Successful numerical weather prediction not only rests upon appropriate modeling of physical processes frequently expressed as partial differential equations and accurate observations used as input data, it also depends on the efficiency and accuracy of the numerical methods. The numerical methods can basically be separated into two groups: finite difference and spectral methods. With the finite difference methods, the spatial and temporal derivatives are evaluated at prescribed points using Taylor series approximations. With the spectral methods, the dependent variables are expressed as the sum of functions that have a prescribed spatial structure and the coefficient associated with each function is generally a function of time. The spectral techniques have been proven extremely worthy in the numerical modeling of the global atmosphere, but have not been used extensively in limited-area models. The atmosphere in a global model is treated as a laterally-closed spherical shell. In contrast, the atmosphere in a limited-area model interacts with its surrounding atmosphere. This open boundary condition is one of the most difficult aspects in limited-area modeling in meteorology. Under this project, a spectral method using the Chebyshev polynomials will be developed for both barotropic and baroclinic limited-area models.
