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DOE OSTI2021

Reproducibility Practice in High-Performance Computing: Community Survey Results

The integrity of science and engineering research is grounded in assumptions of rigor and transparency on the part of those engaging in such research. HPC community effort to strengthen rigor and transparency take the form of reproducibility efforts. In a recent survey of the SC conference community, we collected information about the SC Reproducibility Initiative activities. Here, we present the survey results in this paper. Results show that the reproducibility initiative activities have contributed to higher levels of awareness on the part of SC conference technical program participants, and hint at contributing to greater scientific impact for the published papers of the SC conference series. Stringent point-of-manuscript-submission verification is problematic for reasons we point out, as are inherent difficulties of computational reproducibility in HPC. Future efforts should better decouple the community educational goals from goals that specifically strengthen a research work's potential for long-term impact through reuse 5-10 years down the road.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

2020 Exascale Computing Project Annual Meeting (Executive Summary Report)

The Exascale Computing Project (ECP) delivers specific applications, software products, and outcomes on DOE computing facilities. Integration across these elements for specific hardware technologies for exascale system instantiations is fundamental to ECP success. The outcome of the ECP is the delivery of a capable exascale computing ecosystem to provide breakthrough solutions addressing our most critical challenges in scientific discovery, energy assurance, economic competitiveness, and national security. This outcome is not a matter of ensuring more powerful computing systems. The ECP is designed to create more valuable and rapid insights from a wide variety of applications (“capable”), which requires a much higher level of inherent efficacy in all methods, software tools, and ECP-enabled computing technologies to be acquired by DOE laboratories (“ecosystem”). The ECP annual meeting provides a unique opportunity for the core technical expertise in the United States focused on achieving this next plateau of computational science and computing performance to engage in direct discussions on project execution. Face-to-face gatherings in technical communities like this are common and needed for the exchange of scientific ideas and technical performance. The ECP annual meeting stands apart from other technical conferences and meetings in the computing community as it is uniquely and solely focused on the execution of the ECP and the integration of technical activities leading to the creation of the exascale computing ecosystem for the future. The direct interaction of key critical technical staff, who are leaders in their respective fields, and the resulting give-and-take between software, applications, and hardware and the technical co-design therein, is unique and essential to the effective execution of the ECP. The first annual meeting was held in Knoxville, Tennessee, January 31 – February 2, 2017 and brought together, for the first time, a diverse collection of researchers from 16 DOE national laboratories as well as university computer and computational science researchers to discuss shared problems and joint solutions for the development of a capable exascale computing ecosystem. These interactions resulted in focused technical plans and an energized community centered on advances for ECP. The second annual meeting was held in Knoxville, Tennessee, February 5–9, 2018. It included 643 individual thought leaders and performers in application development, software research and deployment, and hardware research and integrators, all of whom are part of the multifaceted, billion dollar HPC community. This meeting provided a platform to discuss and disseminate numerous examples where researchers with common goals and synergistic solutions came together for the first time to deliver tangible results. Additionally, at the 2018 meeting, ECP researchers had the opportunity to digest all US HPC vendor R&D product roadmaps pointing to exascale – not only to learn how their research can play a role, but, more importantly, to influence those roadmaps to ensure successful delivery on DOE applications that will contribute to (if not solve) problems of national interest in national security, science, energy, and health, as well as growing security threats. The third annual meeting was held in Houston, Texas, January 14–17, 2019. With a 19% increase in the number of registrations (768 people), and the change in location, the third annual meeting was considered the most impactful of the three at the time. The new website provided a better platform for the dissemination of the content, the new venue as a meeting hotel instead of a conference center facilitated interactions and discussions after event hours, and the addition of an award-winning mobile event conference app (Whova) transformed dramatically the attendee experience at the event. This fourth annual meeting was held in Houston, Texas, February 3-7, 2020. This meeting had an increase in the number of attendees for a total of 824 people registered (782 attendees) and included numerous enhancements based on feedback and lessons learned from previous meetings, some of which are listed here: Improved quality of the sessions, their material and the whole program.; Had more industry participation and addition of external collaborators from overseas.; Published the full agenda earlier to better accommodate attendance and travel plans based on schedule.; Centralized all sessions in one venue.; Provided additional hotels and room blocks for the attendees.; Improved communication with the audience (links, material, directions, notifications, etc.) to go paperless.; Enhanced side meeting scheduling, management and user experience.; Made available additional space and tables for impromptu meetings and side discussions.; Improved IT and A/V solutions for speakers. In addition, our final survey captured the following points as opportunities for improvement in future meetings: consider a different meeting location that is more pedestrian friendly, reduce talks during working meals to allow more collaboration and informal time, adapt the agenda to acknowledge attendees from different timezones, consider recording some of the tutorials and/or sessions to share broadly with the HPC community, have a larger poster room, provide additional power strips, and improve the WiFi.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

CMS Computing Resources: Meeting the demands of the high-luminosity LHC physics program

The high-luminosity program has seen numerous extrapolations of its needed computing resources that each indicate the need for substantial changes if the desired HL-LHC physics program is to be supported within the current level of computing resource budgets. Drivers include large increases in event complexity (leading to increased processing time and analysis data size) and trigger rates needed (5-10 fold increases) for the HL-LHC program. The CMS experiment has recently undertaken an effort to merge the ideas behind short-term and long-term resource models in order to make easier and more reliable extrapolations to future needs. Near term computing resource estimation requirements depend on numerous parameters: LHC uptime and beam intensities; detector and online trigger performance; software performance; analysis data requirements; data access, management, and retention policies; site characteristics; and network performance. Longer term modeling is affected by the same characteristics, but with much larger uncertainties that must be considered to understand the most interesting handles for increasing the "physics per computing dollar" of the HL-LHC. In this presentation, we discuss the current status of long term modeling of the CMS computing resource needs for HL-LHC with emphasis on techniques for extrapolations, uncertainty quantification, and model results. We illustrate potential ways that high-luminosity CMS could accomplish its desired physics program within today's computing budgets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Challenges and Opportunities in Magnetospheric Space Weather Prediction

Abstract Space Weather is the study of the dynamics of the coupled Solar‐Terrestrial environment, as these dynamics impact technological systems and human activity. This paper reviews a selection of the advances, challenges, and new opportunities for magnetospheric space weather, and while the focus is on specific phenomena, many other aspects of space weather will have similar challenges and needs. As a scientific field with direct applications, the field of space weather is partly driven by imperatives from both policy and operations. We provide an introduction to some of the context in which the field exists and discuss how this might shape future developments and norms within the space weather enterprise. We briefly examine benchmarking, as a policy and operationally driven activity, as it provides immediate societal relevance and an opportunity to stretch scientific understanding. As numerical space weather prediction now becomes routine, and exascale computing is in the near future, we identify challenges relating to computational expense and big data, capturing and accounting for uncertainties, and specification of boundary conditions. Here, as with the observations supporting numerical space weather prediction, the key challenge lies in extending the lead time of predictions. We also discuss the role of data, particularly in regard to model validation and empirical modeling. Due to the growing societal impact of space weather, we also examine the relationships between space weather and its terrestrial counterpart and look at the importance of continuous evaluation, monitoring progress in predictive capability, and communication with researchers, forecasters, and end users.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Structural Simluation Toolkit (SST) v.11.0

The SST provides a parallel framework to perform system simulation of computer architectures to determine their performance and power consumption. Additionally, the SST contains basic models of a computer processor, and interconnect and can connect to an external memory simulator (DRAMSim II). The SST framework provides a simple interface by which other computer simulation models can be combined under a common parallel discrete event-based simulation environment. This allows design exploration of future architectures, analysis of how current computer programs will function on future architectures. The SST provides a parallel discrete event simulation framework, including partitioning and object distribution over MPI. It also provides a mechanism by which components can report their power consumption for analysis.

Rodrigues, ArunF.↗
DOE OSTI2019

QAOA for Max-Cut requires hundreds of qubits for quantum speed-up

Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in quantum information processing, noisy devices with about 50 qubits are expected to experimentally demonstrate quantum supremacy in the next few years. Defined in terms of artificial tasks, current proposals for quantum supremacy, even if successful, will not help to facilitate solutions to practical problems. In contrast, we believe that future users of quantum computers are interested in actual applications and that noisy quantum devices may still provide value by approximately solving hard combinatorial problems via hybrid classical-quantum algorithms. To lower bound the size of quantum computers with practical utility, we perform realistic simulations of the Quantum Approximate Optimization Algorithm and conclude that quantum speedup will not be attainable, at least for a representative combinatorial problem, until several hundreds of qubits are available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Collaborative Research: Performance Retargeting of Instrumentation, Measurement, and Analysis Technologies for Exascale Computing: the PRIMA-X Project -- Final Technical Report

The PRIMA-X (Performance Retargeting of Instrumentation, Measurement, and Analysis Technologies for Exascale Computing) project was a collaborative research effort between the University of Oregon (UO) (Malony, PI) and the German Research School for Simulation Sciences GmbH (Wolf, PI) originally, later changed to the Technical University of Darmstadt. Our project aims addressed five areas -- scalability, dynamism, heterogeneity, locality, energy -- that present challenges to performance measurement systems at exascale, with emphasis placed on the first three. In essence, the general goal of the project was to prototype new technologies for performance measurement, analysis, and tuning on future exascale-enable computer systems. Each institution followed its research agena, with periodic coordination and sharing of ideas and results. After the 3-year funding, the PRIMA-X grant was extended beyond the 3-year period at no cost until the end of August 2018. This is the final technical report on the University of Oregon's progress during the entire project scope. Our main focus was to address the PRIMA-X challenges both through technological advancements in the TAU Performance System and their application, as well as prototypes developed in association with other exascale-directed research efforts (prior to the Exascale Computing Project (ECP)). Progress in Years 1 and 2 are summarized and our achievements in Year 3 (plus the extension) are discussed in more detail. This includes specific efforts on power, runtime systems, and monitoring infrastructure.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Workshop on Computational Turbulence Modeling

The purpose of this meeting was to discuss the current status and future development of turbulence modeling in computational fluid dynamics for aerospace propulsion systems. Various turbulence models have been developed and applied to different turbulent flows over the past several decades and it is becoming more and more urgent to assess their performance in various complex situations. In order to help users in selecting and implementing appropriate models in their engineering calculations, it is important to identify the capabilities as well as the deficiencies of these models. This also benefits turbulence modelers by permitting them to further improve upon the existing models. This workshop was designed for exchanging ideas and enhancing collaboration between different groups in the Lewis community who are using turbulence models in propulsion related CFD. In this respect this workshop will help the Lewis goal of excelling in propulsion related research. This meeting had seven sessions for presentations and one panel discussion over a period of two days. Each presentation session was assigned to one or two branches (or groups) to present their turbulence related research work. Each group was asked to address at least the following points: current status of turbulence model applications and developments in the research; progress and existing problems; and requests about turbulence modeling. The panel discussion session was designed for organizing committee members to answer management and technical questions from the audience and to make concluding remarks.

Shabbir, A.↗
DOE OSTI2020

A massively parallel and scalable multi-CPU material point method

Harnessing the power of modern multi-GPU architectures, we present a massively parallel simulation system based on the Material Point Method (MPM) for simulating physical behaviors of materials undergoing complex topological changes, self-collision, and large deformations. Our system makes three critical contributions. First, we introduce a new particle data structure that promotes coalesced memory access patterns on the GPU and eliminates the need for complex atomic operations on the memory hierarchy when writing particle data to the grid. Second, we propose a kernel fusion approach using a new Grid-to-Particles-to-Grid (G2P2G) scheme, which efficiently reduces GPU kernel launches, improves latency, and significantly reduces the amount of global memory needed to store particle data. Finally, we introduce optimized algorithmic designs that allow for efficient sparse grids in a shared memory context, enabling us to best utilize modern multi-GPU computational platforms for hybrid Lagrangian-Eulerian computational patterns. We demonstrate the effectiveness of our method with extensive benchmarks, evaluations, and dynamic simulations with elastoplasticity, granular media, and fluid dynamics. In comparisons against an open-source and heavily optimized CPU-based MPM codebase [Fang et al. 2019] on an elastic sphere colliding scene with particle counts ranging from 5 to 40 million, our GPU MPM achieves over 100x per-time-step speedup on a workstation with an Intel 8086K CPU and a single Quadro P6000 GPU, exposing exciting possibilities for future MPM simulations in computer graphics and computational science. Moreover, compared to the state-of-the-art GPU MPM method [Hu et al. 2019a], we not only achieve 2x acceleration on a single GPU but our kernel fusion strategy and Array-of-Structs-of-Array (AoSoA) data structure design also generalizes to multi-GPU systems. Our multi-GPU MPM exhibits near-perfect weak and strong scaling with 4 GPUs, enabling performant and large-scale simulations on a 10243 grid with close to 100 million particles with less than 4 minutes per frame on a single 4-GPU workstation and 134 million particles with less than 1 minute per frame on an 8-GPU workstation.

Wang, Xinlei↗
DOE OSTI2018

Phase field benchmark problems for dendritic growth and linear elasticity

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem for solidifiication and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. As a result, these numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Entanglement rearrangement in self-consistent nuclear structure calculations

Background: Entanglement plays a central role in a diverse array of increasingly important research areas, including quantum computation, simulation, measurement, sensing, and communication. Extensive suites of investigations have been performed to better understand entanglement in atomic and molecular quantum many-body systems, while the exploration of entanglement in the structure of nuclei and their reactions is presently in its infancy. Purpose: The goal of this work is to begin investigating the entanglement properties of nuclei from first-principles nuclear many-body calculations. We attempt to identify common features and emergent structures of entanglement that could ultimately lead to new and natural many-body schemes. With an eye toward quantum accelerators in future hybrid-supercomputers, criteria for partitioning nuclear many-body calculations into quantum and classical components may provide advantages in future large-scale computations. Along the way we look for explanations of the relative success of phenomenological models such as the nuclear shell model, and for better ways to match to low-energy nuclear effective field theories and lattice QCD calculations to nuclear many-body techniques that are based upon entanglement. Method: We explore the entanglement between single-particle states in 4 He and 6 He. The patterns of entanglement emerging from different single-particle bases are compared, and possible links with the convergence of observables are explored, in particular, ground-state energies. The nuclear wave functions are obtained by performing active-space no-core configuration-interaction calculations using a two-body nucleon-nucleon interaction derived from chiral effective field theory. Entanglement measures within single-particle bases exhibiting different degrees of complexity are determined, in particular, harmonic oscillator (HO), Hartree-Fock (HF), natural (NAT) and variational natural (VNAT) bases. Specifically, single-orbital entanglement entropy, two-orbital mutual information, and negativity are studied. Results: The entanglement structures in 4 He and 6 He are found to be more localized within NAT and VNAT bases than within a HO basis for the optimal HO parameters we have worked with. In particular a core-valence structure clearly emerges from the full no-core calculation of 6 He. Here, the two-nucleon mutual information shows that the VNAT basis, which typically exhibits good convergence properties, effectively decouples the active and inactive spaces. Conclusions: Measures of one- and two-nucleon entanglement are found to be useful in analyzing the structure of nuclear wave functions, in particular the efficacy of basis states, and may provide useful metrics toward developing more efficient schemes for ab initio computations of the structure and reactions of nuclei, and quantum many-body systems more generally.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Exascale Multiphysics Nuclear Reactor Simulations for Advanced Designs

ENRICO is a coupled application developed under the U.S. Department of Energy's Exascale Computing Project (ECP) targeting the modeling of advanced nuclear reactors. It couples radiation transport with heat and fluid simulation, including the high-fidelity, highresolution Monte-Carlo code Shift and the Computational fluid dynamics code NekRS. NekRS is a highly-performant open-source code for simulation of incompressible and low-Mach fluid flow, heat transfer, and combustion with a particular focus on turbulent flows in complex domains. It is based on rapidly convergent high-order spectral element discretizations that feature minimal numerical dissipation and dispersion. State-of-the-art multilevel preconditioners, efficient high-order time-splitting methods, and runtime-adaptive communication strategies are built on a fast OCCA-based kernel library, libParanumal, to provide scalability and portability across the spectrum of current and future high-performance computing platforms. On Frontier, Nek5000/RS has recently achieved an unprecedented milestone in breaching over 1 billion spectral elements and 350 billion degrees of freedom. Shift has demonstrated the capability to transport upwards of 1 billion particles per second in full core nuclear reactor simulations featuring complete temperature-dependent, continuous-energy physics on Frontier. Shift achieved a weak-scaling efficiency of 97.8% on 8192 nodes of Frontier and calculated 6 reactions in 214,896 fuel pin regions below 1% statistical error yielding first-of-a-kind resolution for a Monte Carlo transport application.

Hamilton, Steven P.↗
NASA NTRS1990

Navier-Stokes computations useful in aircraft design

Large scale Navier-Stokes computations about aircraft components as well as reasonably complete aircraft configurations are presented and discussed. Speed and memory requirements are described for various general problem classes, which in some cases are already being used in the industrial design environment. Recent computed results, with experimental comparisons when available, are included to highlight the presentation. Finally, prospects for the future are described and recommendations for areas of concentrated research are indicated. The future of Navier-Stokes computations is seen to be rapidly expanding across a broad front of applications, which includes the entire subsonic-to-hypersonic speed regime.

Holst, Terry L.↗
NASA NTRS2017

Automation Rover for Extreme Environments

Almost 2,300 years ago the ancient Greeks built the Antikythera automaton. This purely mechanical computer accurately predicted past and future astronomical events long before electronics existed1. Automata have been credibly used for hundreds of years as computers, art pieces, and clocks. However, in the past several decades automata have become less popular as the capabilities of electronics increased, leaving them an unexplored solution for robotic spacecraft. The Automaton Rover for Extreme Environments (AREE) proposes an exciting paradigm shift from electronics to a fully mechanical system, enabling longitudinal exploration of the most extreme environments within the solar system.

automata↗
DOE OSTI2022

High-throughput native mass spectrometry as experimental validation for in silico drug design

In this project, we developed automated workflows for both experimental validation and computational prediction of protein-ligand interactions. The ultimate goal is to establish an integrated pipeline for high throughput design of inhibitors to enzymes relevant to all areas of biological research. Our experimental approach is based on native mass spectrometry (native MS), which measures accurate masses and quantify the relative abundance of protein-ligand complexes to define binding affinity. We set up an in-house built autosampler with highly flexible configurations to minimize the manual steps for high throughput native MS. In parallel, we also performed manual native MS to characterize the binding of substrates and inhibitors of SARS-Cov-2 nonstructural protein nsp10/16 in order to optimize the experimental parameters for future automation. On the computational side, we streamlined the pipeline to achieve minimal manual intervention for predicting enzyme inhibitors via simulation, using the same nsp10/16 system as an example. Using the native MS method we examined 8 top-ranked designed compounds, 2 of which showed weak binding of ~50 µM. The information from native MS experiment provided critical insights and the foundation for a fully integrated workflow for enzyme inhibitor design.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

VTK-m: Visualization for the Exascale Era and Beyond

A recent trend in modern high-performance computing is the increasing use of hybrid architectures, where the vast majority of performance comes from accelerators. Modern accelerators are based on Graphics Processing Units (GPU) that contain many low power cores that in their aggregate provides an extremely high computation rate. Current and future CPU processors are requiring more explicit parallelism as each successive version of the hardware packs in more cores, and technologies like hyperthreading and vector operations require even more parallel processing to leverage each core’s full potential. As an example, the Frontier supercomputer installed at Oak Ridge National Laboratories recently hit a record breaking 1.1 exaflops1 on the LINPACK HPC benchmark [Shoemaker 2022]. The system contains 37632 AMD MI250x GPUs which requires more than half a billion threads to keep the system fully utilized [Khizeran 2022].VTK-m is a toolkit of scientific visualization algorithms for these emerging processor architectures. VTK-m supports the fine-grained concurrency for data analysis and visualization algorithms required to drive extreme scale computing by providing abstract models for data and execution that can be applied to a variety of algorithms across many different processor architectures.

Bolstad, Mark↗
NASA NTRS1971

Remote Sensing of Snow Fields from Earth Satellites

Considerable effort has gone into snow line delineation using available satellite data. Furthermore, increasing emphasis is being put on automated extraction of such information and generation of a useable product for hydrologists. Implications are clear that the impact from future satellite and sensors systems will create an increased demand for computer processing before the data can be used by the hydrologist. If the coarse-resolution, broad spectral band data available from current satellites already create a demand by hydrologists for computer processing of the data, it is obvious there will be an even greater demand for computer analysis and evaluation when the future ERTS data become available.

Baker, D. R.↗
NASA NTRSDate not supplied

Multi-angle Imaging SpectroRadiometer

MISR views the sunlit Earth simultaneously at nine widely spaced angles and provides ongoing global coverage with high spatial detail. Its imagery is carefully calibrated to provide accurate measures of the brightness, contrast, and color of reflected sunlight. MISR provides new types of information for scientists studying Earth's climate, such as the regional and global distribution of different types of atmospheric particles and aerosols. The change in reflection at different view angles provides the means to distinguish aerosol types, cloud forms, and land surface cover. Combined with stereoscopic techniques, this enables construction of 3-D cloud models and estimation of the total amount of sunlight reflected by Earth's diverse environments. MISR was built for NASA by the Jet Propulsion Laboratory (JPL) in Pasadena, California. It is part of NASA's first Earth Observing System (EOS) spacecraft, the Terra spacecraft, which was launched into polar orbit from Vandenberg Air Force Base on December 18, 1999. MISR has been continuously providing data since February 24, 2000. [Mission Objectives] The MISR instrument acquires systematic multi-angle measurements for global monitoring of top-of-atmosphere and surface albedos and for measuring the shortwave radiative properties of aerosols, clouds, and surface scenes in order to characterize their impact on the Earth's climate. The Earth's climate is constantly changing -- as a consequence of both natural processes and human activities. Scientists care a great deal about even small changes in Earth's climate, since they can affect our comfort and well-being, and possibly our survival. A few years of below-average rainfall, an unusually cold winter, or a change in emissions from a coal-burning power plant, can influence the quality of life of people, plants, and animals in the region involved. The goal of NASA's Earth Observing System (EOS) is to increase our understanding of the climate changes that are occurring on our planet, and the reasons for these changes, so we are better equipped to anticipate and prepare for the future. The MISR instrument is a part of EOS. Its role is to measure the amount of sunlight scattered in different directions under natural conditions. These measurements will help quantify the amount of solar energy that heats the Earth's surface and atmosphere, and the changes that occur in them over the lifetime of the MISR instrument. From the MISR observations, we are also learning more about those components of the Earth's environment that scatter sunlight: particles in the atmosphere, the planet's surface, and clouds. MISR monitors changes in surface reflection properties, in atmospheric aerosol content and composition, and in cloudiness. Scientists use these data to study land use changes, air pollution, volcanic eruptions, as well as processes such as desertification, deforestation, and soil erosion. As part of the EOS program, computer models that predict future climate will be improved by the results of these studies. [Temporal_Coverage: Start_Date=2000-02-24; Stop_Date=] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180].

Diner, David J.↗