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Jan Handwerker and Winfried Straub


Measured raindrop size distributions are often approximated by analytical functions. The parameters determining such functions are usually derived from measured data. This procedure can suffer from various uncertainties. The most important of which are (i) the limited detection range of measuring devices such as, for example, disdrometers, and (ii) poor statistics resulting from the rare appearance of relatively large drops.

One way to derive the parameters is the moments method that has a degree of freedom in the choice of the moments. The aim of this study is to find an optimal choice of moments. To this end, numerical experiments are performed by calculating random samples from drop populations with gamma-shaped size distributions. These samples are evaluated as they were recorded by an ideal disdrometer whose single limitation is the cutoff with respect to very small and very large raindrops. From that data the parameters mentioned above are determined by the moments method. The truncation of the measurement is explicitly taken into account during the retrieval. Further, all possible combinations of three different moments used to derive the gamma parameters are impartially compared.

It turns out that parameters derived on the basis of low-order moments are less affected by biases and noise than parameters derived by larger-order moments, that is, the sampling problem is more severe than the truncation problem, especially because the latter can be overcome much more efficiently within the retrieval algorithm. It is shown that by using very low-order moments and estimating the unmeasured fraction of the moments, optimal results from real measurements can be obtained.

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Katja Träumner, Jan Handwerker, Andreas Wieser, and Jens Grenzhäuser


Remote sensing systems like radars and lidars are frequently used in atmospheric measurement campaigns. Because of their different wavelengths, they operate in different scattering regimes. Combined use may result in new measurement options. Here, an approach to estimate raindrop size distribution using vertical velocities measured by a lidar–radar combination is introduced and tested using a 2-μm Doppler lidar and a 35.5-GHz cloud radar. The lidar spectra are evaluated to deduce air motion from the aerosol peak and the fall velocity of the raindrops from the rain peak. The latter is weighted by the area (D 2) of the scatters. The fall velocity derived from radar measurements is weighted by D 6 (Rayleigh approximation). Assuming a size-dependent fall velocity and an analytical description of the drop size distribution, its parameters are calculated from these data. Comparison of the raindrop size distribution from the lidar–radar combination with in situ measurements on the ground yields satisfying results.

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