352
two choices of moisture transport efficiency 11 in the spinup. The stronger
the Newtonian damping, the less stable are the models, consistent with
the findings of, for example, Zhang et al. (1993), Power and Kleeman
(1994), and Mikolajewicz and Maier-Reimer (1994), who all compare strong
vs. weak Newtonian damping of SST in an ocean GCM, and those of
Rahmstorf and Willebrand (1995) and Pierce et al. (1996), who couple
diffusive, linear energy balance models with fixed moisture transports to
ocean GCMs.
Analytically, the same dependence of model stability on the choice of
n can be shown for infinitesimal perturbations if one considers the steady
limit of eq. (40) for temperature anomalies, which is a good approximation
since typically A »q. It follows that for a given perturbation S',
T' =
2kf3T
s' ~ 2kf3T S'.
A + 2kaT + 2q
A
(45)
For fixed surface freshwater fluxes, the tendency equation (41) for salinity
anomalies gives
S' = -2kaST' + 2(kf3S - q)S'.
(46)
The stabilising first term on the right-hand side of (46) is proportional to
the temperature anomaly, and in the diagnostic limit it is approximately
inversely proportional to the restoring coefficient A and hence to n. All
three stability criteria thus give the same result.
The last feedback this model can exhibit involves the response of the
atmospheric moisture transport to changes in circulation and hence temperatures:
Feedback #4: Atmospheric Moisture Transport Weaker overturning circulation, q' < 0 =} T' > 0 =} Larger meridional temperature contrast
=} Increased atmospheric moisture transport =} Greater surface salinity
contrast =} Even weaker overturning circulation.
This also is a positive, coupled ocean-atmosphere feedback, termed EMT
(for eddy moisture transport) feedback by NSM. It is suppressed by prescribing either SST or SSS. Its effect is demonstrated by Fig. 4, showing
the flow strengths in response to an initial salinity perturbation of -1.6 psu
(polar box) and +1.6 psu (equatorial box) of three models with the same
(linear) atmospheric heat transport, but with moisture transports that are
constant (model #4), linear (#5), or cubic (#7). Model #7 undergoes a
two choices of moisture transport efficiency 11 in the spinup. The stronger
the Newtonian damping, the less stable are the models, consistent with
the findings of, for example, Zhang et al. (1993), Power and Kleeman
(1994), and Mikolajewicz and Maier-Reimer (1994), who all compare strong
vs. weak Newtonian damping of SST in an ocean GCM, and those of
Rahmstorf and Willebrand (1995) and Pierce et al. (1996), who couple
diffusive, linear energy balance models with fixed moisture transports to
ocean GCMs.
Analytically, the same dependence of model stability on the choice of
n can be shown for infinitesimal perturbations if one considers the steady
limit of eq. (40) for temperature anomalies, which is a good approximation
since typically A »q. It follows that for a given perturbation S',
T' =
2kf3T
s' ~ 2kf3T S'.
A + 2kaT + 2q
A
(45)
For fixed surface freshwater fluxes, the tendency equation (41) for salinity
anomalies gives
S' = -2kaST' + 2(kf3S - q)S'.
(46)
The stabilising first term on the right-hand side of (46) is proportional to
the temperature anomaly, and in the diagnostic limit it is approximately
inversely proportional to the restoring coefficient A and hence to n. All
three stability criteria thus give the same result.
The last feedback this model can exhibit involves the response of the
atmospheric moisture transport to changes in circulation and hence temperatures:
Feedback #4: Atmospheric Moisture Transport Weaker overturning circulation, q' < 0 =} T' > 0 =} Larger meridional temperature contrast
=} Increased atmospheric moisture transport =} Greater surface salinity
contrast =} Even weaker overturning circulation.
This also is a positive, coupled ocean-atmosphere feedback, termed EMT
(for eddy moisture transport) feedback by NSM. It is suppressed by prescribing either SST or SSS. Its effect is demonstrated by Fig. 4, showing
the flow strengths in response to an initial salinity perturbation of -1.6 psu
(polar box) and +1.6 psu (equatorial box) of three models with the same
(linear) atmospheric heat transport, but with moisture transports that are
constant (model #4), linear (#5), or cubic (#7). Model #7 undergoes a