Abstract: We compare scalare and vector transform methods for global spectral models of the shallow-water equations. For the scalar transform methods, we demonstrate some economies in the number of Legendre transforms required. It ...

Abstract: Orthogonal vertical normal modes are found for a multilevel sigma-coordinate model, linearized about a state of rest with a nonisothermal mean temperature profile. Orthogonality permits the partitioning of energy into the ...

Abstract: The application of variational normal mode initialization to the ECMWF multilevel grid-point model is described. The technique involves minimizing a variational integral of the changes made by the initialization to the ...

Abstract: It is shown that nonlinear normal mode initialization (NMI) can be implemented without knowing the normal modes of a model. The implicit form of nonlinear NMI is particularly useful for models whose normal modes cannot ...

Abstract: Implicit nonlinear normal mode initialization schemes enable nonlinear NMI to be performed in models whose normal modes cannot readily be computed. Such schemes are algebraically equivalent to conventional (?explicit?) NMI ...

Abstract: It is shown that implicit normal mode initialization can be combined with a variational technique, in order to control the relative magnitudes of the changes to the analyzed mass and wind fields. Since the initialization ...

Abstract: We present the firm application of the semi-implicit semi-Lagrangian integration technique to a finite-element barotropic model using the shallow-water equations on a variable-resolution. Two schemes based on this approach, ...

Abstract: In a previous study based on the shallow-water equations, it was shown that nonlinear normal mode initialization (NMI) can be implemented without knowing the normal modes of a model; this implicit form of nonlinear NMI is ...

Abstract: In Part II of this paper, we describe the nonlinear normal mode initialization applied to the ECMWF multilevel global grid-point model and show that the procedure is highly successful in eliminating spurious high-frequency ...

Abstract: In Part I of this paper we review initialization methods for numerical weather prediction models, leading up to the development of schemes based on the normal modes of the forecast model. We present the derivation of the ...