The multifractal properties of rain are investigated within the framework of universal multifractals. The database used in this study includes measurements performed over several months in different locations by means of a disdrometer, the dual-beam spectropluviometer (DBS). An assessment of the effect of the rain–no rain intermittency shows that the analysis of rain-rate time series may lead to a spurious break in the scaling and to erroneous parameters. The estimation of rain multifractal parameters is, therefore, performed on an event-by-event basis, and they are found to be significantly different from those proposed in scientific literature. In particular, the parameter H, which has often been estimated to be 0, is more likely to be 0.53, thus meaning that rain is a fractionally integrated flux (FIF). Finally, a new model is proposed that simulates high-resolution rain-rate time series based on these new parameters and on a simple threshold.

The present study deals with the development of a low-cost microwave device devoted to the measurement of average rain rates observed along Earth–satellite links, the latter being characterized by a tropospheric path length of a few kilometres. The ground-based power measurements, which are made using the Ku-band television transmissions from several different geostationary satellites, are based on the principle that the atmospheric attenuation produced by rain encountered along each transmission path can be used to determine the path-averaged rain rate. This kind of device could be very useful in hilly areas where radar data are not available or in urban areas where such devices could be directly placed in homes by using residential TV antenna. The major difficulty encountered with this technique is that of retrieving rainfall characteristics in the presence of many other causes of received signal fluctuation, produced by atmospheric scintillation, variations in atmospheric composition (water vapour concentration, cloud water content) or satellite transmission parameters (variations in emitted power, satellite pointing). In order to conduct a feasibility study with such a device, a measurement campaign was carried out over a period of five months close to Paris. The present paper proposes an algorithm based on an artificial neural network, used to identify dry and rainy periods and to model received signal variability resulting from effects not related to rain. When the altitude of the rain layer is taken into account, the rain attenuation can be inverted to obtain the path-averaged rain rate. The rainfall rates obtained from this process are compared with co-located rain gauges and radar measurements taken throughout the full duration of the campaign, and the most significant rainfall events are analysed.

The gamma distribution is often used to characterize raindrop size distributions (DSDs). However, the estimation of measured raindrop distributions suffers from the shortcomings of statistical sampling errors, which become increasingly significant when the collecting surface of the measuring instrument and the integration time are small. Different estimators of the three parameters (N0*, μ, and Dm) that characterize a normalized gamma distribution have been computed from simulated DSD. A database has been established, containing 22 950 simulated DSDs, corresponding to a wide set of various rainfall situations. Moment, least squares, and maximum likelihood estimators have been evaluated. Error measurement considerations are discussed, in particular the difficulty encountered in measuring small drops (diameter <0.5 mm) with a disdrometer. Modified estimation approaches are proposed to compensate for the lack of small drops accounted for by real measurements. For each of the different methods, systematic error analysis is performed, and the estimation error is quantified in terms of its bias and standard deviation. The sensitivity of the various methods to instrumental characteristics is also evaluated. A case study is run to highlight correlation effects in the estimated DSD parameters, resulting from the use of various retrieval techniques. Finally, a criterion is derived that enables the hypothesis of gamma-distributed DSD to be tested. When applied to real data recorded by an optical disdrometer, this criterion shows that approximately 91% of DSDs are of the gamma type. Real gamma DSDs are then used to compare adapted maximum likelihood estimators with the more commonly used methods.