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Guy Delrieu, Hervé Andrieu, and Jean Dominique Creutin

Abstract

The aim of the current study is to quantify attenuation effects that X- and C-band weather radar systems may experience in heavy rainfall. Part of this information can be obtained from power-law relationships between the attenuation coefficient k (dB km−1) and the rain rate R (mm h−1). These relations exhibit a strong dependence on the wavelength used and a significant influence of the raindrop size and temperature distributions. Here the purpose is to go one step further by providing estimates of the path-integrated attenuations (PIAs) that could be observed as a function of range for a given wavelength. Obviously, these values depend on the space and time structure of rainfall and, therefore, refer to a given climatological context. The methodology used consists of using k–R relations to downgrade carefully processed S-band radar data to the corresponding X- and C-band signals. The data were collected in the Cévennes region, a Mediterranean region in France subject to intense and long-lasting rain events during the autumn season. A refined data processing procedure was applied to the available reflectivity measurements, including ground-clutter removal and correction for the effects of the vertical profile of reflectivity as well as a final bias adjustment using rain gauge data. For three rain events, 75 h of instantaneous rain-rate fields thus were available with total rain amounts that exceeded 300 mm over most of the area of interest. Examples of attenuated profiles are presented, and PIA-range-frequency curves are established for the two wavelengths considered under various hypotheses that concern the raindrop size distribution. One of the results is that, at C band, a PIA of 3 dB is exceeded for 5% of the rain-rate profiles at a range of 50 km. Another finding is that a multiplicative factor of about 6 exists between C- and X-band attenuation effects. Implications for rain-rate estimation at X- and C band are discussed.

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Guy Delrieu, Jean Dominique Creutin, and Hervé Andrieu

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The aim of the present study is to characterize mountain returns measured with a ground-based weather radar operating in a mountainous region. A computation code based on the use of a digitized terrain model is developed for calculating the areas illuminated by the radar beam. Partial and total screening effects am accounted for in the calculation. The angular and range weighting functions of the radar measurement am modeled using Gaussian approximations to give the so-called weighted illuminated areas for various sizes of the radar resolution volume. Radar measurements are compared to the computed illuminated areas in order to determine the average backscattering coefficient of partly grass-covered, partly forested mountains: 87% of the measured time-averaged mountain return variance is explained by the computed values when the 15-dB resolution volume is considered. Additional geometrical information, provided by the calculated angles of incidence, is accounted for to yield a linear σ(dB) 0(α) model relevant for the so-called near-grazing region since most of the angles of incidence are in the 70°–900° range. Here 92% of the measurement variance is explained when the σ(dB) 0(α) model is used.

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Guy Delrieu, Lorenz Hucke, and Jean Dominique Creutin

Abstract

This paper is devoted to a sensitivity study of the equation describing attenuation effects in rain for ground-based weather radar systems operating at X- or C-band wavelengths. First, the so-called attenuation equation, also termed the HB solution or HB algorithm in reference to the well-known paper by , is recalled. A procedure aimed at obtaining consistent relations between average values of the equivalent reflectivity factor Z e, the attenuation coefficient k, and the rain rate R as function of two parameters of the drop size distribution (DSD) is also presented. Then, a numerical simulation framework based on a simple description of rainfall characteristics and accounting for some of the radar measurement features is proposed to test the ability of the HB algorithm to perform attenuation correction of hypothetical rain-rate profiles. In a first step, the well-known instability of the solution is illustrated. For instance, it is shown that, even in the absence of radar calibration error and with perfect knowledge of the DSD, the algorithm is not able to correct profiles with path-integrated attenuation (PIA) greater than about 20 dB when typical values are considered for the radar parameters. Owing to this inherent instability, the sensitivity study with respect to the DSD parameters is therefore limited to profiles with PIAs less than 15 dB. The two following results are obtained: 1) a PIA of about 10 dB should be considered as the upper limit that the algorithm is able to correct and 2) given the choice of the (Z e, k, R) relations, optimization of one parameter is necessary and sufficient to obtain improvement over the standard ZR method for this range of PIAs. This parameter plays the role of a correction term for the radar calibration error, the uncertainty in the knowledge of the DSD, and other sources of bias. These results are confirmed by an X-band radar–rain gauge comparison with a dataset collected during the Marseilles Hydrometeorological Experiment.

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Alexis Berne, Guy Delrieu, Herve Andrieu, and Jean-Dominique Creutin

Abstract

The present study aims to demonstrate the major influence of the vertical heterogeneity of rainfall on radar–rain gauge assessment. For this purpose, an experimental setup was deployed during the HYDROMET Integrated Radar Experiment (HIRE-98) based on a conventional S-band weather radar operating at long range (90 km), an X-band vertically pointing radar, and a network of 25 tipping-bucket rain gauges. After calibration and attenuation corrections, the X-band radar data enables the estimation of the vertical profile of reflectivity (VPR) time series. Screening and VPR correction factors are derived for the distant S-band radar measurements. The raw and corrected S-band radar estimates are compared to rain gauge measurements for various integration time steps (6–30 min). Considering about 12 h of intense Mediterranean precipitation, the VPR influence at the X-band radar site is clear for all the time steps considered. For instance, a continuous increase in the Nash efficiency for the corrected radar data compared to the rain gauge data (0.85 for the 6-min time step, up to 0.93 for the 30-min time step) is observed while this criterion remains less than 0.15 for the raw radar data, regardless of the time step. The effect of the low-level reflectivity enhancement on the radar–rain gauge assessment was also found to be very important in the considered configuration. The establishment of reliable VPR climatologies is therefore a challenge in order to better account for such effects that are not observable at long range from the radars. The spatial validity of the VPR correction derived from a point sensor like the vertically pointing radar is also investigated. As a result of the high space–time variability of rainfall, such a punctual VPR correction has an efficiency limited to areas of about 20 km2 (200 km2) for the 6-min (30 min) integration time step.

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Pierre-Emmanuel Kirstetter, Hervé Andrieu, Brice Boudevillain, and Guy Delrieu

Abstract

The vertical profile of reflectivity (VPR) must be identified to correct estimations of rainfall rates by radar for the nonuniform beam filling associated with the vertical variation of radar reflectivity. A method for identifying VPRs from volumetric radar data is presented that takes into account the radar sampling. Physically based constraints on the vertical structure of rainfall are introduced with simple VPR models within a rainfall classification procedure defining more homogeneous precipitation patterns. The model parameters are identified in the framework of an extended Kalman filter to ensure their temporal consistency. The method is assessed using the dataset from a volume-scanning strategy for radar quantitative precipitation estimation designed in 2002 for the Bollène radar (France). The physical consistency of the retrieved VPR is evaluated. Positive results are obtained insofar as the physically based identified VPR (i) presents physically consistent shapes and characteristics considering beam effects, (ii) shows improved robustness in the difficult radar measurement context of the Cévennes–Vivarais region, and (iii) provides consistent physical insight into the rain field.

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Pierre-Emmanuel Kirstetter, Hervé Andrieu, Guy Delrieu, and Brice Boudevillain

Abstract

Nonuniform beam filling associated with the vertical variation of atmospheric reflectivity is an important source of error in the estimation of rainfall rates by radar. It is, however, possible to correct for this error if the vertical profile of reflectivity (VPR) is known. This paper presents a method for identifying VPRs from volumetric radar data. The method aims at improving an existing algorithm based on the analysis of ratios of radar measurements at multiple elevation angles. By adding a rainfall classification procedure defining more homogeneous precipitation patterns, the issue of VPR homogeneity is specifically addressed. The method is assessed using the dataset from a volume-scanning strategy for radar quantitative precipitation estimation designed in 2002 for the Bollène radar (France). The identified VPR is more representative of the rain field than are other estimated VPRs. It has also a positive impact on radar data processing for precipitation estimation: while scatter remains unchanged, an overall bias reduction at all time steps is noticed (up to 6% for all events) whereas performance varies with type of events considered (mesoscale convective systems, cold fronts, or shallow convection) according to the radar-observation conditions. This is attributed to the better processing of spatial variations of the vertical profile of reflectivity for the stratiform regions. However, adaptation of the VPR identification in the difficult radar measurement context in mountainous areas and to the rainfall classification procedure proved challenging because of data fluctuations.

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Guy Delrieu, Soumia Serrar, Elena Guardo, and Jean Dominique Creutin

Abstract

The authors recently showed that when attenuating wavelengths are used mountain returns may allow estimation of path-integrated attenuations (PIAs) between a ground-based weather radar and a given mountain, an application of the well-known Surface Reference Technique originally proposed for spaceborne radar configurations. This information proved to be valuable for the quantitative interpretation of X-band weather radar data in terms of rainfall rate for an urban hydrological application in Marseilles, France. In this paper, a further verification of this concept is presented with the comparison of mountain-derived PIAs and direct measurements obtained by means of a receiving antenna installed in the Balcons de Belledonne mountain ridge near Grenoble, France. Maximum PIAs in the range of 8–16 dB are obtained over the considered 9-km propagation path for various rain events observed between May and July 1997. A physical model of the mountain return power is developed leading to the formulation of two mountain PIA estimators under various hypotheses concerning 1) the stability of both the radar equipment and the electromagnetic properties of the mountain surfaces and 2) the effects of the rain falling over the mountain. A geometric calculation based on the use of a digital terrain model then allows the authors to estimate both the radar-positioning errors and the rain beamfilling factors of the mountain-cluttered radar bins. The dry-weather mountain return time series are also studied, showing a good stability of the average value from one rain event to the next with, however, a marked effect of the wetting of the mountain surfaces. The time variability of these values is also characterized in order to assess the minimum detectable mountain PIA, estimated in the present case to be about 2.25 dB. Finally, a good agreement is observed between the estimated mountain PIAs and the measured ones (with correlation coefficients and regression slopes reaching 0.92 and 0.95, respectively). Assuming that the receiving antenna measurements are error free, the standard error in the mountain PIA estimation is found to be about ±2.5 dB in the considered configuration.

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Nan Yu, Guy Delrieu, Brice Boudevillain, Pieter Hazenberg, and Remko Uijlenhoet

Abstract

This study offers a unified formulation of single- and multimoment normalizations of the raindrop size distribution (DSD), which have been proposed in the framework of scaling analyses in the literature. The key point is to consider a well-defined “general distribution” g(x) as the probability density function (pdf) of the raindrop diameter scaled by a characteristic diameter D c. The two-parameter gamma pdf is used to model the g(x) function. This theory is illustrated with a 3-yr DSD time series collected in the Cévennes region, France. It is shown that three DSD moments (M 2, M 3, and M 4) make it possible to satisfactorily model the DSDs, both for individual spectra and for time series of spectra. The formulation is then extended to the one- and two-moment normalization by introducing single and dual power-law models. As compared with previous scaling formulations, this approach explicitly accounts for the prefactors of the power-law models to yield a unique and dimensionless g(x), whatever the scaling moment(s) considered. A parameter estimation procedure, based on the analysis of power-law regressions and the self-consistency relationships, is proposed for those normalizations. The implementation of this method with different scaling DSD moments (rain rate and/or radar reflectivity) yields g(x) functions similar to the one obtained with the three-moment normalization. For a particular rain event, highly consistent g(x) functions can be obtained during homogeneous rain phases, whatever the scaling moments used. However, the g(x) functions may present contrasting shapes from one phase to another. This supports the idea that the g(x) function is process dependent and not “unique” as hypothesized in the scaling theory.

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Thierry Pellarin, Guy Delrieu, Georges-Marie Saulnier, Hervé Andrieu, Bertrand Vignal, and Jean-Dominique Creutin

Abstract

A simulation procedure has been developed for use in predetermining the expected quality of rain-rate estimates that a given weather radar system operating in a mountainous region may obtain over a given hydrologic catchment. This first application of what is referred to as the “hydrologic visibility” concept focuses on the quantification of the rain-rate error resulting from the effects of ground clutter, beam blockage, and the vertical profile of reflectivity (VPR). The assessment of the impact of the space–time structure of the radar error in terms of discharge at the catchment outlet is also investigated using a distributed hydrologic model. A case study is presented for the Ardèche catchment in France using the parameters of two S-band weather radars operated by Météo-France at Nîmes and Bollène. Radar rain-rate error generation and rainfall–runoff simulations are performed using VPR and areal rainfall time series representative of the Cévennes rain climatology. The major impact of ground clutter on both rainfall and runoff estimates is confirmed. The “hydrologic compositing procedure,” based on the selection of the elevation angle minimizing the rain-rate error at a given point, is shown to be preferable to the “pseudo-CAPPI” procedure based on radar-range considerations only. An almost perfect ground-clutter reduction (GCR) technique is simulated in order to assess the effects of beam blockage and VPR alone. These error sources lead to severe and slight rain underestimations for the Nîmes and Bollène radars, respectively, over the Ardèche catchment. The results, indicating an amplification of the errors on the discharge parameters (peak discharge, runoff volume) compared to the areal rainfall error, are of particular interest. They emphasize the need for refined corrections for ground clutter, beam blockage, and VPR effects, in addition to the optimization of the radar location and scanning strategy, if hydrologic applications are foreseen.

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Guy Delrieu, Brice Boudevillain, John Nicol, Benoît Chapon, Pierre-Emmanuel Kirstetter, Hervé Andrieu, and D. Faure

Abstract

The Bollène-2002 Experiment was aimed at developing the use of a radar volume-scanning strategy for conducting radar rainfall estimations in the mountainous regions of France. A developmental radar processing system, called Traitements Régionalisés et Adaptatifs de Données Radar pour l’Hydrologie (Regionalized and Adaptive Radar Data Processing for Hydrological Applications), has been built and several algorithms were specifically produced as part of this project. These algorithms include 1) a clutter identification technique based on the pulse-to-pulse variability of reflectivity Z for noncoherent radar, 2) a coupled procedure for determining a rain partition between convective and widespread rainfall R and the associated normalized vertical profiles of reflectivity, and 3) a method for calculating reflectivity at ground level from reflectivities measured aloft. Several radar processing strategies, including nonadaptive, time-adaptive, and space–time-adaptive variants, have been implemented to assess the performance of these new algorithms. Reference rainfall data were derived from a careful analysis of rain gauge datasets furnished by the Cévennes–Vivarais Mediterranean Hydrometeorological Observatory. The assessment criteria for five intense and long-lasting Mediterranean rain events have proven that good quantitative precipitation estimates can be obtained from radar data alone within 100-km range by using well-sited, well-maintained radar systems and sophisticated, physically based data-processing systems. The basic requirements entail performing accurate electronic calibration and stability verification, determining the radar detection domain, achieving efficient clutter elimination, and capturing the vertical structure(s) of reflectivity for the target event. Radar performance was shown to depend on type of rainfall, with better results obtained with deep convective rain systems (Nash coefficients of roughly 0.90 for point radar–rain gauge comparisons at the event time step), as opposed to shallow convective and frontal rain systems (Nash coefficients in the 0.6–0.8 range). In comparison with time-adaptive strategies, the space–time-adaptive strategy yields a very significant reduction in the radar–rain gauge bias while the level of scatter remains basically unchanged. Because the Z–R relationships have not been optimized in this study, results are attributed to an improved processing of spatial variations in the vertical profile of reflectivity. The two main recommendations for future work consist of adapting the rain separation method for radar network operations and documenting Z–R relationships conditional on rainfall type.

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