Within geographic information systems (GIS), there is a family of measures that can be used to describe the local characteristics of surface shape. Gradient, sometimes synonymously referred to as slope, describes the steepness of the change in elevation over distance. Aspect is a measure of the compass direction of steepest slope. Within geographic information science, these are most commonly measured from elevation models of terrain. Gradient and aspect have a wide range of applications, such as flood and avalanche prediction, agricultural productivity modeling, civil engineering, and remote-sensing calibration.

Gradient

Most GIS are able to calculate gradient automatically from some form of digital elevation model (DEM). In the simplest case, gradient can be calculated along a linear profile as follows:

where dz represents the difference in elevation between two ...