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NASA NTRS1990

Internal structure of Io and the global distribution of its topography

A global topography is presently calculated for two multilayer Io models in which dissipation occurs in a viscous asthenosphere and a solid mantle: (1) a 'thermal swell' model, in which topography and heat flow are positively correlated, and (2) a 'differentiated lithosphere' model, in which topography and heat flow are negatively correlated. Both the polar topography and the hypsometric distribution of elevations in the differentiated lithosphere model are better matched with observations than the thermal swell model. The shift of the equatorial basin-swell pattern indicates a recent zonal rotation of about 25 deg for Io's lithosphere.

Ross, M. N.↗

NASA NTRS1991

Supercritical baroclinic disturbances under the influence of topography

An Eady model modified to include Ekman dissipation and sloping horizontal boundaries is used to investigate the nonlinear evolution of baroclinic waves in the presence of surface topography. The effectiveness of the topography to phase lock and equilibrate a given mode vs that of baroclinity to propagate and vacillate that mode is found to depend on the topographic height, its zonal structure, and the level of supercriticality. When topography is sinusoidal and of the same wavelength as the baroclinically most unstable mode, it induces a short-period amplitude modulation whose envelope represents the baroclinic evolution. The dynamics of this modulation is explored analytically. When the sinusoidal topography is of a longer zonal wavelength, a 'mixed' wave state persists with amplitude dominance shifting between the topographic mode and the baroclinic mode, depending on the relative strength of form drag and baroclinicity. Model results are also compared, in appropriate parameter limits, with near-resonance asymptotic results and annulus experiments.

Chou, Shih-Hung↗

NASA NTRS1993

Geoid-to-topography ratios on Venus: A global perspective

Recently available spherical harmonic solutions for the geoid and topography of Venus are sufficiently high resolution that they can be used to address questions concerning the relationship between geoid and topography on a regional scale. We have approached this question by mapping the geoid-to-topography ratio (GTR) on a systematic global basis. For a given point on the surface, we consider the geoid and elevation values at all points on a gridded representation of those fields located within a specified distance of the reference point. From the set of paired values, we determine the correlation coefficient and the best-fitting straight line. The latter is the GTR at that position, and the former is a measure of the significance of the derived ratio. This procedure is then repeated for all points on the global grid, yielding maps of the GTR and the correlation coefficient. Unlike previous studies of the GRT on Venus, this apprach permits us to make an objective and systematic search for regions with anomalous GTR's as well as areas that do not demonstrate any strong correlation between geoid and topography. These maps can be updated regularly as new harmonic models of the Venus geoid are produced from new Magellan tracking data. This procedure permits the development of a global perspective on the relationship between GTR and venusian surface tectonics.

Simons, Mark↗

NASA NTRS1994

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Tsaoussi, Lucia S.↗

NASA NTRS1997

Topography of the Moon from the Clementine Lidar

Range measurements from the lidar instrument carried aboard the Clementine spacecraft have been used to produce an accurate global topographic model of the Moon. This paper discusses the function of the lidar; the acquisition, processing, and filtering of observations to produce a global topographic model; and the determination of parameters that define the fundamental shape of the Moon. Our topographic model: a 72nd degree and order spherical harmonic expansion of lunar radii, is designated Goddard Lunar Topography Model 2 (GLTM 2). This topographic field has an absolute vertical accuracy of approximately 100 m and a spatial resolution of 2.5 deg. The field shows that the Moon can be described as a sphere with maximum positive and negative deviations of approx. 8 km, both occurring on the farside, in the areas of the Korolev and South Pole-Aitken (S.P.-Aitken) basins. The amplitude spectrum of the topography shows more power at longer wavelengths as compared to previous models, owing to more complete sampling of the surface, particularly the farside. A comparison of elevations derived from the Clementine lidar to control point elevations from the Apollo laser altimeters indicates that measured relative topographic heights generally agree to within approx. 200 in over the maria. While the major axis of the lunar gravity field is aligned in the Earth-Moon direction, the major axis of topography is displaced from this line by approximately 10 deg to the cast and intersects the farside 24 deg north of the equator. The magnitude of impact basin topography is greater than the lunar flattening (approx. 2 km) and equatorial ellipticity (approx. 800 m), which imposes a significant challenge to interpreting the lunar figure. The floors of mare basins are shown to lie close to an equipotential surface, while the floors of unflooded large basins, except for S.P.-Aitken, lie above this equipotential. The radii of basin floors are thus consistent with a hydrostatic mechanism for the absence of significant farside maria except for S.P.-Aitken, whose depth and lack of mare require significant internal compositional and/or thermal heterogeneity. A macroscale surface roughness map shows that roughness at length scales of 10(exp 1) - 10(exp 2) km correlates with elevation and surface age.

Smith, David E.↗

NASA NTRS1998

MOLA Topography of the Crustal Dichotomy Boundary Zone, Mars

Mars Orbiter Laser Altimeter (MOLA) profiles frequently cross the crustal dichotomy boundary where the transition zone (TZ) between cratered highland terrain (CT) and lowland smooth plains (SP) is marked by mesas and knobby terrain. The detailed topographic character of the boundary zone is longitudinally variable, as is the geomorphology of the TZ. Some portions of the boundary are associated with an outer ring of the Utopia impact basin; MOLA topography is consistent with this. The regional character of the boundary topography is a 2-4 km step function from nearly flat SP to almost as flat CT. This rise has a regional slope of 1-2 degrees, 50-100 times that of the Cr and SP away from TZ, which suggests a significant change in crustal properties (thickness, composition or both) across the TZ. The overall topography is very similar to that at some passive continent-oceanic crustal margins on the Earth, with the seafloor allowed to adjust upward after removal of the overlying water. A possible temporal constraint on the CT/SP elevation difference comes from two MOLA profiles which pass through two large (150 km diameter) craters located at the boundary in Aeolis. The N and S rims of the more degraded crater are at the same elevation; north of the N rim the topography drops by greater than 2 km to the floor of the TZ. This crater predates the elevation offset between CT and TZ floor. The better preserved crater (Gale) has a N rim 2 km lower than its S rim, and appears to have been emplaced on a pre-existing regional slope of about I degree. Gale probably post- dates the elevation difference between CT and TZ floor. Based on the stratigraphy of the units in which these craters are found, the elevation difference appears to have been in place in the Mid to Late Noachian.

Frey, Herbert V.↗

NASA NTRS1999

The Relationship of the MOLA Topography of Mars to the Mean Atmospheric Pressure

The MOLA topography of Mars is based on a new mean radius of the planet and new equipotential surface for the areoid. The mean atmospheric pressure surface of 6.1mbars that has been used in the past as a reference level for topography does not apply to the zero level of MOLA elevations. The MOLA mean radius of the planet is 3389508 meters and the mean equatorial radius is 339600 meters. The areoid of the zero level of the MOLA altimetry is defined to be the potential surface with the same potential as the mean equatorial radius. The MOLA topography differs from the USGS digital elevation data by approximately 1.6 km, with MOLA higher. The average pressure on the MOLA reference surface for Ls =0 is approximately 5.1 mbars and has been derived from occultation data obtained from the tracking of Viking, Mariner, and MGS spacecraft and interpolated with the aid of the Ames Mars GCM. The new topography and the new occultation data are providing a more reliable relationship between elevation and surface pressure.

Smith, David E.↗

NASA NTRS1998

MOLA Topography of Impact Basins in the Northern Hemisphere of Mars

Coverage of the northern hemisphere of Mars by the Mars Orbiter Laser Altimeter (MOLA) during the aerobraking hiatus and the two Science Phasing Operation periods provides improved definition and characterization of large impact basins. Gridded MOLA data show the Utopia Basin has a pronounced bowl-like structure, as opposed to the interior rises suggested by the earlier USGS DEM. The elevation structure is concentric about the basin center as mapped by McGill. In particular, the proposed inner ring closely follows the -4 km contour over much of the southern, western and northwestern sides. Higher topography along portions of the dichotomy boundary aligns with the basin's outer ring. High topography in the polar region also occurs where the outer ring should lie, raising the possibility that perhaps some of the polar topography is due to basin structure as well as ice. Two MOLA passes near Phison Rupes provide evidence for a large "stealth" hole where Viking imagery show little evidence of any major structure. The 2 km deep, 600 km wide depression at 31OW, 3ON is as large as the Cassini impact basin 1000 km to the SW. While Cassini is easily recognized in image data, the "MOLA Hole" is not. If this depression is a deeply eroded and buried impact basin (as perhaps suggested by a decrease in the crater density and somewhat smoother terrain than in adjacent areas), it is not clear why it has managed to maintain its great depth. In Tempe at the dichotomy boundary a 300 km wide impact basin is revealed by pronounced bowl-like topography centered at 87W, 47N, even though only about 1/3 of the basin rim structure is obvious. The basin lies on a sloping boundary zone, with the more buried N rim up to 2 km below the rugged S rim. A similar N-S asymmetry in basin ring structure occurs for the much larger Isidis Basin, where the S rim rises 6 km but the subdued N rim rises barely 2 km above the floor. There is essentially no topographic expression of the main ring in the NE quadrant of Isidis where, if it exists, it lies below Hesperian-age plains.

Frey, Herbert↗

NASA NTRS1999

Southern Hemisphere Storm Zones on Mars: Implications of MOLA Topography

Using the NASA Ames Mars general circulation model and recent Mars orbiter laser altimeter (MOLA) global topography, annual-cycle simulations have been performed corresponding to a lowglobally-averaged atmospheric dust loading (tau= 0 - 3). Comparisons of key global circulation fields as simulated utilizing previous topography datasets and those using the new Mars global topography have been carried out. Values of globally and/or hemispheric averaged kinetic energy associated with the longitudinally averaged (i.e., zonal) circulation and longitudinal departures (i.e., eddy components) as a function of season for simulations using the different topography datasets are provided contributions arising frommeteorological variability associated with thermal tides, stationary circulation components and recurrent weather systems (transient baroclinc and/or barotropic eddies). It can be noted that eddy activity in the northern hemisphere (NH) is substantially diminished using the new topographic data, and that at some seasons, the southern hemisphere (SH) activity is moderately increased. Additional information is contained in the original extended abstract.

Hollingsworth, J. L.↗

NASA NTRS2002

Imaging Laser Altimetry in the Amazon: Mapping Large Areas of Topography, Vegetation Height and Structure, and Biomass

A flight mission of NASA GSFC's Laser Vegetation Imaging Sensor (LVIS) is planned for June-August 2003 in the Amazon region of Brazil. The goal of this flight mission is to map the vegetation height and structure and ground topography of a large area of the Amazon. This data will be used to produce maps of true ground topography, vegetation height, and estimated above-ground biomass and for comparison with and potential calibration of Synthetic Aperture Radar (SAR) data. Approximately 15,000 sq. km covering various regions of the Amazon will be mapped. The LVIS sensor has the unique ability to accurately sense the ground topography beneath even the densest of forest canopies. This is achieved by using a high signal-to-noise laser altimeter to detect the very weak reflection from the ground that is available only through small gaps in between leaves and between tree canopies. Often the amount of ground signal is 1% or less of the total returned echo. Once the ground elevation is identified, that is used as the reference surface from which we measure the vertical height and structure of the vegetation. Test data over tropical forests have shown excellent correlation between LVIS measurements and biomass, basal area, stem density, ground topography, and canopy height. Examples of laser altimetry data over forests and the relationships to biophysical parameters will be shown. Also, recent advances in the LVIS instrument will be discussed.

Blair, J. Bryan↗

NASA NTRS2003

The Influence of Current Density and Magnetic Field Topography in Optimizing the Performance, Divergence, and Plasma Oscillations of High Specific Impulse Hall Thrusters

Recent studies of xenon Hall thrusters have shown peak efficiencies at specific impulses of less than 3000 s. This was a consequence of modern Hall thruster magnetic field topographies, which have been optimized for 300 V discharges. On-going research at the NASA Glenn Research Center is investigating this behavior and methods to enhance thruster performance. To conduct these studies, a laboratory model Hall thruster that uses a pair of trim coils to tailor the magnetic field topography for high specific impulse operation has been developed. The thruster-the NASA-173Mv2 was tested to determine how current density and magnetic field topography affect performance, divergence, and plasma oscillations at voltages up to 1000 V. Test results showed there was a minimum current density and optimum magnetic field topography at which efficiency monotonically increased with voltage. At 1000 V, 10 milligrams per second the total specific impulse was 3390 s and the total efficiency was 60.8%. Plume divergence decreased at 400-1000 V, but increased at 300-400 V as the result of plasma oscillations. The dominant oscillation frequency steadily increased with voltage, from 14.5 kHz at 300 V, to 22 kHz at 1000 V. An additional oscillatory mode in the 80-90 kHz frequency range began to appear above 500 V. The use of trim coils to modify the magnetic field improved performance while decreasing plume divergence and the frequency and magnitude of plasma oscillations.

Hofer, Richard R.↗

NASA NTRS2016

Low-Amplitude Topographic Features and Textures on the Moon: Initial Results from Detrended Lunar Orbiter Laser Altimeter (LOLA) Topography

Global lunar topographic data derived from ranging measurements by the Lunar Orbiter Laser Altimeter (LOLA) onboard LRO mission to the Moon have extremely high vertical precision. We use detrended topography as a means for utilization of this precision in geomorphological analysis. The detrended topography was calculated as a difference between actual topography and a trend surface defined as a median topography in a circular sliding window. We found that despite complicated distortions caused by the non-linear nature of the detrending procedure, visual inspection of these data facilitates identification of low-amplitude gently-sloping geomorphic features. We present specific examples of patterns of lava flows forming the lunar maria and revealing compound flow fields, a new class of lava flow complex on the Moon. We also highlight the identification of linear tectonic features that otherwise are obscured in the images and topographic data processed in a more traditional manner.

Moon↗

DOE OSTI2026

Status and new features of the topography beamline 1-BM after the Advanced Photon Source upgrade

The beamline 1-BM of the Advanced Photon Source (APS), a bending-magnet beamline with an effective X-ray beam size of ~100×4 mm2, has relatively comprehensive synchrotron topography and rocking curve imaging capabilities for characterization of crystals (particularly wide-bandgap semiconductors SiC, AlN, GaN, Ga2O3 etc). It is equipped with a white-beam topography stage for imaging large wafers up to 8 inches. It also has a double-crystal setup, of which the second stage can be used for monochromatic-beam topography. The first stage has different beam conditioners in the grazing-incidence geometry that can expand the vertical beam size from 4 to ~100 mm for double-crystal rocking curve imaging when it is combined with the second stage. Recently APS has been upgraded to a modern 4th-generation light source, and 1-BM has been recommissioned to its normal operation for general users with better performance. The upgraded APS leads to new features at 1-BM. The much smaller source size and higher X-ray coherence significantly improve the image resolution and contrast. The higher flux and brightness of the new source reduce exposure time, which mitigates the mechanical drifting and vibration issues. Here the main capabilities and status of 1-BM together with these new features are introduced.

X-ray topography↗

NASA NTRS2012

SWOT: The Surface Water and Ocean Topography Mission. Wide- Swath Altimetric Elevation on Earth

The elevation of the surface of the ocean and freshwater bodies on land holds key information on many important processes of the Earth System. The elevation of the ocean surface, called ocean surface topography, has been measured by conventional nadirlooking radar altimeter for the past two decades. The data collected have been used for the study of large-scale circulation and sea level change. However, the spatial resolution of the observations has limited the study to scales larger than about 200 km, leaving the smaller scales containing substantial kinetic energy of ocean circulation that is responsible for the flux of heat, dissolved gas and nutrients between the upper and the deep ocean. This flux is important to the understanding of the ocean's role in regulatingfuture climate change.The elevation of the water bodies on land is a key parameter required for the computation of storage and discharge of freshwater in rivers, lakes, and wetlands. Globally, the spatial and temporal variability of water storage and discharge is poorly known due to the lack of well-sampled observations. In situ networks measuring river flows are declining worldwide due to economic and political reasons. Conventional altimeter observations suffers from the complexity of multiple peaks caused by the reflections from water, vegetation canopy and rough topography, resulting in much less valid data over land than over the ocean. Another major limitation is the large inter track distance preventing good coverage of rivers and other water bodies.This document provides descriptions of a new measurement technique using radar interferometry to obtain wide-swath measurement of water elevation at high resolution over both the ocean and land. Making this type of measurement, which addresses the shortcomings of conventional altimetry in both oceanographic and hydrologic applications, is the objective of a mission concept called Surface Water and Ocean Topography (SWOT), which was recommended by the National Research Council's first decadal survey of NASA's Earth science program. This document provides wide-ranging examples of research opportunities in oceanography and land hydrology that would be enabled by the new type of measurement. Additional applications in many other branches of Earth System science ranging from ocean bathymetry to sea ice dynamics are also discussed. Many of the technical issues in making the measurement are discussed as well. Also presented is a preliminary design of the SWOT Mission concept, which is being jointly developed by NASA and CNES, with contributions from the Canadian Space Agency.

altimetry↗

NASA NTRS2011

The Dawn Topography Investigation

The objective of the Dawn topography investigation is to derive the detailed shapes of 4 Vesta and 1 Ceres in order to create orthorectified image mosaics for geologic interpretation, as well as to study the asteroids' landforms, interior structure, and the processes that have modified their surfaces over geologic time. In this paper we describe our approaches for producing shape models, plans for acquiring the needed image data for Vesta, and the results of a numerical simulation of the Vesta mapping campaign that quantify the expected accuracy of our results. Multi-angle images obtained by Dawn's framing camera will be used to create topographic models with 100 m/pixel horizontal resolution and 10 m height accuracy at Vesta, and 200 m/pixel horizontal resolution and 20 m height accuracy at Ceres. Two different techniques, stereophotogrammetry and stereophotoclinometry, are employed to model the shape; these models will be merged with the asteroidal gravity fields obtained by Dawn to produce geodetically controlled topographic models for each body. The resulting digital topography models, together with the gravity data, will reveal the tectonic, volcanic and impact history of Vesta, and enable co-registration of data sets to determine Vesta's geologic history. At Ceres, the topography will likely reveal much about processes of surface modification as well as the internal structure and evolution of this dwarf planet.

dawn↗

DOE OSTI2025

Topography restoration in white-light interferometry using an instrument transfer function evaluated with binary pseudo-random arrays

Accurate knowledge of the instrument transfer function (ITF) is vital for topography measurements using white-light interferometry (WLI). To this end, we derive a complete set of analytical expressions for the power spectral density (PSD) of a discretely sampled binary pseudo-random array (BPRA) as a theoretical benchmark. We then determine the ITF by comparing this theoretical PSD with the measured PSD of the BPRA. For the Zygo ZeGage Pro HR with a objective, the determined ITF closely matches the nominal modulation transfer function (MTF). Accordingly, we integrate the nominal MTF into Fourier-domain restoration filters and apply them to practical WLI topography data, yielding restored topographies that show improved agreement with atomic force microscopy measurements. Overall, our integrated BPRA-based ITF measurement and filtering methodology offers a robust yet practical means of characterizing WLI performance and enhancing the accuracy of surface measurements.

Hirose, Shigenobu [Japan Agency for Marine Earth S↗

NASA NTRS1973

Topography on satellite surfaces and the shape of asteroids.

Consideration of the topography and shape of incompressible, nonrotating, isothermal, spherical objects as an approach to the study of the topography and shape of smaller planetary bodies. A static model and a creep deformation model are applied in the process. Factors and forces which may have a bearing on the geometry and topography of small planetary bodies are discussed.

Johnson, T. V.↗

NASA NTRS1976

Influence of planetary-scale topography on the diurnal thermal tide during the 1971 Martian dust storm

Data obtained with the Mariner 9 infrared spectroscopy experiment during the Martian Dust Storm of 1971 to 1972 are examined for evidence of topographic influence on the atmospheric thermal structure. Temperature perturbations which are well correlated with the planetary scale topography are found superposed on the large amplitude diurnal thermal tide. Applications of tidal theory to the data indicate that the observed perturbations result from the kinematic interaction of the westward traveling diurnal wave with the large scale components of topography. The dominant mode is excited by the wave-number two topography component and is a vertically evanescent eastward traveling wave with an equivalent depth comparable to the atmospheric scale height. The principle dynamic effect of this mode is the enhancement of the amplitude of the near-surface diurnal wind to over 40m/sec in limited areas near 30 deg south latitude. It appears likely that dust was injected into the atmosphere in these regions during the storm.

Conrath, B. J.↗