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Ring curvature

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 co-ordinates, 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 finite-difference methods (e.g., IF-2009 method and IF-1998 method) as well as the universal spectral analytical method.

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: 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:

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 Contents Summary ScienceDirect

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