In mesoscale climate models, 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 the urban climate at the microscale. Reynolds averaged Navier–Stokes simulation (RANS) models have previously been employed to derive vertical profiles of turbulent length scale and drag coefficient for such parameterization. However, there is substantial evidence that RANS models fall short in accurately representing turbulent flow fields in the urban roughness sublayer.
When compared with more accurate flow modeling such as large-eddy simulations (LES), we observed that vertical profiles of turbulent kinetic energy and associated turbulent length scales obtained from RANS models are substantially smaller specifically in the urban canopy. Accordingly, using LES results, we revisited the urban canopy parameterizations employed in the one-dimensional model of turbulent flow through urban areas and updated the parameterization of turbulent length scale and drag coefficient. Additionally, we included the parameterization of the dispersive stress, previously neglected in the 1-D column model. For this objective, the 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. The plan area density (

Schematic of urban canopy parameterization (UCP) in multi-layer column models at mesoscale.

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 the analysis of urban climate and further prediction and management of urban heat and pollution.

In mesoscale models, urban climate variables on timescales of hours to days depend on multiple spatial scales from the street scale to synoptic scales. Given contemporary computational resources, however, it is not feasible to explicitly resolves building shapes (O(1–100 m)) and at the same time span a domain large enough to assess mesoscale impacts on the urban boundary layer (UBL; O(10–100 km)). Therefore, mesoscale models must parameterize the subgrid-scale exchanges of momentum, pollutant, moisture, and heat across the urban canopy layer (UCL) and UBL interface (Fig.

These “subgrid”-scale urban processes may be classified as hydrodynamic (flow) or thermal (e.g., radiation, convection, conduction). In the case of the former (focus of this study), the flow near the surface is being treated with approaches of varying complexity. The simplest and oldest is the bulk transfer approach, with the Monin–Obukhov similarity theory

In the past 2 decades, urban canopy models (UCMs) have been developed to approximate the flow and thermal exchanges within and above neighborhoods and to couple with mesoscale models. Single-layer UCMs

The combined multi-layer urban canopy model, called BEP-Tree

In this study, we aim to investigate the factors contributing to the underestimation of vertical exchange of heat and momentum in the multi-layer column model. We hypothesize that the following factors may be responsible:

Flow chart of the present study. Three-dimensional LES simulations are performed and vigorously tested in an idealized configuration of buildings. Then, using the spatially averaged profiles, urban canopy parameterizations of the multi-layer (column) model are revisited. The updated multi-layer (1-D) model is then evaluated against the UCPs in

Considering that (a) the underestimation of vertical exchange of momentum is also seen in neutral cases and (b) the height variability in the Sunset neighborhood in Vancouver, which was used in

Figure

The momentum equation in mesoscale models undergoes two averaging processes

Accordingly, the first term on the right-hand side (RHS) of Eq. (

To parameterize the contribution of the spatially averaged turbulent momentum flux (first RHS term in Eq.

Plan view of configurations used for LES analyses, representing “staggered”

To calculate the spatially averaged TKE in Eq. (

Accordingly, to solve prognostic Eqs. (

Additionally, analogous to the momentum equation, the source term of TKE due to the conversion of mean kinetic energy into turbulent kinetic energy by the presence of buildings is parameterized as

The LES results are used as a superior method to RANS models for evaluating turbulence characteristics and dispersion behavior in urban canopies

A series of neutral simulations is considered for idealized urban-like configurations with aligned (Fig.

The flow is driven by a pressure gradient of magnitude

The PALM model is widely used and has been validated against various experimental measurements

Comparison of the TKE profile at the center of the canyon with experimental results of

Second, in order to ensure the accuracy of our LES analysis, the choice of simulation setups is rigorously evaluated here, and a series of sensitivity analyses are performed to compare the profiles (time- and ensemble-averaged) of mean flow, TKE, and velocity covariances based on the (1) geometrical configuration (size and height of the domain), (2) grid resolution, and (3) run time parameters (spin-up time, sampling frequency, and time-averaging interval).

We find the domain height to be critical for both staggered and aligned arrays. The domain size of

Regarding the run time calculations, three main parameters are evaluated. First the volume-averaged results are monitored throughout the runs, and the spin-up time (i.e., the initial time interval that is discarded in the subsequent analysis) is chosen to be 3 h, corresponding to 125 eddy turnover time (

Vertical profiles of spatially averaged velocity

Vertical profiles of normalized velocity

Figure

Another investigation made here is regarding the significance of dispersive fluxes in urban canopy parameterizations. In the formulation of the multi-layer urban canopy model, the dispersive transport processes are neglected so far

It is known that the sectional drag coefficient depends on the packing density and the configuration of the array with a strong dependency on height, such that

Variation of

In this section, the length scales obtained from the spatially averaged LES results and the

To assess the dissipation length scale

Three different zones are then defined consistent with

Comparing the turbulent (

Variation in normalized dissipation length scale (

The drag coefficient and length scales (Sect.

Figure

Comparison of the vertical profiles of velocity

Figure

Root mean square error calculated for vertical profiles of velocity (

Lastly, the 1-D multi-layer model is compared with the LES results of

Comparison of vertical profile of velocity

The present study focused on updating the urban canopy parameterizations of drag coefficient and turbulent length scales using large-eddy simulations (LES) results, which is shown to be a superior numerical model for resolving the turbulent flow field compared to Reynolds-averaged Navier Stokes (RANS) previously used in multi-layer UCMs

The detailed analyses of the spatially averaged turbulent field in urban configurations revealed the following: (1) LES results exhibit a significantly higher transport of TKE into the lower canopy compared to RANS; (2) dispersive fluxes are not negligible in the urban canopy, particularly in higher urban packing densities; and (3) the ratio between turbulent and dispersive length scale (commonly described by the model constant

We demonstrated that using LES results as the basis for parameterization, as well as the inclusion of dispersive stress, improves the performance of the multi-layer model, such that spatially averaged profiles of flow, and consequently the turbulent exchange in the urban canopy in realistic neighborhoods, can be predicted more accurately. Additionally, when the updated parameterizations were used in the BEP-Tree model

However, spatially averaged turbulent kinetic energy,

Further analysis is also needed to fully evaluate the effects of idealized configurations in parameterizations and assess the impact of variable building heights and wind directions on turbulent length scales and drag parameterization.

The source code and the supporting data of the updated 1-D Multi-layer Urban Canopy Model (MLUCM v2.0) are publicly available at

NN, ESK, and AM collectively developed and planned the study. AM developed the initial one-dimensional vertical diffusion model, and ESK and AM have continued the parameterization of the 1-D model to include radiation and trees. NN ran the large-eddy simulations and modified the model based on the updated parameterizations of length scales. NN carried out the result analyses and wrote the paper with significant input and critical feedback from ESK and AM.

The authors declare that they have no conflict of interest.

Negin Nazarian acknowledges the support received from the National Research Foundation Singapore under its Campus for Research Excellence and Technological Enterprise program in the initial phases of this analysis. The authors thank Marco Giometto (Columbia University) for discussions throughout the paper and sharing the LES data of realistic configurations and acknowledge discussions with Andreas Christen (Uni Freiburg) and Andres Simon-Moral (NUS).

This research has been supported by the NSF Sustainability Research Network Cooperative Agreement 1444758 and NSF SES-1520803, as well as an NSERC Discovery grant.

This paper was edited by Augustin Colette and reviewed by two anonymous referees.