A Wavelet–Based Approach for Atmospheric Pollution Modeling: Algorithm Development

Abstract

A wavelet-based technique for numerical integration of species-conservation equations describing atmospheric pollutant transport and fate is described. This technique applies hexuplet families of spline-based biorthogonal wavelets using a quasi-Galerkin approach. The wavelet families described here are advantageous because, in addition to their biorthogonal character, they satisfy special relationships enabling straightforward evaluation of function derivatives. Moreover, the compact nature of the wavelets suggests the possibility of performing chemistry calculations efficiently in the wavelet-transform domain. The present article describes the selected wavelet families, their derivative relationships, and the proposed methods for their numerical application. In addition, it presents some simple numerical-integration tests to demonstrate the method and examines the method?s potential for performing chemistry calculations in the wavelet domain. More extensive application of the wavelet-based method is the subject of ongoing research, which will be reported at a later date.