This coupling scheme uses the surface temperature at the last time-step to close the vertical diffusion equations. It simplifies the solution of the surface energy balance equation, as surface temperature is obtained independently of the vertical diffusion scheme. This method is used by a few complex land surface schemes coupled to GCMs. We may cite the Blondin scheme in the ECMWF model [Blondin, 1988] and the ECHAM model [Dümenil and Todini, 1992].
As in the implicit scheme, the coefficient 
and 
need to be computed in order to solve equation 16 to
obtain the new values at the first level. The simplification lies in
the fact that instead of using 
the old surface
temperature 
is used. The following equations are then
used to compute the turbulent fluxes :
These fluxes are then given back to the vertical diffusion which computes the new temperature and humidity profiles.
The derivative of the new surface fluxes with respect to surface temperature are then used to solve the surface energy balance which yields the new surface conditions. Equation 1 is then discretized as :
As this step is usually done after the vertical diffusion parameterization is called, the surface fluxes which correspond to the new surface temperature are different from those received by the atmosphere (eq. 10, 11). To avoid an energy imbalance, this difference has to taken into account in the temperature calculation of the next time step. By design, the semi-implicit coupling only allows for surface temperature changes to feed back to the atmosphere at the next time step.
As the coupling scheme proposed here only requires one call to the land surface parameterization, the new surface temperature will have to be computed just after the surface fluxes. This opens the possibility for the schemes using the semi-implicit coupling to reduce the problem of energy conservation. If a threshold formulation is used for evaporation, equation 12 cannot be solved in the general case. The discontinuity introduced into the calculation of evaporation makes it difficult to compute the derivatives needed in the semi-implicit coupling.
The way this scheme has been implemented amounts to a Dirichlet closure for the vertical diffusion and a Neumann closure for the surface energy balance.
