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Drought is a complex and multi-attribute natural hazard that has worldwide effects. Defined by a commonly used standardized precipitation index (SPI), each drought event is characterized by three correlated attributes: severity, duration and frequency. A probabilistic approach is developed to establish a drought severity-duration-frequency (SDF) relationship. Copulas are employed to construct the joint distribution function of drought severity and duration. Drought frequency, in terms of recurrence interval of drought events, is then related to the copula-based distribution function via a conditional distribution function. The derived analytic drought SDF thus becomes a function of univariate distribution functions of drought severity and duration, a copula function which links the fitted univariate models, and the arrival rate of drought events. In this study, rainfall data for the period of 1954-2003 from two gauge stations in Iran, Abadan in the southwestern semi-arid region and Anzali in the north humid region, are employed as an example to illustrate the proposed approach. From the derived drought SDF, drought severity in Anzali station is greater than those in Abadan station for given drought duration and recurrence interval. The results imply that the drought severity in humid region might be more severe if high rainfall fluctuations exist in that region. Copyright (C) 2009 Royal Meteorological Society