In general, most studies of the surface layer have shown good agreement with prediction from Monin-Obukhov theory, but some parameters have large scatter.
But more recent studies have shown that the surface layer also for slightly unstable conditions is influenced by the circulation in the convective boundary layer. To treat this indirect influence of the convective boundary, the height of the CBL zi must be included as a parameter. One of the first to do this was Panofsky et al. (1977, Boundary-Layer Meteorol.) who found that the standard deviation of the horizontal wind component is a function of zi/L.
A LES-simulation on the convective boundary layer made by Khanna and Brasseur (1997, J. Fluid Mech) showed that there were more surface variables effected by zi than discovered before. By using measurements from two summertime experiment, which include turbulence measurements, profile measurements, airborne measurements and numerous radio soundings, some of the results from their study have been verified.
Khanna and Brasseur (1997) found that the nondimensional wind gradient Phim is dependent on both z/L and zi/L. This is confirmed by the measurements and a new parametrisation of Phim has been made that includes the dependence of zi/L. The nondimensional temperature gradient Phih show however no dependence on zi, in agreement with the LES-results.
The LES-simulation show that the standard deviation of the horizontal wind component is a function of zi/L, as found by Panofsky et al. (1977). Peltier et al. (1996, J. Atm. Sci.) concluded, from a model of the spectrum for the vertical wind component, that also sigmaw/u* depends to some extend on the depth of the convective boundary layer zi.
This expression has, after adjustment of some constants, been found to be in good agreement with the experimental data for -z/L>0.2, but not for -z/L<0.2. For the near neutral range Högström (1990, J. Atm. Sci.) found that the standard deviation of the vertical wind component is a function of the height of the near neutral boundary layer. By combining the two expressions a new one has been made that gives very good agreement with the measurements for the whole range from neutral to free convection.