Quantitative estimate of inter basin exchanges in the Mediterranean Sea
from Lagrangian diagnostics applied to a OGCM
V.Rupolo, D.Iudicone
ENEA (Roma) – LODYC (Paris)
EU TRACMASS project
Lagrangian diagnostics to compute
- the water mass transport in the upper and lower branch of the Mediterranean
thermohaline circulation.
- the spectrum of transit times associated to the different paths of the
Mediterranean THC
Off line lagrangian integration algorithms developped by B. Blanke at LPO
(off line integration – 3D not ispoycnic floats – transport estimate)
http://www.ifremer.fr/lpo/blanke/ARIANE
Eulerian velocity fields (stored every days) from an equilibrium
year of a Mediterranean OGCM (MOM 1.0 0.25°x0.25°x19, Artale et al., 2002)
Details on the integration algorithm and model
implementation in the poster sesion
The Mediterranean is an evaporative basin and the Gibraltar
strait is a source of intermediate water
?
※
In the 90’ have been observed dramatic changes in the deep water formation
and in the vertical stratification in the EM. How/when
they reflect in the Gibraltar Output ?
Qualitative visualisation of the upper branch of the THC
About 60 000 particles uniformly released in the surface layers.
colours indicate depth from surface (blu) to 1000 m. (yellow)
Qualitative visualisation of the lower branch of the THC in the East Mediterranean
About 60 000 particles uniformly released in the surface layers.
colours indicate depth from 200 m (blu) to 1700 m. (yellow)
Qualitative visualisation of the lower branch of the THC in the West Mediterranean
About 60 000 particles uniformly released in the surface layers.
colours indicate depth from 50 m (blu) to 1700 m. (yellow)
The global TH cell appears to be composed by several different paths
- Quantitative estimate by releasing about 500 000 particles in the inflow in the
Alborean Sea and integrating them till they cross again the same section.
- For each particle hydrological characteristics and transit time are stored when
crossing one of the ‘transparent’ sections in the basin.
Sub division in different paths by checking the arrival times in the transparent sections
Total TH cell = Global cell + Western Cell + Fast recirculation
Distribution of arrival times
Western Cell
Global Cell, Upper Branch
Red arrows indicate the lower branch
Global Cell, Lower Branch
Water Mass transformation
SIC
LEV
SIC
ooSARD
Mean
NW
values
ADR ALB
T and S of the outflowing water in the Alborean Sea strongly depend on mixing between
water of eastern origin with fresher and cooler water in the North Western Mediterranean
paths P2 and P3 (strongly depending on deep convection in the NWM)
Global Cell, Lower Branch
Arrival times
Characteristic times
Experimental arrival times distribution P(t)
Tmode : P(Tmode) > P(t) t
Tfirst=first arrival time
Cumulative F(t) = 0t P(t’)dt’ / 0 P(t’)dt’
median tm: F(tm) = 0.5
Percentage of water connecting the two sections
in a time smaller than t
Concentration in the basin C(t)=1-F(t)
Tres 0 C(t’)dt’
Typical times Ti if in some ranges C(t) e –t/Ti
Often to fit the experimental distribution of the arrival times is used - without dynamical
arguments for its revelance – the solution of the one-dimensional advective-diffusive
equation
G(t*, , ) = · (4 2 t*3) –1/2 exp{- 2(t*-1) 2 /4 2 t*},
where is the mean arrival time and is a measure of the width of the curve (dispersal)
, same
Great , diffusive
behaviour (long tails)
Great , advective
behaviour (peaked around )
Global cell, total lower branch
Transit times distribution from Sicily
to Alborean Sea
- - total
P1
P2
P3
Global cell, P1 lower branch
Transit times distribution from Sicily
to Alborean Sea
Global cell, P2 lower branch
Transit times distribution from Sicily
to Alborean Sea
Global cell, P3 lower branch
Transit times distribution from Sicily
to Alborean Sea
Water Mass composition and Age
’Classical’ quantitative Water Mass Analysis: the tracer concentration is expressed
as a linear combination of N source-water values:
= a1 1 + a2 2 + ………….. ….. +aN N ai >0, ai=1
The coefficient ai can be expressed (Haine and Hall, 2002) as:
ai = Ci 0d Gi’(r, | 1), ai >0, ai=1
where Gi’ = distribution of transit times from the source region i to r
Lagrangian approach
The water-mass component is defined by the geographical path from two given initial
and final sections where particles are released and stopped and the related distribution of
the arrival times P() can be subdivided in N distribution P i () corresponding to N
different paths connecting the two sections:
P()= i P i()
In equilibrium the arrival time distributions corresponds to the age spectrum of the considered
transport between the two sections, then it is possible to compute the relative composition of a
water parcel in the final section in terms as a function of the water ‘age’ (elapsed time from
the initial to the final section).
Global cell, total lower branch
Cumulative functions
- - total
P1
P2
P3
Fi/Ftot:
Relative
Composition
As a function
of the age
Summary
- Lagrangian diagnostics powerful tool to fully exploit results
from Eulerian OGCM (detailed description of circulation paths)
- Analysis of the transit times distributions particularly
interesting (transmission of an anomalous signal, accident,
pollution)
Water Mass composition
Quantitative Water Mass Analysis
Composition of a water parcel in terms of the different fractions of source waters.
Tracer concentration as a linear combination of N source-water value:
T= a1T1 + a2T2 + ….. +aNTN
S= a1S1 + a2S2 + ….. +aNSN
ai >0, ai=1
A water-mass component is defined by the geographical location of the
formation site, or (Lagrangian approach) by the geographical path
from two given initial and final sections
Tracer Green’s Function
t (r,t) + [(r,t)] =
S(r,t)
is a linear opeartor including advection and diffusive mixing
S is a tracer source or sink
The Green’s function G(r,t|r’,t’) is the solution to the related problem
t G(r,t) + [G(r,t)] = (r-r’)(t-
t’)
G is the response of tracer concentration to an instantaneous impulse at
time t’ and position r’ in the interior. Considered as a function of r, t, r’ and t.
G captures complete information about transport processes in the flow.
The tracer field from a continuous source is a superposition of individual pulses.
(r,t) =d3r’dt’ S(r’,t)
G(r,t|r’,t’)
S(r’,t’) G(r,t|r’,t’)/ (r,t) is the fraction of tracer at r that released at r’ has resided
In the ocean a time =t-t’ and is a distribution of transit timefrom r to r’.
Tracer Boundary propagator
tG’(r,t) + [G’(r,t)] = 0
The concentration boundary condition are G’= (r-r’,t-t’), where r’ is on the
boundary surface . The interior tracer concentration can be built from G’:
(r,t) = d2r’ tot dt’ (r,t’) G’(r,t|r’,t’)
Where (r,t) (r) is a known time variation of the concentration on
The interior field is obtained by multiplying G’ with the boundary concentration and
integrating. From all the possible pathways from to (r,t), G’(r,t|r’,t’) dt’d2r’ is the
fraction that originated from the boundary region d2r’ in the time interval (t’,t’+dt’).
G’(r,t|r’,t’) is a joint distribution function describing the water-mass composition at r and t
from different surface-source regions and different times.
Considering a surface concentration steady in time and piece-wise constant over a series
of N surface patches 1 … N we then have:
(r) = (1) 1 0d G1’(r, | 1) + … + (N) N 0d GN’(r,
| N)
P()= experimental arrival time distribution that can be
decomposed in N arrival time distribution Pi() : i Pi() =
P() corresponding to N different path connecting initial and final
section
F(t) = 0td P()
(t)= F(t)/F() represents the percentage of water , with regard to
the total flow, connecting the initial and final section in a time
smaller than t
Fi(t) = 0td Pi()
i(t) = Fi(t)/F(t) = 0td Pi() [ 0td P()] –1 , i
i() = 1
i represents the percentage of water, with regard to the flow
younger than t, that connects the initial and final section following
the i-th path.
Global cell, total lower branch
Sezione extra
Arrival times distribution
Total cell
Global cell
Western cell
WC, circulating
In the Tyrrhenian
Fast recirculation
In one dimension, the tracer continuity equation is
t + u · x -k· xx = 0,
where u is the velocity, k is the diffusivity nd the only tracer source is ta x = 0.
The transit time distribution function G(x,t) is the response to a boundary condition (t)
at x = 0. For constant uniform u and k:
G(x,t) = x · (4kt3) –1/2 exp{-(ut-x)2/4kt}
An alternative form is (t*= /t)
G(t*, , ) = · (4 2 t*3) –1/2 exp{- 2(t*-1) 2 /4 2 t*}
This distribution depends on the mean transit time and width , that are simply
Related to u and k (=x/u , =(kx)1/2/u3/2 ).
This solution – without dynamical arguments for the revelance of one-dimensional
Transport - is a convenient form to fit experimental arrival time distribution making
freely vary the parameters (mean age) and (width)
Upwelling through the nutricline: particles are released (homogeneously) at
160 m. of depth and they are integrated till they reach the depth of 30, 15 and
5 m.
standard year
1993:Fully developped
EMT
From 160 to 5: 0.01 Sv From 160 to 5: 0.02 Sv
From 160 to 15: 0.02 Sv From 160 to 15: 0.04 Sv
From 160 to 300: 0.03 Sv From 160 to 300: 0.07 Sv
Time behavior of flux through the ‘nutricline’
Red = flux at the starting section, black= flux at the ending section
standard year
1993
From 160 to 5:
From 160 to 5:
From 160 to 15:
From 160 to 15:
From 160 to 30:
From 160 to 30:
Summary
Relaxing model SST to satellite SST from 1988 to 1993, the general
mechanism of the EMT is reproduced
Lagrangian diagnostics make easier the analysis of the development
of the EMT as it is represented by the model and allows quantitative
estimates, in particular:
i) In a preconditioning phase IW inflow in the Adriatic (Aegean)
decreases (increases). Probably wind induced (Samuel et al, Demirov
and Pinardi)
ii) The EMT fully develops during 1992 and 1993, the overflow from the
Aegean is concentrated during two events (O(months)). The total flow
over the Cretan Arcs is 1.2 1014 m3 (roughly the half of he estimate of
Roether et al.; 1996)
iii) Relaxation toward pre-EMT situatiuon (qualitative behavior and
estimate of characteristic time)
Moreover: Quantitative estimates of vertical transport before and after the
EMT (up lifted water), Time statistics
http://clima.casaccia.enea.it/staff/rupolo