Laboratory measurements on fumigation into a convectively mixed layer indicate how the near surface concentration behaves with time. For two categories of entrainment rate, slow and fast, the experiments indicate how the ensemble-averaged concentration near the surface reaches a greater maximum in less time for the more rapid entrainment. For the two categories of entrainment studied, graphs are presented showing how the maximum time-averaged near-surface concentration in the horizontally homogeneous situation depends on averaging time and upon the angle between the wind velocity inside the mixed layer and just above. In the steady lake-breeze situation the maximum mean value found in the laboratory is an upper limit to the maximum time-averaged value inland of the shoreline because of the absence of downstream diffusion in the laboratory experiments.