law of stream lengths

hydrology

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July 14, 2026

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Horton's laws of drainage composition, developed by Robert E. Horton, describe the quantitative relationships within stream networks. The "law of stream numbers" states that the number of streams of different orders in a drainage basin approximates an inverse geometric series. The "law of stream lengths" posits that the average lengths of streams of each order tend to approximate a direct geometric series. These laws reveal exponential relationships in network morphometry, independent of the specific drainage pattern, and facilitate comparative studies of factors like lithology and climate.12

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Horton’s laws of drainage composition
Law of stream lengths: the average lengths of streams of each of the different orders in a drainage basin tend closely to approximate a direct geometric series in which the first term is the average length of streams of the first order.
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Law of stream lengths: the average lengths of streams of each of the different orders in a drainage basin tend closely to approximate a direct geometric series in which the first term is the average length of streams of the first order.
Read More