Comparison of optimized Dynamic Mode Decomposition vs POD for the shallow water equations model reduction with large-time-step observations

We propose a framework for dynamic mode decomposition of 2D flows, when numerical or experimental data snapshots are captured with large time steps. Such problems originate for instance from meteorology, when a large time step acts like a filter in obtaining the significant Koopman modes, therefore the classic dynamic mode decomposition method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and POD dynamic modes. We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) to derive reduced-order models of Shallow Water Equations (SWE). A new algorithm for extracting the dominant Koopman modes of the flow field and a new criterion of selecting the optimal Koopman modes are proposed. A quantitative comparison of the spatial modes computed from the two decompositions is performed and a rigorous error analysis for the ROM models obtained by the classic POD and the optimized DMD is presented. Copyright © 2014 John Wiley & Sons, Ltd.