Parcel model with "rainbow" ice nucleation from Frostenberg et al 2023

[AgnieszkaMakulska]

Purpose

Add a parcel model example that uses the "rainbow" parameterization the way it was described in Frostenberg et al 2023 . Test the dependency on dt, drawing frequency, etc.

To-do

Content

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• I have read and checked the items on the review checklist.

[codecov]

Codecov Report

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Additional details and impacted files

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[trontrytel]

I left some comments on the draft already. Aside from them, could you also add a small entry to the documentation page with parcel model examples? Including the notes I have in PR 336 and including the plot with the parcel model results. Thank you, this is a really cool example!

[trontrytel]

Here is the final version (I think). Initially I wrote the equations wrong, thinking g = sigma sqrt(2 gamma) But that actually gives us the wrong limit and the noise in the system does not increase as we change the gamma scale. It should be g = sigma (duh...)

Now we see that for large gammas (i.e. short assumed timescales) the solution converges to the mean solution.

I'm not sure if I understand why we converge to the mean when we draw less frequently in the random option (dotted lines)

[trontrytel]

I cleaned up some of the names in the example. Not sure what is the least confusing way of naming/specifying the sampling interval in the random scheme. But at least now on the labels we have the same units (i.e. either the time between sampling in the random case or the assumed process time scale in the stochastic case). The problem is that even if the units are the same the interpretation is the opposite (I think). The larger sampling interval the more close we are to the mean. But the shorter the time scale the closer we are to the mean.

Below I show two plots with the same assumed sampling intervals and timescales, but different model dt of either 0.1s or 1s. It would be better to plot everything on one plot, but I'm thinking how to do it neatly.

[trontrytel]

Yet another attempt at squeezing in more plots:

[haakon-e]

https://en.wikipedia.org/wiki/Euler–Maruyama_method

[haakon-e]

for future implementation: https://github.com/SciML/StochasticDiffEq.jl