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S h is the salinity just below the OML, k is the horizontal diffusivity coefficient
(k * 2,000 ms -2 ). The total entrainment term must be treated differently in case of
upward or downward entrainment, so it is multiplied by a step function C in Eq. ( 1 ).
Indeed, when additional water is included into the mixed layer, its properties are affected
by mixing with the deeper layer: C(w e ) = w e if w e [ 0. On the contrary, if water is
removed from the mixed layer, the properties of the remaining water are conserved and
only its depth h can change: C(w e ) = 0ifw e \ 0. The vertical processes are conveniently
represented by a single entrainment term, consisting of the vertical Ekman advection and
the OML conditions.
The first term in the right-hand side of Eq. ( 1 ) is the net freshwater flux. The impact of
this flux on the surface water strongly depends on the salinity itself. Moreover, SSS has no
direct feedback on the surface flux. These particularities have important consequences on
the salt budget and on the duration of SSS anomalies. The second term is the horizontal
advection of salinity by surface currents that can be separated into a wind-induced com-
ponent, the Ekman transport, and the geostrophic current. Ekman transport is due to wind
friction on the sea surface, which is rotated by the Coriolis force as it penetrates in depth.
The Ekman layer depth is systematically lower than the mixed layer depth, because both
increases with the wind stress, although the depth of the mixed layer also deepens in
response to other processes. Thus, the Ekman transport occurs entirely in the OML. In
addition, the geostrophic current that arises from the balance between the horizontal
pressure force and the Coriolis force can usually be considered constant, with the mixed
layer resulting from the homogeneous density structure.
The value of the SMOS SSS at a fixed point, S(t, r), is obtained by averaging individual
SMOS swath SSS measurements over a considerable time interval (t - s/2, t ? s/2), say
10 days, which is enough to filter out noise in the SSS. S uppose that the climate mean, or
norm, of this SSS (provided by climatology) is S ð t ; r Þ¼ S o ð t ; r Þ . In the following, we
define the SSS anomaly as the departure of the SSS from the norm:
DS ð t ; r Þ¼ S ð t ; r Þ S o ð t ; r Þ
Following approaches traditionally used for studying large-area SST anomalies (Piterbarg,
and Ostrovskii 1997 ), a formal definition can be introduced for the large-area SSS
anomalies. For example, large-area and large-amplitude SSS anomaly comprises the
connected components of the set:
x ; y Þ : DS ð t ; r j j [ S T g
where r = (x, y) and S T is a threshold that can be taken either as a fixed salinity value, for
example, 0.2 pss or as a function of the standard deviation of SSS anomalies, r S , for
example, 0.5 r S . This choice for the threshold depends on the magnitude of the anomaly of
interest.
In the tropical Atlantic, Michel et al. ( 2007 ) and Yu ( 2011 ) have shown that the
dominant terms of the mixed layer salinity balance are horizontal advection by Ekman and
geostrophic currents and the atmospheric forcing fluxes (E - P - R). In that context, the
salinity balance equation in the OML can be simplified as follows:
o S
ot
ð E P R Þ S
h
~r S
ð 2 Þ
Using OSCAR surface current products (which comprise contributions of both Ekman and
geostrophic currents), the horizontal salt advection term ~r S can be deduced from
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