Lots of interesting discussion here, but also a fair bit of confusion so let's try and clear that up.

Radiation Balance:

(1) Rnet = ((1-a) * SWD) + LWD - LWU

- a = albedo (in this case, pertinant to shortwave radiation only - lets say 0.2-4.0 micrometers). a * SWD = upward solar radiation.
- SWD = shortwave radiation, downwards. A function of location and time and atmospheric constituent e.g. water vapor, aerosols, and importantly, clouds
- LWD = longwave radiation, downwards; a function of atmospheric temperature and radiators like water vapor, clouds, CO2 etc. which determine atmospheric emissivity.
- LWU = longwave radiation, upwards; function of surface "skin" (i.e. radiant) temperature and surface emissivity

All terms are in units of Watts per meter squared.

Net radiation can be computed for any "surface" whether that be the ice/ocean/land surface or the top of atmosphere (though I have couched things in terms of an ice surface). A black body has an emissivity of 1.0. Snow often considered close to a blackbody. The atmosphere is grey body (i.e. emissivity below 1.0) - see PDF of lecture notes below.

Be careful to consider your spatial and temporal frame of reference when talking about such quantities - are you talking about a particular hour, month, year or decade; are you talking about a point at the pole, the region north of 65N or the entire planet?

Some reference material by Martin Wild at ETH:

https://www1.ethz.ch/iac/edu/courses/master/modules/radiation_and_climate_change/download/Lecture5_2014Surface energy balance: e.g. for a given ice-atmosphere interface surface:

(2) Rnet = H + E + G

- H = Sensible heat flux; function of temperature gradient from air to surface, wind speed, stability of atmosphere (+ve towards atmo)
- E = Latent heat flux to the atmosphere; often thought of as evaporation+sublimation; function of vapor gradient from air to surface, wind speed, stability of atmo (+ve towards atmo)
- G = flux into the surface. For ice during the melt season, G can be decomposed into a melt flux (which is also a latent flux, though different from E) and a conductive (or diffusive) flux that warms the underlying ice (a function of subsurface temperature & diffusivity properties; the flux that causes the buoy temperature profiles to change). This term will be negative when ice is growing. (+ve into the surface)

Surface radiant temperature (Trad) features in each term of (2). Hence, expand each term and solve for Trad (given all the required inputs/states of SWD, LWD, Tair, humidity, precip, wind, pressure and subsurface temperature). All terms in (2) are in units of Watts per meter squared and the sign convention is given. There are other subtle items such as sub-surface penetration of solar radiation etc. but we'll not go into that.

There is an energy balance at the base of the ice (the ice-ocean interface) but the terms will be of different importance or magnitude and involve a different fluid (sea water) as well as salinity dynamics. Throw a volume between these two energy balances and whacko!, you have yourself a (highly, highly simplified) thermodynamic sea ice model. Now make it all move around properly and you have a neanderthal CICE.

Other item: Latent heat of fusion (J/kg) compared to heat capacity of (sea) ice (J/kg/K).

L(fusion) : 335000 Joules will melt 1kg of pure ice that is at 0C

Specific heat of pure ice at 0C is 2093 J/kg/K.

So if we removed the same amount of energy from the 1kg 0C ice as would be used to melt it (and it was a completely closed system and the heat capacity did not change with temperature), the ice would now be approx. -160 C. Phase change of H2O involves lots of energy! - vaporization even more so.

Of course, salinity will play a (non-linear) role in these thermodynamic quantities in sea ice, as will temperature - just google it if you want to see the curves.

Old question: I don't know who is using CICE5 for operational forecasting. If I was running an operational system of that sort I'd probably wait until the model has had a good thrashing in the academic community before I switched over from an earlier version.