440484035
Dynamic Toxics
Waste Load Allocation Model
(DYNTOX)
USER'S MANUAL
Prepared for:
USEPA Mentoring and Data Support Division
Washington,' D.C.
Prepared by:
Limno-Tech, Inc.
Ann Arbor, Mi.
September 13, 1985
Racy clad/Racy clabla* Printed with Vegetable Oil Based Inks on 100% Recycled Paper (50% Postconsumer) Please recycle as newsprint
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PREFACE
This report represents a Users Manual to explain how to use the DYNTOX
model. This computer model was developed by Limno-Tech, Inc. under
direction from the U.S. Environmental Protection Agency Monitoring and Data
Support Division. It is designed for use in waste load allocation of toxic
substances. It uses three simulation techniques to calculate the frequency
and severity of instream toxicity at different effluent discharge levels.
The report is contained in two volumes, consisting of the User's Manual and
a separately bound appendix. The User's Manual describes the theory behind
each technique, their use in DYNTOX, and briefly discusses how to use
DYNTOX when performing waste load allocations. The appendix provides two
illustrative examples.
This report is not intended to be a discussion of the theoretical
characteristics and practical nuances of the three techniques. Some
introductory remarks are provided in these regards, but the primary
objective of this report is to provide use instructions for the DYNTOX
programs.
This project required the combined efforts of many individuals and
organizations. These are highlighted below:
Funding support was provided by the U.S. Environmental Protection
Agency Monitoring and Data Support Division (Contract #68-03-3131). Dr.
Elizabeth Southerland was project officer and provided invaluable insights
and direction to the project. Messrs. Tim Stuart and Mark Morris of EPA
also provided valuable administrative direction. Jack Kittle of Anderson-
Nichols is thanked for his assistance in supplying updated versions of the
ANNIE program. Dr. Dominic DiToro, Manhattan College is thanked for his
contribution to the log normal analysis aspects of the project. Drs. Paul
Rodgers and Raymond Canale of Limno-Tech, Inc. are thanked for their
conceptual ideas. Tad Slawecki and Dr. Derek Wong, also of Limno-Tech, Inc.
are thanked for their program contributions.
LTI, Limno-Tech, Inc. LTI, Limno-Tech, Inc.
Paul L. Freedman David W. Dilks
President Project Manager
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TABLE OF CONTENTS
TITLE PAGE
LIST OF FIGURES i
LIST OF TABLES iii
I. OVERVIEW 1
Background 1
Concepts 2
Organization of Manual 3
II. COMMON REQUIREMENTS 4
Model Access 4
Upstream Boundary Data 8
System Data 9
Effluent Data 11
III. CONTINUOUS SIMULATION 12
Theory , 12
Input Requirements 16
Program Use 20
IV. MONTE CARLO 34
Theory 34
Input Requirements 37
Program Use 41
V. LOG NORMAL 57
Theory 57
Input Requirements 58
Program Use 61
VI. PERFORMING WASTE LOAD ALLOCATIONS 72
Overview 72
Selecting Between Techniques 72
Allowable Effluent Loads 73
Multiple Discharges 74
Calculating the Return Period 75
Toxic Concentrations 76
VII. REFERENCES 77
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LIST OF FIGURES
FIGURE UILE
1 Example Session with ANNIE (Inexperienced User) ......... 6
2 Example Session with ANNIE (Experienced User)... ........ 7
3 Determination of Time of Travel Input Constants ........ 10
4 Continuous Simulation Modeling Schematic ............... 13
5 Concentration Frequency Curves ......................... 15
6 Hierarchy of Continuous Simulation Subprograms.., ...... 21
7 Example Session with Continuous Simulation Program
Entry ............................................... 22
8 Example Session with Continuous Simulation
System Constants ........................ ........... 2*
9 Example Session with Continuous Simulation
Effluent Specification .............................. 27
10 Example Tabular Display of Continuous Simulation
Inputs ............................... .- .............. 30
11 Example Plot Display of Continuous Simulation Inputs... 32
12 Example Plot Display of Continuous Simulation Results.. 33
13 Schematic of Monte Carlo Technique ..................... 36
14 Example Monte Carlo Input Distributions ................ 40
15 Hierarchy of Monte Carlo Subprograms ................... 42
16 Example Session with Monte Carlo Program Entry ......... 45
17 Example Session with Monte Carlo System Constants ...... 47
18 Example Session with Monte Carlo Specifying Effluent
Distributions ........................................ 48
19 Example Session with Monte Carlo Specifying Triangular
Distribution 52
20 Example Session Specifying Data Defined Distribution.... 54
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LIST OF FIGURES (Continued)
FIGURE TITLE PAGE
21 Example Session with Monte Carlo Viewing Results
in Plot Format 55
22 Example Session with Monte Carlo Viewing Results
in Tabular Format 56
23 Hierarchy of Subprograms for Log Normal 62
24 Example Sessions with Log Normal Program Entry 64
25 Example Session with Log Normal Input Specification 66
26 Example Session Performing Log Normal Simulation 68
27 Example Session with Tabular Output from Log Normal 69
28 Example Session with Plot of Log Normal Inputs 70
29 Example Session with Plot of Log Normal Results 71
ii
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LIST OF TABLES
TABLE TITLE PAGE
1 Input Requirements for the Continuous Simulation
Technique 17
2 Input Requirements for Monte Carlo Technique 38
3 Input Requirements for Log Normal Technique 59
iii
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I. OVERVIEW
Environmental contamination by toxic substances can pose risks to
public and ecological health. "egulttory agencies irt now establishing
regulations and procedures for determining al owable discharge 1 mits to
minimize those risks. Unfortunately, technology to define risks and
quantify allowable discharge limits is new or not widely used or understood.
This document serves to Provide instructions on the use of modeling
techniques for calculating allowable loading limits and the »«ocd
risks These techniques are incorporated in the DYNTOX portion of the ANNIE
interactive program.
Background
At present, most States which have regulations for setting allowable
discharge limits for toxic pollutants use steady state models to assess
exposure and calculate waste load allocations. These models are used to
calculate the allowable effluent load that just meets the chrome toxicity
water quality standard at a critical low flow. These analyses typically do
not consider issues of frequency and duration. They generally consist only
of a simple dilution equation; do not include instreatn processes; and only
examine a single environmental condition for a single discharge at a single
design specification.
In contrast, the extent of biological impairment from toxic discharges
depends on the duration of exposure above certain levels as well as the
number of times (frequency) these violations occur. Water quality criteria
now specify both duration and frequency of compliance. The duration and
frequency of violations depend on the daily variation in receiving water and
effluent flow, combined with daily variation in effluent toxicity. Therefore
dynamic models must be used to calculate'the frequency distribution of in-
stream concentrations for any given duration. The current durations of
interest are four days for chronic toxicity and one hour for acute toxicity.
The one hour duration period generally is approximated as a one day period
because hourly data are generally not available.
Modeling techniques are available that incorporate the effects of both
variable flow and effluent to calculate the frequency and duration of
exposure at different concentration levels. These more thorough methods
simulate the entire distribution of receiving water concentrations
(expressed in a probability distribution) rather than a single worst case
based on critical conditions. This allows each alternative control strategy
to be evaluated in terms of the total risk of toxic concentration. The data
used to define criteria for toxic levels of substances incorporate the
concepts of duration and risk. It is only appropriate that the procedures
used to regulate these substances also incorporate these concepts.
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Concepts
Ideally, it would be desirable to assess the Impacts of toxic
discharges on receiving water quality over the entire range of historical
and future conditions. These conditions would then be analyzed to define
frequency and duration of exposure above specified limits. Unfortunately,
on a practical basis this approach is impossible. However, three procedures
are readily available which estimate this range of conditions. These are:
1. Continuous Simulation
2. Monte Carlo Simulation
3. Log Normal Analysis
All three are included in the DYNTOX program.
Continuous Simulation uses the most direct approach. A mathematical
model is used to simulate a specified period of recorded history. This
approach uses a historical record of river flow and upstream conditions
combined with a historical or projected record of discharge flow and
toxicity. Results from this simulation are then analyzed for frequency and
duration of toxicity which are assumed to statistically describe the entire
record. The procedure requires an extended period of record but is simple
to execute and understand.
The Monte Carlo simulation technique is less direct but also involves a
simple approach. It uses a model as Continuous Simulation, but inputs are
not determined on a continuous basis. Inputs such as river flows, upstream
conditions, effluent flow and effluent toxicity are each defined
statistically by a distribution of historical or potential conditions. The
Monte Carlo model then repetitively selects sets of model inputs randomly
from among these statistical distributions. Statistical theory dictates
that the distribution of results from numerous repetitive simulations will
characterize the actual distribution of potential outcomes. This
distribution can then be used to define frequency and duration of toxics
concentrations. This technique requires either a good statistical
characterization for model inputs or reasonable assumptions.
The Log Normal analysis procedure is computationally less extensive
than the previous two simulation techniques but involves more complex theory
and certain restrictions. This procedure assumes all input parameters
follow a log normal statistical distribution. Statistical theory dictates
that under these conditions for a simple dilution model with one discharge,
the projected outcomes can be numerically determined. The procedure
incorporates the distributions into the model through numerical integration
and thereby defines the distribution of downstream water quality. This
distribution can then be used to define the frequency and duration
of different ' river concentrations. The procedure requires a proper
log normal characterization for all model inputs.
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The DYNTOX programs are at this time designed only for use in rivers
and streams. Kinetic interactions are restricted to first order losses.
Monte Carlo and Continuous Simulation are amenable to more sophisticated
situations which were not included in this study. DYNTOX can be used to set
up inputs for models of lakes and estuaries or for river models with more
complex fate processes. At present DYNTOX does not include models to
address these more complex situations.
Organization of Manual
The first chapter (after the overview) of this report describes those
aspects common to all three simulation techniques. This Includes general
operation of the ANNIE program, how to access the three probabilistic models
in DYNTOX, the required input data, and step by step procedures. The next
three chapters discuss the theory behind Continuous Simulation, Monte Carlo
simulation, and Log Normal. The final section includes a brief discussion
on how to select the most suited technique for an individual wasteload
allocation and qualitatively how to assess the reliability of the results.
Illustrative examples demonstrating the use of each of the three DYNTOX
techniques are bound separately as an appendix to this report. This
appendix also contains information on mainframe and microcomputer
installation of DYNTOX.
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II. COMMON REQUIREMENTS
The three analytical techniques contained in DYNTOX, although
conceptually quite different, have several common requirements. The first
common requirement is that the DYNTOX programs can only be accessed through
the U.S. Geological Survey model pre-processor program ANNIE. This
requirement was brought about to maintain consistency and continuity with
the use of ANNIE as a preprocessor for large mainframe computer models. For
future microcomputer adaptation of DYNTOX, the requirement of ANNIE-only
access may be discontinued.
All three analytical techniques in DYNTOX also require the same three
general types of input data:
1) Upstream data...used to describe flow and concentration in
the river upstream of the discharge(s).
2) System data...used to describe such processes as instream
decay, time of travel between outfalls, etc.
3) Effluent data...used to describe the flow and concentration
of each discharge.
Upstream boundary flow and concentration data can be obtained through
DYNTOX from STORET. In cases where STORET data are not available, the user
may enter data directly from the terminal. System data must be determined
by the user prior to performing any simulations. Effluent data must be
supplied by the user and may either be read from a computer file or entered
directly from the terminal.
This chapter describes the requirements common to all three
techniques: how to access the model and how to obtain the three types of
common required data in the appropriate format. Input format and inputs
specific to a given technique will be discussed later in their respective
chapters.
Model Access
Presently, DYNTOX is accessed through the computer program ANNIE. The
ANNIE program was originally designed and supported by the U.S. Geological
Survey in cooperation with the U.S. Environmental Protection Agency to help
users interactively create, check and update inputs to models and perform
the actual model simulation. Limno-Tech, Inc. has added the capability of
probabilistic simulation. Presently, the only way DYNTOX can be
accessed is through ANNIE. This section briefly describes the ANNIE program
and how it is used to access DYNTOX.
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ANNIE is a Fortran program designed for mini- and microcomputers to
help users interactively create, check, and update inputs to water-related
models. ANNIE can be used to reformat, store, list, update, and plot data
for models that require time-series information. ANNIE can be used to
submit prepared model inputs to their respective models for processing.
After model processing, ANNIE can also be used in the plotting and analysis
of model results. At present, ANNIE is designed to work with the Hydrologic
Simulation Program - Fortran (HSPF) and for the Precipitation/Runoff Model
System. Limno-Tech has now adapted it to include interaction with DYNTOX.
DYNTOX is contained wholly in the ANNIE package; it can only be accessed by
running ANNIE.
The first step in accessing DYNTOX is to install ANNIE on the computer
system to be used. If ANNIE has not yet been installed, this must be done
before DYNTOX can be accessed. Installation of ANNIE and DYNTOX is
described in the Appendix to this report.
Once the ANNIE program is installed and running, accessing DYNTOX is
quite easy. ANNIE is designed to give the model user as much help as
desired in choosing selections, and screens user responses for each question
against acceptable values. For any section, the user need only enter ? to
find the acceptable range of responses. Figure 1 shows the initial portion
of an example session with ANNIE for inexperienced users and Figure 2 for
experienced users. User responses are denoted by arrows. Note thct ajj.
user responses must be In capital letters. The first question determines
how much help information is given to the user. The responses "NO", "LOTS",
or "SOME" are acceptable for using DYNTOX. If the user specifies NO
experience, he will be given the opportunity to view several paragraphs
describing ANNIE. To stop this documentation, type NO when the prompt MORE?
appears. The third question requires the response DYNTOX. (Only enough
letters to distinguish your response from other acceptable responses is
required). Users with experience using ANNIE will be prompted for
information pertaining to User Control Input (UCI) files. This question is
not relevant to the use of DYNTOX and the answer to this question should
always be NO.
At this point in the session the DYNTOX programs are activated, and
the user may choose from the three possible techniques: Continuous
Simulation, Monte Carlo and Log Normal. A Complete description of program
operations for the three techniques will be given in the subsequent
sections, following a description of data required by all three techniques.
The user exits the DYNTOX session by selecting option 4, End Dynamic
Toxics Analysis. There will again be a prompt concerning UCI files. The
correct response to this question is DELETE (Figure 2).
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fEsecutior. begin*
*'
...... WELCOME TO "ANKIE'
...... VERSJOK DATES DECEK3ER 5. 1961
DO T0t5 HAVE MO. SOME, OR LOTS OF EXPERIENCE OSJNG AKKIE?
ANKIE helps prepare or update input to *>odel».
Also. AKKIE helps create and fi* the data for the tine-series
tile (TSS file) that it uaed by »o»e of the models.
Dor't be concerned about bad entries,
ANK1E guides you to acceptable responses.
When a question isn't clear, enter a question Bark bcted Routing R*:niall/Rur.of f prograt.
CREAM OS AR5 rainJall/runcf f Biodel.
RE'ORXA? mefcr»»ts CS6S, HOXA, KSPF sequential files
nc adif data tc TSS file fro: sequential files.
P^CT Piets data fror various sources to plotters.
ET*T3> Dji«ric Tcxicc Analyses.
Vet yet available.
. STAT . PRKS
:**» . 9JCT. . DTKTOX
«ftU- scat. OS PWXCSS DO TO'J WAKT TO OSE?
CT>?^
CTkAf C TUICt »>AiTSES
»r- c» n:"»:ra K TOV WAST TC USE-.
«» t^~:STC71 »IKr-AT:OS: DILUTJOK AJO DECA?
i; itr«-t CAB.S: c:-r7iOK MO DECAT
ijt yx-»3«F^. C:LUT:OK OK-_T
t«i M: ttrTW, HETURK TC AKKIE KEKU
«>n» »uirr:» n-4)
(Hit retorr let 4)
FIGURE 1
Example Session with ANNIE (Inexperienced User)
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/Execution be;in*
*
WELCOME TO "ANKIE"
» VERSION DATES DECEMBER 5. 1964
DO TOO HAVE HO. COKE. OR LOTS OF EXPERIENCE USING ANNIE?
SOME
WHAT MODEL OF PROCESS DO TOO WANT TO USE?
DT
ARE TOO WORM NO FROM AN OLD UCI FILE?
NO
DTKAKIC TOXICS ANALYSES
«-::«: TECHK:OUE DO TOV WAXT TO USE:
(i) COKT: K'JO'JS SIKV^>.TJOK: D:LCT;OK AK; DECAT
(2) MOKTI CARLO: DILUTION AK5 DECAT
(3) LOG-NORXJkL: DILtrTIOK OKLT
(4) EK3 DTKTOI, RETURN TO AKKIE KEN-J
EKTER SELECTION (1-«)
(Hit return for 4)
4
SAVE. LIST. OR DELETE TEKPORART OCI FILE
D
^Execution Terr.in«tei
FIGURE 2
Example Session with ANNIE (Experienced User)
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Upstream Boundary Data
DYNTOX requires data describing the daily river flow upstream of the
effluent discharges. Data describing these flows are maintained for most
rivers by the United States Geological Survey (USGS) and are available
through STORE!. Users should contact USGS State or District Office if they
have questions about whether the flow record needs to be adjusted for point
source inputs or water withdrawals. The first step in obtaining boundary
flow data for DYNTOX is selecting the USGS gaging station to be used. The
recommended location for the USGS gage is the closest gage upstream of the
first discharge. Care should be taken to ensure that no major tributaries
enter the river between the USGS gage and the first outfall. If no stations
are available that meet the above criterion, the nearest gage downstream
should be used. In this case, the user must enter the average point source
flow or water withdrawals above the gage to correct the daily record for
these effects. If the river is ungaged, it may be possible to use the flow
record of a nearby river with similar drainage characteristics and
proportion the daily flows by drainage area.
When the appropriate gage station has been selected, flow values can be
retrieved using the FLOSTR option of STORET. Details for this procedure are
contained in the STORET User Handbook (USEPA, 1982). The user must
determine if the streamflow has been regulated by dams at any time before
retrieving flow data for toxics analysis. This information is available in
the Water Resources Data book published for each state by the USGS. If
stream flow has been regulated, use only the data for the period which
represents existing conditions.
STORET data are also often available for describing upstream
concentration data. Since concentration data are usually taken at USGS
gaging stations, the same station used for flow data should be used for
concentration data. Unlike upstream flow, there are cases when STORET data
for upstream concentrations cannot and should not be used. The first such
case is when the USGS gage is located downstream of one of the modeled
discharges. "Upstream" concentration data in this case would be biased by
the effluent concentration and therefore not representative of conditions
upstream of the discharge.
STORET data are not stored in toxic units and cannot be used for
wasteload allocation modeling conducted using toxic units. In these cases
the user must enter the data manually during program operation.
Fortunately, in these cases a constant value will typically be used for
upstream concentration. This value should be set to zero unless available
data indicate that a different value is in order.
Concentration data is retrieved from STORET using the RETRIEVE command.
Further documentation on STORET retrieval is located in the STORET User
Handbook. Users can retrieve multiple parameters at one session; DYNTOX
will prompt the user for the desired parameter during program operation.
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System Data
Several types of information describing the river system are required.
These include drainage area ratios from each outfall to the USGS gage, time
of travel (velocity), withdrawals, and instream decay. The system data
requirements are very similar between techniques and are discussed in this
section. Specific examples of input for system data specific to each
technique will be given later in their respective sections.
The drainage area ratio from each outfall to the USGS gage is required
to determine the river flow immediately above each outfall by correcting for
other flow inputs. This ratio should be determined by dividing the total
drainage area for the river at the location of the outfall by the drainage
area for the river at the USGS gage. When possible, a planimeter should be
used to determine drainage areas.
Information on time of travel is required by the Continuous Simulation
and Monte Carlo techniques for calculating instream fate processes (instream
decay is not considered in the log normal analysis). Time of travel
information is necessary to describe passage from the upstream boundary
station to the first outfall and for the stretch of river between each
outfall (in multiple discharge situations). Time of travel information can
be obtained in one of two ways. First, dye studies can be conducted to
determine the time of travel for each required stretch of river. Second,
current meters can be used to calculate the average velocity in a reach.
Time of travel information is determined from velocity measurements by
dividing the length of the reach by the average velocity.
The user has two options for specifying time of travel. Time of travel
may be described as constant or varying as a function of flow. Flow-
dependent time of travtl 1$ recommended and is calculated by the equation:
TIM of Travel - aQb (1)
where Q is river flow »»6 a «nd b are constants. The coefficients a and b
can be determined by plotting observed time of travel (distance/velocity)
values at different flow* on a log-log scale (Figure 3). The coefficient a
is the y-intercept cf Iht b«st fit line through the data, while b is the
slope of the line. Hot* that b should be negative, as time of travel will
decrease with increasing flow. Typical values for b range from -0.34 to
-0.70 (Thomann, 1972). Constant time of travel requires only one input
value that will be used for all flow conditions, and should be used when
insufficient data are available to calculate flow-dependent time of travel.
The Continuous Simulation and Monte Carlo techniques in DYNTOX treat
the instream fate of a toxic as a first-order decay and therefore require a
first-order decay rate. Calculating this decay rate requires several data
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In Concentration
5 8
8
a>
i
3
Q)
r-t-
|Mh
O
o
ZJ
a
c
Q)
3
r+
V)
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points taken from different stations on the river with a known time of
travel and no pollutant sources between them. The natural logarithm of the
concentration should be plotted versus time of travel (Figure 3) on semi-log
paper and the decay rate calculated as the slope of the best fit line. This
decay rate can change with changes in treatment for future scenarios.
However, unless data are available to indicate otherwise, the same decay
rate observed in-stream should be used for all wasteload allocation
projections. When no in-stream data are available, the user should assume
zero decay.
The user must also determine if there are significant water withdrawals
(>1% of river flow) at any location over the stream section of interest.
The average daily withdrawal rate will be prompted for in each river reach.
Effluent Data
Effluent data can be entered manually from the terminal during program
operation or read from a previously created file. Required information
consists of the total number of data points, and a date, flow, and
concentration for each value. Care must be taken to use consistent units
between river flow and concentration and effluent flow and concentration.
That is, if river data have been entered using toxic units and cfs, effluent
data must also be in toxic units and cfs.
11
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III. CONTINUOUS SIMULATION
The most direct technique which can be used to simulate a probability
distribution for instream toxics concentrations is Continuous Simulation.
This technique directly predicts the concentration frequency distribution
below an effluent discharge (or series of discharges) based on an observed
history of upstream river flow and concentration. The Continuous Simulation
technique has many advantages as it considers:
o frequency and duration of concentrations;
o instream fate and transport;
o single or multiple pollutant sources; and
o cross-correlation and serial correlation of parameters by using an
actual historical sequence.
The primary disadvantage of the technique is that it requires a large and
mostly complete set of data on historical conditions. Another disadvantage
to Continuous Simulation is that computational requirements are
significantly higher than for steady state modeling or for Log Normal
analysis.
This chapter discusses the theory and application of the Continuous
Simulation technique, and is divided into three sections. The first section
discusses the theory upon which the model is based, and its advantages and
disadvantages. The second section describes the data input requirements.
The third and final section details how to use the computer model of the
Continuous Simulation technique when performing waste load allocations.
Theory
As shown in Figure 4, a Continuous Simulation model uses model inputs
for observed daily effluent flow (Q ) and effluent concentration (C ) and
combines these with daily upstream receiving water flow (Q ) and upstream
concentration (C ) to calculate downstream receiving water concentrations.
The concentrationudirectly below an effluent outfall (Cd) is determined from
the equation:
.?« VV... ,2,
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ime Historical
C-T. , . i . . J
Standard
% Less Than
Continuous Simulation Modeling Schematic
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This technique assumes complete lateral mixing in the river. The
model predicts a simulated history of instream concentrations in
chronological order corresponding to the same time sequence of the model
inputs.
The calculated daily downstream concentrations are ranked from the
lowest to the highest without regard to time sequence. A probability
distribution plot is constructed from these ranked values, and the
recurrence frequency of any concentration of interest can be obtained (Cd
vs. frequency). Running average concentrations for four days, or for any
other averaging period, can also be computed from the simulated
concentrations, ranked in order of magnitude, and also presented as a
probability distribution (see Figure 5).
The Continuous Simulation model can predict the concentration below
each of a series of discharges. Successive concentrations downstream are
calculated progressively from the concentrations upstream on a day by day
basis. Equation (2) is used to calculate the concentration downstream of the
first discharge. The concentration further downstream but immediately
upstream of the next discharge is calculated according to the following:
cu - Cd * O)
where: C - concentration above the second discharge
Cd - concentration below the first discharge
k - first-order decay rate
t - time of travel between discharges
The exponential term including the decay rate k represents any first order
instream loss. Effects of subsequent discharges are calculated successively
using equation (2) and (3). River flow above any particular discharge is the
sum of the upstream boundary flow plus all additional flow inputs, including
discharges.
The probability distribution plot generated by the Continuous
Simulation technique will indicate the predicted frequency of criteria
violations. These frequencies can be compared for different effluent
alternatives. If evaluations of recurrence intervals of 10 or 20 years are
desired, then at least 30 years of flow data should be available. This is
needed to provide a sufficiently long record to estimate the probability of
rare events. (The same data requirements are also true for the Log Normal
and Monte Carlo methods).
The Continuous Simulation model has three primary advantages compared
to steady state modeling, Monte Carlo and Log Normal analysis. First, the
advantage over steady state modeling is that Continuous Simulation can
predict the frequency and duration of toxicant concentrations in a receiving
14
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50
O
30
c
O)
20
c
O
S 10
.O
I day
_^^^ 4days .^--
^' ^.
tar, " 30days_
l
JL
1
99 99-5
Percent of Time Concentration is Less Than or Equal To
i
100
20
Recurrence Interval (years)
FIGURE 5
Concentration Frequency Curves
(from USEPA, 1981)
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water; steady state analysis cannot. Second, the inclusion of Instream
fate processes is an advantage over Log Normal, which cannot simulate
instream fate and is limited to simulations for one effluent discharge.
Third, by using simultaneous observations for all input parameters, the
Continuous Simulation model can directly incorporate the observed effects of
serial and cross correlation of inputs. When calculating four day
average instream concentrations, Continuous Simulation correctly does the
averaging on the model results. Monte Carlo and Log Normal estimate four
day average instream concentrations by averaging model inputs.
The primary disadvantage of Continuous Simulation is the large data
requirement. A long period of historical data is required for all
parameters. Although time series data can be synthesized for missing
parameters, synthesis of time-series data for more than one parameter
greatly reduces the reliability of this technique. Additional data are
required for the calibration/verification of instream fate processes. A
second disadvantage to Continuous Simulation is the large requirement of
computer time and storage; however, recent advances in computer technology
have minimized this problem.
Input Requirements
The model input requirements for all three techniques were discussed
in Chapter 2. This section details the specific input requirements for
the Continuous Simulation technique. The inputs can be generally
categorized into four groups:
o general simulation requirements,
o upstream data.
o effluent data, and
o system physical *nd hydrologic constants.
All of these inputs «rt summarized in Table 1, and will be discussed
individually in thn stctior..
General Siwu'at^o* Requirements: The Continuous Simulation method
requires some general information on the system that will not change between
simulations. The first taste input required for Continuous Simulation is to
establish the period of the simulation. This consists of the beginning
and the end date of tht simulation, which must contain all or a portion of
the streamflow record. This period should be as long as possible, since
the power of the Continuous Simulation technique increases with the amount
of observed data. The user should select a period for which a complete and
consistent data set is available. Caution should also be directed against"
using old data which are no longer representative of current conditions.
16
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o General Information:
- Beginning and end date of simulation
- Number of discharges above flow gage
- Average point source flow above gage
- TSS computer field name
Data Source
USGS flow records
User defined
Treatment records
User defined
o Upstream Data:
- Time series flow data
- Data synthesis technique for flow
- Time series concentration data
- Data synthesis technique for concentration
STORET
User defined
STORET
User defined
o Effluent Data:
- Time series flow data
- Data synthesis technique for flow
- Time series concentration data
- Data synthesis technique for concentration
Treatment records
User defined
Treatment records
User defined
o System Constants:
- Time of travel information
- First order decay rate (s)
- Drainage area ratio (s)
- Water withdrawal rate (s)
Dye studies,
current meters
Instream data
USGS topographic maps
Withdrawal records
Table 1. Input Requirements for the Continuous
Simulation Technique
17
-------
The second basic input required by Continuous Simulation is the number
of discharges in the system. The user must also determine if any of these
discharges are located upstream of the USGS gaging station; if so, the
average point source flow above the gage must be determined in order to
correct recorded streamflows for this input. The final general input
required is a computer file name to store these inputs. Once these general
inputs are specified, they will be stored in this computer file and need not
be specified for later simulations.
Upstream Boundary Data: The Continuous Simulation technique requires time
series information on upstream boundary flow and concentration, and effluent
flow and concentration. The Continuous Simulation technique requires a data
value for each individual day of the simulation. Typically many "holes"
will exist in the data set, days which have no data for a given parameter.
A method to synthesize or fill in data for missing days is required. Three
methods are available for synthesizing missing data for the Continuous
Simulation technique:
1. linear interpolation
2. simple Markov synthesis
3. multi-period Markov synthesis
Each is briefly described here as needed for use in this program. The
reader is referred elsewhere for a more thorough theoretical discussion
(Fiering and Jackson, 1971).
Linear interpolation is the simplest method. It synthesizes missing
data by linearly interpolating between the available observed data values
that bound the missing value. This method should be used in cases where
data are available over the majority of the period of record and only minor
"gaps" need to be filled in. When synthesizing missing upstream flow data,
linear interpolation is the only method which should be used. Also, linear
interpolation will produce a constant value repeated over the entire
simulation when one observed data point exists.
The second method of data synthesis is a first-order, lag-one Markov
process, referred to herein as simple Markov. With this technique, data for
a given day are randomly determined from the overall data mean, overall data
variance, the previous day's value, and an auto-correlation coefficient.
The auto-correlation coefficient is a measure of how closely a given day's
value is related to the previous day's value. The Markov process in DYNTOX
assumes that daily fluctuations jn model inputs are normally distributed.
DYNTOX assumes an initial mean value and generates 50 data points in order
to determine the first value used in the simulation. The only user input
required by the simple Markov process is the auto-correlation coefficient.
These coefficients can be determined using the SAS routine AUTOREG (SAS,
1982). A value for the auto-correlation coefficient of 0.7 is recommended
18
-------
if insufficient data are available for calculation from observed data. All
other coefficients will be determined from the observed data by the program
itself. The only exception is the case where less than three data values
exist, in this situation the user must manually specify mean and variance or
choose another method of data synthesis.
Multi-period Markov synthesis is the third technique and involves a
third, more complex level of synthesis. The simple Markov process assumes
that the process for which data is synthesized is "stationary" over the
period of simulation; that is, the mean and variance remain relatively
constant over the entire period of the simulation. The multi-period Markov
process is designed to handle cases of non-stationary processes, where the
mean and/or variance are known to change over time. The primary example of
a non-stationary process is effluent flow from batch treatment. In this
situation flow may be zero for several days during treatment, then
non-zero for the next few days during discharge. The multi-period Markov
process allows the user to divide a non-stationary process into as many
repeating stationary periods as necessary. Each period requires data
describing its mean value, standard deviation, and auto-correlation. These
values must be calculated before performing a waste load allocation. Using
the batch treatment flow as an example, the user would specify two periods
to describe the process. The first period would have a mean and standard
deviation of zero and a length equal to the duration of the treatment
period. The second period would have an appropriate mean and standard
deviation and a length equal the duration of the discharge. DYNTOX then uses
a Markov process to repeat the two periods until a data value for each day
is generated.
Effluent Data: Similar to upstream data, daily input values are needed in
the model for effluent flow *nd concentration (or toxicity). The source of
these data must be uitr specified. As for the upstream data, gaps are
likely to exist in any data set. Here again, the user must use either
linear interpolation, staple Markov, or multi-period Markov to synthesize
data for missing days. Any downstream tributary inputs occurring between
discharges should be co«Hd«r«d as a separate effluent input.
System Constants: Systt* constants need to be defined for hydro!ogic and
physical characteristics of the system. Model inputs for physical data
include time of passage b«t«»e*n locations and instream loss rates. Time
of passage must be defined for the stream segment between the upstream
boundary station and the first discharge, as well as for the segments
between each discharge. The coefficients used to define the time of passage
were discussed previously in the Common Requirements chapter. Instream
losses are defined by a first-order decay rate, and are held constant in
each reach throughout the simulation period. The method for determining the
first-order decay rate was also discussed in the Data Requirements chapter.
19
-------
Program inputs for hydrologlc data are needed to properly adjust gauged
flow data to determine instream flow at different locations. Ratios are
needed to define the comparison between the gauged drainage basin area and
the drainage basin area at the point of discharge. These ratios adjust the
USGS measured flows for non-point sources, and must be specified regardless
of the location of the gaging station. For discharges located downstream of
the USGS gage the ratio (and adjustment) will be greater than 1.0. For
discharges located upstream of the gage, the ratio will be less than 1.0.
The method to be used for specifying drainage area ratios is described in
the Common Requirements chapter. A second hydrologic adjustment is required
for water withdrawals. If a significant amount of water (>1% of river flow)
is withdrawn from the river at any location, this witnarawal rate must be
specified before performing a Continuous Simulation waste load allocation.
Program Use
The Continuous Simulation program, like the programs for the other
techniques, is divided into menu driven sub-programs (entitled activities)
to allow the user as much flexibility as possible in performing simulations.
The hierarchy of activities for Continuous Simulation is shown in Figure 6.
This section will describe how to use the Continuous Simulation program and
will discuss the options available. It is divided into sections describing
each of the primary activities of Continuous Simulation:
o Program Entry,
o Input Specification,
o Model Simulation,
o Viewing/Analysis of Input Data,
o Viewing/Analysis of Simulation Results, and
o Ending Continuous Simulation
Program Entry: The first activity of the Continuous Simulation technique is
termed Program Entry. This section involves either the initialization and
development of the basic input file or the specification of an existing
file. Initial data include those data and information which typically would
not be changed in alternative simulations. They include the period of data
record (duration of simulation), the number of discharges, and the data base
used to define upstream flows and concentration. Modifications to the data
including data interpolation, loss rates, and effluent inputs are handled in
another activity (entitled Input Specification) because these factors may be
changed in alternative simulations.
Figure 7 shows example sessions with the Program Entry activity. The
first questions in Program Entry concerns the existence and location of the
TSS files used for the simulation. Time Series Store (TSS) files are created
by ANNIE to hold all time series information for a system, such as the
period of simulation and observed flow and concentration data for upstream
20
-------
Input
Specification
Model
Simulation
ro
Program Entry
/Menu j
VI en/Analyze
Inputs
h-
ze
VleN/ Analyze
Kcsults
End
Continuous
Simulation
1
Svsio
Constants
.
LI fluent riu*
1
Concentration
Mdtmauv
Conditions
1
did Input
Spec II leal ion
FIGURE 6
Hierarchy of Continuous Simulation Subprograms
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7b. Existing TSS File
ENTES SELECTION (1-4)
(Hit return for 4)
KAVE YDS PREVIOUSLY CREATE? A TSS FILE FOR THIS SIMULATION?
£"7 JS THE KAKE OF YOUR TSS FILE?
EXAMPLE
terminal Entry of Data
HAVE TO'.' PREVIOUSLY CREATED A TES FILE FOR THIS SIKVLATION?
N"^
Vr:A7 IE THE KAMI OF TCVf NE- TJ5. FILE'
ENTE="BEC:NNIN:. AK: ENDING DATES FOR
EK7ES S7AS71KG DA7E.
EK7E? ES~:NG DATE.
HOV"KASY30-.TFALLS ARE THERE IK THE SYSTEM?
(Hit return lor 1)
HOV KAKT. OUTFALLS LIE ABO^ THE FLOW CAGE?
(Hit return tor 0)
0
PLEASE WAIT VX:LE TOUR TEE F:LE is INITIALIZES ...
INITIALISATION OF TOLTt TSS FILE IS KOK COMPLETE.
DC TOV KA\T A STORE7 FLOW DATA FILE?
j
WXAT IS THE KAKE OF THE STORI7 FILE?
US£ V>::CK SATA SET?
Kit rtt^rr- lor "
WHAT IE THE KAI'.MV. ACCEPTABLE FLOW VALUE?
(Hit return icr 0. )
ei
-------
CONTIK'JO'JS SIMULATION TECHNIQUE
PLEASE CHOOSE FROM THE FOLLOWING:
(1) SPECIFY HODEL INPLTS
(2) RUN THE SIMULATION
(3) V1EW/ANALYIE THE IKPUT DATA
(«) VIEW/ANALYZE THE SIMULATION RESULTS
(5) END CONTINUOUS SIMULATION
ENTER TOOT CHOICE (1 - 5):
(Hit return for 1)
1
PREPARE KODEL INPUT TI MISERIES
(1) SPECIFY SYSTEM CONSTANTS
(2) SPECIFY OUTFALL FLOWS AND CONCENTRATIONS
(3) READ UPSTREAM BO-TCARY FLOWS AND CISCENTRATIONS
(4) EVD T:KESES:ES DEFINITION AW RETURN TO CONTINUOUS
S:KULATION KEKU
ENTER YOUR CHOICE (1 - 4):
(Hit return for 1)
SYSTEM CONSTANTS
IKPUT DATA FOR EACH REACH
SYSTEM CONSTANTS FOR REACH 1. BETWEEN UPSTREAM BOUNDARY AND FIRST OUTFALL
HOW DC YOU VANT TC SPECIFY THE TIKE OF TRAVEL?
(1) CONSTANT
(2) AS A FUNCTION Or FLOW
ENTER YOUR CHOICE (1 OR 2):
(Hit return for 1)
. i
WHAT IS THE TIKE OF TRAVEL IN DAYS
(Kit return for 0.1)
. . 1
WHAT is -THE FIRST ORDER DECAY RATE?
(Kit return for O.D
WHAT is THE AVERASE WITHDRAWAL?
-o.
WHAT is THE DRAINAGE AREA RATIO FROM THE uses GAGE?
(Hit return for 1.)
-1.
FIGURE 8
Example Session with Continuous
Simulation System Constants
24
-------
conditions. The first time a simulation is performed the user should
answer NO to the question asking if a TSS file was previously created
(Figure 7a). This will initiate the process to create a file. The user
should answer YES to this question in subsequent simulations, and no other
information will be required in the Program Entry section (Figure 7b).
For first time entries, the TSS file name must be supplied. Any file
name can be used that is compatible with the computer system. The next
inputs required are the beginning and end dates of the simulation which
define the extent of the input data base. The required format for these
dates are Year/Month/Day. Months and days with only one significant figure
of information may be entered using one digit. Four digits are needed to
define the year. The last question before creation of the TSS file concerns
the number of discharges in the system.
At this point in Program Entry, the TSS file for the system is being
created and initialized. This may take some time, depending on the computer
system used, but the user will be informed when the file initialization is
complete. TSS files created during Continuous Simulation can be used for
either of the three interactive programs contained in DYNTOX.
The final portion of Program Entry concerns defining the upstream
boundary data files. Figure 7a shows an example session where both the
boundary flow and boundary concentration data are located in STORET files.
The user need only specify the location of the STORET data file and
which data set of the STORET retrieval is desired. The data set number
selected by the user should be one, unless multiple data sets were stored in
the same file during the STORET retrieval. This section also provides the
ability to correct the STORET data and screen out flow and concentration
values above acceptable values. Observed data above the maximum acceptable
value are set to this cut-off value.
The final possibility for Program Entry is when the user has no STORET
data and wishes to enter observed flow and concentration data manually from
the terminal. Figure 7c shows an example of this situation. The user is
required to input the number of data values and then the date and
concentration for each value. The proper format is date and value with the
date being in the YYMMDD (two digits for year, two digits for month, two
digits for day) format.
After completing Program Entry, the program enters the main portion of
the Continuous Simulation program. The user will be given the menu shown in
Figure 9 and must select one of the five activities:
1. Input Specification
2. Model Simulation
3. View/Analyze Inputs
4. View/Analyze Results
5. End Simulation
25
-------
Although there is some flexibility 1n the order 1n which activites are
selected, inputs must be specified before choosing any other option (except
ending).
Input Specification: Selecting Input Specification provides a new menu
involving four subtasks: 1) System constants, 2) Effluent flow and
concentrations, 3) Boundary condition data, and 4) Ending input
specifications. These four tasks can be selected in any order desired.
The first task of input specification pertains to the system constants:
time of travel, first-order loss rate, drainage area ratio, and water
withdrawal rate. Program operation for this task is very straightforward,
requiring only the Inputs discussed in the data requirement section. An
example session specifying system constants is shown in Figure 8.
The second subtask of input specification covers effluent flows and
concentrations (Figure 9). The user has the option of entering data
directly from the terminal or having the data read from a file. The
required format in both cases is the number of data points followed by the
date, flow, and concentration for each observation on a line separated by
commas. The proper format for the date is YYMMDD.
Next, the user must specify the desired data synthesis technique used
to define data values missing in the input data file. This method is
selected first for effluent flow and then for effluent concentration. The
specifics of the data synthesis techniques were described in the Upstream
Boundary Data section of this chapter. The implementation of these three
techniques is quite simple. For linear interpolation (see Figure 9a), no
additional user inputs are required. The first-order Markov process
requires user specification only of the auto correlation coefficient (Figure
9a) since the program Internally computes the mean and standard deviation of
the data. The user has the ability to calculate coefficients from the data
or to override the statistics and input any selected values. Where
sufficient data are not available for the program to calculate statistics,
the user must manually specify statistics or choose a new technique. The
multiple-period Markov process requires somewhat more user input than the
other data synthesis techniques (see Figure 9b). The first input is the
number of repeating periods to be used. For each repeating period, the user
must manually specify the mean value, standard deviation, and auto-
correlation coefficient.
The boundary data task involves completing the input data file for
upstream flow and concentration. This also requires the selection of a
technique to fill in missing data. The program requires specification of a
data synthesis technique both for boundary concentration and flow. The same
procedure used for synthesis of effluent data applies for synthesis of
boundary data. Linear interpolation should always be selected as the data
synthesis technique for boundary flow, since a thorough boundary flow data
set is essential to the proper function of Continuous Simulation.
26
-------
9a. Linear Interpolation and Simple Markov
PREPARE M5DEL XKPUT TIKESERIES
(1) SPECIFY SYSTEM CONSTANTS
(2) SPECIFY OUTFALL FLOWS AND CONCENTRATIONS
(3) READ UPSTREA" B3UK3A.P.Y FLOWS AND CONCENTRATIONS
(4) END TIKESERIES DEFIKITIOK AND RETURN TO CONTINUOUS
SIMULATION' K£S"J
ENTER TOUR CHOICE (1-4):
(Hit return for 1)
2
IS TOUR EFFLUENT DATA IN A FILE?
NO
D:SCHAS3E I 1
H5'» MANY POTS DC TO'J HAVE FOR THIS DISCHARGE?
(Hit return Jor 4)
3
EVTES DATE, FLOW. A«O COKCEKTRATIOK FOR EACH SAMPLE:
6CC2C2. 25.. 1.
6::«:4. 22., .
6:cs:3. 2t., .7
3 PC:KTS REA3
DATA STKTHESIS FOR EFFLUEKT FLOW
W-1AT TECHNIQUE DO YOU WAST TO USE TO SYNTHESIZE KISSING DATA
(1) LINEAS INTERPOLATION (OR CONSTANT VALUE)
(2) FIRST CR3ER KARXOV
(3) MULTIPLE PtR:03 KASROV
ENTER 1-3
(Hit return for 1)
- 1
DATA SYNTHESIS FOR EFFLUENT CONCENTRATION
WHAT TECHS:SUE DO TOU WAKT TO USE TO SYNTHESIZE H:SS:NS DATA
(D LINEAR INTE?.PCLAT:ON (OR CCSSTANT VALUE)
(2) FIRST ORZ'ER KARKOV
(3) KJLTIPLE PEruOD KASKOV
ESTER 1-3
(Hit return for 1)
2
KEAN VALUE !S 0.83333
STAVLARD rrviAT:oN is c.iszis
IS TKIS ACCEPTABLE?
Y
WriAT IS THE AUTO-CCK3ELATION CCEFF1CIEKT FOR THIS PARAMETER
(Hit return for 0.)
- .7
FIGURE 9
Example Session with Continuous Simulation
Effluent Specification
27
-------
9b. Multiple Period Markov
DATA SYNTHESIS FOR EFFLUENT FLOW
WHAT TECHNIQUE DO YOV WANT TO L'SE TO SYNTHESIZE KISSING DATA
(1) LINEAR INTERPOLATION (OR CONSTANT VALVE)
(2) FIP.ST CRCER MARKOV
(3) MVLTIPLE PER;os KARKSV
ENTER 1-3
(Kit return for 1)
PARAMETER SPECIFICATION FOR KVLTIPLE PERIOD KARKOV PROCESS
HOW KANY REPEATING PERIODS DO YCV WANT TO USE
(Kit ret-jrn lor 2)
2
DESCRIBE FErlOD 1
HOW KANY DAYS IN THIS FEPIOD
(Hit return for 1C)
10
V>:AT is THE KEAS VALVE FOR THIS FER::D
(Hit return for 1.)
25.
VriAT IS THE STANDARD DEViATICS fZr T.-1I S PE?.ICD
(Hit return for 0.)
-3.
WHAT IS THE A1TO-CCRHE1ATIOK CCE'FICIENT DVr.ISG THIS PERIOD
(Hit return for 0.)
- .7
DESCRIBE PERIOD 2
KO'-- KANT SAYS IN TrIS PERIOD
(H:t return for 10)
-3
WHAT IS THE KEAN VALVE FOR THIS FESICD
(H-.t return for 1.)
- .01
WVAT IS THE STASDASD DEVIATION FOR THIS PERIOD
(Hit return for C.)
- . DC i
WHAT IS THE AVTO-COR?.EI.ATION CCE'-ICIENT CVRIN5 THIS PERIOD
(Hit return for 0.)
- .7
FIGURE 9 Cont'd.
Example Session with Continuous Simulation
Effluent Specification
28
-------
The final task of Input specification Is to end and return to the main
Continuous Simulation menu. This option may be selected at any time;
however, to run a simulation the previous three options must all_ be
successfully executed.
Model Simulation: The model simulation can be conducted any time after the
inputs have been fully specified. No additional inputs are required to run
the simulation. The program will print out each 500 days of program
execution as they are completed so the user can monitor program progress.
View/Analyze Inputs: The user has the ability to view any of the model input
parameters in either tabular or graphic format using any averaging period
(1-day, 4-day, etc.). This activity can be accessed any time after the
inputs have been specified, but need not be conducted. After specifying the
parameter to be viewed, an averaging period must be supplied. The user then
has the option of selecting a table (Figure 10) and/or a plot (Figure 11) of
inputs.
Graphical plots of model inputs show the percentage of the input values
for a particular parameter that occurs in each of ten value ranges.
Tabular results give a statistical evaluation of the parameter of interest
in terms of mean value, standard deviation and coefficient of variation.
The tabular presentation also shows the percentage of the data that exceeds
various values, the return period (recurrence interval) for exceeding these
limits, and the percentage of the data occurring between various limits.
Additional features of tabular results are the ability to determine the
return period for any value of interest and the ability to view the value
that has exactly a three year return period.
View/Analyze Results: This activity of the program can be accessed any time
after a simulation has been run. The format for the activity is identical
to that for the viewing/analysis of inputs. The results shown indicate the
frequency distribution for the in-stream concentration directly at the point
of mix with the specified discharge (Figure 12). Tabular results are
identical to the view/analyze inputs activity section.
End Continuous Simulation: The final option of the Continous Simulation
program is to end and return to the main DYNTOX menu. This option may
be selected at any time during the session.
29
-------
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STATISTICS TABLE
6.53C STAKSARS DEVIATION
COEFF1C1EKT OF VARIATION 0.26*
2.«22
VALUE
C.C
2.5C
S.OC
7 . 5C
1C.O
12.5
15.0
17.5
20.0
22.5
2S.C
t OF TIKI EXCEEDE2
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22.404
3.275
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C .0
1C. 525
23.457
43. US
15.126
3.275
0.0
0.0
0.0
0.0
RETURN PERIOD (TEARS)
O.OC3
c.c::-
C.OC3
0.004
C.012
O.OE4
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FIGURE 10 Cont'd.
Example Tabular Display of Continuous
Simulation Inputs
31
-------
VIEWING/ANALYSIS or IKPUTS
WHICH PARAMETER DO TOV VAKT TO VIEW?
(1) OUTFALL DISCHARGE
(2) OU7FALL COXCESTRA710S
(3) UPS7REAH BOVK3ART DISCHARGE
(4) UPETREAK 8DUK3AR7 COSCESTRATION
EKTER TO'JR CHOICE (1 - 4):
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FIGURE 11
Example Plot Display of Continuous Simulation Inputs
32
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IV. MONTE CARLO
The second technique which can be used to simulate a probability
distribution for instream toxics concentrations 1s Monte Carlo simulation.
This technique combines probabilistic and deterministic analyses, by using a
fate and transport mathematical model with statistically described model
inputs. The Monte Carlo simulation technique has many advantages as it:
o calculates frequency and duration of toxicant concentrations;
o includes instream fate and transport processes;
o simulates single or multiple pollutant sources;
o requires less extensive data than Continuous Simulation;
o model inputs need not follow a specific statistical function;
o incorporates cross and serial correlation.
The primary disadvantage to Monte Carlo is that it still requires extensive
input data to define probability distributions for Inputs. If extensive
data are not available, the user must have enough Information to assume
distributions for the input parameters.
This chapter discusses the theory and application of the Monte Carlo
technique, and is divided Into three sections. The first section discusses
the theory upon which the node! is based, its advantages and disadvantages.
The second section describes the data input requirements. The third and
final section details how to use the computer model of the Monte Carlo
simulation technique w*tn performing waste load allocations.
Theory
Ordinarily, deterministic water quality simulations use single values
for inputs to conduct a single steady state model simulation, providing a
single water quality p^vdictlon. Single values are selected for upstream
flow, upstream conct«tratlon, effluent flow, effluent concentration and
decay rape. The aodtl Is then used to simulate a single water quality
response profile. In Multiple discharge cases, the concentration above each
outfall is determined from the concentration below the previous outfall.
Equations 2, 3 and 4 in Chapter 3 detail the mathematics involved. These
equations are appropriate for all river modeling cases except mixing zone
anaylsis.
34
-------
The Monte Carlo technique is similar to the above, but repeats the
simulation many times. It repetitively selects model inputs according to
defined statistical distributions. The deterministic model 1s repetitively
run for a large number of statistically selected sets of Inputs. Results
when summarized (see Figure 13) show a range of predicted concentrations at
each stream location. This range reflects the range of possible input
conditions and outcomes for the model. The range in predicted
concentrations is characterized by a distribution. This distribution
indicates the probabilities of concentrations over the entire range.
By combining statistical information on environmental conditions with
deterministic model calculations, a statistically predicted forecast of
water quality is obtained. The input distibutions statistically reflect our
best understanding of model inputs. The predicted concentration
distributions, therefore, reflect the best estimate of the range in
predicted water quality conditions. Analysis of this distribution can
provide information on the probability of water quality problems and their
severity. For a more in-depth discussion of using Monte Carlo to perform
waste load allocations, the user is referred to Freedman and Canale (1983).
The Monte Carlo technique has several advantages over steady state
modeling and the non-steady state techniques Continuous Simulation and Log
Normal Analysis. The main advantage over steady state modeling is that
Monte Carlo can predict the frequency and duration of toxicant
concentrations in a receiving water. The inclusion of instream fate
processes is an advantage over Log Normal analysis, which cannot simulate
instream fate and is limited to simulations for one effluent discharge.
Another advantage of Monte Carlo is that model input data are not required
to follow a specific statistical function, as in the Log Normal process.
The Monte Carlo technique can also incorporate cross-correlation, and can
estimate interaction of time varying parameters if the analysis is developed
separately for each season and the results combined. Only Continuous
Simulation can exactly calculate the effect of time varying parameters.
The primary disadvantage of Monte Carlo is the data requirement. Data
on model input parameters are required to define the statistical
distributions or the assumptions therein. Additional data are required for
the calibration/verification of instream fate processes. However, in
contrast to Continuous Simulation, the Monte Carlo Simulation can proceed
and provide good results with a relatively sparse data set. Continuous
Simulation requires a very complete data set. A secondary disadvantage to
Monte Carlo is the inability to directly calculate running averages for
results, as Continuous Simulation is able to do. Monte Carlo, like Log
Normal, cannot directly calculate multiple day average instream
concentrations but must estimate them by using multiple day averages to
describe model inputs. A secondary disadvantage of the Monte Carlo technique-
is the large computational requirement. Like Continuous Simulation, however,
the problem of excessive computer requirements is being minimized through
recent advances in computer technology.
35
-------
u>
MONTE CARLO TECHNIQUE
JO
O
CL
Stat. Selection
ij
1
Water Quality Model
Qu + Cu
FIGURE 13
Schematic of Monte Carlo Technique
JD
O
-------
Input Requirements
The model Input requirements for all three techniques were discussed in
the Common Requirements chapter. This section details the specific input
requirements for the Monte Carlo technique. These inputs are summarized in
Table 2, and will be discussed in detail in this section. The inputs can be
categorized into five groups:
o general simulation requirements,
o upstream data,
o effluent data,
o system physical and hydrological constraints, and
o number of iterations.
General Simulation Requirements: The Monte Carlo method requires some
general information on the system that will not change between simulations.
The first basic input required for Monte Carlo is to establish the period of
observed data to be used. This consists of the first year of observed data
and the total number of years of data to use. The user should be cautious
to select a period of duration for which a consistent data set is available.
The user should not employ old data which are no longer representative of
current conditions.
The second basic input required by Monte Carlo is the number of
discharges in the system. The user must also determine if any of these
discharges are located upstream of the USGS gaging station; if so, Lhe
average point source flow above the gage must be determined in order to
correct the flow record. The final general input required is a computer
file name to store these inputs. Once these general inputs are specified,
they will be stored In this computer file and need not be specified for
later simulations.
Upstream Boundary Data: The Monte Carlo technique requires statistical
input distributions for tht upstream boundary flow and concentration. The
Monte Carlo technique allows the use of assumed data distributions or the
observed data when ttl»ctln$ Input distributions. The latter requires
STORET data defining Ihtit conditions. STORET data defining boundary flow
and concentration should bt retrieved as described in the Data Requirements
chapter, and stored m stp«r«te computer files.
DYNTOX currently allows four input distribution types to be used for
Monte Carlo. The first three are standard statistical distributions:
uniform (rectangular), normal (Gaussian), and triangular. The fourth
distribution type, temed data-defined, is a non-standard statistical
distribution. This choice can be used to simulate statistical distributions
not currently supported by DYNTOX or in cases where the observed data follow
no standard statistical distribution. The parameters required to describe
these data should all be determined using SAS (UNIVARIATE procedure) and are
described below. DYNTOX allows comparison of the observed data to the
distribution selected by the user.
37
-------
Data Source
o General Information:
- Beginning date of observed data
- Number of years of observed data
- Number of discharges above flow gage
- Average point source flow above gage
- TSS computer field name
USGS flow records
USGS flow records
User defined
Treatment records
User defined
o Upstream Data:
- Flow Data
- Statistical Distribution for Flow
- Concentration Data
- Statistical Distribution for Concentration
STORE!
User defined
STORET
User defined
o Effluent Data:
- Flow data
- Statistical distribution for flow
- Concentration data
- Statistical distribution for concentration
Treatment records
User defined
Treatment records
User defined
o System Constants:
- Time of travel information
- First order decay rate (s)
- Drainage area ratio (s)
- Water withdrawal rate (s)
Dye studies,
current meters
Instream data
USGS topographic maps
Withdrawal records
o Number of Iterations
User defined
Table 2. Input Requirements for the
Monte Carlo Technique
38
-------
The uniform distribution represents the case where each value within a
given range has an equal probability of occurrence. Two parameters are
required to define a uniform distribution, the mean value and the range (See
Figure 14).
The normal or Gaussian distribution is also shown in Figure 14. Two
parameters are required to define this distribution, the mean value and
standard deviation. The normal distribution is the only one that DYNTOX
allows to have cross-correlation between parameters. If either effluent
flow and concentration or boundary flow and concentration are specified as
normal, the user may simulate cross-correlation between these parameters
through the use of the bivariate normal distribution. The covariance
between parameters is required if this option is selected, and can be
determined using the COV option of the SAS procedures CORR or FUNCAT.
Triangular distributions are shown in Figure 14. The triangular
distribution requires three parameters - the minimum value, expected value,
and maximum value - and can therefore have a variety of different shapes.
Examples of the data defined distribution are shown in Figure 14. This
distribution can take on an infinite number of shapes and can be used to
simulate any desired distribution. The data defined distribution requires
information on the minimum value, maximum value, and number of intervals to
be used. For each interval, the user must specify the probability of
occurrence for that range. «
Effluent Data: Similar to upstream data, statistical distributions are
needed in the model for effluent flow and concentration (or toxicity). For
each effluent parameter, the user must specify a statistical distribution
using the same technique described in the upstream boundary data section.
Any downstream tributary input should be treated as a separate effluent
input.
System Constants: System constants need to be defined for hydrologic and
physical characteristics of the system. Program inputs for hydrologic data
are needed to properly adjust gaged flow data to determine instream flow at
different locations. Ratios are needed to define the comparison between the
gauged drainage basin area and the drainage basin area at the point of
discharge. These ratios adjust the USGS measured flows for nonpoint
sources, and must be specified regardless of the location of the gaging
station. For discharges located downstream of the USGS gage the ratio (and
adjustment) will be greater than 1.0. For discharges located upstream of
the gage, the ratio will be less than 1.0. The method to be used for
specifying drainage area ratios is described in the Common Requirements
chapter. A second hydrologic adjustment is required for water withdrawals.
If a significant amount of water (>1% of river flow) is withdrawn from the
river at any location, this withdrawal rate must be specified before
performing a Monte Carlo waste load allocation.
39
-------
Probability of
Occurrence
Probability of
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Another system constant required by Monte Carlo is the time-of-travel,
which must be specified for the stream segment between the upstream boundary
station and the first discharge and for the segments between each discharge.
The method for specifying time of travel was discussed in detail in the
Common Requirements chapter. Time of travel information need not be
specified for the upstream segment in cases where the boundary station is
located below a discharge as there is no upstream segment.
The first-order decay rate must be specified for each stream segment
that requires time-of-travel information. The method for determining the
first-order decay rate was discussed in the Data Requirements chapter.
Number of Iterations: The Monte Carlo technique requires a sufficient
number of iterations to adequately define the probability of occurrence of
downstream concentration. However, specifying too many iterations can waste
computer time. The recommended method for determining the proper number of
iterations is to run the Monte Carlo technique for an increasing number of
iterations until the predicted probability distribution remains relatively
constant. Five thousand (5000) iterations can be used as a starting point,
with the number of iterations repetitively doubled until results remain
constant. It is recommended that the three year return period value be
compared when determining the proper number of iterations.
Program Use
The Monte Carlo program, like the programs for the other techniques, is
divided into menu driven sub-programs (entitled activities) to allow the
user as much flexibility as desired in performing simulations. The
hierarchy of activities for Monte Carlo is shown in Figure 15. this section
will describe how to use the Monte Carlo program and will discuss the
options available to the user. It is divided into sections describing each
of the primary activities:
o Program Entry,
o System Constants,
o View Input Data/Specify Distributions,
o Run Model,
o View/Analyze Results, and
o End Monte Carlo.
Program Entry: The first activity of the Monte Carlo technique is termed
Program Entry. This section consists of specification of the time period of
observed STORET data, number of discharges to be simulated, modeled point
source flow above the USGS flow gage, and location of the data describing
boundary conditions.
41
-------
*>
t\>
Program Entry
System
Constants
VI CM Input
Data/Specify
Distribution
v
/Menu}
Run
Hodc I
)
VI en/ Analyze
Results
End Monte
Carlo
FIGURE 15
Hierarchy of Monte Carlo Subprograms
-------
Figure 16 shows example sessions with the Program Entry activity. The
first questions in Program Entry concern the existence and location of the
TSS files for the simulation. TSS (Time Series Store) files are created by
ANNIE to store time series information. The TSS file holds all information
pertaining to the STORET boundary data for the Monte Carlo case. The first
time a simulation is performed, the user should answer NO to the question
asking if a TSS file was previously created, and specify a file name (Figure
16a). This will initiate the process to create a file. The user should
answer YES to this question in subsequent simulations, and no other
information will be required in the Program Entry section except the name of
the TSS file (Figure 16b).
For first time entries, the TSS file name must be supplied. Any file
name can be used that is compatible with the computer system. The next
inputs required are the first year of observed data and the number of years
of data. The required format for the date is Year/Month/Day (Figure 17a).
Months and days with only one significant figure of information may be
entered using only one digit. The next question in Program Entry before
creation of the TSS file concerns the number of discharges in the system.
The TSS file for the system is being created and initialized at this
point in Program Entry. This may take some time, depending on the computer
system used, but the user will be informed when the file initialization is
complete. TSS files created during Monte Carlo can be used for either of
the other two DYNTOX techniques.
The final portion of Program Entry concerns defining the upstream
boundary data files. Figure 16a shows an example session where both the
boundary flow and boundary concentration data are located in STORET files.
The user need only specify the name of the STORET data files and which data
set of the STORET retrieval is to be used. The data set will always be one
unless the user has multiple STORET retrievals stored in the same file. The
section provides the ability to screen out flow and concentration data above
acceptable values.
Another possibility for Program Entry is when the user has no STORET
data and wishes to enter observed data manually from the terminal. Figure
16c shows an example of this situation. The user is required to input the
number of data points, then the date and concentration for each value. The
proper format for the data is (date, value) with the date in the YYMMDD
format. The final option of program entry concerns the case where all input
distributions were calculated off-line before using DYNTOX. In this case,
no raw data need be entered, either from STORET files or from the terminal.
Instead, the user enters only the previously calculated distribution
information, (e.g. Figure 18a).
43
-------
Figure 16 shows example sessions with the Program Entry activity. The
first questions in Program Entry concern the existence and location of the
TSS files for the simulation. TSS (Time Series Store) files are created by
ANNIE to store time series information. The TSS file holds all information
pertaining to the STORET boundary data for the Monte Carlo case. The first
time a simulation is performed, the user should answer NO to the question
asking if a TSS file was previously created, and specify a file name (Figure
16a). This will initiate the process to create a file. The user should
answer YES to this question in subsequent simulations, and no other
information will be required in the Program Entry section except the name of
the TSS file (Figure 16b).
For first time entries, the TSS file name must be supplied. Any file
name can be used that is compatible with the computer system. The next
inputs required are the first year of observed data and the number of years
of data. The required format for the date is Year/Month/Day (Figure 17a).
Months and days with only one significant figure of information may be
entered using only one digit. The next question in Program Entry before
creation of the TSS file concerns the number of discharges in the system.
The TSS file for the system is being created and initialized at this
point in Program Entry. This may take some time, depending on the computer
system used, but the user will be informed when the file initialization is
complete. TSS files created during Monte Carlo can be used for either of
the other two DYNTOX techniques.
The final portion of Program Entry concerns defining the upstream
boundary data files. Figure 16a shows an example session where both the
boundary flow and boundary concentration data are located in STORET files.
The user need only specify the name of the STORET data files and which data
set of the STORET retri**al 1s to be used. The data set will always be one
unless the user has »wUiplt STORET retrievals stored in the same file. The
section provides the ability to screen out flow and concentration data above
acceptable values.
Another possibility for Program Entry is when the user has no STORET
data and wishes to **ttr observed data manually from the terminal. Figure
16c shows an exa*pif o* IMS situation. The user is required to input the
number of data points. tK«n the date and concentration for each value. The
proper format for tM data 1s (date, value) with the date in the YYMMDD
format. The final optic* of program entry concerns the case where all input
distributions were calculated off-line before using DYNTOX. In this case,
no raw data need be entered, either from STORET files or from the terminal.
Instead, the user enters only the previously calculated distribution
information, (e.g. Figure 18a).
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16b. Existing TSS File
HAVE YOU PREVIOUSLY CREATED A TSS FILE FOR THIS SIMULATION?
YES
WHAT IS TriE KAKE OF YOUR TSS FILE?
EXAMPLE
16c. Terminal Entry of Data
HAVE TOU PREVIOUSLY CREATED A TSS FILE FOR THIS SIMULATION?
NO
WHAT IS THE KAKE OF TOUR NEW TSS FILE?
TEST": IE
JO- KANY TEARS OF DATA DO YOU HAVE?
(Hit returr Icr ')
e
HCW KANY OUTFALLS ARE THERE IN THE SYSTEM?
(Hit return {or 1)
1
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(hit return fcr 0)
-0
PLEASE WA:T WHILE YOUR TSS F:LE is INITIALIZES ...
INITIALIZATION OF irjR TSS FILE is NSW COMPLETE.
DO YOU HAVE A STORET FLOW DATA FILE?
- Y
WHAT IS THE KAXE OF THE STORET FILE?
-STCr.ET.FLO
USE WHICH DATA SET?
(Hit return (or 1)
- i
WHAT IS THE KAX'-K-JV. ACCEPTABLE FLOW VALVE?
(H:t returr. tor 0.)
4S99.
£2<5 PC:KTS READ
DO T3'J HAVI A STORET DATA FILE FOR UPSTREAM COSCEKTRATICS?
- NO
DC iO'J WANT TO ESTER CONCENTRATION DATA FROM THE TESX.INXL?
P- YES
HCW KANT SAMPLES DO YO'J HAVE?
(Hit return, for «)
^ 3
ENTE5 3ATE AKD UPSTREAM COSCENTSATIOS FOR EACH SAMPLE:
»-6::-ci, .5
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3 P::KTS READ
FIGURE 16 Cont'd.
Example Session with Monte Carlo Program Entry
46
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-------
Demonstration of Uniform and Normal Distributions
PLEASE CHOOSE ONE:
(1) SP'CIFT EFFL'JEKT FLOW /CONCENTRATION DISTRIBUTION
2 VI Ew bATA/DETERXIKE BO'JKSARl CONCENTRATION 01 STRIB.-TI ON
(3 V'EH DATA/DETESKINE BOUNDARY FLOW DISTRIBUTION
(4) CK3 IKP-JT DEFINITION. RETURN TO MONTE CARLO MENU
tKTER SELECTION (1-4)
(Hit return (or 4)
SPECIFICATION or
SIST?.IB--T:ONS
SPrc:FT FLO« iNr:-RMATios FCS D:SCKAHGE
VriAT TTrE OF D:STR:B~IOK DO TO'J HAKT?
(1) UKIFCRK
(2) N5R.KAL
(3) TSIANCULAR
(«)
ATA DEFINES
EKTES SELECTION (1-4)
(Kit return lor 1)
1
WHAT IS THE KIAS VALUE
(Kit return (or 1.)
25.
WHAT IS THE RANGE
(Kit return (or 0.)
SrECIFT CONCENTRATION IKFCRKATIOK FOR DISCHARGE
VriAT TYPE OF 01 STS: B'.T: OS 35 TOU WANT?
(1) UNIFORM
(2) N:=KAL
(3) T?.:ASG-.'*_AR
(4) DATA DEFINED
ESTER SELECTION (1-4)
(Kit return for 1)
- 2
WHAT IS THE KEAN VALUE
(Kit return tor 1.)
-S.
WAT IS THE STAV=iJO DEVIATION
(Hit return for C.)
ENS CF DISCnAPCE SPECIFICATION SECTION
FIGURE 18
Example Session with Monte Carlo
Specifying Effluent Distributions
48
-------
18b. Bivariate Normal Distribution
SPEC: n CAT: OK or EFFLITENT DISTRIBUTIONS
SPECIFY FLO* INFORMATION FOR DISCHARGE 1
WHAT TTPE OF DISTRIBUTION DO YOU WANT?
( 1) UNIFORM
(2) NSRMAL
(3) TRIANGULAR
(4) DATA DEFINED
ENTER SELECT; OK d-4)
(Hit rtturn for 1)
2
WHAT IS TrE MEAN VALUE
(Hit return for 1.)
25.
WHAT IS THE STANDARD DEVIATION
(Kit return for 0.)
-3.
SPECIFY CONCENTRATION IKFCRMATION FOR DISCKAR3E 1
WHAT TYPE OF DISTRIBUTION DO YOU WANT?
( 1) UNIFORM
(2) K?SMAL
(3) TSIASGULAR
(4) DATA DEFINED
ENTER SELECTION (1-4)
(Hit return for 1)
»2
WHAT is THE KIAN VALUE
(Hit return for 1.)
~S.
WriAT IS THE STAN3AR3 DEVIATION
(Hit ret.rn for 0.)
».1.
IS CONCENTRATION C3R?.ELATED TO FLOW
.TES
ENTER CCVARIASCE BETVEEN CONCENTRATION AND FLOW
(Kit return fsr 0.)
END OF DISCKAR3E SPECIFICATION SECTION
FIGURE 18 Cont'd.
Example Session with Monte Carlo
Specifying Effluent Distributions
49
-------
After completing Program Entry the program enters the main portion of
Monte Carlo. The user will be given the menu shown in Figure 17 and must
select one of the five activities:
1. System Constants
2. View Data/Specify Distributions
3. Run the Simulation
4. View/Analyze Model Results
5. End Simulation
Although there is flexibility in the order in which options are selected,
system constants must be specified before choosing any other option (except
ending).
System Constants: The system constants consist of time of travel, first-
order decay rate, drainage area ratio, and water withdrawal rate. Program
operation for the section is straightforward, requiring only the inputs
discussed in the Common Requirements section. An example session specifying
system constants is shown in Figure 17.
View Data/Specify Distributions: This section allows the user to view and/or
analyze the observed data for the boundary parameters and then requires
specification of the input distribution for these and the effluent
parameters. Upon entry to the section, the user is given a menu (Figure 18)
of four choices:
1) Specify effluent flow/concentration distribution,
2) View data/determine boundary concentration distribution,
3) View data/determine boundary flow distribution,
4) End input definition.
The options may be selected in any order desired; however, options 1-3 must
be successfully completed before ending to successfully perform the model
simulations.
Example sessions using the first option, specification of effluent data
are shown in Figure 18. This session demonstrates use of the uniform and
normal input distributions. A uniform distribution is selected for effluent
flow in this example, and the user is required to supply a mean value and
range (Figure 18a). A normal distribution is selected for effluent
concentration; in this case, the user must supply a mean value and standard
deviation. In the special case where normal distributions are selected for
both flow and concentration, the option exists to specify a covariance term
to represent the cross-correlation between parameters (Figure 18b). The
same option exists when specifying normal distributions for boundary flow
and boundary concentration.
50
-------
When boundary concentration and flow data are available, the user has
the option to view a plot of the actual data distribution or see a table
describing the statistics and distribution of the data. Figure 19 shows an
example session specifying boundary flow, where the user selects to see the
plot of the data. The plot shows the probability of occurrence for the
parameter over a number of ranges. The distribution is selected after
viewing the data plot; in this case a triangular distribution. In cases
where the data has been viewed or analyzed, the option exists to compare the
predicted distribution to the observed data and also to determine its
acceptability. The user is allowed to choose a new distribution for the
parameter in cases where the fit is unacceptable.
Figure 20 shows an example session specifying boundary flow. This
example demonstrates use of the data defined distribution. The sum of
probabilities specified for all of the intervals in data defined must equal
1.0 or they will be rejected by the program and new values required.
In many cases, insufficient data will be available to define
distribution for four-day average values. Based upon the Central Limit
Theorem, users may specify a normal distribution for the parameter in
question, with a standard deviation one half of that in the observed data as
an estimate of the distribution of four day average value. The mean value
will remain constant.
Running the Simulation: Only one input is required when choosing to run the
simulation, the number of iterations. During the simulation, the program
will print a message after the completion of every 2000 iterations to help
in monitoring program progress.
View/Analyze Model Results: Model results can be seen in one of two formats,
as a plot showing probability of exceedance for all concentrations, or as a
statistics table showing statistics on the results along with the frequency
distribution of the results in tabular format. An example session viewing
the results of a model run in plot form is given in Figure 21. Figure 22
shows the results of the same simulation in tabular format. The statistics
table consists of the statistical parameters mean, standard deviation, and
coefficient of variation, along with the probability of occurrence for a
number of intervals. The table also shows the probability of exceedance and
the return period (recurrence interval) for a number of values. The option
exists to view the return period for a value not shown if desired, or to
view the value with a three year return period.
End the'Simulation: Choosing this option allows the user to exit the Monte
Carlo technique and return to the main DYNTOX menu. This option can be
selected at any time during the Monte Carlo simulation.
51
-------
SPECIFICATION OF IKPUT DISTRIBUTIONS
OVER HOW MAH1 DAYS DO TOU «AHT WSOLTS AVWAGED
(Hit return tor t)
PLEASE CHOOSE OHE:
ESTER SELECTION (1-4)
(Kit returr. lor 4)
3
SPECIFICS OK or BOUOARY FLO* B:STR;BOTIOK
^ TO, WAK7 TO SEE A DATA WSTHIWTIC* K.OT BtrOR* CHOOSIHC7
1XTERVM. OR OWJLATIVE FORMAT
lr TOC VAKT TO SEE A STATISTICS TABLE?
' £HAT TITLE DO TOC «AKT FOR TOUR F-OT (60 CHARACTER IU1IN3K)
- B3UK3ART FLOW
20
5 -----»-
0. 500.
FIGURE 19
Example Session with Monte Carlo Specifying
Triangular Distribution
52
-------
SFECJFT BO'JOAR-Y FLOV B: STRIB'-TIOK
WHAT TVPE or »:STA:B-.TJOK B: »oa VAKT?
(i) UN:FORX
(2) K?RKAL
(3) TRIAVS'.'LAS
(4) BAT A BCflKED
EKTEF. SELECT!OK (1-4)
(Hit return lot 1)
3
WHAT IS THE KIKJ»W. VALUE
(Hit return for C.)
U.
WHAT IS THE KAZ:K*jy. VALUE
(K:t return lor 1.)
?5CC.
V>:AT is THE tiPECTED VALVE
(K:t return lor 0.5)
- 6CO.
B: lO'J WAKT 70 CO.".?ARE THE CISTP.: B'JTIOK TO THE ACTUAL BATA?
WHAT T:TLE BO tsv VAST FOR TOVF. PLOT UO CKARACTEK KAZJUJK)
COM?AR: SDK or TRIASSV-AR BISTRJBUTIOK
100
T
I
V.
E
1
K
I
K
T
E
R
V
A
L
6C
«c
2C
f
C.
sec.
K.::. i;:c. 2::?. 2scc.
cof-:?A?.:sos or T?:ASCVLAR
ssco. 4::c. 45c
IF THIS FIT ACCEPTABLE?
T
EKS Or BOUK3ART FLO- SFEC!ri CAT10S SECTION
FIGURE 19 Cont'd.
Example Session with Monte Carlo Specifying
Triangular Distribution
53
-------
SPECIFICATION or BOUNDARY FLOW DISTRIBUTION
SPECIFY BOUNDARY FLOW DISTRIBUTION
VriAT TYPE Or DISTRIBUTION DO TO.. VAST?
(1) UNIFORM
(2) NORMAL
(3) TRIANGULAR
(4) DATA DEFIKEO
ENTER SELECT10NO-4)
(Hit return for 1)
WHAT is THE K:N:KUK. VALUE
(Hit return f er C. )
IE*
HOW KAKT IKTEKW.S DO TO*J WAST TO SPECIFY
(Kit rerurr. lor 2)
K'K-K-JV VA^DI rOR JKTEFVAL 1 JS 160.
WrAT JS THE KAZ:>TJK VA'.VE
(Hit returr, for 1. )
220
WHAT IS THE PROBABILITY Or OCCURREKCE
(Kit return for C.)
KIKIKJK VALUE TO?. ISTEPVAL 2 JS 220.
WHAT IS THE JSAIIKUK VAiUE
(Hit return lor 220.)
WriAT !S THI PROBASILITY Or OCCURREKCE
(Kit returr. let C. )
K-VK-J* VALUE F3f ISTERVAL 3 IS 260.
whAT is TKI KAX:KUV VALUE
(Kit re:urr ler 26C . )
w-n»- is THE PROI«.B:LJTY or OCCURRENCE
(H;t re-.urr to: C.)
K:K:K»' VALUE rsr IKTEFVAL 4 is 32C.
WVIAT :s TKE HAi:»nv VALUE
(K:t re-.ur- ter JZC.)
WH!T is TKI P>;IAB:LITY or
(V:t t»:^r> !e: t.)
:1"! vwr TO CCMFARI THE D:STR:»LT:OS TO THE ACTUAL DATA
Ki
EK- Of »;UV3Af.T FLOW SPECIFICATION" SECTION
FIGURE 20
Example Session Specifying Data Defined Distribution
54
-------
MONTE CARLO TECHNIQUE .
PLEASE CHOOSE FROM THE FOLLOWING:
(1) SPECIFY SYSTEM CONSTANTS
(2) RUN MCOEL
(3) VIEW/ANALYZE RESULTS
(4) EK3 MONTE CARLO SIMULATION, RETURN TO TOXICS WLA MENU
ENTER TOUR CHOICE (1 - 4):
(Hit return for 1)
-3
v:r-:ss 'ANALYSIS or RESULTS
DO YCV VAN? TO SEE A PLOT?
Y
WHAT TITLE DO YCw WAST FOR YCVR PLOT (6: CHARACTER KAXIKVK)
MONTE CARLO CONCENTRATION
» ICC
0 I i
F j . ;
ac i - - -. |
i i *. I
E 6C ! -» *- - j
! '
t * ,
X < ,
c «o ! «.--* - « ;
E !
E !
D
E 2C ! »---»... » -, - ,
D ! « i
I i
! ;
c ---
0.0 0.50 1.CC 1.50 2.CC 2 5'
MONTE CARLO CONCENTRATION
FIGURE 21
Example Session with Monte Carlo
Viewing Results in Plot Format
55
-------
PLEASE CHOOSE FROM THE TO-LOVING:
(1) SPECIFY SYSTEM COKSTAKTS
(2) R'JK MODEL
(3) VIEV'AKALYZE RESULTS
(4) EKD COKTIKUO'JS SIMULATION
EKTEF YOUR CHOICE (1 - 4):
RETURN PERIOD FOR A DIFFEREKT VALUE
(2) CALCULATE THE VALUE WITH A THREE TEAS RETURN PERIOD
OR (3) EKD TABULAR ANALYSIS
3
FIGURE 22
Example Session with Monte Carlo Viewing Results
in Tabular Format
56
-------
V. LOG NORMAL
The third technique that can be used to calculate a probability
distribution for instream toxics concentrations Is Log Normal probabilistic
analysis. This technique assumes that all Input parameters can be described
by a log normal statistical distribution, and uses numerical Integration to
predict the concentration distribution below a single effluent discharge.
The Log Normal technique has many advantages as it:
o predicts frequency and duration of concentrations;
o requires less computational expense than Continuous Simulation or
Monte Carlo;
o does not require extensive time-series data as Continuous Simulation;
o incorporates cross-correlation of parameters.
The primary disadvantages to Log Normal are that extensive data are
required to define input distributions, all parameters are assumed to be log
normally distributed, and instream losses or simulation of more than one
discharge cannot be considered.
This chapter describes the theory and application of the Log Normal
technique, and is divided into three sections. The first section discusses
the theory upon which the Log Normal technique is based, and its advantages
and disadvantages. The second section describes the data input
requirements. The third and final section details how to use the computer
program of the Log Normal technique when performing waste load allocations.
Theory
Continuous Simulation and Monte Carlo and Log Normal analysis are based
upon the same dilution equation, which predicts the concentration below a
discharge (CH) based upon upstream concentration (C), upstream flow (Q )
effluent concentration (Ce), and effluent flow (Qe):u u
This equation is suitable for all in-stream modeling except mixing zone
analysis. Where Continuous Simulation and Monte Carlo analysis solve this
equation many thousands of times using different values for the Inputs, Log
Normal analysis uses a totally different technique.
Log Normal analysis requires that each model input follow a log normal
statistical distribution; this causes the probability distribution for each
equation to be well defined mathematically. The probability* that the
downstream river concentration (Cd) exceeds any given value, C , can be
57
-------
expressed as a multiple integral of the joint probability degsity functions
over the values of flows and concentrations for which Cd > C . Since the
variation of each input variable is defined by a mathematical equation,
numerical integration can be conducted to determine the probability that
C. > C . By repeating this integration for different values of C , the
probability distribution for Cd can be estimated. The probability of
exceedance can be estimated for derations other than one day by using inputs
representative of multiple-day averages. For a more complete description
of the theory behind Log Normal probabilistic analysis, see DiToro (1984).
The primary advantage of the Log Normal technique is the ability to
predict the frequency distribution of the river concentration without the
excessive computational requirements of Continuous Simulation or Monte
Carlo. Whereas Continuous Simulation and Monte Carlo require several
thousand iterations of the model to predict the concentration distribution,
Log Normal can proceed much faster through numerical integration.
The disadvantages of Log Normal are the inability to simulate multiple
discharge situations and the requirement that all parameters follow log
normal distributions. In many cases, parameter data only approximately
conform to a log normal distribution. This introduces errors which are
exagerated at the infrequent recurrence levels of the probablistic
simulation. Log Normal also has the same disadvantage as Monte Carlo in
that multiple day average in-stream concentrations can only be approximated
through the use of averaged inputs. Continuous Simulation is the only
technique that allows exact determination of multiple day average results.
Log Normal analysis also requires significantly more input data than steady
state models, but no more than Continuous Simulation or Monte Carlo.
Input Requirements
The model input requirements for all three techniques were discussed in
the Data Requirements chapter. This section details the specific input
requirements for the Log Normal technique. These inputs are summarized in
Table 3, and will be discussed in detail in this section. The inputs can be
categorized into five groups: general simulation requirements, upstream
data, effluent data, system hydrological constraints, and output range of
interest. However, the data requirements for each are to an extent first
dictated by general information on the simulation.
General Simulation Requirements: Log Normal analysis requires some general
information on the system that will not change between simulations. The
first basic input required for Log Normal Analysis is to establish the
period of observed data to be used. This consists of the first year of
observed data and the total number of years of data to use. The user should
be cautious to select a period of duration for which a complete and
consistent data set is available. Caution should be directed towards using
old data which are no longer representative of current conditions.
The second basic input required by Log Normal is whether the discharge
is located upstream of the USGS gaging station. , If so, the average point
source flow above the gage must be determined. The final general input
required is a computer file name to store these inputs. Once these general
inputs are specified, they will be stored in this computer file and need not
be specified for later simulations.
58
-------
Data Source
o General Information:
- Beginning date of observed data
- No. of years of observed data
- Number of discharges above flow gage
- Average point source flow above gage
- TSS computer file name
USGS flow records
USGS flow records
User defined
Treatment records
User defined
o Upstream Data:
- Mean and 84th percentile value for flow
- Cross-correlation between river flow
and river concentration
- Mean and 84th percentile value for
concentration
- Cross-correlation between river flow
and effluent flow
STORE!
SAS
STORET
SAS
o Effluent Data:
- Mean and 84th percentile value for flow
- Mean and 84th percentile value for
concentration
- Cross-correlatiion between effluent flow
and effluent concentration
STORET
STORET
o System Constants:
- Drainage area ratio
- Water withdrawal rate
USGS topographic maps
Withdrawal records
o Output Interval of Interest:
- Minimum river concentration of interest
- Maximum river concentration of interest
- Interval for output
User defined
User defined
User defined
Table 3. Input Requirements for the
Log Normal Technique
59
-------
Upstream Boundary Data: The Log Normal technique requires the mean and
variance of the input distributions for the upstream boundary flow and
concentration. DYNTOX provides the ability to determine the distribution
parameters from observed upstream boundary flow and concentration. This
requires STORET data defining these conditions.
The required form of this data includes the 50th percentile (mean)
value and 84th percentile value for each parameter. These parameters can
also be determined from SAS, as well as the adequacy of the assumption of
log normality (using the UNIVARIATE procedure on the logarthims of the
observed data). Boundary flow data must be corrected for point source flows
and withdrawals before performing SAS analysis, as they may significantly
affect the assumption of log normality. In addition, this technique
requires information describing the cross-correlation between river flow and
effluent flow, and river flow and river concentration. These cross-
correlations can also be determined using SAS, using the CORR procedure.
Effluent Data: Similar to upstream data, log normal distribution parameters
are needed in the model for effluent flow and concentration (or toxicity).
For each effluent parameter, the user must specify a mean and 84th
percentile using the same technique described in the upstream boundary data
section. DYNTOX does not provide the capability to calculate these values
directly from observed effluent data. However, SAS may be used to calculate
these parameters before performing Log Normal analysis. The final effluent
requirement is the cross-correlation between effluent flow and
concentration. This may also be determined through SAS.
System Constants: Program inputs for hydro!ogic data are needed to properly
adjust gaged flow data to determine instream flow at different locations.
Ratios are needed to define the comparison between the gauged drainage basin
area and the drainage basin area at the point of discharge. This ratio
adjusts the USGS measured flows for nonpoint sources, and must be specified
regardless of the location of the gaging station. For a discharge located
downstream of the USGS gage the ratio (and adjustment) will be greater than
1.0. For a discharge located upstream of the gage, the ratio will be less
than 1.0. The method to be used for specifying drainage area ratios is
described in the Data Requirements chapter. A second hydrologic adjustment
is required for water withdrawals. If a significant amount of water (>1% of
river flow) is withdrawn from the river at any location between the gage and
the outfall, this withdrawal rate must be specified before performing a
waste load allocation.
Output Range of Interest: The user must specify the minimum and maximum
output concentration of interest and desired output interval before running
the simulation, due to the nature of the solution technique. Care should be
taken to choose a minimum value that has a non-zero probability of
exceedance. Minimum values that have an insignificant probability of
exceedance will be rejected by the program, and replacement values will be
required.
60
-------
Program Use
The Log Normal program, like the programs for the other techniques, is
divided into menu-driven subprograms (entitled activities) to allow as much
flexibility as possible in performing the simulation. The hierarchy of
activities for Log Normal analysis is shown in Figure 23. This section will
describe how to use the Log Normal program and will discuss the options
available. It is divided into sections describing each of the primary
activities of Log Normal analysis: Program Entry, Input Specification,
Model Simulation, Statistical Analysis of Inputs/Results, Plots of
Inputs/Results.
Program Entry: The first activity of the Log Normal technique is termed
Program Entry. This section consists of specification of the time period of
observed STORET data, modeled point source flow above the USGS flow gage,
location of the data describing boundary conditions, and withdrawals between
the USGS gage and the effluent outfall.
Figure 24 shows example sessions with the Program Entry activity. The
first questions in Program Entry concern the existence and location of the
TSS files for the simulation. TSS (Time Series Store) files are created by
ANNIE to store time series information. For the Log Normal technique, the
TSS file holds all information pertaining to the STORET boundary data. The
user should answer NO to the question asking if a TSS file was previously
created the first time a simulation is performed, and specify a TSS file
name (Figure 24a). This will initiate the process to create a file. The
user should answer YES to this question in subsequent simulations, and no
other information will be required in the Program Entry section except the
name of the TSS file (Figure 24b). A TSS file created for Log Normal
analysis can also be used for Continuous Simulation or Monte Carlo.
For first-time entries, the TSS file name must be supplied. Any file
name compatible with the computer system in use is acceptable. The next
inputs required of the user are the first year of observed data and the
number of years of data that exist. The required format for the date is
Year/Month/Day (Figure 24a). Months and days with only one significant
figure of information may be entered using only one digit. At this point in
Program Entry, the TSS file for the system is being created and initialized.
This may take some time, depending on the computer system used, but the user
will be informed when the initialization is complete.
The final portion of the Program Entry concerns location of the STORET
data. Figure 24a shows an example session where both the boundary flow and
boundary concentration data are located in STORET files. The user need only
specify the name of the STORET data files and which data set of the STORET
retrieval is to be used. The program provides the capability to screen out
flow and concentration data above acceptable values.
61
-------
Determine
Specify Hodel
Parameters
Run
Model
,
t>o
VICH Inputs/
KCSUltS
End
Log-Nornal
FIGURE 23
Hierarchy of Subprograms for Log Normal
-------
Another possibility for Program Entry is when the user has no STORET
data and wishes to enter data manually from the terminal (Figure 24c). The
user is required to input the number of data points, then the date and
concentration for each value. The proper format for the data is (date,
value) with the date in the YYMMDD format. The final option of the Program
Entry concerns the case where all input distributions were calculated off-
line before using the DYNTOX. In this case, no data need be entered,
either from STORET files or from the terminal, and the user may proceed
directly to Input Specification.
Input Specification: Required inputs include mean (50th percentile) and 84th
percentile values for all model parameters, along with the cross-correlation
between river flow and effluent flow, between river flow and river
concentration, and between effluent flow and effluent concentration. Values
for the 50th and 84th percentile values for the boundary parameters will be
calculated from the observed data when available. An example session
demonstrating Log Normal Input Specification is shown in Figure 25.
In many cases, insufficient data will be available to define
distribution for four-day average values. In these situations, users may
specify a log normal distribution for the parameter in question, with a
standard deviation one half of that in the observed data as an estimate of
the distribution of four day average values.
Model Simulation: Model simulation requires the specification of a minimum
and maximum value of interest and the interval that results are desired. It
is important to note that this interval is in log (base 10) units. When
conducting wasteload allocations, the user should select the minimum,
maximum, and increment value such that the return period for the water
quality criterion will be output. One way to assure this occurrence is to
specify the minimum and/or maximum value to be the criteria. An example
session showing model simulation is given in Figure 26.
Statistical Analysis of Inputs/Results: The user has the ability to view any
of the model input parameters or the simulation results in tabular format,
receiving statistical results and a table of the frequency distribution.
This section can be assessed any time after the simulation has been run.
After specifying the parameter to be viewed and a one-line 80 character
maximum title, results shown in Figure 27 demonstrate this feature using
model results. The output for model input parameters has an identical
format.
Plots of Inputs/Results: The user also has the ability to view any of the
model input parameters frequency distribution in plot form. The plot format
differs slightly between the input parameters and model results. The input
parameters are plotted as the probability of occurrence over a number of
ranges (see Figure 28). The model results are plotted as the overall
probability of exceedance for each value in the specified range (Figure 29).
63
-------
24a. New TSS File
TOXIC SUBSTANCE WAETELOA3 ALLOCATION K32£L!K3
VKICH TECHNIOL'E DO YOU WANT 70 USE:
(1) CONTINUOUS SIKULATION: DILUTIOK AND DECAY
(2) KSXTE CARLO: DILUTION AND DECAY
(3) LOC-K^RKAL: DILUTIOK ONLY
(4) ENS TOXICS WLA. FETUP.K TO ANKIC KEK'J
ENTER SELECTION (1-4)
(Hit return for 4)
DO-YOU HAVE UPSTREAM BOUNDARY DATA FI? ANALYSIS?
HAVE YOU PREVIOUSLY CREATES A TSS FILE FOR THIS SIKULATION?
^-ND
WHAT IS THE KAMZ OF YOUR Kt- TSS FILE?
^-TESTFILE
HO- KASY TEARS OF DATA DO YOU HAVE?
(Kit return tor 1)
^"fc
EKTES STARTING DATE.
»- 1S6I/V1
HOW KASY OUTFALLS ARE THERE IK THE SYSTEK?
(Kit return for 1)
^- i
HOW KASI OUTFALLS LIE ABIVE THE FLOW CAGE?
(Hit return for 0)
*~ PLEASE KAIT WHILE YC'JR TSS FILE IS INITIALIZES ...
INITIALIZATION OF YCVR TSS FILE IS NOW COMPLETE.
DO YOU HAVE A STCrIT FLOW DATA FILE?
^- Y
WHAT IS THE NAME OF THE STCR" FILE?
ST:?.".FLO
USE WHICH DATA SET?
(Kit return for 1)
WHAT IS THE KAXIKUV. ACCEPTABLE FLOW VALUE?
(Hit rtt.rn fcr C.)
>-;9rS.
ez;E PC:KTS READ
D5 YOU HAVE A S"RET DATA FILE FOR UPSTREAM CCSCESTRATICN?
^- YES
WHAT IS THE KAMI OF THE STCnST FILE?
^-STCRET.CON
USE WHICH DATA SET?
(Kit return for O
WHAT IS THE KAXIKUV COSCES'TR».TICN VALUE?
(Hit return for C.)
>-'.0
nj« PC:NTS READ
FIGURE 21
Example Sessions with Log Normal Program Entry
64
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24b. Existing TSS File
HAVE YOU' PREVIOUSLY CREATES A TSS FILE FOR THIS SIKVLAT10K?
>- YES
WHAT IS THE KAV.E OF YOVK TSS FILE?
> EXAMPLE
24c. Terminal Entry of Data
HAVE IOU PREVIOUSLY CREATES A TSS FILE FOR THIS S I KV- AT 1 OK ?
NO
*T-:AT is THE NAME OF vcvs NEW TSS FILE?
7ES7FILE
KZ- Ki.SY YEARS OF SJ7A DO YO'J HAVE?
(Kit r*t_rn lor l)
6
EK7ES S?AST:KC DATE.
HC- KASY O'.TFAILS ARE THERE IN THE SYSTSK?
(Hit return for 1)
- i
HOW KAVY orrrALLS LIE ABOVE THE FLOW CAGE?
(Kit rtturn for C)
-0
PLEASE WA:T »>V:LE »O-JR TSS FILE is INITIALIZED ...
IKITIAllZATISK OF YC'.-S TSS FILE IS NDW COMPLETE.
DO Y=-. KA-.T A ST:F.ET FLOW DATA FILE?
V
V-:AT 3t ?^i ».»VT or THr ST;SIT F:LE?
- S7:;r-.r.e
VSt w-;c> S«*» ltr»
(K.t ft: .f» tar M
. 1
*>»" 1» **t »*»".»' ACCErTASLE FLOW VALUE?
(K.t f»i»f» If C.I
iSfi
r: ir. »* t i-r»iT DA7A FILE FOR UFS7REAM cos:Es7S.A7:os?
r: :. k»»- ; i«-t» c:--:r<-ri7:os TATA FR:M
»;. ».«» »»».»» : Y:V HAVE'
.t .- i»- «)
!«-! >'t »: '.MTSiJ.V CCSCESTRAT1C-N FOR EACH SAMPLE:
*:::. »
t: si-. .«
*!:»!. li
J »: -*i :*:
FIGURE 2^ Cont'd.
Example Sessions with Log Normal Program Entry
65
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AL SIK-JLATIOK TECKNIQ-JE
PLEASE SELECT OUt:
(1) DETERMINE/SPECIFY MODEL PAXAXS7ERS
(2) RUN K:DEL
(3) VIEW K3DEL RESULTS/IKPU7 DISTRIBUTIONS
(4) END LOGNCRXAL, RETURX TO TCXICS WLA KSSU
ENTER SELECTION (1-4)
(Hit return (or 4)
(1) DETERMINE/SPECIFY K.rDEL PARAMETERS
(2) R'.-s K.:;EI
(3) VIEW HC3EL SESV17S/IKPV7 DISTR:EVTIOKS
(4) ES3 LDCSORJ:AT is THE CRrss-ccRRtLATiON SITWEES RIVES FLDW ASD
FLOW
(K>t return fcr 0.)
. 1
WHAT IS TH£ KtCIAN BCVNDARy CONCENTRATION
(Kit return fcr 1.)
- . 1
WV:AT is THE E<\ BCVVDASY CONCENTRATION
(Hit ret^rr. for 1C.)
- .S
Wr.AT IS THE CPCSS-CCSSELATI ON SiT-'EEN FIVES CCNCENT?.ATI OS
RIVER FLO'-
(Kit retjrn for C.)
- . 1
FIGURE 25
Example Session with Log Normal Input Specification
66
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EFFLUENT FLOW SPiZlTl CATION
WHAT IS THE MEDIAN EFFLUENT FLOW
(Kit return lor 1.)
10.
WHAT is rut e<* EFFLUENT FLOW
(Hit return for 10.)
-100.
WHAT JS Ti-E CRCSS-C?S?.ELATiON BETWEEN EFFLUENT FLOW AV3
EFFL'JEs'T CONCESTRAT:OK
(Hit return for 0.)
- . 1
EFFLUENT CONCENTRATION SPECIFICATION
WHAT JS THE KID:AN EFFLUENT CONCENTRATION
(Hit return (er 1.)
- 10.
WHAT 3S THE 64% EFFLVENT CONCENTRATION
(Kit return for 10.)
- 10'C.
FIGURE 25 Cont'd.
Example Session with Log Normal Input Specification
67
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LOGKCRKAL SI»T.:LATIOK
FLEASE SELECT OKE:
(1) DiTERXIKE/SPECJFy MC2EL PARAMETERS
(2) R'jn H.SSEL
(3) VIEW MrrEL RESULTS/IN?'.'- 01STRI B'.'T; OKS
(4) E« L03s;R>y.l. RiTwRK 70 TOXICS WUk KIK'J
tVTER SELECTION' (1-4)
(Hit return (or 4)
2
WXAT IS TKE KIKIK.-y VALUE OF IKTEREST
(Hit return (or 0.>
.01
WHAT is TKE KAX:KW. VALUE or IKTEREST
(Hit rt:urn (or 0.)
100.
AT WVAT 1KCREKEST DO TOL' WAV? RESULTS LISTED (K^TE: THIS
IHCKi«^»;T H'JST BE IN LOG UNITS!)
(Kit rt-.urn (or 0.)
-.&
$:K_-L»r:oK COV?LETE
FIGURE 26
Example Session Performing Log Normal Simulation
68
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LOGNORMAL SIMULATION TECHK10OT
PLEASE SELECT OKE:
(1) DETERMINE/SPECIFY MODEL PARAMETERS
(2) RUN tax;
(3) VIEW MODEL RESULTS/INPUT DISTRIBUTIONS
(4) IKS LOGNORMAL, RETURN TO TOXICS KLA HEK'J
ENTER SELECTION (1-4)
(Hit return for 4)
3
VIEW RESULTS/I KPUTS FOS LOGNDRKAL *N ALTS IS
0: 705 WANT (1) PLOT OF FRiCUENCT DISTRIBUTION
(2) TABULAR OUTPUT
OR (3) EN~ VIE." KG. RETURN TC M>.IK LOGKORKAL KEK:
EKTER SELECT! ON (1- 3 )
(Kit return ler 3)
HKAT DO 70V WANT TO SEE
MD3EL RESL'LTS:
(1) RTVEF CONCENTRATION
IKPLT E:S":B-.TIONS:
(2) UPSTREAM FLOV
(3) DPSTREAV CONCENTRATION
(«) EFFLUENT FLOW
(5) EFFLUENT CONCENTRATION
EKTER SELECTION ( 1-5 )
(Hit return tor 1)
1
VrlAT TITLE K> 70V VANT (EC CHARACTERS KAX1KUM)
LOC-NORKAL RESULTS
tOC-KORKAL RESL'LTS
VALUE
» OF TIKE EXCEEDED 1 OF TIKE IK IKTERVAL RETURN PER:CD (TEARS)
C.100E-01
0.316E-C1
0.100E-00
C.316E-CC
C.100E-C2
0.316£-C2
0.100E-03
9E.67C
S3.2C
34.162
19.111
1C.2E1
S.OBt
2.20E
J.41C
14.429
22.6«S
22.0CC
15.071
6.B6C
5. life
2.676
C.OC3
C.CC3
C.OC3
c.c:s
C.OCE
C.C14
0.027
0.054
0.124
FIGURE 27
Example Session with Tabular Output from Log Normal
69
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LOGNDRXAL SIMULATION' TECHNIQUE
PLEASE SELECT OKE:
(1) DETERMINE/SPECIFY MODEL PARAMETERS
(2) RUN MODEL
(3) VIEW MODEL RESULTS/IKPL'T DISTRIBUTIONS
(4) END IOGNOR.VAL. RETURN TO TOXICS KLA MENU
ENTER SELECTION (1-4)
(Hit return for 4)
3
VIEW RESULTS/INPUTS FOR LOCS2RXAL ANALYSIS
DO YOU VAST d) PLOT or FRE:UEN:Y SISTPIS-.TICN
(2) TASVLAP CVTrVT
CP (3) END V:E"'1K3. RET'JRN TC MAIN LOGSCRy.AL KEN'J
E-JTER SELECTION (1-3)
(Kit return for 3)
1
WHAT DO YOU WANT TO SEE
K:DEL RESULTS:
(1) RIVER CONCENTRATION
:N?UT DISTRIB-TIONS:
(2) UPSTREAV. FLOW
(3) UPSTREAM CONCENTRATION
(4) EFFLUENT FLOW
(5) EFFLUENT CONCENTRATION
ENTER SELECTION ( 1-5 )
(Hit return for 1)
2
PLEASE ENTER TKE TITLE OF THE PLOT (EC CHARACTERS KAXIKUV.)
- U?S?RiS,y FLOW
25.-
t !
T
I 20.'
K
E
N
I
N
T
E
R
V
A
L
I
LOG 0.49 0.93 1.46
1.9S 2.52 3.05
UPSTREAM FLOW
3.58
4.11
4.64
5.17 5.70
FIfiURE 28
Example Session with Plot of Log Normal Inputs
70
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VI EV RESULTS/INPUTS FOR LOGKORKAL ANALYSIS
PC TO'J MART (1) PLOT OF FREDUENCT DISTRIBUTION
(2) TABULAR OUTPUT
OR (3) EK5 VIEVING, RETURN TO MAIN 1OGNORKAL KEK13
EKTEF SELECTION (1-3)
(hit return for 3)
1
WHAT DO 10u WAKT TO SEE
MODEL RESULTS:
(i) R:VER CONCENTRATION
JKrUT DISTRIBUTIONS:
(21 UPSTKEAV FLOV
(3, UPSTMAV. CONCEKTRAT:ON
(i) EFFLUENT CONCENTRATION
EKTE? SELECTION ( 1-£ )
(Hit return tor 1)
PLEASE ENTEK THE TITLE OF Tn£ PLOT <6C CHARACTERS KAZIKUK)
LOC NORMAL RESULTS
I IOC.
0
F
e:.
T
I
Y.
E e:.
E
X
c '«:.
E
E
D
E 2:
LOG -i.CC -C.iC -C.2C
0.20 0.60 1.00 1.40
LOG KORXAL RESULTS
1.60
2.20 2.6C 3.CC
V:E» RISVLT
D; T3'.- WAK7
LOGIORKAL AKAL?S:S
S! STRI BLT1ON
(1) PLCT OF FR
(2) 7ASULAS OL'TP'JT
OR (3) EKS V:E-."NC, RETURX TO KAIK LOGKORKAL KEKU
EN'TEP SELECTION d-3)
(H:i return lor 3)
3
FIGURE 29
Example Session with Plot of Log Normal Results
71
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VI. PERFORMING WASTE LOAD ALLOCATIONS
Overview
Each of the three techniques documented herein - Continuous Simulation,
Monte Carlo, and Log Normal - can potentially be used to perform toxics
waste load allocations. However, not all techniques can be applied in all
situations. In general, Continuous Simulation should be used in cases where
time series information on model inputs is well defined. Log Normal should
be used in single discharge cases where all model parameters are
approximately log normally distributed. Monte Carlo should be used when
neither of the other techniques are applicable, or in conjunction with the
other techniques. In some cases, the data may be insufficient to use any of
the three techniques.
This chapter discusses at an introductory level the conditions where
each of the techniques may be applied, and gives brief guidelines for
selecting between them. The chapter also briefly discusses how to perform a
waste load allocation for single and multiple discharge cases and how to
calculate the return period. Last is a discussion of toxic concentration
criteria. Discussions provided herein are very brief only as necessary to
alert the users to important technical issues. More detailed discussion is
beyond the scope of this users manual.
Selecting Between Techniques
Each of the thret techniques can be applied to perform toxics waste
load allocations and no one technique is necessarily preferable to any other
on a theoretical basis. However, all three techniques are not similarly
accurate or appropriate in all situations. This section highlights when
each technique should bt applied.
Continuous Simulation: Continuous Simulation is the most powerful technique
but only when sufficitnt ti»*-series data are available to define the input
parameters. The povtr of Continuous Simulation decreases significantly when
data must be synthtsutd to replace missing historical values. The
guidelines for selecting Continuous Simulation as a function of time-series
data availability can bt suMtarized as follows:
Time-Series Applicability of
Data Availability Continuous Simulation
All input parameters available Very high
and complete
Only one effluent parameter missing High
or significantly incomplete
Both effluent parameters missing Fair
but other data is complete
All other cases Poor
72
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Continuous Simulation can be very reliable when analyzing the frequency
distribution of concentrations for existing conditions where all parameters
are well defined. However, the technique 1s at best fair when projecting
concentrations for future treatment alternatives because the sequential
nature of effluent flow and concentration cannot typically be defined as
treatment changes. If the user is uneasy about this problem 1t is possible
to use Continuous Simulation to simulate the concentration distribution for
existing conditions and the Monte Carlo technique for projecting the Impact
of future treatment alternatives.
Monte Carlo: Monte Carlo analysis has the least stringent input
requirements of any of the three techniques and therefore the widest
applications. It is best used In situations with limited cross and serial
correlation of parameters; 1n these cases Continuous Simulation is preferred
where data are available. It can be applied 1n cases where the available
data are inadequate for either Continuous Simulation or for Log Normal
analyses. However, if the data are insufficient or inadequate the
reliability of results must be considered. Any of three standard
statistical distributions - uniform, normal, or triangular - should be used
whenever possible to describe input data; but data defined distributions can
also be used. Since data defined distributions can be used for even the
most limited data sets, care should be taken to ensure that sufficient data
exists to provide meaningful results.
Log Normal: The Log Normal technique 1s attractive because it requires far
less computational expense than the other two techniques. However, it can
only be applied for waste load allocation with single discharges and where
all input parameters have been shown to be log normally distributed, The Log
Normal technique can also be used as a lower-cost screening technique when
parameters are not all log normally distributed before conducting more
complex analyses with Continuous Simulation or Monte Carlo. In examining
the consistency of data to log normality special emphasis should be placed
on the "tail ends" of the distribution curves. It is typically at the
extremes of the input distributions where water quality problems occur and
thus where the assumption of log normality must be the most rigorously
justified.
Allowable Effluent Loads
Water quality criteria are currently defined for maximum concentrations
of a constituent for a three year return period. For acute toxicity, the
instream concentration should not exceed 0.3 times the toxic concentration
level (or 0.3 toxic units acute) more than once 1n three years. Although
the critiera were determined for a one hour duration, the criterion will
generally be interpreted on a daily averaged basis because more frequent
calculations cannot be practically supported by data. For chronic toxicity,
the instream concentration for a four day average should not exceed the
chronic toxic level (1.0 toxic units chronic) similarly more than once in
three years. Allowable effluent loads should be calculated to maintain
these conditions.
73
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The waste load allocation process determines the effluent concentration
and flow that will result in a three year return period for the desired in-
stream concentration. DYNTOX allows two ways of determining the allowable
effluent load, both of which are equally valid and consistent:
1) inspection of the return period corresponding to a
desired in-stream concentration;
2) inspection of in-stream concentrations corresponding to
a desired return period.
Using the first method, a user performing an acute waste load allocation
would inspect the return period for an in-stream concentration of 0.3 tua.
If the return period is less than three years, the effluent load is too
large and must be decreased. If the return period is greater than three
years, the effluent load may be increased. The waste load allocation
process using this technique consists of finding the largest effluent load
that will result in an in-stream return period for three years or greater
for the water quality criterion.
The second method for performing a waste load allocation is to
determine the in-stream concentration that has a three year return period.
For the acute toxicity example, the user inspects the in-stream
concentration with a three year return period. If this concentration is
greater than 0.3 tua, the effluent load is too large and must be decreased.
If the in-stream concentration with a three year return period is less than
0.3 tua, the effluent load may be increased. The waste load allocation
process using this technique consists of finding the largest effluent load
that will result in an in-stream three year return period concentration less
than or equal to the water quality criterion.
Multiple Discharges
Establishing allowable toxic loads among multiple discharges in one
system involves technical and policy issues handled differently by different
states. One simple approach is to calculate the maximum allocations
successively, upstream to downstream, ignoring the inherent upstream
preference. A second approach would be to require consistent removal
efficiencies from all discharges ignoring that the assimilative capacity may
not be fully used in all river segments or allowing individual increases. A
third would be to assume no decay and allocate proportional to flow. The
list of options is extensive. The specific policy and procedure is a State
issue which involves technical, policy and political consideration.
However, DYNTOX can generally be adapted to address most any State policy.
In the illustrative examples included in this Appendix, a very simple
approach is used wherein allocations are conducted successively upstream to
downstream. This procedure was chosen only to illustrate the use of DYNTOX
and in no way represents a recommended procedure for allocating among
multiple discharges.
74
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Calculating the Return Period
Two common methods exist to calculate the return period for a given
concentration from probabilistic modeling. They are termed herein as:
1) the percentile method
2} the extrema method
The percentile method uses a listing of all in-stream concentrations and
ranks them. The return period for a concentration is then calculated based
upon percentile occurrence. In the extrema method, only annual extreme
values are used in the ranking. The return period calculated from these two
methods are equally valid statistical representations, but neither
necessarily predicts annual occurrence frequency.
The percentile method assumes that all violations of the in-stream
criteria are independent from each other. Every exceedance of the criteria
is treated equally, including multiple violations in the same year. Results
from this method therefore represent an "average" return period. The
disadvantage to this technique is that multiple violations related to the
same extended event (e.g. drought river flow) are treated as separate
events, which could lead to an estimation of the recurrence interval which
is more frequent than actually characteristic. The advantage to the
percentile technique is that multiple, independent violations occurring in
the same year are correctly incorporated into the return period analysis.
The extrema method uses only the largest concentration for each year in
calculating the return period value. This technique predicts the return
period for an annual extreme value and has the advantage of not "double
counting" multiple violations that are caused by the same event. The
disadvantage to the extrtaa method is that when multiple independent
violations occur in tht itae year, only one violation is considered in the
return period analysis. TMs can lead to an estimate of the return period
which may be longer than tryly characteristic.
For the DYNTOX tinplts provided in this report, as for all analyses
conducted using DWTOI. the percentile method is used. Users have the
ability to perform titrnu analysis by running Continuous Simulation one
year at a time and Rtnvally tabulating the extreme in-stream concentration
for each year. InwtittyatIons are now being conducted to establish the
appropriate application of the two techniques and the need to adapt DYNTOX
to more directly compute the extrema method.
In either case the degree of confidence that can be placed in model
results is directly.related to the amount of input data available and the
return period for the concentration of interest. In general, the longer the
return period the more data that is required. If recurrence intervals of 10
to 20 years are desired, input data should accurately define the 30 year
return value of all input parameters in order to estimate the probability of
such rare events. Although the program will provide results using an
inadequate data base, these results should not be used in performing waste
load allocations.
75
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Toxic Concentrations
Toxic concentration criteria for waste load allocation can be
determined by two methods:
o chemical specific
o effluent toxicity testing
The chemical specific method involves using scientific toxicity data for a
particular toxicant and establishing the concentration level of acute and
chronic toxicity. Limited consideration Is typically given to synergistic
and antagonistic effects with other parameters. On the other hand, effluent
toxicity testing uses an operational approach. Bioassays are performed with
the effluent at different dilution levels to determine Its toxicity as a
whole. Its toxicity is then defined in toxic units where one unit equals
the least concentrated dilution which caused the test endpoint. Other
levels of concentration are described in toxic units which are multiples of
this dilution. Detailed discussion of these concepts is not appropriate for
this users manual and the reader is referred elsewhere (EPA, 1985). However
some comments are appropriate.
Whole effluent toxicity testing has many advantages because 1t directly
considers site specific effluent toxicity and inherently considers multi-
parameter effects. However, on the downside:
o almost no toxic unit data exists for upstream water
quality
o defining combined effects of multiple effluents is
difficult
o quantifying in-stream decay of toxicity is also difficult.
In contrast, chemical specific toxic criteria are simple to use and apply.
They are limited however because they:
o are not site specific
o do not consider synergistic effects
o do not consider antagonistic effects
Both options have advantages and disadvantages. The reader is encouraged to
research these issues in more appropriate technical documents (e.g. EPA,
1985).
76
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VII. REFERENCES
DiToro, D. M. Probability Model of Stream Quality Due to Runoff. Journal
of Environmental Engineering, ASCE, Vol. 110, No. 3, June, 1984.
Fiering, M.B. and B. Jackson. Streamflow Synthesis, American Geophysical
Union, 1971.
Freedman, P.L. and R.P. Canale. Modeling Uncertainty and Variability for
Waste Load Allocations. LTI, Limno-Tech, Inc., prepared for USEPA
Monitoring and Data Support Division, August, 1983.
SAS Institute Inc. SAS User's Guide: Basics, 1982 Edition. Gary, North
Carolina, 1982.
Thomann, R.V. Systems Analysis and Water Quality Management. McGraw-Hill,
New York, 1972.
USEPA Office of Water Technical Support Document for Water Quality - based
Toxics Control. September, 1985.
USEPA Storet User Handbook. USEPA, Washington, D.C., 1982.
77
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