Scaling of raindrop size distributions and classification of radar reflectivity–rain rate relations in intense Mediterranean precipitation †

SummaryIn radar hydrology the relationship between the reflectivity factor (Z) and the rainfall intensity (R) is generally assumed to follow a power law of which the parameters change both in space and time and depend on the drop size distribution (DSD). Based on disdrometer data, this study tries to improve our understanding of the temporal variability of the power-law relationship between Z and R using a scaling-law formalism for the raindrop size distribution proposed in previous contributions. In particular, this study focuses on the inter-event variability of Z–R coefficients and associated DSD-parameters and their relationship to the type of precipitation. This is crucial for developing improved quantitative precipitation estimation algorithms for extreme, flash flood triggering rainfall.Within the DSD scaling-law framework a new normalized parameter estimation method is presented, which calculates significantly faster than the original method and leads to bulk event estimates of the DSD-parameters and associated Z–R coefficients. Based on a 2.5-year disdrometer dataset collected in the Cévennes-Vivarais region in the south of France, comprising a total of 70 events, it is shown that the quality of the resulting Z–R relationships obtained by the new method compares well to two standard least-squares fitting techniques. A major benefit of the new implementation, as compared to such purely statistical methods, is that it also provides information concerning the properties of the DSD.For each of the 70 events this study also estimates the convective activity based on a threshold technique. Results show that convective events generally tend to have smaller Z–R exponents, which is assumed to result from an increased amount of drop interaction. For stratiform events, a much larger range in exponents is obtained, which is thought to depend on differences in meteorological origin (snow vs. ice). For the types of precipitation events observed in the Cévennes region, for a given value of the exponent, the prefactor of the Z–R relation tends to be larger for the more convective type of events. This emphasizes the different meteorological origin of the heavy rainfall observed in the south of France as compared to other regions of the world.

Research highlights
► This study tries to increase the understanding in reflectivity-rain rate (Z–R) relationship variability for Mediterranean precipitation.
► This study proposes a new method to estimate the parameters of the normalized drop size distribution (DSD).
► For a total of 70 different precipitation events, the DSD parameters and Z–R relationships were estimated.
► Larger Z–R prefactors are observed for convective precipitation as compared to stratiform events.
► Stratiform events tend to have a larger range Z–R exponent values as compared to convective events.