## 4 Conclusions  
This study investigated the relationship between ozone concentration in the second and third quarters and the net primary productivity of forest and estimated the damage that is caused by ozone when the ozone concentration was fixed and when it changed. Three phase analyses were conducted; (1) an empirical model was developed that can represent the current net primary productivity of forests, reflecting the concentration of ozone; (2) the relationship between ozone concentration and the current net primary productivity of forests was analyzed by using cross-section time series analysis; and (3) estimates of future net primary productivity of forests and the impact of future ozone concentrations on forest fertility were made using the future ozone concentration data estimated using the temperature and precipitation data of the RCP 8.5 scenario and the NO\(\alpha\) emissions of the SSP scenarios.  
According to the results of this study, the net primary productivity of forests was reduced by 8.25% due to ozone levels at present, and the damage to NPP is estimated to be between 8.47% to 10.55% in the 2050s and 5.85% to 11.15% in the 2090s. Climate change will negatively affect the net primary productivity by an estimated 7.31% in the 2050s and 1.64% in the 2090s. The relationship between carbon dioxide at current or future levels and the productivity of plants is controversial, but the negative relationship between ozone concentration and the net primary productivity of forests is clear, as indicated by the results of this study.  
The significance of this study is that the effect of ozone on the net primary productivity was statistically figured out in macro scale. Also, the estimation of the net primary productivity of forests in the future is reflected not only in the climate data, but also in the concentration of ozone based on emissions in SSP scenarios to calculate future ozone concentrations, rather than to make assumptions based on a simply scenario. This is another significance of this study, as compared to other studies that can estimate the damage due to the changes of carbon dioxide concentration. These findings of this study offer policy implications on climate change mitigation and adaptation or international environmental negotiations. However, in future studies it will be necessary to apply methods which overcome the limitation of the empirical model, as well as to find a method to increase the accuracy of the model.  
In many studies, it is suggested that future ozone concentration is likely to increase due to climate change. This means that future damage to forests due to ozone is expected to increase beyond the current level of damage. Therefore, we consider that the effect of ozone is no longer a problem only in Korea, but rather a problem facing all of East Asia, including China and Japan, and that it also be viewed as a global problem. For more accurate forecasting, cooperation among domestic and international researchers will be needed.  
This work was supported by grants from the National Institute of Environment Research (NIER-2015-02-02-040) and the Public Technology Program based on Environmental Policy (Project No. 2016000210004), which are funded by the Ministry of Environment of Republic of Korea.  
All authors have contributed to the intellectual content of this paper. [PERSON] designed this study and analyzed the data and wrote the manuscript. [PERSON], [PERSON], [PERSON] and [PERSON] contributed to make the data and to analyze. [PERSON], [PERSON] and [PERSON] provided some core advice and checked through the paper's entirety.  
The authors declare no conflict of interest.