Ocean/ice shelf interface

The melt rate in the model is governed by two factors, the thermal driving and the friction velocity that are used in the parameterisation of turbulent heat and fresh water transfer at the ocean/ice shelf interface, described by Holland and Jenkins [1999]. The thermal driving is defined by Holland and Jenkins [1999] as:

T_∗ =TM −TB, (3.1)

where TM is the in situ temperature at the top layer of the model beneath the

ice shelf and TB is the in situ freezing temperature within the ocean/ice bound- ary layer (pressure dependent). In this study, TB is calculated assuming that the pressure and the salinity at the top layer of the model are the same as within the ocean/ice boundary, which is similar to other studies such as Gwyther et al. [2016] and Dansereau et al. [2013]. The friction velocity is directly linked with the current velocity beneath the ice shelf and is calculated as follows:

u_∗ =√Cd UM, (3.2)

where Cd = 0.005 is the dimensionless drag coefficient, spatially constant over the entire ice shelf andUM is the model top layer velocity (m s−1) directly underneath

the ice shelf, which is known to be an important driver of the basal melting [Gwyther et al. 2016; Dansereau et al. 2013].

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The pattern of the ice shelf basal melting for the ‘ref’ simulation (Figure 3.4a – solid line) shows near zero melting at the grounding line, maximum melting at the lower half of the ice shelf (about 40 km north of the grounding line) and refreezing at the ice shelf front. The minimum melt rate (Figure 3.4a) is correlated with the maximum thermal driving (Figure 3.4b) and the minimum value of the friction velocity (Figure 3.4c). The low friction velocity near the southern point of the domain explains the near zero melting while the thermal driving is high. The friction velocity increases along the ice shelf as the ISW plume rises and the thermal driving decreases as glacial meltwater is released into the ocean. The melt rate reaches the maximum value when both thermal driving and friction velocity reach an equilibrium (Figure 3.4d).

It is interesting to note that for the ‘no melt’ simulation the thermal driving is linear along the ice shelf base. For this simulation, no heat and salt fluxes (no melt) are prescribed beneath the ice shelf, so there is no cooling or freshening of the ocean by the ice shelf. However, thermal driving and friction velocity can be calculated. The thermal driving is linear following the change in local freezing temperature due to the change in pressure (Figure 3.4b). However, the friction velocity along the ice shelf draft does not increase linearly (Figure 3.4c), in particular for the upper half of the ice shelf, where T_∗u_∗ is maximum at about 60 km (Figure 3.4d). In parallel,

T_∗ almost doubles in the ‘no melt’ simulation within the ice shelf cavity compared to the ‘ref’ simulation, as no glacial meltwater is released from the melting of the ice shelf to cool the water column within the ice shelf cavity.

The ‘strong’ simulation is similar to the ‘ref’ simulation and the averages of melt rate, T_∗ and u_∗ are about the same, 0.76 m yr−1 _{and 0.78 m yr}−1 _{respectively for}

the melt rate (Table 3.3). However, the ‘low’ forcing experiment is very different with an area-averaged melt rate reaching 8.45 m yr−1 _{(990% higher than the ‘ref’}

simulation). The maximum melt rate is at mid ice shelf (about 50 km from the grounding line) and then plateaus until the ice shelf front, while the thermal driving is maximum at the grounding line and the friction velocity is at its minimum (cor- responding to the minimum area averaged melt rate). The 50 km mark corresponds to an ice draft of about 400 m depth, which is also the depth of the warmest layer from the inflowing mCDW that interacts with the ice shelf (Figure 3.2l).

The ‘low’ forcing experiment is more sensitive to thermal driving than to the friction velocity. The averaged friction velocity in the ‘low’ simulation is only doubled

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compared to the ‘ref’, while the thermal driving is almost 300% higher and the area-averaged melt rate is about 11 times higher (990%, Table 3.3). Gwyther et al. [2016] use the same model, but with a different set up (e.g. wider domain, closed boundary, Coriolis parameter) to perform similar studies focused on the ice shelf melting and its driver for different ocean conditions. They also found that the melt rate distribution in a hot cavity environment (comparable to the ‘low’ forcing simulation here) is more correlated with thermal driving, while in a cold cavity environment (comparable to the ‘ref’ and ‘strong’ forcing simulations here) the melt rate distribution is mostly driven by the ocean circulation.

Table 3.3: Area-averaged melt rate (m), averaged friction velocity (u_∗) and averaged thermal driving (T_∗) along the base of the ice shelf for each experiment. The percentage of change for each simulation compared to the ‘ref’ simulation is given in square brackets. Simulation m (m yr−1_{) u} ∗ (m s−1) T∗ (◦C) Ref 0.78 3.6 e−3 0.15 No melt 0.00 [ - ] 1.3 e−3 _{[-60%] 0.25 [+67%]} Strong 0.76 [-3%] 3.5 e−3 [-3%] 0.15 [ 0%] Low 8.45 [990%] 7.5 e−3 [+108%] 0.59 [293%]

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Figure 3.4: Ice shelf basal melt rate (a), thermal driving (T_∗: b), friction velocity (u_∗: c) and T_∗u_∗ (d) along the ice shelf base for each experiment. As for Figure 3.3 the ‘ref’ simulation is represented with the solid line, ‘no melt’ with grey dots, ‘strong’ with squares and ‘low’ simulation with triangles.