ABSTRACT

We present a study of the Proper Orthogonal Decomposition technique from the perspective of spectral theory of dynamical systems. It is shown that spectral properties of the so called Koopman operator can be translated into a new kind of the decomposition that we call the Mixed Orthogonal Decomposition. This new decomposition separates periodic, predictable part of the dynamics from the aperiodic, stochastic part that is treated using the standard Proper Orthogonal Decomposition. Consequences for predictability of oceanographic processes are discussed. The use of the technique for modelling Lagrangian processes in the ocean is presented.