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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 finitedifference
methods (e.g., IF2009
method and IF1998
method) as well as the universal spectral
analytical method. 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: 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:
