Ensemble-based Atmospheric Data Assimilation: A hybrid ensemble- variational method

1. Ensemble-based Atmospheric Data Assimilation:A hybrid ensemble-variational method • Xuguang Wang • School of Meteorology and Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, OK, USA • Collaborators: Dale Barker, Chris Snyder, Tom Hamill, Yongzuo Li, Ming Xue International Symposium on Radar and Modeling Studies of the Atmosphere, Kyoto, Japan, Nov. 10-13, 2009

2. observations model forecast data assimilation analysis What’s data assimilation (DA)? • DA is a statistical analysis process that combines observations with short-range model forecasts.

3. What’s Hybrid? xb yo xb xa VAR + e.g. ETKF time xb VAR xa xb xa xb xb • HYBRID • Data assimilation part adopts variational framework. • Like EnKF, maintain multiple forecasts and analyses cycles. • Like EnKF, ensemble forecasts involve in the estimate of background error covariance. EnKF Xb: forecast Xa: analysis yo: observation VAR: variational (3DVAR, 4DVAR) method EnKF: ensemble Kalman filter ETKF: ensemble transform Kalman filter

4. Why Hybrid? “Best of both worlds” • Compared to VAR, Hybrid conveniently provides flow-dependent estimate of the background error covariance. Hamill et al. 2006 Wang 2009

5. Why Hybrid? “Best of both worlds” • Study (Caya et al. 2005) shows that for radar DA, 4DVAR spins up faster than EnKF, but EnKF is better in later stage of the DA cycles. Hybrid can take advantage of both • Compared to EnKF, hybrid adopts model space rather than observation space covariance localization, more appropriate for satellite radiance, GPS refractivity assimilation (campbell et al. 2009; Wang 2009b) • VAR framework provides maximum likelihood solution and thus allows non-Gaussian errors (Zupanski 2005). VAR framework can also easily add in dynamic constraint. • Likely to be cost effective with many obs., since minimization does not scale linearly with number of obs. (Wang et al. 2007b). • Good choice for already having an established VAR and ensemble forecast system (Wang et al. 2007ab, 2009) • Minor changes to the existing operational variational framework • Take advantages of existing capability of VAR, e.g., variational data quality control • Static covariance model in advanced VAR can provide sophisticated method to reduce sampling errors in ensemble covariance.

6. Hybrid ETKF-3DVAR for WRF Wang et al. 2008ab, Monthly Weather Review (MWR) • Ensemble covariance is incorporated into WRF VAR using the extended control variable method • The ensemble was generated by the ensemble transform Kalman filter (ETKF, Wang and Bishop 2003; Wang et al. 2004, 2007b)

7. Experiments using the WRF ETKF-3DVAR system • Month-long experiment over North America • Hurricane IKE 2008 5-day track forecast • First radar DA trial

8. Month-long NA Experiment Wang et al. 2008ab, MWR WRF domain, observation locations and verification region • WRF domain: North America; coarse resolution (Δx=200km; 28 levels) • Observation: radiosonde wind and temperature • Test period: Jan 2003 • Ensemble size: 50 members • Verifications: Compare forecasts initialized by the hybrid and 3DVAR analyses.

9. flow-dependent increments by the hybrid 850mb T increment (k) • The hybrid system can provide flow-dependent increments.

10. 12-h wind forecast Why big improvement here? • Forecast initialized from analysis by hybrid DA improved over 3DVAR.

11. flow-dependent cross variable update of moisture field by the hybrid • Although no moisture observations were assimilated, hybrid through cross-variable covariance estimated by the ensemble can update moisture field whereas 3DVAR can not. • In this case, flow-dependent adjustments produced by the hybrid dried the lower troposphere along the front.

12. Hurricane IKE 2008 • WRF Model: Δx=30km; 35 levels • Observations: all conventional in-situ data plus cloud wind and QuikScat wind, no bugus data • Ensemble size: 32 members • DA and forecast: 2-day DA started at Sep. 07 00Z and then run 5-day forecast started at Sep. 9 00Z • Verification: compare forecast initialized by WRF Hybrid with WRF 3DVAR and GFS (US NWS operational analysis which uses bogus data) 14 Tropical storm cat1 cat2 13 cat1 cat3 cat4 12 11 10 9 8 7 5-day forecast 2 day 3hrly DA cycle

13. Track forecast • Track forecast initialized by analysis generated by the hybrid method is much more accurate.

14. 500mb Height analysis at Sep 9 00Z WRF HYBRID • Stronger vortex by the hybrid analysis WRF 3DVAR • Differences in the west periphery of the ridge

15. SLP Increment differences on Sep 8 00z WRF HYBRID increment Ensemble spread WRF 3DVAR increment • Ensemble spread suggested major forecast uncertainty around IKE (“flow- dependent”) • Increment by the hybrid was mostly at TC • 3DVAR background error covariance did not recognize TC well.

16. First Radar DA trial with WRF hybrid Observations: WSR88D radial wind Ensemble size: 40 members WRF model: ∆x=4km

17. Wind increment differences: hybrid vs. 3DVAR • 3DVAR increments produced a double vortex, which is irrelevant to the background weather • Hybrid increments mostly concentrated at the region of active weather (flow-dependent).

18. Conclusion and discussion • WRF Hybrid ETKF-3DVAR has been developed and applied for various applications and was demonstrated to improve the analyses and subsequent forecasts. • Experiments have shown that flow-dependent covariance provided by the ensemble contributes to the better performance by the hybrid. • Such flow-dependency is expected to have the biggest impact on data sparse region (TC over open water), less-observed state variables (e.g., moisture), and retrieval of indirectly observed state variables (e.g., radar reflectivity) • More hurricane cases are being tried (e.g., Rita 2005) and the system is being applied for assimilating ground-based and airborn radar data for IKE. • Experiments using ETKF-4DVAR is on the way!

19. Minimum SLP forecast of IKE 2008