Scale Dependence of Atmosphere-Surface Coupling through Similarity Theory (Invited Presentation)

Surface-layer similarity theory is derived under the assumptions of horizontal heterogeneity and stationarity, but it is used in ever more complex and heterogeneous configurations. We independently assess the scale-dependence of surface-layer similarity theory by obtaining values of the surface friction from wind- and velocity fields within the surface layer. A classical set of Monin-Obukhov similarity functions is inverted analytically; this allows to investigate the joint convergence of individual samples of the wall-friction and its estimate from similarity theory as a function of the spatial and temporal filter scale. Spatially and temporally resolved data originate from a direct numerical simulation of turbulent Ekman flow, an idealized representation of the atmospheric boundary layer. This work focuses on the stable stratification and the neutrally stratified limit.

In neutral conditions, a systematic underestimation of variance in surface fluxes estimated through similarity theory versus the actual flux is found and quantified as a function of height, averaging time and length scale. A sufficient convergence of the local friction estimate by similarity theory to the actual local surface friction is only obtained for averaging box sizes of several thousand wall units, and only for data filtered along both horizontal dimensions; the three-dimensional structure of the turbulence elements appears to limit the convergence of data filtered along any of the single dimensions time, the streamwise or the spanwise direction.

In stable conditions, the bulk profiles agree with similarity theory until the maximum buoyancy flux is reached and the turbulence becomes intermittent. Due to the non-stationarity, convergence is only considered in the spatial domain and only for two-dimensional horizontal box-averages. Due to the turbulence intermittency and a frictional decoupling associated
to the inertial oscillation, similarity theory does not govern the joint fluctuation of wind in the lower part of the surface layer and friction at the surface at any scale; in fact, the skill of similarity in predicting local variations decreases with increasing averaging scale while the mean values are still constrained to within 10\%.

While similarity theory appears appropriate to represent fluctuations for weak stratification and at large scales, the present results suggest a scale on the order of thousands of wall units below which the coupling of fluctuations at the surface and within the surface layer is no longer governed by surface-layer similarity theory such as the Monin-Obukhov Stability Theory. Further, the applicability limit of similarity in terms of a critical stratification is also confirmed in this analysis be a negative skill of similarity in predicting local fluctuations in strongly stable conditions.