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Digital Terrain ModelingA Brief Historical Overview

Topography is one of the main factors controlling processes takingplace in the near-surface layer of the planet (Huggett and Cheesman,2002). In particular, topography is one of the soil-forming factors(Dokuchaev, 1883; Zakharov, 1913; Neustruev, 1927; Jenny, 1941;Huggett, 1975; Fridland, 1976; Gerrard, 1981; Schaetzl and Anderson,2005) since it influences: (1) climatic and meteorological characteristics,which controls hydrological and thermal regimes of soils (Geiger, 1927;Romanova, 1977; Kondratyev et al., 1978; Raupach and Finnigan, 1997;Bohner and Antonic, 2009); (2) prerequisites for gravity-driven overlandand intrasoil lateral transport of water and other substances (Kirkbyand Chorley, 1967; Young, 1972; Speight, 1980); and (3) spatial distribu-tion of vegetation cover (Yaroshenko, 1961; Franklin, 1995). At the sametime, being a result of the interaction of endogenous and exogenousprocesses of different scales, topography can reflect the geological struc-ture of a terrain (Penck, 1924; Gerasimov, 1959; Meshcheryakov, 1965;Ollier, 1981; Ufimtsev, 1988; Burbank and Anderson, 2001; Scheidegger,2004; Lopatin, 2008; Brocklehurst, 2010). In this connection, qualitativeand quantitative topographic information is widely used in thegeosciences.

Before the 1990s, topographic maps were the main source of quantita-tive information on topography. They were analyzed using geomorpho-metric1 techniques to calculate manually morphometric variables (e.g.,slope gradient, drainage density, horizontal curvature, etc.) and producemorphometric maps (Vakhtin, 1930; Weinberg, 1934a; Chentsov, 1940;Horton, 1945; Volkov, 1950; Strahler, 1957; Clarke, 1966; Devdariani, 1967;

1Pike (2000, p. 1) defines geomorphometry as “the quantitative study of topography.”

1Digital Terrain Analysis in Soil Science and Geology © 2012 Elsevier Inc. All rights reserved.

Pannekoek, 1967; Mark, 1975b; Gardiner and Park, 1978; Stepanov et al.,1984; Lastochkin, 1987). Conventional geomorphometric techniques havereceived wide acceptance in geological studies (Berlyant, 1966): torepresent graphically the shape of deposits (Sobolevsky, 1932), to exploreoil and gas bearing and ore controlling structures (Levorsen, 1927;Filosofov, 1960; Murray, 1968; Volchanskaya, 1981; Guberman et al.,1997), to analyze block structure of the Earth’s crust (Orlova, 1975;Glasko and Rantsman, 1996), to study seismicity (Gelfand et al., 1972),and so on. In soil science, conventional geomorphometric techniqueshave been used to investigate relationships between soil cover andtopography (Dokuchaev, 1891; Ototzky, 1901); to predict quantitativesoil properties (Romanova, 1963, 1970, 1971); to produce soil maps(Anisimov et al., 1977; Stepanov et al., 1987, 1998; Stepanov, 1989;Stepanov and Loshakova, 1998); and to study regularities in the struc-ture of the soil cover and its relations with geological features (Filatov,1927; Stepanov and Sabitova, 1983; Kuryakova and Florinsky, 1991;Stepanov, 1996).

In the mid-1950s, a new research field—digital terrain modeling—emerged in photogrammetry (Rosenberg, 1955). Within its framework,digital elevation models (DEMs), two-dimensional discrete functions ofelevation, became the main source of information on topography.DEMs were used to calculate digital terrain models (DTMs), two-dimensional discrete functions of morphometric variables. Initially, dig-ital terrain modeling has mainly been applied to produce raised-reliefmaps using computer-controlled milling machines (Spooner et al., 1957;Lyubkov and Martynenko, 1963), and to design highways and railways(Miller and Leflamme, 1958; Konovalov, 1960).

Subsequent advances in computer, space, and geophysical technolo-gies were responsible for the transition from conventional geomorpho-metry to digital terrain modeling2 (Evans, 1972; Koshkarev, 1982;Burrough, 1986; Dikau, 1988; Serbenyuk, 1990). This was supported bythe development of the physical and mathematical theory of the topo-graphic surface3 in gravity (Krcho, 1973; Evans, 1979; Shary, 1991, 1995;Koenderink and van Doorn, 1994; Rudy, 1999; Shary et al., 2002b).Currently, digital terrain modeling is widely used to solve variousmultiscale problems of geomorphology, hydrology, remote sensing, soilscience, geology, geophysics, geobotany, glaciology, oceanology, clima-tology, planetology, and other disciplines—see reviews (McCullagh,1988; Moore et al., 1991; Shary et al., 1991; Weibel and Heller, 1991;

2Pike (2000, p. 1) noted that geomorphometry “is known variously as terrain

analysis or quantitative geomorphology, although the newer term digital terrain

modelling increasingly seems preferred.”3For the definition of the term topographic surface,, see Section 2.1.

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Band, 1993; Franklin, 1995; Florinsky, 1998b; Pike, 1995, 2000, 2001;Deng, 2007; Brocklehurst, 2010), books (Felicısimo, 1994a; Wilson andGallant, 2000; El-Sheimy et al., 2005; Li et al., 2005; Hengl and Reuter,2009), and bibliography (Pike, 2002). Digital terrain modeling evolvedinto the science of quantitative modeling and analysis of the topo-graphic surface and relationships between topography and other natu-ral and artificial components of geosystems.4

As early as the 1960s, soil science and geology have begun to usemethods of digital terrain modeling. Two DTM-based research avenueshave arisen in that time:

• Analysis of the influence of topography on the formation of soilproperties. In that period, the first attempts were made to model soilproperties with digital topographic data (Troeh, 1964; Walker et al.,1968).

• Study of geological structures using DEMs of both the land surfaceand stratigraphic surfaces (Munoz-Espinoza, 1968; Abelsky andLastochkin, 1969; Robinson et al., 1969). One of the pioneering workswas conducted by Belonin and Zhukov (1968) who studied an upliftevolution of an elevated block using digital models of the Gaussian,mean, and principal curvatures of geological surfaces.

Although the first effective methods to calculate morphometric vari-ables were developed in the 1970�1980s (Young, 1978; Evans, 1979;Zevenbergen and Thorne, 1987; Jenson and Domingue, 1988; Martz andde Jong, 1988), digital terrain modeling was still relatively uncommonin soil and geological studies of this period. In the 1980s, however, twomentioned DTM-based research trends have been further developed inboth soil science (Sinai et al., 1981; Burt and Butcher, 1985; Kachanoskiet al., 1985a, 1985b; Pennock et al., 1987) and geology (Moore andSimpson, 1983; Schowengerdt and Glass, 1983; Onorati et al., 1987;Zeilik et al., 1989). In the 1990s, the widespread use of personal compu-ters was responsible for the mass transition from conventional geomor-phometric techniques to digital terrain analysis in both soil science andgeology. In the first decade of the twenty-first century, advances inaerial, space, and geophysical technologies have opened new horizonsfor digital terrain modeling. First, large-scale and detailed DEMs of theland surface became available due to the progress in kinematic GPS sur-vey (Ghilani and Wolf, 2008) and LiDAR aerial survey (French, 2003).Second, global DEMs marked by a relatively high resolution and accu-racy were produced using satellite surveys (Farr et al., 2007; Hato et al.,2009). Public access to these materials via Internet extended the

4Detailed historical overview of digital terrain modeling can be found elsewhere

(Pike et al., 2009).

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DIGITAL TERRAIN ANALYSIS IN SOIL SCIENCE AND GEOLOGY

capabilities to conduct DTM-based regional geological and soil studies.Finally, the advances in three-dimensional seismic survey (Chopra andMarfurt, 2005, 2007a) enhanced the production of DEMs of geologicalsurfaces.

Currently, there are four main research trends in soil- and geology-oriented digital terrain modeling:

1. Analysis and modeling of relations between soil properties andtopographic characteristics (Chapters 8, 9, and 11).

2. Use of the resulting data and knowledge in predictive mapping ofsoil properties (Chapters 10 and 11).

3. Analysis of forms of geological features, such as folds and domes(Chapter 12).

4. Revealing and analysis of lineaments and faults, as well as theirrelations with other components of geosystems (Chapters 13�15).

Methods of digital terrain modeling are also used in three researchfields, which, from the formal point of view, are associated with geo-logy. However, they have a closer connection with adjacent researchareas, and hence they are not discussed in this book:

1. Study of geodynamics as a factor of terrain evolution (reviews canbe found elsewhere—Codilean et al., 2006; Brocklehurst, 2010). Thisis the subject of tectonic geomorphology.

2. Analysis of microtopography of geological samples (Pollard et al.,2004). To carry out such works, researchers use superdetailed DTMswith resolution of about 0.2 mm. This scientific field is close toindustrial surface metrology (Pike, 2001).

3. Study of geophysical fields using approaches of digital terrainmodeling (e.g., Rybakov et al., 2003). This research trend is, in fact,a modification of the well-known geophysical method of secondderivatives (Elkins, 1951).

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