Skillful subseasonal forecasts beyond 2 weeks are crucial for a wide range of applications across various sectors of society. Recently, state-of-the-art machine learning based weather forecasting models have made significant advancements, outperforming the high-resolution forecast (HRES) from the European Centre for Medium-Range Weather Forecasts (ECMWF). However, the full potential of machine learning models in subseasonal forecasts has yet to be fully explored. In this study, we introduce FuXi Subseasonal-to-Seasonal (FuXi-S2S), a machine learning based subseasonal forecasting model that provides global daily mean forecasts up to 42 days, covering 5 upper-air atmospheric variables at 13 pressure levels and 11 surface variables. FuXi-S2S integrates an enhanced FuXi base model with a perturbation module for flow-dependent perturbations in hidden features, and incorporates Perlin noise to perturb initial conditions. The model is developed using 72 years of daily statistics from ECMWF ERA5 reanalysis data. When compared to the ECMWF Subseasonal-to-Seasonal (S2S) reforecasts, the FuXi-S2S forecasts demonstrate superior deterministic and ensemble forecasts for total precipitation (TP), outgoing longwave radiation (OLR), and geopotential at 500 hPa (Z500). Although it shows slightly inferior performance in predicting 2-meter temperature (T2M), it has clear advantages over land area. Regarding the extreme forecasts, FuXi-S2S outperforms ECMWF S2S globally for TP. Furthermore, FuXi-S2S forecasts surpass the ECMWF S2S reforecasts in predicting the Madden Julian Oscillation (MJO), a key source of subseasonal predictability. They extend the skillful prediction of MJO from 30 days to 36 days.
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