1. 1 A multi-scale three-dimensional variational data assimilation scheme Zhijin Li,, Yi Chao (JPL) James C. McWilliams (UCLA), Kayo Ide (UMD) The 8th International Workshop on Adjoint Model Applications in Dynamic Meteorology May 18-22, 2009, Tannersville, PA

2. 2 Outline 1.Motivations 2.A multi-scale three-dimensional variational data assimilation (MS-3DVAR) scheme 3.Applications and evaluations 4.Summary

3. 3 Data Assimilation and Forecast Cycle 3-day forecast Aug.1 00Z Time Aug.1 18Z Aug.1 12Z Aug.1 06Z Initial condition 6-hour forecast Aug.2 00Z xaxa xfxf 6-hour assimilation cycle Time scales comparable with those of the atmosphere

4. 4 Observations and Data assimilation  T/S profiles from gliders  Ship CTD profiles  Aircraft SSTs  AUV sections  HF radar velocities

5. 5 Comparison of Glider-Derived Currents (vertically integrated current) Black: SIO glider; Red: ROMS SALT(PSU) Performance of ROMS3DVAR: AOSN-II, August 2003 (Chao et al., 2009, DSR) TEMP(C) Glider temperature/salinity profiles

6. 6 Challenge: An Example with SCCOOS Model domain, the resolution of 1km

7. 7 Southern California Coastal Ocean Observing System (SCCOOS) SIO Glider Tracks Challenge: How to assimilate sparse vertical profiles along with high resolution observations for a very high resolution model Aug 2008, simulation without DA

8. 8 Data Assimilation Formulation  prescribed B  optimization algorithm Variational methods (3Dvar/4Dvar): Sequential methods (Kalman filter/smoother)  dynamically evolved B  analytical solution

9. 9 Error Covariance and correlations C : Correlation matrix RMSE diagonal matrix Correlations are the vehicle for spreading out information of observations Correlation scales are about 15-30km

10. 10 Forecast Error Covariance B: Single Observation Experiment One single observation of SSH (increment)

11. 11 Southern California Coastal Ocean Observing System (SCCOOS) SIO Glider Tracks Motivation: assimilating sparse vertical profiles along with high resolution observations for a very high resolution model

12. 12 Multi-Scale Data Assimilation: Concept Background Observation Prerequisites Multi-scale DA SCCOOS Glider Tracks (Boer, 1983, MWR)

13. 13 Multi-Scale Data Assimilation: Scheme Low Resolution (LR) High Resolution (HR) Sparse Obs High Resolution Obs SCCOOS Glider Tracks High resolution HF radar

14. 14 Work Flowchart of MS-3DVAR Satellite SST/SSHHF Radar LR-3DVAR Forecast Smoothed Start HR-3DVAR Increment End Glider/Argo/MooringSmoothed

15. 15 Glider Observations vs Analyses Aug 2008

16. 16 CALCOFI Observations Aug 14-30, 2008 (not assimilated)

17. 17 Aug, 2008 Monthly Means

18. 18 Analysis vs HF Radar Observations Taylor diagram (Taylor, 2001, JGR)

19. 19 Surface Currents Forecasts vs Analyses

20. 20 Summary  A multi-scale 3DVAR (MS-3DVAR) scheme has been formulated and developed.  It has been implemented in support of SCCOOS and AOOS-PWS.  The scheme has demonstrated the capability of assimilating sparse and high resolutions observations simultaneously, effectively and reliably.

21. 21 3 nested levels: L0 / L1 / L2. Resolution : 10km / 3.6km / 1.2 km (L2 : Prince William Sound) Alaska Ocean Observing System -Prince William Sound: AOOS-PWS

22. 22 From USGS Oil Spill: 1989 Exxon Tanker Wreck Prince William Sound, Alaska Today March 24, 1989

23. 23 Decomposition of Large and Small Scales and Estimation of Error Covariance  Generate perturbations: difference between 24h and 48h forecasts, valid at the same time.  Decompose perturbations Large scales: smoothed fields, with weight of where L=25km, which is the decorrelation length scale from Russ’s estimation Small scales: the residuals

24. 24 Observational Errors: Representativeness Errors Large scale observations: T/S vertical profiles from SIO, mooring and Argo Observational errors at the depth of z: Tentative values: briefly and empirically estimated from the RMS profile of the small scale components For temperature For salinity CALCOFI Section

25. 25 Future Coastal Observing System (National Research Council, 2003)  Buoy and glider profiles are sparse, with distances between profiles larger than decorrelation scales  Radar and satellite measurements may have very high resolutions, as high as the model resolution

26. 26 Glider Temperature and Salinity Profiles

27. 27 Surface Tidal Current Comparison (M2) Corr. RMS Mean Sept. 0.43 3.6 6.6 Oct. 0.44 3.8 6.6 Nov. 0.51 3.7 6.3 Length of Major Axis (cm/s)

28. 28 A There-Dimensional Variational Data Assimilation (3DVAR) Real-time capability Implementation with sophisticated and high resolution model configurations Flexibility to assimilate various observation simultaneously Development for more advanced scheme ( Li et al., 2006, MWR; Li et al., 2008, JGR, Li et al., 2008, JAOT )