Reduced order modeling of the upper tropical Pacific ocean model using proper orthogonal decomposition
Yanhua Cao, Jiang Zhu, Zhedong Luo, Navon, I.M.
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, 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 construct 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 is well captured by a low dimensional system of order of 22, which is constructed using 20 snapshots and 7 leading POD basis functions. (2) the RMS errors for the upper ocean layer thickness of the POD model of order of 22 are less than 1m that is less than 1% of the average thickness and the correlations between the upper ocean layer thickness with that from the POD model is around 0.99. (3) Retaining modes that capture 99% energy is necessary in order to construct POD models yielding a high accuracy.
Key words POD, reduced order model, PDE, Galerkin methods, ODE. AMS subject classifications 76N10, 65K10, 49J20, 35C10.