## 3 Results
### Correlation between Inventory and LiDAR Height Metrics  
LiDAR height metrics generally showed a moderate to strong correlation with maximum inventory height (Figures 9 and 10). Correlation between maximum inventory height and maximum LiDAR height was in 0.91 for the 2011-2013 LiDAR data and 0.84 for the 2017-2020 data when the positional difference of plot center was less than 0.1 m. Correlation between maximum inventory height and LiDAR percentile height had a negative trend as the percentile number decreased. Average LiDAR height and maximum inventory height had a correlation coefficient less than 0.75. Figure 8: Visualization of (**a**) canopy height model (CHM) of Indiana, USA, (**b**) CHM in Tippecanoe County, Indiana, USA, and (**c**) CHM in Martell Forest in Tippecanoe County, Indiana, USA. Figure 9: Correlation between LiDAR and inventory height metrics. LiDAR data in 2011–2013 and inventory data in 2008–2012 were used. Forest plots have positional uncertainty approximately less than 0.1 m (\(n\) = 25). Ht: height. Average inventory height and LiDAR height metrics had less positive correlation coefficients between 0.4-0.8. The ninety-ninth percentile of LiDAR height had the strongest correlation of 0.78 and 0.76. A decreasing trend of correlation coefficients between average inventory height and LiDAR height percentiles was observed as percentile number decreased. Correlation between average LiDAR height and average inventory height was 0.6. We also conducted correlation analysis between median inventory height and LiDAR metrics. However, we do not report the result since the correlation was weaker than the above results. The correlation analysis showed that the maximum inventory height was most highly correlated with maximum LiDAR heights. Therefore, we used the term inventory height and LiDAR height in the rest of the paper to indicate maximum inventory and LiDAR height. The size of the clipping area used to obtain LiDAR height did not show a significant effect on the correlation of LiDAR and inventory height (Table 1). Slightly higher correlation coefficients were observed when the clipping radius was either 7.3 or 11.0 m. However, the correlation coefficients did not improve more than 0.1 within the studied range of clipping radius from 3.7 to 14.6 m. Therefore, we used a clipping radius of 7.3 m, i.e., radius of inventory plot, in the rest of the paper to obtain LiDAR height. A substantial difference in the correlation coefficient was shown according to the positional difference of plot location. A higher correlation of 0.8 was observed when the positional difference of the plot was less than 0.1 m.  
A very strong correlation of 0.95 was observed between LiDAR and CHM-based height (Figure 7) from the entire set of inventory plots. Consequently, plot-wise LiDAR tree height was obtained from CHM henceforth, and we refer to it as CHM height. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Correlation of Tree Heights Obtained by**} & \multicolumn{2}{c}{**Correlation of Tree Heights Obtained by**} \\
**Clipping** & **2011–2013 LiDAR and 2008–2012 Inventory Data** & **2017–2020 LiDAR and 2013–2017 Inventory Data** \\
**Radius (m)** & **Positional Difference of Plot Center (GPS)** & **Positional Difference of Plot Center (GPS)** \\  & **Less Than 0.1 m (\(m\) = 25)** & **Unspecified (\(n\) = 4845)** & **Less Than 0.1 m (\(m\) = 25)** & **Unspecified (\(n\) = 4845)** \\ \hline
3.7 & 0.84 & 0.55 & 0.78 & 0.42 \\
7.3 & 0.91 & 0.60 & 0.84 & 0.48 \\
11.0 & 0.89 & 0.56 & 0.86 & 0.49 \\
14.6 & 0.88 & 0.53 & 0.84 & 0.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Effect of clipping area (radius) and positional difference of plot center location on correlation between LiDAR and inventory height. LiDAR height was obtained from a circular area with variable radii, whereas inventory height was acquired within the original plot area with a 7.3 m radius. Figure 10: Correlation between LiDAR and inventory height metrics. LiDAR data in 2017–2020 and inventory data in 2013–2017 were used.