Supplementary Information: the CAM-MLM model

1. The four components of the CAM-MLM modela. Atmosphere, land and ice components
The model atmosphere is the second version of the Community Atmosphere
Model (CAM2.1), primarily developed at the National Center for AtmosphericResearch (NCAR). The AGCM dynamics is based upon an eulerian spectral
scheme solved on a Gaussian grid of about 2.8o x 2.8o latitude-longitude
corresponding to a triangular horizontal truncation at 42 wave numbers. The
vertical resolution is discretized over 26 levels using a progressive vertical hybrid
coordinate. The reader is invited to refer to Kiehl and Gent (2004) for a detailed
description of the model physics package and for its performance.
The land surface and the sea-ice components are the Community Land Model(CLM2, Oleson et al 2004) and the Community Sea-Ice Model (CSIM, Briegleb etal 2004), respectively. The dynamical core of the latter has been turned off in thepresent case.
b. Ocean components
The ocean component (hereafter MLM) consists of single independent column
models with explicit mixed layer physics and no horizontal advection. MLM isbased on Gaspar (1988)’s formulation as implemented by Alexander and Deser(1995). In the present study, we use a modified version of that used in Alexanderet al (2000) where we have first included additional layers at the bottom of theocean now reaching 1500 m or the actual depth which ever is shallower, andwhere we have implemented the coupling between the thermodynamical sea-ice
component of CSIM and the MLM surface layer. Each ocean point has 36 verticallevels with 15 layers in the upper 100m and a realistic bathymetry (Fig. SI1). Veryshallow areas (< 40 m) are treated as a fixed 50m-depth slab ocean. Others havea varying mixed layer depth (h or MLD) computed as a prognostic variable We(vertical entrainment rate) based on turbulent kinetic energy parameterization
when deepening (Eq. SI1)

dhD)
= We = f ( M + B −dt∆ρ − S(Eq. SI1)

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where M is the mechanical turbulence and is function of u* the friction velocity, B
the buoyancy forcing which is function of the net surface heat flux Qnet and thenet water flux (E-P) with E the evaporation and P the precipitation, D thedissipation term, ∆ρ the density jump at base of the mixed layer, and S the wind
induced shear across the mixed layer.
When shoaling, h is a diagnostic quantity based on the balance between windstirring and net surface buoyancy forcing over the depth of the mixed layer (Eq.
SI2):

We = 0 and h = f (M) (Eq. SI2)
B−D

The MLD is not forced to coincide with the levels of the layered model but isconstrained to be greater than 19 m and less than 1350 m or the bottom of theocean when reached.

Fig.SI1: Bathymetry of the MLM model (meters)

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The temperature (TML=SST) and salinity (SML=SSS) tendency of the mixed layer
for open ocean grid points is given by Eq. 3, respectively,

δTML (Qnet + Qcor − Qswh ) We (TML − Tb )κh δTML++ CA +=δt
ρ o C phhh δzz =h(Eq. 3)

δSML SML( E − P) + Scor We( SML − Sb) κs δSML=++δtρohhh δzz =hwhere ρo is the density of seawater, Cp the specific heat of ocean water, We isthe entrainment rate, Tb and Sb are respectively the temperature and salinity at
the model level just below h, Qswh is the penetrating solar radiation at h, Qnet isthe net surface energy flux into the ocean and E-P is the net water flux. CA
stands for convective adjustment occurring when the mixed layer is denser thanthe layer below. кh and кs are the vertical eddy diffusivity coefficient accounting
for small-scale motions and are equal to 9yr-1 and 4yr-1, respectively. Qswh iscalculated up to a depth of 300 meters and is prescribed following Paulson andSimpson (1977). 5 different types of water with different optical properties aretaken into account as shown in Fig. SI2.

Fig.S21: 5 Ocean color types in the MLM model3

c. Coupling
Land, sea-ice and ocean models are aligned with the CAM grid. Coupling
between the ocean and the other components occurs daily, while theatmosphere, ice and land modules exchange flux and mass quantities at theCAM time step (20 minutes).

2. Surface flux correction terms
To prevent the modeled climate system from drifting far away from the observed
mean state, additional flux correction terms (Qcor and Scor, respectively) have to
be included in the computation of temperature and salinity tendency equations.
Those terms compensate for all the missing physics in the ocean such as heatand salinity transport by the mean currents, diffusion etc. Qcor and Scor should not
be compared to the so-called “flux correction approach in Coupled Global
Circulation Models” which are applied to adjust the mean climate state of themodel. In our case, the correction terms are mandatory to simulate a realistic
climate state. They are several orders of magnitude higher and mostly preserve
the observed ratio between atmospheric and oceanic heat transport.
Qcor and Scor are obtained from a stand-alone integration of MLM driven by daily
surface fluxes from a preliminary [CAM+CSIM] uncoupled simulation forced byobserved HadiSST SST and sea-ice extent over 1950-1999 (Rayner et al 2003).
For a given day (d), Qcor(d) is computed from the departure between the modeled
SST(d+1) value given by MLM driven by CAM surface fluxes(d) and the observed
SST(d+1) value. In other words, it corresponds to the energy term necessary for
MLM to realistically reproduce the observed daily SST variation. As described
previously, the departure between observed and modeled SST is mostly
explained by the missing of ocean advection but also by intrinsic errors of CAM
surface fluxes. A similar setup is used to compute Scor based on the Levitus longterm mean dataset of surface salinity (SSS) (Monterey and Levitus 1997).
When ice occurs, two additional terms given by CSIM are added in the Qcor
formulation (daily sea-ice extent estimated from HadiSST are imposed in aforced mode and CSIM only calculates fluxes associated with ice changes). They
correspond to the conductive heat flux at the bottom of the ice layer that ispassed to the ocean, and to the latent heat of fusion due to ice volume changes.
Those two terms are weighted by the observed sea-ice fraction. A similar setup isapplied for Scor under ice. In that case, the additional terms correspond to thewater budget on the surface ice and to the fresh water flux due to ice volume
change, both converted into equivalent salt flux weighted by the observed sea icefraction. The brine rejection when ice is forming is also computed in CSIM and isincluded in the latter term.

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Qcor and Scor climatologies including both CAM and CSIM fluxes contributions arethen obtained daily from the 50-yr integration average. The December-February(DJF) and June-August (JJA) Qcor values are shown in Fig. SI3. Heat is mainly
added in the winter hemisphere oceans while it is extracted year-round in a10oN-10oS latitudinal band especially in the tropical Pacific and tropical Atlantic.
The latter compensates for the missing horizontal ocean advection along theequatorial cold tongues and for their associated upwelling. The former
compensates in DJF and in the northern hemisphere, for the missing heat
meridional advection along the Gulf Stream and its North Atlantic extension, as
well as along the Kuroshio Current in the Pacific (Fig. SI3a). In JJA and in thesouthern hemisphere, austral winter Qcor brings heat along the storm track into
the mixed layer, which is fed in nature by intrusions of warm intermediate watersthat are not simulated in MLM (Fig. SI3b).
In boreal summer, the heat transport by the western boundary currents in thenorthern hemisphere is considerably reduced, but for the Labrador Current
whose cooling action on the atmosphere is strongest (Fig. SI3b). In fact, summer
Qcor mostly accounts for both atmospheric and MLM model errors. In the northernhemisphere, overestimated JJA trade-winds in stand-alone CAM in both thePacific and Atlantic basins tend to overcool the subtropical surface ocean andare compensated by a positive Qcor between 10oN and 45oN (Fig. SI3b). On theocean model side, the stand-alone MLM tends to create a too deep mixed layer
in these areas mostly because of the frequency of coupling between the oceanicand atmospheric models. In the southern hemisphere, austral summer Qcor
mostly cools down the extratropical upper ocean (Fig. SI3a). Such a sign is
explained by the stand-alone MLM tendency to systematically produce tooshallow mixed layer in summertime at midlatitudes (see also in the northern
Atlantic in JJA [40o-70oN], Fig. SI3b).

Fig.SI3: DJF (a) and JJA (b) average surface heat flux correction (W m2). Positive values indicate
heat is added to the ocean. Shading interval is 25 W m2.

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3. Coupled mean state
We performed a 150-yr coupled integration hereafter referred to as CTL whereQcor and Scor flux correction terms are applied. The initial ocean state is derived
from the mean three-dimensional conditions of the off-line MLM simulation used
to compute the daily climatology of Qcor and Scor. The coupled model reproduces
rather well the SST mean state and differences between CTL and observed SST
climatologies are weak as shown in Fig. SI4. Year-round tropical and midlatitude
winter SSTs are very well simulated (within +/-0.3oC bias); the largest errors
occur in the extratropical summer oceans. The latter are overly warm due toshallower-than-observed MLD. Maximum amplitude locally peaks at +1.2oC in
the southern hemisphere for DJF within a 30o-50oS band (Fig. SI4a). A bias of ~+1oC is found basin-wide in the North Pacific and North Atlantic extratropicaloceans in JJA (Fig. SI4b). Despite Qcor, it appears that the stand-alone model
systematic errors are not totally compensated by the flux correction terms incoupled mode. In winter, the strongest bias (~+1oC) occurs in the Labrador Sea
along the Labrador Current (Fig. SI4a). It is attributed to the crude representationof ice and salinity related processes (dynamics in particular) that control a largepart of the ocean vertical profiles in these regions.

Fig.SI4: CTL mean SST bias (oC) for DJF (a) and JJA (b) average given by the difference
between the 150-yr mean climatology of CTL SST and the climatology of HadiSST SST over
1950-1999. The latter period corresponds to the one used to force CAM whose daily surface
fluxes were then subsequently used to compute the CTL flux correction terms. Shading interval is0.3oC

Most of the significant SST biases occur along the ice edge especially in boreal
summer (Fig. SI4b). The arctic domain covered by ice in JJA is too shrunkcompared to observations (Fig. SI5b). Earlier and overestimated melting of seaice in spring in the Hudson Bay and in the subarctic basins (Labrador, Greenlandand Kara Seas) is associated with significantly too warm SSTs in JJA while theLaptev and the East Siberian Seas are significantly too cold due to delayed
melting (Fig. SI4b). In winter, the simulated sea-ice matches very well theestimated observed extent (Fig. SI5a). Marginal errors are found along theGreenland Sea ice tongue that is slightly too broad and in the Labrador Sea6where the winter sea-ice does not penetrate enough southeastward, consistentlywith the warmer SST.

Fig.SI5: 150-yr climatology of simulated sea ice fraction for CTL (shading), for DJF (a) and JJA(b) average. The 0.5 limit for the HadiSST sea ice climatology is superimposed (purple thick line).
Shading interval is 0.1.

In the southern hemisphere, biases are minor for sea-ice (Fig. SI6) especially inwinter. In summer the melting in the Ross and Weddell seas is underestimated.
Note here that the implementation of the fresh water/salinity flux exchanges
between the ocean and ice model components appeared crucial in bothcontrolling the wintertime sea-ice spatial growth and initiating the summertime
melting. For the latter, it significantly shoals the ocean mixed layer, then allowing
for rapid warming of open-waters. For the former, the brine rejection term that
dominates, deepens the ocean mixed layer and delays its rapid cooling. Notealso that in the course of the coupled simulation, Qcor is set to zero whennegative (i.e. when it tends to cool down the SST) when the entire ocean surface
is covered by ice. The latter correction is necessary and physically justified tohave a reasonable seasonal cycle of the sea-ice extent especially during thespring and summer melting seasons.

Fig.SI6: Same as Fig.SI5 but for the southern hemisphere

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The maximum simulated MLD is shown in Fig. SI7 for boreal winter and summer
seasons, respectively. As in observations (see, de Boyer Montegut et al 2004 forinstance), the deepest MLD occurs in the winter hemisphere. In the northernhemisphere, maxima follow the vigorous storm tracks both in the North Pacificand in the North Atlantic with simulated values between 150-200 meters (Fig.
SI7a). Greater depths are found between Greenland and Great Britain as well as
in the Labrador and Norwegian Sea. They correspond to deep water formation
controlled by complex convective processes leading locally to instantaneous
values as high as 1500 m in the observations (Dickson et al 1996). In CTL, even
if some grid points around Iceland and Spitzberg reach 600-700 meters, thenorth Atlantic MLD is clearly underestimated with mean simulated values around250m. Such a weak magnitude is very common for this type of model and thereader is invited to refer to as Alexander et al (2000) for a list of factors that may
contribute to such a model behavior.
Within the subtropical band, as stated previously, MLM tends to produce a too
deep MLD in the trade wind regions in winter with values as high as 120 m
instead of 50-70m estimated in the observations (Fig. SI7a). Such a bias ispersistent in summer especially in the Pacific and Atlantic between 10oN and
30oN where the MLD is twice too deep (Fig. SI7b).
Realistic mixed layer deepening is found along the austral winter storm track.
Note finally that there is no significant drift in the coupled model over open waterin MLD, temperature and salinity. However a clear trend in salinity is found underpermanent sea-ice points.

Fig.SI7: Simulated maximum mixed layer depth (m) for boreal (a) and austral (b) winter. Note thatthe shading interval changes with depth: 25m for h<100, 50m for 100<h<300, and 200m fordeeper h.

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