Harvard University P.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

Harvard University P.F.J. Lermusiaux et al.www.deas.harvard.edu/~pierrel

Harvard University P.F.J. Lermusiaux et al.

Harvard University P.F.J. Lermusiaux et al.

PAA PAO PAB

P = POA POO POB

PBA PBO PBB

Coupled Interdisciplinary Error Covariances

Physics: xO = [T, S, U, V, W]

Biology: xB = [Ni, Pi, Zi, Bi, Di, Ci]

Acoustics: xA = [Pressure (p), Phase ()]

x = [xA xO xB]

xOcO

P = (x – x t ) ( x – x

t )Tˆ ˆ

Harvard University P.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).

Harvard University P.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.

Harvard University P.F.J. Lermusiaux et al.

ESSE filtering estimate

Temperature at 5 m on April 6, 1995.

ESSE smoothing estimate

Harvard University P.F.J. Lermusiaux et al.

Forward filtering (zig-zag)Dots: Filtering estimatesSquares: Forecasts from previous filtering estimate

Backward smoothing (continuous lines)

Dots: Smoothing estimatesSquares: Forecasts from previous smoothing estimate

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

Harvard University P.F.J. Lermusiaux et al.

PHYSICAL-ACOUSTICAL FILTERING IN A SHELFBREAK ENVIRONMENT

Harvard University P.F.J. Lermusiaux et al.

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

Harvard University P.F.J. Lermusiaux et al.

Harvard University P.F.J. Lermusiaux et al.

Harvard University P.F.J. Lermusiaux et al.

Harvard University P.F.J. Lermusiaux et al.

Harvard University P.F.J. Lermusiaux et al.

Harvard University P.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

Harvard University P.F.J. Lermusiaux et al.

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

Harvard University P.F.J. Lermusiaux et al.

ESSE ERROR EIGENMODE 2 (FCST FOR SEP 2)

Harvard University P.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

Harvard University P.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)

Harvard University P.F.J. Lermusiaux et al.

Coupled bio-physical sub-regions of Massachusetts Bay in late summer:

Dominant dynamics for trophic enrichment and accumulation

Harvard University P.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

Harvard University P.F.J. Lermusiaux et al.