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.     

Geomorphometric feature analysis using morphometric parameterization and artificial neural networks

This paper presents a semi-automatic method using an unsupervised neural network to analyze geomorphometric features as landform elements. The Shuttle Radar Topography Mission (SRTM) provided detailed digital elevation models (DEMs) for all land masses between 60°N and 57°S. Exploiting these data for recognition and extraction of geomorphometric features is a challenging task. Results obtained with two methods, Wood's morphometric parameterization and the Self Organizing Map (SOM), are presented in this paper.Four morphometric parameters (slope, minimum curvature, maximum curvature and cross-sectional curvature) were derived by fitting a bivariate quadratic surface with a window size of 5 by 5 to the SRTM DEM. These parameters were then used as input to the two methods. Wood's morphometric parameterization provides point-based features (peak, pit and pass), line-based features (channel and ridge) and area-based features (planar). Since point-based features are defined as having a very small slope when their neighbors are considered, two tolerance values (slope tolerance and curvature tolerance) are introduced. Selection of suitable values for the tolerance parameters is crucial for obtaining useful results.The SOM as an unsupervised neural network algorithm is employed for the classification of the same morphometric parameters into ten classes characterized by morphometric position (crest, channel, ridge and plan area) subdivided by slope ranges. These terrain features are generic landform element and can be used to improve mapping and modeling of soils, vegetation, and land use, as well as ecological, hydrological and geomorphological features. These landform elements are the smallest homogeneous divisions of the land surface at the given resolution. The result showed that the SOM is an efficient scalable tool for analyzing geomorphometric features as meaningful landform elements, and uses the full potential of morphometric characteristics.     

Multi‐scale correlations between topography and vegetation in a hillside catchment of Honduras

All systems have causes and effects that can be appreciated at different spatial scales. Understanding and representing the complexity of multi‐scale patterns in maps and spatial models are key research objectives. We describe the use of three types of correlation analyses: (1) a standard Pearson correlation coefficient, (2) a ‘global’ multi‐scale correlation, and (3) local geographically weighted correlation. These methods were applied to topographic and vegetation indices in a small catchment in Honduras that is representative of the country's hillsides agro‐ecosystem which suffers from severe environmental degradation due to land‐use decisions that lead to deforestation, overgrazing, and unsustainable agricultural. If the geographical scale at which topography matters for land‐use allocation can be determined, then integration of knowledge systems can be focused. Our preliminary results show that: (1) single‐scale correlations do not adequately represent the relationship between NDVI and topographic indices; (2) peaks in the global multi‐scale correlations in agricultural areas coincided with the median farm size, but there was no evidence of any community or larger‐scale land‐use planning or optimization; and (3) local multi‐scale correlations varied considerably from the global results at all scales, and these variations have a strong spatial structure which may indicate local optimization of land use.     

Discrimination of fluvial, eolian and neotectonic features in a low hilly landscape: A DEM-based morphotectonic analysis in the Central Pannonian Basin, Hungary

The Gödöllő Hills, a low-relief terrain within the Central Pannonian Basin in Hungary, is characterised by moderate tectonic deformation rates. Although typical tectonic landforms are not clearly recognisable in the study area, this paper succeeded in discriminating between tectonically controlled landforms and features shaped by fluvial erosion or deflation with no tectonic control.DEM-based morphometric parameters including elevation, slope and surface roughness, enabled the delineation of two NW–SE trending spearhead-shaped ridges separated by a wide rectilinear valley of the same strike. Although directional statistics suggested possible tectonic control of NW–SE striking landforms, precise morphometry completed with an analysis of subsurface structures rejected their tectonic preformation. Deflation plays a significant role in shaping the area, and the presence of two large-scale yardangs separated by a wind channel is proposed. In temperate-continental areas of Europe, no deflational landforms of such scale have been described so far, suggesting that Pleistocene wind power in periglacial areas was more significant than it was previously thought.Characteristic drainage patterns and longitudinal valley profiles enabled the recognition of areas probably affected by neotectonic deformation. A good agreement was observed between locations of Quaternary warping predicted by the morphometric study and subsurface structures revealed by the tectonic analysis. Zones of surface uplift and subsidence corresponded to anticlinal and synclinal hinges of fault-related folds. In low-relief and slowly-deforming areas, where exogenous forces may override tectonic deformation, only the integrated application of morphometric and subsurface-structural indications could assure correct interpretation of the origin of various landforms, while a morphometric study alone could have led to misinterpretation of some morphometric indices apparently suggesting tectonic preformation. On the other hand, the described morphological expression of subsurface structures could verify Quaternary age of the deformation.     

An integrated TIN and Grid method for constructing multi‐resolution digital terrain models

Multi‐resolution terrain models are an efficient approach to improve the speed of three‐dimensional (3D) visualizations, especially for terrain visualization in Geographical Information Systems (GIS). As a further development to existing algorithms and models, a new model is proposed for the construction of multi‐resolution terrain models in a 3D GIS. The new model represents multi‐resolution terrains using two major methods for terrain representation: Triangulated Irregular Network (TIN) and regular grid (Grid). In this paper, first, the concepts and formal definitions of the new model are presented. Second, the methodology for constructing multi‐resolution terrain models based on the new model is proposed. Third, the error of multi‐resolution terrain models is analysed, and a set of rules is proposed to retain the important features (e.g. boundaries of man‐made objects) within the multi‐resolution terrain models. Finally, several experiments are undertaken to test the performance of the new model. The experimental results demonstrate that the new model can be applied to construct multi‐resolution terrain models with good performance in terms of time cost and maintenance of the important features. Furthermore, a comparison with previous algorithms/models shows that the speed of rendering for 3D walking/flying through has been greatly improved by applying the new model.     

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.     

Multi-scale landform characterization

One fundamental objective in geomorphometry is to extract signatures of geomorphologic processes on different spatial scales from digital terrain models (DTMs) and to describe the complexity of landforms as the synthesis of those individual imprints. We present an approach for characterizing land surfaces on multiple, spatially varying local scales. We approximate terrain surfaces locally to calculate surface derivatives at different window sizes. Local scale behaviour diagrams are used to define dominant scale ranges and multiple curvatures for each surface point. Multi-scale landform analysis leads to improved models of surface derivatives and new landform classifications, applicable in geomorphology, soil science and hydrology.     

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.     

中国数字地形学研究进展（英文）

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.     

Multi‐visibility maps of triangulated terrains

Visibility computation on terrain models is an important research topic with many applications in Geographical Information Systems. A multi‐visibility map is the subdivision of the domain of a terrain into regions that, according to different criteria, encodes the visibility with respect to a set of view elements. We present an approach for visualising approximated multi‐visibility maps of a triangulated terrain corresponding to a set of view elements by using graphics hardware. Our method supports heterogeneous sets of view elements containing points, segments, polygonal chains and polygons and works for weak and strong visibility. Moreover, we are also able to efficiently solve approximated point and polygonal region multi‐visibility queries. To illustrate the usefulness of our approach we present results obtained with an implementation of the proposed algorithms.     

产业地理集中、产业集聚与产业集群:测量与辨识

本文综述了产业地理集中、产业地理集聚以及产业集群的测量与辨识方法。传统的测量 产业地理集中方法包括集中系数、变差系数、赫芬代尔系数、赫希曼- 赫芬代尔系数、信息熵、锡尔 系数以及基尼系数等, 这些系数测量产业总体地理集中程度, 没有考虑企业规模分布对产业地理 集中的影响。基于企业区位选择模型, 经济学家发展了测量产业地理集聚的指数, 控制产业内企 业规模分布对产业地理集中的影响。无论地理集中指数还是地理集聚系数都以行政单元为基础, 仅描述单一空间尺度上的产业区位模式。Ripley 的K 函数通过计算某个企业一定距离内的邻居 企业个数来测量产业的地理集聚程度, 可同时反映产业在不同空间尺度的集聚程度。相互联系的 一群企业在地理空间上的集聚构成了产业集群, 产业集群的辨识不仅要测量产业间联系, 也要考 虑产业地理临近性。区位商和标准化区位商法、空间相关与产业联系法、因子分析和聚类分析等 多元统计方法以及基于投入产出关系的图谱分析方法等可以用来作为辨识区域产业集群手段。     

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。     

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.     

Decadal variability in climate and glacier fluctuations on Mt Baker, Washington, USA

Climate variability in the Pacific basin has been attributed to large‐scale oceanic‐atmospheric modulations (e.g. the El Niño‐Southern Oscillation (ENSO)) that dominate the weather of adjacent land areas. The Pacific Decadal Oscillation (PDO) and north Pacific index are thought to be indicators of modulations and events in the northeast Pacific. In this study we find that variations in the PDO are reflected in the terminus position of glaciers on Mt Baker, in the northern Cascade Range, Washington. The initiation of retreat and advance phases of six glaciers persisted for 20–30 years, which relate to PDO regime shifts. The result of this study agrees with previous studies that link glacier mass balance changes to local precipitation anomalies and processes in the Pacific. However, the use of mass balance changes and glacier terminus variation for identification of regime shifts in climate indices is complicated by the lack of standardized measuring techniques, differing response times of individual glaciers to changes in climate, geographic and morphometric factors, and the use of assorted climate indices with different domains and time‐scales in the Pacific for comparison.     

Neighborhood size and spatial scale in raster-based slope calculations

Raster-based slope estimation is routine in GIS. Like many other terrain attributes, the slope at a location is determined from elevations of surrounding cells. This spatial extent – ‘neighborhood size’ – is often treated as the ‘spatial scale’ of the calculation. In fact, neighborhood size and spatial scale are two connected yet different concepts, but few studies have investigated the relationship between them. The distinction is important because neighborhood size is under user control whereas spatial scale is merely implicit in the computational method. This article attempts to clarify and provide a more precise meaning of the two terms by considering slope operators from the standpoint of the frequency (or wavenumber) domain. This article derives analytical expressions for the amplitude response functions of four popular slope estimators. These are used to characterize the individual methods and also to show that the neighborhood size and spatial scale of a slope calculation are not numerically the same. In fact, because there is no single spatial scale that can be unambiguously associated with a given neighborhood size, neighborhood size cannot be an adequate indicator of spatial scale. Furthermore, this article shows that different indices of ‘scale’ yield different impressions about the action of a slope estimator and its response to changing neighborhood size. Therefore, it is necessary to examine the amplitude response function when investigating the spatial scale. The article also provides guidance for GIS practitioners when selecting a slope estimation method.     

Are prominent mountains frequently mentioned in text? Exploring the spatial expressiveness of text frequency

Data-driven GIScience shows a growing interest in making spatial information from large text data. In this paper, we quantify and thus evaluate the relation between text frequency and properties of the outer-text, geographic setting by comparing text frequencies of mountain names to the respective geomorphometric characteristics. We focus on some 2000 unique mountain names that appear some 50,000 times in a large compilation of texts on Swiss alpine history. The results on the full data set suggest only a weak relation: only 5–10% of the variation in the text frequency being explained by the respective geomorphometric characteristics. However, an analysis of multiple scales allows us to identify a Simpson’s Paradox. What appears to be ‘noise’ in the analysis of all mountains in the whole of Switzerland shows significant local signals. Small spatial extents, found all over Switzerland, can show considerably strong correlations between text frequency and spatial prominence, with up to 90% of the total variation explained. We argue that our findings have practical implications for data-driven GIScience. Retrieving meaningful spatial information from text might only be possible if the spatial scale of analysis reflects the spatial scale described in the input text documents.     

Automatic mapping of lunar landforms using DEM-derived geomorphometric parameters

Developing approaches to automate the analysis of the massive amounts of data sent back from the Moon will generate significant benefits for the field of lunar geomorphology. In this paper, we outline an automated method for mapping lunar landforms that is based on digital terrain analysis. An iterative self-organizing (ISO) cluster unsupervised classification enables the automatic mapping of landforms via a series of input raster bands that utilize six geomorphometric parameters. These parameters divide landforms into a number of spatially extended, topographically homogeneous segments that exhibit similar terrain attributes and neighborhood properties. To illustrate the applicability of our approach, we apply it to three representative test sites on the Moon, automatically presenting our results as a thematic landform map. We also quantitatively evaluated this approach using a series of confusion matrices, achieving overall accuracies as high as 83.34% and Kappa coefficients (K) as high as 0.77. An immediate version of our algorithm can also be applied for automatically mapping large-scale lunar landforms and for the quantitative comparison of lunar surface morphologies.     

基于DEM和地貌计量的月球形貌类型自动制图（英文）

Developing approaches to automate the analysis of the massive amounts of data sent back from the Moon will generate significant benefits for the field of lunar geomorphology.In this paper,we outline an automated method for mapping lunar landforms that is based on digital terrain analysis.An iterative self-organizing(ISO)cluster unsupervised classification enables the automatic mapping of landforms via a series of input raster bands that utilize six geomorphometric parameters.These parameters divide landforms into a number of spatially extended,topographically homogeneous segments that exhibit similar terrain attributes and neighborhood properties.To illustrate the applicability of our approach,we apply it to three representative test sites on the Moon,automatically presenting our results as a thematic landform map.We also quantitatively evaluated this approach using a series of confusion matrices,achieving overall accuracies as high as 83.34% and Kappa coefficients(K)as high as 0.77.An immediate version of our algorithm can also be applied for automatically mapping large-scale lunar landforms and for the quantitative comparison of lunar surface morphologies.