On the Diurnal Cycle in a Stratocumulus-Topped Mixed Layer

Mixed-layer theory is used to study the diurnal cycle of the stratocumulus-topped boundary layer (STBL). Our results show that the evolution of cloud thickness subject to diurnally varying radiative forcing is very sensitive to the entrainment closure, as represented by different entrainment efficiencies, denoted by η. For large values of η, like those used in the entrainment closures of previous studies, the model produces a diurnal cycle in which cloud base descends faster than cloud top; this leads to a thickening of the layer during the daytime, which is inconsistent with observations. Simulations that use smaller values of η, such as those inferred from recent field studies, are in better agreement with available data. This sensitivity of the STBL's diurnal cycle is explained by examining the equilibrium response of the cloud boundaries for a given forcing and the timescales for their adjustment to equilibrium. Specifically we show that the differing rates at which cloud base and cloud top adjust to their new equilibrium heights is essential for generating the out-of phase response characteristic of mixed-layer models using vigorously entraining closures. The tendency of the diurnal response of the STBL to improve when given more realistic entrainment formulations Is due to the tendency for the equilibrium response of cloud base to vary little with weaker entrainment efficiencies. Overall these results increase our confidence both in mixed-layer theory and its closure; in particular, they show that decoupling between cloud layer and sub-cloud layer need not be invoked to explain the diurnal variation of cloud thickness in the STBL.