Long-term stability stands as a crucial requirement in data-driven medium-range global weather forecasting. Spectral bias is recognized as the primary contributor to instabilities, as data-driven methods difficult to learn small-scale dynamics. In this paper, we reveal that the universal mechanism for these instabilities is not only related to spectral bias but also to distortions brought by processing spherical data using conventional convolution. These distortions lead to a rapid amplification of errors over successive long-term iterations, resulting in a significant decline in forecast accuracy. To address this issue, a universal neural operator called the Spherical Harmonic Neural Operator (SHNO) is introduced to improve long-term iterative forecasts. SHNO uses the spherical harmonic basis to mitigate distortions for spherical data and uses gated residual spectral attention (GRSA) to correct spectral bias caused by spurious correlations across different scales. The effectiveness and merit of the proposed method have been validated through its application for spherical Shallow Water Equations (SWEs) and medium-range global weather forecasting. Our findings highlight the benefits and potential of SHNO to improve the accuracy of long-term prediction.

引入球谐神经算子 (SHNO) 的研究以改善长期迭代预测，通过减轻球面数据的扭曲并纠正由虚假相关引起的谱偏差，通过应用于球面浅水方程 (SWEs) 和中长期全球天气预报验证了其有效性和优点，强调了 SHNO 提高长期预测准确性的潜力。

数据驱动的全球中期气象预报的长期预测精度提升