As explained in section 2.3, the land surface scheme of current GCMs should provide the radiation scheme with albedo, emissivity and surface radiative temperature as lower boundary conditions and receive in return the net short-wave flux, the zenith angle and the down-welling long-wave flux.
As the radiation parameterizations are computationally very expensive, their time-step is usually longer than the one used by the other components of the GCM. This contrasts to the LSS which uses the shortest time-step of the physical parameterizations as it is closely linked to the turbulent diffusion. Thus the LSS is called more often that the radiation scheme and special attention has to be paid at the interface to ensure conservation of energy.
It should be noted here that in the case where the radiation scheme uses the same time-step as the LSS another coupling method is possible. The long-wave flux balance can be solved with a mixed closure, thus coupling the surface energy balance equation to the radiation code. This approach will certainly result in a better simulation of the radiative cooling of the surface in regions where this process is dominant. However, only one model is known where this approach has been used; the version of the BMRC GCM coupled to the bucket scheme described in McAvaney et al. (1978). Later this coupling was abandoned at BMRC because of its computational cost.
Most radiation schemes will require from the LSS albedos for direct
and diffuse sunlight in the spectral band below and above 
. In order to compute this, the land surface scheme will
require the zenith angle, fraction of diffuse radiation and the
incoming solar radiation. The latter will have to be computed by the
LSS from the net solar radiation and the albedo it provided at the
last call. The downward solar flux is only used to compute albedo and
photosynthetically active radiation and may thus tolerate numerical
approximations if needed. The same argument applies to the choice of
fraction of diffuse short-wave radiation instead of a flux.
Priority is given to the net flux because it is the energy received by the surface as computed in the radiation scheme and it is used in the surface energy balance. This ensures energy conservation through the interface even with the different time-stepings. The LSS will receive the same net solar flux at each time-step between two calls to the radiation scheme. The radiation scheme may choose to use the last albedo provided by the LSS or the average of all values obtained since the last radiation time-step. The GCM has also the responsibility of providing the zenith angle for the next point in time to ensure a correct computation of albedo by the LSS for such critical situation as sunrise.
In the long-wave part of the spectrum the radiation scheme will provide incoming radiation at the surface. On the other hand it needs to receive from the LSS the emissivity to determine the fraction of this flux which will be reflected.
Providing a radiative temperature through the interface has practical
advantages but also a few pitfalls. While solving the surface energy
balance the land surface scheme can use a limited expansion of the
surface temperature around its old value to obtain a value for the
emitted radiation closer to the new temperature. For instance the upward
long-wave flux ( 
) may be determined by :
where 
is surface emissivity and 
the
Stefan-Boltzman constant. The benefits of this approach is to
stabilize the numerical scheme used to solve equation 1
in situation where the long-wave radiation dominates the energy
balance. The intermediate temperature used to determine the upward
long-wave flux will be called the radiative temperature (T) and is
defined by:
It needs to be recomputed once the surface energy balance is solved. As can easily be seen, without the Taylor expansion the radiative temperature is the surface temperature at time t. If this is not done energy will not be conserved in the coupled system as the GCM will receive a long-wave flux different from the one used in the LSS.
When the radiative temperature and the emissivity are passed to the
radiation scheme, they have to be averaged over the time-steps at
which the radiation is not called so that the mean flux emitted from
the surface, as calculated by the LSS, is given to the radiation. This
averaging has to be linear for the emissivity and in the 4th power of
the radiative temperature. In order to perform this process on the fly
we propose the following equations which yield the new averages
( 
, n is the time-step at which radiative temperature
is available between two calls to the radiation) from the mean over
the previous time-steps and the new values:
Using 
and 
in the
next call to the radiation scheme will ensure that the time-averaged
balance of the long-wave radiative fluxes is conserved.
If the land surface scheme includes a sub-grid scale variability of the surface temperature it has to perform the same type of averaging to obtain a mean radiative temperature for the grid. It will also need to compute an averaged emissivity.