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###### Difference curvature

Difference curvature (E) is a half-difference of horizontal and vertical curvatures*. The unit of measurement is m-1.

Once elevations are given by , where x and y are plane Cartesian co-ordinates, difference curvature is a function of the partial derivatives of z:

,

where kh and kv 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 a universal spectral analytical method as well as finite-difference methods (e.g., method 1, method 2, and method 3).

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.

#### ** 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:

 DIGITAL TERRAIN ANALYSIS IN SOIL SCIENCE AND GEOLOGY   2nd revised edition     I.V. Florinsky   Elsevier / Academic Press, 2016 Amsterdam, 486 p.   ISBN 978-0-12-804632-6