## 4 Discussion
Figure 8 shows that the three algorithms have some saturation problems in the training and test phases. In the training phase, the maximum value of the RF estimation (363.63 m\({}^{3}\) ha\({}^{-1}\)) was larger than the other two algorithms (SVR, 336.79 m\({}^{3}\) ha\({}^{-1}\); MLR, 308.39 m\({}^{3}\) ha\({}^{-1}\)), and the minimum value of the RF estimation was smaller (4.97 m\({}^{3}\) ha\({}^{-1}\)) than the other two algorithms (SVR, 6.52 m\({}^{3}\) ha\({}^{-1}\); MLR, 5.52 m\({}^{3}\) ha\({}^{-1}\)). In the test phase, although the maximum value estimated by MLR (290.26 m\({}^{3}\) ha\({}^{-1}\)) was the largest, the minimum value (7.48 m\({}^{3}\) ha\({}^{-1}\)) was the smallest, and the data range of the RF estimated value was the largest (7.48-272.23 m\({}^{3}\) ha\({}^{-1}\)). This indicated that the RF model was the best model with which to estimate the FSV. In addition, the RF exhibited the best performance among the three algorithms according to the \(R^{2}\) and RMSE. When using the RF model to predict the FSV in Hunan Province (Figure 9), we found that the smallest FSV per hectare was 12.7421 m\({}^{3}\), which was larger than the smallest FSV measured in the field (1.42 m\({}^{3}\) ha\({}^{-1}\)), and the largest FSV per hectare was 269.649 m\({}^{3}\), which was smaller than the highest FSV measured (577.50 m\({}^{3}\) ha\({}^{-1}\)). This result indicated that the RF model overestimated the low FSV values and underestimated the high FSV values, which may be due to the common saturation problem in optical remote sensing vegetation analyses [83]. The overestimation problem could be caused by the understory vegetation (e.g., shrub and grass), which typically impacts the reflectance values. The high FSV areas often have complex canopy structures, which may affect the reflectance values. A similar study by [PERSON] et al. [106] also found this was a common problem in the estimation of the FSV or biomass using multispectral remote sensing data. However, if the forest area with a low FSV and the forest area with a high FSV reach a certain ratio, the underestimation and overestimation problems of the RF will reach a certain balance. For this reason, when using the RF to estimate the FSV over a large area, it may offset some errors caused by the defects of the model or the image data. Regarding the SVR model, Figure 8c shows two distinct trend lines consisting of points. This trend was caused by the large data volume (n = 321 in the training phase) and parameter optimization. Due to the parameter optimization, as many samples as possible were within this hyperplane; therefore, many data points were concentrated on the edge. After mapping the FSV for the whole of Hunan Province, a statistic using the ENVI 5.3 \"Quick Stats \" tool (Exelis Visual Information Solutions, Boulder, Colorado) was calculated, and the mean FSV was 39.09 m\({}^{3}\) ha\({}^{-1}\). For comparison, we calculated the mean FSV of Hunan Province based on the Analysis Report of Hunan Forestry Statistics Annual Report in 2017, and found that the value was 42.15 m\({}^{3}\) ha\({}^{-1}\)[107]. The estimation accuracy of the mean FSV reached 92.74%. However, for the sample plot data, the mean values were 121.11 and 120.53 m\({}^{3}\) ha\({}^{-1}\) for the training and test, respectively. This result shows that among the sample plots we selected, there were too few samples with a small FSV. Using these data to directly model may cause some errors in the model prediction results. However,before modeling, a normal transformation was performed, and the mean values were 3.97 (Table 4) and 3.04 (39.09\({}^{3}\)) before and after transformation, respectively (Figure 3). The normal transformation narrowed this gap, which may compensate for the impact of uneven data sampling to some extent [108]. Finally, the total FSV that we predicted in Hunan Province was \(3.50\times 10^{8}\) m\({}^{3}\) in forest areas.