*3.5. Mapping FSV Distribution of Helan Mountains*

Based on the results shown in Figure 8, we have concluded that the BVBM is the best-performing model in this study, and we calculated the FSV of the Helan Mountains by the BVBM combined with the forest distribution pattern. Figure 9 is the final FSV map, the minimum value of the unit area FSV of the Helan Mountains is 9.63 m3ha−<sup>1</sup> and the maximum value is 143.96 m3ha−1. The total amount of FSV in the Helan Mountains was estimated to be 1,062,727.25 m3. According to the FSV data released by the Helan Mountains National Nature Reserve in Ningxia Province (http://www.hlsbhq.com/, accessed on 22 January 2023), the total FSV of the Helan Mountains is 1,320,721.7 m3. Therefore, the accuracy of the BVBM to predict the FSV in the Helan Mountains reached 80.46%.

**Figure 9.** Spatial distribution of the predicted FSV, and forest distribution of the Helan Mountains.

#### **4. Discussion**

The carbon sequestration capacity of montane forest ecosystems is very significant and of prime importance in the global carbon cycle. Due to their geographical location and climatic characteristics, montane forests are an integral part of the entire terrestrial forest ecosystem [35,39]. The Helan Mountains are highly representative of montane forest ecosystems, their FSV estimation has a very high reference value for studies across similar landscapes. However, as a result of the inaccessibility and complex spatial heterogeneity of montane forest ecosystems, it is often a daunting task to obtain a sufficient number and sufficiently representative ground samples to estimate FSV in large-scale areas. Although remote sensing images have made it easier, issues related to low-value overestimation and high-value underestimation still occur [15,17]. However, as more and more red-edge bands in Sentinel-2 data are applied, the accurate estimation of vegetation parameters has been greatly improved [1,2]. For example, based on the red-edge band of Sentinel-2, Liu et al. [27] developed several new vegetation indices to estimate the photosynthetic and non-photosynthetic fractional vegetation cover of alpine grasslands on the Qinghai-Tibetan Plateau. Despite exhibiting a more sensitive response at low vegetation coverage, their study found that compared with traditional vegetation indices, the novel vegetation indices can effectively alleviate the high vegetation saturation problem at low vegetation coverage. In a related study in Zhejiang Province, China, Fang et al. [2] used the optimal variable selection method of different dominant tree species to estimate FSV. Their selected variables included a variety of vegetation indices, such as SRre, MSRre, CIre, and NDI45 developed based on the Sentinel-2 red-edge bands. Almost all of these variables appear in the final variable selection results, which also prove the potential of the red-edge band in estimating forest parameters.

In exploring the potential of *NDVIRE* to estimate FSV based on the Sentinel-2 red-edge bands, in the variable importance results of the VBM and BVBM, the *NDVIRE* ranks first. It is worth mentioning that the introduction of weighting coefficients "*α*" and "*β*" played a key role in the successful construction of the *NDVIRE*. The results of this study also indicate that the model's estimation accuracy of FSV is significantly improved due to the addition of the *NDVIRE*. First of all, an estimation accuracy of 80.46% is impressive in the research on FSV estimation. Moreover, according to Table 6, we found that the minimum and maximum values in the estimated results of the VBM and BVBM with the *NDVIRE* involvement are superior to those in the BBM, indicating that the *NDVIRE* mitigates the issue of light saturation to some extent. In addition, the mean values of FSV predicted by the BVBM in the training phase (56.88 m3ha−1) and the testing phase (60.79 m3ha−1) are also very close to the mean values of the training data (56.66 m3ha−1) and the testing data (63.84 m3ha−1).

Despite the proven efficiency and robustness of the RF algorithm through numerous studies [8,21,35–38], there is still a limitation observed in its ability to predict the minimum and maximum values of FSV in both the training and testing phases when compared to the actual training and testing data. This limitation results in overestimation of low values and underestimation of high values. Therefore, it would be necessary for future studies to incorporate more machine learning algorithms and innovative machine learning algorithms. From another perspective, deep learning, as a kind of non-parametric machine learning algorithm, is widely applied in forest monitoring. Numerous prior studies have demonstrated the outstanding capability of deep learning algorithms when it comes to target detection and vegetation classification [40–44].

Another paramount limitation of this study is the source of sample plot data which were the most recent. Although "one map" contains a large amount of necessary forest information, using these data to carry out research can no longer meet the current requirements for real-time forest monitoring. In order to resolve this problem in future studies, it is necessary to use unmanned aerial vehicles (UAVs) to obtain enough measured sample plots. Similarly, many studies have proposed UAVs equipped with hyper-spectral and LiDAR sensors to obtain the horizontal and vertical structure information of forests [45–51]. Its efficiency in obtaining

forest parameters is unmatched by manual investigation. The accuracy of tree height, DBH, and spectral information extracted using UAVs is very close to manual surveys. Therefore, as an innovative research method, it is recommended to use UAVs to replace manual field survey work to improve research efficiency where high-precision forest estimation results can be obtained.
