## 2 Materials and Methods
### Estimation and Projection Models for the Net Primary Productivity  
For this study, we designed the research method in three stages, as shown in Figure 1. First, we selected and categorized the variables as topographical variables, climate variables, including ozone concentration, and vegetation variables through the literature review. The data was extracted from satellite images or obtained from the data, which was provided by the Ministry of Environment from 2001 to 2010 for the empirical model. Second, we made an empirical model that can determine the relationship between ozone concentration or climate change and the net primary productivity of forests. The model for estimating the net primary productivity can be divided into three categories: remote sensing-based models [38], correlative (biogeographical) models or process-based (biogeochemical) models, and empirical models [39]. The purpose of this study is to predict future forest productivity based on current net primary productivity of forest and to understand how ozone affects current and future forest productivity. However, most of the aforementioned models do not reflect the effects of ozone, and even if the effects of ozone are reflected, there are limitations to the construction of the input data for estimating future forest productivity. Therefore, in this study, a statistical model was developed using the variables that affect the net primary productivity of forests [40]. The empirical model estimates forest productivity based on factors, such as evapotranspiration, stand age, Normal Distribution Vegetation Index (NDVI), and other factors based on temperature and precipitation. However, the disadvantage of the empirical model is that there is a limit to the assumption that changes in forests occur immediately in response to climate change [38]. Nevertheless, the empirical model has a simple structure and can be used as a basis for the calculation of net production [41]. A vector autoregressive model and panel analysis model were used to estimate and predict NDVI and net primary productivity. Finally, the future net primary productivity of forests was estimated using the derived model. The topographical variables were used as-is in this process, and climate variables and ozone parameters were taken from the RCP 8.5 scenario, which reflects the emissions of the SSP scenarios. In the case of the established RCP 8.5 scenario, the scenario reflects not only the SSP scenarios, but also the air pollutants and greenhouse gas emissions from China. The reason for using the RCP 8.5 scenario is that the emissions from SSP scenarios are based on the climate variables in RCP 8.5, which represents the most extreme conditions of all of the RCP scenarios. 2.1. Variables Included in the Models for Estimating the Normal Distribution Vegetation Index and the Net Primary Productivity  
The net primary productivity of forests is based on plant photosynthesis [42; 43; 44]. Therefore, in this study, micro factors that affect the photosynthesis of plants and macroscopic factors that affect the net primary productivity or gross primary productivity were identified. For the climate factors, the highest temperature of the warmest month and the lowest temperature of the coldest month were selected to determine the annual temperature range [9; 42; 44; 45]. Slope, altitude, and aspect were selected as the topographical factors [42; 46]. Leaf Area Index (LAI), NDVI, evapotranspiration, and potential evapotranspiration were considered as factors related to the plants [46; 47]. Since the rate of growth of plants varies according to their stand age [48], we assumed that the previous year's growth would affect the next year's growth. Simultaneously, LAI is known to have different values for different species, depending on leaf area per unit of soil area. In many studies, LAI and NDVI show similar results 70-80% of the time [49; 50; 51], with some studies showing the results matching in as much as 90% of results [52; 53].