Application of Wavelet-based Adaptive Mesh Refinement for Global Atmospheric Chemical Transport Modeling

Accurate numerical modeling of global atmospheric chemical transport presents enormous computational difficulties associated with simulating a wide range of time and spatial scales. These difficulties are exacerbated by the fact that hundreds of chemical species and thousands of chemical reactions are typically used for atmospheric chemical kinetics description. Therefore such numerical simulations are very computationally expensive. As a consequence, relatively crude uniform or quasi-uniform numerical grids with poor spatial resolution that introduces large amount of numerical diffusion into the system are often used for atmospheric chemical transport calculations. It was demonstrated that this spurious diffusion significantly distorts the predictions of pollutant mixing and transport dynamics when a typical grid resolution is used.

In this work we consider a dynamic multilevel Wavelet-based Adaptive Mesh Refinement (WAMR) method for numerical modeling of the atmospheric chemical transport. The adequate spatial resolution is achieved in a computationally inexpensive way by dynamically adding small-scale wavelets in the locations of rapid variation and by coarsening the computational grid in regions where the solution is smooth. The error estimates for the numerical solution are developed and used in conjunction with appropriate refinement criteria to adapt the non-uniform computational grid. The algorithm uses an efficient wavelet spatial discretization, which allows a minimization of the number of degrees of freedom for a prescribed accuracy, a fast algorithm for computing wavelet decomposition and accurate derivative approximations on an irregular grid.

The developed algorithm has been tested for several benchmark problems including numerical simulation of transpacific travel of inert and reactive pollution plumes. The generated plumes are diluted due to turbulent mixing as they advect downwind. Despite this dilution, it was recently discovered that pollution plumes in the remote troposphere can preserve their identity as well-defined structures for two weeks or more as they circle the globe. Presently used Global Chemical Transport Models (CTMs) implemented for uniform or quasi-uniform grids are incapable of reproducing these layered structures because of the large numerical diffusion smearing the physical non-uniformity of atmospheric flows.

The numerical results obtained with the WAMR algorithm have been compared with conventional CTM calculations. It is shown that WAMR solutions with the accuracy comparable to that of conventional numerical techniques are obtained with several orders of magnitude reduction in the number of grid points. Therefore the adaptive algorithm is capable of producing accurate results at a relatively low computational cost. It is also demonstrated that unlike conventional numerical methods that utilize quasi-uniform numerical grids WAMR algorithm applied to traveling plumes accurately reproduces their dynamics over their complete life-time.

This work is supported by a National Science Foundation grant under Award No. HRD-1036563.