Lagrangian Archive from MFS Eulerian Archive'

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WP8620 Lagrangian Diagnostic
Claudia Pizzigalli, Volfango Rupolo, Emanuele
Lombardi, Bruno Blanke

• Lagrangian Archive from MFS Eulerian Archive.
• Seasonal statistics of lagrangian dispersion on
  the Mediterranean Sea Surface (local and global
  maps).
• User friendly visualization tool (web site).
• Validation.

Enea Casaccia Roma -Italy Laboratoire
de Pyisique del Oceans Brest - France

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Lagrangian Archive

• From MFS hindcast Eulerian (daily) velocity
  fields from January 2000 to December 2004.
• Particles are
• released on the sea surface and constrained to
  float at surface
• Integrated for 4 weeks (overlapping) using the
  off-line algorithm developed by B. Blanke
  (Ariane).
• I.C. the Mediterranean Sea is divided into 3/8
  x 3/8 boxes. We put 225 particles in each box.

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Integration
Integration is performed using overlapping time
slots as shown below
For each season we have 50 integrations (10 each
year). For each box (I.C.) , the seasonal
statistics is based on about 11000 trajectories (
225 particles for 50 integrations)
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MFS Eulerian velocity Data

• Hindcast velocity fields from MFSPP-SYS3 (MOM 1/8
  x 1/8 degrees and 31 vertical levels )

Topography of the OGCM
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Web site

• A web site for an easy visualization of surface
  dispersion properties in the Mediterranean Sea
  Surface has been constructed.
• The aim is to obtain a friendly user instrument
  to be used to have a first information on the
  seasonal statistics of dispersion starting from a
  generic point in the Mediterranean Sea Surface.
• The user can choose interactively the initial
  condition, the season and the kind of map.

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Two kinds of map

• LOCAL MAP user, choosing the starting point, can
  visualize local dispersal properties.
• GLOBAL MAP user can visualize synoptic
  properties of dispersion.

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Local interactive Maps

• Density map directly showing the probability of
  dispersion (in term of percentage from all
  realizations in a given season).
• Spaghetti Diagram visualization of centers of
  mass of each realization and of the
  seasonal(from all the realizations) center of
  mass.
• Rectangle of standard deviation meridional and
  zonal standard deviations
• around the Seasonal Center of Mass

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Global synoptic maps

• Maps of standard deviation mean zonal,
  meridional and module of the standard deviations
  around the total (seasonal) center of mass are
  mapped for each season (for fixed times)
• Coastal crash map indicates the probability of
  dangerous approach to the coast. The percentage
  of particles approaching the coasts (two model
  grid points) is mapped at fixed times.

Properties are mapped on the I.C release
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Spaghetti Diagrams

• Visualization of centers of mass of each
  realization and of the seasonal(from all the
  realizations) center of mass

N is the number of particles for each
realization (225)
Total centre of mass
M is the number of realization (50)
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Dangerous Approach (white area)
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Validation

• Using Mediterranean surface drifter database
  (1986-1999).

Pierre Poulain
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Validation

• The Database contains data relative to drifters
  released in several areas of Mediterranean Sea
  and drogued from 0 m to 300 m depth. For our
  purpose we have used only drifters drogued at
  maximum 15 m depth (0m, 4m, 10m and 15m). After
  the screening drifters useful for our purpose are
  229. Moreover, coherently with our previous
  analysis, we have grouped the experimental
  drifters by seasons, as function of their release
  time.

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Validation
A straight validation of this work would imply
the estimate of such seasonal Lagrangian
variability using experimental true
data. Unfortunately, the experimental data set is
quite limited and it do not allow for a straight
validation through the computation of the
seasonal Lagrangian variability from true data.
Nevertheless a first, indirect, validation can be
done measuring, for each season, the distance
between the centres of mass of numerical
particles (for each realization) with drifters
released in the same initial conditions (box of
3/8 x 3/8 large). This distance at a given time
T is defined as follows
where
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Winter
7 days
All basin
winter
winter
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Validation statistical indices of distribution
of distances
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State of art

• Even if the order of magnitude of these values is
  a rather big, especially in view of operative
  purposes, it is important to stress here that
  similar results are obtained when more
  sophisticated models are used to forecast
  Lagrangian trajectories of drifters with direct
  numerical simulations (Edwards et al. 2005,
  Werner et al. 1999, Spaulding et al, 2005).

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Two questions

• 1) Are our probability maps of dispersion
  representative of the lagrangian dispersion?
• 2) Is the prediction of the position of particles
  given by our probability maps better than this
  given by the knowledge of the characteristics
  scales of the velocity field (i.e. D V?T, where
• V is the typical velocity) ?

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1)

• Areas characterized by higher values of distances
  between real drifter and centers of mass (Sicily
  Channel and Otranto Strait) display also higher
  values of numerical lagrangian variability
  (standard deviation of the centres of mass of
  numerical particles)
• A more quantitative estimate of this general
  agreement can
• be obtained through the computation of the
  ratio ,
• where s is the standard deviation around the
  seasonal center
• characteristic of the initial box.

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1)
The histograms show the typical skewed shape with
a greater concentration for values smaller than
the peak that is always near the values 1-1.5,
even if, as usual, long tails for large values
are observed. We believe that this result, even
if obtained through an indirect validation, shows
that the methodology presented here is successful
to estimate the variability of the Lagrangian
dispersal properties.
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2)
The quantitative Lagrangian error metric (Toner
et al. 2001)
(
length of the true trajectory, proxy of D )
Displacement between numerical and observed
drifters normalized by the observed drifters
displacement from to to T. If Ln(T) lt 1,
prediction of position of particles is better
than those given by the knowledge of
characteristics of velocity fields
to T.
).
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Lagrangian error metric
2)
- For large times the information inferred from
our probability maps of dispersion is better than
those given from the characteristics of the
velocity fields. - Worse values for small times
are likely due to or to an inadequate
representation of high frequencies by the OGCM
or to the fact that we use daily mean Eulerian
velocity fields we further smooth energy at high
frequency. -On the other hand the relatively
good skill at large times demonstrate that the
same OGC is successful in representing low
frequency variability of the mean flow.
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• The web site
• clima.casaccia.enea.it/riskmap
• Grazie per la vostra attenzione!

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Select the season
Select the area
Select the kind of map
Select the area
Output