The vertical diffusion of sensible heat and humidity through turbulent mixing can be described by the following generic equation:
where X is potential enthalpy 
(As defined in
equation 21.) or specific humidity (q) and K is the
``eddy-diffusivity''. In the following it will be assumed that the
diffusion coefficients are the same for both variables. The sensible
and latent heat fluxes at the surface are also computed using this
equation but with diffusion coefficients which take into account the
surface properties. At the surface we will write 
and
in order to distinguish the diffusion coefficients for each of
the fluxes. Land surface schemes are thus intimately linked to the
vertical diffusion scheme.
To solve equations 14 over the atmospheric column boundary conditions are needed. Above the planetary boundary layer vertical diffusion becomes sufficiently small that the flux can be considered to vanish. This leads to a zero flux upper boundary condition. The surface is the source of the transported energy and the closure of the equation there is a delicate problem which is discussed in section 4.
