Multifractal analysis of African monsoon rain fields, taking into account the zero rain-rate problem

Abstract

Nonlinear rain dynamics, due to strong coupling with turbulence, can be described by stochastic scale invariant (such as multifractal) models. In this study, attention is focused on the three-parameter fractionally integrated flux (FIF), based on the universal multifractal (UM) model developed by Schertzer and Lovejoy (1987). Multifractal analysis techniques were applied to experimental radar data measured during the African monsoon multidisciplinary analysis (AMMA) campaign, during the summer of 2006. The non-conservation parameter H, which has often been estimated at 0, was found to be more likely close to 0.4, meaning that rain is not a conserved cascade. Moreover, it is shown that the presence of numerous zero values in the data has an influence, which has until now been underestimated, but should in fact be accounted for. UM parameters are therefore estimated from the full dataset, and then only from maps in which almost all pixels have a non-zero value. Significant differences were found, attributed to on–off intermittency, and their role was checked by means of simulations. Finally, these results are compared with those previously based on time series, and collected by a co-localized disdrometer. The sets of parameters obtained in the spatial and time domains are found to be quite close to each other, contrary to most results published in the literature. This generally reported incoherency is believed to result mainly from the influence of on–off intermittency, whose effects are stronger for time series than for selected radar maps.