Estimating and evaluating roughness length and displacement height in heterogeneous urban environments

The roughness length (z₀) and displacement height (z_d) are essential surface-layer parameters in numerical models (e.g., weather, climate, wall-modeled LES, etc.). Approaches to estimating these parameters for heterogeneous urban environments can be separated into three broad groups: rule-of-thumb, morphometric, and anemometric methods. This work evaluates the consistency of z₀ and z_d values estimated using methods from each of these groups, including examining the impacts of urban vegetation. The analysis uses data from two eddy-covariance flux towers (AmeriFlux US-INg and US-INc) in Indianapolis, IN. US-INg sits between a major highway and a vegetated suburban neighborhood, while US-INc sits over a network of intersecting highways surrounded by buildings of various shapes and sizes. Results show significant discrepancies in estimated z₀ and z_d values depending on the choice of method and the consideration of urban vegetation. In addition, no parameters estimated using any method can be used by existing similarity theories to reproduce observed surface-layer flux-profile relationships. These results are consistent with previous observational and modeling studies in urban areas, suggesting limitations in applying similarity theories to urban environments. Specifically, existing similarity theories underestimate integral velocity and length scales, and the degree of underestimation depends on stability conditions. For unstable conditions, accounting for the anisotropy of surface-layer turbulence helps reduce the biases between similarity theories and observations. Future work is needed to identify the cause of such biases for near-neutral conditions.