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DYNAMICAL OCEANOGRAPHY
(2.3) Freshwater balance
Consider the freshwater balance for a thin layer of seawater. The salinity of the
water changes through evaporation (E) and precipitation (P ). The dimension
of E and P is m 3 s −1 per m 2 and hence ms −1 .LetF w be the vertical flux of salt
at the bottom of the layer, which has a salinity S and let F S be the freshwater
flux through the ocean-atmosphere surface.
a. Show that the balance of freshwater can be written as
E − P + F w (1 − S)=0
b. Show that the salt balance can be written as
F w S = F S
c. Derive that, to a good approximation, the flux F S can be written as
F S =(E − P )S
(2.4) Gulf Stream
Warm western boundary currents such as the Gulf Stream play an important
role in the climate system because they contribute to the meridional heat transport. The Gulf Stream is about 100 km wide, has a depth of 500 m and has a
mean speed of 1 ms −1 .
a. Provide an estimate of the volume transport of the Gulf Stream (in Sv).
The meridional heat transport due to the Gulf Stream depends on the temperature difference between the warm water flowing northward and the cooler
water flowing southward.
b. Provide an estimate of this temperature difference and of the meridional
heat transport associated with the Gulf Stream.
(2.5) Mediterranean Outflow
Consider a flow over a sill such as that in the Gibraltar Strait. West of the sill,
the water has a salinity S a =36.2 ppt and east of the sill (in the Mediterranean
basin), the salinity is S b =3 8 .4 ppt. The volume flux of the surface transport
of the Atlantic to Mediterranean is Q a , and the reverse transport at depth has
DYNAMICAL OCEANOGRAPHY
(2.3) Freshwater balance
Consider the freshwater balance for a thin layer of seawater. The salinity of the
water changes through evaporation (E) and precipitation (P ). The dimension
of E and P is m 3 s −1 per m 2 and hence ms −1 .LetF w be the vertical flux of salt
at the bottom of the layer, which has a salinity S and let F S be the freshwater
flux through the ocean-atmosphere surface.
a. Show that the balance of freshwater can be written as
E − P + F w (1 − S)=0
b. Show that the salt balance can be written as
F w S = F S
c. Derive that, to a good approximation, the flux F S can be written as
F S =(E − P )S
(2.4) Gulf Stream
Warm western boundary currents such as the Gulf Stream play an important
role in the climate system because they contribute to the meridional heat transport. The Gulf Stream is about 100 km wide, has a depth of 500 m and has a
mean speed of 1 ms −1 .
a. Provide an estimate of the volume transport of the Gulf Stream (in Sv).
The meridional heat transport due to the Gulf Stream depends on the temperature difference between the warm water flowing northward and the cooler
water flowing southward.
b. Provide an estimate of this temperature difference and of the meridional
heat transport associated with the Gulf Stream.
(2.5) Mediterranean Outflow
Consider a flow over a sill such as that in the Gibraltar Strait. West of the sill,
the water has a salinity S a =36.2 ppt and east of the sill (in the Mediterranean
basin), the salinity is S b =3 8 .4 ppt. The volume flux of the surface transport
of the Atlantic to Mediterranean is Q a , and the reverse transport at depth has