It is possible for a layer of air to be convectively unstable and absolutely stable at the same time.

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Convective instability refers to the tendency of a fluid to overturn due to density differences, while absolute stability refers to the tendency of a fluid to resist overturning due to the presence of a stable density gradient. It is possible for a layer of air to be convectively unstable due to a lapse rate that is greater than the adiabatic lapse rate, but absolutely stable due to the presence of a stable density gradient caused by, for example, a temperature inversion.

It Is Possible for a Layer of Air to Be