Hybrid variational-ensemble data assimilation at NCEP by dfhdhdhdhjr


									Hybrid variational-ensemble data assimilation

                              Daryl T. Kleist1,3

  Dave Parrish1, John Derber1,Jeff Whitaker2, Kayo Ide3, & Xuguang Wang4

1NOAA/NCEP/EMC, 2NOAA/ESRL, 3University   of Maryland-College Park, 4University of Oklahoma

               High Impact Weather Working Group Workshop                                     1
                      24 February, 2011 – Norman, OK
             Variational Data Assimilation

J Var      B   
           1 '
        x  x

                  T    1
                                1 '
                             x  y o  Hx '

                                                          R y
                                                          T    1     '
                                                                      o         
                                                                           Hx '  J c

J : Penalty (Fit to background + Fit to observations + Constraints)
x’ : Analysis increment (xa – xb) ; where xb is a background
BVar : Background error covariance
H : Observations (forward) operator (eg. CRTM)
R : Observation error covariance (Instrument +
yo’ : Observation innovations
Jc : Constraints (physical quantities, balance/noise, etc.)

               B is typically static and estimated a-priori/offline

• Current background error covariance (applied
  operationally) in VAR
  – Isotropic recursive filters
  – Poor handle on cross-variable covariance
  – Minimal flow-dependence added
     • Implicit flow-dependence through linearization in
       normal mode constraint (Kleist et al. 2009)
     • Flow-dependent variances (only for wind, temperature,
       and pressure) based on background tendencies
  – Tuned NMC-based estimate (lagged forecast pairs)
                 Hybrid Variational-Ensemble
• Incorporate ensemble perturbations directly into
  variational cost function through extended control
    – Lorenc (2003), Buehner (2005), Wang et. al. (2007), etc.

    J x ,   f x f B x f   e
         f         
                1 ' T 1 '
                               2
                                                                       
                                     L    1 y 'o  Hx 't T R 1 y 'o  Hx 't
                                 1 T 1
                                                          
                                x  x   k  xe
                                      f         k
                                           k 1

                                      1        1
                                                     1
                                      f       e
f & e: weighting coefficients for fixed and ensemble covariance respectively
xt: (total increment) sum of increment from fixed/static B (xf) and ensemble B
k: extended control variable; x k :ensemble perturbation
L: correlation matrix [localization on ensemble perturbations]                            4
                                     Why Hybrid?

                                 VAR      EnKF Hybrid References
                                 (3D, 4D)
Benefit from use of flow                     x        x          Hamill and Snyder 2000;
dependent ensemble                                               Wang et al. 2007b,2008ab,
covariance instead of static B                                   2009b, Wang 2011; Buehner
                                                                 et al. 2010ab
Robust for small ensemble                             x          Wang et al. 2007b, 2009b;
                                                                 Buehner et al. 2010b
Better localization for                               x          Campbell et al. 2009
integrated measure, e.g.
satellite radiance
Easy framework to add            x                    x
various constraints
Framework to treat non-          x                    x
Use of various existing          x                    x
capabilities in VAR

                                 Acknowledgement: Xuguang Wang                               5
                      Hybrid with (global) GSI

• Control variable has been implemented into GSI 3DVAR*
   – Full B preconditioning (Wang 2011)
        • Working on extensions to B1/2 preconditioned minimization options
   – Spectral filter for horizontal part of A
        • Eventually replace with (anisotropic) recursive filters
   – Recursive filter used for vertical
   – Dual resolution capability
        • Ensemble can be from different resolution than background/analysis
          (vertical levels are the exception)
   – Various localization options for A
        • Grid units or scale height
        • Level dependent (plans to expand)
   – Option to apply TLNMC (Kleist et al. 2009) to analysis increment

                                       ' K              
                                                        
                                x  C x f    k  x e 
                                            k 1        
      *Acknowledgement: Dave Parrish for original implementation of extended control variable
  Single Observation

Single 850mb Tv observation (1K O-F, 1K error)
            Single Observation

Single ps observation (-2mb O-F, 1mb error) near center of Hurricane Ike
                   Single Observation

Single 850mb zonal wind observation (3 m/s O-F, 1m/s error) in Hurricane Ike circulation
                 Dual-Res Coupled Hybrid

                                                  recenter analysis ensemble
 member 1
                                                                               member 1

 member 2                EnKF                                                  member 2
  forecast            member update                                             analysis

                                                                               member 3
 member 3

   high res           GSI              high res
   forecast      Hybrid Ens/Var        analysis

Previous Cycle        Current Update Cycle
            Hybrid Var-EnKF GFS experiment
•   Model
     – GFS deterministic (T574L64; post July 2010 version – current operational version)
     – GFS ensemble (T254L64)
          • 80 ensemble members, EnKF update, GSI for observation operators

•   Observations
     – All operationally available observations (including radiances)
     – Includes early (GFS) and late (GDAS/cycled) cycles as in production

•   Dual-resolution/Coupled
          • High resolution control/deterministic component
                –   Includes TC Relocation on guess
          • Ensemble is recentered every cycle about hybrid analysis
                –   Discard ensemble mean analysis

•   Satellite bias corrections
     – Coefficients come from GSI/VAR

•   Parameter settings
          • 1/3 static B, 2/3 ensemble
          • Fixed localization: 800km & 1.5 scale heights

•   Test Period                                                                            11
     – 15 July 2010 – 15 October 2010 (first two weeks ignored for “spin-up”)
              500 hPa Anom.Corr.
Northern Hemisphere          Southern Hemisphere

Forecast Fits to Obs (Tropical Winds)

    Forecasts from hybrid analyses fit observation much better.
     Tropical Wind Errors (72hr)

Verification against ‘consensus analysis’ [ECMWF, NCEP, UKMET]
Hybrid versus 3DVAR Track Error

Hybrid versus 3DVAR Intensity Bias

            HVEDAS (3D) for GDAS/GFS
• Prototype dual-resolution, two-way coupled hybrid Var/EnKF
  system outperforms standard 3DVAR in GFS experiments
   – 2010 Hurricane Season (August 15 through October 31 2010) run off-
   – Emphasis on AC, RMSE, TC Tracks

• Plan underway to implement into GDAS/GFS operationally
   – Target: Spring 2012 (subject to many potential issues)
       • Porting of codes/scripts back to IBM P6
       • Cost analysis (will everything fit in production suite?)
       • More thorough (pre-implementation) testing and evaluation
           – More test periods (including NH winter)
           – Other/more verification metrics
       • Potential moratorium associated with move to new NCEP facility

• Issues
   – Weighting between ensemble and static B
   – Localization
   – How should EnKF be used within ensemble forecasting paradigm?
         HVEDAS Extension to other Applications
• Expand hybrid to 4D
   – Hybrid within ‘traditional 4DVAR’ (with adjoint)
   – Pure ensemble 4DVAR (non-adjoint)
   – Ensemble 4DVAR with static B supplement (non-adjoint)

• Non-GFS applications in development
   –   NASA GEOS-5 (GMAO)
   –   NAM (Dave Parrish, others)
   –   Hurricanes/HWRF (Mingjing Tong, HFIP, many collaborators)
   –   Storm-scale initialization (Jacob Carley, collaborators)
   –   RR (Xuguang Wang, Ming Xue, Stan Benjamin, Jeff Whitaker, Steve
       Weygandt, others)

• NCEP strives to have single DA system to develop, maintain,
  and run operationally (global, mesoscale, severe weather,
  hurricanes, etc.)
   – GSI (including hybrid development) is community code supported through
   – EnKF used for GFS-based hybrid being expanded for use with other
     applications                                                             18
Backup Slides

               Applications of hybrid DA

•   WRFVAR based hybrid (Wang et al 2008ab, MWR)
•   Application for hurricane track forecasts (Wang 2011, WAF)
•   For radar data assimilation for hurricanes, Li et al.
•   FAA application with GSI-based hybrid, Zhu et al.

                                                         Li et al. 2011
           GSI-based ‘ensemble 4DVAR’

•   A natural extension of 3DVAR-based hybrid with no static covariance B.
•   Temporal evolution of the increment is obtained through evolved ensemble
    perturbations in the assimilation window.
•   ens4dvar is a 4DVAR with no need for tangent linear and adjoint of the
    forecast model (Liu et al. 2009).

                                                     Lei, Wang et al. 2011

         Temporal evolution of the error covariance


                  t-3h             t                 t+3h


                  t-3h             t                 t+3h

          Downstream                      Upstream
          impact                          impact

To top