Including linear eddy model (LEM) in the 1D kinematic driver example

[jtbuch]

Hi @slayoo,

I've been extending a couple PySDM examples to reproduce the effect of cloud seeding, following several very helpful suggestions by @claresinger.

Relatedly, I'm also interested in using the linear eddy model (Kerstein 1998, Hoffmann et al. 2019) to simulate stochastic supersaturation fluctuations over the mean parcel supersaturation in the 1D kinematic driver example. Have you thought about incorporating the LEM into the PySDM dynamics module? If this is something in the project pipeline, I would be interested in contributing toward its development.

Let me know what you think!

[slayoo]

H @jtbuch, I do not know of any considerations to extend PySDM to cover LEM yet. I have close to no experience in modelling subgrid effects, but will happily help in technicalities. If feasible, please outline what would need to be addressed to make PySDM capable of being extended to cover LEM?

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[CappedColumn]

It was great to speak with @jtbuch and @claresinger about pySDM at the Micro2Macro workshop. This looks like a great project. Here are some specifics of how LEM could be useful in pySDM (from my current perspective).

It sounds like LEM in pySDM would look most similar to what Fabian Hoffman has been doing for LEM as a subgrid model. I do not have experience implementing LEM as a set of superdroplets, rather my group essentially uses LEM as the dynamical core in a small domain, where individual droplets respond to supersaturation variability as they are advected through the LEM-induced turbulent domain. That being said, we have some understanding of the numerical implementation of LEM's triplet maps.

What is the primary goal of implementing LEM in pySDM? It may be beneficial to start with a relatively simple SGS model, such as a stochastic supersaturation fluctuation term, with a specifiable intensity. This would avoid any additional computational cost and would be easiest to implement, then work our way up from there.

For the 1D pySDM, a LEM implementation might look like a hybrid version of L3 (Hoffman et al. 2019) and EMPM (Krueger et al. 1997). As in L3, LEM adds stochastic variability by directly manipulating the set of superdroplet properties, but the intensity of the turbulence is specified by the user as in EMPM (as opposed to information provided by the resolved flow). I'm unfamiliar with the dynamical variables of the 1D kinematic setup which could be used to inform LEM.

[slayoo]

Thank you @CappedColumn!

I'm unfamiliar with the dynamical variables of the 1D kinematic setup which could be used to inform LEM.

The single-column examples are based on the Shipway & Hill 2012 framework which has a fixed temperature profile, and only the moisture content is advected vertically with a time-dependent prescribed velocity field. So, there are in fact no dynamical variables. This is prescribed flow. The only Eulerian field is water vapour mixing ratio. Energy is not conserved since the temperature is prescribed, and the latent heat budget is ignored. (The 2D examples use both heat and moisture advection).

[CappedColumn]

Sounds like it is best to prescribe a TKE dissipation rate profile. This would be the easiest implementation (for the coder).

Could also couple TKE dissipation to the local LWC with a (simple) functional form. Not exact, but that would take out the guess-work of determining cloud base and cloud type. Any other ideas/thoughts are welcome.

[claresinger]

https://www.nature.com/articles/s41612-025-01024-w
A new paper that combines a LEM representation of small-scale turbulent fluctuations with a prescribed updraft velocity 1D column simulation. They do it for ice, which was not the goal here, but maybe this provides some good ideas / starting points.
@jtbuch @CappedColumn @slayoo

[jtbuch]

Apologies for the delay in acknowledging this comment. This paper looks very interesting and relevant -- let me know what would be a good place to start contributing!