A multiresolution method for climate system modeling: application of spherical centroidal Voronoi tessellations

Abstract

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 highquality Voronoi diagrams and Delaunay triangulations Responsible Editor: Eric Deleersnijder LA-UR-08-05303. T. Ringler (B) 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, shallowwater equations spanning the entire surface of the sphere. This example is used to elucidate both the potential benefits of this multiresolution method and the challenges ahead.

DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models

“…This has led to the development of the constrained centroidal Voronoi tessellation (CCVT) (Du et al, 2003), which imposes the additional requirement that the set of generators be coincident with the centroids of each polygon. Given a desired polygonal density function, several algorithms have been developed to generate CCVTs both in Cartesian and spherical geometry (i.e., for ocean basins or ice sheets) (Ringler et al, 2008). Figure 3 depicts one such CCVT grid that is compatible with the MPAS model.…”

JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

“…A range of new general circulation models, including the Finite Element Sea Ice-Ocean Model (FESOM) (Wang et al, 2014), the Finite Volume Community Ocean Model (FVCOM) (Chen et al, 2003(Chen et al, , 2007Lai et al, 2010), the Stanford Unstructured Non-hydrostatic Terrain-following Adaptive NavierStokes Simulator (SUNTANS) (Fringer et al, 2006;Vitousek and Fringer, 2014), and the Second-generation Louvainla-Neuve Ice-ocean Model (SLIM) (Bernard et al, 2007;Comblen et al, 2009), are based on semi-structured triangular grids, with the horizontal directions discretised according to an unstructured spherical triangulation, and the ver-D. Engwirda: Unstructured grid-generation for general circulation modelling 2119 tical direction represented as a stack of locally structured layers. The Model for Predication Across Scales (MPAS) (Skamarock et al, 2012;Ringler et al, 2013Ringler et al, , 2008) adopts a similar arrangement, except that a locally orthogonal unstructured discretisation is adopted, consisting of both a Spherical Voronoi Tessellation (SVT) and its dual Delaunay triangulation. The use of fully unstructured representations, based on general tetrahedral and/or polyhedral grids, are also under investigation in the Fluidity framework (Ford et al, 2004a, b;Pain et al, 2005;Piggott et al, 2008).…”

A high-fidelity multiresolution digital elevation model for Earth systems

“…With the success of Earth and environment systems with these scale-diversified processes, persistent demands exist for extending their utility to new and expanding scopes (Ringler et al, 2008;Tarolli, 2014;Wilson, 2012), as exemplified by lapse-rate-controlled functional plant distributions (Ke et al, 2012), orographic forcing imposed on oceanic and atmospheric dynamics (Nunalee et al, 2015;Brioude et al, 2012;Hughes et al, 2015), topographic dominated flood inundations (Bilskie et al, 2015;Hunter et al, 2007), and many other geomorphological (Wilson, 2012), soil (Florinsky and Pankratov, 2015), and ecological (Leempoel et al, 2015) examples from Earth systems. However, as numerical simulation systems evolved to incorporate broader scales and finer processes to produce more exact predictions (Ringler et al, 2011;Weller et al, 2016;Wilson, 2012;Zarzycki et al, 2014), how to accurately assimilate or transform the finePublished by Copernicus Publications on behalf of the European Geosciences Union.…”