QTCM version 2.3 includes a simple atmospheric boundary layer. It assumes a steady state, vertically homogeneous mixed layer of fixed height . This reduces the momentum equation in the boundary layer to a simple balance between the Coriolis force due to the boundary layer wind , the boundary layer's average gradient of the geopotential and the turbulent stress at top and bottom (see Stevens et al. [10]):
The stress at the top of the mixed layer is assumed to be proportional to the velocity jump at the interface with an entrainment velocity as its proportionality constant. For the surface stress the wind speed in the standard bulk formula is augmented by a minimum surface wind speed which crudely parameterizes the additional stress due to surface wind variance not captured in QTCM (gustiness etc.): , . The result is a nonlinear vector equation for the boundary layer wind. In components:
These equations are solved for and in subroutine abl
using
a Newton-Ralphon procedure. The routine uses the surface wind of the prior time
step as the initial guess. Initially, the routine uses the as
the initiall guess(*).
The input of abl
are the surface geopotential gradient
and the velocity at the top of the ABL .
Besides and abl
returns which is then used in the
bulk formulas for the latent and sensible heat fluxes.
The contribution
of the minimum wind speed is incorporated in . The surface wind
components ,
, however, are not augmented by the minimum wind speed and are
thus not directly used as the surface wind in the bulk formulas for scalar fluxes.
(*)The surface wind is currently not saved in the restart file which may make the model not exactly restartable, i.e., the trajectories of a restarted run may diverge from the original trajectory.