The derivation of areal reduction factor of storm rainfall from its scaling properties

We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is widely used in reducing, point rainfall to obtain areal average values for the same duration, probability of exceedance, and specified area. The concepts of scaling and multiscaling, developed in recent years, provide a powerful framework for studying spatial and temporal variability of hydrological processes. It is our view that ARF must reflect the scaling properties of rainfall in space and time. We develop a simple statistical approach to the ARF of extreme storm rainfall based on the scaling properties of the underlying, process in space and time. We derive the scaling relations of mean rainfall intensity over an area A and for a duration T using the concepts of dynamic scaling and statistical self-affinity. A new physically based formula for the ARF is then obtained. Applications are made to observations from the metropolitan area of Milan, Italy, and to data in the United Kingdom, as given in the Natural Environmental Research Council Flood Studies Report. These studies indicate that storm rates in space and time are scaling for extreme events, and hence this concept is shown to provide a useful practical approach to the evaluation of design storms for specified areas.