Prediction and correction of ENSO using an intelligent Air-Sea coupling model based on the Transformer architecture

El Niño-Southern Oscillation (ENSO), as the most prominent interannual variability signal in the climate system, exerts significant impacts on global weather and climate. Under global warming, ENSO evolution has increasingly exhibited the characteristics of complex and diverse rendering its simulation and prediction a particularly challenging subject within climatology. This study introduces 3D-Geoformer, an advanced multi-variable intelligent prediction model for the tropical sea-air system based on Transformer architecture, to conduct error analysis and correction research for ENSO predictions. Unlike many existing models that focus solely on univariate fields or time series related to ENSO, the 3D-Geoformer model achieves accurate characterization and prediction of the multi-variable three-dimensional field of the tropical Pacific sea-air system while preserving the integrity of the physical processes essential for ENSO prediction. To address specific issues in ENSO predictions by the 3D-Geoformer model, such as low spring forecasting skills, weak SST forecasting ability in the western equatorial Pacific, and inadequate forecasting intensity for extreme ENSO events, this study proposes a seasonal forecasting error correction technique based on empirical orthogonal function (EOF) decomposition. This method is applied to correct the prediction results of the 3D-Geoformer model. During the construction phase of the correction relationship, EOF analysis was used to establish the linear relationship between the principal component sequences of the multivariable prediction field and the prediction error field from 1983 to 2009. Subsequently, this relationship was utilized for subsequent error corrections. In the testing phase, the EOF principal component coefficients of the prediction field and their linear relationships with the main components of the error were employed to calculate the corresponding principal components of the prediction error, thereby obtaining the prediction error field and the corrected prediction field. The experimental results indicate that when the 3D-Geoformer model is employed for forecasting the sea - surface temperature (SST) in the western equatorial Pacific, the prediction error remains below 0.15 °C. Notably, the prediction bias of the 3D-Geoformer model regarding the sea temperature in the western equatorial Pacific, induced by the “cold tongue bias” inherent in climate models, is substantially mitigated. Concurrently, there is a remarkable 46.7% reduction in the prediction error of the sea-surface temperature (SST) in the central and eastern equatorial Pacific. Through a meticulous comparison of the disparities in the anomaly correlation coefficients (ACC) between the SST prediction outcomes of the 3D-Geoformer model with and without Empirical Orthogonal Function (EOF) correction in the equatorial Pacific, it is discerned that positive-value regions are consistently present in the ACC differences. This finding strongly suggests that the EOF-corrected model exhibits enhanced prediction accuracy, effectively alleviating the “cold tongue bias” issue arising from the utilization of climate model data from the Sixth Coupled Model Inter-comparison Project (CMIP6) during the training phase of the 3D-Geoformer model. For the 2015−2016 El Niño event, forecast corrections made 12 months in advance show that the SST error in the western equatorial Pacific is controlled within 0.5°C, and the SST error in the eastern equatorial Pacific is reduced by approximately 75%, with the error range narrowed to within ±0.5°C. This study underscores the application value of the seasonal forecast error correction method based on EOF decomposition in enhancing model prediction accuracy, providing a novel approach to improving the precision of ENSO intelligent predictions, and offering new insights into simulation prediction and error analysis in earth science.