A majority of numerical schemes used in computational fluid dynamics are based on finite-difference methods. Despite the sophistication currently allowed by finite-difference methods, they suffer from certain shortcomings when applied to meteorological problems. For example, many schemes result in damping of important waves, inaccurate phase speeds, and computational instabilities [1,2]. Certain computational instabilities can be handled by addition of terms (e.g., artificial viscosity) which may not be entirely representative of the physics of the problem. Other notable shortcomings of finite-difference methods for spatial discretization include the difficulty in accurately describing complex domains, the inability to easily employ nonuniform and nonrectangular meshes in the interest of computational efficiency, and the complexity involved in developing higher order approximations to achieve solution accuracy.