C. \underline{List of the Information Exchanged}

To function properly the Flux Coupler must provide the inputs required by each component model, based on outputs from all the component models. The inputs are primarily fluxes which force the models and in some cases a state variable input array, V⃗. The outputs are primarily state variable arrays, W⃗. Some fluxes are computed by the component models themselves and output to the flux coupler for dissemination to other component models. The purpose of this section is to specify the inputs and outputs exchanged between the coupler and the component models. The flux calculations and exchanges are complicated, as illustrated by the schematic, Fig. 1. In this flux flow diagram, outputs are shown as arrows away from the component models or interfaces, diamond symbols denote partitioning of the fluxes among component models, flux computations by the coupler are represented by circles and encircled crosses indicate that fluxes are combined. The formulae used to compute the fluxes in the coupler are given in Section F. The exchange of state variables is not shown in Fig. 1.

For the present only four component models are to be coupled and these are denoted (e.g., Fig. 1) as follows:

A − Atmosphere (a)
C − Cryosphere (Sea − Ice, i)
B − Biosphere (Land, l)
H − Hydrosphere (Ocean, o)

At present the biosphere component is imbedded within the atmospheric model. In this configuration the latter acts as a passive conduit for information exchange between the coupler and the biosphere.

We first specify the inputs to each component model (Subsections I, II, III and IV), then give the outputs required from each component (Subsections V, VI, VII and VIII). With no biosphere–cryosphere exchanges, contributions to these inputs and outputs come across the following five interfaces (Fig. 1) :

1 − Atmosphere − Cryosphere
2 − Atmosphere − Biosphere
3 − Atmosphere − Hydrosphere
4 − Cryosphere − Hydrosphere
5 − Biosphere − Hydrosphere .

In order to be consistent with the convention that incident solar radiation is positive, all fluxes will be defined as positive downwards. That is, a positive flux of any quantity across an interface acts to increase the value of that quantity in the layer below that interface. For example, the freshwater flux components, precipitation, P, and evaporation, E, are positive and negative, respectively and the wind stress, τ⃗, is positive over both ocean and land.

C-1 I. Inputs to the Atmosphere I.a Fluxes (upward arrows into A, Fig. 1)

Flux inputs to the atmosphere have contributions from the three surfaces (1, 2 and 3) below it. Flux coupler calculations of these fluxes are represented by the four circles below A in Fig. 1. τ⃗_{A}, > 0, the surface drag on the bottom of the atmosphere. Given as zonal, τ_{A}^{λ}, and

meridional, τ_{A}^{φ}, components. H_{A}, the sensible heat flux. L ↑_{A}, < 0, the emitted upward longwave radiation. E_{A}, < 0, the evaporative water flux, proportional to the latent heat flux. LH_{A}, < 0, the latent heat flux, proportional to E_{A}, and therefore not shown in Fig. 1.

I.b The input state variable array V⃗_{A} α⃗_{A}, a four element array containing the effective surface albedos for visible direct, α_{V} (dir),

and diffuse, α_{V} (dif), radiation, and for near-infrared direct, α_{I} (dir), and diffuse, α_{I} (dif), radiation.

T_{A}, surface temperature, averaged over the underlying interfaces. Note, T_{A}, should not be necessary as an atmospheric input and should be removed from the fields to be passed in the future.

I.c Future Atmosphere Inputs τ⃗_{G}, the gravity wave momentum flux due to sub–gridscale orographic variance.

II. Inputs to the Hydrosphere II.a Fluxes (downward arrows into H, Fig.1) τ⃗_{H}, the surface stress on the top of the ocean due to both the wind and relative sea-ice

movement, given as zonal, τ_{H}^{λ}, and meridional, τ_{H}^{φ}, components. It is the vector sum of two flux coupler calculations: the atmospheric stress across interface (3) and the ice-ocean stress across interface (4). In Fig. 1, such summations are represented by encircled crosses.

S_{H}, the net (after reflection) solar radiation directly from the atmosphere plus any solar

radiation penetrating through the sea-ice interface (4). H_{H}, the net non-solar surface heat flux exchanged with the atmosphere and the cryosphere.

It has many contributors, as illustrated by the 3 summations below interface 3 in Fig.1. These are the sensible and latent heat fluxes across interface 3, the net longwave radiation (L ↑_{3} +L ↓_{3}) across interface 3, and the net heat flux across interface 4, H_{4}, which includes the cooling due to snow and ice melt, but not due to the freezing of sea

C-2 water, which is an output, Q_{4}, of the hydrosphere (see Section F and Section H of the Technical Note on the CSM ocean model).

F_{H}, the net surface flux of freshwater. Its components are the evaporation, E_{3}, the total of convective and large scale rainfall and snowfall, P_{3}, and the melting of cryosphere ice and snow, F_{4}, plus runoff from the biosphere, F_{5}. As for H_{H} above, it does not include the freshwater flux due to ocean water freezing (see Section F and Section H of the Technical Note on the CSM ocean model).

III. Inputs to the Cryosphere

III.a Fluxes (arrows pointing towards C, Fig. 1)

τ⃗_{C}, = τ⃗_{1} - τ⃗_{4}, the vector difference between the wind stress on the ice minus the stress of the ice on the underlying water, as represented by the encircled cross inside of area C in Fig. 1. Also see Section G.

S_{1}, > 0, the net (after reflection) solar radiation penetrating the snow/ice surface.

H_{1}, the sum of the latent and sensible heat fluxes and the downward long-wave radiation exchanged with the atmosphere.

L ↑_{1}, < 0, the upward long-wave radiation emitted to the atmosphere. The surface energy balance calculation of surface ice temperature in many ice models requires that this flux remain separate from H_{1}.

Q_{H}, = Q_{4}, the net heat exchange (and implied water flux) between the ice and ocean due to ocean freezing (> 0), or the potential heat available in the upper ocean to melt sea-ice (< 0) (see Section F below and Section H of the Technical Note on the CSM ocean model).

F_{1}, the snowfall (presently all convective and large scale precipitation) onto the ice/snow surface, plus the evaporation of snow and ice.

H′_{4}, = H_{3} + S_{3}, the total surface heat flux through the atmosphere–hydrosphere interface (3). This flux is needed by some ice models to control the rate of lateral ice growth into leads.

III.b The input state variable array V⃗_{C}

∇η, the sea-surface slope.

dH_{1}, the derivative of H_{1} with respect to T_{1}. Used in energy balance determination of T_{1}.

IV. Inputs to the Biosphere

All inputs are for the future as the land model is presently part of the atmospheric model and has access to all atmospheric fields.

IV.a Fluxes (downward arrows at interface 2, Fig. 1)

S_{B}, the net (after reflection) solar radiation across interface 2.

C-3 I⃗_{B}, a four element array containing the four components of incident (before reflection)

downward solar radiation (direct and diffuse visible, and direct and diffuse nearinfrared).

L ↓_{B}, the net downward longwave radiative flux across interface 2.

P⃗_{B}, the precipitation onto the biosphere in two components: P c_{B}, the convective precipi-

tation, and P l_{B}, the large scale precipitation. IV.b The input state variable array V⃗_{B}

This array contains complete information on the state of the atmosphere needed for the computation of atmosphere-biosphere fluxes, such as τ⃗_{2}, H_{2}, E_{2} and the runoff, F_{5}, within the biosphere component model. It is comprised of the complete atmospheric output state variable array W⃗_{A} listed below in subsection V, with the exception of air density.

V. Atmospheric Model Outputs V.a The output state variable array W⃗_{A} Z_{A}, the height of the first atmospheric level. U⃗_{A}, the wind velocity at the first atmospheric level. θ_{A}, the potential temperature at the first atmospheric level. q_{A}, the specific humidity at the first atmospheric level. ρ_{A}, the air density at the first atmospheric level. B_{A}, the barometric pressure at the first atmospheric level. B_{S}, the surface barometric pressure. V.b Flux outputs from the atmosphere (downward arrows from A, Fig.1) S_{A}, the net (after reflection) solar radiation at the bottom of the atmosphere. I⃗_{A}, four components of incident downward solar radiation: direct and diffuse visible, and

direct and diffuse near-infrared. L ↓_{A}, the downward longwave radiation at the bottom of the atmosphere.

P⃗_{A}, a two component precipitation array consisting of P c_{A}, the convective precipitation at the bottom of the atmosphere, and P l_{A}, the large scale precipitation at the bottom of the atmosphere.

V.c Future outputs from the atmosphere P_{S}, the precipitation falling as snow (may not include snowfall explicitly, in which case the

Flux Coupler may compute snowfall over ice from P c_{A}, P l_{A}, and θ_{A}).

α_{a}(dif), the albedo of the atmosphere as seen by upwards diffuse shortwave radiation.

C-4 VI. Hydrospheric Outputs VI.a The output state variable array W⃗_{H} T_{H}, the sea surface temperature. U⃗_{H}, the zonal and meridional components of the first layer water velocity. ∇η, the sea-surface slope. VI.b Fluxes ( upward arrow out of H, Fig. 1) Q_{H}, = Q_{4} the cumulative heat of fusion (and implied water flux) if any sea-ice is formed

(> 0) or the potential to melt sea-ice if ice is present (< 0) (see Section F and Section H of the Technical Note on the CSM ocean model).

VI.c Future outputs from the hydrosphere α⃗_{H}, the ocean albedos for direct, α_{H}(dir) and diffuse, α_{H}(dif) solar radiation, respectively.

Both albedos have two components: for visible and near–infrared wavelengths. These values are presently constants and set in the Flux Coupler.

VII. Cryospheric Outputs VII.a The output state variable array W⃗_{C} U⃗_{C}, the two components of ice velocity. T_{C}, the ice surface temperature. f_{C}, the ice concentration as a fraction. α⃗_{C}, the sea-ice albedos for direct α_{C} (dir) and diffuse, α_{H} (dif) solar radiation, respectively.

Both albedos have two components: for visible and near-infrared wavelengths. d_{C}, the snow depth (or flag) which can be used to compute the final albedos. VII.b Fluxes (downward arrows at interface 4, Fig. 1) S_{4}, > 0, the solar radiation passing through the ice and into the hydrosphere below. H_{4}, < 0, the heat flux into the hydrosphere due to snow/ice melt in response to upper

layer ocean temperatures above freezing as communicated by Q_{H} = Q_{4} < 0. Note, unless all the ice and snow melts, H_{4} = Q_{4}.

F_{4}, > 0, the water flux into the hydrosphere due to snow/ice melt associated both with H_{4} above and with atmospheric heating and rainfall. The H_{4} contribution becomes B_{4} = B_{H}, the net flux of brackish water with the salinity of sea–ice = S_{I}, for S_{I} ≠ 0.

VIII. Biospheric Outputs

All outputs are for the future, as the land model is presently part of the atmospheric model and has access to all atmospheric fields.

C-5 VIII.a The output state variable array W⃗_{B} T_{B}, the surface temperature. α⃗_{B}, the terrestrial albedos for direct α_{B} (dir) and diffuse, α_{B} (dif) solar radiation, respec-

tively. Both albedos have two components: for visible and near-infrared wavelengths. d_{B}, snow depth over land. VIII.b Flux outputs from the biosphere τ⃗_{B}, the surface drag of the biosphere on the atmosphere. Given as zonal, τ_{B}^{λ}, and merid-

ional, τ_{B}^{φ}, components. H_{B}, the sensible heat flux. LH_{B}, the latent heat flux. E_{B}, the evaporative water flux, proportional to the latent heat flux. L ↑_{B}, the emitted upward longwave radiation (not shown in Fig. 1).

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