We introduce an innovative wavelet-based approach to dynamically adjust the local grid resolution to maintain a uniform specified error tolerance. Extending the work of [4], a wavelet multi-scale approximation is used to make dynamically adaptive the TRiSK model [13] for the rotating shallow water equations on the sphere. This paper focuses on the challenges encountered when extending the adaptive wavelet method to the sphere and ensuring an efficient parallel implementation using mpi. The wavelet method is implemented in fortran95 with an emphasis on computational efficiency and scales well up to O(10 2 ) processors for load-unbalanced scenarios and up to at least O(10 3 ) processors for load-balanced scenarios. The method is verified using standard smooth test cases [22] and a nonlinear test case proposed by [5]. 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.

Abstract. In order to easily enforce solid-wall boundary conditions in the presence of complex coastlines, we propose a new mass and energy conserving Brinkman penalization for the rotating shallow water equations. This penalization does not lead to higher wave speeds in the solid region. The error estimates for the penalization are derived analytically and verified numerically for linearized one-dimensional equations. The penalization is implemented in a conservative dynamically adaptive wavelet method for the rotating shallow water equations on the sphere with bathymetry and coastline data from NOAA's ETOPO1 database. This code could form the dynamical core for a future global ocean model. The potential of the dynamically adaptive ocean model is illustrated by using it to simulate the 2004 Indonesian tsunami and wind-driven gyres.

Abstract. An efficient, local, explicit, second-order, conservative interpolation algorithm between spherical meshes is presented. The cells composing the source and target meshes may be either spherical polygons or latitudelongitude quadrilaterals. Second-order accuracy is obtained by piece-wise linear finite-volume reconstruction over the source mesh. Global conservation is achieved through the introduction of a "supermesh", whose cells are all possible intersections of source and target cells. Areas and intersections are computed exactly to yield a geometrically exact method. The main efficiency bottleneck caused by the construction of the supermesh is overcome by adopting tree-based data structures and algorithms, from which the mesh connectivity can also be deduced efficiently.The theoretical second-order accuracy is verified using a smooth test function and pairs of meshes commonly used for atmospheric modelling. Experiments confirm that the most expensive operations, especially the supermesh construction, have O(N log N ) computational cost. The method presented is meant to be incorporated in pre-or post-processing atmospheric modelling pipelines, or directly into models for flexible input/output. It could also serve as a basis for conservative coupling between model components, e.g., atmosphere and ocean.