Slow Manifolds and Multiple Equilibria in Stratocumulus‐Capped Boundary Layers

Abstract

In marine stratocumulus‐capped boundary layers under strong inversions, the timescale for thermodynamic adjustment is roughly a day, much shorter than the multiday timescale for inversion height adjustment. Slow‐manifold analysis is introduced to exploit this timescale separation when boundary layer air columns experience only slow changes in their boundary conditions. Its essence is that the thermodynamic structure of the boundary layer remains approximately slaved to its inversion height and the instantaneous boundary conditions; this slaved structure determines the entrainment rate and hence the slow evolution of the inversion height and can be regarded as a one‐dimensional slow manifold. Slow‐manifold analysis is applied to mixed‐layer model and large‐eddy simulations of an idealized nocturnal stratocumulus‐capped boundary layer. Both models are found to have multiple equilibria; depending on the initial inversion height, the simulations slowly evolve toward a shallow thin‐cloud boundary layer or a deep, well‐mixed thick cloud boundary layer. In the mixed‐layer model, this can be described using a single slow manifold bifurcated by an unstable equilibrium inversion height which separates a branch that evolves toward a deep steady state from a branch which shallows indefinitely. In the large‐eddy simulations, there are two separate slow manifolds (one of which becomes unstable if cloud droplet concentration is reduced). On one, the boundary layer is well‐mixed and deepens to a thick‐cloud steady state. On the other, the boundary layer is decoupled and shallows to a thin‐cloud steady state. If the initial inversion height supports an optically thick but nearly nondrizzling cloud, it evolves onto the well‐mixed manifold; if the initial cloud layer is either too thin to efficiently radiatively cool, or thick enough to heavily drizzle, it evolves onto the decoupled manifold. Applications to analysis of stratocumulus observations and to pockets of open cells and ship tracks are proposed.