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Vertical excess curvature

Vertical excess curvature (kve) is a difference of vertical and minimal curvatures*. The unit of measurement is m-1.

,

where kv, kmin , M, and E are vertical, minimal, unsphericity, and difference curvatures, correspondingly.

Vertical excess curvature describes to what extent vertical curvature is larger than minimal curvature at the given point of the topographic surface.

Like other local morphometric variables, vertical excess 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 vertical excess 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: 373390.

** 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

 

 

 

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