Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the corresponding physical parameters during model configuration can significantly impact the accuracy of model forecasts. There is no combination of physical schemes that works best for all times, at all locations, and under all conditions. It is therefore of considerable interest to understand the interplay between the choice of physics and the accuracy of the resulting forecasts under different conditions.

This paper demonstrates the use of machine learning techniques to study the uncertainty in numerical weather prediction models due to the interaction of multiple physical processes. The first problem addressed herein is the estimation of systematic model errors in output quantities of interest at future times, and the use of this information to improve the model forecasts. The second problem considered is the identification of those specific physical processes that contribute most to the forecast uncertainty in the quantity of interest under specified meteorological conditions. In order to address these questions we employ two machine learning approaches, random forests and artificial neural networks. The discrepancies between model results and observations at past times are used to learn the relationships between the choice of physical processes and the resulting forecast errors.

Numerical experiments are carried out with the Weather Research and Forecasting (WRF) model. The output quantity of interest is the model precipitation, a variable that is both extremely important and very challenging to forecast. The physical processes under consideration include various micro-physics schemes, cumulus parameterizations, short wave, and long wave radiation schemes. The experiments demonstrate the strong potential of machine learning approaches to aid the study of model errors.

复杂的数字天气预报模型包含各种物理过程，每个过程都由具有特定参数的多种替代物理方案描述。在模型配置过程中，物理方案的选择和相应物理参数的选择会严重影响模型预测的准确性。没有任何一种物理方案可以在所有时间，所有地点和所有条件下始终保持最佳状态。因此，非常有必要了解物理选择和在不同条件下所得预测的准确性之间的相互作用。

本文演示了使用机器学习技术来研究由于多个物理过程的相互作用而导致的数值天气预报模型中的不确定性。本文解决的第一个问题是在将来的时间中，对目标输出量中系统模型误差的估计，以及使用此信息来改进模型预测。所考虑的第二个问题是在特定的气象条件下，确定对预期的感兴趣量的不确定性贡献最大的那些特定物理过程。为了解决这些问题，我们采用了两种机器学习方法，即随机森林和人工神经网络。

使用天气研究和预报（WRF）模型进行了数值实验。感兴趣的输出量是模型降水量，该变量对预测非常重要且极具挑战性。正在考虑的物理过程包括各种微物理方案，累积参数化，短波和长波辐射方案。实验证明了机器学习方法有助于研究模型错误的强大潜力。