Note on stratocumulus instability

With the exception of a few numerical modeling studies (e.g. Oliver et al., 1978), investigations of the stratocumulus-topped planetary boundary layer have evolved from Lilly’s (1968) mixed-layer approach (e.g. Schubert, 1976; Deardorff, 1976; Kraus and Schaller, 1978; Schubert et al., 1979a,b). In a discussion of the stability of these cloud decks, Lilly (1968) introduced the concept of moist convective instability, which occurs when very dry air is entrained into the cloud’s top, and becomes negatively buoyant (with respect to the cloud) while becoming saturated. Lilly asserted that this would happen when the difference across the cloud top of moist static energy is negative; Le., when h_c > h_u, where subscripts “c” and “u” to the cloud and upper (clear) air respectively. (Lilly (1968) actually discussed the problem in terms of wet bulb potential temperature, which is equivalent to moist static energy for purposes of this discussion.)