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Difference curvature (E) is a halfdifference
of horizontal and vertical curvatures*. The unit of measurement is m^{1}. Once
elevations are given by , where x and y are plane
Cartesian coordinates, difference curvature
is a function of the partial derivatives of z: , where
k_{h} and k_{v} are horizontal and vertical
curvatures, correspondingly, , , , , . Two mechanisms of flow accumulation, convergence and deceleration, are controlled by
horizontal and vertical curvatures, correspondingly. So, difference
curvature shows to what extent flow deceleration is higher than flow
convergence at the given point of the topographic surface. Like other local morphometric
variables, difference 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 difference 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:
