en ru 
Mean curvature (H) is a
halfsum of curvatures of two orthogonal normal sections of the topographic
surface at the given point*. The unit of measurement is m^{1}. Once
elevations are given by , where x and y are plane Cartesian
coordinates, mean curvature is a function of the partial derivatives of z: , where
k_{min}, k_{max},_{ }k_{h},
and k_{v} are minimal, maximal, horizontal,
and vertical
curvatures, correspondingly; , , , , . Mean
curvature presents convergence and relative deceleration of gravitydriven
flows (controlled by horizontal and vertical curvatures, correspondingly)
with equal weights. Like other local morphometric
variables, mean curvature can be derived from a digital elevation model (DEM) by a universal spectral
analytical method as well as finitedifference methods (e.g., method 1, method 2, and method 3). Example**. A model of mean curvature 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". To deal
with the large dynamic range of this variable, its values were logarithmically transformed. The vertical
exaggeration of the 3D model is 2x. The data processing and modelling were carried out using the software Matlab R2008b. References
*
Shary, P.A., 1995. Land surface in gravity points classification by a
complete system of curvatures. Mathematical Geology, 27 373390.
** 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:
