Hack and Gray have both found that data on mainstream lengths and basin areas can be represented by the equation L′ = CAn′, where C is about 1.4 (measurements in miles), and n′ is about 0.6. Hack has suggested that the deviation of n′ from ½ can be explained by an elongation of drainage basin shapes with increasing area. We point out that variations of stream sinuosity with area can also affect the value of n′. A simple approximate formula is deduced that relates mainstream length, sinuosity, basin shape, and area, and shows how the contributions of sinuosity and shape variation to the quantity (n′ − ½) may be separated and evaluated. Data that illustrate these points are presented for both real and simulated stream systems. Our conclusions are: (1) Variation in mainstream sinuosity with area can be responsible for a significant part of the deviation of n′ from ½. (2) The generally accepted statement that drainage basins become more elongated as their area increases needs further investigation.
Water Resources Research – Wiley
Published: Dec 1, 1967
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