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 finite-difference methods (e.g., IF-2009 method and IF-1998 method) as well as the universal spectral analytical method.
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., 2017. An illustrated introduction to general geomorphometry. Progress in Physical Geography, 41: 723–752. doi pdf
For details and other examples, see: