  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 post-processing 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 is scarce, and our findings suggest that
incorporating domain expertise into postprocessing models allows to optimize
weather forecast information while satisfying application-specific
requirements.
