Voronoi Tessellations and Their Application to Climate and Global Modeling

Ju, Lili; Ringler, Todd D.; Gunzburger, Max D.

doi:10.1007/978-3-642-11640-7_10

Cited by 56 publications

(67 citation statements)

References 74 publications

(79 reference statements)

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“…A full review of SCVTs and their potential benefit in global climate system modeling is provided in Ju et al (2010) and Ringler et al (2008). Our discussion here is restricted to the most salient aspects of SCVTs with a focus on the practical aspect of the meshes.…”

Section: Properties and Generation Of Scvtsmentioning

confidence: 99%

“…1 Neither Sadourny nor Williamson refer to their grids as Voronoi tessellations, but both appeared to use Voronoi tessellations as their base mesh. Even over the last decade there has been much ambiguity with respect to the terminology used to describe these meshes (see Ju et al (2010)). More recently, Voronoi-like meshing of the sphere has found significant success in global atmosphere modeling (Heikes and Randall (1995), Thuburn…”

Section: Introductionmentioning

confidence: 99%

“…Voronoi (1908 generalized the work of Dirichlet to arbitrary dimensions. These tessellations have been given many different names by their reinventors (see Ju et al (2010)) (1997), Ringler et al (2000), Ringler and Randall (2002), Randall et al (2002), Tomita et al (2005, Weller and Weller (2008)). In each of these examples, the use of Voronoi-like tessellations is motivated through their ability to produce high-quality meshes of uniform resolution while at the same time eliminating problematic grid singularities associated with other meshing approaches.…”

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confidence: 99%

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Exploring a Multiresolution Modeling Approach within the Shallow-Water Equations

Ringler

Jacobsen

Gunzburger

et al. 2011

Monthly Weather Review

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122

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The ability to solve the global shallow-water equations with a conforming, variable-resolution mesh is evaluated using standard shallow-water test cases. While our long-term motivation is the creation of a global climate modeling framework capable of resolving different spatial and temporal scales in different regions, we begin with an analysis of the shallow-water system in order to better understand the strengths and weaknesses of our approach. The multiresolution meshes are spherical centroidal Voronoi tessellations where a single, user-supplied density function determines the region(s) of fine-and coarse-mesh resolution. We explore the shallow-water system with a suite of meshes ranging from quasi-uniform resolution meshes, where grid spacing is globally uniform, to highly-variable resolution meshes, where grid spacing varies by a factor of 16 between the fine and coarse regions. We find that potential vorticity is conserved to within machine precision and total available energy is conserved to within time-truncation error. This finding holds for the full suite of meshes, ranging from quasi-uniform resolution and highly-variable resolution meshes. Using shallow-water test cases 2 and 5, we find that solution error is controlled primarily by the grid resolution in the coarsest part of the model domain. This finding is consistent with results obtained by others.When these variable resolution meshes are used for the simulation of an unstable zonal jet, we find that the core features of the growing instability are largely unchanged as the variation in mesh resolution increases. The main differences between the simulations occur outside the region of mesh refinement and these differences are attributed to the additional truncation error that accompanies increases in grid spacing. Overall, the results demonstrate support for this approach as a path toward multi-resolution climate system modeling.1

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Section: Properties and Generation Of Scvtsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Exploring a Multiresolution Modeling Approach within the Shallow-Water Equations

Ringler

Jacobsen

Gunzburger

et al. 2011

Monthly Weather Review

Self Cite

122

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“…Climate modelling is a specific field which has recently begun adopting Voronoi tessellations as well as triangular meshes for the spatial discretization of partial differential equations (Pain et al, 2005;Weller et al, 2009;Ju et al, 2008Ju et al, , 2011Ringler et al, 2011). As this is a special interest of ours, we also develop a new parallel algorithm for the generation of Voronoi and Delaunay tessellations for the entire sphere or some subregion of interest.…”

Section: Introductionmentioning

confidence: 99%

Parallel algorithms for planar and spherical Delaunay construction with an application to centroidal Voronoi tessellations

et al. 2013

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Abstract.A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construction of spherical Delaunay and Voronoi tessellations. The algorithms are then embedded into algorithms for the parallel construction of planar and spherical centroidal Voronoi tessellations that require multiple constructions of Delaunay tessellations. This combination of overlapping domain decompositions with stereographic projections provides a unique algorithm for the construction of spherical meshes that can be used in climate simulations. Computational tests are used to demonstrate the efficiency and scalability of the algorithms for spherical Delaunay and centroidal Voronoi tessellations. Compared to serial versions of the algorithm and to STRIPACK-based approaches, the new parallel algorithm results in speedups for the construction of spherical centroidal Voronoi tessellations and spherical Delaunay triangulations.

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“…See for example Thiessen's classic paper (Thiessen, 1911) on estimating regional rainfall or Harding's work (Harding, 1923) on the estimation of ore reserves. More recent work on related problems includes (Ju et al, 2011;Møller and Skare, 2001). Note that supporting data structures are routinely implemented in GIS systems (Rigaux et al, 2001).…”

Section: Introductionmentioning

confidence: 99%

An introduction to planar random tessellation models

Lieshout¹

2012

Spatial Statistics

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a b s t r a c tThe goal of this paper is to give an overview of random tessellation models. We discuss the classic isotropic Poisson line tessellation in some detail and then move on to more complicated models, including Arak-Clifford-Surgailis polygonal Markov fields and their Gibbs field counterparts, crystal growth models such as the Poisson-Voronoi, Johnson-Mehl and Laguerre random tessellations, and the STIT nesting scheme. An extensive list of references is included as a guide to the literature.

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Voronoi Tessellations and Their Application to Climate and Global Modeling

Cited by 56 publications

References 74 publications

Exploring a Multiresolution Modeling Approach within the Shallow-Water Equations

Exploring a Multiresolution Modeling Approach within the Shallow-Water Equations

Parallel algorithms for planar and spherical Delaunay construction with an application to centroidal Voronoi tessellations

An introduction to planar random tessellation models

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