Estimating open boundary conditions in a GCM
Open
boundary conditions are implemented to the west of the Indonesian Archipelago
and near 30°S (Fig. 1). The approach simultaneously optimizes the initial
conditions of the hydrographic fields, surface fluxes, and the open boundary
conditions (temperature, salinity, and horizontal velocities).
The model configuration is similar to Lee and Marotzke (1997)(LM97).
Wind-driven surface currents
The estimated horizontal velocity is plotted in Fig. 1
for level 1 (12.5~m depth). The wind-driven surface currents are readily
identified, like the westward South Equatorial Current between
10°S and 20°S, the eastward Equatorial Counter Current
near the equator, the Somali Current and the anticyclonic Arabian Sea
gyre. Compared to the closed-domain results of LM97,
the estimated velocity field shows a marked improvement near the southern
boundary, with a reasonably strong (for a model of this resolution)
Agulhas current leaving the model domain. The Indonesian
throughflow (ITF) is estimated as 2.7 Sv westward, which is on the low
end of the range of previous estimates.
Figure 1
Meridional overturning
The zonally integrated meridional overturning stream function is plotted in
Fig. 2. A dominant counterclockwise cell is present in the upper
700 m. Its magnitude is 16 Sv and the maximum is located at 12°S and
about 50 m depth. The northward flowing water upwells continuously north of
12°S, then returns to the wind-driven surface Ekman layer. We
have confirmed that this overturning cell is indeed wind-driven, by
separately turning off wind and surface buoyancy forcing of the optimized
solution (following LM97). The shallow overturning carries equatorial surface
water of high temperature southward and dominates the meridional heat
transport; it
is similar both in magnitude and depth with that estimated by LM97,
who used a closed basin. Hence, we conclude that it was not the presence of
closed boundaries that led to the differences between LM97 (weak deep
inflow) and Toole and Warren (1993)(large deep inflow).
Figure 2
Open boundaries vs sponge layers
An optimization is carried out in which the southern and eastern boundaries
are closed, and sponge layers are employed. The meridional overturning
(Fig. 3) shows
a very strong (16 Sv) clockwise overturning cell in the sponge near the
Indonesian Archipelago. A similar problem is seen in the southern sponge
layer, and we attribute these overly large vertical velocities to the
numerical formulation of
the model, most likely the choice of a ``C'' grid. Our standard experiment
(Fig. 2)
shows that the solution with open boundaries behaves much better numerically,
which is yet another argument for eliminating the closed-wall and sponge
boundary conditions.
Figure 3
Freshwater transport
The divergent model freshwater transport (blue line) and the surface flux
(green line) are reasonably well balanced between the northern sponge layer and the
equator, as evidenced by the flat residual curve (red line) in
Fig. 4.
Freshwater transport is weak
in the northern Indian Ocean, reflecting the large differences in P-E
between the evaporative Arabian Sea and the large precipitation over the
Bay of Bengal. Between the equator and about $10^\circ$S, a southward
freshwater transport reaches 0.29 Sv, which is reduced to about zero by the
strong evaporation over the southern subtropics.
The cyan dotted line represents the freshening of the mean mass flux
associated with the Indonesian throughflow (ITF), and the magenta dotted
line is the ITF freshwater transport relative to the ITF section mean
salinity. Both terms are smaller than the residual.
Hence, in our model, the ITF plays a negligible role in the freshwater budget,
counter to widespread expectation but consistent
with Macdonald and Wunsch (1996) who found their global linear inverse
model to be relatively insensitive to widely varying assumptions about
ITF strength.
Figure 4
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