Statistical-Physical Microphysics Parameterization Schemes: A Proposed Framework for Physically-Based Microphysics Schemes that Learn from Observations

Errors and uncertainties in cloud microphysics parameterization schemes represent a bottleneck for efforts to improve the performance of numerical weather forecasts. This is, in part, because microphysics parameterizations suffer from both sub-grid scale approximations as well as fundamental gaps in the understanding of underlying physics of clouds and precipitation (an issue that affects all schemes, including detailed bin and Lagrangian schemes). Observations have the potential to help resolve this bottleneck, but have seldom been systematically applied to improve schemes. We argue for a statistical-physical framework as the preferred approach for using observations to improve the performance and fidelity of cloud microphysics schemes. In this framework, a priori assumptions (such as the form of the drop size distribution) are avoided and process rates are estimated via Bayesian inference, reducing errors associated with these assumptions and approximations. The few hard physical constraints that do exist, such as mass conservation and monotonicity of drop sedimentation rate, can be naturally integrated into such a scheme. All other scheme information is inferred from observations, including the degree of complexity in the scheme (for example, the number and choice of prognostic drop size distribution moments). We present proof-of-concept examples of development of one such scheme, the Bayesian Observationally-constrained Statistical-physical Scheme (BOSS). We explore using polarimetric radar observations of rain as the source of observational information, as well as tests within idealized kinematic models of shallow warm clouds. Finally, we demonstrate how machine learning tools such as Gaussian process models and neural networks can be used to reduce the computational cost of inference, without loss of physical interpretability of the scheme.