164 IEEEGEOSCIENCEANDREMOTESENSINGLETTERS,VOL.3,NO.1,JANUARY2006 A Statistical Approach to WindSat Ocean Surface Wind Vector Retrieval CraigK.Smith,Member,IEEE,MichaelBettenhausen,Member,IEEE,andPeterW.Gaiser,SeniorMember,IEEE Abstract—WindSat is the first space-based polarimetric mi- TABLE I crowave radiometer. It is designed to evaluate the capability of NOMINAL NEDT VALUES FOR RAIN-FREE OCEAN polarimetric microwave radiometry to measure ocean surface RETRIEVALCELLS(INKELVIN) wind vectors from space. The sensor provides risk reduction for the National Polar-orbiting Operational Environmental Satellite System Conical Scanning Microwave Imager/Sounder, which is planned to provide wind vector data operationally starting in 2010. The channel set also enables retrieval of sea surface temperature, and columnar water vapor and cloud liquid water (W) referenced to 10-m height, compass wind direction , overtheoceans.Wedescribestatisticalalgorithmsforretrievalof theseparameters,andacombinedstatistical/maximum-likelihood columnarwatervapor(V),andcloudliquidwater(L).Thepur- estimator algorithm for retrieval of wind vectors. We present a poseofthiseffortisthreefold:1)obtainaquickinitialassess- quantitative analysis of the initial wind vector retrievals relative ment of WindSat’s wind vector measurement capabilities; 2) toQuikSCATwindvectors. provide a retrieval-oriented test platform for enhancements to Index Terms—Microwave radiometry, polarimetry, retrievals, theWindSatTemperatureandSensorDataRecordalgorithms; wind. and 3) provide either an independent set of retrievals from, or aprioridata for,a physically basedalgorithm.Theregression techniqueandtheselectionofregressiontrainingdatawerede- I. INTRODUCTION signedtofacilitateretrievalofallfiveparameters,asdiscussed WINDSAT is a conically scanning polar-orbiting multi- inSectionsIIandV.However,inthisletterwefocusonappli- frequency microwave radiometer launched in January cationoftheregressionstowindvectorretrieval. 2003. Its objective is to measure the partially polarized emis- sionfromtheoceansurfaceand,therefore,testandfullyeval- uate the viability of using polarimetric microwave radiometry II. REGRESSIONTECHNIQUE to retrieve ocean surface wind vectors. WindSat measures po- Forthisinitialvalidationoftheregressiontechnique,weused larized radiometric brightness temperatures in 16 “chan- WindSat averagedtothelowestresolution(6.8GHz),where nels”: vertically and horizontally polarized ( and ) at the forall16channelsareavailable.The foreachchannel 6.8,10.7,18.7,23.8,and37.0GHz,andthirdandfourthStokes are sampled at approximately 12.5 km along scan and along parameters( and )at10.7,18.7,and37.0GHz. and track and averaged to a common spatial resolution of approx- arederivedfromthedifferenceof linearandleft/rightcir- imately 40 60 km. The nominal measurement noise for the cularpolarizations,respectively.TheWindSatreflectorantenna retrievalcells,specifiedbythenoise-equivalentdifferentialtem- hasan11-feedhorncluster,resultinginfixednominalEarthin- perature(NEDT)formeanoceanscene ,isgiveninTableI. cidenceangles(EIA)rangingfrom50 to56 (allhornswithina The regression training (i.e., regression coefficient determi- frequencybandhavethesameEIA)[1].TheEIAsareknownto nation)isperformedempirically,usingcollocationsofWindSat better than 0.05 [2]. A detailed description of the radiometer with various sources of satellite retrievals and numerical can be found in [1]. WindSat provides risk reduction for the weather prediction model (NWP) data (Section V). Unlike re- ConicallyScanningMicrowaveImager/Soundertobeflownon gressionstrainedusing simulatedwithaphysicalmodel[4], theNationalPolar-orbitingOperationalEnvironmentalSatellite [5],empiricalregressionsautomaticallycompensateforbiaser- System[3]. rorsinthemeasurements,andpotentialproblemssuchastime- We have developed an empirical statistical regression tech- dependentcalibrationerrorsorhighnoiseresultsindeemphasis niqueforretrievalofseasurfacetemperature(SST),windspeed (coefficientsnearzero)fortheaffectedchannel.Therefore,we useall16channelsinallregressions.Regressioncoefficientsare determinedbylinearleastsquares. ManuscriptreceivedDecenber21,2004;revisedAugust5,2005.Thiswork Weusealinearmethodtoretrieveparametersforwhichthe wassupportedinpartbytheU.S.NavyunderGrantN000WX04730023. relationship with the ranges from nearly linear to severely C.K.SmithwaswithComputationalPhysics,Inc.,Springfield,VA22151 nonlinear. Three techniques exist to address this nonlinearity USA. He is nowwith The Aerospace Corporation,Los Angeles, CA90009 USA. problem.Thefirstusesfunctionsofthe thatarelinearwith M. Bettenhausen and P. W. Gaiser are with the Remote Sensing Divi- respecttoagivenretrievalparameterasargumentsintheregres- sion, Naval Research Laboratory, Washington DC, 20375 USA (e-mail: sions [4], [5]. Additionally, terms that are quadratic or higher [email protected]). DigitalObjectIdentifier10.1109/LGRS.2005.860661 orderinthe orthe linearizationfunctionsmay beincluded 1545-598X/$20.00©2006IEEE Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. 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PERFORMING ORGANIZATION Naval Research Laboratory,Remote Sensing Division,4555 Overlook REPORT NUMBER Avenue, SW,Washington,DC,20375 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES The original document contains color images. 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF ABSTRACT OF PAGES RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE 5 unclassified unclassified unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 SMITHetal.:STATISTICALAPPROACHTOWINDSATOCEANSURFACEWINDVECTORRETRIEVAL 165 toallowtheregressiontrainingtoeliminatesomeofthenonlin- The regressions are accomplished using a two-stage tech- earity directly [5]. The second technique is to retrieve a func- nique. In the first stage, the retrievals are performed for , tionofthedesiredparameter,onwhichthe haveanapprox- , and , using regression coefficients trained on the entire imatelylineardependence[5].Thethirdmethodistotrainand trainingdataset(SectionV).Inthesecondstage,thefirst-stage applyregressionsonrestricteddomains(“bins”)ofageophys- regressionresultisusedtodetermineawindspeedbin,from ical parameter on which the have a nonlinear dependence. which regression coefficients are selected to perform the SST The bins are chosen so that the dependence of the on that and through retrievals.Thebinsare2m/swide,andcover parameterisapproximatelylinearwithineachbin[4]. thewindspeedranges0–2,2–4,4–6m/s,etc. The application of these techniques to the retrievals is ex- The second-stage regressions offer significant advantages plained below. We make a significant extension to the second over analogous first-stage regressions. Within each bin the techniquetoretrievewinddirection,forwhichthesignalinall Fouriercoefficientsin(2)areapproximatelylinearfunctionsof the isseverelynonlinear(infactnonunique)anddependson —i.e.,thewinddirectionsignalsareapproximatelylinearin windspeed.There,weperformregressionsforseveralfunctions through —improvingthe through linearregression ofwindspeedanddirection,andthenusetheregressionresults andMLEwinddirectionperformance. in a maximum-likelihood estimator (MLE) for wind direction Second-stageperformanceisimprovedbywideningthebins retrieval,asdiscussedinSectionIII. during regression training, to account for the “misbinning” Theregressionforanyretrievalparameter isoftheform resulting from retrieval error in the first-stage regression [0.8 m/s root mean square (rms) error]. However, the benefit of accommodating misbinning is counterbalanced by the in- (1) creasingnonlinearityof the withrespectto through as the bins are widened. Given the bin width of 2 m/s for the retrievals, a bin width of 4 m/s for the training is optimal; the where is the WindSat brightness temperature for channel binsarethuswidenedby1.0m/soneachsideforsecond-stage , except for the 23.8-GHz channels, where training(0–3,1–5,3–7m/s,etc.). ; the latter serves to linearize with respect to the V signal when water vapor absorption is appreciable [4], III. MAXIMUM-LIKELIHOODESTIMATOR [5], which significantly improves the V retrieval but does not significantly affect any of the other retrievals. The quadratic Following application of the second-stage regressions, terms greatly reduce the nonlinear interactions (“crosstalk”) through areprovidedtotheMLEforwinddirectionretrieval. betweenSST,W,V,andL.InclusionoftheEIAforthe37-GHz Thelikelihoodfunctiontobemaximizedisforestimatingtwo vertical–horizontal(vh)feedhorn(e)reducestheSSTretrieval parameters from four “measurements” ( through error by 5%, but has little effect on the other retrievals. The ) whose errors are correlated and approximately Gaussian small variations from the nominal EIAs for the different feed- distributed[9].Therefore,theMLEfindsmultiplewindvector hornsshowalinearrelationshiptoeachother,sothatinclusion solutions, pairs known as “ambiguities,” as local ofasingleEIAissufficientforalinearregression.Theregres- minimaof sionsallowfordirectretrievalofSST,W,V,andL. The directional component of the microwave sea surface emissivity canbeexpressedasatwo-termFourierseries where in relative wind direction ( , the compass wind direction minus radiometer look direction projected on the Earth) [6]. TheFouriercoefficientsarenonlinearfunctionsofwindspeed thatdependonEarthincidenceangle,frequency,andpolariza- tion [6]. The series is even for and and odd for and [6],[7] is the error covariance matrix of the through re- trievals for the bin determined by the first-stage regression (Section II) and is obtained by running the regressions on the (2) trainingdataset(SectionV).The vectorissimplythediffer- ence between the through regressions and their mathe- Thus, for retrieval, we perform four regressions, for the maticaldefinitionsgiveninSectionII. along-look wind speed , cross-look wind The MLE may appear to be a two-dimensional search for speed , and “second harmonics” of the chi-squareminimainthespaceof .However,itshould along- and cross-look wind speeds ( and be noted that, because through are linear in , mini- ). The along-look wind speed is identical to mization along the axis yields a single, analytical solution the“line-of-sight”windspeedretrievedbyWentz[8].Whilethe for at each value of , denoted . Substitution and regressionsaresufficientforuniquewinddirection of into the definition of the chi-square results in a retrieval, we find significant improvement for m/s by one-dimensionalminimizationalongthe axis.Thisone-di- usingallfourregressionsasinputtoanMLEforwinddirection mensionalminimizationissubjecttothefollowingconditions: retrieval. 1) isnonnegative(physicalsolution);2)thesecond 166 IEEEGEOSCIENCEANDREMOTESENSINGLETTERS,VOL.3,NO.1,JANUARY2006 partialderivativeofthechi-squarewithrespectto ,evaluated SSM/I.GDAS1 1 analysesspatiallyinterpolatedtothelo- at ,ispositive(trueminimumandnotasaddleorin- cationofWindsatmeasurementsareusedforSST,andforwind flectionpoint). vectorswhenaQuikSCATobservationisnotavailable.Thecol- The resulting ambiguities are then ranked locationwithSSM/IisincludedtofacilitatedevelopmentofV by chi-square, with the “first rank” solution having the lowest andLregressions.Thewindvectortestingdatasetisatwo-way chi-square.Itshouldbenotedthatthe through regressions collocationbetweenWindSatandQuikSCAT.Forbothtraining have significantly larger retrieval errors than the first-stage andtesting,thespatialcollocationwindowis25kmforalldata regression, and therefore the ’s are inferior to the first- sources, and the temporal collocation window is 60 min for stage regression result. We therefore use the first-stage GDASandQuikSCATand35minforSSM/I.Beforecolloca- retrievalasthefinalretrievalresult. tion,theeightretrievalcellsalongbothedgesoftheQuikSCAT swathwereremoved,becausetheycontainlessthantheoptimal fourbeamcombinations,andhavedegradedwindvectors[11]. IV. MEDIANFILTER Theregressiontrainingdatasetisqualitycontrolledthrough Duetoregressionerrors,thefirstrank(mostlikely)solution exclusion of every condition listed in the next paragraph and is not always the closest ambiguity to the true wind direction. SDRsthatarelikelyinfluencedbythermalgradientsinthewarm Improvementinambiguityselectionbeyondthefirstrankresult load.Nosuchexclusionsaremadeinthetestingdataset;instead, ismadeinretrievalpostprocessing,whereweapplyavectorme- qualitycontrolflagsaresetduringretrieval. dianfilter(MF)[10]tocorrectisolatedambiguityselectioner- RetrievalsareperformedforallSDRsexceptthoseintheaft rorswhileretainingthelargescalediscontinuities(forexample, scan [1], with surface type other than ocean (no coast or near fronts)foundinnaturalwindfields. coast), with one or more outside the physical bounds for The MF is an iterative spatial filter that selects from the set no or light rain, or with any EIA outside the expected range ofambiguitiesinthecellbeingfilteredtheonemostconsistent (i.e.,morethan0.5 fromnominal).Thefollowingareflagged with the previously selected ambiguities in a window of sur- as“lowconfidenceretrievals”:1)inlakesorinlandseas;2)re- rounding cells. It accomplishes this by minimizing the vector trieval cell may contain rain; 3) in areas found to periodically medianfilterfunction[10],aweightedsumofnormsofvector suffer from radio-frequency interference (RFI) or ice contam- differences between an ambiguity and the previously selected ination; and 4) are likely to suffer land contamination (within ambiguitiesforallcellsinthewindow.AftertheMFisapplied 105kmor1.75retrievalcellHPBWfromnearestland).Condi- to allocean cells inan orbit,the newly selected wind fieldre- tion(2)isdeterminedusinganSSMI-typerainflaggingadapted placesthepreviouswindfield.Theprocessisiterateduntilthe toWindSatfrequencies[13].Static,geographicalmasksdefine windfieldconverges. theotherconditions. Inourapplication,thewindowis7 7cells(inscan-based coordinates) centered on and including the cell being filtered. VI. RETRIEVALPERFORMANCE Missingcellsinthewindow(duetoscanedges,land,ice,etc.), Theretrievalperformanceinthissectionexcludeslowconfi- are “replaced” with the ambiguities from the center cell. Be- dence retrievals, which are 20% of the total.1 The Faraday ro- cause wind direction retrieval performance improves with in- tationcorrectionnecessarytooptimize retrievalperformance creasing (Section VI), the term for each cell in the filter isundervalidation,andhasnotbeenappliedtotheSDRsinthe function is weighted linearly by the retrieved wind speed for regressiontestingandtrainingdatasets. thatcell; forhighconfidencere- Wind vector retrieval errors are computed relative to collo- trievals,andhalfthatforlow-confidenceretrievals(SectionV) catedQuikSCATdata(SectionV).TheQuikSCATtestingdata andforreplacements. haserrorsrelativetoinsitugroundtruth,asdoestheQuikSCAT The MF is initialized with the first rank wind vector from andGDASdatausedforwindvectorregressiontraining.How- each ocean retrieval cell. Optionally, it can be initialized with ever,theerrorscomputedhereshouldbegoodapproximations nudgedwindvectorfields[11];thenudgedfieldisobtainedby (and likely upper bounds) to those that would be obtained by selectingthefirstorsecondrankambiguityforeachcellthatis trainingandtestingwithactualgroundtruthdata(orbytraining closesttothewindvectorobtainedfromtheNCEPGlobalData with simulatedusingaphysicalmodelcalibratedtoground AssimilationSystem(GDAS)1 1 analysisclosestintime, truth,andtestingwithgroundtruth). spatiallyinterpolatedtothecelllocations. Table II shows the overall regression retrieval errors. Given theconsiderationsabove,theoverall rmserroriswellwithin V. ALGORITHMTRAININGANDTESTING 1.0 m/s. Training the regression on a natural, nonuniform distributionofwindspeeds(ascontainedinthecollocateddata) Six months of WindSat version 1.6.1 Sensor Data Records initially resulted in a large bias error at high wind speeds (SDRs),spanningaperiodwhenthermalgradientsinthewarm ( m/sat23m/s).Wegreatlyreducedthisbias(attheexpense load[12]areminimal(September2003throughFebruary2004), havebeencollocatedwithvarioussourcesofNWPandsatellite retrievalsforuseinregressiontrainingandretrievaltesting(al- 189% of low confidence retrievals were flagged for possible rain, 3% for ternatingtwodaystraining,onedaytestingthroughout). RFI/ice,10%forlandcontamination,and1%forinlandlakesandseas;mul- tipleflagscanbesetforeachretrieval.Therainflagwasdevelopedforfiltering ThetrainingdatasetconsistsofcollocationsbetweenWindsat allraincasesfromthetrainingdata,andthereforeerrsonthecautioussideand SDRs,theQuikSCATscienceproduct[11]forwindvectors,and overestimatestheoccurrenceofrain. SMITHetal.:STATISTICALAPPROACHTOWINDSATOCEANSURFACEWINDVECTORRETRIEVAL 167 TABLE II OVERALLRETRIEVALERRORSFORREGRESSIONS Fig.2. WindSatwinddirectionrmserrorsstratifiedbyQuikSCATwindspeed. ErrorsaredeterminedrelativetothecollocatedQuikSCATscienceproduct. Fig.1. WindSatwindspeederrorsstratifiedbyQuikSCATwindspeed. ofintroducingasmalloverallbias)byweightingeachofthecol- locatedobservationsintheregressiontrainingbythereciprocal ofthesquarerootofthewindspeeddistribution[14].Thestrat- ification of the retrieval errors versus the QuikSCAT wind speedisshowninFig.1. The overall regression errors for through in Table II aremuchlargerthanthosefor .Thisoccursbecausethewind speed signal in is large [5], while the directional signals Fig. 3. Wind direction skill and mean number of ambiguities stratified by are relatively small [6], [15]. The through regressions QuikSCATwindspeed. must extract parts of the small directional signals, while com- pensating for atmospheric and SST variations. Because of the ambiguities is low. Due to the requirement that the MLE-re- sine/cosine dependence of the wind direction signals, the trieved wind speed be nonnegative (Section III), there are no and regressionsusemainly and ,whilethe and morethantwoambiguitiesforanyretrieval,2withanaverageof regressionsusemainly and .Becausethewinddirection 1.56overallretrievals.Thus,themedianfiltercannotimprove signalsfor and aresuperposedonalargeandhighlyvari- 44%oftheretrievals.Anotherreasonisthat,whenoneconsiders ablenondirectionalcomponent,theregressionerrorsfor and only retrievals with two ambiguities, the skill is reduced from arelargerthanthosefor and . that shown in the figure; for example the FR skill drops from Fig.2showsthewinddirectionrmserrorsforthefirstranked 84%to76%at5m/s. (FR), median filtered (MF), median filtered with nudging Additionally, MF wind fields show good qualitative agree- (MFNG) ambiguities, and the closest ambiguity to the collo- ment with QuikSCAT wind fields except inside some regions catedwinddirection(CL).Thewinddirectionbiaserroratall where m/sandwinddirectionischangingrapidly;there, issmall(lessthan3 )andisnotshown. low-skilldegradedretrievalsoftenoccurincontiguouspatches. Above12m/s,theagreementbetweenthewinddirectionre- By itself, the median filter rarely improves upon the FR am- trievals and QuikSCAT is excellent for all of the above ambi- biguityinsuchpatches.Analogoustoscatterometerretrievals, guities.Ourinitialwinddirectionperformanceiswithin20 of wehavefoundthattheseparationbetweenthefirstandsecond QuikSCATforwindspeedsabove9.9,8.8,7.6,and7.2m/sfor rankambiguitiesisabout180 ,whichmayfurtherinhibitme- the FR, MF, MFNG, and CL ambiguities, respectively. Below dianfilterperformanceinandnearthepatches.Nudging,which 5 m/s, the wind direction signals are very small [6], [15], and can select the second rank ambiguity to initialize the median thewinddirectionretrievalperformancedegradesaccordingly. Fig.3showstheskill(percentageofretrievalswherethese- 2Withoutthisrequirement,themaximumnumberofambiguitiesis3.How- ever,ambiguitieswithnegativeW alwayshavethehighestchi-squareof lected ambiguity is the CL ambiguity) for the FR, MF, and (cid:0) anyambiguity(oftenbyanorderofmagnitude),haveavaluenear 1m/s, MFNG ambiguities, and the total number of ambiguities. De- regardlessofthemagnitudeofthewindspeedscomputedfrom(U ;U )and spite high FR skill, the median filter by itself makes only a (U ;U )vectors,andappearwhenthesetwowindspeedsaregrosslyincon- sistent.Thus,weconsiderambiguitieswithnegativeW tobeanunphysical smallimprovementinthewinddirectionerror(6 to8 below resultobtainedwhentheMLEisgiveninconsistentvaluesofU throughU . 8 m/s, less than 3 above). One reason is that the number of Assuch,theyshouldbediscarded. 168 IEEEGEOSCIENCEANDREMOTESENSINGLETTERS,VOL.3,NO.1,JANUARY2006 filter,allowssignificantimprovementintheagreementbetween REFERENCES MFNG and QuikSCAT wind fields over the patches, and thus [1] P.W.Gaiser,K.St.Germain,E.M.Twarog,G.A.Poe,W.Purdy,D. in wind direction performance at low and intermediate wind Richardson,W.Grossman,W.L.Jones,D.Spencer,G.Golba,M.Mook, speeds. 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