Speaker

Larry J. Pratt, Ph.D., Senior Scientist, Woods Hole Oceanographic Institution

Koopman Theory Applied to Ocean Data

Abstract

Koopman theory can be useful in the treatment of data from various fields of science and engineering. Applications include the formulation of data-based models, the analysis of data, reduction of order, and handling of certain types of big data. At the heart of the theory is the idea that for many nonlinear models there is an equivalent linear model in which the variables are “observables”. In physical oceanography, these variables consist of state variables (velocity, temperature, etc.) that we observe along with other measurable functions of the state variables: an infinitely long list. The linear model therefore operates in an infinite dimensional space of observation functions whose evolution in time is governed by a linear operator (the Koopman operator). This evlution takes a particularly simple form when voice in terms of the eigenvalues of the operator (Koopman modes) and the Dynamic Mode Decomposition is one method for approximating these modes. I will discuss the theoretical underpinning and implementation of this approach and give an example of application to numerical model data from the western Mediterranean Sea and Strait of Gibraltar, a region characterized by a number of time-dependent, nonlinear processes.