Physics-Constrained Deep Learning Postprocessing of Temperature and Humidity

Abstract

Abstract Weather forecasting centers currently rely on statistical postprocessing methods to minimize forecast error. This improves skill but can lead to predictions that violate physical principles or disregard dependencies between variables, which can be problematic for downstream applications and for the trustworthiness of postprocessing models, especially when they are based on new machine learning approaches. Building on recent advances in physics-informed machine learning, we propose to achieve physical consistency in deep learning–based postprocessing models by integrating meteorological expertise in the form of analytic equations. Applied to the postprocessing of surface weather in Switzerland, we find that constraining a neural network to enforce thermodynamic state equations yields physically consistent predictions of temperature and humidity without compromising performance. Our approach is especially advantageous when data are scarce, and our findings suggest that incorporating domain expertise into postprocessing models allows the optimization of weather forecast information while satisfying application-specific requirements. Significance Statement Postprocessing is a widely used approach to reduce forecast error using statistics, but it may lead to physical inconsistencies. This outcome can be problematic for trustworthiness and downstream applications. We present the first machine learning–based postprocessing method intentionally designed to strictly enforce physical laws. Our framework improves physical consistency without sacrificing performance and suggests that human expertise can be incorporated into postprocessing models via analytic equations.