Rotor (rot) is a curvature of flow lines which are perpendicular to contours*. The unit of measurement is m-1.
Once elevations are given by , where x and y are plane Cartesian co-ordinates, rotor is a function of the partial derivatives of z:
where , , , , .
Rotor is a measure of twisting of flow lines. Flow lines turn clockwise when rot > 0, while flow lines turn anti-clockwise when rot < 0.
Like other local morphometric variables, rotor 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 rotor 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.
* Shary, P.A., 1995. Land surface in gravity points classification by a complete system of curvatures. Mathematical Geology, 27 373-390.
** 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: