372
gradient anomaly shows a more interesting behavior (Fig. 9d), which can
be understood as follows. Since T and S are both positive for all cases
considered here, ' v, > ',0' always and hence v /,0 < -1 in eq. (86). At
t = 0, the square bracket is zero also, and the initial spiciness anomaly
has the same sign as the initial salinity anomaly. As the exponential in the
square bracket decays, however, v /,0 is multiplied by a number approaching
unity, and the term in curly brackets has a zero crossing, which is readily
shown to occur at tv,!, given by
1
elf + {38
tv 1 = -,_,In
T ·
,
2 q
2a
(87)
There must be a maximum in spiciness deviation from equilibrium, of sign
opposite to the initial anomaly, which occurs at
1
aT + (38
tv2 = -,_,In
.
,
2q
aT
(88)
The time for the zero crossing is positive only if aT < (38, i.e., for
low-latitude sinking: The spiciness anomaly decays nearly linearly and
overshoots; the zero crossing occurs after 75 years for the parameters from
Table 1, according to eq. (87) and, consistently, Fig. 9d. An extremum
is reached after 800 years [again consistently from eq. (88) and Fig. 9d),
and finally the spiciness anomaly decays exponentially (not shown). For
high-latitude sinking, the initial perturbation grows linearly and reaches
an extremum after typically 50-100 years, before it decays.
It is not clear how relevant the large excursions of model #1 about its
low-latitude sinking state are. The assumption of fixed surface fluxes is very
strong; in addition, Marotzke (1990) and Marotzke and Willebrand (1991)
discussed how wind forcing in GCMs tends to eliminate the counterparts of
low-latitude sinking states found in box models. On the other hand, Zorita
and Frankignoul (1996) have recently identified modes of North Atlantic
variability in a coupled GCM, on a timescale of decades, with no significant associated response of surface heat flux to SST anomalies. Model
#1 might thus be applicable in some cases. Also, the Atlantic overturning circulation can be viewed as two back-to-back Stommel box models
(Welander, 1986), with the Northern Hemisphere showing thermally direct
circulation and the Southern Hemisphere thermally indirect circulation.
One can then speculate that the neutral model contributes significantly
to drift and variability in the Southern Hemisphere and hence the entire
Atlantic thermohaline circulation.
gradient anomaly shows a more interesting behavior (Fig. 9d), which can
be understood as follows. Since T and S are both positive for all cases
considered here, ' v, > ',0' always and hence v /,0 < -1 in eq. (86). At
t = 0, the square bracket is zero also, and the initial spiciness anomaly
has the same sign as the initial salinity anomaly. As the exponential in the
square bracket decays, however, v /,0 is multiplied by a number approaching
unity, and the term in curly brackets has a zero crossing, which is readily
shown to occur at tv,!, given by
1
elf + {38
tv 1 = -,_,In
T ·
,
2 q
2a
(87)
There must be a maximum in spiciness deviation from equilibrium, of sign
opposite to the initial anomaly, which occurs at
1
aT + (38
tv2 = -,_,In
.
,
2q
aT
(88)
The time for the zero crossing is positive only if aT < (38, i.e., for
low-latitude sinking: The spiciness anomaly decays nearly linearly and
overshoots; the zero crossing occurs after 75 years for the parameters from
Table 1, according to eq. (87) and, consistently, Fig. 9d. An extremum
is reached after 800 years [again consistently from eq. (88) and Fig. 9d),
and finally the spiciness anomaly decays exponentially (not shown). For
high-latitude sinking, the initial perturbation grows linearly and reaches
an extremum after typically 50-100 years, before it decays.
It is not clear how relevant the large excursions of model #1 about its
low-latitude sinking state are. The assumption of fixed surface fluxes is very
strong; in addition, Marotzke (1990) and Marotzke and Willebrand (1991)
discussed how wind forcing in GCMs tends to eliminate the counterparts of
low-latitude sinking states found in box models. On the other hand, Zorita
and Frankignoul (1996) have recently identified modes of North Atlantic
variability in a coupled GCM, on a timescale of decades, with no significant associated response of surface heat flux to SST anomalies. Model
#1 might thus be applicable in some cases. Also, the Atlantic overturning circulation can be viewed as two back-to-back Stommel box models
(Welander, 1986), with the Northern Hemisphere showing thermally direct
circulation and the Southern Hemisphere thermally indirect circulation.
One can then speculate that the neutral model contributes significantly
to drift and variability in the Southern Hemisphere and hence the entire
Atlantic thermohaline circulation.