An Online Spectral Nudging-Based Correction System: Improving Physical Model Forecasts by Incorporating Large-Scale Circulations Derived from Machine Learning Models

Abstract. Traditional numerical weather prediction (NWP) models are constrained by limitations in the representation of physical processes and computational resources, resulting in lengthy development cycles and relatively slow improvements in forecast skill. In recent years, machine learning (ML)-based weather forecasting models have advanced rapidly, and in some aspects, outperform traditional physical models, particularly in forecasting large-scale circulation. However, these ML-based models suffer from notable deficiencies, such as over-smoothing in forecasts and inadequate capability for predicting extreme weather events. In this study, an online correction system based on the spectral nudging (SN) method is developed. In this system, the China Meteorological Administration Global Forecast System (CMA-GFS) is used as the foundational physical model, and a correction term is integrated into the governing equations, such that during numerical integration, the large-scale circulation is constrained to evolve toward the forecasts produced by the ML model FuXi. The performance of the hybrid system on large-scale circulation prediction is comparable to that of the FuXi model, with a substantial extension of forecast leading time and a marked improvement in the stability of forecast skill. Verification against high-impact weather events, including heavy rainfall and tropical cyclones, demonstrates that the hybrid system integrates the strengths of the FuXi model in forecasting circulation patterns, precipitation distribution and tropical cyclone tracks, while preserving the advantages of the CMA-GFS in representing precipitation intensity, tropical cyclone intensity and fine-scale details. Thus, the system demonstrates robust forecasting capability for extreme weather. This proof-of-concept study verifies that the SN-based method can effectively integrate the complementary strengths of ML and physical models, providing a new pathway for the operational NWP.