Learning Propagators for Sea Surface Height Forecasts Using Koopman Autoencoders

Due to the wide range of processes impacting the sea surface height (SSH) on daily-to-interannual timescales, SSH forecasts are hampered by numerous sources of uncertainty. While statistical-dynamical methods like Linear Inverse Modeling have been successful at making forecasts, they often rely on assumptions that can be hard to satisfy given the nonlinear dynamics of the climate. Here, we train convolutional autoencoders with a dynamical propagator in the latent space to generate forecasts of SSH anomalies. Learning a nonlinear dimensionality reduction and the prediction timestepping together results in a propagator that produces better predictions for daily- and monthly-averaged SSH in the North Pacific and Atlantic than if the dimensionality reduction and dynamics are learned separately. The reconstruction skill of the model highlights regions in which better representation results in improved predictions: in particular, the tropics for North Pacific daily SSH predictions and the Caribbean Current for the North Atlantic.