Strahler stream order
The Strahler number of a mathematical tree is a numerical measure of its branching complexity. It is defined on nodes as follows:
- Leaves have a Strahler number of 1.
- For a nonleaf v:
- If v has a child with Strahler number i and all other children have Strahler number less than i, then the Strahler number of v is i.
- If v has two or more children with Strahler number i and there is no child with Strahler number greater than i, then the Strahler number of v is i + 1.
The definition can easily be extended to edges by defining the Strahler number of an edge to be the minimum of the Strahler numbers of its start and end nodes.
See an example beanshell script that you can test on a sample network named test_hydro.gdms.
In OrbisGIS, we can visualize the Strahler number by applying different colors and/or thicknesses to the edges. The edges in the test_hydro.strahler_edges layer resulting from the above example script have Strahler numbers 1, 2, 3 and 4. Below, we increase line thickness with Strahler number, and we apply the following color scheme: 1=blue, 2=green, 3=pink, 4=red. Download this style file to see the details. We obtain the following representation:
Here is the original network, represented in the test_hydro layer:
