A mathematical framework for studying rainfall intensity-duration-frequency relationships

A general formula for the rainfall intensity-duration-frequency (idf) relationship, consistent with the theoretical probabilistic foundation of the analysis of rainfall maxima is proposed. Specific forms of this formula are explicitly derived from the underlying probability distribution function of maximum intensities. Several appropriate distribution functions are studied for that purpose. Simple analytical approximations of the most common distribution functions are presented, which are incorporated in, and allow mathematically convenient expressions of idf relationships. Also, two methods for a reliable parameter estimation of idf relationships are proposed. The proposed formulation of idf relationships constitutes an efficient parameterisation, facilitating the description of the geographical variability and regionalisation of idf curves. Moreover, it allows incorporating data from non-recording stations, thus remedying the problem of establishing idf curves in places with a sparse network of rain-recording stations, using data of the denser network of non-recording stations. Case studies, based on data of a significant part of Greece, briefly presented in the paper, clarify the methodology for the construction and regionalisation of the idf relationship. (C) 1998 Elsevier Science B.V. All rights reserved.