Terrain Analysis

Generically, the term terrain analysis covers all processes that extract information from all kinds of terrain surface representation data. Such representations may include contour lines, profile lines, triangulated irregular networks, and square-grid digital elevation models (DEMs). The primary information extracted from terrain surface representations may be about local morphology or the characteristics of the entire catchment/watershed. Based on this primary information, the movements of materials controlled by gravity and the dynamics of energy [Page 2799]controlled by solar radiation over the land surface can be understood and described, and in turn, complex hydrological, geomorphological, pedological, and biological processes can be modeled. For this reason, terrain analysis has found applications in different fields, including geomorphology, soil science, hydrology, ecology, civil engineering, and environmental science.

The relationships between certain components in the natural system and terrain features have long been studied. A typical example of this type of relationship is the appearance of a “chain” of soils at different terrain positions along a slope. “Catena,” a concept proposed to refer to this soil-terrain pattern, became a cornerstone of the contemporary soil survey and mapping. However, only with the development of the contemporary digital technology did terrain analysis grow into a serious research field. Nowadays terrain analysis is almost a synonym of digital terrain analysis and is a significant aspect of the general spatial analysis that is based on geographical information science and technology. The most widely used terrain surface representation in digital terrain analysis is the square-grid DEM, due to its simplicity of format and easiness of algorithm implementation.

Terrain Attributes Characterizing Local Morphology

In digital terrain analysis, to measure the local morphological features at a given location, including slope gradient, slope aspect, and various types of curvatures, a conceptual procedure is to first represent the actual terrain surface in a mathematical way and then calculate morphological features as the derivatives of the mathematical surface. Specifically, slope gradient and slope aspect are calculated as the first-order derivatives of the surface, and the two most useful curvatures, profile curvature and planform curvature, are modeled as the second-order derivatives of the surface.

With a square-grid DEM, the primary approach to deriving derivatives from a discrete raster representation is the finite difference estimation. The basic idea of this method is to first fit a polynomial to a neighborhood defined by a group of cells (pixels) and then calculate the derivatives of the polynomial surface for the center location of the neighborhood. The two most widely used polynomials for this purpose are the quadratic polynomial,

and the Lagrange polynomial,

In the above equations, Z is the elevation, x and y are geographical coordinates, and a, b,…, u are coefficients whose values need to be derived from the actual terrain surface.

As an example, for a neighborhood typically defined by 3 × 3 cells, the equation for calculating the slope gradient (in angular degrees) for the center cell is as follows:

where p and q are calculated as follows:

where z1, z2, …, z9 are elevation values for the cells in the 3 × 3 neighborhood illustrated in Figure 1 (w is the length of one side of a cell).

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