Proper orthogonal decomposition reduced-order model of a hydrostatic atmosphere

Abstract: A reduced-order model (ROM) of the global atmosphere is developed by projecting the hydrostatic equations of motion onto a proper orthogonal decomposition (POD) basis. This approach transforms a system of partial differential equations dependent upon time and space into a system of ordinary differential equations dependent upon time and POD mode index, massively reducing the dimensionality of the problem. Here, we adopt the Climate Analysis Forecast Ensemble (CAFE) reanalysis dataset, comprising 96 realizations of the dynamically coupled atmosphere and ocean each month. Two POD bases are calculated from the atmospheric data: one for the velocity vector field and another for the scalar temperature field. The POD ROM coefficients are then calculated using a regression approach. Temporal integrations of the POD ROM are able to broadly capture the variability of the underlying atmospheric fields at a fraction of the computational cost. Keywords: Atmosphere, Hydrostatic, Proper Orthogonal Decomposition, Reduced-Order Model