Hack's law is an
empirical relationship
In science
Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural science ...
between the length of
streams
A stream is a continuous body of surface water flowing within the bed and banks of a channel. Depending on its location or certain characteristics, a stream may be referred to by a variety of local or regional names. Long, large stream ...
and the area of their
basins
Basin may refer to:
Geography and geology
* Depression (geology)
** Back-arc basin, a submarine feature associated with island arcs and subduction zones
** Debris basin, designed to prevent damage from debris flow
** Drainage basin (hydrology), ...
. 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
In mathematics, exponentiation, denoted , is an operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, i ...
''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 mi
2, or 20,720 km
2). 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
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*
Hydrology
Rivers
Geomorphology
Water streams
Power laws
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