Exercise #13




  • Problem #1 - 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 #2 - 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.