Hack's law

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

L=CA^{h}\

for some constant C where the exponent h is slightly less than 0.6 in most basins. h varies slightly from region to region and slightly decreases for larger basins (>8,000 mi², or 20,720 km²). In addition to the catchment-scales, Hack's law was observed on unchanneled small-scale surfaces when the morphology measured at high resolutions (Cheraghi et al., 2018).

The law is named after American geomorphologist John Tilton Hack.

References

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.
Cheraghi, M.; Rinaldo, A.; Sander, G. C.; Perona, P.; Barry, D. A. (2018). "Catchment drainage network scaling laws found experimentally in over-land flow morphologies". Geophysical Research Letters. 45 (18): 9614–9622. Bibcode:2018GeoRL..45.9614C. doi:10.1029/2018GL078351. hdl:20.500.11820/2d9254dd-7ad9-40b0-a95f-3abbea834ec8.

Rivers, streams and springs
Rivers (lists)	Alluvial river Braided river Blackwater river Channel Channel pattern Channel types Confluence Distributary Drainage basin Subterranean river River bifurcation River ecosystem River source Tributary
Streams	Arroyo Bourne Burn Chalk stream Coulee Current Stream bed Stream channel Streamflow Stream gradient Stream pool Perennial stream Winterbourne
Springs (list)	Estavelle/Inversac Geyser Holy well Hot spring list list in the US Karst spring list Mineral spring Ponor Rhythmic spring Spring horizon
Sedimentary processes and erosion	Abrasion Anabranch Aggradation Armor Bed load Bed material load Granular flow Debris flow Deposition Dissolved load Downcutting Erosion Headward erosion Knickpoint Palaeochannel Progradation Retrogradation Saltation Secondary flow Sediment transport Suspended load Wash load Water gap
Fluvial landforms	Ait Alluvial fan Antecedent drainage stream Avulsion Bank Bar Bayou Billabong Canyon Chine Cut bank Estuary Floating island Fluvial terrace Gill Gulch Gully Glen Meander scar Mouth bar Oxbow lake Riffle-pool sequence Point bar Ravine Rill River island Rock-cut basin Sedimentary basin Sedimentary structures Strath Thalweg River valley Wadi
Fluvial flow	Helicoidal flow International scale of river difficulty Log jam Meander Plunge pool Rapids Riffle Shoal Stream capture Waterfall Whitewater
Surface runoff	Agricultural wastewater First flush Urban runoff
Floods and stormwater	100-year flood Crevasse splay Flash flood Flood Urban flooding Non-water flood Flood barrier Flood control Flood forecasting Flood-meadow Floodplain Flood pulse concept Flooded grasslands and savannas Inundation Storm Water Management Model Return period
Point source pollution	Effluent Industrial wastewater Sewage
River measurement and modelling	Baer's law Baseflow Bradshaw model Discharge (hydrology) Drainage density Exner equation Groundwater model Hack's law Hjulström curve Hydrograph Hydrological modelling Hydrological transport model Infiltration (hydrology) Main stem Playfair's law Relief ratio River Continuum Concept Rouse number Runoff curve number Runoff model (reservoir) Stream gauge Universal Soil Loss Equation WAFLEX Wetted perimeter Volumetric flow rate
River engineering	Aqueduct Balancing lake Canal Check dam Dam Drop structure Daylighting Detention basin Erosion control Fish ladder Floodplain restoration Flume Infiltration basin Leat Levee River morphology Retention basin Revetment Riparian-zone restoration Stream restoration Weir
River sports	Canyoning Fly fishing Rafting River surfing Riverboarding Stone skipping Triathlon Whitewater canoeing Whitewater kayaking Whitewater slalom
Other topics	Aquifer Aquatic toxicology Body of water Hydraulic civilization Limnology Riparian zone River valley civilization River cruise Surface water Wild river
Rivers by length Rivers by discharge rate Drainage basins Whitewater rivers Flash floods River name etymologies Countries without rivers

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.