Resolution and accuracy of terrain representation by grid DEMs at a micro-scale

This paper examines the impact of DEM resolution on the accuracy of terrain representation and of the gradient determined. The DEMs of three terrain types with diverse complexities were constructed from digitizing contours and then kriging. The accuracy (RMSE) of the DEMs was regressed against contour density (D) and DEM resolution (S) at six resolution levels. It is found that RMSE may be expressed as (7.274 1.666S)D/1000 with an R value of 0.9659. The representation accuracy decreases moderately at an intermediate resolution, but sharply at coarse resolutions for all three terrain types. Resolution reduction profoundly affects the gradient determined from the DEM. While exerting little influence on mean gradient, resolution significantly affects the standard deviation of gradient, especially for a simple terrain. The results obtained in this study may be used to determine the DEM resolution that is appropriate to the accuracy requirements of a particular user.     

Comparison of existing methods for building triangular irregular network,models of terrain from grid digital elevation models

Abstract

Triangulated irregular networks (TINs) are increasingly popular for their efficiency in data storage and their ability to accommodate irregularly spaced elevation points for many applications of geographical information systems. This paper reviews and evaluates various methods for extracting TINs from dense digital elevation models (DEMs) on a sample DEM. Both structural and statistical comparisons show that the methods perform with different rates of success in different settings. Users of DEM to TIN conversion methods should be aware of the strengths and weaknesses of the methods in addition to their own purposes before conducting the conversion.     

Special Issue on parallel processing in GIS

This paper explores three theoretical approaches for estimating the degree of correctness to which the accuracy figures of a gridded Digital Elevation Model (DEM) have been estimated depending on the number of checkpoints involved in the assessment process. The widely used average‐error statistic Mean Square Error (MSE) was selected for measuring the DEM accuracy. The work was focused on DEM uncertainty assessment using approximate confidence intervals. Those confidence intervals were constructed both from classical methods which assume a normal distribution of the error and from a new method based on a non‐parametric approach. The first two approaches studied, called Chi‐squared and Asymptotic Student t, consider a normal distribution of the residuals. That is especially true in the first case. The second case, due to the asymptotic properties of the t distribution, can perform reasonably well with even slightly non‐normal residuals if the sample size is large enough. The third approach developed in this article is a new method based on the theory of estimating functions which could be considered much more general than the previous two cases. It is based on a non‐parametric approach where no particular distribution is assumed. Thus, we can avoid the strong assumption of distribution normality accepted in previous work and in the majority of current standards of positional accuracy. The three approaches were tested using Monte Carlo simulation for several populations of residuals generated from originally sampled data. Those original grid DEMs, considered as ground data, were collected by means of digital photogrammetric methods from seven areas displaying differing morphology employing a 2 by 2 m sampling interval. The original grid DEMs were subsampled to generate new lower‐resolution DEMs. Each of these new DEMs was then interpolated to retrieve its original resolution using two different procedures. Height differences between original and interpolated grid DEMs were calculated to obtain residual populations. One interpolation procedure resulted in slightly non‐normal residual populations, whereas the other produced very non‐normal residuals with frequent outliers. Monte Carlo simulations allow us to report that the estimating function approach was the most robust and general of those tested. In fact, the other two approaches, especially the Chi‐squared method, were clearly affected by the degree of normality of the residual population distribution, producing less reliable results than the estimating functions approach. This last method shows good results when applied to the different datasets, even in the case of more leptokurtic populations. In the worst cases, no more than 64–128 checkpoints were required to construct an estimate of the global error of the DEM with 95% confidence. The approach therefore is an important step towards saving time and money in the evaluation of DEM accuracy using a single average‐error statistic. Nevertheless, we must take into account that MSE is essentially a single global measure of deviations, and thus incapable of characterizing the spatial variations of errors over the interpolated surface.     

The impact of DEM data source on prediction of flooding and erosion risk due to sea-level rise

Digital elevation model (DEM) elevation accuracy and spatial resolution are typically considered before a given DEM is used for the assessment of coastal flooding, sea-level rise or erosion risk. However, limitations of DEMs arising from their original data source can often be overlooked during DEM selection. Global elevation error statistics provided by DEM data suppliers can provide a useful indicator of actual DEM error, but these statistics can understate elevation errors occurring outside of idealised ground reference areas. The characteristic limitations of a range of DEM sources that may be used for the assessment of coastal inundation and erosion risk are tested using high-resolution photogrammetric, low- and medium-resolution global positioning system (GPS)-derived and very high-resolution terrestrial laser scanning point data sets. Errors detected in a high-resolution photogrammetric DEM are found to be substantially beyond quoted error, demonstrating the degree to which quoted DEM accuracy can understate local DEM error and highlighting the extent to which spatial resolution can fail to provide a reliable indicator of DEM accuracy. Superior accuracies and inundation prediction results are achieved based on much lower-resolution GPS points confirming conclusions drawn in the case of the photogrammetric DEM data. This suggests a scope for the use of GPS-derived DEMs in preference to the photogrammetric DEM data in large-scale risk-mapping studies. DEM accuracies and superior representation of micro-topography achieved using high-resolution terrestrial laser scan data confirm its advantages for the prediction of subtle inundation and erosion risk. However, the requirement for data fusion of GPS to remove ground-vegetation error highlighted limitations for the use of side-scan laser scan data in densely vegetated areas.     

Propagation of vertical and horizontal source data errors into a TIN with linear interpolation

Digital elevation models (DEMs) have been widely used for a range of applications and form the basis of many GIS-related tasks. An essential aspect of a DEM is its accuracy, which depends on a variety of factors, such as source data quality, interpolation methods, data sampling density and the surface topographical characteristics. In recent years, point measurements acquired directly from land surveying such as differential global positioning system and light detection and ranging have become increasingly popular. These topographical data points can be used as the source data for the creation of DEMs at a local or regional scale. The errors in point measurements can be estimated in some cases. The focus of this article is on how the errors in the source data propagate into DEMs. The interpolation method considered is a triangulated irregular network (TIN) with linear interpolation. Both horizontal and vertical errors in source data points are considered in this study. An analytical method is derived for the error propagation into any particular point of interest within a TIN model. The solution is validated using Monte Carlo simulations and survey data obtained from a terrestrial laser scanner.     

The impact of resolution on the accuracy of hydrologic data derived from DEMs

1 Introduction Automated extraction of drainage features from DEMs is an effective alternative to the tedious manual mapping from topographic maps. The derived hydrologic characteristics include stream-channel networks, delineation of catchment boundaries, catchment area, catchment length, stream-channel long profiles and stream order etc. Other important characteristics of river catchments, such as the stream-channel density, stream-channel bifurcation ratios, stream-channel order, number…     

The impact of resolution on the accuracy of hydrologic data derived from DEMs

Hydrologic data derived from digital elevation models (DEM) has been regarded as an effective method in the spatial analysis of geographical information systems (GIS). However, both DEM resolution and terrain complexity has impacts on the accuracy of hydrologic derivatives. In this study, a multi-resolution and multi-relief comparative approach was used as a major methodology to investigate the accuracy of hydrologic data derived from DEMs. The experiment reveals that DEM terrain representation error affects the accuracy of DEM hydrological derivatives (drainage networks and watershed etc.). Coarser DEM resolutions can usually cause worse results. However, uncertain result commonly exists in this calculation. The derivative errors can be found closely related with DEM vertical resolution and terrain roughness. DEM vertical resolution can be found closely related with the accuracy of DEM hydrological derivatives, especially in the smooth plain area. If the mean slope is less than 4 degrees, the derived hydrologic data are usually unreliable. This result may be helpful in estimating the accuracy of the hydrologic derivatives and determining the DEM resolution that is appropriate to the accuracy requirement of a particular user. By applying a threshold value to subset the cells of a higher accumulation flow, a stream network of a specific network density can be extracted. Some very important geomorphologic characteristics, e.g., shallow and deep gullies, can be separately extracted by means of adjusting the threshold value. However, such a flow accumulationbased processing method can not correctly derive those streams that pass through the working area because it is hard to accumulate enough flow direction values to express the stream channels at the stream's entrance area. Consequently, errors will definitely occur at the stream’s entrance area. In addition, erroneous derivatives can also be found in deriving some particular rivers, e.g., perched (hanging up) rivers, anastomosing rivers and braided rivers. Therefore, more work should be done to develop and perfect the algorithms.     

Impact of sampling intervals on the reliability of topographic variables mapped from grid DEMs at a micro-scale

This paper explores the quantitative relation between the reliability of slope aspect, gradient, and form mapped from a gridded DEM and the sampling interval (SI) of elevations. Grid DEMs initially interpolated from digitised contours at 10 m were sampled to five other resolution levels. The topographic variables mapped at these SIs were compared with those at 10 m. It is found that the reliability of mapped slope aspect and form is not significantly affected by SI. By comparison, the reliability of slope gradient is more susceptible to SI, especially if it is derived from a gently rolling terrain. Around 90% of the variation in the mapped slope aspect and gradient are accounted for by the inaccuracy of DEMs. A lower percentage exists for slope form. The stability of the mapped topographic variables can be reliably predicted from SI and terrain complexity.     

基于光学立体和InSAR的Grove山地区DEM建立和分析

本文分别利用光学立体和In SAR技术生成了东南极Grove山地区15 m分辨率的ASTER DEM和20 m分辨率的In SAR DEM。在利用ASTER立体像对生成DEM的过程中引入ICESat测高数据作为高程控制以减少错误匹配,提高DEM垂直精度;而在利用ERS tandem数据生成DEM后,选取ICESat测高数据对In SAR DEM进行倾斜面纠正,以消除基线不精确估计等带来的影响。通过与未作控制的ICESat测高数据进行比较,评价了两种DEM的精度并对误差进行了分析。同时,比较了两种DEM的差异,并分析了造成这些差异的原因,探讨了两种技术生成南极冰盖DEM的优势和不足。最后结合两DEM的优势,融合生成了Grove山地区高精度的DEM。     

面向地貌学本源的DEM增值理论框架与构建方法

数字高程模型（DEM）在表达地貌形态、认知地表过程、揭示地学机理等研究中发挥着基础性的作用,是重要的地理空间数据模型,广泛地应用于地学分析与建模中。但是,传统DEM具有属性单一的天然缺陷,难以支撑面向地学过程与机理挖掘的地球系统科学研究。亟待在传统DEM的基础上实现其数据模型的增值,服务于新地貌学研究范式和新对地观测技术背景下的数字地形建模与分析。立足于以上问题,本文构建了DEM增值的理论框架,主要包括DEM增值的概念、内涵、内容、类别、不同增值类别之间的相互关系,以及此理论框架的研究意义和应用范畴。提出了DEM增值的构建方法,包含：① 强调地上地下一体化、时间空间相耦合的DEM空间维度和时间维度增值方法;② 重视地下、地表和地上物质构成,形态属性耦合的物质属性和形态属性增值方法;③ 顾及自然过程、人工作用的地物对象、地貌形态的地物要素和形体要素增值方法。最后,分别以数字阶地模型、数字坡地模型和数字流域模型为例,阐释DEM在面向地貌学本源问题时的不同增值方法及应用场景。期望通过对DEM进行维度、属性和要素3个层面的增值,实现现代对地观测技术背景下数字高程模型表达方法的突破,并支撑知识驱动的数字地貌问题分析。     

Evaluating the Potential of an Airborne Laser-scanning System for Measuring Volume Changes of Glaciers

Airborne laser scanning (ALS) is well suited for the production of digital elevation models (DEM), and can, in contrast to photographic methods, be used to acquire a DEM independently of surface texture and external light sources. ALS thus serves as a tool to generate DEMs of firn areas where photogram- metric methods often fail.
The potential of an integrated ALS system – comprising a laser scanner, precise differential global positioning system, and a gyro platform – for DEM generation of firn areas is currently being assessed. The Unteraargletscher, Bernese Alps, Switzerland, has been chosen as a test site. As part of a pilot project aimed at determining the mass balance distribution of that glacier without the use of in situ information, ALS measurements were conducted in autumn 1997. The DEM derived from laser measurements is extremely sensitive to the position and attitude of the aircraft. Currently the main work focuses on assessing and improving the system's accuracy by error modelling and by the development of error-correction algorithms.
Preliminary results from Unteraargletscher are presented, and the potential of this method for the generation of DEMs of firn areas is discussed.     

不同分辨率DEM提取地面坡度的不确定性模拟:以在黄土高原的试验为例

Slope is one of the crucial terrain variables in spatial analysis and land use planning,especially in the Loess Plateau area of China which is suffering from serious soil erosion. DEM based slope extracting method has been widely accepted and applied in practice. However slope accuracy derived from this method usually does not match with its popularity. A quantitative simulation to slope data uncertainty is important not only theoretically but also necessarily to applications. This paper focuses on how resolution and terrain complexity impact on the accuracy of mean slope extracted from DEMs of different resolutions in the Loess Plateau of China. Six typical geomorphologic areas are selected as test areas, representing different terrain types from smooth to rough. Their DEMs are produced from digitizing contours of 1:10,000 scale topographic maps. Field survey results show that 5 m should be the most suitable grid size for representing slope in the Loess Plateau area. Comparative and math-simulation methodology was employed for data processing and analysis. A linear correlativity between mean slope and DEM resolution was found at all test areas,but their regression coefficients related closely with the terrain complexity of the test areas. If taking stream channel density to represent terrain complexity, mean slope error could be regressed against DEM resolution (X) and stream channel density (S) at 8 resolution levels and expressed as (0.0015S2+0.031S-0.0325)X-0.0045S2-0.155S+0.1625, with a R2 value of over 0.98. Practical tests also show an effective result of this model in applications. The new development methodology applied in this study should be helpful to similar researches in spatial data uncertainty investigation.     

Simulation on slope uncertainty derived from DEMs at different resolution levels： a case study in the Loess Plateau

Slope is one of the crucial terrain variables in spatial analysis and land use planning, especially in the Loess Plateau area of China which is suffering from serious soil erosion. DEM based slope extracting method has been widely accepted and applied in practice. However slope accuracy derived from this method usually does not match with its popularity. A quantitative simulation to slope data uncertainty is important not only theoretically but also necessarily to applications. This paper focuses on how resolution and terrain complexity impact on the accuracy of mean slope extracted from DEMs of different resolutions in the Loess Plateau of China. Six typical geomorphologic areas are selected as test areas, representing different terrain types from smooth to rough. Their DEMs are produced from digitizing contours of 1:10,000 scale topographic maps. Field survey results show that 5 m should be the most suitable grid size for representing slope in the Loess Plateau area. Comparative and math-simulation methodology was employed for data processing and analysis. A linear correlativity between mean slope and DEM resolution was found at all test areas, but their regression coefficients related closely with the terrain complexity of the test areas. If taking stream channel density to represent terrain complexity, mean slope error could be regressed against DEM resolution (X) and stream channel density (S) at 8 resolution levels and expressed as(0.0015S2 0.031S-0.0325)X-0.0045S2-0.155S 0.1625, with a R2 value of over 0.98. Practical tests also show an effective result of this model in applications. The new development methodology applied in this study should be helpful to similar researches in spatial data uncertainty investigation.     

Simulation on slope uncertainty derived from DEMs at different resolution levels: a case study in the Loess Plateau

Slope is one of the crucial terrain variables in spatial analysis and land use planning, especially in the Loess Plateau area of China which is suffering from serious soil erosion. DEM based slope extracting method has been widely accepted and applied in practice. However slope accuracy derived from this method usually does not match with its popularity. A quantitative simulation to slope data uncertainty is important not only theoretically but also necessarily to applications. This paper focuses on how resolution and terrain complexity impact on the accuracy of mean slope extracted from DEMs of different resolutions in the Loess Plateau of China. Six typical geomorphologic areas are selected as test areas, representing different terrain types from smooth to rough. Their DEMs are produced from digitizing contours of 1:10,000 scale topographic maps. Field survey results show that 5 m should be the most suitable grid size for representing slope in the Loess Plateau area. Comparative and math-simulation methodology was employed for data processing and analysis. A linear correlativity between mean slope and DEM resolution was found at all test areas, but their regression coefficients related closely with the terrain complexity of the test areas. If taking stream channel density to represent terrain complexity, mean slope error could be regressed against DEM resolution (X) and stream channel density (S) at 8 resolution levels and expressed as (0.0015S2+0.031S-0.0325)X-0.0045S2-0.155S+0.1625, with a R2 value of over 0.98. Practical tests also show an effective result of this model in applications. The new development methodology applied in this study should be helpful to similar researches in spatial data uncertainty investigation.     

A universal spectral analytical method for digital terrain modeling

There are three major mathematical problems in digital terrain analysis: (1) interpolation of digital elevation models (DEMs); (2) DEM generalization and denoising; and (3) computation of morphometric variables through calculating partial derivatives of elevation. Traditionally, these three problems are solved separately by means of procedures implemented in different methods and algorithms. In this article, we present a universal spectral analytical method based on high-order orthogonal expansions using the Chebyshev polynomials of the first kind with the subsequent Fejér summation. The method is intended for the processing of regularly spaced DEMs within a single framework including DEM global approximation, denoising, generalization, as well as calculating the partial derivatives of elevation and local morphometric variables.

The method is exemplified by a portion of the Great Rift Valley and central Kenyan highlands. A DEM of this territory (the matrix 480 × 481 with a grid spacing of 30″) was extracted from the global DEM SRTM30_PLUS. We evaluated various sets of expansion coefficients (up to 7000) to approximate and reconstruct DEMs with and without the Fejér summation. Digital models of horizontal and vertical curvatures were computed using the first and second partial derivatives of elevation derived from the reconstructed DEMs. To evaluate the approximation accuracy, digital models of residuals (differences between the reconstructed DEMs and the initial one) were calculated. The test results demonstrated that the method is characterized by a good performance (i.e., a distinct monotonic convergence of the approximation) and a high speed of data processing. The method can become an effective alternative to common techniques of DEM processing.     

Methodological sensitivity of morphometric estimates of coarse fluvial sediment transport

The estimation of fluvial sediment transport rate from measurements of morphological change has received growing recent interest. The revival of the ‘morphological method’ reflects continuing concern over traditional methods of rate determination but also the availability of new survey methods capable of high-precision, high-resolution topographic monitoring. Remote sensing of river channels through aerial digital photogrammetry is a potentially attractive alternative to labour intensive ground surveys. However, while photogrammetry presents the opportunity to acquire survey data over large areas, data precision and accuracy, particularly in the vertical dimension are lower than in traditional ground survey methods. This paper presents results of recent research in which digital elevation models (DEMs) have been developed for a reach of a large braided gravel-bed river in Scotland using both digital photogrammetry and high-resolution RTK GPS ground surveys. A statistical level of change detection is assessed by comparing surfaces with independent check points. The methodological sensitivity of the annual channel sediment budget (1999–2000) to the threshold is presented. Results suggest that while the remote survey methods employed here can be used to develop qualitatively convincing, moderate precision DEMs of channel topography (RMSE=±0.21 m), the remaining errors imply significant limits on reliable change detection which lead to important information losses. Tests at a 95% confidence interval for change detection show that over 60% of channel deposition and 40% of erosion may be obscured by the lower level of precision associated with photogrammetric monitoring when compared to ground survey measurements. This bias reflects the difficulty of detecting the topographic signature of widespread, but shallow deposition on bar tops.     

A study on DEM-derived primary topographic attributes for hydrologic applications: Sensitivity to elevation data resolution

Primary topographic attributes play a critical role in determining watershed hydrologic characteristics for water resources modeling with raster-based digital elevation models (DEM). The effects of DEM resolution on a set of important topographic derivatives are examined in this study, including slope, upslope contributing area, flow length and watershed area. The focus of the study is on how sensitive each of the attributes is to the resolution uncertainty by considering the effects of overall terrain gradient and bias from resampling. Two case study watersheds of different gradient patterns are used with their 10 m USGS DEMs. A series of DEMs up to 200 m grid size are produced from the base DEMs using three commonly used resampling methods. All the terrain variables tested vary with the grid size change. It is found that slope angles decrease and contributing area values increase constantly as DEMs are aggregated progressively to coarser resolutions. No systematic trend is observed for corresponding changes of flow path and watershed area. The analysis also suggests that gradient profile of the watershed presents an important factor for the examined sensitivities to DEM resolution.     

Deriving ground surface digital elevation models from LiDAR data with geostatistics

This paper focuses on two common problems encountered when using Light Detection And Ranging (LiDAR) data to derive digital elevation models (DEMs). Firstly, LiDAR measurements are obtained in an irregular configuration and on a point, rather than a pixel, basis. There is usually a need to interpolate from these point data to a regular grid so it is necessary to identify the approaches that make best use of the sample data to derive the most accurate DEM possible. Secondly, raw LiDAR data contain information on above‐surface features such as vegetation and buildings. It is often the desire to (digitally) remove these features and predict the surface elevations beneath them, thereby obtaining a DEM that does not contain any above‐surface features. This paper explores the use of geostatistical approaches for prediction in this situation. The approaches used are inverse distance weighting (IDW), ordinary kriging (OK) and kriging with a trend model (KT). It is concluded that, for the case studies presented, OK offers greater accuracy of prediction than IDW while KT demonstrates benefits over OK. The absolute differences are not large, but to make the most of the high quality LiDAR data KT seems the most appropriate technique in this case.     

Modelling surface drainage patterns in altered landscapes using LiDAR

The detailed topographic information contained in light detection and ranging (LiDAR) digital elevation models (DEMs) can present significant challenges for modelling surface drainage patterns. These data frequently represent anthropogenic infrastructure, such as road embankments and drainage ditches. While LiDAR DEMs can improve estimates of catchment boundaries and surface flow paths, modelling efforts are often confounded difficulties associated with incomplete representation of infrastructure. The inability of DEMs to represent embankment underpasses (e.g. bridges, culverts) and the problems with existing automated techniques for dealing with these problems can lead to unsatisfactory results. This is often dealt with by manually modifying LiDAR DEMs to incorporate the effects of embankment underpasses. This paper presents a new DEM pre-processing algorithm for removing the artefact dams created by infrastructure in sites of embankment underpasses as well as enforcing flow along drainage ditches. The application of the new algorithm to a large LiDAR DEM of a site in Southwestern Ontario, Canada, demonstrated that the least-cost breaching method used by the algorithm could reliably enforce drainage pathways while minimizing the impact to the original DEM.     

DEM提取黄土高原地面坡度的不确定性

选择陕北黄土高原6个典型地貌类型区为试验样区,采用野外实测及高精度的1:1万比例尺DEM为基准数据,研究栅格分辨率及地形粗糙度对DEM所提取地面平均坡度精度的影响。结果显示,对于1:1万比例尺DEM,5 m是保证该地区地形描述精度的理想分辨率尺度;多要素逐步回归模拟的方法进一步揭示了DEM所提取的地面平均坡度误差E与栅格分辨率X以及地形起伏的代表性因子-沟壑密度S之间存在的量化关系为E = (0.0015S2+0.031S-0.0325)X-0.0045S2-0.155S+0.1625,该结果也为确定适用的DEM分辨率提供了理论依据。