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Ensemble 4DVAR and observation impact study with the GSI-based hybrid ensemble-variational data assimilation system for the GFS

Xuguang WangUniversity of Oklahoma, Norman, OK

xuguang.wang@ou.edu

Ting Lei, Govindan Kutty (OU)Jeff Whitaker (NOAA/ESRL)

Dave Parrish, Daryl Kleist, John Derber, Russ Treadon (NOAA/NCEP/EMC)

July 28, 2011

1st GSI workshop, Boulder, CO

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member 1 forecast

member 2 forecast

member k forecast

control forecast GSI-ECV

EnKF

control analysis

EnKF analysis k

EnKF analysis 2

EnKF analysis 1

member 1 forecast

member 2 forecast

member k forecast

data assimilationFirst guess forecast

control forecast

Ensemble covariance

Hybrid GSI-EnKF DA system: 1 way coupling

…… ……

……

Wang et al. 2011

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Hybrid GSI-EnKF DA system: 2 way coupling

member 1 forecast

member 2 forecast

member k forecast

control forecast GSI-ECV

EnKF

control analysis

EnKF analysis k

EnKF analysis 2

EnKF analysis 1

member 1 analysis

member 2 analysis

member k analysis

member 1 forecast

member 2 forecast

member k forecast

data assimilationFirst guess forecast

control forecast

Ensemble covariance

Re-center EnK

F analysis ensemble

to control analysis

……

……

……

……

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Why Hybrid? “Best of both worlds”VAR (3D, 4D)

EnKF hybrid References

Benefit from use of flow dependent ensemble covariance instead of static B

x x Hamill and Snyder 2000; Wang et al. 2007b,2008ab, 2009, Wang 2011; Buehner et al. 2010ab

Robust for small ensemble x Wang et al. 2007b, 2009; Buehner et al. 2010b

Better covariance localization for integrated measure (e.g. satellite radiance; radar with attenuation)

x Campbell et al. 2010

Easiness to add various constraints in VAR

x x

Treatment of nonlinearity with outer loops in VAR

x x

Use of various existing capability in VAR (e.g. variational QC)

x x

5

''1''1

2'1

1'11

211'1

21

21

21

,

HxyHxyαCαxBx

αx

oToTT

oe JJJJ

R

K

k

ekk

1

'1

' xαxx

How to incorporate ensemble in GSI?

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

kx kth ensemble perturbation; '1x 3DVAR increment; 'x total (hybrid) increment; 'oy innovation vector;

H linearized observation operator; 1 weighting coefficient for static covariance;

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

• Ensemble covariance is included in the VAR cost function through augmentation of control variables (Lorenc 2003; Buehner 2005; Wang et al. 2007a, 2008a, Wang 2010) .

• Hybrid formula (Wang 2010 -- formula for GSI with B preconditioning):

Extra term associated with extended control variable

Extra increment associated with ensemble

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Flow-dependent ensemble covariance

K

kk

GSI (static covariance) Hybrid (ensemble covariance)

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• A natural extension of 3DVAR-based hybrid.

• ENS4DVAR is a 4DVAR with no need to develop the tangent linear and adjoint of the forecast model (Liu et al. 2009).

• 4D analyses are obtained through variational minimization within the temporally evolved ensemble forecast space spanning the assimilation window.

Ensemble 4DVAR (ENS4DVAR)

Lei, Wang et al. 2011

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Temporal evolution of the error covariance within the assimilation window by ENS4DVAR

tt-3h t+3h

Temp.

Height

t-3h t t+3h

Upstream impact

Downstream impact

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ExperimentsTest period: winter (Jan. 2010); summer (3 weeks from Aug. 15 2010)

Model: Global Forecast System Model (GFS) T190 64 levels

Observations: all operational data (conventional+satellite)

Data assimilation methods: o GSI oHybrid:

3DVAR based GSI-EnKF hybrid (hybrid1way)ensemble 4DVAR (ens4dvar1way)

1010

RMSE of forecasts for winter

Significant improvement of 3DVAR based hybrid and ensemble 4DVAR over GSIEnsemble 4DVAR showed further improvement over 3DVAR based hybrid especially for wind

w.r.t. in-situ-obs.

Wang et al. 2011 Lei, Wang et al. 2011

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RMSE of forecasts for summer

similar to winter

w.r.t. in-situ-obs.

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Impact of AMSU radiancesw.r.t. in-situ-obs. winter

Forecast from hybrid was more accurate than GSI. Hybrid: Positive impact of AMSU at most levels. GSI: Negative impact of AMSU above ~200mb. Improvement due to assimilation of AMSU is less than that due to using the hybrid DA method.

Kutty, Wang et al. 2011

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Impact of AMSU radiancesw.r.t. ECMWF analyses winter

24h rmse for wind global 24h rmse for temp global

Forecast from hybrid was more accurate than GSI. Hybrid: Positive impact of AMSU for wind for all levels and temp for upper levels. GSI: Positive impact of AMSU for wind except at upper levels; negative/neutral impact of AMSU for temp for most levels. Hybrid makes better use of AMSU than GSI. Improvement due to assimilation of AMSU is less than that due to using the hybrid DA method.

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Impact of AMSU radiancesw.r.t. ECMWF analyses (winter, wind)

GSI hybrid

Pres

sure

leve

ls (m

b)

Latitude LatitudePr

essu

re le

vels

(mb)

m/s m/s

GSI: positive impact at most latitude except southern high latitude and high levels. Hybrid: Positive impact of AMSU at most levels and latitude. More positive impact at southern hemisphere.

Blue (red) means positive (negative) impact.

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Latitude

Impact of AMSU radiancesw.r.t. ECMWF analyses (winter, temp)

GSI hybrid

Pres

sure

leve

ls (m

b)

Pres

sure

leve

ls (m

b)

K KLatitude

GSI: positive impact except southern high latitude high levels. Hybrid: Positive impact except high latitude low levels.

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Summary and future work Tests for GFS showed performance of hybrid was better than GSI. Ensemble 4DVAR (no tangent linear and adjoint needed) was developed for GSI and showed better results than 3DVAR based hybrid. Hybrid better used AMSU than the GSI. Positive impact of hybrid was greater than that of assimilating AMSU. Need more tests/experiments: different periods/cases (e.g., TC)/various configurations. Further enhancement of the hybrid including the GSI-ECV and EnKF components.Further understand the difference among GSI, 3DVAR based Hybrid, ensemble 4DVAR, EnKF. Observation impact study with various other observations. Develop ensemble based (no tangent linear and adjoint needed) observation impact metric for the hybrid. 3DVAR based hybrid and ENS4DVAR for regional application (e.g., RR application, TC forecast with HWRF). Regular 4DVAR (with TLM and adjoint; perturbation method) based hybrid.

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References citedBuehner, 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, 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. Buehner, M, P. L. Houtekamer, C. Charette, H. L. Mitchell, B. He, 2010: Intercomparison of Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part II: One-Month Experiments with Real Observations. Mon. Wea. Rev., 138, 1550-1566. Campbell, W. F., C. H. Bishop, D. Hodyss, 2010: Vertical Covariance Localization for Satellite Radiances in Ensemble Kalman Filters. Mon. Wea. Rev., 138, 282-290.Hamill, T. and C. Snyder, 2000: A Hybrid Ensemble Kalman Filter–3D Variational Analysis Scheme. Mon. Wea. Rev., 128, 2905-2915. 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, 2007a: On the theoretical equivalence of differently proposed ensemble/3D-Var hybrid analysis schemes. Mon. Wea. Rev., 135, 222-227. Wang, X., T. M. Hamill, J. S. Whitaker and C. H. Bishop, 2007b: A comparison of hybrid ensemble transform Kalman filter-OI and ensemble square-root filter analysis schemes. Mon. Wea. Rev., 135, 1055-1076. Wang, X., D. Barker, C. Snyder, T. M. Hamill, 2008a: 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., D. Barker, C. Snyder, T. M. Hamill, 2008b: A hybrid ETKF-3DVar data assimilation scheme for the WRF model. Part II: real observation experiments. Mon. Wea. Rev., 136, 5132-5147. Wang, X., T. M. Hamill, J. S. Whitaker, C. H. Bishop, 2009: A comparison of the hybrid and EnSRF analysis schemes in the presence of model error due to unresolved scales. Mon. Wea. Rev., 137, 3219-3232.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. 2011: Application of the WRF hybrid ETKF-3DVAR data assimilation system for hurricane track forecasts. Wea. Forecasting, accepted.