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'''Hack's law''' is an [[empirical relationship]] between the length of [[streams]] and the area of their [[Drainage basin|basins]]. If ''L'' is the length of the longest stream in a basin, and ''A'' is the area of the basin, then Hack's law may be written as | |||
:<math>L = C A^h\ </math> | |||
for some constant ''C'' where the [[exponent]] ''h'' is slightly less than 0.6 in most basins. Note that ''h'' varies slightly from region to region, and also slightly decreases for larger basins (>8,000 mi², or 20,720 km²). A theoretical value ''h'' = 4/7 ≈ 0.571 for the exponent has been derived (Birnir, 2008). | |||
== References == | |||
* Birnir, B., 2008, "Turbulent rivers", ''Quart. Appl. Math.'', '''66''', 3, pp. 565–594. | |||
* Hack, J., 1957, "Studies of longitudinal stream profiles in Virginia and Maryland", ''U.S. Geological Survey Professional Paper'', 294-B. | |||
* Rigon, R., et al., 1996, "On Hack's law" ''Water Resources Research'', '''32''', 11, pp. 3367–3374. | |||
* Willemin, J.H., 2000, "Hack’s law: Sinuosity, convexity, elongation". ''Water Resources Research'', '''36''', 11, pp. 3365–3374. | |||
{{river morphology}} | |||
[[Category:Hydrology]] | |||
[[Category:Rivers]] | |||
[[Category:Geomorphology]] | |||
[[Category:Water streams]] | |||
[[Category:Power laws]] | |||
Revision as of 09:57, 13 January 2014
Hack's law is an empirical relationship between the length of streams and the area of their basins. If L is the length of the longest stream in a basin, and A is the area of the basin, then Hack's law may be written as
for some constant C where the exponent h is slightly less than 0.6 in most basins. Note that h varies slightly from region to region, and also slightly decreases for larger basins (>8,000 mi², or 20,720 km²). A theoretical value h = 4/7 ≈ 0.571 for the exponent has been derived (Birnir, 2008).
References
- Birnir, B., 2008, "Turbulent rivers", Quart. Appl. Math., 66, 3, pp. 565–594.
- Hack, J., 1957, "Studies of longitudinal stream profiles in Virginia and Maryland", U.S. Geological Survey Professional Paper, 294-B.
- Rigon, R., et al., 1996, "On Hack's law" Water Resources Research, 32, 11, pp. 3367–3374.
- Willemin, J.H., 2000, "Hack’s law: Sinuosity, convexity, elongation". Water Resources Research, 36, 11, pp. 3365–3374.