A causal analysis of error in viewsheds from USGS digital elevation models

Users of GIS are faced with the ongoing and difficult problem of estimating the validity of a GIS output given the uncertainty of the quality of digital mapped data. This research project examines the manner in which error from a digital elevation model (DEM) results in error in an estimate of a viewshed. The data set includes two DEMs for the same study area. A 10-metre DEM serves as the control model to test a United States Geological Survey (USGS) DEM. The amount and spatial pattern of the error in the test DEM is determined by comparing it to the control DEM. A viewshed analysis is then performed at a set of 61 sites. After determining the relative accuracy of the viewsheds thus estimated, a causal model of viewshed error is developed, which links the sources of the DEM error with the error in the viewshed. The most important factor in DEM error is terrain roughness. The error in the viewsheds is a result of the error being propagated from the DEM, with landscape characteristics of the viewpoinr playing a role due to their effect on the error in the DEM. The conceptual path model developed sets the stage for a quancitative approach that will attempt to predict viewshed error from the landscape characteristics without direct knowledge of the error in the DEM.     

基于参考面的可视域算法

与传统基于视线的可视域算法相比，该算法不需进行DEM内插，无冗余计算，计算时间和视点位置与可视域面积无关，受DEM区域影响不大。     

Propagating effects of database generalization on the viewshed

Few studies have systematically examined the effects of different possible generalization methods on the products of GIS operations. In this paper the effects of generalizing a Digital Elevation Model (DEM) on the area which is determined to be visible (the viewshed) is examined. Among the many different methods of generalization which are possible, a limited set of operators is examined here. First, they all fit geometrically from one resolution to another, and they can be grouped into two types: regular sampling and statistical summaries. In the latter class four different operations are used: for any cell at the target resolution, elevations are determined, from the arithmetic mean, the maximum, the minimum, and the maximum difference from the mean of the cells within the kernel at the original scale. Changes in resolution of 0.5, 0.33, 0.25, and 0.2 of the original study area are studied at 100 viewing points in each of two study areas. At the original resolution a 120 × 120 pixel area was examined, giving generalizations to 60 × 60, 40 × 40, 30 × 30, and 24 × 24 pixels. The viewsheds determined over these different resolution DEMs are compared with a number of possible viewsheds derived by generalization of the viewshed over the original DEM. Of those tested, the maximum deviation from the mean within kernel emerges as the most reliable estimate of the pattern and area of the viewshed at all resolutions. The importance of this conclusion is that different generalization operators yield more or less faithful versions of the ungeneralized product (the viewshed), and it seems indicative that a similar variety in stability of the product with generalization operator will result in many, if not all, complex products of spatial analysis.     

基于LiDAR点云数据的可视域计算研究

当前GIS软件中通视分析建立在DEM数据基础上,而DEM中不含植被和建筑物信息,从而会造成通视分析误差。通过Li DAR点云数据获取高精度植被和建筑物高度,提出一种顾及地物的插值算法,生成同一网格大小的DEM与DSM,在其上分别进行通视域分析,并将分析结果进行对比,发现DEM比DSM更容易扩大视域范围,从而产生了分析误差,验证了利用DSM进行通视分析的可行性。     

Spheroidal equal angular DEMs: The specificity of morphometric treatment

Digital elevation models (DEMs) are commonly constructed using two main types of regular grids: plane square grids and spheroidal equal angular grids. Methods and algorithms intended for plane square‐gridded DEMs should not be directly applied to spheroidal equal angular DEMs. This is because these grids have fundamentally different geometry. However, some researchers continue to apply square‐grid algorithms to spheroidal equal angular DEMs. It seems appropriate to consider once again the specifity of morphometric treatment of spheroidal equal angular DEMs. This article, first, demonstrates possibilities of direct calculation of local, nonlocal, and combined morphometric variables from spheroidal equal angular DEMs exemplified by slope gradient, catchment area, and topographic index. Second, the article shows computational errors when algorithms for plane square‐gridded DEMs are unreasonably applied to spheroidal equal angular DEMs. The study is exemplified by two DEMs. A medium‐resolution DEM of a relatively small, high‐mountainous area (Mount Elbrus) was extracted from the SRTM1 DEM. A low‐resolution DEM of a vast region with the diverse topography (the central and western regions of Kenya) was extracted from the SRTM30_PLUS DEM. The results show that application of square‐grid methods to spheroidal equal angular DEMs leads to substantial computational errors in models of morphometric variables.     

Satellite stereo data for dem surfaces and derivatives

Various attributes can be derived from Digital Elevation Model (DEM), which are essential to analyze watershed physical characteristics. This paper discusses utility and accuracy of satellite DEM surfaces and their derivatives. Facilities available in various software packages were compared to generate DEM from satellite data and other sources. For test site at Chamba, Uttaranchal, DEMs produced from various algorithms were evaluated for accuracy of surface and its derivatives. Most of the algorithms have shown correlation coefficient of 0.99 and above but the desirable maximum error in spot height (1/5 of contour interval) is not achieved. Slope and aspect produced from various algorithms were comparable around 70-80%. Comparison of DEM surface and its derivatives were attempted for test sites at Shimla and Nahan using IRS-1C and SPOT PAN stereo pair, respectively. Model accuracy has shown that error in height is higher than planimetry. Surface derivatives from stereo DEM for Shimla and Nahan test sites have shown an overall accuracy of 56.5% and 59.2% for slope; 49.79% and 71.21% for aspect and 74.15% for topographic level slicing, respectively. Accuracy has improved when observed class value was lowered or put-up by one unit.     

Digital close range photogrammetry for measurement of soil erosion

Many of the processes involved in soil erosion have dimensions on the millimetre scale. Modelling and quantification of such processes require information on soil surface topography with adequate resolution. The purpose of this study was to generate digital elevation models (DEMs) from soil surfaces with high spatial and temporal resolution. Digital photogrammetry was applied for measuring erosion rates on complex-shaped soil surfaces under laboratory rainfall conditions. A total of 60 DEMs were generated, covering a planimetric area of 16 m². The DEMs had a grid resolution of 3 mm. A vertical precision of approximately 1 mm was desired for DEM analysis. A consumer-grade digital camera was used for image acquisition. The camera was calibrated using BLUH software. Homologous points in overlapping images were identified with least squares matching software. Irregularly spaced object coordinates were interpolated to a regular grid in a geographic information system. The resulting DEMs represented the soil surface well. A precision of 1·26 mm in the vertical was attained. The precision of DEM production was limited to camera calibration. Improvements of the setup presented could include the use of better control points and more advanced image matching strategies for identification of homologous points. The DEMs allowed for detailed analysis of soil surface evolution.     

A Comparison Between Contour Elevation Data Sources for DEM Creation and Soil Carbon Prediction, Coshocton, Ohio

A raster and vector GIS was created for the North Appalachian Experimental Watershed (NAEW) from legacy (1960) 1:2,400‐scale contour maps. The intent of the study was to use terrain data for the spatial modeling of soil organic carbon. It was hypothesized that DEMs derived from these data would be more accurate and therefore more useful for terrain‐based soil modeling than those from USGS 1:24,000‐scale contour data. Central tasks for this study were to digitally capture the 1:2,400‐scale maps, convert digital contour data sources to raster DEMs at multiple resolutions, and derive terrain attributes. A flexible approach was adopted, using software outside of mainstream GIS sources where scientifically or practically advantageous. Elevation contours and streamlines were converted to raster DEMs using ANUDEM. DEMs ranging in resolution from 0.5–30 m were tested for accuracy against precision carrier‐phase GPS data. The residual standard deviation was 1.68 meters for the USGS DEM and 0.36 meters for the NAEW DEM. The optimal horizontal resolution for the NAEW DEM was 5 m and for the USGS 10 m. Five and 10 m resolution DEMs from both data sources were tested for carbon prediction. Multiple terrain parameters were derived as proxies for surficial processes. Soil samples (n = 184) were collected on four zero‐order watersheds (conventional tillage, no‐till, hay and pasture). Multiple least squares regressions (m.l.s.) were used to predict mass C (kg m^?2, 30 cm depth) from topographic information. Model residuals were not spatially autocorrelated. Statistically significant topographic parameters were attained most consistently from the 5 m NAEW DEM. However, topography was not a strong predictor of carbon for these watersheds, with r² ranging from 0.23 to 0.58.     

Topographic correction of ALOS-PALSAR images using InSAR-derived DEM

Topographic corrections of synthetic aperture radar (SAR) images over hilly regions are vital for retrieval of correct backscatter values associated with natural targets. The coarse resolution external digital elevation models (DEM) available for topographic corrections of high resolution SAR images often result into degradation of spatial resolution or improper estimation of backscatter values in SAR images. Also, many a times the external DEMs do not spatially co-register well with the SAR data. The present study showcases the methodology and results of topographic correction of ALOS-PALSAR image using high resolution DEM generated from the same data. High resolution DEMs of Jaipur region, India were generated using multiple pair SAR images acquired from ALOS-PALSAR using interferometric (InSAR) techniques. The DEMs were validated using differential global positioning system measured elevation values as ground control points and were compared with photogrammetric DEM (advanced spaceborne thermal emission and reflection radiometer – ASTER) and SRTM (Shuttle Radar Topography Mission) DEM. It was observed that ALOS-PALSAR images with optimum baseline parameters produced high resolution DEM with better height accuracy. Finally, the validated DEM was used for topographic correction of ALOS-PALSAR images of the same region and were found to produce better result as compared with ASTER and SRTM-DEM.     

Total 3D‐viewshed Map: Quantifying the Visible Volume in Digital Elevation Models

The 3D perception of the human eye is more impressive in irregular land surfaces than in flat land surfaces. The quantification of this perception would be very useful in many applications. This article presents the first approach to determining the visible volume, which we call the 3D‐viewshed, in each and all the points of a DEM (Digital Elevation Model). Most previous visibility algorithms in GIS (Geographic Information Systems) are based on the concept of a 2D‐viewshed, which determines the number of points that can be seen from an observer in a DEM. Extending such a 2D‐viewshed to 3D space, then to all the DEM‐points, is too expensive computationally since the viewshed computation per se is costly. In this work, we propose the first approach to compute a new visibility metric that quantifies the visible volume from every point of a DEM. In particular, we developed an efficient algorithm with a high data and calculation re‐utilization. This article presents the first total‐3D‐viewshed maps together with validation results and comparative analysis. Using our highly scalable parallel algorithm to compute the total‐3D‐viewshed of a DEM with 4 million points on a Xeon Processor E5‐2698 takes only 1.3 minutes.     

Urban DEM generation,analysis and enhancements using TanDEM-X

This paper analyzes the potential of the TanDEM-X mission for the generation of urban Digital Elevation Models (DEMs). The high resolution of the sensors and the absence of temporal decorrelation are exploited. The interferometric chain and the problems encountered for correct mapping of urban areas are analyzed first. The operational Integrated TanDEM-X Processor (ITP) algorithms are taken as reference. The ITP main product is called the raw DEM. Whereas the ITP coregistration stage is demonstrated to be robust enough, large improvements in the raw DEM such as fewer percentages of phase unwrapping errors, can be obtained by using adaptive fringe filters instead of the conventional ones in the interferogram generation stage. The shape of the raw DEM in the layover area is also shown and determined to be regular for buildings with vertical walls. Generally, in the presence of layover, the raw DEM exhibits a height ramp, resulting in a height underestimation for the affected structure. Examples provided confirm the theoretical background. The focus is centered on high resolution DEMs produced using spotlight acquisitions. In particular, a raw DEM over Berlin (Germany) with a 2.5 m raster is generated and validated. For this purpose, ITP is modified in its interferogram generation stage by adopting the Intensity Driven Adaptive Neighbourhood (IDAN) algorithm. The height Root Mean Square Error (RMSE) between the raw DEM and a reference is about 8 m for the two classes defining the urban DEM: structures and non-structures. The result can be further improved for the structure class using a DEM generated with Persistent Scatterer Interferometry. A DEM fusion is thus proposed and a drop of about 20% in the RMSE is reported.     

基于栅格DEM的地形特征提取与分析

以陕北延安地区燕儿沟流域为实验样区,运用比较分析法和数理统计法进行基于栅格DEM的地形特征提取和分析,以及DEM分辨率对地形特征的影响,并计算和比较了地形特征的空间统计分布。研究表明:一个相对真实的DEM能够通过修改生成DEM的基本材料,以及对DEM进行再加工而获得。由于DEM分辨率的不同,由此得到的地形特征值(如坡度、地形指数、河网密度等)在统计特性上也会随之变化。随着DEM分辨率的降低,坡度减小,地形坦化,地形指数均值变大,流域总面积变大,子流域数量减少,河流总长度减小,河网密度降低。     

QUALITY CONTROL OF PHOTOGRAMMETRICALLY SAMPLED DIGITAL ELEVATION MODELS

The object of this paper is to study the geometric accuracy of photogrammetrically sampled digital elevation models (DEMs)obtained by using an on line graphical DEM editor. As a reference, DEMs obtained by regular grid measurements have been used. Three different test areas are used in the study, each representing different ground types and degrees of homogeneity. The DEMs have been evaluated with respect to their standard errors in elevation, slope and curvature. The results show that the standard errors are not improved by using the on line DEM editor. It is also demonstrated that an increased point density decreases the standard error in elevation while its effect on the standard error in slope is limited. The standard error in curvature is almost independent of the point density.     

机载LiDAR点云生成多尺度DEM方法

为了利用机载激光雷达点云生成高保真、多尺度的数字高程模型(DEM),提出了一种基于综合生成策略的方法:首先,利用点云数据中的地面点生成高分辨率、高保真的DEM作为基础DEM;然后,通过迭代的方式对上一层较高分辨的DEM进行综合获取较低分辨率、高保真的DEM。实验表明,本文方法不仅具有可行性,而且生成的多尺度DEM具有高保真的特性。     

顾及地形坡度的SRTM和ASTER加权融合

为了克服现有SRTM和ASTER各自缺陷,提升公共DEM精度,本文提出了一种顾及地形坡度的SRTM和ASTER加权融合方法。首先对两种DEM进行地理配准;然后计算不同坡度等级下SRTM和ASTER的高程误差,并得到DEM融合权重;最后采用加权平均法对SRTM和ASTER进行融合。高精度控制点的检验表明:融合后DEM精度有明显提高,相比于原始SRTM和ASTER高程误差,标准差分别降低了5.65 m和1.20 m。     

A total error-based multiquadric method for surface modeling of digital elevation models

Digital elevation model (DEM) source data are subject to both horizontal and vertical errors owing to improper instrument operation, physical limitations of sensors, and bad weather conditions. These factors may bring a negative effect on some DEM-based applications requiring low levels of positional errors. Although classical smoothing interpolation methods have the ability to handle vertical errors, they are prone to omit horizontal errors. Based on the statistical concept of the total least squares method, a total error-based multiquadric (MQ-T) method is proposed in this paper to reduce the effects of both horizontal and vertical errors in the context of DEM construction. In nature, the classical multiquadric (MQ) method is a vertical error regression procedure, whereas MQ-T is an orthogonal error regression model. Two examples, including a numerical test and a real-world example, are employed in a comparative performance analysis of MQ-T for surface modeling of DEMs. The numerical test indicates that MQ-T performs better than the classical MQ in terms of root mean square error. The real-world example of DEM construction with sample points derived from a total station instrument demonstrates that regardless of the sample interval and DEM resolution, MQ-T is more accurate than classical interpolation methods including inverse distance weighting, ordinary kriging, and Australian National University DEM. Therefore, MQ-T can be considered as an alternative interpolator for surface modeling with sample points subject to both horizontal and vertical errors.     

GIS结点捕捉的广义算法及误差传播模型

根据最小二乘原理，本文提出了结点捕捉的一种广义算法，并建立了伴随的误差传播模型，针对位于模糊公差范围内待捕捉点组中各点坐标误差统计我的各种可能的特殊情况，进一步导出了相应的简化算法以及其误差传播模型，并从理论和数值模拟两方面系统地分析了结点坐标的相准确性一对捕捉结果的影响，理论推导表明，现有的GIS结点捕捉算法属广义算法的一种特殊情况，最后通过算例说明了广义算法和误差传播模型的实际应用前景。     

The isotropic organization of DEM structure and extraction of valley lines using hexagonal grid

The automatic extraction of valley lines (VLs) from digital elevation models (DEMs) has had a long history in the GIS and hydrology fields. The quality of the extracted results relies on the geometrical shape, spatial tessellation, and placement of the grids in the DEM structure. The traditional DEM structure consists of square grids with an eight‐neighborhood relationship, where there is an inconsistent distance measurement between orthogonal neighborhoods and diagonal neighborhoods. The directional difference results in the extracted VLs by the D8 algorithm not guaranteeing isotropy characteristics. Alternatively, hexagonal grids have been proved to be advantageous over square grids due to their consistent connectivity, isotropy of local neighborhoods, higher symmetry, increased compactness, and more. Considering the merits above, this study develops an approach to VL extraction from DEMs based on hexagonal grids. First, the pre‐process phase contains the depression filling, flow direction calculation, and flow accumulation calculation based on the six‐neighborhood relationship. Then, the flow arcs are connected, followed by estimating the flow direction. Finally, the connected paths are organized into a tree structure. To explore the effectiveness of hexagonal grids, comparative experiments are implemented against traditional DEMs with square grids using three sample regions. By analyzing the results between these two grid structures via visual and quantitative comparison, we conclude that the hexagonal grid structure has an outstanding ability in maintaining the location accuracy and bending characteristics of extracted valley networks. That is to say, the DEM‐derived VLs based on hexagonal grids have better spatial agreement with mapped river systems and lower shape diversion under the same resolution representation. Therefore, the DEMs with hexagonal grids can extract finer valley networks with the same data volume relative to traditional DEM.     

A case study of using external DEM in InSAR DEM generation

Synthetic aperture radar interferometry (InSAR) has been used as an innovative technique for digital elevation model (DEM) and topographic map generation. In this paper, external DEMs are used for InSAR DEM generation to reduce the errors in data processing. The DEMs generated from repeat-pass InSAR are compared. For steep slopes and severe changes in topography, phase unwrapping quality can be improved by subtracting the phase calculated from an external DEM. It is affirmative that the absolute height accuracy of the InSAR DEM is improved by using external DEM. The data processing was undertaken without the use of ground control points and other manual operation.     

LIDAR Data and Hydrological Applications at the Basin Scale

Digital elevation models (DEMs) resulting from LIDAR (light detection and ranging) surveys are now more available in the hydrology and hydraulics (H&H) community, not only for hydraulic applications in small areas close to river networks but also for hydrologic applications in whole basins. Several questions arise when trying to combine LIDAR data and hydrologic models. Despite the long processing time, LIDAR-derived DEMs can provide more accurate information that is useful for basin hydrogeomorphic characterization, in comparison with DEMs at resolutions commonly used in hydrologic applications (cell size 20-30 m). Of particular focus here are river network properties and the instantaneous unit hydrograph (IUH) framework. Two case studies, one in Italy and the other in the USA, are presented in which three DEMs are analyzed with differing resolutions as follows: "standard," i.e., a resolution commonly used in hydrologic applications (cell size 20-30 m), LIDAR (cell size 1-2.5 m), and LIDAR-resampled at the same resolution as the "standard" DEM. Results suggest that the higher spatial resolution LIDAR-derived data are preferable and can introduce more detailed information about basin hydrogeomorphic behavior.