Monte Carlo simulations of randomly distributed falling raindrops: Properties of drop size spectra as measured by a vertically pointing FM-CW Doppler Radar

Vertical profiles of rain drop size distributions near ground can in principle be accurately obtained by a (well designed) FM-CW Doppler radar. However, there are some open questions regarding the theoretical basis of FM-CW Doppler measurements.

In this paper it is presented that a careful derivation of the theoretical power spectrum for a single scatterer differs from that originally given by Strauch (1976) in the sense that a term appears whose consideration leads to a large overestimation of the number of small raindrops in heavy rain (lots of scatterers with differing sizes and radial velocities).

In parallel, this finding is supported by Monte Carlo simulations of drops having a predefined size spectrum which are randomly distributed in and falling through the radar volume. In these simulations, the electric field backscattered by the raindrops and its measurement by a bistatic FM-CW setup is modeled. Then the ordinary FM-CW-algorithm is applied to deduce the drop size distribution. The numerical results show considerable differences between the true and the measured spectra in the small size range of the raindrop spectrum (see attached figure 1), confirming the theoretical considerations. This effect can partly be removed by applying specific window functions in the FFT involved.

Moreover, the model simulations can generally be used to investigate other properties of the FM-CW technique, e.g. spectral leakage and echo statistics.