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.

翻译：天气预报中心目前依赖统计后处理方法最小化预报误差。这虽能提升预报技巧，却可能导致违背物理原理或忽略变量间依赖关系的预测结果，这对下游应用及后处理模型（尤其是基于新型机器学习方法的模型）的可信度构成挑战。基于物理信息机器学习的最新进展，我们提出通过整合以解析方程形式呈现的气象专业知识，在基于深度学习的后处理模型中实现物理一致性。将该方法应用于瑞士地面天气后处理时发现，通过约束神经网络以强制执行热力学状态方程，可在不降低性能的前提下获得温度与湿度的物理一致预测。该方法在数据稀缺场景下尤为有效，研究结果表明，将领域专业知识融入后处理模型既能优化天气预报信息，又可满足特定应用需求。