Physics-constrained postprocessing of surface temperature and humidity

Traditional post-processing methods aim at minimizing forecast error. This often leads to predictions that violate physical principles and disregard dependencies between variables. However, for various impact-based applications such as hydrological forecasting or heat indices, it is important to provide forecasts that not only have high univariate accuracy, but also are physically consistent, in the sense of respecting physical principles and variable dependencies. Achieving physical consistency remains an open problem in the post-processing of weather forecasts, while this question has recently gained a lot of attention in the wider deep learning community and climate field. Recent contributions show that physical consistency may be pursued by applying different forms of constraints to deep learning models. The most widely used approaches are to incorporate physics via regularization, by defining physics-based losses in addition to common metrics such as mean absolute error, or to define custom-designed model architectures, such that the physical constraints are strictly enforced. Including constraints also has the potential to help the training procedure by restraining the hypothesis space of the model and improving generalization capabilities.

This work investigates the application of the aforementioned approaches for the postprocessing of a set of variables related to surface temperature and humidity, specifically temperature, dew point, surface pressure, relative humidity and water vapor mixing ratio. As baseline, we use an unconstrained fully connected neural network. We consider the simple case of postprocessing at a single location, and we show how it is possible to incorporate domain knowledge, specifically thermodynamic relationships, via analytic constraints, to obtain physically consistent postprocessed prediction. We compare different approaches and show that we can enforce physical consistency without degrading performance, or even improving it. Furthermore, we discuss additional advantages and disadvantages of these approaches in the context of post-processing, besides error reduction.