How SAGA calculates Convergence Index

Question

I have calculated convergence index on my DEM with SAGA. Output results seems to be ok (values in range -100;100), but I don't understand how it works.

Here is some sample data from my DEM:

I know that Convergence Index is calculated based on aspect, therefore I've calculated Aspect in SAGA (to understand whole process), however it didn't help me. I still don't know how CI was calculated.

I've found this formula in some paper:

"Where θ denotes average angle between the aspect of adjacent cells and the direction to the central cell."

Can someone explain to me step by step how CI was calculated (for example on values inside red frame)

Answer 1

In the SAGA-GIS Tool Library Documentation (v2.1.3) there is a reference to the method which is used for this calculation:

Koethe, R. & Lehmeier, F. (1996): SARA - System zur Automatischen Relief-Analyse. User Manual, 2. Edition [Dept. of Geography, University of Goettingen, unpublished]

Unfortunately, I wasn't able to get this document, but I found another paper where the above authors are mentioned when the Convergence Index is described. The paper comes from the Journal of Hungarian Geomathematics:

Kiss, R. (2004). Determination of Drainage Network in Digital Elevation Models, Utilities and Limitations, Journal of Hungarian Geomathmatics, 2, 16-29.

and it's freely available here.

I report what it's written at page 22 (the following text and images come from the above mentioned paper, all credits to the cited source and to the authors):

The index is obtained by averaging the bias of the slope directions of the adjacent cells from the direction of the central cell, and subtracting 90 degrees. The possibile values of the index range from -90° to +90° according to Fig.8.

I hope this will help.

Answer 2

https://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-31-stokes-theorem/

Hey if you want to understand this in deep, Try that link.