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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

The Surface-Topography Challenge: A Multi-Laboratory Benchmark Study to Advance the Characterization of Topography

Surface performance is critically influenced by topography in virtually all real-world applications. The current standard practice is to describe topography using one of a few industry-standard parameters. The most commonly reported number is Ra, the average absolute deviation of the height from the mean line (at some, not necessarily known or specified, lateral length scale). However, other parameters, particularly those that are scale-dependent, influence surface and interfacial properties; for example the local surface slope is critical for visual appearance, friction, and wear. The present Surface-Topography Challenge was launched to raise awareness for the need of a multi-scale description, but also to assess the reliability of different metrology techniques. In the resulting international collaborative effort, 153 scientists and engineers from 64 research groups and companies across 20 countries characterized statistically equivalent samples from two different surfaces: a “rough” and a “smooth” surface. The results of the 2088 measurements constitute the most comprehensive surface description ever compiled. We find wide disagreement across measurements and techniques when the lateral scale of the measurement is ignored. Consensus is established through scale-dependent parameters while removing data that violates an established resolution criterion and deviates from the majority measurements at each length scale. Our findings suggest best practices for characterizing and specifying topography. The public release of the accumulated data and presented analyses enables global reuse for further scientific investigation and benchmarking.

42 ENGINEERING↗
DOE OSTI2025

Topography-Induced TKE Budget Behavior Over an Amazon Forest

Data from three different heights (35, 50 and 81 m) of one of the ATTO Project towers in the Amazon forest were used to calculate the TKE (turbulence kinetic energy) budget and some other statistics within the RSL (roughness sublayer). The statistical analyses were carried out for unstable and stable cases. The vertical transport and the vertical advection terms do not explain the imbalances found in the TKE budget, highlighting the impor- tance of horizontal terms in complex terrain. Indeed, patterns independent of the time of day were found for vertical transport, horizontal and vertical velocity skewness, the mean vertical component velocity, and momentum and vertical TKE flux. Here, the highest values of mean vertical velocity were observed from the direction where there is a valley near the tower, which may indicate a topographical effect. Monin-Obukhov Similarity Theory (MOST) predictions for the mean velocity gradient, strictly applicable only in the inertial sublayer (ISL), gave reasonable predictions at 35 and 50 m, but dimensionless dissipation rates displayed large scatter. At 81 m, there were clear deviations from MOST for the two functions, disclosing the effect of topography. In addition, a neutral LES (large-eddy simu- lation) study showed good agreement with tower data for the same general wind direction.

ATTO project↗
NASA NTRS2004

Topography of the Flattest Surface on Earth: using ICESAT, GPS, and MISR to Measure Salt Surface Topography on Salar de Uyuni, Bolivia

Salt flats are aptly named: they are composed largely of salt, and are maintained as nearly equipotential surfaces via frequent flooding. The salar de Uyuni, on the Altiplano in southwestern Bolivia, is the largest salt flat on Earth, with an area of 9,800 sq km. Except for a few bedrock islands, it has less than 40 cm of relief. The upper-most salt unit averages 5 m thick and contains 50 cu km of nearly pure halite. It includes most of the salt that was in solution in paleolake Minchin, which attained a maximum area of 60,000 sq km and a maximum depth of 150 m, roughly 15 kyr ago. Despite approx. 10 m of differential isostatic rebound since deposition, the salar surface has been actively maintained as an extraordinarily flat and smooth surface by annual flooding during the rainy season. We have used the strong optical absorption properties of water in the visible band to map spatial variations in water depth during a time when the salar was flooded. As water depth increases, the initially pure white surface appears both darker and bluer. We utilized MISR images taken during the interval from April to November 2001. The red and infra-red bands (672 and 867 nm wavelength) were most useful since the water depth is small and the absorption at those wavelengths is quite strong. Nadir pointed MISR images have 275 m spatial resolution. To aid in our evaluation of water depth variations over the saiar surface, we utilized two sources of direct topographic measurements: several ICESAT altimetry tracks cross the area, and a 40x50 km GPS grid was surveyed to calibrate ICESAT. A difficulty in using these data types is that both give salt surface elevations relative to the ellipsoid, whereas the water surface will, in the absence of wind or tidal disturbances, follow an equipotential surface. Geoid height is not known to the required accuracy of a few cm in the central Andes. As a result, before comparing optical absorption from MISR to salt surface topography from GPS or ICESAT, we removed the longest wavelengths from both.

Comstock, Robert L.↗
NASA NTRS1993

Can weak crust explain the correlation of geoid and topography on Venus?

The effect on geoid and topography of low viscosity crust overlying a steady-state convecting mantle is estimated under the assumption that the shear between crust and mantle does not alter the mantle flow. The weak crustal layer can change the sign of the geoid to topography ratio (admittance). The positive long wavelength admittance for Venus is consistent with a weak crust overlying a mantle with a viscosity that increases strongly with depth. The accepted interpretation of the strong positive correlation of geoid and topography on Venus, is that the convecting mantle of Venus has a constant viscosity with depth. Topography results from vertical normal stresses caused by mantle convection and highlands occur where mantle upwells. For topography to be supported by normal stress, the time scale for crustal flow must be long compared to the time scale for changes in the pattern of mantle flow. Because the high surface temperature of Venus may cause the crust to have a low viscosity, this assumption may be false. Topography should then be dominated by shear coupling between the crust and mantle. In the absence of a crustal layer, convection in a constant viscosity layer gives rise to a geoid anomaly that correlates positively with surface topography. When the viscosity in the layer increases with depth by several orders of magnitude, the surface topography and geoid anomaly become anti-correlated.

Buck, W. Roger↗
NASA NTRS1987

A fractal interpretation of topography and geoid spectra on the earth, moon, Venus, and Mars

Global spectra are available for topography and geoid on the earth, Venus, Mars, and the moon. If the spectral energy density has a power law dependence on wave number, a fractal is defined. The topography spectrum for the earth is a well-defined fractal with D = 1.5; this corresponds to Brown noise with the amplitude proportional to the wavelength. Although there is more scatter for the other planetary bodies, the data for Mars and the moon correlate well with the data for the earth. Venus topography also exhibits a Brown noise behavior but with a smaller amplitude. The power law dependence of the earth's geoid is known as Kaula's law. It is shown that uncompensated Brown topography gives a geoid with a power law dependence that is in quite good agreement with Kaula's law. However, the required amplitude is only 8 percent of the observed topography. A similar result is found for the other bodies, with the ratio of the amplitude of topography required to explain the geoid to the observed topography increasing to 72 percent for the moon.

Turcotte, Donald L.↗
NASA NTRS1998

The Laser Vegetation Imaging Sensor (LVIS): An Airborne Laser Altimeter for Mapping Vegetation and Topography

The Laser Vegetation Imaging Sensor (LVIS) is an airborne laser altimeter designed to quickly and extensively map surface topography as well as the relative heights of other reflecting surfaces within the laser footprint. Since 1997, this instrument has primarily been used as the airborne simulator for the Vegetation Canopy Lidar (VCL) mission, a spaceborne mission designed to measure tree height, vertical structure and ground topography (including sub-canopy topography). LVIS is capable of operating from 500 m to 10 km above ground level with footprint sizes from 1 to 60 m. Laser footprints can be randomly spaced within the 7 degree telescope field-of-view, constrained only by the operating frequency of the ND:YAG Q-switched laser (500 Hz). A significant innovation of the LVIS altimeter is that all ranging, waveform recording, and range gating are performed using a single digitizer, clock base, and detector. A portion of the outgoing laser pulse is fiber-optically fed into the detector used to collect the return signal and this entire time history of the outgoing and return pulses is digitized at 500 Msamp/sec. The ground return is then located using software digital signal processing, even in the presence of visibly opaque clouds. The surface height distribution of all reflecting surfaces within the laser footprint can be determined, for example, tree height and ground elevation. To date, the LVIS system has been used to monitor topographic change at Long Valley caldera, CA, as part of NASA's Topography and Surface Change program, and to map tree structure and sub-canopy topography at the La Selva Biological Research Station in Costa Rica, as part of the pre-launch calibration activities for the VCL mission. We present results that show the laser altimeter consistently and accurately maps surface topography, including sub-canopy topography, and vegetation height and structure. These results confirm the measurement concept of VCL and highlight the benefits of airborne prototypes of spaceborne instruments.

Bryan, J.↗
NASA NTRS1998

Geoid Anomalies and Dynamic Topography from Time Dependent, Spherical Axisymmetric Mantle Convection

Geoid anomalies and dynamic topography are two important diagnostics of mantle convection. We present geoid and topography results for several time-dependent convection models in spherical axisymmetric geometry for Rayleigh numbers between 10(exp 6) and 10(exp 7) with depth-dependent viscosity and mixtures of bottom and internal heating. The models are strongly chaotic, with boundary layer instabilities erupting out of both thermal boundary layers. In some instances, instabilities from one boundary layer influence the development of instabilities in the other boundary layer. Such coupling between events at the top and bottom of the mantle has been suggested to play a role in a mid-Cretaceous episode of enhanced volcanism in the Pacific. These boundary layer instabilities produce large temporal variations in the geoid anomalies and dynamic nd to the topography associated with the convection. The amplitudes of these fluctuations depend on the detailed model parameter,.% it of this but fluctuations of 30-50% relative to the time-averaged geoid and topography are common. The convective planform is strongly sensitive to the specific initial conditions. Convection cells with larger aspect ratio tend to have larger fractional fluctuations in their geoid and topography amplitudes, because boundary layer instabilities have more time to develop in long cells. In some instances, we observe low-amplitude topographic highs adjacent to the topographic lows produced by cold downwellings. We discuss applications of these results to several situations, including the temporal variability of m basis. hotspots such as Hawaii, the topography of subduction zone outer rises, and the topography of coronae on Venus.

Kiefer, Walter S.↗
NASA NTRS1989

Dynamic sea surface topography, gravity and improved orbit accuracies from the direct evaluation of SEASAT altimeter data

A method for the simultaneous solution of dynamic ocean topography, gravity and orbits using satellite altimeter data is described. A GEM-T1 based gravitational model called PGS-3337 that incorporates Seasat altimetry, surface gravimetry and satellite tracking data has been determined complete to degree and order 50. The altimeter data is utilized as a dynamic observation of the satellite's height above the sea surface with a degree 10 model of dynamic topography being recovered simultaneously with the orbit parameters, gravity and tidal terms in this model. PGS-3337 has a geoid uncertainty of 60 cm root-mean-square (RMS) globally, with the uncertainty over the altimeter tracked ocean being in the 25 cm range. Doppler determined orbits for Seasat, show large improvements, with the sub-30 cm radial accuracies being achieved. When altimeter data is used in orbit determination, radial orbital accuracies of 20 cm are achieved. The RMS of fit to the altimeter data directly gives 30 cm fits for Seasat when using PGS-3337 and its geoid and dynamic topography model. This performance level is two to three times better than that achieved with earlier Goddard earth models (GEM) using the dynamic topography from long-term oceanographic averages. The recovered dynamic topography reveals the global long wavelength circulation of the oceans with a resolution of 1500 km. The power in the dynamic topography recovery is now found to be closer to that of oceanographic studies than for previous satellite solutions. This is attributed primarily to the improved modeling of the geoid which has occurred. Study of the altimeter residuals reveals regions where tidal models are poor and sea state effects are major limitations.

Marsh, J. G.↗
NASA NTRS1994

Accuracy assessment of the large-scale dynamic ocean topography from TOPEX/POSEIDON altimetry

The quality of TOPEX/POSEIDON determinations of the global scale dynamic ocean topography have been assessed by determining mean topography solutions for successive 10-day repeat cycles and by examining the temporal changes in the sea surface topography to identify known features. The assessment is based on the analysis of TOPEX altimeter data cycles 1 through 36. Important errors in the tide model used to correct the altimeter data have been identified. The errors were reduced significantly by use of a new tide model derived with the TOPEX/POSEIDON measurements. Maps of the global 1-year mean topography, produced using four of the most accurate of the marine geoid, show that the largest error in the dynamic ocean topography show expected features, such as the known annual hemispherical sea surface rise and fall and the seasonal variability due to monsoon influence in the Indian Ocean. Changes in the sequence of 10-day topography maps show the development and propagation of an equatorial Kelvin wave in the Pacific beginning in December 1992 with a propagation velocity of approximately 3 m/s. The observations are consistent with observed changes in the equatorial trade winds, and with tide gauge and other in situ observations of the strengthening of the El Nino. Comparison of TOPEX-determine sea surface height at points near oceanic tide gauges shows agreement at the 4 cm root-mean-square (RMS) level over the tropical Pacific. The results show that the TOPEX altimeter data set can be used to map the ocean surface with a temporal resolution of 10 days and an accuracy which is insonsistent with traditional in situ methods for the determination of sea level variations.

Tapley, B. D.↗
NASA NTRS2019

Effects of Topography on Tropical Forest Structure Depend on Climate Context

Topography affects abiotic conditions which can influence the structure, function, and dynamics of ecological communities. An increasing number of studies have demonstrated biological consequences of fine-scale topographic heterogeneity but we have a limited understanding of how We merged high-resolution (1 sq. meter) data on topography and canopy height derived from airborne lidar with ground-based data from 15 forest plots in Puerto Rico distributed along a precipitation gradient spanning ca. 800 to 3,500 mm yr(exp -1). Ground-based data included species composition, estimated above-ground biomass (AGB), and two key functional traits (wood density and leaf mass per area, LMA) that reflect resource-use strategies and a trade-off between hydraulic safety and hydraulic efficiency. We used hierarchical Bayesian models to evaluate how the interaction between topography climate is related to metrics of forest structure (i.e., canopy height and AGB), as well as taxonomic and functional alpha- and beta-diversity. Fine-scale topography (characterized with the topographic wetness index, TWI) significantly affected forest structure and the strength (and in some cases direction) of these effects varied across the precipitation gradient. In all plots, canopy height increased with topographic wetness but the effect was much stronger in dry compared to wet forest plots. In dry forest plots, topographically wetter microsites also had higher levels of AGB but in wet forest plots, topographically drier microsites had higher AGB. Fine-scale topography influenced functional composition but had only weak or non-significant effects on taxonomic and functional alpha- and beta-diversity. For instance, community-weighted wood density followed a similar pattern to AGB across plots. We also found a marginally significant association between variation of wood density and topographic heterogeneity that depended on climate context. Synthesis: The effects of fine-scale topographic heterogeneity on tropical forest structure and composition depend on the climate context. Our study demonstrates how a stronger integration of topographic heterogeneity across precipitation gradients could improve estimates of forest structure and biomass, and may provide insight to the ways that topography might mediate species responses to drought and climate change.

Tropical dry forest↗
DOE OSTI2025

Interplay of Topography, Fire History, and Climate on Interior Alaska Boreal Forest Vegetation Dynamics in the 21st Century: A Landsat Time-Series Analysis

This study investigates vegetation dynamics in boreal forests of Interior Alaska, focusing on topography, fire history, and climate influences. The study area includes Bonanza Creek Experimental Forest (BCEF) and surrounding region, categorized by topography (upland, floodplain, lowland) and fire history. Using Mann–Kendall trend and Theil–Sen slope analyses on Landsat-derived spectral metrics: Normalized Difference Vegetation Index (NDVI) and Normalized Burn Ratio (NBR), we observed a shift from browning to greening trends, particularly in historically burned areas. The photosynthetic activity in burned upland converged with unburned areas ~30 years post-fire, coincident with a shift towards deciduous dominance during post-fire succession. Normalized Difference Moisture Index (NDMI) trends revealed a significant increase in vegetation moisture content across all topographies. We introduce Effective Seasonal Precipitation Index (ESPI), which combines prior-year annual precipitation with current-year spring snow depth. Its positive correlation with NDMI highlights its potential for monitoring vegetation moisture dynamics at the landscape scale. Furthermore, by correlating dendrochronology-based climate indices, we found strong correlation between NDMI and normalized Supplemental Precipitation Index (nSPI), across topographies. Overall, this research provides critical insights into how climate and fire influence interior boreal vegetation, highlighting the effects of increased precipitation, and topography on shaping differential vegetation responses across the landscape.

Google Earth Engine↗
NASA NTRS1987

Linear baroclinic instability in the presence of large scale topography

The effect of a planetary-scale, wavenumber 2 topography on baroclinically active disturbances is investigated for a channel domain in a two-layer, quasi-geostrophic context. When the lower-layer zonal velocity is nonzero, the topography influences the disturbances by forcing a stationary wave, and the topography and the forced wave influence the growth rates and the spatial structures of the time-dependent solutions. The case of zero zonal velocity in the lower layer was also investigated, for which no forced wave exists. Asymptotic forms of the equations, valid when the topographic effect (governed by the ratio of the nondimensional topographic height to the rotational Froude number) is small, are used to obtain both the stationary and time-dependent solutions. The latter are also obtained using a numerical approach, in which is determined the eigenvalues and eigenfunctions of a matrix representing the dynamical equations. Agreement is good between the two approaches. Recent laboratory experiments with a baroclinic annulus in which there is a false bottom with wavenumber 2 topography, are used to select governing parameters. The simultaneous presence of a stationary forced wave of wavenumber 2 and a time-dependent baroclinic wave of wavenumber 4, which has wavenumber 2 and 6 sidebands due to the topography, yields a flow field that exhibits some principal features of the laboratory experiments. The position of the forced wave and the location of an excursion in latitude of the storm track show qualitative resemblance to those features observed in the atmosphere.

Reynolds, Nathaniel Dunton↗
NASA NTRS1993

Spectral analysis of the gravity and topography of Mars

New spherical harmonic models of the gravity and topography of Mars place important constraints on the structure and dynamics of the interior. The gravity and topography models are significantly phase coherent for harmonic degrees n less than 30 (wavelengths greater than 700 km). Loss of coherence below that wavelength is presumably due to inadequacies of the models, rather than a change in behavior of the planet. The gravity/topography admittance reveals two very different spectral domains: for n greater than 4, a simple Airy compensation model, with mean depth of 100 km, faithfully represents the observed pattern; for degrees 2 and 3, the effective compensation depths are 1400 and 550 km, respectively, strongly arguing for dynamic compensation at those wavelengths. The gravity model has been derived from a reanalysis of the tracking data for Mariner 9 and the Viking Orbiters, The topography model was derived by harmonic analysis of the USGS digital elevation model of Mars. Before comparing gravity and topography for internal structure inferences, we must ensure that both are consistently referenced to a hydrostatic datum. For the gravity, this involves removal of hydrostatic components of the even degree zonal coefficients. For the topography, it involves adding the degree 4 equipotential reference surface, to get spherically referenced values, and then subtracting the full degree 50 equipotential. Variance spectra and phase coherence of orthometric heights and gravity anomalies are addressed.

Bills, Bruce G.↗
NASA NTRS1993

An inversion of geoid and topography for mantle and crustal structure on Mars

Mars has the largest amplitude geoid anomalies and surface topography known on the terrestrial planets. A number of prior studies have analyzed Martian gravity anomalies and topography in terms of isostasy and flexure of the crust and lithosphere. Other studies have emphasized the role of mantle convection in producing gravity anomalies and topography in some regions of Mars. Geoid and topography observations for simultaneous estimates of density anomalies in the crust and mantle of Mars are inverted. In performing this study, a recent degree 50 spherical harmonic expansion of the Martian gravity field (GMM-l) and a corresponding resolution expansion of the USGS Mars topography model are used. However, our analysis is restricted to harmonic degrees up to L equals 25, which are better determined than the higher harmonics. This provides a half-wavelength horizontal resolution of 425 km.

Kiefer, Walter↗