Diurnal Surface Heating and Roof Material Effects on Urban Pollution Dispersion: A Coupled Large-eddy Simulation and Surface Energy Balance Analysis

Abstract

We investigate the understudied role of diurnally variable urban surface heating in transport phenomena within an idealized urban environment. We also explore whether heating from different roof materials (asphalt, reflective, and green roofs) at different times of the day affects pollution dispersion and ventilation mechanisms. Results show that the ventilation capacity of urban canyons varies diurnally and is influenced by the buoyancy forces from differentially heated urban surfaces, indicating the highest values in the afternoon and the lowest in the evening. The mechanism of canyon ventilation also varies diurnally. In the morning, the pollutant outflux at the roof level is the principal route of ventilation, while in the evening, lateral outfluxes are dominant and pollutant escape at the roof level is damped because of a local stable air layer. In the afternoon, both vertical and horizontal pollutant outflows contribute similarly to the canyon ventilation. In general, lateral turbulent (rather than mean) fluxes from the side canyon boundaries are the main contributors to the canyon pollutant ventilation throughout the day for all roof-type cases, but their significance slightly decreases from morning to evening. Results reveal that different roof types influence the canyon ventilation mechanism and capacity based on their diurnally-varying surface temperatures and their temperature gradients with respect to other urban surfaces. The existence of the green roof type mainly leads to the generation of a local stable layer and suppression of pollutant escape at the roof level.

Appendices

Appendix 1: The Green Roof Model

The green roof model used in this study is a quasi-steady-state heat and mass transfer model that has been fully validated with laboratory and field experimental data (Tabares-Velasco and Srebric 2012; Tabares-Velasco et al. 2012).

A typical green roof consists of five layers: starting from the top, they are (1) the vegetation layer, (2) the substrate layer (moisture-retaining soil-like layer to support the plant growth), (3) a filter membrane, (4) a drainage layer, and lastly, (5) a root resistance layer. To calculate the temperature of the plant and substrate layers, the energy balance equations for these layers are solved iteratively by Newton’s method. These equations are (Tabares-Velasco and Srebric 2012)

$${R}_{sh,abs,plants}={Q}_{film,plants}+{Q}_{IR,S,P},$$

(3)

$${R}_{sh,abs,substrate}={-Q}_{IR,S,P}+{Q}_{S,S}+{Q}_{conduction}+{Q}_{IR,subs,cov,sky}+{Q}_{E},$$

(4)

where in Eq. 3, ${R}_{sh,abs,plants}$(W m⁻²) is the absorbed solar radiation by the plants, ${Q}_{film,plants}$(W m⁻²) is the heat losses to the surrounding air (through transpiration (${Q}_{T}$), convection (${Q}_{convection, plants}$), and radiation (${Q}_{IR,plants,sky}$)),${Q}_{IR,S,P}$ is the longwave radiative heat transfer between the plant and the top substrate layer. In Eq. 4, ${R}_{sh,abs,substrate}$ (W m⁻²), is the absorbed solar radiation by the substrate, ${Q}_{S,S}$ (W m⁻²) is the substrate-air convective heat transfer, ${Q}_{conduction}$ (W m⁻²) is the conduction through the substrate, ${Q}_{IR,subs,cov,sky}$ is the radiative exchange between the substrate and sky, and ${Q}_{E}$ (W m⁻²) is the substrate evaporation. The equations used for each of the terms, representing radiation, convection, evaporation, transpiration, and conduction are described below.

1.1 Radiation

The absorbed solar radiation by the plants and substrate layers are given by the following equations:

$${R}_{sh,abs,plants}=\left(1-{\rho }_{plants}-{\tau }_{plants, solar}\right) \left(1+{{\tau }_{plants,solar} \rho }_{substrate}\right) {R}_{sh},$$

(5)

$${R}_{sh,abs,substrate}={\tau }_{plants, solar} \left(1-{\rho }_{substrate}\right){R}_{sh}.$$

(6)

Here, ${\rho }_{plants}$ and ${\rho }_{substrate}$ are the plant and substrate reflectivities, ${\tau }_{plants, solar }(={\text{e}}^{-{k}_{s }LAI})$ is the shortwave transmittance of the plant canopy, where ${k}_{s}$ is the extinction coefficient and $LAI$ is the leaf area index, and ${R}_{sh}$ is the shortwave radiation received on the surface.

Thermal radiation between plants and the substrate (${Q}_{IR,S,P}$), between the substrate and the sky (${Q}_{IR,subs,cov,sky}$), and between plants and the sky (${Q}_{IR,plants,sky}$) is calculated using the following equations

$${Q}_{IR,S,P}=\left(1-{\tau }_{plants,IR}\right)\frac{\sigma ({T}_{plants}^{4}-{T}_{top,substrate}^{4})}{\frac{1}{{\varepsilon }_{substrate}}+\frac{1}{{\varepsilon }_{plants}}-1},$$

(7)

$${Q}_{IR,subs,cov,sky}={\tau }_{plants,IR}{ \varepsilon }_{substrate }\sigma \left({T}_{plants}^{4}-{T}_{sky}^{4}\right),$$

(8)

$${Q}_{IR,plants,sky}={(1-\tau }_{plants,IR}) {\varepsilon }_{plants} \sigma \left({T}_{plants}^{4}-{T}_{sky}^{4}\right),$$

(9)

where $\sigma$ is the Stefan–Boltzmann constant (= 5.64 × 10^–8 W m⁻² K⁻⁴), ${\tau }_{plants, IR }(={e}^{-{k}_{s} LAI})$ is the transmittance of the thermal radiation that is not intercepted by any leaf (uses a different ${k}_{s}$ than that in ${\tau }_{plants, solar}$), ${\varepsilon }_{plants}$ is the plant emissivity, ${\varepsilon }_{substrate}$ is the substrate emissivity, and ${T}_{plants}$, ${T}_{top,substrate}$ and ${T}_{sky}$ are the plant, substrate, and sky temperatures respectively.

1.2 Convective Heat Transfer

The sensible heat flux between the plants and air (${Q}_{convection, plants}$), and between the substrate and air (${Q}_{convection, substrate,cov}={Q}_{S,S}$) are determined based on the following equations

$${Q}_{convection, plants}=\beta LAI {h}_{conv} \left({T}_{plants}-{T}_{air}\right),$$

(10)

$${Q}_{convection, substrate,cov}={h}_{sub }\left({T}_{substrate,top}-{T}_{air}\right),$$

(11)

$${h}_{sub}={h}_{por}{ h}_{conv}/({h}_{por}+{h}_{conv}),$$

(12)

where $\beta$ is the green roof roughness; ${h}_{conv}$ (W m⁻² K⁻¹) is based on the Nusselt number for forced, mixed, and natural convection on a flat surface; ${h}_{sub}$ is the convective coefficient for the green roof substrate covered by plants; and ${h}_{por}$ is the convection coefficient for porous media that takes sheltering and roughness effects of the plant layer into account. More details can be found in Tabares-Velasco and Srebric (2012).

1.3 Evapotranspiration

The substrate evaporation (${Q}_{E})$ depends on the vapour pressure differences of the soil and air, as well as the wind speed and is calculated based on Eq. 13, while plant transpiration (${Q}_{T})$ is calculated using Eq. 14

$${Q}_{E}=\frac{{\rho C}_{p}}{\gamma ({r}_{substrate}+{r}_{a})}\left({e}_{soil}-{e}_{air}\right),$$

(13)

$${Q}_{T}=LAI\frac{{\rho C}_{p}}{\gamma ({r}_{s}+{r}_{a})}\left({e}_{s,plants}-{e}_{air}\right).$$

(14)

Here, $\rho$ (kg m⁻³) and ${C}_{p}$ (J kg⁻¹ K⁻¹) are the density and specific heat of air, ${e}_{soil}$ (kPa) is the saturated vapour pressure at the soil/substrate temperature, ${e}_{air}$ (kPa) is the vapour pressure in the air, and ${e}_{s,plants}$ (kPa) is the vapour pressure of air in contact with plants, $\gamma (={C}_{p}P/0.622{ i}_{fg})$ is the psychrometric constant (in which ${i}_{fg}$ is the enthalpy of vapourization and $P$ is the atmospheric pressure),${r}_{a}$ is the aerodynamic resistance to mass transfer, ${r}_{s}$ is the stomatal resistance, and ${r}_{substrate}(=34.5{\left(\frac{VWC}{{VWC}_{sat}}\right)}^{-3.3})$ is the substrate surface resistance to mass transfer that depends on the average substrate volumetric water content (VWC) and the substrate volumetric water content at saturation (${VWC}_{sat}$). The stomatal resistance is calculated using

$${r}_{s}=\frac{{r}_{stomatal,min}}{LAI}{f}_{solar} {f}_{VPD} {f}_{VWC} {f}_{Temperature},$$

(15)

where, ${f}_{solar}$, ${f}_{VPD}$, ${f}_{VWC}$, and ${f}_{Temperature}$ are empirical functions, respectively, representing the roles of solar radiation, vapour pressure deficit, water content, and temperature in the stomal resistance. More details can be found in Tabares-Velasco and Srebric (2012).

1.4 Conductive Heat Flux

Conduction through the substrate layer is given by

$${Q}_{conduction}={k}_{substrate}\frac{{T}_{top,substrate}-{T}_{bottom,substrate}}{{L}_{substrate}},$$

(16)

$${k}_{substrate}={a}_{1}+{a}_{2} VWC,$$

(17)

where ${k}_{substrate}$ (W m⁻² K⁻¹) is the substrate conductivity, ${L}_{substrate}$ (m) is the substrate depth, and ${a}_{1}$(= 0.17) and ${a}_{2}$(= 0.37) are the substrate thermal conductivity coefficients.

Appendix 2: Physical, Thermal, and Radiative Properties of Building Walls, Ground, and Green Roof

See Tables

Table 3 Building and ground material thickness, and thermal and radiative properties by layer (based on Table 1 of Yaghoobian and Kleissl 2012b)

3 and

Table 4 Information of the green roof soil and plant canopy (based on Table 3 of Yaghoobian and Srebric 2015 that follows the construction assembly of an extensive type green roof installed on a commercial building in Chicago, IL (Tabares-Velasco et al. 2012; Zhao et al. 2014))

4.