Estimation of Surface-Layer Scaling Parameters in the Unstable Boundary Layer: Implications for Orographic Flow Speed-Up

Abstract

A method is proposed for estimating the surface-layer depth $$(z_s)$$ and the friction velocity $$(u_*)$$ as a function of stability (here quantified by the Obukhov length, L) over the complete range of unstable flow regimes. This method extends that developed previously for stable conditions by Argain et al. (Boundary-Layer Meteorol 130:15–28, 2009), but uses a qualitatively different approach. The method is specifically used to calculate the fractional speed-up $$(\varDelta S)$$ in flow over a ridge, although it is suitable for more general boundary-layer applications. The behaviour of $$z_s \left( L\right) $$ and $$u_*\left( L\right) $$ as a function of L is indirectly assessed via calculation of $$\varDelta S\left( L\right) $$ using the linear model of Hunt et al. (Q J R Meteorol Soc 29:16–26, 1988) and its comparison with the field measurements reported in Coppin et al. (Boundary-Layer Meteorol 69:173–199, 1994) and with numerical simulations carried out using a non-linear numerical model, FLEX. The behaviour of $$\varDelta S$$ estimated from the linear model is clearly improved when $$u_*$$ is calculated using the method proposed here, confirming the importance of accounting for the dependences of $$z_s\left( L \right) $$ and $$u_*\left( L \right) $$ on L to better represent processes in the unstable boundary layer.