GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus PublicationsGöttingen, Germany10.5194/gmd-10-2849-2017Explicit representation and parametrised impacts of under ice shelf seas in the z∗ coordinate ocean model NEMO 3.6MathiotPierrepierre.mathiot@metoffice.gov.ukhttps://orcid.org/0000-0002-2001-0762JenkinsAdrianHarrisChristopherMadecGurvanBritish Antarctic Survey, Natural Environment Research Council, Cambridge, UKMet Office, Exeter, UKSorbonne Universités (University Pierre et Marie Curie Paris 6)-CNRS-IRD-MNHN, LOCEAN Laboratory, Paris, FrancePierre Mathiot (pierre.mathiot@metoffice.gov.uk)26July20171072849287410February20176March201730May201714June2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://gmd.copernicus.org/articles/10/2849/2017/gmd-10-2849-2017.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/10/2849/2017/gmd-10-2849-2017.pdf
Ice-shelf–ocean interactions
are a major source of freshwater on the Antarctic continental shelf and have
a strong impact on ocean properties, ocean circulation and sea ice. However,
climate models based on the ocean–sea ice model NEMO (Nucleus for European
Modelling of the Ocean) currently do not include these interactions in any
detail. The capability of explicitly simulating the circulation beneath ice
shelves is introduced in the non-linear free surface model NEMO. Its
implementation into the NEMO framework and its assessment in an idealised and
realistic circum-Antarctic configuration is described in this study.
Compared with the current prescription of ice shelf melting (i.e. at the
surface), inclusion of open sub-ice-shelf cavities leads to a decrease in sea
ice thickness along the coast, a weakening of the ocean stratification on the
shelf, a decrease in salinity of high-salinity shelf water on the Ross and
Weddell sea shelves and an increase in the strength of the gyres that
circulate within the over-deepened basins on the West Antarctic continental
shelf. Mimicking the overturning circulation under the ice shelves by
introducing a prescribed meltwater flux over the depth range of the ice shelf
base, rather than at the surface, is also assessed. It yields similar
improvements in the simulated ocean properties and circulation over the
Antarctic continental shelf to those from the explicit ice shelf cavity
representation. With the ice shelf cavities opened, the widely used “three
equation” ice shelf melting formulation, which enables an interactive
computation of melting, is tested. Comparison with observational estimates of
ice shelf melting indicates realistic results for most ice shelves. However,
melting rates for the Amery, Getz and George VI ice shelves are considerably
overestimated.
Introduction
Ice shelf melting, which accounts for 55 % of the ice mass loss from
Antarctica, is one of the main sources of freshwater input to the Antarctic
coastal ocean. The net basal meltwater flux released to the Southern Ocean is
estimated to be 1500 ± 237 Gtyr-1 (or
48 ± 8 mSv), compared with 1265 ± 141 Gtyr-1
(or 39 ± 4 mSv) from iceberg calving (Rignot et al., 2013). The
total Antarctic mass discharge is thus similar to the 76 mSv due to
surface atmospheric forcing (P-E) south of 63∘ S (Silva et al.,
2006). The ice shelf melting contribution to the Southern Ocean freshwater
forcing is different from the iceberg melting and precipitation. Ice shelf
melting is injected into the ocean at depth whereas precipitation is input at
the surface and icebergs inject meltwater at a range of depths, but
primarily in the top ∼ 100 m. Therefore, the effect of ice
shelf melting on coastal ocean stratification and circulation is very
different from that of iceberg melt and precipitation.
The net ice shelf discharge (melting and calving) does not directly
contribute to eustatic sea level change, because ice shelves are already
floating, but does make a small steric contribution, because of the
associated freshening (Jenkins and Holland, 2007). However, the strong
mechanical coupling between ice sheet and ice shelf controls the ice flux
across the grounding line from the ice sheet. Modifications to the ice shelf
geometry associated with changes in ice thickness or extent lead to changes
in buttressing at the grounding line. A reduction in buttressing can trigger
a speed-up of the discharge from the ice sheet, a process that has been
implicated in widespread mass loss from the Antarctic Ice Sheet (Scambos
et al., 2004; Rignot et al., 2004; Favier et al., 2014). Therefore,
understanding of ice-shelf–ocean interaction is a key factor in advancing our
understanding of the ice sheet contribution to sea level rise.
Basal melting of ice shelves is driven by the properties of the water masses
that are present over the continental shelves, enter the ocean cavities and
reach the grounding line where they initiate melting. The associated input of
buoyancy triggers an overturning circulation with inflow at depth and outflow
along the ice shelf base that carries meltwater upward. The process is
referred to as an ice pump when the ascending waters cause refreezing (Lewis
and Perkin, 1986). Jacobs et al. (1992) identified three modes of
overturning, depending on the inflowing water mass, which could be either
high-salinity shelf water (HSSW; mode 1), modified forms of Circumpolar Deep
Water (CDW; mode 2) or less saline water masses that could collectively be
referred to as Antarctic Surface Water (AASW; mode 3). Mode 1 melt is low,
because HSSW has a temperature close to the surface freezing point and can
melt ice at depth only because of the lowering of its freezing point with
increasing pressure. Mode 2 melt can be high if almost unmodified CDW has
access to the sub-ice-shelf cavities. Mode 3 melt is intermediate and
variable, depending on whether only the near-freezing core of ASSW, often
designated winter water (WW), or the seasonally warmer upper layers can
access the cavities. When the inflow has a temperature at or close to the
surface freezing point (HSSW or WW), melting at depth is accompanied by
partial refreezing at higher levels, as the falling pressure results in
a rising freezing point temperature. In this case, the out-flowing water mass
produced is designated as ice shelf water (ISW), and has a temperature below
the surface freezing point. At the edge of the broad continental shelves of
the southern Weddell and Ross seas and along the Adelie Land coast, ISW mixes
with CDW and HSSW to form Antarctic Bottom Water (Foldvik et al., 1985;
Williams et al., 2008) that contributes to the global overturning
circulation. A modelling study (Hellmer, 2004) further suggested that
20 cm of the total sea ice thickness in the Ross and Weddell seas
results from the cooling and freshening of shelf water by ice shelf melting.
To improve the representation of the Antarctic coastal ocean and global sea
level rise in the coupled Ocean–Sea-ice model NEMO (Nucleus for European
Modelling of the Ocean), ice-shelf–ocean interactions need to be properly
included. In previous NEMO simulations, ice-shelf melt was uniformly
distributed around the coast of Antarctica and input at the surface. Global
conservation is an important issue, as the ocean–sea-ice model is also used
as a component within Earth system models. To tackle this issue,
a z∗ vertical coordinate has been included within the NEMO
framework (Madec and the NEMO team, 2016), and the ice shelf module as well
as the ice shelf parametrisation are developed using this vertical
coordinates and considering ice shelf melting as a mass flux.
This study is based on that of Losch (2008) (hereafter L08), describing the
development of an ice shelf module within MITgcm. We follow a similar
strategy to introduce ice-shelf–ocean interactions into the NEMO framework
(Madec and the NEMO team, 2016). The work is a first step towards adding an
ice sheet component and its interaction within NEMO, and including these
interactions within climate models such as IPSL (Dufresne et al., 2013), the
Hadley Centre models (Hewitt et al., 2011, 2016), EC earth (Hazeleger et al.,
2010), CNRM (Voldoire et al., 2013) and CMCC (Scoccimarro et al., 2011).
Ice shelves range in size from the giant Ross ice shelf
(500 000 km2) to the tiny Ferrigno ice shelf
(117 km2). This means that current global ocean model
configurations are not able to resolve explicitly all the ice shelf cavities.
For this reason, a simple way to include unresolved ice shelf melting in the
ocean model that mimics the circulation driven by ice shelf melting at depth
is also presented here.
The paper is structured as follows: first, the NEMO model (Sect. 2.1), as
well as the ice shelf module (Sect. 2.2 and 2.3), are described, then
idealised experiments are presented to validate the ice shelf module
(Sect. 3) and ice shelf parametrisation (Sect. 4), followed by its
application to a realistic circum-Antarctic configuration at 0.25∘
resolution (Sect. 5). The sensitivity of the ocean and sea ice properties to
the inclusion of the ice shelf cavity (Sect. 5.3 and 5.4), the effect of the
ice shelf cavity parametrisation under prescribed ice shelf melting
(Sect. 5.5) and the resulting meltwater flux (Sect. 5.6) are then discussed.
Finally, in a summary section (Sect. 6), the major results as well as the
remaining issues are highlighted, and we conclude with details of code
availability.
Model descriptionOcean model
NEMO is a primitive equation ocean model, and this study uses version 3.6 of
the code. The variables are distributed on an Arakawa C-grid; i.e. the scalar
point (temperature, salinity) is defined on the centre of the cell and the
vector points (zonal, meridional, vertical velocity) are defined on the
centre of each face (Arakawa, 1966). We also make use of the time varying
z∗ vertical coordinate; i.e. the variation of the water column
thickness due to sea-surface undulations is not concentrated in the surface
level, as in the z coordinate formulation, but is distributed over the full
water column (Adcroft and Campin, 2004).
A complete description of the schemes and options available in NEMO is
available in the documentation (Madec and the NEMO team, 2016). A full
description of the configurations used in this study is presented in
Sect. 3.1 for the idealised configuration and in Sect. 4.1 for the realistic
configuration.
The z∗ vertical coordinate can be used with a sea ice model (Campin
et al., 2008) in NEMO (Madec and the NEMO team, 2016). However, modelling the ocean
circulation within an ice shelf cavity in z∗ coordinates requires
some modification of the existing code. Beneath sea ice, the number of ocean
levels is kept constant, and the levels are squeezed between the bottom
surface of the ice and the seabed. The resulting pressure gradient error term
is small because the ratio of sea ice thickness to total water column
thickness is small and almost spatially constant. Within an ice shelf cavity,
a z∗ coordinate used as a surface following coordinate will face
the same limitation as terrain following coordinates, especially along the
ice shelf front. The pressure gradient error will be large, particularly at
the vertical ice front, and the tiny vertical cell thickness where the water
column is thin will limit the stable time step that is achievable.
To avoid these issues, we follow the idea of Grosfeld et al. (1997) for an
s-coordinate model. All cells between the surface (z= 0) and the ice
shelf base are masked at the model initialisation stage. By masking the ice
shelf cells, the z∗ iso-surfaces are close to horizontal and the
associated slopes are small, even at the ice front. Outside the ice shelf
cavity, the definition of the cell thickness and the computation of the
pressure gradient are not changed compared with the original code that
follows Adcroft and Campin (2004). Within the cavities, the ice shelf
thickness and the associated masked cells are constant over time, so the
z∗ iso-surfaces are defined as
Zw(1)=0,ifk<kisf,Zw(k)=∑kz=1k-1dz0,T(kz),ifk≥kisf,Zw(k)=∑kz=1kisf-1dz0,T(kz)+∑kz=kisfk-1dzt,T(kz),dzt,T(kz)=dz0,T(kz)1+ηH,
where Zw is the depth of the w interface (interface between two cells
along the z axis of the Arakawa C-grid, positive down),
dzt,T the vertical level thickness at time t,
dz0,T the vertical level thickness at time 0, k the model
level (k= 1 is the first level), η the sea-surface height
(positive up), H the total water column thickness (sum of all the wet cell
vertical thicknesses at time 0) and kisf the first wet level.
The pressure p at a depth z is computed in a standard way (Beckmann
et al., 1999; L08). We assume the ice shelf to be in hydrostatic equilibrium
in water at the reference density ρisf, taken to be the
density of water at a temperature of -1.9 ∘C (freezing
point) and a salinity of 34.4 PSU (mean salinity over the Antarctic
continental shelves). The total pressure at any depth is computed from the
sum of the ice shelf load and the pressure due to the water column above that
depth. The pressure gradient is formulated as suggested by Adcroft
et al. (2004) for z∗ coordinate models:
p(z)=∫zisf0ρisfgdz+∫zzisfρgdz,∇zp(z)=∇z∗p(z)+ρg∇z∗z,
where p(z) is the pressure at depth z, ρ is the water density at
depth z and zisf is the ice shelf draft. The hydrostatic
pressure gradient at a given level, k, (first term in Eq. 6) is computed by
adding the pressure gradient due to the ice shelf load (defined as the first
term of Eq. 5) to the vertical integral of the in situ density gradient along
the model level from the surface to that level.
In this study, we assume the ice shelf to be in an equilibrium state (i.e.
the ice shelf draft is temporally constant) so that all the ice melted by
the ocean is assumed to be replaced by the seaward advection of new ice. The
pressure of the ice shelf on the ocean therefore stays constant, but the
ocean volume increases due to ice shelf melting. Dealing with an evolving ice
shelf thickness is beyond the scope of this paper.
Representation of the bottom topography is difficult in z coordinate
models. The partial cell scheme allows a more accurate representation of
bottom topography through the use of partially wet cells (Adcroft et al.,
1997). Solutions obtained with this scheme compare favourably with those
obtained with sigma coordinate models (Adcroft et al., 1997) and also with
more realistic solutions (Barnier et al., 2006). Following L08, we apply the
partial cell scheme developed for the bottom topography to the top cells
beneath the ice shelf base. For stability reasons, the minimum thickness of
the bottom and top cells is set to the smaller of 25 m or 20 % of
a full cell. However, representation of density-driven flow in a z coordinate
model (even with partial cells), like the overflow, is challenging (Legg
et al., 2006). Thus, the representation of the buoyancy-driven flow along an
ice shelf base is expected to present analogous problems.
Where the water column is thinner than two cells, vertical circulation cannot
be represented. In order to simulate the overturning circulation generated by
ice shelf melting in such regions, we modify the bathymetry or the ice shelf
draft sufficiently to open a new cell in the water column. In places where
the cavity is thin and the slopes of the bathymetry and ice shelf draft are
steep, it would sometimes be necessary to create more than one new cell in
order to open a minimum of two cells at the velocity points (at the centre of
the cell faces on the Arakawa C-grid). Rather than making such extensive
modifications to the topography, we regard the combination of vertical and
horizontal resolution as too coarse to represent the sub-ice cavity geometry
in these places, and instead we ground the ice shelf. Consequently some ice
shelves have a reduced area.
For regional configurations with open boundaries, the normal barotropic
velocity around the boundary at each time step is corrected to force the
total volume to be constant. The correction ensures that the net inflow (the
combination of inflow at the open boundary, runoff, ice shelf melting and
precipitation) and net outflow (the combination of outflow at the open
boundary, ice shelf freezing and evaporation) are balanced.
Thermodynamics
Two formulations of the ice shelf melt rate are available: a simple one used
in the idealised cases, for consistency with earlier studies and the Ice
Shelf–Ocean Model Intercomparison Project (ISOMIP), and a more sophisticated
one used in the realistic configuration.
For the idealised study, the heat flux and the freshwater flux (negative for
melting) resulting from ice shelf melting–freezing are parameterized
following Grosfeld et al. (1997). This formulation is based on a balance
between the vertical diffusive heat flux across the ocean top boundary layer
and the latent heat due to melting–freezing:
Qh=ρcpγ(Tw-Tf),q=-QhLf,
where Qh (Wm-2) is the heat flux, q
(kgs-1m-2) the freshwater flux, Lf the specific latent
heat, Tw the temperature averaged over a boundary layer below the ice
shelf (explained below), Tf the freezing point computed from
Millero (1978) using the pressure at the ice shelf base and the salinity of
the water in the boundary layer, and γ the thermal exchange
coefficient. Hereafter, Eqs. () and () are referred to as
the ISOMIP formulation.
For realistic studies, the heat and freshwater fluxes are parameterized
following Jenkins et al. (2001, Eq. 24). This formulation is based on three
equations: a balance between the vertical diffusive heat flux across the
boundary layer and the latent heat due to melting–freezing of ice plus the
vertical diffusive heat flux into the ice shelf (Eq. 9); a balance between
the vertical diffusive salt flux across the boundary layer and the salt
source or sink represented by the melting–freezing (Eq. 10); and a linear
equation for the freezing temperature of sea water (Eq. 11; Jenkins,
1991):
cpργT(Tw-Tb)=-Lfq-ρicp,iκTs-Tbhisf,ργS(Sw-Sb)=(Si-Sb)q,Tb=λ1Sb+λ2+λ3zisf,
where Tb is the temperature at the interface, Sb the salinity
at the interface, γT and γS the
exchange coefficients for temperature and salt, respectively,
Si the salinity of the ice (assumed to be 0), hisf
the ice shelf thickness, ρi the density of the ice shelf,
cp,i the specific heat capacity of the ice, κ the thermal
diffusivity of the ice and Ts the atmospheric surface
temperature (at the ice/air interface, assumed to be -20 ∘C). The linear system formed by Eqs. (9) and (10) and the linearised
equation for the freezing temperature of sea water (Eq. 11) can be solved for
Sb or Tb. Afterward, the freshwater flux (q) and the
heat flux (Qh) can be computed. γT and
γS are velocity dependent (Jenkins et al., 2010) and can
be written as:
γT=CduwΓT,γS=CduwΓS,
where uw is the ocean velocity in the top boundary layer, Cd
the drag coefficient and ΓT/S a constant. The choices of the
thermal Stanton number (CdΓT= 0.0011) and the diffusion Stanton number
(CdΓS= 3.1 × 10-5)
are based on the recommendation of Jenkins et al. (2010). The drag
coefficient is chosen to be 1.0 × 10-3. This value lies within
the range used in the literature. However, there are no direct measurements
of the drag coefficient beneath an ice shelf. Dansereau et al. (2014)
highlighted that the range of values used for the top drag coefficient is large
(from 1.0 × 10-3 to 9.7 × 10-3). Furthermore,
uncertainties in the Stanton numbers are also large, as the study used to
determine their values (Jenkins et al., 2010) is based on data from a single
borehole. Parameter values used in Eqs. (7)–(12) are defined in Table 1.
Hereafter, Eqs. (10)–(12) are referred to as the “three equation” ice
shelf melting formulation. Unlike in more sophisticated models of the
freezing process (Galton-Fenzi et al., 2012), the parameters used in the
“three equation” formulation are not dependent of the surface state
(freezing or melting) and the freezing only occurs at the ice–ocean
interface.
Parameters used in the ice-shelf–ocean interaction formulation.
Following L08, in the idealised experiments, the ice shelf forcing is applied
as an effective heat flux and a virtual salt flux (no ocean volume change).
For realistic configurations, the velocity divergence at the ice shelf base
is adjusted in order to apply the ice shelf melting as a volume flux of
freshwater at the freezing point temperature.
List of model runs. Expl. means the ice shelf melt rate is
explicitly calculated. Presc. means the ice shelf melt rate is prescribed
(i.e. independent of ocean temperature and salinity and constant in time).
L08 shows that z coordinate models with partial cells generate a noisy melt
rate pattern due to the variation of the top cell thickness. The melt rate is
proportional to the difference between the in situ basal temperature and
in situ temperature in the first wet cell. Because the largest cells cool
down more slowly than the thinnest cells, for a given initial basal
temperature, the melt rate in the thickest cells is larger than in the
smallest cells. Following L08, the noise due to the spatially varying size of
the top cells is suppressed by computing Tw and Sw in
Eqs. (7), (9) and (10) as the mean value over a constant thickness, assumed
to represent the top boundary layer thickness (HTBL, i.e.
properties are averaged over the cells entirely included in the top boundary
layer and a fraction of the deepest wet cell partly included in the top
boundary required to make up the constant HTBL). The top ocean
velocity uw is defined as the velocity magnitude derived from the mean
zonal/meridional velocity at U/V points within the top boundary layer
averaged at T points. The heat and freshwater fluxes are distributed over
the same constant thickness. If the first wet cell is thicker than the
specified top boundary layer thickness, HTBL is set to the top
cell thickness. A complete description of this parametrisation is available
in L08. Using z∗ instead of pure z coordinates does not alter the
noise seen in the melt rate. Therefore, the parametrisation proposed by L08
is applied in each simulation used in this study. HTBL is set to
a default value of 30 m, but different values are used for the
simulations with various vertical resolutions, as presented in Table 2.
Freshwater and associated latent heat introduced (a) at the
surface (R_noISF), (b) beneath the ice shelf (A_ISF,
R_ISF and R_MLT), (c) at the ice shelf base level
(A_BG03) and (d) over the depth range of the ice shelf base
(A_PAR and R_PAR).
Simplified representation of ice shelf melting
Global ocean model configurations are typically unable to resolve all the ice
shelves around Antarctica. Despite their limited extent, the smaller ice
shelves nevertheless make a significant contribution to the total meltwater
flux from the ice sheet. We therefore need a way to mimic the impact of
unresolved cavities on the ocean.
Beckmann and Goosse (2003, hereafter BG03) suggested a simple parametrisation
for the melting beneath an ice shelf and prescribed the input of meltwater at
the ocean level corresponding to the base of the ice shelf (Fig. 1c). One of
the main issues with this parametrisation is that, for the same ice shelf
melting, the effect on the ocean dynamics will be the same whatever the
grounding line depth is.
The idea tested in this paper is to spread the freshwater due to ice shelf
melting evenly between the grounding line depth and the depth of the calving
front. In this case, the model creates its own plume along the vertical wall
(Fig. 1d, no cavity in this case) and thus an overturning between the
grounding line depth and the equilibrium depth (the depth where the density
of the plume is equal to the density of the ambient water). Figure 1a and b
are discussed in Sect. 5.2.
In this part of the study we focus on how to inject the observed ice shelf
meltwater flux into the ocean model. Therefore, the ice shelf melting is
prescribed and the heat flux is derived from the freshwater flux using
Eq. (8). The computation of the melt rate from the off-shore ocean properties
and ice shelf geometry could be included using the BG03 parametrisation or
some adaptation of the Jenkins (2011) plume model. The parametrisation tested
in this study is kept as simple as possible for ease of use in a wide range
of applications. Further testing of other interactive melt parametrisations
or fresh water distributions that are functions of the ice shelf geometry or
melt rate is beyond the scope of this study.
Academic case
In order to compare the sub-ice shelf cavity capability in NEMO with that in
other models, the idealised configuration used in this study is the one
described in the ISOMIP.
ISOMIP is an open, international effort to identify systematic errors in
sub-ice-shelf cavity ocean models and the reference configuration is based on
a very simple set-up, briefly described below.
Near-steady-state (after 10 000 days) solution of the I_30M
ISOMIP experiment. (a) Horizontal stream function (Psi) in Sv
with a contour interval of 0.02 Sv. (b) Meridional
overturning circulation (moc) in Sv with a contour interval of 0.01.
(c) Melt rate in myr-1 (negative for melting and
positive for freezing) with a contour interval of 0.4 myr-1.
ISOMIP set-up
The ISOMIP set-up follows the recommendations of the inter comparison project
for experiment 1.01 (Hunter, 2006). The geometry is based on a closed domain
with a flat seabed fixed at 900 m. The grid extends over 15∘
in longitude, from 0 to 15∘ E with a resolution of 0.3∘, and
10∘ in latitude, from 80 to 70∘ S with a resolution of
0.1∘. The spatial resolution ranges from 6 km at the southern
boundary to 11 km at the northern boundary. The whole domain is
covered with an ice shelf, and includes no open-ocean region. The ice shelf
draft is uniform in the east–west direction, is set at 200 m between
the northern boundary and 76∘ S and deepens linearly south of
76∘ S down to 700 m at the southern boundary. The water is
initially at rest and has a potential temperature of -1.9 ∘C
and a salinity of 34.4 PSU. No restoring is applied to either the
temperature and salinity.
The vertical resolution is uniform and fixed at 30 m, allowing for
a direct comparison with the results of L08. The density is computed using
the polyEOS80-bsq function. It takes the same polynomial form as the
polyTEOS10 function (Roquet et al., 2015), but the coefficients have been
optimized to accurately fit EOS-80 (Fabien Roquet, personal communication,
2015). The melt formulation is the “ISOMIP” one. All the results presented
are taken from day 10 000 at which time the system is close to a steady
state.
Model comparison
The ISOMIP experiment has been carried out with many models using different
vertical coordinates during the last 10 years, including
ROMS
http://www.ccpo.odu.edu/~msd/ISOMIP/
,
OzPOM
http://staff.acecrc.org.au/~bkgalton/ISOMIP/
, MITgcm
(Losch, 2008) and POP (Asays-Davis, 2012). All these models agree on a common
circulation and melt pattern. The melting and freezing along the base of the
ice shelf drives an overturning circulation of about 0.1 Sv.
Associated with the meridional overturning circulation, all the models
generate a cyclonic gyre with a western boundary current beneath the sloping
ice shelf of about 0.3 Sv. This horizontal circulation drives water
that is warmer than the freezing point into the south-eastern part of the
cavity. The inflow of warm water causes melting at the ice shelf base that is
concentrated along the eastern and southern boundaries. On the western side
of the ice shelf cavity, the boundary current advects colder water towards
the ice front. Shoaling of the ice shelf base causes super-cooling of the
water in contact with the ice and thus drives freezing. A detailed discussion
of this circulation can be found in Grosfeld et al. (1997). The maximum
melting–freezing rates are model dependent. The range is
0.7–1.8 myr-1 for the maximum freezing rate and
0.7–2.4 myr-1 for the maximum melting rate.
(a) Total melting rate versus total freezing rate, and
(b) meridional overturning circulation versus barotropic stream function (bsf) for all the ISOMIP sensitivity experiments (I_5M,
I_10M, I_30M, I_60M, I_100M, I_150M, I_31L,
I_46L and I_75L). The simulations I_XXM are with constant
vertical resolutions of XX m and a HTBLof 30 m,
the simulations I_XXMYYM are with constant vertical resolution of
XX m and a HTBL of YY m, Finally, the simulations
I_XXL are with variable vertical resolution. Details are given in
Table 2.
The NEMO response to the ISOMIP set-up (simulation I_30M) is shown in
Fig. 2. It is similar to that previously simulated with a z coordinate
model (L08). The strength of the overturning circulation is 0.11 Sv.
The transport of the western boundary current generated by the cyclonic gyre
beneath the sloping ice shelf is 0.32 Sv. The pattern of melting and
freezing is similar to that in L08. The melting occurs, as expected, in the
south-eastern corner with a maximum of 2.7 myr-1 and the
freezing takes place beneath the western boundary current with a maximum of
1.9 myr-1. The low noise is the result of the L08
parametrisation (Fig. 2). In simulations without this parametrisation (not
shown) the noise in the melt pattern is as shown in L08.
Sensitivity of ocean circulation to the vertical resolution
Depending on the scientific question to be addressed, the ocean models
commonly used have very different vertical resolutions, ranging from 1 to
100 m. The representation of the top boundary layer is strongly
affected by the choice of vertical resolution. To evaluate the impact of this
choice on the ocean circulation beneath the ice shelf, nine simulations with
vertical resolution ranging from 5 m (I_5M) to 150 m
(I_150M) have been carried out (Table 2).
The choice of vertical resolution and Losh HTBL strongly affects
the ice shelf melting. When HTBL is tied to the vertical
resolution, the finer resolution gives lower melting. Under melting conditions,
a thin, fresh and cold top boundary layer appears in the top metres of the
ocean next to the ice shelf base. With finer vertical resolution, a thinner
and colder top boundary layer can be resolved, resulting in weaker melting
(Fig. 3a). Our sensitivity experiments show a maximum melt rate 4 times
higher in the I_150M simulation (4.3 myr-1) and 3 times
higher in the I_60M simulation (3.1 myr-1) than in the
I_5M simulation (0.9 myr-1) (not shown). In analogous
experiments, L08 found a similar sensitivity, with maximum melting 3 times
larger at 45 m resolution than at 10 m resolution. However,
when HTBL is kept constant (I_5M30M, I_10M30M and
I_30M), the total melt is insensitive to the vertical resolution. The
total melt at high vertical resolution (5 or 10 m) with
a 30 m Losh top boundary layer thickness (respectively I_5M30M
and I_10M30M) is converging toward I_30M (Fig. 3a). This suggests
that a more physical definition of HTBL (based on stratification,
melt rate, etc …), rather than a constant HTBL could
significantly change the melt rate in a high-resolution models (although
investigation of this is beyond the scope of the paper).
With very coarse resolution (I_100M/I_150M), the model is unable to
represent a top boundary layer at all and the total melting saturates. Total
melting is 20 % smaller in the I_5M simulation than in both the
I_100M and I_150M simulations, which have the same total melt
(Fig. 3a). With variable vertical resolution (I_31L, I_46L and
I_75L), such as is typically used in global configurations of NEMO
(Timmermann et al., 2005; DRAKKAR group, 2007; Megann et al., 2014), the
coarsest resolution in the cavity seems to determine the total melt. This is
because more than 50 % of the melting occurs between 500 and
700 m depth where the resolution is coarsest (not shown). This could
be an issue for modelling ice shelf melting with the standard configuration
used for climate applications because Dutrieux et al. (2013) show that, for
some ice shelves with high melt rates, most of the melt may occur over
a small area close to the grounding line, where the resolution is coarsest.
The vertical resolution also has a major impact on the noise pattern
(Fig. 4). As the noise in the melt pattern is closely linked with variations
in the thickness of the first wet cell, the finer the vertical resolution,
the weaker the noise.
Melt rate in (a) the 5M simulation, and (b) the
100M simulation in myr-1 (negative for melting and positive for
freezing) with a contour interval of 0.4 myr-1.
In contrast, the barotropic stream function and the overturning circulation
in the cavity are not altered by any choice of vertical resolution between 5
and 150 m (Fig. 3b). One of the reasons could be that with the bulk
formulation of melting used in the ISOMIP simulations, there is no direct
link between the ocean current velocity at the ice-shelf–ocean interface and
the melt rate, because the thermal exchange coefficient is defined to be
a constant.
Ice shelf cavity parametrisation
While the ice shelf module as described so far works well in idealised cases,
for a wider range of applications (including ice shelves of varying extent at
all likely horizontal resolutions) we also need the capability of
representing the impact of circulation and melting within unresolved
cavities. In this section, we investigate the ability of our ice shelf cavity
parametrisation to mimic the circulation and water mass properties produced
by the full cavity simulation, and compare the results with those produced by
the parametrisation of BG03. Both parametrisations are evaluated in an
idealised configuration derived from the ISOMIP set-up.
The geometry is the one for ISOMIP experiment 2.01, which is the same as that
for ISOMIP experiment 1.01 except in the top 200 m, where the flat
ice shelf is replaced by open water (Fig. 5a). The simulations are
initialised with a warm linear profile typical of conditions on the
continental shelves of the Amundsen and Bellingshausen seas (Fig. 6 in Asay
Davis et al., 2016, with constant value between 720 and 900 m).
Radiative open boundary conditions are applied at the northern boundary
(Treguier et al., 2001). The vertical eddy viscosity and diffusivity, in
unstable conditions, is set to 10 m2s-1 (instead of
0.1 m2s-1 in ISOMIP configuration) to reduce the noise
generated along the ice shelf front.
(a) Zonal mean temperature (∘C) after
30 years of the run; in contour, the meridional overturning stream function
(Meridional Overturning Circulation, MOC) in the A_ISF experiment. (b) Mean temperature difference
(∘C) with respect to A_ISF experiment
(A_PAR-A_ISF); in contour, the MOC in the A_PAR experiment.
(c) as (b) but for A_BG03.
Three experiments are run for 30 years: one with the ice shelf cavity open
(A_ISF, Fig. 1b), but with a steady pattern of basal melt/freeze
imposed; another with the open-ocean circulation driven by the cavity
parametrisation of BG03 (A_BG03, Fig. 1c); and a third with the cavity
parametrised as outlined in Sect. 2.3 (A_PAR, Fig. 1d). In all these
experiments the same heat and freshwater fluxes are applied, derived from the
basal melt/freeze pattern obtained in the last month of a dedicated 30-year
run with explicit ice shelf melting calculated using the “ISOMIP”
formulation.
A_ISF drives a deep inflow toward the ice shelf, and corresponding
outflow in the top 400 m toward the open ocean, of 0.9 Sv at
the northern boundary (Fig. 5a). In a stratified ocean, this circulation has
a crucial effect on the total amount of heat advected toward the ice shelf,
on the properties of the water drawn into the overturning circulation and on
the overall stratification in the basin. In A_BG03 the overturning is
too weak (0.6 Sv compared with 0.9 Sv in A_ISF) and too
shallow (200 m compared with 400 m in A_ISF).
Consequently, the water masses drawn into the overturning come from
a different depth and have different T/S properties, and the resulting
stratification is too strong, with colder surface waters and warmer deep
waters (Fig. 5c). In A_PAR, because the freshwater flux is distributed
over the same depth range as in A_ISF (between 200 and 700 m),
the vertical extent of the overturning and the water masses drawn in are the
same in both A_PAR and A_ISF. The result is a circulation on the
shelf that is similar in depth and magnitude and a stratification that is
similar in strength to those simulated in A_ISF (Fig. 5b).
With far-field conditions typical of the cold, salty continental shelves of
the Ross and Weddell seas, where the water column is well mixed by brine
rejection from growing sea ice in winter and less heat is available at depth,
the differences in the stratification resulting from the two parametrisations
and the simulation with the open ice shelf cavity should be smaller.
Real ocean application
In the ISOMIP test cases, the ocean circulation in the cavity compares well
with that simulated by other models. Furthermore, the suggested
parametrisation of ice shelf melting mimics well the circulation and water
properties generated by the presence of an open ice shelf cavity.
Nevertheless, the bathymetry and ice shelf draft are smooth in these
idealised cases and the heat transfer coefficient is constant, so the
favourable comparison with other models in the idealised ISOMIP set-up between
models as well as the good match between the idealised A_ISF and
A_PAR experiment might not be reproduced in a realistic configuration.
In the next section, we assess both the explicit ocean cavity representation
and the cavity parametrisation in a realistic circumpolar configuration.
Bathymetry (m) over the Antarctic continental shelf and
beneath the ice shelves. Black lines are the cell edges (plotted every
25 cells). The thick grey line is the limit of the Weddell sector of the grid
and the thick dashed grey line is the limit of the Ross, Amudsen and
Bellingshausen sectors.
Antarctic configuration set-up
ePERIANT025 is a circum-Antarctic configuration based on the PERIANT025
configuration (Dufour et al., 2012) covering the ocean from 86.5 to
30∘ S, using a 1/4∘ isotropic Mercator grid. A feature of
the Mercator grid is that the mesh spacing reduces with decreasing distance
from the South Pole, so that the farthest south grid boxes strongly constrain
the model time step. To maintain a model time step equal to that used in
current global 1/4∘ configurations, the Mercator grid is replaced
south of 67∘ S with two quasi-isotropic bipolar grids, one for the
Bellingshausen, Amundsen and Ross sea sector and one for the Weddell sea
sector (Fig. 6). Each sector is built following the semi-analytical method
used to create the tripolar ORCA grid north of 22∘ N (Madec and Imbard, 1996).
The effective resolution is 13.8 km at 60∘ S, increasing to
3.8 km at 86.5∘ S, where a pure Mercator grid would have
a resolution of 2.2 km. The model uses 75 vertical levels with
thicknesses varying from 1 m at the surface to 200 at 6000 m
depth, giving a vertical resolution ranging from 10 to 150 m beneath
the ice shelves. See Sect. 3.3 for the effect of this resolution on ice shelf
melting in an idealised case.
The bathymetry used for the model domain north of the Antarctic continental
shelf is that described by Megann et al., (2014). Over the Antarctic
continental shelves the IBCSO dataset (Arndt et al., 2013) is used. The two
bathymetry datasets are merged between the 1000 and 2000 m isobath
along the Antarctic continental slope. Under the ice shelves, bathymetry
(included in the IBCSO dataset) and ice draft are taken from BEDMAP 2
(Fretwell et al., 2013). The resulting model bathymetry is shown in Fig. 6.
Note that for some ice shelves, Fretwell et al. (2013) enforced flotation by
lowering the seabed. In addition, we impose a minimum of two vertical grid
cells within the ocean cavities so that an overturning cell can develop.
Where necessary, either the bathymetry or the ice shelf draft, depending on
the local configuration, is modified to fit the criterion. If more than one
cell has to be modified to fit the water column criterion, the entire water
column is masked. Using this procedure, Totten and Dalton (Moscow University
in Rignot et al., 2013) ice shelves and the deepest part of Amery Ice Shelf
are almost fully masked.
Other choices (the momentum advection, tracer advection, diffusion,
viscosity, vertical mixing, double diffusion, bottom friction, bottom
boundary layer and tidal mixing parametrisations) are as used in Megann
et al. (2014). For the sea ice we use the Louvain-la-Neuve sea-ice model LIM2
(Fichefet and Morales, 1997) with ice rheology based on an
elasto-visco-plastic law as described in Bouillon et al. (2013).
The geothermal heat flux is assumed to be constant and set to
86 mWm-2 (Emile-Geay and Madec, 2009), while the internal wave
energy used in the tidal mixing parametrisation (0 under the ice shelf for
simplicity) is derived from the tide model FES 2012 (Carrère et al.,
2012). Sea-surface salinity restoring is applied north of 55∘ S,
river runoff comes from Dai and Trenberth (2002), and iceberg melting based
on Rignot et al. (2013) is evenly distributed at the surface along the
Antarctica coast. Ice shelf melt is applied either into the open cavities, at
depth following our parametrisation, or as surface runoff. The total ice
shelf melt in each individual cavity is either interactively computed using
the “three equation” formulation or prescribed following the Rignot
et al. (2013) estimates.
Radiative boundary conditions are applied at the northern open boundary
(Treguier et al., 2001) using velocity, temperature and salinity data from
a global NEMO ORCA025 simulation (Barnier et al., 2012) forced by the DFS5.2
atmospheric forcing developed by the DRAKKAR project. To minimise
inconsistency, the model is also driven by the same DFS5.2 atmospheric
forcing. The methodology applied to build the DFS forcing series is described
in Brodeau et al. (2010), and the details of the DFS5.2 are given in a report
by Dussin et al. (2016). Initial conditions come from the World Ocean Atlas
2013 (Locarnini et al., 2013; Zweng et al., 2013). The model is run for
10 years starting in 1979 and ending in 1988, and the first-order response
is investigated using output from the last year of the simulation.
Experiment description
In order to evaluate both the explicit ice shelf module (Sect. 2.2) and the
improved parametrisation (Sect. 2.3) in this realistic case, four simulations
are run:
R_noISF: a simulation without ice shelf cavities. Both the ice shelf freshwater flux and the latent
heat flux associated with melting of the ice are prescribed at the surface (Fig. 1a).
R_ISF: a simulation with explicit ice shelf cavities (Fig. 1b), but where both the melt rate of the
ice shelves and the latent heat flux at the ice-shelf–ocean interface are specified.
R_PAR: a simulation without ice shelf cavities (Fig. 1d). Both freshwater and latent heat fluxes
from the ice shelves are uniformly distributed along the calving front from its base down to the grounding line depth, or
the seabed if it is shallower.
R_MLT: a simulation with explicit ice shelf cavities and interactive melt rates computed by the
“three equation” formulation (Fig. 1b).
For R_ISF, R_noISF and R_PAR the same total inputs of
freshwater and latent heat are prescribed for each ice shelf and the fluxes
are constant over time; only the location of the input changes. The melting
pattern used in R_ISF is provided by the simulation R_MLT, while
the magnitude is scaled so that the total for each ice shelf matches that
from Rignot et al. (2013). The associated latent heat flux is derived from
the melt rate using Eq. (8).
Initially, results from R_noISF and R_ISF are used to evaluate the
sensitivity of the ocean and sea ice properties to the presence of ice shelf
cavities in a control set-up with prescribed melting. Next, results from
R_PAR are compared with those from R_noISF and R_ISF in order
to evaluate and validate the ice shelf parametrisation in a realistic case.
Finally, results from R_MLT are used to evaluate the modelled ice shelf
melting in our circum-Antarctic configuration using the “three equation”
ice shelf melting formulation.
Sensitivity of ocean properties to the ice shelf cavities
In both R_noISF and R_ISF, large-scale open-ocean features are well
represented. Simulated ACC transport (135 Sv) and Weddell gyre
transport (56 Sv) are similar and compare well with the observations
of 137 Sv for the ACC transport (Cunningham et al., 2003) and
56 Sv for the Weddell gyre transport (Klatt et al., 2005).
Temperature and salinity properties north of the continental shelves are also
similar in both simulations and compare reasonably with WOA2013 (Figs. 7–8).
In contrast, the presence of ice shelf cavities in R_ISF substantially
affects the ocean properties and dynamics in the coastal Antarctic seas
(Figs. 7, 8 and 10).
Temperature (∘C) averaged between 300 and
1000 m (year 10, 1988) from (a) R_ISF,
(b) R_PAR, (c) R_noISF and (d) World Ocean
Atlas 2013 (Locarnini et al., 2013; Zweng et al., 2013).
Over the Bellingshausen and Amundsen seas, the input of freshwater at the
surface in R_noISF leads to strong stratification in the upper
250 m, weak stratification below (Fig. 9), a weak and shallow
vertical circulation (maximum overturning is 0.01 Sv at 70 m
depth) and a weak barotropic circulation over the continental shelf
(Fig. 10). In R_ISF, the input of buoyancy at the ice shelf base
activates the buoyancy-forced overturning, driving upwelling along the
ice-shelf–ocean interface. The overturning circulation entrains 0.23 Sv
of a mix of ambient water (CDW) and meltwater along the ice shelf base. This
upwelling generates a barotropic circulation that follows the f/h contours
over the Amundsen and Bellingshausen sea continental shelf (Fig. 10a and c)
as explained in Grosfeld et al. (1997). The resulting mixture of CDW and
meltwater stabilises at an equilibrium depth between 400 and 60 m
(not shown). The upwelling of CDW into the surface mixed layer weakens the
thermohaline stratification and warms and salinizes the surface layer. These
changes in ocean dynamics on the shelf lead to a more realistic continental
shelf temperature and salinity distribution (Figs. 7–8) and stratification
(Fig. 9) in R_ISF compared with R_noISF.
In Pine Island Bay and elsewhere on the Amundsen and Bellingshausen sea
shelves, the bottom water properties in the over-deepened basins are
determined by the properties in the open ocean at the sill depth (Walker
et al., 2007) close to the shelf break. So the bottom temperature bias
present in R_ISF could be strongly affected by the model bias in the
ACC, the possible sources of which are beyond the scope of this paper. In
R_noISF, as the overturning is not activated, there is no process to
flush the bottom water trapped in the over-deepened basins, so the waters
there are not affected by external forcing, and the bottom properties still
match the initial conditions after 10 years of the run (Fig. 9).
Over the Ross and Weddell sea continental shelves, the cold, salty HSSW in
R_noISF matches the observations and spreads northward across the shelf
break toward the open ocean. In R_ISF, the HSSW produced is too fresh
(-0.2 PSU, Fig. 8). Weak winds in the atmospheric forcing (Dinniman
et al., 2015), in addition to a fresher coastal current (Nakayama et al.,
2014), the opening of a new pathway for HSSW circulation beneath the ice
shelves (Budillon et al., 2003; Nicholls et al., 2009), mixing of HSSW with
light surface waters all year long, and a deficiency of the sea-ice model in
representing coastal polynyas could all help to explain the absence of HSSW
in R_ISF.
Salinity (PSU) averaged between 300 and 1000 m (year 10,
1988) from (a) R_ISF, (b) R_PAR,
(c) R_noISF and (d) World Ocean Atlas 2013 (Locarnini
et al., 2013; Zweng et al., 2013).
Profiles (year 10, 1988) in Pine Island Bay in R_noISF (blue),
R_ISF (red) and R_PAR (green) of (a) salinity and
(b) temperature. Climatology from 1994 to 2012 (Dutrieux et al.,
2014) is in black.
Barotropic stream function (Sv) on the Ross, Amundsen,
Bellingshausen and Weddell continental shelves in (a) R_ISF,
(b) R_PAR and (c) R_noISF. Stream function
isolines out of the ±2 Sv range are not plotted.
Sensitivity of sea ice properties to the ice shelf cavities
Winter sea ice extent compares well with the 18.3 million km2
estimated from satellite observations (Comiso, 2000) in both R_ISF
(18.2 million km2) and R_noISF
(18.4 million km2). The position of the sea-ice edge, being too
far south in the Amundsen Sea and too far north in the Weddell Sea and around
East Antarctica in both simulations, is not changed significantly by the
presence of ice shelf cavities (Fig. 11).
Mean sea ice thickness (m) from September to November (SON)
in colour. Lines represent the sea ice extent (threshold set at 15 % ice
concentration) in the observations of Comiso (2000) (grey) and the
corresponding simulation (black). (a) R_ISF,
(b) R_PAR, (c) R_noISF and (d) Kurtz and
Markus (2012) data. The observational uncertainty is ±40 cm.
Over the warm continental shelves of the Amundsen and Bellingshausen seas,
sea ice is thicker in the R_noISF than in the R_ISF simulation
(+1 m, Fig. 11a). In R_noISF, because the freshwater and the
latent heat sink from the melting of land ice are prescribed at the surface,
the consequent freshening and cooling of the surface waters considerably
enhances the formation of sea ice. This leads to very thick sea ice in
R_noISF, greater than 3 m locally (Fig. 11c). In R_ISF, the
overturning circulation driven by melting at the ice shelf ocean interface
entrains warm CDW and mixes it into the surface layer. This upward heat flux
decreases the sea ice formation and has a direct effect on sea ice thickness
(Fig. 11a).
Over the cold continental shelves of the Ross and Weddell seas and around the
coast of East Antarctica, sea ice thickness differences between R_ISF
and R_noISF are much smaller, typically about 20 cm (Fig. 11).
The ocean is well mixed and the shelf water temperature is close to the
freezing point (Fig. 7). So the amount of heat entrained into the buoyant
overturning along the ice shelf base is smaller, as is the impact on sea ice.
Comparison with spring sea ice thickness estimates derived from sea-ice
freeboard and snow thickness measurements (Fig. 11d; Kurtz and Markus, 2012)
shows that sea ice thickness in R_ISF is closer to observation by about
1 m over the warm shelves of West Antarctica. Over the cold shelves,
the modelled sea-ice thicknesses are similar in both simulations (less than
20 cm differences) and comparable with the observations, which are
subject to ±40 cm uncertainties.
Assessment of the simplified ice shelf representation
The implementation of the ice shelf cavities in a realistic configuration
showed a great improvement in the circulation on the Antarctic continental
shelves, especially in the Amundsen and Bellingshausen seas. However, many
climate models lack the horizontal and vertical resolution needed to
represent all these cavities. Our parametrisation described in Sect. 2.3 has
been developed to address this issue. The evaluation of our parametrisation
in a simple idealised case showed very encouraging results. Here, by
comparing R_ISF and R_noISF with R_PAR, we evaluate the
parametrisation for all ice shelves of the Southern Ocean.
Over the warm shelves of West Antarctica, R_PAR reproduces well the
R_ISF shelf properties and circulation (Figs. 12a and b and 10).
Critically, the prescription of the ice shelf meltwater flux at depth drives
an overturning circulation and spins up the associated gyres within the
over-deepened basins. The magnitudes of the gyres are similar between the
R_ISF and the R_PAR simulations (Fig. 10b and c). Shelf water
properties generated by R_ISF are better reproduced by R_PAR than
by R_noISF over all the West and East Antarctic shelves (Fig. 12a–d).
Over the Amundsen shelf, R_PAR also decreases the stratification and
improves the mean temperature and salinity profiles compared with
R_noISF (Fig. 9).
Map of temperature in ∘C(a, b) and salinity
in PSU(c, d) differences between R_PAR and R_ISF
(a, c) and R_noISF and R_ISF (b, d) averaged
between 300 and 1000 m.
Over the Ross and Weddell sea shelves, HSSW produced in R_PAR is saltier
than in R_ISF (+0.1 PSU). The salinity gradient between the
salty western side and the fresher eastern side of the shelves is larger than
in R_ISF (Fig. 12c) and larger than in the observations (Fig. 8). In
R_PAR, this is due to the lack of a HSSW circulation pathway beneath the
giant Ross (Budillon et al., 2003) and Filchner–Ronne (Nicholls et al., 2009)
ice shelves that in reality carries HSSW formed in the west over to the
central or eastern shelf. Instead of this sub-ice shelf circulation that is
captured in R_ISF (Fig. 10), R_PAR drives individual gyre
circulations within each of the over-deepened basins, similar in structure
to, but stronger than, those in R_noISF.
Sea ice extent and thickness in R_PAR match well the R_ISF sea ice
characteristics (Fig. 11). Thickness is smaller by more than 1 m in
West Antarctica compared with the R_noISF simulation. Around East
Antarctica, and over the Ross and Weddell sea shelves, despite the deficiency
in representing the ocean circulation beneath the giant ice shelves, sea ice
thickness in R_PAR is similar to that in R_ISF.
These comparisons between R_ISF/R_PAR and R_noISF suggest that
not only the presence and the amount of meltwater are important but also
the depth at which it is input to the model. The parametrisation directly
addresses this latter feature of the sub-ice-shelf ocean circulation and so
is able to represent the ocean dynamics associated with the overturning
circulation within the cavity. However, the parametrisation is not fully
adapted to mimic the large-scale horizontal gyre circulation that is spun-up
under the giant ice shelves. This may not be a significant problem because
current coarse-resolution ocean models have a nominal resolution of
1 ∘cos(θ), where θ is the latitude, which
is sufficient to explicitly represent the two giant ice shelves (L08, Hellmer
et al., 2004, 2012).
Ice shelf melting
In the previous section we showed that specifying a realistic melting pattern
at the ice-shelf–ocean interface gives convincing results with major
improvements in the properties and circulation of the ocean beyond the ice
shelves, especially in the Amundsen and Bellingshausen seas. However,
prescribing the freshwater flux represents a strong constraint on the range
of applications, since the specified fluxes will only be valid for the
present oceanic state. To compute melt rates for other oceanic states
interactively, and eventually to couple the ocean model to an evolving ice
sheet model, requires the “three equation” formulation for ice shelf
melting. Next, we evaluate the ability of the described circum-Antarctic
configuration with the “three equation” ice shelf melting formulation to
simulated realistic ice shelf melting.
The total ice shelf melting simulated in R_MLT
(1864 Gtyr-1) is slightly above the range of the observational
estimate of Rignot et al. (2013) (Table 3). In R_MLT, as in the
observations, we can separate the ice shelves into two different regimes
based on the temperature of the water masses on the continental shelves
(Fig. 7d) and the average melt rate: the cold water (Fig. 13b–d) and the
warm water (Fig. 13a) ice shelves. As the ice shelf cavity geometry is based
on recent estimates (Fretwell et al., 2013) and the ice shelf regime modelled
in R_MLT are similar to those in recent observations, the modelled ice
shelf melt rate are compared with the Rignot et al. (2013) estimates.
Basal melt in Gtyr-1 for the last year of simulation in
R_MLT. Observations come from Rignot et al. (2013). Geometry column
indicates the main modification to the BEDMAP2 bathymetry/ice shelf draft as
follows: GL means the GL is moved seaward, “shallow” means the ice shelf is
too shallow away from the grounding line and “narrow” means the narrowest
passage into the cavity is one cell wide. ++/+/0/-/– is a summary of the
ocean temperature condition at the closest non-extrapolated cell in the
WOA2013 observational dataset (Fig. 14). ++ for ocean temperature
differences with regard to WOA2013 of more than 1 ∘C, + differences in
the range 0.5 and 1 ∘C, 0 differences in the range 0.5 and
-0.5 ∘C, - differences in the range -0.5 and
-1 ∘C and – for ocean temperature differences greater than
-1 ∘C.
Ice shelf melting (myr-1, positive values mean melting)
in the R_MLT simulation for (a) the West Antarctic ice shelves,
(b) Ross Ice Shelf, (c) Filchner–Ronne Ice Shelf and
(d) the East Antarctic ice shelves. Note that panels
(a) and (b–d) have different colourbars.
Cold water ice shelves
For the Ross, Weddell and East Antarctic continental shelves, the agreement
between computed and observed ice shelf melt rates varies. The total melt in
R_MLT for these ice shelves (722 Gtyr-1) lies within the
range of the observations (475–867 Gtyr-1) (Table 3). These ice
shelves all experience low melt rates (Fig. 13b–d) due to the presence of
cold water on the shelves (Fig. 8).
For Filchner–Ronne Ice Shelf (FRIS) the total melt in R_MLT is in
agreement with the observation based estimates (Table 3), while the spatial
pattern of melting and freezing is also similar to other simulations without
tidal forcing (Makinson et al., 2011). FRIS experiences strong melt close to
the grounding line, along the ice front and along the paths of the main
inflows. Large freezing rates occur along the paths of the main outflows that
follow the eastern coasts of the Antarctic Peninsula, Berkner Island and
Henry Ice Rise. The latter generates a particularly large area of intense
freezing in the central part of the ice shelf, north of the ice rises, in
agreement with the observation based distributions of Joughin and
Padman (2003) and Moholdt et al. (2014).
For Ross Ice Shelf, R_MLT generates a total melt of
111 Gtyr-1, with high melt rates concentrated along the ice
front, and lower freezing rates in the central part of the ice shelf
(Fig. 13). The total melt is within the range of previous model based
estimates (51–260 Gtyr-1) and the melting–freezing pattern is
in good agreement with earlier modelling studies (Timmermann et al., 2012;
Assmann et al., 2003; Dinniman et al., 2007). However, the total melt
simulated in R_MLT is 30 Gtyr-1 above the observational
range, because melt rates along the ice front and on the western side of the
ice shelf are larger than those inferred from observation (Rignot et al.,
2013; Moholdt et al., 2014).
Total melt of Amery Ice Shelf is overestimated by at least a factor of 5
(Table 3), because the waters on the continental shelf in front of the cavity
are warmer than observed by more than 1.2 ∘C (Fig. 14). As
a consequence, the freezing within the cavity, evaluated from remote sensing
and in situ data (Wen et al., 2010) and simulated by Galton-Fenzi
et al. (2012), is absent in R_MLT.
Shown are 300–1000 m mean temperature differences between R_MLT
(year 10, 1988) and observations from World Ocean Atlas 2013 (Locarnini
et al., 2013; Zweng et al., 2013). Grey area represents ice sheet, ice
shelves or ocean shallower than 300 m. The hatched area limited by
the green line represents where the observational dataset is obtained by
extrapolation.
Warm water ice shelves
The ice shelves along the West Antarctic coastline between the Ross and
Weddell seas experience a large total melt rate in R_MLT
(1142 Gtyr-1) (Fig. 12a), due to the presence of CDW on the
continental shelf. This total melt is about twice the recent observation-based estimate (541 Gtyr-1) (Table 3).
The melt rates in R_MLT are realistic for Abbot Ice Shelf
(52 Gtyr-1) (Table 3), but slightly underestimated for Thwaites
(74 Gtyr-1) and Pine Island Glacier (PIG;
87 Gtyr-1) compared with observation (Table 3). By comparison
with previous modelling studies, R_MLT results for Abbot and PIG ice
shelves are in the range of earlier work (Timmermann et al., 2012; Nakayama
et al., 2014; Shodlock et al., 2016) while for Thwaites the results are above
those obtained previously.
Most of the warm ice shelf melting overestimate in R_MLT comes from Getz
(337 Gtyr-1) and George VI (298 Gtyr-1) ice shelves
(+178 and +181 Gtyr-1 respectively, Table 3). R_MLT
estimates are also well above earlier estimates obtained with FESOM by
Timmermann et al. (2012) and Nakayama et al. (2014) with RTOPO1 bathymetry
(Timmerman et al., 2010), respectively, 164 and 127 Gtyr-1 for
Getz Ice shelf, and 86 and 88 Gtyr-1 for George VI Ice Shelf.
However, Schodlok et al., (2016) obtained similar melt rates using MITgcm
with IBCSO bathymetry (respectively 303.9 and 373.1 Gtyr-1).
These large inter-model differences could have three causes. First, the
bathymetry and ice shelf draft data used in Timmermann et al. (2012) and
Nakayama et al. (2014) come from RTOPO1, whereas Schodlok et al. (2016) and
the present study use bathymetry data from IBCSO and ice shelf draft data
from BEDMAP2. Differences in ice shelf geometry and bathymetry, particularly
the height of seabed sills, can strongly affect ice-shelf melting (Rydt
et al., 2014).
Second, the ability of off-shelf CDW to cross the shelf break and spread
across the continental shelf is a key control on the water mass structure
within the ice shelf cavities. In R_MLT (Fig. 14) and MITgcm (Shodlock
et al., 2016), CDW flow onto the shelf is well established. However, in the
FESOM simulations of Nakayama et al. (2014), the shelf water is colder than
the observations by 0.5 to 3 ∘C, depending of the horizontal
resolution used. Analysis of why CDW can cross the continental shelf break in
some models and not in others is beyond of the scope of this paper.
Finally, NEMO and MITgcm both use z coordinates, while FESOM use
a sigma coordinate around the Antarctic margin. In a sigma-coordinate model the
vertical resolution within the cavity is higher due to the concentration of
level beneath the ice shelf. In R_MLT, the number of wet levels in the
cavities varies from ∼ 10 levels near the ice fronts to two levels at
the grounding line, while in FESOM there are 21 levels everywhere. This
allows for better resolution near the grounding line and in the top boundary
layer. Shodlok et al. (2016) and the sensitivity experiments performed in
Sect. 3.3 show that some ice shelves (West, Dalton, Totten, George VI,
Larsen C and FRIS for example) are highly sensitive to the vertical
resolution, which affects the ocean properties on the continental shelf, the
representation of the top boundary layer beneath the ice shelf, and the
ability to resolve details of the cavity geometry.
Limitations
In addition to the inter-model differences described above, ice-shelf–ocean
models in general are still subject to several limitations. Most of them are
specific to our model set-up as well as the large uncertainties in geometry
and forcing data, and critical gaps in our knowledge of dynamics at the
ice–ocean interface.
The most recent bathymetry and ice shelf draft reconstruction of the Amundsen
Sea (Millan et al., 2017) shows features that are missing in the BEDMAP2
data-set. In BEDMAP2, for many ice shelves, there are only indirect
observations of ice draft, based on satellite surface elevation data, while
the sub-ice bathymetry data are often poorly constrained. For some ice
shelves (Getz, Venable, Stange, Nivlisen, Shackleton, Totten and Dalton ice
shelves, some of the thickest areas of the Filchner, Ronne, Ross and Amery
ice shelves and for the ice shelves of Dronning Maud Land), the flotation
condition had to be enforced by lowering the seabed arbitrarily from a level
that itself was based on nothing more than extrapolation of cavity thickness
from surrounding regions of grounded ice and 100 m thick cavity.
Consequently, more data are needed for effective modelling (Fretwell et al.,
2013), because cavity geometry has a major impact on the simulated melting by
controlling the water mass structure and circulation within the cavity (Rydt
et al., 2014).
Tides have a strong impact on high-frequency variability in melting as well
as the magnitude and spatial pattern of the temporal mean melt rate (Makinson
et al., 2011), but they are not taken into account in the present study.
Subglacial runoff can enhance melting at the ice–ocean interface, especially
near the grounding line (Jenkins, 2011). However, the location, magnitude and
variability of subglacial outflows from beneath the Antarctic Ice Sheet are
poorly known (Dierssen et al., 2002; Fricker et al., 2007).
The drag coefficient, as well as the friction law, affect the top velocity
and hence the turbulent exchange coefficients (Eqs. 12 and 13). The
appropriate drag coefficient for the base of an ice shelf of unknown
roughness is highly speculative, and the range of values discussed in the
literature is wide, ranging from 1.5 × 10-3 (Holland and
Jenkins, 1999) to 9.7 × 10-3 (Jenkins et al., 2010), while the
basal melting simulated in models is sensitive to the value chosen (Dansereau
et al., 2014; Gwyther et al., 2015; Jourdain et al., 2017). Furthermore, the
friction law commonly used to compute the drag is overly simplistic. The same
drag coefficient and friction law are used to compute the stress whatever the
dynamic regime appropriate for the grid point location beneath the ice shelf
(i.e. whether it lies within the boundary layer or the free stream flow
beyond).
Recent observations beneath George VI ice shelf exhibit thermohaline
staircases in the top 20 m below the melting ice shelf base, due to
double-diffusive convection (Kimura et al., 2015). These observations raise
a doubt about the applicability of the widely used three-equation model to
predict the melt rate in regions where the flow beneath the ice shelf is
weak. More experiments, observations and numerical simulations are needed to
fully understand the role of turbulence and thermohaline staircases
controlling the heat flux to melting ice shelves.
In addition, Dutrieux et al. (2013) suggested that melting can be concentrated
around kilometre-scale heterogeneities in ice thickness, such as keels and
channels, especially near the grounding line. Furthermore, Stanton
et al. (2013), from density measurements in the top 30 m of the ocean
beneath Pine Island Glacier, suggest that the top boundary layer can be less
than 5 m thick. This means either very high horizontal and vertical
resolution or a better melt formulation, or both, are needed to improve the
representation of processes near the grounding line and the ice shelf base.
Conclusions
An ice shelf capability has been implemented and evaluated in the NEMO model
framework following Losch et al. (2008). The work represents the first step
toward a couple ice sheet–ocean model. The working hypothesis used here is
that the ice shelf is in equilibrium, with the mass removed by melting being
replenished by the flow of the ice shelf, so the shape of the sub-ice-shelf
cavity remains constant over time.
In an idealised case (ISOMIP set-up), the simulated ocean circulation and ice
shelf melting are similar to those described by Losch et al. (2008) using the
MITgcm model. Ice shelf melting appears to be sensitive to vertical
resolution and top boundary layer definition. When the Losch top boundary
layer thickness is fixed, results are independent of vertical resolution and
converge toward those obtained with a vertical resolution equal to that of
the top boundary layer. When top boundary layer thickness changes with the
vertical resolution under melting conditions, models simulate a cold, fresh,
top boundary layer that tends to decrease the thermal forcing and thus the
simulated melt rate. At coarse resolution, the cold, top boundary layer is
absent, leading to much larger melt rates.
To apply this work to a realistic case, a southward-extended global ORCA grid
(eORCA) has been set up using two quasi-isotropic bipolar grids south of
67∘ S. The impact of including the ice shelf cavities has been
evaluated in a circum-Antarctic version of the eORCA grid, by comparison with
a control simulation without ice shelf cavities. The freshwater and heat flux
resulting from ice shelf melting is specified at the ice-shelf–ocean
interface for the simulation with cavities and at the ocean surface for the
control run.
For warm water shelves, prescribing the ice shelf melting at the surface
(R_noISF) leads to a stratification that is too strong compared with the
observations. With ice shelf cavities included (R_ISF), melting into the
cavity drives a buoyant overturning circulation and entrains warm and salty
CDW into the upwelling branch that subsequently mixes into the cold, fresh
surface layers outside of the cavity. The entrainment of CDW thus weakens the
thermocline by warming and increasing the salinity of the upper ocean layers,
resulting in a decrease of the ocean stratification. The activation of the
overturning circulation also creates a barotropic circulation that follows
f/h contours on the continental shelf.
For cold water shelves, high-salinity shelf water (HSSW) simulated in
R_noISF is slightly less dense than observations, but when ice shelf
cavities are present, the model is unable to maintain HSSW on the shelf at
all. Compared with the simulation without ice shelf cavities, two extra
processes consume the HSSW. The vertical overturning circulation driven by
melting acts to mix the HSSW with the upper layers all year long, and the
presence of new pathways beneath Ross and Filchner–Ronne ice shelves
increases the export of HSSW from its formation location on the western
continental shelf. The loss of HSSW with the ice shelf cavity opened is not
balanced by increased dense water formation at the surface. This could be
a result of deficiencies in any or all of the atmospheric forcing, the
sea-ice model used in this study, or the representation of coastal polynyas.
The effects on sea ice are very dependent on the amount of ocean heat
available at depth. Over warm water shelves, the CDW entrained into the
cavity overturning circulation warms the surface layer all year long and thus
restricts the sea ice formation. This warming of the surface layer leads to
thinning of the sea ice by more than 1 m in coastal regions of the
Bellingshausen and Amundsen seas (2 m locally). Over cold water
shelves, including the sub-ice-shelf cavities has a smaller effect on sea ice
thickness (less than 20 cm).
Hence, the inclusion of the ice shelf capability in NEMO has a major impact
on ocean and sea ice properties. However, the ice shelves vary greatly in
area, from O(100 km2) to O(100 000 km2); therefore, depending
on the application, more or fewer ice shelves will remain unresolved. In our
1/4∘ configuration the unresolved ice shelves contribute 25 %
of the total ice shelf meltwater flux from Antarctica, and at coarser
resolutions the majority of the freshwater source could be missing.
To mimic the circulation driven by these unresolved ice shelves, the ice
shelf melting is uniformly distributed over the depth and width of the
unresolved cavity opening, from the mean ice front draft down to the seabed,
or the grounding line depth if it is shallower. This simple representation of
the ice shelf melting drives a buoyant overturning circulation along the
coast similar to that would be present within the ice shelf cavity.
Idealised and realistic circum-Antarctic experiments show that this
parametrisation mimics the effect of the overturning circulation within small
ice shelf cavities and its impact on water mass properties and circulation on
the continental shelf. However, for large ice shelves, such as Ross and
Filchner–Ronne, the parametrisation is unable to mimic the effect of the
large-scale horizontal ocean circulation beneath the ice shelf. Thus, the
redistribution of meltwater and high-salinity shelf water between the
different troughs on the continental shelf via their connections under the
ice shelf is missing.
The specification of ice shelf melting, either over the area of the ice shelf
base for resolved cavities or over the area of the cavity opening for
unresolved cavities, leads to major improvements in the water mass
properties, ocean circulation and sea ice state on the Antarctic continental
shelf. However, a model that interactively computes ice shelf melting is
crucial for simulating the ocean and ice sheet response to perturbations as
well as for developing coupled ice-sheet–ocean models. With the parametrised
version of the ice shelf presented here, we only explain how to distribute
the meltwater fluxes in an ocean model without ice shelf cavities in
a physically sensible way. We do not describe a way to compute the melt rate
itself. To tackle this issue, this work needs to be combined with
a parametrisation of ice shelf melting (for example Beckmann and Goosse,
2003; Jenkins et al., 2011).
With the ice shelf cavities opened, the widely-used “three equation” ice
shelf melting formulation enables an interactive computation of melting. The
ability of the circum-Antarctic configuration with the “three equation” ice
shelf melting formulation to simulated realistic ice shelf melting has been
assessed. Comparison with observational estimates of ice shelf melting
reported by Rignot et al. (2013) indicates realistic results for most ice
shelves. However, melting rates for Amery, Getz and George VI ice shelves are
considerably overestimated and some key ice shelves, such as Totten and
Dalton, are missing because of inadequate horizontal and vertical resolution.
Possible causes of the overestimated melt rates include poor representation
of shelf water properties, inaccurate or poorly resolved cavity shape,
unknown ice shelf ocean drag coefficient and poor representation of boundary
layer processes.
Despite some deficiencies in the simulation of ice shelf melting and the
parametrisation of ocean processes in unresolved ice shelf cavities, this
work is a step forward toward a better representation of ice-shelf-ocean
interaction in the NEMO framework for all model resolutions. In practice, for
horizontal resolutions finer than 2∘, some of the ice shelf cavities
can be resolved (Ross ice shelf for example) while at almost any useable
resolution some cavities will have to be parametrised. The most suitable
choice of which can be explicitly resolved and which must be parametrised
will depend on the combination of horizontal and vertical resolution used.
To apply this work to a global coupled ice sheet–ocean model, we will need
some further developments. First, a better knowledge of sub-ice-shelf cavity
geometries and key processes that contribute to melting (drag, tides,
boundary layer, etc.) could lead to improvements in the ice shelf
representation. Second, parametrisations need to be developed to represent
the processes (melt and circulation) where the resolution is not fine enough
to represent the ice shelf cavity geometry correctly as at the grounding line
for example. Finally, a conservative wetting and drying scheme needs to be
developed to allow for the grounding line (and calving front) to move back and
forth.
The model code for NEMO 3.6 is available from the NEMO
website (www.nemo-ocean.eu). On registering, individuals can access the
FORTRAN code using the open-source subversion software
(http://subversion.apache.org/). The branch used for both
configurations used in this study is the 2015 development branch named
dev_r5151_UKMO_ISF at revision 5204. The ice shelf module is
now included in the public NEMO distribution.
The ISOMIP configuration is distributed in NEMO version 3.6 as an unsupported
configuration. No file is required to run ISOMIP configuration. For the
circum-Antarctic configuration, the input files (cpp keys, namelist,
bathymetry, ice shelf draft, iceberg runoff, initial condition, river runoff,
tidal mixing and weights for the surface forcings) could be requested from
the authors. The surface forcing and the open boundary were provided by the
DRAKKAR consortium (http://www.drakkar-ocean.eu).
The authors declare that they have no conflict of
interest.
Acknowledgements
The authors acknowledge financial support from the National Environmental
Research Council and the UK Met Office. Computational resources were provided
by the supercomputing facilities of the British Antarctic Survey and the
ARCHER UK National Supercomputing Service. The DFS5.2 forcing fields and the
open boundary conditions from the ORCA025-GRD100 simulation were provided by
the DRAKKAR coordination (CNRS GDRI no. 810). We thank Martin Losch, Julien Le
Sommer, Nicolas Jourdain and Jean-Marc Molines for their useful comments and
suggestions. We thank, Xylar Asay-Davis and one anonymous reviewer for their
detailed and very constructive comments on this work. Edited by: Sophie Valcke Reviewed by: Xylar Asay-Davis and one
anonymous referee
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