Hack's law
Encyclopedia
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).
Empirical relationship
In science, an empirical relationship is one based solely on observation rather than theory. An empirical relationship requires only confirmatory data irrespective of theoretical basis. Sometimes theoretical explanations for what were initially empirical relationships are found, in which case the...
between the length of streams
STREAMS
In computer networking, STREAMS is the native framework in Unix System V for implementing character devices.STREAMS was designed as a modular architecture for implementing full-duplex I/O between kernel or user space processes and device drivers. Its most frequent uses have been in developing...
and the area of their basins
Drainage basin
A drainage basin is an extent or an area of land where surface water from rain and melting snow or ice converges to a single point, usually the exit of the basin, where the waters join another waterbody, such as a river, lake, reservoir, estuary, wetland, sea, or ocean...
. 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).