United States
                    Environmental Protection
                    Agency
 Risk Reduction
 Engineering Laboratory
 Cincinnati, OH 45268
                    Research and Development
 EPA/600/SR-92/145    September 1992
& EPA       Project  Summary
                    AutoMOUSE
                    An  Improvement  to  the  MOUSE
                    Computerized  Uncertainty
                    Analysis System  Operational
                    Manual
                    Albert J. Klee
                     Environmental engineering calcula-
                   tions involving uncertainties in data are
                   well beyond the capabilities of conven-
                   tional analysis for any but the simplest
                   models. There exists a number of gen-
                   eral-purpose computer simulation lan-
                   guages that are capable of such analy-
                   sis,  but these languages are difficult
                   to learn and implement quickly.
                     The original MOUSE (Modular Ori-
                   ented Uncertainty SystEm) system was
                   designed to deal with the problem of
                   uncertainties  in static mathematical
                   models, such as a set of engineering
                   cost or risk analysis equations. It was
                   especially  intended for  use by indi-
                   viduals with little or no knowledge of
                   computer languages, programming, or
                   simulation. The MOUSE system runs
                   on MS-DOS-based personal computers.
                   It is easy and fast to learn and has all
                   of the features needed for substantive
                   uncertainty analysis, such as built-in
                   probability  distributions, plotting and
                   graphing capabilities, sensitivity analy-
                   sis, and interest functions for cost
                   analyses. A series of unique companion
                   utility programs help (1) analyze sample
                   data to determine the probability distri-
                   butions that best fit those data and (2)
                   check each program for errors in syn-
                   tax.
                     AutoMOUSE is  a significant im-
                   provement to  the original MOUSE sys-
                   tem. It  actually writes  the computer
                   program necessary to  carry out the
                   uncertainty analysis. The input to
                   AutoMOUSE consists of the equations
                   of the model and requires no knowledge
                   of computer  programming. It is de-
signed primarily for beginners but is
also of value for those who have some
programming experience and wish to
construct  MOUSE programs more
quickly and with fewer errors.
  Some typical examples of the use of
MOUSE within the U.S. Environmental
Protection Agency include studying the
migration  of pollution plumes in
streams, establishing regulations for
hazardous wastes in landfills, and es-
timating pollution  control costs.
  This Project Summary was developed
by EPA's Risk Reduction Engineering
Laboratory, Cincinnati, OH, to announce
key findings  of the research project
that is fully documented in a separate
report of the same title (see Project
Report ordering information at back).

Introduction
  Models consisting of one or more math-
ematical equations are extremely impor-
tant for  they are used in  a number of
professional disciplines including  eco-
nomics,  engineering, and the health sci-
ences. In environmental engineering, for
example, they are  common in  cost and
risk analysis calculations.  Such models
can be either deterministic (input variables
are single numbers) or stochastic (input
variables are in the form  of probability
distributions  that reflect the uncertainty
about their values). Although the solution
of deterministic models is well understood,
stochastic models are more difficult. The
following simple example will illustrate this
point. It  is  taken  from an actual EPA
problem, where the objective was to de-
velop a method to establish the regulatory
                                                                  Printed on Recycled Paper

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level of wastes disposed of in  a landfill
which pose a hazard due to toxic organic
constituents.  The environment  modeled
was that of a non-secure sanitary landfill
that receives a small amount of toxic in-
dustrial waste.
  In the  model, the  regulatory level
(REGLEV) of a toxic  constituent  was
obtained  by multiplying the maximum
permitted daily  exposure level (DELMAX)
for  the toxic constituent in question by a
suitable factor, i.e.,

REGLEV(ppm) - DELMAX(mg/day) x
FACTOR(days/kg)                 [1]

  The factor involved  four variables as
follows:

FACTOR .
[(attenuation factor x (liters leached/year)
x years]/[(liters consumed/day)  x  (indus-
trial waste quantity, kg)].           [2]

  Defining PRECIP as the annual precipi-
tation, RLEACH as  the rate of  leaching,
DEPTHL as the landfill depth, and WDENS
as waste density, and assuming that: (1)
the (dimensioniess) attenuation factor is
100, (2) there are 2 liters of water con-
sumed per day, (3) the exposure period is
70 yr, and (4) 5% of the waste is  industrial,
the factor becomes:

FACTOR -  70,000*[PRECIP*RLEACH]/
[DEPTHL'WDENS]                [3]

  To  determine a regulatory  level using
the model of Equation 1, a value of FAC-
TOR must first be determined. In Equation
3, using average estimates of annual pre-
cipitation  of 1,143 liters/meter  per year,
rate of  leaching of 0.75, landfill depth of
8.35 meters, and waste density of 415.3
kg/meter3, FACTOR equals 17,303. Based
upon  this value, Table  1 shows the regu-
latory levels for compounds with  varying
DELMAX's.
  Table 1,  however,  is a deterministic
solution; it does not take into account any
uncertainty  in  the four stochastic input
 Table 1.  Regulatory Levels as a Function of
         DELMAX

 Compound      DELMAX    Regulatory
                (mg/day)    Level(ppm)
Compound A
Compound B
Compound C
Compound D
Compound E
Compound F
Compound G
.000001
.00001
.0001
.001
.01
.1
1.0
.017
.17
1.7
17
170
1700
17000
variables.  Table 2 shows the probability
distributions for these variables which re-
flect the best judgment of the investiga-
tors. The  problem was to  calculate the
value of FACTOR, and hence the value of
REGLEV,  given these input probability
distributions. A  common approach to the
solution of mathematical models which in-
volve uncertainty is a form of Monte Carlo
simulation known as Model Sampling:
  (1) A value for each of the input vari-
      ables is drawn at random from their
      respective probability distributions,
      and the model's output is computed
      using this particular set of values.
  (2) The above  process is  repeated
      many times. Since the results vary
      with each iteration, the output  is
      gathered in the  form of a probabil-
      ity distribution.
  Figure 1  shows a Monte Carlo solution
(using  MOUSE) to the distribution of the
variable FACTOR. The statistics reported
include the mean, standard deviation, co-
efficient of variation,  and  minimum and
maximum of the output variable, FACTOR.
Graphical output is provided in the form of
(a)  the frequency distribution (asterisks)
and (b) the cumulative frequency distribu-
tion (circles) of FACTOR. Histogram sta-
tistics are  also provided, such as number
of  entries, percent entries,  cumulative
percent entries, and complement of the
cumulative percent entries for each inter-
val  of the histogram.

AutoMOUSE
  The  MOUSE  program  used  to obtain
Figure  1 is shown in  Figure 2.  It can be
seen that  even this  simple  uncertainty
problem poses a complex task for those
unfamiliar  with programming.  It  is  no
                         wonder then that uncertainty analyses are
                         either left up to highly skilled profession-
                         als, frequently at high costs and long lead
                         times, or else omitted altogether. For this
                         reason,  AutoMOUSE was developed to
                         provide a simple, clean, non-programming
                         interface to the  MOUSE  model. With
                         AutoMOUSE,  anyone can develop  a
                         complete uncertainty analysis model with-
                         out any knowledge of, or contact with, the
                         programming language itself.
                           There are two  major input stages to
                         AutoMOUSE. The first consists of the
                         model equations. This is  followed by the
                         specification of the probability distributions
                         for the uncertain variables  in the model
                         and the arguments for these distributions.
                         AutoMOUSE  operates  in  either  of  two
                         modes: (a) a Non-Expert mode and (b) an
                         Expert mode. The former, intended  for
                         beginners  to the MOUSE system and
                         which places certain restrictions  on the
                         model, will be used in the  following expo-
                         sition.
                           The Non-Expert mode  equation entry
                         screen is  shown  in  Figure 3, with the
                         simple    FACTOR=70000*(PRECIP*
                         RLEACH)/(DEPTHL*WDENS) equation
                         example entered.  The screen consists of
                         three parts: (1) Top: equation/error report-
                         ing area, (2) Middle: equation entry area,
                         and (3) Bottom: equation instruction area.
                         Each equation is allotted 240 characters,
                         denoted by the shaded lines. The instruc-
                         tions for moving around the equation are
                         shown below the  shaded  lines.  Entering
                         Alt-F brings up a help screen that reminds
                         the user of the symbols used for the vari-
                         ous  arithmetic  operations and functions
                         permitted  in  this mode.  The INS  key
                         toggles the insert  mode on and off (when
Table 2. Distributions of the Input Stochastic Variables
Variable
RLEACH
Type
Continuous
Uniform
Outcome
0.5
1.0
Cumulative
Probability
0.00
1.00
                                          Variable
                Type
                                                                                         Parameters
PRECIP
                                          DEPTHL
                                          WDENS
Trapezoidal
                 Trapezoidal
                 Triangular
 762  (= lowest value)
1016  (= most likely value, lower boundary)
1270  (= most likely value, upper boundary)
1524  (= highest value)

 3.0  (= lowest value)
 6.1  (= most likely value, lower boundary)
 9.1  (= most likely value, upper boundary)
 15.2  (= highest value)

 297  (= lowest value)
 415  (= most likely value)
 534  (= highest value)

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insert mode is on, characters are inserted
into  the  lines; when insert  mode  is off,
new characters  overwrite the  old). After
an equation has  been entered and edited,
the user presses the ESC key to continue
to the next equation. After entering all of
the  model's equations, the  ESC key is
pressed  twice to  end model  entry. An
equation can be entered  anywhere within
the shaded  three lines. AutoMOUSE will
                              remove unnecessary spaces when it scans
                              the equation for errors.
                                During equation input and editing, if the
                              user  attempts  to  enter an  illegitimate
                              character or a character that cannot legiti-
                              mately follow the preceding  character,
                              AutoMOUSE will beep  and  reject  the
                              character. An explanation of the error is
                              also displayed on the screen,  just  below
                              the equation  entry  area.  AutoMOUSE
                                                             makes two checks for errors: (1) the pre-
                                                             liminary check, just described, as the user
                                                             enters the equation,  and (2) a more de-
                                                             tailed scan after the  equation is entered
                                                             and the user has pressed the ESC key.
                                                             The more detailed check involves checking
                                                             the equation for legitimate  numbers or
                                                             variable names;  correct use  of parenthe-
                                                             ses,  commas and equal signs; allowable
                                                             functions and function  arguments; etc.  If
                                              DISTRIBUTION FOR QUANTITY  FACTOR
    NUMBER Of ITERATIONS =  5000
                                          MEAN
                                       MINIMUM
                                       MAXIMUM
                                         20361.21000
                                         4219.64600
                                         82200.32000
                                                        STANDARD DEVIATION
                                               COEFFICIENT OF VARIATION. X
                                                                        12154.16000
                                                                           59.69275
     LOWER
     LIMIT

     4200.
     6100.
     8000.
     9900.
    11800.
    13700.
    15600.
    17500.
    19400.
    21300.
    23200.
    25100.
    27000.
    28900.
    30800.
    32700.
    38400.
    40300.
    42200.
    44100.
    47900.
    49800.
    51700.
    53600.
    55500.
    57400.
    59300.
    61200.
    63100.
    65000.
    OVERFLOW
NUMBER OF
  ENTRIES

     60.
    245.
    443.
    585.
    486.
    467.
    381.

    248!
    239.
    194.
    158.
    127.
    121.
    107.
     94.
     95.
     69.
     75.
     70.
     56.
     56.

     3S.
     26.
     24.
     28.
     17.
     11.
     15.
      5.
      6.
      9.
     19.
PERCENT
ENTRIES

 1.20
 4.90
 8.86
11.70
 9.72
 9.34
 7.62
 7.48
 4.96
 4.78
 3.88
 3.16
 2.54
 2.42
 2.14
 1.88
 1.90

 ilso
 1.40
 1.12
 1.12
 1.10
  .70
  .52
  .48
  .56
  .34
  .22
  .30
  .10
  .12
  .18
  .38
CUMULATIVE
 % ENTRIES

  1.20
  6.10
 14.96
 26.66
 53.34
 60.82
 65.78
 70.56
 74.44
 77.60
 80.14
 82.56
 84.70
 86.58
 88.48
 89.86
 91.36
 92.76
 93.88
 95.00
 96.10
 96.80
 97.32
 97.80
 98.36
 98.70
 98.92
 99.22
 99.32
 99.44
 99.62
100.00
CUMULATIVE                 DISTRIBUTIONS
COMPLEMENT    * = FREQUENCY DISTRIBUTION     0 = CUMULATIVE DISTRIBUTION
98.80
93.90
85.04
73.34
c/ oo
?*»•. to
to i 0
39. 18
OO / f
aV .****
25.56
22.40
19.86
17.44
15.30
13.42
11.52
10. 14
8.64
7.24
6.12
5.00
3.90
3.20
2.68
2.20
1.64
1.30
1.08
.78
.68
.56
.38
.00
*0*****
o
...,**.*.2,*,,*,0*«*»**.
o*
***
*************************************

*********************************Q*******


*********************
*****************
**************
**************
************
***********



********
*******
*******

*****
****
****
****
***
**
***
**
**
**
***

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0
0
0
0
0
o
0
0
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    CUMULATIVE   CUMULATIVE
     % ENTRIES   COMPLEMENT
           5.0
          10.0
          25.0
          50.0
          75.0
          90.0
          95.0
          99.0
          95.0
          90.0
          75.0
          50.0
          25.0
          10.0
           5.0
           1.0
                    VALUE OF
                    FACTOR
         5673.
         6936.
         9630.
        14767.
        23536,
        36677,
        44100.
        57906.
     4690
     3430
     4280
     1900
     7100
     3300
     0000
     6700
Figure 1.   Monte Carlo analysis for FACTOR.

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an  error is  detected, AutoMOUSE  will
beep, redisplay the equation, explain the
error in the equation/error reporting area
of the screen, and request correction of
the  equation.
  if AutoMOUSE finds no problem with
an equation, it will ask whether you wish
to continue to the next equation or create
a statistics summary and histogram table
(of the kind shown in Figure 1) for the
dependent variable of the equation. In our
example, the following menu would appear
(the arrow indicates a  highlighted  bar
across the line):
   1. Continue to next equation
   2. Create table for variable factor •
Pressing the Enter key selects the high-
lighted line). No additional input is required
of the user to create a statistics summary
and histogram table for this variable.

Stochastic Variable
Specification
   During  the  processing  of  equations,
AutoMOUSE keeps track of the indepen-
dent variables used in the equations. Since
no numerical values have been specified
for these variables, they are presumed to
be stochastic or uncertain variables. When
equation entry is  completed,  the user is
prompted to specify  for each stochastic
                                variable the nature of its distribution and
                                its parameters using the menu shown in
                                Figure  4. The figure shows the entry for
                                variable PRECIP  where the  trapezoidal
                                probability distribution has been selected,
                                with  parameters 762, 1,016,  1,270, and
                                1,524. The entries for the other variables
                                are similar.
                                  When all of the probability distribution
                                arguments have been supplied, a summary
                                table appears on the screen indicating the
                                number of equations and stochastic vari-
                                ables in the  model and the number of
                                table output lines requested. The MOUSE
                                program shown in  Figure 2 is written to a
                                file, and AutoMOUSE is finished.

                                Error Checking and Avoidance
                                in AutoMOUSE
                                  There are two types of error checking in
                                AutoMOUSE. The first  scans for proper
                                FORTRAN characters and syntax (since
                                MOUSE is based upon that computer lan-
                                guage). One  cannot  have, for example,
                                the character "@" in a  MOUSE program
                                or have plus (+)  follow minus  (-)  in an
                                equation. AutoMOUSE goes even further
                                than  the usual  FORTRAN compiler
                                checker, in that it will not allow taking the
                                square root of a negative number.  In the
                                Expert  mode,  the  second type  of  error
                                checker scans the arguments to MOUSE
                                probability and interest functions. The
                                probability of a "success" in a binomial
distribution, for example, must not be equal
to or greater than one or less  than or
equal to zero and there must be two ar-
guments (i.e., the probability of a success
and the number of trials).  No other error
checking is  necessary since it is  Auto-
MOUSE and not the user that writes all of
the remaining code necessary to complete
the program. Errors made by the user in
writing an  equation or in specifying a
FORTRAN  function or a  MOUSE prob-
ability or. interest function  are caught im-
mediately, and not after the user has en-
tered the complete model.

Summary
  A  comparison  with general purpose
simulation languages has shown  that the
MOUSE/AutoMOUSE system  is the
quickest  and easiest way to  implement
uncertainty in models involving equations.
This  is accomplished  without  sacrificing
any  of the power commonly associated
with  such languages.  Most importantly,
the MOUSE/AutoMOUSE system permits
the user to focus on the model rather than
on the details of coding a program. With-
out a system such as MOUSE, uncertainty
analysis on  any  but the simplest waste
management models  would probably be
skipped and the  decision making  process
would  be noticeably less effective as a
result.
 10

 15
DIMENSION TAB(46)
COMMON/Q1/C80/Q2/JUMP/Q3/LOOP/Q4/SENS/Q5/IDATA/Q6/IOUT/Q7/IPASS/Q8
&/IRAN/Q9/IREAD/Q10/ISCR1/Q11/ISCR2/Q12/ISNAP/Q13/ITER/Q14/ITOG/Q15
&/IWRIT/Q16/IXXX/Q17/OK1/Q18/OK2/Q19/OK3/Q20/OK4/Q21/OK5/Q22/OK6
CALL NAME('(REGULATORY EXAMPLE}')
ITER=5000
D010IXXX=1,ITER
PRECIPsTRA(762.0,1016.0,1270.0,1524.0)
RLEACH=CUNI(.5,1.0)
DEPTHL=TRA{3.0,6.1,9.1,15.2)
WDENS=TRI{297.0,415.0,534.0)
FACTOR=70000*(PRECIP*RLEACH)/(DEPTHL*WDENS)
CALL TABLEfFACTOR.XFACTORX.DUMO.DUMI ,40,TAB)
CONTINUE
GOTO(5.15),JUMP
CONTINUE
END
 Figure 2.  MOUSE program for the regulatory example.

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                                    ENTER EQUATION #1 OF THE MODEL ON THE FOLLOWING LINES.
                                    (Leaving lines blank indicates that there are no more equations to enter.)
        FACTOR=70000*(PRECIP*RLEACH)/(DEPTHL*WDENS)
        To move around use ARROW keys plus HOME/END for start/end of last line, CONTROL LEFT ARROW/CONTROL RIGHT ARROW
        for  end/beginning of line, ENTER for first column of next line, and TAB for right 8 spaces. DEL/BACKSPACE deletes the character
        to the right/left, ESCAPE ends thedata entry, and\toggles between erase/restore all lines. Enter Alt-F to view a summary of permissible
        functions and arithmetic operations in this Non-Expert mode.
                                                    INSERT MODE STATUS IS ON
Figure 3: Equation entry screen, Non-Expert mode.
Stochastic Variable Distribution Choices
1.

2.

3.
4.
5.
6.
7.
Autocorrelation,
Exponential
Autocorrelation,
Linear
Beta, Standard Form
Binomial
Continuous Uniform
Discrete Trapezoidal
Discrete Triangular
8.
9.
10.
11.
12.
13.
14.
15.
16.
Discrete Uniform
Empirical Beta
Empirical Cts
.Empirical Discrete
Erlang
Exponential
Gamma
Hypergeometric
Lognormal
17.

18.
19.
20.
21.
22.
23.
24.
Lognormal,
Alternate Form
Normal
Pascal/Geometric
Poisson
Step Rectangular
Trapezoidal
Triangular
Set = to LOOP

Enter number of probability function desired for variable
PRECIP » 22
                   Trapezoidal Distribution-Example: PRECIP =TRA(2.,5.,7.,9.)where2and9are the
                   lower and upper bounds (Parameters A and D), respectively, of the distribution, and
                   5 and 7 are the lower and upper bounds (Parameters B and C), respectively, of the
                   middle of the distribution. Enter your own PARAMETERS A, B, C, and D, separated
                   by commas or spaces,  e.g.,  2,5,7,9 (or Return to select a different probability
                   distribution):

                   » 762,1016,1270,1524
Figure 4.  Probability distribution specification menu.
                                                                                          •U.S. Government Printing Office: 1992— 648-080/60084

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The EPA author, Albert J. Klee, (also the EPA Project Officer, see below) is with
    the Risk Reduction Engineering Laboratory, Cincinnati, OH 45268
The complete report consists of paper copy and diskette, entitled "AutoMOUSE,
    An Improvement to the MOUSE Computerized Uncertainty Analysis System
    Operational Manual".
       Paper Copy (Order No. PB93-500007AS; Cost: $35.00, subject to
       change)
       Diskette (Order No. PB93-100113AS; Cost: Contact NTIS for pricing
       information)
The above items will be available only from:
       National Technical Information Service
       5285 Port Royal Road
       Springfield, VA 22161
        Telephone: 703-487-4650
The EPA Project Off leer can be contacted at:
       Risk Reduction Engineering Laboratory
        U.S. Environmental Protection Agency
       Cincinnati, OH 45268
   United States
   Environmental Protection Agency
   Center for Environmental Research Information
   Cincinnati, OH 45268

   Official Business
   Penalty for Private Use
   $300
     BULK RATE
POSTAGE & FEES PAID
         EPA
   PERMIT No. G-35
   EPA/600/SR-92/145

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