Filtering Integration Schemes Based on the Laplace and Z Transforms

Abstract

A filtering integration scheme based on a modification of the inversion integral for the Laplace transform (LT) is developed and implemented in a barotropic limited-area model. The LT scheme is compared to a conventional scheme and shown to simulate faithfully the low-frequency evolution of the atmosphere while eliminating high-frequency oscillations. The scheme is combined with a Lagrangian treatment of advection giving stable integrations for long time steps. Simple perturbation experiments show that the LT model can absorb an imposed disturbance without data shock. It is superior in this respect to more conventional schemes and may prove useful for asynoptic data assimilation. An alternative formulation of the filtering scheme using the Z transform is described. This techniques applied to a system of equations that have been discretized with respect to time. The Z-transform scheme is shown to behave in a manner similar to the Laplace-transform scheme.