Fig. 4: Robustness of artificial neural networks (ANNs) in future emission scenarios confirmed by the model-as-truth approach.

a ANN-estimated (red line) and Coupled Model Intercomparison Project (CMIP)-modeled (black line) El Niño-Southern Oscillation (ENSO) sea surface temperature (SST) amplitudes when climate model data are treated as observations. Using the GISS-E2-1-H model as an example, its historical SST mean state is input into the ANNs as synthetic observational data. In the left panel, the ANN estimate shows a strong correlation with the GISS-E2-1-H historical simulations (HIS denotes the historical period; root-mean-square error = 0.05 °C, r = 0.91, p < 0.001). When the future SST mean state from the same model is fed into the ANNs, the estimate remains closely aligned with the model’s projected ENSO SST amplitudes (SSP126-585 denotes the future period across the Shared Socioeconomic Pathway (SSP)1-2.6 to SSP5-8.5 scenarios; root-mean-square error = 0.06, r = 0.90, p < 0.001). The right panel shows the probability density function (fitted to Gaussian distributions) of the bias in projected ENSO SST amplitudes. Thus, when treating GISS-E2-1-H climate model data as pseudo-observations, the uncertainty between ANN-based projections and direct model simulations measures 0.01 ± 0.05 °C across SSP1-2.6 to SSP5-8.5 scenarios. b Correlation coefficients between ANN-estimated and CMIP-modeled ENSO SST amplitudes for historical (blue bars) and future (red bars) periods. The x-axis indicates the climate model simulation treated as synthetic observations. Excluding the climate model simulations subject to unrealistic ENSO physics (shading; these three models perform the worst against observational data and have the largest BJ index errors), ANNs that reproduce the historical response of ENSO SST amplitudes to mean state changes retain their skill under future scenarios. The dashed line represents the historical ANN performance on real observational data. The dependence of future ANN performance on historical skill in the model-as-truth approach suggests that ANNs validated against real-world observations are likely to be robust for real-world future projections.