PRecover 1.0: Process Rate Recovery with Machine Learning

Abstract. Comprehensive information on cloud microphysical process rates from numerical simulations allows for better understanding of precipitation formation pathways and aerosol-cloud interactions. However, resource limitations often make it impractical to include all microphysical process rates in the model output, limiting in-depth analyses. To address this shortcoming, we introduce PRecover, a data-driven post-processing approach to recover microphysical process rates that are not stored during runtime from standard output of a numerical weather prediction model. In particular, we train random forests, gradient boosting models, and feed-forward neural networks to recover microphysical process rates from a two-moment bulk microphysics scheme in the ICOsahedral Nonhydrostatic (ICON) model. We use cloud variables as input, obtained from high-resolution simulations in a limited-area setup over Europe. Warm-rain and ice microphysical process rates are recovered with a two-step classification-regression approach for both instantaneous process rates and process rates accumulated over output time steps ranging from one to 60 minutes. As a physics-based baseline, we assess whether process rates can be directly recalculated from stored ICON output variables. Accurate recalculation is possible for process rates such as accretion and self-collection but not for the autoconversion, rain melting or heterogeneous ice nucleation rate. Using PRecover, we successfully recover most of the process rates that are accumulated over output time steps of 10 minutes or less, but the values are increasingly difficult to recover for rates accumulated over longer accumulation intervals. For a model output time step of 10 minutes, the final combined classification-regression models achieve a deterministic performance of R² = 0.66 for instantaneous process rates and R² = 0.40 for accumulated process rates, respectively. The recovery fails for the heterogeneous ice nucleation rate, likely due to the unavailability of the number of activated ice nuclei in the model output. Excluding QI_HET, the mean scores increase to R² = 0.69 for instantaneous rates and R² = 0.41 for accumulated rates. To quantify predictive uncertainty, we provide calibrated prediction intervals through conformalized quantile regression, achieving a prediction interval coverage probability of 88.09 % and 86.95 % for instantaneous and accumulated process rates, respectively. We demonstrate spatial transferability of the models with two case studies over different regional domains and simulation settings unseen during training. PRecover opens the possibility of obtaining information about microphysical process rates in a more resource-efficient and flexible way, allowing for in-depth studies of cloud microphysics even when the microphysical process rates were not saved initially.