# Air Quality Predictions through Mathematical Modeling for Iron Ore Mine Project
## 3 Methodology
### Air Quality Assessment
#### 3.3.3 Air Quality Modeling  
The ISCST3 model was deployed to assess the air quality impacts of mining operations. This model employs a Gaussian plume approach (Equation (1)), allowing for simultaneous consideration of various source types. The formula used for pollutant-concentration calculation is as follows:  
\[C_{(x,y,0,H)}=\frac{Q}{\pi u\sigma_{y}\sigma_{z}}\exp(-\frac{1}{2}\left(\frac{ y}{\sigma_{y}}\right)^{2})\text{ex}\left(-\frac{1}{2}\left(\frac{H}{\sigma_{z}} \right)^{2}\right) \tag{1}\]  
where \(C_{(x,y,0,H)}\) is the downwind concentration at ground level (g/m3), \(Q\) is the emission rate (g/s), \(\sigma_{y}\) and \(\sigma_{z}\) are the lateral dispersion and vertical dispersion parameters (m), \(u\) is the wind speed (m/s), \(y\) is the crosswind distance (m), and \(H\) is the effective stack height (m) (actual height + plume rise).  
This model employs a short-term area-source approach with numerical integration across upwind and crosswind directions of the Gaussian plume formula, allowing for the inclusion of point, area, line, or volume sources. This flexibility enables the model to account for diverse sources and their contributions to overall air quality by considering source characteristics, meteorological conditions, and plume dispersion patterns.  
Meteorological data of wind speed, direction, temperature rainfall, and relative humidity, recorded at one-hour intervals during the monitoring period by a continuous weather monitoring station, served as the model's input. Table 3 summarizes the distribution of stability classes observed during the pre-monsoon season in the study area. For extrapolating wind speed, the power law relationship was used to calculate wind speed at the stack level, ensuring an accurate estimation of wind conditions at the relevant height for pollutant-dispersion modeling [25]. The mixing-heights criterion from the Central Pollution Control Board (CPCB), India, was adopted in the model due to the absence of site-specific data [34; 35; 36]. This approach facilitates the simulation of a worst-case scenario based on typical pre-monsoon season variations in atmospheric mixing heights (see supplementary data). The complete modeling process of ISCST3 is explained in Figure 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Stability Class**} & \multicolumn{2}{c}{**Standard Deviation of Wind Direction Fluctuation (\(\sigma_{\pi}\)) in Degrees**} & \multirow{2}{*}{**Lateral Dispersion (\(\sigma_{y}\))**} & \multirow{2}{*}{**Vertical Dispersion (\(\sigma_{z}\))**} & **Frequency of Occurrence (\%)** \\ \hline A & \(>\)22.5 & \(0.22x(1+0.0001x)^{-0.5}\) & \(0.20x\) & \(8.33\) \\ B & 22.4–17.5 & \(0.16x(1+0.0001x)^{-0.5}\) & \(0.12x\) & \(8.33\) \\ C & 17.4–12.5 & \(0.11x(1+0.0001x)^{-0.5}\) & \(0.08x(1+0.0002x)^{0.5}\) & \(12.5\) \\ D & 12.4–7.5 & \(0.08x(1+0.0001x)^{-0.5}\) & \(0.06x(1+0.0015x)^{0.5}\) & \(25\) \\ E & 7.4–3.5 & \(0.06x(1+0.0001x)^{-0.5}\) & \(0.03x(1+0.0003x)^{-1}\) & \(16.67\) \\ F & \(<\)3.5 & \(0.04x(1+0.0001x)^{-0.5}\) & \(0.16x(1+0.0003x)^{-1}\) & \(29.17\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Stability classes for wind direction and dispersion parameters influencing the predicted pollutant concentrations for rural conditions and frequency of occurrence (%) in the pre-monsoon season in the study area.