Accurate Subseasonal-to-Seasonal (S2S) forecasting is vital for decision-making in agriculture, energy production, and emergency management. However, it remains a challenging and underexplored problem due to the chaotic nature of the weather system. Recent data-driven studies have shown promising results, but their performance is limited by the inadequate incorporation of climate states and a model tendency to degrade, progressively losing fine-scale details and yielding over-smoothed forecasts. To overcome these limitations, we propose TianQuan-S2S, a global S2S forecasting model that integrates initial weather states with climatological means via incorporating climatology into patch embedding and enhancing variability capture through an uncertainty-augmented Transformer. Extensive experiments on the Earth Reanalysis 5 (ERA5) reanalysis dataset demonstrate that our model yields a significant improvement in both deterministic and ensemble forecasting over the climatology mean, traditional numerical methods, and data-driven models. Ablation studies empirically show the effectiveness of our model designs. Remarkably, our model outperforms skillful numerical ECMWF-S2S and advanced data-driven Fuxi-S2S in key meteorological variables.

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.