Fig. 3: Strategy 2, dynamical-DL based on “First-Guess”.

The colorful and black lines indicate the prediction skill of each dynamical model (a–h) and the dynamic-model mean (i) for the year-round ACC during 1982–2018. The solid lines indicate the prediction skill of the all-ensemble mean. The thin dashed-dot lines indicate the prediction skill based on Strategy 2, where the “Truth” value (i.e., the observation) is an indicator (sub-ensemble members are 50% of all-ensemble members). And the dashed (CNN) and dot (3D-Geoformer) lines indicate the prediction skill based on Strategy 2, where the results of DL models are used as indicators (sub-ensemble members are 50% of all-ensemble members). The shading around the lines denotes the 95% confidence interval, based on the bootstrap method.