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Xuguang Wang University of Oklahoma, Norman, OK xuguang.wang@ou.edu Ting Lei, Govindan Kutty (OU)

Ensemble 4DVAR and observation impact study with the GSI-based hybrid ensemble- variational data assimilation system for the GFS. Xuguang Wang University of Oklahoma, Norman, OK xuguang.wang@ou.edu Ting Lei, Govindan Kutty (OU) Jeff Whitaker (NOAA/ESRL)

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Xuguang Wang University of Oklahoma, Norman, OK xuguang.wang@ou.edu Ting Lei, Govindan Kutty (OU)

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

  2. EnKF analysis 1 EnKF analysis 2 EnKF analysis k control analysis control forecast Hybrid GSI-EnKF DA system: 1 way coupling member 1 forecast member 1 forecast EnKF member 2 forecast member 2 forecast …… …… …… Ensemble covariance member k forecast member k forecast control forecast GSI-ECV First guess forecast data assimilation Wang et al. 2011 2

  3. EnKF analysis k EnKF analysis 2 EnKF analysis 1 control analysis control forecast Hybrid GSI-EnKF DA system: 2 way coupling Re-center EnKF analysis ensemble to control analysis member 1 forecast member 1 analysis member 1 forecast EnKF member 2 forecast member 2 analysis member 2 forecast …… Ensemble covariance …… …… …… member k forecast member k analysis member k forecast control forecast GSI-ECV First guess forecast data assimilation 3

  4. Why Hybrid?“Best of both worlds”

  5. How to incorporate ensemble in GSI? • 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

  6. Flow-dependent ensemble covariance GSI (static covariance) Hybrid (ensemble covariance) K k k 6

  7. Ensemble 4DVAR (ENS4DVAR) • 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. Lei, Wang et al. 2011

  8. Temporal evolution of the error covariance within the assimilation window by ENS4DVAR Temp. t t+3h t-3h Height t-3h t t+3h Downstream impact Upstream impact

  9. Experiments • Test 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: • GSI • Hybrid: • 3DVAR based GSI-EnKF hybrid (hybrid1way) • ensemble 4DVAR (ens4dvar1way)

  10. RMSE of forecasts for winter w.r.t. in-situ-obs. • Significant improvement of 3DVAR based hybrid and ensemble 4DVAR over GSI • Ensemble 4DVAR showed further improvement over 3DVAR based hybrid especially for wind 10 Wang et al. 2011 Lei, Wang et al. 2011

  11. RMSE of forecasts for summer w.r.t. in-situ-obs. • similar to winter

  12. Impact of AMSU radiances w.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

  13. Impact of AMSU radiances w.r.t. ECMWF analyses winter 24h rmse for temp global 24h rmse for wind 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.

  14. Impact of AMSU radiances w.r.t. ECMWF analyses (winter, wind) GSI hybrid Pressure levels (mb) Pressure levels (mb) Blue (red) means positive (negative) impact. m/s m/s Latitude Latitude • 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.

  15. Impact of AMSU radiances w.r.t. ECMWF analyses (winter, temp) GSI hybrid Pressure levels (mb) Pressure levels (mb) K K Latitude Latitude • GSI: positive impact except southern high latitude high levels. • Hybrid: Positive impact except high latitude low levels.

  16. 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.,RRapplication, TC forecast with HWRF). • Regular 4DVAR (with TLM and adjoint; perturbation method) based hybrid.

  17. References cited 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, 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.

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