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 fi 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
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Jery Stedinger and Bryan Tolson  Cornell University   April 20, 2001; revised 4-04; D. Cowen corrected plotting 4-07 ile and enable macros. k. istribution of generated random variables. 1 fits a lognormal dist with this mean and stand. dev. W 8 in macro. Maximum  Concentration #MACRO? #DIV/0! #MACRO? to 'Tools', select 'Macros', then select 'Security' (g/m 3 )
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RANDOM VARIABLE VALUES GENERATED Using Visual functi Basic Macro Functi Emission Rate Windspeed Ambient temperature MAX conc Q (g/s) degrees K/m 494.900 4.382 10.857 0.016 #MACRO? 434.350
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This note was uploaded on 03/29/2009 for the course CEE 5950 taught by Professor Carr during the Fall '08 term at Cornell.

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MC_Demonstration_ver8_Student - Example spreadsheet for...

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