Toward a Multiscale Approach for Computational Atmospheric Modeling

Abstract

Atmospheric motions are generally characterized by a wide range of multiple length and time scales, and a numerical method must use a fine grid to resolve such a wide range of scales. Furthermore, a very fine grid requires an extremely small time step in order to keep explicit time integration schemes stable. Therefore, high-resolution meteorological simulations are very expensive.A novel multiscale modeling approach is, therefore, presented for simulating atmospheric flows. In this approach, a prognostic variable representing a highly intermittent multiscale feature is decomposed into a significant and a nonsignificant part using wavelets, where the significant part is represented by a small fraction of the wavelet modes. The proposed multiscale methodology has been verified for simulating three cases: Smolarkiewicz's deformational flow model, warm thermals in a dry atmosphere, and the dynamics of a vortex pair with ambient stable stratification. Comparisons with benchmark simulations and with a reference model are evidence for the convergence and stability of the proposed model. The comparison with the reference model has revealed that about 93% of the grid points are not necessary to resolve the significant motion in a warm thermal simulation, saving about 96% of the CPU time. Moreover, the CPU time varies linearly with the number of significant wavelet modes, showing that the present fully implicit adaptive model is asymptotically optimal for this simulation. These primary results point toward the benefit of constructing multiscale atmospheric models using the adaptive wavelet methodology.

A multiscale eddy simulation methodology for the atmospheric Ekman boundary layer

“…Domingues et al 2005, Nordbo andKatul 2013). Alam (2011) developed a wavelet-based multiscale model for thermally driven non-hydrostatic circulations in the dry atmosphere. The work of Farge et al (1999) demonstrates decomposition of a turbulent flow into multiple length scales, whereas the present article employs wavelets to model spatial intermittency in the ABL.…”

“…As a result, all eddies at level s + 1 are decomposed into one group at level s via (2a) and another group representing the missing details at level s via (2b). In the present development, we have used 6 nodes for interpolations in (2a,b), which results in 6th order lifted interpolating wavelets (Sweldens 1997, Alam 2011, Stefano and Vasilyev 2013.…”

“…The overall numerical procedure is an extension of the method that was developed in Alam (2011), where methods for approximating spatial derivatives and implementing boundary conditions are briefly outlined (see also Alam 2006). It is important to note that the proposed MES methodology is not strictly dependent on the spatial discretization adopted in the present work, and can also be extended along with an existing ABL code.…”

“…The maximum value of the Courant-Friedrichs-Lewy (CFL) number is 4 for all simulations presented in this article. On each scale, the discrete nonlinear system is approximated only with 3-5 iterations of the Newton-Krylov algorithm presented in Alam (2011). A dynamically adaptive sparse mesh is obtained naturally from the location of significant eddies.…”

“…We employ the secondgeneration interpolating wavelet transform using the lifting scheme with O(N ) operations (Sweldens 1997), where N is the number of resolved eddies. Using the lifting wavelet transform (Sweldens 1997, Alam 2011, we can extract the position, scale, and strength of an eddy. The significant eddies are resolved, and the insignificant eddies are parameterized, where we have investigated and developed a multiscale parameterization scheme for unresolved motion, as well as a fast multiscale solution algorithm.…”