Fig. 3: Projected changes in parameters of two-box recharge oscillation model and theirs effect of spring predictability barrier strength.

a, b The mean values of (a) \({a}_{21}\) (unit: month⁻¹) and b \({a}_{22}\) (unit:  °Cm⁻¹) month⁻¹) in different Coupled Model Intercomparison Project Phase 6 (CMIP6) models over present-day (blue bars) and future (red bars) climate. Error bars are calculated as 1.0 standard derivation of 10,000 inter-realizations of a bootstrap method (see bootstrap test in Methods). Models that are opposite to the multi-model mean result are marked in white shading. c The central Pacific (CP) El Niño-Southern Oscillation (ENSO) persistence barrier (x-axis) and spring predictability barrier (SPB; y-axis) difference against different damping rates (\({a}_{21}\)) and the coupling coefficients between T and h (\({a}_{22}\)). The difference is calculated relative to the case when \({a}_{21}\) is −0.05 month⁻¹ and \({a}_{22}\) is 0.0098  °Cm⁻¹ month⁻¹. The red dots (light to dark) and arrow indicate \({a}_{21}\) ranging from −0.02 to −0.15 month⁻¹. The blue dots (light to dark) and arrow indicate \({a}_{22}\) ranging from 0.0084 to 0.011  °Cm⁻¹ month⁻¹.