Estimation Of Topography Research Articles

Mapping multi-scale vascular plant richness in a forest landscape with integrated LiDAR and hyperspectral remote-sensing.

The central role of floristic diversity in maintaining habitat integrity and ecosystem function has propelled efforts to map and monitor its distribution across forest landscapes. While biodiversity studies have traditionally relied largely on ground-based observations, the immensity of the task of generating accurate, repeatable, and spatially-continuous data on biodiversity patterns at large scales has stimulated the development of remote-sensing methods for scaling up from field plot measurements. One such approach is through integrated LiDAR and hyperspectral remote-sensing. However, despite their efficiencies in cost and effort, LiDAR-hyperspectral sensors are still highly constrained in structurally- and taxonomically-heterogeneous forests - especially when species' cover is smaller than the image resolution, intertwined with neighboring taxa, or otherwise obscured by overlapping canopy strata. In light of these challenges, this study goes beyond the remote characterization of upper canopy diversity to instead model total vascular plant species richness in a continuous-cover North Carolina Piedmont forest landscape. We focus on two related, but parallel, tasks. First, we demonstrate an application of predictive biodiversity mapping, using nonparametric models trained with spatially-nested field plots and aerial LiDAR-hyperspectral data, to predict spatially-explicit landscape patterns in floristic diversity across seven spatial scales between 0.01-900m2 . Second, we employ bivariate parametric models to test the significance of individual, remotely-sensed predictors of plant richness to determine how parameter estimates vary with scale. Cross-validated results indicate that predictive models were able to account for 15-70% of variance in plant richness, with LiDAR-derived estimates of topography and forest structural complexity, as well as spectral variance in hyperspectral imagery explaining the largest portion of variance in diversity levels. Importantly, bivariate tests provide evidence of scale-dependence among predictors, such that remotely-sensed variables significantly predict plant richness only at spatial scales that sufficiently subsume geolocational imprecision between remotely-sensed and field data, and best align with stand components including plant size and density, as well as canopy gaps and understory growth patterns. Beyond their insights into the scale-dependent patterns and drivers of plant diversity in Piedmont forests, these results highlight the potential of remotely-sensible essential biodiversity variables for mapping and monitoring landscape floristic diversity from air- and space-borne platforms.

A Multibeam-Based SLAM Algorithm for Iceberg Mapping Using AUVs

Using autonomous underwater vehicles (AUVs) for mapping underwater topography of sea-ice and icebergs, or detecting keels of ice ridges, is foreseen as enabling technology in future arctic marine operations. Wind, current, and Coriolis forces affect an iceberg’s trajectory, making automated mapping difficult. This paper presents a method aiming at enabling autonomous iceberg mapping using AUVs equipped with a multibeam echosounder by estimating the position and orientation of the iceberg. The method is based on a bathymetric simultaneous localization and mapping (SLAM) algorithm, namely, the bathymetric distributed particle filter SLAM (BPSLAM) algorithm. The proposed method estimates the AUV’s pose in an iceberg-fixed coordinate system. The relative states can be used for both guiding the vehicle to achieve complete coverage, as well as estimation of a consistent iceberg topography. The algorithm also provides an estimate of the iceberg’s drift velocity – an important parameter for the AUV trajectory planning as well as any related ice management (IM) operations. Two new weighting algorithms for the BPSLAM method are proposed, enabling batch processing of multibeam echosounder (MBE) measurements to ensure real-time operation without discarding information. The proposed method is demonstrated using a real iceberg topography taken from the PERD iceberg sightings database, with simulated AUV and MBE range measurements. The algorithm is also evaluated on a real world bathymetric dataset, collected using the HUGIN HUS AUV.

A Cross-Spectral Approach to Measure the Error Budget of the SWOT Altimetry Mission over the Ocean

AbstractThe future Surface Water Ocean Topography (SWOT) mission aims to observe water bodies and short-scale ocean surface topography with unprecedented spatial resolution and accuracy. However, the topography estimates will be contaminated by errors of various signals (geophysical and instrumental) featuring, in large part, strong dependencies on the radar range direction (cross track). This study shows that a cross-spectral analysis performed along track for all cross-track combinations can detect most of these errors and can provide estimates of their power spectral densities. From a series of outputs of the SWOT science team simulator, a cross-spectral method was developed to simulate the estimation of the error budget compared to the actual error budget in the simulator. The study determined that the error spectra of the dominant terms can be estimated at very high accuracy. Beyond the obvious applications for the future SWOT data calibration and validation, the spectral estimates of the error budget will have applications for state estimate problems using SWOT data.

Oceanic Residual Topography Agrees With Mantle Flow Predictions at Long Wavelengths

AbstractDynamic topography, the surface deflection induced by sublithosheric mantle flow, is an important prediction made by geodynamic models, but there is an apparent disparity between geodynamic model predictions and estimates of residual topography (total topography minus lithospheric and crustal contributions). We generate synthetic global topography fields with different power spectral slopes and spatial patterns to investigate how well the long‐wavelength (spherical degrees 1 to 3) components can be recovered from a discrete set of samples where residual topography has been recently estimated. An analysis of synthetic topography, along with observed geoid and gravity anomalies, demonstrates the reliability of signal recovery. Appropriate damping factors, which depend on the maximum degree in the spherical harmonic expansion that is used to fit the samples, must be applied to recover the long‐wavelength topography correctly; large damping factors smooth the model excessively and suppress residual topography amplitude and power spectra unrealistically. Recovered long‐wavelength residual topographies based on recent oceanic point‐wise estimates with different spherical expansion degrees agree with each other and with the predicted dynamic topography from mantle flow models. The peak amplitude of the long‐wavelength residual topography from oceanic observations is about 1 km, suggesting an important influence of large‐scale deep mantle flow.

Geomorphometric analysis of the 2014–2015 Bárðarbunga volcanic eruption, Iceland

Topographical information is of fundamental interest for a wide range of disciplines including glaciology, agriculture, communication network planning, or hazard management. In volcanology, elevation data are of particular importance when assessing material flows throughout a volcanic system. To obtain accurate estimates of time-varying topography in volcanic active regions, high-resolution digital elevation models (DEMs) are required. To monitor and evaluate topographical changes and especially volumetric gains and losses during the 2014–2015 Bárðarbunga eruption, Iceland, multi-temporal TanDEM-X DEM sequences were evaluated.The 2014–2015 volcanic eruption was associated with the rare event of a caldera collapse, visible on the surface of the Vatnajökull glacier, as well as major lava effusion in the Holuhraun plain. Before investigating topographical change at the two study areas, the TanDEM-X DEMs were analysed for absolute and relative height errors resulting from the radar system parameters, the SAR processing or the local environment. The uncertainty investigation determined that acquisitions over the snow-covered Bárðarbunga caldera were primarily affected by microwave penetration into snow and DEMs over the Holuhraun lava field exhibited increased height errors due to active lava flows and dynamic outwash plain.The topographical analysis of the 2014–2015 Bárðarbunga eruption revealed a maximum vertical displacement of approximately −65m and +43m at the study area of the Bárðarbunga caldera and Holuhraun lava field respectively. With a total subsidence volume of −1.40±0.13km3 and a dense-rock equivalent (DRE) lava volume of +1.36±0.07km3, known uncertainties in volume were decreased by approximately 35% and 77% accordingly. Taking into account the calculation of rates, the temporal development of caldera collapse and lava effusion was found to exhibit a near-exponential decrease. The ratio between subsidence and DRE lava volume moreover indicated the coupling between piston collapse and magma drainage.

Geochemical and geophysical constrains on the dynamic topography of the Southern African Plateau

AbstractThe deep mantle African Superswell is considered to contribute to the topographic uplift of the Southern African Plateau, but dynamic support estimates vary wildly depending on the approach and data used. One reason for these large disparities is that the role of lithospheric structure, key in modulating deep dynamic contributions to elevation, is commonly ignored or oversimplified in convection studies. We use multiple high‐quality geophysical data coupled with xenolith‐based geochemical constraints to compute the isostatic lithospheric contribution to the elevation of the Plateau, facilitating isolation of the current dynamic component from the total observed elevation. We employ a multiobservable stochastic algorithm to invert geoid anomaly, surface‐wave dispersion data, magnetotelluric data, and surface heat flow to predict elevation in a fully thermodynamically and internally‐consistent manner. We find that a compositionally layered 230 ± 7 km thick lithosphere is required to simultaneously fit all four data types, in agreement with abundant independent xenolith evidence. Our stochastic modeling indicates a lithospheric contribution to elevation of the order of 670 m, which implies dynamic support arising from the convecting sublithospheric mantle of ∼650 m. Our results have important implications for the understanding of lithospheric‐deep mantle feedback mechanisms and for calibrating dynamic topography estimates from global convection studies.

Underlying Topography Estimation over Forest Areas Using High-Resolution P-Band Single-Baseline PolInSAR Data

This paper discusses the potential and limitations of high-resolution P-band polarimetric synthetic aperture radar (SAR) interferometry (PolInSAR) in underlying topography estimation over forest areas. Time-frequency (TF) analysis in the azimuth direction is utilized to separate the ground scattering contribution from the total PolInSAR signal, without the use of any physical model, because the P-band PolInSAR data have a significant penetration depth and sufficient observation angle interval. To achieve this goal, a one-dimensional polynomial fitting (PF) method is proposed for correcting the residual motion error (RME). The Krycklan catchment test site, which is covered with pine forest, was selected to test the performance of the digital elevation model (DEM) inversion. The results show that the PF method can correct the RMEs for the sub-look interferograms well. When compared to the existing line-fit method, the TF+PF method can provide a more accurate DEM (the accuracy is improved by 26.9%). Moreover, the performance of the DEM inversion is free from the random-volume-over-ground assumption.

Monitoring gully change: A comparison of airborne and terrestrial laser scanning using a case study from Aratula, Queensland

Airborne laser scanning (ALS) and terrestrial laser scanning (TLS) technologies capture spatially detailed estimates of surface topography and when collected multi-temporally can be used to assess geomorphic change. The sensitivity and repeatability of ALS measurements to characterise geomorphic change in topographically complex environments such as gullies; however, remains an area lacking quantitative research. In this study, we captured coincident ALS and TLS datasets to assess their ability and synergies to detect geomorphic change for a gully located in Aratula, southeast Queensland, Australia. We initially used the higher spatial density and ranging accuracy of TLS to provide an assessment of the Digital Elevation Models (DEM) derived from ALS within a gully environment. Results indicated mean residual errors of 0.13 and 0.09m along with standard deviation (SD) of residual errors of 0.20 and 0.16m using pixel sizes of 0.5 and 1.0m, respectively. The positive mean residual errors confirm that TLS data consistently detected deeper sections of the gully than ALS. We also compared the repeatability of ALS and TLS for characterising gully morphology. This indicated that the sensitivity to detect change using ALS is substantially lower than TLS, as expected, and that the ALS survey characteristics influence the ability to detect change. Notably, we found that using one ALS transect (mean density of 5 points/m2) as opposed to three transects increased the SD of residual error by approximately 30%. The supplied classification of ALS ground points was also demonstrated to misclassify gully features as non-ground, with minimum elevation filtering found to provide a more accurate DEM of the gully. The number and placement of terrestrial laser scans were also found to influence the derived DEMs. Furthermore, we applied change detection using two ALS data captures over a four year period and four TLS field surveys over an eight month period. This demonstrated that ALS can detect large scale erosional changes with head cutting of gully branches migrating approximately 10m upslope. In comparison, TLS captured smaller scale intra-annual erosional patterns largely undetectable by the ALS dataset with a large rainfall event coinciding with the highest volumetric change (net change>46m3). Overall, these findings reaffirm the importance of quantifying DEM errors and demonstrate that ALS is unlikely to detect subtle geomorphic changes (<0.45m) potentially missing significant sediment change. TLS was able to detect more subtle intra-annual changes but was limited in its spatial coverage. This suggests TLS and ALS surveys are complementary technologies and when used together can provide a more detailed understanding of gully processes at different temporal and spatial scales, provided the inherent errors are taken into account.

Robust atomic force microscopy using multiple sensors.

Atomic force microscopy typically relies on high-resolution high-bandwidth cantilever deflection measurements based control for imaging and estimating sample topography and properties. More precisely, in amplitude-modulation atomic force microscopy (AM-AFM), the control effort that regulates deflection amplitude is used as an estimate of sample topography; similarly, contact-mode AFM uses regulation of deflection signal to generate sample topography. In this article, a control design scheme based on an additional feedback mechanism that uses vertical z-piezo motion sensor, which augments the deflection based control scheme, is proposed and evaluated. The proposed scheme exploits the fact that the piezo motion sensor, though inferior to the cantilever deflection signal in terms of resolution and bandwidth, provides information on piezo actuator dynamics that is not easily retrievable from the deflection signal. The augmented design results in significant improvements in imaging bandwidth and robustness, especially in AM-AFM, where the complicated underlying nonlinear dynamics inhibits estimating piezo motions from deflection signals. In AM-AFM experiments, the two-sensor based design demonstrates a substantial improvement in robustness to modeling uncertainties by practically eliminating the peak in the sensitivity plot without affecting the closed-loop bandwidth when compared to a design that does not use the piezo-position sensor based feedback. The contact-mode imaging results, which use proportional-integral controllers for cantilever-deflection regulation, demonstrate improvements in bandwidth and robustness to modeling uncertainties, respectively, by over 30% and 20%. The piezo-sensor based feedback is developed using H∞ control framework.

Arctic sea surface height variability and change from satellite radar altimetry and GRACE, 2003–2014

AbstractArctic sea surface height (SSH) is poorly observed by radar altimeters due to the poor coverage of the polar oceans provided by conventional altimeter missions and because large areas are perpetually covered by sea ice, requiring specialized data processing. We utilize SSH estimates from both the ice‐covered and ice‐free ocean to present monthly estimates of Arctic Dynamic Ocean Topography (DOT) from radar altimetry south of 81.5°N and combine this with GRACE ocean mass to estimate steric height. Our SSH and steric height estimates show good agreement with tide gauge records and geopotential height derived from Ice‐Tethered Profilers. The large seasonal cycle of Arctic SSH (amplitude ∼5 cm) is dominated by seasonal steric height variation associated with seasonal freshwater fluxes, and peaks in October–November. Overall, the annual mean steric height increased by 2.2 ± 1.4 cm between 2003 and 2012 before falling to circa 2003 levels between 2012 and 2014 due to large reductions on the Siberian shelf seas. The total secular change in SSH between 2003 and 2014 is then dominated by a 2.1 ± 0.7 cm increase in ocean mass. We estimate that by 2010, the Beaufort Gyre had accumulated 4600 km3 of freshwater relative to the 2003–2006 mean. Doming of Arctic DOT in the Beaufort Sea is revealed by Empirical Orthogonal Function analysis to be concurrent with regional reductions in the Siberian Arctic. We estimate that the Siberian shelf seas lost ∼180 km3 of freshwater between 2003 and 2014, associated with an increase in annual mean salinity of 0.15 psu yr−1. Finally, ocean storage flux estimates from altimetry agree well with high‐resolution model results, demonstrating the potential for altimetry to elucidate the Arctic hydrological cycle.

On the observability of bottom topography from measurements of tidal sea surface height

The question of whether features of the ocean bottom topography can be identified from measurements of water level is investigated using a simplified one-dimensional barotropic model. Because of the nonlinear dependence of the sea surface height on the water depth, a linearized analysis is performed concerning the identification of a Gaussian bump within two specific depth profiles, (1) a constant depth domain, and, (2) a constant depth domain adjoining a near-resonant continental shelf. Observability is quantified by examining the estimation error in a series of identical-twin experiments varying data density, tide wavelength, assumed (versus actual) topographic correlation scale, and friction. For measurements of sea surface height that resolve the scale of the topographic perturbation, the fractional error in the bottom topography is approximately a factor of 10 larger than the fractional error of the sea surface height. Domain-scale and shelf-scale resonances may lead to inaccurate topography estimates due to a reduction in the effective number of degrees of freedom in the dynamics, and the amplification of nonlinearity. A realizability condition for the variance of the topography error in the limit of zero bottom depth is proposed which is interpreted as a bound on the fractional error of the topography. Appropriately designed spatial covariance models partly ameliorate the negative impact of shelf-scale near-resonance, and highlight the importance of spatial covariance modeling for bottom topography estimation.

Estimation of Surface Topography and Wear Loss of Laser Metal‐Deposited Ti6Al4V and Cu

The atomic force microscopy (AFM) analysis is a process that involves the detailed analyses of the surface of a three‐dimensional sample piece. A good image is always generated on such a sample once the settings are implemented correctly. And as such, the amplitude set point plays a vital role in achieving a better image. This paper presents the evolving microstructures and the surface topographies of the laser‐deposited Ti6Al4V/Cu alloys. The formation and the output of the microstructure depend on the laser processing parameters employed. The migration of the β‐phase has been impeded during solidification due to the low strain hardening effect posed by the α‐Ti lamella. A correlation between wear loss and surface roughness has been established among the laser‐deposited samples.

COMPARISON OF ACCURACY CHARACTERISTICS OF THE TWO WAYS TO BUILD AIRCRAFT INTERFEROMETRIC SAR

The paper considers the options for interferometric shooting with synthetic aperture radar (SAR) located aboard an aircraft carrier. Moreover, the paper researches the factors that affect the accuracy characteristics of SAR interferometer, and identifies the specificity of radar interferometric sensing, allowing engineers to minimize the error of the local topography estimation for each of the variants of the interferometer construction.

Double-Tip Artefact Removal from Atomic Force Microscopy Images.

The Atomic Force Microscope (AFM) allows the measurement of interactions at interfaces with nanoscale resolution. Imperfections in the shape of the tip often lead to the presence of imaging artefacts such as the blurring and repetition of objects within images. Generally, these artefacts can only be avoided by discarding data and replacing the probe. Under certain circumstances (e.g., rare, high value samples, or extensive chemical/physical tip modification) such an approach is not feasible. Here, we apply a novel deblurring technique, using a Bayesian framework, to yield a reliable estimation of the real surface topography without any prior knowledge of the tip geometry (blind reconstruction). A key contribution is to leverage the significant recently successful body of work in natural image deblurring to solve this problem. We focus specifically on the 'double-tip' effect, where two asperities 1 are present on the tip, each contributing to the image formation mechanism. Finally, we demonstrate that the proposed technique successfully removes the 'double-tip' effect from high resolution AFM images which demonstrate this artefact whilst preserving feature resolution.

Alternative Methods for the Calculation of Pedestrian Catchment Areas for Public Transit

Federal and local transportation policy aims to reduce vehicle emissions, improve air quality, and promote active lifestyles by investing in sustainable transportation alternatives. Investments in public transportation can be maximized by improving pedestrian connections to transit stops and stations. For pedestrian access to public transportation to be improved, enhancements must be within the pedestrian catchment area of a transit stop or station. This study explored three new approaches for identifying pedestrian catchment areas that incorporate topography, pedestrian facilities, and energy expenditure estimates: the network grade, pedestrian speed, and pedestrian energy methods. This paper includes a description of how to conduct the three spatial analyses and a comparison of results from these methods with the results from two methods widely used in practice: the Euclidian distance and network distance methods. The comparison was carried out by analyzing spatial data from the light rail Expo Line and its surrounding environment in Los Angeles County, California. The results demonstrate significant differences in the size, land use diversity, and transportation facilities captured by the new methods compared with those from the two existing methods.

Fractalness of land gravity data and residual isostatic anomalies map of Argentina, Chile and western Uruguay

Gravity anomalies are often strongly influenced by topography, which effect is mitigated through appropriate reductions. Usually, a standard value of 2670 kg/m3 is used for the density of topography in the absence of specific information. However, various methods have been implemented to obtain density of topography estimates directly from the gravity data. A particularly suitable technique for regional scale studies is based on analyzing the fractal nature of gravity anomalies for a particular region.In this paper the fractalness of the onshore gravity anomalies for Argentina, Chile and part of Uruguay is analyzed by using an updated gravity database. The fractal dimensions of the topography and gravity anomaly data were estimated by means of the variogram technique in the spatial domain. As a result of this analysis, it was found that the optimum density for the studied region has a value of 2300 kg/m3. This density was used to prepare a map of isostatic residual anomalies using the Airy-Heiskanen model. The main anomalies recognized on this map were interpreted in relation to the degree of isostatic balance and the densities of rocks near to the surface.

Radar scattering of linear dunes and mega-yardangs: Application to Titan

The Ku-band (13.8GHz – 2.2cm) RADAR instrument onboard the Cassini-Huygens spacecraft has revealed the richness of the surface of Titan, as numerous seas, lakes, rivers, cryo-volcanic flows and vast dune fields have been discovered. Linear dunes are a major geomorphological feature present on Titan, covering up to 17% of its surface, mainly in equatorial regions. However, the resolution of the RADAR instrument is not good enough to allow a detailed study of the morphology of these features. In addition, other linear wind-related landforms, such as mega-yardangs (linear wind-abraded ridges formed in cohesive rocks), are likely to present a comparable radar signature that could be confused with the one of dunes. We conducted a comparative study of the radar radiometry of both linear dunes and mega-yardangs, based on representative terrestrial analogues: the linear dunes located in the Great Sand Sea in western Egypt and in the Namib Desert in Namibia, and the mega-yardangs observed in the Lut Desert in eastern Iran and in the Borkou Desert in northern Chad. We analysed the radar scattering of both terrestrial linear dunes and mega-yardangs, using high-resolution radar images acquired by the X-band (9.6GHz – 3.1cm) sensor of the TerraSAR-X satellite. Variations seen in the radar response of dunes are the result of a contrast between the dune and interdune scattering, while for mega-yardangs these variations are the result of a contrast between ridges and erosion valleys. We tested a simple surface scattering model, with parameters derived from the local topography and surface roughness estimates, to accurately reproduce the radar signal variations for both landforms. It appears that we can discriminate between two types of dunes – bare interdunes as in Egypt and sand-covered interdunes as in Namibia, and between two types of mega-yardangs – young yardangs as in Iran and older ones as in Chad. We applied our understanding of the radar scattering to the analysis of Cassini RADAR T8 acquisitions over the Belet Sand Sea on Titan, and show that the linear dunes encountered there are likely to be of both Egyptian and Namibian type. We also show that the radar-bright linear features observed in Cassini RADAR T64 and T83 acquisitions are very likely to be mega-yardangs, possible remnants of ancient lake basins at mid-latitude, formed when Titan’s climate was different.

A Multidimensional Extension of the Concept of Coherence in Polarimetric SAR Interferometry

Interferometric synthetic aperture radar (InSAR) is a phase-based radar signal processing technique that has been addressed from a polarimetric point of view since the late 1990s, starting with Cloude and Papathanassiou's foundational work. Polarimeric InSAR (PolInSAR) has consolidated as an active field of research in parallel to non-PolInSAR. Regarding the latter, there have been a number of issues that were discussed in an earlier paper from which some other questions related to Cloude's PolInSAR come out naturally. In particular, they affect the usual understanding of coherence and statistical independence. Coherence involves the behavior of electromagnetic waves in at least a pair of points, and it is crucially related to the statistical independence of scatterers in a complex scene. Although this would seem to allow PolInSAR to overcome the difficulties involving the controversial confusion between statistical independence and polarization as present in PolSAR, Cloude's PolInSAR originally inherited the idea of separating physical contributors to the scattering phenomenon through the use of singular values and vectors. This was an assumption consistent with Cloude's PolSAR postulates that was later set aside. We propose the introduction of a multidimensional coherence tensor that includes PolInSAR's polarimetric interferometry matrix Ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> as its 2-D case. We show that some important properties of the polarimetric interferometry matrix are incidental to its bidimensionality. Notably, this exceptional behavior in 2-D seems to suggest that the singular value decomposition (SVD) of Ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> does not provide a physical insight into the scattering problem in the sense of splitting different scattering contributors. It might be argued that Cloude's PolInSAR in its current form does not rely on the SVD of Ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> but on other underlying optimization schemes. The drawbacks of such ulterior developments and the failure of the maximum coherence separation procedure to be a consistent scheme for surface topography estimation in a two-layer model are discussed in depth in this paper. Nevertheless, turning back to the SVD of Ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> , the use of the singular values of a prewhitened version of Ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> is consistent with a leading method of characterizing coherence in modern Optics. For this reason, the utility of the SVD of Ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> as a means of characterizing coherence is analyzed here and extended to higher dimensionalities. Finally, these extensions of the concept of coherence to the multidimensional case are tested and compared with the 2-D case by numerically simulating the scattered electromagnetic field from a rough surface.

Airborne lidar-based estimates of tropical forest structure in complex terrain: opportunities and trade-offs for REDD+

BackgroundCarbon stocks and fluxes in tropical forests remain large sources of uncertainty in the global carbon budget. Airborne lidar remote sensing is a powerful tool for estimating aboveground biomass, provided that lidar measurements penetrate dense forest vegetation to generate accurate estimates of surface topography and canopy heights. Tropical forest areas with complex topography present a challenge for lidar remote sensing.ResultsWe compared digital terrain models (DTM) derived from airborne lidar data from a mountainous region of the Atlantic Forest in Brazil to 35 ground control points measured with survey grade GNSS receivers. The terrain model generated from full-density (~20 returns m−2) data was highly accurate (mean signed error of 0.19 ± 0.97 m), while those derived from reduced-density datasets (8 m−2, 4 m−2, 2 m−2 and 1 m−2) were increasingly less accurate. Canopy heights calculated from reduced-density lidar data declined as data density decreased due to the inability to accurately model the terrain surface. For lidar return densities below 4 m−2, the bias in height estimates translated into errors of 80–125 Mg ha−1 in predicted aboveground biomass.ConclusionsGiven the growing emphasis on the use of airborne lidar for forest management, carbon monitoring, and conservation efforts, the results of this study highlight the importance of careful survey planning and consistent sampling for accurate quantification of aboveground biomass stocks and dynamics. Approaches that rely primarily on canopy height to estimate aboveground biomass are sensitive to DTM errors from variability in lidar sampling density.Electronic supplementary materialThe online version of this article (doi:10.1186/s13021-015-0013-x) contains supplementary material, which is available to authorized users.

Improving the geoid: Combining altimetry and mean dynamic topography in the California coastal ocean

AbstractSatellite gravity mapping missions, altimeters, and other platforms have allowed the Earth's geoid to be mapped over the ocean to a horizontal resolution of approximately 100 km with an uncertainty of less than 10 cm. At finer resolution this uncertainty increases to greater than 10 cm. Achieving greater accuracy requires accurate estimates of the dynamic ocean topography (DOT). In this study two DOT estimates for the California Current System with uncertainties less than 10 cm are used to solve for a geoid correction field. The derived field increases the consistency between the DOTs and along‐track altimetric observations, suggesting it is a useful correction to the gravitational field. The correction is large compared to the dynamic ocean topography, with a magnitude of 15 cm and significant structure, especially near the coast. The results are evidence that modern high‐resolution dynamic ocean topography products can be used to improve estimates of the geoid.