Physics-Constrained Machine Learning Model Enhances Weather Forecast Accuracy and Physical Consistency

Data-driven weather forecasting models, such as FuXi and Pangu-Weather, have made significant advancements in global forecasting accuracy and computational efficiency. However, these models lack physical constraints, a limitation that traditional numerical weather prediction (NWP) models address through the dynamical core and physical parameterization schemes. Recent efforts, like NeuralGCM and PINNs, have successfully integrated the dynamical core or Navier-Stokes equations with machine learning models. Yet, effective integration of physical parameterization schemes remains uncharted in this field, primarily due to the greater uncertainty and complexity of physical processes compared to the dynamical core. To bridge this gap, we integrated the shortwave radiative transfer scheme with FuXi, by modeling the Rapid Radiative Transfer Model for General Circulation Models Applications (RRTMG) as a neural network. This represents the first successful integration of a physical parameterization scheme with large-scale weather forecasting models. This integration yielded substantial improvements in forecasting performance and physical consistency, reducing root mean square error (RMSE) by approximately 15% for radiatively related variables, such as albedo and cloud water mixing ratio, especially for longer lead times.  Moreover, the optimized model demonstrated significantly enhanced atmospheric moisture energy conservation.  This work provides a promising pathway for integrating physical processes into machine learning based weather forecasting models, paving the way for more accurate and physically consistent weather forecasts.