Reduced Order Modeling of the Upper Tropical Pacific Ocean Model Using Proper Orthogonal Decomposion

The proper orthogonal decomposition (POD) is shown an efficiently model reduction technique in simulating physical processes governed by partial differential equations. In this paper we make an initial effort to investigate problems related to POD reduced modeling of a large-scale upper ocean circulation in the tropic Pacific domain. We constructed different POD models with different choices of snapshots and different number of POD basis functions. The results from these different POD models are compared with that of the original model. The main findings are: (1) the large-scale seasonal variability of the tropic Pacific obtained by the original model can be captured well by a low dimensional system of order of 22, which is constructed by 20 snapshots and 7 leading POD basis functions. (2) RMS errors for the upper ocean layer thickness of the POD model of order of 22 is less than 1m that is less than 1from the POD model is around 0.99. (3) The modes that capture 0.99 energy are necessary to construct POD models in order to yield a high accuracy.