An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with near-optimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.
AbstractThe formulation of a fully compressible nonhydrostatic atmospheric model called the Model for Prediction Across Scales–Atmosphere (MPAS-A) is described. The solver is discretized using centroidal Voronoi meshes and a C-grid staggering of the prognostic variables, and it incorporates a split-explicit time-integration technique used in many existing nonhydrostatic meso- and cloud-scale models. MPAS can be applied to the globe, over limited areas of the globe, and on Cartesian planes. The Voronoi meshes are unstructured grids that permit variable horizontal resolution. These meshes allow for applications beyond uniform-resolution NWP and climate prediction, in particular allowing embedded high-resolution regions to be used for regional NWP and regional climate applications. The rationales for aspects of this formulation are discussed, and results from tests for nonhydrostatic flows on Cartesian planes and for large-scale flow on the sphere are presented. The results indicate that the solver is as acc... Abstract A new global ocean model (MPAS-Ocean) capable of using enhanced resolution in selected regions of the ocean domain is described and evaluated. Three simulations using different grids are presented. The first grid is a uniform high-resolution (15 km) mesh; the second grid has similarly high resolution (15 km) in the North Atlantic (NA), but coarse resolution elsewhere; the third grid is a variable resolution grid like the second but with higher resolution (7.5 km) in the NA. Simulation results are compared to observed sea-surface height (SSH), SSH variance and selected current transports. In general, the simulations produce subtropical and subpolar gyres with peak SSH amplitudes too strong by between 0.25 and 0.40 m. The mesoscale eddy activity within the NA is, in general, well simulated in both structure and amplitude. The uniform high-resolution simulation produces reasonable representations of mesoscale activity throughout the global ocean. Simulations using the second variable-resolution grid are essentially identical to the uniform case within the NA region. The third case with higher NA resolution produces a simulation that agrees somewhat better in the NA with observed SSH, SSH variance and transports than the two 15 km simulations. The actual throughput, including I O, for the x1-15 km simulation is the same as the structured grid Parallel Ocean Program ocean model in its standard high-resolution 0.1° configuration. Our overall conclusion is that this ocean model is a viable candidate for multi-resolution simulations of the global ocean system on climate-change time scales. During the next decade and beyond, climate system models will be challenged to resolve scales and processes that are far beyond their current scope. Each climate system component has its prototypical example of an unresolved process that may strongly influence the global climate system, ranging from eddy activity within ocean models, to ice streams within ice sheet models, to surface hydrological processes within land system models, to cloud processes within atmosphere models. These new demands will almost certainly result in the develop of multiresolution schemes that are able, at least regionally, to faithfully simulate these fine-scale processes. Spherical centroidal Voronoi tessellations (SCVTs) offer one potential path toward the development of a robust, multiresolution climate system model components. SCVTs allow for the generation of high-quality Voronoi diagrams and Delaunay triangulations through the use of an intuitive, user-defined density function. In each of the examples provided, this method results in high-quality meshes where the quality measures are guaranteed to improve as the number of nodes is increased. Real-world examples are developed for the Greenland ice sheet and the North Atlantic ocean. Idealized examples are developed for ocean–ice shelf interaction and for regional atmospheric modeling. In addition to defining, developing, and exhibiting SCVTs, we pair this mesh generation technique with a previously developed finite-volume method. Our numerical example is based on the nonlinear, shallow-water equations spanning the entire surface of the sphere. This example is used to elucidate both the po tential benefits of this multiresolution method and the challenges ahead.