## 3 Results and Discussion
### Spatial-Temporal Distribution Characteristics Analysis
#### 3.1.2 Temporal Distribution Characteristics of Pavement Runoff Pollutants  
Ten samples collected in Site 1 are shown in Figure 7. Visually, the turbidity highly related to the concentration of SS declining with the extension of rainfall duration.  
To better understand the temporal distribution characteristics of pavement runoff pollutants, different elementary functions were adopted to fit the water quality analysis data.  
The natural logarithmic function, shown in Formula (1), was found to fit the cumulative concentration of different pollutants quite well. In the formula, \(C_{c}\) represents the cumulative concentration of different pollutants. \(t\) represents the time point of sampling. \(a\) and \(b\) are the coefficient and constant, respectively. The fitting results for different pollutants at four sites are listed in Table 5.  
\[C_{c}=a\cdot\ln\left(t\right)+b \tag{1}\]  
Taking SS as an example, the correlation curve between time and concentration of SS is plotted in Figure 8.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Items**} & \multicolumn{3}{c}{**Fitting Results**} & \multirow{2}{*}{**R2**} & \multirow{2}{*}{**Items**} & \multicolumn{3}{c}{**Fitting Results**} & \multirow{2}{*}{**R2**} \\ \cline{3-3} \cline{5-10}  & & **a** & & & & **a** & & **b** \\ \hline \multirow{4}{*}{SS} & Site 1 & 1057.20 & 435.25 & 0.95 & & Site 1 & 9.4321 & 5.9133 & 0.99 \\  & Site 2 & 404.07 & 588.65 & 0.95 & & Site 2 & 2.8734 & 4.0392 & 0.94 \\  & Site 3 & 1424.6 & 1054.2 & 0.94 & & Site 3 & 5.2462 & 5.3276 & 0.98 \\  & Site 4 & 578.43 & 636.31 & 0.99 & & Site 4 & 1.4852 & 2.5092 & 0.92 \\ \hline \multirow{4}{*}{Pb} & Site 1 & 3.0108 & \(-\)0.0563 & 0.96 & & & Site 1 & 19.384 & 7.7671 & 0.98 \\  & Site 2 & 0.9459 & 0.1947 & 0.97 & & & Site 2 & 6.305 & 4.1668 & 0.98 \\  & Site 3 & 0.9987 & 0.5371 & 0.98 & & & Site 3 & 13.679 & 7.9176 & 0.99 \\  & Site 4 & 0.7169 & 0.1681 & 0.95 & & & Site 4 & 8.6679 & 4.7657 & 0.99 \\ \hline \multirow{4}{*}{COD} & Site 1 & 1464.2 & \(-\)162.43 & 0.96 & & & Site 1 & 2.8676 & 1.5756 & 0.99 \\  & Site 2 & 1572.3 & \(-\)381.71 & 0.95 & & & Site 2 & 1.9779 & 0.7055 & 0.98 \\  & Site 3 & 1382.71 & \(-\)321.74 & 0.93 & & & Site 3 & 5.3052 & 3.5971 & 0.98 \\  & Site 4 & 1628.7 & \(-\)246.82 & 0.95 & & & Site 4 & 2.7355 & 1.5902 & 0.99 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The fitting results for different pollutants at four sites.  
Figure 7: Samples of pavement runoff.  
The increase of the natural logarithmic function proves the continuous input of pollutants during the entire rainfall event. Additionally, the curve increases sharply at the initial stage and then tends to gradually stabilize. This property is consistent with the first flush effect of rainfall events. The cumulative concentration reached a high level in a very short time and then ascended slowly due to the slight input of pollutants. Although the average concentrations of all pollutants are greater than the limitation in the standard, the real-time concentrations become lower and lower, up to a moment when the concentration was lower than the limitation value. This moment, \(t_{c}\), is defined as the critical time point, for pollution control of pavement runoff. Taking TN at Site 2 as an example, the concentration, 1.048 mg/L, meets the requirement of the standard 50 min after the formation of pavement runoff, which means that the critical time point is between 40 and 50 min. It is not necessary to process the TN in the pavement runoff after this point. However, the concentrations of most pollutants analyzed in this study were not lower than the limitation value within 60 min.