## 3 Results and Discussion
### Spatial Variations of Air Pollutants
#### 3.4.3 Spatial and Temporal Variability of Air Pollutants  
The concentrations of traffic-related air pollutants vary significantly in space and time due to the proximity of emission sources [10; 21; 29]. These spatial and temporal variations can be strongly affected by the surrounding built environment, surface meteorology within the urban-canopy, and emission strengths (e.g., traffic flow rates and fleet composition) [10]. Here, we define the spatial variability of pollutant levels among sub-sites as spatial heterogeneity and the spatial variability of temporal variations as temporal heterogeneity. To quantitatively determine the spatial and temporal heterogeneity of air pollutants in various micro-environments (Sites-1-4), two statistics were calculated: Pearson's correlation coefficient (R) for temporal heterogeneity and the coefficient of divergence (COD) for spatial heterogeneity. Figure 7: Horizontal box plots of the vertical distributions of pollutants at Site-1. The vertical dotted line in the box represents the mean value. (**a**–**d**): summer, (**e**–**h**): cold wave period of winter, and (**i**–**l**): the PM\({}_{2.5}\) pollution event. Ozone data were used only for the period of 11:00–17:00. The COD is widely used as a measure of spatial heterogeneity between a pair of simultaneously obtained time-series (Equation (1)) [30; 31; 32]. \[\text{COD}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(\frac{x_{if}-x_{ih}}{x_{if}+x_{ih} }\right)^{2}}, \tag{1}\]  
where \(n\) is the number of data points, \(f\) and \(h\) are the two observation sites to be compared, and \(x\) is the concentration. A COD value of zero means that the two time-series are perfectly homogeneous, and a COD value \(>0.2\) indicates a spatially heterogeneous distribution [31; 32]. To simultaneously probe the extent of spatial and temporal heterogeneity in air pollutant distributions at each sub-site, we plotted COD vs. R for all sensor locations with respect to the location of sensor-node nearest to AQMS at Site-4 (Figures 1 and S1) where the traffic was minimal (Figure 8). In the plot, the upper left quadrant (I) represents spatially and temporally heterogeneous distributions, the upper right quadrant (II) represents spatially heterogeneous but temporally homogeneous distributions, and the lower right quadrant (IV) represents spatially and temporally homogeneous distributions. For temporal heterogeneity, we arbitrarily chose the criterion value of R = 0.7 (corresponding to an R\({}^{2}\) value of \(\sim\)0.5). Generally, O\({}_{3}\) and NO\({}_{2}\) displayed the largest spatial and temporal heterogeneity among the sub-sites, followed by CO. This heterogeneity was enhanced during daytime when traffic activity was high compared to the nighttime, as reflected in the diurnal variations (Section 3.3.2), whereas PM\({}_{2.5}\) had a homogeneous distribution within the monitoring domain in the summer (Figure 8a). These large variabilities were significantly reduced in winter (Figure 8a vs. Figure 8b). However, when the cold wave period was examined separately, NO\({}_{2}\) and O\({}_{3}\) still had spatially heterogeneous distributions in the daytime (with a reduced extent compared to the summer period), but the nighttime spatial and temporal distributions were homogeneous due to the lower traffic emissions. The spatial and temporal distributions for PM\({}_{2.5}\) were homogeneous and similar to those of the summer period. For the polluted period, all pollutants displayed homogeneous distributions in time and space within the domain (COD \(<0.2\) or close to 0.2 for ozone; R \(\geq 0.7\) except for nighttime NO\({}_{2}\)), implying that the pollution event occurred at a much larger scale than this monitoring domain. The NO\({}_{2}\) was distributed homogeneously in space (COD \(<0.1\)) but the temporal homogeneity was somewhat weak, most likely because concentrations were maintained at a high level over the polluted period.