## 2 Materials and Methods
### Simulating Cumulative Stomatal O\({}_{3}\) Uptake  
COU is given by  
\[\text{COU}=\Sigma F_{\text{st}} \tag{1}\]  
\[F_{\text{st}}=[\text{O}_{3}]/(R_{\text{s\_O3}}+R_{\text{b\_O3}}) \tag{2}\]  
\[R_{\text{s\_O3}}=1/(0.663\times g_{\text{s}}) \tag{3}\]  
\[R_{\text{b\_O3}}=1.3\times 150\times(L_{\text{d}}/u)^{0.5} \tag{4}\]  
where \(F_{\text{st}}\) is the stomatal O\({}_{3}\) uptake, [O\({}_{3}\)] is the atmospheric O\({}_{3}\) concentration, \(R_{\text{s\_O3}}\) and \(R_{\text{b\_O3}}\) are the stomatal resistance and leaf boundary layer resistance to O\({}_{3}\), respectively, \(g_{\text{s}}\) is the stomatal conductance to H\({}_{2}\)O, \(L_{\text{d}}\) is the crosswind leaf dimension, and \(u\) is the wind speed. The \(g_{\text{s}}\) was estimated according to the \(g_{\text{s}}\) model provided by [PERSON] et al. (2019), originally developed by [PERSON] (2017):  
\[g_{\text{s}}=g_{\text{max}}\times f_{\text{phen}}\times f_{\text{light}}\times \text{max}(f_{\text{min}},f_{\text{temp}}\times f_{\text{VPD}}\times f_{ \text{SWC}}\times f_{\text{O3 conc}}) \tag{5}\]  
where \(g_{\text{max}}\) is the maximum \(g_{\text{s}};f_{\text{min}}\) is the ratio of minimum \(g_{\text{s}}\) to \(g_{\text{max}}\); and \(f_{\text{phen}},f_{\text{light}},f_{\text{temp}},f_{\text{VPD}},\)\(f_{\text{SWC}},\) and \(f_{\text{O3 conc}}\) represent responses of \(g_{\text{s}}\)/\(g_{\text{max}}\) to leaf phenology, photosynthetic photon flux density (PPFD), air temperature, vapor pressure deficit, volumetric soil water content, and atmospheric O\({}_{3}\) concentration, respectively. These parameters are species-specific and were essentially based on our previous results (see details in [PERSON] et al. (2019)). The leaf emergence date and leaf senescence date \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value or Source** \\ \hline Targeted year & 2011–2015 \\ \hline Targeted leaves & Sunlit leaves \\ \hline Calculation time step & 1 h \\ \hline Latitude & From 24\({}^{\circ}\) to 46\({}^{\circ}\) \\ \hline Longitude & From 122\({}^{\circ}\) to 154\({}^{\circ}\) \\ \hline Meteorological factors & Japan Meteorological Agency \\  & ([[https://www.data.jma.go.jp/obd/stats/etrn/index.php](https://www.data.jma.go.jp/obd/stats/etrn/index.php)]([https://www.data.jma.go.jp/obd/stats/etrn/index.php](https://www.data.jma.go.jp/obd/stats/etrn/index.php))) \\ \hline Ozone concentration & National Institute for Environmental Studies \\  & ([[https://www.nies.go.jp/igreen/](https://www.nies.go.jp/igreen/)]([https://www.nies.go.jp/igreen/](https://www.nies.go.jp/igreen/))) \\ \hline Tree distribution (45\({}^{\prime\prime}\times 30^{\prime\prime}\) mesh) & Ministry of the Environment \\  & ([[http://www.biodic.go.jp/index.html](http://www.biodic.go.jp/index.html)]([http://www.biodic.go.jp/index.html](http://www.biodic.go.jp/index.html))) \\ \hline Parameters of stomatal conductance model & [PERSON] et al. (2019) \\ \hline Phenology (leaf emergence date, leaf & [PERSON] et al. (2020) \\ senescence date, and \(f_{\text{phen}}\)) & ([[https://doi.org/10.5067/MODIS/MCD12Q2.006](https://doi.org/10.5067/MODIS/MCD12Q2.006)]([https://doi.org/10.5067/MODIS/MCD12Q2.006](https://doi.org/10.5067/MODIS/MCD12Q2.006))) \\ \hline Response of annual photosynthetic CO\({}_{2}\) & [PERSON] et al. (2018) \\ uptake to COU & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation setting and data sources for the impact assessment of O\({}_{3}\) on annual CO\({}_{2}\) uptake. were provided by MODIS Land Cover Dynamics Product, MCD12Q2 v. 006, in 500-m grids in the world. Seasonal changes in enhanced vegetation index (EVI) of the MCD12Q2 were substituted for the \(f_{\rm phen}\). These phenological data were obtained considering tree distribution using vegetation raster data (\(45^{\prime\prime}\times 30^{\prime\prime}\) mesh) of the National Survey on the Natural Environment (Ministry of the Environment), indicating the distribution of dominant species, although uncertainties exist in the dataset because the forest is not necessarily pure.