Effects of Urban Surface Roughness on Potential Sources of Microplastics in the Atmospheric Boundary Layer

Abstract

Understanding the local transport of microplastics (MPs) emitted from the urban environment, such as those from vehicle tire wearing in streets and highways, is a necessary first step for quantifying their global transport cycle. By approximating microplastics as heavy particles, we conduct numerical simulations using large-eddy simulations (LESs) to understand how spatially organized sources and complex urban surface roughness affect their transport. Three sets of cases are considered, namely: (i) spatially uniform source and (ii) spatially organized source, and (iii) spatially organized source with explicitly resolved roughness elements, respectively. Results suggest that for a spatially organized source without buildings, source heterogeneity in streamwise direction only influences the vertical concentration profile up to $z/L_z=0.11$. In contrast, that in spanwise direction influences the profile till $z/L_z=0.58$, where z and $L_z$ are the vertical coordinate and the domain height, respectively. Simulations with buildings reveal that the buildings impede the transport of particles and particles accumulate on the leeward side of the buildings, which are characterized by wake turbulence and relatively quiescent flow. Within the canopy sub-layer, the gravitational settling effect of the particles becomes more significant because of the reduced wind. Because of that, the escape fraction of particles is smaller than in cases with no buildings and it decreases with increasing building height h and increasing building plan area fraction $\lambda _p$. Finally, by finding suitable scalar displacement height $d_s$ and scalar roughness length $z_{os}$, we find that similar to a passive scalar, an inertial sub-layer (ISL) still exists for heavy particles. This study highlights that for spatially organized particle sources, the momentum sinks due to urban roughness and the gravitational settling jointly affect the transport of heavy particles, which implies that the surface heterogeneity effect can be substantial in quantifying the atmospheric transport of microplastics of urban origins.

Appendices

Appendix 1: Particle Wall Model

A particle wall model derived from the Kind model in Kind (1992) is applied to calculate dC/dz at the first level of grid above the ground at $z=dz/2$. The analytical solution of vertical particle concentration is given by Eq. 3. We take the reference height $z_r$ as the roughness length $z_0$ and $C_r$ is equal to the concentration at $z=z_0$. Time $C_r$ to both sides of Eq. 3, and then do a z derivative, we get:

$$\begin{aligned} \frac{dC}{dz} = \left( \frac{\phi _{net}}{w_s}+C_r\right) \left( \frac{z}{z_0}\right) ^{-\gamma _{local}-1}\left( \frac{-\gamma _{local}}{z_0}\right) . \end{aligned}$$

(14)

Here, $\gamma _{local}$ is calculated according to the local $u_*^{local}$ as shown in Eq. 11. From Eq. 3, we can also get:

$$\begin{aligned} \frac{\phi _{net}}{w_s}+C_r = \left( C+\frac{\phi _{net}}{w_s}\right) \left( \frac{z}{z_0}\right) ^{\gamma _{local}}. \end{aligned}$$

(15)

By substituting $\frac{\phi _{net}}{w_s}+C_r$ in Eq. 15 into Eq. 14, and selecting $z=dz/2$ which is the first level of grid, we have:

$$\begin{aligned} \frac{dC}{dz}\arrowvert _{z=dz/2} = \frac{-\gamma _{local}}{dz/2}\left( \frac{\phi _{net}\arrowvert _{z=dz/2}}{w_s}+C\arrowvert _{z=dz/2}\right) . \end{aligned}$$

(16)

Below $z=dz/2$ where LES cannot resolve, we assume that:

$$\begin{aligned} \phi _{net}\arrowvert _{z=dz/2} = \phi _{emi}+\phi _{dep}\arrowvert _{z=dz/2}=\phi _{emi}-w_sC\arrowvert _{z=dz/2}, \end{aligned}$$

(17)

where $\phi _{emi}$ and $\phi _{dep}$ are the emission and deposition flux of the particle, respectively (both positive upwards). Thus, Eq. 16 can be rewritten as follows:

$$\begin{aligned} \frac{dC}{dz}\arrowvert _{z=dz/2} = \frac{-\gamma _{local}}{dz/2}\left( \frac{\phi _{emi}-w_sC\arrowvert _{z=dz/2}}{w_s}+C\arrowvert _{z=dz/2}\right) =\frac{-\gamma _{local}}{dz/2}\left( \frac{\phi _{emi}\arrowvert _{z=dz/2}}{w_s}\right) . \end{aligned}$$

(18)

Appendix 2: Sensitivity Test of the RMSE of the Fitted Aerodynamic Parameters to the Choice of the ISL Range

The impacts of the choice of the ISL range to the RMSE for both velocity and concentration are explored in Figs. 18 and 19. The lower and upper boundaries of ISL are varied from the building top h to 1.875h and from 1.875h to 2.75h, respectively. And the minimum ISL height is set to be 0.875h. It is seen that both $RMSE_m$ and $RMSE_s$ are small within the choice of ISL range. Thus, the conclusions of the paper are deemed robust to uncertainties in the identification of the ISL range.