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The cubed sphere geometry, obtained by inscribing a cube in a sphere and mapping points between the two surfaces using a gnomonic (central) projection, is commonly used in atmospheric models because it is free of polar singularities and is well-suited for parallel computing. Global meshes on the cubed-sphere typically project uniform (square) grids from each face of the cube onto the sphere, and if refinement is desired then it is done with non-conforming meshes - overlaying the area of interest with a finer uniform mesh, which introduces so-called hanging nodes on edges along the boundary of the fine resolution area. An alternate technique is to tile each face of the cube with quadrilaterals without requiring the quads to be rectangular. These meshes allow for refinement in areas of interest with a conforming mesh, providing a smoother transition between high and low resolution portions of the grid than non-conforming refinement. The conforming meshes are demonstrated in HOMME, NCAR's High Order Method Modeling Environment, where two modifications have been made: the dependence on uniform meshes has been removed, and the ability to read arbitrary quadrilateral meshes from a previously-generated file has been added. Numerical results come from a conservative spectral element method modeling a selection of the standard shallow water test cases.

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TYPE Conference YEAR 2010

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The Arctic as a test case for an assessment of climate impacts on national security

Boslough, Mark B.; Taylor, Mark A.; Zak, Bernard D.; Backus, George A.

The Arctic region is rapidly changing in a way that will affect the rest of the world. Parts of Alaska, western Canada, and Siberia are currently warming at twice the global rate. This warming trend is accelerating permafrost deterioration, coastal erosion, snow and ice loss, and other changes that are a direct consequence of climate change. Climatologists have long understood that changes in the Arctic would be faster and more intense than elsewhere on the planet, but the degree and speed of the changes were underestimated compared to recent observations. Policy makers have not yet had time to examine the latest evidence or appreciate the nature of the consequences. Thus, the abruptness and severity of an unfolding Arctic climate crisis has not been incorporated into long-range planning. The purpose of this report is to briefly review the physical basis for global climate change and Arctic amplification, summarize the ongoing observations, discuss the potential consequences, explain the need for an objective risk assessment, develop scenarios for future change, review existing modeling capabilities and the need for better regional models, and finally to make recommendations for Sandia's future role in preparing our leaders to deal with impacts of Arctic climate change on national security. Accurate and credible regional-scale climate models are still several years in the future, and those models are essential for estimating climate impacts around the globe. This study demonstrates how a scenario-based method may be used to give insights into climate impacts on a regional scale and possible mitigation. Because of our experience in the Arctic and widespread recognition of the Arctic's importance in the Earth climate system we chose the Arctic as a test case for an assessment of climate impacts on national security. Sandia can make a swift and significant contribution by applying modeling and simulation tools with internal collaborations as well as with outside organizations. Because changes in the Arctic environment are happening so rapidly, a successful program will be one that can adapt very quickly to new information as it becomes available, and can provide decision makers with projections on the 1-5 year time scale over which the most disruptive, high-consequence changes are likely to occur. The greatest short-term impact would be to initiate exploratory simulations to discover new emergent and robust phenomena associated with one or more of the following changing systems: Arctic hydrological cycle, sea ice extent, ocean and atmospheric circulation, permafrost deterioration, carbon mobilization, Greenland ice sheet stability, and coastal erosion. Sandia can also contribute to new technology solutions for improved observations in the Arctic, which is currently a data-sparse region. Sensitivity analyses have the potential to identify thresholds which would enable the collaborative development of 'early warning' sensor systems to seek predicted phenomena that might be precursory to major, high-consequence changes. Much of this work will require improved regional climate models and advanced computing capabilities. Socio-economic modeling tools can help define human and national security consequences. Formal uncertainty quantification must be an integral part of any results that emerge from this work.

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TYPE SAND Report YEAR 2008

DOI OSTI

Asymmetric cubature formulas for polynomial integration in the triangle and square

Journal of Computational and Applied Mathematics

Taylor, Mark A.

We present five new cubature formula in the triangle and square for exact integration of polynomials. The points were computed numerically with a cardinal function algorithm which does not impose any symmetry requirements on the points. Cubature formula are presented which integrate degrees 10, 11 and 12 in the triangle and degrees 10 and 12 in the square. They have positive weights, contain no points outside the domain, and have fewer points than previously known results. © 2007 Elsevier B.V. All rights reserved.

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TYPE Journal Article YEAR 2008

OSTI Scopus