Learning to Infer Weather States Using Partial Observations

Abstract Accurate state estimation of the high‐dimensional, chaotic Earth's atmosphere marks a Sisyphean task, yet is indispensable for initiating weather forecasts and gauging climate variability. While much effort is devoted to assimilating observations and forecasts to infer weather states, the inherent low‐dimensional statistical structure in atmospheric circulation, shaped by geophysical laws and geographic boundaries, is underutilized as an informative prior for state inference, or as reference for assessing representative of existing observations and planning new ones. We realize these potential by learning climatological distribution from climate reanalysis/simulation, using a deep generative model. For a case study of estimating 2 m temperature spatial patterns, the learned distribution faithfully reproduces climatology statistics. A combination of the learned climatological prior with few station observations yields strong posterior of spatial pattern estimates, which are spatially coherent, faithful and adaptive to observational constraints, and uncertainty‐aware. This allows us to evaluate each observation's value in reducing pattern estimation uncertainty, and guide optimal observation network design by pinpointing the most informative sites. Our study showcases how generative models can extract and utilize information produced in the chaotic evolution of climate system.