## 2 Configuration and Pollutant Dispersion Modelling
### Governing Equations  
The PALM model system, an open-source software that simulates atmospheric and oceanic boundary layers, is used for the present simulations. The Navier-Stokes equations in a non-hydrostatic, filtered, and incompressible form under the Boussinesq approximation are solved. The basic equations for the conservation of mass, momentum, energy, and moisture are defined as:  
\[\frac{\partial u_{i}}{\partial x_{j}}=0 \tag{3}\]  
\[\frac{\partial u_{i}}{\partial t}=-\frac{\partial u_{i}u_{j}}{\partial x_{j}} -\varepsilon_{ijk}f_{j}u_{k}+\varepsilon_{i3j}f_{3}u_{g,j}-\frac{1}{\rho_{0}} \frac{\partial\pi^{*}}{\partial x_{i}}+g\frac{\theta_{v}-\langle\theta_{v} \rangle}{\langle\theta_{v}\rangle}\delta_{3}-\frac{\partial}{\partial x_{j} }\bigg{(}\overline{u^{\prime\prime}_{i}u^{\prime\prime}_{j}}-\frac{2}{3}e \delta_{ij}\bigg{)} \tag{4}\]  
\[\frac{\partial\theta}{\partial t}=-\frac{\partial u_{i}\beta}{\partial x_{j}} -\frac{\partial}{\partial x_{j}}\bigg{(}\overline{u^{\prime\prime}_{j}\theta^ {\prime\prime}}\bigg{)}-\frac{L_{v}}{C_{p}\Pi}\Psi_{qv} \tag{5}\]  
\[\frac{\partial q_{v}}{\partial t}=-\frac{\partial u_{i}q_{v}}{\partial x_{j}} -\frac{\partial}{\partial x_{j}}\bigg{(}\overline{u^{\prime\prime}_{j}q^{ \prime\prime}_{v}}\bigg{)}+\Psi_{qv} \tag{6}\]  
\[\frac{\partial s}{\partial t}=-\frac{\partial u_{j}s}{\partial x_{j}}-\frac{ \partial}{\partial x_{j}}\bigg{(}\overline{u^{\prime\prime}_{j}s^{\prime\prime }}\bigg{)}+\Psi_{s} \tag{7}\]  
where \(i,\ j,\ k\in\{1,\ 2,\ 3\}\), the components of the velocity \((u_{1}=u,\ u_{2}=v\) and \(u_{3}=w)\) are defined by the \(u_{i}\) variable at specific positions in the flow field \(\ x_{i}\), where \(\ x_{1}=x,\ \ x_{2}=y\) and \(x_{3}=z\), and \(t\) is time. \(q_{v}\) and \(s\) are the latent heat transfer and moisture, respectively. The gravitational acceleration is denoted by \(g\), the density of the dry air is defined by \(\rho_{0}\), and \(L_{v}\) is the latent heat of vaporization. The source term of the variable \(q_{v}\), is defined as \(\Psi_{q_{v}}\) and the sink term of the variable \(s\) is defined as \(\Psi_{s}\). The angle brackets correspond to the horizontal averages of the flow field and the double prime indicated the subgrid-scale variables.  
The subgrid-scale turbulence kinetic energy is defined as:  
\[e=\frac{1}{2}\bigg{(}\overline{u^{\prime\prime}_{i}u^{\prime\prime}_{i}}\bigg{)} \tag{8}\]  
The modified perturbation pressure based on the perturbation pressure \(p^{*}\) is defined as:  
\[\pi^{*}=p^{*}+\frac{2}{3}\rho_{0}e \tag{9}\]  
The potential temperature is defined from the equation:  
\[\theta=\frac{T}{\Pi} \tag{10}\]  
where \(T\) is the instantaneous absolute temperature and the Exner function is calculated by the equation:  
\[\Pi=\bigg{(}\frac{p}{p_{0}}\bigg{)}^{\frac{g_{d}}{C_{p}}} \tag{11}\]where \(p\) is the hydrostatic pressure of the air, \(p_{0}=1000\) hPa is the reference pressure, \(R_{d}\) is the specific gas constant for dry air, and \(C_{p}\) is the specific heat capacity under constant pressure.  
The virtual potential temperature is defined by the equation:  
\[\theta_{v}=\theta\bigg{[}1+q_{v}\bigg{(}\frac{R_{v}}{R_{d}}-1\bigg{)}-q_{l} \bigg{]} \tag{12}\]  
where \(R_{v}\) is the specific gas constant for water vapors, and \(q_{l}\) is the liquid water mixing ratio.