data quality of the meteo-france c-band polarimetric radar

Data Quality of the Meteo-France C-Band Polarimetric Radar

JONATHAN J. GOURLEY, PIERRE TABARY, AND JACQUES PARENT DU CHATELET

Direction des Systemes d’Observation, Meteo-France, Trappes, France

(Manuscript received 24 August 2005, in final form 2 February 2006)

ABSTRACT

The French operational radar network is being upgraded and expanded from 2002 to 2006 by Meteo-France in partnership with the French Ministry of the Environment. A detailed examination of the qualityof the raw polarimetric variables is reported here. The analysis procedures determine the precision of themeasurements and quantify errors resulting from miscalibration, near-radome interference, and noise ef-fects. Correction methods to remove biases resulting from effective noise powers in the horizontal andvertical channels, radar miscalibration, and the system offset in differential propagation phase measure-ments are presented and evaluated. Filtering methods were also required in order to remove azimuthaldependencies discovered with fields of differential reflectivity and differential propagation phase. Thedeveloped data quality analysis procedures may be useful to the agencies that are in the process of up-grading their radar networks with dual-polarization capabilities.

1. Introduction

a. Motivation

The Programme Aramis Nouvelles Technologie enHydrometeorologie Extension et Renouvellement(PANTHERE) project of Meteo-France (Parent et al.2003) seeks to improve the density of the French op-erational radar network, to replace old radars, and toconsider an upgrade to dual polarization. The Trappes,France, radar, situated approximately 30 km to thesouthwest of Paris, was equipped with dual-polarizationcapabilities in the spring of 2004 and continues to col-lect data in an operational setting. A specific goal of theproject is to assess the benefits to hydrology and mi-crophysical retrievals afforded by polarization diversityradar in midlatitudes within an operational context.Prior to the development of these quantitative precipi-tation estimation and particle typing algorithms, a rig-orous assessment of the accuracy and precision of eachvariable must proceed. This study identifies errorsources predominant at C band, many of which aredescribed in Keenan et al. (1998), quantifies their ef-fects in a statistically significant manner, and, in some

cases, presents techniques in order to correct for theresulting biases. The approach undertaken is generaland can be easily adapted to other polarized radar sys-tems. This is especially important to the many meteo-rological services that are currently upgrading their ra-dar networks with dual polarization.

b. Background

Biases in measured backscatter and propagationcharacteristics may result due to a variety of reasons.Measurements of differential reflectivity (ZDR) and co-planar cross-correlation coefficient at zero lag [�HV(0)]at low signal-to-noise ratios (SNRs) can be biased nega-tively or positively and expressions exist to correctthem (Liu et al. 1994). It has been shown that thesereceiver noise powers result in biases when the signalstrength is sufficiently low. In this study, the ratio ofeffective noise terms (i.e., those that are both internaland external to the radar system) is estimated and sub-sequently considered in the calculation of ZDR and�HV(0). A parameter describing the ratio of horizontal-to-vertical effective noise powers is optimized usingrainfall measurements at vertical incidence to effec-tively remove biases resulting from noise.

Backscattered reflectivity at horizontal polarization(ZH) and ZDR may be biased either positively or nega-tively due to radar miscalibration. Calibration errors inthe U.S. Weather Surveillance Radar-1998 Doppler

Corresponding author address: Dr. Jonathan J. Gourley, Na-tional Severe Storms Laboratory, 120 David L. Boren Blvd., Rm.4745, Norman, OK 73072.E-mail: [email protected]

1340 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 23

© 2006 American Meteorological Society

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(WSR-88D) network have been noted by several inves-tigators (Bolen and Chandrasekar 2000; Gourley et al.2003). While there is no universal method for radarcalibration (Atlas 2002), the dependence between po-larimetric variables may be used to improve the cali-bration of radar reflectivity (Goddard et al. 1994;Scarchilli et al. 1996; Gorgucci et al. 1999a; Illingworthand Blackman 2002; Ryzhkov et al. 2005). Reception ofsolar radiation and measurements from natural hy-drometeors can be used to calibrate ZDR in an absolutesense (Gorgucci et al. 1999a; Bringi and Chandrasekar2001; Ryzhkov et al. 2005). The differential propaga-tion phase (�DP) and �HV(0) are known to be immuneto radar calibration errors (Zrnic and Ryzhkov 1996).

Molecular absorption and scattering at C band by therain medium reduces the amount of backscattered en-ergy that reaches the radar. This process affects mea-sured ZH and ZDR by reducing their values with in-creasing range. Quantification of attenuation-relatederrors is beyond the scope of study regarding the qual-ity of raw polarimetric variables. Instead, we simplyrestrict our datasets to those that have low values of�DP where attenuation effects are negligible.

In this paper, we will isolate the effects of interfer-ence, system noise, and calibration. Then, we will quan-tify the impact of these errors on each relevant polari-metric variable. These observational errors will also becompared to theoretical expectations, where appli-cable. Section 2 provides operating characteristics ofthe Trappes radar and examines possible interferenceproblems on ZDR resulting from structures in the im-mediate vicinity of the radome. Section 3 reveals theimpact of system noise on ZDR and �HV(0). Section 4explores the calibration of ZH, ZDR, as well as the sys-tem offset of differential propagation phase measure-ments (�o) and aliased measurements. Estimates ofthe precision in differential phase (�DP) and ZDR mea-surements are provided in section 5, and a brief sum-mary follows. It is anticipated that this work may beused as a set of methodologies for other meteorologicalservices that are interested in data quality of their dual-polarization radars.

2. Trappes C-band polarimetric radar

a. Operating characteristics of the radar

A C-band Doppler weather radar system (type 510C)operates continuously as part of the French operationalradar network. The radar is equipped with linear po-larization capabilities in that it transmits horizontallyand vertically polarized waves. The two receiving chan-nels, which have nearly identical waveguide runs, op-

erate in parallel and thus enable the simultaneoustransmission and reception (STAR) mode of polarizedsignals. A diagram of the radar system is provided inFig. 1. A staggered pulse repetition time (PRT) schemewas developed for retrieving and dealiasing Dopplervelocities (Tabary et al. 2005). Technical details of theantenna, transmitter, receiver, and processor are pro-vided in Table 1.

The Trappes radar measures reflectivity at horizontalpolarization (ZH) defined as

ZH � 10 log10��|SHH|2��, �1�

where SHH (SVV) is the copolar horizontal (vertical)component of the backscatter amplitude. The innerbrackets indicate averaging across each ith independentsample in each 240 m � 0.5° pulse volume. Given theoperational values of the Trappes radar’s nominalbeamwidth, pulse repetition frequency, antenna rota-tion rate, and wavelength (see Table 1), the total num-ber of samples at a given bin has been computed to be23. The degree to which these samples are independentdepends on the observed spectrum width. Differentialreflectivity is defined as follows:

ZDR � 10 log10

��|SHH|2��

��|SVV|2��. �2�

The copolar cross-correlation coefficient at zero lag[�HV(0)] is the magnitude of the cross-correlation co-efficient and is defined as

�HV�0� � � �S*HHSVV�

�|SHH|2��|SVV|2��. �3�

FIG. 1. Diagram of the Trappes polarimetric radar system in asimultaneous transmission and reception mode. The triple PRTscheme is described in detail in Tabary et al. (2005).

OCTOBER 2006 G O U R L E Y E T A L . 1341


The differential propagation phase shift (�DP) is theargument of the cross-correlation coefficient as follows:

�DP � arg� �S*HHSVV�

�|SHH|2��|SVV|2��. �4�

The Trappes radar also collects radial velocity measure-ments (Vr) as well as a parameter describing the pulse-to-pulse fluctuations of the instantaneous power(sigma; Nicol et al. 2003). This latter variable has beenshown to be useful in ground clutter recognition andrejection.

The Trappes’ scanning strategy is demonstrated inTable 2. Data are collected at six different elevationangles every 5 min, which comprises a single cycle. Thesecond cycle begins by repeating the lowest four tilts,but changes the elevation angles at the two highest tilts.The same logic is used for the third and final cycle ofthe total volume scan. Note that the first cycle is com-posed of an elevation angle of 90°. As is shown in sec-tions 3 and 4, data collected at vertical incidence have

proven to be quite useful for data quality purposes.Moreover, the antenna is rotated 360° while pointingvertically, thus providing an abundance of samples. Thecombination of all scans over the 15-min period com-prised of all three cycles results in the volume coveragepattern illustrated in Fig. 2. The boldface type at lowelevation angles corresponds to data collected with anantenna rotation rate of 7.5° s1. A faster rotation rateof 15° s1 is used for the highest two tilts for each cycle.

b. Artifacts caused by radome and near-radomeinterference

The radome enveloping the Trappes dish is con-structed with 12 curved panels with seams that arealigned vertically. It has been suggested that the jointsconnecting these panels may result in two-way powerlosses at azimuths near these joints. This potential in-terference problem would be most noticeable withmeasurements of ZDR. A two-way power loss of reflec-tivity at vertical polarization (ZV) would be larger than

TABLE 2. Scanning strategy employed by the Trappes polarimetric radar. The boldface denotes data collected with an antennarotation rate of 7.5° s1.

H → H � 5 H � 5 → H � 10 H � 10 → H � 15 H � 15 → H � 20 . . .

T01 � 2.5° T07 � 2.5° T13 � 2.5° T01 � 2.5° . . .T02 � 6.5° T08 � 4.5° T14 � 3.6° T02 � 6.5° . . .T03 � 0.8° T09 � 0.8° T15 � 0.8° T03 � 0.8° . . .T04 � 1.5° T10 � 1.5° T16 � 1.5° T04 � 1.5° . . .T05 � 90.° T11 � 9.0° T17 � 7.5° T05 � 90.° . . .T06 � 0.4° T12 � 0.4° T18 � 0.4° T06 � 0.4° . . .

TABLE 1. Operating characteristics of the Trappes polarimetric radar. The listed parameters have been measured by the radarmanufacturer.

Antenna Type Center-fed paraboloid

Diameter 3.7 mBeamwidth (3 dB), horizontal (H) and vertical (V) �1.1°Sidelobe level within 5° (H and V) �25 dBSidelobe levels beyond 10° (H and V) �40 dBGain (H and V) �43.8 dBMax cross-polar isolation �30 dBAzimuth travel range 0 → 360° (continuous)Elevation travel range 3 → 183°Azimuth/elevation pointing accuracy 0.1°Azimuth/elevation velocity Up to 36° s1

Transmitter Peak power 250 kWPulse width 2 �sFrequency 5.640 GHzWavelength 5.31 cmPRF Staggered triple PRT: 379, 321, and 305 Hz

Receiver Minimum detectable signal �112 dBmTotal instantaneous dynamic range (H and V) �95 dB

Radar processor Developed by Meteo-France



with ZH at the azimuths corresponding to the verticallyaligned joints, and could possibly increase values ofZDR. To test this hypothesis, analyses are produced forrainfall events that occurred on 17 December 2004,24 March 2005, 13 May 2005, and 29 May 2005. Theseevents are comprised of 23, 283, 24, and 15 respectivetilts of data, all of which are collected at an elevationangle of 1.5°, which is unblocked at this flat radar siting.Modulation of ZDR may be noticeable at 30° intervals ifthe joints are indeed causing transmission and recep-tion losses.

The data sample needs to be free from attenuationeffects, backscatter differential phase resulting fromMie scattering, and nonweather scatterers. Imposing athreshold of �HV(0) � 0.97 improves the quality of thedataset by removing several data points that are fromground clutter and those that are likely biased due tolow SNRs. An additional threshold of SNR � 25 dB isalso enforced in order to mitigate biases in ZDR and�HV(0) at low SNR (see section 3 for the correctiontechnique). Data measured at ranges �5 km aredeemed to be more prone to ground clutter contami-nation and are close to the antenna’s near–field of view.Limiting the dataset to values of �DP � 10° reduceserrors resulting from attenuation and resonance effects.Finally, an altitude threshold of 1.25 km has been im-posed in order to limit the data sample to rain mea-surements below the melting layer. Interference-based

discontinuities will be present, if they indeed exist, aslong as the precipitation is widespread and raindropsizes are approximately constant in the azimuthal di-rection.

The normalized density plot of ZDR as a function ofazimuth in Fig. 3 shows no symmetrical waves at 30°intervals, corresponding to the 12 joints in the radome.Moreover, the interior of the radome was visually in-spected and the joints are merely thin, smooth seamsthat contain no metal screws. It has been suggested thata constant difference in the attenuation of ZV and ZH

may exist because the reflector is always covered bythree–four panel joints. This effect may not be revealedby rotating the antenna alone (i.e., the modulation maynot vary with azimuth). Instead, there may be a depen-dence on elevation angle as the panel joint pattern ap-proaches symmetry (i.e., no effect at 90°). A possiblemethod to identify this radome panel effect is to exam-ine the change in ZDR measurements with increasingelevation angle. The changes should follow the theoryas outlined in Bringi and Chandrasekar (2001, their sec-tion 2.3.3). If not, then there may be a need to correctfor an apparent attenuation in ZDR as a function ofelevation angle, but not azimuth.

While radome interference is not evident with theTrappes radar, it is noted that mean ZDR values for allfour cases examined exhibit nonnegligible, asymmetricvariability as a function of azimuth. In fact, when com-paring the behavior of mean ZDR curves for the differ-ent cases in Fig. 3, they follow a recurring pattern.There are local maxima at approximately 15°, 75°, 130°,195°, 270°, and 315°. A closer examination of structuresin the near vicinity of the radome reveals a securityfence along the perimeter of the square tower as well asa box containing electronics at the top of the tower (seeFig. 4). The box, which provides the capability to con-trol the elevator, has sides that are 20 cm � 27 cm. Theheight of the box is 60 cm and it is mounted on a 1-msupport. It is situated on the north corner of the radomeand is believed to be responsible for the 0.4-dB fluctua-tion between 315° and 360°. The complex behavior ofthe curve may be attributed to the fact that the radar isnot situated directly in the center of the tower. Thus,the distance from the antenna to the fence and afore-mentioned structures varies with azimuth. In addition,similar analyses were performed for higher elevationangles (not shown), and the “near-radome interferenceeffect” was observed to diminish with higher angles.While the azimuthal dependence of ZDR is complex andmust be accounted for, the behavior of the curves fromcase to case exhibits remarkable similarities. This en-ables us to develop an empirical ZDR correction proce-dure that can be applied to the measurements here-

FIG. 2. The operational volume coverage pattern employed bythe Trappes polarimetric radar. The dark gray color correspondsto data that are measured with an antenna rotation rate of7.5° s1. The light gray color refers to a rotation rate of 15° s1.



after. A mask is constructed using all 283 tilts from the24 March 2005 case. This mask, which varies as a func-tion of azimuth, is then subtracted from ZDR measure-ments for all cases previously analyzed in Fig. 3. Theresulting ZDR data are shown to be less affected frominterference due to structures in the radar’s near–fieldof view (Figs. 5a–d). There may be some dependenceon azimuth because of the natural variability of ZDR asa function of space. In any case, most of the artifacts,such as the dip in ZDR measurements between 315° and360°, have been mitigated. In the future, the structureswithin the radar’s field of view will simply be removed.In the meantime, the empirical mask developed hereinwill be implemented to reduce the impacts on raw ZDR

measurements caused by interference.

3. System noise

There are several sources both internal and externalto a radar system that can create noise (Bringi andChandrasekar 2001, their section 5.8). Receiver noise in

both channels may be measured internally. However, itis the contribution of both external and internal noisethat biases measurements of polarimetric variables.Noise from external sources, such as from the radomeand surrounding fence, is difficult to measure. The ap-proach adopted herein is unique in that the effectivenoise is estimated using actual measurements in rainmedia at vertical incidence. While the powers of noiseat both horizontal and vertical polarizations may not beknown precisely, there is a mathematical basis for in-cluding the ratios of horizontal-to-vertical noise powersinto calculations of polarimetric variables (Liu et al.1994). Moreover, the utilization of precipitation mea-surements at vertical incidence yields a known, intrinsicvalue of differential reflectivity (ZDR). This informa-tion allows us to solve for an unknown constant, andthen compute corrected values of polarimetric vari-ables. Without this correction procedure, noise powerswill induce biases in measurements of ZDR and the co-polar cross-correlation coefficient at zero lag [�HV(0)]at SNRs less than 25 dB.

FIG. 3. The normalized density of ZDR (dB) as a function of azimuth for widespread rainfall cases on (a) 17 Dec 2004, (b) 24 Mar2005, (c) 13 May 2005, and (d) 29 May 2005. Data from the 1.5° elevation angle are included in the analysis, and the data sample musthave met the following criteria: ZH � 20 dBZ, �HV(0) � 0.97, �DP � 10°, and range �5 km. Solid line is the mean ZDR; the dotted linescorrespond to one standard deviation. The thin vertically oriented lines represent a third dimension to the figure. They show densitiesof ZDR computed for all 360 azimuthal bins. Note that the densities have been normalized by the maximum number of counts withineach azimuthal bin. These densities have subsequently been “collapsed” onto the x–y plane.



a. Differential reflectivity

The radar-measured ZDR is expressed below to in-clude the contributions of effective noise:

Zdrm �

Zdrin � Zdr

in � snr1

1 � Zdrin � �1 � snr1 . �5�

The differential reflectivity in this case is in linear unitsso the subscript “dr” has been put in lower case. Thesuperscript on Zdr (“m”) refers to the measured value.Equation (5) is expressed in terms of snr (where lowercase implies linear units), the intrinsic differential re-flectivity (Zin

dr), and a parameter used to describe theratio of effective noise in the horizontal channel to thatin the vertical channel (�). Raindrops have circularcross sections at vertical incidence; thus, Zin

DR should be0 dB in the absence of an imprecise antenna-pointingangle, mean canting of the raindrops, or miscalibration(Gorgucci et al. 1999a; Bringi and Chandrasekar 2001,their section 6.3.2). In the case of the Trappes radar, theantenna may be rotated 360° in azimuth while pointingvertically. Once the data are azimuthally averaged, thescatterers no longer need to satisfy azimuthal symmetryin order for the intrinsic ZDR to be 0 dB.

The behavior of Zmdr is evaluated using precipita-

tion at vertical incidence for different values of SNR(Fig. 6). The same 6-h stratiform rainfall event de-scribed in section 2b is used here. The Trappes radarscans in the vertical once every 15 min, resulting in 24scans comprising the dataset. A normalized density plotis created from data points that have values of �HV(0) �0.97 and were measured at altitudes �0.7 km. The�HV(0) criterion improves the quality of the dataset bylimiting it to samples that contain hydrometeors withuniform phases and by reducing contamination fromnonmeteorological scatterers. The altitude threshold of0.7 km ensures that the data in the analysis are collectedin the antenna’s far field (Bringi and Chandraskear2001, their section 6.3.2). No significant differentialphase shifts were noted in the selected data sample,which is to be expected with hydrometeors whose crosssections generally satisfy azimuthal symmetry.

Figure 6 shows that values of measured ZDR increaseslightly as SNRs fall below 15 dB. This trend in thecurve suggests that contributions from noise in the hori-zontal channel induce a small bias in the apparent ZDR

values. Using the vertically pointing observations hereoptimizes the � parameter in Eq. (5) because the in-trinsic ZDR is known to be 0 dB. First, it is noted thatthe mean values of measured ZDR (solid black curve inFig. 6) lie below 0 dB, even at high SNRs where noiseeffects are negligible [see Eq. (5)]. This mean bias isattributed to the miscalibration of ZDR and is exploredin greater detail in the next section. For now, a calibra-tion bias of 0.08 dB is used to simulate measurementsin the presence of errors from miscalibration. The solidgray curve in Fig. 6 shows the theoretical ZDR at ver-tical incidence in the presence of the aforementionedcalibration error. The next procedure uses Eq. (5) tosimulate the combined effects of miscalibration andnoise on ZDR. The dash–dotted curve in Fig. 6 showsthe theoretical ZDR using Eq. (5) with Zin

DR set to 0 dBto accommodate for measurements at vertical inci-dence, for an � setting of 1.76 dB in order to simulatenoise, and for 0.08 dB subtracted out in order to simu-late a calibration error. It is shown that the dash–dottedcurve matches the general trend of the observed ZDR

reasonably well. The value of the � parameter, whichwas found by trial and error, suggests that while thepowers of noise may be quite low (i.e., �0 dBZ), thehorizontal channel apparently has about 50% more ef-fective noise than is present in the vertical channel.

The advantage of this approach is the utilization ofmeasurements in rain media where the combined ef-fects of noise internal and external to the radar systemare considered. The disadvantage is the scarcity of ob-servations that are available at low SNR while the radar

FIG. 4. A picture showing electronics box and a fence on top ofthe Trappes radar tower that have been found to impact ZDR

measurements.



is pointing vertically. Thus, uncertainty exists in the es-timation of � because the tail of the curve at low SNRdictates the optimized value (where there are the few-est number of measurements). Many more ZDR mea-surements at low SNR can be obtained using data col-lected at 1.5°. The intrinsic ZDR is not known at 1.5°.However, a bias will be noticeable if the raindrop sizesare generally constant with range. It is also recom-mended that users combine these tests with internalnoise measurements taken on both channels.

b. Copolar cross-correlation coefficient at zero lag

Analogous to the previous section, measurements of�HV(0) are expressed in terms of snr, Zin

dr, and �,

�hvm �0� �

�hvin �0�

�1 � snr1��1 � Zdrin � �1 � snr1�

. �6�

The behavior of measured �HV(0) in the presence ofcalibration errors and noise effects is compared to theo-retical expectations in Fig. 7. The solid black curveshowing mean �HV(0) values as a function of SNR isvery close to 0.987 at SNRs greater than 25 dB. Thesolid gray curve in Fig. 7 shows what the measured�HV(0) curve should look like if the intrinsic �HV(0) is0.987, ZDR is miscalibrated by 0.08 dB, and there is no

noise in either the horizontal or vertical channels. Dif-ferences between the measured �HV(0) values andthose that simulate ZDR calibration errors alone showthat biases resulting from noise have been introduced inthe �HV(0) measurements at SNR � 25 dB. Finally, thecombination of calibration errors in ZDR and noise ef-fects are simulated in Eq. (6) by setting � to 1.76 dB,intrinsic �HV(0) to 0.987, and intrinsic ZDR to 0.08 dB.The dash–dotted curve in Fig. 7 indicates that simulatednoise and calibration errors match the observationswell. With an optimized setting for �, we can solve Eqs.(5) and (6) for the intrinsic variables, and thus correctthe measured ZDR and �HV(0) for biases introduced atSNR � 25 dB resulting from noise effects.

4. Calibration

a. Horizontal reflectivity

The precision of reflectivity at horizontal polariza-tion (ZH) calibration may be the limiting factor in theaccuracy of rain rates. The required accuracy of ZH

calibration is about 1 dB in order for fractional errors inrain-rate estimates to remain below 15% (Ryzhkov etal. 2005). The absolute calibration of ZH for an opera-tional radar network presents a long-standing challengein radar meteorology. Typically radars may be cali-

FIG. 5. Same as in Fig. 3, except the interference problems with ZDR measurements have been corrected using an empirical mask.



brated through measurements from targets with knownscattering properties, by injecting known signalstrengths to the receiver, and with comparisons withrain gauge accumulations, disdrometer measurements,

and reflectivity from neighboring radars. The strengthsand weaknesses of these approaches are summarized inAtlas (2002). Another option with a polarimetric radaris to capitalize on the redundancy between ZH, differ-

FIG. 7. Same as in Fig. 6, but for SNR (dB) vs 1�HV(0).

FIG. 6. The normalized density of SNR (dB) vs ZDR (dB) for stratiform precipitation measured at verticalincidence. One vertical scan collected every 15 min from 0600 to 1145 UTC 17 Dec 2004 is used in this analysis.Data comprising the plot must have values of �HV(0) � 0.97 and were measured at altitudes �0.7 km. Solid blackcurve is the mean ZDR while the dotted curves correspond to one standard deviation. The solid gray line refers tosimulated ZDR with a 0.08 dB calibration error, and the dash–dotted one corresponds to simulated ZDR with errorscaused by noise and miscalibrated ZDR. Refer to Fig. 3 for a detailed explanation of the vertically oriented lines.



ential reflectivity (ZDR), and specific differential phaseshift (KDP) in rain. This concept, first presented byGoddard et al. (1994), is based on the well-defined be-havior of ZDR versus KDP scaled by ZH (in linear units).This relationship has been shown to be virtually inde-pendent of variations in drop size distributions (DSDs).Moreover, KDP can then be estimated from measuredvalues of ZH and ZDR. Differences between measuredand consistency-based KDP are attributed to miscalibra-tion in ZH and provide a basis for correcting it. A de-tailed study of ZH calibration using the consistencytheory based on the approach reported in Gourley andIllingworth (2005), and the subsequent comparisonwith a disdrometer, is being evaluated and will be re-ported in the near future. An initial evaluation of thecalibration of ZH is performed here using traditionalradar–radar and radar–rain gauge comparisons.

The temporal variability of a radar’s calibration canbe monitored by comparing ZH from two different ra-dars at similar distances and altitudes (Gourley et al.2003; Tabary 2003). Systematic monitoring of these dif-ferences may only provide a relative comparison, butaccommodate large radar networks much more readilythan using deployed targets with known backscatteringproperties. The combination of this approach alongwith radar–rain gauge comparisons is used here to

evaluate the calibration of ZH. Comparisons are madeover a 5-month period from 1 September 2004 to 29January 2005.

The temporal behavior of radar reflectivity from theTrappes radar as compared to data collected at neigh-boring radars is approximately constant (Fig. 8a). Thecomparisons are made in precipitating clouds that aresampled at collocated bins by both radars. A singlevalue is produced for each day that represents the av-erage difference for all times at all collocated bins.Variability may be attributed to differences in beampropagation paths resulting from differing thermo-dynamic profiles near the radars. Comparisons with theBourges radar alone suggest the Trappes radar may bebiased slightly high. However, a similar bias, but in thenegative sense, is evident in comparisons betweenTrappes and Caen. When considering the ensemble ofcomparisons, there appears to be little bias in Trappesreflectivity measurements.

An additional calibration metric is provided here thatsheds light on the absolute calibration of the Trappesradar. For each day in which there is significant rainfall,data from as many as 161 gauges within 100 km of theTrappes radar are collected for comparison to collo-cated ZH measurements. Hourly rainfall accumulationsfrom rain gauges are converted into equivalent reflec-

FIG. 8. Comparisons between horizontal reflectivity from the Trappes radar (a) minus reflectivity from neighboring radars collected atcollocated bins (dB) and (b) minus calculated reflectivity from collocated rain gauges assuming Marshall–Palmer relationship (dB).



tivity factors using the standard Marshall–Palmer re-flectivity-to-rainfall relationship (Marshall and Palmer1948). This reflectivity factor is then compared to thehourly average of reflectivity at the nearest radar bin. Adifference is computed at each gauge location, and agiven point on Fig. 8b represents a daily average of thesedifferences. Variability from these comparisons can re-sult from a host of sources, including spatiotemporal-scale mismatches between gauged and radar-measuredrainfall, DSD variability, variability of reflectivity as afunction of height, etc. Nonetheless, we believe thelarge degree of averaging over space and time shoulddiminish resulting biases. Figure 8b reveals little evi-dence that there is a significant bias in the measure-ments of ZH. It is understood, however, that the uncer-tainty bounds with these analyses are rather large. On-going work will explore more precise ZH calibrationmethods using polarimetric self-consistency principles(see e.g., Gourley and Illingworth 2005).

b. Differential reflectivity

A radar equipped with polarization diversity com-bined with the known scattering properties of hydro-meteors sampled at vertical incidence, as well as solarradiation, allow us to examine the absolute calibrationof ZDR. While the mean canting of raindrops or animprecise pointing angle will lead to more variable ZDR

measurements, an azimuthal average should be 0 dB.The 6-h stratiform rainfall event on 17 December 2004is used here to diagnose calibration errors in ZDR.There are a total of 24 scans comprising the dataset.Normalized density plots are created from data pointsthat have values of �HV(0) � 0.97 and were measured ataltitudes beyond the antenna’s far field (e.g., altitudes�0.7 km). The �HV(0) criterion was implemented inorder to reduce ground clutter contamination in thesidelobes. This threshold may not be sufficient at re-moving echoes from nonprecipitation sources because�HV(0) in ground clutter can be as high as 1.0. Figure 9bshows the distribution of ZDR values as a function ofaltitude at vertical incidence. If sidelobe contaminationwere a problem with the Trappes radar, then the dis-tribution of ZDR values would be wider at lower alti-tudes. Figure 9b shows that the distribution of ZDR

remains constant with altitude, thus the contributionfrom sidelobes is negligible.

The mean ZDR values as a function of azimuth indi-cate that the curve is approximately sinusoidal (see Fig.9a). The amplitude is approximately 0.1–0.2 dB and thewavelength is 180°. This behavior of the curve suggeststhat either the hydrometeors were canted throughoutthe event or the antenna was not pointing at a preciseelevation angle of 90°, but was wobbling while it was

spinning. This effect is removed when the data fromdifferent azimuths are consolidated as in Figs. 9b and9c. Mean ZDR is approximately constant when plottedas a function of altitude (Fig. 9b). Note that this strati-form rainfall event had a melting level at 1.9 km. Thisconfirms that hydrometeors in different phases may beused in calibration experiments of ZDR if the antenna is

FIG. 9. The normalized density of (a) azimuth (°), (b) altitude(km), and (c) ZH (dBZ ) vs ZDR (dB) for stratiform precipitationmeasured at vertical incidence. One vertical scan collected every15 min from 0600 to 1145 UTC 17 Dec 2004 is used in this analysis.Data comprising the plot must have values of �HV(0) � 0.97 andwere measured at altitudes �0.7 km. Solid line is a fit to the meanZDR while the dotted lines correspond to one standard deviation.Refer to Fig. 3 for a detailed explanation of the vertically orientedlines.



rotated 360° at vertical incidence and an azimuthal av-erage is considered. Figures 9a–c all indicate that ZDR

has a slight negative bias. Thus, the calibration error inZDR as computed by precipitation sampling at vertical in-cidence is 0.08 dB, with a standard deviation of 0.9 dB.

The temporal behavior of the ZDR calibration wasexamined for a case that occurred on 13 May 2005, fivemonths after the initial calibration test (not shown).The calibration error for this case was also discoveredto be 0.08 dB; thus, the calibration is assumed to beconstant as long as the waveguide remains unchanged.It is noted that this calibration strategy requires pre-cipitation directly above the radar. This may not beappropriate for a large network of radars or for radarsoperating in dry climates.

The reception of solar radiation has been shown toevaluate the calibration of ZDR (Melnikov et al. 2003;Ryzhkov et al. 2005). Solar radiation has equal power atboth vertical and horizontal polarizations; thus, the in-trinsic ZDR is 0 dB regardless of elevation angle. Datathat were collected near sunrise (0800–0845 UTC) areanalyzed to detect the presence of solar radiation alongeach radial. This analysis is performed on 16 tilts of dataper volume scan (the 9° and 90° data are excluded)from 17 December 2004 to 11 January 2005. Solar ra-diation along a radial, or a “sun spike,” is automaticallyfound if there are at least 500 range gates in an azimuththat meet the following criteria. First, it was observedthat 10 � ZH � 20 dBZ with solar radiation, thus thisthreshold was subsequently imposed. In theory, the co-polar cross-correlation coefficient at zero lag [�HV(0)]should be 0 in a sun spike. This was not always ob-served, yet a threshold of �HV(0) � 0.5 is sufficient todistinguish solar radiation from hydrometeors.

A probability distribution is computed from the sunspike dataset and is shown in Fig. 10. The curve is ap-proximated well as being Gaussian with a mean valueshifted toward negative ZDR values. An average bias of0.2 dB with a standard deviation of 1.4 dB is com-puted using the measurements of ZDR from solar ra-diation. Both ZDR calibration methods are in agree-ment in that they suggest a slight negative bias thatneeds to be corrected. The former analysis that usesmeasurements from hydrometeors at vertical incidenceis capable of testing the combined effects of receptionand transmission on the absolute calibration of ZDR.The “sun spike” analysis tests only the reception com-ponent of the radar, and results from this latter testhave more uncertainty given the larger standard devia-tion. It is thus preferable to use precipitation measure-ments at vertical incidence to calibrate ZDR if this op-tion is available with the radar system. Otherwise, cali-bration using solar radiation may be sufficient.

c. System offset of differential propagation phase

Absolute measurements of �DP have been shown tobe related to attenuation (Bringi et al. 1978) and thusmay be used to correct power measurements in thepresence of attenuation. More importantly, consistencymethods rely on the dependence between ZDR, ZH, andKDP. One approach is to estimate KDP given observa-tions of ZH and ZDR. Space–time averages of observedKDP are then compared to consistency-based KDP

(Ryzhkov et al. 2005). Differences are then attributedto calibration errors on ZH. Another approach (Gour-ley and Illingworth 2005) estimates KDP as discussedabove and then integrates it along the radial directionso that consistency-based �DP may be compared di-rectly to observed �DP. This latter approach is pre-ferred (a) because of possible biases that may be intro-duced in the calculation of KDP from �DP measure-ments (see, e.g., Gorgucci et al. 1999b), (b) becauseKDP has been observed to be noisy in light rain condi-tions, and (c) because KDP is subject to partial beam-filling effects. The technique used to calibrate ZH using�DP measurements found �DP estimated from consis-tency theory increased by about 1.2° (1 dB)1 pertur-bation in ZH (Gourley and Illingworth 2005). Such sen-sitivity requires us to examine raw �DP values and beaware of possible offsets in initial differential phasemeasurements (�o). A nonzero �o may occur prior toencountering a precipitation medium because of veryslight differences between the horizontal and verticalwaveguides. A slight offset in distances can result ineither a positive or negative phase difference.

A probability distribution of raw �DP values iscreated for a stratiform rainfall event from 0600 to1145 UTC 17 December 2004 (Fig. 11a). This analysisuses data collected at 0.8° and 1.5°, which must also be

FIG. 10. The probability density of ZDR (dB) for reception ofsolar radiation. This analysis is comprised of 16 scans of datacollected every 15 min at times near sunrise from 17 Dec 2004 to11 Jan 2005.



measured below the bright band (altitude � 1.25 km).The probability distribution of raw �DP values in strati-form rain (Fig. 11a) shows an apparent bimodal behav-ior with the mode around 350° and a secondary maxi-mum near 0°. The shape of the distribution and themagnitude of the �DP values associated with the modeindicate an aliasing or wrapping problem. The predomi-nance of observations at such large �DP values suggeststhat there is a nonzero system offset and an aliasing

problem. A simple technique is developed to dealias orunwrap �DP measurements.

The �DP dealiasing algorithm simply subtracts 360°from all raw �DP measurements greater than 270°. Thealgorithm has been implemented on the same datasetused above and is evaluated in Fig. 11b. The recovereddistribution has a single peak, and the shape is nearlyGaussian but slightly skewed to the right towardgreater �DP values. The shape of this curve indicates

FIG. 11. The probability densities of (a) raw �DP and (b) dealiased �DP (°) in stratiform rain. Eachanalysis uses 6 h of data from the 0.8° and 1.5° elevation angles from 17 Dec 2004, where 24 scans areavailable each hour. Data are considered in the plot if they were observed below the bottom of themelting layer, which was found to be 1.25 km.



that the initial aliasing problem has been completelyresolved. The suggestion of a tail toward higher �DP

values is associated with instances in which there wasmoderate rain and thus a positive phase difference.Negative �DP values are not expected with stratiformrain, but of course may occur because of fluctuations inraw �DP measurements. However, mean values of �DP

are negative, which suggests that there is an initial sys-tem offset that needs to be corrected. Details in thebehavior of �o are elucidated below.

Analyses are performed on three different rainfallcases to determine the behavior of the initial systemoffset of differential phase measurements. To producea sample of �DP measurements that can be consideredas initial values taken along a radial, the data must haveZH greater than 20 dBZ, but less than 30 dBZ. Theupper limit on ZH reduces positive differential phaseshifts that can be expected in moderate to heavy rain.The lower ZH limit is used in combination with rangerestrictions to ensure that the SNR is reasonably high.Measurements of �DP have been observed to fluctuatesignificantly along their paths in suspected ground clut-ter regions and with measurements taken at low SNR.Candidate �o values must therefore be measured at adistance greater than 5 km from the radar but within50 km. A threshold of �HV(0) � 0.97 is also imposed inorder to refine the dataset to measurements that arelikely observed in precipitation media.

Figure 12 shows the behavior of �o as a function ofazimuth angle for (a) 283 tilts on 24 March 2005, (b) 24tilts on 13 May 2005, and (c) 15 tilts on 29 May 2005.The mean �o is shown to be approximately 6°. If thesystem offset of differential phase shift were constantwith azimuth, then �DP measurements could be ad-justed by simply subtracting out the mean �o value of6°. Closer inspection of the estimated �o trends (seeFigs. 12a–c), however, reveals that they follow a sinu-soid with a wavelength of 360° and an amplitude of2.25°. This sine wave appears to recur with a similarbehavior for all three cases. The wavelength and re-peatability from case to case points to the waveguiderotary joint being the culprit of the �DP dependence onazimuth. It is likely that the mechanical rotation of theantenna has the effect of imparting a very slight differ-ence in length between the horizontal and verticalpaths. This difference results in an apparent phase dif-ference between the two channels. The expected be-havior of this artifact permits us to develop and imple-ment an empirical correction procedure.

The method to correct for artifacts in �DP measure-ments is intended to mitigate the observed azimuthaldependence and remove the negative bias. First, a sinewave is manually fit to the observed mean �o curves

shown in Figs. 12a–c. This sine wave is then shifted 180°in azimuth and then added back to �DP measurements.In addition, a factor of 6° is included in the correctionformula to account for the mean bias in �DP as follows:

�DPin � 2.25 sin�� 230� � �DP

m � 6, �7�

where all values are in degrees and the superscripts “in”and “m” refer to intrinsic and measured values. Equa-tion (7) is then applied to all �DP measurements used inFigs. 12a–c. Figures 13a–c correspond to the same

FIG. 12. The normalized density of �DP (°) as a function ofazimuth for widespread rainfall cases on (a) 24 Mar 2005, (b) 13May 2005, and (c) 29 May 2005. Data from the 1.5° elevationangle are included in the analysis, and data sample must have metthe following criteria in order to estimate the initial system offset(�o): 20 � ZH � 30 dBZ, �HV(0) � 0.97, and 5 � range � 50 km.Solid line is the mean �o. Refer to Fig. 3 for a detailed explanationof the vertically oriented lines.



datasets and thresholds used in Figs. 12a–c, but correctfor initial �DP offset using Eq. (7). The correctionmethod is shown to adequately account for the sinusoi-dal behavior and negative bias present in the original�o measurements. The resulting mean �o values nowhave very little bias and are no longer dependent onazimuth. This simple, empirical procedure is applied toall �DP measurements hereafter.

5. Measurement precision

A major goal in the analysis of data quality is quan-tification of measurement error. Up to this point, errorsrelated to near-radome interference, noise, and miscali-bration have been identified, quantified, and corrected.

The standard deviations of ZDR and �DP are calculatedin light stratiform rain along a nine-gate window andare then compared to theoretical expectations and toexperimental findings from other studies at C band(e.g., Keenan et al. 1998). The accuracy of ZDR neededfor rain-rate estimates with fractional errors less than15% is 0.1–0.2 dB (Ryzhkov et al. 2005). The theoret-ical values are calculated using operating specifics ofthe radar (cf. section 2a) for differing values of spec-trum width. The variances of the estimates of the co-variance matrix elements may be computed theoretical-ly following section 6.5 in Bringi and Chandrasekar(2001).

a. Differential reflectivity

The precision in ZDR is calculated here using datacollected at 0.8° and 1.5° during a 6-h stratiform rainfallevent that occurred from 0600 to 1145 UTC 17 Decem-ber 2004. A standard deviation in ZDR is computed ifthe data are measured below the altitude of the brightband at 1.25 km and have an associated �DP less than10°. These thresholds ensure that the dataset is limitedto hydrometeors in liquid phase and are not biased dueto attenuation or backscatter differential phase effects.The standard deviation in ZDR is compared to theoret-ical expectations for normalized spectrum widths (�vn)of 0.104, 0.208, and 0.312. These values correspond tononnormalized spectrum widths of 1, 2, and 3 m s1,respectively. The theoretical results are computedusing Eq. (6.142) in Bringi and Chandrasekar (2001).Figure 14 shows that observational values of the stan-dard deviation of ZDR fall within theoretical expecta-tions for �vn between 0.104 and 0.208. Spectrum widthvalues were not recorded during this event, yet the val-ues are reasonable for stratiform rainfall. Because theobservations of the variance in ZDR follow theory, wecan anticipate an expected precision for given values of�vn and measurements of �HV(0). Figure 14 indicatesthat ZDR values are precise within 0.2 dB and will thusresult in fractional errors in rain-rate estimates less than15% for �HV(0) values of 0.99. This precision assumesthat interference, noise, calibration, and attenuation ef-fects on ZDR have been successfully mitigated.

b. Differential propagation phase

A similar analysis as above is performed in order toevaluate the precision in �DP measurements as a func-tion of �HV(0). The observed standard deviations of�DP fall within theoretical expectations, assuming thatvalues of �vn were between 0.104 and 0.208, corre-sponding to nonnormalized spectrum widths between1 and 2 m s1 (Fig. 15). These values seem reasonable,which suggests that the expected precision in �DP mea-

FIG. 13. Same as in Fig. 12, but �DP values have been correctedfor initial system offset using Eq. (7). Refer to Fig. 3 for a detailedexplanation of the vertically oriented lines.



surements made by the Trappes radar is 1.8° for strati-form rainfall that has an associated �HV(0) of 0.99. Inthis analysis phase, differences resulting from backscat-ter were mitigated by limiting the dataset to �DP � 10°.Mie scattering effects on �DP measurements can be

reduced using iterative filtering techniques such as inHubbert and Bringi (1995). The precision of �DP mea-surements with the Trappes radar (1.8°) is lower thanthe experimental findings of Keenan et al. (1998) whofound a complete system rms phase noise of 3.8°.

FIG. 15. Same as in Fig. 14, but for the standard deviation of �DP as a function of �HV(0).Theoretical values are from Eq. (6.143) in Bringi and Chandrasekar (2001).

FIG. 14. The normalized density of the standard deviation of ZDR as a function of �HV(0). The dottedcurve represents mean observed values. Theoretical values for normalized spectrum widths of (top)0.104, (middle) 0.208, and (bottom) 0.312 are shown as dashed lines and are computed from Eq. (6.142)in Bringi and Chandrasekar (2001). Observations are from a widespread, stratiform rainfall eventcollected at elevation angles of 0.8° and 1.5° from 0600 to 1145 UTC 17 Dec 2004. Refer to Fig. 3 for adetailed explanation of the vertically oriented lines.



6. Summary

A robust analysis of the quality of polarimetric vari-ables measured by the Trappes radar has been under-taken. A great deal of precision in the variables is re-quired for quantitative precipitation estimation andmicrophysical retrievals. Procedures have been devel-oped to identify, quantify, and correct error sourcesthat are known to impact the quality of raw polarimet-ric variables. Moreover, analyses highlighted previouslyundocumented biases that were caused by interferencein the near vicinity of the radome as well as system-specific offsets. We believe that this study can serve asa guide for users who are in the process of equippingtheir radars with polarimetric capabilities. The analysisprocedures are applicable at X-, C-, and S-band wave-lengths.

The following procedures can be used to identify sig-nificant error sources when examining raw polarimetricradar data.

• Structures situated on top of the radar tower near theradome, such as security fences and electronic boxes,may interfere with measurements of ZH and ZDR.This near-radome interference effect may be testedby examining values of ZDR as a function of azimuthfor several hours of widespread stratiform rainfall. IfZDR is dependent on azimuth and the pattern is re-peatable from case to case, then empirical filteringmethods need to be implemented to correct for theinterference problem.

• System noise results in biased measurements of ZDR

and �HV(0) when data are collected at SNR � 25 dB.The reduction in �HV(0) is significant and requirescorrection. The biases may be effectively removedthrough the optimization of a parameter describing theratio of the effective (both internal and external) noisepowers when the intrinsic values of ZDR and �HV(0)are known. Rainfall measurements at vertical incidencegreatly facilitate this process. If the radar is incapableof pointing vertically, then biases at SNR � 25 dBmay be noticeable with measurements obtained instratiform rain at a lower elevation angle of 1.5°.

• Both ZH and ZDR may be biased either positively ornegatively if the radar is miscalibrated. The calibra-tion of ZDR may be checked by using vertically point-ing measurements where the intrinsic ZDR is knownto be 0 dB. Polarimetric methods exist to calibrateZH; however, automating the procedure presentedseveral challenges. This initial study relies on tradi-tional radar–radar and radar–rain gauge comparisonsfor ZH calibration. Correction procedures simply addor subtract a constant value so that the biases areremoved.

• The �DP values may be aliased toward very high val-ues. A histogram or probability distribution of raw�DP values collected at an elevation angle of 1.5° willelucidate this problem. If the peak of the distributionis at an unrealistically high value, then the measure-ments are likely aliased. This problem is remedied bysimply subtracting 360° from the aliased measure-ments.

• The �DP may have an initial system offset that can bedependent on azimuth. A histogram or probabilitydistribution of �DP measurements obtained near theradar in light, widespread rain may reveal that thereis an overall positive or negative bias. These initial�DP measurements should also be plotted as a func-tion of azimuth. If the mean �o values follow a sinu-soidal pattern with a period of 360° and are repeat-able from case to case, then the waveguide rotaryjoint may be the culprit. This artifact can be allevi-ated by using an empirical filtering technique. It isalso quite simple to manually fit a sine wave to thedata and use the optimized parameters as a basis forcorrecting the azimuthally dependent �DP measure-ments.

• The precision in ZDR and �DP can be found by com-puting the standard deviation of each variable withina small window (e.g., nine gates in the radial direc-tion) for several hours of widespread stratiform rain.These standard deviations may be compared to theo-retical expectations and other experimental findingswhen they are plotted as a function of �HV(0). Thisanalysis provides for an estimate of the expected pre-cision in ZDR and �DP for measurements of �HV(0)and normalized spectrum widths (�vn).

The following quantifies the error sources and re-veals the expected precision of polarimetric measure-ments using several case studies with the Trappes radar.These findings are based on our experience and can beconsidered typical for radars operating at C-band wave-lengths.

• Interference caused by structures on top of the radartower resulted in biases in ZDR as large as 0.4 dB.

• While noise powers in the horizontal and verticalchannels resulted in a �HV(0) reduction of 0.1 for datameasured at SNRs of 10 dB, the effect of noise onZDR may be neglected. The noise in the horizontalchannel was found to be about 1.5 times greater thanthe noise power in the vertical channel, although themagnitude of both powers is less than 0 dB.

• Biases in ZH using traditional, nonpolarimetric meth-ods were difficult to identify. A bias of 0.08 dB wasfound with ZDR through the use of measurements of



rainfall at vertical incidence. This bias remained con-stant over at least a 5-month period.

• Following the dealiasing procedure, the initial systemoffset of �DP measurements was discovered to bebiased negatively by 6°. In addition, the initial �DP

values had a sinusoidal dependence on azimuth, mostlikely because of the waveguide rotary joint. The am-plitude of this wave was 2.25° with a period of 360°and remained constant for at least 3 months.

• After the aforementioned error sources have beenaccounted for, the expected precision in ZDR is0.2 dB and 1.8° in �DP. These values are for �HV(0) of0.99 and are within theoretical expectations.

Future work involves the investigation of new and ex-isting attenuation correction methods based on �DP mea-surements (Gourley et al. 2005) and polarimetric-based calibration of ZH (Gourley and Illingworth 2005).

Acknowledgments. This work was done in the frameof the Programme Aramis Nouvelles Technologie enHydrometeorologie Extension et Renouvellement(PANTHERE) project supported by Meteo-France,the French “Ministere de L’Ecologie et du Develop-pement Durable,” the “European Regional Develop-ment Fund (ERDF)” of the European Union, andCEMAGREF. The authors would like to acknowledgethe advice provided by the PANTHERE scientific re-view committee. Specifically, Anthony Illingworth pro-vided us with many useful insights and suggestions re-garding typical artifacts in the polarimetric variables.Martin Hagen also shared his experiences with polari-metric data with us. Alexander Ryzhkov assisted uswith the mathematical formulas concerning the correc-tion for system noise. The readability of this manuscriptwas improved through the inputs from two independentreviewers. Their assistance is greatly appreciated.

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