Attenuation in rain for X- and C-band weather radar systems: Sensitivity with respect to the drop size distribution

This paper is devoted to a sensitivity study of the equation describing att enuation effects in rain for groundbased weather radar systems operating at X- or C-band wavelengths. First, the so-called attenuation equation, also termed the HE solution or HE algorithm in reference to the well-known paper by Hitschfeld and Bordan, is recalled. A procedure aimed at obtaining cons istent relations between average values of the equivalent reflectivity fact or Z(e), the attenuation coefficient k, and the rain rate R as function of two parameters of the drop size distribution (DSD) is also presented. Then. a numerical simulation framework based on a simple description of rainfall characteristics and accounting for some of the radar measurement features is proposed to test the ability of the HE algorithm to perform attenuation correction of hypothetical rain-rate profiles. In a first step, the well-kn own instability of the solution is illustrated. For instance, it is shown t hat, even in the absence of radar calibration error and with perfect knowle dge of the DSD. the algorithm is nor able to correct profiles with path-int egrated attenuation (PIA) greater than about 20 dB when typical values are considered for the radar parameters. Owing to this inherent instability, th e sensitivity study with respect to the DSD parameters is therefore limited to profiles with PIAs less than 15 dB. The two following results are obtai ned: 1) a PIA of about 10 dB should be considered as the upper limit that t he algorithm is able to correct and 2) given the choice of the (Z(e), k. R) relations, optimization of one parameter is necessary and sufficient to ob tain improvement over the standard ZR method for this range of PIAs. This p arameter plays the role of a correction term for the radar calibration erro r, the uncertainty in the knowledge of the DSD, and other sources of bias. These results are confirmed by an X-band radar-rain gauge comparison with a dataset collected during the Marseilles Hydrometeorological Experiment.