Where is the problem?

I spent some time sending emails back and forth trying to solve the problem of heat exchanges at the air - ice/ocean interface, especially those associated with mass exchanges (i.e. heat content of precipitation and evaporation). I think there is a misunderstanding between what the atmosphere expects to send/receive (from an ice-ocean perspective) and what is really sent/received.

It is time to approach the matter from a different angle. I describe below what we are doing in NEMO and what we think the solution should be, and you can comment on that.

So far, the total non-solar flux is imposed by the atmosphere but it excludes (from what I understand) the heat contents of snow precipitation and rain. It also does not take into account the heat content (if any) of evaporated ice and water (already in vapor form) that the atmosphere should receive. The total non-solar (conservative) flux should then write:

Qns_tot = Qns + Qsnow + Qrain + Qevap

with Qns being the non-solar flux provided by the atmosphere.

Therefore NEMO did a guess on Qsnow, Qrain and Qevap by considering the temperature of falling snow, rain and evaporated water = SST, and temperature of evaporated ice = 0°C. Then,

Qsnow = sprecip * ice_frac * ( Cp * SST - Lfus ) [in W/m2]

Qrain = lprecip * Cp * SST

Qevap (water) = evap * (1 - ice_frac) * Cp * SST

Qevap (ice) = 0

with sprecip = snow precip, lprecip = liquid precip, ice_frac = ice fraction, Cp = specific heat of sea water, Lfus = Latent heat of fusion of pure ice at 0deg, SST = sea surface temperature.
A Voldoire : Concerning Qrain = lprecip * Cp * SST It means that you consider that liquid precipitation temperature is zero and you calculate the energy given to the ocean by changing the temperature from zero to SST? Am I wrong?

In order to be really conservative, the atmosphere should provide those fluxes, or am I completely wrong here?

What is the solution?

I see 2 options here:

1) The atmosphere considers all these fluxes to be 0, that’s ok but NEMO needs to know and we will have to trick the calculation of snow temperature in LIM3 since it is recalculated from Qsnow (see nota bene). You can see that as NEMO business but it is important you know it has consequences on sea ice thermodynamics.

2) The atmosphere provides non-zero fluxes and then it is better if NEMO knows how Qsnow is calculated in the atmosphere, which Cp, temperature and Lfus is used (see why below).

Nota bene
The most important flux here (by far) is Qsnow. When snow falls on ice, its heat content adds up with the pre-existing snow and snow temperature is recalculated with this expression:
q = rho(snow) * ( Cp(snow) * T(snow) - Lfus ) [in J/m3]
Therefore a large difference between the expressions of Qsnow and q would lead to erroneous snow temperatures. One consequence could be a snow that always melts because its temperature is always positive. The largest difference between Qsnow and q is certainly Lfus which may differ greatly between the atmospheric model and LIM3.

LIM3 physical constants

Heat capacity (ice/snow) = 2067

Heat capacity (sea water) = 3991.867957

Latent heat of fusion at 0deg (Lfus) = 334,000 J/kg

Latent heat of sublimation at 0deg = 2,834,000 J/kg

IFS physical constants

Heat capacity (ice/snow) = 2106

Latent heat of fusion at 0deg (Lfus) = 333,700 J/kg

Latent heat of sublimation at 0deg = 2,834,500 J/kg