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Accurately predicting sea-surface temperature weeks to months into the futureis an important step toward long term weather forecasting. Standardatmosphere-ocean coupled numerical models provide accurate sea-surfaceforecasts on the scale of a few days to a few weeks, but many important weathersystems require greater foresight. In this paper we propose machine-learningapproaches sea-surface temperature forecasting that are accurate on the scaleof dozens of weeks. Our approach is based in Koopman operator theory, a usefultool for dynamical systems modelling. With this approach, we predict seasurface temperature in the Gulf of Mexico up to 180 days into the future basedon a present image of thermal conditions and three years of historical trainingdata. We evaluate the combination of a basic Koopman method with aconvolutional autoencoder, and a newly proposed "consistent Koopman" method, invarious permutations. We show that the Koopman approach consistentlyoutperforms baselines, and we discuss the utility of our additional assumptionsand methods in this sea-surface temperature domain.

Analyzing Koopman approaches to physics-informed machine learning for long-term sea-surface temperature forecasting