Physically Constrained Adaptive Deep Learning for Ocean Vertical-Mixing Parameterization

Existing traditional ocean vertical-mixing schemes are empirically developed without a thorough understanding of the physical processes involved, resulting in a discrepancy between the parameterization and forecast results. The uncertainty in ocean-mixing parameterization is primarily responsible for the bias in ocean models. Benefiting from deep-learning technology, we design the Adaptive Fully Connected Module with an Inception module as the baseline to minimize bias. It adaptively extracts the best features through fully connected layers with different widths, and better learns the nonlinear relationship between input variables and parameterization fields. Moreover, to obtain more accurate results, we impose KPP (K-Profile Parameterization) and PP (Pacanowski–Philander) schemes as physical constraints to make the network parameterization process follow the basic physical laws more closely. Since model data are calculated with human experience, lacking some unknown physical processes, which may differ from the actual data, we use a decade-long time record of hydrological and turbulence observations in the tropical Pacific Ocean as training data. Combining physical constraints and a nonlinear activation function, our method catches its nonlinear change and better adapts to the ocean-mixing parameterization process. The use of physical constraints can improve the final results.