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靠统计后处理方法来尽量减少预测误差,这提高了技能,但可能导致预测违反物理原理或无视变量之间的依赖性,这可能会对下游应用和后处理模型的可信赖性造成问题,特别是当后处理模型以新的机器学习方法为基础时。 根据在物理知情的机器学习方面的最新进展,我们建议通过以分析方程式的形式整合气象专门知识,实现深层次学习后处理模型的实际一致性。 应用于瑞士地表气象后处理,我们发现限制神经网络以实施热力学状态方程式,可以对温度和湿度作出符合实际的预测,而不会损害性能。 在数据稀缺时,我们的方法特别有利,我们的调查结果表明,将域专门知识纳入后处理模型可以优化天气预报信息,同时满足具体应用的要求。