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GSI-based four dimensional ensemble-variational (4DEnsVar) data assimilation: formulation and single resolution experiments with real data for NCEP GFS Ting Lei, Xuguang Wang University of Oklahoma, Norman, OK, USA Wang and Lei, MWR, 2013

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GSI-based four dimensional ensemble-variational (4DEnsVar) data assimilation: formulation and single resolution experiments with real data for NCEP GFS

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6th WMO Symposium on data assimilation College Park, MD, USA

  • Oct. 7-11, 2013

Ting Lei, Xuguang Wang University of Oklahoma, Norman, OK, USA

Wang and Lei, MWR, 2013

Daryl Kleist (NCEP): dual resolution 4DEnsVar

Acknowledgement: NCEP DA team (John Derber, Dave Parrish, Russ Treadon, Miodrag Rancic) and Jeff Whitaker (NOAA ESRL)

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Background

 Over the past three years, significant efforts were conducted to develop GSI hybrid system and test with US operational Global Forecast System (GFS). The GSI hybrid DA system showed significant improvement compared to GSI 3DVAR and became operational on May 22, 2012 for GFS.  It has also been extended to a 4DEnsVar hybrid (“Tangent linear and adjoint model free”) and showed further improvements.  Efforts are being conducted to further develop and research GSI hybrid DA for operational regional forecast systems, e.g.,

  • Xu Lu poster on GSI hybrid for Hurricane-WRF (HWRF)
  • Xuguang Wang Thur. talk on convective scale weather over

CONUS

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control forecast GSI control analysis data assimilation First guess forecast control forecast Ensemble covariance EnKF EnKF analysis k member 1 forecast member 2 forecast member k forecast EnKF analysis 2 EnKF analysis 1 member 1 forecast member 2 forecast member k forecast member 1 analysis member 2 analysis member k analysis Re-center EnKF analysis ensemble to control analysis

GSI-based hybrid ensemble-variational DA system

Wang, Parrish, Kleist, Whitaker, MWR, 2013

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Various hybrid schemes

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Wang and Lei, MWR, 2013

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NCEP pre-implementation test of 3DEnsVar hybrid

http://www.emc.ncep.noaa.gov/gmb/wd20rt/experiments/prd12q3s/vsdb/

  • Significant improvement of operational GFS forecasts
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GSI hybrid for GFS: GSI 3DVar vs. 3DEnsVar vs. EnKF

Wang, Parrish, Kleist and Whitaker, MWR, 2013

  • Hybrid was better than

3DVar due to use of flow-dependent ensemble covariance

  • Hybrid was better than

EnKF due to the use of tangent linear normal mode balance constraint (TLNMC)

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  • Account for temporal evolution of error covariance that was ignored

in 3DEnsVar hybrid.

  • Still need to improve computational efficiency of traditional TL/ADJ

4DVAR being developed for GSI (Rancic et al. 2012).

  • An alternative to TL/ADJ 4DVar, i.e., 4D-Ensemble-Variational method

(4DEnsVar) is therefore developed

  • Conveniently avoid TL/ADJ of forecast model like earlier work and also

applied localization inside variational minimization (e.g., Buehner et

  • al. 2010)

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GSI-based 4DEnsVar hybrid: motivation

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T t t

  • t

t

  • t

T static T

  • e

y y J J J J

1 t 1

  • t

T t 1 2 ' 1 1 ' 1 1 2 1 1 ' 1

) '-H ( R ) '-H ( 2 1 2 1 2 1 , x x α C α x B x α x

K k t e k k t 1 ' 1 '

) (x α x x 

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B stat 3DVAR static covariance; R observation error covariance; K ensemble size; C correlation matrix for ensemble covariance localization;

e k

x kth ensemble perturbation;

' 1

x 3DVAR increment;

'

x total (hybrid) increment;

'

  • y innovation vector;

H linearized observation operator;

1 weighting coefficient for static covariance; 2 weighting coefficient for ensemble covariance; α extended control variable.

GSI-based 4DEnsVar hybrid: formulation

  • Naturally extended from and unified with GSI-based 3DEnsVar hybrid

formula (Wang 2010, MWR), which uses extended control variables to incorporate ensemble like in Lorenc 2003, Buehner 2005, Wang et al., 2007, Wang et al. 2008)

Add time dimension in 4DEnsVar

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Experiment Design

  • Time period: Aug. 15 2010 – Sep. 20 2010;
  • Model: GFS T190L64
  • Observations: all operational data
  • Verification: global forecast and hurricane track forecasts.

Experiment Description GSI3DVar The GSI 3DVar experiment 4DEnsVar 4D ensemble-variational DA experiment with hourly ensemble perturbations 4DEnsVar-2hr 4D ensemble-variational DA experiment with 2-hourly ensemble perturbations 3DEnsVar 3D ensemble-variational DA experiment 4DEnsVar-nbc Same as “4DEnsVar-2hr” except without the use of the tangent linear normal mode balance constraint (TLNMC)

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One obs. example for TC

  • 3h 0 3h

*

4DEnsVar 3DEnsVar –3h increment propagated by model integration t=0 t=0 t=0 time

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Another example

Downstream impact Upstream impact

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Temp. Height

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Global forecasts verified against ECMWF analyses

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  • Forecasts from 3DEnsVar are

more skillful than GSI3DVar.

  • 4DEnsVar further improves

the skill of the forecasts compared to 3DEnsVar.

  • The improvement of

4DEnsVar relative to 3DEnsVar is smaller than the improvement of 3DEnsVar relative to GSI3DVar.

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  • 3DEnsVar and 4DEnsVar are

more accurate than GSI3DVar at most levels.

  • More appreciable improvement

is seen in the wind than the temperature forecasts.

  • Over NH and SH, 4DEnsVar

shows consistent improvement relative to 3DEnsVar for wind forecasts and neutral or slightly positive impact for temperature forecast.

  • Over TR, 4DEnsVar shows mostly

neutral impact compared to 3DEnsVar for both wind and temperature forecasts (not show).

6-hour forecasts verified against conv. obs.

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K m/s

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  • Temperature forecasts from

4DEnsVar show overall positive impact relative to 3DEnsVar for both NH and SH.

  • 4DEnsVar shows neutral

impact on wind forecasts

  • ver NH and positive impact
  • ver SH.
  • Over TR, 4DEnsVar shows

positive impact relative to 3DEnsVar only for wind forecasts at low level (not show)

96-hour forecasts verified against conv. obs.

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K m/s

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Verification of hurricane track forecasts: cases

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16 named storms in Atlantic and Pacific basins during 2010

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  • 3DEnsVar outperforms GSI3DVar.
  • 4DEnsVar are more accurate than 3DEnsVar after the 2-

day forecast lead time.

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Verification of hurricane track forecasts: RMSE and percentage of better forecast

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Impact of number of time levels of ensemble perturbations and TLNMC

  • Negative impact of less

time levels of ensemble perturbations.

  • Positive impact of TLNMC

for global forecasts.

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  • Negative impact of less time levels of ensemble perturbations

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Impact of number of time levels of ensemble perturbations and TLNMC

  • Negative impact of TLNMC on TC track forecasts
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  • Slightly slower

convergence for the first

  • uter loop and slightly

faster convergence for the second outer loop

  • The cost of 4DEnsVar

variational minimization is approximately 1.5 times of that of 3DEnsVar.

Convergence rate and computational cost

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 GSI based 4DEnsVar was developed and tested for NCEP GFS.  4DEnsVar further improved upon 3DEnsVar

  • At short lead times, the improvement of 4DEnsVar relative to 3DEnsVar over NH was

similar to that over SH. At longer forecast lead times, 4DEnsVar showed more improvement in SH than in NH.

  • The improvement of 4DEnsVar over TR was neutral or slightly positive when forecasts

were verified against the in-situ observations.

  • The hurricane track forecasts initialized by 4DEnsVar were more accurate than

3DEnsVar after the 2-day forecast lead time.

 Temporal localization is being developed within GSI-based 4DEnsVar. Preliminary tests showed positive impact of the temporal localization.  Further development of TLNMC.  Tests of 4DEnsVar at dual resolution mode (Daryl Kleist)

Summary and Discussion

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Cited references

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  • Buehner, M., 2005: Ensemble-derived stationary and flow-dependent background-error

covariances: evaluation in a quasi-operational NWP setting.Quart. J. Roy. Meteor. Soc.,131,1013-1043.

  • Buehner, M.,P. L. Houtekamer, C. Charette, H. L. Mitchell, and B. He, 2010: Intercomparison of

Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part I: Description and Single-Observation Experiments. Mon. Wea. Rev.,138, 1550-1566.

  • Lorenc, A. C. 2003: The potential of the ensemble Kalman filter for NWP – a comparison with

4D-VAR. Quart. J. Roy. Meteor. Soc.,129, 3183-3203.

  • Wang, X., C. Snyder, and T. M. Hamill, 2007: On the theoretical equivalence of differently

proposed ensemble/3D-Var hybrid analysis schemes. Mon. Wea. Rev., 135, 222-227.

  • Wang, X., D. Barker, C. Snyder, T. M. Hamill, 2008: A hybrid ETKF-3DVAR data assimilation

scheme for the WRF model. Part I: observing system simulation experiment. Mon. Wea. Rev., 136, 5116-5131.

  • Wang, X., 2010: Incorporating ensemble covariance in the Gridpoint Statistical Interpolation

(GSI) variational minimization: a mathematical framework. Mon. Wea. Rev., 138,2990-2995.

  • Wang, X., D. Parrish, D. Kleist and J. S. Whitaker, 2013: GSI 3DVar-based Ensemble-Variational

Hybrid Data Assimilation for NCEP Global Forecast System: Single Resolution Experiments.

  • Mon. Wea. Rev., in press.