Nearly steady convection and the boundary-layer budgets of water vapor and sensible heat

The budgets of water vapor and sensible heat in the convective atmospheric boundary (mixed) layer are analyzed by means of a simple slab approach adapted to steady large-scale advective conditions with radiation and cloud activity. The entrainment flux for sensible heat is assumed to be a linear function of the surface flux. The flux of water vapor at the top of the mixed layer is parameterized by extending the first-order Betts-Deardorff approach, i.e., by adopting linear changes for both the specific humidity and the flux across the mixed layer and across the inversion layer of finite thickness. In this way the dissimilarity of sensible heat and water vapor transport in the mixed layer can be taken into account. The experimental data were obtained from the Air Mass Transformation Experiment (AMTEX). The entrainment constant for sensible heat at the top of the mixed layer was found to have values similar to those observed in other weakly convective situations, i.e., around 0.4 to 0.6. This appears to indicate that the effect of mechanical turbulence was not negligible; however, the inclusion of this effect in the formulation did not improve the correlation. In contrast to the first-order approach, the zero-order approach, i. e., the jump equation commonly used for the flux of a scalar at the inversion, (ovwc )_h = w_e c (where w_e is the entrainment velocity and c the concentration jump across the inversion), was found to be invalid and incapable of describing the data.