Scale Dependence of Atmosphere–Surface Coupling Through Similarity Theory

Monin–Obukhov similarity theory (MOST) applies for homogeneous and stationary conditions but is used in ever more complex and heterogeneous configurations. Here, it is used to estimate the surface friction velocity u_ from the wind speed and temperature in the atmospheric surface layer (ASL). Filters of varying scale and direction are applied to wind speed and temperature in the ASL before MOST is used to estimate u_ . This procedure unveils the scale dependence of coupling between the ASL and the surface. Direct numerical simulation of turbulent Ekman flow above a smooth surface is used to explicitly resolve the near-wall dynamics. It is found that the viscous sub-layer may cease to exist, even in continuously turbulent neutral conditions, while the ASL covers more than one decade of variation in height. An underestimation in the variance of u_ estimated through MOST versus its actual variance is quantified as a function of height, averaging time, and length scale. For large filter scales, the variance exhibits a purely statistical convergence—there is no signature of long-term memory beyond the scale of coherent turbulent motion. Joint convergence of u_ estimated by MOST and the actual u_ is obtained for filter scales beyond several thousand wall units, and only for data filtered along both horizontal dimensions; the three-dimensional structure of the turbulence elements limits the convergence of data filtered along any of the single dimensions: time, the streamwise or spanwise direction. In stably stratified conditions, MOST is found to have no or negative skill in locally estimating ASL properties from u_ and should therefore only be applied to filtered quantities.