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NASA NTRS1993

A predictability study of Lorenz's 28-variable model as a dynamical system

The dynamics of error growth in a two-layer nonlinear quasi-geostrophic model has been studied to gain an understanding of the mathematical theory of atmospheric predictability. The growth of random errors of varying initial magnitudes has been studied, and the relation between this classical approach and the concepts of the nonlinear dynamical systems theory has been explored. The local and global growths of random errors have been expressed partly in terms of the properties of an error ellipsoid and the Liapunov exponents determined by linear error dynamics. The local growth of small errors is initially governed by several modes of the evolving error ellipsoid but soon becomes dominated by the longest axis. The average global growth of small errors is exponential with a growth rate consistent with the largest Liapunov exponent. The duration of the exponential growth phase depends on the initial magnitude of the errors. The subsequent large errors undergo a nonlinear growth with a steadily decreasing growth rate and attain saturation that defines the limit of predictability. The degree of chaos and the largest Liapunov exponent show considerable variation with change in the forcing, which implies that the time variation in the external forcing can introduce variable character to the predictability.

Krishnamurthy, V.↗

NASA NTRS1924

The Inertial Coefficients of an Airship in a Frictionless Fluid

This report deals with the investigation of the apparent inertia of an airship hull. The exact solution of the aerodynamical problem has been studied for hulls of various shapes and special attention has been given to the case of an ellipsoidal hull. In order that the results for this last case may be readily adapted to other cases, they are expressed in terms of the area and perimeter of the largest cross section perpendicular to the direction motion by means of a formula involving a coefficient K which varies only slowly when the shape of the hull is changed, being 0.637 for a circular or elliptic disk, 0.5 for a sphere, and about 0.25 for a spheroid of fineness ratio 7. For rough purposes it is sufficient to employ the coefficients, originally found for ellipsoids, for hulls otherwise shaped. When more exact values of the inertia are needed, estimates may be based on a study of the way in which K varies with different characteristics and for such a study the new coefficient possesses some advantage over one which is defined with reference to the volume of fluid displaced. The case of rotation of an airship hull has been investigated also and a coefficient has been defined with the same advantages as the corresponding coefficient for rectilinear motion.

Bateman, H↗

NASA NTRS1930

Flow and Force Equations for a Body Revolving in a Fluid

Part I gives a general method for finding the steady-flow velocity relative to a body in plane curvilinear motion, whence the pressure is found by Bernoulli's energy principle. Integration of the pressure supplies basic formulas for the zonal forces and moments on the revolving body. Part II, applying this steady-flow method, finds the velocity and pressure at all points of the flow inside and outside an ellipsoid and some of its limiting forms, and graphs those quantities for the latter forms. Part III finds the pressure, and thence the zonal force and moment, on hulls in plane curvilinear flight. Part IV derives general equations for the resultant fluid forces and moments on trisymmetrical bodies moving through a perfect fluid, and in some cases compares the moment values with those found for bodies moving in air. Part V furnishes ready formulas for potential coefficients and inertia coefficients for an ellipsoid and its limiting forms. Thence are derived tables giving numerical values of those coefficients for a comprehensive range of shapes.

Zahm, A F↗

NASA NTRS1994

Progress in navigation filter estimate fusion and its application to spacecraft rendezvous

A new derivation of an algorithm which fuses the outputs of two Kalman filters is presented within the context of previous research in this field. Unlike other works, this derivation clearly shows the combination of estimates to be optimal, minimizing the trace of the fused covariance matrix. The algorithm assumes that the filters use identical models, and are stable and operating optimally with respect to their own local measurements. Evidence is presented which indicates that the error ellipsoid derived from the covariance of the optimally fused estimate is contained within the intersections of the error ellipsoids of the two filters being fused. Modifications which reduce the algorithm's data transmission requirements are also presented, including a scalar gain approximation, a cross-covariance update formula which employs only the two contributing filters' autocovariances, and a form of the algorithm which can be used to reinitialize the two Kalman filters. A sufficient condition for using the optimally fused estimates to periodically reinitialize the Kalman filters in this fashion is presented and proved as a theorem. When these results are applied to an optimal spacecraft rendezvous problem, simulated performance results indicate that the use of optimally fused data leads to significantly improved robustness to initial target vehicle state errors. The following applications of estimate fusion methods to spacecraft rendezvous are also described: state vector differencing, and redundancy management.

Carpenter, J. Russell↗

NASA NTRS1994

Differential GPS and system integration of the Low Visibility Landing and Surface Operations (LVLASO) demonstration

The LVLASO Flight Demonstration of ASTA concepts (FDAC) integrates NASA-Langley's electronic moving map display and Transport Systems Research Vehicle (TSRV) (a modified Boeing 737 aircraft); ARINC's VHF data link, GPS ground station, and automated controller workstation; and Norden's surface radar/airport movement safety system. Aircraft location is shown on the electronic map display in the cockpit. An approved taxi route as well as other aircraft and surface traffic are also displayed. An Ashtech Z12 Global Positioning System (GPS) receiver on the TSRV estimates the aircraft's position. In Differential mode (DSPS), the Ashtech receiver accepts differential C/A code pseudorange corrections from a GPS ground station. The GPS ground station provides corrections up to ten satellites. The corrections are transmitted on a VHF data link at a 1 Hz. rate using the RTCM-104 format. DGPS position estimates will be within 5 meters of actual aircraft position. DGPS position estimates are blended with position, velocity, acceleration, and heading data from the TSRV Air Data/Inertial Reference System (ADIRS). The ADIRS data is accurate in the short-term, but drifts over time. The DGPS data is used to keep the ADIRS position accurate. Ownship position, velocity, heading, and turn rate are sent at a 20 Hz. rate to the electronic map display. Airport traffic is detected by the airport surface radar system. Aircraft and vehicles such as fuel trucks and baggage carts are detected. The traffic's location, velocity, and heading are sent to the TSRV. To prevent traffic symbology from jumping each second when a location update arrives, velocity and heading are used to predict a new traffic location for each display update. Possible runway incursions and collisions can be shown on the electronic map. Integrating the different systems used in the FDAC requires attention to the underlying coordinate systems. The airport diagram displayed on the electronic map is obtained from published navigational charts. The charts reference the North American Datum of 1927 (NAD27) or a local state-plane coordinate system. GPS uses the World Geodetic Standard of 1984 (WGS84). Both NAD27 and WGS84 model the Earth as an ellipsoid, however, they use a different origin and different size ellipsoids. Latitudes and longitudes given in these systems can be converted to a Cartesian system with the origin at the Earth's center. The surface radar detects traffic in a locally-level, rho-theta coordiante system. The electronic airport diagram is stored using a flat XY coordinate system. The map origin is at the tower and is referenced as True North up. All ownship and other traffic positions must be converted to the electronic map's frame of reference for display.

Rankin, James M.↗

NASA NTRS1994

Geometrical evidence for dark matter: X-ray constraints on the mass of the elliptical galaxy NGC 720

We describe (1) a new test for dark matter and alternate theories of gravitation based on the relative geometries of the X-ray and optical surface brightness distributions and an assumed form for the potential, of the optical light, (2) a technique to measure the shapes of the total gravitating matter and dark matter of an ellipsoidal system which is insensitive to the precise value of the temperature of the gas and to modest temperature gradients, and (3) a new method to determine the ratio of dark mass to stellar mass that is dependent on the functional forms for the visible star, gas and dark matter distributions, but independent of the distance to the galaxy or the gas temperature. We apply these techniques to X-ray data from the ROSAT Position Sensitive Proportional Counter (PSPC) of the optically flattened elliptical galaxy NGC 720; the optical isophotes have ellipticity epsilon approximately 0.40 extending out to approximately 120 sec. The X-ray isophotes are significantly elongated, epsilon = 0.20-0.30 for semimajor axis a approximately 100 sec. The major axes of the optical and X-ray isophotes are misaligned by approximately 30 deg +/- 15 deg. Spectral analysis of the X-ray data reveals no evidence of temperature gradients or anisotropies and demonstrates that a single-temperature plasma (T approximately 0.6 keV) having subsolar heavy element abundances and a two-temperature model having solar abundances describe the spectrum equally well. Considering only the relative geometries of the X-ray and optical surface brightness distributions and an assumed functional form for the potential of the optical light, we conclude that matter distributed like the optical light cannot produce the observed ellipticities of the X-ray isophotes, independent of the gas pressure, the gas temperature, and the value of the stellar mass; this comparison assumes a state of quasi-hydrostatic equilibrium so that the three-dimensional surfaces of the gas emissivity trace the three-dimensional isopotential surfaces -- we discuss the viability of this assumption for NGC 720. Milgrom's Modification of Newtonian Dynamics (MOND) cannot dispel this manifestation of dark matter. Hence, geometrical considerations require, without mention of pressure or temperature, the presence of an extended, massive dark matter halo in NGC 720. Employing essentially the technique of Buote & Canizares (1992; Buote 1992) we use the shape of the X-ray surface brightness to constrain the shape of the total gravitating matter. The total matter is modeled as either an oblate or prolate spheriod of constant shape and orientation having either a Ferrers (rho approximately r(exp -n)) or Hernquist density. Assuming the X-ray gas is in hydrostatic equilibrium, we construct a model X-ray gas distribution for various temperature profiles. We determine the ellipticity of the total gravitating matter to be epsilon approximately 0.50-0.70. Using the single-temperature model we estimate a total mass approximately (0.41-1.4) x 10(exp 12) h(sub 80) solar mass interior to the ellipsoid of semimajor axis 43.6 h(sub 80) kpc. Ferrers densities as steep as r(exp -3) do not fit the data, but the r(exp -2) and Hernquist models yield excellent fits. We estimate the mass distributions of the stars and the gas and fit the dark matter directly. For a given gas equation of state and functional forms for the visible stars, gas, and dark matter, these models yield a distance-independent and temperature-independent measurement of the ratio of dark mass to stellar mass M(sub DM)/M(sub stars). We estimate a minimum M(sub DM)/M(sub stars) greater than or equal to 4 which corresponds to a total mass slightly greater than that derived from the single-temperature models for distance D = 20h(sub 80) Mpc.

Buote, David A.↗

NASA NTRS1994

Method for confining the magnetic field of the cross-tail current inside the magnetopause

A method is presented for analytically representing the magnetic field due to the cross-tail current and its closure on the magnetopause. It is an extension of a method used by Tsyganenko (1989b) to confine the dipole field inside an ellipsoidal magnetopause using a scalar potential. Given a model of the cross-tail current, the implied net magnetic field is obtained by adding to the cross-tail current field a potential field B = - del gamma, which makes all field lines divide into two disjoint groups, separated by the magnetopause (i.e., the combined field is made to have zero normal component with the magnetopause). The magnetopause is assumed to be an ellipsoid of revolution (a prolate spheroid) as an approximation to observations (Sibeck et al., 1991). This assumption permits the potential gamma to be expressed in spheroidal coordinates, expanded in spheroidal harmonics and its terms evaluated by performing inversion integrals. Finally, the field outside the magnetopause is replaced by zero, resulting in a consistent current closure along the magnetopause. This procedure can also be used to confine the modeled field of any other interior magnetic source, though the model current must always flow in closed circuits. The method is demonstrated on the T87 cross-tail current, examples illustrate the effect of changing the size and shape of the prescribed magnetopause and a comparison is made to an independent numerical scheme based on the Biot-Savart equation.

Sotirelis, T.↗

NASA NTRS1995

Effect of Gravity on the Mammalian Cell Deformation

The effect of human cell immersed in culture liquid under a micro-gravity environment has been investigated. The study is based on the numerical simulation of the configuration of human cell affected by the time dependent variation of gravity acceleration ranging from 10(exp -3) to 2 g(sub o) (g(sub o) = 9.81 m/s(exp 2)) in 15 seconds. Both the free floating cell and the cell contacted to the upper and lower inclined walls imposed by the time-dependent reduced gravity acceleration are considered in this study. The results show that the cell configuration changes from spherical to horizontally elongated ellipsoid for both the free floating cell and the cell sitting on the lower inclined wall while the cell configuration varies from spherical to vertically elongated ellipsoid for the cell hanging to the upper inclined wall when the gravity acceleration increases. Experimental observations, carried out of human cells exposed to the variation of gravity levels, show that the results of experimental observations agree exactly with the theoretical model computation described in this paper. These results sre significant for humans exposed to the micro-gravity environment.

Hung, R. J.↗

NASA NTRS1998

Heat Conduction in Ceramic Coatings: Relationship Between Microstructure and Effective Thermal Conductivity

Analysis of the effective thermal conductivity of ceramic coatings and its relation to the microstructure continued. Results (obtained in Task 1) for the three-dimensional problem of heat conduction in a solid containing an inclusion (or, in particular, cavity - thermal insulator) of the ellipsoidal shape, were further advanced in the following two directions: (1) closed form expressions of H tensor have been derived for special cases of ellipsoidal cavity geometry: spheroid, crack-like spheroidal cavity and needle shaped spheroidal cavity; (2) these results for one cavity have been incorporated to construct heat energy potential for a solid with many spheroidal cavities (in the approximation of non-interacting defects). This problem constitutes a basic building block for further analyses.

Kachanov, Mark↗

NASA NTRS1996

An Electrothermodynamic Model with Distributed Properties for Effective Permittivities of Sea Ice

This paper presents a model to calculate the temperature dependence of effective permittivities for sea ice, a heterogeneous medium containing multiphase scatterers. With the strong permittivity fluctuation approach the model accounts for the electrodynamic scattering effect together with the quasi-static characteristics of multiple species and subspecies of inhomogeneities with distributed orientations, sizes, and shapes. Because of a preferential direction in the orientation distribution, the medium is effectively anisotropic. The size distribution is described with a probability density function in terms of normalized volumetric sizes. Scatterer shapes are nonuniform and have a general ellipsoidal form characterized by arbitrary axial ratios of correlation lengths which are related to physical geometries of the scatterers. In this formulation, sea ice consisting of solid ice, liquid brine, and gaseous inclusions is modeled to derive effective permittivities with thermodynamic phase redistribution and structural metamorphism. Theoretical results are in good agreement with experimental data at the C band frequency of 4.8 GHz for saline ice undergoing warming and cooling cycles. A competitive effect between the increase of liquid brine and the shape rounding of ellipsoidal scatterers at increasing temperatures explains the trend observed in measured data. Sensitivities of effective permittivities to structural and physical parameters characterizing sea ice are also studied.

Nghiem, S. V.↗

NASA NTRS1996

Shape and Orientation of Mercury from Radar Ranging Data

If Mercury's radius is expanded in Legendre functions to the second degree and order, the systematic error in radar ranging can be reduced significantly. We interpret the expansion coefficients in terms of a best-fit ellipsoid displaced with respect to the center of mass in the equatorial plane. The ellipsoid's principal axes are rotated in the equatorial plane such that the long axis is aligned with cartographic longitude 15.3 deg +/- 2.9 deg (west). The pole location is consistent with the IAU pole, normal to Mercury's orbital plane. There is a significant equatorial ellipticity (a - b)/a = (540 +/- 54) x 10(exp -6). The center of figure is offset from the center of mass (C.F.-C.M.) by 640 +/- 78 m in the equatorial plane in the direction of cartographic longitude 319.5 deg +/- 6.9 deg. The magnitude of the equatorial center of figure offset implies an excess crustal thickness of 12 km or less, comparable to the Moon's excess. By comparing the equatorial ellipticity with the Mariner 10 gravity coefficient C(sub 22) and assuming Airy isostatic compensation, we conclude that Mercury's crustal thickness is in the range from 100 to 300 km.

Anderson, J. D.↗

NASA NTRS2000

Feeling Gravity's Pull: Gravity Modeling. The Gravity Field of Mars

Most people take the constant presence of gravitys pull for granted. However, the Earth's gravitational strength actually varies from location to location. This variation occurs because mass, which influences an object's gravitational pull, is not evenly distributed within the planet. Changes in topography, such as glacial movement, an earthquake, or a rise in the ocean level, can subtly affect the gravity field. An accurate measurement of the Earth's gravity field helps us understand the distribution of mass beneath the surface. This insight can assist us in locating petroleum, mineral deposits, ground water, and other valuable substances. Gravity mapping can also help notice or verify changes in sea surface height and other ocean characteristics. Such changes may indicate climate change from polar ice melting and other phenomena. In addition, gravity mapping can indicate how land moves under the surface after earthquakes and other plate tectonic processes. Finally, changes in the Earth's gravity field might indicate a shift in water distribution that could affect agriculture, water supplies for population centers, and long-term weather prediction. Scientists can map out the Earth's gravity field by watching satellite orbits. When a satellite shifts in vertical position, it might be passing over an area where gravity changes in strength. Gravity is only one factor that may shape a satellite's orbital path. To derive a gravity measurement from satellite movement, scientists must remove other factors that might affect a satellite's position: 1. Drag from atmospheric friction. 2. Pressure from solar radiation as it heads toward Earth and. as it is reflected off the surface of the Earth 3. Gravitational pull from the Sun, the Moon, and other planets in the Solar System. 4. The effect of tides. 5. Relativistic effects. Scientists must also correct for the satellite tracking process. For example, the tracking signal must be corrected for refraction through the atmosphere of the Earth. Supercomputers can calculate the effect of gravity for specific locations in space following a mathematical process known as spherical harmonics, which quantifies the gravity field of a planetary body. The process is based on Laplace's fundamental differential equation of gravity. The accuracy of a spherical harmonic solution is rated by its degree and order. Minute variations in gravity are measured against the geoid, a surface of constant gravity acceleration at mean sea level. The geoid reference gravity model strength includes the central body gravitational attraction (9.8 m/sq s) and a geopotential variation in latitude partially caused by the rotation of the Earth. The rotational effect modifies the shape of the geoid to be more like an ellipsoid, rather than a perfect, circle. Variations of gravity strength from the ellipsoidal reference model are measured in units called milli-Galileos (mGals). One mGal equals 10(exp -5) m/sq s. Research projects have also measured the gravity fields of other planetary bodies, as noted in the user profile that follows. From this information, we may make inferences about our own planet's internal structure and evolution. Moreover, mapping the gravity fields of other planets can help scientists plot the most fuel-efficient course for spacecraft expeditions to those planets.

Lemoine, Frank↗

NASA NTRS2002

Manipulability, force, and compliance analysis for planar continuum manipulators

Continuum manipulators, inspired by the natural capabilities of elephant trunks and octopus tentacles, may find niche applications in areas like human-robot interaction, multiarm manipulation, and unknown environment exploration. However, their true capabilities will remain largely inaccessible without proper analytical tools to evaluate their unique properties. Ellipsoids have long served as one of the foremost analytical tools available to the robotics researcher, and the purpose of this paper is to first formulate, and then to examine, three types of ellipsoids for continuum robots: manipulability, force, and compliance.

Non-NASA Center↗

NASA NTRS1995

(abstract) A Polarimetric Model for Effects of Brine Infiltrated Snow Cover and Frost Flowers on Sea Ice Backscatter

A polarimetric scattering model is developed to study effects of snow cover and frost flowers with brine infiltration on thin sea ice. Leads containing thin sea ice in the Artic icepack are important to heat exchange with the atmosphere and salt flux into the upper ocean. Surface characteristics of thin sea ice in leads are dominated by the formation of frost flowers with high salinity. In many cases, the thin sea ice layer is covered by snow, which wicks up brine from sea ice due to capillary force. Snow and frost flowers have a significant impact on polarimetric signatures of thin ice, which needs to be studied for accessing the retrieval of geophysical parameters such as ice thickness. Frost flowers or snow layer is modeled with a heterogeneous mixture consisting of randomly oriented ellipsoids and brine infiltration in an air background. Ice crystals are characterized with three different axial lengths to depict the nonspherical shape. Under the covering multispecies medium, the columinar sea-ice layer is an inhomogeneous anisotropic medium composed of ellipsoidal brine inclusions preferentially oriented in the vertical direction in an ice background. The underlying medium is homogeneous sea water. This configuration is described with layered inhomogeneous media containing multiple species of scatterers. The species are allowed to have different size, shape, and permittivity. The strong permittivity fluctuation theory is extended to account for the multispecies in the derivation of effective permittivities with distributions of scatterer orientations characterized by Eulerian rotation angles. Polarimetric backscattering coefficients are obtained consistently with the same physical description used in the effective permittivity calculation. The mulitspecies model allows the inclusion of high-permittivity species to study effects of brine infiltrated snow cover and frost flowers on thin ice. The results suggest that the frost cover with a rough interface significantly increases the backscatter from thin saline ice and the polarimetric signature becomes closer to the isotropic characteristics. The snow cover also modifies polarimetric signatures of thin sea ice depending on the snow mixture and the interface condition.

thin sea ice radar backscatter frost flowers snow ↗

NASA NTRS1991

Variable magnification variable dispersion glancing incidence imaging x-ray spectroscopic telescope

A variable magnification variable dispersion glancing incidence x-ray spectroscopic telescope capable of multiple high spatial revolution imaging at precise spectral lines of solar and stellar x-ray and extreme ultraviolet radiation sources includes a pirmary optical system which focuses the incoming radiation to a primary focus. Two or more rotatable carries each providing a different magnification are positioned behind the primary focus at an inclination to the optical axis, each carrier carrying a series of ellipsoidal diffraction grating mirrors each having a concave surface on which the gratings are ruled and coated with a mutlilayer coating to reflect by diffraction a different desired wavelength. The diffraction grating mirrors of both carriers are segments of ellipsoids having a common first focus coincident with the primary focus. A contoured detector such as an x-ray sensitive photogrpahic film is positioned at the second respective focus of each diffraction grating so that each grating may reflect the image at the first focus to the detector at the second focus. The carriers are selectively rotated to position a selected mirror for receiving radiation from the primary optical system, and at least the first carrier may be withdrawn from the path of the radiation to permit a selected grating on the second carrier to receive radiation.

Hoover, Richard B.↗

NASA NTRSDate not supplied

MISR Geometric Parameters (MIB2GEOP_V1)

SOLAR AZIMUTH ANGLE↗

NASA NTRSDate not supplied

MISR Level 1B2 Terrain Data (MI1B2T_V1)

The MISR instrument consists of nine pushbroom cameras which measure radiance in four spectral bands. Global coverage is achieved in nine days. The cameras are arranged with one camera pointing toward the nadir, four cameras pointing forward and four cameras pointing aftward. It takes 7 minutes for all nine cameras to view the same surface location. The view angles relative to the surface reference ellipsoid, are 0, 26.1, 45.6, 60.0, and 70.5 degrees. The spectral band shapes are nominally gaussian, centered at 443, 555, 670, and 865 nm. The Terrain data are re-projected to the terrain altitude. In this product, surface data from all cameras will appear in the same geographic location. Thus, this product is the primary input to Level 2 aerosol/surface processing, which requires co-registration of the L1B2 imagery at the surface. Clouds will still be displaced due to their elevation above the surface, but this time with respect to the terrain rather than the ellipsoid. (The mountain location T is now assigned the geographic location at T, and the Cloud at F appears at the geographic location T.) In Level 2 aerosol/surface processing, algorithms are applied to screen out the clouds. Terrain data only exist for MISR blocks containing some land. [Temporal_Coverage: Start_Date=2000-02-24; Stop_Date=] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=563.2 km (cross-track); Longitude_Resolution=140.8 km (along-track).; Temporal_Resolution=about 15 orbits/day; Temporal_Resolution_Range=about 15 orbits/day].

NEAR IR WAVELENGTHS↗

NASA NTRSDate not supplied

MISR Level 1B2 Terrain Data (MI1B2T_V2)

The MISR instrument consists of nine pushbroom cameras which measure radiance in four spectral bands. Global coverage is achieved in nine days. The cameras are arranged with one camera pointing toward the nadir, four cameras pointing forward and four cameras pointing aftward. It takes 7 minutes for all nine cameras to view the same surface location. The view angles relative to the surface reference ellipsoid, are 0, 26.1, 45.6, 60.0, and 70.5 degrees. The spectral band shapes are nominally gaussian, centered at 443, 555, 670, and 865 nm. The Terrain data are re-projected to the terrain altitude. In this product, surface data from all cameras will appear in the same geographic location. Thus, this product is the primary input to Level 2 aerosol/surface processing, which requires co-registration of the L1B2 imagery at the surface. Clouds will still be displaced due to their elevation above the surface, but this time with respect to the terrain rather than the ellipsoid. (The mountain location T is now assigned the geographic location at T, and the Cloud at F appears at the geographic location T.) In Level 2 aerosol/surface processing, algorithms are applied to screen out the clouds. Terrain data only exist for MISR blocks containing some land. [Location=GLOBAL LAND] [Temporal_Coverage: Start_Date=2000-02-24; Stop_Date=] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=563.2 km (cross-track); Longitude_Resolution=140.8 km (along-track).; Temporal_Resolution=about 15 orbits/day; Temporal_Resolution_Range=about 15 orbits/day].

SPECTRAL BANDS↗