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Atmospheric Boundary Layer

 

QTCM version 2.3 includes a simple atmospheric boundary layer. It assumes a steady state, vertically homogeneous mixed layer of fixed height tex2html_wrap_inline3000 . This reduces the momentum equation in the boundary layer to a simple balance between the Coriolis force due to the boundary layer wind tex2html_wrap_inline3002 , the boundary layer's average gradient of the geopotential tex2html_wrap_inline3004 and the turbulent stress tex2html_wrap_inline3006 at top and bottom (see Stevens et al. [10]):

equation898

The stress tex2html_wrap_inline3008 at the top of the mixed layer is assumed to be proportional to the velocity jump at the interface tex2html_wrap_inline3010 with an entrainment velocity tex2html_wrap_inline3012 as its proportionality constant. For the surface stress the wind speed tex2html_wrap_inline3014 in the standard bulk formula is augmented by a minimum surface wind speed tex2html_wrap_inline3016 which crudely parameterizes the additional stress due to surface wind variance not captured in QTCM (gustiness etc.): tex2html_wrap_inline3018 , tex2html_wrap_inline3020 . The result is a nonlinear vector equation for the boundary layer wind. In components:

eqnarray910

These equations are solved for tex2html_wrap_inline3022 and tex2html_wrap_inline3024 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 tex2html_wrap_inline3026 as the initiall guess(*). The input of abl are the surface geopotential gradient tex2html_wrap_inline3028 and the velocity at the top of the ABL tex2html_wrap_inline3030 . Besides tex2html_wrap_inline3022 and tex2html_wrap_inline3024 abl returns tex2html_wrap_inline3036 which is then used in the bulk formulas for the latent and sensible heat fluxes. The contribution of the minimum wind speed tex2html_wrap_inline3016 is incorporated in tex2html_wrap_inline3022. The surface wind components tex2html_wrap_inline3022, tex2html_wrap_inline3024 , 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.



Climate Systems Interaction Group
Sun Aug 25 00:58:46 PDT 2002