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R. Sorgente et al.: Seasonal variability in the Central Mediterranean Sea circulation
where C is the coefficient of Smagorinsky diffusivity. This
parameter is nondimensional and is known as the Horcon pa-
rameter (Mellor, 1998). In this application C = 0.1.
The derivation of the sigma coordinate equations, from
(x, y, z, t) to (x ,y ,σ ,t ) coordinates where:
x = x, y = y, σ = z−η ,t = t, (9)
H +η
can be found in Blumberg and Mellor (1987). In Eq. (9),
H (x,y) is the bottom topography and η(x, y, t) is the free
surface elevation. The main advantage of the σ system is that
a smooth representation of bottom topography is obtained,
and the use of the sigma coordinate system is a useful at-
tribute in domains with significant variability in the topogra-
phy, such as in the Central Mediterranean.
3.2 The model domain
It extends from 9.0◦ E to 17.1◦ E and from 31.2◦ N to 39.5◦ N
(Fig. 2). The grid resolution is chosen to be 1/20◦ for a better
representation of the mesoscale eddy activity and of the ex-
changes through the Strait of Sicily. This resolution is below
the first internal Rossby radius of deformation, about 10 km
long (Send et al., 1999). The number of grid points used
are 163 (x-direction), 168 (y-direction) and 22 sigma levels
in the vertical. The sigma levels are bottom following, with
logarithmic distribution near the surface. The external time
step is set to 8 s with an internal integration every 240 s.
3.3 Bathymetry and initial condition
The model bathymetry is based on the U.S. Navy bathymet-
ric database DBDB1 with bilinear interpolation of depth data
(mapped at 1/60◦). Additional light smoothing is applied to
reduce the sigma coordinate pressure gradient error (Mellor
et al., 1994). The resulting topography is shown in Fig. 2.
The maximum depth is about 4000 m. The model was initial-
ized with the temperature and salinity fields from the eight-
year long OGCM perpetual year simulation (Demirov and
Pinardi, 2003). It starts from the first of January with zero
initial velocity.
3.4 Lateral open boundary conditions
The model has three open boundaries located in the south-
ern Tyrrhenian Sea (along 39.5◦ N), in the Sardinia Chan-
nel (along 9◦ E) and in the open Ionian Sea (along 17.1◦ E).
At the lateral open boundaries the regional model receives
information of temperature, salinity and velocity fields by
one-way off-line nesting to the coarse resolution basin scale
model in which it is embedded. The grid-nesting ratio be-
tween the two models is 2.5. The one-way nesting enables
the transmission of information at the interconnecting bound-
aries from the coarse resolution grid to the fine resolution
(nested) grid at each external time step, using a linear inter-
polation in time of 10-day averaged coarse model fields. On
the vertical plane, the coarse and fine resolution models have
different vertical coordinate systems. The coarse resolution
303
model uses a z-level discretisation model, while the high res-
olution model uses a sigma-coordinate system. The main ad-
vantage with the latter vertical discretisation is that a smooth
representation of the bottom topography can be obtained. In
a recent study, Bell (1997) has shown that, especially with
finer grids, the step structure of a z-level model can lead to
vorticity errors and consequently, to errors in the barotropic
component of the flow, leading to rather large temperature er-
rors. In the sigma-coordinate system, the top numerical level
(k = 1) follows the free sea surface, while the lowest numer-
ical level (k = kb) follows the bottom depth; for 1 < k < kb
the distance between the levels is fixed in proportion to each
other, independent of elevation or depth.
At the open boundaries, the normal and tangential total
velocity components are fully specified by a bilinear interpo-
lation of the 10-day averaged coarse resolution model fields
(MOM) onto the high resolution model grid (POM), then
Upom = Umom (10)
with the exception of the eastern open boundary, where the
following radiation condition is used:
∂ Upom ± ce ∂ Upom = 0; ce = gH . (11)
∂t ∂x
Since the coarse resolution model is a rigid-lid model, the
barotropic normal velocities need to be adjusted to ensure
conservation of volume. They are specified at each external
time step by the following equation:
H (12)
U pom = U mom H + η ,
where U pom is the vertically integrated velocity in the high
resolution model, U mom is the vertical integral of the veloc-
ity prescribed from the coarse model, and η is the free sur-
face elevation. The matching of the fields at the common
boundaries between the two models must also ascertain that
the mass transport at each respective open boundary is con-
strained to remain equal to that prescribed from the coarse
model. This means that the total velocity component on the
boundary of the high resolution grid needs to be adjusted so
as to preserve the net transport across the boundary as speci-
fied on the coarse grid. Then,
l2 η Uptootmdzdl = l2 η Umtoot m d zd l .
(13)
l1 Hcoarse l1 Hhigh
The free surface elevation is not nested (zero gradient bound-
ary condition). However, the free surface coarse resolution
field enters indirectly through the specification of the bound-
ary condition for the normal barotropic velocity component
(Eq.12).
An upstream advection scheme is used for temperature and
salinity:
∂ (θ, S) ∂ (θ, S) (14)
+ U = 0.
∂t ∂x
In the case of outflow through the open boundaries, temper-
ature and salinity are prescribed from the coarse resolution