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Joël Jaffrain and Alexis Berne

Abstract

The spatial structure of the raindrop size distribution (DSD) conveys crucial information for reliable quantitative estimation of rainfall using remote sensing techniques. To investigate this question, a network of 16 optical disdrometers has been deployed over a typical weather radar pixel (~1 × 1 km2) in Lausanne, Switzerland. A set of 36 rainfall events has been classified according to three types: convective, transitional, and frontal. In a first step, the spatial structure of the DSD is quantified using spatial correlation for comparison with the literature, showing good agreement with previous studies. The spatial structure of important quantities related to the DSD—namely, the total concentration of drops Nt, the mass-weighted diameter Dm, and the rain rate R—is quantified using variograms. Results clearly highlight that DSD fields are organized and not randomly distributed even at a scale below 1 km. Moreover, convective-type rainfall exhibits larger variability of the DSD than do transitional and frontal rainfall. The temporal resolution is shown to have an influence on the results: increasing time steps tend to decrease the spatial variability. This study presents a possible application of such information by quantifying the error associated with the use of point measurements as areal estimates at larger scales. Analyses have been conducted for different sizes of domain ranging from 100 × 100 to 1000 × 1000 m2. As expected, this error is increasing with the size of the domain. For instance, for a domain of ~1000 × 1000 m2, the error associated with rain-rate estimates is on the order of 25% for all types of rain.

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Marc Schleiss and Alexis Berne

Abstract

A stochastic method to disaggregate rain rate fields into drop size distribution (DSD) fields is proposed. It is based on a previously presented DSD simulator that has been modified to take into account prescribed block-averaged rain rate values at a coarser scale. The integral quantity used to drive the disaggregation process can be the rain rate, the radar reflectivity, or any variable directly related to the DSD. The proposed method is illustrated and qualitatively evaluated using radar rain rate data provided by MeteoSwiss for two rain events of very contrasted type (stratiform versus convective). The evaluation shows that both types of rainfall are correctly disaggregated, although the general agreement in terms of rain rate distributions, intermittency, and space–time structures is much better for the stratiform case. Possible extensions and generalizations of the technique (e.g., using radar reflectivities at two different frequencies or polarizations to drive the disaggregation process) are discussed at the end of the paper.

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Joël Jaffrain and Alexis Berne

Abstract

This work aims at quantifying the variability of the parameters of the power laws used for rain-rate estimation from radar data, on the basis of raindrop size distribution measurements over a typical weather radar pixel. Power laws between the rain rate and the reflectivity or the specific differential phase shift are fitted to the measured values, and the variability of the parameters is analyzed. At the point scale, the variability within this radar pixel cannot be solely explained by the sampling uncertainty associated with disdrometer measurements. When parameters derived from point measurements are applied at the radar pixel scale, the resulting error in the rain amount varies between −2% and +15%.

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Joël Jaffrain and Alexis Berne

Abstract

The variability of the (rain)drop size distribution (DSD) in time and space is an intrinsic property of rainfall, which is of primary importance for various environmental fields such as remote sensing of precipitation, for example. DSD observations are usually collected using disdrometers deployed at the ground level. Like any other measurement of a physical process, disdrometer measurements are affected by noise and sampling effects. This uncertainty must be quantified and taken into account in further analyses. This paper addresses this issue for the Particle Size Velocity (PARSIVEL) optical disdrometer by using a large dataset corresponding to light and moderate rainfall and collected from two collocated PARSIVELs deployed during 15 months in Lausanne, Switzerland. The relative sampling uncertainty associated with quantities characterizing the DSD—namely the total concentration of drops Nt and the median-volume diameter D 0—is quantified for different temporal resolutions. Similarly, the relative sampling uncertainty associated with the estimates of the most commonly used weighted moments of the DSD (i.e., the rain-rate R, the radar reflectivity at horizontal polarization Zh, and the differential reflectivity Z dr) is quantified as well for different weather radar frequencies. The relative sampling uncertainty associated with estimates of Nt is below 13% for time steps longer than 60 s. For D 0, it is below 8% for D 0 values smaller than 1 mm. The associated sampling uncertainty for estimates of R is on the order of 15% at a temporal resolution of 60 s. For Zh, the sampling uncertainty is below 9% for Zh values below 35 dBZ at a temporal resolution of 60 s. For Z dr values below 0.75 dB, the sampling uncertainty is below 36% for all temporal resolutions. These analyses provide relevant information for the accurate quantification of the variability of the DSD from disdrometer measurements.

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Marc Schneebeli and Alexis Berne

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The different quantities measured by dual-polarization radar systems are closely linked to each other. An extended Kalman filter framework is proposed in order to make use of constraints on individual radar observables that are induced by these relations. This new approach simultaneously estimates the specific differential phase on propagation K dp, the attenuation-corrected reflectivity at horizontal polarization Zh, and the attenuation-corrected differential reflectivity Z dr, as well as the differential phase shift on backscatter δ. In a simulation experiment it is found that K dp and δ can be retrieved with higher accuracy and spatial resolution than existing estimators that solely rely on a smoothed measurement of the differential phase shift Ψdp. Attenuation-corrected Zh was retrieved with an accuracy similar to standard algorithms, but improvements were found for attenuation-corrected Z dr. In addition, the algorithm can be used for radar calibration by comparing the directly retrieved differential phase shift on propagation Φdp with the accumulated K dp estimates. The extended Kalman filter estimation scheme was applied to data collected with an X-band polarimetric radar in the Swiss Alps in 2010. Radome attenuation appears to be significant (up to 5 dB) in moderate to intense rain events and hence needs to be corrected in order to have reliable quantitative precipitation estimates. Measurements corrected for radome and propagation attenuation were converted into rain-rate R with a newly developed relation between R, K dp, and Z dr. The good agreement between rain-rate values inferred from ground observations and from the radar measurements confirms the reliability of the proposed radar processing technique.

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Timothy H. Raupach and Alexis Berne

Abstract

Double-moment normalization of the drop size distribution (DSD) summarizes the DSD in a compact way, using two of its statistical moments and a “generic” double-moment normalized DSD function. Results are presented of an investigation into the invariance of the double-moment normalized DSD through horizontal and vertical displacement in space, using data from disdrometers, vertically pointing K-band Micro Rain Radars, and an X-band polarimetric weather radar. The invariance of the double-moment normalized DSD is tested over a vertical range of up to 1.8 km and a horizontal range of up to approximately 100 km. The results suggest that for practical use, with well-chosen input moments, the double-moment normalized DSD can be assumed invariant in space in stratiform rain. The choice of moments used to characterize the DSD affects the amount of DSD variability captured by the normalization. It is shown that in stratiform rain, it is possible to capture more than 85% of the variability in DSD moments zero to seven using the technique. Most DSD variability in stratiform rain can thus be explained through the variability of two of its statistical moments. The results suggest similar behavior exists in transition and convective rain, but the limited data samples available do not allow for robust conclusions for these rain types. The results have implications for practical uses of double-moment DSD normalization, including the study of DSD variability and microphysics, DSD-retrieval algorithms, and DSD models used in rainfall retrieval.

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Timothy H. Raupach and Alexis Berne

Abstract

The drop size distribution (DSD) describes the microstructure of liquid precipitation. The high variability of the DSD reflects the variety of microphysical processes controlling raindrop properties and affects the retrieval of rainfall. An analysis of the effects of DSD subgrid variability on areal estimation of precipitation is presented. Data used were recorded with a network of disdrometers in Ardèche, France. DSD variability was studied over two typical scales: 5 km × 5 km, similar to the ground footprint size of the Global Precipitation Measurement (GPM) spaceborne weather radar, and 2.8 km × 2.8 km, an operational pixel size of the Consortium for Small-Scale Modeling (COSMO) numerical weather model. Stochastic simulation was used to generate high-resolution grids of DSD estimates over the regions of interest, constrained by experimental DSDs measured by disdrometers. From these grids, areal DSD estimates were derived. The error introduced by assuming a point measurement to be representative of the areal DSD was quantitatively characterized and was shown to increase with the size of the considered area and with drop size and to decrease with the integration time. The controlled framework allowed for the accuracy of retrieval algorithms to be investigated. Rainfall variables derived by idealized simulations of GPM- and COSMO-style algorithms were compared to subgrid distributions of the same variables. While rain rate and radar reflectivity were well represented, the estimated drop concentration and mass-weighted mean drop diameter were often less representative of subgrid values.

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Marc Schleiss, Joel Jaffrain, and Alexis Berne

Abstract

A method for the stochastic simulation of (rain)drop size distributions (DSDs) in space and time using geostatistics is presented. At each pixel, the raindrop size distribution is described by a Gamma distribution with two or three stochastic parameters. The presence or absence of rainfall is modeled using an indicator field. Separable space–time variograms are used to estimate and reproduce the spatial and temporal structures of all these parameters. A simple and user-oriented procedure for the parameterization of the simulator is proposed. The only data required are DSD time series and radar rain-rate (or reflectivity) measurements. The proposed simulation method is illustrated for both frontal and convective precipitation using real data collected in the vicinity of Lausanne, Switzerland. The spatial and temporal structures of the simulated fields are evaluated and validated using DSD measurements from eight independent disdrometers.

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Hidde Leijnse, Remko Uijlenhoet, and Alexis Berne

Abstract

Microwave links can be used for the estimation of path-averaged rainfall by using either the path-integrated attenuation or the difference in attenuation of two signals with different frequencies and/or polarizations. Link signals have been simulated using measured time series of raindrop size distributions (DSDs) over a period of nearly 2 yr, in combination with wind velocity data and Taylor’s hypothesis. For this purpose, Taylor’s hypothesis has been tested using more than 1.5 yr of high-resolution radar data. In terms of correlation between spatial and temporal profiles of rainfall intensities, the validity of Taylor’s hypothesis quickly decreases with distance. However, in terms of error statistics, the hypothesis is seen to hold up to distances of at least 10 km. Errors and uncertainties (mean bias error and root-mean-square error, respectively) in microwave link rainfall estimates due to spatial DSD variation are at a minimum at frequencies (and frequency combinations) where the power-law relation for the conversion to rainfall intensity is close to linear. Errors generally increase with link length, whereas uncertainties decrease because of the decrease of scatter about the retrieval relations because of averaging of spatially variable DSDs for longer links. The exponent of power-law rainfall retrieval relations can explain a large part of the variation in both bias and uncertainty, which means that the order of magnitude of these error statistics can be predicted from the value of this exponent, regardless of the link length.

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Marc Schleiss, Sabine Chamoun, and Alexis Berne

Abstract

A particular aspect of the nonstationary nature of intermittent rainfall is investigated. It manifests itself in the fact that the average rain rate varies with the distance to the surrounding dry areas. The authors call this fundamental link between the rainfall intensity and the rainfall occurrence process the “dry drift.” Using high-resolution radar rain-rate maps and disdrometer data, they show how the dry drift affects the structure and the variability of intermittent rainfall fields. They provide a rigorous geostatistical framework to describe it and propose an extension of the concept to more general quantities like the (rain)drop size distribution.

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