As in the previous method, the explicit coupling uses the atmospheric and surface values at different time steps to compute the fluxes. In the present case the emphasis is put on a coherent calculation of the surface energy balance. The old atmospheric conditions are used, as it can be assumed that their variations over time are smaller than those at the surface. This method is used in CCM2 coupled to BATS (Dickinson et al. 1993) and in CCM3 coupled to LSM [Bonan, 1996].
The first step is to solve the surface energy balance using the old atmospheric conditions. Equation 1 is thus discretized as:
It may be solved either by expanding the saturated humidity as is done in the implicit coupling or by using an iterative procedure. The latter one is suited for land surface schemes with a threshold formulation for evaporation. When solving equation 13 for the new surface temperature an iteration scheme has to be chosen which ensures convergence towards a physical correct solution. This is not a trivial task for all atmospheric conditions. If the stability dependence of the surface transfer coefficients is updated at each step of the iteration convergence is improved (Desborough, personal communication). Thus, these schemes may need to modify the surface transfer coefficient given by the GCM. It must be noted that when an iterative procedure is used, the scheme can become computationally very expensive and does not always converge to an unique solution.
The surface fluxes determined for the new surface temperature will then be used to complete the back-substitution of the vertical diffusion after computing the new variables at the first atmospheric level.
This approach has the advantage over the semi-implicit coupling that energy will be conserved. The fluxes obtained by solving the surface energy balance are those which are given to the atmosphere. Its drawback, on the other hand, is that the atmospheric feedback to the surface is only felt from one time step to the other. As in general temperature variations are slower at the lowest level of the atmosphere than at the surface, this approximation seems to be better than the one used in the semi-implicit coupling. This needs to be verified in numerical experiments.
This type of coupling facilitates the ``tile'' modeling as is allows multiple surface energy balances to be computed. The fluxes are then averaged before they are passed to the vertical diffusion.
