Introduction
The Marine Ice Sheet–Ocean Model Intercomparison Project (MISOMIP) is
a targeted activity of the World Climate Research Programme's Climate and
Cryosphere (CliC) project. MISOMIP is a community effort aimed at better
quantifying sea-level change induced by increased mass loss from the West
Antarctic Ice Sheet (WAIS), particularly the Amundsen Sea region. At the
first MISOMIP workshop,
participants decided that intercomparisons of ice sheet–ocean dynamics in
realistic configurations would be more credible if it was preceded by a more
idealized intercomparison and evaluation process for the stand-alone
components and coupled models involved. While MISOMIP's longer-term goal is
to investigate WAIS, participants in the workshop felt that the idealized
model intercomparison projects (MIPs) would be applicable to a wide variety of models used to investigate
a number of processes related to ice sheet and glacier interactions with the
ocean. In addition to model evaluation, these idealized MIPs should be
designed as a framework for exploring and comparing emergent properties of
the coupled system.
Marine Ice Sheet Model Intercomparison Projects (MISMIPs)
At the time of the workshop, two previous MIPs focused on verifying and evaluating stand-alone ice-sheet models for
marine ice sheets had taken place and a third was under development. The
first MISMIP compared the grounding-line dynamics between
14 models with a total of 27 unique configurations, and with a semi-analytic
solution . The MISMIP experiments were designed
for flow-line models in which topography and other model fields varied in only
one horizontal dimension (1HD). Within each experiment, a parameter (the ice
softness) was varied through a series of discrete values, leading to advance
and subsequent retreat of the grounding line. At each stage of the advance
and retreat cycle, the model was allowed to reach steady state, typically
over timescales of thousands to tens of thousands of years. The results
showed that steady-state grounding-line positions could differ markedly
depending on the resolution, type of stress approximation, and discretization
methods employed. Comparison between the semi-analytic solution and
high-resolution models with adaptive grids allowed the community to assess
which model configurations gave accurate results and which configurations
were likely not appropriate for marine ice-sheet studies. An important
finding of MISMIP related studies
was that models with fixed
grids (as opposed to those that track the grounding line in time) and without
sub-grid-scale parameterizations of the grounding line require grounding-line
resolution on the order of hundreds of meters to accurately reproduce
grounding-line dynamics.
The second ice-sheet MIP, MISMIP3d , aimed at exploring
grounding-line dynamics on centennial timescales in a configuration that
varied in 2HDs. Dynamic changes were induced
through a perturbation in the basal slipperiness in the center of the domain
near the grounding line. MISMIP3d also tested the reversibility of the
grounding-line position once the perturbation was removed. Results from 16
models with a total of 33 unique configurations showed that initial steady
states as well as the reversibility of the dynamics differed significantly
depending on the stress approximation and horizontal resolution.
Both MISMIP and MISMIP3d provided a basis for a number of follow-up studies
focused on both improvements in numerical methods
e.g., and exploring
changes in the model topography and physics parameterizations
e.g.,.
The third marine ice-sheet MIP (MISMIP+), described in
Sect. , examines marine ice-sheet dynamics in 2HDs with strong
buttressing. An idealized bedrock topography, based on the work of
and , was designed to produce
a steady state featuring a grounding line lying partly on a retrograde slope
in the absence of ice shelf melt. The three major MISMIP+ experiments
prescribe melt rates varying from no melt in a control experiment, to strong
melt rates, concentrated either close to or far from the grounding line,
which
are expected to drive rapid grounding-line retreat (up to ∼50 km per century), followed by re-advance when the melt rates are
restored to zero.
Ice Shelf–Ocean Model Intercomparison Projects (ISOMIPs)
ISOMIP was designed in an effort to identify systematic differences between
ocean models with sub-shelf cavities. The specifications for the first ISOMIP
included three idealized experiments with
sub-ice-shelf cavities based on . In the first
experiment, the entire domain was covered by an ice shelf while the second
and third experiments included a sharp calving front and a region of open
ocean with simplified atmospheric/sea ice forcing in the form of surface
restoring of temperature and salinity. The restoring was constant in time for
the second experiment and varied seasonally in the third. Each experiment was
prescribed to run for 30 years, at which point the ocean was expected to be
close to steady state.
Unfortunately, ISOMIP results were never collected and compared in a formal
publication. The few ISOMIP results that have been published or made publicly
available (; ; ) suggest that melt
rates as well as barotropic and overturning circulations varied between
models depending on the vertical discretization and resolution of the model.
In Sect. , we describe the design for a second ocean MIP with
ice-shelf cavities, ISOMIP+, which aims to improve upon the original ISOMIP
in several ways. Bedrock and ice-shelf topographies, based on MISMIP+
results, are more like those of realistic ice shelves in that the
water-column thickness goes to zero at the grounding line and the topography
varies in 2HDs, rather than 1HD. The melt parameterization and parameter
choices for horizontal mixing are closer to those used in realistic
applications. As opposed to forcing only at the ocean surface, ISOMIP+ uses
far-field restoring throughout the water column following
and , an approach more
similar to those commonly used in forced regional climate experiments.
Importantly, preliminary results show that restoring with a relatively warm
far-field temperature profile leads to a quasi-steady state within 1 to 2
year, whereas the 30-year ISOMIP experiments approached, but did not reach,
a steady state in which the ocean was at the freezing point everywhere.
Whereas ISOMIP used static ice-shelf topography, two ISOMIP+ experiments
prescribe dynamic topography, allowing models to test their ability to handle
moving boundaries and to see the effects that moving topography has on ocean
dynamics.
ISOMIP+ will also improve upon ISOMIP in terms of organized community
involvement as well as scientific developments. ISOMIP+ is expected to
benefit from the organization and active community of MISOMIP, as well as the
close relationship of ISOMIP+ to both MISMIP+ and MISOMIP1 (through the
shared experimental design and development towards coupled ice–ocean
models). These factors are likely to lead a larger number of ISOMIP+
participants and formal publication of the analysis, both of which were
lacking in ISOMIP.
Coupled ice sheet–ocean modeling
While no previous MIP has been performed with coupled ice sheet–ocean models,
a number of studies have used coupled ice sheet–ocean models, most in
idealized configurations. performed offline-coupled
simulations of a three-dimensional (3-D) ocean and 2-D ice-sheet model including dynamic calving
of tabular icebergs using idealized topography based on the Filchner–Ronne
Ice Shelf. and used
idealized, coupled modeling in 2-D (one horizontal and one vertical
dimension) to show that warm ocean conditions and variations in ice basal
sliding affected grounding-line motion and ice-shelf topography on decadal
timescales. coupled 3-D ice-sheet and ocean models to study
the dynamics of a sub-glacial lake. used the same
models to perform ice-sheet simulations driven by melt rates computed in the
ocean model, showing hysteresis following a melt perturbation applied to
idealized ice-sheet topography. showed
results from idealized, coupled experiments spanning 250 years using four
different profiles for the ambient water temperature. They showed that
feedbacks between the ocean and ice-sheet components led to steepening of the
ice draft near the grounding line and strong melting in a channel on the
western flank of the ice shelf. performed coupled
simulations of an idealized ice shelf based on Petermann Glacier with the
plume ocean model in 2HDs of , showing the influence of
channelization on total melt fluxes and melt distribution.
used the same plume model to further explore melt
channels in idealized configurations. used a plume
ocean model in 1HD to show that ice-shelf topography is
controlled by a balance between ice advection and either ice deformation or
ocean melting, depending on the temperature of the ambient ocean water.
used coupled 1-D flow-line models to explore the effects of
different melt parameterizations on coupled dynamics. A study by
used a coupled ice sheet–ocean model in an idealized
configuration similar to Pine Island Glacier to show the effect a seabed
ridge can have on grounding-line stability. They also concluded that coupled
ice–ocean modeling was required in their problem because commonly used
parameterizations of ice-shelf basal melting differed from those produced by
their ocean model by more than 40 %. While these individual studies have
advanced our understanding of ice sheet–ocean processes, a MIP involving
coupled ice sheet–ocean models is likely to improve our confidence in the
models through greater understanding of the variability and the causes of
differences in model results.
In Sect. , we describe the first Marine Ice Sheet–Ocean
Model Intercomparison Project (MISOMIP1), which combines elements from
MISMIP+ and ISOMIP+. In some ways, the MISOMIP1 setup is similar to that
of in that it includes a narrow channel
with strong ice-shelf buttressing and strong far-field restoring in the
ocean. MISOMIP1 differs from this previous work in having (1) steeper channel
walls, meaning a stronger change in buttressing as the ice-shelf thickness
changes, (2) a larger region of open ocean allowing for ocean dynamics both
inside and outside the cavity, and (3) a bedrock topography with an
upward-sloping region in the ice-flow direction, allowing us to investigate
the possibility that thinning or other changes in the state of the ice sheet
could trigger marine ice-sheet instability MISI;
e.g.,.
Goals of the three new MIPs
The MIPs were designed with three main goals in mind. As in their
predecessors (ISOMIP, MISMIP and MISMIP3d), the first goal of the MIPs is to
provide a controlled forum for researchers to compare their model results
with those from other models during model development. Furthermore, it is
hoped that researchers will publish their MIP results and/or submit them to
the relevant MIP database when they introduce new ice sheet models, ocean
models with ice-shelf cavities or coupled ice sheet–ocean models. Differences
between models should be investigated, understood and explained. We have
endeavored to keep the MIP setups relatively simple to make them relevant and
accessible to the largest possible number of potential contributors and to
make them easy to duplicate, while still capturing physical processes
relevant to ice sheet–ocean dynamics.
The second goal is for the three MIPs to provide a path for testing
components in the process of developing a coupled ice sheet–ocean model.
Within ISOMIP+, the experiments progress from static to dynamic (but
prescribed) ice topography with the same goal in mind. Meeting this goal has
required that all three MIPs be designed simultaneously, ensuring that they
use the same bedrock topography (bathymetry) and compatible domains.
Grounding-line dynamics in MISMIP+ is controlled by a melt profile that
adapts to the ice topography and qualitatively mimics example results from
ISOMIP+. Ice topography (both static and dynamic) for ISOMIP+ comes from
example MISMIP+ results. In addition, two ISOMIP+ experiments have been
designed to produce large changes in melting over a short period of time
(less than a decade), mimicking the abrupt changes in the melt rate applied in
MISMIP+. All three MIPs include an experiment with 100 years of ice retreat
followed by 100 years of re-advance, allowing evaluation of stand-alone and
coupled simulations of essentially the same problem.
Our third goal is that each MIP should provide a basic setup from which
a large variety of parameter and process studies can usefully be performed.
Each MIP setup uses idealized topography and simplifies or ignores known
physics. These simplifications leave opportunities for others to study the
effects of adding missing processes (e.g., a more realistic calving law,
a basal hydrology model, sub-glacial meltwater runoff across the grounding
line, wind stresses, sea-ice formation and export, tides, time-varying
far-field ocean forcing). Results may be affected by parameterizations (e.g.,
ice sliding law, melt parameterization, mixing schemes in the ocean, equation
of state) and other choices (e.g., horizontal and vertical resolution,
coupling interval, ice rheology) that the community may choose to
explore in more detail.
MISMIP+ design
A number of previous MIPs not specifically focused on marine ice sheets have
explored model physics EISMINT;, provided benchmarks for
higher-order stress approximations ISMIP-HOM; and
demonstrated modes of internal variability ISMIP-HEINO;,
improving our understanding of ice-sheet models. The previous Marine Ice
Sheet MIPs, MISMIP and MISMIP3d, tested the capabilities of ice sheet models
to simulate advance and retreat cycles under changes in ice softness and
basal sliding, respectively, each teaching the community a great deal about
the numerical behavior of ice-sheet models of various types. Nonetheless, it
was clear in discussions of a follow-up intercomparison exercise that the
MISMIP3d experimental design had three shortcomings as a test of 2HD marine
ice sheet models. First, it started from a steady state that was invariant in
the crossflow direction – that is, 1HD – meaning it did not involve
significant lateral stresses. Second, the initial grounding lines of the
shallow-shelf approximation (SSA) models were around
80 km downstream from the Stokes models, but the grounding line only moved
about 20 km in the perturbation experiment. That left an obvious
question entirely unanswered: in a realistic simulation with the model
parameters chosen to match geometry and velocity derived from observations,
and thus with prescribed initial conditions, does the SSA provide a good
approximation to the Stokes model? Third, grounding-line migration was driven
by changes to the basal-traction field, rather than the ice shelf melting
that is thought to be the dominant driver of present-day grounding-line
retreat in West Antarctica .
Parameters for the MISMIP+ experiments.
Parameter
Value
Description
Lx
640 km
Domain length (along ice flow)
Ly
80 km
Domain width (across ice flow)
B0
-150.0 m
Bedrock topography at x=0
B2
-728.8 m
Second bedrock topography coefficient
B4
343.91 m
Third bedrock topography coefficient
B6
-50.57 m
Fourth bedrock topography coefficient
x¯
300 km
Characteristic along-flow length scale of the bedrock
fc
4.0 km
Characteristic width of the side walls of the channel
dc
500 m
Depth of the trough compared with the side walls
wc
24.0 km
Half-width of the trough
zb,deep
-720 m
Maximum depth of the bedrock topography
xcalve
640 km
The location in x beyond which ice is removed
ρi
918 kgm-3
Density of ice
ρsw
1028 kgm-3
Density of seawater
Ω
0.2 a-1
Melt-rate rate factor
z0
-100 m
Depth above which the melt rate is zero
Hc0
75 m
Reference ocean-cavity thickness
a
0.3 ma-1
Accumulation rate
A
6.338×10-25 Pa-3s-1
Glen's law coefficient
= 2.0×10-17 Pa-3a-1
n
3
Glen's law exponent
m
3
Friction-law exponent
α2
0.5
Coulomb law friction coefficient
β2
3.160×106 Pam-1/3s1/3
Power-law friction coefficient
= 1.0×104 Pam-1/3a1/3
g
9.81 ms-2
Acceleration of gravity
–
31 556 926 sa-1
Seconds per year (defined to have 365.2422 days)
MISMIP+ has been designed to address each of these shortcomings. Regarding
the first, the chosen geometry, based on , results in
strong lateral stresses that buttress the ice stream. The particular
parameters chosen for MISMIP+ result in a stable grounding line crossing
a retrograde slope, a configuration not possible in 1HD. Regarding the
second, modelers are free to choose certain model parameters so that their
initial grounding line at the center of the domain is within a tolerance of
a prescribed location. Preliminary simulations with the BISICLES ice sheet
model with two stress approximations that showed large
differences in grounding-line position in the MISMIP3d experiments have been
found to have grounding lines within a few kilometers of one another in the
MISMIP+ steady state. Finally, extensive grounding-line retreat is driven
by sub-shelf melt rates.
Experimental setup
The MISMIP+ domain is a box bounded by 0≤x≤640 km and
0≤y≤80 km. The bedrock topography,
shown in Fig. , is a smaller version of that given in
and :
zb(x,y)=maxBx(x)+By(y),zb,deep,
Bx(x)=B0+B2x̃2+B4x̃4+B6x̃6,x̃=x/x¯,By(y)=dc1+e-2y-Ly/2-wc/fc+dc1+e2y-Ly/2+wc/fc,
where the parameter values used in these equations, along with several others
related to the MISMIP+ experiment, are given in
Table . As in , there is
a no-slip boundary condition at x=0 and free-slip boundaries at y=0 and
80 km. Ice is removed from the domain beyond xcalve=640 km but no other calving criterion is specified.
Englacial deviatoric stresses τij are related to strain-rates Dij
through Glen's flow law. As in previous MISMIP exercises,
τij=A-1/nDe1/n-1Dij,
where n=3. De is the second scalar invariant of the strain-rate,
given by 2De2=DijDji, with the usual summation convention.
The ice is isothermal, with a constant rate factor A independent of space,
with a value determined by the participant as discussed below.
As in the previous MISMIP experiments, MISMIP+ uses a symmetry boundary
condition at the ice divide, ocean pressure (up to sea level) at the
ice–ocean interface, and stress-free boundary conditions at the upper surface
seefor details. Where the ice is grounded,
the tangential component of the basal traction
τntzb is given by any of three relationships:
a power law, a modified power-law relation introduced by , or
a second modified power-law relation introduced by and
explored by and . Participants are
free to choose any or all of these.
The bedrock topography for the three MIPs as defined by
Eqs. ()–(). (a) The variability of the
bedrock topography in the x direction. The topography through the central
trough, Bx(x), is shown in blue and on the side walls is shown in red.
(b) By(y), the shape of the bedrock topography in the
y direction relative to that at the center of the trough. Note that
By(y) is not a transect of the topography because Bx(x) is
never equal to zero. (c) The topography in 3-D at 1 km
resolution. Sea level is shown in translucent blue.
The power law is
τntizb=β2ub1/m-1uti(i=1,2),
where uti are the two tangential components of the velocity with magnitude ub,
m=3, and β2 is a friction coefficient, which is invariant in space and with
a suggested value given in Table . The value of β2 may
be modified by the participant (see below).
Evolution of the basal traction
τntzb and ice shelf melt rate mi
fields during the Ice1r and Ice1ra experiments from a BISICLES run. Melt
rates are applied when 0<t<100 a, causing the ice shelf to
thin and grounding line to retreat. Once t>100 a, no melt is
applied, the ice shelf thickens, and the grounding line advances. The choice
of the traction law ensures that
τntzb is continuous across the grounding line
but large ∼1 km upstream. Similarly, the factor tanhHc/Hc0 ensures that mi is
continuous across the grounding line but large ∼10 km
downstream.
The first modified law differs from the power law by preventing the basal
traction from exceeding the value given by a Coulomb law, that is, a fraction
of the effective pressure N:
τntizb=minα2N,β2ub1/mub-1uti(i=1,2),
where α2=0.5. N should be constructed by assuming a perfect
hydrological connection with the ocean so that
N=-σnn-ρswgzd.
Hydrostatic models should approximate the normal stress σnn in the
usual way, giving
N=ρig(h-hf),
where g is the acceleration of gravity, h is the ice thickness and
hf=max0,-ρswρizb
is the flotation thickness given the bedrock elevation zb and the
reference densities of ice and seawater ρi and ρsw.
Expressing the basal traction in this way ensures that it is continuous
(though not differentiable) across the grounding line, but grows to ∼10–100 kPa over the region ∼1 km upstream (see
Fig. ).
The second modified law has the same limits as the first modified law (the power law
for large effective pressure, and the Coulomb law near the grounding line where the effective
pressure approaches zero) but transitions between these limits more smoothly:
τntizb=β2ub1/mα2Nβ2mub+α2Nm1/mub-1uti(i=1,2).
In this form, basal traction remains continuous everywhere and differentiable
everywhere except across the grounding line.
We note that Eq. () is a zeroth-order hydrology
model that assumes connectivity to the ocean throughout the domain and is
likely only valid within a few tens of kilometers of the grounding line
. It is likely that simulations using more realistic
topography would require a more sophisticated hydrology model to produce
results consistent with observations inland of the grounding line.
We prescribe that the steady-state grounding line should cross the centerline
of the trough at x=450±10 km, ensuring that all models start
from similar initial states. Participants should adjust the grounding-line
position by modifying first the values of A and, if necessary, the value of
β2 beginning with the suggested values given in
Table . We have adopted this approach for model
initialization to be more consistent with the methods used to initialize
models for real-world problems: unknown parameters or fields are determined
by search or inversion techniques so that initial conditions are consistent
with observations. The precise method used to adjust A and/or β2 and
for finding the steady state is left up to the participant. Some participants
will spin up their models for tens of thousands of years with different
parameter values until the grounding line lies within the desired position.
Others might construct a more formal optimization problem and solve it with
variational methods.
A constant accumulation rate a, with the value given in
Table , is applied over the entire ice surface. One of
the three MISMIP+ experiments uses a parameterization of basal melting
below the ice shelf, obtained by balancing the latent heat of melting with
parameterized turbulent heat flux within the ocean ,
neglecting the heat flux into the ice:
mi=ρiρfwmw=ρicwΓTρfwLu*Tw-Tf,
where mi is the basal melt rate of ice, mw is the same
melt rate expressed in water equivalent (weq), ρfw
is the density of fresh water, cw is the heat capacity of seawater,
L is the latent heat of fusion, ΓT is the heat-transfer
coefficient, u* is the ocean friction velocity and T*=(Tw-Tf) is the thermal driving, the difference between the ambient ocean
water temperature Tw and the local freezing point Tf.
For the purposes of model intercomparison, we have developed an ad hoc,
simplified parameterization of basal melting based on results from the
Parallel Ocean Program v. 2x (POP2x) using cavity shapes from a MISMIP+
simulation. The parameterization prescribes melt rates as follows:
mi=ρicwΓTρfwLu*(Hc)T*(zd),
u*(Hc)=u*,0tanhHcHc0,T*(zd)=T*,0zrefmaxz0-zd,0,Hc=zd-zb,
where zd is the elevation of the ice–ocean interface (ice draft),
Hc is the water-column thickness, and u*,0, Hc0,
T*,0 and zref are fitting constants.
The POP2x results suggest that the friction velocity u* increases linearly
near the grounding line (for small Hc) but saturates to a nearly
constant value when the ocean-cavity thickness exceeds a threshold thickness
Hc0=75 m. also showed that
melt rates tend to approach zero near the grounding line in a number of
experiments, though he found that glacial meltwater fluxes can lead to
increased melt rates immediately adjacent to the grounding line. Glacial
meltwater fluxes are neglected here. In their idealized simulations studying
the behavior of meltwater impeded by a bathymetric ridge,
saw a similar tapering of the melt rate near the
grounding line. It should be noted that melt rates near grounding lines are
not well constrained by observations and that ocean models may have
particular difficulty in these regions. Therefore, the dependence upon water-column thickness should be treated as an ad hoc formulation for the purpose
of a model intercomparison and not necessarily as a realistic representation
of melting near grounding lines.
(a) A schematic showing the ice draft (zd), the
bedrock elevation (zb), the cutoff depth (z0) above which the
melt rate is zero, the ocean column thickness (Hc) and the
reference thickness Hc0. (b) The melt parameterization
given by Eq. (). Melting increases linearly with
decreasing zd below z0 and is independent of Hc when
the ocean column is thick and zero near the grounding line as the ocean column
thins.
The POP2x simulations used to calibrate the parameterization had
a temperature profile that increased linearly with depth (similar to the
profiles described in Sect. ), leading to a thermal
driving that also increased approximately linearly with depth. Thermal
driving, and therefore melting, reached zero at a depth z0∼-100 m. Though the simulations showed some freezing above this
depth, our parameterization assumes for simplicity that no melting or
freezing occurs at depths shallower than z0≡-100 m.
We simplify mi by lumping various constants and coefficients from
Eqs. ()–() into a single coefficient
Ω:
mi=ΩtanhHcHc0maxz0-zd,0.
Fig. shows a schematic of the ice shelf, labeling
the various depths and thicknesses involved in the melt parameterization, as
well as the melt rate as a function of zd and Hc. Again,
the parameter values are given in Table . The
coefficient Ω has been given a value of 0.2 a-1,
corresponding to a maximum ambient ocean temperature ∼1.0 ∘C, which leads to a melt rate with a maximum value of
mi≈75 ma-1 of ice near the grounding line of
the BISICLES initial condition (see Fig. ). We reiterate
that the formulation given by Eq. () is an ad hoc
parameterization appropriate only for this intercomparison and not
appropriate for other geometries, ocean ambient temperatures, etc. The melt
parameterization is missing known physics such as dependence on the slope of
the ice draft and superlinear dependence on ambient
ocean temperature .
Experiments
MISMIP+ consists of three experiments with different melt rates. Each
experiment is initialized with mi=0 (no melting), and should
begin with a stable grounding line crossing the center of the channel on the
retrograde slope around x=450±10 km. Stable in this case
means that the ice sheet thickness and the grounding-line position is
permitted to fluctuate, but any fluctuations should average to zero over
time, and should be of low amplitude compared to the response to
perturbations. Preliminary experiments indicate that, starting from a uniform
thickness of 100 m, a stable state is found after around
20 000 a. One experiment (Ice0) is simply a control, where the melt
rate is maintained at mi=0 for 100 years, while the other two
(Ice1 and Ice2) are intended to study the response to substantial ice shelf
ablation.
List of the MISMIP+, ISOMIP+ and MISOMIP1 experiments.
MIP
Experiment
Description
MISMIP+
Ice0
100-year control simulation with no melting
MISMIP+
Ice1r
100-year run with melt-induced retreat
MISMIP+
Ice1ra
100-year (or optionally up to 900-year) simulation
from end of Ice1r with no melting
MISMIP+
Ice1rr
Continue Ice1r for a further 900 years (optional)
MISMIP+
Ice2r
100-year “calving-event” simulation
MISMIP+
Ice2ra
100-year (or optionally up to 900-year) simulation
from end of Ice2r with no melting
MISMIP+
Ice2rr
Continue Ice2r for a further 900 years (optional)
ISOMIP+
Ocean0
1-year run with static topography, WARM initial
conditions and WARM forcing
ISOMIP+
Ocean1
20-year run with static topography, COLD initial
conditions and WARM forcing
ISOMIP+
Ocean2
20-year run with static topography, WARM initial
conditions and COLD forcing
ISOMIP+
Ocean3
100-year run with dynamic topography, WARM initial
conditions and WARM forcing
ISOMIP+
Ocean4
100-year run with dynamic topography, COLD initial
conditions and COLD forcing
MISOMIP1
IceOcean1r
100-year coupled run with no dynamic calving,
COLD initial conditions and WARM forcing
MISOMIP1
IceOcean1ra
100-year coupled run from end of IceOcean1r with
no dynamic calving and COLD forcing
MISOMIP1
IceOcean2r
Optional: 100-year coupled run with dynamic calving,
COLD initial conditions and WARM forcing
MISOMIP1
IceOcean2ra
Optional: 100-year coupled run from end of
IceOcean2r with dynamic calving and COLD forcing
Experiment Ice1 is divided into several parts, all beginning with Ice1r,
where the melt rate given in Eq. () is applied from
t=0 to t=100a, and is expected to produce thinning of the ice
shelf, a loss of buttressing, and grounding-line retreat. Ice1ra starts from
the state computed at the end of the Ice1r simulation and runs at least until
t=200 a, and optionally until t=1000 a, with no
melting, so that the ice shelf thickens, buttressing is restored and the
grounding line advances. Preliminary simulations have shown that the
grounding-line position does not reach its initial steady state within even
1000 years. Finally, Ice1rr is optional and continues Ice1r, with the melt
rate of Eq. (), until t=1000 a.
Figure shows example basal-traction and melt-rate fields
calculated at several points during the Ice1r and Ice1ra experiments.
Experiment Ice2 is structured in the same way as Ice1, but a different melt
rate is applied. The Ice1 melt rate adjusts to pursue the grounding line as
it retreats, preventing the formation of a substantive ice shelf. In
contrast, Ice2r prescribes a sub ice-shelf melt-rate of
100 ma-1, where x>480 km and no melt elsewhere from
t=0 to t=100 a, resulting in substantial loss of ice concentrated
away from the grounding line, as in a sequence of extensive calving
events. Preliminary calculations show that the grounding line
retreats for more than 20 km but begins to stabilize as a thick ice
shelf forms in its wake. Ice2ra takes the endpoint of the Ice2r experiment as
its initial state, and evolves the ice sheet with no melting until t=200 a and optionally until t=1000 a, while Ice2rr is
optional and continues Ice2r to t=1000 a.
As an example, Fig. plots grounded area
against time for all of the MISMIP+ experiments carried out with BISICLES
using SSA. We emphasize that the example results shown in this figure are
not intended as a benchmark for other simulations, but simply to
demonstrate generally what type of behavior might be expected in each
experiment. Table gives a brief summary of the
MISMIP+ experiments, as well as those from the other two MIPs.
Grounded area plotted against time for the MISMIP+ experiments,
computed using BISICLES with the SSA and the basal traction.
The Ice0, Ice1r and Ice2r experiments all start from steady-state, and apply
either zero melt (Ice0) or melt rates derived from simple formulae (Ice1r and
Ice2r) from t=0 to t=100 a. Following on from Ice1r, the Ice1ra
and Ice1rr experiments evolve the ice sheet until at least t=200 a and optionally to t=1000 a, with the melt rate set
to zero in Ice1ra and derived from the same formula as Ice1r in Ice1rr.
Ice2ra and Ice2rr follow on from Ice2r in a similar
fashion.
Figure shows the sensitivity of the
BISICLES Ice1r results to various choices of basal traction, stress
approximation, and values of A. Results are nearly insensitive to the
differences between the basal-traction parameterizations of
and , and also to differences between two stress
approximations, SSA and SSA* . However, the simulations
with the basal traction of show a significant difference
in both the initial grounded area and the rate of retreat compared with the
other parameterizations. Furthermore, even when A is adjusted so that the
initial grounding-line position (and therefore the grounded area) is in
agreement with the other configurations, the rate of retreat remains
significantly slower than for the other parameterizations.
Requested output
MISMIP+ requested output is divided into compulsory and optional parts. The
compulsory components will be used to write an analysis paper, along the
lines of the MISMIP3d paper . The optional data will be
included with the compulsory data in an open-access database.
Participants are required to supply point data at the grounding line, along
the same lines as MISMIP3d, as well as integrated quantities such as volume
above flotation, at set times throughout the experiments. Data should be
stored in a single NetCDF 4 file for each experiment with the file-naming
convention of [expt]_[MODEL].nc, where [expt] is
an experiment name from Table and [MODEL] is
a unique identifier for the participant. For the core experiments, where 0≤t≤200, data should be provided every 10 years starting from t=0, while for the optional extensions, data should be provided every
100 years starting from t=200. Since the length of the grounding line
varies over time, we expect that the number of point data required to describe
it will vary over time in all models. It will be left to each participant to
decide how to determine location of the grounding-line points (e.g., taking
cell edges between grounded and floating regions or performing sub-grid-scale
interpolation).
We ask participants to use the variable and dimension names given in bold and
units given in square brackets as follows:
nPointGL: an unlimited dimension – a netCDF4 feature that allows nPointGL to be
decided as the data are written;
nTime: a fixed dimension;
time(nTime) [a]: the time in years since the beginning of the experiment;
iceVolume(nTime) [m3], iceVAF(nTime) [m3], groundedArea(nTime)
[m2]:
the ice volume, volume above flotation, and the grounded area, integrated
over the domain;
xGL(nPointGL,nTime), yGL(nPointGL,nTime) [m]: the x and y coordinates of a given point on the grounding line;
iceThicknessGL(nPointGL,nTime) [m]: ice thickness at the grounding line;
uBaseGL(nPointGL,nTime), vBaseGL(nPointGL,nTime) [ma-1]: the x and y components of the basal velocity;
uSurfaceGL(nPointGL,nTime), vSurfaceGL(nPointGL,nTime) [ma-1]: the x and y components of the surface velocity;
uMeanGL(nPointGL,nTime), vMeanGL(nPointGL,nTime) [ma-1]: the x and y components of the vertical mean of the velocity.
Since the number of grounding-line points n(t) will vary over time, most of
the slices xGL(:,t) will contain missing values, which should be
filled with the default value NC_FILL_FLOAT. In Python, C and
Fortran this can be achieved by writing data for each time step in turn into
the first n(t) elements of the slice xGL(:,t). At the same time,
the unlimited dimension nPointGL will be automatically adjusted by
the netCDF library routines to the maximum value of n(t). Two python
programs are included in the Supplement: write_example.py creates a netcdf
file given data in the MISMIP3d text file format, and plot_example.py reads
example netcdf files, constructs a plot like
Fig. , and takes advantage of numpy's masked
array class to show the changing shape of the grounding line.
BISICLES parameter sensitivity in the MISMIP+ Ice1r experiment.
The and basal-traction laws lead to
similar initial states and rates of retreat, as do the SSA and SSA* stress
approximations, given the same rate factor A0=2.0×10-17 Pa-3a-1. On the other hand the, the Weertman basal-traction law results in a grounding line some way upstream given the same
rate factor, a closer grounding line when the rate factor is increased to
A1=2.2×10-17 Pa-3a-1, and a far slower rate of
retreat in either case.
All submissions should include a brief model description, in a pdf file,
which summarizes the stress approximation and parameters used, and evidence
that simulations are adequately resolved. The model summary should be
an enumerated list, indicating
Parameters shared between all five ISOMIP+ experiments.
Parameter
Value
Description
x0
320 km
Southern boundary of the domain
y0
0
Eastern boundary of the domain
Lx
480 km
Domain length (south to north, along ice flow)
Ly
80 km
Domain width (east to west, across ice flow)
Hcalve
100 m
Minimum thickness of ice, below which it is removed
θc
75∘ S
Latitude of the center of the domain
γ0
10 days-1
Restoring decay rate at the northern boundary
xr0
790 km
Southern edge of the restoring region
xr1
800 km
Northern edge of the restoring region
model: the name of the model (e.g., BISICLES), with a citation if available;
repository: a link to the repository where the model can be
downloaded (if public) and specific tag, branch or revision (if available);
englacial stresses: the stress approximation and coefficients (e.g., SSA, A=2.0×10-17 Pa-3a-1);
basal traction: the choice of law and coefficients, e.g., |τb|=β2ub1/3, β2=104 Pam-1/3a1/3;
space discretization: e.g., finite volume, adaptive non-uniform grid, square cells 0.25 km < Δx<4.0 km;
time discretization: e.g., Piecewise Parabolic Method, explicit, Δt<Δx/(4|u|);
grounding line: any special treatment of the grounding line, e.g., one-sided differences of surface elevation;
MISMIP3d name: the name of the model in MISMIP3d, with any relevant differences, e.g., DMA6 (different mesh resolution).
Evidence that the submissions are adequately resolved will vary from model to
model. Typically, models should simply carry out a convergence study of
experiment Ice1r and Ice1ra, showing that the grounding-line shape and
positions at the start and end of Ice1r and the volume-above-flotation curves
throughout the experiments converge with mesh refinement and differ by
a fraction at the finer resolutions. An example model description is included
in the Supplement.
Optionally, participants can add further high-volume data to their NetCDF
file. These consist of several fields on a uniform 1 km grid, and are
the same fields requested in the coupled IceOcean experiments. They will not
be used in the MISMIP+ analysis paper, but will be freely available once
the analysis is published. The optional fields are
nx,ny. fixed dimensions, cell-centered points on an 800×80 grid of 1 km squares;
x(nx) and y(ny) [m] cell centers of the output grid as vectors. The grid spacing is 1 km;
iceThickness(nTime,ny,nx) [m] ice thickness;
upperSurface(nTime,ny,nx), lowerSurface(nTime,ny,nx) [m] upper and lower surface
elevation;
basalMassBalance(nTime,ny,nx) [ma-1] of ice (not water equivalent) basal mass balance (melt rate), positive for melting and negative for
freezing;
groundedMask(nTime,ny,nx), floatingMask(nTime,ny,nx) the fraction of grounded or floating ice in a given
cell;
basalTractionMagnitude(nTime,ny,nx), [Pa] the magnitude of the tangential basal-traction field
τnt|b;
uBase(nTime,ny,nx), vBase(nTime,ny,nx) [ma-1] x and y components of the basal
velocity;
uSurface(nTime,ny,nx), vSurface(nTime,ny,nx) [ma-1] x and y components of the surface
velocity;
uMean(nTime,ny,nx), vMean(nTime,ny,nx) [ma-1] x and y components of the vertical mean of the velocity.
ISOMIP+ design
The ISOMIP+ experiments have been designed to make a number of improvements
on the original ISOMIP experiments. Whereas ISOMIP used highly idealized
topography (the ocean column at the grounding line was 200 m thick,
the ice draft sloped linearly with latitude and was invariant with longitude,
and the bedrock was perfectly flat), ISOMIP+ makes use of relatively
complex topography from MISMIP+ BISICLES simulations, including an ocean
cavity that reaches zero thickness at the grounding line. Where ISOMIP uses
a velocity-independent, two-equation formulation of the melt boundary
conditions, ISOMIP+ uses the velocity-dependent three-equation formulation
e.g., more commonly used in realistic
model configurations. ISOMIP specified ∼10 km resolution, too
coarse to resolve the 9 km Rossby radius of deformation
, and large values of the horizontal viscosity and
diffusivities, leading to a laminar flow that evolved toward steady state
without eddies or other fluctuations. In contrast, ISOMIP+ runs will
typically use smaller horizontal viscosity and diffusivities and higher
resolution (∼2 km), allowing for mesoscale eddies and unsteady
flow. A smaller computational domain makes the experiments computationally
feasible despite the higher resolution. ISOMIP+ should provide more
appropriate test cases than the original ISOMIP for realistic experiments,
particularly for those focused on the Amundsen Sea region of WAIS.
ISOMIP+ prescribes five experiments, Ocean0 through Ocean4. Ocean0–2 have
fixed topography while Ocean3–4 have prescribed, evolving ice topography.
The experiments are summarized in Table .
Shared setup across the five experiments
We request that ISOMIP+ participants perform each experiment once at
a common resolution and with a common set of parameters (hereafter, the COM
configuration), and once at a typical resolution and with typical parameters
they would use for a realistic problem (hereafter, the TYP configuration).
TYP allows participants to choose resolution, parameters and
parameterizations typical to each model as it is most often used. We ask
participants who do not feel they have time to perform both the COM and TYP
experiments to prioritize the COM experiments.
Parameters recommended for the common (COM) experiments.
Parameter
Value
Description
Δx=Δy
2 km
Horizontal resolution
cw
3974 J∘C-1kg-1
Specific heat capacity of seawater
L
3.34×105 Jkg-1
Latent heat of fusion of ice
λ1
-0.0573 ∘CPSU-1
Liquidus slope
λ2
0.0832 ∘C
Liquidus intercept
λ3
-7.53×10-8 ∘CPa-1
Liquidus pressure coefficient
ΓT
model specific
Nondimensional heat-transfer coefficient
ΓS
ΓT/35
Nondimensional salt-transfer coefficient
CD,top
2.5×10-3
Top drag coefficient
CD,bot
2.5×10-3
Bottom drag coefficient
utidal
0.01 ms-1
RMS velocity associated with tides
κi
0
Heat diffusivity into ice (perfectly insulating)
νunstab
0.1 m2s-1
Convective vertical viscosity
κunstab
0.1 m2s-1
Convective vertical diffusivity
νstab
1×10-3 m2s-1
Stable vertical eddy viscosity
κstab
5×10-5 m2s-1
Stable vertical eddy diffusivity
νH
6.0 m2s-1
Horizontal eddy viscosity
κH
1.0 m2s-1
Horizontal eddy diffusivity
ρfw
1000 kgm-3
Density of fresh water
ρsw
1028 kgm-3
Reference density of seawater
Tref
-1 ∘C
Reference potential temperature for linear equation of state (EOS)
Sref
34.2 PSU
Reference salinity for linear EOS
ρref
1027.51 kgm-3
In situ density for linear EOS
αlin
3.733×10-5 ∘C-1
Thermal expansion coefficient for linear EOS
βlin
7.843×10-4 PSU-1
Salinity contraction coefficient for linear EOS
The purpose of COM is to produce results that can be more easily
intercompared. We would like to discover the consequences of certain modeling
choices (e.g., the horizontal and vertical discretization), keeping as many
aspects of the configuration as possible common to all participating models.
TYP will allow us to compare the results of models as they are configured for
real problems and to better understand the diversity of results that
different modeling choices produce. Given that there is currently no
“right” answer to the ISOMIP+ experiments – there are no observations or
exact mathematical solutions with which to compare – the spread in TYP model
results is expected to give us insight into how uncertainties reflected in
parameter choices affect model solutions.
Parameters general to both COM and TYP runs are given in
Table , while parameters specific to the COM runs are
given in Table .
Domain and topography
The ISOMIP+ domain is a Cartesian box bounded by 320 km ≤ x≤800 km and 0≤y≤80 km, overlapping with the
right half of the MISMIP+ domain. To aid in describing features within the
domain, we define positive x as pointing north (the flow direction of most
Antarctic ice shelves) and positive y as pointing west. These directions
have no dynamic consequences. A region of open ocean extends beyond the edge
of the MISMIP+ calving front (which is not allowed to advance beyond
xcalve=640 km) on the northern side of the domain. The
southern boundary has been placed far enough south to accommodate the
retreated ice-shelf topography used in Ocean2, which is also the most
retreated state in Ocean3 and Ocean4.
The Coriolis parameter requires latitude to be defined over the domain. We
prescribe an f plane configuration (, Chapt. 7;
, Chapt. 6)
at 75∘ S latitude, although models that
do not support an f plane should vary latitude in the x direction with
75∘ S at the center of the domain (and mention this in the description pdf
that participants will submit with their results).
Longitude plays no role in the dynamics, and can be defined
arbitrarily.
The bathymetry is the same as in Eq. (). Because the ice-draft
topography is derived from ice-sheet model results, it cannot be described by
an analytic function. Instead, both the topography used for Ocean0–2 and the
snapshots used to produce the dynamic topography for Ocean3–4 come from
MISMIP+ BISICLES results, and are available in NetCDF format for download
. The topography data come from the BISICLES model
in the SSA configuration. The topography is provided on
a uniform 1 km grid so that participants can process the data as they
require. We prescribe a slightly coarser resolution, 2 km, for COM
runs, since POP2x simulations indicated that 1 km resolution would be
too time consuming and resource intensive for some participants in the MIP.
For both COM and TYP runs, participants are expected to interpolate the
ice-sheet topography to the ocean grid as part of whatever processing is
required to make the data ocean-model friendly. To aid later analysis of the
effect these modifications to the topography might have on the results,
participants are asked to provide a description of their model specific
modifications, e.g., smoothing, determining regions of land, open ocean and
ice-shelf cavity, and expanding the water column to a minimum thickness. The
calving criterion, described below, should also be applied during this
processing step.
Some participating ocean models require a surface pressure rather than the
ice draft as the upper boundary condition. These models are free to compute
the ice thickness from the ice surface elevation and ice draft provided in
the input geometry, and multiply these by ρig to get a pressure.
Equivalently, the pressure can be derived from the ice draft as
pzd=-ρswgzd. The elevation of the
ice–ocean interface in the model will differ slightly from the prescribed
zd because of the dynamic pressure and variations in the ocean
density, but the slight variation in topography across models is not expected
to contribute significantly to differences between model results.
Calving
The MISMIP+ experiments explicitly exclude a dynamic calving criterion,
allowing the ice to become arbitrarily thin without calving. We felt that it
was important that ISOMIP+ include the effects of a cliff-like calving
front so that participating ocean models will be required to demonstrate
their ability to handle advance and retreat of this jump in topography. We
feel that this is important because ocean models will require this capability
to handle real-world problems with dynamic calving fronts. Therefore, we
prescribe a calving criterion on the MISMIP+ topography used in ISOMIP+:
Ice thinner than Hcalve=100 m (equivalent to an ice draft
above ∼-90 m) is considered to have calved and the ice draft is
set to zero. This threshold was chosen to eliminate the thinnest ice on
eastern and western flanks of the ice tongue while maintaining the tongue
itself. A thicker threshold, more consistent with typical Antarctic ice
shelves, would eliminate large portions of the ice shelf during retreat and
make analysis of the evolving melt-rate field more challenging.
Ocean1 and Ocean2 have stationary topography, so the calving criterion needs
to be applied only once when setting up the model domain. Ocean3 and Ocean4
have dynamic topography so it will be necessary to apply calving as the
topography is interpolated in time. To accommodate models that wish to
interpolate the MISMIP+ topography in time for Ocean3 and Ocean4 (see
Sects. and ), we have not
applied the calving criterion to the provided topography. Calving must be
applied as part of setting up the topography. This prevents the cliff face at
the calving front from pinching off vertically over the course of a year
(because of interpolation between large thickness and zero thickness) instead
of advancing or retreating horizontally in time. Models that do not support
a sheer calving face or which update the ice topography at each time step
will likely need to smooth the calving face over several horizontal grid
cells and/or to relax to the new geometry gradually over time. In such cases,
it is suggested that participants interpolate the geometry in time, then
apply the calving criterion, and finally apply whatever smoothing or
relaxation is required. This way, the (smoothed) calving front is expected to
move relatively continuously in the horizontal direction, rather than
abruptly jumping to the new location each year as the ice between the old and
new calving fronts thins to zero.
Calved ice is simply removed from the domain, and contributes no freshwater
flux to the ocean. We feel this is justified partly because it keeps the
problem as simple as possible and partly because an Antarctic iceberg would
be transported out of the ISOMIP+ domain in a matter of months, meaning
most meltwater would be deposited elsewhere in a real-world problem.
Forcing
There is no forcing at the surface of the open ocean (i.e., no atmospheric or
sea-ice fluxes) in any of the experiments. Aside from melt fluxes under the
ice shelf, the only forcing is via 3-D restoring within 10 km of
the northern boundary. In the restoring region, potential temperature and
salinity are restored to prescribed profiles with the following tendencies:
∂T∂tres=-γ(x)T-Tres(z),∂S∂tres=-γ(x)S-Sres(z),
where Tres(z) and Sres(z) are the restoring profiles for
potential temperature and salinity, respectively, and γ(x) is the
decay rate, which increases linearly from zero (no restoring) at xr0=790 km to γ0=10 days-1 at the northern boundary,
xr1=800 km:
γ(x)=γ0max0,x-xr0xr1-xr0.
The relatively fast restoring rate, corresponding to a restoring timescale
of 0.1 days, was chosen following
.
WARM and COLD temperature, salinity and density profiles used in all
five ISOMIP+ experiments. In Ocean1, the COLD profile specifies the initial
condition and the WARM profile is used in the restoring, while in Ocean2 the
profiles are switched. Ocean3 uses both WARM initial conditions and restoring
whereas Ocean4 uses both COLD initial conditions and restoring. The WARM
profiles were designed to qualitatively approximate observations in the
Amundsen Sea Embayment near Pine Island Glacier . The
COLD profile is at the surface freezing temperature at all depths and has
a salinity such that the densities of the WARM and COLD profiles are nearly
identical.
For the ocean initial conditions and boundary forcing, linear profiles for
potential temperature and salinity as functions of depth are given by
Tres(z)=T0+Tbot-T0zzb,deep,Sres(z)=S0+Sbot-T0zzb,deep,
where values at the surface (T0 and S0) and at the ocean floor
(Tbot and Sbot) correspond to either the COLD
(Fig. and Table ) or WARM profiles
(Fig. and Table ), depending on the
experiment. The WARM profiles were chosen to produce strong thermal driving
at depth but potential temperatures near freezing at the surface,
qualitatively mimicking observations of deep, warm water observed in the
Amundsen Sea region . These relatively warm conditions,
which result in large melt rates, are consistent with “warm” Antarctic ice
shelves like those bordering the Amundsen and Bellingshausen Seas. The COLD
profiles are consistent with ocean properties of “cold” Antarctic ice
shelves like those bordering the Weddell and Ross Seas. The COLD potential
temperature profile is constant at the surface freezing temperature
throughout the water column and has a lower salinity, resulting in WARM and
COLD density profiles that are nearly identical throughout the water column,
thus reducing convective instabilities resulting from the transitions between
COLD and WARM conditions that occur in Ocean1–2 as well as the MISOMIP1
IceOcean1–2 experiments.
Parameters for the COLD profiles.
Parameter
Value
Description
T0
-1.9 ∘C
Surface temperature
Tbot
-1.9 ∘C
Temperature at the ocean floor
S0
33.8 PSU
Surface salinity
Sbot
34.55 PSU
Salinity at the ocean floor
Boundary and initial conditions
In the COM configuration, we request that participants use no-slip lateral
boundary conditions at all walls including the northern wall adjacent to the
restoring region and the calving front. We realize that free-slip or open
boundary conditions may be more physically justifiable but no-slip boundary
conditions are likely to be supported by the largest number of models. Also
we prescribe no melting or drag from vertical ice faces (e.g., the calving
front) both for simplicity and because many models do not support melting on
vertical faces. Participants that use other boundary conditions should note
this when they submit their results. The momentum boundary conditions at the
ice-shelf base and seabed are quadratic drag with coefficients given in
Table .
The ocean is initialized at rest with potential temperature and salinity
profiles that are horizontally constant. The vertical functional forms of the
initial profiles differ between the experiments, and are described below.
Parameters for the WARM profiles.
Parameter
Value
Description
T0
-1.9 ∘C
Surface temperature
Tbot
1.0 ∘C
Temperature at the ocean floor
S0
33.8 PSU
Surface salinity
Sbot
34.7 PSU
Salinity at the ocean floor
For TYP runs, no other model parameters or choices of model physics are
prescribed. For COM runs, the recommended values for several relevant
parameters are given in Table .
COM grid resolution
The nominal horizontal resolution for COM runs is 2 km. We leave it
at the discretion of modelers with horizontally unstructured grids to
determine what a characteristic resolution of 2 km means for their
model.
Given the diversity of ocean-model vertical coordinates,
it is not possible or useful to specify a vertical resolution that applies to all models.
For this reason, we specify that all models should have 36 vertical layers,
but we leave it at the modeler's discretion how the layers are distributed.
Many models will require a minimum ocean-column thickness. We recommend that
models make the minimum ocean column as thin as can reasonably be achieved
while retaining numerical stability and accuracy. For z level models, the
minimum thickness is likely to be approximately two grid cells (∼40 m
if z levels are equally spaced).
Models with other vertical coordinates may be less restricted, but some modification
of the topography may be required to maintain a minimum ocean-column thickness.
In locations where the ocean column is too thin, participants will need to decide
for themselves whether it is more practical to modify the topography (ice draft,
bathymetry or both) or to remove the column from the ocean (i.e., mark it as “land”).
We recommend that z level models use both partial top and bottom cells, if they
are supported, for increased accuracy.
COM mixing parameterizations
Mixing is typically computed separately in the “horizontal” direction
(i.e.,
within a model layer) and in the “vertical” direction (i.e., between model
layers), regardless of which vertical coordinate is being used. To keep the
experiments simple, we ask participants to perform “vertical” mixing with
harmonic diffusion and the constant vertical viscosities and diffusivities
given in Table . However, enhanced vertical
mixing near the ice–ocean interface may be appropriate for models with high
vertical resolution near the ice–ocean interface, since the buoyant
sub-ice-shelf plume likely induces enhanced turbulent mixing that entrains
ambient fluid. Models using non-constant vertical mixing should document the
mixing scheme along with their results. Most models (e.g., those using the
hydrostatic approximation) do not explicitly model convective instability. We
prescribe a large vertical viscosity/diffusivity to be applied when the local
stratification is unstable, with values given in the table. Participants
whose models do not support this convective parameterization should note what
other scheme was used to handle unstable stratification (e.g., convective
adjustment or explicit modeling of convection).
“Horizontal” mixing should be parameterized with harmonic diffusion using
a constant eddy viscosity/diffusivity. The values of the “horizontal” eddy
viscosity and diffusivity have been chosen to be small but (hopefully)
sufficient to damp grid-scale numerical noise at the COM resolution.
Participants may need to increase these values for numerical stability, in
which case this should be noted with their results (see
Sect. ). The vertical eddy viscosity and diffusivity
have the same values as in the original ISOMIP experiment. We note that, in
many models, it may be that numerical diffusion is larger than the explicit
mixing.
COM equation of state
We prescribe a linear equation of state (EOS) with coefficients in
Table :
ρ=ρref1-αlinT-Tref+βlinS-Sref.
For models that do not support a linear equation of state, we ask
participants to note this and to describe the EOS they used in the pdf
describing their model. Any model that requires ρref to be equal
to ρsw should use ρref for both values, and should
note this difference along with their output.
COM melt parameterization
The recommended melt-rate formulation is the three-equation formulation with
constant nondimensional heat- and salt-transfer coefficients
(ΓT and ΓS). Following ,
Eqs. (1), (3), (4) and (5), we have
ρfwmwL=-ρswcwu*ΓTTzd-Tw,Tzd=λ1Szd+λ2+λ3pzd,ρfwmwSzd=-ρswu*ΓSSzd-Sw,u*2=CD,topuw2+utidal2,
where mw is the melt rate expressed in water equivalent
(weq), u* is the friction velocity, Tzd,
Szd and pzd are the potential temperature, salinity
and pressure at the interface, and uw, Tw and Sw are the
velocity magnitude, potential temperature and salinity some distance below
the ice-shelf interface, as discussed below.
Because of differences in vertical resolution, vertical mixing and the method
for computing uw, Tw and Sw, appropriate values of the heat-
and salt-transfer coefficients, ΓT and ΓS, are
likely to vary significantly between models. In Sect. ,
we prescribe a procedure for tuning these coefficients to achieve a desired
mean melt rate. With the exception of ΓT and
ΓS, we prescribe values for the coefficients in
Eqs. ()–() in
Table .
The liquidus coefficients in Eq. () are based on values from
but have been modified to compute the potential
freezing point. This should save modelers the trouble of converting the
boundary-layer potential temperature to in situ temperature before
computing the thermal driving. Modelers will need to determine the best
method for computing the pressure at the ice–ocean interface,
pzb, as we do not prescribe a method for doing so here. One
commonly used method computes pzb by
integrating a reference density profile from sea level to the ice draft.
For simplicity, the ice is considered to be perfectly
insulating. This means that modelers should not use the advection–diffusion scheme from
to determine the heat flux into the ice shelf, as is common
practice in ice-shelf cavity modeling. Top and bottom friction are computed
with a quadratic drag law (surface stresses are proportional to the square of
the local ocean flow speed) using drag coefficients from
, as given in the table. The root-mean-square “tidal” velocity,
utidal, is used to parameterize the turbulent mixing that would be induced
by tides if they were present and is used to prevent the friction velocity (and thus the melt
rate) from going to zero when there is no motion under the ice shelf.
The computation of top and bottom drag do not incorporate utidal.
Methods for computing the “far-field” potential temperature, salinity and
velocity (Tw, Sw and uw) differ across models. Some models
sample these fields at a fixed distance below the ice draft
e.g., while others average the fields over a prescribed
thickness e.g.,. Participants are asked to describe how
Tw, Sw and uw are computed in the pdf included with their
results.
Some models will use virtual salt fluxes, while others will use volume fluxes
(or perhaps mass fluxes) at the ice–ocean boundary. The freshwater, heat and
salt fluxes for models using virtual salt fluxes should be computed following
as
Ffw=0,FH=-cwρswu*ΓT+ρfwmwTzd-Tw,FS=-ρswu*ΓS+ρfwmwSzd-Sw.
If volume fluxes are used instead, the same fluxes are given by
Ffw=ρfwmw,FH=-cwρfwmwTzb+ρswu*ΓTTzd-Tw,FS=0.
Though we do not require it, models may wish to distribute melt fluxes over
several vertical grid cells, as in . This approach
parameterizes additional vertical mixing within the boundary layer and may
prevent noise and/or time-step restrictions in models with very thin cells
below the ice–ocean interface. This is an alternative approach to
representing the enhanced turbulent mixing near the ice–ocean interface
mentioned in Sect. .
Models using volume or mass fluxes will need a strategy for removing mass in
the open ocean to compensate for the volume of meltwater that enters the
domain. Because of the small size of the domain, without such a strategy, sea
level would likely rise by hundreds of meters in simulations with large melt
rates (Ocean1 and Ocean3). One possible approach is to impose an artificial
evaporative flux in the restoring region (x>790 km).
Corresponding salt and heat fluxes will be needed to prevent the top cells
from becoming cooler and saltier as mass leaves the cell:
Fe=-ρswmwAshelfAres,
FH,e=cwT0Fe,FS,e=S0Fe,
where Fe, FH,e and FS,e are the evaporative
mass, heat and salt flux, respectively, Ares is the area of the
restoring region, T0 and S0 are the prescribed temperature and salinity
at the ocean surface in the restoring profile, and mw
is the melt rate averaged over the area of the ice shelf Ashelf and
over a suitable period of time (perhaps 1 month). Participants are welcome
to use alternative strategies. They are asked to document whichever approach
(if any) they use for removing excess mass in their description pdf.
Experiments
Ocean0–2 involve static ice-shelf topography, making them accessible to
a wider range of ocean models. They are intended to represent the most
advanced and most retreated states in the coupled ice sheet–ocean system to
come later. These experiments are designed to test how changes in far-field
ocean forcing result in changes in melt rates, which would drive ice-sheet
dynamics in the coupled system. Preliminary simulations with POP2x suggest
that, in each experiment, the system will experience an initial shock lasting
a few days as the ocean water in contact with the ice shelf adjusts to the
melting/freezing boundary conditions. In Ocean0, strong melting begins
immediately, and the system reaches a quasi-equilibrium within a few months.
In Ocean1 and Ocean2, far-field changes in ocean properties take several
years to propagate into the ice-shelf cavity, leading to a substantial
increase (in Ocean1) or decrease (in Ocean2) in melting.
Ocean3 and Ocean4 make use of dynamic ice topography that evolves over
100 years. Whereas preliminary results suggest that Ocean0–2 approach or
have reached quasi-equilibria by the end of each experiment, Ocean3–4 do not
reach steady state because of the evolving topography.
Figure shows time series of area-averaged melt
rate for four of the five ISOMIP+ experiments from example POP2x
simulations. Melt rates from Ocean0, not shown, are nearly indistinguishable
from the first year of the Ocean3 experiment.
Example results from POP2x simulations showing melt rates averaged
over the shelf area as functions of time for Ocean1–4. Melting increases by
nearly 2 orders of magnitude in Ocean1, and decreases by about the same
order in Ocean2, demonstrating that changes in far-field forcing can greatly
increase or reduce melting. After a decade or two of initial adjustment, the
melt rates in Ocean3 and Ocean4 remain relatively steady in time despite the
changing topography in those experiments, suggesting that the total cavity
size has relatively little impact on total
melting.
In the following sections, we present further results from these POP2x
simulations. In each case, we show the evolution of a transect through the
ocean temperature field through the center of the domain, which also
indicates how the ice topography evolves (if at all) over time. We emphasize
that we do not intend these results to be treated as a benchmark for
other participants to try to match. Instead, the examples show that the
simulations can be performed and that they achieve their intended purposes.
They should give the participants a qualitative idea of what to expect. After
all, the MIP is not to attempt to produce identical results with all models
but rather to try to understand the differences that occur.
Example results from a 1-year Ocean0 simulation with the
POP2x model using heat-transfer coefficient ΓT=0.11. Panels
show the progression in time of transects of monthly averaged ocean
temperature through the center of the domain (y=40 km). The initial
conditions and far-field restoring at the right-hand side of the domain both
use the WARM profiles from Fig. . The ice draft does not
evolve in time. The simulation reaches a quasi-steady state with relatively
strong melting
within a few months.
Ocean0: warm initial conditions and forcing with static
ice-shelf topography
Ocean0 uses steady-state ice topography, as shown in the transects in
Fig. , from the initial steady state of the MISMIP+ Ice1
experiment (see Sect. ) produced with BISICLES
using the SSA and no melting. The ocean is initialized with the WARM profiles
in Fig. and restored the same profile in the far field.
The combination of warm initial conditions and restoring is expected to lead
the system to reach a quasi-equilibrium with strong melting over a few months
to a year, based on preliminary results. The duration of the run should be
the time needed to reach a quasi-equilibrium melt rate plus 6 months, so
that time averages without trends may be taken over the final 6 months of
the simulation. We expect the total run duration to be between 1 and 2
years.
Because Ocean0 is expected to reach a quasi-equilibrium within approximately
1 year, this experiment is well suited to parameter studies. In particular,
we use this experiment to calibrate the values of the heat- and salt-transfer
coefficients, ΓT and ΓS to achieve a target
melt rate:
mw=30±2ma-1,
where the brackets indicate the average of mw over the area where
zb<-300 m and over the final 6 months of the simulation.
We focus on the melt rate over the deeper portion of the ice draft because we
expect larger (therefore more dynamically relevant) melt rates in this
region. Participants should use an optimization approach such as sampling or
a continuation method to find a value of ΓT such that
mw lies within the prescribed bounds. At each stage,
the value of ΓS should also be modified such that
ΓS=ΓT/35 . Fits
to observations suggest that the thermal Stanton number is on the order of
St=CD,topΓT=1.1×10-3
, suggesting that ΓT=2.2×10-2
might be a good initial guess. Figure shows
an example of the tuning process applied in POP2x, plotting
mw for various values of ΓT. The melt
rate is ∼30 ma-1 when ΓT≈0.11 for
this model. Figure shows example Ocean0 results from POP2x
with ΓT≈0.115.
Example results from a series of POP2x simulations of Ocean0 showing
the dependence of the mean melt rate mw averaged over
locations below zd=-300 m and over the final 6 months of
the simulation for various values of the turbulent heat-transfer coefficient
ΓT. Based on these results, the value ΓT≈0.11, corresponding to a mean melt rate mw≈30 ma-1, was used for subsequent ISOMIP+ and MISOMIP1
simulations.
Models with high resolution near the ice–ocean interface may wish to deviate
from the prescribed value of CD,top in addition to tuning
ΓT and ΓS.
For example, at high vertical resolution (higher than 0.1–1 m),
the log law of the wall, in which CD is a function of the log of
the distance from the interface, is used in some models .
Participants that use a value or functional form for
CD,top other than that given in
Table should document this with their submitted
results.
Ocean1: cold initial conditions and warm forcing with static
ice-shelf topography
Ocean1 uses the same topography and restoring as Ocean0 but is initialized to
a colder, fresher profile (COLD from Fig. ) that is
expected to result in low melt rates during the first several years of the
simulation. Far-field restoring to the WARM profiles leads to warmer and
saltier water in the far field at depth.
It is worth noting that this COLD-to-WARM scenario represents a transition
between the two extremes of water masses observed on the Antarctic continental shelf,
and is therefore an unrealistic scenario designed to test the response of models
to an extreme forcing.
Example results from POP2x as in Fig. but for
Ocean1 (top) and Ocean2 (bottom) simulations each lasting 20 years. In both
experiments, the ice draft is held fixed in time. Ocean1 is initialized with
COLD profiles and restored to WARM profiles. Melt rates are initially low and
the overturning strength is initially relatively weak, so that warm, deep
water takes several years to reach the back of the sub-ice-shelf cavity, at
which point melting increases by several orders of magnitude, reaching
a quasi-steady state for approximately the second half of the experiment.
Ocean2 is initialized with WARM profiles and restored to COLD profiles,
leading to a melt rate that decays by several orders of magnitude over the
duration of the simulation. Ocean2 does not reach a quasi-steady state within
its 20-year duration.
The duration of the experiment is exactly 20 years (from the beginning of the
date 1 January 0000 to the end of 31 December 0019), which preliminary
results suggest is sufficient time to reach a quasi-steady state. Melt rates
as well as the strengths of the barotropic and overturning circulations
toward the end of the simulation are expected to be significantly larger than
those within the first few years because of the warming.
Example results from a POP2x Ocean1 simulation, the top row of
Fig. , show that warm water at depth gradually advects and
mixes into the cavity during the first decade, becoming quasi-steady over the
second decade. Melt rates from Fig. are initially
low, corresponding to a relatively weak overturning circulation. This weak
circulation means that warm, deep water is pulled into the cavity only
gradually over most of the first decade. As warmer water reaches the back of
the cavity, melt rates increase, driving stronger overturning and drawing
more warm water. This positive feedback saturates over the coarse of several
years once melt rates have increased by several orders of magnitude. The
system remains in quasi-steady state for approximately the second half of the
experiment.
Ocean2: warm initial conditions and cold forcing with static
ice-shelf topography
In Ocean2, the topography is from the end of Ice1r (see
Sect. ) using BISICLES with the SSA. A temperature
transect through the center of the domain can be seen in each panel of the
bottom row of Fig. . The ocean is initialized with the WARM
profiles and restored to the COLD profiles in Fig. ,
with parameters given in Tables and .
Again, the experiment should run for 20 years. As in Ocean1, the abrupt
change between forcing profiles is unrealistically strong and is designed to
test how the participating models respond to extreme changes.
The bottom row of Fig. and the green curve in
Fig. show example POP2x results from Ocean2.
Initially, strong circulation driven by warm ocean temperatures and rapid
melting pull in cold water from the far field. As this cold water reaches the
back of the cavity within the first year, the melt rate begins to fall,
decreasing by several orders of magnitude over the course of the simulation.
The slower overturning during much of the simulation means that the timescale
required to reach a quasi-steady state is longer for Ocean2 than for Ocean1
and equilibrium has not been reached after 20 years.
Ocean3: warm initial conditions and forcing with retreating ice-shelf
topography
Ocean3 begins with the same topography as Ocean1, but in this experiment the
ice draft evolves over time according to a prescribed data set covering
100 years of ice retreat from Ice1r. Ocean3 is initialized and forced with
the WARM profile. We expect strong melting to begin immediately as the
sub-ice-shelf circulation spins up, consistent with the conditions for Ice1r
used to generate the topography, and to persist for the duration of the
experiment.
The topography for Ocean3, available through , includes snapshots of
the ice draft and ice surface at yearly intervals on
a 1 km grid. We expect that the frequency with which
ocean models can update their topography may vary considerably, from once per time step
in some models to monthly or yearly in others. Participants wishing to update more
frequently than yearly should interpolate the ice draft linearly between
subsequent geometries to determine the topography at intermediate times. As
previously mentioned, we have not applied the calving criteria to the topography
provided because calving should be applied only after interpolation in
time and space. This means that models that update the topography only every year and
thus require no interpolation in time will need to apply the calving criteria
themselves.
The red curve in Fig. shows melt rates from
Ocean3, and the top row of Fig. shows a transect of
monthly-averaged temperature as well as the evolving ice topography at four
points in time. Mean melt rates remain strong throughout the simulation. As
the ice draft steepens, melting becomes concentrated near the grounding line
within the trough. As the cavity grows, melt fluxes remain strong but the
mean melt rate decreases somewhat because of the increased area.
Ocean4: cold initial conditions and forcing with advancing ice-shelf
topography
Conceptually, Ocean4 is an extension of Ocean3. The ice-draft topography from
Ice1ra was produced by abruptly shutting off melting at year 100 and allowing
the ice to re-advance for 100 years (see Sect. ).
Thus, Ocean4 begins with the final topography from Ocean3 (which is also the
same topography as in Ocean2). This time, we prescribe both initialization
and restoring to the COLD salinity and potential temperature profile, which
should lead to very low melt rates, consistent with the lack of melting in
the MISMIP+ run that produced the ice topography. As in Ocean3, yearly
topography data at 1 km resolution are provided through
. Once again, participants will need to apply the calving
criteria to these data.
Example results from POP2x as in Fig. but for
Ocean3 (top) and Ocean4 (bottom) simulations each lasting 100 years. In these
experiments, the ice draft evolves in time. Ocean3 prescribes WARM initial
conditions and restoring, producing strong melting throughout the experiment,
consistent with the retreating ice. The melt rate declines slightly over the
course of the simulation as the ice retreats to shallower depths, associated
with colder ocean temperatures. Ocean4 is initialized and forced with COLD
profiles, which lead to relatively low melt rates, fitting with the advancing
ice topography. Meltwater cools the sub-shelf cavity, leading to several
decades of decreasing melt rates followed by quasi-steady values for the
remainder of the simulation.
Example results from POP2x show that melt rates remain low for the duration
of the simulation (cyan curve in Fig. ) and that
temperatures in the cavity evolve toward the freezing point over the first
several decades, reaching a quasi-steady state after ∼ 30 years. A
transect through the temperature field in the bottom row of
Fig. also shows the evolving ice topography.
Requested output
Participants are asked to supply a number of fields interpolated to
a standard grid. NetCDF files with example output on the standard grid are
available for download (see Sect. ). Participants are
asked to supply a single NetCDF4 file for each experiment with the
file-naming convention of [expt]_COM_[MODEL].nc, where
[expt] is an experiment name from Table , COM
or TYP indicates the type of run and [MODEL] is a unique identifier
for the participant (e.g., the name of the ocean model and/or the institute).
We ask participants to provide all fields in 32-bit floating-point precision
using the variable and dimension names given in bold and units given in
square brackets as follows.
nx, ny, nz and nTime dimensions.
x(nx), [m] vector of cell centers in the x direction
on the output grid with 2-km spacing, 3.21×105, 3.23×105, … 7.99×105.
y(ny), [m] vector of cell centers in the y direction
on the output grid with 2-km spacing, 1.0×103, 3.0×103, … 7.9×104.
z(nz), [m] vector of cell centers in the z direction
on the output grid with 5-m spacing, -2.5, -7.5 … -717.5.
time(nTime) [s] from the start of the simulation as
a vector running over the full duration of the simulation (20 years for
Ocean1 and Ocean2, 100 years for Ocean3 and Ocean4). The time interval
between entries is 1 month, using a standard 365 day calendar with
no leap years.
meanMeltRate(nTime) [ms-1] weq, the melt rate, positive for melting and negative for freezing, averaged
over the ice-shelf base.
totalMeltFlux(nTime) [kgs-1], the total mass flux of
freshwater across the ice–ocean interface, positive for melting and negative
for freezing.
totalOceanVolume(nTime) [m3], the total volume of the ocean.
meanTemperature(nTime) [∘C], the potential temperature averaged
over the ocean volume.
meanSalinity(nTime) [PSU], the salinity averaged
over the ocean volume.
iceDraft(nTime,ny,nx) [m], the elevation of the ice–ocean interface (zd). Dependence on time is only needed for Ocean3 and Ocean4.
bathymetry(nTime,ny,nx) [m], the elevation of the bathymetry (zb). Dependence on time is only needed for Ocean3 and Ocean4.
meltRate(nTime,ny,nx) [ms-1] weq, the melt rate, positive for melting and negative for freezing.
frictionVelocity(nTime,ny,nx) [ms-1], the friction
velocity u* used in melt calculations.
thermalDriving(nTime,ny,nx) [∘C], the thermal
driving used in the melt calculation. The thermal driving is the difference
between the potential temperature in the boundary layer, Tw,
and the freezing potential temperature at the ice–ocean interface, Tzd.
halineDriving(nTime,ny,nx) [PSU], the haline
driving used in the melt calculation. The haline driving is the difference
between the salinity in the boundary layer, Sw and the salinity at the
ice–ocean interface, Szd.
uBoundaryLayer(nTime,ny,nx) and vBoundaryLayer(time, y,
x) [ms-1], the components of the velocity in the boundary layer
that were used to compute u*.
barotropicStreamfunction(nTime,ny,nx) [m3s-1],
the barotropic streamfunction, ψxy, such that the barotorpic velocity,
U, is (U=-∂ψxy/∂y,
V=∂ψxy/∂x).
overturningStreamfunction(nTime,nz,nx) [m3s-1],
the overturning streamfunction, ψxz, in x–z such that the zonal-mean
velocity, u¯, is (u¯=-∂ψxz/∂z,
w¯=∂ψxz/∂x).
bottomTemperature(nTime,ny,nx) [∘C] and
bottomSalinity(nTime,ny,nx) [PSU], the potential temperature and
salinity in the bottom-most cell in each ocean column.
temperatureXZ(nTime,nz,nx) [∘C] and
salinityXZ(nTime,nz,nx) [PSU], the potential temperature and salinity
transects in x–z plane through the center of the domain, y=40 km.
temperatureYZ(nTime,nz,ny) [∘C] and
salinityYZ(nTime,nz,ny) [PSU], the potential temperature and salinity
transects in y–z plane outside the cavity x=520 km.
Invalid values (e.g., field locations that lie within the ice shelf or
bedrock) should be masked out using a fill value. In C and Fortran, this can
be accomplished by assigning a value of NC_FILL_FLOAT and setting
the _FillValue attribute of the NetCDF variable to this value. In
Python, invalid data can be masked by using numpy masked arrays to assign to
netCDF4 variables.
We ask participants to supply monthly mean values of all time-dependent
quantities (except iceDraft and bathymetry, which should be
snapshots), where the values in the time array indicate the
beginning of the period being averaged. Participants who are unable to
compute monthly mean values may supply snapshots instead but should indicate
this with their submission.
We note that many functions are typically computed on staggered grids. For
example, the barotropic streamfunction is typically computed at horizontal
cell corners (vertices) and the overturning streamfunction is typically
computed at cell corners on the vertical grid. Velocity components
(uBoundaryLayer and vBoundaryLayer) are typically located
at cell edges (on a C-grid) or cell corners (on a B-grid). Additionally, for
most models, potential temperature and salinity fields will not have values
exactly at y=40 km as requested in temperatureXZ and
salinityXZ (and similarly for the y–z transects). To aid in
analysis and comparison of results, we ask all participants to interpolate
these fields to the standard grid. The standard grid has a high vertical
resolution (Δz=5 m) in an attempt to accommodate models
with a variety of vertical coordinates. Participants are welcome to provide
plots of their results on their model's native grid in addition to
supplying the output on the standard grid.
Participants are asked to provide the iceDraft and
bathymetry, which are time dependent for Ocean3 and Ocean4, to show
how topography has been modified (interpolated in time, smoothed, the ocean
column thickened, etc.).
Two python scripts for plotting the contents of a properly formatted results file are available in the
Supplement (plotMISOMIPOceanData.py and plotMISOMIPOceanMetrics.py).
Plots of the example POP2x simulation results produced with this script are available for download
(see Sect. ).
We ask participants to include a description of the result in a pdf file
(using the same naming convention as the results, i.e.,
[expt]_COM_[MODEL].pdf) describing several specific properties of
their model and its ISOMIP+ configuration. If appropriate, a single pdf can
be used to describe Ocean1–4 results, as has been done in the example
included in the Supplement. These include
model: the name and version of the model used (as specifically as possible, including a citation if
available);
repository: a link to the repository where the model can be downloaded (if public) and specific tag,
branch or revision (if available);
vertical coordinate: description of the vertical coordinate of the model (z level, z*,
terrain, isopycnal, etc.);
horizontal mixing: description of how “horizontal” mixing was performed (harmonic, biharmonic, etc.;
within model levels, along geopotentials, along isopycnals, etc.);
vertical mixing: description of how “vertical” mixing was performed (constant diffusivity, k profile
parameterization, etc.; harmonic, biharmonic, etc.);
advection: description of the momentum- and tracer-advection schemes used (centered,
third-order with limiter, etc.);
EOS: description of the equation of state;
convection: description of the procedure for handling convection (explicitly modeled,
parameterized using strong vertical mixing, etc.);
melt parameterization: description of how Tw, Sw and uw in the melt parameterization
are computed from T, S and u fields (e.g., averaging over the
boundary layer, sampling at a fixed distance);
topography: description of procedure for interpolating, smoothing or otherwise modifying the ice draft and/or
bedrock topography;
maintaining sea level: description of strategy (if any) for maintaining sea level when volume or
mass fluxes are used (e.g., use of Eq. );
moving boundaries: for Ocean3 and Ocean4, a description of how the moving boundary is implemented
(e.g., how T, S and u are computed in cells or ocean columns that were previously
ice-filled and redistributed, if at all, when a cell or column is filled with
ice);
TYP parameters: for TYP results, details on resolution as well as melt and mixing
parameterizations;
TYP problem: for TYP results, a description of the types of problems the participant
would typically apply the model to using this configuration (e.g., which region;
over what time span; with what kind of initialization, forcing and boundary
conditions);
COM deviations: for COM results, details anywhere the model deviated from the COM
resolution or the COM melt and mixing parameterizations;
COM parameters: for COM results, the values of ΓT and ΓS. Also, the value
of CD,top if different from the prescribed value;
ΓT figure: for COM Ocean0 results, a figure similar to Fig. showing
how the melt rate for zd<-300 m varies with
ΓT.
We provide an example in the Supplement.
MISOMIP1 design
MISOMIP1 prescribes two coupled ice sheet–ocean experiments (IceOcean1–2,
summarized in Table ), each with two parts. We expect
the MISOMIP1 experiment to play an analogous role in evaluating coupled ice
sheet–ocean systems to that of the ISOMIP projects for stand-alone ocean
models with ice-shelf cavities and the MISMIP projects for ice-sheet models.
We ask participants to first perform the MISMIP+ and ISOMIP+ experiments,
so that the behavior of each component on its own has been documented, before
proceeding to MISOMIP1.
For both MISOMIP1 experiments, the bedrock topography is the same as for
MISMIP+ and ISOMIP+, as given by
Eqs. ()–(). Ice-sheet parameters are the same
as for MISMIP+ except where noted below. To simplify the coupled problem,
we prescribe a constant ice temperature as in MISMIP+ and set the thermal
conductivity of ice to zero (so that there is no sensible heat flux into ice
at the ice–ocean interface). Thus, the only flux across the ice–ocean
interface is of meltwater. As in ISOMIP+, freshwater fluxes come only from
melting. Calved ice disappears abruptly (or as abruptly as the ocean
component can handle, since some ocean models will need a finite period of
adjustment to prevent tsunamis) without producing a freshwater flux into the
ocean.
IceOcean1: retreat and re-advance without dynamic calving
IceOcean1 begins with the ice-sheet steady state that also served as the
initial conditions for the MISMIP+ Ice0, Ice1 and Ice2 experiments (see
Sect. ). Unlike in ISOMIP+, IceOcean1 does not
include a dynamic calving criterion. Ice is allowed to become as thin as the
ice sheet and ocean components permit (potentially zero thickness) without
calving. As in MISMIP+ and ISOMIP+, ice beyond x=640 km is
considered to have calved.
Example results from POPSICLES simulations of IceOcean1 (no dynamic
calving) and IceOcean2 (thickness-based calving criterion) using SSA and the
sliding law from showing melt rates averaged over the
shelf area (top panel) and the grounded area as functions of time (bottom
panel). Though melt rates are initially similar, after about year 40 the
dynamic calving in IceOcean2 begins to remove substantial areas of the ice
shelf (notably when an iceberg is removed just after year 60), resulting in
larger mean melt rates (but similar total melt fluxes) for that experiment.
IceOcean2 loses substantially more grounded area than IceOcean1 during
retreat (the first 100 years), presumably due to a loss of buttressing from
the ice shelf, which has nearly completely calved away. The grounding line
re-advances at approximately the same rate in both experiments because the
advancing shelf it thick enough not to calve.
Example results from POPSICLES plotted as in Fig.
but for IceOcean1 (top) and IceOcean2 (bottom) simulations each lasting
200 years. Both simulations begin with ice shelves that are in steady state
without melting and with COLD ocean conditions. The WARM far-field restoring
in the ocean causes the melt rate to increase by several orders of magnitude
over the first decade and for the ice shelf to thin over the remainder of the
retreat phase (100 years). In IceOcean2, dynamic calving significantly
reduces the size of the ice shelf compared with IceOcean1. During the final
100 years, the switch to COLD far-field restoring leads to cold ocean
temperatures, melt rates are reduced by several orders of magnitude, and the
ice shelf begins to re-advance; 100 years is not long enough for the
ice shelf in either simulation to re-advance to its initial steady
state.
The experiment consists of two phases – a 100-year retreat phase,
IceOcean1r, and a 100-year re-advance phase, IceOcean1ra. At the beginning of
IceOcean1r, the ocean component is initialized with the steady-state ice
topography from the ice-sheet component and the COLD salinity and temperature
profiles from Fig. and Table . The
initial state should be cold enough to produce low melt rates
(∼0.2 ma-1 in preliminary tests) that are approximately
consistent with the ice sheet's initial state. For the 100-year duration of
IceOcean1r, restoring to the WARM profile (see Fig. and
Table ) is applied near the ocean's northern boundary. As
in ISOMIP+ Ocean1, the warm water is expected to reach the ice-shelf cavity
within the first decade, at which point it should induce strong melting and
subsequent rapid ice retreat.
The re-advance phase, IceOcean1ra, begins where IceOcean1r ends but abruptly
switches to the COLD restoring profile at the ocean's northern boundary. The
simulation evolves for another 100 years, during the first decade of which
the ocean should cool and the melt rate should be greatly reduced, similarly
to Ocean2. The reduced melting should allow ice to re-advance for the
remainder of the simulation.
The blue curves in Fig. shows the mean melt rate
and the grounded area and from an IceOcean1 simulation using the POPSICLES
model (coupled POP2x and BISICLES). The top row of Fig.
shows the evolution of the ice draft and ocean temperature over the course of
the simulation. The mean melt rate is initially relatively small, increasing
by several orders of magnitude over the first decade as warm water reaches
the cavity and initiating grounding-line retreat. Because of the ocean
temperature profile, the melt rate is a strong function of the depth of the
ice–ocean interface. As the ice shelf thins, melting becomes concentrated
over a steep region within the channel near the grounding line. As the
grounding line retreats, the area of the cavity increases (no calving occurs
except beyond x=640 km) while the total melt flux remains nearly
constant, meaning that the mean melt rate gradually decreases. Between
year 100 and about year 130, the melt rate decays by several orders of
magnitude, reaching a nearly steady value for the remainder of the simulation
as the ice shelf thickens and the grounding line begins to re-advance.
IceOcean2 (optional): retreat and re-advance with dynamic calving
Specifying calving was a major challenge in the design of MISOMIP1. There was
general agreement in the community that ice-sheet models have not been shown
to behave reliably with dynamic calving, while there is a lack of consensus
about which calving parameterizations are appropriate or physically
realistic. In Antarctica, calving events tend to be infrequent, producing
large tabular icebergs, a process that is not well modeled by a continuous
calving velocity or a simple calving criterion based on ice thickness (e.g.,
Sect. ). Nevertheless, we felt that it was important
for testing the robustness of the ice-sheet and ocean components in MISOMIP1
that there be an experiment with a dynamic, sheer cliff at the calving front.
We include an optional coupled experiment, IceOcean2, that is identical to
IceOcean1 except that it includes dynamic calving in the ice-sheet component.
This experiment is designed test the ability of the ice-sheet component to
apply dynamic calving, including detecting disconnected icebergs and the
ability of the ocean component to handle abrupt changes in ice topography.
Whereas the MISMIP+ experiments do not include a dynamic calving front,
IceOcean2 prescribes the same simple calving criterion used in ISOMIP+: ice
thinner than Hcalve=100 m (equivalent to an ice draft
above ∼-90 m) should be calved and the ice thickness set to
zero. This thickness threshold was chosen for consistency with ISOMIP+, and
allows the ice shelf to become thinner than would typically be observed in
Antarctica. We also maintain the fixed-front calving condition from MISMIP+
that ice beyond xcalve=640 km is removed. The calving
criteria should be enforced in the ice-sheet component.
Because the calving criterion will change the steady state of the ice sheet,
IceOcean2 should begin with a new steady-state ice-sheet initial condition,
again without melting but with the calving criterion imposed. For models that
are performing a spinup to steady state, we recommend starting with the
IceOcean1 initial condition. This may also be an appropriate starting guess
for those using continuation methods to find the initial steady state. As in
MISMIP+, participants should modify the ice softness (A) and, if
necessary, the basal-traction coefficient (β2) so that the
steady-state grounding line crosses the center of the trough at x=450±10 km. Participants are asked to perform both the Ice0 and Ice1
experiments with the calving criterion. These results should be submitted
along with the IceOcean2 results. This will allow for a more complete
analysis of the effects of calving on both the coupled and uncoupled systems.
Mean melt rates and grounded area from an example POPSICLES IceOcean2
simulation are shown in the green curves in
Fig. , and the evolution of the ice draft and
ocean temperature are shown in the bottom row of Fig. .
The beginning of the retreat phase of IceOcean2 proceeds similarly to
IceOcean1, with small differences due to the smaller, thinner ice shelf in
the steady state with the calving criterion. Starting at around year 30,
dynamic calving removes significant portions of the ice shelf. Although the
melt flux remains relatively steady, the mean melt rate increases as the
ice-shelf area decreases. Just after year 60, a large iceberg breaks off from
the ice shelf, leading to an abrupt decrease in ice-shelf area and a
corresponding increase in the mean melt rate. For the remainder of the
retreat phase, the ice shelf exists only as a small remnant of its initial
size close to the grounding line. The re-advance phase begins at year 100
when the far-field restoring is switched to the COLD profiles. As the ocean
cools, the melt rate decreases by several orders of magnitude. The ice-shelf
area remains much smaller than in IceOcean1ra while melt fluxes are similar,
meaning that the mean melt rate is nearly an order of magnitude higher.
Component resolutions and parameterizations
As in the ISOMIP+ experiments, we ask participants to perform the MISOMIP1
experiment once in a “common” (COM) configuration similar to that of
ISOMIP+. For this configuration, the ocean component should have the same
resolution and parameters as in the ISOMIP+ COM run. We do not prescribe
the resolution of the ice-sheet component because the wider use of
unstructured, dynamic and adaptive grids as well as higher-order elements in
ice-sheet models compared with ocean models make it impractical to provide
specifications that are appropriate for all models. Also, grounding-line
dynamics in ice-sheet models have been shown to converge with resolution
e.g.,, whereas the same has not
been shown for melt rates produced by ocean models.
Whereas we prescribed a “typical” run for ISOMIP+ with resolution and
parameters that the ocean model typically uses for Antarctic regional
simulations, it is not obvious that this is appropriate for MISOMIP1 models.
Coupled ice sheet–ocean models are not well enough established to have
typical resolutions and parameters. Therefore, we invite participants to
submit several sets of results with parameter choices at their discretion in
addition to the COM run and ensure these are well documented in the pdf
describing the model and results.
The coupling interval for the model is left to each participant to decide. We
recommend that participants perform a relatively short test with strong melting
(e.g., initializing and forcing the coupled model with WARM conditions)
to demonstrate convergence of the results with decreasing coupling intervals.
For example, in POPSICLES, we have found in several tests that
the mean melt rate and volume above flotation converge with coupling interval
only when the coupling interval is 6 months or shorter.
In the example results, POPSICLES was coupled monthly.
We ask participants who are able to do so to
provide multiple sets of results using different coupling intervals.
Requested output
We request that participants supply separate NetCDF files for their ice-sheet
and ocean MISOMIP1 results. This allows the results to be supplied on
different grids and is expected to simplify comparing the final results.
NetCDF files with example output on the standard grids for each component are
available (see Sect. ). Participants are asked to
supply all fields in 32-bit floating-point precision, with the file-naming
convention of [expt]_COM_[component]_[MODEL_CONFIG].nc, where
[expt] is the experiment name from Table , COM
indicates a verification run and is omitted for non-COM runs,
[component] is either ice or ocean and [MODEL_CONFIG] is
a unique identifier for the coupled-model configuration (e.g., the name of the
model, the institute, ice stress approximation).
The requested ocean fields and the output grid are the same as in
Sect. . The requested output from the ice-sheet
component is the same as in MISMIP+ (see Sect. )
with the exception that time is sampled monthly, the 2-D fields are
required, rather than optional, and any units involving time should be given
in s rather than a for consistency with the ocean output. As in
MISMIP+, the 2-D ice-sheet fields should be interpolated from the ice-sheet
model's native grid to the standard 1 km grid to simplify analysis.
The results should be accompanied by a pdf file giving details about the coupled model.
In addition to the information requested in Sects. and ,
this file should include a description of the coupling scheme and the length of the coupling interval.