1. Jidong Gao and David Stensrud Some OSSEs on Assimilation of Radar Data with a Hybrid 3DVAR/EnKF Method

2. OUTLINE OUTLINE  Why hybrid 3(4)DVAR/EnKF ?  Brief description of the method.  OSSEs with a supercell storm.  Conclusion. Goal: To test if the hybrid 3DVAR/EnKF scheme is good for convective scale DA and WoF strategy

3. Why hybrid 3(4)DVAR/EnKF ? EnKF can use statistical info. more effectively by,  providing flow-dependent background error covariances.  model errors can be handled by multi-physics ens.  but may contain sampling error due to small ens. size. 3(4)DVAR can use model’s dynamic info. more effectively by,  adding model equations as strong & weak constraints.  sampling error in static bkgrd. error statistics can be small.  but does not carry bkgrd. error coaraince B through cycles so B is not explicitly flow-independent. Hybrid 3(4)DVAR/EnKF may combine dynamic and statistical information in an optimal way.

4. Hybrid 3DVAR/EnKF Formulation (Lorenc 2003, QJ; Buehner 2005, QJ; Wang et al.2007, MWR) The cost function in preconditioned incremental form: v  is 3DVAR control variables;  is extended control variables When β 1 =1, β 2 =0, a pure 3(4)DVAR method; When β 1 =0, β 2 =1, a method equivalent to an EnKF method; In between, a hybrid method with different combinations. β 1 is weighting for static B; β 2 is weighting for ens. P e

5. Illustration of Hybrid 3(4)DVAR/EnKF mem 2 forecast mem 1 forecast mem N forecast mem 1 analysis mem 2 analysis mem N analysis Control forecast Why extra control forecast ? Gao and Xue, Hybrid EnKF, dual-resolution (2008, MWR) EnKF analysis update only 3DEnVAR analysis inflation, or relaxing to prior

6. OSSEs with a Simulated Supercell Storm A truth simulation is created using ARPS with the Del City supercell sounding. The model domain: 57 x 57 x 16 km 3. Horizontal:  x = 1 km, vertical:  z = 500 m. Both Vr and Z are assimilated at 5 min intervals, similar to Gao and Stensrud (2012, JAS).

7. List of OSSEs Exp. NoDescription 1Single-observation experiment 2OSSEs as a function of ens. size and coeff. for ens. covariance β 2. 3OSSEs as a function of number of alpha control variables

8. 1.Single observation experiment put Vr = 34 m/s within the storm with N=50 ens. members β 2 =1, full ens. covariance

9. Increments for α in response to the single ob. Same pattern but with different values for every member -0.321 -0.628 0.2130.610 allows each ensemble member to give the different degree of contribution to the analysis.

10. Derived analysis Increments for some model variables Different flow- dependent structure for every variable.

11. 2. OSSE Experiments A function of ens. size N = 5, 10, 50, 100 & β 2 =0.0, 0.2, 0.5, 0.8, 1.0

13. The rms errors for the analysis and forecast cycles red, green, blue, purple and baby-blue lines are corresponding to weighting value of ensemble covariance with β 2 = 0.0, 0.2, 0.5, 0.8, and 1.0 respectively. N=5 N=50 N=10 N=100

14. -8.37-10.65 -9.31-8.95 -8.68 -5.89

15. V (vectors), θ (contours), and simulated reflectivity Z (shaded contours) at surface for: (a)β 2 =0.2; (b)β 2 =0.5; (c) β 2 =0.8; (d)β 2 =1.0. All experiments with 100 ensemble members. All exp. are pretty close to the truth simulations! -8.70 -8.55 -8.38 -7.17 Truth simulation: -8.37

16. 3. OSSE Experiments for the size of extra control variables A function of ensemble size, dimensions of coordinates, number of analysis variables. 1.Control Exp: a function of ensemble size and 3D of coordinates. 2.2D Exp: a function of ensemble size and horizontal 2D of coordinates. 3.Big size: a function of ensemble size and 3D and also number of analysis variables.

18. The rms errors for the analysis and forecast cycles In each panel, red, green and blue lines are corresponding to CtrCV, BigCV; and 2dCV exp. respectively.

19. Summary The hybrid 3DVAR/EnKF allows each ens. member to give the different degree of contribution to the analysis through ens. derived covariance. Even with a very small ens. size, the hybrid method performs better than pure 3DVAR. More weighting should be given to ens. derived covariance. The best results are obtained when the number of the augmented control vectors is a function of the ensemble size and 3 dimensions of coordinates. Future work Test the hybrid scheme with a small ensemble size, and dual- resolution strategy (Gao and Xue 2008, MWR) for the purpose of greatly reducing the computational cost for WoF project.