High resolu,on mapping of 3D semigeostrophic dynamics from a combina,on of ARGO measurements and satellite observa,ons Bruno Buongiorno Nardelli Consiglio Nazionale delle Ricerche, Italy
High resolu,on mapping of 3D semi-‐geostrophic dynamics from a combina,on of ARGO measurements and satellite observa,ons Bruno Buongiorno Nardelli Consiglio Nazionale delle Ricerche, Italy
High resolu,on mapping of 3D semi-‐geostrophic dynamics from a combina,on of ARGO measurements and satellite observa,ons àanalyze mesoscale dynamics from observa6ons àver6cal exchanges àmechanisms with poten6al impact on biology
Single observa,ons give us informa,on on some of the variables used to describe the ocean state (u,v,w,T,S,…)àlimited view
ARGO CTD/XCTD
ALTIMETRY
SeaSurfaceTemperature
Analyzing 3D Mesoscale dynamics: background
The degrees of freedom of the system are reduced by dynamical constraints, leading to autocorrela6on/correla6ons among ocean state variables
ARGO CTD/XCTD
ALTIMETRY
Analyzing 3D Mesoscale dynamics: background
SeaSurfaceTemperature
Take advantage of correla,ons between the variables describing the ocean state to retrieve mesoscale dynamics from observa6ons
ARGO CTD/XCTD
ALTIMETRY
Analyzing 3D Mesoscale dynamics: strategy
SeaSurfaceTemperature
High resolu6on 3D tracer fields Temperature Salinity Density
àbuild high resolu,on surface fields àver,cal extrapola,on
Analyzing 3D Mesoscale dynamics: approach and methodologies
High resolu6on 3D tracer fields Temperature Salinity Density
àbuild high resolu,on surface fields àver,cal extrapola,on
Analyzing 3D Mesoscale dynamics: approach and methodologies
High resolu6on 3D tracer fields Temperature Salinity Density
àbuild high resolu,on surface fields àver,cal extrapola,on
Analyzing 3D Mesoscale dynamics: approach and methodologies
High resolu6on 3D tracer fields Temperature Salinity Density
àbuild high resolu,on surface fields àver,cal extrapola,on
Analyzing 3D Mesoscale dynamics: approach and methodologies
Test areaà North Atlan6c/Gulf Stream
àGeostrophic (only horizontal component) àQuasi Geostrophic (QG Omega equa,onàw) àSemi Geostrophic (SG Omega equa,onàw)
High resolu6on 3D tracer fields Temperature Salinity Density
High resolu6on 3D velocity fields
àbuild high resolu,on surface fields àver,cal extrapola,on
Analyzing 3D Mesoscale dynamics: approach and methodologies
àGeostrophic (only horizontal component) àQuasi Geostrophic (QG Omega equa,onàw) àSemi Geostrophic (SG Omega equa,onàw)
High resolu6on 3D tracer fields Temperature Salinity Density
High resolu6on 3D velocity fields
àbuild high resolu,on surface fields àver,cal extrapola,on
Analyzing 3D Mesoscale dynamics: approach and methodologies
Study areaà Agulhas Current
àGeostrophic (only horizontal component) àQuasi Geostrophic (QG Omega equa,onàw) àSemi Geostrophic (SG Omega equa,onàw)
High resolu6on 3D tracer fields Temperature Salinity Density
High resolu6on 3D velocity fields
Lagrangian trajectories 3D advec,on
àbuild high resolu,on surface fields àver,cal extrapola,on
Analyzing 3D Mesoscale dynamics: approach and methodologies
Study areaà Agulhas Current
àrelevant for biology àmay help interpreta,on à…
àGeostrophic (only horizontal component) àQuasi Geostrophic (QG Omega equa,onàw) àSemi Geostrophic (SG Omega equa,onàw)
High resolu6on 3D tracer fields Temperature Salinity Density
High resolu6on 3D velocity fields
Lagrangian trajectories 3D advec,on
àbuild high resolu,on surface fields àver,cal extrapola,on
àrelevant for biology àmay help interpreta,on à…
Analyzing 3D Mesoscale dynamics: approach and methodologies
Study areaà Agulhas Current
àHR SSS needed by 3D reconstruc,on method ànew product poten,ally useful in combina,on with SMOS data Hypothesis: high correla6on between sea surface temperature (SST) and sea surface salinity (SSS) varia,ons can be expected (in the open ocean) at scales significantly smaller than the ones domina6ng atmospheric variabilityàboth T and S basically modified through advec,on and diffusion Proposed technique: op,mal interpola,on (Bretherton-‐like) algorithm that includes satellite (spa,ally high-‐pass filtered) SST differences in the covariance es,ma,on
)()( . backgroundobsbackgroundanalysis xyCRCxx −++= −1
222
⎟⎟⎠
⎞⎜⎜⎝
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⎠⎞
⎜⎝⎛ Δ−⎟
⎠⎞
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=ΔΔΔ TSST
Lrt filtered
eeeSSTtr τ),,(CCovariance func6on parameters (i.e. spa,al (L), temporal (τ) and thermal (T) decorrela,on scales and spa,al filtering) determined empirically minimizing errors vs independent surface observa6ons
Mul6-‐parameter HR interpola6on of surface salinity data: method
Mul6-‐parameter HR interpola6on of surface salinity data: method
àHR SSS needed by 3D reconstruc,on method ànew product poten,ally useful in combina,on with SMOS data Hypothesis: high correla6on between sea surface temperature (SST) and sea surface salinity (SSS) varia,ons can be expected (in the open ocean) at scales significantly smaller than the ones domina6ng atmospheric variabilityàboth T and S basically modified through advec,on and diffusion Proposed technique: op,mal interpola,on (Bretherton-‐like) algorithm that includes satellite (spa,ally high-‐pass filtered) SST differences in the covariance es,ma,on
)()( . backgroundobsbackgroundanalysis xyCRCxx −++= −1
222
⎟⎟⎠
⎞⎜⎜⎝
⎛ Δ−⎟
⎠⎞
⎜⎝⎛ Δ−⎟
⎠⎞
⎜⎝⎛ Δ−
=ΔΔΔ TSST
Lrt filtered
eeeSSTtr τ),,(CCovariance func6on parameters (i.e. spa,al (L), temporal (τ) and thermal (T) decorrela,on scales and spa,al filtering) determined empirically minimizing errors vs independent surface observa6ons
Same test performed on simulated observa6ons taking MERCATOR model output as ‘true’ SSS field
in situ SSS Red dots (input) 30 days window, centered on interpola,on dayà MyOcean INSITU-‐TAC ARGO, CTD and XCTD, referenced to 5 m depth Blue dots (valida6on) (only for interpola,on day) GOSUD and LEGOS TSG data
Mul6-‐parameter HR interpola6on of surface salinity data: test datasets
Background SSS (1/2°) MyOcean CORIOLIS SSS objec,vely analyzed maps (ISAS)
in situ SSS Red dots (input) 30 days window, centered on interpola,on dayà MyOcean INSITU-‐TAC ARGO, CTD and XCTD, referenced to 5 m depth Blue dots (valida6on) (only for interpola,on day) GOSUD and LEGOS TSG data
Mul6-‐parameter HR interpola6on of surface salinity data: test datasets
Background SSS MyOcean CORIOLIS SSS objec,vely analyzed maps
in situ SSS Red dots (input) 30 days window, centered on interpola,on dayà MyOcean INSITU-‐TAC ARGO, CTD and XCTD, referenced to 5 m depth Blue dots (valida6on) (only for interpola,on day) GOSUD and LEGOS TSG data
Background
ODYSSEA L4 SST (1/10°, daily)
Mul6-‐parameter HR interpola6on of surface salinity data: test datasets
Backgrou
nd
MESCLA
MESCLA high resolu6on SSS field and derived SSS gradient reveal more realis,c and smaller scale structures than those visible in CORIOLIS-‐SSS product.
Mul6-‐parameter HR interpola6on of surface salinity data: results
Mul6-‐parameter HR interpola6on of surface salinity data: results
Simulated dataset from MERCATOR model L= 475km τ=10 days T=1.75 °C Noise-‐to-‐signal=0.3 HR SSS RMSE reduced to <50% of corresponding ISAS error
In Situ/ODYSSEA SST observa6ons L= 400 km τ=6 days T=2.75 °C signal-‐to-‐noise=0.01 HR SSS RMSE reduced to <75% of corresponding ISAS error
Mul6-‐parameter HR interpola6on of surface salinity data: results
∑=
=n
kkk zLtatzT
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Ver6cal extrapola6on: Mul6variate EOF Reconstruc6on (mEOF-‐R)
à mul6variate Empirical Orthogonal Func6on (mEOF) decomposi,on of T,S,SH from ARGO profiles àhypothesis that few modes explain the major part of the variability and that surface values of the parameters considered are known àincluding Steric Heights profiles in state vector provides dynamical informa,on
∑=
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332211Core of mEOF-‐R method
Buongiorno Nardelli B., Santoleri R., J. Atmos. Ocean. Tech. 2005 Buongiorno Nardelli B. et al., J. Geophys. Res.2006 Buongiorno Nardelli B. et al., Ocean Sci.2012 (accepted last week)
In situ profiles (used to tain the model): Quality Controlled ARGO/CTD profiles provided by Coriolis (used in their OA) through MyOcean catalogue àProfiles already QC à Profiles were interpolated at regular pressure bins (10 dbar) Surface input (daily): SH extracted from AVISO ADT maps (updated 1/3° product, daily, upsized to 1/10°) Odyssea SST L4 (1/10°, daily) MESCLA SSS L4 (1/10°, daily)
Ver6cal extrapola6on: study area and input observa6ons
Study area: Agulhas Current Focus on eddies Period: 1st September 2010-‐18th November 2010
SYNTHETIC PROFILES RECONSTRUCTION ERRORS
Different configura6ons tested: à mEOFs computed from ARGO profiles selected within a moving monthly window à no further geographical subseing (one set of mEOFs for whole domain) à First three modes generally explaining >99% of variance, third mode O(10-‐4) à Errors minimized using only first two modes (blue and green)
First three modes
Ver6cal extrapola6on: mul6variate EOFs (T-‐S-‐SH)
−0.15 −0.1 −0.05 0 0.05 0.1
0
100
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pres
sure
(dba
r)
SH mEOF modes
mode 1mode 2mode 3
−0.1 −0.05 0 0.05 0.1
0
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pres
sure
(dba
r)
T mEOF modes
mode 1mode 2mode 3
−0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2
0
100
200
300
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pres
sure
(dba
r)
S mEOF modes
mode 1mode 2mode 3
SYNTHETIC PROFILES RECONSTRUCTION ERRORS
hindcast on training dataset (i.e. using surface values as input to mEOF-‐reconstruc,on)
−0.5 0 0.5 1 1.5
0
100
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pres
sure
(dba
r)
temperature errors (°C)
HINDCAST mEOF−R
STDEMBE
−0.5 0 0.5 1 1.5
0
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pres
sure
(dba
r)
temperature errors (°C)
satellite surface input mEOF−R
STDEMBE
−0.05 0 0.05 0.1 0.15
0
100
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pres
sure
(dba
r)
salinity errors (psu)
HINDCAST mEOF−R
STDEMBE
−0.05 0 0.05 0.1 0.15
0
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pres
sure
(dba
r)
salinity errors (psu)
satellite surface input mEOF−R
STDEMBE
Ver6cal extrapola6on: errors on one snapshot
matchup between synthe,c profiles and ARGO profiles
Ver6cal extrapola6on: surface and 3D fields
à It allows to es,mate w from density field and geostrophic veloci,es à It retains ageostrophic advec,on in the equa,ons à Improved accuracy over an extended range of dynamical condi,ons (larger Rossby numbers)
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The eq. is derived applying a change of coordinates (see above), but it can be solved in the original coordinates (amer a lot of algebra… see also Viudez and Dritschel, J. Phys. Ocean., 2004)
geostrophic coordinates geostrophic vorAcity
Semi-‐geostrophic Omega equa6on: formula6on
QG Omega eq. SG Omega eq. PE solu6on (MERCATOR Model)
Tested using MERCATOR model output as simulated observa,ons and applying the simplified QG and SG diagnos,c models:
100 m 100 m 100 m
though not all the features are reproduced by QG and SG, SG improves the ver6cal velocity es6mates (look at the scales)
Semi-‐geostrophic Omega equa6on: valida6on
Some slides here originally contained recent (s6ll) unpublished results Please contact [email protected] for further informa6on
UNPUBLISHED RESULTS: work in progress
Conclusions and perspec,ves
Mesoscale resolving 3D tracer fields can be obtained by combina6on of different/complementary observa6ons ànot going to work everywhere and every,me, but improvements can be expected with SWOT al,metry and comparing different techniques Semi-‐geostrophic omega equa6on can be used to retrieve 3D ver6cal veloci6es from synthe6c 3D tracer fields à beper diagnos,c (working also at high Rossby numbers) à limi,ng factor mostly related to true resolu,on of input surface fields and mEOF
trunca,ons (only looking at dominant modes) Evidence (?) of Vortex Rossby Waves modula6ng the evolu6on of eddies is seen in SG ver6cal veloci6es àrarely observed in the oceans, widely studied in the atmosphere à3D Lagrangian trajectories seem to indicate they might be relevant mechanisms driving ver,cal exchanges of nutrients (at ,mescales comparable to biological ones)