Investigation of Rossby and inertia gravity waves based on proper orthogonal decomposition (POD) in beta plain

In the present work properties of Rossby and inertia gravity waves are investigated based on proper orthogonal decomposition (POD) functions. The POD functions are constructed using analytical, experimental or numerical data recorded as snapshots. The POD basis can be carried out to make a reduced order model by Galerkin projection of governing equations onto these functions. In this paper, the analytical solutions of Rossby and inertia gravity waves obtained from linearized shallow water equations (SWEs) are applied to form the POD basis. In order to analyse Rossby and gravity waves based on POD functions, the linearized SWEs are projected onto the POD basis and as a result the partial differential equations are converted to few ordinary differential equations. This reduced order model makes a framework to study the behaviour of Rossby and gravity waves. It was discovered that, in order to capture the dynamics of a Rossby wave 2 POD modes are needed, whereas to capture an inertia gravity wave, 4 POD modes are required. Furthermore, one can predict one Rossby wave accurately up to 120 h using a reduced order model formed by 100 recorded snapshots during 5 h or 24 h of beginning of integration time. However, to predict an inertia gravity wave accurately up to 96 h, 400 snapshots during 0.1 h are needed.