GCOMS needs air-sea forcing fluxes suitable for its global domain. POLCOMS relies on very simple bulk formula tuned for the North-East European Shelf. Thus we have to include parameterisations adapted to all the shelf seas of the World's ocean, independently of their latitude, climate, depth, etc.

• Why using bulk formulas?

An Ocean General Circulation Model can be forced using 2 methods: - applying directly surface fluxes (from a meteorological model or an observed dataset) - using meteorological and oceanic variables (simulated or observed) to compute the fluxes from a set of bulk formula The bulk formula approach is chosen in POLCOMS, because it allows the ocean model to modify the air-sea fluxes interactively.

• Which fluxes are needed?

Three different air-sea fluxes are necessary to force the full physical model: - surface wind stress (, in N.m-2) - net surface heat flux (Qnet, in W.m-2) - net surface freshwater flux (E-P, in m.s-1 or mm/day)

The heat and freshwater fluxes are composed of several parts. The freshwater flux consists in an advective and a turbulent component:

E : evaporation/condensation P : precipitations (rain and snow)

The net heat flux consists in radiative and turbulent components:

Qsol : solar short-wave (visible light) radiation Qther : thermal long-wave (infra-red) radiation Qsen : sensible turbulent flux (due to heat conduction) Qlat : latent turbulent flux (due to water evaporation and condensation)

• What is the theory behind bulk formulas?

The bulk scaling theory enables to express the turbulent part of these fluxes from observable mean quantities: - wind stress from the mean wind speed and gustiness - sensible heat flux from the wind speed and air-sea temperature difference - latent heat flux from the wind speed and air-sea specific humidity difference

The turbulent surface fluxes can be formulated from the Monin–Obukhov similarity theory (MOST). We denote x an observable property at the interface (u, v wind components, potential temperature  or water vapour specific humidity q) and X is its large-scale mean value. The turbulent flux across the surface is equal to the covariance of the vertical velocity w and the property x:

cx : bulk transfer coefficient for the variable x cd : bulk transfer coefficient for the wind speed Cx : total transfer coefficient X : air–sea difference in the mean value of x

S : bulk wind speed (relative to the ocean surface), composed of a mean vector part (U and V components) and a gustiness part (Ug)

• How to estimate the transfer coefficients?

In the bulk scaling theory, the transfer coefficients depend on the surface stability parameter :

cxn : transfer coefficient at neutral stability ( = 0)

 : Von Karman’s constant (~ 0.40) x : profile stability function for variable x (empirical) z: height of measurement of the mean quantity X(z) zox : roughness length for variable x

In COARE parameterisations, the stability parameter is estimated as follows:

g : gravitational acceleration (~ 9.81 m.s-2) T : bulk air temperature  : potential temperature of air q : specific humidity of air u : wind velocity Using simplified notations, this can be written:

where the MOST scaling parameters for velocity, temperature and humidity are defined as:

• What is needed to compute the turbulent fluxes?

Applying the above formulas to the wind velocity (x = u), the wind stress can be written:

a : volumic mass of air ( 1.2 kg.m-3) s : volumic mass of seawater ( 1020 kg.m-3) Cd : momentum transfer coefficient (drag coefficient) Uw : bulk wind velocity at height z (in m.s-1) Us : sea surface current in the wind direction (in m.s-1)

Applied to the temperature (x =  ), the formulas lead to the sensible heat flux:

Cpa : specific heat of air ( 1004 J.kg-1) Ch : heat transfer coefficient (Stanton number) Ta : bulk air temperature at height z (in C) Ts : sea surface temperature (in C)

Applied to the humidity (x = q), the formulas lead to the latent heat flux:

Le : latent heat of air ( 2.5x106 – 2300 Ta) Ce : moisture transfer coefficient (Dalton number) qa : bulk air temperature at height z (in C) qs : sea surface temperature (in C)

• Case of the POLCOMS standard parameterisations:

The drag coefficient is proportional to the wind velocity: Cd = (0.63 + 0.066 Uw)x10-3 The wind gustiness is ignored and the sea surface current is neglected:

U, V : eastward and northward component of the wind velocity (in m.s-1)

The heat and moisture transfer coefficients are set to constants, equal to the average values from the North Sea Project observations. Ch = 1.1 Ce = 1.5 The volumic mass of air is also set to a constant value: a : volumic mass of air ( 1.25 kg.m-3) The specific humidity of air qa is computed from the surface atmospheric pressure p, the air temperature Ta and the relative humidity rh. The specific humidity of air qs is computed from the surface atmospheric pressure p and the sea surface temperature Ts.

-- SylvainMichel - 11 Jan 2007