Data-Driven Modelling and Assimilation of the Sub-Seasonal Evolution of Sea Surface Temperature

Sea Surface Temperature (SST), due to its influence on air-sea interactions, is a critical input into weather models. While physics-based ocean models are continually improving to better represent SST in weather models, data-driven methods offer a promising alternative. In this work, we present an implementation of nonlinear operator inference on a satellite-based SST field (10 km spatial resolution, 1 day temporal resolution) in the northern Indian Ocean, which is known to significantly impact the Indian monsoon. For the prediction of SST, a reduced-order model with a polynomial structure is built non-intrusively from satellite data over a 30-day training period, showing the first five proper orthogonal decomposition modes to capture the SST evolution. A moving-window assimilation scheme utilises the reduced-order model adjoint to correct the prior state, enforcing the model equations over the assimilation window with state observations. Results show that this framework corrects drift, extending the prediction horizon from one week to twenty days. We demonstrate the efficacy of the discovered models using error metrics and their ability to accurately capture lateral SST gradients. Importantly, the inferred operators from the reduced-order model enable the derivation of an explicit adjoint directly from the data, overcoming the computational constraints of General Circulation Models that prohibit rapid adjoint-based assimilation. The performance of the reduced-order model over multiple seasons will also be presented, including the effects of training with data from several years.