A One-Dimensional Model of Turbulent Flow Through ‘Urban' Canopies: Updates Based on Large-Eddy Simulation

Mesoscale meteorology is of particular interest for urban climate analysis: many weather phenomena that directly impact human activities occur at this scale; and the effects of urban roughness, heat, pollutant, and moisture on the atmospheric boundary layer (characterized as Urban Boundary Layer) have important mesoscale implications. Accordingly, mesoscale modeling is a powerful tool for analysis of urban climate and dispersion. Given contemporary computational resources, however, it is not feasible to have a high resolution that explicitly resolves building shapes (O(1-100m)), and at the same time spans a domain large enough to assess synoptic and mesoscale impacts on the UBL (O(10-100km)). Therefore, mesoscale models must parameterize the subgrid-scale exchanges of momentum, pollutant, moisture and heat across the Urban Canopy Layer (UCL) and Urban Boundary Layer (UBL) interface.

Urban canopy flow is typically parameterized in terms of the horizontally-averaged (1-D) flow and scalar-transport, and these parameterizations can be informed by computational fluid dynamics (CFD) simulations of urban micrometeorology. For instance, Santiago and Martilli (2010) employed RANS simulations to derive vertical profiles of turbulent length scale and drag coefficient as a function of built density, and parameterized a 1-D turbulent flow model for urban areas. However, when compared to wind tunnel experiments and Large Eddy Simulations, RANS models can fall short in accurately representing turbulent flow field in the urban roughness sublayer.  Additionally, Krayenhoff (2014, PhD thesis) observed that the 1D model of Santiago and Martilli (2010) contributed to underestimation of the venting in UCL, and the discrepancy has been traced to turbulent length scales derived from the RANS simulations. With these new findings, and considering the recent advancements in the high-performance computing, we revisit these parameterizations with a more accurate flow model.

In this study, we aim to update the parameterization of turbulent length scale and drag coefficient in the one-dimensional model of turbulent flow through urban areas developed by Santiago and Martilli (2010). PArallelized Large-Eddy Simulation Model (PALM) is used and a series of simulations in an idealized urban configuration with aligned and staggered arrays are considered. Plan area density is varied in both configurations to span a wide range of urban density (from sparsely developed to compact midrise neighbourhoods). In order to ensure the accuracy of simulation results, we rigorously evaluate PALM by comparing the vertical profiles of turbulent kinetic energy and Reynolds stresses with wind tunnel experiment data (Brown et al. 2001), as well as other available LES studies (Kanda et al. 2004). Vertical profiles of turbulent kinetic energy and associated turbulent length scales obtained from LES are substantially larger than in RANS results (especially in the urban canopy), and the 1-D parameterization is updated accordingly.  

After implementing the updated drag coefficients and turbulent length scales in the 1-D model of urban canopy flow, we evaluate the results by a) testing the 1-D model against the original LES results, and demonstrating the differences in predictions between new (derived from LES) and old (derived from RANS) versions of the 1-D model, and more importantly, b) testing the 1-D model against LES results for real geometries (e.g., Giometto et al. 2016). Results suggest a more accurate prediction of vertical turbulent exchange in urban canopies, and consequently an improved prediction of urban heat and pollutant dispersion at the mesoscale.

References:

_{[1] Santiago, J. L., and Martilli. A. "A dynamic urban canopy parameterization for mesoscale models based on computational fluid dynamics Reynolds-averaged Navier–Stokes microscale simulations." Boundary-layer meteorology 137.3 (2010): 417-439.}

_{[2] Krayenhoff, E. S. “A multi-layer urban canopy model for neighbourhoods with trees.” Diss. University of British Columbia, (2014).}

_{[3] Brown, M. J., Lawson, R. E., DeCroix, D. S., and Lee, R. L. "Comparison of centerline velocity measurements obtained around 2D and 3D building arrays in a wind tunnel." Int. Soc. Environ. Hydraulics, Tempe, AZ (2001).}

_{[4] Kanda, M., Moriwaki, R.  and Kasamatsu. F. "Large-eddy simulation of turbulent organized structures within and above explicitly resolved cube arrays." Boundary-Layer Meteorology 112.2 (2004): 343-368.}

_{[5] Giometto, M. G., Christen, A., Meneveau, C., Fang, J., Krafczyk, M., and Parlange, M. B. "Spatial Characteristics of Roughness Sublayer Mean Flow and Turbulence Over a Realistic Urban Surface." Boundary-Layer Meteorology (2016): 1-28.}