The Numerical Representation of Entrainment in Parameterizations of Boundary Layer Turbulent Mixing

Abstract

Problems have been identified with parameterizations of convective boundary layers, in particular with their numerical treatment of the capping inversion. It is shown that the turbulence scheme can combine with the numerical representation of subsidence to produce unphysical entrainment, as was also identified by Lenderink and Holtslag. A correction is proposed for the Lock et al. boundary layer parameterization in which a discontinuous inversion is diagnosed from the mean thermodynamic profiles every time step. This then allows a consistent treatment of subgrid-scale processes in the region of the inversion. In particular, the parameterized turbulent entrainment flux can be adjusted to allow for the spurious entrainment arising from the conflicting representations of turbulent mixing and vertical advection. It also allows a direct coupling between the turbulent and radiative fluxes to ensure that cloud-top radiative cooling is correctly distributed between the inversion grid level and the mixed layer. The revised scheme demonstrates a much improved representation of stratocumulus-capped boundary layers, not only in single-column model tests but also in a climate-resolution GCM. In the latter, the semipermanent subtropical stratocumulus sheets appear realistic, both in terms of their cloud amount and their evolution. This suggests that a significant cause of the lack of stratocumulus in many GCMs may not be the inaccuracy of the parameterizations employed, but rather their numerical implementation.