  Accurately predicting sea-surface temperature weeks to months into the future
is an important step toward long term weather forecasting. Standard
atmosphere-ocean coupled numerical models provide accurate sea-surface
forecasts on the scale of a few days to a few weeks, but many important weather
systems require greater foresight. In this paper we propose machine-learning
approaches sea-surface temperature forecasting that are accurate on the scale
of dozens of weeks. Our approach is based in Koopman operator theory, a useful
tool for dynamical systems modelling. With this approach, we predict sea
surface temperature in the Gulf of Mexico up to 180 days into the future based
on a present image of thermal conditions and three years of historical training
data. We evaluate the combination of a basic Koopman method with a
convolutional autoencoder, and a newly proposed "consistent Koopman" method, in
various permutations. We show that the Koopman approach consistently
outperforms baselines, and we discuss the utility of our additional assumptions
and methods in this sea-surface temperature domain.
