Evaluation on the accuracy of digital elevation models

There is a growing interest in investigating the accuracy of digital elevation model (DEM). However people usually have an unbalanced view on DEM errors. They emphasize DEM sampling errors, but ignore the impact of DEM resolution and terrain roughness on the accuracy of terrain representation. This research puts forward the concept of DEM terrain representation error (Et) and then investigates the generation, factors, measurement and simulation of DEM terrain representation errors. A multi-resolution and multi-relief comparative approach is used as the major methodology in this research. The experiment reveals a quantitative relationship between the error and the variation of resolution and terrain roughness at a global level. Root mean square error (RMS Et) is regressed against surface profile curvature (V) and DEM resolution (R) at 10 resolution levels. It is found that the RMS Et may be expressed as RMS Et = (0.0061 × V+ 0.0052) × R - 0.022 × V + 0.2415. This result may be very useful in forecasting DEM accuracy, as well as in determining the DEM resolution related to the accuracy requirement of particular application.     

Characterizing errors in digital elevation models and estimating the financial costs of accuracy

Digital topographic models are the foundation of more advanced modeling applications and ultimately inform planning and decision making in many fields. Despite this, the error associated with these models and derived attributes is commonly overlooked. Little attention has been given in the scientific literature to the benefits gained from having less error in a model or to the corresponding cost associated with reducing model error by choosing one product over another. To address these gaps in knowledge we evaluated the error associated with five digital elevation models (DEMs) and derived attributes of slope and aspect relative to the same attributes derived from LiDAR data. We also estimated the acquisition and processing costs per square kilometer of the five test models and the LiDAR models. We used three measures to characterize model error: (1) root mean square error, (2) mean error (and standard deviation), and (3) area of significant elevation error. We applied these measures to DEM products that are used extensively across a range of applications for planning and managing natural resources. We depicted the relationship between model accuracy (the inverse of error) and cost in two ways. One was accuracy/cost ratio for each model. The other used separate data on accuracy and cost to better guide potential users in choosing between models or deciding on necessary expenditure on models. The main conclusion of our work was that accounting for error in DEMs can inform choice of models and the need for financial outlays.     

Loess terrain segmentation from digital elevation models based on the region growth method

Regional automatic segmentation – automatic terrain segmentation according to terrain features – is significant for modern geographical analysis. We propose a new approach of terrain region segmentation based on the region growth method. This method features actual runoff nodes as seed points. The corresponding growth threshold is defined based on statistical analysis of quantitative indexes of topographic features. Terrain segmentation of some regions is completed using the growth threshold. The corresponding edge boundaries of different terrain regions are extracted by image processing. Thus, the automatic segmentation of the terrain region is realized by the edge boundary. The application of the method to a typical Chinese loess landform area and automatic segmentation of three types of terrain regions – gully interfluve land, gully slope land, and gully groove land – are achieved by analyzing characteristics of the curvature structure of surface profiles. Segmentation results, compared with results of visual interpretation from a high-precision digital orthophoto map, show an average accuracy of segmentation of 93.51%. Topographic factor features of segmentation results are statistically analyzed. This study presents an effective and practical approach for segmenting terrain regions. This approach may be incorporated into the theory and method system of digital terrain analysis.     

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.     

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…     

数字高程模型地形描述误差的量化模拟--以黄土丘陵沟壑区的实验为例

本研究以陕北黄土高原丘陵沟壑区为试验样区 ,综合运用统计分析及比较分析的原理与方法 ,通过数学模拟、对比分析、误差可视化分析 ,研究不同空间尺度下DEM地形描述误差的数学转换模型。实验结果证明 ,目前适用于欧洲地区的地形描述误差的模拟方程EtD=q·a·(EtD′) b,经过参数的修正 ,在我国黄土高原丘陵沟壑区具有较高的模拟精度。该模型的建立可以实现应用低空间分辨率的DEM数据在栅格水平模拟高空间分辨率DEM所提取的地形描述误差 ,从而 ,在一定精度范围内大大提高Et的计算速度和计算效率。并且 ,对我国其它地貌类型区类似模型的建立 ,都具有重要的参考意义     

顾及数据特性的格网DEM分辨率计算

水平分辨率是格网DEM的决定性变量之一,直接决定着DEM对地形的逼近程度和地形参数计算、地学模拟的精度。基于地统计学理论和非参数密度估计方法,提出了地形宏观变异和微观变异相结合的DEM适宜分辨率计算方法。即首先按系列支撑对采样数据进行格网划分,形成具有不同尺度的支撑域;然后利用正则化理论,对高程点数据进行正则化变换,通过不同支撑上正则化变量的半变异函数分析,探索不同支撑尺度上的地形宏观变异规律,从而确定地形宏观变异的最佳支撑尺度;第三,在所确定的宏观变异最佳支撑尺度内,借鉴非参数密度估计中直方图的理论方法,从微观角度计算DEM适宜分辨率。最后通过陕北黄土高原的实际采样数据,对本文提出的方法进行了验证。     

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.     

Parallel identification and filling of depressions in raster digital elevation models

With the increasing sizes of digital elevation models (DEMs), there is a growing need to design parallel schemes for existing sequential algorithms that identify and fill depressions in raster DEMs. The Priority-Flood algorithm is the fastest sequential algorithm in the literature for depression identification and filling of raster DEMs, but it has had no parallel implementation since it was proposed approximately a decade ago. A parallel Priority-Flood algorithm based on the fastest sequential variant is proposed in this study. The algorithm partitions a DEM into stripes, processes each stripe using the sequential variant in many rounds, and progressively identifies more slope cells that are misidentified as depression cells in previous rounds. Both Open Multi-Processing (OpenMP)- and Message Passing Interface (MPI)-based implementations are presented. The speed-up ratios of the OpenMP-based implementation over the sequential algorithm are greater than four for all tested DEMs with eight computing threads. The mean speed-up ratio of our MPI-based implementation is greater than eight over TauDEM, which is a widely used MPI-based library for hydrologic information extraction. The speed-up ratios of our MPI-based implementation generally become larger with more computing nodes. This study shows that the Priority-Flood algorithm can be implemented in parallel, which makes it an ideal algorithm for depression identification and filling on both single computers and computer clusters.     

Uncertainty modeling and analysis of surface area calculation based on a regular grid digital elevation model (DEM)

In the field of digital terrain analysis (DTA), the principle and method of uncertainty in surface area calculation (SAC) have not been deeply developed and need to be further studied. This paper considers the uncertainty of data sources from the digital elevation model (DEM) and SAC in DTA to perform the following investigations: (a) truncation error (TE) modeling and analysis, (b) modeling and analysis of SAC propagation error (PE) by using Monte-Carlo simulation techniques and spatial autocorrelation error to simulate DEM uncertainty. The simulation experiments show that (a) without the introduction of the DEM error, higher DEM resolution and lower terrain complexity lead to smaller TE and absolute error (AE); (b) with the introduction of the DEM error, the DEM resolution and terrain complexity influence the AE and standard deviation (SD) of the SAC, but the trends by which the two values change may be not consistent; and (c) the spatial distribution of the introduced random error determines the size and degree of the deviation between the calculated result and the true value of the surface area. This study provides insights regarding the principle and method of uncertainty in SACs in geographic information science (GIScience) and provides guidance to quantify SAC uncertainty.     

栅格数字地形分析中的尺度问题研究方法

栅格数字高程模型（DEM）固有的尺度特征给以栅格DEM为基本输入的数字地形分析带来各种尺度问题。对栅格数字地形分析中涉及的尺度进行梳理,以分辨率和分析窗口为重点,对栅格数字地形分析中的多尺度表达、尺度效应、适宜尺度选择、尺度转换等尺度问题及其相互关系进行阐述;分别介绍各类尺度问题的现有定量研究方法,尤其对尺度效应定量刻画和适宜尺度选择方法,根据不同方法计算定量指标所利用的信息类别进行分类归纳;最后讨论了其中有待进一步开展研究的几方面工作。     

DEM采样间隔对地形描述精度的影响研究

数字高程模型(DEM)的精度包括采样点数据精度和地形描述精度两方面,前人对DEM精度的研究多集中在DEM采样点精度,而忽视了地形描述精度。该文提出基于窗口曲面拟合计算拟合曲面系列参数与"实际地形"曲面参数的标准差来衡量地形描述精度的方法,研究发现DEM地形描述精度随采样间隔的增大呈降低趋势;并利用坡度频率曲线和坡度累计频率曲线研究对DEM精度敏感的坡度因子与DEM采样间隔的关系,认为随DEM采样间隔增大,坡度衰减(变缓)的速率加快。     

Effects of DEM resolution and source on soil erosion modelling: a case study using the WEPP model

Digital elevation models (DEMs) vary in resolution and accuracy by the production method. DEMs with different resolutions and accuracies can generate varied topographic and hydrological features, which can in turn affect predictions by soil erosion models, such as the WEPP (Water Erosion Prediction Project) model. This study investigates the effects of DEMs on deriving topographic and hydrological attributes, and on predicting watershed erosion using WEPP v2006.5. Six DEMs at three resolutions from three sources were prepared for two small forested watersheds located in northern Idaho, USA. These DEMs were used to calculate topographic and hydrological parameters that served as inputs to WEPP. The model results of sediment yields and runoffs were compared with field observations. For both watersheds, DEMs with different resolutions and sources generated varied watershed shapes and structures, which in turn led to different extracted hill slope and channel lengths and gradients, and produced substantially different erosion predictions by WEPP.     

论DEM地形分析中的尺度问题

DEM及其地形分析具有强烈的尺度依赖特征。本文以黄高原地区的研究为例,结合地学建模和地学模拟的需求,重点讨论DEM地形分析中的尺度问题。文中从DEM建立与应用出发,首先建立了DEM地形分析中的尺度概念体系,剖析了各类尺度之间的关系,其次讨论了尺度所引起的各种地形分析效应问题,最后探讨了DEM地形分析中的尺度转换类型和方法。     

Reducing the grid orientation dependence of flow routing on square-grid digital elevation models

Topographical parameters derived from digital elevation models by employing flow routing algorithms may depend on the orientation of the square grid. Grid orientation dependence results from the insufficient isotropy of square grid and affects the flow directions and subsequent calculations based on flow routing. In this article, a systematic approach for analysing the rotational invariance of flow accumulation calculations is presented and applied. Computed flow accumulation maps are found to depend strongly on the grid orientation, especially if flow routing methods with low dispersion are used. It is also shown that isotropy of flow routing algorithms can be significantly improved by introducing a numerical parameter resulting in adjustable weighting for cardinal and diagonal directions in flow routing. The actual value of this parameter depends on the used flow routing method.     

Order classification of river watershed divides based on processing digital elevation models

The principles and the algorithm of order classification of river watershed divides are outlined. It is shown that a formal application of any available order classification procedures for river watershed divides is not theoretically grounded as well as being impractical, because the physical mechanisms for formation of watershed divide network are different from those operating in the river network. We have formulated the basic principle of determining the watershed divides order on the basis of a serial sequence of sections constituting the travel path of an arbitrary water drop from the watershed divide to the outlet section of the basin. It is suggested that the order N should be assigned to the section of the watershed divide belonging to the full divide line of the N-order basin only if the travel path from it to the N-order stream is “full” in the topological sense, i.e. includes sections of all orders, from 1 to N. Also, we present a variant of determining the order on the basis of so-called higher-order triplets, incomplete sequences of sections of three neighboring orders along the travel path, with the higher of them determining the watershed divide order. The use of triplets is a subjective procedure of generalization that eliminates the influence of recent random erosional incisions on the forms of stable high-order watersheds. We outline the variants of the technique for identifying the network of watershed divides and calculating their orders, based on processing the digital elevation models (DEM) through the use of standard GIS ArcMap tools. Results are obtained in the form of a correlated classification of river and watershed networks which are rationally interpreted and hold promise for investigating the structure, functioning and evolution of river systems. The study revealed the existence of formation “cores” of river systems, i.e. regions within which the system reaches a higher stream order and which are bounded by watersheds of the same order.     

联合GPS和SARAL卫星测高数据构建南极Dome A区域DEM

南极冰盖数字高程模型(digital elevation model,DEM)对南极环境变化和地形研究具有重要作用,利用GPS实测数据和卫星测高数据建立DEM是构建南极冰盖表面DEM的重要方法。考虑到实测GPS数据的精度较高,而卫星测高的空间分辨率占优,本文探讨综合利用这两种数据构建南极Dome A区域DEM。法国国家空间研究中心和印度空间研究组织共同研制的SARAL卫星是Envisat的后续卫星,搭载的Alti Ka雷达高度计首次采用了Ka波段,可以极大减小电离层的影响,提高测距精度和卫星数据的空间分辨率。本文首先利用中国南极第29次科学考察在Dome A区域的实测GPS数据对SARAL数据进行精度评定,然后利用实测GPS数据对SARAL测高数据进行高程修正,联合GPS数据获取得到了Dome A区域300 m分辨率的DEM。结果表明SARAL的高程精度为0.615 m,而联合GPS数据能改善DEM精度,提高到0.261 m。