WRF 4D-Var 4-Dimensional Variational Data Assimilation for the by wuyunyi

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									                         WRF 4D-Var
                    Hans Huang, MMM/NCAR

    1.     A short introduction to WRF 4D-Var
    2.     The current status: The basic system
    3.     The structure function: single ob exp
    4.     Results from cold-start experiments
    5.     Results from cycling experiments
    6.     Our first radar data assimilation experiments
    7.     Summary

Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007     1
            WRF 4D-Var developers

                      Xiang-Yu Huang,
 Qingnong Xiao, Dale Barker, Xin Zhang, John Michalakes, Wei
  Huang, John Bray, Zaizhong Ma, Tom Henderson, Jimy Dudhia,
  Xiaoyan Zhang, Duk-Jin Won, Yongsheng Chen, Yongrun Guo,
          Juanzhen Sun, Hui-Chuan Lin, Ying-Hwa Kuo




Acknowledgments. The WRF 4D-Var development has been primarily
supported by the Air Force Weather Agency (AFWA). The Korean Meteorological
Administration (KMA) also funded some 4D-Var tasks.
Hans Huang: WRF 4D-Var      MMM Seminar, 13 December 2007                     2
         4D-Var: 4-Dimensional Variation
              data assimilation
                                            (new)




                                                    (initial condition for NWP)
                           (old forecast)




Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007                            3
                 WRF 4D-Var: J=Jo +Jb +Jc
 J b x 0  
                1
                2
                                         
                  x0  xb  B1 x0  xb 
                            T                                                 80000

                                                                              70000                               Jb
                                                                                                                  Jo
             1 K
                                                    
                                                                              60000
 J o x 0    H k x k  y k  R 1 H k x k  y k 
                                T                                                                                 Jc




                                                              cost function
             2 k1                                                            50000

             
                                                        
                                                                              40000
 J c x 0   df  x N 2  x df 2  C1  x N 2  x df 2 
                                    T
                               N                    N
              2                                                               30000

              df                                           
                                        T
                           N          1          N                   20000
              x N 2   fix i  C  x N 2   fix i 
                                                           
                                                                              10000
               2 
                          i0                    i0    
                                                             
                                                              
                                                                                 0
              df  N                         
                              T
                           1  N                                              0   4   9   14 18 23 28 33 37 42
                                      
               hix i  C  hix i 
                                                                                                iterations
               2  i0
                   
                                i0      
                                              
                                               
where:
       f , if i  N 2
 hi   i
       fi , if i  N 2
       1

Hans Huang: WRF 4D-Var                        MMM Seminar, 13 December 2007                                              4
                         Why 4D-Var?
   •      Use observations over a time interval,
          which suits most asynoptic data and use
          tendency information from observations.
   •      Use a forecast model as a constraint,
          which enhances the dynamic balance of
          the analysis.
   •      Implicitly use flow-dependent background
          errors, which ensures the analysis quality
          for fast developing weather systems.
   •      NOT easy to build and maintain!
Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007   5
                   A short 4D-Var review
     •   The idea: Le Dimet and Talagrand (1986); Lewis and Derber (1985)
     •   Implementation examples:
          – Courtier and Talagrand (1990); a shallow water model
          – Thepaut and Courtier (1991); a multi-level primitive equation model
          – Navon, et al. (1992); the NMC global model
          – Zupanski M (1993); the Eta model
          – Zou, et al. (1995); the MM5 model
          – Sun and Crook (1998); a cloud model
          – Rabier, et al. (2000); the ECMWF model
          – Huang, et al. (2002); the HIRLAM model
          – Zupanski M, et al. (2005); the RAMS model
          – Ishikawa, et al. (2005); the JMA mesoscale model
          – Huang, et al. (2005); the WRF model
          – Xu, et al. (2005); NAVDAS-AR
          – Gauthier, et al. (2007); MSC
     •   Operation: ECMWF, Meteo France, JMA, UKMO, MSC.
     •   Pre-operation: HIRLAM, NAVDAS-AR


Hans Huang: WRF 4D-Var           MMM Seminar, 13 December 2007                    6
        Necessary components of 4D-Var
      • H observation operator, including the tangent linear operator H
        and the adjoint operator HT.
      • M forecast model, including the tangent linear model M and
        adjoint model MT.
      • B background error covariance (N*N matrix).
      • R observation error covariance, which includes the representative
        error (K*K matrix).




Hans Huang: WRF 4D-Var     MMM Seminar, 13 December 2007                    7
                 WRF 4D-Var milestones
      2003: WRF 4D-Var project.                           ?? FTE
      2004: WRF SN (simplified nonlinear model).          1.5 FTE
            Modifications to WRF 3D-Var.
      2005: TL and AD of WRF dynamics.                    1.5 FTE
            WRF TL and AD framework.
            WRF 4D-Var framework.
      2006: The WRF 4D-Var prototype.                     2.5 FTE
            Single ob and real data experiments.
            Parallelization of WRF TL and AD.
            Simple physics TL and AD.
            JcDF
      2007: The WRF 4D-Var basic system.                  2.5 FTE


Hans Huang: WRF 4D-Var    MMM Seminar, 13 December 2007             8
Basic system: 3 exes, disk I/O, parallel, full dyn, simple phys, JcDF

                 WRF               I/O                   VAR

                                                     Outerloop   xb
               WRF_NL            WRFINPUT

WRFBDY                             call                  Mk      B
                              NL(1),…,NL(K)              dk
                                                                 R
                                                                 y1
                 WRF+     BS(0),…,BS(N)              Innerloop   …

                                  TL00                   U       yK
               WRF_TL              call                  Mk
                               TL(1),…,TL(K)
                                                         Hk
                          TLDF
                                                          T
                              AF(K),…,AF(1)              Hk
              WRF_AD                                       T
                                   call                  Mk
                                   AD00                  UT      xn

Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007                  9
            Single observation experiment
     The idea behind single ob tests:
     The solution of 3D-Var should be

                                                                                   y  Hx 
                                                                                   1
                         x  x  BH HBH  R
                         a           b                T         T                                       b


     Single observation
                     x  x  Bi   
                         a
                                 
                                 b                    2
                                                      b         y  x 
                                                              2 1
                                                              o            i            i
        
     3D-Var  4D-Var: H  HM; H  HM; HT  MTHT
     The solution of 4D-Var should be
       
             x  x  BM H HMBM   R                                                                        
                                                                                             1
              a      b
                                 H   T        T                    T           T
                                                                                                   y  HMx b
     Single observation, solution at observation time
                     Mx  x a            b
                                               MBM       T               2
                                                                               b            y  x 
                                                                                            2 1
                                                                                            o       i       i
                                                                       i

Hans Huang: WRF 4D-Var                   MMM Seminar, 13 December 2007                                              10
        Analysis increments of 500mb q
               from 3D-Var at 00h and from 4D-Var at 06h
                  due to a 500mb T observation at 06h




                              +                                        +




               FGAT(3D-Var)                                   4D-Var
Hans Huang: WRF 4D-Var        MMM Seminar, 13 December 2007                11
500mb q increments at 00,01,02,03,04,05,06h to a 500mb T ob at 06h




                                                         +   OBS




Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007             12
          500mb q difference at 00,01,02,03,04,05,06h from
     two nonlinear runs (one from background; one from 4D-Var)




                                                         +   OBS




Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007             13
         500mb q difference at 00,01,02,03,04,05,06h from
     two nonlinear runs (one from background; one from FGAT)




                                                         +   OBS




Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007             14
            Real Case: Typhoon Haitang
          Experimental Design (Cold-Start)
 •    Domain configuration: 91x73x17, 45km
 •    Observations from Taiwan CWB operational database.
 •    5 experiments are conducted before Haitang’s landfall at
      0000 UTC 18 July 2005.
           FGS – forecast from the background [The background fields are
            6-h WRF forecasts from National Center for Environment
            Prediction (NCEP) GFS analysis.]
           AVN- forecast from the NCEP AVN analysis
           3DVAR – forecast from WRF-Var3d using FGS as background
           FGAT - forecast from WRF-Var3dFGAT using FGS as
            background
           4DVAR – forecast from WRF-Var4d using FGS as background

Hans Huang: WRF 4D-Var       MMM Seminar, 13 December 2007                  15
Observations used in a 4D-Var experiment
          Table 1. The numbers of different observation types assimilated
                      by WRF 4D-Var at 0600 UTC 16 July.
           U(m/s)     V(m/s)      T(K)       P(Pa) Q(kg/kg) DZ(m)           REF(m)
   TEMP      858         857      1054                    841
 TEMPsurf     9          10        12          12          12
  SYNOP      229         232       240        237         238
 GEOAMV     2569        2569
   AIREP     932         933       947
   PILOT     124         121
  METAR      128         130       154                    144
    SHIP     55          58        64          64          58
  GPSREF                                                                     162
  SATEM                                                              851
  QSCAT     2597        2610
   BUOY      66          65                    65
  BOGUS     1200        1200       788        788          80




 Hans Huang: WRF 4D-Var         MMM Seminar, 13 December 2007                        16
                   Typhoon Haitang 2005
                             2005.07.16.00Z




Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007   17
                   Typhoon Haitang 2005




Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007   18
                 A KMA Heavy Rain Case
   Period: 12 UTC 4 May - 00 UTC 7 May, 2006

   Assimilation window: 6 hours

   Cycling (6h forecast
   from previous cycle as

   background for analysis)
   All KMA operational data

   Grid : 60x54x31
   Resolution : 30km
   Domain size: the same as the
   KMA operational 10km domain.
Hans Huang: WRF 4D-Var    MMM Seminar, 13 December 2007   19
            Observations used in 3D-Var
                                                                             Water
                         U wind       V wind     Temperature      Pressure
                                                                             vapor
        SOUND             459          464            519            -        385

     SONDE_SFC             14           15             15           15        15

        SYNOP              67           59             73           71        72

       GEOAMV              74           76              -            -         -

        PILOT             182          195              -            -         -

        METAR             559          551            614           33        36

         SHIP              1             1             2             2         1




Hans Huang: WRF 4D-Var            MMM Seminar, 13 December 2007                      20
            Observations used in 4D-Var
                                                                             Water
                         U wind       V wind     Temperature      Pressure
                                                                             vapor
        SOUND             456          461            519            -        384

     SONDE_SFC             14           14             15           14        15

        SYNOP             253          212            268           191       204

       GEOAMV              -             -              -            -         -

        PILOT             185          194              -            -         -

        METAR             2636         2402           2957          218       240

         SHIP              1             1             2             2         1




Hans Huang: WRF 4D-Var            MMM Seminar, 13 December 2007                      21
                                                  Observations Verification
                                                                                                                                                                                24 hours forecasted ve rification -TEM P V
                                                                           24 hours forecast verification -SYNOP U                       3DVar_Ave              4DVar_Ave
                       3DVar_Ave                   4DVar_Ave
                                                                                                                                                     5.00
                                   4.00

                                   3.50                                                                                                              4.50




                                                                                                                                        RMSE (m/s)
                                   3.00
                      RMSE (m/s)




                                                                                                                                                     4.00

                                   2.50
                                                                                                                                                     3.50
                                   2.00

                                                                                                                                                     3.00
                                   1.50

                                   1.00                                                                                                              2.50
                                              0                   6                             12                       18        24                       0               6                    12                          18   24
                                                                                      FCST Verification                                                                                   FCST Verification


                                                                                                                                                                                24 hours forecasted ve rification -TEM P U
                                                                                                                                         3DVar_Ave              4DVar_Ave


                                                                                                                                                     5.00


                                                                                                                                                     4.50




                                                                                                                                        RMSE (m/s)
                                                                             QuickTime™ and a
                                                                         TIFF (LZW) decompressor                                                     4.00
                                                                      are needed to see this picture.

                                                                                                                                                     3.50


                                                                                                                                                     3.00


                                                                                                                                                     2.50
                                                                                                                                                            0               6                    12                          18   24

                                                                                                                                                                                          FCST Verification

                                                                                                                                                                                24 hours forecasted verification -TEM P T
                                                                                                                                         3DVar_Ave              4DVar_Ave
                                                                        24 hours forecasted verification -SYNOP T
               3DVar_Ave                          4DVar_Ave                                                                                          3.00
                           4.00

                           3.50
                                                                                                                                                     2.50
                                                                                                                                        RMSE (m/s)




                           3.00
         RMSE (m/s)




                           2.50
                                                                                                                                                     2.00
                           2.00

                           1.50

                                                                                                                                                     1.50
                           1.00
                                                                                                                                                            0               6                   12                           18   24
                                          0                   6                            12                       18        24

                                                                                   FCST Verification
                                                                                                                                                                                          FCST Verification



Hans Huang: WRF 4D-Var                                                                                     MMM Seminar, 13 December 2007                                                                                               22
                                         Precipitation Verification

                                 0.1 mm Precipitation                                            5mm Precipitation

               0.7                                                             0.9
                                                                               0.8
               0.6
                                                                               0.7
               0.5
                                                                               0.6
               0.4                                                             0.5
                                                                 3dvar                                                           3dvar
         CSI




                                                                         CSI
               0.3                                               4dvar         0.4                                               4dvar

                                                                               0.3
               0.2
                                                                               0.2
               0.1
                                                                               0.1
                0                                                               0
                         3   6     9    12   15   18   21   24                           3   6     9    12   15   18   21   24
                                   FCST Time (hours)                                              FCST Time (Hours)



                                 15 mm Precipitation                                             25 mm Precipitation

                0.4                                                            0.16

               0.35                                                            0.14

                0.3                                                            0.12

               0.25                                                             0.1
                                                                 3dvar                                                           3dvar
         CSI




                                                                         CSI
                0.2                                                            0.08
                                                                 4dvar                                                           4dvar
               0.15                                                            0.06

                0.1                                                            0.04

               0.05                                                            0.02

                     0                                                               0
                         3   6      9   12   15   18   21   24                           3   6      9   12   15   18   21   24
                                   FCST Time (Hours)                                               FCST Time (Hours)




Hans Huang: WRF 4D-Var                             MMM Seminar, 13 December 2007                                                         23
                    Observation Verification: Precipitation, CSI
                         CSI (0.1mm)
                                                                               CSI (5.0 mm)
                            3DVAR       4DVAR
                                                                                   3DVAR      4DVAR
       1                                                          1
      0.9                                                        0.9
      0.8                                                        0.8
      0.7                                                        0.7
      0.6                                                        0.6




                                                           CSI
CSI




      0.5                                                        0.5
      0.4                                                        0.4

      0.3                                                        0.3

      0.2                                                        0.2

      0.1                                                        0.1

       0                                                          0
            3   6    9       12        15   18   21   24               3   6   9     12     15        18   21   24
                             FCST. Time                                              FCST. Time




      Hans Huang: WRF 4D-Var                     MMM Seminar, 13 December 2007                                       24
                        Observation Verification: Precipitation, BIAS

                         BIAS (0.1mm)                                              BIAS (5.0mm)

                             3DVAR      4DVAR                                          3DVAR      4DVAR

        2                                                             1

                                                                     0.9
       1.8
                                                                     0.8
       1.6                                                           0.7

                                                                     0.6
       1.4
BIAS




                                                              BIAS
                                                                     0.5
       1.2
                                                                     0.4

        1                                                            0.3

                                                                     0.2
       0.8
                                                                     0.1
       0.6                                                            0
               3    6    9    12     15     18   21      24                3   6   9    12     15     18   21   24
                             FCST. Time                                                FCST. Time




             Hans Huang: WRF 4D-Var                   MMM Seminar, 13 December 2007                                  25
  First radar data assimilation
  experiment using WRF 4D-Var

  Yong-Run Guo and Juanzhen Sun




Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007   26
  The OSSE setup
                         061301Z, 4VAR Exp. Initial time

  061212Z                            061300Z                              061312Z



                                         Convection period

                                                   4DVAR time window


 • 12/4-km WRFV2.2 run
      – Initial and boundary conditions: Eta 3-hly analysis starting at
      2002061212Z
      – Domain size: 271x241x31 (12-km) and 325x280x31 (4km)

      –The control experiment with the domain2 (325x280x31):



Hans Huang: WRF 4D-Var        MMM Seminar, 13 December 2007                         27
            Domain settings                               height




                                                         landuse




Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007             28
Hourly rainfall forecast from the control run starting from 2002061212Z




 Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007              29
Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007   30
Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007   31
               WRF 4D-Var Experiment design

  • Physics option as the control run (truth)
  • Initial time for Experiments at 2002061301Z (the 13-h
    forecast starting from 2002061212Z)
  • Domain size: 151x118x31, covered the convective cells.
  • Grid size: 4-km, Time step: 20 seconds
  • First guess from NCEP GFS analysis
  • Time window for WRF 4DVar:
       0.25-h, 45 steps
             0.5-h, 90 steps (?)
  • Forecast length: 11-h.
  • BES interpolated from 12km IHOP BES (Hongli Wang)
Hans Huang: WRF 4D-Var      MMM Seminar, 13 December 2007    32
                   Control run 4-km domain




                                  118
             280




                                            151


                    WRF 4DVar Exp 4-km Domain


                                 325


Hans Huang: WRF 4D-Var       MMM Seminar, 13 December 2007   33
                         OSSE Radar data generation
• Gaussian random perturbation (0,1), Xpert, added to truth
• The truth is obtained by using iowrf utility to extract a box-
  domain <x121to 271, y94to211> from the 4-km control run
  <325x280> domain.
• Soichiro Sugimoto’s code as the reference
• The Radius of Radar OBS: 200km
• When Rain water mixing ratio > 1.e-7, the reflectivity truth
  will be computed as Xtdbz

                         X   o
                                 dbz   X     t
                                                  dbz   X    pert

• It is regarded as clear air when Xodbz < 5, no clear air radar obs
  considered.
• When the bean angle > 20o, no radar obs
• The radial velocity data are generated in the same way as
  reflectivity
Hans Huang: WRF 4D-Var             MMM Seminar, 13 December 2007       34
        Rain water mixing ratio every 5 minutes from 130100 to 130130

      130100             130105                 130110          130115




      130120             130125                 130130




Hans Huang: WRF 4D-Var     MMM Seminar, 13 December 2007                 35
                         OSSE Radar data coverage




      10 NEXRAD Radar sites                      OSSE Radar data coverage
      over the Exp. Domain                        at 0100 UTC 13 June 20
Hans Huang: WRF 4D-Var       MMM Seminar, 13 December 2007                  36
                         Experiment design
• TRUTH ----- Initial condition from TRUTH (13-h forecast
  initialized at 2002061212Z from AWIPS 3-h analysis) run
  cutted by ndown, boundary condition from NCEP GFS data.
• NODA ----- Both initial condition and boudary condition from
  NCEP GFS data.
• 3DVAR ----- 3DVAR analysis at 2002061301Z used as the
  initial condition, and boundary condition from NCEP GFS.
  Only Radar radial velocity at 2002061301Z assimilated (total
  # of data points = 65,195).
• 4DVAR ----- 4DVAR analysis at 2002061301Z used as initial
  condition, and boundary condition from NCEP GFS. The radar
  radial velocity at 4 times: 200206130100, 05, 10, and 15, are
  assimilated (total # of data points = 262,445).

Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007            37
   INCREMENTS (A-B): B is the NCEP GFS analysis at 2002061301Z
      Truth Temperature/wind at             (Truth-FG) Temperature/wind
            lowest h level                         at lowest h level




    (3DVAR-FG) Temperature/wind         (4DVAR15m-FG) Temperature/wind
          at lowest h level                    at lowest h level




Hans Huang: WRF 4D-Var     MMM Seminar, 13 December 2007                  38
                Hourly precipitation ending at 01-h forecast
      TRUTH                                      NODA




       3DVAR                                     4DVAR




Hans Huang: WRF 4D-Var      MMM Seminar, 13 December 2007      39
                Hourly precipitation ending at 03-h forecast
             TRUTH                                 NODA




             3DVAR                                  4DVAR




Hans Huang: WRF 4D-Var      MMM Seminar, 13 December 2007      40
                Hourly precipitation ending at 06-h forecast
          TRUTH                                   NODA




         3DVAR                                    4DVAR




Hans Huang: WRF 4D-Var      MMM Seminar, 13 December 2007      41
                           Summary
    1.     A short introduction to WRF 4D-Var
    2.     The current status: The basic system
    3.     The structure function: single ob exp
    4.     A cold-start experiment
    5.     A cycling experiment
    6.     First radar data assimilation experiment



Hans Huang: WRF 4D-Var   MMM Seminar, 13 December 2007   42

								
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