348
Model # Definition
Comments
1
Xo"o,B = 0
Fixed surfacefluxes
2
Xoo,B -t 00
Fixed temperatures
3
XO, /0
Radiative restoring
4
Xl, /0
Diffusive + fixed E-P
5
Xl,/l
MS
6
X3, /1
7
Xl, /3
8
X3, /3
~NSM
Table 2: Definition of the models. The indices on X and ' Y indicate the powers of the heat
and moisture transport laws, respectively.
3.2 Modelling strategy
In the following, 8 combinations of nand m are used in the power laws
for atmospheric transports, (9) and (10). The models are listed in Table
2, along with some comments. Models 1-3 have been characterised above;
model 4 is the simplification to two horizontal boxes of linear diffusive
atmospheric transport, as recently used with oceanic GeMs by Rahmstorf
and Willebrand (1995) and Pierce et al. (1996). Model 5 is the reference
one (MS); Models 6 and 7 use combinations of linear and cubic laws, and
Model 8 is closest to the one used by NSM.
The goal is to characterise the stability of the high-latitude sinking
equilibrium of each model, and to assess how the feedbacks reinforce or
counteract each other. To this end, steady state A of Fig. 2 is subjected to
an initial anomaly in salinity gradient, such that the amount t6..S is taken
out of the polar box and added to the equatorial one. There are at least
three measures of stability that are readily used for this type of experiment,
i) The critical perturbation in salinity, t6..Sc, defined as the minimum necessary to induce a transition to the low-latitude sinking equilibrium.
The smaller t6..Sc, the less stable is the model.
ii) The time it takes a model to make a transition, for a perturbation
greater than t6..Sc• The shorter the transition time, the less stable is
the model.
iii) The time constant of the exponential decay of small (sub critical) perturbations. The slower the decay, the less stable is the model.
Model # Definition
Comments
1
Xo"o,B = 0
Fixed surfacefluxes
2
Xoo,B -t 00
Fixed temperatures
3
XO, /0
Radiative restoring
4
Xl, /0
Diffusive + fixed E-P
5
Xl,/l
MS
6
X3, /1
7
Xl, /3
8
X3, /3
~NSM
Table 2: Definition of the models. The indices on X and ' Y indicate the powers of the heat
and moisture transport laws, respectively.
3.2 Modelling strategy
In the following, 8 combinations of nand m are used in the power laws
for atmospheric transports, (9) and (10). The models are listed in Table
2, along with some comments. Models 1-3 have been characterised above;
model 4 is the simplification to two horizontal boxes of linear diffusive
atmospheric transport, as recently used with oceanic GeMs by Rahmstorf
and Willebrand (1995) and Pierce et al. (1996). Model 5 is the reference
one (MS); Models 6 and 7 use combinations of linear and cubic laws, and
Model 8 is closest to the one used by NSM.
The goal is to characterise the stability of the high-latitude sinking
equilibrium of each model, and to assess how the feedbacks reinforce or
counteract each other. To this end, steady state A of Fig. 2 is subjected to
an initial anomaly in salinity gradient, such that the amount t6..S is taken
out of the polar box and added to the equatorial one. There are at least
three measures of stability that are readily used for this type of experiment,
i) The critical perturbation in salinity, t6..Sc, defined as the minimum necessary to induce a transition to the low-latitude sinking equilibrium.
The smaller t6..Sc, the less stable is the model.
ii) The time it takes a model to make a transition, for a perturbation
greater than t6..Sc• The shorter the transition time, the less stable is
the model.
iii) The time constant of the exponential decay of small (sub critical) perturbations. The slower the decay, the less stable is the model.