In Section 7.5 we saw how results were dependent on the number of computational particles used.
In this section we will discuss this dependence in more detail.
Concentrations are estimated from the distribution of the computational particles and some uncertainty is introduced by this process.
The relative uncertainty in the concentration is proportional to 1/√N so increasing the number of particles will decrease the
uncertainty due to the particle number. A simulation should utilize enough computational particles to ensure that the uncertainty
is within a range acceptable to the end user. By varying the random seed we can create a series of simulations, the variations of which
express this uncertainty.
The approach shown here can be useful in deciding how many particles are needed for a simulation and what is the error due to particle number variations.
A similar approach would be to set the namelist parameter KRAND=4 or SEED, which uses a different method to set a
variable seed for the random numbers. krand and SEED can be used with any concentration model executable.
It is not limited to the variance version of the code. The KRAND and SEED options cannot be set through the GUI.
- Before running a simulation, we should delete all the ensemble files left over from the previous section. There is a Special Runs / Ensemble / cleanup tab that opens the menu. There are no options, just press Execute Script and all ensemble related files will be deleted from the working directory. Only the model output concentration files with the root name set in the Grid menu with the .000 suffix will be deleted.
- Start by retrieving the saved ensemble_control.txt and ensemble_setup.txt settings into the GUI menu. For this simulation, from the Setup Run menus, change the release height back to 10 m and change the output file from ensemble to a unique name such as ensturb.
- After the Setup Run and the Advanced Configuration menus have been retrieved, open the Advanced / Configuration Setup / Concentration / Menu #4 and change the particle release per cycle from 5000 to 1852. Although the turbulence ensemble can be composed of any number of members, to parallel the meteorological grid ensemble, 27 variations are also run in this case. The 1852 is determined by dividing 50000 (from the original simulation) by the number of members to maintain about the same total particle number when computing the mean concentration.
- After saving the change, press the Special Runs / Ensemble / Turbulence menu tab. There are no data entry options, just a prompt menu to ask if you really want to continue with the ensemble turbulence calculation. The calculation will start and as each member calculation is completed, a message is added to the simulation log and finally a completion message when member 27 finishes.
- Following the same procedure as previously with the meteorological ensemble, select the Display / Ensemble / Create Files menu tab. This step is required to display probability maps or box plots because it invokes the pre-processor step that creates the probability files from the individual concentration simulations. When finished, open the box plot menu and enter the same position 42.25 -78.80, sampler 510 (Little Valley, NY), used in the previous section.
- The resulting box plot is similar to the previous example,
but with a somewhat lower range between low and high concentrations; note that the ordinate scale is different.
For instance, the time period with the initial measured concentration (26 18), shows the 90th percentile concentration uncertainty range (5th to 95th)
is about a factor of four rather than a factor of 10 from the meteorological grid ensemble.
- Optional Exercise: Repeat the exercise using 50000 particles in each simulation. The resulting box plot and
member distribution plot show that there is much less difference between the simulations than when using only 1852 particles. Note that the mean from the 27 runs with 1852 particles
is about the same as the one run with 50000 particles.
Note that taking the mean of two simulations with different random seeds and 10000 particles each is the same as running one simulation with 20000 particles.
Further reading Section 2.4 and Appendix A of The Use of Gaussian Mixture Models with Atmospheric Lagrangian Particle Dispersion Models for
Density Estimation and Feature Identification. Atmosphere 2020, 11(12)
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