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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 BLX-83 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 surfacelayer frequency distribution of temperature into a corresponding entrainment zone distribution is shown to approximate the hysteresis evolution to first order. The following paper has been accepted for publication by the Journal of Applied Meteorology. "Lidar observations of linear convection during BLX-83" R.A.Ferrare, J.L.Schols and E.W.Eloranta