Developments in Normal Mode Initialization. Part II: A New Method and its Comparison with Currently Used Schemes

Abstract

The analysis of Part I suggested that the temporal characteristics of the nonlinear terms in the equations of motion could introduce convergence problems in currently used schemes for normal mode initialization (NMI). In Part II we 1) introduce a new scheme that is more robust, 2) use a large complex model to verify the existence of problem characteristics in some of the nonlinear parameterizations, and 3) make intercomparisons between new and old schemes. We find that the time scales of some parameterizations used in models of the atmosphere are associated directly with the length of the time step. Some of these parameterizations are used routinely in almost all large numerical models; others provide insight into problems with similar parameterizations. This sensitivity of time scale to time step is due partly to the formulation of the parameterizations, and partly to their highly nonlinear nature and the inconsistency between spectral and grid resolutions in a Galerkin spectral transform model. For the model used here moist and dry convective adjustment, and large scale condensation are primarily responsible for the short time scale forcing. This short time scale forcing is the primary reason for failure of current NMI schemes. The new scheme adjusts to the impact of the forcing on the mode, and converges in situations where the others diverge (during diabatic initializations and initializations of normal modes with small equivalent depths). The Hadley circulation, eliminated in adiabatic initializations, can now be retained. The specification of the moisture field is important in retaining this circulation. The diabatic initialization shows a small improvement over the adiabatic initialization when compared with the balance condition defined by the model itself.