WHOI PO

Title: Applying Koopman Theory to  Oceanographic Data

Abstract: Koopman theory can be useful in thetreatment of data from various fields of science and engineering. Applications include the formulation of data-based models, the analysisof data, the reduction of order, and the handling of certain types of big data.  At the heart of the theory is the idea that for many nonlinear modelsthere is an equivalent linear model in which the variables are"observables".   In physical oceanography, these variablesconsist of state variables (velocity, temperature, etc.)  that we observealong with other measurable functions of the state variables: an infinitelylong list. The linear model therefore operates in an infinite dimensional spaceof observation functions whose evolution in time is governed by a linearoperator (the Koopman operator).  This evolution takes a particularlysimple form when voiced in terms of the eigenvalues of the operator (Koopmanmodes) and the Dynamic Mode Decomposition is one method for approximating thesemodes.   I will discuss the theoretical underpinning and implementation ofthis approach and give an example of application to numerical model data fromthe western Mediterranean Sea and Strait of Gibraltar, a region characterizedby a number of time-dependent, nonlinear processes.