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<p>Numerical modelling is an important method for the investigation of urbanization effect on weather and climate. Single-layer urban canopy models (SLUCMs) are most widely used in numerical models, such as WRF and CESM to represent the momentum and heat exchange between urban land surface and the atmosphere. Within SLUCMs, the bulk momentum roughness length constitutes a fundamental parameter that regulates the fluxes exchange between the urban canopy and the atmosphere and thus exerts a substantial influence on overall simulation. The roughness length is typically estimated using morphological approaches, yet commonly adopted formulations omit building-height heterogeneity, leading to a systematic underestimation. To address this issue, this study develops an improved algorithm by incorporating the probability density function of building heights (<i>PDF</i>(<i>h</i>)) into an existing morphological framework. An exponential approximation method is further proposed to simplify the formulation while preserving physical interpretability. Large-eddy simulations are used to evaluate the new scheme and the results demonstrate that the exponential approximation method achieves the best agreement with reference values, reducing the mean relative error from − 73.6% (conventional formulations) to 11.2% and the root mean square error from 5.83 to 2.23&#xa0;m. The <i>PDF</i>(<i>h</i>)-based method shows moderate performance, which tends to overestimate roughness length by ~ 38.1% on average. These results highlight that incorporating the statistical characteristics of building-height distributions—particularly through exponential approximation—can substantially improve the accuracy of urban roughness length.</p>

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Incorporating Building-Height Distributions into Roughness Length Calculations for Urban Environments

  • 期刊论文

  • 发表日期：

    2026年5月25日

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  • Liao Zhou,
  • Ning Zhang,
  • Xin Shao,
  • Dahu Yang,
  • Yong Sun

摘要

Numerical modelling is an important method for the investigation of urbanization effect on weather and climate. Single-layer urban canopy models (SLUCMs) are most widely used in numerical models, such as WRF and CESM to represent the momentum and heat exchange between urban land surface and the atmosphere. Within SLUCMs, the bulk momentum roughness length constitutes a fundamental parameter that regulates the fluxes exchange between the urban canopy and the atmosphere and thus exerts a substantial influence on overall simulation. The roughness length is typically estimated using morphological approaches, yet commonly adopted formulations omit building-height heterogeneity, leading to a systematic underestimation. To address this issue, this study develops an improved algorithm by incorporating the probability density function of building heights (PDF(h)) into an existing morphological framework. An exponential approximation method is further proposed to simplify the formulation while preserving physical interpretability. Large-eddy simulations are used to evaluate the new scheme and the results demonstrate that the exponential approximation method achieves the best agreement with reference values, reducing the mean relative error from − 73.6% (conventional formulations) to 11.2% and the root mean square error from 5.83 to 2.23 m. The PDF(h)-based method shows moderate performance, which tends to overestimate roughness length by ~ 38.1% on average. These results highlight that incorporating the statistical characteristics of building-height distributions—particularly through exponential approximation—can substantially improve the accuracy of urban roughness length.