  Climate models play a critical role in understanding and projecting climate
change. Due to their complexity, their horizontal resolution of about 40-100 km
remains too coarse to resolve processes such as clouds and convection, which
need to be approximated via parameterizations. These parameterizations are a
major source of systematic errors and large uncertainties in climate
projections. Deep learning (DL)-based parameterizations, trained on data from
computationally expensive short, high-resolution simulations, have shown great
promise for improving climate models in that regard. However, their lack of
interpretability and tendency to learn spurious non-physical correlations
result in reduced trust in the climate simulation. We propose an efficient
supervised learning framework for DL-based parameterizations that leads to
physically consistent models with improved interpretability and negligible
computational overhead compared to standard supervised training. First, key
features determining the target physical processes are uncovered. Subsequently,
the neural network is fine-tuned using only those relevant features. We show
empirically that our method robustly identifies a small subset of the inputs as
actual physical drivers, therefore, removing spurious non-physical
relationships. This results in by design physically consistent and
interpretable neural networks while maintaining the predictive performance of
unconstrained black-box DL-based parameterizations.
