Scaling the Vertical-Velocity Variance During the Very Late Afternoon Transition of the Convective Boundary Layer

In the bulk of the convective boundary layer driven by surface heating, the vertical-velocity variance is known to scale with the convective velocity scale. This scaling relies on the quasi-equilibrium assumption that the surface heat flux (H , the water-vapor contribution to buoyancy is neglected) varies slowly compared to the adjustment time scale of the large scale convective eddies (or the eddy turnover time), a condition which over land is typically satisfied from the late morning to the early afternoon transition. Later on, when the surface heat flux starts decaying moderately compared to the eddy turnover time, a departure from the quasi-equilibrium regime is expected. A recent idealized large-eddy simulations (LES) study proposed a parameter for describing such departure during the late afternoon transition: r ≡ H^-1dH/dt^-1/t_*, where t_* is the eddy turnover time. The quasi-equilibrium assumption applies when r >> 1, and breaks down when r ∼ 1. Building on these results, we further investigate the scaling for the vertical-velocity variance during the very late afternoon transition, i.e. in the regime r << 1 where the surface heat flux decays rapidly compared to the eddy turnover time. In a first step, we use LES to reveal that the regime r << 1 is characterized by a new velocity scale w_*r ≡ ((g/θ )dH/dtzi²)^1/4 . Within the specific framework of this study using the parameter r for identifying the out-of-equilibrium regime r << 1, the proposed scaling is implicitly dependent on the surface heat flux magnitude at the initial state when r ≈ 0.1, through the definition of the parameter r . In a second step, we demonstrate that the new velocity scale can be deduced from scaling arguments applied to the budget-equation of the vertical turbulent heat flux.