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.     

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.     

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.     

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.     

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.     

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.     

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。     

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。     

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.     

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.     

Detecting the order of spatial dependence via symbolic analysis

In this article, we have proposed a simple diagnostic statistical procedure for testing the order of dependence of a spatial process. The proposed test is of nonparametric nature, and it is able to deal with potential nonlinear spatial dependencies. An added value is that from a methodological point of view, the new test is based on symbolic dynamics and hence on information theory. We characterized the behavior of a symbolic entropy measure in the presence of spatial dependencies of order higher than 1. The good power performance of the new method in detecting higher order spatial lags is notable and gives rise to an expectation that it may form a suitable basis for constructive specification searches.     

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.     

Dealing with double vagueness in DEM morphometric analysis

A method is presented to explicitly incorporate spatial and scale vagueness – double vagueness – into geomorphometric analyses. Known limitations of usual practices include using a single fixed set of crisp thresholds for morphometric classification and the imposition of a single arbitrary number of scales of analysis to the entire digital elevation model (DEM). Among the advantages of the proposed method are: fuzzification of morphometric classification rules, scale-dependent adaptive fuzzy set parametrization and an objective definition of maximum scale of analysis on a cell-by-cell basis. The method was applied to several DEMs ranging from the ocean floor to surface landscapes of both Earth and Mars. The result was evaluated with respect to modal morphometric features and to characteristic scales, suggesting a more robust method for deriving both morphometric classifications and terrain attributes. We argue that the method would be preferable to any single-scale crisp approach, at least in the context of preliminary hands-off morphometric analyses of DEMs.     

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.     

数字地形分析的理论、方法与应用

数字高程模型自20世纪50年代首次被提出以来,就以其简洁的数据组织方式、对地形的直观表达、简单高效的地形因子解译方法而显示了其在地学领域应用的巨大潜力。本文在全面检索和分析前人相关研究成果的基础上,首先将数字地形分析 (Digital Terrain Analysis,简称DTA) 的各种分析方法总结为四类,即坡面地形因子分析、特征地形要素分析、地形统计分析以及基于DEM的地学模型分析,并简要总结了每种分析方法的主要内容;其次,探讨了数字地形分析的精度及尺度问题,指出尺度效应、最适宜尺度选择以及尺度转换是DEM地形分析中的基本尺度问题;然后,论文介绍了DTA在地貌、水文、土壤、地质灾害、农业等领域的应用现状;最后,提出了数字地形分析发展方向,指出数字地形分析的概念框架亟待完善、模型构建精度有待提高、地形分析方法需要扩展,尤其是实现DEM模型嵌入的一体化分析方法,以求得到与现实世界地理环境更为接近的模拟。     

Measuring the significance of a divide to local drainage patterns

This article presents a framework for estimating a new topographic attribute derived from digital elevation models (DEMs) called maximum branch length (B _max). Branch length is defined as the distance travelled along a flow path initiated at one grid cell to the confluence with the flow path passing through a second cell. B _max is the longest branch length measured for a grid cell and its eight neighbours. The index provides a physically meaningful method for assessing the relative significance of drainage divides to the dispersion of materials and energy across a landscape, that is, it is a measure of ‘divide size’. B _max is particularly useful for studying divide network structure, for mapping drainage divides, and in landform classification applications. Sensitivity analyses were performed to evaluate the robustness of estimates of B _max to the algorithm used to estimate flow lengths and the prevalence of edge effects resulting from inadequate DEM extent. The findings suggest that the index is insensitive to the specific flow algorithm used but that edge effects can result in significant underestimation along major divides. Edge contamination can, however, be avoided by using an appropriately extensive DEM.     

发展时态GIS的可操作性时空数据模型

当前GIS广泛采用的空间数据模型不足以满足时态GIS发展的需要。该文探讨时态GIS所需的、可操作性时空数据模型,并且以土地利用和交通发展的时空相互作用为例,说明如何设计和实施相关的时空数据模型,用于支持发展时态GIS。     

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。     

Morphometric characterisation of landform from DEMs

We describe a method of morphometric characterisation of landform from digital elevation models (DEMs). The method is implemented first by classifying every location into morphometric classes based on the mathematical shape of a locally fitted quadratic surface and its positional relationship with the analysis window. Single‐scale fuzzy terrain indices of peakness, pitness, passness, ridgeness, and valleyness are then calculated based on the distance of the analysis location from the ideal cases. These can then be combined into multi‐scale terrain indices to summarise terrain information across different operational scales. The algorithm has four characteristics: (1) the ideal cases of different geomorphometric features are simply and clearly defined; (2) the output is spatially continuous to reflect the inherent fuzziness of geomorphometric features; (3) the output is easily combined into a multi‐scale index across a range of operational scales; and (4) the standard general morphometric parameters are quantified as the first and second order derivatives of the quadratic surface. An additional benefit of the quadratic surface is the derivation of the R ² goodness of fit statistic, which allows an assessment of both the reliability of the results and the complexity of the terrain. An application of the method using a test DEM indicates that the single‐ and multi‐scale terrain indices perform well when characterising the different geomorphometric features.