SuperdropNet: Machine Learning Parameterization for Super-droplet Cloud Microphysics Scheme

In weather and climate models, physical processes that can’t be explicitly resolved are often parameterized. Among them is cloud microphysics that controls the formation of clouds and rain. Existing parameterization schemes available for cloud microphysics suffer from an accuracy/speed trade-off. The most accurate schemes based on Lagrangian droplet methods, such as the superdroplet method (SDM), are computationally expensive and are only used for research and development. On the other hand, more widely used approaches such as bulk moment schemes simplify the particle size distributions into the total mass and number density of cloud and rain droplets. While these approximations are fairly realistic in many cases, they struggle to represent more complex microphysical scenarios. This gap can be bridged through the development of computationally inexpensive proxies for expensive droplet simulations.

Here we train a neural network to mimic the behavior of SDM simulations in a warm-rain scenario in a dimensionless control volume. We call this SDM emulator SuperdropNet. The network behaves akin to a dynamical system that converts cloud droplets to rain droplets–represented as bulk moments–with only the current system state as the input. We use a multi-step training loss to stabilize the network over long integration periods. We find that the network is stable across various initial conditions and in many cases, emulates the SDM simulations better than the traditional bulk moment schemes. Our network also performs better than any previous ML-based attempts to learn from SDM.

It is common for ML based emulators to perform well on their own but fail when coupled to a numerical model. This can happen due to out of distribution values that are produced due to the compounded effects from other processes. To test the emulator's performance in a coupled scenario, we couple it to a warm-bubble simulation in ICON (Icosahedral Non-hydrostatic) model with the help of a FORTRAN-Python bridge. We analyze the evolution of the warm-bubble simulation, when using the default two moment bulk scheme versus SuperdropNet. Here we find that SuperdropNet produces physically plausible results that remain stable throughout the duration of the simulation. When compared with the two-moment bulk scheme, SuperdropNet produces a similar pattern of rain formation. On the other hand, certain other quantities demonstrate a considerable divergence which we attribute to the differences in the estimation of rain mass and the late onset of rain.

Our study proves the feasibility of employing ML based proxies for droplet simulations, which have been made possible due to specialized data generation and training techniques. We attribute SuperdropNet’s stability to an exhaustive training process involving droplet simulations with various initial conditions. We plan on expanding this work by creating ML based emulators for other cloud microphysical processes such as sedimentation and condensation/evaporation by using superdroplet simulations.