From stable online coupling to decade-long climate simulations: A machine learning parameterization for cloud microphysics in ICON

Abstract

The representation of cloud microphysics and its nonlinear character and scale-dependence is a remaining source of uncertainty in Earth system models (ESMs). Here, we develop and couple online a machine learning (ML)-based cloud microphysics parameterization with the Icosahedral non-hydrostatic modeling framework (ICON). The primary challenge is achieving numerically stable, long-term online coupling when transitioning from training with km-scale data to application in coarse-scale simulations, where the coupled system encounters atmospheric states and feedbacks not seen during training. The training data is obtained from a global convection-permitting ICON simulation at 5 km resolution. The ML microphysics scheme uses a two-stage design: a classifier to identify active grid cells and a regressor to predict cloud microphysical tendencies. Physical constraints such as enforcing mass positivity and overshoot prevention prove essential for numerical stability in the coupled system. We demonstrate that achieving stable online coupling requires enforcing physical constraints and careful dataset curation, and that strong offline performance alone is insufficient. The coupled model maintains numerical stability over decade-long simulations with a performance in reproducing the observed climate comparable to the classical graupel scheme. The ML-based scheme eliminates two microphysics-specific tuning parameters of the classical graupel scheme, though systematic improvements in long-term mean-state biases are not yet realized. This study demonstrates that stable, decade-long climate simulations with an ML-based cloud microphysics scheme trained on convection-permitting data are feasible, providing a foundation for future hybrid ESMs.