A novel approach for absolute radar calibration: formulation and theoretical validation

Abstract. The theoretical framework of a novel approach for absolute radar calibration is presented and its potential analysed by means of synthetic data to lay out a solid basis for future practical application. The method presents the advantage of an absolute calibration with respect to the directly measured reflectivity, without needing a previously calibrated reference device. It requires a setup comprising three radars: two devices oriented towards each other, measuring reflectivity along the same horizontal beam and operating within a strongly attenuated frequency range (e.g. K or X band), and one vertical reflectivity and drop size distribution (DSD) profiler below this connecting line, which is to be calibrated. The absolute determination of the calibration factor is based on attenuation estimates.

Using synthetic, smooth and geometrically idealised data, calibration is found to perform best using homogeneous precipitation events with rain rates high enough to ensure a distinct attenuation signal (reflectivity above ca. 30 dBZ). Furthermore, the choice of the interval width (in measuring range gates) around the vertically pointing radar, needed for attenuation estimation, is found to have an impact on the calibration results.

Further analysis is done by means of synthetic data with realistic, inhomogeneous precipitation fields taken from measurements. A calibration factor is calculated for each considered case using the presented method. Based on the distribution of the calculated calibration factors, the most probable value is determined by estimating the mode of a fitted shifted logarithmic normal distribution function. After filtering the data set with respect to rain rate and inhomogeneity and choosing an appropriate length of the considered attenuation path, the estimated uncertainty of the calibration factor is of the order of 1 to 11 %, depending on the chosen interval width. Considering stability and accuracy of the method, an interval of eight range gates on both sides of the vertically pointing radar is most appropriate for calibration in the presented setup.