-normal. Thus, only the ratio of the average flows,
WOE, is required. A convenient normalization using ratios that are
more, readily available results if the average effluent and stream flows
are standardized relative to design stream flow (here designated by 7Q1Q).
Defining
.. , Fl = 7Q10/QS ' (D-12)
F2 = 7Q10/QF ". _. {D.13)
Then
' ; \Wqr- F2/F1 ; (
and
These ratios, Fl and F2. together with the coefficients of variation,
VQS.VQE, and VCE, completely specify the characteristics of the random
variables in the normalized dilution Equation D-ll. R specifies the
effe,ct of permit averaging period and p, the acute to chronic criteria ,
ra-tio, specifies the toxicity behavior of the substance being considered.
This completes the normalization.
D~2- Description of Program Use
The program is easy to use. The values of the input variables are
sequentially requested on the CRT. Once the input values are entered, a
summary of the input data is printed out, as is a tabular listing of the
, : . D-s
-------
VII (D)
. Revision No. 0
results of the calculations. The user should be thoroughly familiar with
the theoretical and practical bases for the PDM-PS as described in Chap- -.
tens 2 and 3 before attempting to use the PDM-PS.
* • •
USER: Initiates program execution.
PRINTER: Writes'title.
CRT: Displays title and general descriptive material shown in
Figure D-l. • ;
CRT: Question #1 is displayed: "Enter coefficient of varia-
tion of QS, QE, and CE:"
USER: Enters the values of VQS, VQE and VCE, separated by
commas. *- . .
CRT: question #2 is displayed: "7Q10/avg QS?"
USER: Enters the ratio of the 7Q10 flow to the average stream
flow (TJS).
CRT: Question #3 is displayed: "7Q10/avg QE?"
USER: Enters the design dilution ratio, i.e., the ratio of 7Q10
flow rate to the average effluent flow rate (T|E").
CRT: Question #4 is displayed: "avg CE/EL?"
USER: Enters the ratio of the average effluent concentration
which the treatment plant will be designed to produce
(avg CE), to the effluent concentration derived from the
D-6
-------
VII (0)
Revision No. 0
WLA analysis (EL). This latter value is that concentra-
tion in the effluent which will result in the stream
target concentration being met, when the following flow
conditions prevail: , ,.
Stream flow (QS) is at the 7Q10 flow rate.
Effluent flow (QE) is at the average discharge rate of
f 1 ow.
PRINTER: Prints a tabular summary of the input data selected.
CRT: Question #5 is displayed: "Enter lowest, highest and
increment of multiple of target for which % exceedence -is
desired."
USER: Decides on a range of stream concentrations (expressed as
multiples of the target concentration1, CL) for which the
probability of occurrence and the recurrence interval are
desired. The user enters,(1) the lowest value, (2) the
highest value and (3) the incremental step desired for -
values between the highest and lowest.
PRINTER: Prints tabular listing of results. For each multiple of
CL, the exceedence frequency and return period are
listed. When the'printing is completed, a tone sounds
and Question 5 is repeated.
USER: Enters a new set of values for multiples of CL, if
D-7
-------
VII (D)
Revision No. 0
desired. This allows the user to conveniently search out
• •.,. .
the ranges of interest and select the most appropriate
levels of incremental.detail. When the desired amount of
output has been obtained9 the program is interrupted, and
begun again at Question #1 to examine another set of
conditions. The user can formally "end" the program by
entering 0,0,0 in response to Question 5»
D-8
-------
POINT SOURCE - RECEIVING WATER
CONCENTRATION ANALYSIS
INPUTS: COEF VAR OF QS,QE,C£
RATIO... 7Q10/avgQS
RATIO... 7Q10/avgQE
RATIp...ayg CE/EL
BACKGROUND STREAM CONC (CS)
IS ASSUMED TO BE ZERO
VII (D)
Revision No. 0
GENERAL DESCRIPTIVE MATERIAL
ENTER COEF VAR OF QS,QE,C£?
QUESTION
ENTER FOLLOWING RATIOS:
7QIO/avg QS ?
' '
.05
.7Q10/avg QE ?
.avg CE/ EL? -
•.67
ENTER LOWEST, HIGHEST, AND INCREM
ENT OF MULT OF TARGET FOR WHICH
% EXCEED IS DESIRED
?
ENTER LOWEST,HIGHEST,AND INCREM
ENT OF MULT OF TARGET FOR WHICH
% EXCEED IS DESIRED
7
2.5, 3, .05 . , ••..'..•
QUESTION #2
QUESTION #3
QUESTION #4 ,
QUESTION #5 (CONTINUES TO REPEAT
AS NEEDED)
Figure D-l - CRT displays,
'D-9
-------
VII (D)
Revision
No. 0
•***********************.**********
RECEIVING WATER CONC (CO)
PROBABILITY DISTRIBUTION
AND RETURN PERIOD
- FOR MULTIPLES OF TARGET CONC
DUE TO POINT SOURCE LOADS
*********************************
COEF VAR..»..QS =
COEF VAR.....QE =
COEF VAR.....CE =•
7Q10/avg QS =
7Q10/avg QE -
avg CE/ EL *
VIOLATION PERCENT
MULT OF OF TIME
TARGET EXCEEDED
1.00 0.894
2.00 0.112
3.00 0.024
• 4.00 0.007 •
5.00 0.002
2.50 0.050
2.55 0.046
2.60 0.043
2.65 0.040
2.70 0.037
2.75 0.034
2.80 0.032
2.85 0.030
• 2.90 0.028
2.95 0.026
3.00 0.024
1.50
0.20
0.70
0.05
3.00
0.67
RETURN
PERIOD
( YEARS)
0.3
2.4
11.3
39.4
114.4
5.5
5.9
6.4
6.9
7.4
8.0
8.6
9.2
9.9
10.6
11.3
TITLE
SUMMARY OF INPUT DATA
CALCULATED RESULTS .
Figure D-2 - Example of printed output
D-10
-------
t
Start
Clear screen
Print header
messages
Prompt for and
input coef. of
variations for
QS, QE.-CE
Prompt for and
input ratios
of 7Q10/QS,
7Q10/QE,
and avg. CE/CL
Compute normal
and reverse normal
coefficients
Prompt for and'input
lowest, highest, and
delta increment of
multiples of CO/CL
to use
. Print input values
and table header
1
Iterate on CO/CL values
Evaluate Q(x)
Compute return
. . period
Print CO/CL, % of time.
exceeded, and
•, return period
Next CO/CL
Figure D-3 - Flow chart for PDM-PS program.
-------
VII (D)
Revision No. 0
10
20
30
40
50
60
70
80
90
100
110
128
13©
140
150
170
180
190
200
210
220
233
240
259
260
270
280
290
380
1
i
!
i
i
i
i
i
i
i
i
t
t
I
!
t
i
i
i.
i"
t
i
i
;*
j
i
i
i
D
POM-PS
PROBABALI3TIC
DILUTION MODEL
FOR POINT SOURCE DISCHARGE
DEFINITION - INPUT TERM*
QS « STREAM FLOW
GE » EFFLUENT FLOW
CE - EFFLUENT CONCENTR.
7Qi0/av-gi3S = RATIO
SPECIFIED STREAM FLOW'i
7Q10/av-3i?E - DESIGN
EFFLUENT DILUTION RATIO
av^CE/EL = RATIO OF
THE SPECIFIED AVERAGE
PLANT EFFLUENT CONCENTR.
-TO THE EFFLUENT LIMIT
CONCENTRATION.
EL IS THE EFFL
CONC THAT PRODUCES THE
STREAM TARGET CONC WHEN-
AND QE=av-9i3E
DIM R5<32),Z5t32>
DIM R<8>,S8<8>
DIM PC
PRINT .
PRINT " RECEIVING WATER
NC PROBABILIT
ISTRIBUTION "
PRINT " • AND RETURN
IGD"
PRINT " FOR-,MULTIPLES OF
GET CONC. DUE TO POINT
URGE LOADS"
PRINT
320
330
340
350
360
370
380 D.ISP "POINT SOURCE - RECIEVI
NG WATER"
390 DISP " CONCENTRATION ANALtS
IS"
430 DISP
410 DISP "•
CO
Y D
PER-
TAR-
SO
420 DISP "INPUTS-- COEF VAR OF QS
RATIO...7(
RATIO...7C
450 DISP " RATIO... av<3 CE
•*30 DISP
v^QS"
440 DISP
470
480
490.
560
510
520
530
549
550
560
570
580
530
680
610
62>3
630
640
658
660
670
680
690
DISP
DISP "
C
BE ZERO
DISP
BACKROUHD STREAM
IS ASSUMED TO
DISP
DISP
ENTER .COEF VAR OF OS, ft
INPUT V1,V2.'..'3
DISP "ENTER FOLLOWING RATIOS
QS ".
i3E -,
EL " ?
COEF ;
COEF .
.COEF 5
Cli
• f *• + -r 4. 4.
DISP " ..
INPUT Fl
DISP "
INPUT F2
DISP " . i . . . av;-^
ERCENT" ; TAB <25 > .= " RETURN "
PRINT " TARGET "; TAB< 13) .= "OF
TIME"; TAB (. 25 > ; " PER IOD "
PRINT " "jTAB<13>;"EX
CEEDED";TAB(25>;" >
W3=SQR
-------
VII (0)
Revision No. 0
850
860
870
890
920
930
940
950
' .
960
970
980
990
1910
1 020
1030
1040
1 850
1070
1080
1090
1100
1119
1120
.1130
1140
1150
1160
1170
1180
1190
1200
1210
1220
1230
1240
1250
1260
1270
1230
,1290
1300
1310
1320
1330
1340
1350
1360
INPUT. B1,B2,B3
IF B1+B2+B3-9 THEN 1199
! - LOAD QUAD. WGTS. & ROOTS
GOSU8 1488
! - COMPUTE PORTION OF' GKH)
ARGUMENT IHDEP OF C©
DIM Z9<32>
FOR 1=1 TO NO
! - EVALUATE USING INV PROB
TRANSFORMATION
P9=R5
GOSUB 1380
Z9 < I > =LOG < 1 + EXP < U9-W9#X9 > > -U
3 ' • . . " ' ; ' .
NEXT I
! - CONCENTRATION LOOP
FOR C0=B1 TO BZ STEP B3
15=0
! — QUAD LOOP— EVALUATE. CK
X> = F AND SUM
FOR 1=1 TO N0
X= CLOG < C0 > +Z9 < I » /M3
X0=SGN
X=ABS-;X>
F= 1 +X* < 0 1 +X-* -, D2+X* < 03+X* < 04
+X* (. 05+X*06 ;• > > > ;
F=.-'5*FA-lb . • • .
IF X0>0 THEN 1090
F=1-F ' . '
I5=I5+F*Z5
NEXT I-
! — COMPUTE RETURN PERIOD
15=100*15
PRINT USING 1150'.: C8.I5.I0'-
IMAGE 2DZ.DD,5X,2DZ.3D, 5X,3
DZ.3D
NEXT C8
PRINT 8 BEEP
GOTO 840 -
FOR L=l TO 7
PRINT
NEXT L '
END
! -SUBROUTINE TO LOAD NORMA
L AND REVERSE NORMAL COEFFI
CIENTS
01=. 0,49867347
D2=;.0211410061 ,
03=.0032776263
D4=.0000380036
D5=.0000483986
D6=.000005383
! -n-t-++++++-
El=2.515517
E2=.802853
E3=.010328
E4=l.432788
E5=.189269
F6=.001388
1370 RETURN
1380 ! -SUBROUTINE TO COMPUTE IN
VERSE NORMAL TRANSF
1390 ! POLYNOMIAL APPP.OX TO INVE
RSE NORMAL TABLE
1400 DEF FNC*S9
RETURN
! -QUADRATURE SUBROUTINE -
'COMPUTE ROOTS AND WEIGHTS
! 15 = INTEGRAL
! R5 = N0 ROOTS C+- GR
USSIAN ROOTS «. N9/-2 LAGRR R
OOTS> ' .-•'.'
! Z5CN0.) = H0 WEIGHTS
!
! LOAD ROOTS AND WEIGHTS C0
R 32nd ORDER QUADS
! FIRST THE GAUSSIAN AND TK
EN THE LAGUERRE TERMS
! -QUAD ROOTS & WEIGHTS
16th ORDER GAUSSIAN
Rl=8
989400935 .
944575023
86563 12024
7554044084
R < 1 > =- .
R<2>=-.
R<3>=-.
R<4>=-.
R<5>=-.
R<6^=-.
6178762444
4530 1677.76
RC8>=-.
88. =.
S8<2>=.
S8<3>=.
S8<4>=.
S8<5>=. '
S8<6>=.
S8<7>=.
S8<8>=.
N0=4#P1
! CONVERT
WEIGHTS FOR
NTVL
09501250984
02 7. 1-5245942
06225352394
09515851168
1246289713
1495959888
1691565194
1826034154
1894506.105
(0,1''
ROOTS
INTEGP
.
1750 ! AND DIVIDE BY THO FOR COM
POSITE FORMULA
1760 FOR K2=l TO Rl
1770 R5=.5+.5*RCK2>
1780 R5=.5-.5*R
1790 Z5=S8X4
I860 Z5=Z5'
1810 NEXT K2 ,
1820 ! -LOAD THE LAGUERRE PfOOTS
- AND WEIGHTS, PROPERLY CON'VE
RTED
Figure D-4 (cont'd.)
0-13
-------
VII (D)
Revision No,
1S30 ! -loth ORDER LfiGUERRE ROOT
S & WEIGHTS
184Q P<1>=51.7011603395
1850 P<2>=41.9494526477
1860 P<3>-34.5333987023
1870 P<4>-28.5787297429
1880 P<5>=23.515905694
1898 P<6>=19.1301568563
19013 P<7>=15.4415273683
1919 P<8>=12.2142233689
1920 P<9>=9.43831433639
1938 P<10>^7.07033353505
1940 P-5.07801861455
1950 P<12>s3.43708663389
I960 P<13>=2.1292836451
1970 P<14>=1.14105777433
1980 P<15>s.462696328915
1990 P<16)=8.76494l04739E-2
2000 Q-4.16146237E-22
£810 Q<2>=5 0504737E-'13
2020 Q<3>-6.297967003E-15
2030 Q<4>=2.127079033E-12
2040 Q<5>=2.862350243E-18
2Q50 Q<6>sl.8S1024841E-8
2060 €K7>=6.828319331E-7
2076 Q<8>-1.4S4458687E-5
2030 Q<9^2.042719153Er4
2090 Q<10>-l.S4907094353E-3
2106 6<11>=1.12999000803E-2
2110 Q<12)=4.732S9286941E-2
2120 Q<13>=.136296934296
£130 Q<14>-.265795777644
2140 Q<15>=.331057854951
2150 Q<16>=.206151714953
2160 FOR K2-1 TO N0/2
2170
2180
2130 NEXT K2
2200 RETURN
Figure D-4 (cont'd.)
n-u
-------
VII (0) ,
Revfsfon Wo. 0
A>TYPE B:DILMOB.BAS -
10 REM -H.+-M.-M. PDM-PS
20 REK / • PROEABALISTIC
30 EEt-- DILUTION MODEL
40 REM FOB POINT SOURCE DISCHARGE
50 EEH. ' ' ' . ' • .
'55' EEK- AUGUST, 1984
60 REJa , IBK-PC AMD MS-DOS COMPATIBLE VERSION
70 REM HORIZON SYSTEl-S CORPORATION
80 EEK , (703) 471-0460
85 REM .
90 REIi •+*+-M
300 DIM R5#(32),Z5#(32)
310 DIM R#(8),S8>(8)
320 DIM P#(16),Q#(16),Z9#(32)
321 CLS
322 KEY OFF ;.'.•
330 PHINT n**
340 PRINT » BECEIVING WATER CQNC (CO) PROBABILITY DISTRIBUTION «
350 PRINT » AND RETURN PERIOD"
360 PRINT » • FOR MULTIPLES OF TARGET CONG"
370 PRINT « DUE TO POINT SOURCE LOADS"
380 PRINT f******«*****«**5*»***»s.*«»**«K«
390 PRINT "POINT SOURCE - RECEIVING WATER"
^00 PRINT "CONCENTRATION ANALYSIS"
•410 PRINT ' .
•420 FRUIT "H •! •! i i .
•430 PRINT "INPUT COEF OF VAR OF QS,QE,CE«
•440 PRINT " RATI0...7Q10/AVGQS"
450 PRINT n RATIO... 7Q10/AVGQS"
•460 PRINT "• RATIO... AVG CE/CL"
470 PRINT " BACKGROUND STREAM CONC (CS) IS ASSOKED' TO BE ZERO"
480 PRINT
490 PRINT
500 PRINT "ENTER COEF OF VAR OF QS.QE.CE"
510 'INPUT V1,V2,V3
520 PRINT "EHTEB THE FOLLOWING RATIOS:"
530 INPUT " ..... ..7Q10/AVG QS ";F1
540 INPUT "... ---- 7Q10/AVG QE tt;F2
550 INPUT "... ---- ..AVG CE/EL ":F3
560 PRINT
565 CLS
570 PRINT " COEF OF VAR.....QS = ";V1
580 PRINT » COEF OF VAR ..... QE, = «;V2
581 PRINT " COEF OF VAR, ____ CE = "-V3
590 PRINT '
600 PRINT « 7Q10/AVG QS = ";F1
610 PRINT " 7Q10/AVG QE = "jF2
620 PRINT " . AVG CE/EL = »:F3
630 PRINT ' '. ' . •
640 PBINT "-S-H
Figure D-5 - PDM-PS program listing - IBM-PC and MS-DOS compatible.
-------
VII (D)
Revision No. 0
720 i
730 V2cSQR(LOG(1+V2"2))
740 H3-SQR(LOG(1-f-V3~2})
750 W9=SQR(in"2+W2~2)
760 U9sLOGCF2/F1)+LOG(SQR(1+V2''2)/SGR(1+Vl''2))
770 L3=LOC-(F3*(1+F2)/SQR(1-t-V3~2))
7SO GOSDB 1160
790 PRINT "ENTER LOWEST, HIGHEST, AND IHCEEKEKT OF KULT OF TARGET FOR"
795 INPUT "WHICH $ EXCEED IS DESIRED";B1,E2,B3
796 IF B1+B2+B3=0 THEN GOTO 1120
797 CLS
BOB PRINT w COEF OF VAR QS = ";VT
804 PRINT « COEF OF VAR QE = ";V2
805 PRINT * COEF'OF'VAH CE = n;V3 .
806 PRINT
807 PRINT « '7Q10/AVG QS = ";F1
808 PRINT « 7010/AVG QE = ";F2
809 PRINT • AVG CE/EL = ";F3
810 PRIIJT ,
811 PRINT "•! I •! I -I 'I •! '1
812 PRINT ,
813 PRINT « STREAK COMC (CO)"
EU PRINT
.815 -PRINT n MULT OF";TAB( 13) ;nPERCEKT"-;TAB(25); "RETURN",
816 PRINT " TARGET ";TAE(13);"OF TIME";TAB(25);"PERIOD"
817 PRINT "(CO/CL) ";TAB(13);"EXCEEDED";TAE(25);"(YEARS)"
818 PRINT " «;TAB(13);" ";TA3(25);" "
820 EEM - LOAD QUAD. WGTS & ROOTS
83t) GOSUB 1410 ,
S^K) REI-1 COiffDT PORTION OF Q(X) ARGUMENT IIIDEP OF CO
850 FOR 1=1 TO NO
860 REK - EVALUATE USING IHV PROB TRANSFORMATION
870 P9£=R5£(I)
880 GOSUE 1310
S90 Z9f(I)sLOG(1-i-EXP(U9-W9sX9))-U3
900 NEXT I
910 EEK - CONG LOOP
520 F.OR CO=B1 TO E2 STEP 33
930 15=0
SlJO REK - QUAD LOOP - EVALUATE Q(X) = F AND SUM
950 FOR 1=1 TO KO
960 X={LOG(CO
970 XO=SGN(2)
980 X=
990 F=1
1000 F=.5*F"(-16)
1010 IF X0>0 THEii GOTO 1030
T020 Fs1-F
1030 I5=I5+F«Z5#(I)
1040 EEXT I
1050 REI« COHPUTE RETURN PERIOD
1060 10=1/365/15
' Figure D-5 (cont'd.) -j
D-16
-------
VII (D).
Revision No. 0
1070 15=100*15 -
1080 PRINT USING "###.### "; CO, 15, 10
1090 NEXT CO ••'.-.
1100 P?:INT CER$(7)
1101 INPUT "ENTER TO CONTINUE, OR 'STOP' ";A$ ' x
1102 IF A$OnSTOPw THEN GOTO 560 ' '"
1110 £EM GOTO 790 , .
1120 FOR L=1 TO 7 )
1130 PRINT . '•
1140 NEXT L •
1 1 45 KEY OH
1150 END
1160 HEM SUBROUTINE TO LOAD. NORMAL AND REVERSE NOBK4L COEFFIC^rTS
11~r LI =.049867347* ?
1180 D2=..021U10001-'- •
'ISO D3a.0032776263#
1200 D4=3.80036E-05
1210 D5=4.88906E-05 . -
1220 D6s5.383E-06 .
1230 REl'i
1240 El =2.51 5517 •
1250 E2=.302S53 " .
1260 E3=. 010328 .-.••-,
1270 £4=1.432788
1280 S5=. 189269 ' , .
1290 E6 = . 00.1308
1300 RETURN ' • ,
1310 RET: SUBROUTINE TO COMPUTE INVERSE iiOFj-iAL
1320 BEM POLYNOMIAL APPROX TO INVERSE TABLE
1330 EEF FlICa#)= X-J-(E1-i-E2*X#-hE
1340 S9=1
1349 IF P9#<1E-18 THEN P9#=1E-18
'1350 IF P9#<.5 TKBT GOTO 1380
1360 P9,?=i
1370 S9=-1
1380 P9i
1390 X9=FKC(P9#)*S9
1400 .RETURN
1410 REM QUADRATURE SUBROUTINE - COMPUTE ROOTS AND WEIGHTS
1420'REM I5=INTEGRAL
1430 REM R5(KO)= NO ROOTS
1440 REM Z5(KO)= NO WEIGHTS
1450 REM LOAD ROOTS AND WEIGHTS FOR 32ND ORDER QUADS
1460 REM, FIRST THE GAUSSIAN, THEN THE LAGUERRE TERt-S
1470 REK QUAD ROOTS & WEIGHTS FOR 16TH ORDER GAUSSIAN
T480 R1=8 •
1490 R#(1) =-.989400935*
1500 R#(2)=-. 944575023*
1510 R#(3)=-.8656312024#
1520 R#(4).=-.7554C44084# ;
1530 R#(5)=-.617S762444# ' ...'•-
'1540 R#(6)=-.458oi67776#
1550 E#(7) =-.2816035508* - -
Figure D-5 (cont'd.)
n_i7
-------
VII (D)
Revision No.
1560 M( 8)=-:. 09501250984*
1570 S8£(1)=.02715245942* ' ''
1580 S8£<2)=.06225352394* • '"
1590 S8£(3)=.Q9515851168* ' . ' '
1600 S8#(4)=.1246289713*
1610 S8£(5)=.1495959888* ' . . .
1620 S8#(6)=,1691565194* •
1630 S8#(7)=.1826034154*
1640 SS*(8)=.1894506105*
1650 KO=4*R1
1660 HEM CONVERT GAUSSIAN HOOTS & WEIGHTS FOR (0,1) INTEGR. INTERVAL
1670 REH AED DIVIDE BY TUO FOR COMPOSITE FORMULA
1680 FOR K2=1 TO R1
1690 R5#(K2)=.5+.5*R*(K2)
1710 Z5*(K2)=S8*(K2)/4 ' . .
1730 IffiXT K2
1740 REM LOAD THE LAGUERRE ROOTS AND WEIGHTS, PROPERLY CONVERTED
1750 'REH 16TH ORDER LAGUERRE ROOTS AND WEIGHTS
1760 P#(1)=51.7011603395*
1770 P#(2)=41,9404526477*
1780 P*C3)=34.5833987023*
1790 P£(4)=28.5787297429*
1800 ?£(5)=23.515905694*
1-310 P*(6)=19.1301568568* ' .
1820 P*(7)=15.4415273688* '
1830 P#(8)=12.2142233689*
1840 Pf(9)=9.43831433639* • -
1850 P#(10)=7.07033853505*
1860 P*(11)=5.07801861455*
1870 P#(12)=3-43708663389*
1880 P*{13)=2.1292836451*
1390 P*( 1-4) =1.14105777483*
1900 P#{15)=.462696328915*
1910 ?#(16)=.0876494104789*
1920 Q£(1)=4.l6l46237D-22
1930 Q£(2)=5.05C4737D-18
1940 p£(3)=6.297967003D-15 '
1950 Q^C-4) =2.1270790330-12
I960 G£t5)=2.862350243D-10 -
1970 Qf-(6) =1.8810248410-08
1980 Q#(7)=.0000006828319331*
1990 Ojf(8)=.0000l484458687*
2000 Q*(9)=.0002042719153*
2010 Q*(10)=,00184907094353*
2020 Q*(11)=.0112999000803*
2030 Q*(12)=.0473289286941*
2040 q*(133=.136296934296*
2050 QS( 1-4) =.265795777644*
2060 Q$(15)s.331057854951* '
2070 ^(163=.206151714958* '
Figure D-5 (cont'd.)
D-18
-------
VII (D)
Revision Wo. 0
2080 FOB K2=1 TO
2090 P.5£(X2+NO/2) =EXP(-P#(K2);
2100 Z5#(K2+NO/2)=Q#(K2)/2
2110 NEXT IC2
2120 RETURN •
A> - •' ' • ' ' •
RECEIVING" WATER CONG (co) PROBABILITY DISTRIBUTION
AND RETURN PERIOD
FOR MULTIPLES OF TARGET CONG
DUE TO POINT SOURCE LOADS
*«******««»«««*«$*«*»*»«*»*««****«***«*«***«*«*«£«**
POINT SOURCE - RECEIVING WATER
CONCENTRATION ANALYSIS
INPUT COEF OF' VAR OF QS,QE,CE
RATIO...7Q10/AVGQS
RATIO...7Q10/AVGQE
.RATIO...AVG CE/CL
'BACKGROUND .STREAM CONG (CS) IS ASSUMED TO BE ZERO
ENTER COEF OF VAR OF QS,QE,CE
71.5.2.7 '
ENTER. THE FOLLOWING RATIOS:
... ----- 7Q10/AVG QS ? .05 '
----- '...7Q10/AVG QE ? 3.0
.. ------ ..AVG CE/EL ? .67
COEF OF VAR.....QS =1.5
COEF OF VAR ..... QE = .2
COEF OF VAR ---- .CE = .7
7Q10/AVG QS = .05
7Q10/AVG QE = 3
:AVG CE/EL = .67
ENTER LOWEST, HIGHEST, AND INCREMENT OF MULT OF TARGET FOR
WHICH % EXCEED IS DESIRED? 1,5,1
COEF OF VAR QS' = 1.5
COEF OF VAR .QE = .2
COEF OF VAR CE s .7
7Q10/AVG QS = .05
7Q10/AVG QS a 3
AVG CE/EL = .67.
Figure D-5 (cont'd.)
D-19
-------
VII (D)
Revision No. 0^
STREAM COHC (CO)
MULT OF PERCENT
TARGET OF TIME
(CO/CL) EXCEEDED
1.000 0.894
2.000 0.112
3.000 0.024
4.000 0.007
5.000 0.002
ENTER TO CONTINUE
COEF OF VAR QS =
COEF OF VAR QE =
COEF OF VAR CE =
7Q10/AVG QS =
7Q10/AVG QE =
AVG CE/EL =
RETURN
PERIOD
(YEARS)
0.306
2.443
11.313
39.429
114.356
, OR 'STOP' ?
1.5.
.2
.7
.05
3
.67
ENTER LOWEST, HIGHEST, 'AND INCREMENT OF MULT OF TARGET FOR
WHICH % EXCEED IS DESIRED? 2.5,3,..1
COEF OF VAE QS' =
COEF OF VAR QE =
COEF OF VAR CE =
7Q10/AVG QS =
7Q10/AVG QE =
AVG CE/EL '=
Jlllllllllllllll'l I1 'I11! TTH
STREAM CONG (CO)
MULT OF PERCENT
TARGET OF TIME
(CO/CL), EXCEEDED
2.500 0.050
2.600 0.043
2.700 0.037 •
2.800 0.032
2.900 0.028
3.000 0.024
1.5
.2
.7
.05
3 •
.67
.RETURN
PERIOD
(YEARS)
5.501 -
6.395
7.410
8.558
9.854 .
11.313
ENTER TO CONTINUE, OR 'STOP' ? STOP
Figure D-5 (cont'd.)
-------