[You have to work with a dimensionless number]

A measure of how slim or rounded your catchments are is (A/P^2, or Area/perimeter/perimeter)

There is a range between a circle and a very long rectangle. That range is being used for estimation of "longest flow path" in many hydrology works in particular when a distinctive ditch or channel do not exists in a watershed. Although it is not exactly your answer but I think you can use that measure for clustering your catchments. On practical advantage of that measure is you can use it very easily without any extra coding efforts in GIS.

Hope it helps,

Kaveh

Hello

Please see hydrology book

Dear Kaveh

This paper https://iopscience.iop.org/article/10.1088/1755-1315/118/1/012028/pdf provides a review of various parameters via which catchments can be classified relating to various physical characteristics. This paper may also be of use: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.671.3027&rep=rep1&type=pdf

This paper here also details the application of an elongation ratio see: https://www.iasj.net/iasj?func=fulltext&aId=89687

I hope these are of help.

Darren

Puede relacionar las cuencas en función de su tiempo de concentración.

Hi Florian,

The first reference from Darren Lumbroso is pretty good. Thanks Darren! I skimmed through it, and the closest classification seems to be either the form factor (ratio of the basin area to the square of the basin length, cites Horton), or the circularity ratio (similar to what Kaveh Zamani suggested in his answer).

I am also interested in this question. If you find something else on this topic please let me know.

Ilhan