Hack's law
{{Short description|Hydrological relationship}}
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. 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
- {{Cite report |url=https://pubs.usgs.gov/pp/0294b/report.pdf |title=Studies of Longitudinal Stream Profiles in Virginia and Maryland |last=Hack |first=John T. |date=1957 |doi=10.3133/pp294B |pages=45–97 |id=U.S. Geological Survey (USGS) Professional Paper 294-B |author-link=John Tilton Hack |archive-url=https://web.archive.org/web/20240711121213/https://pubs.usgs.gov/publication/pp294B |archive-date=2024-07-11 |url-status=live |series=Shorter Contributions to General Geology}}
- {{Cite journal |last1=Rigon |first1=Riccardo |last2=Rodriguez-Iturbe |first2=Ignacio |last3=Maritan |first3=Amos |last4=Giacometti |first4=Achille |last5=Tarboton |first5=David G. |last6=Rinaldo |first6=Andrea |date=November 1996 |title=On Hack's law |url=https://agupubs.onlinelibrary.wiley.com/doi/10.1029/96WR02397 |journal=Water Resources Research |language=en |publisher=American Geophysical Union |volume=32 |issue=11 |pages=3367–3374 |doi=10.1029/96WR02397 |bibcode=1996WRR....32.3367R |issn=0043-1397 |via=Wiley|url-access=subscription }}
- {{Cite journal |last=Willemin |first=James H. |date=November 2000 |title=Hack's law: Sinuosity, convexity, elongation |url=https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2000WR900229 |journal=Water Resources Research |language=en |publisher=American Geophysical Union |volume=36 |issue=11 |pages=3365–3374 |doi=10.1029/2000WR900229 |bibcode=2000WRR....36.3365W |issn=0043-1397 |via=Wiley}}
- {{cite journal|last1=Cheraghi|first1=Mohsen|last2=Rinaldo|first2=Andrea|last3=Sander|first3=Graham C.|last4=Perona|first4=Paolo|last5=Barry|first5=D. A.|title=Catchment drainage network scaling laws found experimentally in over-land flow morphologies|journal=Geophysical Research Letters|volume=45|issue=18|pages=9614–9622|doi=10.1029/2018GL078351|bibcode=2018GeoRL..45.9614C|doi-access=free|hdl=20.500.11820/2d9254dd-7ad9-40b0-a95f-3abbea834ec8|hdl-access=free|url=https://www.research.ed.ac.uk/en/publications/catchment-drainage-network-scaling-laws-found-experimentally-in-o|date=28 September 2018|publisher=American Geophysical Union}}
{{Rivers, streams and springs}}
{{geomorph-stub}}