GSI fundamentals (4): Background Error Covariance and Observation Error

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1 27 GSI Community Tutorial July 2, 27, College Park, MD GSI fundamentals (4): Background Error Covariance and Observation Error Ming Hu Developmental Testbed Center

2 Outline GSI fundamentals (): Setup and Compilation GSI fundamentals (2): Run and Namelist! GSI fundamentals (3): Diagnostics!!! GSI fundamentals (4): Background Error and Observation Error! Background error covariance! Observation error!! GSI fundamentals (5): PrepBUFR and BUFR format GSI fundamentals (6): Review and Applications 2

3 GSI input and output files Analysis results; stdout and diagnostic files, J(x) = (x-xb)tb-(x-xb)+(y-h[x])tr-(y-h[x]) + Jc Background file Observations files Background covariance file CRTM coefficients Observation error file Control and state variable info file Observation data control info files Fixed files Namelist Radiance bias correction coefficient files 3

4 Background Error (BE) Covariance What BE does and structure of a GSI BE? Options to tune a GSI BE? Generate your own BE: GenBE Setup EnVar hybrid analysis 4

5 Background Error Covariance (BE)! In 3D-Var analysis, background error covariance (BE) is the most important and complex part, which includes three pieces of information:! Variance: represents the quality of the background. Ratio of background error variance and observation error variance decides the fit of analysis to the observation.! Horizontal and vertical impact scale: decide the area and depth of the observation information should spread.! Balance: relation between different analysis variables, such as temperature and wind. 5

6 GSI BE structure! BE is huge matrix that cannot be calculate explicitly. In GSI, the B matrix is decomposed into the following form: B = BbalanceVBZ(BxByByBx)BZVBTbalance Balance among different variables represented with pre-computed regression coefficients Pre-calculated square root of variance Vertical impact is modeled as a Gaussian distribution with pre-computed lengthscale parameters in recursive filter Horizontal impact is modeled as a Gaussian distribution with pre-computed lengthscale parameters in recursive filter 6

7 GSI BE structure Table 6. The information on arrays used by GSI background error matrix Category Bbalance BTbalance Array name agvi Balance (Horizontal wgvi regression coefficients) bvi hwll BZ (BxByByBx) BZ V Dimension :mlat+,:nsig,:nsig :mlat+,:nsig :mlat+,:nsig Content Regression coefficients for stream function and temperature Regression coefficients for stream function and surface pressure Regression coefficients for stream function and velocity potential :mlat+,:nsig,:nc3d horizontal lengthscales for stream function, unbalanced velocity potential, Horizontal unbalanced temperature, and relative and vertical humidity influence hwllp :mlat+, nc2d horizontal lengthscale for unbalanced scale surface pressure vz :nsig, :mlat+, :nc3d Vertical lengthscale for stream function, unbalanced velocity potential, unbalanced temperature, and relative humidity corz :mlat,:nsig,:nc3d Square root of variance for stream function, unbalanced velocity potential, variance unbalanced temperature, and relative humidity corp :mlat,nc2d Square root of variance for unbalanced surface pressure Note: mlat = number of latitude in original background error coefficient domain, nsig = number of vertical levels in analysis grid nc3d = number of 3 dimensional analysis variables nc2d = number of 2 dimensional analysis variables 7

8 BE Tuning Options! In GSI namelist: BZ vs scale factor for vertical correlation lengths for background error nhscrf number of horizontal scales for recursive filter (Bx hzscl(3) scale factor for horizontal smoothing. Specifies factor by which to reduce horizontal scales (i.e. 2 would then B yb y apply /2 of the horizontal scale) B x) hswgt(3) empirical weights to apply to each horizontal scale! In anavinfo! Column as under section control_vector:: V control_vector::!var level itracer as/tsfc_sdv sf 4. vp 4. ps.5 t 4.7 q 4.7 an_amp source state state state state state funcof u,v u,v prse tv q 8

9 Fat-tailed Power Spectrum for horizontal impact Horizontal impact is modeled by the combination of three recursive filters that have different impact scales Yellow: filter (wide) Green: filter 2 (middle) White: filter 3 (narrow) Red: combined to make fat-tail impact pattern Courtesy of Wan-Shu Wu 9

10 GSI BE in release Package! nam_nmmstat_na.gcv : contains the regional background error statistics! Computed using forecasts from the NCEP s NAM model covering North America.! Covers the northern hemisphere with 93 latitude lines from -2.5 degree to 89.5 degree! With 6 vertical sigma levels from to.364.! nam_glb_berror.f77.gcv : contains the global background errors! Based on the NCEP s GFS model, a global forecast model.! Covers global with 92 latitude lines from -9 degree to 9 degree and! With 42 vertical sigma levels from to.383.! Global BE:! Many GFS BE files match different versions of operational GFS.

11 Column # Content Unit Pressure hpa 2 T degree C 3 q percent/ 4 UV m/s 5 Ps mb 6 Pw 2 kg/m (or mm) Reference values for BE Tuning options fixed B matrix vs hzscl hswgt ss/tsfc_sdv Global nam_glb_berror.f77.gcv.7.7,.8,.5.45,.3,.25 control_vector::!var as/tsfc_sdv sf.6 vp.6 ps.75 t.75 q.75 oz.75 sst. cw. stl 3. sti 3. Regional nam_nmmstat_na.gcv..373,.746,.5.45,.3,.25 control_vector::!var as/tsfc_sdv sf. vp. ps.5 t.7 q.7 oz.5 sst. cw. stl. sti. GSI run scripts in community release can pick right values based the set of choice to bkcv_option=(global or NAM)

12 BE tuning examples! Through single observation test, we can see how those BE tuning option works! Check fundamental talks on setting up single observation test! Regional BE nam_nmmstat_na.gcv is used! In GSI namelist:! Horizontal impact scale of BE before tuning: hzscl_op='.373,.746,.5,'! Vertical impact scale of BE before tuning: vs_op='.,' Courtesy of Min Sun 2

13 Single Obs(U) Test with BE tuning Single observation test parameters Parameter Value ΔU m/s Observation Error 2m/s Horizontal Location Domain Center Vertical Location 7hPa Horizontal impact scale tuning Horizontal Test hzscl Value Original.373,.746,.5 /2.865,.373,.75 /4.9325,.865,.375 / ,.9325,.875 / ,.46625,.9375 / ,.23325, Vertical impact scale tuning Vertical Test vs Value original. /2.5 /4.25 Courtesy of Min Sun 3

14 Analysis Increment from Single Obs(U) Test Horizontal Vertical Horizontal Vertical Horizontal Vertical T U V Default hzscl & vs /2 hzscl Courtesy of Min Sun /2 vs 4

15 Horizontal Cross Section of U Increment zoom in Change hzscl_op not only change the horizontal influence scale, but also the weight (how much analysis results fit to the observations)! Courtesy of Min Sun 5

16 Vertical Cross Section of U Analysis Increment Courtesy of Min Sun 6

17 Two Ways to Change Horizontal Influence Scale " By changing parameter hzscl in namelist " By reading BE matrix directly and changing hwll array which stores horizontal influence scales Same! How to change the horizontal influence scale, meanwhile do not affect the weight? Courtesy of Min Sun 7

18 Change Variance in BE How to change the horizontal influence scale, meanwhile do not influence the weight? Change the arrays which store horizontal influence scales hwll and variance of BE simultaneously! Both hwll and variance are divided by 2 Only hwll is divided by 2 Courtesy of Min Sun 8

19 GEN-BE! Reference 22 GSI tutorial: Community Tools: gen_be! GenBE version with WRF-DA Syed RH Rizvi National Center For Atmospheric Research (NCAR) NESL/MMM/DAG, Boulder, CO-837, USA GEN_BE v2.: August, 22 GSI Tutorial Community Tools "gen_be" Syed RH Rizvi! Gael Descombes (25)! Included in GSI package under directory util/gen_be_v2.! No support from DTC. 9

20 GSI Variational-Ensemble (EnVar) hybrid Important way to construct background error covariance in GSI Details will be covered in Daryl s talk tomorrow morning Only introduce the setup of GSI EnVar hybrid here 2

21 Setup GSI hybrid Table the list of ensemble be read by GSI hybrid! Step : Link the5.ensemble membersforecasts to thethat GSIcanrun directory regional_ensemble explanation _option GFS ensemble internally interpolated to hybrid grid 2 ensembles are in WRF NMM (HWRF) format 3 ensembles are in ARW netcdf format 4 ensembles are in NEMS NMMB format GSI recognized ensemble file names filelist : a text file include path and name of ensemble files d_en, d_en2, wrf_en, wrf_en2, nmmb_ens_mem, nmmb_ens_mem2,! Step 2: Setup namelist (Daryl s talk) 3D EnVar Hybrid: 4D EnVar hybrid: Basic Practical case 4 Advanced Practical case A4 Advanced Practical case C 2

22 Observation Error Introduction to observations errors External observation error table for conventional obs Satellite radiance observation error Radar radial wind observations error Adaptive Tuning of Observation Error 22

23 Introduction to observation errors! Observation error has to be available for variational analysis! Observation error decides the impact of this observation in varataional analysis. The ratio of observation error and background error decide how much analysis results fit to the observation value.! For most of observations, observation errors are unrelated! Each type of observations has their own way to set error:! Error for conventional observation:!read in from the PrepBUFR file for Global analysis when oberrflg set to false.!calculated based on an external observation error table for regional analysis or for global analysis when oberrflg set to true.! Satellite radiance! Radar radial wind! 23

24 External observation error table Column # 2 2 OBSERVATION TYPE.E+4.267E+.5E+4.332E+.E+4.47E+.95E E+.9E E+.85E E+.563E+.6326E E+.8635E E+.2E+.685E+.685E+.685E+.737E E E+ 22 OBSERVATION TYPE.E+4.5E+4.E+4.95E+3.9E+3.85E+3.772E+.2338E E E E+.2575E+ Column # Content Unit Pressure hpa 3 2 T degree C 4 3 q percent/ 5 4 UV m/s 6 5 Ps mb 6 Pw 2 kg/m (or mm) For each observation, error is from a vertical interpolation based on error table Global Regional fixed B matrix nam_glb_berror.f77.gcv nam_nmmstat_na.gcv 24

25 Satellite radiance observation error! In satinfo file, observation error is set based on sensor, satellite, and channel:!sensor/instr/sat amsua_n5 amsua_n5 amsua_n5 amsua_n5... amsua_n5 hirs3_n7 hirs3_n7... hirs3_n7 chan iuse error error_cld ermax var_b.... var_pg.... cld_det Observation error for clear radiance Observation error for cloudy radiance 25

26 Radar radial wind observation error! Level II radial wind observations are superobed as new radial wind observations and the observation error for new radial velocity is: 2 r error = V Vr 2 where, Vr is a vector includes all level-ii radial wind observations in a superob box.! The observation error can be inflated through a namelist variable erradar_inflate in section /obsqc/. The default value is. 26

27 Gross check! Gross check is a QC check to exclude questionable obs that degrade the analysis! Users can adjust thresholds for data types in convinfo:!otype ps ps t t type Gross check controlled by these columns sub iuse twindow numgrp ngroup nmiter gross ermax ermin var_b var_pg ithin If ratio > gross: observation rejected ratio = (Observation-Background)/max(ermin,min(ermax,obserror)) Rejected observations will show up in fit files under rej

28 Adaptive Tuning of Observation Error! Talagrand (997) on E ( J (Xa) )! Desroziers & Ivanov (2) E( Jo )= ½ Tr ( Ip HK) E( Jb )= ½ Tr (KH) where Ip is identity matrix with order p K is Kalman gain matrix H is linearized observation forward operator! Chapnik et al.(24): robust even when B is incorrectly specified More details please see Wan-Shu Wu s talk in 23 GSI summer tutorial: Background and Observation Error Estimation and Tuning Courtesy of Wan-Shu Wu 28

29 Questions?

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