Evaluating the effects of height-variable reflectivity and antenna sidelobes on the radar equation

Using radar observations to quantify precipitation intensity requires the intervention of the radar equation, which converts the precipitation signal into reflectivity units. This equation generally assumes that the reflectivity is uniform within each sampling gate and that the sidelobes of the antenna pattern are negligible. The purpose here is to provide a more realistic approach that eliminates these assumptions when computing profiles of precipitation intensity (by using a height-variable reflectivity and antenna pattern of significant sidelobes to compute profiles of a radar reflectivity factor). To achieve this, simultaneous observations of collocated vertically pointing radars operating in the VHF and X bands were obtained. Raindrop measurements were used to correct for attenuation in the precipitation signal at the X band. Then the precipitation signal in the VHF radar was simulated by combining this X-band signal and the VHF antenna pattern into a general version of the radar equation. The simulated precipitation signal at VHF compares well with actual measurements of the rain signal (range gates centered at 2.5, 3.0, and 3.5 km) by the VHF radar, and this validates the analysis methods. In conclusion, the analysis indicates that VHF reflectivity at gates above the melting layer is artificially enhanced by the precipitation signal collected in the sidelobe direction. Similar enhancement will be expected wherever there is a strong vertical gradient of reflectivity (i.e., on the order of 10 dB km(-1) or larger).