ON HACKS LAW

Hack's law is reviewed, emphasizing its implications for the elongatio n of river basins as well as its connections with their fractal charac teristics. The relation between Hack's law and the internal structure of river basins is investigated experimentally through digital elevati on models. It is found that Hack's exponent, elongation, and some rele vant fractal characters are closely related. The self-affine character of basin boundaries is shown to be connected to the power law decay o f the probability of total contributing areas at any link and to Hack' s law. An explanation for Hack's law is derived from scaling arguments . From the results we suggest that a statistical framework referring t o the scaling invariance of the entire basin structure should be used in the interpretation of Hack's law.