Estimating and Evaluating Roughness Length and Displacement Height in Heterogeneous Urban Environments

The roughness length ( $z_0$ ) and displacement height ( $z_d$ ) are essential surface-layer parameters in numerical models (e.g., weather, climate, wall-modeled LES, etc.). This work evaluates the consistency of $z_0$ and $z_d$ estimates from morphometric and anemometric methods using data from two eddy-covariance flux towers (AmeriFlux US-INg and US-INc) in Indianapolis, IN. Results show inconsistencies in estimated $z_0$ and $z_d$ values depending on the chosen method. The two evaluated anemometric methods estimate non-physical values of $z_d$ when compared to roughness elements surrounding both towers. Additionally, predictions of mean wind speed using surface-layer similarity theory with morphometric estimates exhibit a bias during near-neutral and stable conditions relative to observations. The overestimation of mean wind speed by surface layer similarity theory is consistent with previous observational and modeling studies in urban areas, suggesting that the application of similarity theories to urban environments may have limitations. Differentiation of vegetation from built structures appears to impact morphometric $z_0$ and $z_d$ estimates, particularly where vegetation is abundant; however, it has little impact on correcting biases in the similarity theory. Specifically, we find that existing similarity theories using morphometric estimates underestimate integral velocity and length scales, and the degree of underestimation depends on the stability conditions. Accounting for the degree of anisotropy in surface-layer turbulence helps reduce the biases between similarity theories and observations during unstable conditions, but not in near-neutral cases. Future work is needed to identify the cause of such biases for near-neutral conditions.