Transcript 1차원 변분법 흐름도
The usage of the ATOVS data in the Korea Meteorological Administration (KMA) Sang-Won Joo Korea Meteorological Administration History of the satellite sounding assimilation in KMA • Feb. 1999 : TOVS data assimilation in the Global model (1DVAR) • Nov. 2001 : AOTVS(HIRS+AMSU-A) assimilation in the Global Model (1DVAR) Numerical Weather Prediction Division Introduction 1. 1DVAR in KMA - Background error implies geographical variation - Observation error is calculated from the innovation and background error • Evaluation of effect on the model performance - Evaluation of the time averaged fields - Typhoon track forecast error Numerical Weather Prediction Division Inhomogeneous background error Background Error Correlation (N.H.) Distribution of Background Error 25 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 80 NH TR SH 20 Control Variables 40 15 10 20 5 0 -6 -4 -2 0 2 4 Background Error Correlation (Tropics) TTB-BTB [K] 6 8 5 25 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 20 15 15 5 5 15 Control Variables 20 25 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 20 10 10 25 25 10 5 10 15 20 Background Error Correlation (S.H) Control Variables Control Variables -8 Control Variables Frequency 60 5 10 15 20 25 Control Variables Numerical Weather Prediction Division Methodology Error variance changes but correlation is fixed Damping area is assigned eb 15enh (25 )etr ,15N 25N eb 15esh (25 )etr ,15S 25S e esh 90S eb etr 20S Eq. eb 20N enh 90N Error covariance becomes Cv1 , v2 j e j v1 Rv1 , v2 e j v2 Inverse matrix of error covariance becomes C 1 v1 , v 2 j e j 1 v1 R 1 v1 , v2 e j 1 v2 Numerical Weather Prediction Division Observation error Statistical Method for observation error Assumption 1. Tangent linear approximation 2. No correlation between background error and RTM error 3. Biases are well removed Derivation H xb H xt Hx Ht xt H xt Hx 1st assumption H xb yo Ht xt H ( xt ) Hx yt y H xt Hx y H xb yo H xb yo T RTM error F H xxT HT yy T 2nd assumption F E H xxT H T H x H T y 2 R H xb y o H xb y o T HBHT 2 3rd assumption Numerical Weather Prediction Division Meaning of the resulting equation R H xb y o H xb y o T • Observation error • Square of innovation • RTM error and instrument error • First estimates of Derber and Wu (1999) HBHT • Background error in radiance space • Innovation is the sum of observation error and background error if there is no correlation • The resulting equation says the above statement in radiance space. Numerical Weather Prediction Division Feedback of observation error OBSERVATION 1DVAR ANALYSIS R INNOVATION MODEL BACKGROUND B Benefits of our method • Relationship exists between observation error and NWP analysis through B • Improvement of background error can readily affect the observation error • The error ratio (eigenvlaue) is changed automatically Numerical Weather Prediction Division Description of the Global Model MODEL ANALYSIS Basic Equation Primitive Equation Resolution Triangular truncation of 213 in horizontal and 30 levels sigma-p hybrid coordinate from surface to 10hPa Numerical Scheme Semi-implicit time integration, spherical harmonics for horizontal representation and finite difference in the vertical Radiation Lacis and Hansen (1974) for short-wave and water vapor, carbon dioxide and ozone for long-wave Convective Parameterization Kuo type(1974) Large Scale Condensation Kanamitsu et. al. (1983) Shallow Convection Tiedke(1985) Gravity Wave Drag Iwasaki et. al. (1989) PBL scheme 2 Layer method from Yamada and Meller (1982) Land Surface Processes SiB Method 3 Dimensional Multivariate Optimum Interpolation Resolution 0.5625 degrees Update Cycle 6 hourly Numerical Weather Prediction Division Observation (ATOVS TBB Data=OTB) CHANNEL CHANNEL CHANNEL CHANNEL CHANNEL HIRS1 HIRS6 HIRS12 AMSU5 HIRS10 HIRS2 HIRS7 HIRS13 AMSU6 HIRS11 HIRS3 HIRS8 HIRS14 AMSU7 HIRS12 HIRS4 HIRS10 HIRS15 HIRS8 AMSU13 HIRS5 HIRS11 AMSU4 HIRS9 AMSU14 Background (Profile=BPR) Variable Level Source Element Temperature [K] Surface – 10 hPa 6 hour forecast from GDAPS 1-16 Temperature [K] 10 hPa – 0.4 hPa NESDIS retrieval 17-20 Specific Humidity [g/g] Surface – 300 hPa 6 hour forecast from GDAPS 21-27 Skin Temperature Surface NOAA weekly SST analysis 28 Pressure [hPa] Sea Level 6 hour forecast from GDAPS 29 U [m/s] Surface 6 hour forecast from GDAPS 30 V [m/s] Surface 6 hour forecast from GDAPS 31 CTP [hPa] NESDIS retrieval 32 Cloudness NESDIS retrieval 33 Numerical Weather Prediction Division Others • Quality control(Eyre, 1992) • Forward operator: RTM(RTTOV version 6) + Vertical interpolation • Minimization algorithm: BFGS method (quasi-Newtonian algorithm) • Dimension reduction to the TOVS BUFR format • Optimum interpolation interface (Lorence 1986, Eyre 1993) • Bias correction: Scan angle and air mass bias correction (Joo and Okamoto, 2000) Numerical Weather Prediction Division Flowchart PREFIX: Background(B), Observation(O), Analysis(A) Departure(D) SURFIX: Profile(PR) Brightness Temperature(TB) BFGS Physical Space BPR 1st no MINIMIZATION Background Error - yes DPR APR APR ADJOINT J& J RTM DTB_B OTB ATB - BIAS C. DTB BIAS C. Observation Error Radiance Space OTB_B Numerical Weather Prediction Division Flow chart of the 1DVAR with NWP analysis B Background Error R B 1 D V A R 1DVAR background Tv 24 and 48 hour Forecasts for 1 Month Bias Observation error 3D O.I. Global Model Bias O-B for 1 Month ATOVS data Synoptic Obs. 6 hour forecast 10 day forecast FEP Diagnostics Numerical Weather Prediction Division Analysis verification (September 2001) ANALYSIS VERIFICATION of 500hPa GPH(Northern Hemisphere) 1DVA 120 OPER 100 RMSE [m] 80 ANALYSIS VERIFICATION of 500hPa GPH(Tropics) 60 1DVA 18 OPER 40 16 20 14 0 24 48 72 96 120 144 168 192 216 240 FORECAST HOUR RMSE [m] 12 0 ANALYSIS VERIFICATION of 500hPa GPH(Southern Hemisphere) 1DVA 160 10 8 6 OPER 4 140 2 120 0 RMSE [m] 0 100 24 48 72 96 120 144 168 192 FORECAST HOUR 80 60 40 20 0 0 24 48 72 96 120 144 FORECAST HOUR 168 192 216 240 Numerical Weather Prediction Division 216 240 Observation verification(Sep. 2001) OBERVATION VERIFICATION of 500hPa GPH(Northern Hemisphere) OBERVATION VERIFICATION of 500hPa GPH(ASIA) 1DVA 80 OPER 1DVA 120 70 OPER 100 60 RMSE [m] RMSE [m] 80 50 40 30 60 40 20 20 10 0 0 0 24 48 72 96 120 144 168 192 216 0 240 1DVA OPER 48 72 96 120 144 168 192 216 240 FORECASTofHOUR OBERVATION VERIFICATION 500hPa GPH(Southern Hemisphere) FORECAST HOURof 500hPa GPH(TROPICS) OBERVATION VERIFICATION 20 24 1DVA 120 OPER 18 100 16 80 RMSE [m] RMSE [m] 14 12 10 8 60 40 6 4 20 2 0 0 0 24 48 72 96 120 144 FORECAST HOUR 168 192 216 240 0 24 48 72 96 120 144 168 192 216 240 FORECAST HOUR Numerical Weather Prediction Division Averaged typhoon track forecast error (TY0111-TY0123) AVERAGED TYPHOON TRACK ERROR TRACK ERROR[km] 600 500 OPER 1DVA 400 300 200 100 0 12 24 36 48 60 72 FORECAST HOUR Numerical Weather Prediction Division Summary • The 1DVAR is developed in KMA to assimilate the ATOVS data • The statistics shows positive effect mostly and also in ASIA • Typhoon track is well predicted with the 1DVAR and it is mainly caused by the better specification of the Pacific High • The 1DVAR is in operation from 1 November, 2001 Numerical Weather Prediction Division Future Plans • Improvement of the bias correction scheme • Utilization of the ATOVS data over the land • Improvement of cloud detection scheme • Implementation of the 1DVAR in the regional model Numerical Weather Prediction Division Verification with RAOB RMSD of Tv Error of BG, Anal and D from RAOB (NH) RMSD of Tv Error of BG, Anal and D from RAOB (TR) RMSD of Tv Error of BG, Anal and D from RAOB (NH) RMSD of Tv Error of BG, Anal and D from RAOB (TR) 30 10 30 10 70 30 100 70 bg anal 100 70 300 100 300 100 500 300 500 300 700 500 700 500 1000 700 0 1000 700 1 2 3 1 2 4 3 4 30 10 70 30 100 70 300 100 300 100 500 300 500 300 700 500 1 2 3 4 5 Mean Virtual Temperaure [K] 0 1 2 3 4 Mean Virtual Temperaure [K] • Poor performance near surface and tropopause bg anal 70 30 100 70 bg anal 70 30 100 70 1000 700 RMSD of Tv Error BG, Anal and D [K] from RAOB (SH) MeanofVirtual Temperaure 30 10 bg anal 700 500 1000 700 0 RMSD of Tv Error BG, Anal and D [K] from RAOB (SH) MeanofVirtual Temperaure 0 Layer [hPa - hPa] Layer [hPa - hPa] 30 10 70 30 bg anal Layer [hPa - hPa] Layer [hPa - hPa] Layer [hPa - hPa] Layer [hPa - hPa] 30 10 70 30 bg anal • Large improvement in the S.H. 100 70 300 100 • We need more improvement in the N.H. and Tropics. 300 100 500 300 500 300 700 500 700 500 1000 700 1 2 3 1000 700 4 5 6 Mean Virtual Temperaure [K] 1 2 3 4 Mean Virtual Temperaure [K] 5 6 Numerical Weather Prediction Division 5 ATOVS Information CNTL (NB) 8 True Value(T) Wrong Information 2 Right Information T-B B.G.(B) Anal(A) Obs(O) (TTB-BTB) [K] 1 0 -8 0 O-B (T-B) X (O-B) > 0 -8 (OTB-BTB) [K] • Observation should be in the same direction as RAOB from background • The 2nd and 4th quadrants data mislead the analysis. • There are many data in the 2nd quadrant. 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