A conservative adaptive wavelet method for the shallow-water equations on the sphere

We introduce an innovative wavelet-based approach to adjust local grid resolution dynamically to maintain a uniform specified error tolerance. Extending the work of Dubos and Kevlahan, a wavelet multiscale approximation is used to make the Thuburn-Ringler-Skamarock-Klemp (TRiSK) model dynamically adaptive for the rotating shallow-water equations on the sphere. This article focuses on the challenges encountered when extending the adaptive wavelet method to the sphere and ensuring an efficient parallel implementation using message passing interface (MPI). The wavelet method is implemented in Fortran 95 with an emphasis on computational efficiency and scales well up to O(102) processors for load-unbalanced scenarios and up to at least O(103) processors for load-balanced scenarios. The method is verified using standard smooth test cases and a nonlinear test case proposed by Galewsky et al. The dynamical grid adaption provides compression ratios of up to 50 times in a challenging homogenous turbulence test case. The adaptive code is about three times slower per active grid point than the equivalent non-adaptive TRiSK code and about four times slower per active grid point than an equivalent spectral code. This computationally efficient adaptive dynamical core could serve as the foundation on which to build a complete climate or weather model.