Gridded Elevation Research Articles

Gamma‐SLAM: Visual SLAM in unstructured environments using variance grid maps

AbstractThis paper describes an online stereo visual simultaneous localization and mapping (SLAM) algorithm developed for the Learning Applied to Ground Robotics (LAGR) program. The Gamma‐SLAM algorithm uses a Rao–Blackwellized particle filter to obtain a joint posterior over poses and maps: the pose distribution is estimated using a particle filter, and each particle has its own map that is obtained through exact filtering conditioned on the particle's pose. Visual odometry is used to provide good proposal distributions for the particle filter, and maps are represented using a Cartesian grid. Unlike previous grid‐based SLAM algorithms, however, the Gamma‐SLAM map maintains a posterior distribution over the elevation variance in each cell. This variance grid map can capture rocks, vegetation, and other objects that are typically found in unstructured environments but are not well modeled by traditional occupancy or elevation grid maps. The algorithm runs in real time on conventional processors and has been evaluated for both qualitative and quantitative accuracy in three outdoor environments over trajectories totaling 1,600 m in length. © 2008 Wiley Periodicals, Inc.

Peer-to-peer visualization of very large 3D landscape and city models using MPEG-4

The recent availability of broadband Internet access and web-based visualization techniques is paving the way for a large scale use of 3D landscape and city models in a great variety of professional and mass market services. To make such services appealing to a large audience, these 3D models must reach a sufficient level of realism and accuracy. Many solutions are now available to automatically generate 3D models of huge urban environments. Geographic information system (GIS) databases (i.e., terrain elevation grids, orthophotographs, buildings, footprint and height) provide a good basis for generating such models at affordable cost with minimum human intervention. However, the growing size of the generated representations will favor streaming over download-and-play. Moreover, the new market for virtual worlds is likely to be soon demanding interoperability. The goal of this paper is to show how solutions based on hierarchical level of detail (LOD) models and view-dependent progressive streaming can efficiently be implemented using the MPEG-4 AFX standard in peer-to-peer network architectures, solving both streaming and interoperability issues.

FA2BOUG—A FORTRAN 90 code to compute Bouguer gravity anomalies from gridded free-air anomalies: Application to the Atlantic-Mediterranean transition zone

In this paper we present a computer program written in FORTRAN 90 specifically designed to determine the Bouguer anomaly from publicly available global gridded free-air anomaly and elevation database sets. FA2BOUG computes the complete Bouguer correction (i.e. Bullard A, B and C corrections) for both land and sea points in several spatial domains according to the distance between the topography and the calculation point. In each zone a different algorithm is used. In a distant zone we consider the harmonic spherical expansion of the potential of each right rectangular prism representing an elevation grid point. In an intermediate zone we compute the gravitational attraction produced by each prism using the analytic formula. Finally, an inner zone contribution is divided into two parts: a flat-topped prism with a height equal to the elevation of the calculation point, and four quadrants of a conic prism sloping continuously from each square of the inner zone to the calculation point. The program has been applied to the Atlantic-Mediterranean transition zone to obtain a complete Bouguer anomaly map of the area, integrating available onshore Bouguer anomaly with satellite-derived free-air anomaly data. Positive Bouguer anomalies are found in the Atlantic oceanic domain (240–300 mGal), central and eastern Alboran Basin (40–160 mGal) and SW Iberian Peninsula (>40 mGal). Major negative Bouguer anomalies are located beneath the west Alboran Basin (<−40 mGal), the Rif, the Rharb Basin and the Atlas Mountains (<−120 mGal). An isostatic residual anomaly map of the study area has been computed and compared with the crustal and lithospheric structure inferred from previous work.

Scaling and parametrization of clear‐sky solar radiation over complex topography

Solar radiation at the land surface is influenced by slope, aspect, shadows, and obstruction of the sky, all of which vary over a wide range of length scales in regions of complex topography, with important consequences for the surface energy balance. Atmospheric models, however, generally assume the surface to be flat on subgrid scales. For four areas in North America, ranging in latitude from 39°N to 69°N and in topography from rolling to mountainous, we simulate spatial patterns of clear‐sky incoming solar radiation. It is found that distributions of slope components and variations in shaded area with solar elevation can be approximated by simple functions that scale to each of the areas studied. From these results, parametrizations are developed for averages, standard deviations, and distributions of direct‐beam and diffuse solar radiation. Results from these parametrizations, and from a modified form of a simpler parametrization presented previously, compare well with statistics from the spatial simulations. The only topographic input required by the parametrizations is the standard deviation of slope components; this parameter is again found to have simple scaling relationships with the resolution and extent of the underlying elevation grid and with the standard deviation of elevation.

ICONE15-10422 Comparing Two Models of Determining Fuel Assembly In-Grid Stiffness

Currently, in Pressurized Water Reactor (PWR) core seismic analysis, various testing methods are used to determine in-grid stiffness and ingrid damping. In-grid stiffness is the effective horizontal stiffness between all of the fuel rods at a grid elevation and a center point of the grid. This stiffness is determined by fuel-assembly lateralimpact tests, in air, at room temperature. In-grid stiffness and damping data are currently being derived from fuel-assembly-grid-impact data obtained with a single beam (one-beam) per assembly model. In this paper, a better correlation with the fuel-assembly lateral-impact test data is achieved by utilizing a "two-beam' fuel-assembly model. The "two-beam" model employs the rudimentary finite element technique of grouping items with common properties and boundary conditions as they would exhibit common behaviors. The first beam represents the total number of fuel rods. The second beam represents all of the guide tubes and the instrument tube. Horizontal springs representing in-grid stiffness are incorporated in the "two-beam" model between the fuel-rods beam and the guide-tubes beam at each spacer grid position. In the "one-beam" model, the fuel assembly is represented with a single vertical beam. That is, all of the fuel rods, guide tubes and instrument tube are lumped into one beam. The model extends from the top surface of the bottom nozzle to the bottom surface of the top nozzle. The upper and the lower ends of the beam are assumed fixed. In the "two-beam" model, only the guide-tube beam is assumed to be fixed at the upper and lower nozzles, while the fuel-rod beam is not fixed at the upper and lower nozzles. This set of end conditions is representative of the actual fuel assembly structure; hence, this model results in more realistic shear forces and moments on the top and bottom nozzles. With the "two-beam" linear model, it is possible to benchmark more closely to both the first natural frequency and lateral stiffness, since it represents the more realistic boundary conditions.

Summer Temperature Variations in the European Alps, a.d. 755–2004

Abstract Annually resolved summer temperatures for the European Alps are described. The reconstruction covers the a.d. 755–2004 period and is based on 180 recent and historic larch [Larix decidua Mill.] density series. The regional curve standardization method was applied to preserve interannual to multicentennial variations in this high-elevation proxy dataset. Instrumental measurements from high- (low-) elevation grid boxes back to 1818 (1760) reveal strongest growth response to current-year June–September mean temperatures. The reconstruction correlates at 0.7 with high-elevation temperatures back to 1818, with a greater signal in the higher-frequency domain (r = 0.8). Low-elevation instrumental data back to 1760 agree with the reconstruction’s interannual variation, although a decoupling between (warmer) instrumental and (cooler) proxy data before ∼1840 is noted. This offset is larger than during any period of overlap with more recent high-elevation instrumental data, even though the proxy time series always contains some unexplained variance. The reconstruction indicates positive temperatures in the tenth and thirteenth century that resemble twentieth-century conditions, and are separated by a prolonged cooling from ∼1350 to 1700. Six of the 10 warmest decades over the 755–2004 period are recorded in the twentieth century. Maximum temperature amplitude over the past 1250 yr is estimated to be 3.1°C between the warmest (1940s) and coldest (1810s) decades. This estimate is, however, affected by the calibration with instrumental temperature data. Warm summers seem to coincide with periods of high solar activity, and cold summers vice versa. The record captures the full range of past European temperature variability, that is, the extreme years 1816 and 2003, warmth during medieval and recent times, and cold in between. Comparison with regional- and large-scale reconstructions reveals similar decadal to longer-term variability.

A mixture‐model based algorithm for real‐time terrain estimation

AbstractA real‐time terrain mapping and estimation algorithm using Gaussian sum elevation densities to model terrain variations in a planar gridded elevation model is presented. A formal probabilistic analysis of each individual sensor measurement allows the modeling of multiple sources of error in a rigorous manner. Measurements are associated to multiple locations in the elevation model using a Gaussian sum conditional density to account for uncertainty in measured elevation as well as uncertainty in the in‐plane location of the measurement. The approach is constructed such that terrain estimates and estimation error statistics can be constructed in real‐time without maintaining a history of sensor measurements. The algorithm is validated experimentally on the 2005 Cornell University DARPA Grand Challenge ground vehicle, demonstrating accurate and computationally feasible elevation estimates on dense terrain models, as well as estimates of the errors in the terrain model. © 2006 Wiley Periodicals, Inc.

A comparison of SRTM and high‐resolution digital elevation models and their use in catchment geomorphology and hydrology: Australian examples

AbstractThe recently released Shuttle Radar Topography Mission (SRTM) 3‐arc second digital elevation data set provides a complete global coverage of the Earth's land surface. In this paper we examine the SRTM data for three catchments in Australia over a range of climates, geology and resultant geomorphology. To test this new data set the SRTM data are compared with high resolution digital elevation models. We use basic hydrological and geomorphological statistics and descriptors such as the area–slope relationship, cumulative area distribution and hypsometric curve, along with Strahler and networking statistics. The above measures describe the surface morphology of a catchment, therefore integrating catchment geology, climate and vegetation. The SRTM data were also assessed as input into the SIBERIA landscape evolution and soil erosion model as were runoff properties, using a wetness index. The results demonstrate that the 90 m SRTM data provide a poor catchment representation. Hillslopes appear as a linked set of facets and display little of the complex curvature that is observed in high resolution data. While catchment area–slope and area–elevation (hypsometry) properties are largely correct, catchment area, relief and shape (as measured by the width function) are poorly captured by the SRTM data. Catchment networking statistics are also variable. The large grid size of the SRTM data also results in incorrect drainage network patterns and different runoff properties. Consequently, care must be used for quantitative assessment of catchment hydrology and geomorphology, as in all cases SRTM‐derived catchment area is incorrect and smaller digital elevation grid sizes are required for accurate catchment‐wide assessment. While only a limited number of catchments have been examined, we believe our findings are applicable to other areas. © Crown Copyright 2006. Reproduced with the permission of the Controller of HMSO. Published by John Wiley &amp; Sons, Ltd.

The use of digital elevation models in the identification and characterization of catchments over different grid scales

This study examines the ability of well-known hydrological and geomorphological descriptors and statistics to differentiate between catchments with spatially varying geology, size and shape subject to the same climate in the Northern Territory, Australia. The effect of digital elevation model grid resolution on these statistics is also examined. Results demonstrate that catchment descriptors such as the area–slope relationship, cumulative area distribution and hypsometric curve can differentiate between catchments with different geology and resultant morphology, but catchment network statistics are insensitive to differences in geology. Examination of the effects of digital elevation model grid scale demonstrates that while considerable catchment information can be gained at digital elevation grids greater than 10 m by 10 m, hillslope and hydrological detail can be lost. Geomorphic descriptors such as the area– slope relationship, cumulative area distribution, width function and Strahler statistics were shown to be sensitive to digital elevation model grid scale, but the hypsometric curve was not. Consequently, caution is needed when deciding on an appropriate grid resolution as well as the interpretation and analysis of catchment properties at grid scales greater than that for optimal hillslope and area aggregation definition. Copyright  2005 John Wiley & Sons, Ltd.

Probability maps as a measure of reliability for indivisibility analysis

Digital terrain models (DTMs) represent segments of spatial data bases related to presentation of terrain features and landforms. Square grid elevation models (DEMs) have emerged as the most widely used structure during the past decade because of their simplicity and simple computer implementation. They have become an important segment of Topographic Information Systems (TIS), storing natural and artificial landscape in forms of digital models. This kind of a data structure is especially suitable for morph metric terrain evaluation and analysis, which is very important in environmental and urban planning and Earth surface modeling applications. One of the most often used functionalities of Geographical information systems software packages is indivisibility or view shed analysis of terrain. Indivisibility determination from analog topographic maps may be very exhausting, because of the large number of profiles that have to be extracted and compared. Terrain representation in form of the DEMs databases facilitates this task. This paper describes simple algorithm for terrain view shed analysis by using DEMs database structures, taking into consideration the influence of uncertainties of such data to the results obtained thus far. The concept of probability maps is introduced as a mean for evaluation of results, and is presented as thematic display.

Terrain correction computation using Gaussian quadrature

A method and a program (tcq) in FORTRAN 90 based on Gaussian quadrature are developed to compute the terrain correction (TC). TCs were determined on 1010 benchmarks using the Gaussian quadrature, prism and FFT methods using a 3″×3″ elevation grid for the inner zone and a 30″×30″ elevation grid for the outer zone. In order to achieve a 0.1 mgal accuracy in TC while reducing the computing time, the best inner and outer radii for TC computation are 20 and 200 km , respectively. The Gaussian quadrature is a highly accurate numerical integrator and yields results that outperform those from the prism method and the FFT method. The singular problem of the kernel function in TC is treated by considering the innermost zone effect, which can be expressed as a complete elliptic integral of the first kind. The innermost zone effect must be taken into account if the required accuracy of TC is at a 1-mgal level.

EXTRACTING MEANINGFUL SLOPES FROM TERRAIN CONTOURS

Good quality terrain models are becoming more and more important, as applications such as runoff modelling are being developed that demand better surface orientation information than is available from traditional interpolation techniques. A consequence is that poor-quality elevation grids must be massaged before they provide useable runoff models. Rather than using direct data acquisition, this project concentrated on using available contour data because, despite modern techniques, contour maps are still the most available form of elevation information. Recent work on the automatic reconstruction of curves from point samples, and the generation of medial axis transforms (skeletons) has greatly helped in expressing the spatial relationships between topographic sets of contours. With these techniques the insertion of skeleton points into a TIN model guarantees the elimination of all "flat triangles" where all three vertices have the same elevation. Additional assumptions about the local uniformity of slopes give us enough information to assign elevation values to these skeleton points. In addition, various interpolation techniques were compared using the enriched contour data. Examination of the quality and consistency of the resulting maps indicates the required properties of the interpolation method in order to produce terrain models with valid slopes. The result provides us with a surprisingly realistic model of the surface - that is, one that conforms well to our subjective interpretation of what a real landscape should look like.

A Comparison of Moisture Scalars and Water Budget Methods to Assess Vegetation-Site Relationships

Quantification of vegetation-site relationships is often required in biogeographic research. Methods linking species to particular sites typically assess evaporative demand and soil moisture availability at the site, though methods differ in how these factors are assessed. This study compares three approaches—a water-budget approach, and field-based and map-based moisture scalars—in their ability to predict the occurrence of a single species, American beech (Fagus grandifolia), observed in 102, 0.04 ha plots in SE Ohio. Actual evapotranspiration and deficit provided results superior to field-based and map-based scalars. Map-based techniques are potentially limited at fine spatial scales, due to the large discrepancy between observed topographic variables, and those modeled with 7.5-minute elevation grids. The study concludes that a water budget approach is applicable to a wide range of studies exploring vegetation-site linkages. It has advantages of being objective in its computation, and applicable at a wide range of spatial scales. Perhaps most importantly with regard to global change research is the dynamic nature of the method: a site's classification will change concurrently with changes in climate.

傾斜地の標高補間に用いられる３次エルミート関数の性質について

The cubic Hermite function was used as an interpolation method to generate the Digital Map 50m Grid (Elevation) by the Geographical Survey Institute of Japan. A Few studies have been reported concerning the reliability of cubic Hermite function for slope interpolation. However, these studies were mostly based on empirical observations without discussions about the cubic Hermite function's mathematical properties. In this paper, we investigate the applicability of the cubic Hermite function for slope interpolation using the mathematical relations between the trajectories of the cubic Hermite function and its tangent values at the both ends of the interpolation interval. The result shows that a proper slope interpolation can be achieved if and if only the trajectories' values are up to three times of the tangent's value.

An image-enhanced DEM of the Greenland ice sheet

AbstractWe have assembled an elevation grid for the Greenland ice sheet using a combination of the best current digital elevation model (DEM) (Bamber and others, 2000a, 2001) and 44 Advanced Very High Resolution Radiometer satellite images acquired in spring 1997. The images are used to quantitatively enhance the representation of surface undulations through photoclinometry. Gridcell spacing of the new DEM is 625 m. To validate the new DEM, we compared profiles extracted from it and the Bamber and others DEM with airborne laser altimetry profiles collected in the 1990s by the Airborne Topographic Mapper (Krabill and others, 1995). The image-enhanced DEM has a greatly improved representation of decameter-relief surface features &lt;15 km in lateral extent, and reduces the mean elevation error in regions having these features by 20–50%. Root-mean-squared errors are typically 7–15m in the Bamber DEM, and 4–10m after image enhancement. However, the photoclinometry process adds some noise. In very smooth portions of the ice sheet where decameter undulationsare absent, the photoclinometry process caused a slight increase in the rms error, from ~1 min the Bamber and others DEM to ∼2.5 min the image-enhanced DEM. The image-enhanced DEM will be useful for inferring accumulation-rate variations over the undulation field, or for improving maps of bedrock elevation through inversion of surface elevation, for example. We briefly explore the preliminary steps of this latter application.

Estimation of surface runoff and water-covered area during filling of surface microrelief depressions

During the filling of surface microrelief depressions the precipitation excess (precipitation minus infiltration and interception) is divided between surface storage and runoff, i.e. runoff starts before the surface depressions are filled. Information on the division of precipitation excess is needed for modelling surface runoff during the filling of surface depressions. Furthermore, information on the surface of the area covered with water is needed for calculating infiltration of water stored in soil surface depressions. Thirty-two soil surface microreliefs were determined in Danish erosion study plots. The slope was c. 10% for all plots. Data were treated initially by removing the slope, after which 20 ‘artificial’ slopes (1–20%) were introduced producing 640 new data sets. Runoff during filling of the microrelief storage was calculated for each of the 640 data sets using a model developed for calculating surface storage and runoff from grid elevation measurements. Runoff started immediately after the first addition of water for all data sets. On a field scale, however, runoff has to travel some distance as overland flow and storage in smaller and larger depressions below the runoff initiation point must be taken into consideration. The runoff increases by intermittent steps. Whenever a depression starts to overflow to the border of the plot, the runoff jumps accordingly. In spite of the jumps, the distribution between surface storage and runoff was closely related to the quotient between precipitation excess and depression storage capacity. Surface area covered with water was exponentially related to the amount of water stored in surface depressions. Models for calculating surface storage and runoff from grid elevation measurements are cumbersome and require time-consuming measurements of the soil surface microrelief. Therefore, estimation from roughness indices requiring fewer measurements is desirable. New improved equations for such estimations are suggested. Copyright © 2000 John Wiley & Sons, Ltd.

Estimating the ground-water contribution in wetlands using modeling and digital terrain analysis

Wetland classification and management often requires information on the contribution of ground water to a wetland’s water budget. Direct estimation of this parameter, however, is time-consuming, expensive, and can typically only be accomplished for small areas. Thus, a method to characterize ground-water flow in wetland areas and regions may be useful in many applications. The estimation technique described combines the use of a digital elevation model (DEM) with transient numerical modeling and assumes that the water table reflects the general pattern of surface topography. The DEM grid elevations are used as initial heads in the model. Stepwise ground-water drainage from the flow domain is simulated until a reasonable match is obtained between the observed and model water tables. By knowing or assuming hydraulic conductivity and using the model water-table configuration, an estimate for ground-water flow to and from each discretized grid node can be estimated from Darcy’s Law and the Dupuit approximation. The net result, when mapped, shows the simulated distribution of recharge and discharge within and surrounding the wetland. Two examples from the Shingobee River headwaters in central Minnesota indicate how the method may be used. Geologically recent development of glacial landforms has led to numerous lakes, ponds, and wetlands in the region. Using a 30-m, 1∶24,000 scale DEM grid in combination with data from the U.S. Fish and Wildlife National Wetlands Inventory, the model predicts the most likely areas of ground-water interaction in and near wetlands and lakes. More quantitative results can be obtained by applying observed water budget and soil/aquifer parameter data.

Mariculture siting: a GIS description of intertidal areas

Variations in habitat parameters greatly affect the physiological state and the growth of bivalves. To achieve success in shellfish mariculture, environmental parameters favorable to the cultured species must be determined and then characteristics of potential grow-out sites evaluated. An intertidal bay in Eastern Maine was described in a GIS (geographical information system), which incorporated infrared aerial photographs and maps of bottom types, topography and bathymetry. Data layers included elevations from both nautical charts and GPS measurements made in the bay. From the elevation data, a series of programs was developed to generate a triangulated irregular network and a grid of elevations. A numerical flow model used the elevation grid to simulate a time series of tidal current vectors and free surface elevations. Gridded data from the numerical model were imported into the GIS and displayed as false color images of elevations, maximum current velocities and tidally averaged current velocities. Current vectors were layered over aerial photos showing sediment transport in the water. The GIS can be queried to identify sites for mariculture. A sample query identified sites for shellfish grow-out.

Digital elevation analysis for distributed hydrological modeling: Reducing scale dependence in effective hydraulic conductivity values

The recent widespread availability of digital terrain data has made automatic procedures for topographic analyses popular. Previous studies have shown that hydrological models and their effective parameter values are dependent on the resolution of the elevation grid. This paper examines the analysis of raster elevation data within the topography‐based model, TOPMODEL, framework. It is demonstrated that the algorithm used in processing channel pixels in calculating the topographic index k=ln(a/tanβ) can have a dramatic effect on the sensitivity of effective parameter values to the grid size. Suggestions are made for calculating the topographic index of channel pixels, consistent with the TOPMODEL assumptions, that strongly decrease the sensitivity of the calibrated effective hydraulic conductivity values to grid size.

Generation of a virtual terrain

A computer software package, TERAN, has been written for the generation of a virtual terrain. Originally intended for use in defining the topology in complex, individual-oriented ecosystem models, TERAN is sufficiently versatile that it may be used to create elevation grids for a wide variety of applications. Moreover, it is structured so that the existing features of the software can be easily modified, and new features added without difficulty. First, the user to define the dimensions and resolution of a rectangular coordinate grid. The user is then able to choose from a variety of models for the overall surface configuration, surface roughness, and up to 100 major surface disturbances. Parameter values are then input for each of these, and the resulting terrain definition can be saved to file for subsequent retrieval and modification. After terrain definition is complete, the surface elevation is calculated for every point in the coordinate grid, taking into account the influence of each topographical feature by invoking the appropriate mathematical model and then summing the elevation increments. The completed rectangular matrix of elevation values is exported in ASCII format for use with other applications (e.g. modeling packages, GIS, graphical display).