## 2 Model Description  
### Model Reactions  
The TKM has been developed in the previous study [10] with the assumption of horizontally homogeneous and vertically heterogeneous CBL in a quasi-steady-state characteristic of a summer cloud-free daytime as shown schematically in Figure 1a for the CBL with coupled chemical kinetics [10]. The TKM includes an asymmetric turbulent transport process to explain the macromixing influence represented by top-down and bottom-up(TDBU) diffusion of two species using the concept of the asymmetric convective model(ACM) [30] presented in Figure 1b. Figure 1c reveals elements of the 1-D TKM structure: The source is expressed by an emission term, a transport process (vertical mixing by turbulence), a transformation process (photochemical reaction, thermal chemical reaction, removal by dry deposition process expressed by a sink term), and output. In this study, the TKM is applied to the daytime essential NO\({}_{\text{x}}\)-O\({}_{3}\)-RH photochemical system [25] with the reactions listed in Table 1 and Figure 1d. The species in the system are ozone (O\({}_{3}\)), the oxides of nitrogen (NO, NO\({}_{2}\) and HNO\({}_{3}\)), the oxides of hydrogen (OH, HO\({}_{2}\), H\({}_{2}\)O, and H\({}_{2}\)O\({}_{2}\)), and a generic hydrocarbon (RH). All but HNO\({}_{3}\) and H\({}_{2}\)O\({}_{2}\) have lifetimes similar to or shorter than the turbulent time scale (667 s in this paper). A constant CO concentration represents all the carbon species that have long lifetimes compared to the turbulent time scale (e.g., methane and CO). Water vapor is considered to be present at a constant concentration [25]. The product species HNO\({}_{3}\) and H\({}_{2}\)O\({}_{2}\) are not reactive and their concentrations increase with time in the model simulations, which assume they are not removed by dry deposition. Although this mechanism is oversimplified in its representation of atmospheric chemistry, it contains most of the key features included in more detailed mechanisms. Thus, this chemical mechanism can be used to illustrate the qualitative features of the general hydrocarbon-NO\({}_{\text{x}}\)-O\({}_{3}\) chemistry in the troposphere. The mechanism consists of the reactions listed in Table 1 and Figure 1d. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Reactions**} & \multirow{2}{*}{**Reactants**} & \multirow{2}{*}{**Products**} & \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**Rate Constant at 298 \({}^{\circ}\)K**} \\ \cline{5-6}  & & & & \multicolumn{1}{c}{**S90 [FOOTNOTE:]Footnote : All reaction rate constants are taken from [31]. Photolysis frequencies are given in s\({}^{-1}\). Reaction rates are given in ppb\({}^{-1}\).s\({}^{-1}\). The factor \(f\) that appears in the reaction rate of RH + OH is variable and ranges from 100 to 300. Initially, \(f\) is set to 100. A constant Relative humidity (Rh) is assumed as 45\%. \({}^{\mathrm{b}}\) J\({}_{\mathrm{I}}\) is the product of the photolysis frequency for O\({}_{3}\) + \(h\
u\rightarrow\) O\({}^{\mathrm{(}}\mathrm{}^{\mathrm{D}}\mathrm{)}+\) O\({}_{2}\) multiplied by the yield of the reaction O(\({}^{\mathrm{(}}\mathrm{}^{\mathrm{D}}\mathrm{)}+\)HO\({}_{2}\). Sources: [25]. \({}^{\mathrm{c}}\) Reaction rate constants are taken from Carbon-bonding mechanism IV ([PERSON], [[http://arisite.unc.edu/soft/cb4/cb4](http://arisite.unc.edu/soft/cb4/cb4) main.html]([http://arisite.unc.edu/soft/cb4/cb4](http://arisite.unc.edu/soft/cb4/cb4) main.html)) [32] except those for R\({}_{\mathrm{I}}\), R\({}_{\mathrm{2}}\), and R\({}_{\mathrm{I}}\).[32] & \multicolumn{1}{c}{} \\ \hline \hline \end{tabular}
\end{table}