Ensemble 4DVAR and observa3on impact study with the GSIbased hybrid ensemble varia3onal data assimila3on system. for the GFS

Transcription

1 Ensemble 4DVAR and observa3on impact study with the GSIbased hybrid ensemble varia3onal data assimila3on system for the GFS Xuguang Wang University of Oklahoma, Norman, OK Ting Lei, Govindan KuGy (OU) Jeff Whitaker (NOAA/ESRL) Dave Parrish, Daryl Kleist, John Derber, Russ Treadon (NOAA/NCEP/EMC) July 28, st GSI workshop, Boulder, CO 1

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

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

4 Why Hybrid? Best of both worlds VAR (3D, 4D) EnKF hybrid References Benefit from use of flow dependent ensemble covariance instead of sta3c 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 BeGer covariance localiza3on for integrated measure (e.g. satellite radiance; radar with agenua3on) Easiness to add various constraints in VAR Treatment of nonlinearity with outer loops in VAR Use of various exis3ng capability in VAR (e.g. varia3onal QC) x Campbell et al x x x x x x 4

5 How to incorporate ensemble in GSI? Ensemble covariance is included in the VAR cost func3on through augmenta3on of control variables (Lorenc 2003; Buehner 2005; Wang et al. 2007a, 2008a, Wang 2010). Hybrid formula (Wang 2010 formula for GSI with B precondi3oning): Extra increment associated with ensemble Extra term associated with extended control variable 5

6 Flow dependent ensemble covariance GSI (sta3c 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 model (Liu et al. 2009). 4D analyses are obtained through varia3onal minimiza3on within the temporally evolved ensemble space spanning the assimila3on window. Lei, Wang et al

8 Temporal evolu3on of the error covariance within the assimila3on window by ENS4DVAR Temp. t 3h t t+3h Height t 3h t t+3h Downstream impact Upstream impact 8

9 Experiments Test period: winter (Jan. 2010); summer (3 weeks from Aug ) Model: Global Forecast System Model (GFS) T levels ObservaNons: all opera3onal data (conven3onal+satellite) Data assimilanon methods: o GSI o Hybrid: 3DVAR based GSI EnKF hybrid (hybrid1way) ensemble 4DVAR (ens4dvar1way) 9

10 RMSE of s 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 Wang et al Lei, Wang et al

11 RMSE of s for summer w.r.t. in situ obs. similar to winter 11

12 Impact of AMSU radiances w.r.t. in situ obs. winter Forecast from hybrid was more accurate than GSI. Hybrid: Posi3ve impact of AMSU at most levels. GSI: Nega3ve impact of AMSU above ~200mb. Improvement due to assimila3on of AMSU is less than that due to using the hybrid DA method. KuGy, Wang et al

13 Impact of AMSU radiances w.r.t. ECMWF analyses winter 24h rmse for wind global 24h rmse for temp global Forecast from hybrid was more accurate than GSI. Hybrid: Posi3ve impact of AMSU for wind for all levels and temp for upper levels. GSI: Posi3ve impact of AMSU for wind except at upper levels; nega3ve/neutral impact of AMSU for temp for most levels. Hybrid makes beger use of AMSU than GSI. Improvement due to assimila3on of AMSU is less than that due to using the hybrid DA method. 13

14 GSI Impact of AMSU radiances w.r.t. ECMWF analyses (winter, wind) hybrid Pressure levels (mb) Pressure levels (mb) Blue (red) means posi3ve (nega3ve) impact. La3tude m/s La3tude GSI: posi3ve impact at most la3tude except southern high la3tude and high levels. Hybrid: Posi3ve impact of AMSU at most levels and la3tude. More posi3ve impact at southern hemisphere. m/s 14

15 GSI Impact of AMSU radiances w.r.t. ECMWF analyses (winter, temp) hybrid Pressure levels (mb) Pressure levels (mb) La3tude K La3tude K GSI: posi3ve impact except southern high la3tude high levels. Hybrid: Posi3ve impact except high la3tude low levels. 15

16 Summary and future work Tests for GFS showed performance of hybrid was beger than GSI. Ensemble 4DVAR (no tangent linear and adjoint needed) was developed for GSI and showed beger results than 3DVAR based hybrid. Hybrid beger used AMSU than the GSI. Posi3ve impact of hybrid was greater than that of assimila3ng AMSU. Need more tests/experiments: different periods/cases (e.g., TC)/various configura3ons. Further enhancement of the hybrid including the GSI ECV and EnKF components. Further understand the difference among GSI, 3DVAR based Hybrid, ensemble 4DVAR, EnKF. Observa3on impact study with various other observa3ons. Develop ensemble based (no tangent linear and adjoint needed) observa3on impact metric for the hybrid. 3DVAR based hybrid and ENS4DVAR for regional applica3on (e.g., RR applica3on, TC with HWRF). Regular 4DVAR (with TLM and adjoint; perturba3on method) based hybrid. 16

17 References cited Buehner, M., 2005: Ensemble derived sta3onary and flow dependent background error covariances: evalua3on in a quasi opera3onal NWP seqng. Quart. J. Roy. Meteor. Soc., 131, Buehner, M, P. L. Houtekamer, C. ChareGe, H. L. Mitchell, B. He, 2010: Intercomparison of Varia3onal Data Assimila3on and the Ensemble Kalman Filter for Global Determinis3c NWP. Part I: Descrip3on and Single Observa3on Experiments. Mon. Wea. Rev., 138, Buehner, M, P. L. Houtekamer, C. ChareGe, H. L. Mitchell, B. He, 2010: Intercomparison of Varia3onal Data Assimila3on and the Ensemble Kalman Filter for Global Determinis3c NWP. Part II: One Month Experiments with Real Observa3ons. Mon. Wea. Rev., 138, Campbell, W. F., C. H. Bishop, D. Hodyss, 2010: Ver3cal Covariance Localiza3on for Satellite Radiances in Ensemble Kalman Filters. Mon. Wea. Rev., 138, Hamill, T. and C. Snyder, 2000: A Hybrid Ensemble Kalman Filter 3D Varia3onal Analysis Scheme. Mon. Wea. Rev., 128, Lorenc, A. C. 2003: The poten3al of the ensemble Kalman filter for NWP a comparison with 4D VAR. Quart. J. Roy. Meteor. Soc., 129, Wang, X., C. Snyder, and T. M. Hamill, 2007a: On the theore3cal equivalence of differently proposed ensemble/ 3D Var hybrid analysis schemes. Mon. Wea. Rev., 135, 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, Wang, X., D. Barker, C. Snyder, T. M. Hamill, 2008a: A hybrid ETKF 3DVar data assimila3on scheme for the WRF model. Part I: observing system simula3on experiment. Mon. Wea. Rev., 136, Wang, X., D. Barker, C. Snyder, T. M. Hamill, 2008b: A hybrid ETKF 3DVar data assimila3on scheme for the WRF model. Part II: real observa3on experiments. Mon. Wea. Rev., 136, 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, Wang, X., 2010: Incorpora3ng ensemble covariance in the Gridpoint Sta3s3cal Interpola3on (GSI) varia3onal minimiza3on: a mathema3cal framework. Mon. Wea. Rev., 138, Wang, X. 2011: Applica3on of the WRF hybrid ETKF 3DVAR data assimila3on system for hurricane track s. Wea. Forecas5ng, accepted. 17