Extreme rainfall climatology from weather...
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44 | Triennial Scientific Report Extreme rainfall climatology from weather radar Aart Overeem, Iwan Holleman and Adri Buishand Introduction Extreme rainfall events have a large impact on society and can lead to loss of life and property. Weather radars give quantitative precipitation estimates over large areas with a high spatial and temporal resolution unmatched by conventional rain gauge networks. The current quality of quantitative precipitation estimation with radar and the length of the available time series make it feasible to derive a radar-based extreme rainfall climatology. KNMI has an archive of 11 years of radar rainfall depths for the entire land surface of the Netherlands. Aſter adjustment using rain gauge data a high-quality rainfall climato- logy is obtained. Subsequently, a generalized extreme value (GEV) distribution is fied to annual radar rainfall maxima and rainfall depth-duration-frequency (DDF) curves are derived, which describe the extreme rainfall depth as a function of duration for given return periods. It is shown that weather radar is suitable to derive the statistics of extreme rainfall, which can, for example, be used for design purposes in water management or the evaluation of the rarity of severe weather. Radar and rain gauge data KNMI operates two C-band Doppler weather radars, from which rainfall intensities were obtained with a 2.4 km spatial resolution and a 5-min temporal resolution for the period 1998-2008 with a data availability of approximately 82%. The radars are located in the Nether- lands in De Bilt and Den Helder, see Figure 1. From the rainfall intensities, accumulations were derived for dura- tions of 15 min to 24 h. Accumulation images from both radars were combined into one composite covering the land surface of the Netherlands (35 500 km 2 ). Quantita- tive precipitation estimation with radar can become less accurate due to, for example, overshooting of precipi- tation by the radar beam, variability of the drop-size distribution and aenuation in the case of strong preci- pitation or a wet radome. Rain gauges are considered to produce accurate point measurements. Because of this, rain gauge networks (Figure 1) were utilized to adjust the radar-based accumulations: an automatic network with 1-h rainfall depths for each clock-hour (≈ 1 station per 1000 km 2 ) and a manual network with 24-h 08-08 UTC rainfall depths (≈ 1 station per 100 km 2 ). A daily spatial adjustment is applied to the 24-h 08 UTC rainfall depths using the manual gauge network. A mean-field bias (MFB) adjustment is applied to the 1-h unadjusted radar rainfall depths using the automatic gauge network. Both adjustment procedures were combined and are denoted by mean-field bias and spatial (MFBS) adjustment. Verification The radar data set of rainfall depths was verified using rain gauges for the period 1998-2007. The bias in unad- justed daily radar rainfall depths with respect to manual rain gauge depths is -0.88 mm, which is a considerable underestimation since the average daily manual rain gauge depth is 2.55 mm. The MFB and MFBS adjustment methods reduce the bias to respectively -0.15 and -0.03 mm. The residual standard deviation is reduced from 2.71 (unadjusted) to 2.14 mm (MFB) and 1.03 mm (MFBS). Rain gauges produce point measurements, whereas radar KNMI has an archive of 11 years of radar rainfall depths for the entire land surface of the Netherlands
Transcript of Extreme rainfall climatology from weather...
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
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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
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x(T) =µ 1 + 1 - - In 1 - for κ = 0 (1) γκ
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x(T) =µ 1 - In - In 1 - for κ = 0 γ 1T
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interestingforshortdurationsforwhichfewraingaugedataareavailable.Forthe11-yearperiod,eachpixelcontains11annualmaxima,whichareabstractedfordurationsDof15minto24h.Foreachindividualduration,GEVdistributionsarefittedtothe6190(pixels)×11(years)annualmaximaassumingthatthedispersioncoefficientandshapeparameterareconstantovertheNetherlands.
ForlongerdurationsthevalidityofthisassumptionisdemonstratedbyBuishandetal.inthisTriennialReport.Thelocationparameterisestimatedforeachradarpixelseparately.Inthisparagraph,theestimatedlocationparametersfortheindividualpixelsareaveragedtoobtainonevalueofthisparameterforeachD.Relati-onshipsarefound,whichmodeltheGEVparametersasfunctionof(inh):
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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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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.
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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
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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
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Weather radar is suitable to estimate extreme rainfall depths for chosen return periods
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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
