Publications

J. Comput. Phys.

Taylor, Mark A.

Abstract not provided.

Mon. Weather Review

Taylor, Mark A.

Abstract not provided.

Levy, Michael N.; Overfelt, James R.; Taylor, Mark A.

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.

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.

Taylor, Mark A.

Abstract not provided.

J. Comput. Appl. Math.

Taylor, Mark A.

Abstract not provided.

Backus, George A.; Boslough, Mark B.; Taylor, Mark A.; Strickland, James H.

Abstract not provided.

Backus, George A.; Boslough, Mark B.; Strickland, James H.; Taylor, Mark A.

Abstract not provided.

Boslough, Mark B.; Taylor, Mark A.

Abstract not provided.

Taylor, Mark A.; Strickland, James H.

Abstract not provided.

Boslough, Mark B.; Sprigg, James A.; Backus, George A.; Taylor, Mark A.; McNamara, Laura A.; Murphy, Kathryn M.; Malczynski, Leonard A.

This white paper represents a summary of work intended to lay the foundation for development of a climatological/agent model of climate-induced conflict. The paper combines several loosely-coupled efforts and is the final report for a four-month late-start Laboratory Directed Research and Development (LDRD) project funded by the Advanced Concepts Group (ACG). The project involved contributions by many participants having diverse areas of expertise, with the common goal of learning how to tie together the physical and human causes and consequences of climate change. We performed a review of relevant literature on conflict arising from environmental scarcity. Rather than simply reviewing the previous work, we actively collected data from the referenced sources, reproduced some of the work, and explored alternative models. We used the unfolding crisis in Darfur (western Sudan) as a case study of conflict related to or triggered by climate change, and as an exercise for developing a preliminary concept map. We also outlined a plan for implementing agents in a climate model and defined a logical progression toward the ultimate goal of running both types of models simultaneously in a two-way feedback mode, where the behavior of agents influences the climate and climate change affects the agents. Finally, we offer some ''lessons learned'' in attempting to keep a diverse and geographically dispersed group working together by using Web-based collaborative tools.

Taylor, Mark A.

The diagonal-mass-matrix spectral element method has proven very successful in geophysical applications dominated by wave propagation. For these problems, the ability to run fully explicit time stepping schemes at relatively high order makes the method more competitive then finite element methods which require the inversion of a mass matrix. The method relies on Gauss-Lobatto points to be successful, since the grid points used are required to produce well conditioned polynomial interpolants, and be high quality 'Gauss-like' quadrature points that exactly integrate a space of polynomials of higher dimension than the number of quadrature points. These two requirements have traditionally limited the diagonal-mass-matrix spectral element method to use square or quadrilateral elements, where tensor products of Gauss-Lobatto points can be used. In non-tensor product domains such as the triangle, both optimal interpolation points and Gauss-like quadrature points are difficult to construct and there are few analytic results. To extend the diagonal-mass-matrix spectral element method to (for example) triangular elements, one must find appropriate points numerically. One successful approach has been to perform numerical searches for high quality interpolation points, as measured by the Lebesgue constant (Such as minimum energy electrostatic points and Fekete points). However, these points typically do not have any Gauss-like quadrature properties. In this work, we describe a new numerical method to look for Gauss-like quadrature points in the triangle, based on a previous algorithm for computing Fekete points. Performing a brute force search for such points is extremely difficult. A common strategy to increase the numerical efficiency of these searches is to reduce the number of unknowns by imposing symmetry conditions on the quadrature points. Motivated by spectral element methods, we propose a different way to reduce the number of unknowns: We look for quadrature formula that have the same number of points as the number of basis functions used in the spectral element method's transform algorithm. This is an important requirement if they are to be used in a diagonal-mass-matrix spectral element method. This restriction allows for the construction of cardinal functions (Lagrange interpolating polynomials). The ability to construct cardinal functions leads to a remarkable expression relating the variation in the quadrature weights to the variation in the quadrature points. This relation in turn leads to an analytical expression for the gradient of the quadrature error with respect to the quadrature points. Thus the quadrature weights have been completely removed from the optimization problem, and we can implement an exact steepest descent algorithm for driving the quadrature error to zero. Results from the algorithm will be presented for the triangle and the sphere.