Sphere Fusion Forecast (SFF): A Neural Operator–Based Model for Global Weather Forecasting

Weather forecasting is crucial for human activities, yet traditional numerical models often face limitations due to complex physical processes and high computational cost. Deep learning–based neural networks offer a promising alternative. The Spherical Fourier Neural Operator (SFNO) model introduces the Spherical Harmonic Transform to maintain SO(3) rotational invariance, ensuring long-term stability in forecasts and preventing early collapse. However, we have identified two key shortcomings in SFNO: high memory consumption and limited ability to capture high-frequency information due to the truncated of spectrum.

To address these issues, we propose the SFF model, which improves upon the well-known SFNO model primarily in the following ways:

• a) U-Structure: We add up-sampling and down-sampling operators between SFNO blocks, allowing the initial and final stages of the SFNO block chain to handle broader frequency spectra, while the middle layers focus on relatively low-frequency information. Under a limited memory budget, this design enables us to increase the number of SFNO blocks or enlarge the embedding dimension, thereby enhancing forecast accuracy.
• b) Vision Transformer-like Residual Connection: We introduce a Vision Transformer–like architecture between the encoder and decoder as the skip connection, and specialize it to focus on local features. This strengthens the model's ability to capture high-frequency information, enhances its capacity for local feature learning, and leads to more robust and accurate predictions.

 

Considering the discontinuous occurrence and development of precipitation, SFF employs an independent precipitation model which can be easier to learn the physical processes of precipitation and leverages classification weighting to improve the detection and prediction accuracy of heavy rainfall, further extending the effective lead time of precipitation forecasts through joint training.

 

We conducted experiments on ERA5 dataset, using data from 1979–2017 for training, 2018 for validation, and 2020 for testing. The experiment results demonstrate that SFF can generate  stable 30-day forecasts cost-effectively on a single NVIDIA H20 GPU, with key metrics—such as the root mean square error (RMSE) and anomaly correlation coefficient (ACC) for Z500/t2m/t850 comparable to the well-established IFS model, and better than the SFNO model. Meanwhile, for precipitation predictions, SFF also exhibits a forecast skill level comparable to that of the IFS model. Moreover, for heavy rainfall prediction, SFF achieves a Threat Score (TS) of over 0.25 in single-step forecasts for 70 mm of precipitation. After joint training of SFF and the precipitation model, the precipitation score within 10-day forecasts can be improved by 5% compared to direct coupling. This study underscores the potential of Neural Operator–Based AI models in advancing weather forecasting and extreme weather prediction.