A heat-flux history length scale for the nocturnal boundary layer

A height scale, H = ∫Q_H d/(p^C_pΔθ_s), based on the night-time heat-flux (Q_H) history is proposed here as being a relevant scale for the nocturnal boundary layer temperature structure. This scale, together with the surface temperature decrease since sunset, Δθ_s. are shown to be sufficient to define a common similarity shape for the potential temperature profile. An equation for this shape based on Wangara field experiment data is Δθ_s/Δθ_s = exp (−0.77z/H). This curve is then tested against the Koorin boundary-layer data set, and is shown to provide a good fit to the data. Such a potential-temperature profile equation suggests that the top of the boundary layer is at about 5H, and that 23% of the cooling within that depth is caused directly by radiation. The definition for H, above, is shown to be a simple means of expressing much of the same information as Nieuwstadt's rate equation.