____________________________________________

Corresponding author: Wiwiana Szalinska,Address: Centre de Meteorologie Radar, DSO, Meteo France,

7 rue Teisserenc-de-Bort 78195, Trappes, France;email: wiwiana.szalinska@meteo.fr

P6R.12 CONDITIONAL EVALUATION OF CONVENTIONAL VS. POLARIMETRIC QPE at C-band

Wiwiana Szalinska1,2), Pierre Tabary2), and Hervé Andrieu3)

1) Cemagref, UR Hydrosystèmes et bioprocédés, Antony Cedex, France2) Meteo-France, DSO, Centre de Meteorologie Radar, Trappes, France

2) Laboratoire Central des Ponts et Chaussées, Division Eau et Environnement, Bouguenais, France

1. INTRODUCTION

Measurement of rainfall with conventional radars issubject to numerous sources of errors. Significantprogress has been made during recent decades to copewith these error sources: partial beam blockage, VPRinfluence, anomalous propagation, attenuation, etc. Thephysics of the conventional radar measurement is wellestablished, allowing the design of radar simulators(Caumont et al., 2005). Despite the progress, somemeasurement difficulties have not yet been solved. Thedrop size distribution (DSD) is subject to variations andthe attenuation correction algorithms (for C and X bandradars) are subject to instabilities which prevent theiroperational application. Dual-polarization which hasbeen a very active research field during the last twentyyears overcome these problems and may improve theaccuracy of rainfall measurement (Bringi andChandrasekar, 2001).

Different approaches have been proposed to benefitfrom polarimetric parameters for rain rate estimation. Afrequent approach extends the conventional R(Z)relationship by expressing rainfall rate R as a function ofpolarimetric radar parameters. Three types ofrelationships have been proposed: R(Z,ZDR), R(KDP,ZDR)and R(KDP) (Ryzhkov et al., 2003). Validation studiesshow that polarimetric relationships result in animprovement of rainfall measurement in comparisonwith R(Z) relationships (to include two references).These findings have been confirmed by the JPOLEexperiment (Ryzhkov et al., 2003) who comparedvarious polarimetric relationships based on a large dataset measured by the S-Band radar in Oklahoma. Thisdata set is mostly composed of convective rain eventsbut also includes stratiform situations. The authorsconclude that most of the polarimetric algorithmsperform better than conventional R(Z) at distance lessthan 125 km and that the best results are obtained witha R(Z,KDP,ZDR) algorithm. The improvement was shownto be significant for stratiform rain events. Alternativeapproaches have been proposed. Brandes et al. (2003)base their rainfall estimation scheme on DSD retrieval.Testud et al. (2000) have developed the algorithm ZPHIwhich uses polarimetric data to reduce the uncertaintyof the classical R(Z) estimate and to correct radar datafor attenuation which is of particular importance for Cand X band radar. ZPHI has been successfully testedand compared to a conventional R(KDP) approach (LeBouar et al., 2001).

In order to objectively assess the benefits of dual-polarization at C-band in an operational context, a one-year experiment has been set up 30 km South Westfrom Paris starting January 2005. Specification of theradar and scanning strategy of Trappes radar aresummarized in the Table 1.

Table 1 Trappes C-band GEMATRONIK radar specification andscanning strategy

RADAR SPECIFICATIONAntenna diameter 3.7 mBeam width (3dB) H and V < 1.1°Pulse width 2 microsecondsFrequency 5.640 GHzWavelength 5.31 cmPRF Staggered-PRT : 379, 321 and 305 HzRange resolution 240 m

Scanning strategyH → H+5 H+5→ H+10 H+10→H+15 H+15→H+20 …

2.5, 6.5,0.81.5, 90., 0.4

2.5, 4.5, 0.8,1.5, 9.0, 0.4

2.5, 3.6, 0.8,1.5, 7.5, 0.4

2.5, 6.5, 0.8,1.5, 90., 0.4

...

Three different Quantitative Precipitation Estimations(QPE) are produced in real-time on a 5-minute basis:the first one, referred to as CONV, is an estimation thatis based entirely on horizontal reflectivity. It serves asthe benchmark to beat in the conditional evaluation. Thetwo other estimations, referred to as POL1 and POL2,are obtained with ZPHI algorithm (Testud et al., 2000)that is implemented on the real time data stream.

The three radar QPEs are compared on an hourly basiswith a dense Meteo France raingauge network of about100 raingauges within a distance of 100 km from theradar (Fig. 1). All the recorded rainfall episodes areincluded in the comparison. The basic idea of thevalidation procedure is to perform a conditionalevaluation that is designed to isolate and quantify thefollowing error sources: ground clutter, attenuation, DSDvariation, bright band contamination and partial beamblocking. From isolated comparison points concernedwith each type of error or free of any error, the capabilityof polarimetric data for each condition is evaluated.

Fig 1 Meteo France raingauge network within the distance of 100 km

2. RADAR QPE ALGORITHMS

2.1 Conventional rainfall estimate

The new operational radar QPE algorithm developed byMeteo France (Tabary et al. 2005) currently corrects forground-clutter, orogenic partial beam blocking,advection and VPR effect. Each pixel of each PPI iscorrected for the various identified error source and thefinal surface rainfall estimation is obtained through aweighted linear combination of all availablemeasurements. In conventional estimate (CONV) therainfall rate is recalculated from the horizontal reflectivityusing the relation R=3.34*10-2Z0.6. The coefficient in theZ-R relation (a=282, b=1.66) were chosen by analyzingdisdrometer measurements of convective and stratiformrainfall during three weeks in 1999 (Testud, personalcommunication).

2.2 Polarimetric rainfall estimate

Before entering the QPE algorithm chain polarimetricradar measurements are processed by ZPHI algorithm(Testud, 2000, Le Bouar et al. 2001). ‘ZPHI’ is a rainprofiling algorithm that retrieves profiles of the rainfallrates. The base of ZPHI algorithm is an inverse modelof three empirical relationships between the integratedparameters of DSD - rainfall rate R (mm h-1), equivalentreflectivity Ze (mm6 m-3), specific attenuation A (dB km-1)and specific differential phase shift Kdp (deg km-1). Theprimary products of ZPHI algorithm are the profile alongthe beam of specific attenuation and the interceptparameter (N0*) of the normalised gamma form of DSD.The rainfall rate is estimated through the rainfall toattenuation relationship adjusted for the value of N0*.

POL2 is the polarimetric estimation of the surfacerainfall accumulation that takes full advantage of ZPHI

algorithm including correction for attenuation andadjustment of the N0* parameter. The rainfall rate is

estimated through an R-A relation dh

d ANcR −= 1*0 ][

where c and d coefficients depend on temperature(Testud et al. 2000, Le Bouar et al. 2001).

POL1 only includes the correction for attenuationestimated by ZPHI and rainfall is calculated through Z-Rrelation.

2.3 Comments

It is important to notice that all pixels of the three QPEscome from the same tilt, which ensures that they havethe same properties in terms of ground clutter,attenuation, height, degree of blocking, DSD variation,and VPR effect. Differences are attributed to the rainfallestimation and applied corrections schemes.

The coefficients of Z-R relation used to estimate rainfallin CONV and POL1 correspond to the logarithm value ofthe ‘normalized’ intercept parameter of gammadistribution of 6.3 m-4. This value is also taken as afixed value for N0

* to run ZPHI when differential phaseshift (∆_DP) is smaller than 6º. In such cases N0* can notbe derived with sufficient accuracy due to the directrelation between error in N0* and uncertainty inestimated ∆_DP (see Le Bouar et al., 2001)

3. VALIDATION PROCEDURE

The conditional evaluation consists of grouping radarmeasurements that have the same characteristics.Criteria required to divide the data set into subsets areeither generated by the radar QPE procedure or by theZPHI algorithm.

In this paper conditioning was aimed at investigating theimprovement of polarimetry for correcting for attenuationand DSD variability while reducing the other source oferrors.

As the validation concerns hourly accumulation, a vitalstage of conditioning is temporal integration of errorcharacteristics. While it is not an issue for fixed andpermanent errors like ground clutters or shielding, itplays a major role for meteorological and rainfalldependent source of errors like attenuation or DSD.This is done differently for each of the error source.

The criteria to survey the variation in DSD were valuesof the ‘normalized’ intercept parameter N0

* retrieved inZPHI algorithm. The discriminator for N0

* parameterover an hour is computed as mean of twelve N0

* valuesweighted by the rainfall rate. This formulation aims tocharacterize the hourly rainfall accumulation with thevalue of N0* retrieved for the most intensive amongtwelve estimated rainfall rates.

To discriminate and stratify the severity of attenuationaffecting radar measurements over an hour, a specialfunction was applied to weight mean attenuation by therainfall intensity. The form of the weighting function wasdeduced by assuming that Z-R relationship provides agood estimate of raingauge measurement so that radar

rainfall estimate (CR) differs from raingauge (CG) only byloss in reflectivity caused by attenuation

6.16

66.1

1

10

10282

10)(

dB

dBATT

G

ATTTRUE

dBTRUE

R CZ

ATTZRC−

−

⋅=

⋅

=−=

Mean attenuation over an hour would be though alogarithm of hourly radar estimates to hourly raingaugeestimate obtained by cumulating 5-min estimates. Eachof the 5-min radar estimates could be expressed as afunction of 5-min raingauge rainfall accumulation and 5-min path integrated attenuation.To evaluate severity of attenuation in reference torainfall intensity, 5-min raingauge rainfall measurementswere expressed by 5-min POL2 rainfall estimates thatbelieved to be the best surface rainfall estimates. Hourlymean value of attenuation was though calculated as:

⋅

⋅−=

∑

∑

=

=

−

12

12

12

1

6.16

)(

2

10

)(

10)(log6.16

i

i

iATT

dB

iPOL

iPOLATT

where i is the number of radar to raingaugeobservations, POL2(i) and ATT(i) are 5-minutes secondpolarimetric estimate and path integrated attenuationrespectively given by ZPHI algorithm.

4. RESULTS

The multi-event data set consists of 22 rainfall eventsrecorded from December 2004 up to August 2005comprising a wide spectrum of rainfall from lightstratiform to heavy convection as illustrated by a caseon 28 July, when raingauges recorded 18 mm of rainfallduring 6 minutes. The data set contained 4137 couplesof hourly raingauges and radar accumulations where allthree radar estimates were available (CONV, POL1 andPOL2) and 8082 couples where only CONV and POL1could be compared (POL2 was not available due todifferent then rain precipitation type and by thisinadequateness of the inverse model employed inZPHI). Errors that may arise due to the scaling of radar-based estimates down to the raingauges wereneglected. Comparisons between raingauges data andradar QPEs were performed for selected subsets havingcommon characteristics. The examined criteria tomeasure the quality of different rainfall estimators werenormalized bias NB and Nash criterion N (Nash et al.1970 )

( )

∑

∑

=

=

−= N

i

ig

N

i

ig

ir

RN

RRN

NB

1

1

1

1

∑

∑

=

=

−

−−= N

i

gig

N

i

ig

ir

RR

RRN

1

2

1

2

)(

)(1

where Rr – rainfall estimated by radar and Rg – rainfallmeasured by raingauges. The results are presented asradar to raingauge correlation plots with displayedvalues of sample size, correlation coefficient, RMSE andexamined criteria. A scatter diagram of RMSE vs.correlation coefficient is also produced.

4.1. Attenuation conditioning

In the first conditioning analyzed data subset contained39 comparison points affected by at least 3 dB of hourlymean attenuation. The comparison showed thatsignificant improvement is obtained with polarimetricmeasurements (Fig. 2). Presence of attenuation mainlyaffects the normalized bias and this indicator was –0.43for CONV, -0.03 for POL1 and 0.12 for POL2, meaningthat the CONV estimate was underestimatingraingauges by 43% on average. Also the other scoreswere better for polarimetric estimates, Nash coefficientin particular was 0.25 for CONV while 0.46 for bothPOL1 and POL2.

Fig. 2 Correlations plots and examined scores results for three radarestimates CONV, POL1 and POL2 versus raingauges measurementsconditioned by value of attenuation (mean attenuation oven an hour ≥3dB).

4.2 DSD conditioning

Discriminating the dataset according to DSD variabilitywas done using the weighted mean value of the N0*parameter. The reference value for was log(N0*)=6.3 m-4

which corresponds to the implicit value of the‘normalized’ intercept parameter characterizing DSD inCONV and POL1. Once retrieved values of N0* wereclose to reference value, Z-R relationship was supposedto correspond well to the real rainfall characteristic.Values smaller then 6.2 meant more stratiform rainfallfor which assumed Z-R relationship was likely to resultin overestimation of rainfall rate. For values bigger then6.4, typical for convective rainfalls, assumed Z-R mightresults in underestimation. This analysis were confirmedby conditional evaluation.

Selecting comparison pairs of mean attenuation lessthen 2 dB and mean value of N0* parameter close toreference value, showed that in this ‘ideal’ conditionssatisfied by 214 cases, all three estimates were of thesame, good accuracy confirmed by the 0.5 of Nash

criterion. No bias was observed for radar estimates,confirming adequateness of Z-R relationship (Fig. 3).

Fig. 3 Correlations plots and examined scores results for three radarestimates CONV, POL1 and POL2 versus raingauges measurementsconditioned by absence of attenuation and mean value of log(N0*) closeto 6.3

Selecting comparison points of mean attenuationsmaller then 2 dB and mean N0* value smaller then 6.2are presented on Fig. 4. They confirmed tendency tooverestimate rainfall rate for CONV and POL1 (NB=0.32 for CONV and 0.47 for POL1). POL2 estimate,through tuning to retrieved N0* value, showed littlepositive bias (0.12) but much satisfactory values ofNash coefficient +0.33 to be compared to the poorvalues obtained by CONV (0.08) and POL1 (–0.6).

Fig. 4 Correlations plots and examined scores results for three radarestimates CONV, POL1 and POL2 versus raingauges measurementsconditioned by absence of attenuation and of mean value log(N0*) lessthen 6.2

Inversing condition on N0* and selecting pairscharacterized by bigger then 6.4 log(N0*) values alsoconfirmed expected underestimation generated by usedZ-R relation (Fig. 5). It especially concerned the highestrainfall rates. Total underestimation was however notvery significant (-0.13 for CONV) due to the fact thatconvective cells characterized by higher values of N0*are usually related to stronger attenuation, so not manycases of intensive rainfall and small attenuation wereobserved. All three estimates were of good accuracyaccording to Nash criterion (around 0.5). Theimprovement introduced by N0* adjustment mainlyaffect ing correlat ion coeff ic ient. Observedoverestimation of POL2 estimates might be caused bythe problems in retrieving the N0* values in stratiformlight rain caused by the increased of statistical error in∆_DP estimation that is proportional to the N0* retrievalerror (Le Bouar et al., 2001)

Fig. 5 Correlations plots and examined scores values for three radarestimates CONV, POL1 and POL2 versus raingauges measurementsconditioned by absence of attenuation and mean value of log(N0*)greater then 6.4

From subset of comparison points affected by meanattenuation bigger then 2 dB, three different N0*characteristics were examined – values of log(N0*) closeto 6.3, smaller and bigger. Because attenuation iscorrelated with N0*, the first two subsets were small andwere evaluated together. The analysis confirmedexpected performance. That is, for the cases ofstratiform rain characterized by smaller values of N0* butalso affected by attenuation, two antagonistic processescan be observed. Not suitable Z-R relation causingoverestimation and signal attenuation resulting in rainfallunderestimation. Due to these effects, no bias andsatisfactory value of Nash coefficient (0.36) wereobtained for CONV in contrary to POL1 when effect ofZ-R overestimation was enhanced by correctingreflectivity for attenuation (Fig. 6). Because of bothattenuation correction and N0* retrieval POL2 estimatereached very good accuracy of 0.7 Nash criterion value

reducing overestimation caused by attenuationcorrection only .

Fig. 6 Correlations plots and examined scores results for three radarestimates CONV, POL1 and POL2 versus raingauges measurementsconditioned by presence of attenuation and mean value of log(N0*) lessthen 6.3

Cases of big attenuation and big value of N0* are theones of the greatest concern as they are usuallyconnected with strong convection and heavy rainfalls.They are also the most difficult to estimate. From multi-event data set, 20 comparison pairs were characterizedby big attenuation of mean value bigger then 2 dB andby big values of ‘normalized’ intercept parameter N0*.Results presented on Fig 7 confirmed the improvementintroduced by polarimeric measurements for bothcorrecting for attenuation in POL1 and correcting forattenuation and tuning N0* in POL2. CONV estimatewas severely underestimated by 46% on averagebecause of attenuation and not suitable Z-R relation.Correcting for attenuation (POL1) helped to reduceunderestimation to the level of 17 % on average, butretrieval of N0* (POL2) removed underestimationcompletely. This efficiency of the two polarmetricestimates were confirmed by the good values of Nashcoefficient of 0.68 for POL1 and 0.73 for POL1 to becompared to 0.17 for CONV.

4.3 CONV vs. POL1 evaluation

The improvement of polarimetric measurements tocorrect for attenuation could be verified by comparingCONV and POL1. The data subset was larger becauseit also included cases of when snow was present in theradar beam. The errors caused by presence of brightband were corrected. Comparison pairs were stratifiedby the value of mean attenuation every 1 dB up to 4 dBand values higher then 4dB.

As the value of mean attenuation increased, CONVestimate was more and more biased with the respect toraingauges while bias for POL1 remained stable (see

Fig 8). The improvement brought up by ZPHI algorithmby correcting reflectivity for attenuation was alsoevidenced by the behavior of Nash criterion valueincreasing for POL1 and decreasing for CONV andreaching for the mean attenuation bigger than 4 dB thevalue of 0.6 for POL1 and 0.1 for CONV.

Fig. 7 Correlations plots and examined scores values for three radarestimates CONV, POL1 and POL2 versus raingauges measurementsconditioned by absence of attenuation and and mean value of log(N0*)greater then 6.4

Normalised bias

0,13

0,67

-0,09

-0,28-0,45

-0,55

0,13 0,17 0,160,05

-0,06 -0,09

-0,8

0

0,8

0 0 - 1 1 - 2 2 - 3 3 - 4 > 4

mean ATTENUATION

CONV POL1

RMSE

1,1

33,7

2,7

65,23

1

3,1

4,45

0,27

4,9

3,5

0

7

0 0 - 1 1 - 2 2 - 3 3 - 4 > 4

mean ATTENUATION

CONV POL1

correlation

0,71 0,7

0,76 0,75

0,58

0,72

0,73 0,71

0,770,75

0,62

0,78

0,5

0,8

0 0 - 1 1 - 2 2 - 3 3 - 4 > 4

mean ATTENUATION

CONV POL1

Nash

0,23

0,45 0,48 0,44

0,08 0,13

0,25

0,4

0,26

0,450,37

0,59

0

1

0 0 - 1 1 - 2 2 - 3 3 - 4 > 4

mean ATTENUATION CONV POL1

Fig 8 Scores on comparing CONV and POL2 for different level ofattenuation

5. CONCLUSION

The validation methodology is quite original in the sensethat a careful examination of the various error sources isdone and the improvement of polarimetry is evaluatedfor each error type. Special emphasis was put onvariation in drop size distribution and attenuation whenthe impact of other sources of errors like VPR effects,ground clutter, orogenic and non orogenic shielding wasreduced to minimum.

The improvement introduced by polarimetry on rainfallmeasurements was especially evident for the convectivesituations and intense rain events characterized bystrong attenuation. For these cases accuracy ofevaluated polarimetric algorithm ZPHI reachedremarkable level of 0.7 of Nash criterion. The results areyet not very robust due to sample size meeting thiscondition, but the multi-event data would be expendedas the rain events would be recorded. For all otherconditions prone to error in radar rainfall estimates likenon-attenuated stratiform rain, attenuated stratiform rainor non-attenuated convective cells characterized bydifferent then conventionally assumed DSD, theevaluated criteria indicated the positive enhancementfor POL2 estimate. Even for the cases whenimprovement was not spectacular as there was noattenuation and the implicit DSD was close to the realone, polarimetric estimate was the one of the greatestcorrelation and value of Nash coefficient.

The improvement of polarimetric measurementsprocessed by ZPHI algorithm to correct for attenuationcould be documented by comparing CONV estimatewith POL1 estimate. The improvement grown as theimpact of attenuation increased.

The problem is the accuracy of retrieved N0* valueslimited by the accuracy of estimating ∆_DP. This resultedin regularly observed ray-wise pattern of N0* valuescaused by the inability to retrieve intercept parametervalue as the differential phase shift along the ray issmaller then assumed threshold.

6. FUTUR WORK

The validation of polarimetry on rainfall estimation wouldbe continue by evaluating other polarimetric algorithmsand attenuation correction schemes, Already recorded,and continually upgraded multi-event data set would thebase for comparative studies on different polarinmetricrainfall estimates as R(Zh, Zdr), R(KDP), R(Kdp, Zdr).

7. ACKNOWLEDGEMENTS

This work was done in the frame of the PANTHEREProject (Programme Aramis Nouvelles Technologies enHydrometeorologie Extension et REnouvellementsupported by Meteo-France, the French “Ministere deL’Ecologie et du Developpement Durable”, the“European Regional Development Fund (ERDF)” of theEuropean Union and CEMAGREF.

8. REFERENCES

Brandes E., Zhang G., Vivekanandan J., 2003: AnEvaluation of a Drop Distribution–Based PolarimetricRadar Rainfall Estimator. Journal of AppliedMeteorology: Vol. 42, No. 5, pp. 652–660.

Bringi, V.N., and V. Chandrasekar, 2001: PolarimetricDoppler Weather Radar Radar. Principles andApplications, Cambridge University Press, 636 p.

Caumont O., Ducrocq V., Delrieu G., Gosset M., PintyJP, Parent du Chatelet J., Andrieu H., Lemaitre Y.,Scialom G., 2005, a radar simulator for high-resolutionnon-hydrostatic models, submitted to J. Atmos. OceanicTechnol.

Le Bouar E., Testud J. , Keenan T.D., 2001, Validationof the rain profiling algorithm « ZPHI » from the C-Bandpolarimetric weather radar in Darwin, J. Atmos. OceanicTech., 18, 1819-1837

Nash, J. E., and J. V. Sutcliffe, 1970: River flowforecasting through conceptual models. I. A discussionof principles. J. Hydrol., 10, 282–290

Ryzhkov, A., Giangrande, S. and T. Schuur, 2003:Rainfall Measurements with the polarimetric WSR-88DRadar, NSSL Report

Testud J., Le Bouar E. , Obligis E., Ali-Mehenni M.,2000, The Rain Profiling Algorithm Applied toPolarimetric Weather Radar. Journal of Atmosphericand Oceanic Technology: 17, 332–356

Tabary P., Desplats J., Eideliman F., Gueguen C.,Lamarque P., Parent-Du-Chatelet J., 2005, The newFrench radar rainfall product. Part I : methodology,submitted to Wea. Forecasting