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Dynamic Toxics 

Waste Load Allocation Model 

(DYNTOX) 

USER'S MANUAL 

Prepared for: 

USEPA Monitoring and Data Support Division 

Washington, D.C. 

Prepared by: 

Limno-Tech, Inc. 

Ann Arbor, Mi. 

September 13, 1985 
PREFACE 

This report represents a Users Manual to explain how to use the DYNTOX 

model. This computer models 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 AndersonNichols 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 Wang, also of Limno-Tech, Inc. 

are thanked for their program contributions. 

LTI, Limno-Tech, Inc. 

Paul L. Freedman 

President 

LTI, Limno-Tech, Inc. 

David W. Dilks 

Project Manager 
I. 

II. 

III. CONTINUOUS SIMULATION.................................... 12 

IV. MONTE CARLO .............................................. 34 

V. LOG NORMAL ............................................... 57 

VI. PERFORMING WASTE LOAD ALLOCATIONS........................ 72 

VII. 

TABLE OF CONTENTS 

TITLE PAGE 

LIST OF FIGURES .......................................... 

LIST OF TABLES ........................................... 

OVERVIEW ................................................. 

Background.. 

Concepts.... 

Organization 

COMMON REQUIREMENTS 

....................................... 

....................................... 

of Manual .............................. 

...................................... 

Model Access ........................................ 

Upstream Boundary Data .............................. 

System Data ......................................... 

Effluent Data ....................................... 

Theory .............................................. 12 

Input Requirements .................................. 16 

Program Use ......................................... 20 

Theory .............................................. 34 

Input Requirements .................................. 37 

Program Use ......................................... 41 

Theory .............................................. 57 

Input Requirements .................................. 58 

Program Use ......................................... 61 

Overview ............................................ 

Selecting Between Techniques ........................ 

Allowable Effluent Loads ............................ 

Multiple Discharges ................................. 

Calculating the Return Period ....................... 

Toxic Concentrations ................................ 

REFERENCES ............................................... 77 

i 

iii 

1 

2 

3 

4 

8 

9 

11 

72 

72 

73 

74 

75 

76 
FIGURE TITLE PAGE 

LIST OF FIGURES 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

I5 

16 

17 

18 

19 

20 Example Session Specifying Data Defined Distribution.... 54 

Example Session with ANNIE (Inexperienced User)......... 6 

Example Session with ANNIE (Experienced User) .......... 7 

Determination of lime of Travel Input Constants ........ 10 

Continuous Simulation Modeling Schematic ............... 13 

Concentration Frequency Curves ......................... 15 

Hierarchy of Continuous Simulation Subprograms ......... 21 

Example Session with Continuous Simulation Program 

Entry ............................................... 22 

Example Session with Continuous Simulation 

System Constants .................................... 24 

Example Session with Continuous Simulation 

Effluent Specification .............................. 27 

Example Tabular Display of Continuous Simulation 

Inputs .............................................. 30 

Example Plot Display of Continuous Simulation Inputs ... 32 

Example Plot Display of Continuous Simulation Results .. 33 

Schematic of Monte Carlo Technique ..................... 36 

Example Monte Carlo Input Distributions ................ 40 

Hierarchy of Monte Carlo Subprograms ................... 42 

Example Session with Monte Carlo Program Entry ......... 45 

Example Session with Monte Carlo System Constants ...... 47 

Example Session with Monte Carlo Specifying Effluent 

Distributions ........................................ 48 

Example Session with Monte Carlo Specifying Triangular 

Distribution ......................................... 52 

i 
FIGURE TITLE PAGE 

21 

22 

23 

24 

25 

26 

27 

28 

29 

LIST OF FIGURES (Continued) 

Example Session with Monte Carlo Viewing Results 

in Plot Format. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Example Session with Monte Carlo Viewing Results 

in Tabular Format. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Hierarchy of Subprograms for Log Normal.............. 

Example Sessions with Log Normal Program Entry....... 

Example Session with Log Normal Input Specification.. 

Example Session Performing Log Normal Simulation..... 

Example Session with Tabular Output from Log Normal.. 

Example Session with Plot of Log Normal Inputs....... 

Example Session with Plot of Log Normal Results...... 

55 

56 

62 

64 

66 

68 

69 

70 

71 

ii 
LIST OF TABLES 

TABLE 

1 

2 

3 

TITLE PAGE 

Input Requirements for the Continuous Simulation 

Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 

Input Requirements for Monte Carlo Technique........... 38 

Input Requirements for Log Normal Technique............ 59 

iii 
I. OVERVIEW 

Environmental contamination by toxic substances can pose risks to 

public and ecological health. Regulatory agencies are now establishing 

regulations and procedures for determining allowable discharge limits 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 associated 

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 chronic 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 instream 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 instream 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. 

1 
Concept s 

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 

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. 

2 
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. 

3 
II. COMMON REQUIREMENTS 

The three analytical techniques contained in DYNTOX, 

conceptually quite different, have several common requirements. 

al though 

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 

DYNTOX from STORET. 

through 

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. 

Presently, DYNTOX is accessed 

ANNIE program was originally designed and supported by the U.S. Ge ological 

Survey in cooperation with the U.S. Environmental Protection Agency 

users interactively create, check and update inputs to models and 

the actual model simulation. Limno-Tech, Inc. has added the capabi lity of 

probabilistic simulation. Presently, the only way DYNTOX 

accessed is through ANNIE. This section briefly describes the ANNIE 

and how it is used to access DYNTOX. 

through the computer program ANNIE. The 

to help 

perform 

can be 

program 

4 
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 

system to be used. If ANNIE has not yet been 

before DYNTOX can be accessed. Installat 

described in the Appendix to this report. 

install ANNIE on the computer 

installed, this must be done 

ion of ANNIE and DYNTOX is 

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 use rs. User responses are denoted by arrows. Note that all 

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 

not relevant to the U 

always be NO. 

to User Control Input (UCI) files. This question is 

se of DYNTOX and the answer to this question should 

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). 

5 
.1.....1..1.......1.t...............,,.............,...., 

. . . ..a VLLCOtC TQ -ANNif . . . ..I 

. . ...* VERSION DAfLS DLCLK3ER 5. 198b . . . . . . 

. . . . . . . . . ..1..........~.................................. 

I)y TO:’ wn UC, SD4CC, DP WTS Or LfPtfi:trCt CC”J- ‘“‘: t’ 

C NC 

~lrc. AN1;:f hr:ps cremte rnC fir the drtm for thr tire-rerirr 

file ITS !11e) thmt ia used by l oae of thr rodrlr. 

Dor’t be concr:nrC l bout b+C rrtraes. 

W*lt 9urdrr JCL tc l cct;t4t;e resp:nscs. 

L’r.t - . q&St10 lC?‘t Ci*l:. t-cer a qhJtrt:or mArs 0). 

Ha-y O! tht OF:lOnS l rt prt Of 1OOpS. b-htr you have iaraarhed 

l :: l ctiv:tlea r:tt.;r l l tt of oFtIons. l nttr do?t tc 

*sit iron tht 100~. 

W2P.c 

Slr,lrtior: of hydrology using HSPf. 

Interactively crrrte/mdC/~,3d;fy/llrt TSS file. 

Strtarticml l r.r:yrlr of tine-•rrier data. 

Sir,:rtiot ritt Pre:lp./Runc!f Hadtl Syrtea. 

D:rtrlbLteC R-&tins k:n!rl;/Rut.~ff pro;rar. tt 

US AR! rr:r.!aL:/ru?c!! rodtl. l m 

mt!cr?rts cszs. YXL, b!SPf st;utTtial t rles 

l nC rdis drtm tc YSS !:lt fro- l t;atrt:m: lilts. 

P:ctr data froc various soJrc*s to plotters. 

D>-.rr;c fcl;cr Ar~c!yrrr. 

. . Ntt ytt rvr.;a:lr. 

FIGURE 1 

Example Sesslon with ANNIE (Inexperlenced User) 

6 
.1......11....,........*.....................*........... 

.L..., vLLCcx.c To l AWh:t’ .,.... 

,...I, VEPSION DATE3 DtCWl3LR 5. 1964 . . . . . . 

.~~~....~...~.~......,,,..........~.~..~....~~.~~~~~.~..~ 

DC To3 IUUVL Y3. SW. OP LO% OF U?LK:tr;Ct US:YG ANK:t? 

* s3E 

w+.r: MXXZ on PmcLSS no TX WAN? T-2 USE? 

t 01 

DTKW: C TcI:CS ANALTSES 

EC:TCP SLLtC,!Oh (l-4) 

(H:t rrturc (or 4 1 

>8 

SALT, Ll Sf , OE DLXTf tL<?3MRT DC1 ?lLt 

*D 

FlGURE 2 

Example Sesslon with ANNIE (Experienced User) 

7 
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 STORET. 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, 

should be used. 

the nearest gage downstream 

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. 

contained 

Details for this procedure are 

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 

corcentration 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 ccnditions 

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 

Fortunately, 

program operation. 

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. 
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 outfaT: LJ 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 (instreas 

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, 

curren? 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. Flowdependent time of travel is recommended and is calculated by the equation: 

Time of Travel - aQb (1) 

where Q is river flow and a and b are constants. The coefficients a and b 

can be determined by plotting observed time of travel (distance/velocity) 

values at different flows on a log-log scale (Figure 3). The coefficient a 

is the y-intercept of the best fit line through the data, while b is the 

slope of the line. Note 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 

9 
. Doto 

- Best fit line 

b = Ay /Ax = -0.4 /day 

1 I 234567891 

In Q kfs) 

l Doto 

- Best fit line 

k= Ay/Ax=0.4/doy 

I I 1 I 

I 2 3 4 

Time of Travel (days) 

FIGURE 3 

Determlnatfon of Input Constants 
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. Uhen 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 
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: 

• frequency and duration of concentrations; 

• instream fate and transport; 

• single or multiple pollutant sources: and 

• 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. 

to Continuous Simulation 

Another disadvantage 

is that computational requirements are 

significantly higher 

analysis. 

than for steady state modeling or for Log Normal 

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 (Qe) and effluent concentration (Ce) and 

combines these with daily upstream receiving water flow (Qu) and upstream 

concentration (C ) to calculate downstream receiving water concentrations. 

The concentration directly below an effluent outfall (Cd) is determined from. 

the equation: 

(2) 

12 
FIGURE 4 

Continuous Simulation Modeling Schematic 

(from USEPA 1984) 

13 
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 1s constructed from these ranked values, and the 

recurrence frequency of any concentration of interest can be obtained (C 

vs. frequency). Running average concentrations for four days, or for an 4 

other averaging period, can also be computed from the simulated 

concentrations, ranked in order of magnitude, and a lso presented as a 

probability distribution (see Figure 5). 

The Continuous Simulation model can predict the concentration below 

each of a series of discharges. Successive concentrat ions 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: 

C, - Cd l (emk’) (3) 

where: C 

$ 

= concentration above the second discharge 

= concentration below the first discharge 

- 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 

I4 
50 

- 

? 

z40 

30 

20 

. 

01 I I I I I I I I I 

99 99.5 IC 

Percent of Time Concentration is Less Than or Equal To 

I 05 I 

Recurrence Interval (years) 

F IGIJRE 5 

Conccntrat 1 on Frerlwncy Curves 

(from USCPA, 1 !IWr) 
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 carrel at ion 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 

l:e 

Chapter 2. This section detalis the specific input requirements for 

Continuous Simulation technique. The inputs can be generally 

categorized into four groups: 

0 general simulation requirements, 

0 upstream data, 

Q effluent data, and 

o system physical and hydrologic constants. 

All of these inputs are summarized in Table 1, and will be discussed 

individually in this section. 

General Simulation Requirements: The Continuous Simulation method 

requires some general information on the system that will not change between 

simulations. The first basic input required for Continuous Simulation is to 

establish the period of the simulation. This consists of the beginning 

and the end date of the 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 
Data Source 

o Genera? Information: 

- Beginning and end date of simulation 

- Number of discharges above flow gage 

- Average point source flon above gage 

- TSS computer field name 

o Upstream Data: 

- Time series flow data 

- Data synthesis technique for flow 

- Time series concentration data 

- Data synthesis technique for concentration 

o Effluent Data: 

- Time series flow data 

- Data synthesis technique for flow 

- Time series concentration data 

- Data synthesis technique for concentration 

0 System Constants: 

- Time of travel information 

- First order decay rate (s) 

- Drainage area ratio (s) 

- Water withdrawal rate (s) 

USGS flow records 

User defined 

Treatment records 

User defined 

STORET 

User defined 

STORET 

User defined 

Treatment records 

User defined 

Treatment records 

User defined 

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 Ccntinuous 

Simulation technique: 

:: 

linear interpolation 

simple tlarkov 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 in 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 and concentration (or toxicity). The source of 

these data must be user specified. As for the upstream data, gaps are 

likely to exist in any data set. Here again, the user must use either 

linear interpolation, simple Markov, or multi-period Markov to synthesize 

data for missing days. Any downstream tributary inputs occurring between 

discharges should be considered as a separate effluent input. 

System Constants: System constants need to be defined for hydrologic and 

physical characteristics of the system. Model inputs for physical data 

include time of passage between 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 hydrologic 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 (>lX of river flow) 

is withdrawn from the river at any location, this withdrawal rate must be 

specified before performing a Continuous Simulation waste load allocation. 

Program 

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, 

0 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 
Inuut blulf21 View/Analyze Vle*/AnalYle Con t I nuous 

!aeclf IcatIon Sllltilat IOfl lnwts Hcsul ts Slmulat 100 

h . 1 b 1 & 4 

i 

FlGURE 6 

HlerarChY of Continuous Simulation Subproqrams 

21 
7a. Nero TSS File 

FlGURE 7 

Example Session with Continuous Simulation 

Program Entry 
7b. Existing TSS File 

Terminal Entry of Date 

FIGURE 7 Cont'd. 

Example Session nith Contlnuous Slmulatlon 

Program Entry 

23 
FIGURE 8 

Example Session Hith Continuous 

Simuiation System Constants 
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 b;g,,ificant 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 useI- 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 STORE1 

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 fnput 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 in the order in which actlvites 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 1s 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 Harkov 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 Harkov process requires somewhat more user input than the 

other data synthesis techniques (see Figure gb). 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 autocorrelation 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 Interpclatlon and Simple Markov 

:C.SS 

Cf\Th*T:OhS 

f; CChTI hl-‘L’S 

s::E b’:SS:h; 3hYA 

FIGURE 9 

Example Sesslon nith Continuous Slmulatjon 

Effluent Specifkation 

27 
9b. Mu1 tiple Period Markov 

k 1 

FlGURE 9 Cont’d. 

Example Session with Continuous Simulation 

Effluent SPeclfication 

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 

successiully executed. 

Model Simulation: The model simu lation can be conducted any time after the 

inputs have been fully specified. No additional inputs are required to run 

the simulation. The program w ill 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 

(l-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 mLst be supplied. The user theri 

has the option of selecting a table (Figure IO) and/or a plot (Figure II) 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 viewl'analyze cnputs 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 
FIGURE 10 

Example Tabular Display of Continuous 

Simulation inputs 

30 
VAb.’ - 6.53: C-b.,h’;ARf Df’-‘Af:O\ . 

CjL’i:::LC: OF \‘AK;AY;Oh :’ C.iEl’ 2.4:: 

r.c 

i.!: 

5.c: 

7 .5: 

:: .c 

Ii.! 

1I.C 

17 .5 

2E.C 

2i.5 

2F.C 

rc: .c:: 

,,- ,-- L. .,.. 

eS.C” 

C! .!7< 

I?.(:( 

3.i75 

C.C 

C.C 

t.c 

C.C 

t.: 

: 

1’ L 

22 

43 

1s 

3 

C 

c 

t 

C 

c 

5;: 

45' 

1t5 

72t 

27s 

c 

C 

C 

C 

c.c:: 

c ;:I 

; .c:: 

c.c:< 

C.C’2 

C.CC4 

-55c.c:: 

-955.c:: 

-S!F.:c: 

-oci.c:c 

-FF'.C:: 

FIGURE 10 Cont’d. 

Example Tabular Display of Contlnuous 

Simulation Inputs 

3f 
v:fi’*- . . AhALTS:S OF ISPITS 

W-: CI! PAK4ETLR DC 13, YAY: f; V:L’d? 

( 1) OL’TFAL; D: S:hAR;L 

(2 : O”T’A.‘-L c C3~:LcfKr-r: 04 

(31 UPSTRLW Bt’s :;AFY D: SthAF;t 

(4 I UPSfRLV B:“h34RT COh;‘h’:fiAf:oK 

-3 

D: It’,‘ &AK‘: f, 5” A P’--’ .- s.. 

NT 

: 4’:;; .‘A.. OF C.y.‘;A::Vl F;R”J: 

5: .-..-........-...-..-..~.---................~.......................... 

I 

I . 

(y .~..~...--..~...~.~...-~~,~..~...~..~~......~.~...~....~.~............. 

I . 

I 

, . 

0 

. 

j: -------.---..-.------.--..-~.----.-~------.------~------.------.------~ 

. , 

. I 

. . * 

;: .-.---..------.-.-,.-.-.-,...-.~....-.............--......--..........- 

. . . , 

I . . 8 

. . . 

, 

.,: . . . ..--........--..~-......-.....-...---...-.---..---..-..--......-.... 

9 

. . . . 

I 

. . . . 

I 

I I . . . . , 

c .‘--,-‘.--.,-‘.---,-..---,-..-......---.--.---.-..--.,--..--........... 

c.: 2.5 5.c 7.: 1: .: Ii .S YE.0 17 ‘ 2:.c 2i.5 2z.c 

LfF.‘::..: C3s:L’T~~:Os *- 

FIGURE 11 

Example Plot Display of Continuous Simulation Inputs 

37 
D: TO; UAKT T: SLt A PLY 

1 

L--.4: f:‘X D- - 1;‘. WAY: (E: Chr=~fTfF VAAL:FTJ” 

C3h’Ti h;‘CL’S s:&:; Oh C3h:EY:id:: Oh 

0 

. 

(: .-------------.-------------...,,.,.....,..*.......,.,.,,,...*...,..,.. 

C.C t.5: 1 .c: 1.5: i.C: i.“ .L 

CQC'T:h"J;;'S S:K" b7;3N C3h:EVTM::Oh .- 

FIGURE 12 

Example Plot Display of Continuous Simulation Results 

33 
IV. MONTE CARLO 

The second technique which can be used to simulate a probability 

distribution for instream toxics concentrations is 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: 

• calculates frequency and duration of toxicant concentrations; 

• includes instream fate and transport processes; 

• simulates single or multiple pollutant sources; 

• requires less extensive data than Continuous Simulation; 

• model inputs need not follow a specific statistical function; 

• 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 model 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 when 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 prediction. Single values are selected for upstream 

flow, upstream concentration, effluent flow, effluent concentration and 

decay rate. The model 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 

analysis. 

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 is 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 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 distributions 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 
MONTE CARLO TECHNIQUE 

A’= I, n 

, Water Quality Model 

, Cd = + 1 QU ClJ + Qe ce 

Qu + cu 

t 

FIGURE 13 

Schmatlc of Monte Carlo Technicluc 
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 Honte 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: 

0 general simulation requirements, 

0 upstream data, 

o effluent data, 

0 system physical and hydrological constraints, and 

number of iterations 

Generil 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 c' 

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, the 

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 the upstream boundary flow and concentration. The 

Monte Carlo technique allows the use of assumed data distributions or the 

observed data when selecting input distributions, The latter requires 

STORET data defining these conditions, STORET data defining boundary flow 

and concentration should be retrieved as described in the Oata Requirements 

chapter, and stored in separate 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, termed 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 (UNIVARSATE 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 USGS flow records 

- Number of years of observed data USGS flow records 

- Number of discharges above flow gage User defined 

- Average point source flow above gage Treatment records 

- TSS computer field name User defined 

0 Upstream Data: 

- Flow Data 

- Statistical Distribution for Flow 

- Concentration Data 

- Statistical Distribution for Concentration 

o Effluent Data: 

- Flow data 

- Statistical di 

- Concentration 

- Statistical d 

STORET 

User defined 

STORET 

User defined 

stribution for flow 

data 

stribution for concentration 

Treatment records 

User defined 

Treatment records 

User defined 

0 System Constants: 

- Time of travel information 

- First order decay rate (s) 

- Drainage area ratio (s) 

- Water withdrawal rate (s) 

o Number of Iterations 

Dye studies, 

current meters 

Instream data 

USGS topographic maps 

Withdrawal records 

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 OYNTOX 

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 'Jser 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 Comnon 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 
. 

Value 

Value 

Data Defined 1 

Value 

01 

Value 

01 

Value 

FlGURE 14 

Example Monte Carlo Input Distributions 

40 
Another system constant required by Honte 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 w25?c 

computer time. The recommended method for determining the proper nur.ber of 

iterations is to run the Monte Carlo techniqlre 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. 

Proqram w 

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: 

0 Program Entry, 

0 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 
svs tea View lnnlt 1 Run Vlew/AnaIy7e End fbnte 

Constalts mta/SPPclfY Mork!I Rt!SUI ts lIlstrlhltlm Carlo 

t . 

, 

FIGURE 15 

HLerarchy of Monte Carlo SubPrograms 

42 
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 {ear/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 STORE1 

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 lea). 

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. 755 (lime 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 questlon 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 STORE: 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 

16~ 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 STORE1 files or from the terminal. 

Instead, the user enters only the previously calculated distribution 

information. (e.g. Figure 18a). 

44 
162. Nek TSS File 

.- 

Example Session nlth Monte Carlo Program Entry 

45 
16~. Terminal Entry of Data 

7 

HAVE TO;’ PIEVIO~SLT CRLAYLC A TSS I:L t r3R W!S s:rC,“*TION? 

t HZ 

PL’rS’ LA,:: b--::t T:;P fSS f”t .C IS 1h:T:AL:Zt: . . . 

1K:T:At:ZAf;Ol OF Tt,R ?SS f:LL IS NW CP!-‘,tff. 

ldb. Existing TSS file 

c 

hb’.‘: TX P2S’.‘:C’,SLT CRZhTE,Z A TSS T:LL r3R tH:S S:KiLATiOh:' 

t YES 

b--h: IS TrE NAVY OF Tt,R fSS f:Lt’ 

t tAhu?Lf 

J 

L 

FIGURE 16 Cont'd. 

Example Session nith Honte Carlo Program Entry 

46 
PLTASC Sfl’Ct ONE: 

( 1) SP’CITT STST’! COSS:A~fS 

(2) V:LZ lb?‘” DATA/S;Z::~T 31STR:BL’TIOSS 

(3) R’,‘c r:xL’ 

:c\s’ 

L\TfF sf-E:T:3\ t '-5) 

(r t rr:-TT fc: 0 

-1. 

(hit rr:,a:n for 1) 

t1 

Y-A: IS 7:: T:M Or ;U’s’fL :N >A?$ 

(h:t rrturn for 0.) 

t. 1 

WA: IS frt FIRS: CF:IEa 3ECAT KATE TR3P’ 

T-L BC3AZT TC fr.L fiRSY L:StkARSt 

i’SE L’S::S OF (l,‘:AT) 

(h-it rt:-:r. for C.) 

t .' 

L--A? IS '6: L':f-Z:A-'A'- Rb:t 

* 0.t 

b--A: :$ Tr: ;?A:'iA;L APiA KAT;C Or C:SC'4?ZE I 1 

72 TnE :‘SGS GAGE 

(k:t I,:-::, fcr 1.1 

D 1. 

:P FRY 

FIGURE 17 

Example Session with Monte Carlo System Constants 

47 
182. Densnstratlon of Uniform and Normal Distributions 

FlGURE 18 

Example Sesslon with Monte Carlo 

Specifying Effluent Distributions 
18b. Blvarlate NDmal Distribution 

(3) TR:A’.‘;L’LAR 

(0 DATA DifiKE3 

Ch’TLR SLLLcf;Or; ( l-4 1 

tHrt rtturn for 1) 

-2 

b--.4: IS 7:rt ELK VAL’,‘L 

It.: re:-rr for 1.1 

> 2s. 

k,s:ST;E ;,“‘;A? 3E’::A::OS 

- . 

W:A: 

1b.t 

*3. 

S?L: 

b--A: 

(1) 

II) 

0) 

(41 DATA 3LC:sES 

CKTLR SELE:T:3h 1 :-a) 

(Hlc re:irn for 1) 

-7 L-SAY IS TiL +!!A% VALUL 

(Hit rt:Lrn for 1.) 

WS. 

b-547 s :S Tn'f S.AS;A;W D,“.‘:AT;ON 

(E;c ret,:3 for 0.1 

sp:::rT r;3s :hf:~v41::0h rtn c:s:-razz 

b-hb: TIPE. Of 3:$:::9;Ti3h h’ YCL’ UAhT’ 

(1) LXIFZ’R’! 

0) NtR”AL 

FIGURE 18 Cont’d. 

Example Session nlth 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 

1 View Data/Specify Distributions 

Run the Simulation 

View/Analyze Model Results 

End Simulation 

f 

4 

5 

Although there is fl 

system constants must 

ending). 

exibility in the order in which options are selected, 

be specified before choosing any other option (except 

System Constants: The system constants consist of time of travel, firstorder decay rate, drainage area ratio, and water withdrawal rate. ProgriT 

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 l-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 
LPtCIFlCAflDh Of 1L’PiiT DlSfR:BLC:lONS 

O\‘lZC MC%’ KANT DAIS DC TO;’ WANT RESULTS AVERACt 

(Hit rrturn (or 1) 

w ’ 

PLEASE CHaost OWL: 

SPf::r:CAT:Oh Or IXhYhRT tZDb D:SfR:BZi3h’ 

I 

DC to3 L’Ah-7 Cc SLt A DATA D:STC:ILITi Oh P;of BLf3Rt CHX%:NC? 

-t 

1 NXPVA: OR CU’T--AT:- ?3RlUf I 

I 

&r 7zri1 DC 19:’ YW: TOR T;=R ~Lof 1 c3 cbiuuc7m ~U:KW) 

W- B:;T1;3ART ILo*‘ 

I 

1DC .------.-----*------.----------,------.------.-- ----.------.------. -..----. 

s I , 

I 1 

? I I 

I 0: .------*------.------.----------,------.------------.------*------.------. 

It I 1 

t I I 

I 

I 6: *------..-----.------.------.------.------. ------.------r------.------. 

K I ! 

I , 

I I I 

b ,t .------,------.------.------.------.------.-----~.------.------...-----. 

f I . I 

L I . I 

1, I . . I 

v 2: -------.---,--.---.--.-------------------. 

A I . . . 9 

*& I l . . . . I 

I . . . . . . I 

0 .---,--r---,--.---, --.---,--.---.--.*-. ---*---.--.---.--*---.--.---.-- 

0. 333. 103c. 153t. 2CCC. 21-c 

Bx.h3AR; -Lob 

3:cc. 353:. 4coc. .I\. . . . . 

“C’ 5”” 

FIGURE 19 

Example Session nith Monte Carlo Speclfylng 

Triangular Distribution 

52 
1tt .------1------.------.------.------.------.*-----*------.------*------. 

t , 1 

I , 

7 I I 

I &: .------.------.------.------.------.------. ------.-r---r.------*----r 

)! , I 

t I I 

I 

I 6: 

I 

.------.------.------.------.------.------.------.------.------.------. 

c 1 

~ : 

, 

I ; . 

(: .------.--.F.-.------.------.------.------.----~-.------.------.------ 

T I . ? 

f ! ? 

P 1 

.------.------*---;.-.------.-- 

4 

\' 2: ----.------.------.------.------.------. 

A ! P -I 

1 ! l ; . 

1 ! 

c ..-----.------.-.----.------.---p--.-- ;- r*--.------.-.r---.--.---,--. 

t. 5Ct. . . . . ___. iI::. ,", (t-7 i!::. 31-* . . . 3I:: 4;::. 45::. 5::: 

cj.';h.-: SJ,4 or fj:b.\-." cm- bF r'cTj:E,y;oh .- 

IF T:r:S tlf ACCtFTb.tlt' 

-1 

fh': or DJ.‘KJAKY - r ;S;’ S;t::T;CA?;Oh Sf;T:ON 

FIGUi?E 19 Cont’d. 

Exainple Sesslon with Monte Carlo Specifying 

Triangular Dlstrlbution 

53 
FIGURE 20 

Example Sessfon Soeclfylng Data Defined Dlstrlbution 
FIGURE 21 

Example Session with Monte Carlo 

Viewing Results In Plot Format 

55 
PLLASL CM33SL TRW THL tO,L3K:WC: 

r-*4 . C.hFb s~hh’;hR; Df.h’: b’: 3s - C.lCY 

C2LFf:c:LC: OT vAK:AT:oh = C.CSj 

VL’JL % or T:E LI~LL3LS I or 7:KL IL IKfLP’.‘AL RL?nJ. PLK: 3: ITLAPS ’ 

c.c :;: .C” c. c.c:3 

4: .2b( 

c.25: :5.75t C.Cf! 

3t .CE’ 

c.5:: 2C.C” . ” C.CCC 

11.3Ei 

c.75: lE.lSS c.c.5 

‘t.lf: 

,.c: i.CZ3 C.‘3! 

2.C:: 

‘.I! C.C -55s.c:: 

c .c 

1.5: C.C “CCC Q’,’ _-_. . . 

c.c 

\ .‘f C.C -52C.CL: 

C.C 

i.CL c.c -5os.c:: 

c, . c 

2.25 0.c -SFS.C?C 

c.0 

2.5: C.C -cFS.Cc: 

0; TCL‘ L;A~: T-2: (1 1 SLE b RLT,‘FJ. PLF:CD r3F A C:TTLkL\-Y VAL:T 

ii 1 cA;C;-"A'L ?dL VAL’L U:Tk A 5riML TLA.F llL,im. PLKl33 

OF 0 1 Ch3 TArL’LAP rr;ALTS:S 

3 

FlGURE 22 

Example Session Hi th Mnte Carlo Viewing Results 

In Tabular Format 
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 (Cd) based upon upstream concentration (Cu), upstream flow (Qu) 

effluent concentration (Ce), and effluent flow (Qe): 

Qu Cu + Qe Ce 

Cd Qu +Qe 

(4) 

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 
> C*. Since the 

variation of each input variable is defined by a mathematical equation, 

numerical integration can be conducted to determine the probability that 

Cd > repeating C*. By this integration for different values of C*, the 

probability distribution for Cd can be estimated. The probability of 

exceedance can be estimated for durations 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). 

expressed as a multiple integral of the joint probability density functions 

over the values of flows and concentrations for which Cd 

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 

exaggerated 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 
Oata 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 

o Upstream Data: 

- Mean and 84th percentile value for flak: 

- Cross-correlation between river flow 

and river concentration 

- Mean and 84th percentile value for 

concentration 

- Cross-correlation between river flow 

and effluent flow 

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 

0 System Constants: 

- Drainage area ratio 

- Water withdrawal rate 

USGS flow records 

USGS flow records 

User defined 

Treatment records 

User defined 

STORET 

SAS 

STORET 

SAS 

STORET 

STORET 

USGS topographic maps 

Withdrawal records 

0 Output Interval of Interest: 

- Minimum river concentration of interest User defined 

- Maximum river concentration of interest User defined 

- Interval for output User defined 

Table 3. Input Requirements for the 

Log Normal Technique 

59 
Upstream 8oundary Data: The Log Normal technique requires the mean and 

variance of the input distributions for the upstream boundary flow and 

concentration. OYNTOX provides the ability to determine the distribution 

parameters from observed upstream boundary flow and concentration. This 

requires STORE1 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 UNlVARIATE 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-correlatjon between river flow and 

effluent flow, and river flow and river concentration. These crosscorrelations 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 ard 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 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. 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 (>lX 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 @ 

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 

Program Entry. This section consists of specification of the time 

observed STORET data, modeled point source flow above the USGS f 

location of the data describing boundary conditions, and withdrawa 

the USGS gage and the effluent outfall. 

is termed 

period of 

low gage, 

1s between 

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 STORE1 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 
Iktcrrlne 

SlwKltv Moclel Run View Inputs/ ml 

ParimJctcr s HwJi!I Hcsul ts Cowuoraal 

4 4 8 4 L 

I 

4 

FIGURE 23 

Hierarchy of Subprograms for Cog NormaI 

62 
Another possibility for Program Entry is when the user has no STORE1 

data and wishes to enter data manually from the terminal (Figure 24~). 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 YYWIDD format. The final option of the Program 

Entry concerns the case where all input distributions were calculated offline 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. Neh- TSS FlIe 

FIGURE 24 

Example Sesslons Hith Log Normal Program Entry 

64 
ttI'i31. .4 

tt !:c’5. .73 I 

FIGURE 24 Cont’d. 

Example Sessions nith Log Normal Program Entry 

65 
FIGURE 25 

Example Session nlth Log Normal input Speclficatlon 

66 
FIGURE 25 Cont’d. 

Example Sesslon with Log Normal Input Specification 

67 
FIGURE 26 

Example Session Performing Log Normal Simulation 

68 
V4Lrx 1 or f:E UtLfJt~ 

---------------___------------- 

c. !c:r-cl 91 .CIC 

C.3:CL-Cl s3.2t: 

c. lOOf-@: 7C.EZl 

C.376f-CC %L.lEi 

C.'CtE-Cl 36.182 

C.316t*Cl lS.111 

0. ‘C3L.C? lC.?51 

0.316L*C? 5.066 

O.lC@L-33 2.206 

-- .---------_-_-____-_ -----_--------- 

c.c:: 

5.4lC 

C.CZ? 

14.425 

C.CC? 

2i.64: 

c.c:5 

2i.c:- 

C.::C 

15.c71 

C.Cl4 

E.86t 

c.c27 

5.166 

c.c54 

2.C76 

c. 124 

_-_-----__----__---_-------------------------------------------------------- 

-- 

1 

FIGURE 27 

Example Sesslon with Tabular Output from Log Norma] 

69 
..-----.-_.___. 

FIGURE 28 

Example Session with Plot of Log Normal Inputs 

70 
, ,ct.*------.------.------.------.------.------*------.------.------.------. 

I 

0 ; , 

r I 

6:,.------..-----.------.------.------.------.------.------*------.------. 

7 , 

I I 0 

v ’ 

t t:,.------.---------,---.------.------*------.------.------.------.------. 

L 9 

f ! . 

c (:.*------.-------------.------.------*------.------.------.------.------. 

t f 

L . 

D 

t 2:,.------.-------------.--~---.------.------.-,----.------.-------------- 

D ! 

9 . 

. 

t.*------.------.------.------*------.------.------.------*------.------, 

L3; -1.c: -C.CC -t.2: C.?C O.6t 1.0: 1.4C 1.6: 2.2: i.6: 3.t: 

LOG L’3R”AL RLS’J;TS 

FIGURE 29 

Example Session Mth Plot of Log Normal Results 
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 

On a theoretical basis. However, all three techniques are not 

accurate or appropriate in all situations. This section highlights when 

each technique should be applied. 

similarly 

Each of the three techniques can be applied to perform toxics waste 

load allocations and no one technique is necessarily preferable to any other 

Continuous Simulation: Continuous Simulation is the most powerful 

but only when sufficient time-series data are available to define the 

parameters. The power of Continuous Simulation decreases significantly when 

data must be synthesized to replace missing historical values 

guidelines for selecting Continuous Simulation as a function of time-series 

data availability can be summarized as follows: 

technique 

input 

The 

and complete 

Time-Series Applicability of 

Data Availability Continuous Simulation 

All input parameters available Very high 

High 

Fair 

Poor 

Only one effluent parameter missing 

or significantly incomplete 

Both effluent parameters missing 

but other data is complete 

All other cases 

72 
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 is 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 it 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; in these cases Continuous Simulation is preferred 

where data are available. It can be applied in 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 is 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 

complex 

conducting more 

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 in three years. Although 

the criteria 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 
The waste load allocation process determines the effluent concentration 

and flow that will result in a three year return period for the desired instream 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 nethod, 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 
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 wthod 

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 v4olations 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 

frequent than actually characteristic. 

~~r-c~~~P,e technique is that multiple, 

The advantage to the 

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 extrema method is that when multiple independent 

violations occur in the same year, only one violation is considered in the 

re:urn period analysis. This can lead to an estimate of the return period 

which may be longer than truly characteristic. 

For the DYNTOX examples provided in this report, as for all analyses 

conducted using DYNTOX, the percentile method is used. Users have the 

ability to perform extrema analysis by running Continuous Simulation one 

year at a time and manually tabulating the extreme in-stream concentration 

for each year. Investigations are now being conducted to establish the 

appropriate application of the two techniques and the need to adapt OYNTOX 

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 
Toxic Concentrations 

Toxic concentration criteria for waste load allocation can be 

determined by two methods: 

o chemical specific 

0 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 toxfcity 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 

this 

some 

cons 

dilution. Detailed discussion of these concepts is not appropriate for 

users manual and the reader is referred elsewhere (EPA, 1985). However 

comments are appropriate. 

Whole effluent toxicity testing has many advantages because it directly 

ders site specific effluent toxicity and inherently considers multi- 

_- 

parameter effects. However, on the downside: 

0 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: 

0 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 
VII. REFERENCES 

DiToro, D. H. 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. Cary, 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.