JuliaCon 2026

Physical effects in oceans span a vast range of both temporal and spatial scales, making it difficult to ensure that a single numerical model resolves all relevant processes within realistic computational limits. To capture effects that occur outside of the resolved scales, models need to include parameterizations that approximate the missing physics. In this work, we explore the use of online learning for parameterizations in a Julia based shallow water model.

Here we use ShallowWaters.jl, a single layer ocean model, to test the capabilities of online learning for eddy backscatter parameterizations. Backscatter parameterizations represent the influence of geostrophic eddies, small-scale turbulent processes that play a large role in ocean energy dynamics. In particular, eddies facilitate the transfer of kinetic energy from small to large scales, an essential process for general ocean circulation. In the online learning framework our backscatter parameterization is given by a neural network (NN), converting ShallowWaters into a hybrid ocean model based on both physics and machine learning. To train the NN parameterization to capture sub-grid scale physics we use data assimilation techniques, and in particular this relies on the automatic differentiation (AD) tool Enzyme.jl to compute full-model gradients. This further expands ShallowWaters to be a fully differentiable shallow water model. Different loss functions are implemented, both spectral and state, to determine which most effectively improves the parameterization, and the resulting NN parameterizations are compared to an equation-discovery closure. This work expands on prior online learning research and further advances hybrid approaches for gradient-based model calibration in comprehensive, differentiable, ocean general circulation models.