**4. Discussion**

The modeling results of mangrove AGB retrieval in the CGBSR obtained by the five ML models (XGBR, GBR, GPR, SVR, and RFR) are given in Table 6. Clearly, the XGBR model yielded the highest performance, with an *R*<sup>2</sup> and RMSE of 0.805 and 28.13 Mg ha−1, respectively. The worst performing model was GPR, with an *R*<sup>2</sup> and RMSE of 0.378 and 50.23 Mg ha−1, respectively. Both the XGBR model

(*R*<sup>2</sup> = 0.805) and GBR model ( *R*<sup>2</sup> = 0.632) were good predictors of mangrove AGB, indicating that the GBDT regression models were applicable to the study area, where the mangrove biomass is higher than in other mangrove regions of Vietnam. As shown in Table 7, the combined S-2 and ALOS-2 PALSAR data significantly improved the performance of estimating the mangrove AGB in the study area. These results are consistent with a recent previous study [50]. Overall, the XGBR model outperformed the existing algorithms in retrieving the mangrove AGB in a Vietnamese biosphere reserve.

Previous studies reported that long-wavelength PolSAR data, such as the L and the P bands, are well correlated with mangrove forest structures. Among these data, crossed-polarized HV appears to be most correlated with biophysical attributes [13,66,67]. The variable-importance analysis revealed that crossed-polarization HV is more sensitive to mangrove AGB in the study area than HH polarization (Figure 6), consistent with previous results [26,29]. However, mangrove forests in a biosphere reserve exhibit unique stand structures and species compositions that may saturate multispectral and SAR sensors. Data saturation of multispectral sensors such as Landsat TM, ETM+ or OLI, and the S-2 sensor degrades the prediction accuracy of mangrove AGBs in dense forest canopies. The saturation range of multispectral data reaches 100–150 Mg ha−<sup>1</sup> in complex tropical forests, much higher than in mixed and pine forest ecosystems (with a saturation range of >150 to <160 Mg ha−1) [68,69]. In several recent investigations, the saturation levels of the mangrove AGBs retrieved from SAR data ranged from above 100 Mg ha−<sup>1</sup> [20] to below 150 Mg ha−<sup>1</sup> [21,26]. This large range probably manifests from the root systems of di fferent mangrove species in intertidal tropical and sub-tropical regions [13]. The sigma backscatter coe fficients of the dual polarimetric data of ALOS-2 PALSAR-2 increased when the mangrove AGB fell below 100 Mg ha−<sup>1</sup> and then saturated at a higher AGB because the high mangrove cover density extinguished the radar signals [70,71].

Biosphere reserves often consist of various mangrove species. The species types (i.e., *R. appiculata*, *B. gymnorrhiza*, and *S. caseolaris*) are densely grown and characterized by high DBH and tall height. Some species, such as *A. germinans* and *C. decandra*, form small but high-density mangrove patches in which high and low biomasses are easily underestimated and overestimated, respectively, by machine learning algorithms. In the current study, the XGBR model possibly over-estimated the low mangrove AGBs (below 50 Mg ha−1) and under-estimated the high values (over 250 Mg ha−1). Despite these limitations, the combined ALOS-2 PALSAR-2 and S-2 data sensitively detected mangrove AGBs exceeding 200 Mg ha−<sup>1</sup> in the CGBRS (See Figure 5). Our findings agree with the conclusions of prior research on biosphere reserves [17,65]. Given the species complexity in mangrove biosphere reserves, we recommend the inclusion of species classification or richness indices for improved mangrove AGB estimation in future work [19,21].

In the variable-importance results, the mangrove AGB in the study area was largely retrieved from the Red band and the Vegetation Red Edge band. A similar result was reported elsewhere [18,72]. The vegetation red edge, narrow NIR, and SWIR reflectance are likely to be more strongly correlated with forest biomass and carbon stock volume than visible reflectance [17]. Accordingly, the new vegetation index ND145, which is computed from the Sentinel-2 data bands, is a probable sensitive indicator of mangrove AGB. Band 8A in the narrow NIR and band 11 in the SWIR (1613 nm) also played a crucial role in the AGB retrieval. Interestingly, the IRECl derived from S-2 was strongly correlated with mangrove AGB in the biosphere reserve. More in-depth studies would elucidate the e ffectiveness of image transformations involving new vegetation indices derived from the Narrow NIR bands, SWIR of S-2 data, and other image transformations computed from the fully polarized data (HH, HV, VH, and VV) of the Gaofeng-3 and the ALOS-2 PALSAR-2 sensors in biosphere reserves.

To accurately estimate mangrove AGBs, researchers attempted multi-linear regression, which performed poorly with *R*<sup>2</sup> ranging from 0.43–0.65 [13,21,73], and various ML algorithms such as GPR, MLPNN, SVR, and RFR [17,18,29]. ML approaches have proven more successful in mangrove AGB than multi-linear regression and other parametric methods [18,47], but the *R*<sup>2</sup> has rarely exceeded 0.70. Therefore, novel approaches for mangrove AGB estimation are urgently needed. In this research, the performance of the XGBR model was boosted by incorporating data from the ALOS-2 PALSAR-2, S-2 sensors. The result (*R<sup>2</sup>* = 0.805 for the AGB of a mangrove biosphere reserve in the tropics) demonstrates the promise of this approach. Despite the good fit between the XGBR-predicted and measured-mean mangrove AGBs, the range of the predicted mangrove AGBs did not reach the extrema of the actual distribution range, which was maximized at 305.41 Mg ha−<sup>1</sup> and minimized at 26 Mg ha−<sup>1</sup> (Table 5). The predicted results may have been degraded by the saturation levels of the S2 MSI sensor and the dual polarimetric L-band ALOS-2 PALSAR-2 when retrieving mangrove AGB in intertidal areas. Although the AGB was well predicted by the XGBR model, the *R*<sup>2</sup> values in the training and testing phases were significantly different (Table 6). This difference is likely attributable to the mixed mangrove species planted in the CGBRS and the number of plots. To archive a more accurate forest AGB map, we should exploit the advantages of various novel GBDT algorithms with multi-sensor data integration [74]. In more intensive works, novel boosting decision tree techniques should exploit the full capability of multi-source EO data in different mangrove communities occupying tropical intertidal areas at different geographical locations, particularly those of biosphere reserves. Such developments are needed for rapid mangrove AGB monitoring in the future.
