Abstract
The Monin–Obukhov Similarity Theory (MOST) is a cornerstone of boundary layer meteorology and the basis of most parameterizations of the atmospheric surface layer. Due to its significance for observations and modelling, we generalize the dimensional analysis of MOST by considering the bulk gradient directly, enabling the study of any sublayer of the atmospheric surface layer. This results in a family of similarity relations describing all gradients from the local gradient to the full-layer bulk gradient. By applying the profiles derived from the law-of-the-wall and MOST, we are able to derive analytic expressions for this family of similarity relations. Under stable conditions, we discover that the log-linear profile of Businger–Dyer generalizes from the local to the bulk shear where the slope is dependent on the choice of the layer. The simplicity of the general log-linear relation allows for estimating the influence of stability on the non-dimensional gradients. It is shown that bulk gradients are less sensitive to stability than the local gradient. By correctly filtering cases where the full-layer bulk gradient is influenced by stability, we demonstrate that MOST is compatible with the Hockey-Stick Transition. For unstable conditions, the Kader and Yaglom (J Fluid Mech 212(151):637-662, 1990) model represents the local gradient well but was not successful in representing the bulk gradient, demonstrating the need for further analysis of scaling relations for the unstable atmospheric surface layer.