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ADVANCED INTERDISCIPLINARY DATA ASSIMILATION: FILTERING AND SMOOTHING VIA ESSE

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. ERROR SUBSPACE STATISTICAL ESTIMATION (ESSE) PHYSICAL SMOOTHING IN THE LEVANTINE SEA

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ADVANCED INTERDISCIPLINARY DATA ASSIMILATION: FILTERING AND SMOOTHING VIA ESSE

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  1. 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 ERROR SUBSPACE STATISTICAL ESTIMATION (ESSE) PHYSICAL SMOOTHING IN THE LEVANTINE SEA PHYSICAL-ACOUSTICAL FILTERING IN A SHELFBREAK ENVIRONMENT BIOGEOCHEMICAL-PHYSICAL SMOOTHING IN MASSACHUSETTS BAY CONCLUSIONS

  2. www.deas.harvard.edu/~pierrel

  3. P =e{(x–xt ) (x – xt)T} ˆ ˆ Coupled Interdisciplinary Error Covariances x = [xAxOxB] Physics: xO = [T, S, U, V, W] Biology: xB = [Ni, Pi, Zi, Bi, Di, Ci] Acoustics: xA = [Pressure (p), Phase ()] xO cO PAA PAO PAB P = POA POO POB PBA PBO PBB

  4. 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). 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).

  5. Surface expected normalized mesoscale error variances (0–1) of the hydrographic data used in the smoothing, as computed by 2D objective analysis.

  6. Temperature at 5 m on April 6, 1995. ESSE smoothing estimate ESSE filtering estimate

  7. RMS differences between T data at 5 m and ESSE T estimates at data-points, on 6 days • 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

  8. PHYSICAL-ACOUSTICAL FILTERING IN A SHELFBREAK ENVIRONMENT

  9. Acoustic paths considered (as in Shelfbreak-PRIMER), overlaid on bathymetry.

  10. BIOGEOCHEMICAL-PHYSICAL SMOOTHING IN MASSACHUSETTS BAY • 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)

  11. ESSE BIOGEOCHEMICAL-PHYSICAL ERROR COVARIANCE (FCST FOR SEP 2)

  12. ESSE ERROR EIGENMODE 2 (FCST FOR SEP 2)

  13. 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

  14. 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)

  15. Coupled bio-physical sub-regions of Massachusetts Bay in late summer: Dominant dynamics for trophic enrichment and accumulation

  16. 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 Conclusions

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