## 2 Materials and Methods
### Causality Analysis--SURD  
The SURD analysis method was used for the simulation results. SURD is a component that decomposes causal relationships into synergistic relationships, uniqueness, and redundancy [57]. SURD quantifies causality as the increments of redundant(R), unique(U), and synergistic(S) information gained about future events from past observations. It is conducive to exploring the influence process of factors such as ozone-meteorological factors and carbon dioxide on the productivity of the woodland ecosystem over a long time series. The original SURD component was only used for analyzing the site. The SURD component was compiled based on Python 3.9 to be used for temporal causal analysis of region-scale raster data. The time series of each meteorological variable is constructed in a single grid to analyze the causal relationship between GPP. As a result, since each variable generates R, U and S causal relationships with other variables, fully presenting the causal relationships of the data is a huge and complex process. \begin{table}
\begin{tabular}{c c c c} \hline
**Site Name** & **Site Coordinates** & **Vegetation Type** & **Year of Observation GPP** \\ \hline HaiBei & 101.25 N, 37.6 E & Shrub & 2009–2010 \\ Changbaishan & 128.1 N, 42.4 E & Conifer & 2009–2010 \\ Dinghushan & 112.5 N, 23.5 E & Hardleaf & 2016, 2010 \\ \hline \end{tabular}
\end{table} 
Table 1: Basic information about three forest sites. \begin{table}
\begin{tabular}{c c c c} \hline
**Experiment No.** & **Climate** & **History\_O\({}_{3}\)** & **History\_CO\({}_{2}\)** \\ \hline E1 & ✓ & & \\ E2 & ✓ & ✓ & ✓ \\ E3 & ✓ & ✓ & \\ E4 & ✓ & & ✓ \\ \hline \end{tabular}
\end{table} 
Table 2: Model simulation experiment protocol to investigate the interactive effects of climate change, [CO\({}_{2}\)] and [O\({}_{3}\)] on woodland GPP in 2001–2020. This study focuses on demonstrating the causal relationship between O\({}_{3}\) and CO\({}_{2}\) and GPP. Firstly, we obtain the causal relationship analysis of all variables through SURD; secondly, we split it into R, U and S relationships; thirdly, we extract the variable combinations with the maximum values in R, U and S, respectively, to determine whether the IDs corresponding to CO\({}_{2}\) and O\({}_{3}\) exist among them. If IDs exist, we pass out the values. For instance, when the independent variable is GPP and the dependent variables are six factors including CO\({}_{2}\), O\({}_{3}\), temperature, a combination of causal analysis factors is generated within the SURD, as shown in Table 3. In this study, we first extracted the maximum values from R and S, and then determined whether there were simultaneously ID values for O\({}_{3}\) and CO\({}_{2}\). If such values existed, we returned that number. For the U value, if the U values corresponding to CO\({}_{2}\) and O\({}_{3}\) are ranked in the top two, then that value is extracted. The causal relationship of the specified variable is presented through filtering, eliminating the complex process of plotting and data filtering. When the independent variable is GPP and the dependent variables are six factors including CO\({}_{2}\) (id: 1), O\({}_{3}\) (id: 2), temperature (id: 3), the combination of variables shows an exponential growth in the form of an array. The more variables there are, the more complex the variable combinations become. In the SURD analysis, each independent variable has a combination of three values: S, U, and R. Their total sum is 1, representing the impact of different variable combinations on the dependent variable. This method utilizes the concept of stepwise regression. Through multiple regressions, it gradually incorporates each variable one by one. Each time a new observation variable is added, the total specific mutual information in the system is recalculated after the addition of the new variable. If the newly added variable merely provides duplicate information of the existing variables, then this increment is classified as redundant information.