Multiresolution wavelet-based simulation of transport and photochemical reactions in the atmosphere

We propose a novel approach for coarsening of computational grids that are used in the modelling of air pollution problems and climate change phenomena at large length scales. The method is based on the use of wavelet transformations. Starting with a fine-scale computational grid, the resolution of which depends on the amount of the experimental data that are available, as well as the topography of the area under study, a wavelet transformation is used to systematically coarsen the grid in those zones in which the fine details of the grid are not necessary, while preserving all the important information and the grid resolution in those regions where large-scale variations in the properties of interest occur. The coarsening can be static and fixed, based on the topography alone, or can be dynamic so as to produce a grid structure that varies with the time. We show that the computations for modelling transport and photochemical reactions (and the associated air pollution problems) with the new approach are orders of magnitude more efficient than the most efficient method currently available, and may render unnecessary use of massively parallel or vectorized computational strategies. To demonstrate the efficiency of the method, we study transport and photochemical reactions of 51 species, involving 117 nonlinear reactions, in the atmosphere of Tehran, Iran, a large urban area with severe air pollution problems.