Optimal Combination of Predictors and Algorithms for Forest Above-Ground Biomass Mapping from Sentinel and SRTM Data

Accurate forest above-ground biomass (AGB) mapping is crucial for sustaining forest management and carbon cycle tracking. The Shuttle Radar Topographic Mission (SRTM) and Sentinel satellite series offer opportunities for forest AGB monitoring. In this study, predictors filtered from 121 variables from Sentinel-1 synthetic aperture radar (SAR), Sentinal-2 multispectral instrument (MSI) and SRTM digital elevation model (DEM) data were composed into four groups and evaluated for their effectiveness in prediction of AGB. Five evaluated algorithms include linear regression such as stepwise regression (SWR) and geographically weighted regression (GWR); machine learning (ML) such as artificial neural network (ANN), support vector machine for regression (SVR), and random forest (RF). The results showed that the RF model used predictors from both the Sentinel series and SRTM DEM performed the best, based on the independent validation set. The RF model achieved accuracy with the mean error, mean absolute error, root mean square error, and correlation coefficient in 1.39, 25.48, 61.11 Mg·ha−1 and 0.9769, respectively. Texture characteristics, reflectance, vegetation indices, elevation, stream power index, topographic wetness index and surface roughness were recommended predictors for AGB prediction. Predictor variables were more important than algorithms for improving the accuracy of AGB estimates. The study demonstrated encouraging results in the optimal combination of predictors and algorithms for forest AGB mapping, using openly accessible and fine-resolution data based on RF algorithms.


Introduction
Forest carbon stocks have a key role in mitigation and adaptation with climate change.A substantial portion (70-90%) of forest carbon is stored in above-ground biomass (AGB) [1][2][3][4][5].Forests absorb large amounts of atmospheric carbon dioxide (CO 2 ) in terrestrial land and soil [6,7].The spatial distribution of forest AGB remains inadequately quantified with certain uncertainty, especially when AGB values are higher than 150 Mg•ha −1 or lower than 40 Mg•ha −1 , with large trees and tropical issues [8,9].This is particularly true when considering practical difficulties in inventory over broad geographic scales and complexity of the forest ecosystems [10][11][12].Therefore, accurate estimation and rapid monitoring of forest AGB is recognized as a research challenge.
Well-known sources for mapping AGB include field-based measurements with allometric functions and data from passive and active remote sensors [13][14][15].In contrast to forest inventories and Light Detection and Ranging equipment (LiDAR) surveys, satellite images cover larger areas in a more cost-effective and comparable manner [16,17].The common approach for the upscaling of accurate forest inventories or airborne LiDAR-derived AGB estimations were coupling reference values with satellite data, and then using spatial predictive algorithms to acquire spatially explicit AGB distributions [18][19][20].Progress has been made in mapping forest AGB by optimal combinations of satellite data-derived predictors and modeling algorithms, based on multisource remote sensing techniques [21][22][23][24].Those predictive algorithms were divided into two categories, i.e., physical and empirical regression models, and the latter include conventional regression and machine learning techniques [25,26].Founded on physical principles with two main examples of radiative transfer and geometric optical models, physical models conventionally depend on a number of factors to simulate canopy reflectance, such as leaf area index, chlorophyll concentration, water and matter contents, soil reflectance, and bidirectional reflectance distribution function, while those are often not readily available [27][28][29].On contrary, empirical regression techniques require support from a large number of ground measurements, and they depend on the modeling relationship between spectral signals and field-measured AGB samples.Common methodologies include stepwise regression (SWR), partial least squares regression (PLSR), geographically weighted regression (GWR), k-nearest neighbor (KNN), artificial neural network (ANN), support vector machine for regression (SVR), and random forest (RF) [30][31][32][33].Most of reported studies employed one method, however, there is lack of comparison of performances from multiple algorithms.
The recent launch of Sentinel series, e.g., Sentinel-1 synthetic aperture radar (SAR) and Sentinel-2 multispectral instrument (MSI), provides new effective data for monitoring and mapping of AGB [34][35][36].Sentinel-1 SAR data are available in C-band HH (horizontal transmit-horizontal) + HV (horizontal transmit-vertical) or VV (vertical transmit-vertical) + VH (vertical transmit-horizontal) polarizations [37].Sentinel-2 MSI data include three vegetation red edge, two infrared, visible, and near infrared bands [38].The Sentinel series data have been applied in a variety of vegetation studies [39][40][41].However, using Sentinel data for forest AGB mapping deserves further exploration.The Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) were globally consistent and openly available for providing topographic indices that are helpful for estimating forest biomass [42][43][44].Thus, data mining can be done from those free-access data for forest AGB mapping.
The specific objectives of this study included: (1) determining the best predictors for forest AGB prediction among four groups of variables, i.e., Sentinel-1 (S1), Sentinel-2 (S2), Sentinel series (S) including S1 and S2, and combination of S and SRTM DEM (S + S); (2) identifying the most accurate algorithm for modeling the relationship between field-measured AGB and the above four groups of predictors among linear regression (SWR and GWR) and machine learning (ANN, SVR and RF) algorithms; (3) revealing the optimal combination of predictors and algorithms for forest AGB mapping.

Study Site and Field-Measured Above-Ground Biomass
This study area covers 17,481 hectares of forests (Figure 1).The site is located within the eastern mountainous area of Jilin Province, northeast China.This region has a four-season, monsoon-influenced, humid continental climate, with an annual average temperature of 3.28 • C and an annual precipitation of 632 mm.Characterized by dense forest cover of the Changbai Mountains, the major forest types include deciduous broadleaved forest (90.7%) and mixed broadleaf-conifer forest (6.4%).Typical tree species include Mongolian oak (Quercus spp.), Betula platyphylla (Suk.),Tilia amurensis (Rupr.), and Fraxinus mandschurica (Rupr.).The field campaign was carried out in July, 2017.The distribution of sampling plots was randomly generated, and non-forest areas were masked out.A total of 1,162 10 m × 10 m plots were located and sampled (Figure 1).The plots included 982 for broadleaved deciduous forests, 94 for mixed broadleaf-conifer forests, 59 for deciduous-coniferous forests, and 27 for evergreen coniferous The field campaign was carried out in July, 2017.The distribution of sampling plots was randomly generated, and non-forest areas were masked out.A total of 1,162 10 m × 10 m plots were located and sampled (Figure 1).The plots included 982 for broadleaved deciduous forests, 94 for mixed broadleaf-conifer forests, 59 for deciduous-coniferous forests, and 27 for evergreen coniferous forests.Based on allometric equations [45][46][47][48], measured diameter at breast height (1.3 m from the ground) and tree height, field-based forest AGB at each plot was calculated.The forest AGB samples were from 0.67 to 533.60 Mg•ha −1 , with the median value being between 103.36 to 143.64 Mg•ha −1 (Figure 2a), and mainly below 200 Mg•ha −1 with 77.8% (Figure 2b).The 1,162 sampling sites were randomly divided into training (n = 775) and validation (n = 387) sets (Figure 1) for establishing and examining the performance of the models.
The procedures were illustrated in Figure 3. SNAP software (version 6.0, European Space Agency) was used to pre-process the Sentinel-1 and Sentinel-2 images.The steps based on the Sentinel-1 Toolbox of acquiring an accurate radar intensity backscatter coefficient with a map projection from the SAR images consisted of image calibration, speckle reduction using the Refined Lee Filter, and terrain correction by the Range-Doppler [36,49].A bottom-of-atmosphere-corrected reflectance image was atmospherically corrected and processed from the Sentinel-2 Level 1C data by the radiative transfer model-based SEN2COR atmospheric correction processor (version 2.5.5,European Space Agency).The pre-processed Sentinel series images and the SRTM DEM data were registered into UTM Zone 52 WGS84 projection, and resampled to 10 m pixel sizes.
Uncertainties for the estimated AGB have been considered an important issue associated with modeling, based on remote sensing-derived variables [50,51].For example, reported studies suggested that improved spatial resolution from the Sentinel series helped to reduce the uncertainty, and improved the accuracy of AGB mapping at finer scale [52,53].Promising results demonstrated that texture measurement of SAR data with higher spatial resolution could improve biomass estimation [54,55].However, uncertainties in implementing the texture measurement for biomass estimation were reported, due to the selection of window size [56,57].Vegetation indices and biophysical variables are strongly related to reflectance, but they showed uncertainties for the estimated AGB in spectral sensitivity [58,59].The reported study suggested that the red edge bands of Sentinel-2 (band 5, 6, 7, and 8A) were sensitive to phenological dynamics in vegetation, and that they were helpful for reducing the uncertainty [60,61].In this study, 121 variables, including those
The procedures were illustrated in Figure 3. SNAP software (version 6.0, European Space Agency) was used to pre-process the Sentinel-1 and Sentinel-2 images.The steps based on the Sentinel-1 Toolbox of acquiring an accurate radar intensity backscatter coefficient with a map projection from the SAR images consisted of image calibration, speckle reduction using the Refined Lee Filter, and terrain correction by the Range-Doppler [36,49].A bottom-of-atmosphere-corrected reflectance image was atmospherically corrected and processed from the Sentinel-2 Level 1C data by the radiative transfer model-based SEN2COR atmospheric correction processor (version 2.5.5,European Space Agency).The pre-processed Sentinel series images and the SRTM DEM data were registered into UTM Zone 52 WGS84 projection, and resampled to 10 m pixel sizes.
Uncertainties for the estimated AGB have been considered an important issue associated with modeling, based on remote sensing-derived variables [50,51].For example, reported studies suggested that improved spatial resolution from the Sentinel series helped to reduce the uncertainty, and improved the accuracy of AGB mapping at finer scale [52,53].Promising results demonstrated that texture measurement of SAR data with higher spatial resolution could improve biomass estimation [54,55].However, uncertainties in implementing the texture measurement for biomass estimation were reported, due to the selection of window size [56,57].Vegetation indices and biophysical variables are strongly related to reflectance, but they showed uncertainties for the estimated AGB in spectral sensitivity [58,59].The reported study suggested that the red edge bands of Sentinel-2 (band 5, 6, 7, and 8A) were sensitive to phenological dynamics in vegetation, and that they were helpful for reducing the uncertainty [60,61].In this study, 121 variables, including those that were suggested to be helpful in reducing uncertainties in forest AGB estimation, were selected and extracted for comparison evaluation [48,[54][55][56][57][60][61][62][63][64].A total of 109 variables were derived from the Sentinel series images, including 83 from Sentinel-1 SAR and 26 from Sentinel-2 MSI, and 12 topographic indices from SRTM DEM were also included (Table 1).The variables derived from the Sentinel series were conducted in the Sentinel-1 and Sentinel-2 Toolboxes of SNAP, and that from SRTM DEM were calculated in Spatial Analyst of ArcGIS (Figure 3).The biophysical variables were also calculated in SNAP from their biophysical processor by the reflectance of bands 3-8A, band 11, band 12 and geometric parameters, which used a neural network algorithm based on the PROSAIL radiative transfer model [65,66].that were suggested to be helpful in reducing uncertainties in forest AGB estimation, were selected and extracted for comparison evaluation [48,[54][55][56][57][60][61][62][63][64].A total of 109 variables were derived from the Sentinel series images, including 83 from Sentinel-1 SAR and 26 from Sentinel-2 MSI, and 12 topographic indices from SRTM DEM were also included (Table 1).The variables derived from the Sentinel series were conducted in the Sentinel-1 and Sentinel-2 Toolboxes of SNAP, and that from SRTM DEM were calculated in Spatial Analyst of ArcGIS (Figure 3).The biophysical variables were also calculated in SNAP from their biophysical processor by the reflectance of bands 3-8A, band 11, band 12 and geometric parameters, which used a neural network algorithm based on the PROSAIL radiative transfer model [65,66].

Modeling Algorithms and Evaluation
Firstly, a pairwise Pearson's product-moment correlation analysis was operated to determine the relationship between field-based AGB and multisensor-derived indices, and collinearity among variables.Then the variance inflation factor (VIF) was calculated to delete the redundancy among variables (Figure 3).Variables that were highly correlated (r ≥ 0.8), and that had high VIF (VIF ≥ 10) in regression analysis were excluded from predictors of the modeling [48,73].Those analyses were performed using SPSS (version 21.0, IBM, Armonk, NY, USA).
Sentinel series and SRTM DEM data were composed into four variable groups, including S1, S2, S, and S + S (Figure 3).The first group of variables (S1) was related to AGB with Sentinel-1 SAR polarization channels (i.e., VH and VV) and texture characteristics in four window sizes.The second group of variables (S2) was related AGB with Sentinel-2 multispectral bands, vegetation indices, and biophysical variables.The third group of variables was a combination of S1 and S2.The fourth group of variables used the factors of the combination of S1, S2, and topographic indices derived from SRTM DEM.
The five tested algorithms were listed in Table 2. Linear regression algorithms included SWR and GWR, which were implemented in SPSS and GWR software (version 4.0, Ritsumeikan University, Kyoto, Japan), respectively.SWR is a global fitting regression model.SWR selects vital variables automatically.The contribution of variables to SWR can be determined by the coefficients [74].GWR estimates individual parameters for each estimation location as a spatial model, the closer to the location of an observation, the greater the weight in a GWR model [75].Machine learning algorithms were modeled in WEKA software (version 3.8, The University of Waikato, Hamilton, NZ).The ANN is a multi-layer perception neural network.Its architecture consists of input, hidden, and output layers, along with interconnection weights characterizing the connection strength.The algorithm takes the back-propagation learning rule to minimize the mean square error between the desired target and the actual output vectors [79].The initial weights are assigned randomly, and when developing the network, the interconnection weights are adjusted to minimize the prediction error.SVR can construct an optimal hyperplane by projecting the data onto a new hyperspace based on means of kernel functions.The hyperplane can fit data with a modeling function that minimizes empirical risk and complexity when representing non-linear patterns [80].
RF combines bagging with random variable selections at each node to iteratively generate a large group of classification and regression trees.Every node in trees is a condition on a single feature, designed to split the dataset into two.Impurity is a measure that is based on the locally optimal condition that is chosen.For regression trees, it is variance.Thus, when training a tree, it can be computed to learn how much each feature decreases the weighted impurity in a tree.For a forest, the impurity decrease from each feature can be averaged, and the features are ranked according to this measure.In other words, the attribute importance in RF algorithms were calculated based on the mean decrease variance.The classification output represents an average from the whole ensemble for regression.Hence, it achieves a more robust result than a single classification tree that is produced by a single model run [81].The performances of SWR, GWR, ANN, SVR, and RF algorithms of each variables group were tested and compared, based on the root mean squared error (RMSE, Equation ( 1)), mean absolute error (MAE, Equation ( 2)), mean error (ME, Equation ( 3)), and correlation coefficient between the measured and predicted AGB (r, Equation ( 4)) [36,82].The algorithm with the highest accuracy was selected for use in the predictive mapping of the AGB distribution in each group of variables.Four predictive maps were produced, which were derived from S1, S2, S, and S + S variables.
where ŷi is the estimated AGB value of each model, y i is the measured AGB value, and n is 387 in this study.The RMSE, MAE, and ME should be as small as possible, while r should be larger.

Relationship between Field-Measured Biomass with Sentinel-Based and Topographical Variables
Among the S1 variables, 54 were significantly related to forest AGB (p < 0.05), including two backscatter values (VV, VH), four window sizes of VH_MEA, VH_VAR, VH_COR, and all 10 texture variables of VV.The backscatter values were positively related to AGB.With the growth of the window size, the r values of those 13 texture variables increased.Except for four sizes of VV_CON, VV_DIS and VV_ENT were negatively related to AGB, and the other 40 texture variables showed positive correlations.In other words, increasing the smoothness and the order of the VV backscatter indicated the decrease of the forest AGB.The top five AGB-related S1 variables were VV_ASM 11 , VV_ENE 11 , VV_MAX 11 , VV_ENT 11 , and VV_HOM 11 .
As for S2, 21 variables were significantly related to forest AGB, excluding B5, 12, TSAVI, S2REP, and Cwc.The reflectance of B2-B4 were negatively related to AGB, while the other 18 variables showed the positive correlation.The reflectance of B2, NDI45, PSSRa, MCARI, and GNDVI displayed the strongest correlation with AGB.The vegetation indices that were calculated and synthesized by characteristic bands of S2 to monitor the chlorophyll of the vegetation were more distinguished and important for predicting forest AGB.
There were four topographical variables, i.e., H, M, TWI, and SPI, that obtained significant correlation with forest AGB, while impacts from the other eight factors were marginal.Elevation and wetness derived from SRTM DEM showed a positive influence on the increase of AGB; however, the surface roughness was negative.Hybrid macro-topographic indicators, as well as elevation, were more useful than other variables from SRTM DEM.Above all, 79 variables acquired from Sl, S2, and SRTM DEM explained the valid information of forest AGB.Based on the average response of the entire samples, elevation, the texture characteristics of the VV channel in the 11×11-pixel window size, and the vegetation indices were comparatively vital for the forest AGB prediction.

Predictors Selection and Descriptive Statistics
Based on the result from Section 3.1, 42 variables that had p values for the correlation analysis with AGB were above 0.05 were excluded.Then, 64 variables that had r values of the correlation analysis among predictors above 0.8 were disposed from the remaining 79 variables.Specifically, r values among VH_MEA and VH_VAR of four window sizes, as well as VH, were above 0.8, so that VH_MEA 11 with the highest r values of the correlation analysis with AGB was chosen as a predictor.Similarly, VH_COR 11 was chosen from VH_COR of four window sizes, then VV_DIS 11 was selected from VV_CON and VV_DIS of four window sizes, and VV_ASM 11 was selected from VV_HOM 5/7/9/11 , VV_ASM 5/7/9/11 , VV_ENE 5/7/9/11 , VV_MAX 5/7/9/11 and VV_ENT 5/7/9/11 , while VV_VAR 9 was elected from VV_MEA 5/7/9/11 , VV_VAR 5/7/9/11 and VV_COR 5/7/9/11 .B2 was selected rather than B3, B4, NDI45, and PSSRa, and B6 was chosen on behalf of B7, B8, B8A, IRECI, LAI, FVC, FAPAR, and Cab.The GDNVI was selected, on behalf of NDVI, TNDVI, and ARVI.As for the topographical variables, SPI was chosen rather than TWI.Among the remaining 15 variables, B6 and GNDVI, whose VIF exceeded the threshold of 10 were deleted.The predictors involved in modeling were the following 13 shown in Table 3. Their r values, which represent the simple linear relationship with AGB, were relatively low.It was revealed that combing predictors from multiple sources and modeling algorithms were necessary.3 displays the basic statistics of the measured AGB and the multiple remote sensor predictors used as explanatory variables.The AGB of all the samples varied from 0.67 to 533.60 Mg•ha −1 , with a standard deviation and coefficient of variation (CV) of 100.07 and 0.73, respectively, which indicated moderate variability.For the explanatory variables, the CV of surface roughness was 0.03, which showed the least variability.The CV of VV_DIS 11 , SPI, VV, and VH_MEA 11 were 4.02, 0.73, 0.65, and 0.58, indicating a stronger variability than the other predictors, respectively.The kurtosis of AGB was 0.49, and the skewness was 0.92, indicating that the AGB data had an approximately normal distribution.

Linear Regression
The four SWR models automated the selection of the best explanatory variables based on different predictors groups (Table 4).According to the formula and the p-values of the F-test, the four SWR models were strongly significant, while the factors influencing forest AGB varied.Specifically, VV_ASM 11 and VH_COR 11 were factors of forest AGB based on S1 predictors, and their impacts were significantly active, which was consistent with the above correlation analysis.B2 and B11 represented S2 indices for predicting AGB and explaining its variation significant influence.In accordance with adjusted R 2 , AGB predicted by the SWR model based on S2 fit the measured AGB better that that based on S1.When combining S1 and S2, MTCI became much more important by replacing VH_COR 11 , and the effect of B2 turned out to be unclear, due to the insignificance of its coefficient.In regard to the S+S variables, all four predictors from S1 and S2 models were retained.Among three predictors from SRTM DEM, only elevation showed a significant impact.Overall, VV_ASM 11 , B2, B11, and H were relatively essential for AGB modeling, based on the SWR algorithm, and the SWR model based on predictors from S + S explained more of the information on forest AGB then the other three, on the basis of the highest adjusted R 2 .The GWR models were the Gaussian approach, where the weight function was an adaptive Gaussian kernel.The models found the optimal bandwidth by using a golden section search and the corrected Akaike information criterion (AICc, small sample bias corrected AIC).The GWR was a local regression method whose parameters in the formula varied across the study area.The top three predictors with the largest absolute mean values of coefficients in each GWR model were recorded in Table 5. B2 and B11 were relatively important in GWR modeling for predicting forest AGB in the study area.According to the values of the adjusted R 2 of four models, predictors from S2 were more influential than that from S1 on forest AGB prediction.However, the effective information decreased when S1 variables or topographic indices were added, as indicated by the lowest value of AICc of the S2 model, among the four.
To sum up, both global and local linear regression algorithms indicated that predictors from S2 performed better than those from S1. Combining all of the factors from S1, S2, and SRTM DEM improved the ability of the linear regression models to predict forest AGB.

Machine Learning Algorithms
The necessary parameters of machine learning models are shown in Table 6.The optimized ANN architecture of the S1 model used 13 input nodes in the input layer, six nodes in the hidden layer with the unipolar sigmoid as the transfer function, and one node in the output layer (i.e., 13-16-1).Using the Levenberg-Marquardt learning algorithm, the best learning rate, momentum, and training time obtained were determined to be 0.1, 0.2, and 500, respectively.Likewise, the other three ANN models were built with parameters in Table 6.As for the SVR models, using the SMO (sequential minimal optimization) algorithm with Shevade et al. [83] and the RBF (radial basis function) kernel, the best parameters for C and σ that were obtained were both five and five, respectively.With a tree number of 1000, and feature numbers of four, two, five, and eight, the RF models based on S1, S2, S, and S+S were acquired, respectively.The attribute importance for the four RF models was calculated based on the mean decrease variance, and illustrated in Figure 4.In detail, VH_COR 11 was the most important factor of the RF model based on the S1 predictors, which was in accordance with the linear regression models.In the S2 RF model, MCARI was the most needed predictor, which was different to the linear models.When integrating S1 and S2 to build the RF models, the attribute importance ranking of the S1 variables changed a little, which was that VH_MEA 11 turned out to be more important than VV_ASM 11 .While the attribute importance ranking of the S2 variables changed, B2 surpassed MTCI and MCARI, and became the primary predictor.Additionally, predictors from S2 were more crucial than those from S1, due to the higher importance in the S model.After adding topographic indices to the S RF model, the attribute importance ranking of factors from S1 remained the same, while that from S2 changed, where MTCI was shown to be the most important among the S2 predictors.Elevation was the most essential factor, followed by MTCI and SPI.In short, predictors from S2 were more vital than that from S1, which was also found by linear models, and elevation from SRTM DEM contributed to a lot of RF modeling for predicting forest AGB.

Models Assessment and Biomass Mapping.
Calculated by an independent validation dataset, the accuracies of the five algorithms were depicted in Figure 5.All five S1 models underestimated AGB, except for the ANN model.The S1 RF model, with the lowest RMSE (19.90 Mg•ha −1 ), MAE (30.31 Mg•ha −1 ), and ME (2.65 Mg•ha −1 ) as well as the highest r (0.9781), was an algorithm chosen to predict forest AGB based on S1 indices.The S2 models all underestimated the AGB.The RF algorithm also was considered the optimal one, where the RMSE, MAE, ME, and r were 21.37, 28.61, 1.37 Mg•ha −1 , and 0.9715, respectively.Coupling the S1 and S2 explanatory variables, the accuracies of all the models increased, and the RF was also the most accurate algorithm with the lowest RMSE (12.51 Mg•ha −1 ), MAE (27.15 Mg•ha −1 ), and ME (1.15 Mg•ha −1 ), as well as the highest r (0.9790).The models combining the explanatory variables from S1, S2, and SRTM DEM all showed the tendency for underestimation.Although the ANN algorithm obtained the lowest RMSE and ME among the S + S models, its value of ME was relatively high, and r was low.Thus, the RF model was selected again with the lowest MAE (25.48 Mg•ha −1 ) and the highest r (0.9769), where the RMSE and ME were 61.11 and 1.39 Mg•ha −1 , respectively.In summary,

Models Assessment and Biomass Mapping.
Calculated by an independent validation dataset, the accuracies of the five algorithms were depicted in Figure 5.All five S1 models underestimated AGB, except for the ANN model.The S1 RF model, with the lowest RMSE (19.90 Mg•ha −1 ), MAE (30.31 Mg•ha −1 ), and ME (2.65 Mg•ha −1 ) as well as the highest r (0.9781), was an algorithm chosen to predict forest AGB based on S1 indices.The S2 models all underestimated the AGB.The RF algorithm also was considered the optimal one, where the RMSE, MAE, ME, and r were 21.37, 28.61, 1.37 Mg•ha −1 , and 0.9715, respectively.Coupling the S1 and S2 explanatory variables, the accuracies of all the models increased, and the RF was also the most accurate algorithm with the lowest RMSE (12.51 Mg•ha −1 ), MAE (27.15 Mg•ha −1 ), and ME (1.15 Mg•ha −1 ), as well as the highest r (0.9790).The models combining the explanatory variables from S1, S2, and SRTM DEM all showed the tendency for underestimation.Although the ANN algorithm obtained the lowest RMSE and ME among the S + S models, its value of ME was relatively high, and r was low.Thus, the RF model was selected again with the lowest MAE (25.48 Mg•ha −1 ) and the highest r (0.9769), where the RMSE and ME were 61.11 and 1.39 Mg•ha −1 , respectively.In summary, all of the models underestimated forest AGB except for the ANN one based on the S1 factors, and four RF algorithms were selected to map forest AGB distribution.
The predicted values of forest AGB of the study area ranged from 5.91 to 442.82 Mg•ha −1 (Figure 6).For a better comparison among the four models, the values were divided into seven levels by intervals of measured AGB values in Figure 2a.All maps showed that the southern part of the study area was a high AGB region, with values ranging from 208.06 to 442.82 Mg•ha −1 .Low AGB (5.91 to 53.37 Mg•ha −1 ) zones were located close to non-forest areas.Comparing the predicted and measured AGB (Figure 2), the RF model built by multisource explanatory variables from S1, S2, and SRTM DEM performed the best (Figure 6a).The map produced from the RF model based on six S1 predictors displayed the fragmentation of AGB, where spatial distribution was rather random (Figure 6d).Although there were only four predictors from S2, they demonstrated better performance compared to S1 factors on forest AGB mapping by the RF algorithm (Figure 6c), but it was still difficult to predict high values of forest AGB (238-533.06Mg•ha −1 , shown in Figure 2a).The distribution of forest AGB predicted by the RF model using S1 and S2 predictors (Figure 6b) was similar with that by the S2 RF model.This S model made progress in high values of forest AGB; however, it overestimated low values of AGB (0.67-29.83Mg•ha −1 , shown in Figure 2a).It had a great improvement on the accuracy of forest AGB mapping, where topographic indices from SRTM DEM were joined to the explanatory variables of the RF model (Figure 6a).In detail, the distribution of the predicted values of forest AGB by the Sentinel series, combined with the SRTM DEM model depicted in Figure 6a, was relatively in keeping with the field data (Figure 2).all of the models underestimated forest AGB except for the ANN one based on the S1 factors, and four RF algorithms were selected to map forest AGB distribution.The predicted values of forest AGB of the study area ranged from 5.91 to 442.82 Mg•ha −1 (Figure 6).For a better comparison among the four models, the values were divided into seven levels by intervals of measured AGB values in Figure 2a.All maps showed that the southern part of the study area was a high AGB region, with values ranging from 208.06 to 442.82 Mg•ha −1 .Low AGB (5.91 to 53.37 Mg•ha −1 ) zones were located close to non-forest areas.Comparing the predicted and measured AGB (Figure 2), the RF model built by multisource explanatory variables from S1, S2, and SRTM DEM performed the best (Figure 6a).The map produced from the RF model based on six S1 predictors displayed the fragmentation of AGB, where spatial distribution was rather random (Figure 6d).Although there were only four predictors from S2, they demonstrated better performance compared to S1 factors on forest AGB mapping by the RF algorithm (Figure 6c), but it was still difficult to predict high values of forest AGB (238-533.06Mg•ha −1 , shown in Figure 2a).The distribution of forest AGB predicted by the RF model using S1 and S2 predictors (Figure 6b) was similar with that by the S2 RF model.This S model made progress in high values of forest AGB; however, it overestimated low values of AGB (0.67-29.83Mg•ha −1 , shown in Figure 2a).It had a great improvement on the accuracy of forest AGB mapping, where topographic indices from SRTM DEM were joined to the explanatory variables of the RF model (Figure 6a).In detail, the distribution of the predicted values of forest AGB by the Sentinel series, combined with the SRTM DEM model depicted in Figure 6a, was relatively in keeping with the field data (Figure 2).This study revealed that the relationships of the measured AGB with Sentinel-based and topographical predictors varied by modeling the algorithms according to parameters from the SWR and GWR formulas, and the attribute importance from RF models.VV_ASM11 and VH_COR11 were

Sentinel-Based and Topographical Predictors of Forest AGB Mapping
This study revealed that the relationships of the measured AGB with Sentinel-based and topographical predictors varied by modeling the algorithms according to parameters from the SWR and GWR formulas, and the attribute importance from RF models.VV_ASM 11 and VH_COR 11 were the most important variables among the S1 variables for explaining the observed spatial patterns of forest AGB both in the linear global and local regression, and this was also shown in the RF models.Texture features were usually calculated for forest AGB mapping, with one fixed window size [15,67,84].It was helpful to note that the texture characteristics of the Sentinel SAR backscatters with a larger window size (i.e., 11 × 11) achieved a greater potential for mapping forest AGB, based on the correlation analysis.The backscatter coefficients of S1 and their calculation were useful as common predictors [36,85,86].The study indicated that direct use of the backscatter coefficients from the SAR C band might not be appropriate.The lack of penetrability could affect biomass information retrieval.Meanwhile, the variation and disorder of backscatters showed in texture might be caused by vegetation diversity and density.These texture characteristics denoted a significant relationship with AGB.In other words, vegetation diversity and density was reflected as variation of backscatter texture, resulting in higher forest AGB.Some of the S2 variables showed a significant relationship with forest AGB [87][88][89].This indicated that the selection of predictors were necessary for S2-based prediction.Owing to the acquisition from the band calculation, two vegetation indices were deleted in the S2 SWR model, while they showed a greater impact on GWR and RF modeling of forest AGB.It revealed that variables obtained from the operation of S2 multispectral bands, especially vegetation indices representing chlorophyll characteristics, were more efficient for complex regression algorithms, whereas the reflectance of multispectral bands as the direct information of S2 were more important for simple global linear modeling.However, collinearity and redundancy of the predictors decreased the effective information of models, and this pre-processing for modeling needs to be improved in future work.It was supposed that predictors were obtained by synthesizing indices such as principal component analysis, rather than simply deleting variables with lower correlation with forest AGB.
The strongest related predictor was elevation, as shown in Table 3 and Figure 4.The vital role of topography was also reported in other studies by influencing water and sunlight supply and storage [36,44,64].As a proxy for the potential soil-water storage for vegetation [90], TWI was reported as being an important factor for estimating forest AGB, using nonlinear regression models [64].However in this study, it was replaced by SPI, which was more relative to measured AGB.SPI was the third important predictor of the RF model (Figure 4), after H and MTCI, and it is also listed in the SWR model.It demonstrated that SPI was an essential predictor for forest AGB mapping.Due to the close correlation between AGB and TWI and SPI, it was proposed that both indices should be tested in other geographical settings that are different than this study.Surface roughness (M) was also a vital predictor in this study, both in linear regression and machine learning models, which had a greater influence than S1 predictors.Predictors from S2 were comparatively primary for forest AGB prediction.Factors from SRTM DEM were effective compared to that from S1 in complex AGB modeling, while S1 texture features were useful in simple AGB models.It is suggested that texture characteristics measured in an 11×11-pixel window of S1, and the reflectance and vegetation indices of S2, as well as elevation, SPI, TWI, and M be recommended predictors for forest AGB mapping.

Optimal Combination of Predictors and Modeling Algorithms
Based on the predictor selection in Section 3.2.1, the best predictors for forest AGB mapping were determined to be those listed in Table 3, which belong to the four variable groups, S1, S2, S and S + S. In contrast, the optimal modeling algorithm for predictors from the four variable groups were all the RF algorithm.This study revealed the powerful capacity of the RF algorithm to predict forest AGB, as in other reported studies [88,[91][92][93].The SVR algorithm, however, performed the worst for S1 variables, while the SWR algorithm performed the worst for S2 and S, as well as S+S modeling.Different from other studies [29,33,91], the performances of linear regression algorithms in this research were closer to that by machine learning.The improvement might be from the contribution of the localized spatial scale of the study, and the density of representative field samples of forest AGB.It was demonstrated that SVR algorithm was suitable for limited samples prediction, in agreement with other studies [25,48,94].Figure 5 indicated that predictor variables were more important than algorithms for remote sensing-based estimations of forest AGB.The linear regression depended more on predictors than on machine learning algorithms.
L-and P-band SAR, as well as LiDAR were crucial for prediction of high forest AGB values.Although C band SAR and optical multispectral have demonstrated the saturation for detecting the sensibility of forest AGB, the Sentinel series, and SRTM DEM in fine-resolution with full coverage provided critical information for applications in comparison to forest AGB estimation.

Figure 1 .
Figure 1.The outline of the study area, sampling sites, and the coverage of Sentinel-1 synthetic aperture radar (SAR), Sentinel-2 multispectral instrument (MSI), and Shuttle Radar Topographic Mission (SRTM) data.

Figure 1 .
Figure 1.The outline of the study area, sampling sites, and the coverage of Sentinel-1 synthetic aperture radar (SAR), Sentinel-2 multispectral instrument (MSI), and Shuttle Radar Topographic Mission (SRTM) data.
Remote Sens. 2019, 11, x FOR PEER REVIEW 4 of 20forests.Based on allometric equations[45][46][47][48], measured diameter at breast height (1.3 m from the ground) and tree height, field-based forest AGB at each plot was calculated.The forest AGB samples were from 0.67 to 533.60 Mg•ha −1 , with the median value being between 103.36 to 143.64 Mg•ha −1 (Figure2a), and mainly below 200 Mg•ha −1 with 77.8% (Figure2b).The 1,162 sampling sites were randomly divided into training (n = 775) and validation (n = 387) sets (Figure1) for establishing and examining the performance of the models.

Figure 2 .
Figure 2. The values of measured above-ground biomass (AGB).(a) Field plot profiles of AGB in the study site from Plot 1 to 1,162; (b) Components of AGB.

Figure 2 .
Figure 2. The values of measured above-ground biomass (AGB).(a) Field plot profiles of AGB in the study site from Plot 1 to 1,162; (b) Components of AGB.

Figure 3 .
Figure 3. Flowchart for the evaluation of the optimal combination of predictors, and modeling algorithms for forest above-ground biomass mapping from Sentinels and the SRTM data.

Figure 3 .
Figure 3. Flowchart for the evaluation of the optimal combination of predictors, and modeling algorithms for forest above-ground biomass mapping from Sentinels and the SRTM data.

Figure 4 .
Figure 4.The attribute importance based on the average impurity decrease for the four RF models.

Figure 4 .
Figure 4.The attribute importance based on the average impurity decrease for the four RF models.

Figure 6 .
Figure 6.Maps of AGB prediction in the study area derived from the best combination of predictors and models, based on the Sentinel series and the SRTM DEM data: (a) S+S with RF; (b) S with RF; (c) S2 with RF; (d) S1 with RF.

Table 1 .
Remote sensing indices from the Sentinel series and SRTM digital elevation model (DEM) data for AGB mapping.

Table 3 .
Descriptive statistics of field-measured forest AGB, Sentinel-based, and topographical predictors. *Table

Table 4 .
Summary of AGB models by SWR.
* denotes significance with a p-value of t-test below 0.05; ** denotes strong significance with a p-value below 0.01.

Table 5 .
Summary of AGB models by GWR.

Table 6 .
Summary of AGB models by ANN, SVR and RF.