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.

Accurate prediction of precipitation intensity is of crucial importance for both human and natural systems, especially in a warming climate more prone to extreme precipitation. Yet climate models fail to accurately predict precipitation intensity, particularly extremes. One missing piece of information in traditional climate model parameterizations is sub-grid scale cloud structure and organization, which affects precipitation intensity and stochasticity at the grid scale. Here we show, using storm-resolving climate simulations and machine learning, that by implicitly learning sub-grid organization, we can accurately predict precipitation variability and stochasticity with a low dimensional set of variables. Using a neural network to parameterize coarse-grained precipitation, we find mean precipitation is predictable from large scale quantities only; however, the neural network cannot predict the variability of precipitation (R 2 ∼ 0.4) and underestimates precipitation extremes. Performance is significantly improved when the network is informed by our novel organization metric, correctly predicting precipitation extremes and spatial variability (R 2 ∼ 0.95). The organization metric is implicitly learned by training the algorithm on high-resolution precipitable water, encoding organization degree and humidity amount at the subgrid-scale. The organization metric shows large hysteresis, emphasizing the role of memory created by sub-grid scale structures. We demonstrate this organization metric can be predicted as a simple memory process from information available at the previous time steps. These findings stress the role of organization and memory in accurate prediction of precipitation intensity and extremes and the necessity of parameterizing sub-grid scale convective organization in climate models to better project future changes in the water cycle and extremes.