Multifractal modeling of anomalous scaling laws in rainfall

Abstract

The coupling of hydrological distributed models to numerical weather predictions outputs is an important issue for hydrological applications such as forecasting of flood events. Downscaling meteorological predictions to the hydrological scales requires the resolution of two fundamental issues regarding precipitation, namely: 1) understanding the statistical properties and scaling laws of rainfall fields; 2) validation of downscaling models that are able to preserve statistical characteristics observed in real precipitation. In this paper we discuss the first issue by introducing a new multifractal model that appears particularly suitable for random generation of synthetic rainfall. We argue that the results presented in this paper may be also useful for the solution of the second question. Statistical behavior of rainfall in time is investigated through a high resolution time series recorded in Genova (Italy). The multifractal analysis shows the presence of a temporal threshold, localized around 10÷20 hours, which separates two ranges of anomalous scaling laws. Synthetic time series, characterized by very similar scaling laws to the observed one, are generated with the multifractal model. The potential of the model for extreme rainfall event distributions is also discussed. The multifractal analysis of GATE radar fields have shown that statistical properties of rainfall in space depend on time durations over which precipitation is accumulated. Further analysis of some rainfall fields produced with a meteorological limited area model exhibited the same anomalous scaling as the GATE fields