Towards a wavelet-based dynamically adaptive climate model

Dynamically adaptive climate or weather models have the potential to significantly improve the accuracy and efficiency of climate models by refining or coarsening the computational grid as needed to ensure uniform numerical accuracy at all times and locations (or to provide more resolution where desired).  However, such models have not yet become operational because of challenges in conserving desirable mimetic properties of the underlying numerical scheme and concerns about physical subgrid scale parameterizations.

In a series of papers (Kevlahan, Dubos, Aechtner 2015; Aechtner, Kevlahan; Dubos 2015, Dubos and Kevlahan 2013) we have developed a general framework for a wavelet-based multiscale dynamically adaptive climate model. This method is based on iterative dyadic refinement of the icosahedron, which generates a sequence of approximation subspaces (i.e. different grid levels) with arbitrarily fine local resolution determined by a single parameter that controls the errors in the tendencies at each time step. Biorthogonal wavelets are used to measure local error and to restrict or prolongate fluxes between different grid levels. The adaptivity is designed to preserve the mimetic properties (such as mass conservation) of the underlying discretization.  The grid is adapted horizontally using the strictest condition over all vertical layers and the Lagrangian vertical coordinates are conservatively remapped as required onto the initial grid (Chen 2013), or onto an optimized isopycnal grid (in the case of ocean models). For the shallow water equations we have developed a Brinkman type penalization technique to approximate no-slip lateral boundary conditions. 

I will present results from the 2D shallow water equations (e.g. tsunami propagation) and a number of validations of the 3D code (e.g. from the DCMIP test case series). The goal of this project is to help assess the potential of dynamical adaptivity to improve the computational performance and numerical accuracy of climate models.