William F. Spotz

Bio: William F. Spotz is an academic researcher from Sandia National Laboratories. The author has contributed to research in topics: NumPy & Solver. The author has an hindex of 9, co-authored 20 publications receiving 455 citations. Previous affiliations of William F. Spotz include National Center for Atmospheric Research.

High-Resolution Mesh Convergence Properties and Parallel Efficiency of a Spectral Element Atmospheric Dynamical Core

Abstract: We first demonstrate the parallel performance of the dynamical core of a spectral element atmospheric model. The model uses continuous Galerkin spectral elements to discretize the surface of the Earth, coupled with finite differences in the radial direction. Results are presented from two distributed memory, mesh interconnect supercomputers (ASCI Red and BlueGene/L), using a two-dimensional space filling curve domain decomposition. Better than 80% parallel efficiency is obtained for fixed grids on up to 8938 processors. These runs represent the largest processor counts ever achieved for a geophysical application. They show that the upcoming Red Storm and BlueGene/L super-computers are well suited for performing global atmospheric simulations with a 10 km average grid spacing. We then demonstrate the accuracy of the method by performing a full three-dimensional mesh refinement convergence study, using the primitive equations to model breaking Rossby waves on the polar vortex. Due to the excellent parallel performance, the model is run at several resolutions up to 36 km with 200 levels using only modest computing resources. Isosurfaces of scaled potential vorticity exhibit complex dynamical features, e.g. a primary potential vorticity tongue, and a secondary instability causing roll-up into a ring of five smaller subvortices. As the resolution is increased, these features are shown to converge while potential vorticity gradients steepen.

Guest Editors' Introduction: Climate Modeling

Abstract: This special issue on climate modeling presents a snapshot of some of the researchscientists are conducting to improve our climate modeling capabilities. We present articles on promising atmospheric and ocean models, meshing issues for geophysicalapplications, implementation on distributed computer architectures, atmospheric-chemistry models, and the testing and evaluation of models.These articles, taken together, provide a good indication of the problems facing climate modelers today andsome of the solutions they are pursuing.

Accuracy and performance of numerical wall boundary conditions for steady, 2D, incompressible streamfunction vorticity

Abstract: Three recent papers have studied fourth-order compact discretizations of the streamfunction vorticity equations. They differed primarily in how the no-slip wall boundary conditions were handled. In this paper, these different formulas are compared to one another, as well as to three newly proposed formulas. Special consideration is paid to the truncation errors; in particular, it is shown that many well-known formulations are actually more accurate by O(h) than previously reported, where h is the mesh size. These new theoretical error rates are confirmed with an analytical model problem. The different formulas are then compared with published driven cavity results, both in terms of accuracy and performance, and the newly proposed high-order Jensen formula is judged to have the marginally best combination of these properties. © 1998 John Wiley & Sons, Ltd.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Abstract: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Numerical Heat Transfer And Fluid Flow

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Radiative Forcing of Climate Change

Abstract: Our current understanding of mechanisms that are, or may be, acting to cause climate change over the past century is briefly reviewed, with an emphasis on those due to human activity. The paper discusses the general level of confidence in these estimates and areas of remaining uncertainty. The effects of increases in the so-called well-mixed greenhouse gases, and in particular carbon dioxide, appear to be the dominant mechanism. However, there are considerable uncertainties in our estimates of many other forcing mechanisms; those associated with the so-called indirect aerosol forcing (whereby changes in aerosols can impact on cloud properties) may be the most serious, as its climatic effect may be of a similar size as, but opposite sign to, that due to carbon dioxide. The possible role of volcanic eruptions as a natural climate change mechanism is also highlighted.

CAM-chem: description and evaluation of interactive atmospheric chemistry in the Community Earth System Model

Abstract: . We discuss and evaluate the representation of atmospheric chemistry in the global Community Atmosphere Model (CAM) version 4, the atmospheric component of the Community Earth System Model (CESM). We present a variety of configurations for the representation of tropospheric and stratospheric chemistry, wet removal, and online and offline meteorology. Results from simulations illustrating these configurations are compared with surface, aircraft and satellite observations. Major biases include a negative bias in the high-latitude CO distribution, a positive bias in upper-tropospheric/lower-stratospheric ozone, and a positive bias in summertime surface ozone (over the United States and Europe). The tropospheric net chemical ozone production varies significantly between configurations, partly related to variations in stratosphere-troposphere exchange. Aerosol optical depth tends to be underestimated over most regions, while comparison with aerosol surface measurements over the United States indicate reasonable results for sulfate , especially in the online simulation. Other aerosol species exhibit significant biases. Overall, the model-data comparison indicates that the offline simulation driven by GEOS5 meteorological analyses provides the best simulation, possibly due in part to the increased vertical resolution (52 levels instead of 26 for online dynamics). The CAM-chem code as described in this paper, along with all the necessary datasets needed to perform the simulations described here, are available for download at www.cesm.ucar.edu .