A nonlinear explainable method for data-driven forecasting models in Earth system science

Gradient-based eXplainable AI (XAI) methods that leverage automatic differentiation are widely used to reveal predictor-sensitive areas (or rather patterns) and to infer latent physical mechanisms in forecasts. However, these methods heavily rely on linear assumption when calculating gradients, which underrepresent the influence of large-amplitude features in strongly nonlinear Earth system dynamics. To this end, we introduce the conditional nonlinear optimal perturbation (CNOP) method as a novel XAI technique, which can effectively identify crucial sensitive areas that have the profound both nonlinear and linear impact on forecasts. We compare the sensitive areas for forecasts of typhoon tracks and ENSO diversity identified by both CNOP and gradient-based methods within two skillful AI models. CNOP can capture more dominant sensitive patterns in strongly nonlinear phenomena, revealing physical mechanisms of nonlinear development that are more consistent with known dynamical processes. For Earth system processes governed by more linear dynamics, both methods identify similar sensitive areas, indicating the broad applicability and robustness of CNOP. Furthermore, perturbing or denoising CNOP-identified areas produces significantly larger forecast degradations or improvements. These findings highlight nonlinear sensitivity analysis should be incorporated into XAI for Earth system, and CNOP provides a reliable tool to extract physically meaningful mechanisms from AI models.