Representing cloud microphysical processes in large scale atmospheric models is challenging because many processes depend on the details of the droplet size distribution (DSD, the spectrum of droplets with different sizes in a cloud). While full or partial statistical moments of droplet size distributions are the typical basis set used in bulk models, prognostic moments are limited in their ability to represent microphysical processes across the range of conditions experienced in the atmosphere. Microphysical parameterizations employing prognostic moments are known to suffer from structural uncertainty in their representations of inherently higher dimensional cloud processes, which limit model fidelity and lead to forecasting errors. Here we investigate how data-driven reduced order modeling can be used to learn predictors for microphysical process rates in bulk microphysics schemes in an unsupervised manner from higher dimensional bin distributions, by simultaneously learning lower dimensional representations of droplet size distributions and predicting the evolution of the microphysical state of the system. Droplet collision-coalescence, the main process for generating warm rain, is estimated to have an intrinsic dimension of 3. This intrinsic dimension provides a lower limit on the number of degrees of freedom needed to accurately represent collision-coalescence in models. We demonstrate how deep learning based reduced-order modeling can be used to discover intrinsic coordinates describing the microphysical state of the system, where process rates such as collision-coalescence are globally linearized. These implicitly learned representations of the DSD retain more information about the DSD than typical moment-based representations.

In this study, we find significant sensitivity to the choice of time step for the Energy Exascale Earth System Model's atmospheric component, leading to large decreases in the magnitude of cloud forcing when the time step is reduced to 10 seconds. Reducing the time step size for the microphysics increases precipitation, leading to a drying of the atmosphere and an increase in surface evaporation. This effect is amplified when the microphysics is substepped together with other cloud physics processes. Coupling the model's dynamics and physics more frequently reduces cloud fraction at lower altitudes, while producing more cloud liquid at higher altitudes. Reducing the deep convection time step also reduces low cloud mass and cloud fraction. Together, these results suggest that cloud physics in a global circulation model can depend strongly on time step, and in particular on the frequency with which cloud-related processes are coupled with each other and with the model dynamics.

Warm rain collision coalescence has been persistently difficult to parameterize in bulk microphysics schemes. Here we use a flexible bulk microphysics scheme with bin scheme process parameterizations, called AMP, to investigate reasons for the difficulty. AMP is configured in a variety of ways to mimic bulk schemes and is compared to simulations with the bin scheme upon which AMP is built. We find that the biggest limitation in traditional bulk schemes is the use of separate cloud and rain categories. When the drop size distribution is instead represented by a continuous distribution with or without an explicit functional form, the simulation of cloud-to-rain conversion is substantially improved. We find that the use of an assumed double-mode gamma distribution and the choice of predicted distribution moments do somewhat influence the ability of AMP to simulate rain production, but much less than using a single liquid category compared to separate cloud and rain categories. Traditional two category configurations of AMP are always too slow in producing rain due to their struggle to capture the emergence of the rain mode. Single category configurations may produce rain either too slowly or too quickly, with too slow production more likely for initially narrow droplet size distributions. However, the average error magnitude is much smaller using a single category than two categories. Optimal moment combinations for the single category approach appear to be linked more to the information content they provide for constraining the size distributions than to their correlation with collision-coalescence rates.

The Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS) is a bulk microphysics framework that calculates process rates using generalized power laws of the moments of the droplet size distribution. Formula parameters are inferred with Monte Carlo methods, evaluating a proposed set of parameter values by comparing model outputs to observations. In this study, we produce a set of 2- and 3-moment BOSS schemes that effectively emulate the behavior of a bin microphysics model, using an idealized 1D driver for various forcing conditions that produce either non-precipitating or drizzling cloud. In this driver, BOSS is fully responsible for collision-coalescence, condensation/evaporation, and calculation of hydrometeor fall speeds, with only dynamical forcing and droplet activation handled externally. Comparing BOSS schemes with different terms and different numbers of prognostic cloud moments allows us to evaluate whether the model benefits from the added complexity of these changes. BOSS also has an advantage over black-box machine-learning methods in that the process rate formulas are “human-readable”, allowing us to analytically identify potential sources of instability.