Multifractality and rainfall extremes: A review

The multifractal representation of rainfall and its use to predict rainfall extremes have advanced significantly in recent years. This paper summarizes this body of work and points at some open questions. The need for a coherent overview comes in part from the use of different terminology, notation and analysis methods in the literature and in part from the fact that results are dispersed and not always readily available. Two important trends have marked the use of multifractals for rainfall and its extremes. One is the recent shift of focus from asymptotic scaling properties (mainly for the intensity-duration-frequency curves and the areal reduction factor) to the exact extreme distribution under non-asymptotic conditions. This shift has made the results more relevant to hydrologic applications. The second trend is a more sparing use of multifractality in modeling, reflecting the limits of scale invariance in space-time rainfall. This trend has produced models that are more consistent with observed rainfall characteristics, again making the results more suitable for application. Finally we show that rainfall extremes can be analyzed using rather rough models, provided the parameters are fitted to an appropriate range of large-deviation statistics.