Local Similarity Scaling in the Nocturnal Boundary Layer over Heterogeneous Terrain

A proper representation of turbulence is particularly important for parameterization of surface-atmosphere exchange processes in atmospheric models (e.g., dispersion, numerical weather prediction or regional models). These models use similarity scaling to model flow characteristics and dispersion. In this study we investigate the applicability of Nieuwstadt's (1984) local scaling formulation for the stable boundary layer over a truly heterogeneous terrain. It is well known that even modest surface heterogeneity can significantly influence the nocturnal boundary layer (NBL) and lead to turbulence at higher Richardson number in comparison with homogeneous surfaces. Therefore, this study relates to the approach of Grachev et al. (2013), who distinguished between Kolmogorov and non-Kolmogorov turbulence. Here we evaluate local similarity scaling in terms of flux-variance and flux-gradient relationships.

The data for this study stem from a tall tower within a small forest patch situated in heterogeneous terrain influenced by a mixture of forest, agricultural and industrial surfaces in different upwind sectors. The 62 m tower (levels 20, 32, 40, 55 and 62 m above ground) was situated in the middle of some 120 m x 480 m area of 18 m high trees. The heterogeneity of the surface was characterized by spatial variability of both roughness and topography.

The analysis shows that local similarity approach is valid at a forested site with highly inhomogeneous fetch. It was found that flux-variance and flux-gradient relationships respond differently to inhomogeneity. While the roughness sublayer influence was observed for the flux-variance relationships, it did not show any significant effect on dimensionless wind shear (Φ_m). Despite the inhomogeneous surface conditions, flux-gradient relationship showed similar distinction between Kolmogorov and non-Kolmogorov turbulence as found under ideal conditions. After removing data points associated with the flux Richardson number (Rf) greater than 0.25 (supercritical regime), dimensionless wind shear supports classical linear expressions even over inhomogeneous terrain. Deviations from linear expressions were found to be mainly due to the small-scale turbulence rather than due to the surface heterogeneities.