Stability of cloud‐topped boundary layers

According to the thermodynamic theory of cloud top evaporative instability, persistent stratocumulus should be observed only when the cloud top jumps in equivalent potential temperature θ and total water mixing ratio r satisfy the stability condition Δθ > k(L/cp)Δr, where k ± 0.23. Using observations of persistent mid‐latitude and subtropical stratocumulus we find that the above stability condition is violated in many cases. In an attempt to understand how stratocumulus can persist under apparently unstable conditions we first review the thermodynamic instability theory and then develop a dynamical framework using a two‐dimensional Boussinesq moist convection model with spectral discretization and with resolution sufficient to simulate cloud top processes. Idealized initial value experiments confirm that, when the above condition is violated, evaporative instability leads to cloud breakup through sequential dissections of existing cloud. However, initial conditions close to the critical stability line (e.g. Δθ, (L/cp)Δr = –6K, –15 K) lead to cloud breakup with a characteristic cloud half‐life of several hours, while physically realistic initial conditions far from the critical stability line (e.g. Δθ, (L/cp)Δr = –16 K, –25 K) lead to more rapid breakup, with a cloud half‐life on the order of 1/2 hour. When evaporative instability is so weak that the associated cloud half‐life is as long as several hours, other physical processes (such as surface evaporation) can apparently moisten the boundary layer rapidly enough to mask the cloud breakup process.