## 4 Discussion
### Degradation of Free Estrogen  
From the results in Figure 3 and Table 4, E1, E2 and E3 had significantly decreased over time. According to Equation (1), Figure 4 shows that the average estrogen concentration ratio ln (C\({}_{\text{n}}\)/C\({}_{0}\)) changed with time and displayed a linear regression for E1, E2, and E3. The linear regression was statistically tested and the results are listed in Table 5. For each site, the statistical results of ln (Cn/C0) changing with time are listed in Table 6. The linear regression of the average ln (C\({}_{\text{n}}\)/C\({}_{0}\)) over time had a statistically significant linear relationship (\(p\) = 0.006-0.001) for E1, E2 and E3 (Figure 4). Figure 4 shows that concentrations of free estrogen rapidly decreased during the initial 12 h period, but average concentrations were not further reduced between the 12 and 24 h period. Since the rapid concentration decreased in the initial 12 h, it suggested that the microbial population had adapted to the river water environment. Thus, microbes can effectively degrade the relatively high concentrations of free estrogen in the river. Because estrogen concentrations were not further degraded during the 12 to 24 h period, the degradation rate constants were taken from regression data of concentration degradation during 0-12 h. The E1 first-order rate constants (k) were between 0.11 and 0.37 h\({}^{-1}\) (Table 6), and the k value was 0.154 h\({}^{-1}\) for the average concentration of the six stations (Table 5). The E2 rate constants were between 0.01 and 0.08 h\({}^{-1}\), and the k value was 0.034 h\({}^{-1}\) for the average concentration of the six stations. The E3 rate constants were between 0.04 and 0.16 h\({}^{-1}\), and the k value was 0.102 h\({}^{-1}\) for the average concentration of 5 stations. The slopes of the average concentration of the three free estrogens are shown in Figure 4. The E1 half-lives (T\({}_{1/2}\)) ranged from 1.9 to 6.5 h, and the average half-life was 4.5 h. The E2 half-lives ranged from 8.6 to 49.5 h, and the average half-life was 20.4 h. The E3 half-lives ranged from 4.3 to 18.8 h, and the average half-life was 6.8 h. Figure 5 shows a box-plot of half-life for the free estrogens E1, E2, and E3, and the figure also shows the median half-life values were 4.4, 27.0 and 8.6 h for E1, E2, E3, respectively. The T\({}_{1/2}\) values of the average and the median half-lives were very close for the free estrogens. Compared to laboratory experiments, the field was more complex, and many factors can affect estrogen degradation in the environment [32]. A similar, previous review study on nonylphenol microbial degradation from contaminated environments showed that the k value had significant variation from 0.02 to 0.8 day\({}^{-1}\) at the different mediums of seawater, sediment, activated sludge, wastewater, and soil [32]. The estrogen half-life differs in the environment setting and depends on oxygen availability and degradation rate [1; 4; 48]. For estrogen soil research under aerobic microorganism degradation, the half-lives ranged \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & **E1** & & & **E2** & & & **E3** & \\ \hline
**Site** & **k (h\({}^{-1}\))** & **R\({}^{2}\)** & \(p\)** & **k (h\({}^{-1}\))** & **R\({}^{2}\)** & \(p\)** & **k (h\({}^{-1}\))** & **R\({}^{2}\)** & \(p\)** \\ \hline WL1 & 0.112 & 0.55 & 0.093 & 0.026 & 0.42 & 0.168 & 0.081 & 0.63 & 0.108 \\ WL2 & 0.251 & 0.96 & \textless{}0.001 & 0.051 & 0.56 & 0.087 & 0.092 & 0.77 & 0.051 \\ WL3 & 0.371 & 0.97 & \textless{}0.001 & 0.081 & 0.86 & 0.007 & 0.162 & 0.88 & 0.006 \\ WL4 & 0.107 & 0.45 & 0.142 & 0.014 & 0.13 & 0.486 & 0.072 & 0.76 & 0.023 \\ WL5 & 0.183 & 0.98 & \textless{}0.001 & 0.026 & 0.75 & 0.026 & 0.037 & 0.46 & 0.140 \\ WL6 & 0.138 & 0.71 & 0.035 & 0.025 & 0.27 & 0.286 & NA & NA & NA \\ \hline \hline \end{tabular}  
NA: Not available.  
\end{table} 
Table 6: The kinetic rates of degradation for free estrogens at sampling sites. from 2.8-4.9, 0.8-1.1, and 0.7-1.7 days for E1, E2, and E3, respectively [62].