GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus GmbHGöttingen, Germany10.5194/gmd-8-2991-2015The Louvain-La-Neuve sea ice model LIM3.6: global and regional capabilitiesRoussetC.clement.rousset@locean-ipsl.upmc.frVancoppenolleM.https://orcid.org/0000-0002-7573-8582MadecG.https://orcid.org/0000-0002-6447-4198FichefetT.FlavoniS.BarthélemyA.BenshilaR.ChanutJ.LevyC.MassonS.VivierF.Sorbonne Universités (UPMC Paris 6), LOCEAN-IPSL,
CNRS/IRD/MNHN, Paris, FranceCentre Georges Lemaître for Earth and Climate
Research, Université catholique de Louvain, Louvain-la-Neuve,
BelgiumCNRS/LEGOS, Toulouse, FranceMercator Ocean, Ramonville Saint-Agne,
FranceC. Rousset (clement.rousset@locean-ipsl.upmc.fr)1October20158102991300524March201529April20153August201517September2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://gmd.copernicus.org/articles/8/2991/2015/gmd-8-2991-2015.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/8/2991/2015/gmd-8-2991-2015.pdf
The new 3.6 version of the Louvain-la-Neuve sea ice model (LIM) is presented,
as integrated in the most recent stable release of Nucleus for European
Modelling of the Ocean (NEMO) (3.6). The release will be used for the next
Climate Model Inter-comparison Project (CMIP6). Developments focussed around
three axes: improvements of robustness, versatility and sophistication of the
code, which involved numerous changes. Robustness was improved by enforcing
exact conservation through the inspection of the different processes driving
the air–ice–ocean exchanges of heat, mass and salt. Versatility was
enhanced by implementing lateral boundary conditions for sea ice and more
flexible ice thickness categories. The latter includes a more practical
computation of category boundaries, parameterizations to use LIM3.6 with a
single ice category and a flux redistributor for coupling with atmospheric
models that cannot handle multiple sub-grid fluxes. Sophistication was
upgraded by including the effect of ice and snow weight on the sea surface.
We illustrate some of the new capabilities of the code in two standard
simulations. One is an ORCA2-LIM3 global simulation at a nominal 2∘
resolution, forced by reference atmospheric climatologies. The other one is a
regional simulation at 2 km resolution around the Svalbard Archipelago in
the Arctic Ocean, with open boundaries and tides. We show that the LIM3.6
forms a solid and flexible base for future scientific studies and model
developments.
Introduction
Sea ice covers 3–6 % of the Earth's surface and is characterized by
ample seasonal variations, making it one of the most influential geophysical
features in the Earth system (Comiso, 2010). Mostly because of its high
albedo and thermal insulation power, sea ice affects the weather and more
generally the climate (e.g., Budkyko, 1969; Vihma, 2014). The seasonal cycle of
ice growth and melt strongly impacts the vertical upper ocean density
structure and is a key driver of the ocean circulation at a global scale
through dense water formation (Aagaard and Carmack, 1989; Goosse and
Fichefet, 1999). Sea ice also influences marine primary productivity and
carbon export to depth (e.g. Thomas and Dieckmann, 2010; Vancoppenolle et
al., 2013), and constitutes a habitat for Arctic and Antarctic fauna,
including specific microbial, birds and mammal species (Croxall et al., 2002;
Atkinson et al., 2004).
Given the difficulty to observe polar regions, numerical modelling is
essential to understand sea ice processes and their influence on the other
components of the Earth system. Indeed, a sea ice component is presently
included in virtually all ocean and Earth modelling systems (e.g. Flato et
al., 2013; Danabasoglu et al., 2014). The contemporary use of sea ice models
encompasses a wide range of applications, from large-scale climate to
small-scale process studies and operational forecasts. The physical processes
at stake need to be well resolved at the appropriate spatial and temporal
scales. Hence, sea ice models must be both physically reliable and versatile
in a wide range of scales, at a reasonable computational cost (e.g. Hunke et
al., 2010).
In order to match these constraints, a number of changes have been made into
the Louvain-la-Neuve sea ice model (LIM3; Vancoppenolle et al., 2009a),
leading to the 3.6 version of the code. Along with the interface for Community Ice CodE
(CICE)
(Hunke et al., 2013), LIM3.6 is now the reference sea ice model in the
Nucleus for European Modelling of the Ocean (NEMO) in its 3.6 version just
released in June 2015. NEMO-LIM3.6 is expected to have a long life time, as
it will form the base of the ocean and sea ice representation in several
forthcoming Earth system models for the Coupled Model Inter-comparison Project 6 (CMIP6) (Meehl et al., 2014): the Institut Pierre-et-Simon Laplace (IPSL) Earth system model (Dufresne et
al., 2013), EC-Earth (Hazeleger et al., 2010) and Centro Euro-Mediterraneo sui Cambiamenti Climatici Climate Model (CMCC-CM) (Scoccimarro et
al., 2011). Therefore, we found it timely and appropriate to present the new
characteristics and possibilities made possible by LIM3.6 in this paper.
The modifications made to LIM mainly improve the robustness, versatility
and sophistication of the code, aiming at satisfying the needs of a large
community of users. A major goal was to reach an exact conservation of mass,
heat and salt, which is essential for climate simulations but was not
satisfied in LIM3 until now. For that purpose, the time stepping scheme was
reshaped and several minor conservation leaks were found and corrected. New
capabilities have also been developed: open-boundary conditions for sea ice
(which enables regional studies in ice-covered areas), more flexible
thickness category boundaries, mono-category parameterizations, more
realistic ice–ocean interactions, and more flexible ice–atmosphere
exchanges.
The representation of sea ice physics in LIM is described in Sect. 2.
Section 3 is dedicated to the new developments of the sea ice model. Some of
these developments are illustrated in two simulations using the latest stable
release of NEMO-LIM: a large-scale global 2∘-resolution configuration
(Sect. 4); and a regional 2 km resolution configuration around the Svalbard
Archipelago (Sect. 5), a region well-suited to study various sea ice regimes
as well as transient events such as polynyas. Conclusions and perspectives
are presented in Sect. 6.
Model description
LIM was originally a B-grid sea ice model developed by Fichefet and
Morales-Maqueda (1997), including ice dynamics based on the viscous-plastic
(VP) rheology (Hibler III, 1979), the three-layer thermodynamic formulation of
Semtner Jr. (1976), the second-order moment-conserving advection scheme of
Prather (1986) and various sea ice physical parameterizations. Some years
later LIM became LIM2 when it was rewritten in Fortran 90 and coupled to Ocean Parallelise (OPA),
a C-grid, finite difference, hydrostatic, primitive equation ocean general
circulation model (Madec, 2008). LIM2 was later on integrated into the NEMO
system, for the global reference configuration ORCA2-LIM (Timmermann et al.,
2005).
Recently, LIM was improved towards a better account of sub-grid-scale
physics, giving birth to LIM3 (Vancoppenolle et al., 2009a, b). LIM3, as
other multi-category models (e.g. CICE; Hunke et al., 2013), is based on the
Arctic Ice Dynamics Joint Experiment (AIDJEX) framework (Coon et al., 1974). LIM3 mostly differs from other
multi-category models in terms of parameterizations and implementation
details. The new features of LIM3 are mainly multiple ice categories to
represent the sub-grid-scale ice thickness distribution (Thorndike et al.,
1975), multi-layer halo-thermodynamics including brine dynamics and their
impact on thermal properties and ice–ocean salt exchanges (Vancoppenolle et
al., 2009b) and a C-grid formulation (Bouillon et al., 2009) for ice
dynamics using the modified elastic-viscous-plastic (EVP) rheology (Bouillon et
al., 2013), instead of the more computationally expensive VP rheology (Hibler III, 1979).
Conservation of area and ice thickness categories
To account for unresolved sub-grid-scale variations in ice thickness (h),
the state of sea ice is given by a thickness distribution function g(x,y,h,t) (Thorndike et al., 1975), defined as the limit
g=limdh→0dAdh,
where dA is the areal fraction of a small control surface with
thickness between h and h+dh.
Invoking continuity, the conservation of area can be written as
∂g∂t=-∇⋅gu+ψ-∂∂hfg.
The terms on the right-hand side are (i) divergence of the flux of g, with
u being the horizontal ice current, (ii) mechanical redistribution
(ψ) (i.e. ridging/rafting) and (iii) thermodynamical processes, with
f=dh/dt the net ice growth/melt rate. In practice, the
thickness distribution is discretized over (typically 5) thickness categories
(Bitz et al., 2001; Lipscomb, 2001), each characterized by a specific areal
fraction (referred to as concentration). The ice thickness in each
category is free to evolve between fixed boundaries.
The state of the ice is defined by a series of state variables, X(x,y,h,t,z), namely ice concentration, ice volume per unit area, ice internal energy,
ice salt content, snow volume per unit area and snow internal energy. Ice
internal energy is the only state variable that also depends on the vertical
depth in the ice (z). Ice salt content does not depend on z since
implicit vertical salinity profiles are assumed. Following the discretization
of thickness space, state variables are characterized by specific values in
each category. In addition, in order to resolve the vertical profiles of
internal energy, each category is further vertically divided into one layer
of snow and several ice layers of equal thicknesses.
In practice, sea ice state variables follow an equation of the form
∂X∂t=-∇⋅Xu+ΨX+ΘX,
where∇⋅Xu is the divergence of the flux
of X, ΨX is the ridging/rafting and ΘX is the
halo-thermodynamics.
Dynamics
Ice dynamics (momentum equation, advection and diffusion of state variables)
is formulated on a C-grid, which is a specificity of LIM3.
Momentum equation
The ice velocity is considered the same for all categories and is determined
from the two-dimensional momentum equation
m∂u∂t=Aτa+τw-mfk×u-mg∇η+∇⋅σ,
where m is the ice mass per unit area, A is concentration,
τa and τw are the air–ice and ocean–ice stresses,
-mfk×u is the Coriolis force, -mg∇η is the
pressure force due to horizontal sea surface tilt and ∇⋅σ
refers to internal forces arising in response to deformation. Momentum
advection is at least 1 order of magnitude smaller than acceleration and is
neglected (Leppäranta, 2005). The external stress terms are multiplied by
concentration to satisfy free drift at low concentration (Connolley et al.,
2004). The stress tensor σ is computed using the C-grid
EVP formulation of Bouillon et al. (2009, 2013).
EVP (Hunke and Dukowicz, 1997) regularises the original VP
approach (Hibler III, 1979). VP assumes a viscous ice flow (stress
proportional to deformation) at very small deformations, and a plastic ice
flow (stress independent of deformation) above a plastic failure threshold.
This threshold lies on a so-called yield curve that depends on the ice
strength determined by default from Hibler III (1979):
P=P∗H‾e-C(1-A),
where P* and C are empirical positive parameters, and H‾ is the
ice volume per grid cell area. Other strength formulations are available in
the code (e.g. Rothrock, 1975; Lipscomb et al., 2007); see Vancoppenolle et
al. (2012) for details. By introducing artificial damped elastic waves and a
time-dependence to the stress tensor, the EVP method enables an explicit
resolution of the momentum equation with a reasonable number of sub-time
steps (∼ 100) and easy implementation on parallel architectures.
However, EVP has to be used carefully since even the modified EVP of Bouillon
et al. (2013) hardly converges to the VP solution unless a very large number
(> 500) of iterations is used (Kimmritz et al., 2015).
Horizontal transport and diffusion
The sea ice state variables are transported horizontally using the
second-order moment-conserving scheme of Prather (1986). This scheme is
weakly diffusive and preserves positivity of the transported ice fields. To
smooth the ice fields and dampen instabilities, a horizontal diffusion of the
form D∇2X is implemented in Eq. (3), where D is a diffusion
coefficient that is proportional to mean grid cell size (the reference value
is 350 m2 s-1 at 2∘ resolution). Horizontal diffusion is
solved using a Crank–Nicholson scheme, with a prescribed diffusivity within
the ice pack that drops to zero at the ice edge. Horizontal diffusion should
be understood as a numerical artefact introduced to avoid non-linearities
arising from the coupling between ice dynamics and transport; hence, D
should be as small as possible.
Ridging and rafting ΨX
The dissipation of energy associated with plastic failure under convergence
and shear is accomplished by rafting (overriding of two ice plates) and
ridging (breaking of an ice plate and subsequent piling of the broken ice
blocks into pressure ridges). Thin ice preferentially rafts whereas thick ice
preferentially ridges (Tuhkuri and Lensu, 2002). In LIM3.6, the amount of ice
that rafts/ridges depends on the strain rate tensor invariants (shear and
divergence) as in Flato and Hibler (1995), while the ice categories involved
are determined by a participation function favouring thin ice (Lipscomb et
al., 2007). The thickness of ice being deformed (h′) determines whether ice
rafts (h′<0.75 m) or ridges (h′>0.75 m), following Haapala (2000).
The deformed ice thickness is 2h′ after rafting, and is distributed between
2h′ and 2H∗h′ after ridging, where H*=100 m
(Hibler III, 1980). Newly ridged ice is highly porous, effectively trapping
seawater. To represent this process, mass, salt and heat are extracted from
the ocean into a prescribed volume fraction (30 %) of newly ridged ice
(Leppäranta et al., 1995). Hence, in contrast with other models, the net
thermodynamic ice production during convergence is not zero in LIM, since
mass is added to sea ice during ridging. Consequently, simulated new ridges
have high temperature and salinity as observed (Høyland, 2002). A fraction
of snow (50 %) falls into the ocean during deformation.
Halo-thermodynamics ΘX
Thermodynamics refers to the processes locally affecting the ice mass and
energy, and involving energy transfers through the air–ice–ocean interfaces.
Halo-dynamics refers to the processes impacting sea ice salinity. In the
code, both processes are assumed purely vertical and their computations are
repeated for each ice category. Therefore, the reference to ice categories
is implicit in this section.
Energy
The change in the vertical temperature profile, T(z,t), of the snow–ice
system derives from the heat diffusion equation
ρ∂E(S,T)∂t=∂∂zk(S,T)∂T∂z+R,
where z is the vertical (layer) coordinate, ρ the snow/ice density
(assumed constant), E the snow/ice internal energy per unit mass (Schmidt
et al., 2004), S the salinity, k the thermal conductivity (Pringle et
al., 2007) and R the internal solar heating rate. The effect of brine
inclusions is represented through the S and T dependency of E and k
(e.g. Untersteiner, 1964; Bitz and Lipscomb, 1999). The surface energy
balance (flux condition) and a bottom ice temperature at the freezing point
provide boundary conditions at the top and bottom interfaces, respectively.
Equation (6) is non-linear and is solved iteratively. Change in ice salinity
is assumed to conserve energy; hence, any salt loss implies a small
temperature increase.
The solar energy is apportioned as follows. The net solar flux penetrating
through the snow–ice system is 1-αFsol,
where α is the surface albedo and Fsol is the incoming
solar radiation flux. Only a prescribed fraction i0 of the net solar
flux penetrates below the surface and attenuates exponentially, whereas the
rest is absorbed by the surface where it increases the surface temperature.
The radiation term in Eq. (6) derives from the absorption of the penetrating
solar radiation flux R=-∂/∂zio1-αFswexp-zκ,
where κ=1 m-1 is the attenuation coefficient in sea ice, in the
range of contemporary observations (Light et al., 2008). At this stage no
shortwave radiation penetration is allowed when snow is present (i0=0). The solar radiation flux penetrating down to the ice base is sent to the
ocean. The surface albedo is a function of the ice surface temperature, ice
thickness, snow depth and cloudiness (Shine and Henderson-Sellers, 1985).
Mass
The ice mass increases by (i) new ice formation in open water,
(ii) congelation at the ice base, (iii) snow–ice formation at the ice surface
and (iv) entrapment and freezing of seawater into newly formed ridges. It
decreases by melting at both (v) the surface and (vi) the base. The snow mass
increases by snowfall and reduces by surface melting, sublimation, snow–ice
formation and snow loss during ridging/rafting.
Freezing and melting (i, ii, v, vi) depend on the appropriate interfacial net
energy flux (open water–atmosphere, ice–atmosphere or ice–ocean) ΔQ
(W m-2) such that the ocean-to-ice mass flux Fm
(kg m-2 s-1) is written as
Fm=ΔQΔE.ΔE (J kg-1) is the energy per unit mass required for the phase
transition. For new ice formation in open water, the new ice thickness must
be prescribed (usually 10 cm) and the fractional area is derived from
Eq. (7). For surface melting, ΔQ is different from zero only if the
surface temperature is at the freezing point.
Snow-ice formation requires negative freeboard, which occurs if the snow
load is large enough for the snow–ice interface to lie below sea level
(Leppäranta, 1983). Seawater is assumed to flood the snow below sea
level and freeze there, conserving heat and salt during the process
(Fichefet and Morales Maqueda, 1997; Vancoppenolle et al., 2009b). The
associated ocean-to-ice mass flux is
Fm=ρi-ρs∂h∂t.
Every ice–ocean mass exchange involves corresponding energy and salt
exchanges (Schmidt et al., 2004). For instance, seawater freezing involves a
change in energy ΔE=Ei(S,T)-Ew(Tw),
where Ei is the internal energy of the frozen ice at its new
temperature and salinity and Ew is the internal energy of the
source seawater at its original temperature. To ensure heat conservation in
the ice–ocean system, the heat flux Qm=Ew(Tw)Fm is extracted from the ocean. Conversely, when ice melts the
internal energy of melt water is sent to the ocean. Salt exchanges are
detailed hereafter.
Salt
The salinity of the new ice formed in open water is determined from ice
thickness, using the empirical thickness–salinity relationship of
Kovacs (1996). One originality of LIM3 is that the vertically averaged ice
salinity S‾ (in ‰) evolves in time, following
Vancoppenolle et al. (2009a, b):
∂S‾∂t=∑jνjSw-S‾h∂hj∂t+∑jIjSj-S‾Tj.
The first term on the right-hand side is the salt uptake summed over the
three ice growth processes (ii, iii and iv), each characterized by a growth
rate ∂hj/∂t and a coefficient νj that
determines the fraction of trapped oceanic salinity Sw. For basal
freezing, νj is a function of growth rate (Cox and Weeks, 1988). For
snow–ice formation, it is a function of snow and ice densities. For ridging,
it depends on ridge porosity. The second term on the right-hand side is the
salt loss summed over the two parameterized brine drainage processes (gravity
drainage and flushing; see Notz and Worster, 2009). Ij is 1 if the
drainage process is active and 0 if it is not. Gravity drainage occurs if ice
is growing at the base; flushing occurs if the snow/ice is melting at the
surface. Sj (5 ‰ for gravity drainage; 2 ‰ for
flushing) is the restoring salinity for each drainage process and Tj is
the corresponding timescale (20 days for gravity drainage, 10 days for
flushing).
The shape of the vertical salinity profile depends on S‾, so that
ice with S‾>4.5 ‰ has a constant vertical profile. By
contrast, ice fresher than this threshold has a linear profile with a lower
salinity near the surface. This difference is important to properly represent
the impact of brine on thermal properties (Vancoppenolle et al., 2005). Ice
formation retrieves salt from the ocean, but the conjunction with water mass
loss makes the ocean surface saltier. Conversely, ice melting releases salt
but makes the ocean fresher. Because the ice density is assumed constant,
brine drainage cannot be associated with an ice–ocean water mass exchange
(the ice density would have to change to be conservative). The brine drainage
flux is therefore represented as a salt flux, which directly increases ocean
salinity.
Transport in thickness space
Ice growth or melt in a given category involves a transfer of ice to neighbour
categories, which is formally analogous to a transport in thickness space
with a velocity equal to the net growth rate dh/dt. This
transport in thickness space is solved using the semi-Lagrangian linear
remapping scheme of Lispcomb (2001). This scheme is weakly diffusive,
converges with a few categories and its computational cost is minimal, which
is an important property since transport operates over each ice category.
Transport in thickness space is applied to all other state variables as
well.
New features in LIM3.6Control of the mass, heat and salt budgets
Mass, heat and salt must be perfectly conserved over sufficiently long timescales in an ice–ocean modelling system, especially for climate studies.
Moreover, a clear identification of the different physical processes and
their contributions to the air–ice–ocean exchanges is needed. These
requirements were not satisfied in LIM3.0 mostly because of the temporal
scheme and numerous small conservation leaks, which have necessitated a
large rewriting of the code.
The changes in the sea ice state variables due to dynamics and thermodynamics
were previously calculated in parallel, starting from the same initial state
(Fig. 1a). Both tendencies were then combined to calculate the new state
variables. This method, numerically stable and matching NEMO's philosophy,
required, however, a final correction step to impose that ice losses (by
melting and/or divergence) did not exceed the ice initially available. This
correction step could be as important as the physical processes in some
cases, and could not be attributed to a specific process. The modified
temporal scheme is fractional (as for most sea ice models), removing the need
for a correction step. The dynamic and thermodynamic processes are split in
time and are applied sequentially (Fig. 1b), which allows for consistent
diagnostics of the processes contributing to the air–ice–ocean exchanges
without altering the general model behaviour (not shown). These process
diagnostics are illustrated for global and regional simulations in Sects. 4
and 5.
Illustration of the changes in the time scheme. (a) The
original time scheme used in LIM3.0 treats ice dynamics and thermodynamics in
parallel, requiring a correction step to ensure that the ice mass is strictly
positive. (b) The new scheme of version 3.6 uses an operator
splitting approach, so that dynamics is calculated before thermodynamics,
and therefore no correction is needed.
Based on these modifications, the conservation of mass, salt and heat was
then carefully inspected, leading to several small corrections. In
particular, the space-centred implicit backward-Euler scheme used to solve
the heat diffusion equation (Eq. 6, Bitz and Lipscomb 1999) does not strictly
conserve heat. The scheme is the same as in CICE, for which the problem was
already reported but not yet resolved (Hunke et al., 2013). Because Eq. (6)
is non-linear (E and k depend non-linearly on T), the numerical
procedure has to be iterative. The iteration stops once the temperature
change is less than 10-5∘C or after 50 iterations. The scheme
does not strictly converge, leading to an error on the heat conduction flux
of ∼ 0.005 W m-2, averaged over the ice pack for a global
2∘-resolution simulation, with maxima reaching in some rare cases O
(10 W m-2). These errors are similar to those reported in CICE user's
guide (0.01 W m-2, Hunke et al., 2013). Therefore, to ensure strict
conservation, either the heat conduction fluxes or the ice temperature must
be adjusted at the end of iteration. We chose to keep the ice temperature
unchanged and to recalculate the net downward heat flux reaching the ocean,
which could be easily implemented in other models using the same scheme.
Lateral boundary conditions
NEMO can be used in regional configurations. The BDY tool, handles the
specification of boundary conditions in NEMO, with possible inflows/outflows
through open boundaries (Chanut, 2005). The ocean temperature, salinity and
baroclinic velocity are treated with a flow relaxation scheme (Engedahl,
1995), while the Flather (1976) radiation condition is well-suited for tidal
forcing and therefore is used for both the barotropic ocean velocity and sea
surface height. However, sea ice was missing from BDY, which restricted the
use of regional configurations to ice-free areas. New developments to BDY
were introduced to accommodate sea ice. The treatment of open boundaries in
the
sea ice model is not very much documented in the literature; hence, we found
it difficult to compare this new approach to what is done in other models.
The sea ice state variables imposed at the boundary depend on the direction
of ice velocity in a similar way to an upstream advection scheme. They are
relaxed toward interior domain values where ice exits the domain, and toward
external boundary data where ice enters the domain. External boundary data
can either come from observations, reanalyses or reference simulations. As
ice velocities in these external files are not always well determined, they
need to be defined at the boundary. The tangent ice velocity is imposed to 0.
The normal ice velocity depends on the presence of ice in the adjacent cell:
if ice-free, ice velocity is relaxed to ocean velocity; otherwise, velocity is
relaxed to the ice velocity of the adjacent cell.
Most boundary data sets do not include multiple ice categories. Hence, a
strategy to fill in thickness categories in a smooth and consistent way with
the external data set is defined, following the algorithm used to initialise
the sea ice state variables (Vancoppenolle et al., 2012). The basic
assumption relies on a distribution of ice concentration as a function of ice
categories following a Gaussian law in a volume-conserving way, preserving
positivity. The largest concentration is associated with the category where
the mean thickness (over the grid cell) lies. Illustration of the capability
of LIM3 in a regional domain is presented in Sect. 5.
Category boundaries
The original discretization of the thickness category boundaries in LIM3
follows the hyperbolic tangent formulation from CICE (Hunke et al., 2013).
The formulation proved to be suitable to simulate the Arctic ice pack with
only five ice categories, but cannot be easily adjusted to different ice
conditions. For instance, thin ice can only be finely discretized by
augmenting the number of ice categories, and de facto increasing
computational cost. Multiple simulations, in particular for regional
configurations, call for more flexibility without additional cpu consumption.
Therefore, a new discretization was implemented that can adjust the expected
mean ice thickness (h‾) over the domain. Category boundaries lie
between 0 and 3h‾ and are determined using a fitting function
proportional to (1+h)-α, where α=0.05. For h‾=2 m, the new formulation is very similar to the original one. For
h‾=1 m, boundaries tighten within 3 m, providing more
resolution for thin ice (Fig. 2).
Thickness category boundaries (m) as a function of categories (5 or
10). The tanh formulation from CICE, which is used in the former version 3.0
of LIM, is represented in grey and black for 5 and 10 categories,
respectively. The formulation used in the new version 3.6 of LIM is
proportional to (1+h)-α , where α=0.05, and does not
depend on the number of categories. It is displayed above for three different
mean ice thicknesses h‾ (1, 2 and 3 m), h‾=2 m
being the closest to the tanh formulation.
Virtual thickness distribution
Some users may want to run LIM3.6 at the smallest possible computational
cost. The most efficient way to achieve this is to use a single ice
thickness category (mono-category). However, this deteriorates the results
because of the poor representation of the growth and melt of thin ice, which
typically reduces the amplitude of the seasonal cycle of ice extent (Holland
et al., 2006; Massonnet et al., 2011). To lessen this problem, two
parameterizations from LIM2 (Fichefet and Morales Maqueda, 1997) were
implemented in LIM3.6. The first parameterization enhances the sea ice and
snow thermal conductivities, in order to increase basal ice growth, as thin
ice would do if it was properly resolved. The second parameterization aims
at representing the impact of melting thin ice on ice concentration. With
these two parameterizations, a mono-category simulation mostly reproduces
the global mean volume and extent of a multi-category simulation, but
regional differences subsist. In addition, although the mono-category
approach in LIM3 is conceptually comparable to LIM2, simulations using the
two sea ice models would show different results because of the different
representations of halo-thermodynamics. This will be described in more
details in a forthcoming contribution.
Embedded sea ice
Sea ice has been considered so far as levitating above the ocean in LIM3,
and all the studies (including this one) have been based on this
approximation. Even though exchanges between the levitating ice and the
ocean modify the sea surface height and thermohaline structure of the ocean
surface, the sea surface depression resulting from the weight of the ice and
snow cover was not taken into account. The effect of embedding ice into the
ocean can now be activated at will (not illustrated in this study). It
improves the physical realism and influences ocean dynamics (mostly at the
ice edge) via strengthened gradients of sea surface height, but does not
directly affect ice dynamics (Campin et al., 2008).
A flux redistributor for the ice–atmosphere interface in coupled
mode
NEMO-LIM3.6 can also be coupled to atmospheric models. Some atmospheric
models only provide ice–atmosphere heat or mass fluxes (<F>) for the entire
grid cell, and not for each thickness category, as LIM needs. Yet the
ice-atmosphere flux strongly depends on the ice surface temperature, which
substantially differs among categories. To better estimate the ice–atmosphere
flux in the lth category (Fl), a “flux redistributor” has been
implemented using the following linearisation: Fl=<F>+∂F∂Tsu(Tlsu-<Tsu>), where
∂F∂Tsu is the flux derivative given by the
atmospheric model. Tlsu, is the ice surface temperature in the
lth category and <Tsu> is the average over the categories,
weighted by their areal fractions. The flux redistributor proves much closer
to an exact computation of ice–atmosphere fluxes than a category-averaged
flux.
Inputs and outputs
LIM3.6 has been interfaced with XIOS (XML input output server;
http://forge.ipsl.jussieu.fr/ioserver/), a new and innovative library
developed at Institut Pierre-et-Simon Laplace (IPSL) and dedicated to climate
modelling data output. XIOS combines flexibility and performance. It
considerably simplifies output definition and management by outsourcing
output description in an external XML file. In addition, the interface offers
numerous possibilities for variables manipulations such as complex temporal
operations and computations involving several variables. XIOS also achieves
excellent performance on massively parallel supercomputers by using several
server processes exclusively dedicated to output files. File system
writing is performed concurrently with computation.
Global ice–ocean simulation: ORCA2-LIM3Experimental set-up and observation data sets
The simulation presented here is the standard simulation that can be
performed with the most recent 3.6 version of NEMO right after downloading
the code, in one of the main supported NEMO configurations (ORCA2-LIM3), and
forced by the reference CORE normal year forcing directly provided with the
code. This is not the best simulation that can be produced, but rather the
one that a user starting with the model would perform.
In ORCA2-LIM3, NEMO comprises the ocean general circulation model OPA
version 3.6 (Madec, 2008) and LIM (Vancoppenolle et al., 2009a) in its 3.6
version presented above, running on the same 2∘-resolution grid
(ORCA2). More details can be found in Mignot et al. (2013). The atmospheric
state is imposed using the CORE normal year forcing set proposed by Large and
Yeager (2009), developed to inter-compare ice–ocean models (e.g. Griffies et
al., 2009). It is based on a combination of NCEP/NCAR reanalyses (for wind,
temperature and humidity) and various satellite products (for radiation), has
a 2∘ resolution and near-zero global mean heat and freshwater fluxes.
The so-called normal year data set superimposes the 1995 synoptic variability
on the mean 1984–2000 seasonal cycle. The simulation lasts 100 years, much
longer than needed for sea ice to reach equilibrium. Most diagnostics
presented hereafter are seasonal averages over the last 10 years of the
simulation. The computational cost of such a simulation is about 12 h on 64
processors of an IBM Power6, with LIM3.6 consuming less than 25 % of this
time.
Mean sea ice concentrations from the simulation ORCA2-LIM3 and the
observations OSI-SAF for March and September in the Arctic (left panels) and
February and September in the Antarctic (right panels). The white line
indicates the 15 % ice concentration contour.
The observed ice extent is derived from ice concentration retrievals of the
EUMETSAT Ocean and Sea Ice Satellite Application Facility (OSI-SAF; Eastwood
et al., 2010) and is presented here as 1984–2000 monthly means. To put the
simulated ice volume in context, we do not use satellite estimates, for which
uncertainties are very large (e.g. Zygmuntowska et al., 2014), but instead
the 1979–2011 reanalysis PIOMAS in the Arctic (Schweiger et al., 2011), and
the NEMO-LIM2-EnKF reconstruction in the Antarctic (Massonnet et al., 2013).
Ice concentration and thickness
Neither the model nor the atmospheric forcing are precisely tuned to get the
most realistic sea ice simulation, because this depends on forcing,
resolution and user wishes. Instead, we choose the model default parameters
with the standard reference forcing and show that the simulated ice
concentrations and thicknesses are in reasonable agreement with
observations.
Mean seasonal cycle of sea ice extent (i.e. area inside the 15 %
concentration contour) in the Northern (in blue) and Southern (in cyan)
hemispheres from the ORCA2-LIM3 simulation (solid lines) and as derived from
OSI-SAF observations (dashed lines). Units are in 106 km2.
Figure 3 shows the ice concentrations at the model maximum and minimum extent
in ORCA2-LIM3 and OSI-SAF (March and September for the Arctic; February and
September for the Antarctic). The simulated ice distribution is relatively
close to the observations, with some common defects. In the boreal winter, the
ice extends too much southward covering a large part of the Greenland Sea,
while it almost disappears near Antarctica. These biases have unclear origins
and we do not intend to resolve them but some leads can be proposed. In the
Northern Hemisphere, we notice a low ocean heat supply by the North Atlantic
Current and an overestimated ice volume export through Fram Strait, which
could explain some of the bias. But other factors as the forcing or model
physics, in particular dynamics, cannot be ruled out. In the Southern
Hemisphere, we notice a wrong position of the Antarctic Circumpolar Current
and an overestimated ocean convective activity, which melts ice by mixing
relatively warm and salty water at depth with cold and fresh surface waters,
and which could explain the ice loss. Such problems are common in global
ocean models (Kim and Stössel, 2001), and vertical physics in the ocean
should certainly be tuned to improve the realism of the simulated ice
characteristics.
Mean simulated sea ice thicknesses (m) at the time of maximum ice
volume: for March in the Northern Hemisphere and for September in the
Southern Hemisphere.
The seasonal cycle of the sea ice extent (i.e. the area enclosed within the
15 % ice concentration contour, white lines in Fig. 3) is presented in
Fig. 4 for both hemispheres. The model reproduces the amplitude of the
observed seasonal variations of ice extent but is biased low all year long,
and especially in austral summer.
The simulated ice thickness distributions are displayed in Fig. 5 for both
hemispheres, at the time of maximum extent (March and September). The ice
thickness exceeds 3 m in the central Arctic, reaching 5 m along the
Canadian and Greenland coasts. This is in rough agreement with the submarine
thickness retrievals (3.4 m in the central Arctic in February–March 1988;
Kwok and Rothrock, 2009). The spatial distribution follows expectations,
except a spurious band of thick ice along the East Siberian shelf. The
simulated Arctic ice volume ranges from 17 000 km3 in September to
35 000 km3 in March–April, i.e. somewhat higher than Pan-arctic
Ice-Ocean Modeling and Assimilation System (PIOMAS) reanalyses. In the
Southern Hemisphere, the ice is generally thinner than in the Arctic, with a
modal value of nearly 1 m. The model underestimates the thickness of thick
ice in the Weddell and Amundsen seas (Worby et al., 2008; Kurtz and Markus,
2012). The band of thick ice along the east side of the Antarctic Peninsula
is missing, which is attributed to misrepresented NCEP winds in the region
(Timmermann et al., 2005; Vancoppenolle et al., 2009b). The simulated ice
volume (0 to 14 000 km3) is somewhat larger than the reanalysis values
(2000–10 000 km3; F. Massonnet personal communication, 2015) and
satellite estimates (3000–11 000 km3, Kurtz and Markus, 2012).
Simulated mean seasonal cycles of the different ice mass balance
processes in the ORCA2-LIM3 simulation: Arctic (left panel) and
Antarctic (right panel). Ice grows from the base (magenta), in open water
(red), by snow–ice formation (orange) or by freezing of sea water trapped in
the ridges (green). Ice melts at the base (blue) and surface (cyan). Ice
advection is nil here since diagnostics are hemispheric. The black line is
the net ice production (i.e. the sum of all the processes). Units are in
cm month-1. Positive and negative values represent creation and
destruction of sea ice, respectively.
This simulation could obviously be improved through careful calibration,
which depends on resolution and forcing. Calibration can be achieved by
adjusting the atmospheric forcing and vertical ocean physics, and by tuning
the most influential ice parameters. For instance, the Arctic ice thickness
can be increased substantially by increasing the albedo, decreasing the
minimum lead fraction or decreasing ice strength.
Mass and salt balances
The new developments allow for an examination of the ice mass, heat and salt
budgets seasonally and over the different processes. Seven processes affect
the ice mass (see Sect. 2.3.2). Five belong to vertical thermodynamics: new
ice growth in open water, basal growth and melt, surface melt and snow–ice
formation. Two are dynamical processes: advection and entrapment and freezing
of seawater in newly built ridges. Changes in the heat and salt contents
involve the same processes, plus the changes in internal temperature (for
heat budget) and internal salinity due to brine drainage (for salt budget).
We focus on the mass budget for illustration and present its different
contributors integrated over the Northern and Southern hemispheres in Fig. 6.
In both hemispheres, the dominant balance is between basal ice growth and
melt. Surface melting is also important but only in the Arctic during boreal
summer. Contributions of secondary importance are new ice formation in open
water during the cold season (both hemispheres) and snow–ice formation
during Antarctic spring. Note that the contribution from advection is
obviously nil when integrated over a hemisphere. The maximum growth rate is
about the same in both hemispheres (slightly larger than
20 cm month-1). Basal melt is remarkably weaker in the Arctic than in
the Antarctic (maximum at 40 and 70 cm month-1, respectively). This is
because in the Arctic, the ice is constrained by continents to stay at high
latitudes, where the ocean stratification is strong and the ocean heat flux
is weak. Overall, about 26 000 km3 of ice are formed and melted each
year in the Arctic, which corresponds to about 2 m of ice. About 320 Gt of
salt are extracted from the ocean during freezing and released during ice
desalinisation and melting. These mean values are similar in the Antarctic:
22 000 km3 of annual ice production (∼ 1.8 m) and 320 Gt of
salt.
This integrated view masks strong geographic disparities. In Fig. 7 we show
the geographical distribution of some of the processes in March in the
Arctic. The interior of the ice pack still grows from the bottom, while the
base of the ice edge melts, resulting in snow–ice formation where snow is
thick enough. As expected, the strongest thickness changes due to advection
are near the ice edge. Ice formation in open water is globally weak but
becomes one of the main processes in some regions of climate importance (see
next section).
Horizontal distribution of the five relevant processes contributing
to the sea ice mass balance in March in the Northern Hemisphere, from the
ORCA2-LIM3 simulation. Units are in cm day-1. Positive and negative
values represent creation and destruction of sea ice, respectively.
Regional configurationsExperimental set-up
To illustrate the capability of NEMO-LIM3 in regional ice-covered domains, we
designed an experiment in a regional configuration (500 × 500 km)
around the Svalbard Archipelago. This region was chosen because of the
diverse conditions encountered and strong tides (a tidal gauge at Ny-Ålesund,
on the west coast of Svalbard, records tidal amplitudes up to 2 m). North of
the archipelago, lies the perennial ice pack of the Arctic Ocean
transitioning southwards to a seasonal ice zone. The domain also includes the
large Storfjorden polynya, frequently open during winter. Polynyas are small
(10–105 km2) and sporadic by nature, but their role in climate is
important (e.g. Morales Maqueda et al., 2004). In winter, the ocean heat loss
in polynyas is considerable, producing large amounts of sea ice, as well as
dense water sinking towards the deep ocean basins. At the onset of melting
season, polynyas enhance ice melting as the open waters capture more heat
than ice-covered areas.
Horizontal resolution is very high (2 km) in order to properly represent
fine-scale processes taking place in polynyas. The basin is vertically
discretized by 75 non-uniform ocean levels, with a resolution of 1 m at the
surface. The domain is open at the four boundaries and conditions there are
set up using the BDY tool, modified as described in Sect. 3.2. Bathymetry is
interpolated from etopo1 (Amante and Eakins, 2009), which actually retrieves
data from IBCAOv2 north of 64∘ N (Jakobsson et al., 2008). Tides are
important drivers for high-frequency processes. Therefore, they are included
here as well as the non-linear free surface (z* coordinates system). A
third-order upstream biased advection scheme is used for ocean tracers and
momentum (instead of the flux corrected transport used in ORCA2-LIM3). Such a
scheme is indeed more precise and has implicit diffusion. It also minimizes
diffusion; hence, the oceanic structures can develop without being impeded by
homogeneous diffusion. The k-ε closure scheme using generic
length-scale turbulent mixing is chosen (Umlauf and Burchard, 2003; Reffray
et al., 2015). The simulation is forced at the surface by a 6-hourly,
3/4∘× 3/4∘ ERAI data set, and at the boundaries by
5-day outputs from a DRAKKAR 1/4∘ global reference simulation
ORCA025-MJM (an update to ORCA025-G70; Barnier et al., 2006; Molines et al.,
2007; DRAKKAR group, 2007). We also prescribe tidal sea surface height and
barotropic velocity at the boundaries from FES2012 (Carrère et al.,
2012). The simulation is conducted over 1999–2009 in order to capture
inter-annual variability.
The model behaviour at the boundary is satisfactory. No noise or wave
reflection pollutes the basin despite strong in and out flows and the
presence of tides (not shown). The simulation is also able to represent
transient polynya occurrence. As an example, Fig. 8 shows the simulated ice
concentrations on 22 May 2002 around Svalbard (right panel) as well as the
corresponding observations (left panel). At this date, northeastern winds
were sufficiently strong to open the Storfjorden polynya by pushing sea ice
towards the western side of the fjord. The simulated opening of polynyas –
in terms of timing, location and size – is reasonable in Storfjorden and
elsewhere, though polynyas are somewhat smaller than observed and their
location is not precisely captured. This is likely due to the low
spatio-temporal variability of the ERAI surface forcing, as highlighted by
previous studies (Skogseth et al., 2007). Downscaling the forcing with a
regional atmospheric model is probably required to further improve the
simulation. The Storfjorden polynya is not exactly found where it should be,
north of Storfjorden (Fig. 8), which could be due to the atmospheric forcing
or to the absence of a representation of landfast ice in the model and must
be further investigated.
(Left)satellite MODIS image of the Svalbard Archipelago
(22 May 2002). Note that clouds and sea ice are both white. (Right) 1-day
averaged simulated sea ice concentrations at the same date from the
high-resolution regional simulation. In both pictures, ice is pushed away
from the shore by northeasterly winds, allowing formation of a polynya along
the east coast of Storfjorden.
Mass and salt balances in Storfjorden
Figure 9 shows the 10-year variability of the different mass balance
processes over the 13 000 km2 of the Storfjorden region (see Fig. 8).
The sea ice mass balance is dominated by basal growth
(16 km3 year-1) and new ice growth in open water
(12 km3 year-1), compensated by export out of the domain (not
shown) and basal melt (11 km3 year-1). Surface melt can be
significant (up to one third of total melt) but only at the beginning of
summer. As expected, ice growth in open water is a crucial process here,
while it is weak once averaged over the Arctic basin (see previous section).
The net ice production is +17 km3 year-1 on average, with
strong inter-annual variability (from 23 km3 in 2001–2002 to
10 km3 in 2006–2007). This corresponds to a salt flux from the ocean
to the ice of about 150 Mt year-1. Over a year, the net production
almost balances ice export (not shown), so there is no long-term accumulation
of ice in the basin. However, at timescales shorter than a year, ice can pile
up in the Storfjorden.
A 10-year inter-annual variability of the processes involved in ice
evolution integrated over the Storfjorden area from the regional simulation.
Processes are the same as in Fig. 6, plus an advection term corresponding to
ice coming in and out of the area, which is not shown for more clarity. Units
are in cm day-1. Positive and negative values represent creation and
destruction of sea ice, respectively. Note that for more readability,
variations are smoothed with a Hanning filter at a period of 2 months.
By combining AMSR-E sea ice concentrations and atmospheric forcing from
ERA-interim, Jardon et al. (2014) estimated a mean ice production of
47 km3 in winter between 2002 and 2011. With a similar approach,
Skogseth et al. (2004) found a mean ice production of 40 km3 during
1998–2002. In our simulation, this production amounts to 33 km3 for
the period 1999–2009. This value is reasonable, though it is smaller than
observational retrievals and reanalyses. This could be related to the small
size of the simulated polynya and/or to the lack of high-resolution,
high-frequency winds in the ERAI forcing and should be further investigated.
Conclusions
The Louvain-la-Neuve sea ice model (LIM) has evolved considerably during the
past decade. Two versions have been developed and have coexisted up until
now. LIM2 is based on a Hibler III (1979) mono-category approach, and was
integrated in the NEMO system about 1 decade ago (Timmermann et al., 2005).
It was the reference model to date and was used in a variety of simulations
including CMIP5. LIM3 is a more sophisticated model developed 5 years ago
(Vancoppenolle et al., 2009a), including a better representation of sub-grid-scale ice thickness distribution and salinity processes. Several
modifications to LIM3 have been done recently to make it more robust,
versatile and sophisticated, leading to LIM3.6, described in this paper.
LIM3.6 is the reference model for the forthcoming CMIP6 simulations, while
LIM2 is no longer the reference and will be discontinued in the next NEMO
release.
LIM3 has been improved for a use in various configurations, from climate to
regional studies, with a large range of resolutions and complexities. Three
main developments were required. First, the code has been made strictly
conservative. For that purpose, the general time stepping has changed from
parallel to a splitting approach. In other words, thermodynamics processes
are now performed after dynamics, which enables the discrimination of the
different processes contributing to the mass, heat and salt exchanges across
the interfaces between air, ice and ocean. Conservation in the code has been
carefully examined by comparing these exchanges with thermodynamical and
dynamical ice evolution, which has led to several small corrections to reach
a strictly conservative code. In particular, the iterative procedure to solve
the heat diffusion equation (Eq. 6) did not exactly converge, leading to
small heat leaks. The leaks are now corrected by recalculating heat fluxes.
Second, version 3.6 of LIM is the first to handle open-boundary conditions
for regional simulations in ice-covered areas. The sea ice state variables at
the boundary depends on the direction of the normal ice velocity to allow
realistic inflows and outflows with the rest of the ocean. Boundary
conditions are flexible enough so that ice boundary data sets can either
integrate a sub-grid-scale ice thickness distribution or not. In addition,
the formulation of the discretization of ice categories boundaries has
changed to adapt a simulation to different ice thickness conditions, as
encountered in regional configurations. Third, LIM3.6 sophistication and
versatility have further increased. A mono-category capability has been
implemented with the parameterization of thin ice melting, especially for
users needing an ice model at minimal computational cost. A flux
redistributor at the top of the ice categories has been coded for the
coupling with atmospheric models that cannot handle multiple fluxes over a
grid cell. Finally, the effect of the ice and snow weight on the sea surface
height has been implemented.
To illustrate some of the new capabilities of LIM3, we present 100 years of
the 2∘-resolution forced simulation ORCA2-LIM3, and 10 years of a
regional simulation at 2 km resolution around the Svalbard Archipelago,
which hosts the recurrent Storfjorden polynya. We mainly focus on the ice
mass budget and show how they differ, depending on the region studied. At the
global scale, the dominant processes are basal ice growth and basal ice melt
for both hemispheres, but other processes matter locally. In the Storfjorden,
new ice growth in open water is nearly as large as basal growth. The entire
ice production is exported out of Storfjorden annually. Production presents
large inter-annual variability over the 10 years of the experiment
(1999–2009), with maximum values exceeding twice the minimum.
There are also ongoing and upcoming developments for LIM.
The compatibility between the Adaptive Grid Refinement In Fortran
(AGRIF; Debreu et al., 2008) and LIM3 to run global simulations is yet to be
achieved and work is in progress to use LIM2–AGRIF interface (Talandier
et al., 2014) and apply it to LIM3.
The melt pond parameterization of Flocco and Feltham (2007), as
implemented by Lecomte et al. (2015), exists in a branch of the code and is
expected soon in the reference version.
In the future, LIM will continue to be developed, including, among others,
sea ice biogeochemistry (Vancoppenolle and Tedesco, 2015; Moreau et al.,
2015), an elasto-brittle rheology (Girard et al., 2011), improved snow
physics (Lecomte et al., 2013, 2015) and a sub-grid-scale representation of
ice–ocean exchanges (Barthélemy et al., 2015).
Code availability
The version 3.6 of LIM3 is incorporated in the reference version of NEMO
(currently v3.6 stable) and can be downloaded from the NEMO web site
(http://www.nemo-ocean.eu/) at this address:
https://forge.ipsl.jussieu.fr/nemo/browser/branches/2015/nemo_v3_6_STABLE/NEMOGCM/NEMO/LIM_SRC_3.
Acknowledgements
We thank the two anonymous reviewers for their thorough reading and
constructive comments, which helped improving the manuscript. The present work
was supported by the French National Research Agency (ANR) as part of the
OPTIMISM project (ANR-09-BLAN-0227-01), the European Community's Seventh
Framework Program FP7/SPACE (MyOcean2, grant 283367), IS-ENES2 (grant 312979)
and BISICLO (FP7 CIG 321938). Computational resources have been provided by
the French Institut du Développement et des Ressources en Informatique
Scientifique (IDRIS). The Antarctic sea ice concentration reprocessed data set
was provided by the Ocean and Sea Ice Satellite Application Facilities
(OSISAF) and is available at http://osisaf.met.no. The MODIS image is
courtesy of the online Data Pool at the NASA Land Processes Distributed
Active Archive Center (LP DAAC), USGS/Earth Resources Observation and Science
(EROS) Center, Sioux Falls, South Dakota
(https://lpdaac.usgs.gov/data_access).
Edited by: P. Huybrechts
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