base of the mixed layer modify the properties of
the waters that are released into the thermocline
(subducted). We then present our best description
of ocean surface density from post-WOCE knowledge of the global Sea Surface Temperature (SST)
and Sea Surface Salinity (SSS). A new set of surface
fluxes appropriate for the WOCE period is then
compiled. Finally, we apply the water mass transformation formalism to these data sets, and produce estimates of water mass transformation in
various oceans and subregions of the oceans.
We will compare our results with those of Speer
et al. (1995a), who used different flux and density
fields.
5.1.2 Theory of surface water mass
transformation
5.1.2.1 The diapycnal circulation
In a pioneering work, Walin (1982) presented a
view of the circulation in terms of the flow of water
across isotherms being driven by heating and cooling. This work can be generalized to link the diapycnal flow to diabatic forcing of (potential) density
(Speer and Tziperman, 1992; Tziperman, 1986),
and indeed to link flow across surfaces of any property to forcing of that property (Viudez, 2000). In
principle, the water mass formation rate – the convergence of the diapycnic flow – may be diagnosed
from only the diabatic forcing without requiring
any additional information about the circulation or
dynamics.
The total globally integrated diapycnal flow
across any isopycnal must be zero in the time
mean. Diapycnal flow in the mixed layer driven by
surface forcing, lateral mixing, and entrainment
must be balanced by diapycnal flow in the thermocline driven by diffusion, or possibly by opposite
diapycnal flow in the mixed layer in different parts
of the global ocean.
In this section we focus on the surface water
mass transformation: that is the diapycnal flow in
the surface mixed layer, which creates the water
masses that are mixed by the diffusive processes in
the thermocline. Model diagnostics (Marshall et al.,
1999; Nurser et al., 1999) and scaling analysis
(Garrett and Tandon, 1997; Nurser et al., 1999;
Tandon and Zahariev, 2000) seem to show that
the surface fluxes dominate the entrainment and
lateral mixing in setting this diapycnal flow, at
least for the denser waters.
The formation rate of water masses of various
densities in the North Atlantic was estimated from
climatological surface heat and freshwater fluxes
by Speer and Tziperman (1992), while Speer et al.
(1995a) considered global formation rates. Garrett
et al. (1995) considered transformation rates in
a simple model of the Red Sea, while Tziperman
and Speer (1994) studied transformation rates in
the Mediterranean. Recently, Marsh (2000) has
looked at the year-to-year variability of surface
water mass transformation in the North Atlantic.
Speer extended Walin’s theory to consider formation rates in T–S space, and found (Speer, 1993;
Speer et al., 1995a) that the surface fluxes implied
core water mass properties consistent with observations of mode waters revealed in Worthington’s
volumetric census of T and S (Worthington, 1976,
1981).
5.1.2.2 Water mass formation and diapycnal
volume fluxes
Consider the volume sandwiched between the
isopycnal surfaces with potential densities and
;⌬. We consider a limited area of the ocean,
such as the North Atlantic, with an open boundary (Fig. 5.1.1a).
Strictly speaking, it is mass rather than volume
that is conserved (Viudez, 2000). However, if the
Boussinesq approximation is made and the ocean
is assumed to be incompressible, we can consider
volume rather than mass budgets, and define
water mass formation using a volume budget of a
density layer. We write ⌬V as the volume of fluid
with density between and ;⌬, ⌬ the volume
flux of fluid with density between and ;⌬
out of the domain, and G(), G(;⌬) the diapycnal volume flux of fluid crossing the and ;⌬
isopycnals respectively. Note that Garrett et al.
(1995) and Speer et al. (1995a) denote this term
by A. The sign convention is (Fig. 5.1.1a) that G is
positive if directed towards increasing .
By incompressibility, the volume budget of the
control volume bounded by and ;⌬ isopycnals, the ocean surface, and the open boundary is
;⌬
:G()9G(;⌬); ͵ outcrop 0
91
F in dA
(5.1.1)
where ͵ outcrop 0
91
F in dA is the net surface influx (of
volume) at the surface over the outcrop, with 0
Ѩ⌬V
ᎏ
Ѩt
SECTION 5 FORMATION AND TRANSPORT OF WATER MASSES
318
the waters that are released into the thermocline
(subducted). We then present our best description
of ocean surface density from post-WOCE knowledge of the global Sea Surface Temperature (SST)
and Sea Surface Salinity (SSS). A new set of surface
fluxes appropriate for the WOCE period is then
compiled. Finally, we apply the water mass transformation formalism to these data sets, and produce estimates of water mass transformation in
various oceans and subregions of the oceans.
We will compare our results with those of Speer
et al. (1995a), who used different flux and density
fields.
5.1.2 Theory of surface water mass
transformation
5.1.2.1 The diapycnal circulation
In a pioneering work, Walin (1982) presented a
view of the circulation in terms of the flow of water
across isotherms being driven by heating and cooling. This work can be generalized to link the diapycnal flow to diabatic forcing of (potential) density
(Speer and Tziperman, 1992; Tziperman, 1986),
and indeed to link flow across surfaces of any property to forcing of that property (Viudez, 2000). In
principle, the water mass formation rate – the convergence of the diapycnic flow – may be diagnosed
from only the diabatic forcing without requiring
any additional information about the circulation or
dynamics.
The total globally integrated diapycnal flow
across any isopycnal must be zero in the time
mean. Diapycnal flow in the mixed layer driven by
surface forcing, lateral mixing, and entrainment
must be balanced by diapycnal flow in the thermocline driven by diffusion, or possibly by opposite
diapycnal flow in the mixed layer in different parts
of the global ocean.
In this section we focus on the surface water
mass transformation: that is the diapycnal flow in
the surface mixed layer, which creates the water
masses that are mixed by the diffusive processes in
the thermocline. Model diagnostics (Marshall et al.,
1999; Nurser et al., 1999) and scaling analysis
(Garrett and Tandon, 1997; Nurser et al., 1999;
Tandon and Zahariev, 2000) seem to show that
the surface fluxes dominate the entrainment and
lateral mixing in setting this diapycnal flow, at
least for the denser waters.
The formation rate of water masses of various
densities in the North Atlantic was estimated from
climatological surface heat and freshwater fluxes
by Speer and Tziperman (1992), while Speer et al.
(1995a) considered global formation rates. Garrett
et al. (1995) considered transformation rates in
a simple model of the Red Sea, while Tziperman
and Speer (1994) studied transformation rates in
the Mediterranean. Recently, Marsh (2000) has
looked at the year-to-year variability of surface
water mass transformation in the North Atlantic.
Speer extended Walin’s theory to consider formation rates in T–S space, and found (Speer, 1993;
Speer et al., 1995a) that the surface fluxes implied
core water mass properties consistent with observations of mode waters revealed in Worthington’s
volumetric census of T and S (Worthington, 1976,
1981).
5.1.2.2 Water mass formation and diapycnal
volume fluxes
Consider the volume sandwiched between the
isopycnal surfaces with potential densities and
;⌬. We consider a limited area of the ocean,
such as the North Atlantic, with an open boundary (Fig. 5.1.1a).
Strictly speaking, it is mass rather than volume
that is conserved (Viudez, 2000). However, if the
Boussinesq approximation is made and the ocean
is assumed to be incompressible, we can consider
volume rather than mass budgets, and define
water mass formation using a volume budget of a
density layer. We write ⌬V as the volume of fluid
with density between and ;⌬, ⌬ the volume
flux of fluid with density between and ;⌬
out of the domain, and G(), G(;⌬) the diapycnal volume flux of fluid crossing the and ;⌬
isopycnals respectively. Note that Garrett et al.
(1995) and Speer et al. (1995a) denote this term
by A. The sign convention is (Fig. 5.1.1a) that G is
positive if directed towards increasing .
By incompressibility, the volume budget of the
control volume bounded by and ;⌬ isopycnals, the ocean surface, and the open boundary is
;⌬
:G()9G(;⌬); ͵ outcrop 0
91
F in dA
(5.1.1)
where ͵ outcrop 0
91
F in dA is the net surface influx (of
volume) at the surface over the outcrop, with 0
Ѩ⌬V
ᎏ
Ѩt
SECTION 5 FORMATION AND TRANSPORT OF WATER MASSES
318