Estimation of Koopman transfer operators for the Equatorial Pacific SST

In many cases, ensembles have been used as an approximation to the probability distribution that has acquired more and more a central role, as the importance of a single trajectory, or member, was recognized as less informative.

This paper shows that using results from the dynamical systems and more recent results from the machine learning and AI communities, we can arrive at a direct estimation of the probability distribution evolution and also at the formulation of predictor systems based on a nonlinear formulation. The paper introduces the theory and demonstrates its application to two examples. The first is a one-dimensional system based on the Nino-3 index; the second is a multidimensional case based on time series of monthly mean SST in the Pacific.