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Accumulation
curvature (K_{a}) is a product of horizontal and vertical
curvatures*. The unit of measurement is m^{2}. Once
elevations are given by , where x and y are plane Cartesian
coordinates, accumulation curvature is a function of the partial derivatives
of z: , where
k_{h} and k_{v} are horizontal and vertical curvatures,
correspondingly; ,
,
,
,
. Accumulation
curvature is used in combination with mean curvature to map accumulation,
transit and dissipation zones of the land surface. Like other local morphometric
variables, accumulation 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 accumulation 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:
