44 | Triennial Scientific Report

Extreme rainfall climatology from weather radar

Aart Overeem, Iwan Holleman and Adri Buishand

IntroductionExtremerainfalleventshavealargeimpactonsocietyandcanleadtolossoflifeandproperty.Weatherradarsgivequantitativeprecipitationestimatesoverlargeareaswithahighspatialandtemporalresolutionunmatchedbyconventionalraingaugenetworks.Thecurrentqualityofquantitativeprecipitationestimationwithradarandthelengthoftheavailabletimeseriesmakeitfeasibletoderivearadar-basedextremerainfallclimatology.KNMIhasanarchiveof11yearsofradarrainfalldepthsfortheentirelandsurfaceoftheNetherlands.Afteradjustmentusingraingaugedataahigh-qualityrainfallclimato-logyisobtained.Subsequently,ageneralizedextremevalue(GEV)distributionisfittedtoannualradarrainfallmaximaandrainfalldepth-duration-frequency(DDF)curvesarederived,whichdescribetheextremerainfalldepthasafunctionofdurationforgivenreturnperiods.Itisshownthatweatherradarissuitabletoderivethestatisticsofextremerainfall,whichcan,forexample,beusedfordesignpurposesinwatermanagementortheevaluationoftherarityofsevereweather.

Radar and rain gauge dataKNMIoperatestwoC-bandDopplerweatherradars,fromwhichrainfallintensitieswereobtainedwitha2.4kmspatialresolutionanda5-mintemporalresolutionfortheperiod1998-2008withadataavailabilityof

approximately82%.TheradarsarelocatedintheNether-landsinDeBiltandDenHelder,seeFigure1.Fromtherainfallintensities,accumulationswerederivedfordura-tionsof15minto24h.AccumulationimagesfrombothradarswerecombinedintoonecompositecoveringthelandsurfaceoftheNetherlands(35500km2).Quantita-tiveprecipitationestimationwithradarcanbecomelessaccuratedueto,forexample,overshootingofprecipi-tationbytheradarbeam,variabilityofthedrop-sizedistributionandattenuationinthecaseofstrongpreci-pitationorawetradome.Raingaugesareconsideredtoproduceaccuratepointmeasurements.Becauseofthis,raingaugenetworks(Figure1)wereutilizedtoadjusttheradar-basedaccumulations:anautomaticnetworkwith1-hrainfalldepthsforeachclock-hour(≈1stationper1000km2)andamanualnetworkwith24-h08-08UTCrainfalldepths(≈1stationper100km2).Adailyspatialadjustmentisappliedtothe24-h08UTCrainfalldepthsusingthemanualgaugenetwork.Amean-fieldbias(MFB)adjustmentisappliedtothe1-hunadjustedradarrainfalldepthsusingtheautomaticgaugenetwork.Bothadjustmentprocedureswerecombinedandaredenotedbymean-fieldbiasandspatial(MFBS)adjustment.

VerificationTheradardatasetofrainfalldepthswasverifiedusingraingaugesfortheperiod1998-2007.Thebiasinunad-justeddailyradarrainfalldepthswithrespecttomanualraingaugedepthsis-0.88mm,whichisaconsiderableunderestimationsincetheaveragedailymanualraingaugedepthis2.55mm.TheMFBandMFBSadjustmentmethodsreducethebiastorespectively-0.15and-0.03mm.Theresidualstandarddeviationisreducedfrom2.71(unadjusted)to2.14mm(MFB)and1.03mm(MFBS).Raingaugesproducepointmeasurements,whereasradar

KNMI has an archive of 11 years of radar rainfall depths for the entire land surface of the Netherlands

Triennial Scientific Report | 45

0 50

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De Bilt

Den Helder

Figure 1. Maps of the Netherlands with left the locations of the weather radars in De Bilt and Den Helder, their 200-km range (circles), and the 33

automatic rain gauges (squares) and right the locations of the 326 manual rain gauges.

samplesavolumewithahorizontalsurfaceof5.7km2.Thestandarddeviationofthedifferencesindailyrainfalldepthsbetweenmanualandautomaticraingaugeswithina2.4-kmradiusis1.06mm.Thisindicatesthatanimportantpartinthedifferencesbetweenradarandraingaugeaccumulationsiscausedbysub-pixelvariation.

Toinvestigatethespatialqualityofrainfalldepths,biasesinthemeandailyrainfallandtheresidualstandarddeviationarecalculatedforeachradar-gaugepairfortheMFBandMFBSadjustments.IntheMFBadjustmentmethodaconstantfactorisappliedtotheentireradarimage,sothatregionaldifferencesinthebiasesarenottakenintoaccount.Figure2showsthatsuchanadjustmentresultsinquitenegativebiasesnearthebordersoftheNetherlandsandquitepositiveonesinthemiddleofthecountry.Aconstantadjustmentfactoronlypartlycorrectsthelargenegativebiasesinwinterduetopartialovershootingofprecipitationfromshallowstratiformclouds,andturnsthesmallernegativebiasesatshortrangesintoanoverestimation.TheMFBSadjustmentclearlyremovesrangedependenciesinradarrainfalldepths.The1-hradarrainfalldepthsarealsoverifiedagainstthedepthsobtainedfromtheautomaticraingauges.Bothadjustmentmethodsaresuccessfulinremovingthebiasinthemeanhourlyrainfalldepthandinreducingtheresidualstandarddeviation.Ifonlyradarand/orraingaugedepthslargerthan5mmin1hareconsidered,thebiasintheunadjustedradarrainfalldepthsis-3.81mm.Thisisreducedto-0.82mmfortheMFB-adjusteddataand-0.51mmfortheMFBS-adjusteddata.Fortheseextremeevents,theresidualstandarddeviation

decreasesfrom4.60mm(unadjusted)to3.96mm(MFB)and3.80mm(MFBS).Thisimpliesthatadailyadjustmentusingadensegaugenetwork,whichimprovesthespatialqualityoftherainfalldepths,hasaddedvalueifappliedtoalreadyMFB-adjusted1-hrainfalldepths.

Fitting a GEV distributionDatasetsareusuallytooshorttoaccuratelyestimateextremerainfalldepthsfordesignpurposesinwatermanagement.Oftenextrapolationisneeded.Awell-establishedmethodistoabstractannualrainfallmaximafromaraingaugerecordforagivendurationandmodeltheseextremeswithaGEVdistribution.ThequantilefunctionofthisdistributioncanbeusedtoestimaterainfalldepthsforgivenaveragereturnperiodsT,andisgivenby:

(1)

withμthelocationandκtheshapeparameterofthedistribution;γ isthedispersioncoefficient.Thevalueofκdeterminesthetypeofdistribution,iftheGumbeldistributionisobtained.

Rainfall depth-duration-frequency curvesAnovelapproachistoestimateextremerainfalldepthsbasedonweatherradardata,whichisparticularly

0 50

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x(T) =µ 1 + 1 - - In 1 - for κ = 0 (1) γκ

1T

κ

x(T) =µ 1 - In - In 1 - for κ = 0 γ 1T

x(T) =µ 1 + 1 - - In 1 - for κ = 0 (1) γκ

1T

κ

x(T) =µ 1 - In - In 1 - for κ = 0 γ 1T

46 | Triennial Scientific Report

Bia

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Figure 2. Spatial verification of 24-hour 0800 UTC rainfall depths of radar composites against manual gauges for MFB- and MFBS-adjusted radar data:

bias in the mean (upper panel) and residual standard deviation (lower panel).

interestingforshortdurationsforwhichfewraingaugedataareavailable.Forthe11-yearperiod,eachpixelcontains11annualmaxima,whichareabstractedfordurationsDof15minto24h.Foreachindividualduration,GEVdistributionsarefittedtothe6190(pixels)×11(years)annualmaximaassumingthatthedispersioncoefficientandshapeparameterareconstantovertheNetherlands.

ForlongerdurationsthevalidityofthisassumptionisdemonstratedbyBuishandetal.inthisTriennialReport.Thelocationparameterisestimatedforeachradarpixelseparately.Inthisparagraph,theestimatedlocationparametersfortheindividualpixelsareaveragedtoobtainonevalueofthisparameterforeachD.Relati-onshipsarefound,whichmodeltheGEVparametersasfunctionof(inh):

Triennial Scientific Report | 47

Inμ=2.559+0.318D (2)γ = 0.312-0.025D (3)κ= -0.163 (4)

Theserelationshipsaresimilartothosefoundusingraingaugedata1).SubstitutingtheminEq.(1)givesageneralexpressionfortherainfalldepthquantilex(T),whichcanbeusedtoobtainrainfallDDFs.AnexampleofsucharainfallDDFcurveisgiveninFigure3forT=50yearsbasedonradardatafromthisstudy(solidline)andbasedon514annualmaximafrom12raingauges1)(dashedline).Mostraingaugedatarefertotheperiod1977-2005.Forinstance,forareturnperiodof50yearsthe60-minradarextremerainfallis35mm.Theunderestimationofrainfalldepthswithrespecttoraingaugesforshortdurationsmayberelatedtoremainingerrorsintheradardata.

ItisimportanttoestimatetheuncertaintyinDDFcurvesandtotakethisuncertaintyintoaccountinthedesignofhydraulicstructures.ThebootstrapmethodisemployedtoassesstheuncertaintyintheestimationoftheGEVparameters,i.e.samplingerrors.Inthebootstrapmethodnewsamples(bootstrapsamples)aregeneratedbysamplingwithreplacementfromtheoriginalsample.The95%-confidenceintervalsfortherainfalldepthquantilesareshownasalightgray-shadedarea(radar)oradarkgray-shadedarea(raingauge).Theoverlapregionoftheraingaugeandradar-basedconfidenceintervalsisshowningray.Fortheradardatauncertaintiesbecomeratherlargeforthelongestdurations.Forexample,the95%-confidenceintervalrangesfrom72to92mmforD=24handT=50years,whichisduetotherelativelysmallsizeoftheradardatasetforcalculatingthestatis-ticsofextremerainfall.Nevertheless,theuncertaintiesfortheradardataaresmallforshortdurations.Thisisbecauseofthelowspatialcorrelationofshort-durationrainfall.Thelargenumberofobservationsinspacethencompensatesforthesmallnumberofobservationsintime.Theeffectivelengthofthe11-yearradardatasetrangesfromapproximately80yearsforD=24htoafewhundredyearsforD=15min.

Local rainfall depth-duration-frequency curvesDuetospatialvariationofthevalueofthelocationparameter,theaverageDDFcurveinFigure3cannotbeusedeverywhereintheNetherlands.Figure4showsthelocationparametersforD=60minand24handgivestherainfalldepthsforD=24handT=20years.Mostnoticeablearethehighvaluesofthelocationparameterinthewesternpartofthecountry,nearthecoast,forD=24h,whichareconsiderablylargerthanthoseinthe

restofthecountry.ThisisincorrespondencewithresultspresentedbyBuishandetal.inthisTriennialReport,whereannualdailyrainfallmaximawereobtainedfrom55-yearrecordsof141manualraingauges.However,inradar-baseddatalargerspatialdifferencesinthelocationparameterarefound,resultinginrainfalldepthsrangingfrom48to94mmforT=20yearsandD=24h.ForD=60min,severalisolatedareaswithhighvaluesofthelocationparametercanbedistinguished,butnoclearspatialpatternisrevealed.AlthoughregionalvariabilityintheGEVlocationparameterintheNetherlandsisstatisticallysignificantformostdurations,animportantpartofthedifferencescanbeattributedtorandomness,whichwillberelativelylargeforan11-yeardataset.

IfDDFcurvesarederivedforeachradarpixel,theuncertaintiesintheestimatedquantilesofrainfalldepthsbecomeratherlarge.Asacompromise,localDDFcurvesarederivedfortheareasindicatedbythewhiteboxesinFigure4b.For24h,areaAisoneofthe‘driest’areasandareaBoneofthe‘wettest’areasintheNetherlands.LocalDDFcurvesfor50yearsareshowninFigure5,togetherwiththeir95%-confidencebands.Fordurationslongerthanapproximately4hours,the95%-confidencebandsfortheDDFcurvesofareasAandBdonotoverlapimplyingtheseDDFcurvesdiffersignifi-cantly.Ingeneral,the95%-confidencebandsarewiderthanthosefortheaverageDDFcurvefortheNetherlands,showninFigure3,duetothelargeruncertaintyofthelocationparameter.

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Figure 3. Rainfall depth-duration-frequency curves for a return period

of 50 years based on rain gauge data1) (dashed line) and based on radar

data (solid line). Also shown are pointwise 95%-confidence intervals: dark

gray for the rain gauge data, light gray for the radar data. The overlap

region of these confidence intervals is shown as gray.

48 | Triennial Scientific Report

Annual maxima 1998−2008, kappa = −0.172 , gamma = 0.315

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Figure 4. The location parameter for 60 min (left) and 24 h (middle) and the 24-h rainfall depth for a return period of 20 years (right) for each pixel in

the Netherlands.

ConclusionUsingweatherradaran11-yearrainfallclimatologywasconstructedfortheNetherlandsfordurationsof15minto24h.Theadjustmentofradarrainfalldepthsemployingraingaugesresultsinhigh-qualityradarrain-fallcompositeswithaspatiallyhomogeneousquality,whichcoversthelandsurfaceoftheNetherlands.Foranextensivedescriptionoftheadjustmentandverification,see2,3).Ithasbeenshownthatweatherradarissuitabletoestimateextremerainfalldepthsforchosenreturnperiods3).Theradardatasetispotentiallyusefulforrainfallparameterizationinweatherandclimatemodelsandforuseinhydrologicalmodels.Theclimatologicalradardatasetof1-hrainfalldepthsforeveryclock-hourisavailableattheClimateServicesdivision.

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Figure 5. Local rainfall depth-duration-frequency curves for the two areas

indicated in Fig. 4b for a return period of 50 years based on radar data

and their pointwise 95%-confidence bands.

Weather radar is suitable to estimate extreme rainfall depths for chosen return periods

Triennial Scientific Report | 49

References1) Overeem A., T.A. Buishand and I. Holleman, 2008. Rainfall depth-duration-frequency curves and their uncertainties. J. Hydrol., 348, 124-134, doi:10.1016/j.jhydrol.2007.09.0442) Overeem A., I. Holleman and A. Buishand, 2009. Derivation of a 10-year radar-based climatology of rainfall. J. Appl. Meteor. and Climatology, 48, 1448-1463, doi:10.1175/2009JAMC1954.13) Overeem A., T.A. Buishand and I. Holleman, 2009.Extreme rainfall analysis and estimation of depth-duration-frequency curves using weather radar. Water Resour. Res., 45, W10424, doi:10.1029/2009WR007869