Parameterization of sheared entrainment in a well-developed CBL. Part I: Evaluation of the scheme through large-eddy simulations

The entrainment flux ratio A e and the inversion layer (IL) thickness are two key parameters in a mixed layer model. A e is defined as the ratio of the entrainment heat flux at the mixed layer top to the surface heat flux. The IL is the layer between the mixed layer and the free atmosphere. In this study, a parameterization of A e is derived from the TKE budget in the firstorder model for a well-developed CBL under the condition of linearly sheared geostrophic velocity with a zero value at the surface. It is also appropriate for a CBL under the condition of geostrophic velocity remaining constant with height. LESs are conducted under the above two conditions to determine the coefficients in the parameterization scheme. Results suggest that about 43% of the shear-produced TKE in the IL is available for entrainment, while the shear-produced TKE in the mixed layer and surface layer have little effect on entrainment. Based on this scheme, a new scale of convective turbulence velocity is proposed and applied to parameterize the IL thickness. The LES outputs for the CBLs under the condition of linearly sheared geostrophic velocity with a non-zero surface value are used to verify the performance of the parameterization scheme. It is found that the parameterized A e and IL thickness agree well with the LES outputs.