MC_Demonstration_ver8_Student

# MC_Demonstration_ver8_Student - Example spreadsheet for...

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Example spreadsheet for Monte Carlo Uncertainty Analysis for air pollution modelling example. Spreadsheet considers uncertainty in four variables. Instructions: ENTER MEAN and STANDARD DEVIATION in yellow cells for each variable using the units of that variable Summary statistics appear in the green areas below. and change the security level to medium. Then, close and reopen the fil The Worksheet 'Analysis' has several answers to that you can check your work Four CDFs' provides examples of the graph of the cumulative dis INPUT FOR MONTE CARLO ANALYSIS    Variables: Emission Rate Windspeed Ambient temperature Q (g/s) degrees K/m N=0/LN=1 1 1 0 0 < Mean 400.0 4.0 15.0 0.020 Stand. Deviation 75.0 0.5 3.0 0.004 1.  N=normal distribution, LN=lognormal distribution (natural logartithm) 2.  All other variables for the Gaussian plume model set equal to their values from HW 3.  CDFs of these 4 random variables are plotted in sheet 'Four CDFs'. 4.  To set the variables to deterministic values, assign Standard  deviations  values of 0.0001, 0.0001, 0.0001 and 0.000001 to Q, Us, Ta and dq/dz, respectively,  for the variable of interest. For the lognormal distribution Computed Value of Log-Space Mean and Log-Space Standard Deviation log-mean 5.9742 1.3785 - - log-St. Deviation 0.1859 0.1245 - - Computed Skew for selected model Real-space skew 0.57 0.38 0.00 0.00 MONTE CARLO RESULTS Generated Values Emission Rate Windspeed Ambient temperature (500 samples) Q (g/s) degrees K/m Sample Average 407.54 3.99 14.89 0.02 Sample Stan. Dev. 80.23 0.50 3.01 0.004 Sample Skew 0.51 0.31 -0.16 0.07 AFTER inputs are entered:   Press   F9   to  RE-CALCULATE  all spreadsheet cells. WARNING : If you could not enable macros when the spreadsheet was opened, go to d θ/ dz U s  (m/s) T a  (degrees C) d θ/ dz U s  (m/s) T a  (degrees C)

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Summary of Monte Carlo Analysis Maximum Concentrations Min #MACRO? Lower Quartile #MACRO? Median #MACRO? Upper Quantile #MACRO? Maximum #MACRO? g/m 3
Jery Stedinger and Bryan Tolson  Cornell University   April 20, 2001; revised 4-04; D. Cowen corrected plotting 4-07 le and enable macros. k. stribution of generated random variables. 0 fits a normal dist. with this mean & stand. dev. 1 fits a lognormal dist with this mean and stand. dev. W 8 in macro.   Maximum  Concentration #MACRO? #DIV/0! #MACRO? o 'Tools', select 'Macros', then select 'Security' (g/m 3 )

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RANDOM VARIABLE VALUES GENERATED Using Visual functio Basic Macro Functio Emission Rate Windspeed Ambient temperature MAX conc Q (g/s) degrees K/m 494.900 4.382 10.857 0.016 #MACRO? 434.350 3.865 9.831 0.015 #MACRO? 641.915 4.893 11.494 0.023 #MACRO? 331.881 3.358 19.036 0.021 #MACRO? 320.031 4.710 18.225 0.013 #MACRO? 360.486 3.733 16.220 0.015 #MACRO? 393.103 3.089 13.844 0.019 #MACRO? 362.329 4.896 16.866 0.019 #MACRO? 526.312 4.176 15.841 0.021 #MACRO? 372.534 3.887 14.775 0.019 #MACRO? 392.769 3.479 10.977 0.024 #MACRO? 374.860 4.714 6.479 0.021 #MACRO?

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• Fall '08
• CARR
• Enable Macros, and enable macros, file and enable, Generated DATA, Emission Rate Windspeed, Spreadsheet considers uncertainty

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