## 2 Model Description
### Model Approaches  
The major governing equations solved in the TKM are the same as those described in the previous study [10]. The symbols and subscripts have, in general, the same meanings, but now the subscript \(i\) denotes species NO, O\({}_{3}\), NO\({}_{2}\), RH, HO\({}_{2}\), and OH, and subscript \(j\) denotes the partner of species \(i\) for chemical reactions detailed in Table 1 (e.g., for \(NO\) in a reaction, \(R_{3}\), \(i\) = NO and \(j\) = O\({}_{3}\)). Similarly, the source, sink and reaction rate terms are formulated to account for surface sources of NO and RH, dry deposition removal of species, entrainment of species from the free troposphere above the CBL, and the reactions listed in Table 1. The overall effective reaction rate (\(\mathrm{ppb\cdot s^{-1}}\)) for species \(i\) is  
\[\overline{R}_{e_{i}}=\sum R_{k} \tag{4}\]  
where \(R_{k}\) represents an individual reaction and subscript \(k\) denotes reaction number in Table 1 for all reactions of species involving species \(i\). For example, the overall effective reaction rate of the species NO is  
\[\overline{R}_{e_{i}}=\sum R_{k}=R_{2}-R_{3}-R_{6} \tag{5}\]  
The individual reaction \(R_{k}\) between species \(i\) and \(j\) is expressed in terms of the segregation coefficient \(I_{s_{ij}}\) as  
\[\overline{R}_{k}=-k\Big{(}1+I_{s_{ij}}\Big{)}\overline{\mathcal{C}}_{i} \overline{\mathcal{C}}_{j}\text{ or }\overline{R}_{k}=-k\Big{(}1+I_{s_{ij}}\Big{)}\left( \overline{\mathcal{C}}_{i}^{I}-\overline{\xi}_{i}\right)\left(\overline{ \mathcal{C}}_{j}^{I}-\overline{\xi}_{j}\right) \tag{6}\]  
\[I_{s_{ij}}=\left\{\frac{\varphi_{ij}\Big{[}1+I_{s_{ij}}^{I}\Big{]}\Big{[}1- \left(1-\mu_{i}\right)\overline{\mathcal{C}}_{i}^{I}/\overline{\mathcal{C}}_{i} \Big{]}\Big{[}1-\left(1-\mu_{j}\right)\overline{\mathcal{C}}_{j}^{I}/\overline{ \mathcal{C}}_{j}\Big{]}}{\mu_{i}\mu_{j}}\right\}-1 \tag{7}\]where \(I_{s_{ij}}^{I}\) is the intensity of segregation for inert species \(I_{s_{ij}}^{I}=\left(\overline{c_{i}^{I^{\prime}}c_{j}^{I^{\prime}}}\right)/ \left(\overline{c}_{i}^{I}\overline{c}_{j}^{I}\right)\); \(\mu_{i}\) and \(\mu_{j}\) are the mixing parameters \(\mu_{i}=\left(1+I_{s_{ij}}^{I}\right)/\left(1+I_{jj}^{I}\right)\) with \(I_{jj}^{I}=\overline{\left(c_{j}^{I\prime}\right)^{2}}/\left(\overline{c}_{j} ^{I}\right)^{2}\) and \(\mu_{j}=\left(1+I_{s_{ij}}^{I}\right)/\left(1+I_{ii}^{I}\right)\) with \(I_{ii}^{I}=\overline{\left(c_{i}^{I\prime}\right)^{2}}/\left(\overline{c}_{i }^{I}\right)^{2}\); and \(\varphi_{ij}\) is the reaction parameter as below:  
\[ \begin{array}{ll}\frac{1}{\overline{\varphi}_{ij}}\frac{\partial\varphi_{ij }}{\partial t}=&\frac{2D}{I_{\bar{2}}^{2}}\Bigg{[}1-\frac{\mu_{i}\mu_{j}}{ \left(1+I_{ij}^{I}\right)}\Bigg{]}\\ &-\Bigg{\{}\frac{2D}{I_{\bar{2}}^{2}}\Bigg{[}1-\frac{\left(\overline{c}_{i}- \left(1-\mu_{i}\right)\overline{c}_{i}^{I}\right)\left(\overline{c}_{j}- \left(1-\mu_{j}\right)\overline{c}_{j}^{I}\right)}{\left(1+I_{ij}\right) \overline{c}_{i}\overline{c}_{j}}\Bigg{]}\\ &+k\Big{[}\left(1-\mu_{i}\right)\overline{c}_{i}^{I}+\left(1-\mu_{j}\right) \overline{c}_{j}^{I}\Big{]}\Big{\}}\frac{\varphi_{ij}\left(1+I_{ii}^{I}\right) }{\mu_{i}\mu_{j}}\\ &+\frac{\left(\overline{c}_{i}-\overline{c}_{i}^{I}\right)}{\mu_{i}\overline{ c}_{i}^{I}\left(\overline{c}_{i}-\overline{c}_{i}^{I}+\mu_{i}\overline{c}_{i}^{I} \right)}\left(\mu_{i}\frac{\partial\overline{c}_{i}^{I}}{\partial t}+ \overline{c}_{i}^{I}\frac{\partial\mu_{i}}{\partial t}\right)\\ &+\frac{\left(\overline{c}_{i}-\overline{c}_{j}^{I}\right)}{\mu_{i}\overline{ c}_{j}^{I}\left(\overline{c}_{j}-\overline{c}_{j}^{I}+\mu_{i}\overline{c}_{j}^{I} \right)}\left(\mu_{j}\frac{\partial\overline{c}_{i}^{I}}{\partial t}+ \overline{c}_{j}^{I}\frac{\partial\mu_{j}}{\partial t}\right)\end{array}