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It's known that stream orders are highly regular:

Horton showed that stream order is related to number of streams, channel length, and drainage area by simple geometric relationships; that is, stream order plots against these variables as straight lines on semilogarithmic paper.

[...] Among many samples of basins in the United States the bifurcation ratio tends closely to equal 3.5. There are variations, of course. In the examples of basins cited by Horton (1945, p. 290) values of the bifurcation ratio range from 2 to 4.

Fluvial Geomorphology, p.137

The stream bifurcation ratio is so regular in any given drainage basin that it's actually remarkable to look at a graph - as in these Indian continent sub-basins.

The process Fluvial Geomorphology describes for the evolution of these basins involves the random weathering of locally-level surfaces by rain, melt, or less commonly other liquid weathering. Small rivulets form via random depressions in the surface of the earth, which then merge into larger streams of higher order. But this got me thinking...

If the emergence of initial rivulets is a random process, shouldn't that random process be biased towards wherever the drainage basin happens to be the most erodible? I'd only expect this kind of macro-level structure to necessarily emerge if the earth were homogeneous in the drainage basin, but in practice this doesn't seem to need to be required in order for a drainage basin following a regular bifurcation ratio to emerge.

My questions are related:

  1. Are there any known criteria for which drainage basins do not evolve in a way that produces regular stream orders? (When) has this happened?
  2. Is my assumption that this macro-level order should only emerge for homogeneous substrate incorrect?
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There are what are called "structure driven" stream courses, these occur where the formations underlying the stream bed have a large impact on the fluvial forms in the drainage basin. This is most common where the substrate has been fractured by tectonic motion or where there are inconsistencies in unit erodibility in bedded formations. These conditions force streambeds to follow lines of weakness that inhibit many "normal" behaviours such as bifurcation rates.

You can also get direct tectonic effects on the paths of streambeds where they cross faultlines. This can be in the form of damming, ponding, and overflow episodes after earthquakes. Waterfalls across surface faults are not uncommon. Nor are gorges where a river has cut across a fault driven orographic zone. One can also see "kinked" river beds where a river flowing across a faultline is bent by movement along the fault, in this case the river will follow the line of the fault for some distance before regaining the bed that has been displaced by it's motion.

I hope that answers your question but hit me up in the comments if you want more.

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