The CIOM was described in great detail in the model development and application to the pan-Arctic region (Wang et al. 2002). In the following, we only describe the parts necessary for the completeness of this paper.

Sea-ice model
The sea ice component of the coupled model is a thermodynamic model based on multiple categories of ice thickness distribution function (Throndike et al. 1975; Hibler 1980) and a dynamic model based on a viscous-plastic sea ice rheology (Hibler 1979).
The evolution of the thickness distribution function satisfies a continuity equation
(1)

where is velocity vector (u, v), g is the sea ice thickness distribution function, and g(h)dh is defined as the fraction of area covered by the ice with thickness between h and h+dh. The averaged thickness and concentration A of sea ice in a grid is expressed from g(h) as
(2)
and
(3)
? is the mechanical redistribution function, which represents the creation of open water and ridging during ice deformation. The redistribution process conserves ice volume. The redistribution function is parameterized as described by Yao et al. (2000). f(h) is the thermodynamic vertical growth rate of ice.
The vertical growth rate f(h) of ice thickness is determined by the ice thermodynamics. The model thermodynamic interactions between ice, ocean and atmosphere are shown in Fig. 2. The heat budget on the upper ice surface is
(4)
where ai is the albedo of sea ice (0.75 during the freezing period from October to March, 0.65 during the melting period from April to September). When snow exists, ice albedo is replaced by the snow albedo a (0.9); ei is the emissivity of ice. I0 is the short wave solar radiation reaching the ice surface; QSi, QEi , and QL are the sensible heat flux, the latent heat flux, and the effective longwave radiation flux from ice surface, respectively. QSi, QEi and QL are parameterized by the following formulae,
(5)
(6)
(7)
where qa and Ta are the specific humidity and air temperature of air; q0 is the saturated specific humidity on ice; T0 is the surface ice temperature. Cp is the specific heat of air at constant pressure. Le is the latent heat sublimation on the ice surface. Cs and Ce are the sensible heat and latent heat bulk transfer coefficients, respectively. ea is the emissivity of air. s is Stefan-Boltzman constant. kc is the cloud factor and CL is the cloud fraction. Ta is the air temperature, a and b are empirical constants (a=0.254, b=4.95×10-5). The surface ice temperature T0 is determined from the surface heat balance equation,
(8)
where Qc is the internal conductive heat flux through ice. A linear ice temperature profile and a constant thermal conductive coefficient ki are used in this study. Thus, for the ice category with thickness h,
(9)
where T is the freezing temperature of seawater on bottom ice surface, which is a function of the salinity of seawater (=-0.0544S +237.15K, where S is the salinity of upmost ocean grid, in part per thousand, ppt). For the snow-covered ice, the conductive coefficient will be replaced by , where hs is the snow depth.
If the calculated T0 is found to be over 0oC, it is forced to be 0 oC. The extra heat of equation (8) is used to melt the ice at the upper surface, and the melted water will drain to the ocean immediately. The volume flux of melting water WAI is
(10)
The growth rate at the bottom of the sea ice is
(11)
where L is the volume latent heat of fusion and FT is the oceanic heat flux out of the ocean surface (assumed to be uniform over a model grid cell). Thus, the growth rate f(h) for sea ice with thickness h is the sum of (10) and (11), i.e.
(12)
For the open water in the ice zone, the growth rate of sea ice is
(13)
where QAW is the heat budget between the atmosphere-ocean interface, excluding the solar radiation that is absorbed in the water column. QAW is calculated using a similar parameterization to (4) but without the solar radiation terms, i.e.
(14)
where ew is the emissivity of water. Tw is the sea surface temperature (SST). QSw, QEw , and QL are the sensible heat flux, the latent heat flux and the effective longwave radiation flux from water surface, which are parameterized similar to (5)-(7). When the WAW is negative, the “melting” of ice to water is implied. In this case, the equivalent heat is redistributed to melt the remaining ice. The total ice growth rate is integral over various ice thicknesses with weight g(h).
The ice velocity is determined from the momentum equation
(15)
where f is the Coriolis force and m is the ice mass in a grid. ?H is the gradient of sea surface elevation, is the internal stresses (see Hibler 1979; Wang et al. 1994a), and and are the air and water stresses, respectively. They are determined by the bulk formulae
(16)
(17)
where is wind velocity vector. is the current velocity vector of the upmost ocean layer. Ca (=1.2×10-3) and Cw (=5.5x10-3 ) are the bulk coefficients of wind stress and water stress, respectively. ?a is the air density, and ?w the seawater density. is the two-dimensional internal ice stress tensor, which is derived from the viscous plastic rheology with elliptical yield curve rate e=2 of Hibler (1979) and involves a compressive ice strength
(18)
where P* and C are empirical constants (here 2.5×104Nm-2 and 20, respectively). e is the ratio of principal axes of the ellipse, P is the ice strength, and C is the ice strength decay constant. This formulation requires that the ice strength strongly depends on the amount of thin ice, characterized by (1-A), which is also allows the ice to strengthen as it becomes thicker, as measured by thickness.
The redistribution function is parameterized as described by Thorndike et al. (1975) and Yao et al. (2000). Unlike the treatment by Hibler (1980), they used a given thickness to ridged ice of a single thickness (the multiplication factor is chosen as 15). Table 1 lists the parameters, their values and units that are used in this model.

Ocean model
The Princeton Ocean Model (Blumberg and Mellor, 1987; Mellor, 1996; Wang 2001) is used as the ocean component of the coupled mode in this study. The model has a free surface, uses sigma coordinates in the vertical, and employs a mode-split technique. The model embeds a second-order turbulence closure sub-model. Smagorinsky diffusivity along sigma surfaces is employed in the horizontal diffusion.
The governing equations of temperature and salt are
(19)
(20)
and the surface heat forcing is
(21)
in the ice-free grid cell , and
(22)
in the ice-covered grid cell.

Ice-ocean coupling
Heat and salt fluxes at the ice-ocean interface are governed by the boundary processes as discussed by Mellor and Kantha (1989). In grid cells in which ice is present, the heat flux out of the ocean is
(23)
where Cp is the specific heat of seawater and T is the ocean temperature at the uppermost model grid (in our model the midpoint of the uppermost ocean layer). The heat transfer coefficient CTz is given by
(24)

where u* is the friction velocity, Prt is a turbulent Prantl number, z is the vertical coordinate corresponding to the temperature T, z0 is the roughness length, and k is the von Karman constant. The molecular sublayer correction is represented by BT where Pr is a molecular Prantl number, ? is the kinematic viscosity, and b is an empirical constant (= 3). The salt flux out of the ocean is
(25)
where SI is the salinity of ice (=5% ), S is the salinity at the uppermost model grid point, and (P-E) is the volume flux of precipitation minus evaporation.
Analogous to the heat flux (23), the salt flux is defined as
(26)
where S0 is the salinity at the ice-ocean interface. The salt transfer coefficient CSz is
(27)
where Sc is a Schmidt number. Since Sc =2432 and Pr=12.9, CTz>CSz, this can lead to the production of frazil ice in the water column as discussed by Mellor and Kantha (1989). Frazil ice is immediately added to the floating ice.
The ice-water stress is

where is the ocean velocity vector at the uppermost model grid.

References
Wang, J., Q. Liu and M. Jin, 2002. A User’s Guide for a Coupled Ice-Ocean Model (CIOM)
in the Pan-Arctic and North Atlantic Oceans. International Arctic Research Center-Frontier
Research System for Global Change, Tech. Rep. 02-01, 65 pp.

Wang, J., Q. Liu, M. Jin, M. Ikeda and F.J. Saucier, 2005. A coupled ice-ocean model in
the pan-Arctic and the northern North Atlantic Ocean: Simulation of seasonal cycles.
J. Oceanogr., 61, 213-233.