AbstractSubstantial numerical difficulties associated with the computational modeling of multiscale global atmospheric chemical transport impose severe limitations on the spatial resolution of nonadaptive fixed grids. The crude spatial discretization introduces a large amount of numerical diffusion into the system, which, in combination with strong flow stretching, causes large numerical errors. To resolve this issue, we have developed an optimized wavelet‐based adaptive mesh refinement (OWAMR) method. The OWAMR is a three‐dimensional adaptive method that introduces a fine grid dynamically only in the regions where small spatial structures occur. The algorithm uses a new two‐parameter adaptation criterion that significantly (by factors between 1.5 and 2.7) reduces the number of grid points compared with the more conventional one‐parameter grid adaptation used by wavelet‐based adaptive techniques and high‐order upwind schemes, which enable one to increase the accuracy of approximation of the advection operator substantially. It has been shown that the method simulates the dynamics of a pollution plume that travels on a global scale, producing less than 3% error. To achieve such accuracy, conventional three‐dimensional nonadaptive techniques would require five orders of magnitude more computational resources. Therefore, the method provides a realistic opportunity to model accurately a variety of the most demanding multiscale problems in the area of atmospheric chemical transport, which are difficult or impossible to simulate on existing computational facilities with conventional fixed‐grid techniques.