Koopman Analysis of Sea Surface Temperature with a Signature Kernel

TL;DR

This paper introduces a novel Koopman-based method using signature kernels to analyze and forecast sea surface temperature dynamics, capturing memory effects and improving multi-year prediction accuracy.

Contribution

It develops a trajectory-based Koopman approach with signature kernels for SST, enabling better forecasting and spectral analysis of high-dimensional ocean data.

Findings

Enhanced multi-year SST forecast skill over baseline methods

Revealed coherent spectral modes in SST data

Operates effectively on high-dimensional trajectory segments

Abstract

We develop a trajectory-based Koopman method for sea surface temperature (SST) that lifts annual SST segments using a signature kernel -- a reproducing kernel Hilbert space (RKHS) kernel that compares paths via iterated-integral features -- and learns the one-year shift operator. By operating on annual trajectory segments rather than instantaneous fields, the method encodes finite-time history, which helps capture memory effects in SST-only evolution. The resulting operator improves out-of-sample multi-year forecast skill relative to a climatology baseline and reveals coherent spectral modes. We implement the approach via kernel extended dynamic mode decomposition (EDMD) on signature-kernel Gram matrices, yielding a single pipeline for forecasting and spectral diagnostics of high-dimensional SST dynamics.