Optimized wavelet‐based adaptive mesh refinement algorithm for numerical modeling of three‐dimensional global‐scale atmospheric chemical transport

Abstract

Substantial 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.

Islet: interpolation semi-Lagrangian element-based transport

“…Remapping among subcomponent grids is less common. Recent examples include separate physics parameterizations and dynamics grids in the atmosphere (Herrington et al, 2019;Hannah et al, 2021); adaptive mesh refinement (AMR) of a tracer (Chen et al, 2021;Semakin and Rastigejev, 2020); and local vertical refinement in physics parameterizations relative to the shared background vertical grid, the Framework for Improvement by Vertical Enhancement (FIVE) (Yamaguchi et al, 2017;Lee et al, 2020).…”

Islet: Interpolation semi-Lagrangian element-based transport

“…These act together as the physics parameterizations subcomponent, and the dycore is the other subcomponent of the atmosphere component. Recent examples in atmosphere models of remapping data among multiple subcomponent grids include separate physics parameterizations and dynamics grids in the atmosphere (Herrington et al, 2019;Hannah et al, 2021); adaptive mesh refinement (AMR) of a tracer (Chen et al, 2021;Semakin and Rastigejev, 2020); and local vertical refinement in physics parameterizations relative to the shared background vertical grid, the Framework for Improvement by Vertical Enhancement (FIVE) (Yamaguchi et al, 2017;Lee et al, 2020). We use the ideas in Hannah et al (2021) directly in this article.…”

Adaptive Wavelet Methods for Earth Systems Modelling

“…Adaptive wavelet methods for geophysical flows have been limited primarily to the two-dimensional shallow water equations on the plane [24][25][26], and small-scale twodimensional test cases of small scale atmospheric convection [27] and atmospheric boundary layer flow [28]. In addition, a wavelet method has been proposed for three-dimensional atmospheric chemical transport in flat topology [29]. To date, the only global adaptive wavelet models of atmosphere and ocean flow are our WAVETRISK family of models that will be reviewed in Section 4 [30][31][32][33].…”