Robert E. Horton coined these four laws: the law of stream numbers, the law of stream lengths, the limits of infiltration capacity, and the runoff-detention-storage relation.

What are they specifically? Googling only yielded me paywalled articles and test questions. A good answer will state the laws and provide a brief explanation of what they mean. I want to understand what they tell me about river systems and what comparisons between different rivers I can make based on them. I'm not looking for an in-depth examination, or for an excourse on the purely mathematical side.

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    $\begingroup$ wou.edu/las/physci/taylor/g322/drainage_anal.pdf maybe, so never mind. I leave it to others to decide wether you want this question and an answer on the site or rather close as trivially googled. Linked paper is, again, a test but provides at least a bit of explanation. $\endgroup$
    – mart
    Apr 14, 2015 at 10:58
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    $\begingroup$ Yes, please write up an answer when you are ready. $\endgroup$ Apr 14, 2015 at 12:21

1 Answer 1


Physicalgeography.net and the Colorado State basic hydraulic page have a good explanation of Horton's Laws.

The first thing that needs to be done in analysing a drainage basin is to classify the stream segments in a basin according to Strahler's method. For each stream order tabulate:

  • the number of segments
  • the average length of the segments
  • the average area of drainage for the segments

According to Physicalgeography.net the bifurcation ratio is the ratio between the number of stream segments in one order and the number of stream segments in the next order.

Horton saw that the bifurcation ratio was always around 3, this he called the Law of Stream Numbers. Apparently a bifurcation ratio of 3 also applies to plant roots, branching of woody plants, veining in leaves and the human circulatory system. I get the impression that without knowing about it, Horton was laying some ground work for fractal mathematics that came to prominence in the 1980s, with the work of Benoit Mandelbrot.

With the Law of Stream Lengths, the average length of stream for each order is calculated, then cumulate lengths found before length ratios between segment orders can be calculated.

Colorado State basic hydraulic page has a more mathematical approach to explaining Horton's Laws, but it's very good. It gives a worked example of how to determine the all the coefficients.

Additional information is also on this site as well.


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