Radar rainfall estimation in the context of post-event analysis of flash ...

Journal of Hydrology xxx (2010) xxx–xxx

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Journal of Hydrology

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Radar rainfall estimation in the context of post-event analysis of flash-flood events

Ludovic Bouilloud a, Guy Delrieu a,*, Brice Boudevillain a, Pierre-Emmanuel Kirstetter b

a Laboratoire d0étude des Transferts en Hydrologie et Environnement (LTHE), Grenoble, Franceb Laboratoire Atmosphères, Milieux et Observation Spatiale (LATMOS), Vélizy, France

a r t i c l e i n f o s u m m a r y

Article history:Available online xxxx

Keywords:Extreme rainfall eventsFlash-floodsRadar quantitative precipitation estimation

0022-1694/$ - see front matter � 2010 Published bydoi:10.1016/j.jhydrol.2010.02.035

* Corresponding author. Address: LTHE, BP 53, F-380Tel.: +33 4 76 82 50 94.

E-mail address: [email protected] (G. Delrie

Please cite this article in press as: Bouilloud, L.,doi:10.1016/j.jhydrol.2010.02.035

A method to estimate rainfall from radar data for post-event analysis of flash-flood events has beendeveloped within the EC-funded HYDRATE project. It follows a pragmatic approach including carefulanalysis of the observation conditions for the radar system(s) available for the considered case. Clutterand beam blockage are characterised by dry-weather observations and simulations based on a digital ter-rain model of the region of interest. The vertical profile of reflectivity (VPR) is either inferred from radardata if volume scanning data are available or simply defined using basic meteorological parameters (idea-lised VPR). Such information is then used to produce correction factor maps for each elevation angle tocorrect for range-dependent errors. In a second step, an effective Z–R relationship is optimised to removethe bias over the hit region. Due to limited data availability, the optimisation is carried out with referenceto raingauge rain amounts measured at the event time scale. Sensitivity tests performed with two well-documented rain events show that a number of Z = aRb relationships, organised along hyperbolic curvesin the (a and b) parameter space, lead to optimum assessment results in terms of the Nash coefficientbetween the radar and raingauge estimates. A refined analysis of these equifinality patterns shows thatthe ‘‘total additive conditional bias” can be used to discriminate between the Nash coefficient equifinalsolutions. We observe that the optimisation results are sensitive to the VPR description and also thatthe Z–R optimisation procedure can largely compensate for range-dependent errors, although this shiftsthe optimal coefficients in the parameter space. The time-scale dependency of the equifinality patterns issignificant, however near-optimal Z–R relationships can be obtained at all time scales from the event timestep optimisation.

� 2010 Published by Elsevier B.V.

Introduction

The HYDRATE project, funded by the European Community(http://www.hydrate.tesaf.unipd.it/), aims to improve the scien-tific basis of flash-flood forecasting by extending the understand-ing of past flash-flood events, advancing and harmonising aEuropean-wide innovative flash-flood observation strategy anddeveloping a coherent set of technologies and tools for effectiveearly warning systems. Quantitative precipitation estimation(QPE) is particularly crucial and difficult in this context since thecausative rain events may develop over very short space and timescales (Krajewski and Smith, 2002; Creutin and Borga, 2003). Anal-ysis of 24 flash-flood cases within the HYDRATE project reveals anumber of specific problems regarding QPE. In terms of data avail-ability, rainfall measurements from operational raingauge net-works or amateur devices are often available at the event time

Elsevier B.V.

41 Grenoble Cedex 9, France.

u).

et al. Radar rainfall estimation i

scale but more rarely for the time steps required to describe rain-fall–runoff dynamics, i.e. hourly or even shorter time steps for ur-ban environments (Berne et al., 2004). The development ofweather radar networks in industrial countries now makes it pos-sible to obtain continent-wide rainfall data with adequate space–time resolution (averaged over Cartesian meshes of 1 km2 at inter-vals of 5 min typically) for the hydrological applications at hand.However, the quality of radar data may vary greatly dependingon the location of the flash-flood with respect to the radar sys-tem(s) available. An inherent limitation is related to the radar net-work density. The practical limit for radar QPE is about 100 kmwhile the average radar spacing is about 160 km for the ARAMISnetwork in France and 250 km for the NEXRAD network in theUSA. In addition, flash-floods often occur in mountainous and/orurbanised regions, where environmental noise and visibility prob-lems are aggravated by the intervening relief and infrastructures.Note also that the operating and maintenance protocols for certainradar networks may not be optimal for radar QPE. This is especiallytrue for the electronic calibration procedures and volume scanningstrategies, although they have been considerably improved overrecent years on operational weather radar networks. Two factors

n the context of post-event analysis of flash-flood events. J. Hydrol. (2010),

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reduce the complexity of the problem. First, we are working in thepost-event context, which is much easier than performing andchecking the quality of radar QPE in the real-time context. Second,flash-floods generally result from convective rainfall which makesthe visibility problem less stringent due to the extended verticaldimension of the precipitating clouds. In addition, phase changesbetween ice and water, resulting for instance in bright bands,may have less impact on radar QPE under these extreme conditionsthan in more current rainfall situations.

The present article describes a practical method aimed at mak-ing the best use of available radar and raingauge data for rainfallestimation in the context of post-event analysis. It is based onand contributes to the enhancement of a radar data processing sys-tem called Traitements Régionalisés et Adaptatifs de Données ra-dar pour l’Hydrologie (TRADHy) (i.e. regionalised and adaptiveradar data processing for hydrological applications) initiated in2002 and being developed at LTHE (Delrieu et al., 2009) as partof the activities of the Cévennes–Vivarais Mediterranean Hydro-meteorological Observatory (CVMHO; Delrieu et al., 2005). Afterdescribing the method in ‘‘description of the radar data processingmethod”, two intense and well-documented rain events observedin 2002 in the CVMHO pilot site will be considered in ‘‘illustrationand sensitivity study based on two well-documented intense rainevents” to illustrate the methodology and perform sensitivity stud-ies. ‘‘application of the methodology to two other historical flash-flood events” deals with the application of the method to two otherless documented rain events that occurred in south-eastern Francein 1997 and 1999. Three of the four events studied in this articlebelong to the 24 flash-flood cases from Spain, France, Italy, Austria,Greece and UK that were documented in the HYDRATE project. Thefourth event (24 November 2002), corresponding to a less extremecase, is included to highlight the differences between extreme andmore current situations.

Description of the radar data processing method

In ‘‘regionalised and adaptive radar data processing for hydrol-ogy”, we will first briefly review the TRADHy radar data processingsystem. Delrieu et al. (2009) give a detailed description of the var-ious algorithms and a comparative assessment of several non-adaptive, time-adaptive and space–time adaptive radar data strat-egies based on the datasets collected during the Bollène 2002experiment. An in-depth analysis of radar QPE errors with refer-ence to the CVMHO raingauge datasets is presented in a compan-ion paper (Kirstetter et al., this issue) to initiate work on an errormodel for the Bollène radar. Some adaptation of TRADHy has beennecessary to reach the objectives of the present study dedicated tothe processing of extreme rainfall events, wherever they occur.This will be described in ‘‘proposed adaptations in the context offlash-flood post-event analysis”.

Regionalised and adaptive radar data processing for hydrology

The TRADHy processing system is focused on radar QPE fromnon-coherent volume scanning radar data. Initially developed fornon-attenuating radars, it consists of four steps:

(1) Pre-processing: The pre-processing step is aimed at checkingradar calibration stability, characterising dry-weather clut-ter and determining beam blockage for all elevation angles(Delrieu et al., 1995).

(2) Clutter and rain type identification: During the course of a rainevent, identification techniques are implemented to dynam-ically determine clutter on the one hand, and rain typesalong with the corresponding vertical profiles of reflectivity

Please cite this article in press as: Bouilloud, L., et al. Radar rainfall estimation idoi:10.1016/j.jhydrol.2010.02.035

(VPR) on the other. In the context of the Bollène 2002 exper-iment, clutter identification was based on a pulse-to-pulsereflectivity variability criterion used in sinergy with dry-weather clutter data. Regarding the identification of raintypes, variants of the algorithms by Steiner et al. (1995)and Sanchez-Diezma et al. (2000) are used to determine con-vective and widespread (stratiform) rainfall, respectively.

(3) Reflectivity correction: Cluttered pixels are then corrected byrefined interpolation techniques and correction factor mapsare plotted for each elevation angle to correct for range-dependent error sources such as beam blockage, VPR inte-gration within the radar resolution volume and conversionof the reflectivity measured aloft into its counterpart atground level.

(4) Rainrate estimation: Rainfall estimation at ground level isfinally performed by first computing a weighted average ofthe corrected reflectivities for the various available elevationangles, the weights depending on the correction factor val-ues. The reflectivities are then converted into rainratesand, finally, an advection scheme based on a simple cross-correlation technique is applied to account for the discretetime sampling and smooth the cumulated rain fields.

Rain typing may or may not be accounted for in steps 3 and 4 byconsidering that VPRs and reflectivity–rainrate relationships (Z–Rrelationships) are conditional or not on the rain types. The mainparameters to be specified are: (1) an eventual radar electronic cal-ibration error and (2) the coefficients of the Z–R relationship(s),with Z ¼ aiR

bi ; i denoting a given rain type. Other parameters (e.g.reflectivity thresholds in the rain typing identification, data andparameter variances and covariances in the VPR identification,weights of the mean reflectivity value estimated at ground level)likely affect the performance of the identification, correction andestimation procedures, however they were dealt with during thedevelopment and testing of the algorithms and we assume theyare fixed for the purposes of the present study.

Two alternative approaches could be used for the specifica-tion of the main parameters (radar calibration error and Z–Rrelationships coefficients). A physically-based approach wouldrequire the highest possible accuracy in radar calibration anduse dropsize distribution measurements to define Z–R relation-ships representative of the rainfall climatology of the region ofinterest. On the other hand, an optimisation-based approachwould favour optimisation of the set of parameters using directrainfall measurements at ground level provided by raingaugenetworks (e.g. Seo et al., 2000; Dinku et al., 2002). In standardpractice, a simpler solution is often implemented with the a pri-ori choice of Z–R relationship(s) from the literature and estima-tion of a ‘‘mean field bias” (MFB) from radar–raingaugecomparisons aimed at compensating for the radar calibration er-ror and partly for Z–R relationship mis-specification, and eventu-ally their variation in time (Smith and Krajewski, 1991). In suchan approach, it is implicitly assumed that range-dependent er-rors are negligible or have been previously corrected. Determin-istic (e.g. Brandes, 1975) or geostatistical (e.g. Krajewski, 1987;Creutin et al., 1988; Velasco-Forero et al., 2009) merging tech-niques have also been proposed for spatially-variable adjust-ments of the radar QPE fields. Although based on the sametype of information, such a merging approach inherently differsfrom the optimisation-based approach since it is not used toparameterise the radar data processing system but rather to ob-tain an effective solution. All these parameterisation and merg-ing techniques have their own merits and limitations due tothe high rainfall space–time variability, instrumental errors andsampling properties of the sensors used, as well as the datasetsavailable in a given context.



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Proposed adaptations in the context of flash-flood post-event analysis

With respect to the TRADHy processing strategy summarised inthe previous subsection, the following adaptations are proposed inthe context of flash-flood post-event radar QPE analysis.

A first difference lies in the fact we are interested in a particularevent, generally extreme, that occurred at a given location. Radarprocessing must therefore start with the collation of data fromthe existing radar(s), including the metadata (parameters, operat-ing protocols, description of the raw data and/or the elaboratedproducts, maintenance operations, etc.). When possible, raw datawithout clutter filtering should be collected, including measure-ment periods prior to and after the rain event, to characterisedry-weather noise and the radar signal stability. For radar operat-ing at attenuating frequencies, rainfall attenuation effects can alsobe detected and quantified during the course of the rain event withsuch ground-cluttered data (Bouilloud et al., 2009). Ground clutteris also useful to check the radar antenna positioning and other pos-sible geographical errors by comparing observations and simula-tions based on the use of digital terrain models.

The clutter, rain type and VPR identification step depends onthe radar datasets available. Concerning clutter, filters based ondifferent principles are now generally implemented in modern ra-dar systems. Residual clutter may however remain, in particular atthe edge of permanent ground-cluttered regions. We propose tosimply test the clutter filter efficiency by cumulating radar prod-ucts at the event time scale. A simple procedure, based on rainfallgradient thresholding, has been developed to detect residual clut-ter. Concerning the identification of rain types and VPRs, little can

Fig. 1. Location of the CVMHO window, a region of 32,000 km2 in south-eastern France (tevent time scale for the 8–9 September 2002 (bottom left) and 24 November 2002 (bottavailable raingauges (+) and location of the Bollène radar with 50 km range markers are


be done without volume scanning radar data. Note however thatthe Steiner algorithm (Steiner et al., 1995) can be applied to detectconvection in single elevation radar measurements. Regarding VPR,we will define and test ‘‘idealised VPRs” in the following sections,for cases where the vertical profile of reflectivity cannot be inferredfrom radar data.

Once the beam blockages have been determined and the VPRs(either inferred or idealised) specified, we can proceed with TRAD-Hy step 3 to produce correction factor maps for each elevation an-gle to cope with the range-dependent errors. Depending on theavailable information on the VPRs, such correction factor mapsmay be static (one specific VPR for the entire rain event), time-adaptive (one specific VPR for each time step) or space–time adap-tive (with several specific rain-typed VPRs for each time step andthe need to account for the rain-typed regions identified for eachtime step).

In terms of parameterisation of the radar data processing (step4), we opt for an optimisation-based approach aimed at defining asingle effective Z–R relationship by comparing the radar andraingauge rain amounts at the event time scale in the region hitby the rain event. The term ‘‘single” is used since we will not tryhere, for the sake of simplicity, to optimise rain-typed Z–R relation-ships, even when we use rain-typed VPRs. The term ‘‘effective” re-fers to the fact that such Z–R relationship will compensate in partfor various error sources, e.g. radar calibration and eventuallyrange-dependent error sources. The event time step was chosenfor two reasons. First, as already mentioned, raingauge data aregenerally available for flash-flood events at this time step whileraingauge time series are much rarer. Second, unbiased rainfall

op) and rainfall amounts derived from the raingauge network through kriging at theom right) rain events. The rainfall isolines (thick black curves) are rated in mm. The

indicated. The thin grey curves represent terrain contours with 500 m intervals.




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volumes at the event time step are a critical requirement forhydrological applications to work.

Illustration and sensitivity study based on two well-documented intense rain events

Selected rain events

Details concerning the region of interest, the available hydro-meteorological observation systems and the rain events ob-served in recent years in the CVMHO pilot site can be foundin Delrieu et al. (2005, 2009), and Bonnifait et al. (2009). We

Fig. 2. Vertical profiles of reflectivity (VPR) identified from volume radar data for the 8–9the grey curves correspond to individual VPRs identified for a given time step using a mothe rain event and the dashed curves are the 10% and 90% quantiles of the VPR distribuseparation) while the middle and right graphs correspond to VPRs identified for the convof reflectivity” for details) are represented by the thick black dash-dotted lines on the le


simply recall here that the Bollène radar system (Fig. 1) is partof the French ARAMIS weather radar network. It is an S-bandradar system with a 6.2 m antenna (beamwidth of 1.28� at halfpower). At the time of the Bollène 2002 experiment, it wasoperated with a volume scanning protocol that included eightplan-position indicators (PPI) every 5 min with the followingalternated cycles:

Cycle 1: Elevation angles of 0.4�, 14.0�, 9.0�, 6.0�, 3.6�, 1.8�, 1.2�,and 0.8�.Cycle 2: Elevation angles of 17.0�, 11.0�, 7.2�, 4.8�, 2.4�, 1.8�,1.2�, and 0.8�.

September 2002 (top) and 24 November 2002 (bottom) rain events. For each graph,ving time window of 1 h; the black continuous curve represents the median VPR fortion. The left graphs correspond to VPRs estimated globally (i.e. without rain typeective and stratiform regions, respectively. The idealised VPRs (see ‘‘vertical profilesft graphs.




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Due to the vulnerability of the region to intense rain events, theraingauge networks are particularly dense over the CVMHO win-dow (area of 32,000 km2) with 250 hourly raingauges (density ofapproximately 128 km�2) and 160 additional daily raingauges(resulting in a density of about 78 km�2 at the daily time step).The CVMHO team critically analyses raingauge datasets using ageostatistical data quality control technique (Kirstetter et al., thisissue). The raingauge rainfall maps displayed in Fig. 1 were estab-lished using the anisotropic kriging technique.

The two selected events occurred under southern meteorologi-cal conditions leading to the advection of Mediterranean hot andhumid air masses over land. The 8–9 September 2002 event wasa V-shape mesoscale convective system (MCS) that remained sta-tionary for about 28 h over the Gard plains (south-eastern part ofthe CVHMO window). This deep-convective event produced oneof the most devastating floods ever occurring in France with 24casualties and economic damage evaluated at 1.2 billions Euros.Rainfall amounts reached 700 mm at certain locations and ex-ceeded 100 mm and 200 mm over areas of about 9000 and

Fig. 3. Examples of correction factor maps for range-dependent errors for the 24 Novembmeasured reflectivities expressed in mm6 m�3. The maps are plotted for the 0.8� elevationwith �2 dB km�1 slope, and (d) idealised VPR with �8 dB km�1 slope.


6000 km2, respectively. The Bollène radar observation conditionswere good since the event occurred within the 100 km range in arelatively flat region (range of altitudes: 50–300 m ASL). The 24November 2002 event is more typical of the so-called ‘‘pluiescévenoles” (Cévennes rainfall events) characterised by orographicforcing of Mediterranean air masses, resulting in shallow convec-tive and widespread rainfall with moderate intensity but longduration over the Cévennes mountain ridge. For this case, the totalrain amounts are not particularly remarkable for the region(150 mm in 18 h) but this event is of interest in relation to itsmeteorological features (shallow convection in a mountainous set-ting) and the radar observation conditions (radar range between 50and 120 km and altitude range from 200 to 1700 m ASL).

Vertical profiles of reflectivity

Fig. 2 displays the normalised VPRs that were identified fromthe available volume radar data (Delrieu et al., 2009). We focushereafter on the analysis of the shapes of the VPRs identified at

er 2002 case. The correction factors are multiplicative terms (dimensionless) for theangle for four VPRs: (a) median convective, (b) median stratiform, (c) idealised VPR




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each time step globally over the CVMHO window, and for the con-vective and stratiform regions identified with the rain-typing algo-rithms. The vertical extension of the 8–9 September 2002 event isnoteworthy, in comparison with the 24 November 2002 event, forboth the convective and stratiform regions. The MCS convectiveVPRs display a gradient ranging between �2.5 and �4.5 dB/kmabove 3 km MSL. The stratiform VPR revealed a bright band alti-tude of 3.2 km and a peak of about 5 dB as well as a gradient of�2.5 dB/km above 5 km MSL. The VPRs decrease much faster as afunction of altitude for the 24 November 2002 case, e.g. with gra-dients between �3.5 and �7 dB/km for the convective VPRs above2.5 km ASL. The shapes of the convective and stratiform VPRs areclearly distinct for each single rain event and the global VPR liesbetween the two. The identified bright band altitudes are consis-tent with the available radio soundings since the 0 �C isothermwas positioned at an average altitude of 3300 m ASL for the Sep-tember case and 2500 m ASL for the November case. Note also thatthe spread of VPR distributions is rather limited for each rain event,indicating that the mean VPR time variability remains relativelylow. In addition, erratic individual VPRs are visible (e.g. for the con-vective and stratiform inversions for the November 2002 rainevent) as a result of insufficient data information for the consid-ered time steps. For these reasons, we have decided to work withthe median profiles in the following simulations instead of thetime-adaptive VPRs.

We have also defined idealised VPRs to simulate the situation inwhich the VPRs could not be inferred from radar data. For this pur-pose, we assume that the major contribution to the total rainamounts is associated with convection. We subsequently chooseto neglect the possible radar QPE overestimations associated withbright bands by considering idealised VPRs without bright bands.We use the average 0 �C isotherm altitude available from sound-ings and we assume the normalised VPR to be equal to 1 (or0 dB) below the 0 �C isotherm and to evolve linearly (in dB values)as a function of altitude above the 0 �C isotherm. For both rainevents, we consider hereafter two extreme altitude gradients of�2 and �8 dB/km corresponding to high and low vertical exten-sion of the precipitating clouds above the 0 �C isotherm, respec-tively (see Fig. 2, left graphs).

Correction maps for range-dependent errors

Fig. 3 provides examples of correction factor maps to be appliedto measured reflectivities to cope with the combined effects ofbeam blockages and VPR and estimate the reflectivity at ground le-vel. Pellarin et al. (2002) provide details concerning the correctionfactor expression and its numerical evaluation. The maps are plot-ted for one of the lowest elevation angles (0.8�) in order to showthe impact of beam blockages on such correction factors. Beamblockages also affect the 1.2� elevation angle but not the upper ele-vation angles (1.8� and greater). The two maps on the top of Fig. 3are established with the median convective (a) and stratiform (b)VPRs for the 24 November 2002 case. The correction factors forthe convective VPR increase regularly from 1 to 4 (correspondingto additive corrections of 0–6 dBZ) in the south-west quadrant asthe result of the VPR decrease with altitude. In the north-westquadrant, the correction factors account in addition for the powerloss due to the beam blockages. The bright band strongly influ-ences the stratiform correction factor map (Fig. 3b) with values<1 between ranges 25 and 125 km and minimum values of about0.4 at 80 km for the 0.8� elevation angle. At this point, it may beuseful to clarify how the correction works when rain typing is ac-counted for. For a given time step, pixel and elevation angle, welook in the rain type map established for the considered time stepand then simply multiply the measured reflectivity value by therain-typed dependent correction factor calculated for the consid-


ered elevation angle. Fig. 3c and d displays the correction factormaps corresponding to the 24 November 2002 idealised VPRs with�2 and �8 dB km�1 slopes, respectively. The convective VPR cor-rection factor map (Fig. 3a) lies between the two idealised VPR cor-rection maps, but is closer to the �8 dB km�1 case for this shallowconvective event.

Optimising an effective Z–R relationship with raingauge data

Principle and example of resultsRather than directly implementing an optimisation technique,

we explore hereafter the parameter space defined by the two coef-ficients of the Z–R relationship. The parameter range consideredextends from 25 to 600 for the prefactor a (with an incrementalstep of 25) and from 1 to 2 for the exponent b (with an incrementalstep of 0.05), including the range of physical values reported in theliterature (e.g. Battan, 1973; Steiner et al., 2004). For the assess-ment, the reference values are the raingauge kriged values forthe 1-km2 radar pixels containing at least one raingauge (Kirstetteret al., this issue). For the optimisation, we choose to use raingaugemeasurements at the event time step for domains encompassingthe hit region. Three classical assessment criteria are considered,i.e. the mean error (ME ¼ R� G, where R and G denote the mean ra-dar and raingauge values, respectively), the determination coeffi-cient (square of the correlation coefficient, representing thepercentage of variance explained by the linear regression) andthe Nash criterion ðN ¼ 1� EðG� RÞ2=EðG� GÞ2Þ. The Nash crite-rion is sensitive to both bias and scatter, and as such summarisesthe two other criteria.

Fig. 4 illustrates the results obtained for the two rain eventswhen the rain-typed VPRs are considered for the derivation ofthe correction factor maps and all the elevation angles are usedfor the estimation of the reflectivity at ground level. In terms ofbias, note that the mean error evolves as a hyperbolic curve inthe (a and b) space, separating regions of mean radar overestima-tion (low a and low b values) and radar underestimation (high aand high b values). Being insensitive to linear transformations,the determination coefficient does not depend on the prefactor a.Note that this coefficient varies only slightly as a function of bfor the 8–9 September 2002 event (between 0.87 and 0.93) and sig-nificantly more for the 24 November 2002 event (between 0.60and 0.84), increasing with b for both events. The Nash isolinesare organised around the 0 ME curve. The performance obtainedfor the 8–9 September 2002 event is superior to that of the 24November 2002 case, both in terms of determination coefficientand Nash coefficient. This is related to the observation conditionswhich are much favourable for the 8–9 September 2002 event.Interestingly, these figures indicate the existence of a series of (aand b) coefficients providing optimal results in terms of Nash coef-ficient. For instance, the Z–R relationships Z = 75R1.75 andZ = 250R1.4 are equifinal with a Nash coefficient of 0.91 for the 8–9 September 2002 case. The 0.85 Nash coefficient isoline crossesthe entire range of physically plausible (a and b) values. For the24 November 2002 event, the so-called ‘‘equifinality pattern” interms of Nash coefficient is shifted towards higher and less physi-cal b values (from 1.45 up to 2 for the 0.75 Nash coefficient isoline).Such equifinality properties have already been described for rain-fall retrieval at attenuating frequencies in spaceborne (Haddadet al., 1995) and ground-based (Delrieu et al., 1999) radar configu-rations. To further investigate this point, Fig. 5 presents the scatter-plots associated with the two equifinal Z–R relationshipsmentioned above for the 8–9 September 2002 case. It is clear fromthese graphs that, although equivalent in terms of Nash coefficient(0.91) as well as in terms of mean error (+9.1 and +9.4 mm) anddetermination coefficient (0.926 and 0.913), the two results arenot similar with a significant underestimation of the rain amounts



Fig. 4. Radar–raingauge assessment criteria as a function of the Z–R relationshipcoefficients for the 8–9 September 2002 (top) and the 24 November 2002 (bottom)rain events. The mean error (in mm) is represented by the thick black isolines. Thedotted lines parallel to the a-axis are the determination coefficient isolines. TheNash coefficient values are represented by the thin black isolines. The VPRs used inthe simulation are the rain-typed VPRs. All the elevation angles are accounted for inthe rainrate estimation at ground level.

Fig. 5. Scatterplots of two equifinal Z–R relationship parameterisations in terms ofNash coefficient (0.91) for the 8–9 September 2002 event with Z = 75R1.75 (top) andZ = 250R1.4 (bottom). The linear regression (radar vs. raingauge) is displayed by thedashed line, the additive conditional bias calculated for several rain amount classes(see text for details) by the black dots and the one-to-one line by the black line.


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>450 mm for the Z = 75R1.75 relationship (Fig. 5a). From the hydro-logical point of view, such underestimations of the highest rainfallvolumes are not acceptable. In an attempt to discriminate betweenthe Nash equifinal relationships, we thus considered an additionalcriterion proposed by Ciach et al. (2000), the so-called ‘‘total addi-tive conditional bias”, defined as:

CBtot ¼ VarðCBaðgÞÞ ð1Þ

where CBa(g) is the radar additive conditional bias for a givenraingauge rain amount g:

CBaðgÞ ¼ EðRjG ¼ gÞ � g ð2Þ

The additive conditional bias, displayed in Fig. 5, confirms thepotential of this criterion to detect the underestimation of thehighest rain amounts in Fig. 5a. Examples of the evolution of theCBtot criterion are displayed together with the Nash criterion inFig. 6 for the 8–9 September 2002 and the simulation conditionsof Fig. 5. As expected, the CBtot criterion is slightly inferior for thecase corresponding to Fig. 5b; however, the CBtot criterion has avery large amplitude of variation making it a difficult criterion tomap, even if transformed into dB values as in Fig. 6. Consequently,we recommend using first the Nash criterion and then refining theanalysis with the total additive conditional bias.


Dependency on the VPRs and the availability of volume dataIn this section, we propose to test the dependency of the opti-

misation procedure on the VPRs and on the number of elevationangles used for the estimation of the reflectivity at ground level.We have implemented the optimisation procedure for five cases:(1) use of the rain-typed VPRs (the median convective and strati-form VPRs for all time steps, as in previous section); (2) use ofthe global VPRs (the median global VPR for all time steps); (3)use of the idealised VPR with low vertical extension (slope of�8 dB km�1); (4) use of the idealised VPR with high vertical exten-sion (slope of �2 dB km�1); and finally (5) the case without VPRcorrection. Concerning estimation of the reflectivity at ground le-vel, we consider all the available elevation angles (8 in 5 min) forthe first two cases and only one elevation angle (1.8�) for the lastthree cases corresponding to the idealised VPRs and the case with-out VPR correction. Doing so, the last three cases are simulated forthe situation with poor data availability since we assume no vol-ume data for the VPR inference and only one elevation angle everyfive 5-min. Although somewhat ‘‘extreme” with respect to current



Fig. 6. The total additive conditional bias and the Nash coefficient as a function ofb for two values of the Z–R relationship prefactor: (a) a = 75 and (b) a = 250, for the8–9 September 2002 rain event and the simulation conditions of Fig. 5.

Fig. 7. Equifinality patterns of the Z–R relationship optimisation for the (a) 8–9September 2002 and (b) 24 November 2002 rain events for various VPRs and use ofvolume information in the rainrate estimation at ground level (see ‘‘dependency onthe VPRs and the availability of volume data”). The values of the displayed isolinesare indicated in the legend. They correspond to the maximum Nash value in the (aand b) space �0.05. For instance, in (b), for the idealised VPR with �2 dB km�1

slope, ‘‘Nash = 0.73” in the legend means that the represented isoline is for a Nashcoefficient of 0.73 and that the maximum Nash value in the (a and b) space is equalto 0.78.


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practice in operational radar networks, this situation is representa-tive for several events collected during the HYDRATE project and,for instance, for the two events presented in ‘‘Application of themethodology to two other historical flash-flood events”.

The results are displayed in Fig. 7. For each case, we restrict thedisplay of the equifinality patterns to one particular Nash isolinecorresponding to the maximum Nash value observed in the (aand b) space minus 0.05. For the 8–9 September 2002 case, the ob-served equifinality patterns are quite well superimposed. The max-imum Nash criterion is 0.92, 0.91, 0.86, 0.88, and 0.87 for the fivecases listed above, respectively This means that, for this event,(1) the rain-typing VPRs only bring a slight (if any) advantage overthe global VPRs and (2) performance for the cases with idealisedVPRs or with no VPR correction and a single elevation angle is alsovery good. These two results, plus the fact that the equifinality pat-terns remain similar, can be explained by the high vertical exten-sion of this event and the very good observation conditions ofthe Bollène radar. Actually, the radar observations were mostlymade below the 0 �C isotherm at 3300 m ASL, explaining the smallinfluence of the upper part of the VPR, including the bright bandeffect in the stratiform (and less intense) rainfall. The small de-crease between the rain-typed or global VPR cases and the otherthree cases may even be due to the reduced time sampling (one va-lue in 5 min instead of eight values in 5 min) rather than to the VPRinfluence.

The results obtained for the 24 November 2002 event are alsoon interest: (1) the performance is lower for this event and themaximum Nash coefficients are 0.80, 0.84, 0.82, 0.78, and 0.69for the five cases, respectively and (2) the equifinality patternsare very different from one case to the next. Looking closer, wenote the performance obtained for the rain-typed VPRs to be signif-icantly lower than with the global VPRs. Note also that the equifi-


nality pattern is narrower for the rain-typed VPRs and the twopatterns are significantly shifted in the (a and b) space. This inferi-ority of the rain-typing VPR case was already explained in Delrieuet al. (2009) by the influence of the sampling limitations on therain-typing algorithms in the mountainous part of the CVMHOwindow for such shallow convective events. The performance ob-tained with the idealised VPRs is just below that of the globalVPR, however with a significant shift of the equifinality pattern to-wards higher a and b values for the �8 dB km�1 VPR and a nar-rower equifinality pattern for the �2 dB km�1 VPR. Note that theperformance obtained with no VPR correction is significantly infe-rior (Nash coefficient of 0.69; narrow equifinality pattern), indicat-ing the importance of the VPR correction in that case.

Dependency on the accumulation time stepKrajewski and Smith (2002) evoke the possible time-scale

dependency of the Z–R relationship optimisation. Due to the prob-lem of raingauge data availability for flash-flood QPE, this could bean important limitation for the proposed method. Given the rela-tively dense raingauge network available at the hourly time stepfor the CVMHO, it was possible to investigate this critical point.



Fig. 8. Influence of the accumulation time step on the Z–R relationship optimisationslope for the (a) 8–9 September 2002 and (b) 24 November 2002 rain events. Theequifinality patterns are displayed with the same convention as in Fig. 7. Theidealised VPRs with �2 dB km�1 slope were used. The isocontours refer to the 1-h(grey), 6-h (dotted), 12-h (dashed) and event (continuous black curve) time scales,respectively.


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A new set of optimisations was thus produced with reference toraingauge rain amounts at the 1-h, 6-h and 12-h time steps.Fig. 8 displays an example of the results obtained for the two rain

Table 1Main parameters of the radar systems and other relevant parameters for the application o

Nîmes radar

Geographical coordinates X = 774.46 kmExtended Lambert 2 for X and Y Y = 1869.66 km

Z = 76 m ASLWavelength (cm) 10.714 (S-band)3 dB beamwidth (�) 1.8‘‘Pseudo-CAPPI” scanning protocol Revisit time of 5 min

Elevation angles and range o2.5�; 0–22 km1.3�; 22–80 km0.6�; 80–253 km

Avène case:Radar–rain event distance About 50 kmMean 0 �C isotherm altitude 3700 m ASLBeam blockages (percent of screened energy) Between 3% and 10% for theAude case:Radar–rain event distance Between 150 and 220 kmMean 0 �C isotherm altitude 2400 m ASLBeam blockages (percent of screened energy) Between 15% and 25% for the


events using the idealised VPR with the �2 dB km�1 slope, repre-sentative for all the other studied VPR cases. As expected, the max-imum Nash coefficient tends to decrease with the time step with atypical drop of 10 points between the event and the hourly timestep. The equifinality patterns grow as the time step decreasesand progressively shift towards higher a-values. However, theevent time step equifinality pattern remains included in the otherpatterns, indicating the possibility of obtaining near-optimal Z–Rrelationships at all scales from the event time step optimisation.

Application of the methodology to two other historical flash-flood events

In addition to the 8–9 September 2002 event, two other histor-ical flash-flood cases in France were re-analysed within this work.These events occurred in 1997 and 1999. At that time, the ARAMISnetwork was not as dense as today (five radars have been set up inthe French Mediterranean region since then). Operation was lim-ited to 2 or 3 elevation angles every 5 min and the archived prod-ucts are pseudo-CAPPI composites (Table 1). Therefore, for eachsingle pixel, there is only one reflectivity measurement archivedevery 5 min. In terms of basic processing, we checked the collectedradar datasets for residual ground clutter according to the proce-dure described in ‘‘Proposed adaptations in the context of flash-flood post-event analysis”.

The first event, known as the Avène event, was described byGaume et al. (2003). It occurred in the CVMHO window on 6–7October 1997. The elongated watershed (57 km2) of the Avène, aleft bank tributary of the Gardon river (Fig. 9), experienced thatday a flash-flood with a peak discharge estimated between 600and 900 m3 s�1, i.e. a peak specific discharge of between 10 and15 m3 s�1 km�2. The causative rainfall was estimated to be greaterthan 300 mm falling in a period of about 6 h in the downstreampart of the watershed. The rain event was highly localised with atriangular shape typical of the mesoscale convective systemsaffecting the Mediterranean regions (Fig. 9a). The operationalraingauge network ‘‘missed” the core of the rainfall event. At thattime, the closest radar was the S-band Nîmes radar of theMétéo–France network (Table 1). The observation conditions weregood with a radar-catchment range of about 50 km, limited beamblockages for the available elevation angle (1.3�) and a high alti-tude for the 0 �C isotherm (3700 m ASL). In addition to the Z–Rrelationship, we tried to optimise the slope of the VPR above the0 �C isotherm, using both the Nash and the total additive condi-

f the radar QPE method to the Avène and Aude cases.

Toulouse radar

X = 522.39 kmY = 1842.03 kmZ = 179 m ASL5.357 (C-band)1.3Revisit time of 5 min

f distances: Elevation angles and range of distances:1.4�; 0–40 km0.8�; 40–253 km

1.3� elevation angle

Between 80 and 170 km

0.6� elevation angle Between 1% and 15% for the 0.8� elevation angle




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tional bias. As expected the VPR slope had no influence on the re-sults, due to the high altitude of the 0 �C isotherm and the shortdistance between the radar and the rainfall event. In addition tothe obtained radar QPE map, Fig. 9 displays the radar–raingaugescattergraph for the selected Z–R relationship (Z = 150R1.40) witha Nash coefficient value of 0.73 over the 34 comparison pairs.

The second event, known as the Aude event, was described byDucrocq et al. (2003), and Gaume et al. (2004). Like the 8–9 Sep-tember 2002 Gard case, the Aude event is a spatially extensiveevent reaching rain amounts of 700 mm in 48 h and exceeding300 mm over an area of about 2500 km2 for the domain presentedin Fig. 10a. This event led to severe flash-floods in the upstreamwatersheds of the hit region and an extensive flood of the Aude riv-er. The event was observed with two radars of the ARAMIS network(Table 1). The first radar was again the S-band Nîmes radar. For theelevation angle (0.6�) available for the considered range of dis-tances (80–253 km), the inherent (the 3 dB beamwidth is 1.8�)beam blockages were aggravated in the south part of the regionof interest by small hills located in the vicinity of the radar site.In addition, the range of distances of the rain event with respectto the radar site (150–220 km) and the low altitude of the 0 �C iso-therm (2400 m ASL) represent poor observation conditions for thisevent. Attempts to establish correction factor maps led to very high

Fig. 10. The 12–13 November 1999 case: (a) radar QPE at the event time scale deriveraingauge scatterplot for the chosen optimal Z–R relationship with the radar vs. raingau

Fig. 9. The 6–7 October 1997 Avène flash-flood case: (a) radar QPE at the event time scalthick black contour) and (b) radar–raingauge scatterplot for the chosen optimal Z–R rela(black dots).


correction factors (>20) over most of the hit region and very poorassessment results (negative Nash coefficients), indicating that ra-dar QPE for this event is not feasible with this radar. The second ra-dar was the Toulouse radar (Table 1), with significant beamblockages in the north part of the hit region due to the mountaincalled Montagne Noire. The range of distances between the radarand the hit region (80–170 km) and the low altitude of the 0 �C iso-therm (2400 m ASL) represent observation conditions only slightlybetter than those of the Nîmes radar. A further complication is re-lated to the C-band frequency used by the Toulouse radar which islikely to be severely attenuated in heavy rainfall. Bouilloud et al.(2009) recently proposed a radar QPE study for an intense rainfallevent observed with a C-band radar in Slovenia. They applied theso-called Mountain Reference Technique, based on the estimationof path-integrated attenuation (PIA) from mountain returns, toconstrain forward attenuation correction schemes, known to bevery unstable if not carefully controlled. Due to the lack of appro-priate data (nonclutter-filtered radar data), this method is notapplicable for the Aude event. However, we used one of the obser-vations made in their article (their Fig. 5), i.e. that the attenuationcorrection slightly modifies (increases to be more precise) theslope of the inferred VPR above the 0 �C isotherm. Besides the Z–R relationship, we therefore also optimised the slope of the VPR

d from the proposed methodology with the toulouse radar dataset and (b) radar–ge linear regression line and the conditional bias (black dots).

e derived from the proposed methodology (the hit watershed is delineated with thetionship with the radar vs. raingauge linear regression line and the conditional bias




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for this particular case. Optimal values of �6 dB km�1 andZ = 100R1.8 were found for the VPR slope and Z–R relationship coef-ficients, resulting in a Nash coefficient of 0.70 for the radar–rainga-uge comparison at the event time scale (Fig. 9b).

Summary and conclusions

We have presented a method for radar rainfall estimation in thecontext of post-event analysis of flash-flood events. This pragmaticapproach is based on a careful analysis of the observation condi-tions for the radar system(s) available for the considered case.The interactions between the radar waves and the relief are char-acterised thanks to dry-weather observations and simulationsbased on a digital terrain model of the region of interest. The ver-tical profile of reflectivity is either inferred from radar data if vol-ume scanning data are available or simply defined with the 0 �Cisotherm altitude and the slope of the VPR above the 0 �C isotherm.In the first case (inferred VPRs), we distinguish rain-typed VPRsand VPRs inferred globally over the detection domain. For the lattercase (idealised VPRs), we derived extreme VPR slope values of�2 dB km�1 and �8 dB km�1 from observations.

Such information is then used to produce correction factormaps for each elevation angle to correct for range-dependent er-rors and estimate the reflectivity close to ground level from thereflectivities measured aloft. In a second step, rather than applyinga radar–raingauge merging technique, we optimise an effective Z–R relationship with reference to raingauge rain amounts measuredat the event time scale over the hit region. This procedure is aimedat ensuring that the radar QPE estimates are unbiased at the eventtime scale, a basic condition for hydrological applications.

The sensitivity tests performed with two well-documented rainevents occurring within the CVMHO window show that there ex-ists a number of Z–R relationships, organised along hyperboliccurves in the (a and b) parameter space, that lead to optimumassessment results in terms of Nash coefficient. Refining the anal-ysis of these equifinality patterns, we observe that the ‘‘total addi-tive conditional bias” can be used to discriminate between theseequifinal solutions. Next, comparing optimisations with variousways of specifying the VPRs (including the case with no VPR cor-rection), we observe that the results are sensitive to the VPRdescription and also that the Z–R optimisation procedure can lar-gely compensate for such range-dependent errors, although thisshifts the optimal coefficients in the (a and b) parameter space.The time-scale dependency of the equifinality patterns was shownto be significant. However, the event time step equifinality patternfortunately remains included in the other patterns, indicating thepossibility of obtaining near-optimal Z–R relationships at all timescales from the event time step optimisation. Besides the practicaladvantages of the method, which was applied in ‘‘application of themethodology to two other historical flash-flood events” to twoother events of the HYDRATE database, we believe this optimisa-tion–based approach to be complementary to the physical ap-proaches based on the characterisation of the drop sizedistribution (e.g. Hazenberg et al., 2009).

Acknowledgements

We would like to thank the two anonymous reviewers for theirvaluable comments. This study was funded by the HYDRATE pro-ject of the European Community (GOCE 037024).

References

Battan, L.J., 1973. Radar Observation of the Atmosphere. The University of ChicagoPress. 324 p..


Berne, A., Delrieu, G., Creutin, J.D., Obled, C., 2004. Temporal and spatial resolutionof rainfall measurements required for urban hydrology. Journal of Hydrology299, 166–179.

Bonnifait, L., Delrieu, G., Le Lay, M., Boudevillain, B., Masson, A., Belleudy, P., Gaume,E., Saulnier, G.-M., 2009. Hydrologic and hydraulic distributed modelling withradar rainfall input: reconstruction of the 8–9 September 2002 catastrophicflood event in the Gard region, France. Advances in Water Resources 32, 1077–1089.

Bouilloud, L., Delrieu, G., Boudevillain, B., Borga, M., Zanon, F., 2009. Radar rainfallestimation for the post-event analysis of a Slovenian flash-flood case:application of the Mountain Reference Technique at C-band frequency.Hydrological and Earth System Sciences 13, 1349–1360.

Brandes, E.A., 1975. Optimizing rainfall estimates with the aid of radar. Journal ofApplied Meteorology 14, 1339–1345.

Ciach, J.G., Morrissey, M.L., Krajewski, W.F., 2000. Conditional bias in radar rainfallestimation. Journal of Applied Meteorology 39, 1941–1946.

Creutin, J.D., Borga, M., 2003. Radar hydrology modifies the monitoring of flash floodhazard. Hydrological Processes 17, 1453–1456.

Creutin, J.D., Delrieu, G., Lebel, T., 1988. Rain measurement by raingauge-radarcombination: a geostatistical approach. Journal of Atmospheric and OceanicTechnology 5, 102–115.

Delrieu, G., Creutin, J.D., Andrieu, H., 1995. Simulation of radar mountain returnsusing a digitized terrain model. Journal of Atmospheric and Oceanic Technology12, 1038–1049.

Delrieu, G., Hucke, L., Creutin, J.D., 1999. Attenuation in rain for X- and C-bandweather radar systems: sensitivity with respect to the drop size distribution.Journal of Applied Meteorology 38, 57–68.

Delrieu, G., Ducrocq, V., Gaume, E., Nicol, J., Payrastre, O., Yates, E., Kirstetter, P.E.,Andrieu, H., Ayral, P.A., Bouvier, C., Creutin, J.D., Livet, M., Anquetin, S., Lang, M.,Neppel, L., Obled, C., Parent-du-Chatelet, J., Saulnier, G.M., Walpersdorf, A.,Wobrock, W., 2005. The catastrophic flash-flood event of 8–9 September 2002in the Gard region, France: a first case study for the Cevennes–VivaraisMediterranean Hydrometeorological Observatory. Journal of Hydrometeorology6, 34–52.

Delrieu, G., Boudevillain, B., Nicol, J., Chapon, B., Kirstetter, P.-E., Andrieu, H., Faure, D.,2009. Bollène 2002 experiment: radar rainfall estimation in the Cevennes–Vivarais region. Journal of Applied Meteorology and Climatology 48, 1422–1447.

Dinku, T., Anagnostou, E.N., Borga, M., 2002. Improving radar-based estimation ofrainfall over complex terrain. Journal of Applied Meteorology 41, 1163–1178.

Ducrocq, V., Aullo, G., Santurette, P., 2003. Les précipitations intenses et lesinondations des 12 et 13 novembre 1999 sur le sud de la France (the 12–13November 1999 intense precipitations and floods in southern France). LaMétéorologie 42, 18–27.

Gaume, E., Livet, M., Desbordes, M., 2003. Study of the hydrological processesduring the Avene river extraordinary flood (south of France): 6–7 October 1997.Physics and Chemistry of the Earth 28, 263–267.

Gaume, E., Livet, M., Desbordes, M., Villeneuve, J.-P., 2004. Hydrological analysis ofthe river Aude, France, flash flood on 12 and 13 November. Journal of Hydrology286, 135–154.

Haddad, Z.S., Eastwood, I., Durden, S.L., 1995. Intrinsic ambiguities in the retrieval ofrain rates from radar returns at attenuating wavelengths. Journal of AppliedMeteorology 34, 2667–2679.

Hazenberg, P., Yu, N., Boudevillain, B., Delrieu, G., Uijlenhoet, R., (2009). On thevariability of dropsize distributions for extreme precipitation events and theirconsequences on the Z–R relationships for the Cévennes–Vivarais region,France. Journal of Hydrology, (Unpubished manuscript).

Kirstetter, P.-E., Delrieu, G., Boudevillain, B., Obled, C., this issue. Toward an errormodel for radar quantitative precipitation estimation in the Cévennes–Vivaraisregion, France. Journal of Hydrology.

Krajewski, W.F., 1987. Cokriging radar–rainfall and rain gage data. Journal ofGeophysical Research 92 (D8), 9571–9580.

Krajewski, W.F., Smith, J.A., 2002. Radar hydrology–rainfall estimation. Advances inWater Resources 25, 1387–1394.

Pellarin, T., Delrieu, G., Saulnier, G.M., Andrieu, H., Vignal, B., Creutin, J.D., 2002.Hydrologic visibility of weather radar systems operating in mountainousregions: Case study for the Ardeche Catchment (France). Journal ofHydrometeorology 3, 539–555.

Sanchez-Diezma, R., Zawadzki, I., Sempere-Torres, D., 2000. Identification of thebright band through the analysis of volumetric radar data. Journal ofGeophysical Research – Atmospheres 105 (D2), 2225–2236.

Seo, D.-J., Breidenbach, J.P., Fulton, R.A., Miller, D.A., O’Bannon, T., 2000. Real-timeadjustment of range-dependent biases in WSR-88D rainfall estimates due tononuniform vertical profile of reflectivity. Journal of Hydrometeorology, 222–240.

Smith, J.A., Krajewski, W.F., 1991. Estimation of the mean field bias of radar rainfallestimates. Journal of Applied Meteorology 30 (4), 397–412.

Steiner, M., Houze, R.A., Yuter, S.E., 1995. Characterization of three-dimensionalstorm structure from operational radar and rain gauge data. Journal of AppliedMeteorology 34, 1978–2007.

Steiner, M., Smith, J.A., Uijlenhoet, R., 2004. A microphysical interpretation of radarreflectivity–rainrate relationships. Journal of the Atmospheric Sciences 61,1114–1131.

Velasco-Forero, C.A., Sempere-Torres, D., Cassiraga, E.F., Gomez-Hernandez, J.J.,2009. A non-parametric automatic blending methodology to estimate rainfallfields from rain gauge and radar data. Advances in Water Resources 32 (7), 986–1002.



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