Sensitivity analysis of attenuation in convective rainfall at X-band frequency using the mountain reference technique

Abstract

The RadAlp experiment aims at improving quantitative precipitation estimation (QPE) in the Alps thanks to X-band polarimetric radars and in situ measurements deployed in the region of Grenoble, France. In this article, we revisit the physics of propagation and attenuation of microwaves in rain. We first derive four attenuation–reflectivity (AZ) algorithms constrained, or not, by path-integrated attenuations (PIAs) estimated from the decrease in the return of selected mountain targets when it rains compared to their dry weather levels (the so-called mountain reference technique – MRT). We also consider one simple polarimetric algorithm based on the profile of the total differential phase shift between the radar and the mountain targets. The central idea of the work is to implement these five algorithms all together in the framework of a generalized sensitivity analysis in order to establish useful parameterizations for attenuation correction. The parameter structure and the inherent mathematical ambiguity of the system of equations makes it necessary to organize the optimization procedure in a nested way. The core of the procedure consists of (i) exploring with classical sampling techniques the space of the parameters allowed to be variable from one target to the other and from one time step to the next, (ii) computing a cost function (CF) quantifying the proximity of the simulated profiles and (iii) selecting parameters sets for which a given CF threshold is exceeded. This core is activated for a series of values of parameters supposed to be fixed, e.g., the radar calibration error for a given event. The sensitivity analysis is performed for a set of three convective events using the 0∘ elevation plan position indicator (PPI) measurements of the Météo-France weather radar located on top of the Moucherotte mountain (altitude of 1901 m a.s.l. – above sea level). It allows the estimation of critical parameters for radar QPE using radar data alone. In addition to the radar calibration error, this includes the time series of radome attenuation and estimations of the coefficients of the power law models relating the specific attenuation and the reflectivity (A–Z relationship) on the one hand and the specific attenuation and the specific differential phase shift (A–Kdp relationship) on the other hand. It is noteworthy that the A–Z and A–Kdp relationships obtained are consistent with those derived from concomitant drop size distribution measurements at ground level, in particular with a slightly non-linear A–Kdp relationship (A=0.28 Kdp1.1). X-Band radome attenuations as high as 15 dB were estimated, leading to the recommendation of avoiding the use of radomes for remote sensing of precipitation at such a frequency.