# 7.2. Oceanic forcing¶

## 7.2.1. Sea level¶

The sea level surrounding the simulated ice sheet determines the land area available for glaciation. The level \(z=0\) corresponds to the mean sea level at present day, and the SICOPOLIS variable `z_sl`

denotes the sea level relative to this reference.

Two different options for prescribing the sea level are available, selected in the run-specs headers by the parameter `SEA_LEVEL`

:

`1`

: Temporally constant sea level z_sl, specified by the parameter`Z_SL0`

.`3`

: Time-dependent sea level (e.g., reconstruction from data) from an input file (ASCII or NetCDF), specified by the parameter`SEA_LEVEL_FILE`

.

Both options assume a spatially constant sea level. However, the variable `z_sl`

is actually a 2D field, so that SICOPOLIS can handle in principle a spatially variable sea level as well.

## 7.2.2. Ice-shelf basal melting¶

The parameter `FLOATING_ICE_BASAL_MELTING`

in the run-specs headers allows specifying the melting rate under ice shelves (floating ice), \(a_\mathrm{b}\). For all terrestrial ice sheets, the following options can be chosen:

`1`

: Constant values for the continental shelf (\(a_\mathrm{b}^\mathrm{c.s.}\)) and the abyssal ocean (\(a_\mathrm{b}^\mathrm{a.o.}\)), respectively:(7.5)¶\[\begin{split}a_\mathrm{b} = \left\{ \begin{array}{ll} a_\mathrm{b}^\mathrm{c.s.} & \mbox{if}\;\; z_\mathrm{l} > z_\mathrm{abyss}\,, \\ a_\mathrm{b}^\mathrm{a.o.} & \mbox{if}\;\; z_\mathrm{l} \le z_\mathrm{abyss}\,, \end{array} \right.\end{split}\]where \(z_\mathrm{l}\) is the seabed (lithosphere surface) elevation and \(z_\mathrm{abyss}\) the threshold seabed elevation that separates the continental shelf from the abyssal ocean. The parameters \(a_\mathrm{b}^\mathrm{c.s.}\), \(a_\mathrm{b}^\mathrm{a.o.}\) and \(z_\mathrm{abyss}\) can be set in the run-specs headers (

`QBM_FLOAT_1`

,`QBM_FLOAT_3`

and`Z_ABYSS`

, respectively).`4`

: Local parameterization as a function of the oceanic thermal forcing \(T_\mathrm{f}=T_\mathrm{oc}-T_\mathrm{b}\) (difference between the ocean temperature \(T_\mathrm{oc}\) and the ice-shelf basal temperature \(T_\mathrm{b}\)):(7.6)¶\[a_\mathrm{b} = \Omega\,T_\mathrm{f}^\alpha\,.\]The parameters \(T_\mathrm{oc}\), \(\Omega\) and \(\alpha\) can be set in the run-specs headers (

`TEMP_OCEAN`

,`OMEGA_QBM`

and`ALPHA_QBM`

, respectively). The ice-shelf basal temperature is computed as(7.7)¶\[T_\mathrm{b} = -\beta_\mathrm{sw} d - \Delta{}T_\mathrm{m,sw}\,,\]where \(d\) is the draft (depth of the ice-shelf base below sea level), \(\beta_\mathrm{sw}=7.61\times{}10^{-4}\,\mathrm{K\,m^{-1}}\) the Clausius-Clapeyron gradient and \(\Delta{}T_\mathrm{m,sw}=1.85^\circ\mathrm{C}\) the melting-point lowering due to the average salinity of sea water.

For the Antarctic ice sheet, two additional options are available:

`5`

: Sector-wise, local parameterization as a function of the thermal forcing (Greve and Galton-Fenzi [34]). This parameterization is modified after Beckmann and Goosse [4], with a linear dependence on the thermal forcing \(T_\mathrm{f}\) and an additional power-law dependence on the draft \(d\):(7.8)¶\[a_\mathrm{b} = \frac{\rho_\mathrm{sw}c_\mathrm{sw}\gamma_\mathrm{t}}{\rho L} \,\Omega\,\bigg(\frac{d}{d_0}\bigg)^\alpha \,T_\mathrm{f}\,,\]where \(\rho\) and \(\rho_\mathrm{sw}\) are the ice and sea-water densities, \(L\) is the latent heat of melting (all defined in the run-specs header), \(c_\mathrm{sw}=3974\,\mathrm{J\,kg^{-1}\,K^{-1}}\) is the specific heat of sea water, \(\gamma_\mathrm{t}=5\times{}10^{-5}\,\mathrm{m\,s^{-1}}\) is the exchange velocity for temperature and \(d_0=200\,\mathrm{m}\) is the reference draft.

The parameters \(\Omega\) and \(\alpha\) result from a tuning procedure for eight different sectors, using observed present-day melt rates as a target (as explained in the main part and appendix of Greve and Galton-Fenzi [34]). For the thermal forcing \(T_\mathrm{f}\), \(T_\mathrm{oc}\) is chosen for each sector as the sector-averaged temperature at 500 metres depth just outside the ice-shelf cavity (computed with data from the World Ocean Atlas 2009 [46]), while \(T_\mathrm{b}\) is computed by Eq. (7.7).

`6`

: “ISMIP6 standard approach”: Sector-wise, non-local quadratic parameterization for the 18 IMBIE-2016 sectors (Rignot and Mouginot [53], The IMBIE Team [61]), where the two sectors feeding the Ross ice shelf and the two sectors feeding the Filchner–Ronne ice shelf are combined, leaving 16 distinct sectors (Jourdain et al. [42], Seroussi et al. [56]). The parameterization depends on the local thermal forcing \(T_\mathrm{f}\) and the sector-averaged thermal forcing \(\langle{}T_\mathrm{f}\rangle{}_\mathrm{sector}\) as follows:(7.9)¶\[a_\mathrm{b} = \gamma_0 \bigg(\frac{\rho_\mathrm{sw}c_\mathrm{sw}}{\rho L}\bigg)^2 \, (T_\mathrm{f} + \delta{}T_\mathrm{sector}) \, |\langle{}T_\mathrm{f}\rangle{}_\mathrm{sector} + \delta{}T_\mathrm{sector}|\,,\]where \(\rho\), \(\rho_\mathrm{sw}\), \(L\) and \(c_\mathrm{sw}\) are defined as in Eq. (7.8). The coefficient \(\gamma_0\), similar to an exchange velocity, and the sectorial temperature offsets \(\delta{}T_\mathrm{sector}\) are obtained by calibrating the parameterization against observations (see Jourdain et al. [42]).

The thermal forcing at the ice–ocean interface is derived by extrapolating the oceanic fields from GCMs into the ice-shelf cavities. Following the ISMIP6-Antarctica protocol, it must be provided as NetCDF input files that contain for each year the mean-annual, 3D thermal forcing for the entire computational domain. Thereby, this option allows prescribing a time-dependent thermal forcing (which is currently not the case for the other options). For the detailed parameter settings, see the description in the run-specs headers.

For all cases, an additional scaling factor \(S_\mathrm{w}\) can be applied (\(a_\mathrm{b}\rightarrow{}S_\mathrm{w}\,a_\mathrm{b}\)), defined as

This factor reduces the melting rate close to the grounding line where the water column \(H_\mathrm{w}\) is thin. The parameter \(H_\mathrm{w,0}\) can be set in the run-specs headers (`H_W_0`

). A value recommended by Asay-Davis et al. [2] is \(75\,\mathrm{m}\), while Gladstone et al. [18] used \(36.79\,(=100/e)\,\mathrm{m}\). Setting this parameter to zero results in \(S_\mathrm{w}=1\) everywhere; the scaling is then switched off.

## 7.2.3. Ice-shelf calving¶

The options for calving of ice shelves (floating ice) can be selected in the run-specs headers by the parameter `ICE_SHELF_CALVING`

:

`1`

: Unlimited expansion of ice shelves, no calving.`2`

: Instantaneous calving of ice shelves if the thickness is less than a threshold thickness, specified by the parameter`H_CALV`

.`3`

: “Float-kill”: Instantaneous removal of all floating ice.

For the Antarctic ice sheet, yearly ISMIP6-type ice-shelf collapse masks can be prescribed (Seroussi et al. [56]). This requires the setting `ICE_SHELF_COLLAPSE_MASK = 1`

and additional parameters as described in the run-specs headers.

## 7.2.4. Marine-ice calving¶

For calving of grounded marine ice, the following options are available:

Parameterization for “underwater-ice” calving (Dunse et al. [15]), to be selected by the following combination of run-specs-header parameters:

`MARGIN = 2`

,`MARINE_ICE_FORMATION = 2`

,`MARINE_ICE_CALVING = 9`

. This parameterization is an adaption of the law by Clarke et al. [14], but acts here as an additional surface ablation rather than calving at a vertical front:(7.11)¶\[Q_\mathrm{c} = k_\mathrm{c} H^{r_1} D_\mathrm{w}^{r_2}\,,\]where \(Q_\mathrm{c}\) is the calving flux, \(H\) the ice thickness (taken to some power \(r_1\)), \(D_\mathrm{w}\) the water depth (taken to some power \(r_2\)) and \(k_\mathrm{c}\) the calving parameter (see also Fig. 7.3). The two exponents and the calving parameter can be set in the run-specs headers as parameters

`R1_CALV_UW`

,`R2_CALV_UW`

and`CALV_UW_COEFF`

, respectively.

For the Greenland ice sheet, yearly ISMIP6-type retreat masks can be prescribed (Goelzer et al. [20]). This requires the setting `RETREAT_MASK = 1`

and additional parameters as described in the run-specs headers.