Spherical multigrid neural operator for improving autoregressive global weather forecasting

Data-driven approaches for global weather forecasting have shown great potential. However, conventional architectures of these models struggle with spherical distortions, leading to unstable autoregressive forecasts. Although methods such as spherical Fourier neural operator (SFNO) based on spherical harmonic convolution can alleviate these problems, they face the challenge of high computational cost. Here, we introduce a spherical multigrid neural operator (SMgNO) that integrates spherical harmonic convolution and low resolution SFNO in the multigrid framework, effectively alleviating data distortions while requiring few computational resources. Experiments for spherical shallow water equations and medium-range global weather forecasting demonstrate the effectiveness and robustness of SMgNO. For 500 hPa geopotential height with a 7 days lead time, SMgNO achieves a 9.31% and 6.83% improvement in anomaly correlation coefficient over IFS T42 and SFNO, respectively. Furthermore, SMgNO requires only 10% floating-point operations of SFNO for forward propagation and 30.90% less GPU memory than SFNO during training.