Digital elevation models (DEMs) provide fundamental depictions of the three-dimensional shape of the Earth’s surface and are useful to a wide range of disciplines. Ideally, DEMs record the interface between the atmosphere and the lithosphere using a discrete two-dimensional grid, with complexities introduced by the intervening hydrosphere, cryosphere, biosphere, and anthroposphere. The treatment of DEM surfaces, affected by these intervening spheres, depends on their intended use, and the characteristics of the sensors that were used to create them. DEM is a general term, and more specific terms such as digital surface model (DSM) or digital terrain model (DTM) record the treatment of the intermediate surfaces. Several global DEMs generated with optical (visible and near-infrared) sensors and synthetic aperture radar (SAR), as well as single/multi-beam sonars and products of satellite altimetry, share the common characteristic of a georectified, gridded storage structure. Nevertheless, not all DEMs share the same vertical datum, not all use the same convention for the area on the ground represented by each pixel in the DEM, and some of them have variable data spacings depending on the latitude. This paper highlights the importance of knowing, understanding and reflecting on the sensor and DEM characteristics and consolidates terminology and definitions of key concepts to facilitate a common understanding among the growing community of DEM users, who do not necessarily share the same background.

We study the accuracy of data on some local topographic attributes derived from digital elevation models (DEMs). First, we carry out a test for the precision of four methods for calculation of partial derivatives of elevations. We find that the Evans method is the most precision algorithm of this kind. Second, we produce formulae for root mean square errors of four local topographic variables (gradient, aspect, horizontal and vertical landsurface curvatures), provided that these variables are evaluated with the Evans method. Third, we demonstrate that mapping is the most convenient and pictorial way for the practical implementation of the formulae derived. A DEM of a part of the Kursk Region (Russia) is used as an example. We find that high errors of data on local topographic variables are typical for flat areas. Results of the study can be used to improve landscape investigations with digital terrain models.

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.

The central problem of a combined analysis of digital terrain models (DTMs) and other landscape data is determination of a DTM grid size (w) providing a correct study of relationships between topographic variables and landscape properties. Generally, an adequate w is determined by an expert estimate, and solutions are largely subjective. We developed an experimental statistical method to determine an adequate w for DTMs applied to landscape studies. The method includes the following steps: (a) derivation of a DTM set using a series of w_i , (b) performance of a correlation analysis of data on a landscape property and a topographic variable estimated with various w_i , (c) plotting of correlation coefficients obtained versus w, and (d) determination of smoothed plot portions indicating intervals of an adequate w. We applied the method developed to study the ifluence of topography on the spatial distribution of soil moisture (M) at a micro-scale. We investigated the dependence of M on gradient (G), horizontal (k_h ), vertical (k_v ), and mean (H) landsurface curvatures. For DTM derivation, we used 13 values of w_i from 1 to 7m. An interval of adequate w_i for M falls between 2.25 and 3.25m in the given terrain conditions. In absolute magnitudes, correlation coefficients are largest within this interval; correlation coefficients of M with G, k_h , k_v and H are 0.28, 0.52, 0.50 and 0.60, respectively, for w = 3m. The results obtained demonstrate that the method actually works to identify an adequate w at a micro-scale. The method developed allows estimation of an adequate area of landform which realise a topographic control of landscape properties.