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.     

Cartography: visualization of spatial data (3rd ed.), by Menno-Jan Kraak and Ferjan Ormeling

Conventionally, a raster operation that needs to scan the entire image employs only one scanning order (i.e., single scanning order (SSO)), and the scan usually runs from upper left to lower right and row by row. We explore the idea of alternately applying multiple scanning orders (MSO) to raster operations that are based on the local direction, using the flow accumulation (FA) calculation as an example. We constructed several FA methods based on MSO, and compared them with those widely used methods. Our comparison includes experiments over digital elevation models (DEMs) of different landforms and DEMs of different resolutions. For each DEM, we calculated both single-direction FA (SD-FA) and multi-direction FA (MD-FA). In the theoretical aspect, we deducted the time complexity of an MSO sequential algorithm (MSOsq) for FA based on empirical equations in hydrology. Findings from the experiments include the following: (1) an MSO-based method is generally superior to its counterpart SSO-based method. (2) The advantage of MSO is more significant in the SD-FA calculation than in the MD-FA calculation. (3) For SD-FA, the best method among the compared methods is the one that combines the MSOsq and the depth-first algorithm. This method surpasses the commonly recommended dependency graph algorithm, in both speed and memory use. (4) The differences between the compared methods are not sensitive to specific landforms. (5) For SD-FA, the advantage of MSO-based methods is more obvious in a higher DEM resolution, but this does not apply to MD-FA.     

Automatic determination of stream networks from DEMs by using road network data to locate culverts

Determining stream networks automatically from digital elevation models is an issue that is actively being studied. The quality of elevation models has increased over time, but many hydrologically critical features, such as culverts, are often missing from the elevation data. To analyze the surficial water flow, one must either prepare a special elevation model or post-process an already-existing model.

This study builds on the traditional, well-established method of determining the stream network from digital elevation models. We have extended the traditional method by locating culverts automatically, using road network data as an input. We show, by comparison to the reference data, that the culverts being most relevant for the stream network can be found with good accuracy. We demonstrate that by including the automatically located culverts in the automatic stream network determination, the quality of the generated network can be noticeably improved.     

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。     

The smoothness of HASM

To smooth noises inherent in uniformly sampled dataset, the smoothness of high accuracy surface modeling (HASM) was explored, and a smoothing method of HASM (HASM-SM) was developed based on a penalized least squares method. The optimal smoothing parameter of HASM-SM was automatically obtained by means of the generalized cross-validation (GCV) method. For an efficient smoothing computation, discrete cosine transform was employed to solve the system of HASM-SM and to estimate the minimum GCV score, simultaneously. Two examples including a numerical test and a real-world example were employed to compare the smoothing ability of HASM-SM with that of GCV thin plate smoothing spline (TPS) and kriging. The numerical test indicated that the minimum GCV HASM-SM is averagely more accurate than TPS and kriging for noisy surface smoothing. The real-world example of smoothing a lidar-derived Digital Elevation Model (DEM) showed that HASM-SM has an obvious smoothing effect, which is on a par with TPS. In conclusion, HASM-SM provides an efficient tool for filtering noises in grid-based surfaces like remote sensing–derived images and DEMs.     

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...     

Third-order geomorphometric variables (derivatives): definition,computation and utilization of changes of curvatures

Third-order geomorphometric variables (based on third derivatives of the altitudinal field) have been neglected in geomorphometry, but their application to the delimitation of surface objects will lead to their increasing significance in future. New techniques of computation, presented and evaluated here, facilitate their use. This paper summarizes recent knowledge concerning definition, computation and geomorphologic interpretation of these variables. Formulae defining various third-order variables are unified based on the physical definition of slope gradient. Methods for their computation are compared from the point of view of method error and error generated by digital elevation model (DEM) inaccuracy. For exact mathematical test surfaces, the most natural and simple variant of the method of central differences (CD2) shows a method error 2–3 times smaller than the other methods used recently in geomorphometry. However, success in coping with DEM inaccuracy depends (for a given grid mesh) on the number and weighting of points from which the derivative is computed. This was tested for surfaces with varying degrees of random error. Here least squares-based methods are the most effective for mixed derivatives (especially for finer grids and less accurate DEMs), while a variant of the CD method, that repeats numerical evaluation of first derivatives (CD1), is the most successful for derivatives in cardinal directions. The CD2 method is generally the most successful for coarser grids where the method error is dominant.

Utilization of third-order variables is documented from examples of terrain feature (ridge, valley and edge) extraction and from a first statistical test of the hypothesis that real segments of the land surface have a tendency to a constant value of some morphometric variable. For detection of (sharp) ridges and valleys, it is shown that the rate of change of tangential curvature is inadequate: rate of change of normal curvature is also required. A basic confirmation of the constant-value tendency is provided.     

Exploring the sensitivity of coastal inundation modelling to DEM vertical error

As sea level is projected to rise throughout the twenty-first century due to climate change, there is a need to ensure that sea level rise (SLR) models accurately and defensibly represent future flood inundation levels to allow for effective coastal zone management. Digital elevation models (DEMs) are integral to SLR modelling, but are subject to error, including in their vertical resolution. Error in DEMs leads to uncertainty in the output of SLR inundation models, which if not considered, may result in poor coastal management decisions. However, DEM error is not usually described in detail by DEM suppliers; commonly only the RMSE is reported. This research explores the impact of stated vertical error in delineating zones of inundation in two locations along the Devon, United Kingdom, coastline (Exe and Otter Estuaries). We explore the consequences of needing to make assumptions about the distribution of error in the absence of detailed error data using a 1 m, publically available composite DEM with a maximum RMSE of 0.15 m, typical of recent LiDAR-derived DEMs. We compare uncertainty using two methods (i) the NOAA inundation uncertainty mapping method which assumes a normal distribution of error and (ii) a hydrologically correct bathtub method where the DEM is uniformly perturbed between the upper and lower bounds of a 95% linear error in 500 Monte Carlo Simulations (HBM+MCS). The NOAA method produced a broader zone of uncertainty (an increase of 134.9% on the HBM+MCS method), which is particularly evident in the flatter topography of the upper estuaries. The HBM+MCS method generates a narrower band of uncertainty for these flatter areas, but very similar extents where shorelines are steeper. The differences in inundation extents produced by the methods relate to a number of underpinning assumptions, and particularly, how the stated RMSE is interpreted and used to represent error in a practical sense. Unlike the NOAA method, the HBM+MCS model is computationally intensive, depending on the areas under consideration and the number of iterations. We therefore used the HBM+ MCS method to derive a regression relationship between elevation and inundation probability for the Exe Estuary. We then apply this to the adjacent Otter Estuary and show that it can defensibly reproduce zones of inundation uncertainty, avoiding the computationally intensive step of the HBM+MCS. The equation-derived zone of uncertainty was 112.1% larger than the HBM+MCS method, compared to the NOAA method which produced an uncertain area 423.9% larger. Each approach has advantages and disadvantages and requires value judgements to be made. Their use underscores the need for transparency in assumptions and communications of outputs. We urge DEM publishers to move beyond provision of a generalised RMSE and provide more detailed estimates of spatial error and complete metadata, including locations of ground control points and associated land cover.     

Spatial analysis of geometric design consistency and road sight distance

Because of the high number of crashes occurring on highways, it is necessary to intensify the search for new tools that help in understanding their causes. This research explores the use of a geographic information system (GIS) for an integrated analysis, taking into account two accident-related factors: design consistency (DC) (based on vehicle speed) and available sight distance (ASD) (based on visibility). Both factors require specific GIS software add-ins, which are explained. Digital terrain models (DTMs), vehicle paths, road centerlines, a speed prediction model, and crash data are integrated in the GIS. The usefulness of this approach has been assessed through a study of more than 500 crashes. From a regularly spaced grid, the terrain (bare ground) has been modeled through a triangulated irregular network (TIN). The length of the roads analyzed is greater than 100 km. Results have shown that DC and ASD could be related to crashes in approximately 4% of cases. In order to illustrate the potential of GIS, two crashes are fully analyzed: a car rollover after running off road on the right side and a rear-end collision of two moving vehicles. Although this procedure uses two software add-ins that are available only for ArcGIS, the study gives a practical demonstration of the suitability of GIS for conducting integrated studies of road safety.     

The domestic divide: Access to the Internet in New Zealand

We use unit records of the 2006 census to show that access to the Internet in the home varies geographically in New Zealand primarily as a result of demographic and socio‐economic differences among individuals. Of particular significance is the much lower rates of domestic access experienced by Māori and Pacific Island individuals even after controlling for differences in their age, gender, education, income, occupation and settlement type. While differences in Internet access by ethnicity has been noted before, it is the magnitude and persistence of this difference in New Zealand after controlling for correlated factors that renders this study unique. Our results have important implications in an education environment increasingly reliant on Web access, but they also raise questions about the extent of access to the Internet outside the home.     

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。     

Mark on the globe: a quest for scientific bases of geographic information and its international influence

David M. Mark published his first journal article in 1970. Since then, he has written or coauthored more than 220 publications over a period of 40 years as of 28 May 2012. Based on data from Web of Science (WoS) and Google Scholar, Mark’s publications have been cited over 7410 times by researchers in more than 80 countries or regions as of 28 May 2012, when this paper was first prepared. The geographic extent of Mark’s scholarly influence is truly global. An examination of his 20 most cited articles reveals that his work in diverse areas as digital elevation models, geomorphology, geographic cognition, and ontology of the geospatial domain enjoyed a lasting impact worldwide.     

Spatial structure analysis of a reptile community with airborne LiDAR data

The analysis of the spatial structure of animal communities requires spatial data to determine the distribution of individuals and their limiting factors. New technologies like very precise GPS as well as satellite imagery and aerial photographs of very high spatial resolution are now available. Data from airborne LiDAR (Light Detection and Ranging) sensors can provide digital models of ground and vegetation surfaces with pixel sizes of less than 1 m. We present the first study in terrestrial herpetology using LiDAR data. We aim to identify the spatial patterns of a community of four species of lizards (Lacerta schreiberi, Timon lepidus, Podarcis bocagei, and P. hispanica), and to determine how the habitat is influencing the distribution of the species spatially. The study area is located in Northern Portugal. The position of each lizard was recorded during 16 surveys of 1 h with a very precise GPS (error < 1 m). LiDAR data provided digital models of surface, terrain, and normalised height. From these data, we derived slope, ruggedness, orientation, and hill-shading variables. We applied spatial statistics to determine the spatial structure of the community. We computed Maxent ecological niche models to determine the importance of environmental variables. The community and its species presented a clustered distribution. We identified 14 clusters, composed of 1–3 species. Species records showed two distribution patterns, with clusters associated with steep and flat areas. Cluster outliers had the same patterns. Juveniles and subadults were associated with areas of low quality, while sexes used space in similar ways. Maxent models identified suitable habitats across the study area for two species and in the flat areas for the other two species. LiDAR allowed us to understand the local distributions of a lizard community. Remotely sensed data and LiDAR are giving new insights into the study of species ecology. Images of higher spatial resolutions are necessary to map important factors such as refuges.     

Geomorphometry on the surface of a triaxial ellipsoid: towards the solution of the problem

Existing algorithms of geomorphometry can be applied to digital elevation models (DEMs) given with plane square grids or spheroidal equal angular grids on the surface of an ellipsoid of revolution or a sphere. Computations on spheroidal equal angular grids are trivial for modelling of the Earth, Mars, the Moon, Venus, and Mercury. This is because: (a) forms of these celestial bodies can be described by an ellipsoid of revolution or a sphere and (b) for these surfaces, there are well-developed theory and algorithms to solve the inverse geodetic problem as well as to determine spheroidal trapezoidal areas. It is advisable to apply a triaxial ellipsoid for describing the forms of small moons and asteroids. However, there are no geomorphometric algorithms intended for such a surface. In this article, first, we formulate the problem of geomorphometric modelling on a triaxial ellipsoid surface. Then, we recall definitions and formulae for coordinate systems of a triaxial ellipsoid and their transformation. Next, we present analytical and computational solutions, which provide the basis for geomorphometric modelling on the surface of a triaxial ellipsoid. The Jacobi solution for the inverse geodetic problem has a fundamental mathematical character. The Bespalov solutions for determination of the length of meridian/parallel arcs and the spheroidal trapezoidal areas are computationally efficient. Finally, we describe easy-to-code algorithms for derivation of local and non-local morphometric variables from DEMs based on a spheroidal equal angular grid of a triaxial ellipsoid.     

基于不同算法等高线曲率的提取与分析

等高线曲率是一个重要的地形属性,反应了地形表面在水平方向的凹凸性,表达了地表物质运动的发散和汇合模式。基于安塞县县南沟小流域的矢量等高线数据和DEM,分别利用圆拟合算法(相邻三点法、间隔三点法和最小二乘法)和曲面拟合模型(E模型、S模型和Z模型)提取等高线曲率,通过对实地地形的对比分析,结果表明:(1)在矢量等高线数据的计算结果中,三点拟合法计算结果相比最小二乘法结果差异大,对等高线曲率空间格局分布描述更准确;(2)最小二乘法计算的结果频数分布集中程度最高,两种三点拟合法计算结果频数曲线差别微小;(3)在栅格数字高程模型的计算结果中,基于S模型计算结果在空间格局上较E模型和Z模型的结果差别大,基于E模型的计算结果对等高线曲率描述效果更好。结果能准确说明采用不同算法计算等高线曲率的差别,对在实际数字地形分析中有重要的意义,可为等高线曲率计算提供重要参考。     

Differential effect of neotectonic process on stream characteristics: a geomorphologic evaluation of the Meenachil River basin,Kerala, India

Morphotectonic characteristics of the Meenachil River and its major tributaries in Kerala, India, were evaluated to understand the effects of tectonic processes on stream characteristics. Parameters such as longitudinal profile, stream length-gradient index (SL index), SL anomaly index, and transverse topographic symmetry factor (T) were considered. Longitudinal profiles of all the rivers show convexity and knickpoints in the segments between the headwaters and middle reaches, and further follow smooth profiles. Anomalies in longitudinal profiles were confirmed by the relatively high SL indexes. The SL anomaly index categorizes stream segments based on the severity of anomalies. The T index indicates the differential effect of tectonic processes in the river basin and in channel characteristics by showing spatial variation in its magnitude and orientation. Variations in the SL index, SL anomaly index, and T index in rivers flowing through similar lithology confirm the influence of differential effects of tectonic processes over the stream and networks and the nonequilibrium condition of the Meenachil River basin as a single unit.     

地形湿度指数算法误差的定量评价

地形湿度指数(TWI)能够定量指示地形对土壤湿度空间分布的控制,是一种应用广泛的地形属性.目前基于栅格DEM的TWI计算方法结果各异,因此有必要对'TWI算法进行定量评价.对TWI算法通常是应用实际DEM数据进行评价.但实际DEM中存在的数据源误差会干扰对算法误差的评价.针对该问题,本文介绍了一种用不含数据源误差的人造...     

基于GRID-TIN混合格网DEM的旱作梯田数值模拟模型研究

旱梯田地形具有独特的平面和剖面形态特征,现有DEM难以对其地貌形态特征进行准确描述,无法满足构建旱梯田地形数值模拟模型的需求。为此,以黄土高原典型旱梯田地形为切入点,基于Grid-TIN混合格网DEM和面向对象技术构建出水平梯田等典型旱梯田数值模拟模型。根据旱梯田地形的独特地貌形态特征,提出能够对旱梯田地形的高程、坡度进行准确计算的数字地形分析方法。该研究成果是对基于DEM的旱梯田地形数值模拟模型研究的有益尝试,对于探讨利用DEM实现旱梯田地形的有效数字表达与分析具有重要理论意义。     

我国数字高程模型与数字地形分析研究进展

数字高程模型是最重要的国家基础地理信息数据,基于GIS的数字地形分析的理论、方法与应用,是当今地理学、地貌学界,特别是地理信息科学研究的热点问题。本文从DEM的数据模型、数字地形分析的不确定性、分析方法、尺度效应、高性能计算方法以及地学应用等方面,对我国学者在该领域的研究情况,特别是研究成果进行较全面的梳理与分析。综述显示,我国具有一批从事数字高程模型与数字地形分析的高水平研究力量,研究方向紧跟国际前沿,并取得了丰硕的成果,部分研究内容具有显著创新,年轻一代科学家正加速成长。在黄土高原、青藏高原的区域数字地形分析方面更彰显我国科学家的优势与特色,在国际学术界产生了重要的影响。