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