Modelling of Shallow Water Equations and the Weather Research and Forecasting Model (WRF)

The goal of this report is to analyze various computational techniques applied to model physical phenomena in the area of oceanography and atmospheric sciences. Cases are discussed, wherein, mathematical models are developed using the programming language MATLAB followed by implementing NCAR’s (National Center for Atmospheric Research) WRF (Weather Research and Forecasting) model consisting of built in code and physics modeling capabilities. Before numerical modelling is carried out, various problems of interest, issues and generalized models regarding dynamics of coastal basins are put forth. Shallow water equations (SWE) form a reasonable starting point as far as modelling of physical, biological and chemical processes in lakes and coastal basins are concerned. Finite difference and Fourier methods along with various numerical schemes implemented to model SWE’s are compared and analyzed. A small discussion on the implementation of an advantageous MATLAB function profile is provided. Producing results of idealized cases within the WRF model is carried out to test the modelling capabilities, especially, in light of capturing the physics. Studying the boundary layer parametrizations of the WRF model along with a brief description of the Large-Eddy Simulation (LES) configuration is discussed.