A NEW METHOD FOR IMPROVING SCATTEROMETER WIND QUALITY CONTROL

A NEW METHOD FOR IMPROVING SCATTEROMETER WIND QUALITY CONTROL M. Portabella (, A. Stoffelen (, A. Verhoef (, J. Verspeek ( ( Undad de Tecnología Marna CSIC, Pg. Marítm Barceloneta 37-9, 3 Barcelona, Span ( Royal Netherlands Meteorologcal Insttute (KNMI, Postbus, 373 AE De Blt, The Netherlands Emal: portabella@cmma.csc.es ABSTRACT An mportant part of the scatterometer wnd data processng s the qualty control (QC. Ths paper shows the mplementaton of a new scatterometer QC procedure, based on a comprehensve analyss of the wnd nverson resdual, whch sgnfcantly mproves the effectveness of the wnd data QC. The method s appled on a European scatterometer, the so-called ASCAT, but s generc and can therefore be appled to any scatterometer system.. INTRODUCTION Scatterometers are satellte-based real aperture radar nstruments known to provde accurate mesoscale (5-5 km resoluton sea surface wnd feld nformaton used n a wde varety of applcatons, ncludng Numercal Weather Predcton (NWP data assmlaton, nowcastng, and clmate studes. The radar antenna geometry, the measurement nose, as well as nonlneartes n the relatonshp between the backscatter measurements n a Wnd Vector Cell (WVC and the mean wnd vector complcate the wnd retreval process. In addton, scatterometers are senstve to geophyscal phenomena other than WVC-mean wnd, such as local wnd varablty, confused sea state, ran, and land & ce contamnaton of the radar footprnt. These phenomena can dstort the wnd sgnal, leadng to poor-qualty retreved wnds. As such, elmnaton of poor qualty data s a prerequste for the successful use of scatterometer wnds. The Metop-A satellte was launched on 9 October and carres the Advanced Scatterometer (ASCAT. The radar operates at C band and s vertcally polarzed, wth three fan beam antennas pontng at each sde of the sub-satellte track. An mportant tool n the nterpretaton of the ASCAT data s the vsualzaton of trplets of radar backscatter or σ measurements (correspondng to the three antenna beams n the 3- dmensonal measurement space at each cross-track WVC []. For such gven WVC poston, the ASCAT measured trplets are dstrbuted around a well-defned concal surface (see Fgure and hence the sgnal largely depends on just two geophyscal parameters,.e., wnd speed and drecton, snce geometrcal aspects are rather constant over the orbt. Such cone conssts of the so-called Geophyscal Model Functon (GMF, whch represents the best ft to the measured trplets. The magntude of the trplet departures from the twoparameter functon (.e., the GMF s correlated wth the qualty of the wnd retrevals []. A way to nvestgate such departures s to look at the nverson resdual or maxmum lkelhood estmator (MLE parameter, whch can be nterpreted as a measure of the dstance between the set of radar measurements (trplets and the cone surface n a slghtly transformed measurement space. In general, the trplets le close to the cone surface (.e., low MLE values, further valdatng the two-parameter (.e., wnd-vector dependent GMF. As shown by several QC procedures developed for prevous scatterometer mssons (e.g., [], a large nconsstency wth the GMF results n a large absolute MLE, whch ndcates geophyscal condtons other than those modelled by the GMF, such as local wnd varablty, ran, confused sea state, or ce, and as such, the MLE provdes a good ndcaton for the qualty of the retreved wnds. However, no work has been done to nvestgate the correlaton between the qualty of the retreved wnds and the MLE sgn,.e., postve (negatve for trplets located nsde (outsde the cone surface. In ths paper, we propose a QC method, whch not only depends on the magntude of the MLE but also on the sgn. In Secton, the ASCAT operatonal QC s ntroduced. In Secton 3, the MLE sgn computaton s presented. The analyss of the MLE sgn n terms of a wnd qualty ndcator s descrbed n Secton. Fnally, t s concluded n Secton 5 that the MLE sgn s very benefcal for QC.. ASCAT OPERATIONAL WIND QUALITY CONTROL The most common approach used for scatterometer wnd nverson s the Bayesan approach, whch leads to the so-called Maxmum Lkelhood Estmator (MLE technque [], [3], [], [5]. For the ERS and ASCAT scatterometers, the followng smplfed MLE functon s mnmzed []: 3 MLE = ( z o z s ( 3 = o. where s the measurement ndex, zo o s the o. transformed backscatter measurement, and zs s s the transformed backscatter smulated through the

GMF. The C-band GMF,.e., the so-called CMOD5n [], s represented n z-space n the followng way:.5 z s v, φ= B v [+ B v cosφ + B v cos( φ ] ( where θ, φ, and v are the ncdence angle, azmuthal wnd drecton angle and wnd speed, respectvely. B, B, and B are functons of wnd speed and ncdence angle and were obtaned by fttng the GMF to ERS scatterometer data whch covers an ncdence angle range of -55. Fgure. Vsualzaton of the CMOD5n GMF (blue surface and the ASCAT trplets (black dots n 3D measurement space, for WVC number 3. The axes represent the fore-, aft- and md beam backscatter n z- space,.e., (z fore, z aft, z md where z=(σ.5. Dfferent wnd speed and drecton tral values are used n the GMF n order to mnmze the MLE (Eq.. Neglectng the GMF uncertanty, the followng equaton o. s used: zo s + ε, where ε s the backscatter error wth relatve error ε Kp =, to determne the o σ s expectaton value of Eq. by usng a Taylor expanson: 3 < MLE >= (. z s Kp (3 3 = The MLE nverson technque s also used for other scatterometers, albet usng a slghtly dfferent formulaton [3] and therefore a slghtly dfferent expectaton value []. The expected MLE (Eq. 3 s very valuable for QC [], [] and wnd retreval purposes [7], []. Detaled nformaton on the estmaton of measurement errors (Kp can be found n [9]. Several studes [], [], [9] show that Kp msestmaton leads to dfferences n the expected MLE across the sub-satellte track. As such, an addtonal emprcally-derved WVCdependent normalzaton s generally derved for QC and wnd retreval purposes [], []. In summary, scatterometer wnd QC s generally based on the MLE normalzed by the measurement nose and a WVCdependent factor. For ASCAT, the QC procedure mplemented n AWDP durng the frst three years of the MetOp-A msson, was also based on the normalzed MLE, smlar to that of the ERS scatterometer [9]. The nverson resdual or MLE was normalzed by the measurement nose [9] and a WVC-dependent factor. A fxed threshold value of ths normalzed MLE (hereafteeferred to as MLE,.e.,., s used n AWDP to dscrmnate between poor and good qualty wnd data. As such, a WVC wth MLE value below (above. s accepted (rejected n the processng chan. Table summarzes the overall performance of the ASCAT MLE-based QC. The mean vectooot-mean-square (VRMS dfference between ASCAT and European Centre for Medum-range Forecasts (ECMWF model wnds s used as a qualty ndcator. The substantal dfference n terms of qualty (relatve to ECMWF model wnds between accepted and rejected WVCs denotes an effectve QC. QC Fracton of VRMS (m/s data (% Accepted 99..7 Rejected..5 Table. Percentage and Mean VRMS dfference between ASCAT and ECMWF wnds for accepted and rejected data. 3. MLE SIGN Fgure shows a schematc llustraton of a cross secton of the cone surface shown n Fgure. Note that such cross secton s almost perpendcular to the cone, and manly shows the varaton due to wnd drecton (ø at approxmately constant wnd speed. By r computng the nner product of H = zs A and r M = z s z o (see Fgure, one can straghtforwardly determne whether the measurement trplet s nsde or outsde the cone surface,.e., the nner product wll be postve when the trplet ( z r s nsde the cone and negatve when the trplet s outsde the cone. The trplets on the GMF surface,.e., z r s, are gven by the nverson. The ASCAT mnmzaton procedure (Eq. generally produces wnd vector solutons. For each wnd soluton [ vsol, φ ], a sol z r can be derved usng Eq. s. Lkewse, the cone s major axs locaton can be. 5 derved from Eq.,.e., A = B vsol. As such, for each mnmum MLE value n Eq.,.e., MLE sol (nverson resdual correspondng to a wnd soluton, a sgn can be added n the followng way: ' H M MLEsol = MLE (5 sol H M To mmc the old (sgnless MLE-based procedure wth the new parameter MLE, the ASCAT QC threshold

(. needs to be appled to ts absolute value,.e., MLE. followng secton s therefore focused on scatterometer wnds above m/s. 3 ASCAT Wnd Speed (m/s. Fgure. Schematc llustraton of a cross secton of the CMOD5n GMF shown n Fgure.Note that z r s refers to a pont on the cone surface as determned by nverson; A epresents the major axs locaton at ths cross secton; and z r represents the measurement trplet. Fgure 3 shows a -D hstogram of the MLE rank dstrbuton as a functon of MLE value and retreved wnd speed, where rank means the absolute mnmum n Eq.,.e., the closest dstance between the ASCAT trplet and the CMOD5n cone surface. A good ft of CMOD5n to the ASCAT measurements s represented by a symmetrc MLE dstrbuton n Fg. 3,.e., same MLE dstrbuton nsde and outsde the cone. For md to hgh wnds ths s roughly the case. However, at low wnds, a very dstnct behavour s shown. Around m/s most of the trplets le nsde the cone, ndcatng a clear msft of the CMOD5n GMF. At very low wnds (below m/s, we see the opposte behavour,.e., most of the trplets le outsde the cone. Ths s due to the closng of the cone as t approaches ts orgn,.e., the orgn of the measurement space (z fore, z aft, z md = (,,. By constructon the CMOD5n z s values for the dfferent beams (ncdence angles wll converge at zero wnds, whch leads the cone cross secton (as llustrated n Fg. to vrtually dsappear. At very low wnds and 5-5 km resoluton cells, the scatterometer manly observes wnd varablty rather than a WVC-mean (close to m/s vector wnd and wth lttle backscatter ansotropy, such that the concal surface closes and no trplets can resde nsde the cone (see Fgure, whch therefore mostly le outsde the (very small cone cross secton. Although, due to the effects descrbed above, the scatterometer wnd drecton skll s low at low wnds, the scatterometer wnd vector error s about the same at low wnds than at moderate and hgh wnds []. Moreover, t s most relevant to study the effect of the MLE sgn on QC above m/s. The analyss n the.5 3.5.5.5. - - MLE Fgure 3. Two-dmensonal hstogram of the ASCAT retreved wnd speed versus MLE value for the st -rank soluton (.e., correspondng to closest dstance between the trplet and the cone surface. The contour lnes are n logarthmc scale: every two steps s a factor of and the lowest level s at WVCs per bn.. ANALYSIS OF QC WITH MLE SIGN To characterze the correlaton between the MLE and the qualty of retreved wnds, ECMWF wnds are used as reference. One year ( of collocated ASCAT and ECMWF data are used n the analyss. Fgure shows the mean VRMS dfference between ASCAT and ECMWF wnds as a functon of the MLE magntude and sgn. There s a clear dstnct behavour for postve and negatve MLEs n terms of data qualty. On the one hand, ASCAT wnds derved from trplets located nsde the cone rapdly decrease n qualty as the trplet s dstance to the cone surface ncreases (.e., see steep ncrease of VRMS as a functon of MLE, for postve MLE values. On the other hand, for trplets lyng outsde the cone surface, the ASCAT wnd qualty degradaton s generally small regardless of the trplet dstance to the cone (see the relatvely small slope of the VRMS curve as a functon of MLE, for negatve MLE values. As such, snce January, the AWDP QC procedure was updated to account for the MLE sgn. In partcular, the new QC procedure does not reject any wnd data from trplets located outsde the cone surface (.e., wth negatve MLE values. The MLE threshold value s kept the same (., although t s not appled to the absolute value of the MLE but to the MLE value tself. Fgure 5 shows the hstogram of the wnd drecton relatve to the ASCAT md beam drecton for two dfferent wnd sources,.e., ASCAT (sold and

ECMWF (dotted, and for three dfferent MLE ntervals: -. < MLE <. (top, MLE >. (md, and MLE < -. (bottom. Note that the top (md panel represents QC-accepted (QC-rejected WVCs n both the prevous (before January and the current AWDP QC. The bottom panel shows the WVCs prevously rejected and currently accepted. Mean Vector Dfference ASCAT - ECMWF (m/s - - MLE Fgure. Mean vectooot-mean-square (VRMS dfference between ASCAT and ECMWF wnds as a functon of MLE. Note that negatve (postve values correspond to trplets outsde (nsde the cone surface. The top and mddle panels correspond to the MLE ntervals where both old and new QCs concde. The ASCAT wnd drecton dstrbuton s very smlar to that of ECMWF for the QC-accepted WVCs (top, followng the good agreement between both wnd sources n Table. However, foejected WVCs (md, the ASCAT dstrbuton s substantally dfferent from that of ECMWF. The former has clear artfcal (non geophyscal accumulatons at certan wnd drectons (see sold curve peaks whle the dotted curve s rather flat. Ths systematc effect n the drecton retrevals s well known n scatterometry and has been reported by several authors (e.g., [5], []. It s undesrable and therefore mportant to remove or at least to mtgate. As such, by detectng such artefacts, the QC shows good performance. Regardng the MLE nterval where old and new QCs dffer (bottom panel, although ASCAT wnd drectons present a somewhat more modal dstrbuton than that of ECMWF, t s clear that both dstrbutons are rather smlar, ndcatng a far ASCAT wnd drecton skll for MLE < -.. Ths s consstent wth the rather small VRMS values shown n Fg. at such MLE nterval. The reason for the dfferent wnd drecton skll (and therefore wnd vector skll for trplets located far nsde and far outsde the cone surface s the followng. Let s assume, for example, a true wnd wth a crosswnd drecton (relatve to md beam, whch can be represented n Fg. by a pont at the bottom of the cross secton. Take a measurement trplet ( z r nsde the cone and close to the true wnd drecton and move t away from the surface. At a certan pont, the trplet may le closer to the opposte sde of the cross secton,.e., the top part (upwnd/downwnd drectons, therefore leadng to a set of very wrong wnd drectons n the retreval process. Another nterestng effect s that when the trplet les close to the centre of the cross secton, the number of retreved wnd drecton ambgutes ncreases from two (typcal case for ASCAT to four (not shown. Now, take the same crosswnd trplet, but ths tme located outsde the cone, and move t away from the surface. The trplet s closest dstance to the cone wll reman n the crosswnd regon, ndcatng that the wnd drecton skll s not much affected n ths case. Moreover, the number of retreved ambgutes remans the same,.e., two (not shown. Smlarly, non-perpendcular,.e., sdeways, nose contrbutons cause larger wnd drecton errors for trplets wthn the cone than for trplets outsde the cone (not shown. 5. CONCLUSIONS The ASCAT QC s mproved by takng nto account the MLE sgn n addton to the MLE magntude. It s found that for trplets lyng outsde the cone, the ASCAT retreved wnds are generally of good qualty, as compared to ECMWF wnds. For ASCAT trplets located far away from the cone surface (MLE >., the wnd drecton skll s found to be poor when trplets are nsde the cone (MLE >. and reasonably good when the trplets are outsde the cone (MLE < -.. As such, the AWDP QC has been updated n January to account for the sgn of the MLE value. Ths method s generc and opens the grounds for a more sophstcated QC for both past and future scatterometer mssons. The MLE analyss s also relevant n the context of a GMF mprovement. A good GMF ft of the backscatter measurements should result n approxmately the same amount of measurement trplets nsde and outsde the GMF cone surface (except for very low wnds. An analyss of the current C-band GMF, the so-called CMOD5n, reveals that for wnds around m/s, the majorty of trplets le nsde the cone, therefore ndcatng a GMF msft (see secton 3. Furthermore, spatal patterns (.e., maps of the MLE sgn are found to be correlated wth sub-cell wnd varablty, ndcatng the potental senstvty of scatterometer systems to the presence of, e.g., wnd gustness.

Normalzed hstogram (% Normalzed hstogram (% Normalzed hstogram (% 5 9 35 5 7 35 3 Wnd Drecton (deg 5 9 35 5 7 35 3 Wnd Drecton (deg 5 9 35 5 7 35 3 Wnd Drecton (deg Fgure 5. Wnd drecton (wth respect to the ASCAT md beam azmuth hstograms for ASCAT (sold and ECMWF (dotted wnds for -. < MLE < (top, < MLE < (mddle and - < MLE < - (bottom. ACKNOWLEDGEMENTS The work has been funded under the EUMETSAT Ocean and Sea Ice (OSI Satellte Applcaton Faclty (SAF Assocated Scentst project reference CDOP- SG-VS3. The ASCAT level b data are provded by EUMETSAT. The software used n ths work has been developed through the EUMETSAT Numercal Weather Predcton SAF. REFERENCES [] Stoffelen, A., and Anderson, D., Scatterometer data nterpretaton: measurement space and nverson, J. Atmos. and Oceanc Technol., vol. (, 9-33, 997. [] Portabella, M., and Stoffelen, A. (. Ran detecton and qualty control of SeaWnds. J. Atm. and Ocean Techn., (7, pp. 7-3. [3] Person, W.J., Probabltes and statstcs for backscatter estmates obtaned by a scatterometer, J. Geophys. Res., vol. 9, no. C7, pp. 973-9759, 99. [] Cornford, D., Csató, L., Evans, D. J., and Opper, M., Baysan analyss of the scatterometer wnd retreval nverse problems: some new approaches, J. R. Statst. Soc. B, vol., no. 3, pp. 9-,. [5] Stoffelen, A., and Portabella, M. (. On Bayesan scatterometer wnd nverson. IEEE Trans. Geosc. Rem. Sens., (, do:.9/tgrs.5.5, pp. 53-533. [] Hersbach, H., A. Stoffelen, and S. de Haan (7. The mproved C-band ocean geophyscal model functon: CMOD-5. J. Geophys. Res.,, C3, do:.9/jc373. [7] Stles, B.W., Pollard, B.D., Dunbar, R.S., Drecton nterval retreval wth thresholded nudgng, IEEE Trans. Geosc. Rem. Sens., vol., no., pp. 79-9,. [] Portabella, M., and Stoffelen, A., A probablstc approach for SeaWnds data assmlaton, Quart. J. R. Met. Soc., vol. 3, no. 59, pp. 7-5,. [9] Portabella, M., and Stoffelen, A., Scatterometer backscatter uncertanty due to wnd varablty, IEEE Trans. Geosc. Rem. Sens., (, do:.9/tgrs..7795, pp. 335-33,. [] Huddleston, J.N., and Stles, B.W., A Multdmensonal Hstogram Technque for Flaggng Ran Contamnaton on QukSCAT, Proc. of IEEE Internatonal Geoscence and Remote Sensng Symposum, Vol. 3, Honolulu (USA, IEEE, pp. 3-3,. [] Stoffelen, A., Error modelng and calbraton: towards the true surface wnd speed, J. Geophys. Res., vol. 3, no. C, pp. 7755-77, 99. [] Ebuch, N., and Graber, H. C. (99. Drectvty of wnd vectors derved from the ERS-/AMI scatterometer. J. Geophys. Res., vol. 3(C, pp. 777-779.