Statistical mechanics in climate emulation: Challenges and perspectives

Climate emulators are a powerful instrument for climate modeling, especially in terms of reducing the computational load for simulating spatiotemporal processes associated with climate systems. The most important type of emulators are statistical emulators trained on the output of an ensemble of simulations from various climate models. However, such emulators oftentimes fail to capture the "physics" of a system that can be detrimental for unveiling critical processes that lead to climate tipping points. Historically, statistical mechanics emerged as a tool to resolve the constraints on physics using statistics. We discuss how climate emulators rooted in statistical mechanics and machine learning can give rise to new climate models that are more reliable and require less observational and computational resources. Our goal is to stimulate discussion on how statistical climate emulators can further be improved with the help of statistical mechanics which, in turn, may reignite the interest of statistical community in statistical mechanics of complex systems. Impact Statement This perspective paper assesses the potential for improving the performance of climate emulators with the help of techniques from machine learning and statistical mechanics. It is meant to be accessible to a wide readership and to shed light on this emerging field of climate modeling. The paper is jointly written by a physicist, a statistician, and a computational scientist, which guarantees a multifaceted view.