440484035
                            Dynamic  Toxics
                     Waste Load Allocation Model
                               (DYNTOX)

                            USER'S MANUAL
                            Prepared  for:
             USEPA  Mentoring and  Data Support Division
                           Washington,'  D.C.
                              Prepared by:
                           Limno-Tech, Inc.
                            Ann  Arbor, Mi.
                          September 13, 1985
Racy clad/Racy clabla* Printed with Vegetable Oil Based Inks on 100% Recycled Paper (50% Postconsumer) • Please recycle as newsprint

-------

-------
                                  PREFACE
     This report represents a Users  Manual  to  explain  how to use the  DYNTOX
model.    This  computer  model   was developed  by  Limno-Tech,   Inc.   under
direction from the U.S.  Environmental  Protection Agency Monitoring and Data
Support Division.   It is designed for  use  in  waste load allocation of toxic
substances.   It uses three simulation  techniques to calculate the frequency
and  severity of instream toxicity at different effluent  discharge  levels.
The report is contained in two volumes,   consisting of the User's Manual and
a separately bound appendix.   The User's Manual describes the theory behind
each  technique,  their  use in DYNTOX,   and  briefly  discusses how  to  use
DYNTOX  when performing waste load allocations.  The appendix  provides  two
illustrative examples.

     This  report  is  not intended to  be a discussion  of  the  theoretical
characteristics  and  practical   nuances  of  the  three  techniques.   Some
introductory  remarks  are  provided  in  these  regards,  but  the  primary
objective  of  this  report is to provide use  instructions  for  the  DYNTOX
programs.

     This  project  required the combined efforts of  many  individuals  and
organizations.  These are highlighted below:

     Funding  support  was  provided by the  U.S.  Environmental  Protection
Agency  Monitoring  and Data Support Division   (Contract  #68-03-3131).   Dr.
Elizabeth  Southerland was project officer and provided invaluable  insights
and  direction to the project.   Messrs.  Tim Stuart and Mark Morris of  EPA
also provided valuable administrative direction.   Jack Kittle of  Anderson-
Nichols  is thanked for his assistance in supplying updated versions of  the
ANNIE  program.   Dr.  Dominic DiToro,   Manhattan College is thanked for his
contribution to  the log normal analysis aspects of the project.   Drs.  Paul
Rodgers  and  Raymond  Canale of Limno-Tech,   Inc.  are  thanked  for  their
conceptual ideas.  Tad Slawecki and Dr. Derek Wong, also of Limno-Tech, Inc.
are thanked for  their  program contributions.
 LTI,  Limno-Tech,  Inc.                       LTI,  Limno-Tech,  Inc.
 Paul  L.  Freedman                            David W.  Dilks
 President                                  Project Manager

-------

-------
                             TABLE OF CONTENTS


                                   TITLE                                PAGE



             LIST OF FIGURES	    i

             LIST OF TABLES	  iii

  I.          OVERVIEW	    1

                  Background	    1
                  Concepts	    2
                  Organization of Manual	    3

 II.          COMMON REQUIREMENTS	    4

                  Model Access	    4
                  Upstream Boundary Data	    8
                  System Data	    9
                  Effluent Data	   11

III.          CONTINUOUS SIMULATION	   12

                  Theory	,	   12
                  Input Requirements	   16
                  Program Use	   20


 IV.          MONTE CARLO	   34

                  Theory	   34
                  Input Requirements	   37
                  Program Use	   41

  V.          LOG NORMAL	   57

                  Theory	   57
                  Input Requirements	   58
                  Program Use	   61

 VI.          PERFORMING WASTE LOAD  ALLOCATIONS	   72

                  Overview	•	   72
                  Selecting  Between Techniques	   72
                  Allowable  Effluent  Loads	   73
                  Multiple Discharges	   74
                  Calculating the Return  Period	   75
                  Toxic Concentrations	   76

 VII.        REFERENCES	   77

-------

-------
                              LIST OF  FIGURES

FIGURE                           UILE
   1           Example Session with ANNIE  (Inexperienced User) .........   6
   2           Example Session with ANNIE  (Experienced User)... ........   7
   3           Determination of Time of Travel  Input Constants ........   10
   4           Continuous Simulation Modeling Schematic ...............   13
   5           Concentration Frequency Curves .........................   15
   6           Hierarchy of Continuous Simulation Subprograms.., ......   21
   7           Example Session with Continuous Simulation Program
                  Entry ...............................................   22
   8           Example Session with Continuous Simulation
                  System Constants ........................ • ...........   2*
   9           Example Session with Continuous Simulation
                  Effluent Specification ..............................   27
   10           Example Tabular Display of Continuous Simulation
                  Inputs ............................... .- ..............   30
   11           Example Plot Display of Continuous Simulation  Inputs...   32
   12           Example Plot Display of Continuous Simulation  Results..   33
   13           Schematic of Monte  Carlo Technique .....................   36
   14            Example Monte  Carlo Input  Distributions ................    40
   15            Hierarchy of Monte  Carlo Subprograms ...................    42
   16            Example Session with Monte Carlo Program Entry .........    45
   17            Example Session with Monte Carlo System Constants ......    47
   18           Example Session with Monte Carlo Specifying Effluent
                   Distributions ........................................  48
    19            Example Session with Monte Carlo Specifying Triangular
                   Distribution	   52
    20            Example Session Specifying Data Defined Distribution....   54

-------
                        LIST OF FIGURES (Continued)

FIGURE                            TITLE                                 PAGE

  21           Example Session with Monte Carlo Viewing Results
                  in Plot Format	    55
  22           Example Session with Monte Carlo Viewing Results
                  in Tabular Format	    56
  23           Hierarchy of Subprograms for Log Normal	    62
  24           Example Sessions with Log Normal Program Entry	    64
  25           Example Session with Log Normal Input Specification	    66
  26           Example Session Performing Log Normal Simulation	    68
  27           Example Session with Tabular Output from Log Normal	    69
  28           Example Session with Plot of Log Normal Inputs	    70
  29           Example Session with Plot of Log Normal Results	    71
                                      ii

-------
                               LIST OF TABLES


TABLE                             TITLE                                PAGE


  1            Input Requirements for the Continuous Simulation
                  Technique		   17

  2            Input Requirements for Monte Carlo Technique	   38

  3            Input Requirements for Log Normal Technique	   59
                                     iii

-------

-------
                                I.   OVERVIEW


     Environmental   contamination  by   toxic  substances  can   pose   risks   to
public  and  ecological  health.    "egulttory  agencies  irt  now  establishing
regulations  and  procedures for determining   al  owable  discharge  1  mits   to
minimize  those  risks.    Unfortunately,   technology   to  define  risks   and
quantify allowable discharge limits is  new or not widely used or understood.
This  document  serves  to  Provide instructions   on   the  use  of  modeling
techniques  for  calculating  allowable loading limits  and   the  »«oc™d
risks   These techniques are incorporated in  the  DYNTOX  portion of the ANNIE
interactive program.


Background

     At  present,  most States which have regulations  for  setting   allowable
discharge  limits  for toxic pollutants use steady state  models  to  assess
exposure  and  calculate waste load allocations.   These  models are  used  to
calculate  the allowable effluent load that just  meets the chrome  toxicity
water quality standard at a critical low flow.   These analyses typically do
not consider issues of frequency and duration.   They generally consist  only
of a  simple dilution equation;  do not include instreatn processes;  and  only
examine  a single environmental condition for a single discharge at a single
design  specification.

      In  contrast, the  extent of biological  impairment from toxic discharges
depends  on  the duration of exposure  above  certain levels as  well  as  the
number  of  times  (frequency) these  violations  occur.   Water quality criteria
now   specify   both  duration and  frequency of compliance.   The duration  and
frequency  of violations  depend  on  the  daily  variation in  receiving water and
effluent flow,  combined  with daily variation in  effluent  toxicity. Therefore
dynamic  models  must  be  used to calculate'the frequency distribution  of  in-
 stream  concentrations   for any given  duration.    The current  durations   of
 interest are  four days  for  chronic toxicity  and  one hour  for acute  toxicity.
 The  one hour  duration  period  generally  is approximated as  a one  day  period
 because hourly data are generally not  available.

      Modeling  techniques are available  that incorporate  the effects  of  both
 variable  flow  and  effluent to calculate the   frequency  and duration  of
 exposure  at  different concentration levels.   These more  thorough  methods
 simulate   the  entire  distribution  of  receiving  water   concentrations
 (expressed  in a probability distribution) rather than  a  single  worst  case
 based on critical conditions.  This allows each alternative control strategy
 to be evaluated in terms of the total risk of toxic concentration.  The data
 used  to  define criteria for  toxic  levels  of  substances   incorporate  the
 concepts  of duration and risk.    It  is only appropriate that the procedures
 used to regulate these  substances  also  incorporate these concepts.

-------
Concepts

     Ideally,  it  would  be  desirable  to  assess  the  Impacts  of  toxic
discharges  on  receiving water quality over the entire range of  historical
and  future conditions.   These conditions  would then be analyzed to  define
frequency and duration of exposure above specified  limits.    Unfortunately,
on a practical basis this approach is impossible.  However,  three procedures
are readily available which estimate this range of conditions.   These are:

               1.  Continuous Simulation
               2.  Monte Carlo Simulation
               3.  Log Normal Analysis

All  three  are included in the DYNTOX  program.

     Continuous  Simulation uses the most direct approach.    A  mathematical
model  is  used to simulate a specified period of  recorded   history.   This
approach  uses  a  historical record of river flow and  upstream  conditions
combined  with  a  historical  or projected record  of  discharge  flow  and
toxicity.   Results from this simulation are then analyzed for frequency and
duration of toxicity which are assumed to statistically describe the  entire
record.   The  procedure requires an extended period of record but is simple
to execute and understand.

     The Monte Carlo simulation technique is less direct but also involves a
simple approach.   It uses a model as Continuous Simulation,  but inputs are
not determined on a continuous basis.  Inputs such as river  flows,  upstream
conditions,   effluent   flow  and  effluent  toxicity  are    each   defined
statistically by a distribution of historical or potential  conditions.   The
Monte  Carlo  model then repetitively selects sets of model  inputs  randomly
from  among these statistical distributions.   Statistical  theory   dictates
that  the distribution of results from numerous repetitive simulations  will
characterize   the   actual  distribution  of  potential   outcomes.    This
distribution  can  then be used to define frequency and duration  of  toxics
concentrations.    This   technique  requires  either  a  good   statistical
characterization for model inputs or reasonable assumptions.

     The  Log  Normal analysis procedure is computationally  less  extensive
than the previous two simulation techniques but  involves more complex theory
and  certain  restrictions.   This procedure assumes  all  input  parameters
follow a log  normal statistical distribution.   Statistical  theory  dictates
that  under  these conditions for a simple dilution model with one discharge,
the  projected   outcomes  can  be  numerically  determined.    The  procedure
incorporates  the distributions into the model through numerical   integration
and   thereby defines the distribution of downstream  water  quality.  This
distribution  can then be  used to define  the   frequency   and    duration
of  different  ' river concentrations.    The procedure  requires  a  proper
log  normal characterization  for all model  inputs.

-------
     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.

-------
                          II.   COMMON  REQUIREMENTS


     The   three  analytical   techniques  contained   in    DYNTOX,    although
conceptually quite different,   have  several  common requirements.    The first
common  requirement is that the DYNTOX programs  can only  be accessed through
the  U.S.   Geological  Survey  model   pre-processor  program  ANNIE.   This
requirement  was brought about to maintain consistency and continuity  with
the use of ANNIE as a preprocessor for large mainframe computer models.  For
future  microcomputer  adaptation of DYNTOX,   the requirement of   ANNIE-only
access may be discontinued.

     All three analytical techniques in DYNTOX also require   the  same  three
general types of input data:

          1)    Upstream  data...used  to  describe flow and concentration  in
                the river upstream of  the discharge(s).

          2)   System  data...used to   describe such  processes  as  instream
               decay, time of travel between outfalls, etc.

          3)   Effluent  data...used to describe the  flow and  concentration
               of  each discharge.

Upstream  boundary  flow  and concentration  data can  be   obtained   through
DYNTOX from STORET.   In cases where  STORET data are not  available,  the user
may enter data directly from the terminal.     System  data must be determined
by  the  user prior to performing any  simulations.    Effluent data  must  be
supplied  by the user and may either be read from a computer  file or entered
directly from the terminal.

     This   chapter   describes  the  requirements  common  to   all   three
techniques:   how  to access the model and  how to  obtain the  three types  of
common   required  data in the appropriate format.    Input format and   inputs
specific  to a given  technique will  be discussed later  in  their  respective
chapters.


Model  Access

      Presently,   DYNTOX  is accessed through the computer  program ANNIE.   The
ANNIE   program  was  originally  designed and  supported by the  U.S.   Geological
Survey in  cooperation with the U.S.   Environmental Protection  Agency to  help
users   interactively create,   check and  update  inputs to  models  and  perform
the actual  model  simulation.    Limno-Tech,  Inc. has  added the  capability  of
probabilistic  simulation.     Presently,  the  only way   DYNTOX   can  be
 accessed is through ANNIE.  This section briefly describes the ANNIE program
 and how it is used to access DYNTOX.

-------
     ANNIE  is  a Fortran program designed  for mini-  and  microcomputers  to
help users interactively create,   check,  and update  inputs  to water-related
models.   ANNIE can be used to reformat,  store,  list,  update, and plot data
for  models  that require time-series information.     ANNIE  can be  used  to
submit  prepared  model inputs to their respective  models  for  processing.
After model processing,  ANNIE can also be  used in  the plotting and analysis
of model results.  At present, ANNIE is designed to work with the Hydrologic
Simulation  Program - Fortran (HSPF) and for the Precipitation/Runoff  Model
System.   Limno-Tech  has now adapted it to include interaction with DYNTOX.
DYNTOX  is contained wholly in the ANNIE package; it  can only be accessed by
running ANNIE.

     The first step in accessing DYNTOX is  to install ANNIE on the  computer
system to be used.   If ANNIE has not yet been installed,  this must be done
before  DYNTOX  can  be  accessed.   Installation of  ANNIE  and  DYNTOX  is
described in the Appendix to this report.

     Once  the ANNIE program is installed and running,  accessing DYNTOX  is
quite  easy.    ANNIE  is designed to give the model  user as  much  help  as
desired in choosing selections, and screens user responses for each question
against acceptable values.  For any section, the user need only enter  ?  to
find   the acceptable range of responses.  Figure 1 shows the  initial portion
of  an example session with ANNIE for inexperienced users and Figure  2  for
experienced  users.   User responses are denoted by arrows.   Note thct  ajj.
user   responses  must be In capital letters.  The first question  determines
how much help  information  is given to the user.  The responses "NO", "LOTS",
or  "SOME"   are  acceptable for  using  DYNTOX.   If the  user  specifies  NO
experience,  he  will  be  given the opportunity  to view  several  paragraphs
describing ANNIE.  To  stop this documentation, type NO when the prompt MORE?
appears.   The   third  question requires the response DYNTOX.     (Only enough
letters  to  distinguish your response from other  acceptable  responses  is
required).     Users  with  experience  using  ANNIE  will  be  prompted  for
information  pertaining to  User Control  Input  (UCI) files.   This  question is
not   relevant  to  the  use  of  DYNTOX  and  the  answer  to  this question   should
always be  NO.

      At   this  point  in the session  the  DYNTOX  programs are   activated,   and
the  user   may  choose  from  the  three   possible   techniques:    Continuous
 Simulation,   Monte Carlo and Log  Normal.    A Complete description of program
 operations  for  the  three  techniques will   be  given  in   the  subsequent
 sections,  following a description of data  required by all  three techniques.

      The  user exits the DYNTOX session by selecting option 4,  End  Dynamic
 Toxics  Analysis.  There will again be a prompt concerning UCI  files.   The
 correct response to this question is DELETE (Figure  2).

-------
  fEsecutior. begin*
  •••••••••••••••••••••••*••••••••••••••••••••••••••'••••••
  ......            WELCOME TO  "ANKIE'              ••••••
  ......     VERSJOK DATES DECEK3ER  5.  1961         ••••••
  DO T0t5 HAVE MO. SOME, OR LOTS OF EXPERIENCE OSJNG AKKIE?

  ANKIE helps prepare or update input  to *>odel».

  Also. AKKIE helps create and fi* the data  for the tine-series
       tile (TSS file) that it uaed  by »o»e  of the models.

  Dor't be concerned about bad entries,
       ANK1E guides you to acceptable  responses.

  When a question  isn't clear, enter a question Bark  bcted  Routing R*:niall/Rur.of f  prograt.   ••
  CREAM     OS AR5 rainJall/runcf f Biodel.  ••
   RE'ORXA?   mefcr»»ts CS6S, HOXA, KSPF sequential files
             •nc adif  data tc TSS file fro: sequential files.
   P^CT      Piets data  fror various sources to plotters.
   ET*T3>     Dji«ric Tcxicc Analyses.
             •• Vet yet  available.
                         .   STAT       .  PRKS
      :**»•  .  9JCT.      .   DTKTOX

   «ftU- scat. OS PWXCSS DO TO'J WAKT TO OSE?
   CT>?^
   CTkAf C TUICt »>AiTSES

   »r- c» n:"»:ra K TOV WAST TC USE-.

     «•» t^~:STC71 »IKr-AT:OS: DILUTJOK AJO DECA?
     i;  itr«-t CAB.S: c:-r7iOK MO DECAT
     ijt yx-»3«F^. C:LUT:OK OK-_T
     t«i M: ttrTW, HETURK TC AKKIE KEKU

    «>n» »uirr:»  n-4)
    (Hit retorr let  4)
                            FIGURE  1

Example  Session  with  ANNIE  (Inexperienced User)

-------
    /Execution be;in*
    • ••••••••••••••••••••••••••••••••••••••*•••••••••••••••••
    ••••••            WELCOME TO "ANKIE"              ••••••
    • ••••»      VERSION DATES DECEMBER 5. 1964         ••••••
    DO TOO HAVE HO.  COKE. OR LOTS OF EXPERIENCE USING ANNIE?
    SOME
    WHAT MODEL OF PROCESS DO TOO WANT TO USE?
    DT
    ARE TOO WORM NO FROM AN OLD UCI FILE?
    NO
    DTKAKIC TOXICS ANALYSES

    «-::«•: TECHK:OUE DO TOV WAXT TO USE:

      (i) COKT: K'JO'JS SIKV^>.TJOK: D:LCT;OK AK; DECAT
      (2) MOKTI CARLO: DILUTION AK5 DECAT
      (3) LOG-NORXJkL: DILtrTIOK OKLT
      (4) EK3  DTKTOI, RETURN TO AKKIE KEN-J

    EKTER SELECTION (1-«)
     (Hit return  for 4)
    4
    SAVE. LIST.  OR DELETE TEKPORART OCI FILE
   • D
    ^Execution Terr.in«tei
                          FIGURE 2

Example Session with  ANNIE  (Experienced  User)

-------
Upstream Boundary Data

     DYNTOX    requires data describing the daily  river  flow upstream of the
effluent  discharges.  Data describing these flows are maintained   for  most
rivers  by  the  United States Geological  Survey (USGS)   and  are   available
through STORE!.   Users should contact USGS State  or District Office if they
have  questions about whether the flow record needs to be adjusted  for point
source  inputs or water withdrawals.    The first step in obtaining   boundary
flow data for DYNTOX  is selecting the USGS gaging station to be used.   The
recommended  location for the USGS gage is the closest gage  upstream of  the
first discharge.   Care should be taken to ensure  that no major  tributaries
enter the river between the USGS gage and  the first outfall.   If no stations
are  available  that meet the above criterion, the nearest  gage  downstream
should be used.   In this case, the user must enter the  average point source
flow  or  water withdrawals above the gage to correct the daily  record  for
these effects.  If  the river is ungaged,  it may be possible to use the flow
record   of  a   nearby river with similar   drainage  characteristics   and
proportion the daily flows by drainage area.

     When the appropriate gage station has been selected, flow values can be
retrieved using the FLOSTR option of STORET.  Details for this procedure are
contained  in  the  STORET User Handbook  (USEPA,   1982).    The  user  must
determine  if  the streamflow has been regulated by dams at  any time  before
retrieving flow data for toxics analysis.   This information  is available  in
the  Water  Resources Data book published  for each state by   the  USGS.   If
stream  flow  has  been regulated,  use only the data for the period  which
represents existing conditions.

     STORET   data  are  also  often  available for   describing    upstream
concentration  data.   Since  concentration data are usually taken   at  USGS
gaging  stations,  the  same station used  for flow data  should be   used  for
concentration data.   Unlike upstream flow, there  are cases  when STORET data
for  upstream concentrations cannot and should not be used.    The first such
case  is  when  the USGS gage is located downstream of one   of the  modeled
discharges.     "Upstream" concentration data in this case would be  biased by
the  effluent concentration and therefore  not representative  of  conditions
upstream of the discharge.

     STORET  data  are  not  stored in toxic units and cannot be   used  for
wasteload  allocation modeling conducted using toxic units.   In these  cases
the   user   must  enter  the  data  manually  during    program   operation.
Fortunately,   in  these  cases a constant  value will typically be   used  for
upstream concentration.    This value should be set to zero  unless  available
data indicate  that a different value is in order.

     Concentration data is retrieved from STORET  using the  RETRIEVE command.
Further  documentation  on STORET retrieval is located  in  the  STORET  User
Handbook.   Users  can retrieve multiple parameters at  one   session;  DYNTOX
will prompt the user for the desired parameter during  program operation.

-------
System Data

     Several  types of information describing  the river system are required.
These include drainage area ratios from each outfall  to the USGS gage,   time
of  travel (velocity),  withdrawals,   and instream decay.    The system  data
requirements  are very similar between techniques and are  discussed in  this
section.   Specific  examples  of  input for system data  specific  to  each
technique will be given later in their respective sections.

     The drainage area ratio from each outfall  to the USGS gage is  required
to determine the river flow immediately above  each outfall by correcting for
other  flow inputs.   This ratio should be determined by dividing the  total
drainage  area for the river at the location of the outfall by the  drainage
area for the river at the USGS gage.    When possible, a planimeter should be
used to determine drainage areas.

     Information  on time of travel is required by the Continuous Simulation
and Monte Carlo techniques for calculating instream fate processes (instream
decay  is  not  considered in the log  normal   analysis).    Time  of  travel
information  is  necessary  to describe passage from  the  upstream  boundary
station  to  the  first outfall and for the stretch of  river  between  each
outfall (in multiple discharge situations).   Time of travel information can
be  obtained in one of two ways.   First,  dye studies can be  conducted  to
determine  the time of travel for each required stretch of  river.   Second,
current  meters  can be used to calculate the  average velocity in  a  reach.
Time  of  travel  information is determined from  velocity  measurements  by
dividing the length of the reach by the average velocity.

    The user has two options for specifying time of travel.   Time of travel
may  be  described  as constant or varying as  a  function   of  flow.   Flow-
dependent time of travtl  1$ recommended and is calculated   by the equation:


                    TIM  of Travel -  aQb                                  (1)


where   Q  is  river  flow  »»6 a  «nd  b are  constants.    The coefficients  a  and  b
can   be determined  by  plotting  observed time of   travel   (distance/velocity)
values  at different flow* on  a  log-log  scale  (Figure 3).    The  coefficient  a
 is  the  y-intercept  cf Iht b«st fit  line through the data,  while b  is   the
 slope of  the line.    Hot* that  b should be negative,  as  time  of travel  will
 decrease  with increasing flow.    Typical   values  for b  range  from -0.34 to
 -0.70  (Thomann,   1972).    Constant  time of travel requires only  one  input
 value  that  will  be used for all flow conditions,  and should be used  when
 insufficient data are available to calculate  flow-dependent time of  travel.

      The  Continuous Simulation and Monte Carlo techniques in  DYNTOX  treat
 the  instream fate of a toxic as a first-order decay and  therefore require a
 first-order decay rate.   Calculating this decay rate requires several  data

-------
  In Concentration
5       8
                                           8
a>
—i
3


Q)
r-t-
|Mh
O


o
ZJ
•a
c
Q)
3
r+
V)
           
-------
points  taken  from  different stations on the river with a  known  time  of
travel and no pollutant sources between them.   The natural logarithm of the
concentration should be plotted versus time of travel (Figure 3) on semi-log
paper and the decay rate calculated as the slope of the best fit line.  This
decay  rate  can  change  with changes in treatment  for  future  scenarios.
However,  unless  data are available to indicate otherwise,  the same  decay
rate  observed  in-stream  should  be  used  for  all  wasteload  allocation
projections.   When no in-stream data are available,  the user should assume
zero decay.

     The user must also determine if there are significant water withdrawals
(>1%  of  river flow) at any location over the stream section  of  interest.
The average daily withdrawal rate will be prompted for in each river reach.


Effluent Data

     Effluent data can be entered manually from the terminal during  program
operation  or  read from a previously created  file.   Required  information
consists  of  the  total   number of data  points,   and  a  date,  flow,   and
concentration for each value.    Care must be taken to use consistent   units
between  river  flow and concentration and effluent flow and  concentration.
That is, if river data have been entered using toxic units and cfs, effluent
data must also be in toxic units and cfs.
                                      11

-------
                        III.   CONTINUOUS  SIMULATION
     The  most direct technique which  can  be  used  to  simulate a  probability
distribution  for  instream toxics  concentrations  is  Continuous  Simulation.
This  technique  directly predicts  the concentration  frequency  distribution
below  an effluent discharge (or series of discharges)  based on an  observed
history of upstream river flow and  concentration.   The  Continuous Simulation
technique has many advantages as it considers:

   o  frequency and duration of concentrations;

   o  instream fate and transport;

   o  single or multiple pollutant  sources; and

   o  cross-correlation  and serial correlation  of parameters  by  using  an
      actual historical sequence.

The  primary disadvantage of the technique is that it requires a  large  and
mostly complete set of data on historical  conditions.   Another disadvantage
to   Continuous   Simulation   is  that   computational   requirements   are
significantly  higher  than  for steady  state modeling or  for  Log  Normal
analysis.

     This  chapter  discusses the theory and application of  the  Continuous
Simulation technique, and is divided into three  sections.  The first section
discusses the theory upon which the model  is based,  and its advantages  and
disadvantages.   The  second section describes the data input  requirements.
The  third  and final section details how to use the computer model  of  the
Continuous Simulation technique when performing  waste load allocations.

Theory

     As   shown  in  Figure 4,  a Continuous Simulation model uses model inputs
for  observed daily  effluent flow  (Q  ) and effluent concentration   (C )  and
combines  these  with daily  upstream  receiving water flow (Q  ) and  upstream
concentration   (C  )  to  calculate downstream receiving water   concentrations.
The  concentrationudirectly  below an effluent outfall (Cd) is  determined  from
the  equation:
                    .?« VV...                                       ,2,

-------
         ime         Historical
C-T.  ,    .  i  .  .  J
                              	Standard
                    % Less Than
      Continuous  Simulation Modeling Schematic

-------
This   technique  assumes  complete  lateral  mixing  in   the   river.   The
model   predicts   a  simulated  history  of   instream   concentrations   in
chronological  order  corresponding to the same time sequence of  the  model
inputs.

     The  calculated  daily  downstream concentrations are ranked  from  the
lowest  to  the  highest without regard to time  sequence.    A  probability
distribution  plot  is  constructed  from  these  ranked   values,   and  the
recurrence  frequency of any concentration of interest can be  obtained  (Cd
vs.  frequency).   Running average concentrations  for four days,  or for any
other   averaging   period,   can  also  be  computed  from  the   simulated
concentrations,  ranked  in  order of magnitude,  and also  presented  as  a
probability distribution (see Figure 5).

     The  Continuous  Simulation model can predict the concentration  below
each  of a series of discharges.  Successive  concentrations  downstream  are
calculated  progressively  from the concentrations upstream on a day by  day
basis. Equation (2) is used to calculate the  concentration downstream of the
first  discharge.   The  concentration  further downstream  but  immediately
upstream of the next discharge is calculated  according to the following:



              cu - Cd *                                            O)

    where:  C     - concentration above the second discharge
            Cd     - concentration below the  first discharge
            k      - first-order decay rate
            t      - time of travel between discharges


The  exponential term including the decay rate k represents any first  order
instream loss.  Effects of subsequent discharges are calculated successively
using equation  (2) and (3). River flow above  any particular discharge is the
sum of the upstream boundary flow plus all additional flow inputs, including
discharges.

     The   probability   distribution  plot  generated  by  the   Continuous
Simulation  technique  will  indicate the predicted  frequency  of  criteria
violations.   These  frequencies  can  be compared  for  different  effluent
alternatives.   If evaluations of recurrence intervals of 10 or 20 years  are
desired,  then  at least 30 years of flow data should be available.   This is
needed  to provide a sufficiently long record to estimate the probability of
rare  events.    (The same data requirements are also true for the Log  Normal
and Monte Carlo methods).

      The  Continuous Simulation model has three primary advantages  compared
to steady state modeling, Monte Carlo   and Log Normal analysis.  First, the
advantage  over  steady   state modeling is that  Continuous  Simulation  can
predict the  frequency  and duration of toxicant concentrations in a receiving
                                         14

-------
  50
O

   30
c
O)
   20
 c
 O
•S  10
.O
                                      I day
                                  _^^^ 4days .^--
                        	^—'	^.	
 tar,	  "	            30days_
                                  l
                                              JL
1
99                         99-5
    Percent of Time Concentration is Less Than or Equal To
                                                     i
                                                            100
                                                              20
                      Recurrence Interval (years)
                          FIGURE 5
                 Concentration Frequency Curves
                      (from  USEPA, 1981)

-------
water;  steady  state analysis cannot.    Second,   the inclusion  of Instream
fate  processes  is  an advantage  over  Log   Normal,   which   cannot  simulate
instream  fate  and is limited to  simulations  for  one  effluent  discharge.
Third,  by  using  simultaneous observations for  all  input   parameters,  the
Continuous Simulation model  can directly incorporate  the observed effects of
serial  and cross correlation   of  inputs.     When  calculating  four   day
average  instream concentrations,   Continuous  Simulation correctly does  the
averaging  on the model results.   Monte Carlo and Log Normal  estimate  four
day average instream concentrations by  averaging  model inputs.

     The  primary  disadvantage of Continuous  Simulation is the  large  data
requirement.   A  long  period  of  historical data   is required  for  all
parameters.   Although  time  series data  can be  synthesized  for  missing
parameters,  synthesis  of  time-series  data  for more  than  one  parameter
greatly  reduces  the reliability  of this technique.    Additional  data  are
required  for  the calibration/verification of instream fate  processes.   A
second  disadvantage  to Continuous Simulation is the large  requirement  of
computer time and storage;  however, recent advances in computer technology
have minimized this problem.


Input Requirements

     The  model input requirements for  all  three  techniques  were  discussed
in   Chapter 2.    This section details the specific  input  requirements  for
the   Continuous  Simulation  technique.    The  inputs  can  be   generally
categorized into four groups:

     o  general simulation requirements,
     o  upstream data.
     o  effluent data, and
     o  system physical *nd hydrologic  constants.

All  of  these  inputs  «rt summarized  in Table 1,  and  will  be  discussed
individually  in thn  stctior..
      General   Siwu'at^o*  Requirements:  The  Continuous  Simulation  method
 requires  some general  information on the system that will not change  between
 simulations.   The first taste  input required for Continuous Simulation  is  to
 establish the period of the  simulation.   This consists  of  the    beginning
 and  the  end date of tht  simulation, which must contain  all or  a   portion  of
 the streamflow  record.   This period  should be as long  as  possible,  since
 the  power of the Continuous Simulation technique  increases with  the   amount
 of observed data.   The  user should select a period  for  which a complete and
 consistent  data set is  available.   Caution should  also be directed  against"
 using old data which are no  longer representative  of current conditions.
                                         16

-------
o General Information:

  - Beginning and end date of simulation
  - Number of discharges above flow gage
  - Average point source flow above gage
  - TSS computer field name
                                                      Data Source
USGS flow records
User defined
Treatment records
User defined
o Upstream Data:

  - Time series flow data
  - Data synthesis technique for flow
  - Time series concentration data
  - Data synthesis technique for concentration
STORET
User defined
STORET
User defined
o Effluent Data:

  - Time series flow data
  - Data synthesis technique for flow
  - Time series concentration data
  - Data synthesis technique for concentration
Treatment records
User defined
Treatment records
User defined
o System Constants:

  - Time of travel information

  - First order decay rate (s)
  - Drainage area ratio (s)
  - Water withdrawal rate (s)
Dye studies,
  current meters
Instream data
USGS topographic maps
Withdrawal records
              Table 1.  Input Requirements for the Continuous
                                Simulation Technique
                                 17

-------
     The  second basic input required  by  Continuous  Simulation  is  the number
of discharges in the system.   The  user must  also determine  if  any of  these
discharges  are  located upstream of the  USGS gaging  station;   if  so,  the
average  point  source  flow above  the gage must be  determined  in   order  to
correct  recorded  streamflows  for this  input.   The   final  general  input
required is a computer file name to store these  inputs.    Once  these general
inputs are specified, they will be  stored in  this computer file and need not
be specified for later simulations.


Upstream  Boundary Data:  The Continuous  Simulation  technique requires  time
series information on upstream boundary flow  and concentration, and effluent
flow and concentration.  The Continuous Simulation technique requires a data
value  for each individual day of the  simulation.    Typically   many  "holes"
will  exist in the data set,  days  which  have no data  for a  given  parameter.
A method to synthesize or fill in data for missing days is required.   Three
methods  are  available  for synthesizing missing data  for  the  Continuous
Simulation technique:

                    1.  linear interpolation
                    2.  simple Markov  synthesis
                    3.  multi-period Markov  synthesis


Each  is  briefly described here as needed for use   in  this program.   The
reader  is  referred  elsewhere for a  more thorough  theoretical  discussion
(Fiering and Jackson, 1971).

     Linear  interpolation  is the simplest method.    It synthesizes  missing
data  by linearly interpolating between  the  available  observed   data  values
that  bound the missing value.    This method should be used in cases  where
data  are available over the majority  of the period  of record  and  only minor
"gaps" need to be filled in.   When synthesizing missing upstream flow data,
linear interpolation  is the only method  which  should  be used.   Also, linear
interpolation  will   produce   a  constant value  repeated  over  the  entire
simulation when one observed data  point  exists.

     The   second method of  data  synthesis is a first-order,   lag-one  Markov
process,  referred to  herein as simple Markov.  With this technique,  data  for
a  given day  are  randomly determined from the overall data mean, overall data
variance,  the   previous day's value,  and an auto-correlation  coefficient.
The  auto-correlation coefficient  is  a measure of how closely  a given   day's
value  is  related  to the previous day's value.  The  Markov process  in  DYNTOX
assumes   that  daily fluctuations  jn  model inputs are normally distributed.
DYNTOX  assumes  an  initial  mean value and generates 50 data points in   order
to  determine the first value used in the simulation.  The  only  user  input
required  by the simple Markov process is the auto-correlation coefficient.
These  coefficients  can be determined using the SAS  routine   AUTOREG  (SAS,
 1982).   A  value for the auto-correlation coefficient  of 0.7  is  recommended
                                         18

-------
if insufficient data are available  for calculation  from observed  data.    All
other coefficients will  be determined  from the  observed data  by the  program
itself.   The  only exception is the case where less  than  three data  values
exist, in this situation the user must manually specify mean  and  variance or
choose another method of data synthesis.

     Multi-period  Markov  synthesis is the third technique and  involves  a
third,  more complex level of synthesis.    The  simple Markov  process assumes
that  the  process  for which data  is  synthesized is  "stationary"  over  the
period  of  simulation;   that is,  the mean and variance  remain   relatively
constant over the entire period of  the simulation.    The multi-period Markov
process is designed to handle cases of non-stationary processes,   where  the
mean and/or variance are known to change over time.   The  primary example of
a  non-stationary  process is effluent flow from batch treatment.   In  this
situation   flow  may be zero for several  days  during   treatment,   then
non-zero  for  the next few days during discharge.    The multi-period Markov
process  allows  the  user to divide a non-stationary process into  as  many
repeating  stationary  periods  as  necessary.   Each   period   requires  data
describing its mean value,  standard deviation, and auto-correlation.  These
values must be calculated before performing a waste load allocation.   Using
the batch treatment flow as an example,  the user would specify two  periods
to  describe the process.   The first  period would  have a  mean and  standard
deviation  of  zero  and  a length  equal  to the duration  of   the  treatment
period.   The  second  period would have an appropriate mean   and   standard
deviation and a length equal the duration of the discharge. DYNTOX then uses
a  Markov process to repeat the two periods until a data value for each  day
is generated.


Effluent  Data:  Similar to upstream data,  daily input values are needed in
the model for effluent flow *nd concentration (or toxicity).    The source of
these  data  must be uitr specified.   As for the upstream  data,  gaps  are
likely  to  exist in any data set.    Here again,  the user must  use  either
linear interpolation,  staple Markov,   or multi-period Markov to   synthesize
data   for missing days.   Any downstream tributary inputs  occurring  between
discharges should be co«Hd«r«d as  a separate effluent input.


System Constants:  Systt*  constants  need to be defined for hydro!ogic  and
physical  characteristics  of the  system.   Model  inputs for  physical  data
include time  of  passage  b«t«»e*n  locations  and  instream  loss  rates.    Time
of   passage   must   be defined for  the  stream segment   between  the   upstream
boundary  station   and  the  first discharge,  as  well  as   for  the   segments
between  each  discharge.   The  coefficients  used  to  define the time  of passage
were  discussed   previously in  the Common   Requirements  chapter.    Instream
losses  are  defined by  a first-order  decay rate,   and are held   constant  in
each reach  throughout  the simulation  period.   The  method  for determining the
first-order   decay rate was also discussed in  the  Data Requirements chapter.
                                         19

-------
     Program inputs for hydrologlc data are needed to properly  adjust gauged
flow  data  to determine instream flow at different locations.    Ratios  are
needed  to define the comparison between the gauged drainage  basin area  and
the drainage basin area at the  point of discharge.   These  ratios adjust the
USGS measured flows for non-point sources,  and must be specified regardless
of the location of the gaging station.  For discharges located  downstream of
the  USGS  gage the ratio (and  adjustment) will be greater  than  1.0.   For
discharges  located upstream of the gage,  the ratio will be  less than  1.0.
The  method to be used for specifying drainage area ratios  is  described  in
the Common Requirements chapter.  A second hydrologic adjustment is required
for water withdrawals.  If a significant amount of water  (>1% of river flow)
is  withdrawn from the river at any location,  this  witnarawal rate must be
specified before performing a Continuous Simulation waste load  allocation.


Program Use

     The  Continuous  Simulation  program,  like the programs  for  the  other
techniques,   is divided into menu  driven  sub-programs   (entitled activities)
to allow the  user as much flexibility  as  possible in  performing simulations.
The hierarchy of activities for Continuous Simulation  is  shown  in Figure  6.
This   section will describe how to use  the Continuous  Simulation program and
will discuss  the options available.   It  is divided  into  sections  describing
each of the primary  activities of Continuous  Simulation:

     o Program  Entry,
     o Input Specification,
     o Model Simulation,
     o Viewing/Analysis of  Input Data,
     o Viewing/Analysis of  Simulation Results,  and
     o Ending Continuous Simulation


Program Entry:   The  first activity of the Continuous Simulation  technique  is
termed Program  Entry.   This section involves either the initialization   and
development   of   the  basic  input file or the specification  of  an   existing
file.   Initial  data  include  those data and information which typically would
not  be changed  in alternative  simulations.   They include  the  period of  data
record (duration of  simulation), the number of discharges, and the  data  base
 used to  define  upstream flows  and concentration.   Modifications to the  data
 including data interpolation,  loss rates, and effluent inputs  are handled in
 another  activity (entitled Input Specification)  because  these  factors may be
 changed  in alternative simulations.

      Figure  7 shows example sessions with the Program Entry  activity.   The
 first  questions in Program Entry concerns the existence and location of the
 TSS files used for the simulation. Time  Series Store  (TSS) files are created
 by ANNIE to  hold all time  series  information   for   a   system,  such as the
 period  of simulation  and observed flow and  concentration  data for  upstream
                                          20

-------
                 Input
              Specification
  Model
Simulation
ro
                                                Program Entry
                                                 /Menu j


VI en/Analyze
Inputs
h-
ze



VleN/ Analyze
Kcsults



End
Continuous
Simulation

	 1
Svsio
Constants

. 	 	 —
LI fluent riu*
1
Concentration

—
Mdtmauv
Conditions

— 1
did Input
Spec II leal ion
                                                  FIGURE 6

                             Hierarchy of  Continuous Simulation Subprograms

-------



-o
—1
Q}
3
m
•-+
*
*<











m
X
Q)
X3
cn
01
O
3
Er cr>
«w
o ^>
o m
»-~
^^
a
o
c
(/>
00
_.
c:
|_tf
Q)
O
3

Y Y Y Y Y Y .U
--*?!-ssnj;R8 r3?r?snr8
£°i!ii iiTii-1"?! ^35 s'sPs ^
?! i" t'sisS 5 v ^ £5to3 I
3 3f4 3oxft JS ^-w 3S '; J
vaS s' 1 « R ?- ^ i n
g :5 ^ o ^ G ^ =3 o i

" i-w " H ?
^ '" Ti S «
ii •' 15 m »:
H "] * s ^ "
' ' •« 1 •»! "1
? r 5? o P R
^ " c: • ^ J 'J
s M rl
'" y: "
•^
0
^
n
PI
V.
5
'i
o
*J





JJ
M
.1
9
q
•1
in
in
•1
i;
VI
r
V!
o
o
•3
• !•
PI
H
pi











T
•wo
PI
in
PI
r
-«
o
Vi
in
in
pi
»4
VI
1
!*
M
W
U

,
•









T I T T T t
in*53s33ir.5r!!iH==s
.5 .5^-'^w"i'!- - s^s^.S
«•> •»•/: »JPI^V<«WIIW o *!S28y2
sj i:=§-5R a ^ iESSaa
3^ 5^-5 ^5. » R 33?.Sn§
?? ?? « 5V 5 g »9S,^a
2:: "j: r, o° 15 ° -«."!. I,"
„„, -,n PI J-^ Q «; »--t,"^
"^1-. *~ y pii.i *i *^ irlr*ni^
"-* 7^ "PIMIO *^cir2r*r*
>• ? il S > *o"«
S r M ^ * H1**5?
fc| minv* It O cj
? M •* ^ n R ?3
o (n ^] p n S: 5"
o >n wi -j 11 >;
6 a Is 5 i
^ -j i >• Jj
Li *4 r»
* Y J*
o j; -•
..'
W»
P

^J
p
•j

/



ryKfcv.:c TOIJCS AKMT
VrilCK TECKKJO'Jt TO T
0 VI
« PI
y "
T'.
•I
3
V>
PI















0*
3j»
—I
to
to
Tl
ft)


















-------
7b.   Existing  TSS File
              ENTES SELECTION  (1-4)
              (Hit return for  4)
              KAVE YDS PREVIOUSLY CREATE? A TSS FILE  FOR  THIS SIMULATION?
              £"7 JS THE KAKE OF YOUR TSS FILE?
              EXAMPLE
      terminal  Entry of Data
              HAVE TO'.'  PREVIOUSLY  CREATED A TES FILE FOR THIS  SIKVLATION?
              N"^
              Vr:A7 IE THE KAMI OF  TCVf NE- TJ5. FILE'

              ENTE="BEC:NNIN:. AK:  ENDING DATES FOR
              EK7ES S7AS71KG DA7E.
               EK7E? ES~:NG DATE.

               HOV"KASY30-.TFALLS ARE THERE  IK THE SYSTEM?
               (Hit return lor 1)

               HOV KAKT. OUTFALLS LIE ABO^  THE FLOW CAGE?
               (Hit return tor 0)
               0

               PLEASE WAIT VX:LE TOUR TEE F:LE is INITIALIZES ...

               INITIALISATION OF TOLTt TSS FILE IS KOK COMPLETE.

               DC TOV KA\T A STORE7 FLOW DATA FILE?
               j
               WXAT IS THE KAKE  OF THE STORI7 FILE?
               US£ V>::CK SATA SET?
               • Kit rtt^rr- lor "

               WHAT IE THE KAI'.MV. ACCEPTABLE FLOW VALUE?
               (Hit return icr 0. )
                ei
-------
CONTIK'JO'JS SIMULATION TECHNIQUE

    PLEASE CHOOSE FROM THE FOLLOWING:

    (1) SPECIFY HODEL INPLTS
    (2) RUN THE SIMULATION
    (3) V1EW/ANALYIE THE IKPUT DATA
    («) VIEW/ANALYZE THE SIMULATION RESULTS
    (5) END CONTINUOUS SIMULATION

    ENTER TOOT CHOICE (1 - 5):
 (Hit  return for 1)
 1


 PREPARE KODEL INPUT TI MISERIES

    (1) SPECIFY SYSTEM CONSTANTS
    (2) SPECIFY OUTFALL FLOWS AND  CONCENTRATIONS
    (3) READ UPSTREAM BO-TCARY FLOWS  AND  CISCENTRATIONS
    (4) EVD T:KESES:ES DEFINITION  AW RETURN TO CONTINUOUS
       S:KULATION KEKU

    ENTER YOUR CHOICE (1 - 4):
 (Hit  return for 1)
    	  SYSTEM CONSTANTS 	

    IKPUT  DATA FOR EACH REACH


 SYSTEM CONSTANTS FOR REACH 1. BETWEEN UPSTREAM  BOUNDARY AND FIRST OUTFALL
    HOW DC YOU VANT TC SPECIFY THE TIKE OF TRAVEL?

    (1) CONSTANT
    (2) AS A FUNCTION Or  FLOW

    ENTER  YOUR CHOICE (1  OR 2):
 (Hit  return for  1)
. i
 WHAT IS THE TIKE OF TRAVEL IN DAYS
 (Kit  return for  0.1)
. . 1
    WHAT is -THE FIRST ORDER DECAY RATE?
 (Kit return for  O.D

    WHAT is THE AVERASE WITHDRAWAL?
-o.
    WHAT is THE DRAINAGE AREA RATIO FROM THE uses GAGE?
 (Hit return for  1.)
•-1.
                             FIGURE  8

             Example  Session  with Continuous
                Simulation  System  Constants
                                    24

-------
conditions.    The  first  time a simulation  is  performed   the  user  should
answer  NO  to  the  question asking if a TSS file  was  previously  created
(Figure  7a).   This will initiate the process to create a file.    The  user
should answer YES to this question in subsequent simulations,   and no  other
information will be required in the Program Entry section  (Figure 7b).

     For first time entries,   the TSS file name must  be supplied.  Any file
name  can  be  used that is compatible with the  computer  system.  The  next
inputs  required  are the beginning and end dates of   the   simulation  which
define  the  extent of the input data base.   The required format for  these
dates are  Year/Month/Day.   Months and days with only  one  significant figure
of  information may be entered using one digit.   Four digits  are needed  to
define the year.  The last question before creation of the TSS file concerns
the number of discharges in the system.

     At  this point in Program Entry,  the TSS file for  the system is  being
created and  initialized.  This may take some time,  depending on the computer
system used,  but the user will be informed when the  file  initialization  is
complete.    TSS  files created during Continuous Simulation can be used  for
either of  the three interactive programs contained  in  DYNTOX.

     The   final  portion  of Program Entry concerns  defining   the  upstream
boundary   data  files.   Figure 7a shows an example session where  both  the
boundary   flow and boundary concentration data are  located in  STORET  files.
The  user  need  only specify the location of the STORET  data    file   and
which  data  set  of  the  STORET retrieval is desired.  The data set number
selected by  the user should be one, unless multiple data sets  were stored in
the  same  file during the STORET retrieval.  This  section  also provides  the
ability  to  correct the STORET data and screen out flow  and  concentration
values above acceptable values.   Observed data above the  maximum acceptable
value are  set to this cut-off value.

     The final possibility  for Program Entry is when  the user has no  STORET
data  and  wishes to enter observed flow and concentration data manually from
the terminal.    Figure  7c shows an example of this situation.    The user  is
required   to  input  the  number  of data values  and  then  the  date   and
concentration  for  each  value.   The proper format is  date and value with the
date  being  in  the  YYMMDD  (two digits  for year,  two digits for   month,  two
digits  for day)  format.

      After completing  Program Entry,   the  program enters  the main portion of
the  Continuous Simulation  program.   The  user  will be given  the menu  shown in
 Figure  9 and must select one of  the five  activities:

                            1. Input Specification
                            2. Model  Simulation
                            3. View/Analyze Inputs
                            4. View/Analyze Results
                            5. End Simulation
                                      25

-------
Although  there  is  some flexibility 1n the  order 1n  which  activites  are
selected,  inputs must be specified before choosing any other option (except
ending).


Input  Specification:  Selecting  Input  Specification  provides  a   new  menu
involving  four  subtasks:   1)   System constants,  2)    Effluent   flow  and
concentrations,   3)    Boundary  condition  data,   and   4)  Ending  input
specifications.  These four tasks can be selected in any order desired.

     The first task of input specification pertains to  the system  constants:
time  of  travel,  first-order loss rate,  drainage area  ratio,   and  water
withdrawal  rate.   Program operation for this  task is  very straightforward,
requiring  only the Inputs discussed in the data  requirement section.   An
example session specifying system constants is  shown in Figure 8.

     The  second  subtask of input specification covers effluent   flows  and
concentrations  (Figure  9).   The  user  has the option  of  entering  data
directly  from  the   terminal or having the  data read   from  a  file.   The
required  format in both cases is the number  of data points followed by  the
date,  flow,  and concentration  for each observation on a line separated  by
commas.  The proper format for the date is YYMMDD.

     Next,  the  user must specify the desired  data synthesis technique used
to  define  data  values missing in the input data  file.    This   method  is
selected first  for effluent flow and then for  effluent concentration.   The
specifics  of the data synthesis techniques were described in the  Upstream
Boundary  Data section of this chapter.   The implementation of these  three
techniques is  quite simple.   For linear interpolation (see Figure 9a),  no
additional  user  inputs  are  required.   The   first-order  Markov  process
requires user specification only of the auto  correlation coefficient (Figure
9a) since the program Internally computes the mean and  standard deviation of
the data.   The user has the ability to calculate coefficients from the data
or  to  override  the  statistics and  input  any  selected  values.   Where
sufficient  data are not available for the program to calculate  statistics,
the  user must manually specify statistics or choose a  new  technique.   The
multiple-period  Markov  process requires somewhat more user input than  the
other  data synthesis techniques (see Figure  9b).   The first input  is  the
number of repeating periods to be used.  For  each repeating period, the user
must  manually  specify  the  mean  value,  standard deviation,   and  auto-
correlation coefficient.

     The  boundary  data  task involves completing the  input data   file  for
upstream  flow  and concentration.   This also  requires the selection  of  a
technique to fill in missing data.  The program  requires specification of a
data synthesis technique both for boundary concentration and flow.  The same
procedure   used  for  synthesis of effluent data applies  for  synthesis  of
boundary data.   Linear  interpolation  should always be selected  as the  data
synthesis   technique for boundary flow,   since a thorough boundary flow data
set  is  essential to  the  proper function  of Continuous Simulation.


                                      26

-------
9a.   Linear  Interpolation and Simple  Markov
        PREPARE M5DEL XKPUT TIKESERIES

           (1) SPECIFY SYSTEM CONSTANTS
           (2) SPECIFY OUTFALL FLOWS AND CONCENTRATIONS
           (3) READ UPSTREA" B3UK3A.P.Y FLOWS AND CONCENTRATIONS
           (4) END TIKESERIES DEFIKITIOK AND RETURN TO CONTINUOUS
               SIMULATION' K£S"J

           ENTER TOUR CHOICE (1-4):
        (Hit return for 1)
        2
        IS TOUR EFFLUENT DATA IN A FILE?
        NO

        D:SCHAS3E I  1
        H5'» MANY POTS DC TO'J HAVE FOR THIS DISCHARGE?
        (Hit return Jor 4)
       • 3
        EVTES DATE, FLOW. A«O COKCEKTRATIOK FOR EACH SAMPLE:
       • 6CC2C2. 25.. 1.
        6::«:4. 22., .•
       • 6:cs:3. 2t., .7
            3 PC:KTS REA3

        DATA STKTHESIS FOR EFFLUEKT FLOW

        W-1AT TECHNIQUE DO YOU WAST TO USE TO SYNTHESIZE  KISSING DATA
        (1) LINEAS INTERPOLATION  (OR CONSTANT VALUE)
        (2) FIRST CR3ER KARXOV
        (3) MULTIPLE PtR:03 KASROV
        ENTER  1-3
        (Hit return for  1)
       - 1

        DATA SYNTHESIS FOR EFFLUENT CONCENTRATION

        WHAT TECHS:SUE DO TOU WAKT TO USE TO SYNTHESIZE  H:SS:NS DATA
        (D LINEAR INTE?.PCLAT:ON  (OR CCSSTANT VALUE)
        (2) FIRST ORZ'ER  KARKOV
        (3) KJLTIPLE PEruOD KASKOV
        ESTER  1-3
        (Hit  return for  1)
       • 2
        KEAN  VALUE  !S  0.83333
        STAVLARD rrviAT:oN  is  c.iszis
        IS TKIS ACCEPTABLE?
       • Y
        WriAT  IS THE AUTO-CCK3ELATION CCEFF1CIEKT FOR THIS PARAMETER
         (Hit  return for  0.)
       - .7
                                     FIGURE  9

              Example  Session  with Continuous Simulation
                            Effluent Specification
                                            27

-------
9b.   Multiple Period Markov
         DATA SYNTHESIS FOR EFFLUENT FLOW

         WHAT TECHNIQUE DO YOV WANT TO L'SE TO SYNTHESIZE KISSING DATA
         (1) LINEAR INTERPOLATION (OR CONSTANT VALVE)
         (2) FIP.ST CRCER MARKOV
         (3) MVLTIPLE PER;os KARKSV
         ENTER 1-3
         (Kit return for 1)

         PARAMETER SPECIFICATION FOR KVLTIPLE PERIOD KARKOV PROCESS

         HOW KANY REPEATING PERIODS DO YCV WANT TO USE
         (Kit ret-jrn lor 2)
         2
         DESCRIBE FErlOD   1
         HOW KANY DAYS IN THIS FEPIOD
         (Hit return for 1C)
        • 10
         V>:AT is THE KEAS VALVE FOR THIS FER::D
         (Hit return for 1.)
        • 25.
         VriAT IS THE STANDARD DEViATICS fZr T.-1I S PE?.ICD
         (Hit return for 0.)
        -3.
         WHAT IS THE A1TO-CCRHE1ATIOK CCE'FICIENT DVr.ISG THIS  PERIOD
         (Hit return for 0.)
        - .7
         DESCRIBE PERIOD   2
         KO'-- KANT SAYS IN TrIS PERIOD
         (H:t return for  10)
        -3
         WHAT IS THE KEAN VALVE FOR THIS FESICD
         (H-.t return for  1.)
        - .01
         WVAT IS THE STASDASD DEVIATION FOR THIS PERIOD
         (Hit return for  C.)
        - . DC i
         WHAT IS THE AVTO-COR?.EI.ATION CCE'-ICIENT CVRIN5 THIS PERIOD
         (Hit return  for  0.)
        - .7
                                FIGURE 9  Cont'd.
              Example  Session  with  Continuous  Simulation
                            Effluent  Specification
                                            28

-------
     The final task of Input specification  Is  to  end and return to the  main
Continuous  Simulation  menu.    This   option may  be  selected  at  any  time;
however,  to  run  a  simulation  the previous three  options  must  all_  be
successfully executed.


Model  Simulation:  The model  simulation can be conducted any time after the
inputs have been fully specified.    No additional  inputs are required to run
the  simulation.   The  program  will print out each  500  days  of  program
execution as they are completed so the user can monitor program progress.


View/Analyze  Inputs: The user has the ability  to  view any of the model input
parameters  in  either tabular or graphic format  using any averaging  period
(1-day,  4-day,  etc.).   This  activity can be accessed any time after  the
inputs have been specified, but need not be conducted.  After specifying the
parameter to  be viewed, an averaging period must  be  supplied.  The user then
has the option of selecting a table (Figure 10) and/or a plot (Figure 11) of
inputs.

     Graphical plots of model  inputs show the  percentage of the input values
for  a  particular  parameter  that  occurs in each   of  ten  value  ranges.
Tabular  results give a statistical evaluation of the parameter of  interest
in  terms of  mean value,  standard deviation  and coefficient  of  variation.
The  tabular  presentation also shows the percentage  of the data that exceeds
various values,  the return period (recurrence interval) for exceeding these
limits,  and  the percentage of the data occurring between  various  limits.
Additional  features  of  tabular results are  the ability to  determine  the
return  period for  any value of interest and  the ability to view  the  value
that has exactly a  three year return period.


View/Analyze  Results:  This activity of the program can be accessed any time
after  a simulation  has been run.   The format for the activity  is  identical
to that for the  viewing/analysis of  inputs.   The results shown indicate the
frequency distribution for  the  in-stream concentration directly at the point
of  mix  with  the  specified discharge  (Figure  12).   Tabular  results  are
identical to  the view/analyze  inputs activity section.


End   Continuous  Simulation:  The   final  option of  the  Continous   Simulation
program is  to end and return to the  main   DYNTOX  menu.     This  option  may
be  selected at any time  during the session.
                                      29

-------
-








Ul
H
,1
i* r-
M :t '*.
bl bl O
M •• "
O > l<
Z < X bl <
. . i- o n 11 IK
:« < ... a: i- it i •
u o o i • o .-< v.

i» Ti j-.iP •• * ij i'»
-• O ; i ; i < -~ .c if. ui v.
z it, IA n. v . i m U o . • o
re J- -^..r; u> ..no

bl X O. O *~* ••* I > O bl -t >• !••
H H 'J. •-« bl bl IA •- O. »• 11 IK IK l«

x x *" •< H !•< ui " o •cv.no
O n ,i.i n w an: M s. v.
-. tt bi:»bibio u b. uo:in
I* b. oxx'-in -•— o w in y. ii «i
< O">->.-j: o- M . .omo»
.1 bl XWI.I.I.. T Ul I- CIO
: i IA •<•<»• o>- ..i.i >• j
x n >• ui v y v. o ui i' . i . i -» -<
M X >->Hv.XU :i .1 IK U •< H (K
U O :i U O C X -< b. b. 1 • 1 •
Ul I.I -Jt. bl bl n » »• X. O. 1 • 1 • Ul IA
:> bi a.r>««*-«'.£ *i •< viMn.n*
O IA IA  > bl IK ." '-^ U O IJ :> U
: i ^ i.i «i o u

'£ •" Ul
O X .«
U — r> >
A

IK
1.1
ni
ft
•*
.1
.1
b.
J.

O —

IK >• ^•
M -C M
1- O .1
•j. m
MX •<
— t- I-

|. Ul
IA 1) 0
1.1 U •-•

•» 1.1 i>: ui
1 • i.i o. . .
I VC n. !• !•
^« o •<
•- n .11-
— b. -J. O. IA
O
bl 11 < <
O IA <
• « ^* ^« '^ IK -^ bl b!
O — *- bl •- 1.1 bl
X -i '.• IA Ul
O *• .1 *" •< *•
O < 0 0 O O
'.1 1 • bl
o c :> c i • c i- i-
>. 1. O >• V. 1. V. V.
3 3 bl :>•<-<
IK •> :i: » •• u U
bl 41 O • to t
v. ji! fi ii
xx x o n
•- « «- IN — ••> n ic a >•
A A A A A
X
j;

IK
I.I
-C
IK
:"•
o

o
Ul


bl
. I
III
•{
»•

O.

tl


IK
O
b.

1-
V.
^4

; j
ii bl
in
Ol-

bl Ul
. IU

.. |.
I-IA
*i*.
U 
      X
      UJ

-------
                          STATISTICS TABLE

                6.53C        STAKSARS DEVIATION •
      COEFF1C1EKT OF VARIATION •      0.26*
2.«22
VALUE
C.C

2.5C
S.OC
7 . 5C

1C.O
12.5

15.0

17.5

20.0

22.5


2S.C
t OF TIKI EXCEEDE2
10C.OCC

ioc.c:c
6S.C71
61.574

22.404
3.275

O.C

c.o

c.o

O.C


0.0
\ OF TIKE IX 1K7ERVAI.

C .0
1C. 525
23.457

43. US
15.126

3.275

0.0

0.0

0.0

0.0


RETURN PERIOD (TEARS)
O.OC3

c.c::-
C.OC3
0.004

C.012
O.OE4

-995. OCO

-995. OOC

-9P5.00C

-955. OOC

-epc .ocj

DC TO'J KAKT TO: (0 SEE A Rrr.TU-- PEr.IO: FOR A riFTEREKT Vy.'JE
     O CA-.C-.--ATI THE VAL-JE W:TK A THRSE TEAR RTT-JJU; PER.OD
 OR  (3) EK~ TAB'.'-AR AKAITSIS
3
rs'TER VALVE
iK;t  returr lor 1.)
1 i,
THE RETURN PERIOD FOR
                      11. Ot
                                 IS
                                          C.02
                                                 TEARS
                     FIGURE  10  Cont'd.

        Example  Tabular Display of  Continuous
                     Simulation Inputs
                                  31

-------
  VIEWING/ANALYSIS or IKPUTS

    WHICH PARAMETER DO TOV VAKT TO VIEW?

     (1) OUTFALL DISCHARGE
     (2) OU7FALL COXCESTRA710S
     (3) UPS7REAH BOVK3ART DISCHARGE
     (4) UPETREAK 8DUK3AR7 COSCESTRATION

    EKTER TO'JR CHOICE (1 - 4):
  (Hit  return lor 1)

  2 WH:CH OITFALL JS OF INTEREST (ESTER OLTFALL KUKSSR)?
  (Hit  return fer 1)

         ES7E? AVERAGING PE?.:C: us 5>.is):
  (Kit  return lei 1)

  K 70U VAST TC  SEE A PLOT?
  J
  INTERVAL OF CU>T.-LA7:Vt FCR>y.7

 ' fcV»-  TITLE D: TO'J VAST F?R  70VF. FL07 (6C CHARACTER KAilKLV.)
  EfFLUEST COSCEK7RA7IOS
T !
j 4C . 	 . 	 « 	 	 	
H 1
E !
I 3C 	 * 	 • 	
K !
1 !
K 2C - 	 »—
t !
E !
R 1
v 10 » 	 	 *---
A !
L 1
1
c .---•--« 	 •---
O.C 2.5 5.0








-
.



7.S U.O ^2.5 ^S.O 17.5 20.0 22.5 25. C
*Err;/JiKT COSCEKTRATIOK
                              FIGURE  11

Example Plot Display of  Continuous  Simulation  Inputs
                                     32

-------
X
CO
3
                                                    OWWMWIMM
O
9.
CD
-Q

o
:
*^ * I
t/> I
•o
Q)
*<

° 2

n cr>
o c:
j—»- m
n^ 1 ' 1
>«*•
33 ~*
C« ^^j
O
in

CO
H-**
3
ST
r+
»•«•
0
Z3

CD
to
C
(-»•

0 O
•
o



o
u>
O"
§
-1

o
t;
VI -•
•e o
1 . O
i •

*••
p
O
o
y.
o -•
w»
• 1 r?
•ll
^«
, I
wi
O

K>
C3



r»
^

** **








•
• "
J

















rs





, »
. *
J '






















o
... 4 •- —


.


























CD
r>
.* — 4 •—


• "
























._ .. .- 4

0
., .- .- 4
•
•



























^ k| P « •* *\
O • * ** " M 5
(* i • x r M >* c
** rt r '4 Ti > TO
M M 11 1 * O
!?!f5 ;| ~« ^ ~»
?«, 3 ?> 2 Sn
rq •" _# '" _5
*t *** *~* 21 -2 "™* o
95 *• "}• *"
n'' ? «•• " -
r •» > i -o i ' <

n ?i w o>
r. n •-• "
C >• *-*
M? —
O'l *
T5 o
Jw

5»n
"™*

^
~^ *











                                                                                                                                                                  t-   q

                                                                                                                                                                  ?    h

                                                                                                                                                     i/»

-------
                              IV.   MONTE  CARLO


     The  second  technique  which  can  be  used  to   simulate   a  probability
distribution  for instream toxics concentrations 1s  Monte  Carlo  simulation.
This technique combines probabilistic and deterministic  analyses,  by using a
fate  and  transport mathematical model with  statistically described  model
inputs. The Monte Carlo simulation  technique  has many advantages  as it:

     o  calculates frequency and duration of  toxicant concentrations;

     o  includes instream fate and  transport  processes;

     o  simulates single or multiple pollutant  sources;

     o  requires less extensive data than Continuous Simulation;

     o  model  inputs need not follow a specific statistical  function;

     o  incorporates cross and serial correlation.

The  primary disadvantage to Monte  Carlo  is that it  still  requires extensive
input  data  to define probability  distributions for Inputs.    If  extensive
data  are  not available,  the user must  have enough Information   to  assume
distributions for the input parameters.

     This  chapter discusses the theory and application  of the  Monte  Carlo
technique,  and is divided Into three sections.   The first section discusses
the theory upon which the node! is  based,  its advantages  and disadvantages.
The  second section  describes the  data input requirements.   The third  and
final  section  details  how to use the computer model of   the  Monte  Carlo
simulation technique w*tn performing waste load allocations.


Theory

     Ordinarily,  deterministic  water quality simulations use single values
for  inputs to conduct a single steady state model  simulation,  providing   a
single  water quality p^vdictlon.     Single values are selected for   upstream
flow,  upstream  conct«tratlon,  effluent flow,  effluent concentration  and
decay  rape.    The  aodtl  Is  then used to simulate a single  water  quality
response  profile.   In Multiple discharge cases, the concentration above each
outfall   is   determined  from the concentration below  the  previous   outfall.
Equations 2,   3  and  4  in Chapter 3 detail the mathematics  involved.   These
equations  are   appropriate for all  river modeling  cases except mixing  zone
anaylsis.
                                      34

-------
     The  Monte  Carlo technique is similar to the above,   but  repeats  the
simulation  many times.   It repetitively selects model  inputs according  to
defined statistical distributions.   The  deterministic model  1s repetitively
run  for a large number of statistically selected sets  of  Inputs.   Results
when  summarized (see Figure 13) show a range of predicted concentrations at
each  stream  location.   This range reflects the range   of  possible  input
conditions   and   outcomes  for  the  model.    The  range   in   predicted
concentrations  is  characterized  by   a  distribution.   This  distribution
indicates the probabilities of concentrations over the entire range.

     By  combining statistical information on environmental conditions  with
deterministic  model  calculations,  a statistically predicted  forecast  of
water quality is obtained.  The input distibutions statistically reflect our
best   understanding   of  model  inputs.    The   predicted   concentration
distributions,  therefore,  reflect  the  best  estimate  of  the  range  in
predicted  water  quality  conditions.   Analysis of this   distribution  can
provide  information on the probability of water quality problems and  their
severity.   For  a more in-depth discussion of using Monte Carlo to  perform
waste load allocations, the user is referred to Freedman and Canale (1983).

     The  Monte  Carlo technique has several advantages   over  steady  state
modeling  and the non-steady state techniques Continuous Simulation and  Log
Normal  Analysis.   The  main advantage over steady state  modeling  is  that
Monte   Carlo   can   predict  the  frequency  and  duration   of   toxicant
concentrations  in  a  receiving water.   The  inclusion  of  instream  fate
processes  is an advantage over Log Normal analysis,  which cannot  simulate
instream  fate  and  is limited to simulations for one  effluent  discharge.
Another  advantage of Monte Carlo is that model input data are not  required
to  follow a specific statistical function,  as in the Log  Normal  process.
The  Monte Carlo technique can also incorporate cross-correlation,  and  can
estimate interaction of time varying parameters if the analysis is developed
separately  for  each  season and the  results  combined.    Only  Continuous
Simulation can exactly calculate the effect of time varying parameters.

     The primary disadvantage of Monte Carlo is the data requirement.   Data
on   model   input  parameters  are  required  to  define   the   statistical
distributions or the assumptions therein.   Additional data are required for
the  calibration/verification  of  instream  fate  processes.   However,  in
contrast  to Continuous Simulation,  the Monte Carlo Simulation can  proceed
and  provide  good results with a relatively  sparse  data  set.  Continuous
Simulation  requires a very complete data set.  A secondary disadvantage  to
Monte  Carlo  is  the  inability to directly calculate running  averages  for
results,  as  Continuous Simulation is able to do.   Monte Carlo,  like  Log
Normal,   cannot   directly   calculate  multiple   day    average   instream
concentrations  but  must  estimate them by using multiple day  averages  to
describe model  inputs. A secondary disadvantage of the Monte Carlo technique-
is the large computational requirement.  Like Continuous  Simulation, however,
the  problem of excessive computer requirements is being  minimized  through
recent advances  in  computer technology.
                                     35

-------
u>
                   MONTE CARLO TECHNIQUE
JO
O
CL
                             Stat. Selection
                                         ij
                                  1
                           Water Quality Model
                                   Qu + Cu
                              FIGURE 13
                      Schematic of Monte Carlo Technique
                                                JD
                                                O

-------
Input Requirements

     The model Input requirements for all  three techniques were discussed in
the  Common Requirements chapter.   This  section details  the specific  input
requirements for the Monte Carlo technique.    These  inputs are summarized in
Table 2, and will be discussed in detail  in  this section.   The inputs can be
categorized into five groups:

     o  general simulation requirements,
     o  upstream data,
     o  effluent data,
     o  system physical and hydrological  constraints,  and
     o  number of iterations.
General  Simulation  Requirements:    The   Monte Carlo  method  requires  some
general information on the system that will  not change between  simulations.
The first basic input required for Monte  Carlo is to establish the period of
observed data to be used.   This consists  of the first year of observed data
and  the total number of years of data to  use.   The user should be cautious
to select a period of duration for which  a consistent  data set is available.
The  user should not  employ old data which  are no longer representative  of
current conditions.

     The  second  basic  input  required  by  Monte Carlo  is  the  number  of
discharges  in  the system.   The user must  also determine if any  of  these
discharges  are  located upstream of the  USGS gaging  station;  if  so,  Lhe
average  point  source flow above the gage must be determined  in  order  to
correct  the  flow record.   The final general input required is a  computer
file name to store these inputs.   Once these general  inputs are  specified,
they  will  be  stored In this computer file and need  not be  specified  for
later simulations.


Upstream  Boundary  Data:   The Monte Carlo  technique   requires  statistical
input  distributions for tht upstream boundary flow  and  concentration.  The
Monte  Carlo technique allows the use of  assumed data  distributions  or  the
observed  data  when  ttl»ctln$ Input distributions.   The  latter  requires
STORET data defining Ihtit conditions.    STORET data  defining boundary flow
and concentration should bt retrieved as  described in  the Data  Requirements
chapter, and stored m stp«r«te computer  files.

     DYNTOX  currently  allows four input distribution types to be used  for
Monte  Carlo.   The  first  three are  standard  statistical  distributions:
uniform  (rectangular),  normal  (Gaussian),  and triangular.   The  fourth
distribution  type,  temed  data-defined,  is  a non-standard  statistical
distribution.  This choice can be used to simulate statistical distributions
not currently supported by DYNTOX or in cases where  the observed data follow
no  standard statistical distribution.   The parameters required to describe
these data should all be determined using SAS (UNIVARIATE procedure) and are
described  below.   DYNTOX  allows comparison of the observed  data  to  the
distribution selected by the user.


                                     37

-------
                                                     Data  Source
o General Information:

  - Beginning date of observed data
  - Number of years of observed  data
  - Number of discharges above flow gage
  - Average point source flow above gage
  - TSS computer field name
USGS flow records
USGS flow records
User defined
Treatment records
User defined
o Upstream Data:

  - Flow Data
  - Statistical Distribution for Flow
  - Concentration Data
  - Statistical Distribution for Concentration
STORE!
User defined
STORET
User defined
o Effluent Data:

  - Flow data
  - Statistical distribution for flow
  - Concentration data
  - Statistical distribution for concentration
Treatment  records
User defined
Treatment  records
User defined
o System  Constants:

  - Time  of  travel  information

  - First order  decay rate (s)
  - Drainage area  ratio  (s)
  - Water withdrawal rate  (s)
 Dye  studies,
   current meters
 Instream data
 USGS topographic maps
 Withdrawal records
 o Number of Iterations
 User defined
                     Table 2.  Input  Requirements  for  the
                            Monte Carlo  Technique
                                  38

-------
     The  uniform distribution represents the case where each value within a
given  range  has an equal probability of occurrence.    Two  parameters  are
required to define a uniform distribution, the mean value and the range (See
Figure 14).

     The  normal or Gaussian distribution is also shown in Figure  14.   Two
parameters  are  required to define this distribution,  the mean  value  and
standard  deviation.   The normal distribution is the only one  that  DYNTOX
allows  to  have cross-correlation between parameters.   If either  effluent
flow  and concentration or boundary flow and concentration are specified  as
normal,  the  user may simulate cross-correlation between  these  parameters
through  the  use  of the bivariate  normal  distribution.   The  covariance
between  parameters  is  required if this option is  selected,  and  can  be
determined using the COV option of the SAS procedures CORR or FUNCAT.

     Triangular  distributions  are  shown in  Figure  14.   The  triangular
distribution requires three parameters - the minimum value,  expected value,
and maximum value - and can therefore have a variety of different shapes.

     Examples of the data defined distribution are shown in Figure 14.  This
distribution  can  take on an infinite number of shapes and can be  used  to
simulate   any desired distribution.   The data defined distribution requires
information on  the minimum value,  maximum value, and number of intervals to
be  used.   For each interval,  the user must specify  the  probability  of
occurrence  for  that range.                         «


Effluent   Data:  Similar  to  upstream data,   statistical  distributions  are
needed  in  the model for effluent flow and concentration  (or toxicity).   For
each   effluent  parameter,  the  user must  specify a statistical  distribution
using   the  same technique described  in  the  upstream  boundary data   section.
Any  downstream tributary  input should  be  treated as   a  separate   effluent
input.


System  Constants:   System   constants need  to be defined  for  hydrologic   and
physical  characteristics  of the system.   Program  inputs for  hydrologic   data
are   needed to  properly  adjust  gaged  flow data to  determine  instream flow at
different  locations.   Ratios are needed to define  the comparison  between the
gauged  drainage  basin   area and  the drainage basin  area at  the  point of
discharge.   These  ratios   adjust  the USGS  measured  flows  for  nonpoint
 sources,   and  must  be  specified  regardless of the  location  of  the  gaging
 station.    For discharges located  downstream of the  USGS gage the ratio (and
 adjustment)  will  be greater than  1.0.    For discharges located upstream of
 the   gage,  the  ratio  will be less than 1.0.   The method to  be  used  for
 specifying  drainage  area ratios is described in  the  Common   Requirements
 chapter.  A  second hydrologic adjustment is required for water withdrawals.
 If  a significant amount of water (>1% of river flow) is withdrawn from  the
 river  at  any  location,  this withdrawal rate  must  be  specified  before
 performing a Monte Carlo waste load allocation.


                                      39

-------
             Probability of
             Occurrence
  Probability of
  Occurrence
X
Q)
3
n

n>
CD
           c
           CD
                     O

                     a
                     CD
                     CD
                     O.
           o
           D
           «o
                                                      Probability of   Probability of
                                                      Occurrence     Occurrence
                                                    CD
o.
•*^*
to
CT
c
o
a
01
            C
            CD
C
CD
                                 O
                                      C
                                      CD
3
3=
i

-------
     Another  system constant required by Monte Carlo is the time-of-travel,
which must be specified for the stream segment between the upstream boundary
station and the first discharge and for the segments between each discharge.
The  method  for specifying time of travel was discussed in  detail  in  the
Common  Requirements  chapter.   Time  of  travel  information  need  not  be
specified  for the upstream segment in cases where the boundary  station  is
located below a discharge as there is no upstream segment.

     The  first-order  decay rate must be specified for each stream  segment
that  requires time-of-travel information.   The method for determining  the
first-order decay rate was discussed in the Data Requirements chapter.


Number  of  Iterations:   The Monte Carlo technique  requires  a  sufficient
number  of iterations to adequately define the probability of occurrence  of
downstream concentration.  However, specifying too many iterations can waste
computer time.   The recommended method for determining the proper number of
iterations  is to run the Monte Carlo technique for an increasing number  of
iterations  until the predicted probability distribution remains  relatively
constant.   Five thousand (5000) iterations can be used as a starting point,
with  the  number  of iterations repetitively doubled until  results  remain
constant.   It  is  recommended that the three year return period  value  be
compared when determining the proper number of iterations.


Program Use

     The Monte Carlo program, like the programs for the other techniques, is
divided  into  menu driven sub-programs (entitled activities) to  allow  the
user  as  much  flexibility   as  desired  in  performing   simulations.  The
hierarchy of activities  for Monte Carlo is shown in Figure 15.  this section
will  describe  how  to  use the Monte Carlo program  and  will  discuss  the
options available to the user.   It  is divided into sections describing each
of  the primary activities:

     o  Program  Entry,
     o  System Constants,
     o  View  Input  Data/Specify Distributions,
     o  Run Model,
     o  View/Analyze  Results, and
     o   End  Monte  Carlo.


 Program  Entry:   The  first activity of the Monte Carlo technique is  termed
 Program Entry.   This section consists of specification of the time period of
 observed  STORET data,   number of discharges to be simulated,  modeled  point
 source  flow above the USGS flow gage,  and location of the data  describing
 boundary conditions.
                                      41

-------
*>
t\>
                                                 Program Entry


System
Constants


•
VI CM Input
Data/Specify
Distribution

— v

                                                   /Menu}
                                                     Run

                                                    Hodc I
) 	 	



VI en/ Analyze
Results



End Monte
Carlo
                                                 FIGURE 15


                                  Hierarchy of Monte  Carlo Subprograms

-------
     Figure 16 shows example sessions with the Program Entry activity.    The
first  questions in Program Entry concern the existence and location of  the
TSS files for the simulation.   TSS (Time Series Store) files are created by
ANNIE to store time series information.    The TSS file holds all  information
pertaining to the STORET boundary data for the Monte Carlo case.    The  first
time  a simulation is performed,  the user should answer NO to the  question
asking if a TSS file was previously created,  and specify a file name (Figure
16a).   This  will initiate the process to create a file.   The user  should
answer  YES  to  this  question in  subsequent  simulations,  and  no  other
information will be required in the Program Entry section except the name of
the TSS file (Figure 16b).

     For first time entries,  the TSS file name must be supplied.   Any file
name  can  be used that is compatible with the computer  system.    The   next
inputs  required are the first year of observed data and the number of years
of data.   The required format for the date is Year/Month/Day (Figure  17a).
Months  and  days  with only one significant figure of  information  may  be
entered  using  only one digit.   The next question in Program Entry  before
creation of the TSS file concerns the number of discharges in the system.

     The  TSS file for the system is being created and initialized  at   this
point in Program Entry.   This may take some time, depending on the computer
system  used,  but the user will be informed when the file initialization is
complete.   TSS  files created during Monte Carlo can be used for either  of
the other two DYNTOX techniques.

     The  final  portion  of Program Entry concerns  defining  the  upstream
boundary  data files.   Figure 16a shows an example session where  both  the
boundary  flow and boundary concentration data are located in STORET  files.
The  user need only specify the name of the STORET data files and which data
set of the STORET retrieval is to be used.  The data set will always be  one
unless the user has multiple STORET retrievals stored in the same file.  The
section provides the ability to screen out flow and concentration data above
acceptable values.

     Another  possibility   for Program Entry  is when the user has no  STORET
data and wishes to enter observed data manually from the  terminal.   Figure
16c  shows an example  of this  situation.   The user is required to  input the
number of data  points,  then the date and concentration  for  each value.  The
proper   format  for the data is  (date,   value) with the  date  in  the  YYMMDD
format.  The  final option  of program  entry concerns the  case where  all  input
distributions were calculated  off-line before using DYNTOX.    In this   case,
no raw  data  need  be  entered,   either  from STORET  files or  from the  terminal.
 Instead,   the   user   enters only   the   previously calculated  distribution
 information,   (e.g.  Figure 18a).
                                      43

-------
     Figure 16 shows example sessions with the Program Entry  activity.    The
first  questions in Program Entry concern the existence and location of  the
TSS files for the simulation.   TSS  (Time Series Store) files are  created by
ANNIE to store time series information.   The TSS file holds  all information
pertaining to the STORET boundary data for the Monte Carlo case.    The  first
time  a simulation is performed,  the user should answer NO to the  question
asking if a TSS file was previously  created, and specify a file name (Figure
16a).   This  will initiate the process to create a file.   The user should
answer  YES  to  this  question in   subsequent  simulations,   and   no  other
information will be required in the  Program Entry section except the name of
the TSS file (Figure 16b).

     For first time entries,  the TSS file name must be supplied.    Any file
name  can  be used that is compatible with the computer  system.    The   next
inputs  required are the first year  of observed data and the  number of  years
of data.   The required format for the date is Year/Month/Day (Figure  17a).
Months  and  days  with only one significant figure of  information  may  be
entered  using  only one digit.   The next question in Program Entry before
creation of the TSS file concerns the number of discharges in the  system.

     The  TSS file for the system is being created and initialized  at   this
point in Program Entry.   This may take some time, depending  on the computer
system  used,  but the user will be  informed when the file initialization is
complete.   TSS  files created during Monte Carlo can be used for  either  of
the other two DYNTOX techniques.

     The  final  portion  of Program Entry concerns  defining the  upstream
boundary  data files.   Figure 16a shows an example session where   both  the
boundary  flow and boundary concentration data are located in STORET  files.
The  user need only specify the name of the STORET data files and  which data
set of the STORET retri**al 1s to be used.  The data set will always be  one
unless the user has »wUiplt STORET  retrievals stored in the  same  file.  The
section provides the ability to screen out flow and concentration  data  above
acceptable values.

     Another  possibility  for Program Entry  is when the  user has  no  STORET
data and wishes to **ttr observed data manually from the   terminal.   Figure
16c  shows an exa*pif  o* IMS situation.   The user  is  required  to input the
number  of data  points.  tK«n the  date  and  concentration  for  each value.  The
proper   format  for tM data 1s  (date,   value) with  the  date in   the  YYMMDD
format.  The  final optic* of program entry concerns  the  case where all  input
distributions were calculated off-line before using  DYNTOX.    In this  case,
no  raw  data  need  be entered,  either from STORET  files  or from the terminal.
Instead,  the  user   enters  only   the  previously  calculated  distribution
information,   (e.g.  Figure  18a).

-------

m
X
Q)
O>
CO
ft
V)
c^
*—*
o
X

_^
» » "^^
^ I—I
3 g
O -T1

O) _»
o
Q)

O

-o
o
(O
"^
Q)
m
3
-i

. 	 	 	 	 	 —
Y Y Y Y Y t Y Y
^^r--c«n r,*o ~~5^C|-:3 *!MI8
7 T 'J I in • 1 :i. 11 < ' <*> '" T -f- x "\, ~-L
— riZ-y- •-• 11 " > "* K> «>••»• ~ i! i _,
2 Z- *5?S- ?•"•'"-- "M~ 2
" ^ k*?^" f^ eo ^si1^ >
T} 3S 3or-S PIM 3S ao°S 3
" ?j ~fj r >^ ?J ~J * >
*1n*4n.-lS^^ ••• WlHti
> 'J 15 f > 6 o x - 11 o
u p :e, ^11 o y ° . g ^. ^| 13 w

" ^0 0 ' S "•
S " ", S '" o
R i > S " r-
-ri i! - * 5 S
r, ?, s" u '••: >
o - 3 ? « 2
r. « O «T i-« r-
• j: " ? Si R

\- '" s >
S s S
> •*!
:c
0
ri
11
V.
•1
b
7.
•o


. 	 	 	 	 	 ' 	
Y Y Y Y Y Y Y Y
7 ???g-£ow5"*o"53»;3»M*" 	 -~ ?:
^ 5 1;" «>:Srj "^rir' •'•''"rs ^g^--- 3
n : -i slsn ?.!K= s j jjjsSSljij a
M S So So 5 ^x x •» 5 Spuii-i" x
3 e ~"J ~'-i » "•» r ™ R S" o o 5 5 ° P
^-*fc*"^t-l vpl tjl'^t '**^^*s^4
M** r* ^ ^ ^ ^-r**-*ll*4
oo £ S' ?»«»o «-ar-i!o
51 ^ £ ^ o § > H HO— «
*^ ** W :«. X • 1 X cl^OO>'
w Jj * J g 9 r r! i i» S _ ^ * 's
w* v* 5 i; b« t*i tJ >• •TO***"'
-••^ «"*3 Hr=?oM
p P s ; !: H T, o 0>O':e
= s ? s s : : :^ 5 sg R
- ^ r in r ••* "> n^r.
*• ' Tl Ml* tJ
V r; o U 3 U S |5 >;
o 3 5 g o ? S S
s r. !- 5 ?> F: s
"' ~ "r in >
PI PI ; . . . K
r! u - »
* in

J:
:",
o
V.
'
-


H
o
X
o
I/I
t:
IU
in
• 1
o
Pi
in
• 1
11
I-
O
u
^ •
O
o
;l
7.

\ )
U
11
I-
7,
Cl










ai
a>
— t
to
to
-n
•-••
n>



















.


-------
16b.   Existing  TSS File
               HAVE YOU PREVIOUSLY CREATED A TSS FILE FOR THIS SIMULATION?
               YES
               WHAT IS TriE KAKE OF YOUR TSS FILE?
               EXAMPLE
16c.   Terminal  Entry of Data
               HAVE TOU PREVIOUSLY CREATED A TSS FILE FOR THIS SIMULATION?
              •NO
               WHAT IS THE KAKE OF TOUR NEW TSS FILE?
              •TEST": IE
               JO- KANY TEARS  OF DATA DO YOU HAVE?
               (Hit returr Icr ')
              • e
               HCW KANY OUTFALLS ARE THERE IN THE  SYSTEM?
               (Hit return {or 1)
              • 1
               HCW KAKY OUTFALLS LIE ABOVE THE FLO'-' CAGE?
               (hit return fcr 0)
              -0

               PLEASE  WA:T WHILE YOUR TSS F:LE is  INITIALIZES ...

               INITIALIZATION OF irjR TSS FILE is  NSW COMPLETE.

               DO YOU  HAVE A STORET FLOW DATA FILE?
              - Y
               WHAT  IS THE KAXE OF THE  STORET FILE?
              -STCr.ET.FLO
               USE WHICH  DATA SET?
                (Hit  return (or 1)
              - i
               WHAT IS THE KAX'-K-JV. ACCEPTABLE FLOW VALVE?
                (H:t  returr. tor 0.)
                4S99.
                 £2<5 PC:KTS READ

                DO T3'J HAVI A  STORET DATA FILE FOR  UPSTREAM COSCEKTRATICS?
              - NO
                DC iO'J WANT TO ESTER CONCENTRATION  DATA FROM THE TESX.INXL?
              P- YES
                HCW KANT SAMPLES DO YO'J HAVE?
                (Hit return, for «)
              ^ 3

                ENTE5  3ATE AKD UPSTREAM COSCENTSATIOS FOR  EACH SAMPLE:
              »-6::-ci, .5
                       .4
                   fcU. .23
                    3  P::KTS READ
                                FIGURE 16  Cont'd.

            Example  Session  with  Monte Carlo Program  Entry
                                              46

-------
s
8

j

bi
O
;/•
u:
u
B
g
•^
i .
^

M
O
.1
PC
<
U
bl
O
X








••
bl
O
tj
14
IA
PLEASE
in
O
n
»«
DC
H
M
H
in
H >•
V. b.
l-o
in M
6 In


bi •<
in
*• t
wibj
n. M
>« * n
b. ~ 1)
o :•
:>
V.
*
U1
W*
if
>i
l>
I*
t J
H
y.
o:
f!
y

o
* <•
-<
4/1 L !
fii/i
in
blO

1C
bl X
»*
. 1 M
< !•
•J. 's.
•4 1 1
!i







m
i

«• «
o o
i'
1 1 C
bl 1*
. 1 U

bl W UL bl M I/I •>
O. ~: 1 ..If. b,
M > PC > bl 1C
1.1 **
•- f* m *» in X X



in
I-
V.
i-
in
l.
u
T
bl
1-
in
I-
M

b.
O
'&
O
SFECIFI
a
x
in
6
n
. i
bl
.1
1C
b.
O
b| bl
... rr.
H «:
bl U
u: m
l!°
b! H
^* in
u PC
bl .*
0. b.
in
MI
n '£
fr" !••
kg
5Ek
:>•<-<
O It 1 •







8
U.
u.
O

x *•
»-» b«
i* °
^I^C
-s.

20 o m *.
M U < 1*
:« M — — i • •_••
X
0
PC
b.
bl
in bi o
f. |.(K
g 2*
o
Z «" «
OQ
|j Ol-
1$ nr. K
b.— oi-j^-

O 1 • •• J • **
bl C bl M O
t' u X <4
*- 2 '"?r
u> ^ M ^i .
in w */• - * • •
>-. W »1 I 1 X
H w H
< .. -f bl bl
:i: x - p: :i: w
•- U — -it- ui —
CHARGE 1 1
IA
r .
Q
b>
O
O
b, 2
•< •*
a. M
.1 4
3 "

V '
1 < *
'* t
M» Wt
»- ••
<0 *
"• ii: o i









M
*
a
«*








-


*
&
tot *•
H -
g£-
                                                      c
                                                      CO
                                                      c
                                                      o
                                                      o
                                                      0)
                                                      JJ

                                                      ^O


                                                      00


                                                      o
                                                rx   CO
                                                r-   O


                                                uj   a>
                                                   c
                                                CD   O
                                                      g
                                                      I/I
                                                      a>

                                                      "S
                                                      e
                                                      ro
                                                      x
                                                      UJ

-------
Demonstration  of Uniform and  Normal  Distributions
                 PLEASE CHOOSE ONE:

                  (1)  SP'CIFT EFFL'JEKT FLOW /CONCENTRATION DISTRIBUTION
                   2  VI Ew bATA/DETERXIKE BO'JKSARl CONCENTRATION 01 STRIB.-TI ON
                  (3  V'EH DATA/DETESKINE BOUNDARY FLOW DISTRIBUTION
                  (4)  CK3 IKP-JT DEFINITION. RETURN TO MONTE CARLO MENU

                 tKTER SELECTION (1-4)
                 (Hit  return (or 4)
                  SPECIFICATION or
                                          SIST?.IB--T:ONS
                  SPrc:FT FLO« iNr:-RMATios FCS D:SCKAHGE
                  VriAT TTrE  OF D:STR:B~IOK DO TO'J HAKT?
                   (1) UKIFCRK
                   (2) N5R.KAL
                   (3) TSIANCULAR
                   («)
                       ATA DEFINES
                  EKTES SELECTION  (1-4)
                  (Kit return lor  1)
                  1
                  WHAT IS THE KIAS VALUE
                  (Kit return (or  1.)
                  25.
                  WHAT IS THE RANGE
                  (Kit return (or  0.)

                  SrECIFT CONCENTRATION IKFCRKATIOK  FOR DISCHARGE
                  VriAT TYPE OF 01 STS: B'.T: OS 35 TOU WANT?
                   (1) UNIFORM
                   (2) N:=KAL
                   (3) T?.:ASG-.'*_AR
                   (4) DATA DEFINED
                  ESTER  SELECTION (1-4)
                  (Kit return for 1)
                 - 2
                  WHAT IS THE KEAN VALUE
                  (Kit return tor 1.)
                 -S.
                  WAT IS THE STAV=iJO DEVIATION
                   (Hit return  for C.)
                    ENS CF DISCnAPCE SPECIFICATION SECTION
                                FIGURE  18
                Example Session with  Monte  Carlo
                Specifying  Effluent  Distributions
                                          48

-------
18b.   Bivariate  Normal Distribution
                      SPEC: n CAT: OK or EFFLITENT DISTRIBUTIONS

                     SPECIFY FLO*  INFORMATION  FOR DISCHARGE   1
                     WHAT TTPE OF  DISTRIBUTION DO YOU WANT?
                      ( 1) UNIFORM
                      (2) NSRMAL
                      (3) TRIANGULAR
                      (4) DATA DEFINED
                     ENTER SELECT; OK  d-4)
                     (Hit rtturn for  1)
                     2
                     WHAT IS TrE MEAN VALUE
                     (Hit return for  1.)
                    • 25.
                     WHAT IS THE STANDARD DEVIATION
                     (Kit return for  0.)
                    -3.
                     SPECIFY CONCENTRATION IKFCRMATION FOR DISCKAR3E   1
                     WHAT TYPE OF DISTRIBUTION DO YOU WANT?
                      ( 1) UNIFORM
                      (2) K?SMAL
                      (3) TSIASGULAR
                      (4) DATA DEFINED
                     ENTER SELECTION  (1-4)
                     (Hit return  for  1)
                    »2
                     WHAT is THE KIAN VALUE
                     (Hit  return  for  1.)
                    ~S.
                     WriAT IS THE  STAN3AR3 DEVIATION
                     (Hit  ret.rn  for  0.)
                    ».1.
                     IS CONCENTRATION C3R?.ELATED TO  FLOW
                    •.TES
                     ENTER  CCVARIASCE BETVEEN CONCENTRATION AND FLOW
                      (Kit return  fsr 0.)
                       END OF DISCKAR3E SPECIFICATION SECTION
                               FIGURE  18  Cont'd.
                     Example  Session  with  Monte Carlo
                    Specifying Effluent  Distributions
                                             49

-------
     After  completing Program Entry the program enters  the main portion  of
Monte  Carlo.   The user will be given the menu shown in Figure 17 and  must
select one of the five activities:

                    1.  System Constants
                    2.  View Data/Specify Distributions
                    3.  Run the Simulation
                    4.  View/Analyze Model Results
                    5.  End Simulation

Although  there  is flexibility in  the order in which options are  selected,
system constants must be specified  before choosing any other option  (except
ending).


System  Constants:  The system constants consist of time of  travel,  first-
order decay  rate,  drainage area ratio,  and water withdrawal rate.  Program
operation  for  the section is straightforward,  requiring only  the  inputs
discussed in the Common Requirements section.  An example session specifying
system constants is shown in Figure 17.


View Data/Specify Distributions: This section allows the user to view and/or
analyze  the observed  data for the boundary parameters and  then  requires
specification   of  the  input  distribution  for  these  and  the   effluent
parameters.  Upon entry to the section,  the user is given a menu  (Figure  18)
of  four choices:

      1) Specify effluent  flow/concentration distribution,
      2) View data/determine  boundary concentration distribution,
      3) View data/determine  boundary flow distribution,
      4) End  input  definition.


The options  may be selected  in any order desired;  however,  options 1-3 must
be   successfully  completed  before ending to successfully  perform the  model
 simulations.

      Example sessions using  the first option,  specification of effluent data
 are  shown in Figure 18.    This session demonstrates use of the uniform  and
 normal  input distributions.   A uniform distribution  is  selected for effluent
 flow  in this example,  and the user is required to  supply a mean value  and
 range  (Figure  18a).   A  normal   distribution  is   selected  for  effluent
 concentration;  in this case, the  user must supply a mean value and standard
 deviation.   In the  special  case where normal distributions are selected for
 both flow and concentration,  the option exists to specify a covariance term
 to  represent the cross-correlation between parameters   (Figure  18b).   The
 same  option  exists when specifying normal distributions for boundary  flow
 and boundary concentration.
                                      50

-------
     When  boundary concentration and flow data are available,  the user has
the  option  to view a plot of the actual data distribution or see  a  table
describing the statistics and distribution of the data.   Figure 19 shows an
example session specifying boundary flow,  where the user selects to see the
plot  of  the data.   The plot shows the probability of occurrence  for  the
parameter  over  a  number of ranges.   The distribution is  selected  after
viewing  the data plot;  in this case a triangular distribution.   In  cases
where the data has been viewed or analyzed, the option exists to compare the
predicted  distribution  to  the observed data and  also  to  determine  its
acceptability.   The  user  is allowed to choose a new distribution for  the
parameter in cases where the fit is unacceptable.

     Figure  20  shows an example session specifying  boundary  flow.   This
example  demonstrates  use  of the data defined distribution.   The  sum  of
probabilities specified for all of the intervals in data defined must  equal
1.0 or they will be rejected by the program and new values required.

     In  many  cases,   insufficient  data  will  be  available  to   define
distribution  for  four-day average values.   Based upon the  Central  Limit
Theorem,  users  may  specify  a normal  distribution for  the  parameter  in
question, with a standard deviation one half of that in the observed  data as
an  estimate of the distribution of four day average value.    The mean value
will remain constant.


Running the Simulation:   Only one input  is required when choosing to  run the
simulation,   the number of iterations.    During the simulation,   the  program
will  print a message  after the completion of every 2000 iterations  to help
in monitoring program progress.


View/Analyze Model  Results:  Model results can be seen in one of two formats,
as a plot showing probability of exceedance for all concentrations,  or as  a
statistics  table showing statistics on  the results along with the frequency
distribution of the results in tabular format.   An example session  viewing
the  results of a model  run in plot form is given in Figure 21.    Figure  22
shows the results of the same simulation in tabular format.    The statistics
table consists of the statistical parameters mean,   standard deviation,  and
coefficient  of  variation,  along with the probability of occurrence for  a
number of intervals.  The table also shows the probability of exceedance and
the return period (recurrence interval)  for a number of values.    The option
exists  to view the return period for a value not shown if  desired,   or  to
view the value with a three year return period.


End  the'Simulation:  Choosing this option allows the user to exit the Monte
Carlo  technique  and return to the main DYNTOX menu.   This option  can  be
selected at any time during the Monte Carlo simulation.
                                     51

-------
  SPECIFICATION OF IKPUT DISTRIBUTIONS

 OVER HOW MAH1 DAYS DO TOU «AHT WSOLTS AVWAGED
 (Hit return tor t)

 PLEASE CHOOSE OHE:






  ESTER SELECTION (1-4)
  (Kit returr. lor 4)
  3
  SPECIFICS OK or BOUOARY FLO* B:STR;BOTIOK

  ^ TO, WAK7 TO SEE A DATA WSTHIWTIC* K.OT BtrOR* CHOOSIHC7

  1XTERVM. OR OWJLATIVE FORMAT

  lr TOC VAKT TO SEE A STATISTICS TABLE?

'  £HAT TITLE DO TOC «AKT FOR TOUR F-OT  (60 CHARACTER IU1IN3K)
-  B3UK3ART FLOW
      20
       5 •---•--»-
         0.   500.
                            FIGURE  19

       Example Session with  Monte  Carlo Specifying
                    Triangular  Distribution
                                    52

-------
  SFECJFT BO'JOAR-Y FLOV B: STRIB'-TIOK
 WHAT TVPE or »:STA:B-.TJOK B: »oa VAKT?
  (i) UN:FORX
  (2) K?RKAL
  (3) TRIAVS'.'LAS
  (4) BAT A BCflKED
 EKTEF. SELECT!OK  (1-4)
 (Hit return lot  1)
 3
 WHAT IS THE KIKJ»W. VALUE
 (Hit return for  C.)
• U.
 WHAT IS THE KAZ:K*jy. VALUE
 (K:t return lor  1.)
 ?5CC.
 V>:AT is THE tiPECTED VALVE
 (K:t return lor  0.5)
- 6CO.
 B: lO'J WAKT 70 CO.".?ARE THE  CISTP.: B'JTIOK TO THE  ACTUAL BATA?

 WHAT T:TLE BO tsv VAST FOR  TOVF. PLOT UO CKARACTEK KAZJUJK)
 COM?AR: SDK or TRIASSV-AR BISTRJBUTIOK
   100
 T
 I
 V.
 E

 1
 K

 I
 K
 T
 E
 R
 V
 A
 L
6C
«c
2C
       f
       •
        C.
            sec.
             K.::.  i;:c.   2::?.  2scc.
               cof-:?A?.:sos  or  T?:ASCVLAR
                                                  ssco.  4::c.   45c
  IF THIS FIT ACCEPTABLE?
  T

  EKS Or BOUK3ART FLO- SFEC!ri CAT10S SECTION
                     FIGURE 19 Cont'd.
   Example  Session  with  Monte Carlo  Specifying
                 Triangular  Distribution
                               53

-------
      SPECIFICATION or BOUNDARY FLOW DISTRIBUTION
      SPECIFY  BOUNDARY FLOW DISTRIBUTION
      VriAT TYPE Or DISTRIBUTION DO TO.. VAST?
       (1) UNIFORM
       (2) NORMAL
       (3) TRIANGULAR
       (4) DATA DEFIKEO
      ENTER SELECT10NO-4)
      (Hit return for 1)

      WHAT is THE K:N:KUK. VALUE
      (Hit return f er C. )
      IE*
      HOW KAKT IKTEKW.S DO TO*J WAST TO SPECIFY
      (Kit rerurr. lor 2)

      K'K-K-JV VA^DI  rOR JKTEFVAL 1 JS   160.
      WrAT JS THE KAZ:>TJK  VA'.VE
       (Hit returr,  for  1. )
      220
      WHAT IS THE PROBABILITY Or OCCURREKCE
       (Kit return for  C.)

      KIKIKJK VALUE  TO?. ISTEPVAL 2 JS   220.
       WHAT IS THE JSAIIKUK VAiUE
       (Hit return lor 220.)

       WriAT !S THI PROBASILITY  Or OCCURREKCE
       (Kit returr. let C. )

       K-VK-J* VALUE F3f ISTERVAL  3  IS   260.
       whAT is TKI KAX:KUV VALUE
       (Kit re:urr ler 26C . )

       w-n»- is THE PROI«.B:LJTY or  OCCURRENCE
       (H;t re-.urr to: C.)

       K:K:K»' VALUE rsr  IKTEFVAL 4 is    32C.
       WVIAT :s TKE HAi:»nv VALUE
        (K:t re-.ur-  ter  JZC.)

       WH!T is TKI  P>;IAB:LITY or
        (V:t t»:^r>  !e:  t.)
         :1"! vwr TO CCMFARI  THE D:STR:»LT:OS TO THE ACTUAL DATA
        Ki

        EK- Of  »;UV3Af.T FLOW SPECIFICATION" SECTION
                               FIGURE 20

Example  Session Specifying Data  Defined  Distribution
                                      54

-------
 MONTE CARLO TECHNIQUE .

    PLEASE CHOOSE FROM THE FOLLOWING:

    (1) SPECIFY SYSTEM CONSTANTS
    (2) RUN MCOEL
    (3) VIEW/ANALYZE RESULTS
    (4) EK3 MONTE CARLO SIMULATION,  RETURN TO TOXICS WLA MENU

    ENTER TOUR CHOICE (1  - 4):
 (Hit return for 1)
-3

 v:r-:ss 'ANALYSIS or RESULTS

 DO  YCV VAN? TO SEE A PLOT?
•Y
 WHAT TITLE DO YCw WAST FOR YCVR PLOT  (6: CHARACTER KAXIKVK)
•MONTE CARLO CONCENTRATION
 »  ICC •••••
 0    I                                                                  i
 F    j    .                                                              ;
    ac i	•	-	-	-.	|


 i   i    *.                                                            I
 E  6C !	•	-»		•		*-	-	j

      !       •                                                          '
 t    *        •                                                         ,
 X    <                                                                  ,
 c  «o !	«.--*	-		«	;
 E    !
 E    !
 D    •
 E  2C !	»---»...	»	—	-,	-	,
 D    !                    •«                                            i
      I                      •••                                         i
      !                         •                                        ;
    c	•---	
    0.0           0.50         1.CC         1.50         2.CC          2  5'
                        MONTE CARLO CONCENTRATION
                    FIGURE  21

    Example Session with Monte  Carlo
      Viewing  Results  in  Plot  Format
                           55

-------
     PLEASE CHOOSE FROM THE TO-LOVING:

     (1) SPECIFY SYSTEM COKSTAKTS
     (2) R'JK MODEL
     (3) VIEV'AKALYZE RESULTS
     (4) EKD COKTIKUO'JS SIMULATION
     EKTEF YOUR CHOICE (1  - 4):
   RETURN  PERIOD FOR A DIFFEREKT VALUE
        (2) CALCULATE THE VALUE WITH A THREE TEAS RETURN PERIOD
     OR  (3) EKD TABULAR ANALYSIS
    3
                           FIGURE 22
Example  Session  with  Monte Carlo  Viewing Results
                      in Tabular Format
                                  56

-------
                               V.  LOG NORMAL


     The  third  technique  that  can be used  to  calculate  a  probability
distribution  for instream toxics concentrations Is Log Normal probabilistic
analysis.  This technique assumes that all Input parameters can be described
by a log normal statistical distribution,  and uses numerical Integration to
predict  the  concentration distribution below a single effluent  discharge.
The Log Normal technique has many advantages as it:

     o  predicts frequency and duration of concentrations;

     o  requires  less computational expense than Continuous  Simulation  or
        Monte Carlo;

     o  does not require extensive time-series data as Continuous Simulation;

     o  incorporates cross-correlation of parameters.

     The  primary  disadvantages to Log Normal are that extensive  data  are
required to define input distributions, all parameters are assumed to be log
normally  distributed,  and instream losses or simulation of more  than  one
discharge cannot be considered.

     This  chapter  describes the theory and application of the  Log  Normal
technique,  and is divided into three sections.  The first section discusses
the theory upon which the Log Normal technique is based,  and its advantages
and   disadvantages.    The   second  section  describes  the   data   input
requirements.   The  third and final section details how to use the computer
program of the Log Normal technique when performing waste load allocations.


Theory

     Continuous Simulation and Monte Carlo and Log Normal analysis are based
upon  the same dilution equation,  which predicts the concentration below  a
discharge  (CH) based upon upstream concentration (C),  upstream flow  (Q )
effluent concentration (Ce), and effluent flow (Qe):u                     u

This  equation   is  suitable for all in-stream modeling except  mixing  zone
analysis.   Where Continuous Simulation and Monte Carlo analysis solve  this
equation many thousands of times using different values for the Inputs,  Log
Normal analysis  uses a totally different technique.

     Log Normal  analysis requires that each model input follow a log  normal
statistical distribution;  this causes the probability distribution for each
equation  to  be well defined mathematically.   The  probability* that  the
downstream  river concentration (Cd) exceeds any given value,   C ,  can  be

                                     57

-------
expressed  as a multiple integral  of  the joint probability degsity functions
over  the values of flows and concentrations  for which  Cd >  C  .    Since  the
variation  of  each input variable is defined by   a  mathematical   equation,
numerical  integration can  be conducted to   determine  the probability  that
C.  >  C .   By repeating this integration for different values  of  C ,  the
probability  distribution  for  Cd can  be  estimated.   The  probability  of
exceedance can be estimated for derations other than one day by  using inputs
representative of multiple-day averages.    For a  more  complete  description
of the theory behind Log Normal probabilistic analysis, see  DiToro (1984).

     The  primary  advantage of the Log Normal technique is  the  ability  to
predict  the  frequency distribution  of the river  concentration  without  the
excessive  computational  requirements  of Continuous   Simulation   or  Monte
Carlo.  Whereas  Continuous  Simulation and  Monte  Carlo   require  several
thousand iterations of the model to predict the concentration  distribution,
Log Normal can proceed much faster through numerical integration.

     The  disadvantages of Log Normal are the inability to simulate multiple
discharge  situations  and the requirement that all  parameters   follow  log
normal  distributions.  In  many cases, parameter data only   approximately
conform  to  a log normal distribution.  This  introduces  errors  which  are
exagerated   at  the  infrequent  recurrence   levels   of  the    probablistic
simulation.   Log  Normal also has the  same disadvantage as  Monte   Carlo  in
that  multiple day average in-stream  concentrations can only be  approximated
through  the  use of averaged inputs.  Continuous Simulation   is   the  only
technique  that allows exact determination of multiple day average  results.
Log  Normal analysis also requires significantly more  input  data than steady
state models, but no more than Continuous Simulation or Monte  Carlo.


Input Requirements

     The model  input requirements for all  three techniques were discussed in
the  Data  Requirements chapter.   This section details the   specific  input
requirements  for the Log Normal technique.    These  inputs  are summarized in
Table 3,  and will be discussed  in detail  in  this  section.   The inputs can be
categorized  into five groups:   general  simulation   requirements,  upstream
data,  effluent data,  system  hydrological  constraints,  and output range of
interest.    However,  the data  requirements  for each  are to an extent  first
dictated  by  general  information on the simulation.

General  Simulation  Requirements:   Log Normal analysis requires some general
 information   on  the system that  will  not change  between  simulations.    The
 first   basic  input required for  Log  Normal Analysis  is  to  establish   the
 period   of  observed data to be used.   This consists  of the first  year of
 observed data and the total  number of  years  of data to use.  The  user  should
 be  cautious  to  select  a  period  of duration for  which  a   complete   and
 consistent data set is available.   Caution  should be  directed  towards using
 old data which are no longer representative  of current conditions.

      The second basic input required by Log  Normal is  whether the  discharge
 is  located upstream of the USGS gaging station.  , If so,   the  average point
 source  flow  above the gage must be determined.   The final  general   input
 required is a computer file name to  store these inputs.   Once  these general
 inputs are specified, they will be stored in this computer  file and need not
 be specified for later simulations.

                                        58

-------
                                                      Data Source
o General Information:

  - Beginning date of observed data
  - No. of years of observed data
  - Number of discharges above flow gage
  - Average point source flow above gage
  - TSS computer file name
USGS flow records
USGS flow records
User defined
Treatment records
User defined
o Upstream Data:

  - Mean and 84th percentile value for flow
  - Cross-correlation between river flow
       and river concentration
  - Mean and 84th percentile value for
       concentration
  - Cross-correlation between river flow
    and effluent flow
STORE!

SAS

STORET

SAS
o Effluent Data:

  - Mean and 84th percentile value for flow
  - Mean and 84th percentile value for
       concentration
  - Cross-correlatiion between effluent flow
       and effluent concentration
STORET

STORET
 o  System  Constants:

   -  Drainage  area  ratio
   -  Water withdrawal  rate
 USGS topographic maps
 Withdrawal records
 o Output Interval  of Interest:

   -  Minimum river concentration of interest
   -  Maximum river concentration of interest
   -  Interval for output
 User defined
 User defined
 User defined
                     Table 3.  Input Requirements for the
                               Log Normal Technique
                                  59

-------
Upstream  Boundary  Data:   The Log  Normal  technique  requires  the   mean  and
variance  of  the  input distributions  for  the  upstream   boundary   flow  and
concentration.  DYNTOX  provides the ability  to determine  the  distribution
parameters  from  observed upstream  boundary  flow  and concentration.    This
requires STORET data defining these  conditions.

     The  required  form of this data includes  the 50th   percentile  (mean)
value  and 84th percentile  value for each  parameter.   These  parameters can
also  be determined from SAS,  as well  as the adequacy of the  assumption  of
log  normality  (using  the UNIVARIATE procedure on the   logarthims  of  the
observed data).  Boundary flow data  must be corrected for point  source flows
and  withdrawals before performing SAS analysis,   as  they may  significantly
affect  the  assumption  of log  normality.  In   addition,  this   technique
requires information describing the  cross-correlation between  river flow and
effluent  flow,  and  river  flow and  river  concentration.   These  cross-
correlations can also be determined  using SAS,  using  the  CORR  procedure.


Effluent Data:  Similar to upstream  data, log normal  distribution  parameters
are  needed in the model for effluent flow  and  concentration  (or  toxicity).
For  each  effluent  parameter,  the  user  must specify   a mean   and  84th
percentile  using the same technique described  in  the upstream boundary data
section.   DYNTOX  does not provide  the capability to calculate  these values
directly from observed effluent data.  However, SAS may be used  to calculate
these parameters before performing Log Normal analysis.    The  final effluent
requirement   is   the   cross-correlation    between   effluent    flow   and
concentration.  This may also be determined through SAS.


System Constants:  Program inputs for hydro!ogic data are needed to properly
adjust  gaged flow data to determine instream flow at different  locations.
Ratios are needed to define the comparison  between the gauged  drainage basin
area  and  the drainage basin area at the point of discharge.   This  ratio
adjusts the USGS measured flows for nonpoint  sources,  and must  be specified
regardless of the location of the gaging station.     For  a discharge located
downstream  of the USGS gage the ratio (and adjustment) will  be  greater than
1.0.   For a discharge located upstream of  the  gage,   the ratio  will be less
than  1.0.   The  method to be used for specifying drainage area  ratios  is
described  in the Data Requirements chapter.  A second  hydrologic adjustment
is  required for water withdrawals.   If a significant  amount of water (>1% of
river flow) is withdrawn from the river at  any  location between the gage and
the outfall,  this  withdrawal rate must be specified before  performing   a
waste load  allocation.


Output   Range   of  Interest:  The  user must specify the minimum  and  maximum
output  concentration of interest  and desired output  interval  before  running
the simulation,  due  to  the  nature of the solution technique.  Care should be
taken   to  choose   a minimum   value that  has  a  non-zero   probability  of
exceedance.    Minimum  values   that  have  an   insignificant   probability  of
exceedance  will  be  rejected by the program,   and replacement values will be
required.


                                      60

-------
Program Use

     The Log Normal program,   like the programs  for  the  other techniques,  is
divided  into menu-driven subprograms (entitled  activities)  to allow as much
flexibility  as  possible in  performing the simulation.    The  hierarchy  of
activities for Log Normal analysis is shown in Figure  23.  This section will
describe  how  to use the Log Normal  program and will  discuss  the  options
available.   It  is  divided   into sections describing each  of  the  primary
activities  of Log Normal analysis:   Program Entry,   Input  Specification,
Model   Simulation,   Statistical   Analysis  of   Inputs/Results,    Plots  of
Inputs/Results.


Program  Entry:  The  first activity of the Log  Normal technique  is  termed
Program Entry.  This section  consists of specification of the time period of
observed  STORET data,  modeled point source flow above  the  USGS flow  gage,
location of the data describing boundary conditions, and withdrawals between
the USGS gage and the effluent outfall.

     Figure 24 shows example  sessions with the Program Entry activity.   The
first  questions in Program Entry concern the existence  and  location of  the
TSS files for the simulation.   TSS (Time Series Store)  files are created by
ANNIE to store time series information.   For the Log Normal technique,  the
TSS file holds all information pertaining to the STORET  boundary  data.  The
user  should  answer NO to the question asking  if a TSS  file was  previously
created  the first time a simulation is performed,  and  specify a  TSS  file
name (Figure 24a).     This will initiate the process to create a file.  The
user  should answer YES to this question in subsequent simulations,  and  no
other  information will be required in the Program Entry section except  the
name  of  the  TSS file  (Figure 24b).   A TSS file created  for  Log  Normal
analysis can also be used for Continuous Simulation or Monte Carlo.

     For first-time entries,   the TSS file name  must be supplied.   Any file
name  compatible with the computer system in use is acceptable.    The  next
inputs  required  of  the user are the first year of observed data  and  the
number  of years of data that exist.   The required format for the  date  is
Year/Month/Day   (Figure  24a).   Months and days with only  one  significant
figure of  information may be entered using only one digit.  At this point in
Program Entry, the TSS file for the  system is being created and initialized.
This may take  some time, depending on the computer  system used, but the user
will be informed when the initialization is complete.

     The   final  portion  of the  Program  Entry concerns location of  the  STORET
data.   Figure 24a  shows an  example  session where both  the  boundary flow  and
boundary  concentration data  are located in STORET files.  The user need only
specify   the name  of the STORET data files and  which  data set of the   STORET
retrieval  is to be used.  The  program provides the capability to  screen  out
flow and  concentration data  above acceptable values.
                                      61

-------


Determine
Specify Hodel
Parameters


Run
Model
	 ,
t>o
                                                                VICH  Inputs/
                                                                  KCSUltS
   End
Log-Nornal
                                                   FIGURE 23
                                   Hierarchy  of Subprograms for Log Normal

-------
     Another  possibility for Program Entry is  when  the user has  no  STORET
data and wishes to enter data manually from the terminal  (Figure 24c).   The
user  is  required  to input the number of data points,  then the  date  and
concentration  for  each value.    The proper format  for the data  is  (date,
value) with the date in the YYMMDD format.   The final  option of the Program
Entry  concerns the case where all input distributions  were calculated  off-
line  before  using the  DYNTOX.   In this case,  no data need  be  entered,
either  from  STORET files or from the terminal,  and the user  may  proceed
directly to Input Specification.


Input Specification: Required inputs include mean (50th percentile) and 84th
percentile values for all model  parameters, along with  the cross-correlation
between  river  flow  and  effluent  flow,  between   river  flow  and  river
concentration,  and between effluent flow and effluent  concentration. Values
for the 50th and 84th percentile values for the boundary parameters will  be
calculated  from  the  observed data when  available.   An  example  session
demonstrating Log Normal Input Specification is shown in Figure 25.

      In   many  cases,   insufficient  data  will  be  available  to  define
distribution for four-day average values.   In these situations,  users  may
specify  a  log normal distribution for the parameter in  question,  with   a
standard  deviation one  half of that in the observed data as an estimate  of
the distribution of four day average values.


Model   Simulation:  Model simulation requires the specification of  a minimum
and maximum value of  interest and the  interval that results are desired.  It
is  important   to note that this  interval  is in log  (base   10)  units.  When
conducting  wasteload  allocations,  the   user  should  select  the  minimum,
maximum,   and   increment value such that  the return period  for  the  water
quality criterion  will  be  output.   One  way to assure this occurrence is to
specify the minimum  and/or maximum value  to be the  criteria.   An  example
session showing model  simulation  is given  in Figure  26.


Statistical Analysis  of  Inputs/Results: The user  has the  ability  to view  any
of  the model  input parameters  or the  simulation  results  in tabular  format,
receiving   statistical   results and a  table of the   frequency   distribution.
This   section   can  be assessed  any time after  the simulation has   been   run.
After  specifying  the  parameter to be viewed and  a one-line   80  character
maximum  title,  results shown  in Figure  27 demonstrate  this  feature  using
model  results.   The  output  for model  input parameters has   an  identical
 format.


 Plots  of Inputs/Results:  The user also has the ability to view any of  the
 model input parameters  frequency distribution in plot  form.  The plot format
 differs slightly between the input parameters and model  results.   The input
 parameters  are  plotted as the probability of occurrence over a  number  of
 ranges  (see  Figure  28).   The model results are plotted  as  the  overall
 probability of exceedance for each value  in the specified range (Figure 29).
                                      63

-------
24a.   New TSS  File
            TOXIC SUBSTANCE WAETELOA3 ALLOCATION K32£L!K3

            VKICH TECHNIOL'E DO YOU WANT 70 USE:

              (1) CONTINUOUS SIKULATION: DILUTIOK AND DECAY
              (2) KSXTE CARLO: DILUTION AND DECAY
              (3) LOC-K^RKAL: DILUTIOK ONLY
              (4) ENS TOXICS WLA.  FETUP.K TO ANKIC KEK'J
             ENTER SELECTION (1-4)
             (Hit return for 4)

             DO-YOU  HAVE UPSTREAM BOUNDARY DATA FI? ANALYSIS?

             HAVE YOU PREVIOUSLY CREATES A TSS  FILE FOR THIS SIKULATION?
          ^-ND
             WHAT  IS THE KAMZ OF YOUR Kt- TSS FILE?
          ^-TESTFILE
             HO- KASY TEARS  OF DATA DO YOU HAVE?
             (Kit  return tor  1)
          ^"fc
             EKTES STARTING  DATE.
          »- 1S6I/V1
             HOW KASY  OUTFALLS ARE THERE IK  THE SYSTEK?
             (Kit return for 1)
          ^- i
             HOW KASI OUTFALLS LIE ABIVE THE FLOW CAGE?
             (Hit return for 0)

          *~ PLEASE KAIT WHILE  YC'JR TSS FILE IS INITIALIZES ...

             INITIALIZATION OF  YCVR TSS FILE IS NOW COMPLETE.

             DO YOU HAVE  A STCrIT FLOW DATA FILE?
          •^- Y
             WHAT IS THE NAME OF  THE  STCR" FILE?
              ST:?.".FLO
             USE WHICH DATA SET?
              (Kit return for 1)

              WHAT  IS THE KAXIKUV. ACCEPTABLE FLOW VALUE?
              (Hit  rtt.rn fcr C.)
           >-;9rS.
               ez;E  PC:KTS READ
              D5 YOU HAVE A  S"RET DATA FILE FOR  UPSTREAM CCSCESTRATICN?
           ^- YES
              WHAT IS  THE KAMI OF THE STCnST FILE?
           ^-STCRET.CON
               USE WHICH DATA SET?
               (Kit return  for O

               WHAT IS THE  KAXIKUV COSCES'TR».TICN VALUE?
               (Hit  return  for C.)
            >-'.0
                nj« PC:NTS READ
                                      FIGURE 21

            Example Sessions with Log  Normal  Program  Entry
                                              64

-------
24b.   Existing  TSS File
                HAVE  YOU' PREVIOUSLY CREATES A TSS FILE FOR  THIS SIKVLAT10K?
             >- YES
                WHAT  IS THE KAV.E  OF YOVK TSS FILE?
             >• EXAMPLE
24c.   Terminal  Entry  of Data
                HAVE  IOU PREVIOUSLY CREATES A TSS FILE FOR THIS S I KV- AT 1 OK ?
               •NO
                *T-:AT  is THE NAME OF vcvs NEW TSS FILE?
               •7ES7FILE
                KZ- Ki.SY YEARS OF SJ7A DO YO'J HAVE?
                (Kit  r*t_rn lor l)
               •6
                EK7ES S?AST:KC DATE.
                HC- KASY O'.TFAILS  ARE THERE IN THE SYSTSK?
                (Hit return for 1)
               - i
                HOW KAVY orrrALLS  LIE ABOVE THE FLOW CAGE?
                (Kit rtturn for C)
               -0

                PLEASE WA:T »>V:LE  »O-JR TSS FILE is INITIALIZED  ...

                IKITIAllZATISK OF  YC'.-S TSS FILE IS NDW COMPLETE.

                DO Y=-. KA-.T A ST:F.ET FLOW DATA FILE?
               „ V
                V-:AT 3t ?^i ».»VT or THr ST;SIT F:LE?
               - S7:;r-.r.e
                VSt w-;c> S«*» ltr»
                (K.t ft: .f» tar M
               . 1
                *•>»" 1» **t »*»".•»' ACCErTASLE FLOW VALUE?
                (K.t f»i»f» If C.I
               • iSfi
                r: ir.  »* t • i-r»iT DA7A FILE FOR UFS7REAM cos:Es7S.A7:os?

                r: •:.  k»»- •; i«-t» c:--:r<-ri7:os TATA FR:M

                »•;. ».«» »»•».»» •: Y:V HAVE'
                • ••.t •••.-• i»- «)
                !«-•!• >'t •»: '.MTSiJ.V CCSCESTRAT1C-N FOR EACH SAMPLE:
               •*:::.   »
               •t: si-.  .«
               •*!:»•!.   li
                    J »: -*i  •:*:
                                FIGURE  2^  Cont'd.

           Example  Sessions with Log  Normal  Program  Entry
                                            65

-------
                    AL SIK-JLATIOK TECKNIQ-JE

              PLEASE SELECT OUt:

               (1) DETERMINE/SPECIFY MODEL PAXAXS7ERS
               (2) RUN K:DEL
               (3) VIEW K3DEL RESULTS/IKPU7 DISTRIBUTIONS
               (4) END LOGNCRXAL, RETURX TO TCXICS WLA KSSU

              ENTER SELECTION (1-4)
              (Hit return (or 4)

               (1) DETERMINE/SPECIFY K.rDEL PARAMETERS
               (2) R'.-s K.:;EI
               (3) VIEW HC3EL SESV17S/IKPV7 DISTR:EVTIOKS
               (4) ES3 LDCSORJ:AT is THE CRrss-ccRRtLATiON  SITWEES RIVES FLDW  ASD
              FLOW
              (K>t return fcr 0.)
             • . 1
              WHAT IS TH£ KtCIAN BCVNDARy  CONCENTRATION
              (Kit  return fcr 1.)
             - . 1
              WV:AT is THE E<\ BCVVDASY CONCENTRATION
               (Hit  ret^rr. for 1C.)
             - .S
              Wr.AT IS THE CPCSS-CCSSELATI ON SiT-'EEN  FIVES  CCNCENT?.ATI OS
              RIVER  FLO'-
               (Kit retjrn  for C.)
             - . 1
                              FIGURE  25

Example  Session  with  Log  Normal  Input  Specification
                                     66

-------
                     EFFLUENT FLOW SPiZlTl CATION

                     WHAT IS THE MEDIAN EFFLUENT FLOW
                     (Kit return lor 1.)
                     10.
                     WHAT is rut e<* EFFLUENT FLOW
                     (Hit return for 10.)
                     -100.
                     WHAT JS Ti-E CRCSS-C?S?.ELATiON BETWEEN EFFLUENT  FLOW AV3
                     EFFL'JEs'T CONCESTRAT:OK
                     (Hit return for 0.)
                     - . 1
                     EFFLUENT CONCENTRATION  SPECIFICATION

                     WHAT JS THE KID:AN EFFLUENT CONCENTRATION
                     (Hit return (er 1.)
                     - 10.
                     WHAT 3S THE 64% EFFLVENT CONCENTRATION
                     (Kit return for 10.)
                     - 10'C.
                      FIGURE  25  Cont'd.

Example  Session with  Log Normal  Input  Specification
                                   67

-------
         LOGKCRKAL SI»T.:LATIOK

         FLEASE SELECT OKE:

           (1) DiTERXIKE/SPECJFy MC2EL PARAMETERS
           (2) R'jn H.SSEL
           (3) VIEW MrrEL RESULTS/IN?'.'- 01STRI B'.'T; OKS
           (4) E« L03s;R>y.l. RiTwRK 70 TOXICS WUk KIK'J

         tVTER SELECTION' (1-4)
         (Hit return  (or 4)
         • 2
         WXAT IS TKE  KIKIK.-y VALUE OF IKTEREST
         (Hit return  (or 0.>
         • .01
         WHAT is TKE  KAX:KW. VALUE or IKTEREST
         (Hit rt:urn  (or 0.)
         •100.
         AT WVAT 1KCREKEST DO TOL' WAV? RESULTS LISTED (K^TE: THIS
         IHCKi«^»;T H'JST BE IN LOG UNITS!)
         (Kit rt-.urn  (or 0.)
         -.&

         $:K_-L»r:oK COV?LETE
                           FIGURE 26

Example  Session  Performing Log  Normal  Simulation
                                  68

-------
        LOGNORMAL SIMULATION TECHK10OT

        PLEASE SELECT OKE:

         (1) DETERMINE/SPECIFY MODEL  PARAMETERS
         (2) RUN tax;
         (3) VIEW MODEL RESULTS/INPUT DISTRIBUTIONS
         (4) IKS LOGNORMAL, RETURN TO TOXICS KLA HEK'J
        ENTER SELECTION (1-4)
        (Hit return for 4)
        3
        VIEW RESULTS/I KPUTS FOS LOGNDRKAL *N ALTS IS

        0: 705 WANT (1) PLOT OF FRiCUENCT DISTRIBUTION
                   (2) TABULAR OUTPUT
               OR  (3) EN~ VIE." KG.  RETURN TC M>.IK LOGKORKAL KEK:
        EKTER SELECT! ON (1- 3 )
        (Kit return ler 3)
        HKAT DO 70V WANT TO SEE
            MD3EL RESL'LTS:
        (1) RTVEF CONCENTRATION
            IKPLT E:S":B-.TIONS:
        (2) UPSTREAM FLOV
        (3) DPSTREAV CONCENTRATION
        («) EFFLUENT FLOW
        (5) EFFLUENT CONCENTRATION
        EKTER SELECTION ( 1-5 )
        (Hit return tor 1)
        1
        VrlAT TITLE K> 70V VANT (EC CHARACTERS KAX1KUM)
        LOC-NORKAL RESULTS

                                    tOC-KORKAL RESL'LTS
          VALUE
                    » OF TIKE EXCEEDED  1  OF TIKE IK IKTERVAL  RETURN  PER:CD  (TEARS)
         C.100E-01

         0.316E-C1

         0.100E-00

         C.316E-CC
          C.100E-C2

          0.316£-C2

          0.100E-03
9E.67C

S3.2C
34.162

19.111

1C.2E1

 S.OBt

 2.20E
 J.41C

14.429

22.6«S

22.0CC

15.071

 6.B6C

 5. life

 2.676
C.OC3

C.CC3

C.OC3

c.c:s

C.OCE

C.C14

0.027

0.054

0.124
                              FIGURE  27

Example  Session with Tabular Output  from Log Normal
                                      69

-------
  LOGNDRXAL SIMULATION' TECHNIQUE

  PLEASE SELECT OKE:

   (1) DETERMINE/SPECIFY MODEL PARAMETERS
   (2) RUN MODEL
   (3) VIEW MODEL RESULTS/IKPL'T DISTRIBUTIONS
   (4) END IOGNOR.VAL. RETURN TO TOXICS KLA MENU
  ENTER SELECTION (1-4)
  (Hit return for 4)
  3
  VIEW RESULTS/INPUTS FOR  LOCS2RXAL ANALYSIS

  DO YOU VAST d) PLOT  or  FRE:UEN:Y SISTPIS-.TICN
             (2) TASVLAP  CVTrVT
         CP  (3) END V:E"'1K3. RET'JRN TC MAIN LOGSCRy.AL KEN'J
  E-JTER SELECTION (1-3)
  (Kit  return for 3)
  1
  WHAT  DO YOU WANT TO SEE
     K:DEL RESULTS:
  (1) RIVER CONCENTRATION
     :N?UT DISTRIB-TIONS:
  (2) UPSTREAV. FLOW
  (3) UPSTREAM CONCENTRATION
  (4) EFFLUENT FLOW
  (5) EFFLUENT CONCENTRATION
  ENTER SELECTION ( 1-5 )
  (Hit  return  for 1)
 • 2
  PLEASE  ENTER TKE TITLE OF THE  PLOT  (EC  CHARACTERS  KAXIKUV.)
 - U?S?RiS,y  FLOW
     25.-
   t     !

   T
   I  20.'
   K
   E
   N

   I
   N
   T
   E
   R
   V
   A
   L
         I
   LOG  0.49   0.93    1.46
1.9S   2.52   3.05

     UPSTREAM FLOW
                                                 3.58
                                                        4.11
                                                               4.64
                                                                      5.17 5.70
                           FIfiURE 28

Example Session  with  Plot  of  Log Normal  Inputs
                                  70

-------
    VI EV RESULTS/INPUTS FOR LOGKORKAL ANALYSIS

    PC TO'J MART (1)  PLOT OF FREDUENCT DISTRIBUTION
               (2)  TABULAR OUTPUT
           OR  (3)  EK5 VIEVING, RETURN TO MAIN  1OGNORKAL KEK13

    EKTEF SELECTION  (1-3)
    (hit return for  3)
    1
    WHAT DO 10u WAKT TO SEE
       MODEL RESULTS:
    (i) R:VER CONCENTRATION
       JKrUT DISTRIBUTIONS:
    (21 UPSTKEAV FLOV
    (3, UPSTMAV. CONCEKTRAT:ON

    (i) EFFLUENT CONCENTRATION
    EKTE? SELECTION  ( 1-£  )
    (Hit return tor  1)

    PLEASE ENTEK THE TITLE OF Tn£ PLOT <6C CHARACTERS KAZIKUK)
    LOC NORMAL RESULTS
    I IOC.

    0
    F
       e:.
    T
    I
    Y.
    E  e:.

    E
    X
    c '«:.
    E
    E
    D
    E  2:
     LOG -i.CC  -C.iC  -C.2C
                        0.20   0.60   1.00   1.40

                           LOG KORXAL RESULTS
                                                         1.60
                                                               2.20   2.6C 3.CC
V:E» RISVLT

D; T3'.- WAK7
                           LOGIORKAL AKAL?S:S

                                     S! STRI BLT1ON
                (1)  PLCT  OF FR
                (2)  7ASULAS OL'TP'JT
            OR  (3)  EKS V:E-."NC, RETURX TO KAIK LOGKORKAL KEKU
     EN'TEP SELECTION d-3)
     (H:i return lor 3)
     3
                           FIGURE 29

Example Session  with  Plot of  Log  Normal  Results
                                  71

-------
                   VI.  PERFORMING  WASTE  LOAD ALLOCATIONS


Overview

     Each of the three techniques documented herein  -  Continuous  Simulation,
Monte  Carlo,  and  Log Normal  - can  potentially  be  used to   perform  toxics
waste load allocations.   However,  not all techniques can be applied in all
situations.  In general, Continuous Simulation  should  be used in  cases where
time series information on model inputs is well defined.   Log Normal should
be   used  in  single  discharge  cases   where  all  model   parameters   are
approximately  log  normally distributed.  Monte  Carlo should be   used  when
neither of the other techniques are applicable,   or  in conjunction with  the
other techniques.  In some cases, the data may  be insufficient to use any of
the three techniques.

     This  chapter discusses at an  introductory level  the  conditions  where
each  of  the  techniques may be applied,  and  gives  brief   guidelines  for
selecting between them.  The chapter  also briefly discusses  how to perform a
waste  load  allocation for single  and multiple discharge  cases and  how  to
calculate  the return period.  Last  is a discussion of toxic  concentration
criteria.   Discussions provided herein are very  brief only  as necessary  to
alert the users to important technical issues.    More  detailed discussion is
beyond the scope of this users manual.


Selecting Between Techniques

     Each  of  the thret techniques can be applied to  perform  toxics  waste
load allocations and no one technique is  necessarily preferable to any other
on  a theoretical basis.   However,  all  three  techniques  are not  similarly
accurate  or  appropriate in all situations.    This  section  highlights  when
each technique should bt applied.

Continuous Simulation:  Continuous  Simulation  is  the most  powerful technique
but only when sufficitnt ti»*-series  data are  available to define the  input
parameters.  The povtr of Continuous  Simulation decreases  significantly when
data  must  be  synthtsutd  to  replace  missing  historical  values.   The
guidelines  for selecting Continuous  Simulation as a function of  time-series
data availability can bt suMtarized as follows:
            Time-Series                      Applicability of
         Data  Availability                Continuous Simulation

   All  input parameters  available             Very high
     and  complete
   Only one effluent parameter missing           High
     or significantly incomplete
   Both effluent parameters missing              Fair
     but  other data is complete
   All  other cases                              Poor
                                      72

-------
     Continuous Simulation can be very reliable when analyzing the frequency
distribution of concentrations for existing conditions where all  parameters
are  well defined.  However,  the technique 1s at best fair when  projecting
concentrations  for  future  treatment alternatives because  the  sequential
nature  of  effluent flow and concentration cannot typically be  defined  as
treatment changes.   If the user is uneasy about this problem 1t is possible
to use Continuous Simulation to simulate the concentration distribution  for
existing  conditions and the Monte Carlo technique for projecting the Impact
of future treatment alternatives.

Monte   Carlo:    Monte  Carlo  analysis  has  the  least  stringent   input
requirements  of  any  of  the three techniques  and  therefore  the  widest
applications.   It is best used In situations with limited cross and  serial
correlation of parameters; 1n these cases Continuous Simulation is preferred
where  data are available.   It can be applied 1n cases where the  available
data  are  inadequate  for either Continuous Simulation or  for  Log  Normal
analyses.   However,   if  the  data  are  insufficient  or  inadequate  the
reliability   of  results  must  be  considered.    Any  of  three  standard
statistical distributions - uniform,  normal, or triangular - should be used
whenever possible to describe input data; but data defined distributions can
also  be used.   Since data defined distributions can be used for  even  the
most limited data sets,  care should be taken to ensure that sufficient data
exists to provide meaningful results.


Log  Normal:  The Log Normal technique 1s attractive because it requires far
less computational expense than the other two techniques.   However,   it can
only  be applied for waste load allocation with single discharges and  where
all input parameters have been shown to be log normally distributed,  The Log
Normal  technique can also be used as a lower-cost screening technique  when
parameters  are  not  all log normally distributed  before  conducting  more
complex  analyses with Continuous Simulation or Monte Carlo.   In  examining
the  consistency of data to log normality special  emphasis should be   placed
on  the  "tail ends" of the distribution curves.   It is  typically  at  the
extremes  of the input distributions where water quality problems occur  and
thus  where  the  assumption of log normality must be  the  most  rigorously
justified.


Allowable Effluent Loads

     Water quality criteria are currently defined for maximum concentrations
of a constituent for a three year return period.   For acute  toxicity,  the
instream  concentration should not exceed 0.3 times the toxic  concentration
level  (or 0.3 toxic units acute) more than once 1n three  years.   Although
the  critiera  were determined for a one hour duration,  the criterion  will
generally  be  interpreted on a daily averaged basis because  more  frequent
calculations cannot be practically supported by data.  For chronic toxicity,
the  instream  concentration for a four day average should  not  exceed  the
chronic  toxic  level (1.0 toxic units chronic) similarly more than once  in
three  years.   Allowable  effluent loads should be calculated  to  maintain
these conditions.
                                     73

-------
     The waste load allocation process determines the effluent concentration
and flow that will result in a three year return period for the desired  in-
stream concentration.   DYNTOX allows two ways of determining the  allowable
effluent load, both of which are equally valid and consistent:

     1)   inspection  of  the  return period corresponding   to  a
          desired in-stream concentration;

     2)   inspection of in-stream concentrations corresponding to
          a desired return period.

Using  the first method,  a user performing an acute  waste   load  allocation
would  inspect the return period for an in-stream concentration of 0.3  tua.
If  the  return period is less than three years,  the effluent load  is  too
large  and  must be decreased.   If the return period is greater than  three
years,  the  effluent  load may be increased.    The  waste   load  allocation
process  using this technique consists of finding the largest effluent  load
that  will  result in an in-stream return period for  three  years or  greater
for the water quality criterion.

     The  second  method  for  performing a  waste load allocation  is  to
determine  the in-stream concentration that has a three year return  period.
For   the   acute  toxicity  example,   the  user  inspects  the   in-stream
concentration  with a three year return period.   If  this  concentration  is
greater than 0.3 tua,  the effluent load is too large and must be decreased.
If  the in-stream concentration with a three year return period is less than
0.3  tua,  the effluent load may be increased.   The  waste   load  allocation
process  using this technique consists of finding the largest effluent  load
that will result in an in-stream three year return period concentration less
than or equal to the water quality criterion.


Multiple Discharges

     Establishing  allowable  toxic loads among multiple discharges  in  one
system involves technical and policy issues handled differently by different
states.   One  simple  approach  is  to calculate  the  maximum  allocations
successively,   upstream  to  downstream,  ignoring  the inherent  upstream
preference.   A  second  approach  would be to  require  consistent  removal
efficiencies from all discharges ignoring that the assimilative capacity may
not be fully used in all river segments or allowing individual increases.  A
third  would be to assume no decay and allocate proportional to  flow.   The
list of options is extensive.   The specific policy and procedure is a State
issue  which  involves  technical,   policy  and  political   consideration.
However, DYNTOX can generally be adapted to address most any State policy.

     In  the illustrative examples included in this Appendix,  a very simple
approach  is used wherein allocations are conducted successively upstream to
downstream.   This procedure was chosen only to illustrate  the use of DYNTOX
and  in  no  way represents a recommended  procedure   for  allocating  among
multiple discharges.
                                     74

-------
Calculating the Return Period

     Two  common  methods exist to calculate  the  return  period for  a  given
concentration from probabilistic modeling.  They  are  termed  herein as:

     1)   the percentile method

     2}   the extrema method

The  percentile  method uses a listing  of all  in-stream   concentrations  and
ranks them.   The return period for a concentration is then  calculated  based
upon  percentile  occurrence.   In the  extrema method,   only annual   extreme
values are used in the ranking.  The return period calculated from these two
methods   are  equally  valid  statistical  representations,    but   neither
necessarily predicts annual  occurrence  frequency.

     The  percentile  method assumes that all  violations  of  the   in-stream
criteria are independent from each other.   Every exceedance of the criteria
is treated equally, including multiple  violations in  the same year.   Results
from  this  method  therefore represent an  "average" return  period.    The
disadvantage  to  this technique is that multiple violations related to  the
same  extended  event  (e.g.  drought river flow) are treated  as  separate
events,  which could lead to an estimation of the recurrence interval   which
is  more  frequent  than  actually characteristic.    The  advantage  to  the
percentile technique is that multiple,   independent violations occurring  in
the same year are correctly incorporated into the return period analysis.

     The extrema method uses only the largest concentration  for each year in
calculating  the  return period value.   This technique  predicts the  return
period  for  an annual extreme value and has  the  advantage  of  not  "double
counting"  multiple  violations  that are caused  by   the  same  event.    The
disadvantage  to  the  extrtaa  method  is  that   when multiple independent
violations  occur in tht itae year, only one violation  is considered in the
return period analysis.   TMs can lead to an estimate of the return  period
which may be longer than tryly characteristic.

     For  the DYNTOX tinplts provided  in this report,   as for all  analyses
conducted  using  DWTOI.  the percentile method  is used.   Users   have  the
ability  to  perform titrnu analysis by running  Continuous   Simulation  one
year  at a time and Rtnvally tabulating the extreme  in-stream  concentration
for  each  year.   InwtittyatIons are now being  conducted to  establish  the
appropriate  application of the two techniques and  the need  to adapt  DYNTOX
to more directly compute the extrema method.

     In  either  case the degree of confidence that can  be placed   in  model
results  is directly.related to the amount of input data available  and  the
return period for the concentration of  interest.   In  general, the  longer the
return period the more data that is required.  If recurrence intervals of 10
to  20  years are desired,   input data  should accurately define the 30  year
return value of all  input parameters in order to estimate the probability of
such  rare  events.   Although  the program will  provide  results   using  an
inadequate data base,  these results should  not be  used  in performing  waste
load allocations.
                                     75

-------
Toxic Concentrations

     Toxic   concentration  criteria  for  waste  load  allocation  can   be
determined by two methods:

     o  chemical specific

     o  effluent toxicity testing

The  chemical specific method involves using scientific toxicity data for  a
particular  toxicant  and establishing the concentration level  of acute  and
chronic toxicity.   Limited consideration Is typically given to  synergistic
and antagonistic effects with other parameters.   On the other hand, effluent
toxicity testing uses an operational approach.   Bioassays are performed with
the  effluent  at different dilution levels to  determine Its toxicity  as  a
whole.   Its  toxicity is then defined in toxic units where one unit  equals
the  least  concentrated  dilution which caused the  test  endpoint.   Other
levels of concentration are described in toxic  units which are multiples  of
this dilution.  Detailed discussion of these concepts is not appropriate for
this users manual and the reader is referred elsewhere (EPA,  1985). However
some comments are appropriate.

     Whole effluent toxicity testing has many advantages because 1t directly
considers  site specific effluent toxicity and inherently  considers  multi-
parameter effects.  However, on the downside:

     o   almost  no  toxic  unit data  exists  for  upstream  water
         quality

     o   defining    combined  effects  of  multiple  effluents    is
         difficult

     o   quantifying in-stream  decay of  toxicity  is also difficult.

 In  contrast,   chemical  specific  toxic  criteria  are  simple  to  use  and  apply.
They are limited however because  they:
      o  are not site specific

      o  do not consider synergistic effects

      o  do not consider antagonistic effects

 Both options have advantages and disadvantages.   The reader is encouraged to
 research  these  issues in more appropriate technical documents  (e.g.  EPA,
 1985).
                                      76

-------
                              VII.  REFERENCES


DiToro,  D.  M.  Probability Model of Stream Quality Due to Runoff.  Journal
     of Environmental Engineering, ASCE, Vol. 110, No. 3, June, 1984.

Fiering,  M.B.  and B.  Jackson.  Streamflow Synthesis, American Geophysical
     Union,  1971.

Freedman,  P.L.  and R.P.  Canale.  Modeling Uncertainty and Variability for
     Waste   Load Allocations.   LTI,  Limno-Tech,  Inc.,  prepared for USEPA
     Monitoring and Data Support Division, August, 1983.

SAS Institute Inc.   SAS User's Guide:   Basics,  1982 Edition.  Gary, North
     Carolina, 1982.

Thomann, R.V.   Systems Analysis and Water Quality Management.  McGraw-Hill,
     New York, 1972.

USEPA  Office of Water Technical Support Document for Water Quality  - based
     Toxics  Control.  September, 1985.

USEPA Storet User Handbook.  USEPA, Washington,  D.C., 1982.
                                     77

-------

-------