This study offers a unified formulation of single- and multimoment normalizations of the raindrop size distribution (DSD), which have been proposed in the framework of scaling analyses in the literature. The key point is to consider a well-defined "general distribution" g(x) as the probability density function (pdf) of the raindrop diameter scaled by a characteristic diameter D_c. The two-parameter gamma pdf is used to model the g(x) function. This theory is illustrated with a 3-yr DSD time series collected in the Cévennes region, France. It is shown that threeDSD moments (M₂,M₃, and M₄) make it possible to satisfactorily model the DSDs, both for individual spectra and for time series of spectra. The formulation is then extended to the one- and twomoment normalization by introducing single and dual power-law models. As compared with previous scaling formulations, this approach explicitly accounts for the prefactors of the power-law models to yield a unique and dimensionless g(x), whatever the scaling moment(s) considered. A parameter estimation procedure, based on the analysis of power-law regressions and the self-consistency relationships, is proposed for those normalizations. The implementation of this method with different scaling DSD moments (rain rate and/or radar reflectivity) yields g(x) functions similar to the one obtained with the three-moment normalization. For a particular rain event, highly consistent g(x) functions can be obtained during homogeneous rain phases, whatever the scaling moments used. However, the g(x) functions may present contrasting shapes from one phase to another. This supports the idea that the g(x) function is process dependent and not "unique" as hypothesized in the scaling theory.

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This paper presents a novel approach to estimate the vertical profile of reflectivity (VPR) from volumetric weather radar data using both a traditional Eulerian as well as a newly proposed Lagrangian implementation. For this latter implementation, the recently developed Rotational Carpenter Square Cluster Algorithm (RoCaSCA) is used to delineate precipitation regions at different reflectivity levels. A piecewise linear VPR is estimated for either stratiform or neither stratiform/convective precipitation. As a second aspect of this paper, a novel approach is presented which is able to account for the impact of VPR uncertainty on the estimated radar rainfall variability. Results show that implementation of the VPR identification and correction procedure has a positive impact on quantitative precipitation estimates from radar. Unfortunately, visibility problems severely limit the impact of the Lagrangian implementation beyond distances of 100 km. However, by combining this procedure with the global Eulerian VPR estimation procedure for a given rainfall type (stratiform and neither stratiform/convective), the quality of the quantitative precipitation estimates increases up to a distance of 150 km. Analyses of the impact of VPR uncertainty shows that this aspect accounts for a large fraction of the differences between weather radar rainfall estimates and rain gauge measurements. Key Points A new Lagrangian based VPR identification methodRadar rainfall uncertainty estimation from spatial precipitation variabilityImproved weather radar based surface rainfall estimation

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This study offers an approach to estimate the rainfall kinetic energy (KE) by rain intensity (I) and radar reflectivity factor (Z) separately, or jointly, based on the one- or two-moment scaled raindrop size distribution (DSD) formulation, which contains (a) I and/or Z observations, (b) dimensionless probability density function (pdf) and (c) some intrinsic parameters. The key point of this formulation is to explain all variability of the DSD by the evolution of observations, hence the paland intrinsic parameters are considered as constants. A robust method is proposed to estimate the climatic values for these parameters, and our 28-month DSD data are used to test this estimation process. The results show that three relationships (KE-I, KE-Z and KE-IZ) which link the observations (I and/or Z) to rainfall kinetic energy (KE) are well established based on the climatic scaled DSD formulation. In particular, the combination of Iand Z yields a significant improvement of estimation of KE.@en

This study offers an approach to estimate the rainfall kinetic energy (KE) by rain intensity (R) and radar reflectivity factor (Z) separately or jointly on the basis of a one- or two-moment scaled raindrop size distribution (DSD) formulation, which contains (1) R and/or Z observations and (2) the dimensionless probability density function (pdf) of a scaled raindrop diameter. The key point is to explain all variability of the DSD by the evolution of the explaining moments (R and Z); hence the pdf is considered as constant. A robust method is proposed to estimate the climatological values of the parameters with a 28 month DSD data set collected in the Cévennes-Vivarais region of France. Three relationships (KE-R, KE-Z, and KE-RZ), which link the observations (R and/or Z) to rainfall kinetic energy (KE), are established. As expected, the assessment using the disdrometer data indicates that (1) because of the proximity of the moment orders, the KE-Z relationship exhibits less variability than the KE-R relationship and (2) the combination of R and Z yields a significant improvement of the estimation of KE compared to the single-moment formulations. Subsequently, a first attempt to spatialize the kinetic energy using radar and rain gauge measurements is presented for a convective event, showing a promising potential for erosion process studies. Different from the application with the disdrometer data, the performance of the KE-Z relationship degrades compared to the KE-R relationship as a result of a bias and/or the sampling characteristics of the radar data.

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In 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.@en

The Mountain Reference Technique (MRT) was proposed as a means to perform a self-calibration of a weather radar system operating at an attenuating wavelength in a mountainous environment. Two convective rain events observed during the Grenoble 97-98 Experiment are selected here for an illustration and a further verification of the method at X band: the June 16, 1997, event is a medium event with maximum path-integrated attenuations (PIAs) of about 15 dB over a 9-km path, while the July 3, 1998, event is quite extraordinary with (1) a maximum PIA of 50 dB over the same distance and (2) the temporary presence of hail. An improved scheme is proposed for the MRT parameter estimation procedure with a more satisfactory treatment of such high-attenuation effects. It is shown that the optimal calibration factors obtained for the two rain events are almost equal to each other, a comforting result with respect to the radar equipment stability during the corresponding 1-year period. Although the MRT is based on reflectivity and attenuation measurements only, validation of the rain rate retrieval algorithms with respect to rain gage data for the June 16, 1997, rain event showed that this technique is relevant in terms of rain rate estimation. In particular, the MRT-calibrated Hitschfeld-Bordan algorithm provides satisfactory results for this medium-attenuation event. However, the July 3 case clearly demonstrates that this algorithm cannot correct for such high-attenuation effects because of its inherent instability. For both rain events the Marzoug-Amayenc algorithm, originally proposed for spaceborne configurations, is found to be stable and efficient in terms of rain rate estimation. These interesting features are counterbalanced by the fact that the algorithm implementation is limited to directions for which PIA measurements are actually available.@en

The HYDROMET Integrated Radar Experiment (HIRE) international radar-hydrological experiment was initiated to test the hydrological relevance of different types of weather radars in an urban Mediterranean environment. The experiment involved a vertically pointing X-band radar, an X-band radar performing RHI scans and an S-band radar performing PPI scans. Preliminary analyses of the collected data suggest the success of the experiment, from the scientific point of view.@en