Strategies for Model Reduction: Comparing Different Optimal Bases

Abstract

Several different ways of constructing optimal bases for efficient dynamical modeling are compared: empirical orthogonal functions (EOFs), optimal persistence patterns (OPPs), and principal interaction patterns (PIPs). Past studies on fluid-dynamical topics have pointed out that EOF-based models can have difficulties reproducing behavior dominated by irregular transitions between different dynamical states. This issue is addressed in a geophysical context, by assessing the ability of these strategies for efficient dynamical modeling to reproduce the chaotic regime transitions in a simple atmosphere model. The atmosphere model is the well-known Charney? DeVore model, a six-dimensional truncation of the equations describing barotropic flow over topography in a ?-plane channel geometry. This model is able to generate regime transitions for well-chosen parameter settings. The models based on PIPs are found to be superior to the EOF- and OPP-based models, in spite of some undesirable sensitivities inherent to the PIP method.