Sensitivity to SST ∗

In all models regions of high sensitivity to SST∗ _{are associated with convection}

in the forward model, as perturbations to SST∗ _{in these regions are mixed to a}

greater depth and effect a larger volume of water. In all models convection is most frequent and deepest along the northern boundary of the channel (figure 4.2D-F). There are also shallower bands of convection associated with upwelling south of the front between 49◦_{N and 50}◦_{N in the 0.1}◦ _{models and between 47}◦ _{and 50}◦_N

in the 0.48◦ _{model (figure 4.2D-F). In the undamped 0.1}◦ _{model there is also a}

band of convection at 52◦_{N (figure 4.2E) this is associated with upwelling south}

of the secondary zonal jet (section 2.3.4) . Sensitivity of H to SST∗

The sensitivity of H to SST∗_{, in the 0.48}◦ _{model is highest along the northern}

boundary, and south of the front at 48◦_{N where there is convection in the forward}

model (figure 4.3C). After 278 days both the damped and undamped 0.1◦ _models

have regions of high sensitivity of H to SST∗_{, at the northern boundary and at}

Figure 4.2: Number of timesteps convection occurs averaged over 278 days. Top row (A-C) convection between the top two model layers. Bottom row (D-F) zonally averaged convection. Left (A,D): undamped 0.1◦ _{model, centre (B,E):}

Figure 4.3: Sensitivity of H to the restoring SST∗ _{as calculated by the adjoint}

model at T=0 in a 278 day integration. A: undamped 0.1◦ _{model B: damped 0.1}◦

C: 0.48◦ _{model. Due to the extremely high sensitivity to SST}∗ _{along the northern}

boundary in both 0.1◦ _{models, a different scale is used north of 53.5}◦_{N (black line}

in panels A and B, and 2 sets of numbers along the colour key). Also note the difference in scale between the panels.

discernible band of high sensitivity at 52◦_{N (figure 4.3B). At 52}◦_{N the convection}

is confined to the second model layer (figure 4.2E), so that a SST∗ _perturbation

in this region effects the shallow surface layers only . Sensitivity of D to SST∗

In the damped 0.1◦ _{model there is a band of high negative sensitivity at the}

northern boundary and a band of positive sensitivity at 48◦_{N (figure 4.4B). In the}

undamped model the thermocline depth is 738m and is similar to the maximum depth of convection at the northern boundary (figure 4.2E). An increase in SST∗

at the northern boundary is thus able to reach the depth of the thermocline in the damped 0.1◦ _{model, causing it to deepen (D becomes more negative). The}

band of convection at 50◦_{N is only 150m deep (figure 4.2E), and the integration}

time is insufficient for an increase in SST∗ _{in this region to diffuse down to the}

thermocline, and the resulting warming is all above the level of the thermocline. The sensitivity of D to SST∗ _{is positive throughout the channel in the 0.48}◦

model, including the northern boundary (figure 4.4C). In the 0.48◦ _{model the}

Figure 4.4: Sensitivity of D to SST∗ _{as calculated by the adjoint model after}

278 days of a 690 day integration. A: the undamped 0.1◦ _{model; B: the damped}

0.1◦ _{model; C: the 0.48}◦ _{model. Due to the extremely high sensitivity to SST}∗

along the northern boundary in both 0.1◦ _{models, a different scale is used north}

of 53.5◦_{N (black line in panels A and B and 2 sets of numbers along the colour}

key). Also note the difference in scale between the panels.

(figure 4.2F), so that throughout the entire channel the increase in SST∗ _{all the}

heat uptake due to an increase in SST∗_{is above the thermocline. In the undamped}

0.1◦ _{model there is a band of positive sensitivity at 50}◦_{N but it is less distinct}

than in the damped 0.1◦ _{model. No band of high sensitivity can be seen at the}

northern boundary due to the small scale patches of extremely high sensitivity similar to those seen in the heat content.

Sensitivity of K to SST∗

In the 0.48◦ _{model the sensitivity of K associated with convection at the north-}

ern boundary is negative, where an increase in SST∗ _{would tend to decrease the}

meridional temperature gradient and the available potential energy, and positive at 48◦_{N where an increase in SST}∗ _{would tend to increase the meridional temper-}

ature gradient and the available potential energy. There is no obvious pattern in the sensitivity ofK to SST∗ _{in the damped or undamped 0.1}◦ _{model at 278 days,}

due to patches of extremely high sensitivity at the northern boundary, similar to those seen in the sensitivity of H to the SST∗ _{(figure 4.5A and B).}

Figure 4.5: Sensitivity of K to the restoring SST∗ _{as calculated by the adjoint}

model at T=0 in a 278 day integration. A: undamped 0.1◦ _{model B: damped 0.1}◦

C: 0.48◦ _{model. Due to the extremely high sensitivity to SST}∗ _{along the northern}

boundary in both 0.1◦ _{models, a different scale is used north of 53.5}◦_{N (black line}

in panels A and B, and 2 sets of numbers along the colour key). Also note the difference in scale between the panels.

Sensitivity of A to SST∗

The sensitivity of A to SST∗ _{in the 0.48}◦ _{model is negative everywhere (fig-}

ure 4.6C). Warming the surface of the channel increases the static stability and reduces the available potential energy. This dominates the sensitivity of A to SST∗ _{in the 0.48}◦ _{model, so that the effect of changing the meridional temper-}

ature gradient, which is clearly visible, in the sensitivity of K to SST∗_{, is not}

seen. Again the sensitivity is most negative where there is convection, as the temperature perturbations are mixed to a greater depth effecting a larger volume of water.

In the damped and undamped 0.1◦ _{models there are bands of high positive}

sensitivity of A to SST∗ _{at 50}◦_{N, and bands of negative sensitivity along the}

northern boundary (figure 4.6B). Again these correspond to bands of convection in the forward model. Although all three models have negative sensitivity along the northern boundary, the bands of sensitivity associated with convection due to upwelling at the south of the front are of opposite sign in the 0.1◦ _{models and}

Figure 4.6: Sensitivity of A to SST∗ _{as calculated by the adjoint model after}

278 days of a 690 day integration. A: the undamped 0.1◦ _{model; B: the damped}

0.1◦ _{model; C: the 0.48}◦ _{model. Due to the extremely high sensitivity to SST}∗

along the northern boundary in both 0.1◦ _{models, a different scale is used north}

of 53.5◦_{N (black line in panels A and B and 2 sets of numbers along the colour}

key). Also note the difference in scale between the panels.

gradient and hence the available potential energy. Different processes dominate the sensitivity of the available potential energy to SST∗ _{in the different resolution}

models.