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Horizontal excess curvature (k_{he}) is a
difference of horizontal and minimal curvatures*. The unit of measurement is
m^{‑1}. , where
k_{h}, k_{min }, M, and E are horizontal, minimal, unsphericity, and difference curvatures, correspondingly. Horizontal excess curvature describes to what extent
horizontal curvature is larger
than minimal curvature at the given point
of the topographic surface. Like other local morphometric
variables, horizontal excess
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 horizontal excess 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:
