Ensemble 4DVAR for the NCEP hybrid GSI EnKF data assimilation system and observation impact study with the hybrid system

Transcription

1 Ensemble 4DVAR for the NCEP hybrid GSI EnKF data assimilation system and observation impact study with the hybrid system Xuguang Wang School of Meteorology University of Oklahoma, Norman, OK OU: Ting Lei, Govindan Kutty, Yongzuo Li, Ming Xue, Brian Holland, Terra Thompson NOAA/NSSL: Lou Wicker NOAA/ESRL: Jeff Whitaker NOAA/NCEP/EMC: Daryl Kleist, Dave Parrish, Russ Treadon, John Derber University of Maryland, Weather & Chaos seminar Feb. 20,

2 Outline Part 1: Ensemble 4DVAR for the NCEP hybrid GSI EnKF data assimilation system Part 2: Observation impact study with the hybrid DA system Part 3: Improving high resolution TC prediction using hybrid DA Part 4: LETKF related work 2

3 Part 1: Ensemble 4DVAR for NCEP hybrid GSI EnKF data assimilation system 3

4 Hybrid GSI EnKF DA system member 1 forecast member 2 forecast member k forecast EnKF Ensemble covariance EnKF analysis 1 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 forecast member 2 forecast member k forecast control forecast GSI -ECV control analysis control forecast Wang et al data assimilation First guess forecast 4 4

5 NCEP pre implementation test of hybrid DA 5

6 Ensemble 4DVAR for GSI: motivation Observations (e.g., satellite) are spreading through the DA window. Current GSI EnKF hybrid is 3DVAR based temporal evolution of error covariance within DA window not considered. ENS4DVAR is a natural extension of the current 3D GSI EnKF hybrid. Temporal evolution of the error covariance within the assimilation window is realized through the use of ensemble perturbations (e.g., Qiu et al. 2007) Lei, Wang et al

7 Ensemble 4DVAR for GSI: method Extended control variable method in 3D GSI hybrid (Wang 2010, MWR): J x ' 1, α 1J1 2J e J o 1 ' T 1 ' 1 x1 B x1 2 2 K e α k x k ' ' x x 1 k α T Add time dimension in ENS4DVAR C 1 α 1 2 Extra increment associated with ensemble o ' ' T 1 o y Hx R y ' Hx ' Extra term associated with extended control variable B 3DVAR static covariance; R observation error covariance; K ensemble size; C correlation matrix for ensemble covariance localization; x kth ensemble perturbation; ' ' o' x 1 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. e k 7

8 One obs. example for TC 3h increment propagated by model integration ens4dvar ens3dvar t=0 t=0 t=0 * 3h 0 3h time 8

9 Another example Temp. t 3h t t+3h Height t 3h t t+3h Downstream impact Upstream impact 9

10 Why Hybrid? Best of both worlds Benefit from use of flow dependent ensemble covariance instead of static B VAR (3D, 4D) EnKF hybrid References (examples) x x Hamill and Snyder 2000; Lorenc 2003, Wang et al. 2007b,2008ab, 2009b; Zhang et al. 2009; Buehner et al. 2010ab; Wang 2011; Robust for small ensemble x Wang et al. 2007b, 2009b; Buehner et al. 2010b Better localization for integrated measure, e.g. satellite radiance; radar with attenuation Easiness to add various x x constraints Outer loops x x x Campbell et al More use of various existing x capability in VAR Summarized in Wang 2010, MWR x 10

11 Experiments Test period: Aug Sep Model: GFS T levels Observations: all operational data Data assimilation methods: o GSI (gsi) o 3D GSI EnKF (hybrid1way) o ensemble 4DVAR: 2 hourly frequency (ens4dvar1way) 1 hourly frequency (ens4dvar1way hrly) o excluding the balance constraint: hybrid1way nb ens4dvar1way nb 11

12 Hurricane track forecasts 2010 hurricanes ens3dvar hybrid better than GSI and further improvement by ens4dvar hybrid. Balance constraint in GSI hurt TC forecast for both ens3dvar and ens4dvar hybrid.12

13 Global forecasts verified against EC analyses Height Temperature ens3dvar hybrid better than GSI and further improvement by ens4dvar hybrid. Balance constraint in GSI help both ens3dvar and ens4dvar hybrid. 13

14 Global forecasts verified against conv. obs. 6h wind 6h temp Significant improvement of ens3dvar hybrid and ens4dvar hybrid over GSI ens4dvar showed further improvement over ens3dvar especially for wind 14

15 Global forecasts verified against conv. obs. 96h wind 96h temp Significant improvement of ens3dvar hybrid and ens4dvar hybrid over GSI ens4dvar showed further improvement over ens3dvar especially when nb balance constraint seems helpful at early lead time, but hurt at later lead time for hybrid 15

16 Summary Ensemble 4DVAR capability was developed for GSI and tested for GFS. Ensemble 4DVAR further improved upon the ENS3DVAR hybrid for TC track forecasts, global forecasts verified against EC and obs. Depending on the specific forecasts, the balance constraint in the GSI can benefit or hurt the forecasts. Improvements on balance constraint needed. 16

17 Part 2: Observation impact study with the hybrid DA system 17

18 Introduction Modern data assimilation systems assimilate millions of observations each day to produce initial conditions for numerical weather forecasts. What are the impacts of the obs. from different platforms? Are impacts dependent on DA methods and how? Are impacts dependent on how impacts are assessed and how? 18

19 Increments with static and flow dependent B 19

20 Increments by GSI and hybrid: AMSU 20

21 Introduction (cont d) Various methods have been used to assess the impacts of observations Observing System Experiments (OSE; e.g., Zapotocny et al., 2007, etc.) Adjoint method (e.g., Baker and Daley, 2000; Gelaro et al., 2008, etc.) Ensemble based method (e.g., Liu and Kalnay, 2008; Kalnay 2011; Kunii et al. 2012, etc.) 21

22 Experiment design Test period : Dec. 15 Jan Model: Global Forecast System Model (GFS) T levels Observations denied: AMSU, Rawinsonde Data assimilation methods: GSI Hybrid GSI EnKF (one way coupled) 6 experiments for OSE GSI assimilating all obs. (gsi) GSI denied rawinsonde (gsi noraob) GSI denied AMSU (gsi noamsu) Hybrid assimilating all obs. (hybrid) Hybrid denied rawinsonde (hybrid noraob) Hybrid denied AMSU (hybrid noamsu) Kutty, Wang et al

23 Experiment design (cont d) Ensemble based obs. impact estimate (Kalnay 2011) Goal evaluate the quality of the estimate for the hybrid system research to further improve the estimate compare with other obs. impact metric, e.g., OSE Initial experiments Estimate of rawinsonde temp. impact for temp. and wind forecasts. Verified w.r.t actual impact. Same for satellite data (e.g., AMSU) 23

24 RMSE of global forecasts w.r.t EC analysis 24h wind 24h temperature 24h spec. humidity 24

25 RMSE of global forecasts w.r.t obs. 24h wind 24h temperature 25

26 Zonally averaged impact (wind RMSE difference) 26

27 Zonally averaged impact (temp. RMSE difference) 27

28 Zonally averaged impact (humid. RMSE difference) 28

29 Relative impact (500mb Height) (a) gsi noamsu (b) gsi noraob (c) hybrid noamsu (d) hybrid noraob 29

30 Ensemble based obs. impact estimate for the hybrid system global 200hPa 250hPa 300hPa 500hPa 700hPa 850hPa 925hPa 1000hPa Rawinsonde temp. impact for 24h temp. fcst estimate actual global 200hPa 250hPa 300hPa 500hPa 700hPa 850hPa 925hPa 1000hPa Rawinsonde temp. impact for 24h wind. fcst estimate actual error reduction / gridpoint (K 2 ) error reduction /grid point (ms -1 ) 2 30

31 Summary OSE Forecasts by hybrid DA was better than GSI in both control and data denial experiments. In some verifications, the hybrid assimilating less data was even better than the GSI assimilating all obs. Magnitude and distribution of obs. impact depend on the obs. and the DA methods. The relative impact between rawinsonde and AMSU depends on DA methods and verifications. Ensemble based obs. impact estimate for the hybrid Initial results showed the estimate was promising. The quality of the estimate can be dependent on obs. and forecasts of interest, forecast lead time, etc. 31

32 Part 3: Improving high resolution TC prediction using hybrid DA 32

33 Radar hybrid DA for Ike 2008 IKE 2008 WRF: Δx=5km Observations: radial velocity from two WSR88D radars (KHGX, KLCH) Li, Wang, Xue 2012, MWR 33

34 Temperature increment 3DVARb Hybrid1 Hybrid.5 34

35 Wind and pot. temperature analyses No Radar DA 3DVARb Cold core Hybrid1 Hybrid.5 Warm core 35

36 Wind and Precipitation forecasts 36

37 Part 4: LETKF related work Effects of sequential or simultaneous assimilation and localization methods on the performance of ensemble Kalman filter Doppler Radar data assimilation using the LETKF 37

38 Motivation Popular EnKF schemes contain differences (1) Stochastic versus deterministic EnKF vs. LETKF, EnSRF, ETKF, etc. (2) Simultaneous vs. Sequential LETKF vs. EnSRF, EnKF (3) If and how localization is applied B vs. R localization Previous studies (e.g. Kepert 2009; Greybush et al. 2011; Janjic 2011) related to (2) & (3) did not reach consensus Rigorous study on whether the choice of (2) and (3) has an effect on EnKF accuracy o Optimally tuned o Study the effect of (2) and (3) in isolation and their interaction o Comparison in variety of contexts Holland and Wang, 2012, QJRMS

39 Experimental Design 2 layer dry global primitive equation model (Zou et al. 1993) Model error: T31 model truncation, T127 Truth run Observations = truth run + added error Comparison in various contexts Baseline experiments: 50 member, Surface π &Interface height obs. Other experiments: with digital filter initialization, adding more observation types, reducing observation number, increasing ensemble size, decreasing P b /R ratio.

40 Scheme Breakdown Scheme Serial/ simultaneous Localization Algorithm Bserial Serial B EnSRF Rserial Serial R EnSRF Bsimult Simult B EnSRF Rsimult Simult R EnSRF LETKF Simult R LETKF LETKF: Hunt et al EnSRF: Whitaker and Hamill 2002

41 Baseline experiments: Analysis Error

42 Baseline experiments: imbalance

43 Explore imbalance difference using non cycling experiments Surface π tendency increment difference (Bsimult Rsimult) Wind and height gradient increment difference (Bsimult Rsimult)

44 Conclusion Baseline experiment: Effects of sequential vs. simultaneous assimilation depend on whether B or R localization was being used (Bsimult worse than Bserial; Rsimult better than Rserial) Effects of B or R localization depend on simultaneous or serial assimilation was being used (Bserial ~ Rserial; Bsimult worse than Rsimult) Schemes that produced less accurate analyses tended to be least balanced. Sensitivity experiments: Difference among the schemes reduced when digital filter initialization was used, both wind and mass observations were assimilated, the number of observations was decreased, the ensemble size was increased, and the ratio of forecast error to observation error in the system was decreased. 44

45 Doppler Radar Data Assimilation Using LETKF Apply LETKF to storm scale radar data assimilation Study the effect of simultaneous/serial assimilation and localization methods for storm scale by comparing with serial EnSRF Study the scalability of parallel LETKF. Thompson, Wicker and Wang, 2012

46 Preliminary OSSE results after 1 hour of DA Truth LETKF EnSRF Vertical Velocity Reflectivity

47 Ongoing and future work Working with collaborators, further develop, test and research on ens4dvar and TL/ADJ 4DVAR hybrid for Global DA. Working with collaborators, further test and research the hybrid (ens3dvar, ens4dvar) for regional NWP. Conduct OSE for hybrid DA for other data and other forecasts of interest. Conduct OSE using ens4dvar. Research and improve the ensemble based obs. impact estimation for different data types and different forecasts for the hybrid DA system. Research on obs. impacts inferred by e.g., OSE, ensemble based method and adjoint method. Continue efforts on LETKF for storm scale radar assimilation. 47

48 References Campbell, W. F., C. H. Bishop, D. Hodyss, 2010: Vertical Covariance Localization for Satellite Radiances in Ensemble Kalman Filters. Mon. Wea. Rev., Lorenc, A. C. 2003: The potential of the ensemble Kalman filter for NWP a comparison with 4D VAR. Quart. J. Roy. Meteor. Soc., 129, Buehner, M., 2005: Ensemble derived stationary and flow dependent background error covariances: evaluation in a quasioperational NWP setting. Quart. J. Roy. Meteor. Soc., 131, Hamill, T. and C. Snyder, 2000: A Hybrid Ensemble Kalman Filter 3D Variational Analysis Scheme. Mon. Wea. Rev., 128, 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, 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 assimilation scheme for the WRF model. Part I: observing system simulation experiment. Mon. Wea. Rev., 136, 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, 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: Incorporating ensemble covariance in the Gridpoint Statistical Interpolation (GSI) variational minimization: a mathematical framework. Mon. Wea. Rev., 138, Wang, X. 2011: Application of the WRF hybrid ETKF 3DVAR data assimilation system for hurricane track forecasts. Wea. Forecasting, in press. Li, Y, X. Wang and M. Xue, 2011: Radar data assimilation using a hybrid ensemble variational analysis method for the prediction of hurricane IKE Mon. Wea. Rev., submitted. 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, 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, Holland, B. and X. Wang, 2011: Effects of sequential or simultaneous assimilation of observations and localization methods on the performance of the ensemble Kalman filter. Q. J. R. Meteo. Soc., submitted 48

49 Flow dependent covariance GSI (static covariance) Hybrid (ensemble covariance) K k k Wang et al

50 Track and intensity forecasts No radar No radar Li et al

51 Wind increment 3DVAR with untuned static covariance (3DVARa) 3DVAR with tuned static covariance (3DVARb) Hybrid with full ensemble covariance (hybrid1) Li et al Hybrid with half ensemble covariance and half static covariance (hybrid.5) 51