Drop by drop backscattered signal of a 50 × 50 × 50 m³ volume: A numerical experiment

The goal of this paper is to analyse the influence of individual drop positions on a backscattered radar signal. This is achieved through a numerical experiment: a 3D rain drop field generator is developed and implemented over a volume of 50 × 50 × 50 m³, and then the sum of the electromagnetic waves backscattered by its hydrometeors is computed. Finally the temporal evolution over 1 s is modelled with simplistic assumptions. For the rainfall generator, the liquid water content (LWC) distribution is represented with the help of a multiplicative cascade down to 0.5 m, below which it is considered as homogeneous. Within each 0.5 × 0.5 × 0.5 m³ patch, liquid water is distributed into drops, located randomly uniformly according to a pre-defined drop size distribution (DSD). Such configuration is compared with the one consisting of the same drops being uniformly distributed over the entire 50 × 50 × 50 m³ volume. Due to the fact that the radar wave length is much smaller than the size of a rainfall "patch", it appears that, in agreement with the theory, we retrieve an exponential distribution for potential measures on horizontal reflectivity. Much thinner dispersion is noticed for differential reflectivity. We show that a simple ballistic assumption for drop velocities does not enable the reproduction of radar observations, and turbulence should be taken into account. Finally the sensitivity of these outputs to the various model parameters is quantified.