## 3 Results and Discussion  
### Relationships between the Net Primary Productivity and Ozone Concentration  
The Carnegie Ames Stanford Approach (CASA)-NPP values used in the model were developed using the 10-year average of 592.53 \(\mathrm{tC/km^{2}/year}\) (SD: 213.72 \(\mathrm{tC/km^{2}/year}\)); over the last decade the ozone concentration in the forest areas in the second and third quarters had a mean of 0.0867 ppm (SD 0.0395 ppm). First, we estimated the future NDVI using a vector autoregressive model to reflect changes in vegetation over time, such as future forest distribution. The NDVI estimation model was developed using variables that affect vegetation activity. The independent variables used in the NDVI estimation model are the previous year's NDVI, annual precipitation, and annual temperature range (Table 2). The higher the NDVI value in the previous year, the higher the NDVI value in the year being observed. Higher annual precipitation and a higher annual temperature range lead to a higher NDVI value. Second, we estimated the future NPP using a panel analysis model to reflect the ozone concentration. This is the result of panel analysis model selection before the panel analysis result. A one-way time and random effect model was selected as the most suitable panel analysis model among the various panel analysis models considered in this study. Specifically, we selected the time effect model of the one-way model through the Least Square Dummy Variable (R-sq. : 0.9746) and Chow-test (F-value: 70.63, Sig. : 0.000). Next, we determined that random effects model is more significant through the Breusch and Pagan Lagrangian Multiplier test (see Table 10) and the Hausman test (see Table 10). The Breusch and Pagan Lagrangian Multiplier test results showed that both of the models were significant, but the random effect model was chosen because the null hypothesis, where the difference in coefficients was not systematic, could not be rejected by Hausman test. Finally, one-way time and random effects models were selected by this process. Also, the rho value in context of the random effect model indicates the estimated proportion of the between variance at the total variance was about 0.86. In addition, the Durbin-Watson test value was 1.722, indicating that there was no time-series autocorrelation between each variable. The independent variables used to develop the net primary productivity of the forest impact model when considering the effects of ozone are NDVI, solar radiation, altitude, and average concentration of ozone in the second and third quarters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variables** & **Coef.** & **Std. Error** & **Std. Coef.** & \(t\)**-Statistic** & \(p\)**-Value** \\ \hline (Constant) & \(-574.602\) & 323.55 & & \(-1.78\) & 0.076 \\ Previous year NDVI & 0.881 & 0.02 & 0.879 & 46.16 & 0.000 \\ Precipitation (mm) & 0.222 & 0.08 & 0.052 & 2.82 & 0.005 \\ Annual Temperature & 248.263 & 82.74 & 0.057 & 3.00 & 0.003 \\ \hline \hline \end{tabular} \({}^{*}\) Dependent Variable: NDVI, ** R-sq. 0.816, *** F-value: 836.813 (Sig. 0.000); 1 Annual temperature range is obtained by subtracting minimum temperature of coldest month from maximum temperature of warmest month.  
\end{table} 
Table 2: The result of the first-step model for estimating Normalized Difference Vegetation Index (NDVI) of the Korea forest. According to the results, NPP tends to increase, and NPP increases with increasing NDVI and solar radiation. However, as the altitude increased, NPP decreased, as shown in Table 3. The concentration of ozone has a negative effect on NPP. The analysis suggests that the ozone concentration begin exerting effects to the NPP, about 68.10 tC/km\({}^{2}\)/year decrement per 0.01 ppm increment. NDVI and previous year NDVI, annual precipitation, annual temperature range, solar radiation, altitude, and average ozone concentrations in the second and third quarters were found to have an impact on vegetation growth.