Power law distribution of catastrophic floods, in The Extremes of the Extremes: Extraordinary Floods

This paper is based on the conjecture that catastrophic events follow a simple pattern as inferred by Feder (1988), Turcotte (1992) and Bak (1997) which were derived from observations of different geophysical, geological and biological phenomena. The spatial distribution of catastrophic floods, i.e. floods that cause damage and loss of life, is investigated here by combining the scaling properties of extreme floods with those of river network composition. Accordingly the spatial pattern of catastrophic floods is described by a power law in the form Pr[g > q] ~ a^(-b/m) which indicates that the probability of occurrence of a flood exceeding a value of q is a power law function of basin area. The exponent b/m is determined from the parameters characterizing river flows, m, and river network composition, b. An application using major floods in Thyrrhenian Liguria, northwestern Italy, during one century successfully tests this conjecture.