Maximal curvature

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Maximal curvature

Maximal curvature (k_max), one of two principle curvatures, is a curvature of a normal section BPB’ with the highest value of curvature among all normal sections at the given point P of the surface*. The unit of measurement is m^-1.

where M and H are unsphericity and mean curvatures, correspondingly.

Geomorphologically, positive values of maximal curvature correspond to ridges, while its negative values relate to local concave landforms.

Like other local morphometric variables, maximal 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 maximal 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

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