Hack's law

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The Hacksche law derived from the 1957 [JT Hack (1957)], and describes in the hydrology the fractal length surfaces ratio of basins . There is a relationship between the length of the watercourse (main channel) and the size of the catchment area. A double logarithmic representation results in a linear relationship, which indicates the fractality of the relationship.

The statement of Hack's Law consists in the fact that the size increases as the catchment area grows, but the shape basically remains the same:

${\displaystyle {\frac {L^{n}}{L^{n-1}}}=A^{h}}$

No matter how chosen, is constant ${\displaystyle n}$ ${\displaystyle h}$

L ... length of the main channel ${\displaystyle [L]}$

A ... catchment area ${\displaystyle [L^{2}]}$

n ... flow order number [-]

h ... slope , lies between and [-] ${\displaystyle 0{,}57}$ ${\displaystyle 0{,}6}$

literature

• Ignacio Rodríguez-Iturbe, Andrea Rinaldo : Fractal River Basins. Chance and self-organization. Cambridge University Press, Cambridge et al. 2001, ISBN 0-521-00405-5 .
• BS Daya Sagar, Charles Omoregie, BS Prakasa Rao: Morphometric Relations of Fractal-Skeletal Based Channel Network Model. Hindawi Publishing Corporation, Visakhapatman India 1997.