Entrainment in stratocumulus-topped mixed layers

Abstract

Mixed-layer theory is used to synthesize and evaluate recently proposed entrainment parametrizations (rules) for the stratocumulus-topped boundary layer. The results illustrate that recently proposed entrainment rules exhibit marked differences. Significant differences are found between rules derived from a single set of simulations and rules derived from different sets of simulations. Such differences imply steady-state boundary layers that can differ by as much as a factor of two in climatologically important properties such as vertically integrated liquid water and boundary-layer depth. In addition, surface fluxes depend significantly on entrainment, as do different measures for the limits of applicability of the mixed-layer theory. Moreover, differences among proposed entrainment rules yield steady states with different equilibrium sensitivities; models closed with some rules are more sensitive to divergence while others are more sensitive to variations in the sea surface temperature. Overall we expect that these differences should be evident in the climatology and climate sensitivity of stratocumulus derived from models which use these rules. This degree of sensitivity encourages attempts to bound entrainment rules observationally, by requiring consistency with the observed stratocumulus climatology. The analysis also encourages the use of somewhat simpler strategies for the parametrization of the stratocumulus-topped boundary layer in large-scale models.