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At least 541 records · Page 30

Long-Term Trends in the Concentrations of SF6, CHClF2, and COF2 in the Lower Stratosphere from Analysis of High-Resolution Infrared Solar Occultation Spectra

Long-term trends in the concentrations of SF6, CHClF2 (CFC-22), and COF2 in the lower stratosphere have been derived from analysis of ca. 1980 and more recent infrared solar occultation spectra recorded near 32 deg N latitude at approx. 0.02/ cm resolution. Consistent sets of line parameters and spectral calibration methods have been used in the retrievals to minimize systematic error effects. Quoted error limits are 1 sigma estimated precisions. The SF6 and CHClF2 results are based on spectra recorded by balloon-borne interferometers in March 1981 and June 1988 and a comparison of these results with the Atmospheric Trace Molecule Spectroscopy (ATMOS) Experiment/Spacelab 3 measurements obtained in May 1985 near 30 deg N latitude. In the 13-18 km altitude range the mean measured SF6 mixing ratio in parts per trillion by volume (pptv) increased from 1.17 +/- 0.21 in March 1981 to 2.02 +/- 0.20 pptv in June 1988, and the CHClF2 mixing ratio below 15 km altitude increased from 51 +/- 8 pptv in March 1981 to 102 +/- 10 pptv in June 1988. The CHClF2 retrievals used new empirical CHClF2 line parameters derived from 0.03/cm resolution laboratory spectra recorded at six temperatures between 203 and 293 K; the derived mixing ratios are approx. 30% higher than obtained with earlier sets of line parameters, thereby removing a large discrepancy noted previously between IR and in situ measurements of CHClF2. Assuming an exponential growth model for fitting the trends, SF6 and CHClF2 mean increase rates of 7.4% +/- 1.9% and 9.4% +/- 1.3% /year, are obtained, respectively, which correspond to cumulative increases by factors of approx. 1.7 and -2.0 in the concentrations of these gases over the 7.2-year measurement period. Analysis of spectra recorded in October 1979 and April 1989 yields COF2 volume mixing ratios that are respectively 0.44 +/- 0.17 and 1.21 +/- 0.24 times the ATMOS/Spacelab 3 values, from which an average COF2 increase rate of 10.3 +/- 1.8%/ year over this time period has been estimated. The present results are compared with previously reported observations and trends and with one-dimensional model calculations. The model calculated trends are in reasonably good agreement with the observations.

Rinsland, C. P.↗

Sedimentary Facies Analysis Using AVIRIS Data: A Geophysical Inverse Problem

AVIRIS data can be used to quantitatively analyze and map sedimentary lithofacies. The observed radiance spectra can be reduced to 'apparent reflectance' spectra by topographic and reflectance characterization of several field sites within the image. These apparent reflectance spectra correspond to the true reflectance at each pixel, multiplied by an unknown illumination factor (ranging in value from zero to one). The spatial abundance patterns of spectrally defined lithofacies and the unknown illumination factors can be simultaneously derived using constrained linear spectral unmixing methods. Estimates of the minimum uncertainty in the final results (due to noise, instrument resolutions, degree of illumination and mixing systematics) can be made by forward and inverse modeling. Specific facies studies in the Rattlesnake Hills region of Wyoming illustrate the successful application of these methods.

Boardmann, Joe W.↗

The Effect of Two-Dimensional Forcing on Self-Similar Turbulent Plane Wakes

Three direct numerical simulations of time-evolving turbulent plane wakes with velocity deficit Reynolds numbers of about 2,000 have been simulated using a spectral numerical method with up to 600 x 260 x 160 modes. The initial conditions for the simulations are generated from direct numerical simulations of a turbulent boundary layer (momentum thickness Reynolds number of 670), and varying amounts of additional two- dimensional, forcing. In order to preserve the self-similar flow evolution, the forcing is implemented by multiplying all the two-dimensional modes in the initial condition by a constant factor. In the "natural" case no additional forcing is used; in the "forced" and "heavily forced" cases this factor is 5 and 20, respectively. The wake spreading rate Is increased by factors of 1.7 and 7.1 for the two forced cases. The Reynolds stresses are also increased by a similar or even larger factor. These results indicate that the plane wake is much more sensitive to initial forcing than the plane mixing layer. As in the plane mixing layer, two-dimensional forcing promotes more organized large-scale vortical flow structures and these structures axe sometimes separated by "braid regions" containing streamwise "rib" vortices, unlike in the unforced wake.

Rogers, M. M.↗

Unstructured Adaptive Meshes: Bad for Your Memory?

This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.

Biswas, Rupak↗

Discovery of a Three-Layered Atmospheric Structure in Accretion Disks around Stellar-Mass Black Holes

We have carried out systematic modeling of the X-ray spectra of the Galactic superluminal jet sources GRS 1915+105 and GRO J1655-40, using our newly developed spectral fitting methods. Our results reveal, for the first time, a three-layered structure of the atmosphere in the inner region of the accretion disks. Above the conanonly known, cold and optically thick disk of a blackbody temperature 0.2-0.5 keV, there is a layer of warm gas with a temperature of 1.0-1.5 keV and an optical depth of around 10. Compton scattering of the underlying disk blackbody photons produces the soft X-ray component we comonly observe. Under certain conditions, there is also a much hotter, optically thin corona above the warm layer, characterized by a temperature of 100 keV or higher and an optical depth of unity or less. The corona produces the hard X-ray component typically seen in these sources. We emphasize that the existence of the warm layer seem to be independent of the presence of the hot corona and, therefore, it is not due to irradiation of the disk by hard X-rays from the corona. Our results suggest a striking structural similarity between the accretion disks and the solar atmosphere, which may provide a new stimulus to study the common underlying physical processes operating in these vastly different systems. We also report the first unambiguous detection of an emission line around 6.4 keV in GRO J1655-40, which may allow further constraining of the accretion disk structure. We acknowledge NASA GSFC and MFC for partial financial support. (copyright) 1999: American Astronomical Society. All rights reverved.

Zhang, S. N.↗

Numerical Simulation of Roughness-Induced Transient Growth in a Laminar Boundary Layer

Numerical simulations are used to examine the roughness-induced transient growth in a laminar boundary-layer flow. Based on the spectral element method, these simulations model the stationary disturbance field associated with a nonsmooth roughness geometry, such as the spanwise periodic array of circular disks used by White and co-workers during a series of wind tunnel experiments at Case Western Reserve University. Besides capturing the major trends from the recent measurements by White and Ergin, the simulations provide additional information concerning the relative accuracy of the experimental findings derived from two separate wall-finding procedures. The paper also explores the dependence of transient growth on geometric characteristics of the roughness distribution, including the height and planform shape of the roughness element and the ratio of roughness due to spacing between an adjacent pair of elements. Results are used for a preliminary assessment of the differences between recently reported theoretical results of Tumin and Reshotko and the measurements by White and Ergin.

Fischer, Paul↗

Temporal Large-Eddy Simulation

In 1999, Stolz and Adams unveiled a subgrid-scale model for LES based upon approximately inverting (defiltering) the spatial grid-filter operator and termed .the approximate deconvolution model (ADM). Subsequently, the utility and accuracy of the ADM were demonstrated in a posteriori analyses of flows as diverse as incompressible plane-channel flow and supersonic compression-ramp flow. In a prelude to the current paper, a parameterized temporal ADM (TADM) was developed and demonstrated in both a priori and a posteriori analyses for forced, viscous Burger's flow. The development of a time-filtered variant of the ADM was motivated-primarily by the desire for a unifying theoretical and computational context to encompass direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds averaged Navier-Stokes simulation (RANS). The resultant methodology was termed temporal LES (TLES). To permit exploration of the parameter space, however, previous analyses of the TADM were restricted to Burger's flow, and it has remained to demonstrate the TADM and TLES methodology for three-dimensional flow. For several reasons, plane-channel flow presents an ideal test case for the TADM. Among these reasons, channel flow is anisotropic, yet it lends itself to highly efficient and accurate spectral numerical methods. Moreover, channel-flow has been investigated extensively by DNS, and a highly accurate data base of Moser et.al. exists. In the present paper, we develop a fully anisotropic TADM model and demonstrate its utility in simulating incompressible plane-channel flow at nominal values of Re(sub tau) = 180 and Re(sub tau) = 590 by the TLES method. The TADM model is shown to perform nearly as well as the ADM at equivalent resolution, thereby establishing TLES as a viable alternative to LES. Moreover, as the current model is suboptimal is some respects, there is considerable room to improve TLES.

Pruett, C. D.↗

Optimal Reconfiguration of Tetrahedral Formations

The problem of minimum-fuel formation reconfiguration for the Magnetospheric Multi-Scale (MMS) mission is studied. This reconfiguration trajectory optimization problem can be posed as a nonlinear optimal control problem. In this research, this optimal control problem is solved using a spectral collocation method called the Gauss pseudospectral method. The objective of this research is to provide highly accurate minimum-fuel solutions to the MMS formation reconfiguration problem and to gain insight into the underlying structure of fuel-optimal trajectories.

Huntington, Geoffrey↗

Lunar and Planetary Science XXXVI, Part 5

Topics discussed include: Automation Recognition oF Crater-Like Structures in Terrestrial and Plantary Images; Condensation from Cluster-IDP Enriched Vapor Inside the Snow Line: Implications for Mercury, Asteroids, and Enstatite Chondrites; Tomographic Location of Potential Melt-Bearing Phenocrysts in Lunar Glass Spherules; Source and Evolution of Vapor Due to Impacts into Layered Carbonates and Silicates; Noble Gases and I-Xe Ages of the Zag Meteorite; The MArs Hand Lens Imager (MAHLI) for the 209 Mars Science Laboratory; The Sedimentary Rocks of Meridiani Planum, in Context; Three-System Isotopic of Lunar Norite 78238: Rb-Sr Results; Constraints on the Role of Curium-247 as a Source of Fission Xenon in the Early Solar System; New Features in the ADS Abstract Service; Cassini RADAR's First Look at Titan; Volcanism and Volatile Recycling on Venus from Lithospheric Delamination; The Fate of Water in the Martian Magma Ocean and the Formation of an Early Atmosphere; Mars Odyssey Neutron Spectrometer Water-Equivalent Hydrogen: Comparison with Glacial; Landforms on Tharsis; Using Models of Permanent Shadow to Constrain Lunar Polar Water Ice Abundances; Martian Radiative Transfer Modeling Using the Optimal Spectral Sampling Method; Petrological and Geochemical Consideration on the Tuserkanite Meteorite; and Mineralogy of Asteroids from Observations with the Spitzer Space Telescope.

Source record↗

Long-wavelength Radar Studies of the Lunar Maria

Radar measurements at 70 cm and 7.5 m wavelengths provide insight into the structure and chemical properties of the upper 5-100 m of the lunar regolith and crust. Past work has identified a number of anomalous regions and changes in echo strength, some attributed to differences in titanium content. There has been little opportunity, however, to compare calibrated long-wavelength backscatter among different units or to theoretical model results. We combine recent high-resolution (3-5 km) 70-cm radar data for the nearside with earlier calibrated full-disk observations to provide a reasonable estimate of the true lunar backscatter coefficient. These data are tested against models for quasi-specular scattering from the surface, echoes from a buried substrate, and Mie scattering from surface and buried rocks. We find that 70 cm echoes likely arise from Mie scattering by distributed rocks within the soil, consistent with earlier hypotheses. Returns from a buried substrate would provide a plausible fit to the observations only if the regolith depth were ~3 m or less and varied little across the maria. Depolarized echoes are due to some combination of single and multiple scattering events, but it appears that single scattering alone could account for the observed echo power, based on comparisons with terrestrial rocky surfaces. Backscatter strength from the regolith is most strongly affected by the loss tangent, whose variation with mineral content is still poorly defined. We compared the backscatter values for the mare deposits to the oxide contents inferred from spectral ratio methods, and found that in general the unit boundaries evident in radar images closely follow those seen in color difference images. The 70-cm data are not well correlated with TiO2 values found using the Charette relationship nor with Fe abundances derived from Clementine observations. The lack of a relationship between radar echo and Fe content is reasonable given the distribution of iron among various mineral phases, but ilmenite content (FeTiO3) has typically been cited as the dominant cause of changes in loss tangent (and thus the radar absorption). The lack of correlation between the radar data and TiO2 estimates may arise from uncertainties in the Charette technique, subtle differences in the upper surface and bulk properties of the regolith, mineralogic effects on the radar not linked to titanium content, or to some combination of these factors. Dark crater haloes in the mare and highlands, and low radar returns from apparent cryptomare regions, are used to illustrate the role radar data can play in identifying changes in regolith composition; low-return haloes around craters such as Petavius may indicate 5-25% contamination of the highlands soil by excavated mare material or a layer of rock-poor ejecta at least several meters deep. The 7.5-m data were shown to correlate to a reasonable degree with estimates of Fe abundance, suggesting that this component of the mare basalts is primarily responsible for attenuation losses at very long wavelengths. The different sensitivities of the two radar wavelengths and multispectral data offers the potential for future deep mapping of the mare lava flows and regolith.

Lunar MariaRadarLunar Studies↗

Long-wavelength Radar Studies of the Lunar Maria

Radar measurements at 70 cm and 7.5 m wavelengths provide insight into the structure and chemical properties of the upper 5-100 m of the lunar regolith and crust. Past work has identified a number of anomalous regions and changes in echo strength, some attributed to differences in titanium content. There has been little opportunity, however, to compare calibrated long-wavelength backscatter among different units or to theoretical model results. We combine recent high-resolution (3-5 km) 70-cm radar data for the nearside with earlier calibrated full-disk observations to provide a reasonable estimate of the true lunar backscatter coefficient. These data are tested against models for quasi-specular scattering from the surface, echoes from a buried substrate, and Mie scattering from surface and buried rocks. We find that 70 cm echoes likely arise from Mie scattering by distributed rocks within the soil, consistent with earlier hypotheses. Returns from a buried substrate would provide a plausible fit to the observations only if the regolith depth were approx.3 m or less and varied little across the maria. Depolarized echoes are due to some combination of single and multiple scattering events, but it appears that single scattering alone could account for the observed echo power, based on comparisons with terrestrial rocky surfaces. Backscatter strength from the regolith is most strongly affected by the loss tangent, whose variation with mineral content is still poorly defined. We compared the backscatter values for the mare deposits to the oxide contents inferred from spectral ratio methods, and found that in general the unit boundaries evident in radar images closely follow those seen in color difference images. The 70-cm data are not well correlated with TiO2 values found using the Charette relationship nor with Fe abundances derived from Clementine observations. The lack of a relationship between radar echo and Fe content is reasonable given the distribution of iron among various mineral phases, but ilmenite content (FeTiO3) has typically been cited as the dominant cause of changes in loss tangent (and thus the radar absorption). The lack of correlation between the radar data and TiO2 estimates may arise from uncertainties in the Charette technique, subtle differences in the upper surface and bulk properties of the regolith, mineralogic effects on the radar not linked to titanium content, or to some combination of these factors. Dark crater haloes in the mare and highlands, and low radar returns from apparent cryptomare regions, are used to illustrate the role radar data can play in identifying changes in regolith composition; low-return haloes around craters such as Petavius may indicate 5-25% contamination of the highlands soil by excavated mare material or a layer of rock-poor ejecta at least several meters deep. The 7.5-m data were shown to correlate to a reasonable degree with estimates of Fe abundance, suggesting that this component of the mare basalts is primarily responsible for attenuation losses at very long wavelengths. The different sensitivities of the two radar wavelengths and multispectral data offers the potential for future deep mapping of the mare lava flows and regolith.

Lunar Studies↗

The Calibration of AVHRR/3 Visible Dual Gain Using Meteosat-8 as a MODIS Calibration Transfer Medium

This viewgraph presentation reviews the NOAA-17 AVHRR visible channels calibrated against MET-8/MODIS using dual gain regression methods. The topics include: 1) Motivation; 2) Methodology; 3) Dual Gain Regression Methods; 4) Examples of Regression methods; 5) AVHRR/3 Regression Strategy; 6) Cross-Calibration Method; 7) Spectral Response Functions; 8) MET8/NOAA-17; 9) Example of gain ratio adjustment; 10) Effect of mixed low/high count FOV; 11) Monitor dual gains over time; and 12) Conclusions

Avey, Lance↗

Obtaining Electron Temperatures and Flow Speeds from Thomson Scattered Coronal Emission Observed during the 29 March 2006 Total Solar Eclipse in Libya

An experiment to measure the electron temperature and flow speed in the solar corona by observing the visible K-coronal spectrum was conducted during the total solar eclipse on 29 March 2006 in Libya. New corona1 models accounting for the effect of electron temperature and flow on the resulting K-corona spectrum were used to interpret the observations. Results show electron temperatures of 1.10 +/- 0.05, 0.98 +/- 0.12, and 0.70 +/- 0.08 MK, at l.l{\it R)$-{\odot)$ in the solar north, east and west, respectively, and 0.93 +/- 0.12 MK, at 1.2 R(sub sun) in the solar east. The corresponding outflow speeds obtained from the spectral fit are 103 +/- 92, 0 + 10, 0 + 10, and 0 + 10 km/s. Since the observations are taken only at 1.1 and 1.2 R(sub sun) these velocities , consistent with zero outflow, are in agreement with expectations and provide additional confirmation that the spectral fitting method is working.

Davila, Joseph M.↗

NASA Tech Briefs, July 2009

Topics covered include: Dual Cryogenic Capacitive Density Sensor; Hail Monitor Sensor; Miniature Six-Axis Load Sensor for Robotic Fingertip; Improved Blackbody Temperature Sensors for a Vacuum Furnace; Wrap-Around Out-the-Window Sensor Fusion System; Wide-Range Temperature Sensors with High-Level Pulse Train Output; Terminal Descent Sensor Simulation; A Robust Mechanical Sensing System for Unmanned Sea Surface Vehicles; Additive for Low-Temperature Operation of Li-(CF)n Cells; Li/CFx Cells Optimized for Low-Temperature Operation; Number Codes Readable by Magnetic-Field-Response Recorders; Determining Locations by Use of Networks of Passive Beacons; Superconducting Hot-Electron Submillimeter-Wave Detector; Large-Aperture Membrane Active Phased-Array Antennas; Optical Injection Locking of a VCSEL in an OEO; Measuring Multiple Resistances Using Single-Point Excitation; Improved-Bandwidth Transimpedance Amplifier; Inter-Symbol Guard Time for Synchronizing Optical PPM; Novel Materials Containing Single-Wall Carbon Nanotubes Wrapped in Polymer Molecules; Light-Curing Adhesive Repair Tapes; Thin-Film Solid Oxide Fuel Cells; Zinc Alloys for the Fabrication of Semiconductor Devices; Small, Lightweight, Collapsible Glove Box; Radial Halbach Magnetic Bearings; Aerial Deployment and Inflation System for Mars Helium Balloons; Steel Primer Chamber Assemblies for Dual Initiated Pyrovalves; Voice Coil Percussive Mechanism Concept for Hammer Drill; Inherently Ducted Propfans and Bi-Props; Silicon Nanowire Growth at Chosen Positions and Orientations; Detecting Airborne Mercury by Use of Gold Nanowires; Detecting Airborne Mercury by Use of Palladium Chloride; Micro Electron MicroProbe and Sample Analyzer; Nanowire Electron Scattering Spectroscopy; Electron-Spin Filters Would Offer Spin Polarization Greater than 1; Subcritical-Water Extraction of Organics from Solid Matrices; A Model for Predicting Thermoelectric Properties of Bi2Te3; Integrated Miniature Arrays of Optical Biomolecule Detectors; A Software Rejuvenation Framework for Distributed Computing; Kurtosis Approach to Solution of a Nonlinear ICA Problem; Robust Software Architecture for Robots; R4SA for Controlling Robots; Bio-Inspired Neural Model for Learning Dynamic Models; Evolutionary Computing Methods for Spectral Retrieval; Monitoring Disasters by Use of Instrumented Robotic Aircraft; Complexity for Survival of Living Systems; Using Drained Spacecraft Propellant Tanks for Habitation; Connecting Node; and Electrolytes for Low-Temperature Operation of Li-CFx Cells.

Source record↗

Theory and Simulation of Real and Ideal Magnetohydrodynamic Turbulence

Incompressible, homogeneous magnetohydrodynamic (MHD) turbulence consists of fluctuating vorticity and magnetic fields, which are represented in terms of their Fourier coefficients. Here, a set of five Fourier spectral transform method numerical simulations of two-dimensional (2-D) MHD turbulence on a 512(sup 2) grid is described. Each simulation is a numerically realized dynamical system consisting of Fourier modes associated with wave vectors k, with integer components, such that k = |k| less than or equal to k(sub max). The simulation set consists of one ideal (non-dissipative) case and four real (dissipative) cases. All five runs had equivalent initial conditions. The dimensions of the dynamical systems associated with these cases are the numbers of independent real and imaginary parts of the Fourier modes. The ideal simulation has a dimension of 366104, while each real simulation has a dimension of 411712. The real runs vary in magnetic Prandtl number P(sub M), with P(sub M) is a member of {0.1, 0.25, 1, 4}. In the results presented here, all runs have been taken to a simulation time of t = 25. Although ideal and real Fourier spectra are quite different at high k, they are similar at low values of k. Their low k behavior indicates the existence of broken symmetry and coherent structure in real MHD turbulence, similar to what exists in ideal MHD turbulence. The value of PM strongly affects the ratio of kinetic to magnetic energy and energy dissipation (which is mostly ohmic). The relevance of these results to 3-D Navier-Stokes and MHD turbulence is discussed.

Shebalin, John V.↗

Single-lens computed tomography imaging spectrometer and method of capturing spatial and spectral information

Computed tomography imaging spectrometers ("CTISs") employing a single lens are provided. The CTISs may be either transmissive or reflective, and the single lens is either configured to transmit and receive uncollimated light (in transmissive systems), or is configured to reflect and receive uncollimated light (in reflective systems). An exemplary transmissive CTIS includes a focal plane array detector, a single lens configured to transmit and receive uncollimated light, a two-dimensional grating, and a field stop aperture. An exemplary reflective CTIS includes a focal plane array detector, a single mirror configured to reflect and receive uncollimated light, a two-dimensional grating, and a field stop aperture.

Wilson, Daniel W.↗

Spectral-Spatial Classification of Hyperspectral Images Using Hierarchical Optimization

A new spectral-spatial method for hyperspectral data classification is proposed. For a given hyperspectral image, probabilistic pixelwise classification is first applied. Then, hierarchical step-wise optimization algorithm is performed, by iteratively merging neighboring regions with the smallest Dissimilarity Criterion (DC) and recomputing class labels for new regions. The DC is computed by comparing region mean vectors, class labels and a number of pixels in the two regions under consideration. The algorithm is converged when all the pixels get involved in the region merging procedure. Experimental results are presented on two remote sensing hyperspectral images acquired by the AVIRIS and ROSIS sensors. The proposed approach improves classification accuracies and provides maps with more homogeneous regions, when compared to previously proposed classification techniques.

Tarabalka, Yuliya↗

Electron Temperatures and Flow Speeds of the Low Solar Corona: MACS Results from the Total Solar Eclipse of 29 March 2006 in Libya

An experiment was conducted in conjunction with the total solar eclipse on 29 March 2006 in Libya to measure both the electron temperature and its flow speed simultaneously at multiple locations in the low solar corona by measuring the visible K-coronal spectrum. Coronal model spectra incorporating the effects of electron temperature and its flow speed were matched with the measured K-coronal spectra to interpret the observations. Results show electron temperatures of (1.10 +/- 0.05) MK, (0.70 +/- 0.08) MK, and (0.98 +/- 0.12) MK, at 1.1 Solar Radius from Sun center in the solar north, east and west, respectively, and (0.93 +/- 0.12) MK, at 1.2 Solar Radius from Sun center in the solar west. The corresponding outflow speeds obtained from the spectral fit are (103 +/- 92) km/s, (0 + 10) km/s, (0+10) km/s, and (0+10) km/s. Since the observations were taken only at 1.1 Solar Radius and 1.2 Solar Radius from Sun center, these speeds, consistent with zero outflow, are in agreement with expectations and provide additional confirmation that the spectral fitting method is working. The electron temperature at 1.1 Solar Radius from Sun center is larger at the north (polar region) than the east and west (equatorial region).

Reginald, Nelson L.↗