## 3 Results
### Variable Correlation Analysis  
In this study, a total of thirty-three characteristic variables were obtained, including fourteen vegetation vertical structure characteristics data from GEDI, nine vegetation indices and seven band reflectances from Landsat 9, and three topographic factors (slope, aspect, and elevation). \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Parameter Name** & **Model** & **R\({}^{2}\)** & **Residual SS** & **Nugget** & **Sill** & **Structural Ratio** & **Range** \\ \hline \multirow{3}{*}{digital\_elevation\_ model} & Linear & 0.97 & 5.75 \(\times\) 10\({}^{9}\) & 158,182.97 & 492,097.45 & 0.68 & 0.93 \\  & Spherical & 0.96 & 6.02 \(\times\) 10\({}^{9}\) & 151,000.00 & 647,400.00 & 0.77 & 1.91 \\  & Exponential & 0.95 & 7.56 \(\times\) 10\({}^{9}\) & 130,000.00 & 671,000.00 & 0.81 & 2.86 \\  & Gaussian & 0.94 & 9.80 \(\times\) 10\({}^{9}\) & 195,000.00 & 539,300.00 & 0.64 & 1.20 \\ \hline \multirow{3}{*}{modis\_treecover} & Linear & 0.41 & 1.82 & 4.66 & 5.60 & 0.17 & 0.93 \\  & Spherical & 0.60 & 1.23 & 0.18 & 5.24 & 0.97 & 0.07 \\  & Exponential & 0.72 & 0.88 & 0.61 & 5.28 & 0.88 & 0.11 \\  & Gaussian & 0.60 & 1.23 & 0.74 & 5.24 & 0.86 & 0.06 \\ \hline \multirow{3}{*}{fhd\_normal} & Linear & 0.06 & 5.30 \(\times\) 10\({}^{-3}\) & 0.35 & 0.36 & 0.04 & 0.93 \\  & Spherical & 0.44 & 3.18 \(\times\) 10\({}^{-3}\) & 0.02 & 0.36 & 0.95 & 0.06 \\ \cline{1-1}  & Exponential & 0.42 & 2.94 \(\times\) 10\({}^{-3}\) & 0.04 & 0.36 & 0.89 & 0.07 \\ \cline{1-1}  & Gaussian & 0.44 & 3.18 \(\times\) 10\({}^{-3}\) & 0.06 & 0.36 & 0.84 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of variance function of all models. To analyze the interaction between different remote sensing characteristics and _Quercus aquifoloides_ carbon storage as well as to compare the estimation accuracy of different regression models, Pearson correlation analysis was carried out between the remote sensing characteristic factors extracted from GEDI and Landsat 9 images and the _Quercus aquifoloides_ carbon storage in the sample sites using R software. The correlation coefficient matrix was displayed in Figure 5. The Pearson correlation coefficient between remote sensing variables and carbon storage ranged from \(-0.228\) to \(0.307\), with five variables significantly associated with carbon storage (\(p<0.05\)). Among these variables, digital_elevation_model, modis_treecover, dem, fhd_normal, and B1 had the highest correlation coefficients with carbon storage (\(0.307\), \(0.254\), \(0.234\), \(-0.228\), and \(0.217\), respectively). The band composition of Landsat 9 remote sensing variables shows that the sensitivity of vegetation indices composed of each band to carbon storage was low, while the sensitivity of single band reflectance was relatively high. In addition, digital_elevation_model, modis_treecover, and fhd_normal were significantly positively correlated to carbon storage, indicating that the waveform data provided by GEDI contained information affecting vegetation carbon storage. The remaining variables related to topography and vegetation, such as the atmospherically resistant vegetation index (ARVI), the visible atmospherically resistant index (VARI), the integration of vegetation components in the waveform (rv), and the height from the beginning of the received waveform signal (rh100), also contributed to the evaluation of carbon storage, but the effect was not significant. The importance of each variable was ranked via random forest (Figure 6). The brown line is the connecting line of the %incMSE value of each variable. Because % IncMSE  
Figure 5: The correlation coefficient between carbon storage and each explanatory variable. is verified by OOB data, and the reliability of feature selection is high. Therefore, this paper chose the results of % IncMSE for feature selection. By combing Pearson correlation analysis, the characteristic variables that were significantly correlated at the 0.05 level were screened.