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 ------- 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) ------- 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******* ********************* ***************** ************** ************** ************ *********** ******** ******* ******* ***** **** **** **** *** ** *** ** ** ** *** o ** o 0 0 0 0 0 o 0 0 o o o 0 o 0 o o o o 0 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. ------- 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. ------- 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 ------- ------- ------- 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 ------- |