Exercise #13

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  • Problem #1 - In the last part of the section on estimating emissions from an unknown source, the inverse emission value at the suspected source location was extracted using Convert to Station utility program because the contours in the plot automatically generated by the GUI had insufficient detail. Can you redraw the graphic with more detailed contours?

  • Hint - Use one of the routine concentration display programs to redraw the cmean file that was generated from the cden output files using a finer contour interval.

  • Solution - The concentration contour graphic with a finer contour interval, also shows a value of 5E-16 (or 0.5x10-15) near 43N 75W. However, that region also shows a considerable North-South spatial gradient at that location, suggesting a much larger uncertainty in the emission estimate, given typical model transport and dispersion errors.


  • Problem #2 - Using the five TCM output files from the previous section, determine the time variation of the emission rate using the ratio method.

  • Hint - Instead of using a simple ratio of Measured/Calculated (M/C) to determine the release rate time period, use the values already tabulated in the coefficient matrix (c2array.csv) to compute a regression of M/C using the Excel slope function.

  • Solution - The Excel release rate solution shown on line 29 shows considerable variability about the correct solution of 3000 g/h. The original SVD solution using the same coefficient matrix showed considerably less variability. The SVD solution incorporates all time periods into the solution rather than treating them individually.


  • Problem #3 - Both the SVD and Cost function solutions are very sensitive to model error. We can assume that much of the model error, at least in this hypothetical case, was due to the simplifications introduced to speed up the computations. Re-run the simulation with a finer concentration grid and more particles to see if it improves the results.

  • Hint - Try a 0.05 degree concentration grid and 50,000 particles, either using the GUI or an edited version the script.

  • Solution - The SVD solution now shows almost perfect results, while the cost function solution, although improved, is not as good as the SVD solution. The Cost function solution is also dependent upon the first-guess as well as the error definitions.

    • 14 m 26 s