A study on characteristics of thickness of the entrainment zone above the mixed layer in the daytime

An explanation about the first-order model of Deardorff is given. Based on this explain, the turbulent kinetic energy equation is analyzed, and the contribution to evolution of the convective boundary layer is divided into two parts: buoyant production and mechanical production. Thereout, a new velocity scale, top velocity scale of mixed layer, is proposed. At the same time, the full Richardson number is defined. And a new parameterization of thickness of entrainment zone is concluded. It gives a good agreement with the data of Boers and Eloranta measured by lidar. When the entrainment zone thickness normalized by mixed-layer depth is ploted as a function of the entrainment Richardson number or the entrainment rate normalized by the convective velocity scale, the curve of the function behaves as hysteresis. A preliminary interpretation is made to this phenomenon.