A mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event (e.g. its size), the frequency is said to follow a power law. Thus, Hack’s law (Hack, (1957), US Geol. Surv. Prof. Pap. 294-B:45) states that the length l of the main stream of a river basin scales like a power h of the basin’s area a :
and Li et al. (2011) Geomorph. 130 (2011) 221 find a power law relationship between rainfall and the frequency of landslides in Zhejiang province, China.