A theory is developed in a stochastic climate model for understanding the general features of the seasonal predictability barrier (PB), which is characterized by a band of maximum decline in autocorrelation function phase-locked to a particular season. Our theory determines the forcing threshold, timing, and intensity of the seasonal PB as a function of the damping rate and seasonal forcing. A seasonal PB is found to be an intrinsic feature of a stochastic climate system forced by either seasonal growth rate or seasonal noise forcing. A PB is generated when the seasonal forcing, relative to the damping rate, exceeds a modest threshold. Once generated, all the PBs occur in the same calendar month, forming a seasonal PB. The PB season is determined by the decline of the seasonal forcing as well as the delayed response associated with damping. As such, for a realistic weak damping, the PB season is locked close to the minimum SST variance under the seasonal growth-rate forcing, but after the minimum SST variance under the seasonal noise forcing. The intensity of the PB is determined mainly by the amplitude of the seasonal forcing. The theory is able to explain the general features of the seasonal PB of the observed SST variability over the world. In the tropics, a seasonal PB is generated mainly by a strong seasonal growth rate, whereas in the extratropics a seasonal PB is generated mainly by a strong seasonal noise forcing. Our theory provides a general framework for the understanding of the seasonal PB of climate variability.

Improving the prediction skill of El Niño-Southern Oscillation (ENSO) is of critical importance for society. Over the past half-century, significant improvements have been made in ENSO prediction. Recent studies have shown that deep learning (DL) models can substantially improve the prediction skill of ENSO compared to individual dynamical models. However, effectively integrating the strengths of both DL and dynamical models to further improve ENSO prediction skill remains a critical topic for in-depth investigations. Here, we show that these DL forecasts, including those using the Convolutional Neural Networks and 3D-Geoformer, offer comparable ENSO forecast skill to dynamical forecasts that are based on the dynamic-model mean. More importantly, we introduce a combined dynamical-DL forecast, an approach that integrates DL forecasts with dynamical model forecasts. Two distinct combined dynamical-DL strategies are proposed, both of which significantly outperform individual DL or dynamical forecasts. Our findings suggest the skill of ENSO prediction can be further improved for a range of lead times, with potentially far-reaching implications for climate forecasting.

Statistical model results suggest that the declining growth rate from autumn to spring is the key to cause El Niño‐Southern Oscillation (ENSO) spring persistence barrier (SPB). Using a dynamical approach, we develop the physical mechanisms responsible for ENSO SPB in the framework of recharge oscillator by adding a seasonally varying Bjerknes (BJ) stability index and linking it with ENSO growth rate. By decomposing BJ index, it is indicated that seasonal thermodynamic damping and thermocline positive feedback play an important role in determining the ENSO SPB. We further show that the increasing/decreasing upper‐level cloud/low‐level cloud and the deepening thermocline from autumn to spring are the main factors to control the SPB of ENSO. Our proposed mechanisms also have useful implications for the understanding of ENSO prediction.

This paper investigates potential factors that control the El Niño–Southern Oscillation (ENSO) Spring Persistence Barrier (SPB) strength in two different ENSO regimes and apply it to explain the ENSO SPB strength modulation after the 21st century. In a damped, noise‐driven model, the theoretical solution of SPB strength illustrates that a weaker ENSO growth rate strengthens SPB. In the self‐sustained regime, as in the Cane‐Zebiak model (chaotic system), the strengthened thermodynamic damping and weakened thermocline positive feedback lead to a more negative ENSO growth rate and, in turn, a stronger SPB. Therefore, in both ENSO regimes, a weaker ENSO growth rate intensifies the SPB. The application of the theory to the real world suggests that a more negative ENSO growth rate, corresponding to a more damped feedback system, is responsible for the stronger SPB in recent decades than in 1980–2000.