Lovejoy and Schertzer (1990a) presented a statistical analysis of blotting paper observations of the (twodimensional) spatial distribution of raindrop stains. They found empirical evidence for the fractal scaling behavior of raindrops in space, with potentially far-reaching implications for rainfall microphysics and radar meteorology. In particular, the fractal correlation dimensions determined from their blotting paper observations led them to conclude that "drops are (hierarchically) clustered" and that "inhomogeneity in rain is likely to extend down to millimeter scales". Confirming previously reported Monte Carlo simulations, we demonstrate analytically that the claims based on this analysis need to be reconsidered, as fractal correlation dimensions similar to the ones reported (i.e. smaller than the value of two expected for uniformly distributed raindrops) can result from instrumental artifacts (edge effects) in otherwise homogeneous Poissonian rainfall. Hence, the results of the blotting paper experiment are not statistically significant enough to reject the Poisson homogeneity hypothesis in favor of a fractal description of the discrete nature of rainfall. Our analysis is based on an analytical expression for the expected overlap area between a circle and a square, when the circle center is randomly (uniformly) distributed inside the square. The derived expression (πr2-8r 3/3+r4/2, where r denotes the ratio between the circle radius and the side of the square) can be used as a reference curve against which to test the statistical significance of fractal correlation dimensions determined from spatial point patterns, such as those of raindrops and rainfall cells.@en

A stochastic model of the microstructure of rainfall is used to derive explicit expressions for the magnitude of the sampling fluctuations in rainfall properties estimated from raindrop size measurements in stationary rainfall. The model is a marked point process, in which the points represent the drop centers, assumed to be uniformly distributed in space. This assumption, which is supported both by theoretical and by empirical evidence, implies that during periods of stationary rainfall the number of drops in a sample volume follows a Poisson distribution. The marks represent the drop sizes, assumed to be distributed independent of their positions according to some general drop size distribution. Within this framework, it is shown analytically how the sampling distribution of the estimator of any bulk rainfall variable (such as liquid water content, rain rate, or radar reflectivity) in stationary rainfall converges from a strongly skewed distribution to a (symmetrical) Gaussian distribution with increasing sample size. The relevant parameter controlling this evolution is the average number of drops in the sample ns. For a given sample size, the skewness of the sampling distribution is found to be more pronounced for higher order moments of the drop size distribution. For instance, the sampling distribution of the normalized mean diameter becomes nearly Gaussian for ns > 10, while the sampling distribution of the normalized rain rate remains skewed for ns ∼ 500. Additionally, it is shown analytically that, as a result of the mentioned skewness, the median Q50 as an estimator of a bulk rainfall variable always underestimates its population value Qp in stationary rainfall. The ratio of the former to the latter is found to be Q50 / Qp = 1 - b / ns + O (ns- 2), where b is a constant depending on the drop size distribution. For bulk rainfall variables this constant is positive and therefore the median always underestimates the population value. This provides a theoretical confirmation and explanation of previously published simulation results. Finally, relationships between the expected number of raindrops in the sample ns and the rain rate are established for different parametric forms of the raindrop size distribution. These relationships are first compared to experimental results and then used to provide examples of sampling distributions of bulk rainfall variables (in this case rain rate) for different values of the average rain rate and different integration times of the disdrometric device involved (in this case a Joss-Waldvogel disdrometer). The practical relevance of these results is (1) that they provide exact solutions to the sampling problem during (relatively rare) periods of stationary rainfall (e.g., drizzle), and (2) that they provide a lower bound to the magnitude of the sampling problem in the general situation where sampling fluctuations and natural variability co-exist.@en

The Mountain Reference Technique (MRT) was proposed as a means to perform a self-calibration of a weather radar system operating at an attenuating wavelength in a mountainous environment. Two convective rain events observed during the Grenoble 97-98 Experiment are selected here for an illustration and a further verification of the method at X band: the June 16, 1997, event is a medium event with maximum path-integrated attenuations (PIAs) of about 15 dB over a 9-km path, while the July 3, 1998, event is quite extraordinary with (1) a maximum PIA of 50 dB over the same distance and (2) the temporary presence of hail. An improved scheme is proposed for the MRT parameter estimation procedure with a more satisfactory treatment of such high-attenuation effects. It is shown that the optimal calibration factors obtained for the two rain events are almost equal to each other, a comforting result with respect to the radar equipment stability during the corresponding 1-year period. Although the MRT is based on reflectivity and attenuation measurements only, validation of the rain rate retrieval algorithms with respect to rain gage data for the June 16, 1997, rain event showed that this technique is relevant in terms of rain rate estimation. In particular, the MRT-calibrated Hitschfeld-Bordan algorithm provides satisfactory results for this medium-attenuation event. However, the July 3 case clearly demonstrates that this algorithm cannot correct for such high-attenuation effects because of its inherent instability. For both rain events the Marzoug-Amayenc algorithm, originally proposed for spaceborne configurations, is found to be stable and efficient in terms of rain rate estimation. These interesting features are counterbalanced by the fact that the algorithm implementation is limited to directions for which PIA measurements are actually available.@en

In order to investigate to what extent rainfall fluctuations observed with different types of instruments reflect the properties of the rainfall process itself and to what extent they are merely instrumental artefacts we are in the process of developing a stochastic model of rainfall. The starting point for the development of the model has been the notion that at the spatial and temporal scales associated with many types of surface rainfall measurements, rainfall is a discrete process describing the arrival of raindrops of different sizes at the ground. A fundamental question is whether this raindrop arrival process can be considered a homogeneous (Poisson) process or whether it behaves as a clustering (or possibly even scaling) process, as has recently been proposed in the literature. We have tested the classical Poisson homogeneity hypothesis in rainfall on a 35 min time series of 10 s raindrop size spectra collected with a 50 cm2 optical disdrometer. The rain rates calculated from the spectra indicated roughly uncorrelated fluctuations around a constant mean rain rate of about 3.5 mm h-1. Two types of analysis of the drop counts were carried out, a global analysis taking into account all drops regardless of their size and an analysis considering the drop counts in the 16 0.21 mm diameter intervals separately. The first type of analysis revealed that even for the more or less stationary time series under consideration the total raindrop arrival rate was overdispersed with respect to the homogeneous Poisson process. The second type of analysis demonstrated that this rejection of the homogeneity hypothesis could be attributed entirely to raindrops with diameters smaller than 1.14 mm. Although these drops account for 66% of the raindrop concentration in the air and 55% of the raindrop arrival rate at the ground, they only account for 14% of the rain rate and 2% of the radar reflectivity factor (on the basis of the mean drop size distribution during the experiment). In other words, although clustering may be a significant phenomenon for the smallest raindrops, the analyzed data seem to indicate that for moderate rain rates the arrival rate fluctuations of the raindrops which contribute most to rain rate and radar reflectivity factor behave according to Poisson statistics.@en

The HYDROMET Integrated Radar Experiment (HIRE) international radar-hydrological experiment was initiated to test the hydrological relevance of different types of weather radars in an urban Mediterranean environment. The experiment involved a vertically pointing X-band radar, an X-band radar performing RHI scans and an S-band radar performing PPI scans. Preliminary analyses of the collected data suggest the success of the experiment, from the scientific point of view.@en