Large-eddy simulation study of urban-like topography statistical moments relevant to setting roughness length via a priori models

A priori estimation of aerodynamic roughness length, z0, based on geometric attributes of an underlying topography, remains an open line of inquiry in planetary boundary layer research. At regional scales and for the conditions of a horizontally homogeneous, neutrally stratified atmospheric boundary layer (ABL), z0 represents the elevation at which the mean (logarithmic) streamwise velocity is zero. Thus, z0 falls within the roughness sublayer depth, and models exist that relate z0 to the characteristic vertical scale of an obstacle, h. Urban topographies -- the topic of this study -- exhibit spatial heterogeneities associated with variability of building height, width, and proximity with adjacent buildings; such variability renders a priori, prognostic z0 models appealing. Here, large-eddy simulation (LES) has been used in an extensive parametric study to characterize the ABL response (and z0) to a range of synthetic, urban-like topographies wherein statistical moments of the topography have been systematically varied. This approach yields two complementary insights. First, it offers a means to characterize the hierarchical influence of different topographic moments, and we demonstrate that while standard deviation and skewness are important, kurtosis may be neglected. This finding is reconciled with a model recently proposed by researchers from the engineering roughness community (Flack and Schultz, 2010: J. Fluids Eng. 132, 041203), who demonstrate that z0 can be modeled with standard deviation, skewness, and two empirical parameters (one for each moment). In a noted difference, however, we find that the empirical parameter related to skewness is not constant with standard deviation. For the range of cases considered, we demonstrate strong performance of the generalized Flack and Schultz, 2010: J. Fluids Eng. 132, 041203 model.