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Chengsi Liu, Ming Xue, and Rong Kong Center for Analysis and Prediction of Storms

Implementation and Testing of 3DEnVAR and 4DEnVAR Algorithms within the ARPS Data Assimilation Framework. Chengsi Liu, Ming Xue, and Rong Kong Center for Analysis and Prediction of Storms University of Oklahoma. Outline. ARPS 4DEnVar framework design OSSE for a storm case Only Vr

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Chengsi Liu, Ming Xue, and Rong Kong Center for Analysis and Prediction of Storms

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  1. Implementation and Testing of 3DEnVAR and 4DEnVAR Algorithms within the ARPS Data Assimilation Framework Chengsi Liu, Ming Xue, and Rong Kong Center for Analysis and Prediction of Storms University of Oklahoma

  2. Outline • ARPS 4DEnVar framework design • OSSE for a storm case • Only Vr • Vr + reflectivity • Vr + reflectivity + mass continuity constraint • Conclusions • On-going work

  3. Hybrid En-4DVar (Lorenc 2003, Clayton et al 2012) Ensemble covariance part Static B part Localization matrix Alpha control variable Analysis increment and cost function innovation

  4. 4DEnVar-NPC (Non-Propagation of alpha Control variable) Two approximations (1) Neglecting temporal propagation of alpha control variable by TLM AJM avoided !! (2) Use nonlinear model ensemble forecasts to replace the temporal propagation of perturbations by the TLM TLM avoided !!

  5. The hybrid 4DEnVAR DA system based on the ARPS variational DA framework • 4DEnVar-NPC is adopted as ARPS hybrid variational algorithm because: • Adjoint and tangent linear model are not good approximations in convective scale DA. • High resolution observations, like Radar, are main observation source for convective DA. • The alternative observation-space-perturbation-based 4DEnVar algorithm(Liu et al 2008, 2009) is computationally more expensive.

  6. The ARPS 4DEnVar characteristics • 3D-recursive filter is used for ARPS-4DEnVar localization. • The capabilities for convective-scale radar DA ( Vr and reflectivity) • Physical constraint terms (e.g. mass continuity constraint) can be considered in the cost function.

  7. Radar data operators

  8. EnKF-En4DVar Hybrid Obs Obs Obs Obs Obs Obs Obs EnKF En4DVar Obs Obs 4D Assimilation Window – 1 cycle t1 t0

  9. OSSE for a storm case • Tested with simulated data from a classic supercell storm of 20 May 1977 near Del City, Oklahoma • Domain : 35 x 35 x 35 grids. 2km horizontal resolution • 70-min length of simulation, 5-min cycle intervene

  10. Experiment Design • ARPS 3DVar and ARPS En3DVar with full ensemble covariance • Only Vr • Vr + Z • Vr + Z + mass continuity constraint • Vr + Z + mass continuity constraint and model error

  11. True reflectivity and wind at 850Hpa

  12. Reflectivity 3DVar Vr+Z 3DVar Vr Truth En3DVar Vr+Z En3DVar Vr

  13. Reflectivity 3DVar Vr+Z 3DVar Vr Truth En3DVar Vr En3DVar Vr+Z

  14. Vertical Velocity 3DVar Vr+Z 3DVar Vr Truth En3DVar Vr+Z En3DVar Vr

  15. Pot. Temp. Pert 3DVar Vr 3DVar Vr+Z Truth En3DVar Vr+Z En3DVar Vr

  16. RMSE for 3DVar-Vr, 3DVar-Vr+Z, En3dVar-Vr, En3DVar-Vr+Z U V 3DVar-Vr 3DVar-Vr+Z En3dVar-Vr En3DVar-Vr+Z PT W

  17. RMSE for 3DVar-Vr, 3DVar-Vr+Z, En3dVar-Vr, En3DVar-Vr+Z Qh Qv Qr 3DVar-Vr 3DVar-Vr+Z En3dVar-Vr En3DVar-Vr+Z Qs Qc Qi

  18. Mass Continuity Constraint Test Exp 1 : 3DVar Vr + Z Exp 2 : 3DVar Vr + Z + Constraint Exp 3 : En3DVar Vr + Z Exp 4 : En3DVar Vr + Z + Constraint

  19. w and T 3DVar-CS 3DVar Truth En3DVar-CS En3DVar

  20. RMSE for 3DVar-CS, 3DVar, En3DVar-CS, En3DVar V U W PT

  21. RMSE for 3DVar-CS, 3DVar, En3DVar-CS, En3DVar Qr Qv Qh Qs Qi Qc

  22. Divergence Constraint term testwith model error • Model error is introducing by using a different microphysical scheme in DA • Truth simulation: Ice microphysics (LINICE) • DA: WRF WSM6 scheme (WSM6WR) • Smaller and larger weights for constraint term are tested (CSSW, CSLW) • Both Vr and Z data

  23. Vertical Velocity and T En3DVar Truth En3DVar CSLW En3DVar CSSW

  24. RMSE forEn3DVar, En3DVar-CSSW, En3DVar-CSLW U V W

  25. Summary 3DEnVar/4DEnVar algorithms are being implemented within the ARPS variational DA framework, coupled with the ARPS EnKF system; The systems can assimilate both radar Vr and Z data; Cycled DA OSSEs were performed to compare performances of 3DVar and En3DVar, assimilating Vr and both Vr and Z; Much better state analyses were obtained using En3DVar assimilating both Vr and Z data; Adding Z in 3DVAR improved very little (hydrometero classification of Gao and Stensrud 2012 should help – not shown); Mass continuity constraint hurts En3DVar analyses, and improves w analysis in 3DVar with a perfect model; Analysis errors are much larger in the presence of mirophysics-related model error – adding mass continuity improves results slightly. 3DEnVar and EnKF results similar for single time analysis; cycled results to be compared (using deterministic background forecasts in EnKF)

  26. On-going Research • ARPS 4DEnVar is being tested with OSSEs; • Time localization is being considered on 4DEnVar; • The 4DEnVar results will be compared with 3DEnVar and 4DEnSRF; • Potential benefits of EnVar for assimilating attenuated X-band reflectivity will be evaluated. • Will include other data sources and test with real cases. • The entire system will directly support WRF model also. The EnKF system already does.

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