A Differentiable Framework to Reduce Structural and Parametric Uncertainty in Cloud Microphysics Parameterizations Online

Representing clouds at the climate scale necessitates developing bulk parameterizations of microphysical processes. Parameterizations of processes such as collision-coalescence are known to suffer from both parametric and structural uncertainty. Recent studies have used machine learning to develop parameterizations for microphysical processes from box model simulations of super-droplets, which provide a higher fidelity ground truth data set. However, machine learning-based parameterizations trained offline frequently struggle to generalize when implemented online in models [Seifert and Rasp, 2020; Gettelman et al. 2021]. Moreover, such machine learning approaches have focused on individual processes, without exploring potential reductions in complexity due to multiple process rates acting on a population of hydrometeors simultaneously [Proske et al. 2024].

I will discuss our work towards the development of a differentiable framework to learn cloud microphysical process rates in bulk parameterizations online from higher fidelity models using machine learning. This framework, which is implemented in Jax, is fully differentiable and can exploit automatic differentiation to learn moment-based parameterizations in a fully online fashion. Our approach enables the simultaneous evaluation of multiple process rates and facilitates reduced order modeling to simplify cloud microphysical schemes.

We also explore the applications of this framework to parameterize collision-coalescence processes using learned representations of the droplet size distribution and a Koopman operator-based linearization [Lamb et al. 2024]. Preliminary results indicate that the Koopman operator representation maintains long-term stability and may lead to more optimal bulk representations of warm rain processes. This work represents a significant step toward reducing the complexity and uncertainty in cloud microphysics parameterizations, with implications for improved climate model accuracy.