A non-intrusive framework for learning corrections to long time climate simulations from short time training data

Quantifying the risks of extreme weather events is becoming increasingly challenging due to our rapidly changing climate, and yet remains a critical step in the implementation of strategies to mitigate their impact on society. The vast range of scales relevant to the Earth’s turbulent atmosphere renders direct numerical simulation intractable over the multi-century time horizons needed for converged rare event statistics. On the other hand, coarse scale simulations that parametrize or insufficiently resolve the dynamics at the smallest scales generally suffer from an inability to generalize beyond the parameter regimes for which they were designed. This is because these “sub-grid” scales nontrivially affect the dynamics and statistics of large-scale phenomena in ways that are not universally understood. Here we present a general nonintrusive machine learning framework to correct the output of long-time coarse-resolution climate simulations. The framework -- which acts as a post-processing operation -- relies on training data pairs that have minimal chaotic divergence – namely a reference trajectory and a coarse simulation nudged towards that reference. Training on these specific trajectories allows our approach to generalize to unseen chaotic climate realizations, even when these are much longer than those seen in training. Furthermore, the post-processing nature ensures that our method is stable over indefinitely long-time horizons. We illustrate our approach on the E3SM climate model with 100km resolution, where with only 8 years of training data we can significantly reduce the error in global and regional 40-year statistics relative to ERA5 reanalysis data.