Climate-Adaptive and Cascade-Constrained Machine Learning Prediction for Sea Surface Height under Greenhouse Warming
Machine learning (ML) has achieved remarkable success in climate and marine science. Given that greenhouse warming fundamentally reshapes ocean conditions such as stratification, circulation patterns and eddy activity, evaluating the climate adaptability of the ML models is crucial. While physical constraints have been shown to enhance the performance of ML models, kinetic energy (KE) cascade has not been used as a constraint despite its importance in regulating multi-scale ocean motions. Here we develop two sea surface height (SSH) prediction models (with and without KE cascade constraint) and quantify their climate adaptability at the Kuroshio Extension. Both models exhibit only slight performance degradation under greenhouse warming conditions. Incorporating the KE cascade as a physical constraint significantly improves the model performance, reducing eddy kinetic energy errors by 14.7% in the present climate and 15.9% under greenhouse warming. Additional validations using satellite observations and in the Gulf Stream region further confirm the robustness of the proposed models. Compared with the KE spectrum constraint, both constraints improve the cross-scale transfer and spectrum of KE, but the KE cascade constraint yields larger improvements in the cross-scale transfer. This work presents the first application of the KE cascade as a physical constraint for ML-based ocean state prediction and demonstrates its robust adaptability across climates, offering guidance for the further development of global ML models for both present and future conditions.