Observation quality control: methodology and applications

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Rudolf Hill
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1 Observatin qualit cntrl: methdlg and applicatins Pierre Gauthier Department f Earth and Atmspheric Sciences Université du Québec à Mntréal CANADA) Presentatin at the 010 ESA Earth Observatin Summer Schl n Earth sstem mnitring and mdeling Frascati, Ital, 13 August

2 Intrductin Nature f data received and used at peratinal centres * Wide variet f data that cme frm numerus surces * Man pssible prblems can crrupt the data Incrrect data can have a significant impact n the assimilatin Data acquisitin and qualit cntrl * Receptin f the data * Check the qualit f the data and reject data that have a high prbabibilit f being errneus.

3 Eample: least-square fit invlving an errneus datum frm Tarantla, 005) Least-square fit f data: = a + b 3.

Impact f an errneus datum n the analsis Reprt frm a drifting bu:p = 101.

4 Impact f an errneus datum n the analsis Reprt frm a drifting bu:p = hpa 10 hpa t lw) Analsis with QC in black Analsis withut QC in blue 4.

5 Qualit Cntrl Surces f errrs : * measurement errrs inherent in the instruments * errr f representativeness * imprperl calibrated instruments * incrrect registratin f bservatins * data cding errrs * data transmissin errrs Gals : * reject all errrs ther than measurement errrs * assciate predefined flags with each bservatin thrughut its assimilatin

6 Qualit Cntrl Preliminar checks fr individual reprts : * at decding stage, verificatin f bservatin surce and lcatin * hdrstatic checks fr temperatures and geptential heights frm upper air sundings * check fr limiting wind shear in wind prfiles frm upper air sundings * verificatin f deviatin frm climatlgical values

7 Qualit Cntrl Limit values fr surface temperature Winter Summer Area Min Min1 Ma1 Ma Min Min1 Ma1 Ma 45S - 45N -40C -30C +50C +55C -30C -0C +50C +60C 45N - 90N 45S - 90S -90C -80C +35C +40C -40C -30C +40C +50C Limit values fr surface dew-pint temperature Winter Summer Area Min Min1 Ma1 Ma Min Min1 Ma1 Ma 45S - 45N -45C -35C +35C +40C -35C -5C +35C +40C 45N - 90N 45S - 90S -99C -85C +30C +35C -45C -35C +35C +40C Data Prcessing 7.

8 Ntatins Mdel state : mdel state cmprising 3D and surface atmspheric fields N= NV3D NLEVELS NI NJ ~ 10 8 ) b : t : b = b - t : Observatins backgrund state a priri estimate f the state f the atmsphere) true unknwn state) f the atmsphere backgrund errr : bservatin vectr M~10 6 ) t : = - t : true bservatins bservatin errr

9 Ntatins Observatin peratr H: bservatin peratr prducing a mdel equivalent f all bservatins R N R M ) H = H/) Errr statistics : Jacbian f the bservatin peratr linear peratr assciated with an MN) matri) R: bservatin errr cvariance matri MM) diag R = bservatin errr variances) B: backgrund errr cvariances b diag B = backgrund errr variances) HBH T : image in bservatin space f the backgrund errr cvariances

10 Infrmatin cntained in innvatins Innvatin vectr: * shrt-term frecast backgrund) cntains infrmatin gained frm past bservatins * Cmparisn f bservatins against the backgrund which is ur a priri knwledge f the state f the atmsphere * Offers a cmmn grund against which it is pssible t cmpare all bservatins Mnitring f bservatins * innvatins are represented b bservatin tpes and averaged ver a large number f data, binned accrding t different categries * Allws t detect sstematic prblems with bservatins dh b 10.

11 71165 : Rae Lakes NWT Canada : Prter Lake NWT Canada : Pwder Lake NWT Canada wrngl assigned statin elevatin Data Prcessing 11.

12 7386 : Las Vegas Nev USA 7488 : Ren Nev USA wrngl assigned statin pressure 1.

13 Mnitring and qualit cntrl Statistics based n innvatins -HX b ): eample frm TOVS radiances

14 Mnitring Web Site f the Canadian Meterlgical Centre CMC) ring/ User: Passwrd: mnitring CMC with CMC in uppercase.

15 Verificatin against the backgrund state Observatin departure frm b : H ) H H' T H' ) H' ) RH' BH' b b b t t b t t b H' Fr a single bservatin: H X b ) Need t cmpute H'BH' T which can be dne b a randmizatin methd b H T d H b b Observatin is rejected if ˆ H with being large enugh. b b ) 1/ 15.

16 Difficulties that arise with the backgrund-check prcedure V bs. Frecast Lw V bs. V bs. V bs. Analsis Lw V bs. 16.

17 Qualit cntrl based n lcal analses Cnsider a set f k bservatins 1,..., k Prbabilit f 1 = t assuming that all the ther bservatins are true Analsis is made using all bservatins but 1 and then cmparing 1 against the resulting analsis k 1) H ) a a ˆ H k 1) a a ) 1/ T avid cntaminatin b errneus data, the prcedure is repeated until n mre data are being rejected 17.

18 Drpsnde data rejected b Bgnd Check 18.

19 Baesian apprach t inverse prblems * A priri pdf P): prbabilit f = t * Eample: the Gaussian case in which we knw the errr cvariance and we have b as the nl realizatin f. 19. ) ) ep 1 ) 1 1 b T b C P B d p P d p P ), ), ), ) Jint prbabilit distributin functin pdf): p,) Assciated marginal prbabilit densities in nrmall distributed with mean b and cvariance B In absence f an ther infrmatin, = b is the mst prbable state

20 Similarl, fr P), if stands fr the actual bservatin, P) : prbabilit f = t Estimate f the mean : = Gaussian case : P ) 1 C ep 1 ) T R 1 ) * Nrmall distributed with mean and cvariance R 0.

21 Baes Therem Cnditinal prbabilit distributin Prbabilit f having given that = t 1. ) ), ), ), ) P p d p p p Prbabilit f having given that = ) ) ) ) ), t t t t P p P p p Thus, ) ) ) ) t t p P p P Baes Therem: ) ), ), ), ) t t t t t P p d p p p

22 Cnditinal prbabilit p ): prbabilit that = t given that = has been bserved * A psteriri prbabilit distributin assciated with that f the analsis errr p = t ): prbabilit f given that is the true value * H: estimate f the mean value f. If = t, then H t = t. * - H) = t + H t = * - H) is nrmall distributed with zer mean and cvariance R p ) 1 C 3 ep 1 H) T R 1 H).

23 Representatin f the assciated prbabilit distributins Rdgers, 000) P ) H b t = H P) X t b X P)

24 Mde: d d Frm Baes therem: p ln ) ep C p ) 1 p dp d ln p 0 0 In the case f Gaussian errr statistics, the maimum likelihd and the minimum variance estimate cincide. dp d 1 T 1 1 T 1 H R H ep b) B b ) T 1 ep R J ) 1 1 T 1 T T 1 B ) H ) R H ) C b b 1 Frmulatin includes the case where H) is nnlinear. 4.

25 References Rdgers, R.D., 000: Inverse Methds fr Atmspheric Sunding: ther and practice. Wrld Scientific Series On Atmspheric and Planetar Phsics, vl., 38 pages. Tarantla, A., 005: Inverse prblem ther and methds fr mdel parameter. SIAM, Philadelphia, USA, 34 pages. 5.

26 Variatinal Qualit Cntrl QC-Var) Dharssi et al. 199), Ingleb and Lrenc 1993), Anderssn and Järvinen 1999) Prbabilit f having a grss errr * cnsider that t D/ t D/ 1 P) 1 t ) p ) P/ D ep p) t 6.

27 QC-Var Definitin f the cst functin where 7. ˆ) ep / ln )) ln )) ˆ ) J C D P H p J J N QC QC 1 ) ) 1 ˆ ˆ 1 )) ˆ T N H J R

28 Gradient f the QC-Var cst functin N ep J ) N N ˆ ) ˆ ˆ) ˆ ˆ J J WQCJ ) N ep J ) W QC H ) ) * H J ) ) W QC H ) ) where P ) /1 P) D W QC depends n the current estimate f the state. A psteriri weights are then based n the departure frm the analsis 8.

29 Representatin f the QC-Var cst functin P = 0.01) H) / 9.

30 QC-Var cst functin with different prbabilities f grss errrs P = 0.01 and 0.1) 30.

31 Observatin - Frecast - H b )) AIREP temperatures Perid: March-April 00 Rejected b backgrund check 303) Rejected b QC-Var 103) Accepted 31,96) Ttal Number f data

32 Estimatin f the prbabilit f grss errr Distributin f innvatins Gaussian: ˆ ln p ˆ) ˆ ln p ˆ) C Prbabilit f grss errr is btained in the limit where ˆ frm Järvinen and Anderssn, 1999) 3.

33 Cmparisn f the tw QC prcedures Obs. Tpe Obs. Quantit Rejectin Rati %) Apprimate Rejectin Limits VarQC OIQC VarQC OIQC SYNOP Pressure height) hpa n/a T- Td ) K K Tem perature K 16.6 K SHIP W ind m/s 19 m/s Pressure height) hpa n/a T- Td ) K 6 K Tem perature K 11.7 K DRIBU Pressure height) hpa n/a Tem perature K 6. K TEMP W ind m/s 11-0 m/s T- Td ) K 14 - K Temperature K K 33.

34 Obs. Tpe Obs. Quantit Rejectin Rati %) Apprimate Rejectin Limits VarQC OIQC VarQC OIQC AMDAR Wind m/s 15 m/s Temperature K 5.0 K SATOB Wind m/s m/s AIREP Wind m/s 9 m/s Temperature K 9. K ACARS Wind m/s 14 m/s Temperature K 5.0 K 34.

35 Cmments When bservatin errr is uncrrelated: * QC-Var is eas t implement and cmputatinall inepensive * A number f iteratins need t be dne withut the W QC t crrect main deficiencies that ma eist in the backgrund state assuming the bulk f the bservatins t be gd nes) Prcedure aims at detecting punctual bservatins that ma be in errr Cmpleities arise when bservatin errrs are crrelated but the can be addressed Järvinen et al.,1999) 35.

36 Gaussian + flat PDF Sum f Gaussians Isaksen, 010 ECMWF)

37 Recent develpments in variatinal qualit cntrl Isaksen, L., 010: presentatin at the ECMWF training curse) Huber nrm * Adds sme weight n bservatins with large departures * A set f bservatins with cnsistent large departures will influence the analsis Isaksen, 010 ECMWF)

38 Definitin f the pdf assciated with the Huber nrm 1 a ep ad if a d b ep bd if d b p ep d if a d b with d H

39 Aircraft temperature and winds Nrthern Hemisphere Huber nrm distributed with sme deviatin fr cld departures Nrmalized departures Nrmalized departures Isaksen, 010 ECMWF)

40 Cmparing bservatin weights: Huber nrm red) versus Gaussian+flat blue) Mre weight in the middle f the distributin Mre weight n the edges f the distributin Mre influence f data with large departures Weights: 0 5% Isaksen, 010 ECMWF)

41 7 Dec 1999 French strm 18UTC Eample frm Isaksen, 010 ECMWF) Era interim analsis prduced a lw with min 970 hpa Lwest pressure bservatin SYNOP: red circle) hpa supprted b neighburing statins) At this statin the analsis shws 977 hpa Analsis wrng b 16.5 hpa! Isaksen, 010 ECMWF)

42 Data rejectin and VarQC weights Isaksen 010) fg rejected used

43 Data rejectin and VarQC weights with Huber nrm frmulatin Isaksen, 010)

44 Cnclusin Qualit cntrl is a crucial cmpnent f an data assimilatin sstem Acceptance f bad data and rejectin f gd data happens * t avid this as much as pssible, the errr characteristics need t be regularl reestimated e.g., prbabilit f grss errr, eistence f biases, backgrund and bservatinal errr cvariances). In 4D-Var, small changes t the analsis can lead t substantial differences in the frecast * Impact f accepting bad data r rejecting gd nes can be significant Management f a huge database f infrmatin assciated with the bservatins is technicall challenging 44.

46 frm Auligné. McNall and Dee, QJ 007)

47 A quick intrductin t bias crrectin Sstematic errrs in the analsis can be attributed t bservatin and/r backgrund errr Biases can be bserved in innvatins fr a particular instrument * If n bias is bserved fr ther instruments, then it is likel the bservatins that is biased Principle in bias crrectin schemes * Find a wa t detect biases e.g., mnitring) and relate it t likel causes f the surce f sstematic errr and crrect it * Eample: sstematic errr assciated with the scan angle f a satellite instruments.

48 Static bias crrectin Cnsider innvatins d = H b ) ver a perid f time rder f a mnth) Mdif the bservatin peratr as, H H P Find the cefficients b minimising 1 T J H b, H b, The quantities P i ) are the predictrs which relate t the measurements N i0 i i

49 Predictrs used fr different satellite instruments Instrument Predictrs AIRS ATOVS GEOS TCWV SSMI V s T s TCWV Geptential thicknesses fr the laers cmprised between the pressures in hpa) TCWV: ttal cntent in water vaprt V s : surface wind speed T s : skin temperature

50 Limitatins f the static scheme Bias is assumed t be cnstant ver the perid * Inapprpriate t detect instrument prblems Based n the assumptin that the backgrund errr itself is unbiased * Backgrund errr is cnstrained b all bservatins Justified where H unbiased bservatins are available e.g., b Hb Hb radisndes)

51 Adaptive ffline scheme Bias crrectin is recalibrated befre ever analsis 1 Secnd term acts as a memr T 1 J H f past evaluatins b, R H b, * Culd be interpreted 1 as a static T scheme applied with a running 1 mean. b B b

52 Adaptive nline scheme: Var-BC Bias crrectin is incrprated within the assimilatin scheme itself 1 T 1 J H b, R H b, 1 T 1 b B b Mre apt t distinguish 1 Tbetween 1 mdel bias and bservatin biases. b B b

53 Auligné et al. 007): cmparaisn between VarBC and static bias crrectin

54 Results fr AMSU-a channel 14 peak at 1hPa) average ver 3 weeks) Auligné et al. 007) N assimilatin f satellite data H a Offline bias crrectin

55 Results fr AMSU-a channel 14 average ver 3 weeks) Auligné et al. 007) Var-BC bias crrectin Var-BC bias crrectin using a mask

56 Sensitivit t temperature fr different channels f AMSU-a

57 Cnclusins Distinguishing between mdel and bservatin biases remains delicate VarBc autmates the bias crrectins and has shwn sme skill t in distinguishing between the tw Chice f the predictrs is being revisited regularl t reflect the nature f the instrument Lng term drift ma result due t the interactin between QC-Var and Var-BC Auligné and McNall, 007) * Imprtant fr reanalses as biases in the analses ma be wrngl interpreted as a climate drift.

Comparison of hybrid ensemble-4dvar with EnKF and 4DVar for regional-scale data assimilation

Comparison of hybrid ensemble-4dvar with EnKF and 4DVar for regional-scale data assimilation Cmparisn f hybrid ensemble-4dvar with EnKF and 4DVar fr reginal-scale data assimilatin Jn Pterjy and Fuqing Zhang Department f Meterlgy The Pennsylvania State University Wednesday 18 th December, 2013