Derived distribution of floods based on the concept of partial area coverage with a climatic appeal

A new rationale for deriving the probability distribution of floods and hel p in understanding the physical processes underlying the distribution itsel f is presented. On the basis of this a model that presents a number of new assumptions is developed. The basic ideas are as follows: (1) The peak dire ct streamflow Q can always be expressed as the product of two random variat es, namely, the average runoff per unit area u(a) and the peak contributing area a; (2) the distribution of u(a) conditional on a can be related to th at of the rainfall depth occurring in a duration equal to a characteristic response time tau(a) of the contributing part of the basin; and (3) tau(a) is assumed to vary with a according to a power law. Consequently, the proba bility density function of Q can be found as the integral, over the total b asin area A, of that of a times the density function of u(a) given a. It is suggested that u(a) can be expressed as a fraction of the excess rainfall and that the annual flood distribution can be related to that of Q by the h ypothesis that the flood occurrence process is Poissonian. In the proposed model it is assumed, as an exploratory attempt, that a and u(a) are gamma a nd Weibull distributed, respectively. The model was applied to the annual f lood series of eight gauged basins in Basilicata (southern Italy) with catc hment areas ranging from 40 to 1600 km(2). The results showed strong physic al consistence as the parameters tended to assume values in good agreement with well-consolidated geomorphologic knowledge and suggested a new key to understanding the climatic control of the probability distribution of flood s.