1. LOCAL ENSEMBLE KALMAN FILTER (LETKF) ANALYSIS OF LOOP CURRENT & EDDY IN THE GULF OF MEXICO Fanghua Xu 1, Leo Oey 1, Yasumasa Miyazawa 2, Peter Hamilton 3 IWMO, 2012 1: Princeton University 2: JAMSTEC 3: SAIC

2. mpiPOM-LETKF gues/restart.ncLETKF anal/restart.nc mean/ sprd/ ensfcst(mpiPOM) obs SSHA SST T&S U&V +2d Observation increments/innovations

3. LETKF runnumobs data used 012SSHA (>500m)+MCSST+parm_infl (42%) 013SSHA (>500m)+MCSST+parm_infl (10.5%) 014SSHA(>500m) +MCSST+LC(uv, err = 0.05 m/s) 015SSHA(>500m)+MCSST +parm_infl (21%) 016SSHA(>500m) +MCSST+LC(uv, err = 0.1 m/s) OISSHA(>500m)+MCSST 90-day Experiments (2010/04/22 – 2010/07/21) LETKF parameters Horizontal localization scale7 (number of grids,1/3 degree) vertical localization scale (m)2000 Covariance inflation parameter (%)21 (10.5, 42) Observation error of SSHA (m)0.2 (0.1 & 0.05) Observation error of T ( 0 C)1.0 ( ) Time interval of LETKF (day)2 ensemble members20

4. LETKF015 Positions of the observation data assimilated in GOM, red: satellite SST; blue: AVISO SSHA Mooring locations near the Loop currents, red: measurements from ~80m to ~3000m Blue: measurements in deep (about 3000m) Loop Currents mooring locations

5. Model results are compared with 1. Satellite Sea Surface height (SSH); AVISO NRT map data (http://www.aviso.oceanobs.com/)http://www.aviso.oceanobs.com/ 2. Loop Currents mooring data; (Dr. Peter Hamilton) 3. ADCP data. (http://www.ndbc.noaa.gov/maps/ADCP_WestGulf.shtml)http://www.ndbc.noaa.gov/maps/ADCP_WestGulf.shtml

6. Comparison between model and AVISO SSH Color: model SSH; white line: AVISO SSH=0 line OI LETKF015

7. OI for the first 30 days OI for the entire 90 days 015 for the first 30 days 015 for the entire 90 days Blue: mooring; red: model -100m

8. OI for the first 30 days015 for the first 30 days -500m OI for the entire 90 days015 for the entire 90 days Blue: mooring; red: model

9. run V. Corrskillmean Std R. Rθuv spd ratio αm-αoαm-αo OI0.4130 o 0.730.770.58-44 o 0.99 0150.4130 o 0.94 0.95-23 o 0.70 0140.3030 o 0.900.830.68-40 o 0.83 0130.3452 o 0.93 0.96-23 o 0.82 0120.3438 o 0.930.940.95-16 o 0.76 0160.3525 o 0.950.810.71-28 o 0.75 90 days Vector Corr Coef (R) & Angles averaged over 4 moorings as a function of depth

11. runRθ skillmean std ratio uv m-o OI0.5153 o 0.360.700.85-14 o 0.94 0150.5992 o 0.310.750.79-2 o 0.69 0140.5362 o 0.310.700.74-16 o 0.67 0130.6672 o 0.290.760.96-12 o 0.98 0120.6872 o 0.270.690.87-6 o 0.92 Comparison between model & d moorings (54 days) Vector Corr Coef (R) & Angles ( θ ) at d moorings

12. OI 015 Blue: mooring; red: model 014013 Comparison of model and mooring D over 54 days

13. LETKF comparison with 3 ADCPs 20100501~20100721 OI012

14. Summary  The LETKF data assimilation results are in good agreement with the observation data, including satellite SSH, ADCPs, and moorings.  LETKF data assimilation improves model simulation significantly, compared with the traditional OI assimilation results;  The Loop current and its eddies are well represented, especially in mid water depth.

16. Principles X b : background field Y o : observed variable H : the observation operator that performs the necessary interpolation and transformation from model variables to observation space H(X b ): background or first guess of observations W: weights determined by the estimated statistical error covariance of the forecast and the observations. X a : analysis Observation increments/innovations SCM, OI, 3D-Var, and KF…

17. OI 015 014 013

21. Corr. & RMS error of model with satellite SSHA (h>500m) in GOM

22. runRθskillmeanstd ratio uv m-o OI 0.41-0.1 o 0.260.691.4-110 o 0.26 012 0.66-16 o 0.050.572.7-214 o 0.40 013 0.58-33 o 0.040.533.8-88 o 0.38 014 0.56-23 o 0.040.563.3-208 o 0.36 015 0.4715 o 00.612.9-1820.28 runRθskillmeanstd ratio uv m-o OI 0.36-14 o 00.481.7-129 o 0.41 012 0.50-20 o 0.930.650.70-7 o 0.82 013 0.42-16 o 0.600.240.42-5 o 0.73 014 0.47-12 o 0.750.420.585o5o 0.81 015 0.44-6 o 0.730.620.50-7 o 0.71 500m 100m Model comparison with ADCP in the northern Gulf

23. LETKF$runnumstatusobs data used 001C(90 days)SSHA only (msla) 002C (30days)SSHA+MCSST 003C(90 days)SSHA+T(ship) 004C(90 days)SSHA+TS(ship) 005C(90days)SSHA(>500m)+MCSST 006C(90 days)SSHA trackdata(>500m) 007C(90 days)SSHA trackdata(>500m)+MCSST 008C(90 days)SSHA trackdata(>500m)+MCSST+TS(ship) 009C(90days)SSHA (msla, >500m)+MCSST+TS(ship) 012C(90 days)SSHA (>500m)+MCSST+parm_infl (42%)