1. Harvard UniversityP.F.J. Lermusiaux et al. ADVANCED INTERDISCIPLINARY DATA ASSIMILATION: FILTERING AND SMOOTHING VIA ESSE P.F.J. Lermusiaux, A.R. Robinson, P.J.H. Haley and W.G. Leslie OCEANS 2002, Biloxi, MS, Oct. 29, 2002 1.ERROR SUBSPACE STATISTICAL ESTIMATION (ESSE) 2.PHYSICAL SMOOTHING IN THE LEVANTINE SEA 3.PHYSICAL-ACOUSTICAL FILTERING IN A SHELFBREAK ENVIRONMENT 4.BIOGEOCHEMICAL-PHYSICAL SMOOTHING IN MASSACHUSETTS BAY 5.CONCLUSIONS

2. Harvard UniversityP.F.J. Lermusiaux et al. www.deas.harvard.edu/~pierrel

3. Harvard UniversityP.F.J. Lermusiaux et al.

4. Harvard UniversityP.F.J. Lermusiaux et al. P AA P AO P AB P = P OA P OO P OB P BA P BO P BB Coupled Interdisciplinary Error Covariances Physics: x O = [T, S, U, V, W] Biology: x B = [N i, P i, Z i, B i, D i, C i ] Acoustics: x A = [Pressure (p), Phase (  )] x = [x A x O x B ] xOxO cOcO P =   (x – x t ) ( x – x t ) T  ˆˆ

5. Harvard UniversityP.F.J. Lermusiaux et al. Main upper-thermocline features: Asia Minor Current (1), Mid-Mediterranean Jet (2), Rhodes Gyre (3), West Cyprus Gyre (4), Ierapetra Eddy (5), a lobe of the Mersa Matruh Gyre (6) and main anticyclone in the Mersa Matruh-Shikmona Gyre complex (7). PHYSICAL SMOOTHING IN THE LEVANTINE SEA ESSE analysis for March 27, 1996 Potential density   at 105 m, overlaid with horizontal velocity vectors at 5 m (vectors plotted only if analyzed ||u|| ≥ 6 cm/s).

6. Harvard UniversityP.F.J. Lermusiaux et al. Surface expected normalized mesoscale error variances (0–1) of the hydrographic data used in the smoothing, as computed by 2D objective analysis.

7. Harvard UniversityP.F.J. Lermusiaux et al. ESSE filtering estimate Temperature at 5 m on April 6, 1995. ESSE smoothing estimate

8. Harvard UniversityP.F.J. Lermusiaux et al. Forward filtering (zig-zag) Dots: Filtering estimates Squares: Forecasts from previous filtering estimate Backward smoothing (continuous lines) Dots: Smoothing estimates Squares: Forecasts from previous smoothing estimate RMS differences between T data at 5 m and ESSE T estimates at data-points, on 6 days

9. Harvard UniversityP.F.J. Lermusiaux et al. PHYSICAL-ACOUSTICAL FILTERING IN A SHELFBREAK ENVIRONMENT

10. Harvard UniversityP.F.J. Lermusiaux et al. Acoustic paths considered (as in Shelfbreak-PRIMER), overlaid on bathymetry.

11. Harvard UniversityP.F.J. Lermusiaux et al.

12. Harvard UniversityP.F.J. Lermusiaux et al.

13. Harvard UniversityP.F.J. Lermusiaux et al.

14. Harvard UniversityP.F.J. Lermusiaux et al.

15. Harvard UniversityP.F.J. Lermusiaux et al.

16. Harvard UniversityP.F.J. Lermusiaux et al. Cartoon of horizontal circulation patterns for stratified conditions in Massachusetts Bay, overlying topography in meters (thin lines). Patterns drawn correspond to main currents in the upper layers of the pycnocline where the buoyancy driven component of the horizontal flow is often the largest Patterns are not present at all times Most common patterns (solid), less common (dashed) BIOGEOCHEMICAL-PHYSICAL SMOOTHING IN MASSACHUSETTS BAY

17. Harvard UniversityP.F.J. Lermusiaux et al. ESSE BIOGEOCHEMICAL-PHYSICAL ERROR COVARIANCE (FCST FOR SEP 2)

18. Harvard UniversityP.F.J. Lermusiaux et al. ESSE ERROR EIGENMODE 2 (FCST FOR SEP 2)

19. Harvard UniversityP.F.J. Lermusiaux et al. Cross-sections in Chl-a fields, from south to north along main axis of Massachusetts Bay, with: a) Nowcast on Aug. 25 b) Forecast for Sep. 2 c) 2D objective analysis for Sep. 2 of Chl-a data collected on Sep. 2–3 d) ESSE filtering estimate on Sep. 2

20. Harvard UniversityP.F.J. Lermusiaux et al. e) Difference between ESSE smoothing estimate on Aug. 25 and nowcast on Aug. 25 f) Forecast for Sep. 2, starting from ESSE smoothing estimate on Aug. 25 (g): as d), but for Chl-a at 20 m depth (h): RMS differences between Chl-a data on Sep. 2 and the field estimates at these data- points as a function of depth (specifically, “RMS-error” for persistence, dynamical forecast and ESSE filtering estimate)

21. Harvard UniversityP.F.J. Lermusiaux et al. Coupled bio-physical sub-regions of Massachusetts Bay in late summer: Dominant dynamics for trophic enrichment and accumulation

22. Harvard UniversityP.F.J. Lermusiaux et al. Conclusions Physics-acoustics-biology: single multi-scale coupled problem, for the first-time ESSE smoothing in the Eastern Mediterranean provides dynamically consistent fields superior to those obtained by statistical methods alone –Sub-mesoscale variability found important and increased skill ESSE nonlinear filtering capable of recovering fine-scale TL structures and mesoscale physics from coarse TL and/or C data –Shoreward meander of upper-front leads to less loss in acoustic waveguide on shelf –Corresponding thickening of thermocline at the front induces phase shifts in ray patterns on the shelf ESSE smoothing for coupled physical-biological simulations in Massachusetts Bay ideal to investigate summer-to-fall ecosystem transition –Evidence of patchiness in Chl-a field on several scales –Increasing storms and sub-mesoscale to mesoscale variability, decreasing light levels ESSE: sub-optimal reduction of errors is itself optimal

23. Harvard UniversityP.F.J. Lermusiaux et al.