Slope gradient is an angle between the tangential and horizontal planes at a given point of the topographic surface*. The unit of measurement is degree.
Once elevations are given by , where x and y are plane Cartesian co-ordinates, slope gradient is a function of the partial derivatives of z:
where and .
Slope gradient determines the velocity of gravity-driven flows.
Like other local morphometric variables, slope gradient can be derived from a digital elevation model (DEM) by a universal spectral analytical method as well as finite-difference methods (e.g., method 1, method 2, and method 3).
Example**. A model of slope gradient was derived from a DEM of Mount Ararat by the universal spectral analytical method. The model includes 779,401 points (the matrix 1081 x 721); the grid spacing is 1". The vertical exaggeration of the 3D model is 2x. The data processing and modelling were carried out using the software Matlab R2008b.
* Shary, P.A., 1995. Land surface in gravity points classification by a complete system of curvatures. Mathematical Geology, 27 373-390.
** Florinsky, I.V., 2016. An illustrated introduction to geomorphometry. Almamac Space and Time, 11 (1): 20 p. (in Russian, with English abstract). Article at the journal website
For details and other examples, see: