A Prognostic Relationship for Entrainment Zone Thickness

The thickness of the entrainment zone at the top of the atmospheric mixed layer is analyzed using measurements made with a ground-based lidar during the BLX83 and CIRCE field programs. When the entrainment-zone depth normalized by mixed-layer depth is plotted as a function of the entrainment rate normalized by the convective velocity scale, with time as a parameter, a hysteresis curve results. Although portions of the curve can be approximated by diagnostic relationships, the complete hysteresis behavior is better described with a prognostic relationship. A simple thermodynamic model that maps the surface-layer frequency distribution of temperature into a corresponding entrainment zone distribution is shown to approximate the hysteresis evolution to first order.