Uncertainty due to DEM error in landslide susceptibility mapping

Terrain attributes such as slope gradient and slope shape, computed from a gridded digital elevation model (DEM), are important input data for landslide susceptibility mapping. Errors in DEM can cause uncertainty in terrain attributes and thus influence landslide susceptibility mapping. Monte Carlo simulations have been used in this article to compare uncertainties due to DEM error in two representative landslide susceptibility mapping approaches: a recently developed expert knowledge and fuzzy logic-based approach to landslide susceptibility mapping (efLandslides), and a logistic regression approach that is representative of multivariate statistical approaches to landslide susceptibility mapping. The study area is located in the middle and upper reaches of the Yangtze River, China, and includes two adjacent areas with similar environmental conditions – one for efLandslides model development (approximately 250 km²) and the other for model extrapolation (approximately 4600 km²). Sequential Gaussian simulation was used to simulate DEM error fields at 25-m resolution with different magnitudes and spatial autocorrelation levels. Nine sets of simulations were generated. Each set included 100 realizations derived from a DEM error field specified by possible combinations of three standard deviation values (1, 7.5, and 15 m) for error magnitude and three range values (0, 60, and 120 m) for spatial autocorrelation. The overall uncertainties of both efLandslides and the logistic regression approach attributable to each model-simulated DEM error were evaluated based on a map of standard deviations of landslide susceptibility realizations. The uncertainty assessment showed that the overall uncertainty in efLandslides was less sensitive to DEM error than that in the logistic regression approach and that the overall uncertainties in both efLandslides and the logistic regression approach for the model-extrapolation area were generally lower than in the model-development area used in this study. Boxplots were produced by associating an independent validation set of 205 observed landslides in the model-extrapolation area with the resulting landslide susceptibility realizations. These boxplots showed that for all simulations, efLandslides produced more reasonable results than logistic regression.     

地形复杂度对坡度坡向的影响

采用三阶不带权差分算法，研究了地形复杂度与坡度坡向的关系，澄清了目前关于坡度坡向误差空间分布的矛盾观点，并分别在凹向椭球和高斯合成曲面数学模型曲面DEM上对其进行验证。通过研究得出：①坡度、坡向误差与坡度值正相关；②坡度坡向误差主要分布在平坦地区；③坡向误差较坡度误差对DEM高程数据误差敏感，较小的DEM误差引起较大的坡向误差。     

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。     

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.     

DEM误差对滑坡危险性评价模型的影响

基于数字高程模型(DEM)计算得到的坡度、坡向等地形属性是滑坡危险性评价模型的重要输入数据, DEM误差会导致地形属性计算结果不确定性, 进而影响滑坡危险性评价模型的结果。本文选择基于专家知识的滑坡危险性评价模型和逻辑斯第回归模型, 采用蒙特卡洛模拟方法, 研究DEM误差所导致的滑坡危险性评价模型结果不确定性。研究区位于长江中上游的重庆开县, 采用5 m分辨率的DEM, 以序贯高斯模拟方法模拟了不同大小(误差标准差为1 m、7.5 m、15 m)和空间自相关性(变程为0 m、30 m、60 m、120 m)的12 类DEM误差场参与滑坡危险性评价。每次模拟包括100 个实现, 通过对每次模拟分别计算滑坡危险性评价结果的标准差图层和分类一致性百分比图层, 用以评价结果不确定性。评价结果表明, 在不同的DEM精度下, 两个滑坡危险性评价模型所得结果的总体不确定性随空间自相关程度的变化趋势并不相同。当DEM空间自相关性程度不同时, 基于专家知识的滑坡危险性评价模型的评价结果总体不确定随着DEM误差增加而呈现不同的变化趋势, 而逻辑斯第回归模型的评价结果总体不确定性随着DEM误差大小增加而单调增加。从评价结果总体不确定性角度而言, 总体上逻辑斯第回归模型比基于专家知识的滑坡危险性评价模型更加依赖于DEM数据质量。     

Quantifying local flow direction uncertainty

Absolute elevation error in digital elevation models (DEMs) can be within acceptable National Map Accuracy standards, but still have dramatic impacts on field-level estimates of surface water flow direction, particularly in level regions. We introduce and evaluate a new method for quantifying uncertainty in flow direction rasters derived from DEMs. The method utilizes flow direction values derived from finer resolution digital elevation data to estimate uncertainty, on a cell-by-cell basis, in flow directions derived from coarser digital elevation data. The result is a quantification and spatial distribution of flow direction uncertainty at both local and regional scales. We present an implementation of the method using a 10-m DEM and a reference 1-m lidar DEM. The method contributes to scientific understanding of DEM uncertainty propagation and modeling and can inform hydrological analyses in engineering, agriculture, and other disciplines that rely on simulations of surface water flow.     

Geomorphology-oriented digital terrain analysis: Progress and perspectives

Digital terrain analysis(DTA) is one of the most important contents in the research of geographical information science(GIS). However, on the basis of the digital elevation model(DEM), many problems exist in the current research of DTA in geomorphological studies. For instance, the current DTA research appears to be focused more on morphology, phenomenon, and modern surface rather than mechanism, process, and underlying terrain. The current DTA research needs to be urgently transformed from the study of landform morphology to one focusing on landform process and mechanism. On this basis, this study summarizes the current research status of geomorphology-oriented DTA and systematically reviews and analyzes the research about the knowledge of geomorphological ontology, terrain modeling, terrain derivative calculation, and terrain analytical methods. With the help of DEM data, DTA research has the advantage of carrying out geomorphological studies from the perspective of surface morphology. However, the study of DTA has inherent defects in terms of data expression and analytic patterns. Thus, breakthroughs in basic theories and key technologies are necessary. Moreover, scholars need to realize that DTA research must be transformed from phenomenon to mechanism, from morphology to process, and from terrain to landform. At present, the research development of earth science has reached the critical stage in which the DTA research should focus more on geomorphological ontology. Consequently, this study proposes several prospects of geomorphology-oriented DTA from the aspects of value-added DEM data model, terrain derivatives and their spatial relations, and macro-terrain analysis. The study of DTA based on DEM is at a critical period along with the issue on whether the current GIS technology can truly support the development of geography. The research idea of geomorphology-oriented DTA is expected to be an important exploration and practice in the field of GIS.     

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。     

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.     

山区地形开阔度的分布式模型

 地形开阔度是影响山地辐射平衡及其分量的重要地形因子,是山区散射辐射、地形反射辐射等计算的重要参数。在复杂的地形条件下,地形开阔度的计算很难用数学公式描述。 利用数字高程模型（DEM）,全面考虑了坡地自身遮蔽和周围地形相互遮蔽的影响,提出了山区地形开阔度的分布式模型和算法。以1 km×1 km分辨率的DEM数据作为地形的综合反映,计算了起伏地形下中国地形开阔度的空间分布。同时,利用100 m和1 km两个分辨率的DEM数据,从不同DEM分辨率和不同地貌类型两个方面探讨了地形开阔度的空间尺度效应,阐明了区域地形开阔度随地形地貌和空间分辨率的变化规律。所提供的山地开阔度的数据可作为基础地理数据供相关研究应用。     

起伏地形下黄河流域太阳直接辐射分布式模拟

1 Introduction Directsolarradiation (DSR)isthe key com ponentofthe globalradiation reaching the Earth.For the influence of terrain factors,calculation of DSR quantity of rugged terrain is considerably com plex (Oliphantetal.,2003). The solarradiation quan…     

Evaluation on the accuracy of digital elevation models

1 IntroductionDigital elevation model (DEM) is digital representation of relief. It is one of the most important components in the database of GIS. At present, DEM is playing a key role in the field of survey and mapping, remote sensing and almost all the terrain related geographical analyses. DEM can be grouped into regular grids (raster) and triangulated irregular networks (TIN). Both have their advantages and disadvantages in application. It is generally believed that grid DEM will …     

起伏地形下黄河流域太阳直接辐射分布式模式

基于数字高程模型(DEM)数据和气象站观测资料建立了起伏地形下太阳直接辐射分布式计算模型,模型充分考虑了地形因子(坡向、坡度、地形相互遮蔽)对起伏地形下太阳直接辐射空间分布的影响;以1km×1km分辨率的DEM数据作为地形的综合反映,计算了起伏地形下黄河流域1km×1km分辨率太阳直接辐射的空间分布;深入分析了起伏地形下太阳直接辐射受地理、地形因子影响的变化规律.结果表明受地形起伏和坡向、坡度等局地地形因子的影响,山区年太阳直接辐射量的空间差异比较明显,向阳山坡(偏南坡)的年直接辐射量明显高于背阴山坡(偏北坡).     

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。     

面向地貌学本源的数字地形分析研究进展与展望

数字地形分析（DTA）是地理信息科学（GIS）研究的热点。但是,当前基于数字高程模型（DEM）的数字地形分析在地貌学研究中存在重形态轻机理、重现象轻过程、重地上轻地下等问题,急需从单一的地貌形态分析,迈向面向成因、过程与机理等地貌学本源问题的研究转变。据此,本文系统梳理了面向地貌学本源的数字地形分析的相关研究现状,并从地貌学本源认识、地貌形态建模、地形因子提取、以及其他地形分析方法等研究进行了系统的回顾、梳理与分析。研究表明,基于DEM的数字地形分析虽具有地貌特征分析的潜力与优势,但是,数字地形分析存在数据表达与分析模式上的先天缺陷,亟待通过基础理论与关键技术的突破,实现理论与方法的创新发展,实现从“坡面”走向“区域”,从“形态”走向“过程”,从“地形”走向“地貌”。而当今地球系统科学的研究发展态势也到了数字地形分析研究从重视地貌形态走向揭示地貌学本源的关键阶段。因此,本文从DEM数据模型增值、地形因子及其地形空间关系、以及宏观地形分析等侧面展望了面向地貌学本源的数字地形分析研究。当今基于DEM的数字地形分析研究,正像当前的GIS是否能够真正支撑地理学发展一样,已经处于一个非常关键的十字路口。面向地貌学本源的数字地形分析研究思路可望成为地理信息科学领域理论与方法创新的一次重要探索与实践。     

地形信息对确定DEM适宜分辨率的影响

分辨率会直接影响基于栅格数字高程模型（DEM）的数字地形分析结果,因此在实际应用中,需要选择适宜的DEM分辨率。目前采取的基本方法,基于某种地形信息定量刻画尺度效应曲线,从而确定DEM适宜分辨率,但对于采用不同地形信息时所产生的影响尚缺乏研究。本文针对该方法中通常采用的坡度、剖面曲率、水平曲率等3 种地形信息,每种地形信息提取时,分别使用两种不同的常用算法,在3 个不同地形特征的研究区中,逐一计算其在不同分辨率下的局部方差均值,以刻画尺度效应曲线,确定相应的DEM适宜分辨率,并进行对比分析。结果表明：① 采用剖面曲率或水平曲率所得适宜分辨率结果基本相同,但采用坡度所得出的适宜分辨率结果则有明显差别,后者所得的适宜分辨率更粗;② 采用不同地形信息时,越是在平缓地形为主的研究区,所得的适宜分辨率结果越相近,在复合地形特征的研究区所得到的适宜分辨率区间均明显较宽;③ 地形属性计算时所用的算法对适宜分辨率结果的影响不明显。     

A partition‐based serial algorithm for generating viewshed on massive DEMs

As increasingly large‐scale and higher‐resolution terrain data have become available, for example air‐form and space‐borne sensors, the volume of these datasets reveals scalability problems with existing GIS algorithms. To address this problem, a kind of serial algorithm was developed to generate viewshed on large grid‐based digital elevation models (DEMs). We first divided the whole DEM into rectangular blocks in row and column directions (called block partitioning), then processed these blocks with four axes followed by four sectors sequentially. When processing the particular block, we adopted the ‘reference plane’ algorithm to calculate the visibility of the target point on the block, and adjusted the calculation sequence according to the different spatial relationships between the block and the viewpoint since the viewpoint is not always inside the DEM. By adopting the ‘Reference Plane’ algorithm and using a block partitioning method to segment and load the DEM dynamically, it is possible to generate viewshed efficiently in PC‐based environments. Experiments showed that the divided block should be dynamically loaded whole into computer main memory when partitioning, and the suggested approach retains the accuracy of the reference plane algorithm and has near linear compute complexity.