Bias of footprint dependant on particle number

[cluekenwinkels]

Hello,
I currently use FLEXPART-WRF in an urban setting on roughly 1 km resolution. In a test for the statistical error due to the limited particle number, I found not only statistical, but systematic differences (bias) between runs with different particle numbers. In particular, the sum of the footprints entries grows with the particle number.
As I understand it the footprints' values should not generally grow with larger partical numbers, but become more and more consistent, which is not the case here.
The same footprint was calculated for 10, 50, 250, and 500 thousand particles with very different results for the same release location, time and meteorology.
The lowest paritcle number is chosen due to the vaule in reviewed papers using FLEXPART-WRF in an urban/meso scale setting:

• Cui 2015 ​https://doi.org/10.1002/2014JD023002 (10,000 particles per release)
• Nathan 2021 ​https://doi.org/10.5194/acp-2020-1303 (10,000 particles per release).

[pesei]

Thank you for reporting this, if it is really true it might be a serious issue.

Could you please

• be a bit more specific about how you calculate the so-called footprint, and which relevant settings in the input (parameters and release) you use?
• provide a graph or concrete numbers illustrating the dependency on the particle numbers?

[cluekenwinkels]

The "footprints" are calculated by adding the CONC field in the flxout....nc files along the temporal axis Time (the other dimensions besides longitude and latitude are one-dimensional). I will add the plots and the respective input files to the Attachments. The graphs show the following additional information:

• n_parts: Number of particles of the plotted release
• n_parts_total: Number of total particles in the FLEXPART-WRF run (here, the same as n_parts)
• sum: Sum of all cells that are displayed

Additionally I will add the (cellwise) difference of the two footprints. Here, one can see that not only finer structures emerge with the larger particle number (which would be expected), but also larger values are found in general (which should not be the case on average).

[cluekenwinkels]

During my investigation of the problem, I discovered an additional artifact that suggests the total number of particles in a run may have an impact, rather than just the number of particles in a single release:

I compared the results of a run with one release containing 50,000 particles to a run with 10 releases, each containing 50,000 particles (for a total of 500,000 particles in the second run). If the positions and times of all releases are the same, they should produce similar footprints since each release has the same number of particles. I found that the 10 footprints of the second run matched (with statistical variations). However, when compared to the first run, I observed the same differences as described in the original problem. Additionally, the footprints of the second run more closely matched those of a run with a single release of 500,000 particles.

I can provide corresponding plots and input files upon request.

[cluekenwinkels]

Is there any progress concernig the matter or are there problems in reporducing the effect?

[cluekenwinkels]

A solution was found for the problem:
There seems to be a problem with the default random number generator parameters for large particle numbers. There are two solutions to the problem by adjusting parameters in the par_mod.f90 file:

1) Raise the value of maxrand to a larger value (this will require more memory) to sample more random numbers. For less memory usage in serial mode you can also set MAX_STREAM=1 and maxomp=1.
2) Change the parameter newrandomgen from 0 to 1 (this is a bit slower).

[massimo]

The solutions fix the issue, maxrand should be signficantly larger compared to the particle number, e.g. x100 or more.
Solution (2) ensures the correct statistical performances.