[1] A number of studies have shown that rainfall processes may be described by stochastic scaling models in the time domain. However, most of the data sets have a resolution that is too limited to perceive the internal structure and variability of rain events. In this study, we analyze high-resolution (15 s) disdrometer time series, of total duration 2 years, obtained in Palaiseau, France. Monofractal and multifractal analysis tools are applied to the data set in order to investigate the scaling properties of the process, especially within the framework of universal multifractals (UMs). From spectral analysis and first-order structure function, it is shown that rainfall should be modeled by nonconservative (integrated) processes at small scales (hourly or finer) but not at larger scales. Multifractal analysis shows that two multiscaling regimes should be distinguished, i.e., ∼3 days to 30 min and 15 min to 15 s, with different UM parameters. The former is likely to represent the interevent variability, and the latter is likely to represent the event internal variability. Moreover, most data points contain zero values, which are susceptible to bias multifractal analysis results. In order to assess the effect of the zeros on multifractal analysis results, the UM parameters are also estimated from two variants: from uninterrupted rain events (with almost no zeros) and from a modified (weighted) version of analysis procedure that overweights nonzero values. The parameters are shown to depend noticeably on the proportion of zeros. We propose an approach based on a scaling support of the time series and derive semitheoretical formulas for the bias in the parameters, which are applied in our case study. Finally, we discuss the advantages and drawbacks of some models for numerical simulation of multifractal fields containing a lot of zeros.Citation: Verrier, S., C. Mallet, and L. Barthès (2011), Multiscaling properties of rain in the time domain, taking into account rain support biases,

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[1] Estimation of rainfall intensities from radar measurements relies to a large extent on power-laws relationships between rain rates R and radar reflectivities Z, i.e., Z = a*R^b. These relationships are generally applied unawarely of the scale, which is questionable since the nonlinearity of these relations could lead to undesirable discrepancies when combined with scale aggregation. Since the parameters (a,b) are expectedly related with drop size distribution (DSD) properties, they are often derived at disdrometer scale, not at radar scale, which could lead to errors at the latter. We propose to investigate the statistical behavior of Z-R relationships across scales both on theoretical and empirical sides. Theoretically, it is shown that claimed multifractal properties of rainfall processes could constrain the parameters (a,b) such that the exponent b would be scale independent but the prefactor a would be growing as a (slow) power law of time or space scale. In the empirical part (which may be read independently of theoretical considerations), high-resolution disdrometer (Dual-Beam Spectropluviometer) data of rain rates and reflectivity factors are considered at various integration times comprised in the range 15 s -64 min. A variety of regression techniques is applied on Z-R scatterplots at all these time scales, establishing empirical evidence of a behavior coherent with theoretical considerations: a grows as a 0.1 power law of scale while b decreases more slightly. The properties of a are suggested to be closely linked to inhomogeneities in the DSDs since extensions of Z-R relationships involving (here, strongly nonconstant) normalization parameters of the DSDs seem to be more robust across scales. The scale dependence of simple Z = a*R^b relationships is advocated to be a possible source of overestimation of rainfall intensities or accumulations. Several ways for correcting such scaling biases (which can reach >15-20% in terms of relative error) are suggested. Such corrections could be useful in some practical cases where Z-R scale biases are significant, which is especially expected for convective rainfall.Citation: Verrier, S., L. Barthe`s, and C. Mallet (2013), Theoretical and empirical scale dependency of Z-R relationships: