Best-member-selection as part of an ensemble based data ... - Cosmo

Eidgenössisches Departement des Innern EDIBundesamt für Meteorologie und Klimatologie MeteoSchweizBest-member-selectionas part of an ensemble baseddata assimilation approachTanja Weusthoff 1 , Daniel Leuenberger 1 ,Christian Keil 2 , George Craig 21MeteoSwiss, 2 DLRCOSMO/CLM User Seminar, Langen, 09.-11.03.2009

New data assimilation approach: SIRFDriving EPS(SREPS)Assimilation periodtimeCOSMO-DE-EPSBest-Member-Selection 1Best-Member-Selection 2EnsembleEnhancement/ResamplingBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.2

ObjectivesWP1: Evaluation of classical and spatial metrics for the determination ofweighting schemes for ensemble members (DLR, MeteoSchweiz)WP1.1 Implement spatial metrics and evaluation on selected COPS eventsFQM of Keil and Craig (2007), which is already available,SAL (Wernli et al. 2007)fuzzy verification package of Ebert (2007).WP1.2 Implement classical metrics for conventional observationsWP1.3 Investigate correlation of metrics between models of differentresolutionWP1.4 Compare object-oriented and classical metricsWP1.5 Investigate persistence of skill in different metrics and differentmeteorological situationsBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.3

ConceptApply classical quadratical error measure for conventional observations:[ y−H ( x)]TR−1[ y−H ( x)]( R2⎧ 1/iji = j= ⎨⎩ 0 else−1 σ)ijIn order to give more important observations a higher weighting („tuning“),an additional matrix A is multiplied to the error covariance matrix Rcontaining the setting of the weights.m = [ y −H ( x)]TAR−1[ y −H ( x)]y = vector of observationsH(x) = vector of forecastsH = forward operator,H(x) = observation equivalent, calculated from model state xR = covarianz-matrix of the observation errors, DiagonalmatrixA = additional matrix for the weightings of parameters, DiagonalmatrixAij⎧ αii = j= ⎨⎩ 0 elseBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.4

Quality measure m= distance of model member x (k) to observationsm= [ y−H ( x)]TAR−1[ y−H ( x)]~ ( k )( k )i= yi− H ( xd)i =1,...YY = # variables * # stations * # levelsm( k ) ~ ~ k=ii[ ]( k ) T−1( )d AR dk =1,...KK = # memberm( k )Y= ∑αi=1i~[ ]( k )diσ2ii2m ( k)= D⋅αoptimal weighting α to be determinedBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.5

Quality measure m= distance of model member x (k) to observationsm k)= D⋅α(⎟ ⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟ ⎠⎛m⎜⎜m⎜⎜...⎜⎜⎜⎝ m(1)(2)K⎞⎟⎟⎟⎟⎟⎟⎟⎠=⎛ d1⎜⎜ d1⎜⎜...⎜⎜ ( K⎝d1(1)(2))ddd(1)2(2)2...( K)2d(1)3......( K)Y⎛α1⎞⎜⎜α2⎞ ⎜α3⎟ ⎜⎟ ⎜ ...⎟⋅⎜⎟ ⎜⎟ ⎜⎟ ⎜⎠ ⎜⎜⎜⎝αYBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al....dd(1)Y...6

Forecast: COSMO-DE-EPS• High resolution ensemble with 20 members, 00 UTC runs• 4 driving models:• Member 1-5 EZMWF• Member 6-10 GME• Member 11-15 NCEP• Member 16-20 UKMO• 5 perturbations of model physics• Members 1, 6,11,16 Entrainment rate (entrscv=0.002)• Members 2, 7,12,17 Cloud cover at saturation (clc_diag=0.5)• Members 3, 8,13,18 Laminar layer depth (rlam_heat=50)• Members 4, 9,14,19 Laminar layer depth (rlam_heat=0.1)• Members 5,10,15,20 Turbulent lengh scale (tur_len=150)Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.7

ObservationsBest-member-selection based on standard observations like Synop(hourly), Radiosondes (6 hourly or less), …First investigation with radiosondes• Variables on pressure levels:• temperature,• relative humidity,• u- and v- wind components• …• Integrated variables:• CAPE• CIN• integrated water vapour (IWV)• …Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.8

Weighting …Seven variablesTemperature T,relative humidity RH,Wind components U and VCAPEIWVCIN21levelssinglelevelsThree level regions1000 – 700 hPa650 – 400 hPa350 – 100 hPa Weightings of variables andlevels are multiplied!Initial Weighting everything is set to the same weight 1T RH U V CAPE IWV CIN1 1 1 1 1 1 11000-700650-4001 1 1350-100Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.9

… & EvaluationQ: Do the target quality measure and our m identify the same bestmembers?1. Correlation between target quality r and mcor=covrr,mσ ⋅σm2. Distance between the two quality measures:r − m Need m (k) and r (k) in the same range, e.g. [0,1] in order to determinethe optimal weighting α = [0,1] such thatr− m=r−D ⋅α= minHere: Target quality r = DASBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.10

Target Quality: DAS• The target quality r of the ensemble is provided by the quality measure withrespect to precipitation (radar) the Displacement and Amplitude ScoreDAS (Keil and Craig, 2009)• DAS is based on an areal image matcher using classical optical flowtechnique & has 2 components:• displacement error field DIS• amplitude error AMP (RMS of observed and morphed forecast imagery)D maxI 0maximum search distancecharacteristic intensityBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.11

Target Quality: DASEZMWFGMENCEPUKMO DAS at specifictime DAS, is highlycorrelated with 6-hhourly calculatedmeanDAS,6-hourly mean(forward averaged)DAS,every 6 h(at start time ofaveraging period)Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.12

First Results… investigated period: 08.-16.08.200710738 Stuttgart - Echterdingen14sunshine duratiomcloud coverage [1/8]rain amountrelative humidity100rain sum [mm] and total sunshineduration [h]12108642908070605040302010mean relative humidity [%]020070808 20070810 20070812 20070814 200708160Mesoscale forcingConvectionMesoscale forcingBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.13

First Results… investigated period: 08.-16.08.2007… 8 radiosondes within considered DAS area1 DeBilt2 Payerne4 53 Nancy4 Schleswig196785 Greifswald6 Emden7 Bergen8 Lindenberg9 Essen1110131610 Meiningen11 Idar-Oberstein12 Stuttgart31213 Kuemmersbruck2151414 Muenchen15 Hohenpeissenberg16 PragBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.14

Equally weighted variables and levelsmEZMWFGMENCEPUKMOdasMaximum in the afternoon,minimum in the morning(new run);Partly clustering memberswith same driving modelsBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.15

Scatterplots (m vs DAS)EZMWFGMENCEPUKMOBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.16

Scatterplots (m vs DAS),Individual membersRange ofcorrelation…EZMWF0.11 – 0.19GME0.22 – 0.33NCEP0.11 – 0.24UKMO-0.01 - 0.08Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.17

CorrelationIndividual time steps… large variation ofcorrelation with time correlation apparentlyhigher for mesoscaledriven days…Mesoscale forcingConvectionMesoscale forcingBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.18

Frequency distributionhistogram of normalizedquality measures:das/max(das) andm/(max(m))same as above, but: das x=das 2 PDF become more similar, Decrease in |das-m|Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.19

Sensitivity studies1. VariablesT RH U V CAPE IWV CIN0.5 0.5 0.5 0.5 0.5 0.5 0.51000-700650-4001 1 1350-100Procedure: Set all variables to 0.5, vary each variable from 0to 1.0 in steps of 0.1. Level weightings stay 1.RH and CAPE showstrongest (positive)response to weightingBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.20

Sensitivity studies2. LevelsT RH U V CAPE IWV CIN1 1 1 1 1 1 11000-700650-400350-1000.5 0.5 0.5Procedure: Set all levels to 0.5, vary each level from 0 to 1.0 insteps of 0.1. Level weightings stay 1.Levels between 650 and 400hPa show strongest (positive)response to weightingBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.21

Combination of variables and levels …mT RH U V CAPE IWV CIN0.4 1 0.4 0.6 0.1 0.1 0.11000-700650-4000 1 0350-100dasEZMWFGMENCEPUKMOBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.22

Scatterplots (m vs DAS),Individual membersRange ofcorrelation…(for equallyweighted)EZMWF0.32 – 0.40(0.11 – 0.19)GME0.39 – 0.53(0.22 – 0.33)NCEP0.25 – 0.31(0.11 – 0.24)UKMO0.31 - 0.38(-0.01 - 0.08)Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.23

Comparison• Equally weighted • Combined weightingT RH U V CAPE IWV CIN1 1 1 1 1 1 1T RH U V CAPE IWV CIN0.4 1 0.4 0.6 0.1 0.1 0.11000-700650-4001 1 1350-1001000-700650-4000 1 0350-100Corr(m,das)0.170.37TOTAL(|das-m|)241.93242.62Corr(m,das²)0.160.36TOTAL(|das²-m|)108.68109.36 Rarely a change in distance |das - m|, but increase in correlation!Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.24

Preliminary Fazit• Radiosondes do give information on best members in terms ofprecipitation forecast (as measured by DAS).• Test with radiosoundings reveal a sensitivity of the best memberselection with respect to parameter and heights.• The correlation with DAS could be improved by using radiosondesdata with different weightings for variables and heights.• The correlation between the two quality measures DAS and m isapparently time-dependent.• The correlations are in the order of 0.4, while DAS values at startingtime of averaging period are highly correlated with DAS averaged overnext 6 hours the precipitation measure DAS provides a good basis for the bestmember selection. The use of standard observation as alternativequality measure seems to be appropriate.Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.25

Outlook• find suitable combination of only a few parameters fromradiosondes and synop stations (e.g. total energy)• determine optimal weighting of those parameters withrespect to target quality measure r• expand best member selection to driving ensembleBest-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.26

Thank you for the attention!Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.27

Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.28

Reference: Keil, C. and G. C. Craig, 2009: A displacement andamplitude score employing an optical flow technique, submitted toWea. and Forecasting.Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.29

Calculation of variablesIntegrated Water VapourIWV = ∫ ρ dz = ∫ q dzwρq = spezifische FeuchteCAPE, CIN…(max CAPE)Best-member-selection as part of an ensemble based data assimilation approach | COSMO/CLM User SeminarTanja Weusthoff et al.30