Reduced order ocean model using proper orthogonal decomposition

Abstract

The proper orthogonal decomposition (POD) is shown to be an efficient model reduction technique for simulating physical processes governed by partial differential equations. In this paper, a POD reduced model of a barotropic ocean circulation for coastal region domains was made. The POD basis functions and the results from this POD model were constructed and compared with that of the original model. The main findings were: 1) the variability of the barotropic circulation obtained by the original model is well captured by a low dimensional system of order of 22, which is constructed using 15 snapshots and 7 leading POD basis functions; 2) the RMS errors for the POD model is of order 10$^{ - 4}$ and the correlations between the original results with that from the POD model of more than 0.99; 3) the CPU model time solution is reduced is five times less than the original one; and 4) it is necessary to retain modes that capture more than 99% of the energy is necessary in order to construct POD models yielding a high accuracy.