On the topology of topography: a review

Clarke, Keith; Romero, Boleslo E.

doi:10.1080/15230406.2016.1164625

Cited by 18 publications

(9 citation statements)

References 66 publications

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“…Although structural lines have been mathematically studied for many decades, an analytical solution based on local differential geometric criteria has not yet been found (see reviews: Koenderink and van Doorn, 1993, 1994). At the same time, crests and thalwegs can be considered as two topologically connected tree-like hierarchical structures (Clarke and Romero, 2017). Maxwell (1870) defined a ridge as a slope line connecting a sequence of local maximal and saddle points, and a thalweg as a slope line connecting a sequence of local minimal and saddle points.…”

Section: Discussionmentioning

confidence: 99%

“…Koenderink and van Doorn (1993) supposed that crests and thalwegs are the special type of slope lines where other ones converge, and they also argued that local differential geometric criteria for crests and thalwegs cannot exist. Since the problem of analytical description of structural lines has not been resolved, practical derivation of crests and thalwegs is mainly carried out by flow routing algorithms, similar to calculations of non-local variables (see reviews: Clarke and Romero, 2017; López et al, 1999; Tribe, 1992). Hopefully, these three interrelated problems will be solved in the near future.…”

Section: Discussionmentioning

confidence: 99%

“…Currently, geomorphometric methods are widely used to solve various multiscale problems of geomorphology, hydrology, remote sensing, soil science, geology, geophysics, geobotany, glaciology, oceanology, climatology, planetology and other disciplines; see reviews (Clarke and Romero, 2017; Deng, 2007; Florinsky, 1998b; Jordan, 2007; Lecours et al, 2016; Minár et al, 2016; Moore et al, 1991; Pike, 2000; Wasklewicz et al, 2013; Wilson, 2012) and books (Florinsky, 2016; Hengl and Reuter, 2009; Li et al, 2005; Wilson and Gallant, 2000).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An illustrated introduction to general geomorphometry

Florinsky

2017

Progress in Physical Geography: Earth and Environment

102

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Geomorphometry is widely used to solve various multiscale geoscientific problems. For the successful application of geomorphometric methods, a researcher should know the basic mathematical concepts of geomorphometry and be aware of the system of morphometric variables, as well as understand their physical, mathematical and geographical meanings. This paper reviews the basic mathematical concepts of general geomorphometry. First, we discuss the notion of the topographic surface and its limitations. Second, we present definitions, formulae and meanings for four main groups of morphometric variables, such as local, non-local, two-field specific and combined topographic attributes, and we review the following 29 fundamental morphometric variables: slope, aspect, northwardness, eastwardness, plan curvature, horizontal curvature, vertical curvature, difference curvature, horizontal excess curvature, vertical excess curvature, accumulation curvature, ring curvature, minimal curvature, maximal curvature, mean curvature, Gaussian curvature, unsphericity curvature, rotor, Laplacian, shape index, curvedness, horizontal curvature deflection, vertical curvature deflection, catchment area, dispersive area, reflectance, insolation, topographic index and stream power index. For illustrations, we use a digital elevation model (DEM) of Mount Ararat, extracted from the Shuttle Radar Topography Mission (SRTM) 1-arc-second DEM. The DEM was treated by a spectral analytical method. Finally, we briefly discuss the main paradox of general geomorphometry associated with the smoothness of the topographic surface and the non-smoothness of the real topography; application of morphometric variables; statistical aspects of geomorphometric modelling, including relationships between morphometric variables and roughness indices; and some pending problems of general geomorphometry (i.e. analysis of inner surfaces of caves, analytical description of non-local attributes and structural lines, as well as modelling on a triaxial ellipsoid). The paper can be used as a reference guide on general geomorphometry.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An illustrated introduction to general geomorphometry

Florinsky

2017

Progress in Physical Geography: Earth and Environment

102

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“…The user is then left with the dilemma that they cannot determine whether the failure of a model to fit perfectly is due to the model itself, or to the relatively 'coarse' resolution of the elevation data, or both [1]. Relatively little attention has been given to the topological relationships among topographic features and this state-of-affairs helps to explain why all computed surface networks are scaledependent, fuzzy, and vague and why their undisputed calculation remains elusive [2].…”

Section: Current State-of-the-artmentioning

confidence: 99%

Geomorphometry: Today and Tomorrow

Wilson

2018

Preprint

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This paper summarizes the current state-of-the-art in geomorphometry and describes the innovations that are close at hand and will be required to push digital terrain modeling forward in the future. These innovations will draw on concepts and methods from computer science and the spatial sciences and require greater collaboration to produce “actionable” knowledge and outcomes. The key innovations include rediscovering and using what we already know, developing new digital terrain modeling methods, clarifying and strengthening the role of theory, developing high-fidelity DEMs, developing and embracing new visualization methods, adopting new computational approaches, and making better use of provenance, credibility, and application-content knowledge.

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“…Digital Terrain analysis (DTA) and modeling has been a flourishing interdisciplinary field for decades, with applications in hydrology, geomorphology, soil science, engineering projects and computer sciences [1][2][3][4][5][6][7][8][9][10][11][12][13]. DTA is not so much a single technique, but rather a set of multiple algorithms developed from theory and principles of earth and planetary science, mathematics, and computer science.…”

Section: Introductionmentioning

confidence: 99%

Leading Progress in Digital Terrain Analysis and Modeling

Sofia

Eltner

Nikolopoulos

et al. 2019

IJGI

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Digital Terrain analysis (DTA) and modeling has been a flourishing interdisciplinary field for decades, with applications in hydrology, geomorphology, soil science, engineering projects and computer sciences. Currently, DTA is characterized by a proliferation of multispectral data from new sensors and platforms, driven by regional and national governments, commercial businesses, and scientific groups, with a general trend towards data with higher spatial, spectral or temporal resolutions. Deriving meaningful and interpretable products from such a large pool of data sources sets new challenges. The articles included in this special issue (SI) focuses on terrain analysis applications that advance the fields of hydrology, geomorphology, soil science, geographic information software (GIS), and computer science. They showcase challenging examples of DTA tackling different subjects or different point of views on the same subject.

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On the topology of topography: a review

Cited by 18 publications

References 66 publications

An illustrated introduction to general geomorphometry

An illustrated introduction to general geomorphometry

Geomorphometry: Today and Tomorrow

Leading Progress in Digital Terrain Analysis and Modeling

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