FINMED Preparing next generation fine scale experiments in Med Sea 26-28 Juin 2017 The automatic eddy detection algorithm AMEDA and the cyclo-geostrophic correction in the Mediterranean Sea. B. Le Vu (1) A. Ioannou (1) A. Tuel (1) F. Dumas (2) A. STEGNER (1) (1) Laboratoire de Météorologie Dynamique, CNRS, Ecole Polytechnique, Palaiseau, France. (2) SHOM, Brest, France
Coastal Oceanography 80 surface vorticity ( time = 100 days ) vort/f 0.5 60 0.25 Y [km] 40 1800 1800 0 20 1600 1400 1200 1600 1400 1200 50 100 150 200 250 X [km] 0.25 0.5 In-situ & remote sensing measurements Idealized numerical simulations (Mkhinini et al, 2014; Ioannou et al. 2017) (Cimoli et al. 2017) Alex Stegner (astegner@lmd.polytechnique.fr) Laboratoire de Météorologie Dynamique, CNRS, Ecole Polytechnique
Coastal Oceanography Laboratory experiments Small and large rotating tank (Teinturier et al. 2010) Stability analysis (Lazar et al. 2013) Alex Stegner (astegner@lmd.polytechnique.fr) Laboratoire de Météorologie Dynamique, CNRS, Ecole Polytechnique
DYNamical EDdies - Atlas Dynamical data base of meso-scale eddies in Med Sea (2000-2015) 3 laboratories Navy oceanography 2 SME
Are we able to monitor continuously meso-scale eddies in the Mediterranean Sea?
Satellite Altimetry JASON-2 Altimeter Multiple satellites (Jason-2, EN, AltiKa, Cryosat-2, HY-2A)
Satellite Altimetry AVISO gridded maps (1/4 or 1/8 ) SLA (Sea Level Anomaly) ADT (Absolute Dynamic Topography) Optimal interpolation Le Traon et al. (1998) Altimetric tracks SLA
Eddy detection Algorithm AVISO 1/8 gridded maps (MED) geostrophic velocities AMEDA Angular Mometum Eddy tracking algorithm! $ % = ( ) *+ centers characteristic contours Mkinhini et al. (2014), Le Vu et al. (2017)
Eddy detection Algorithm AVISO geostrophic velocities OKUBO-WEISS CRITERION W = σ n 2 +σ s 2 ζ 2 σ n = x u y v σ s = x v + y u strain, shear ζ = x v y u vorticity W < 0.2 σ W Isern-Fontanet et al. (2003)
Eddy dtection Algorithm AVISO geostrophic velocities OKUBO-WEISS CRITERION W = σ n 2 +σ s 2 ζ 2 σ n = x u y v σ s = x v + y u strain, shear ζ = x v y u vorticity W<-2 10-12 s -1 Chelton et al. (2007)
Algorithm AMEDA AVISO geostrophic velocities Local Normalized Angular Momentum EDDY CENTERS
Algorithm AMEDA AVISO geostrophic velocities Local Normalized Angular Momentum Closed streamlines around eddy centers CHARACTERISTIC CONTOURS
Algorithm AMEDA (a) CHARACTERISTIC CONTOURS LNAM(LOW<0) 1 40 o N 1500 0.8 V end 300 V max 0.6 (b) 39 o N A 300 0.4 0.2 V max 1500 Vend C2 0 38 o N C1 0.2 0.4 (c) 37 o N 1500 300 1500 300 0.6 0.8 V max V end 4 o E 5 o E 6 o E 7 o E 8 o E 1 anticyclones (blue) cyclones (red) Le Vu et al. (2017)
Eddy characterization COMPARISONS WITH IN-SITU MEASUREMENTS EGYPT campaign (2006) CTD Transect
Eddy characterization COMPARISONS WITH IN-SITU MEASUREMENTS EGYPT campaign (2006)
Algorithm AMEDA COMPARISONS WITH IN-SITU MEASUREMENTS 50 B-59751 B-59748 (R i,v i ) In-situ drifters 40 30 V max (cm/s) 20 10 Geostrophic velocity profile 0 0 10 20 30 40 50 60 R max (km) Ro = V max f R max
Eddy characterization COMPARISONS WITH IN-SITU MEASUREMENTS BOUM campaign (2008) VMADCP LADCP
Eddy characterization SYSTEMATIC UNDER ESTIMATION OF THE INTENSITY OF MESO SCALE ANTICYCLONES WITH AVISO PRODUCTS! Name Year Campaign Instruments Ro (AVISO) Ro (In-situ) Error Ierapetra 05 2006 EGYPT-1 Drifters, CTD 0.09 0.13-35 % Ierapetra 04 2006 EGYPT-1 Drifters, CTD 0.085 0.12-30 % Ierapetra 05 2008 BOUM VMADCP, LADCP 0.05 0.085-40 % Libyan Eddy 2006 EGYPT-1 Moorings 0.075 0.15-50% Algerian Eddy 2014 SOMBA VMADCP 0.11 0.15-36 % Baleares Eddy 2016 PROTEVS MED LADCP, Drifters 0.07 0.1-32 %
Trajectories of long-lived eddies EDDY TRACKING / MERGING-SPLITTING / EDDY LIFE TIME Ioannou et al. (2017)
EDDY TRACKING ERRORS: A typical example of bias of the altimetric detection CHLOROPHYL SST GRIDDED MAP ALONG-TRACK Antoine Delpoule
GEOSTROPHIC CIRCULAR VELOCITY PROFILE (AVISO+AMEDA) $ % = ( ), -+ Ro = 0.14 z /f ~ - 0.45 CYCLOGEOSTROPHIC CORRECTION $. / + ) $ = ) $ % Ro = 0.21 z /f ~ - 0.8 Ioannou et al. (2017)
GEOSTROPHIC/CYCLO GEOSTROPHIC CIRCULAR VELOCITY PROFILES CYCLONE-ANTICYCLONE ASYMMETRY a a ΔRo = Ro Ro geo Ro = V max f R max Anticyclones Cyclones Anticyclones are much more impacted than cyclones by cyclo geostrophic correction Penven et al. (2014)
IERAPETRA ANTICYCLONES Annual maximum of vortex intensity Even large meso scale eddies could experience cyclogeostrophic balance and finite relative vorticity! Ioannou et al. (2017)
CYCLOGEOSTROPHIC CORRECTIONS (non-circular eddies) : automatic process Iterative method V n+1 = V g + 1 f k ( V n. ) V n Knoxx & Ohmann (2006) We stop the iteration when V n+1 V n starts to increase In practice 4-5 iterations are enough after ten or more iterations strong divergence occurs
CYCLOGEOSTROPHIC CORRECTIONS : depends on eddy size and intensity Cyclo-geostrophic V c (r) Ro = 0.44 Geostrophic V g (r) Ro = 0.2
CYCLOGEOSTROPHIC CORRECTIONS : depends on eddy size and intensity
CYCLOGEOSTROPHIC CORRECTIONS : depends on eddy size and intensity
CYCLOGEOSTROPHIC CORRECTIONS : depends on eddy size and intensity
CYCLOGEOSTROPHIC CORRECTIONS : depends on eddy size and intensity RO > 0.2 Limits of the iterative method - Eddy radius smaller or equal to grid size - Intense eddies Ro > 0.2-0.3 R max < Dx (1/8 ) = 14km
CYCLOGEOSTROPHIC CORRECTIONS IN THE MEDITERRANEAN SEA Examples of intense ( Ro geo > 0.15 ) meso scale ( R max R d ) eddies in the Mediterranean Sea? Cyclones Anticyclones
CYCLOGEOSTROPHIC CORRECTIONS AT SUB MESOSCALE SWOT Med Area 2021 Simulated Ro= V max / fr max ~ 0.15-0.3 q=39-40 N f ~ 10-4 s -1 V max = 20-50 cm/s Dx = 3-5 km R max = 15 km? Iterative methods might not be fully accurate for cyclo-geostrophic corrections at sub mesocale?
Eddy detection algorithm and cyclo-geostrophic correction in the Mediterranean Sea. Summary - R max, V max allows simple comparison with in situ measurements - Identify the merging and the splitting events and long term eddy tracking - Erroneous detection due to bias in gridded map (local deficit in tracks) - Need for cyclo geostrophic corrections especially for small meso-scale! - DYNED-Atlas data set dedicated to co-location of other in-situ (ARGO, SVP, gliders)
Bibliography - A.Ioannou, A.Stegner, B.Levu and I.Taupier-Letage Dynamical evolution of the Ierapetra Eddy: a 20 year analysis submitted to J. Geophys. Res. Oceans, (2017) - B.Levu, A.Stegner, T. Arsouze «Angular Momentum Eddy Detection and tracking Algorithm (AMEDA) and its application to coastal eddy formation» in press J. Atmos. Oceanic Technol. (2017) - L.Cimoli, G.Roullet, A.Stegner «Meanders and eddies generation from a buoyant coastal current above a bathymetric slope.» in press Ocean Science. (2017) - Penven, P., I. Halo, S. Pous, and L. Marié (2014), Cyclogeostrophic balance in the Mozambique Channel", Journal of Geophysical Research: Oceans, 119(2), 1 14, doi:10.1002/2013jc009528. - N.Mkhinini, A.L. Santi-Coimbra, A.Stegner, T. Arsouze, I. Taupier-Letage and K. Béranger «Long-lived mesoscale eddies in the Eastern Mediterranean Sea: analysis of 20 years of AVISO geostrophic velocities» J. Geophys. Res. Oceans, 119, 8603 8626, doi:10.1002/ 2014JC010176 (2014). - A. Lazar, A. Stegner, R. Caldeira, C. Dong, H. Didelle, S. Vuiboud «Inertial instability of intense and stratified anticyclones. Part II : laboratory experiments» Journal of Fluid Mech. v.732, 485-509 (2013). - S. Teinturier, A. Stegner, S. Viboud and H. Didelle «Small-scale instabilities of an island wake flow in a rotating shallow-water layer» Dynamics of Atmosphere and Ocean, v.39, 1-24 (2010) DOI 10.1016/J.Dynatmoce.2008.10.006. - Chelton, D. B., M. G. Schlax, R. M. Samelson, and R. A. de Szoeke, 2007: Global observations of large oceanic eddies. Geophysical Research Letters, 34 (15), doi:10.1029/2007gl030812, URL http://dx.doi.org/10.1029/2007gl030812. - Isern-Fontanet, J., E. GarcÃŋa-Ladona, and J. Font (2006), Vortices of the Mediterranean Sea: An Altimetric Perspective", Journal of Physical Oceonography, 36(1), 87 103, doi:10.1175/jpo2826.1.