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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 0.25x0.25x19, Artale et al.,
2002) Details on the integration algorithm and
model implementation in the poster sesion
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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 ?
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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)
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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)
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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)
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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
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Total TH cell Global cell Western Cell Fast
recirculation
Distribution of arrival times
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Western Cell
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Global Cell, Upper Branch
Red arrows indicate the lower branch
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Global Cell, Lower Branch
Water Mass transformation
SIC SARD NW ALB
LEV SIC ADR
oo
Mean values
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)
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Global Cell, Lower Branch
Arrival times
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Characteristic times
Experimental arrival times distribution
P(t) Tmode P(Tmode) gt P(t) ? t Tfirstfirst
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
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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 ?t3) 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 ?)
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Global cell, total lower branch Transit times
distribution from Sicily to Alborean Sea
- - total P1 P2 P3
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Global cell, P1 lower branch Transit times
distribution from Sicily to Alborean Sea
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Global cell, P2 lower branch Transit times
distribution from Sicily to Alborean Sea
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Global cell, P3 lower branch Transit times
distribution from Sicily to Alborean Sea
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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 gt0, ? ai1
• The coefficient ai can be expressed (Haine and
  Hall, 2002) as
• ai Ci ? 0?d ? Gi(r, ? ?1), ai gt0, ?
  ai1
• 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).
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Global cell, total lower branch Cumulative
functions
- - total P1 P2 P3
Fi/Ftot Relative Composition As a function of
the age
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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)

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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 gt0, ? ai1
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
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Tracer Greens 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 Greens function G(r,tr,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,tr,t)
S(r,t) G(r,tr,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.
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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,tr,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,tr,t)
dtd2r is the fraction that originated from the
boundary region d2r in the time interval
(t,tdt). G(r,tr,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 ? 0?d ? G1(r, ? ?1)
?(?N) ?N ? 0?d ? GN(r, ? ?N)
? t-t0
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• 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.

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Global cell, total lower branch
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Sezione extra
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Arrival times distribution
Total cell Global cell Western cell WC,
circulating In the Tyrrhenian Fast recirculation
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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 (4?kt3) 1/2 exp-(ut-x)2/4kt
An alternative form is (t ?/t)
G(t, ?, ?) ? (4 ?2 ?t3) 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)
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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
1993Fully 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
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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
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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
• In a preconditioning phase IW inflow in the
  Adriatic (Aegean) decreases (increases). Probably
  wind induced (Samuel et al, Demirov and Pinardi)
• 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)
• 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