# Exercise #7 Previous Next

• Problem #1 - Repeat the Single Particle Trajectory calculation but now show the hour‐to‐hour variation of the particle height.

• Hint - Use the Center‐of‐Mass trajectory option to display the height variation of a concentration calculation.

• Solution - You should see a very large initial displacement between the first and second hours and then varying between 1000 and 2000 m AGL.

• Problem #2 - The multiple particle release section showed that when the particle number was increased from 100 to 1000 and then again from 1000 to 10000, each time the maximum concentration decreased by about half during the last sampling time period (0500 UTC). The 100,000 particle simulation was not shown, but the maximum concentration would have only decreased by 10% from the 10000 particle simulation, suggesting that a 10,000 particle release was sufficient for the 0.05 deg resolution concentration grid. How coarse a resolution concentration grid could be utilized if the simulation were to consist of only 1000 particles?

• Hint - Retrieve conc_test_control.txt and conc_test_setup.txt and reconfigure the tests for different grid resolutions or simply edit the conc_part.bat (or .sh) file.

• Solution - The 1000 particle simulation could permit a concentration grid resolution of 0.20 deg or greater for the maximum concentration to no longer be sensitive to the particle number, that is, similar to the 10,000 particle simulation. See these example results.

A too small a concentration grid may result in under-sampling if an insufficient number of particles have been released. An explanation for this result might be inferred from this illustration. In this case the under-sampling is shown for n=6 but for n>=12, the larger number of particles in the sampling box does not change the maximum concentration because each particle contains a proportionally smaller fraction of the mass.
• 1 m 24 s

• Problem #3 - From the previous problem, can you explain the changes to the minimum concentration? Minimum concentrations can be important, especially when comparing calculations to measurements where the instrument has a detection threshold.

• Hint - Unfortunately, the minimum concentration values shown by the concplot program in the previous graphics cannot be used because they are an artificial result of interpolation by the contouring program. Maximum concentrations are set explicitly. Instead rerun the script but use the program gridplot and view the output file plot.html. No other changes are required.

• Solution - You should get values of 5.3E-15, 5.3E-16, 5.3E-17, and 5.3E-18,respectively, with each factor of 10 increase in particle number from 100 to 1000 to 10000 to 100000! The minimum value is directly proportional to the particle number because the minimum concentration is the result of one particle residing in one concentration grid cell.

Using a calculator, how would you compute the expected minimum concentration for the 10,000 particle simulation with the 0.20 degree by 5 km depth concentration grid?
• 1 m 24 s