Decision? (Update 2016/05/19)

If the atm sends to the ocean/ice: Qsnow = Cp(snow) * Tsnow, and Qrain = Cp(rain) * Train, and Qevap(ice) = Cp(ice) * Tice, and Qevap(ocean) = Cp(ocean) * Toce, then heat is conserved and the differences between atm. physical constants and ocean/ice physical constants are mostly unimportant (except maybe for the snow falling onto the ice). If the atm does not provide these fluxes, then we will make a guess and we have to make sure to have the same constants between Atm. models and NEMO. This is not yet the case.

Klaus: shouldn't it read Qsnow = sprecip * Cp(snow) * Tsnow, etc ?

C Rousset: yes indeed with Temperature in degC.

Klaus: Let's assume we can send these fluxes from IFS to NEMO. Who takes care of the coupling interface in NEMO? It would be stupid if we had one solution for IFS and a different solution for IPSL and yet another one for Arpege. When could such an updated coupling interface be in place?

C Rousset: we just had a meeting today with IPSL and it has been decided that the fluxes will be integrated in the coupler soon (by the beginning of June). Then I will take care of the interface with NEMO. We will let you know asap what are the fields, names, conventions adopted.

Klaus: EC-EARTH uses conservative coupling, e.g. we send the total precipitation (rain+snow) and snow. Could we for consistency have a similar setup for the flux of internal energy, e.g. send the sum of Qrain+Qsnow and Qsnow?

C Rousset: yes, we will see what LMDz will deliver.

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 (Qns) is imposed by the atmosphere but it excludes (from what I understand) the heat contents of snow precipitation (Qsnow) and rain (Qrain). It also does not take into account the heat content (if any) of evaporated ice and water (Qevap, already in vapor form) that the atmosphere should receive. The total non-solar (conservative) flux should thus be written (including the snow melting when it reaches the ocean):

Qns_tot = Qns + Qsnow + Qrain + Qevap + "Snow-melt"

So far, as an input from the atmosphere, NEMO only had Qns. Therefore NEMO had to make 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,

(O Marti : when it's snowing on sea ice, using the surface temperature (snow/ice) would be a better first guess. But the actual flux from ATM is still needed to be conservative)

C Rousset: I agree but I do not think we have access to ice surface temperature at this stage (not sure though)?

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

Qrain = lprecip * Cp * SST

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

Qevap (ice) = 0

"Snow-melt" = sprecip * ( - Lfus )

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?

O Marti. The temperature is not 0. But NEMO doesn't know at which temperature the precips are leaving the ATM realm to enter the OCE realm, and should make a guess.

A. Voldoire I agree with Olivier that the temperature is not 0, but it is the assumption you make in this equation, am I wrong? (it was just to be sure...) . As W. Klaus said, in our model the hydrometeor are in quasi-equilibrium with the ambient air. So the best assumption would be to consider that their temperature is SST.

My understanding is that in order to be fully conservative, the atmosphere should provide those fluxes, or am I completely wrong here?

O Marti : OK with that. When its rains, some matter is leaving the ATM realm, and an energy is associated with it and given to the OCE realm.

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 and Lfus (see nota bene). You can see that as NEMO business but it is important you know it has consequences on sea ice thermodynamics.

O Marti: Not exactly. The flux from atmosphere is not 0. But atmosphere doesn't need to compute it. You could diagnose the actual flux by computing the total ATM enthalpy before and after the rains leaves ATM.

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

Nota bene
The most important flux here (by far) is Qsnow. When snow falls on ice, its enthalpy adds up with the pre-existing snow to give a total enthalpy equal to q 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 - sprecip*Lfus) 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 is certainly Lfus which may differ greatly between the atmospheric model and LIM3.

At this point I expect to receive from you the Qsnow, Qevap(ocean & ice) and Qrain (whether you think it should be zero or a value defined by your atmospheric model calculations). If you do not think this is needed please send me comments based on the above equations so that we can move on in a constructive way.

LIM3 physical constants

Heat capacity (ice/snow) = 2067 J/kg/K

Heat capacity (water) = 3991.86795711963 J/kg/K

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

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

Reference temperature (Tref=0 degC) = 273.15 K

IFS physical constants

Heat capacity (ice/snow) = 2106 J/kg/K

Heat capacity (freshwater at 0deg) = 4218 J/kg/K

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

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

LMDz physical constants

Arpege physical constants