Effect of Nonuniform Beam Filling on the Propagation of the Radar Signal at X-Band Frequencies. Part I: Changes in the k(Z) Relationship

Abstract

Most attenuation correction algorithms are based on the assumption of an average, range-independent power-law relationship, k = aZb, between attenuation k and reflectivity Z. This paper analyzes how nonuniform beam filling (NUBF) of the radar beam can modify the value of the coefficients a and b with distance. This analytical study shows that there are two mechanisms in which NUBF affects the apparent attenuation. One is the global averaging performed by the radar beam within the sampling volume itself. This tends to increase the apparent attenuation. The other mechanism is the gradual building of an angular weighting function due to the accumulated attenuation by a nonuniform rain field between the radar and the sampling volume. This can cause a serious decrease in the apparent specific and path-integrated attenuations. The practical consequences of these analytical results and their quantitative effects on rain retrieval with an X-band ground-based radar are then analyzed by simulations. A radar simulator ?scanning? on a real, high-resolution reflectivity field is used to study the scatter in the relationship between the specific attenuation and Z. It is shown that in a typical horizontal rain structure, the two mechanisms responsible for overestimation or underestimation of the specific attenuation tend to compensate each other with distance. The resulting effect of NUBF from the point of view of ground-based radar is quite neutral.