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.     

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。     

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 点位地形信息量化模型研究

针对DEM 点位, 首先应用微分几何法对其所负载的语法信息量进行测度, 其次根据地形特征点类型及地形结构特征确定其语义信息量, 然后基于信息学理论构建了DEM 点位地形信息综合量化模型。在此基础上, 以黄土丘陵沟壑区作为实验样区, 对DEM 点位地形信息量提取方法及其在地形简化中的初步实例应用进行了探讨和验证。实验结果显示, 所提出的DEM 点位地形信息量化方案可行;基于DEM 地形信息量指数的多尺度DEM 构建方案, 具有机理明确、易于实现的特点, 并通过优先保留地形骨架特征点, 可以有效减少地形失真, 从而满足不同层次的多尺度数字地形建模和表达要求。对DEM 点位地形信息进行有效量化, 为认识DEM 地形信息特征提供了一个新的切入点, 同时为多尺度数字地形建模提供理论依据与方法支持。     

典型黄土地貌类型区的地形复杂度分形研究

黄土高原地貌形态与地形复杂度自南向北有序变化,构成了举世瞩目的独特的地理景观。选择陕西省南北剖面六个典型黄土地貌样区为基本实验区,以其1∶1万栅格DEM为数据源,探讨典型黄土地貌类型区的地形复杂度分形与空间分异特征。首先提出的元分维模型方法,以计算得到的DEM元分维值作为特征指标,研究样区的地形复杂度问题。这种通过滑动窗口的扩展分维分析方法,既可以用于分析该区域不同尺度下的地形复杂度变化情况,也可以探讨区域的局部单元复杂程度及其空间分布,从而不再局限于对全区域的单一分维评价。以此为基础,进一步应用元分维谱方法,研究地貌网格单元的元分维分级分布情况。实验结果表明:以绥德和延川为代表的黄土峁状丘陵沟壑区最为复杂,以宜君和甘泉为代表的梁状丘陵沟壑区居中,而以淳化为代表的黄土塬区和以神木为代表的风沙黄土过渡区最为平缓。实验进一步证明了扩展分形方法在黄土地貌研究中的可行性。     

Chinese progress in geomorphometry

Geomorphometry, the science of digital terrain analysis (DTA), is an important focus of research in both geomorphology and geographical information science (GIS). Given that 70% of China is mountainous, geomorphological research is popular among Chinese scholars, and the development of GIS over the last 30 years has led to significant advances in geomorphometric research. In this paper, we review Chinese progress in geomorphometry based on the published literature. There are three major areas of progress: digital terrain modelling methods, DTA methods, and applications of digital terrain models (DTMs). First, traditional vector- and raster-based terrain modelling methods, including the assessment of uncertainty, have received widespread attention. New terrain modelling methods such as unified raster and vector, high-fidelity, and real-time dynamic geographical scene modelling have also attracted research attention and are now a major focus of digital terrain modelling research. Second, in addition to the popular DTA methods based on topographical derivatives, geomorphological features, and hydrological factors extracted from DTMs, DTA methods have been extended to include analyses of the structure of underlying strata, ocean surface features and even socioeconomic spatial structures. Third, DTMs have been applied to fields including global climate change, analysis of various typical regions, lunar surface and other related fields. Clearly, Chinese scholars have made significant progress in geomorphometry. Chinese scholars have had the greatest international impact in areas including high-fidelity digital terrain modelling and DTM-based regional geomorphological analysis, particularly in the Loess Plateau and the Tibetan Plateau regions.     

多分析尺度下综合判别的地形元素分类方法

地形元素（如山脊、沟谷等）是地表形态类型基本单元,通过地形元素的不同空间组合可形成更高级别的地貌类型。现有的地形元素提取方法大多依靠地形属性计算,难以克服地形元素的空间相关性表达与局部地形属性计算存在不对应的矛盾,Jasiewicz和Stepinski提出的Geomorphons方法——基于高程相对差异信息进行地形元素分类,可避免这一问题,但Geomorphons方法本质上是在单一分析尺度上选择地形特征点用于判别,易受局部地形起伏的影响而造成误分类。针对这一问题,设计出一种多分析尺度下综合判别的地形元素分类方法。应用结果表明：相比Geomorphons方法,利用该方法得到的地形元素的分类结果更为合理。     

Terrain complexity and uncertainties in grid‐based digital terrain analysis

The objective of this research is to study the relationship between terrain complexity and terrain analysis results from grid‐based digital elevation models (DEMs). The impact of terrain complexity represented by terrain steepness and orientation on derived parameters such as slope and aspect has been analysed. Experiments have been conducted to quantify the uncertainties created by digital terrain analysis algorithms. The test results show that (a) the RMSE of derived slope and aspect is negatively correlated with slope steepness; (b) the RMSE of derived aspect is more sensitive to terrain complexity than that of derived slope; and (c) the uncertainties in derived slope and aspect tend to be found in flatter areas, and decrease with increasing terrain complexity. The study shows that although primary surface parameters can be well defined mathematically, the implementation of those mathematical models in a GIS environment may generate considerable uncertainties related to terrain complexity. In general, when terrain is rugged with steep slopes, the uncertainty of derived parameters is quite minimal. While in flatter areas, the DEM‐based derivatives, particularly the aspect, may contain a great amount of uncertainty, causing significant limitation in applying the analytical results.     

Drainage basin object-based method for regional-scale landform classification: a case study of loess area in China

Landform classification is one of the most important procedures in recognizing and dividing earth surface landforms. However, topographical homogeneity and differences in regional-scale landforms are often ignored by traditional pixel- and object-based landform classification methods based on digital elevation models (DEMs). In this work, a drainage basin object-based method for classifying regional-scale landforms is proposed. Drainage basins with least critical areas are first delineated from DEMs. Then, terrain derivatives of mean elevation, mean slope, drainage density, drainage depth, and terrain texture are employed to characterize the morphology of the drainage basins. Finally, a decision tree based on the topographical characteristics of the drainage basins is constructed and employed to determine the landform classification law. The experiment is validated in the landform classification of regional-scale loess areas in China. Results show that clear boundaries exist in different landforms at the regional scale. Landform type in a specific region shows significant topographical homogeneity under its specific regional geomorphological process. Classification accuracies are 87.3 and 86.3% for the field investigation and model validation, respectively. Spatial patterns of classified landforms and their proximity to sediment sources and other factors can be regarded as indicators of the evolutionary process of loess landform formation.     

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.     

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.     

土地覆被类型空间格局与地形因子的定量关联及其应用

以全国1∶25万土地覆被数据、全国公里网格DEM数据和县级行政区划数据为基础,首先,在国家尺度上宏观分析地形因子对土地覆被类型空间分布格局的影响,土地覆被类型空间分布宏观格局受海拔高度、坡度、地表起伏度的影响明显,而与坡向的关系并不显著;其次,以县级行政单元为统计分析样本,利用多元线性回归分析方法,在国家和区域两个尺度建立土地覆被类型面积占比与主要地形因子之间的定量模型,在6类土地覆被类型中,除草地以外,其他5类土地覆被类型的面积占比均与地形因子之间呈显著相关关系,显著性由高到低的排列顺序依次为森林、农田、荒漠、聚落和湿地水体;最后,以相关性最好的森林的空间分布为例,说明了将所建立的模型应用于栅格单元上某种土地覆被类型面积占比估算的可能性,虽然估算结果与实际情况存在差异,但总体趋势基本保持一致,特别是土地覆被类型面积占比大的区域。     

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...     

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。     

GIS-based modelling of topography-induced solar radiation variability in complex terrain for data sparse region

Solar radiation not only sustains the lives on the Earth, but also creates spatial and temporal variations of hydrological ingredients, such as vegetation, soil moisture, and snow. Precise quantification of spatial solar radiation incident on the Earth's surface which accounts for the topographic modulation, especially in complex terrain, underpins the study of many catchment hydro-meteorological and hydro-ecological processes. Topography is a key parameter that affects the spatial solar radiation pattern across different scales. This article addresses the issue of modelling spatial variability of actual solar radiation caused by topography from the hydrological perspective. Models with different algorithms and different complexities, from the simple empirical equations to process-based physical approach, have been developed to parameterize and calculate the potential radiation (under clear-sky condition) and the actual radiation (under overcast cloudy condition). Based on a review of the general steps of solar radiation modelling and the corresponding models for each step, two models with easily or globally available data for spatial solar radiation modelling in complex terrain, namely, the physically parameterized, remote-sensing-oriented Heliosat-2 model and the sunshine duration-based Angström–Prescott regression model are selected and implemented in a GIS framework. The capability of both models for simulation of cloudy-sky radiation on horizontal surfaces has been verified against observed station data showing an R ² greater than 0.9. The validity of the models for modelling inclined surface is tested by comparing against each other, which has shown a satisfactory agreement and demonstrated that the simple Angström–Prescott method performed reasonably well compared with the more elaborate Heliosat-2 method. Scale sensitivity of the models and the shading effect are examined with different digital elevation model (DEM) resolutions from 30 to 500 m and reveal the existence of a threshold grid size to resolve the topography-induced spatial solar radiation variability. Spatial mapping of potential solar radiation and actual solar radiation has been demonstrated in a small catchment in Southern Germany, with a spatial difference up to 30% in winter and 5% in summer. This may lead to a significant difference for the energy-limited hydrological processes, such as snowmelt, and evapotranspiration.     

Computation of the third‐order partial derivatives from a digital elevation model

Loci of extreme curvature of the topographic surface may be defined by the derivation function (T) depending on the first‐, second‐, and third‐order partial derivatives of elevation. The loci may partially describe ridge and thalweg lines. The first‐ and second‐order partial derivatives are commonly calculated from a digital elevation model (DEM) by fitting the second‐order polynomial to a 3×3 window. This approach cannot be used to compute the third‐order partial derivatives and T. We deduced formulae to estimate the first‐, second‐, and third‐order partial derivatives from a DEM fitting the third‐order polynomial to a 5×5 window. The polynomial is approximated to elevation values of the window. This leads to a local denoising that may enhance calculations. Under the same grid size of a DEM and root mean square error (RMSE) of elevation, calculation of the second‐order partial derivatives by the method developed results in significantly lower RMSE of the derivatives than that using the second‐order polynomial and the 3×3 window. An RMSE expression for the derivation function is deduced. The method proposed can be applied to derive any local topographic variable, such as slope gradient, aspect, curvatures, and T. Treatment of a DEM by the method developed demonstrated that T mapping may not substitute regional logistic algorithms to detect ridge/thalweg networks. However, the third‐order partial derivatives of elevation can be used in digital terrain analysis, particularly, in landform classifications.     

Hybrid terrain rendering based on the external edge primitive

Hybrid terrain models combine large regular data sets and high-resolution irregular meshes [triangulated irregular network (TIN)] for topographically and morphologically complex terrain features such as man-made microstructures or cliffs. In this paper, a new method to generate and visualize this kind of 3D hybrid terrain models is presented. This method can integrate geographic data sets from multiple sources without a remeshing process to combine the heterogeneous data of the different models. At the same time, the original data sets are preserved without modification, and, thus, TIN meshes can be easily edited and replaced, among other features. Specifically, our approach is based on the utilization of the external edges of convexified TINs as the fundamental primitive to tessellate the space between both types of meshes. Our proposal is eminently parallel, requires only a minimal preprocessing phase, and minimizes the storage requirements when compared with the previous proposals.     

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.     

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。