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Ring curvature (K_{r}) is a product of
horizontal excess and vertical excess curvatures*. The unit of measurement is
m^{2}. Once
elevations are given by , where x and y are plane
Cartesian coordinates, ring curvature is a function of the partial
derivatives of z: , where k_{he},
k_{ve} , M, and E are horizontal
excess, vertical excess, unsphericity, and difference curvatures,
correspondingly; ,
,
,
,
. Ring
curvature measures twisting of flow lines. Like other local morphometric
variables, ring 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 ring 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:
