1. Mesoscale Assimilation of Rain-Affected Observations Clark Amerault National Research Council Postdoctoral Associate - Naval Research Laboratory, Monterey, CA Xiaolei Zou – Florida State University James Doyle – Naval Research Laboratory

2. Outline Adjoint Model Description Sensitivity Results – Predictability over Topography Idealized Data Assimilation Experiments – Moist Physics Hurricane Initialization – Assimilate Synthetic Observations Microwave Radiances in Precipitation – Ice Channels

3. Components of the COAMPS Adjoint Model Parameterizations in M and M T : Boundary layer TKE (Mellor and Yamada 1982) Surface Fluxes (Louis 1979) Explicit Moist Physics (Rutledege and Hobbs 1983) Cumulus (Kuo 1965) Element of the state vector x: π Exner pressure θ potential temperature u zonal wind speed v meridional wind speed w vertical velocity q v water vapor e TKE q c cloud water q i cloud ice q r rain q s snow q g graupel Hand and Automatic Coding (Giering and Kaminski 1998) RAMDAS Adjoint (Zupanski et al. 2005) also includes hydrometeors

4. Variational Assimilation Experiments Generic strong constraint 4D-Var cost function Gradient needed to minimize cost function Ingredients: M M T (included) R B (crude approximations, diagonal) H H T (only a few) A quasi-Newton minimization algorithm is used for data assimilation experiments No model error assumed (not weak constraint) Nonlinear model is run for each iteration of the minimization (not incremental) COAMPS Nonlinear Model COAMPS Adjoint Model

5. Twin Experiment 2D 200 horizontal points (4 km grid spacing) 45 vertical level Initialized from an unstable sounding Small bubble of elevated θ (3 K) and q v (3 g/kg) values in lower center of domain Model is run for 1 h to create initial state 10 min window, observations are 30 min forward q v (shaded, g/kg) and w (contour, m/s) at 1 h x (km) σ z (m) Sounding State Initial State (1 h) Window (10 min) Observations (30 min later) COAMPS Nonlinear Model COAMPS Adjoint Model

6. Twin Experiment t=10 min x (km) σ z (m) t=60 min Observations Optimal Control qsqs qrqr Forecast after assimilation matches well with observations

7. Twin Experiment Correlation Coefficients Between Observations and Forecasts TWE1 – All Variables Assimilated TWE2 – Only Conventional Data Assimilated / No Hydrometeor Adjustment TWE3 – Only Conventional Data Assimlated / Hydrometeors Adjust CTL – No Assimilation Assimilating only conventional variables will improve hydrometeor forecasts

8. Assimilate infrared radiances to improve cloud hydrometeors (Vukicevic et al. 2004) using RAMDAS ECMWF utilizes microwave radiances in a 1D+4D- Var process (Moreau et al. 2003, 2004) VDRAS (Sun and Crook 1997) improves forecasts of thunderstorms in reflectivity space Ensemble Kalman Filter with ice microphysics and Doppler radar data (Tong and Xue 2005) Assimilating Microwave Radiances Most work has focused on liquid hydrometeors

9. Assimilating Microwave Radiances A Radiative Transfer Model (Liu 1998) and its adjoint (Amerault and Zou 2003) are linked to the COAMPS Adjoint Model Observations are SSM/I Microwave Radiances (19V, 22V, 37V, 85V) from Hurricane Bonnie (1200 UTC August 23 1998) 1 h window – Assimilation every 6 min – 30 km horizontal grid spacing Rain flag is used to modify the background hydrometeor field MVOI Analysis 0000 UTC 8/23/1998 Initial State 1200 UTC Window (60 min)

10. q s perturbation – J at 0 h Gradients q s perturbation – J at 1 h q v perturbation – J at 0 h q v perturbation – J at 1 h J is difference in 85V T b s Perturbations (shading, g/kg) at ~ 6000 m Background q s (left: contours 0.1 g/kg) q v (right: contours 1.0 g/kg) 85V SSM/I Obs.

11. Assimilating Microwave Radiances SSM/I 85V T b s 12 UTC August 23 1998 After Assimilation (0 h) RMSE = 5.1 K Control (0 h) RMSE = 11.4 K Initial Time Error reduced by > 50% Similar for other channels

12. Assimilating Microwave Radiances Model Fields ~ 6000 m q s OPT (g/kg) q v OPT (g/kg) q s CTL (g/kg) q v CTL (g/kg) Hydrometeors adjusted Complex structures in other model variables

13. Assimilating Microwave Radiances SSM/I 85V T b s 12 UTC August 23 1998 After Assimilation (12 h) RMSE = 9.7 K Control (12 h) RMSE = 15.6 K 12 h Forecast Error reduced by ~ 33% at 12 h

14. Summary COAMPS adjoint model provides gradients with respect to hydrometeors and conventional variables on small scales Idealized experiments demonstrate the ability to assimilate rain-affected observations A complete data assimilation system could benefit from adjoint models with complex parameterizations

15. Backup Slides

16. Gradients θ perturbation (K) – J at 1 h Horizontal wind (vectors) Vertical Velocity (shading, m/s) J at 1 h Gradients are physically consistent What do they mean?