Estimating Aboveground Biomass of Mangrove Forests in Indonesia Using Spatial Attention Coupled Bayesian Aggregator

Abstract

Mangroves play a crucial part in the worldwide blue carbon cycle because they store a lot of carbon in their biomass and soil. Accurate estimation of aboveground biomass (AGB) is essential for quantifying carbon stocks and understanding ecological responses to climate and human disturbances. However, regional-scale AGB mapping remains difficult due to fragmented mangrove distributions, limited field data, and cross-site heterogeneity. To address these challenges, we propose a Spatial Attention Coupled Bayesian Aggregator (SAC-BA), which integrates field measurements with multi-source remote sensing (Landsat 8, Sentinel-1), terrain data, and climate variables using advanced ensemble learning. Four machine learning models (Random Forest (RF), Cubist, Support Vector Regression (SVR), and Extreme Gradient Boosting (XGBoost)) were first trained, and their outputs were fused using Bayesian model averaging with spatial attention weights and constraints based on Local Indicators of Spatial Association (LISAs), which identify spatial clusters (e.g., high–high, low–low) to improve accuracy and spatial coherence. SAC-BA achieved the highest performance (coefficient of determination (${\mathrm{R}}^2$) = 0.82, root mean square error = 29.90 Mg/ha), outperforming all individual models and traditional BMA. The resulting 30-m AGB map of Indonesian mangroves in 2017 estimated a total of 217.17 × ${\mathrm{10}}^6$ Mg, with a mean of 103.20 Mg/ha. The predicted AGB map effectively captured spatial variability, reduced noise at ecological boundaries, and maintained high confidence predictions in core mangrove zones. These results highlight the advantages of incorporating spatial structure and uncertainty into ensemble modeling. SAC-BA provides a reliable and transferable framework for regional AGB estimation, supporting improved carbon assessment and mangrove conservation efforts.

1. Introduction

Mangroves are vital ecosystems located in the intertidal zones of tropical and subtropical coastlines, serving as critical interfaces between land and sea. They provide essential ecological and economic services, such as purifying seawater, preventing coastal erosion, sequestering carbon, and supporting rich biodiversity [1,2]. Mangroves are among the most efficient natural carbon sinks, capable of storing up to 1023 Mg C/ha in biomass and soils, far exceeding many terrestrial forests [3,4]. Due to their high carbon sequestration capacity and long-term carbon storage in anaerobic sediments, mangroves are recognized as key blue carbon ecosystems that play a vital role in mitigating climate change. Although they occupy only about 2% of the world’s coastal area, mangroves account for 10%–15% of carbon burial in coastal oceans globally, with annual sequestration rates ranging from 174 to 265 g ${\text{C/m}}^2$/year [4,5]. Despite comprising just 0.7% of tropical forest area [6], mangroves possess among the highest carbon densities of any forest type, particularly in the Indo-Pacific region [3], with total ecosystem carbon stocks exceeding 1000 Mg C/ha. These properties make mangroves disproportionately important in the global carbon budget relative to their areal extent.

However, the survival of mangroves is increasingly threatened by climate change and human activities. Global economic expansion and the widespread burning of fossil fuels have accelerated carbon emissions, intensifying global warming and associated climate challenges [7]. At the same time, deforestation, aquaculture development, and coastal urbanization have led to widespread degradation and loss of mangrove habitats, making them one of the most endangered tropical ecosystems [7,8,9,10]. Given the critical role of mangroves in carbon storage and climate regulation, accurately estimating their aboveground biomass (AGB) is essential. Reliable AGB estimates are crucial for quantifying carbon losses due to habitat destruction and for informing strategies aimed at conservation, restoration, and sustainable management of mangrove ecosystems.

The methods for estimating mangrove AGB can be broadly divided into three categories: parametric models, non-parametric statistical models, and machine learning (ML) models.

Parametric models, such as species-specific allometric equations, rely on ecological and biophysical principles to estimate biomass from structural attributes of mangrove trees, including height, diameter at breast height (DBH), and canopy width. These models assume predefined functional relationships among variables and are typically derived from destructive sampling and site-specific field measurements. While they offer accurate estimations at the plot level, their applicability is often constrained by labor intensity and limited scalability across larger or heterogeneous regions [11,12].

Non-parametric models estimate mangrove AGB based on empirical relationships with environmental indicators, often using regression or machine learning (ML) without predefined functional forms. Optical imagery from Landsat and Sentinel-2 is widely used for regional AGB mapping. For example, Pramaditya et al. [13] used Landsat 8 and stepwise regression to estimate AGB, while Mariano et al. [14] combined vegetation indices (e.g., normalized difference vegetation index (NDVI), Soil Adjusted Vegetation Index (SAVI), and enhanced vegetation index (EVI)) from Landsat 8 and Sentinel-2B, finding NDVI most effective. Radar data such as PALSAR has also been applied; Hamdan et al. [15] linked backscatter coefficients to AGB in Malaysian mangroves using regression models. Some hybrid models like InVEST and MCAT-DNDC also fall under this category. InVEST estimates carbon pools using land use and socio-economic inputs, but assumes constant carbon density, potentially reducing accuracy [16]. MCAT-DNDC simulates mangrove carbon fluxes at 30 m resolution but is mainly applied in the Americas [17].

ML models represent a more recent and powerful class of tools that leverage high-dimensional, multi-source data, such as satellite imagery, UAV observations, and climate variables, to learn complex nonlinear relationships through algorithmic training. These models have become increasingly popular for regional AGB estimation. Li et al. [18] combined UAV LiDAR and multispectral data to extract vegetation indices, canopy height, and texture features, comparing multiple ML algorithms including Random Forest (RF), Support Vector Regression (SVR), and Artificial Neural Networks (ANNs). Their results showed that RF outperformed many satellite-based models in predictive accuracy. Similarly, Tian et al. [19] used UAV-derived canopy height, texture metrics, and field plot data to assess the performance of eight ML algorithms in estimating AGB across species in the Beibu Gulf. Their findings highlighted the superior accuracy of XGBoost in integrating ground observations with low-altitude remote sensing data.

Parametric models are limited by site-specific empirical relationships [20], while non-parametric remote sensing approaches struggle with ecological complexity [21]. Although ML models can capture nonlinear patterns, their predictions often lack spatial coherence in heterogeneous landscapes [22].

To address this issue, spatial statistical tools such as Local Indicators of Spatial Association (LISAs) [23] have been widely used to detect spatial clusters and outliers. LISA provides a local measure of spatial autocorrelation, helping to characterize and preserve spatial structure in geospatial data. Building on this insight, we propose Spatial Attention Coupled Bayesian Aggregator (SAC-BA), a spatially explicit ensemble framework that couples Bayesian model averaging (BMA) with spatial attention mechanisms and LISA-based structural constraints. By prioritizing ecologically similar regions and penalizing spatially inconsistent predictions, SAC-BA enhances both predictive accuracy and spatial consistency in AGB mapping.

The main objectives of this study are

• To develop, evaluate, and compare the performance of four ML models (RF, Cubist, SVR, and XGBoost) for estimating AGB;
• To design a spatial attention mechanism that incorporates slope and LISA clustering to account for spatial heterogeneity in AGB distribution;
• To propose a novel SAC-BA that integrates spatial statistics and model uncertainty into Bayesian model averaging for generating high-resolution AGB maps.

2. Materials and Methods

2.1. Materials

2.1.1. Study Area

Indonesia, the world’s largest archipelago, consists of over 17,000 islands and spans the equator from 12° S to 7° N, between longitudes 95° E and 141° E. Its extensive geography supports a wide variety of ecosystems and climate zones. The country has a tropical climate, with average annual temperatures ranging from 26 °C to 28 °C, maintaining a warm and moist environment all year round. Yearly rainfall often exceeds 2000 mm in the western and central regions, with a rainy season typically lasting from November to March [24]. Indonesia is home to the largest mangrove forest in the world, covering approximately 2.94 million hectares, accounting for about 20% of the global mangrove area [25,26]. Indonesian mangroves are primarily distributed along coastal zones, particularly in tidal flats across Sumatra, Kalimantan, Java, Papua, Sulawesi, and surrounding islands [27]. Dominant mangrove species vary by region, with Rhizophora spp., Avicennia spp., Sonneratia alba Sm., Nypa fruticans Wurmb, Bruguiera gymnorrhiza (L.) Lam., and Rhizophora apiculata Blume being the most prevalent [28]. Typically, Indonesian mangroves exhibit an average tree height ranging from 10 to 25 m, depending on species and geomorphic settings, with tree densities varying between 500 to 2000 stems per hectare [3,10]. The long-term influence of the tropical climate has fostered the development of these extensive and diverse mangrove ecosystems, which play a crucial role in coastal protection, carbon sequestration, and biodiversity conservation.

2.1.2. The Field Observation Data

Field observation data form the basis for estimating mangrove carbon stocks. In this study, we collected plot-level AGB data from published literature and open-access biomass databases. Searches in Google Scholar and Web of Science used keywords such as “mangrove”, “biomass”, and “carbon sequestration”, focusing on studies from 2015 onward [29]. Records based on remote sensing-derived canopy height (e.g., radar altimetry, LiDAR) were excluded due to higher uncertainties [30], as field studies typically apply species-specific allometric equations. Using the mangrove cover map, all sample locations were manually verified, and duplicate coordinates were averaged [31]. As shown in Figure 1, 89 plots were selected, with higher densities near Java and Papua Islands. To ensure transparency and reproducibility, the compiled dataset, including AGB values, coordinates, and original literature references, has been published on Figshare and is accessible at the DOI https://doi.org/10.6084/m9.figshare.29400035.v1 (accessed on 7 August 2025).

2.1.3. Satellite Remote Sensing Data

This study uses Sentinel-1 and Landsat 8 data from the Google Earth Engine (GEE) platform, with image selection covering the period from 1 January 2017, to 1 January 2018. Sentinel-1 is the first satellite launched as part of the European Space Agency’s (ESA) Copernicus Global Earth Observation System (GEMS). In this study, we employed dual-polarization C-band Synthetic Aperture Radar (SAR) data, focusing on the Vertical–Vertical (VV) and Vertical–Horizontal (VH) polarization bands. We calculated the ratio between VV and VH polarization, which was then added as a new band. Landsat 8, a satellite jointly launched by NASA and the United States Geological Survey (USGS), provides valuable remote sensing data. In our study, we utilized the Landsat 8 Surface Reflectance (SR) dataset, which has been atmospherically corrected to improve surface reflectance accuracy. By analyzing multiple bands (such as blue, green, red, and near-infrared), we extracted several vegetation indices, including the normalized difference vegetation index (NDVI), enhanced vegetation index (EVI), Normalized Difference Water Index (MNDWI), Normalized Difference Built-up Index (NDBI), and Bare Soil Index (BSI). These indices serve as effective spectral features for estimating mangrove carbon stocks.

2.1.4. Explanatory Variables from Additional Data Sources

Variables like precipitation, temperature, and elevation have been demonstrated to improve AGB estimation at the regional scale [32]. As a result, these explanatory variables were incorporated into the AGB prediction model. The annual precipitation (AP) and mean annual temperature (MAT) datasets for 2017 were obtained from the Climate Research Unit (CRU) dataset, developed by the UK’s National Centre for Atmospheric Science (NCAS), with a spatial resolution of 0.5° (https://crudata.uea.ac.uk/cru/data/hrg/) (accessed on 7 August 2025). Terrain information was obtained from the Copernicus GLO-30 Digital Elevation Model (DEM) dataset, provided by the U.S. Geological Survey (USGS) via GEE. Appendix

Table A1. All explanatory variables used in this study.

Data Name	Variable Index	Variable Name	Description	Spatial Resolution
Sentinel-1	1	VV	Radar band with vertical	10 m
			transmission and vertical reception
	2	VH	Radar band with vertical
			transmission and horizontal reception
	3	VV/VH	Ratio of VV to VH bands
Landsat 8	4	SR_B1	Coastal aerosol band	30 m
	5	SR_B2	Blue band
	6	SR_B3	Green band
	7	SR_B4	Red band
	8	SR_B5	Near-infrared band
	9	SR_B6	Shortwave infrared band 1
	10	SR_B7	Shortwave infrared band 2
	11	ST_B10	Thermal infrared band
	12	BSI	(SR_B6 + SR_B4 − SR_B5 − SR_B2)/
			(SR_B6 + SR_B4 + SR_B5 + SR_B2)
	13	EVI	2.5 × (SR_B5 − SR_B4)/
			(SR_B5 + 6 × SR_B4 − 7.5 × SR_B2 + 1)
	14	MNDWI	(SR_B3 − SR_B6) / (SR_B3 + SR_B6)
	15	NDBI	(SR_B6 − SR_B5) / (SR_B6 + SR_B5)
	16	NDVI	(SR_B5 − SR_B4) / (SR_B5 + SR_B4)
Copernicus DEM	17	DEM	Digital elevation model	30 m
	18	Slope	The steepness of the terrain
Climate Research Unit	19	MAT	Mean Annual temperature	${\mathrm{0.5}}^{\circ }$
	20	AP	Annual precipitation

summarizes all the variables used.

To ensure spatial consistency among datasets with differing native resolutions, all input layers were resampled to a common 30m resolution prior to analysis. Bilinear interpolation was used for continuous variables, including spectral reflectance, vegetation indices, elevation, and climatic parameters. This resampling step ensured that all predictors were spatially aligned and suitable for pixel-wise integration and modeling.

2.2. Methods

As shown in Figure 2, to improve the accuracy of AGB estimation under spatial heterogeneity, this study proposes a fusion model that integrates a spatial attention mechanism with an uncertainty-based cooperative weighting strategy: SAC-BA. This approach combines the prediction results and associated uncertainties from four base ML models (RF, SVR, XGBoost, and Cubist), along with spatial similarity relationships between pixels and local LISA clustering patterns, to ultimately generate a mangrove AGB map.

2.2.1. Four Machine Learning (ML) Methods and Feature Selection

Four machine learning algorithms were applied to estimate mangrove AGB: Random Forest (RF), Extreme Gradient Boosting (XGBoost), Support Vector Regression (SVR), and Cubist. RF, proposed by Breiman [33], is a Bagging-based ensemble of decision trees, known for its robustness and ability to model nonlinear relationships [18,34]. XGBoost [35] is a gradient-boosting method that iteratively improves decision trees, offering high accuracy and efficiency [36,37]. SVR [38] employs statistical learning theory to fit an optimal hyperplane, making it suitable for small, high-dimensional datasets [39,40,41]. Cubist [42] is a rule-based regression tree model combining decision rules with multivariate linear regressions, allowing for extrapolation beyond sample coverage [43,44,45].

Each model was evaluated using 10-fold cross-validation, where data were split into 10 subsets with iterative training and testing. Performance was assessed using the coefficient of determination (${\mathrm{R}}^2$) and root mean square error (RMSE).

Considering all possible variable combinations during model development, and to further enhance modeling efficiency and interpretability, we used SHapley Additive exPlanations (SHAP) to assess the contribution of each feature to the model’s output. Based on the Akaike Information Criterion (AIC), we selected the feature subset with the highest accuracy and compared it with a model that includes all 20 variables.

SHAP is a tool derived from the Shapley value in cooperative game theory, used to explain ML model predictions. It provides a systematic approach to quantify the contribution of each feature to the model’s prediction. The main idea is to decompose the model prediction into individual contributions from each feature, offering deeper insights into the decision-making process. AIC is a statistical method used for model selection, which strikes a balance between goodness of fit and model complexity, preventing overfitting by considering the number of parameters. The formula for calculating AIC is shown in Equation (1).

$$AIC=2(k)-2ln(L)$$

(1)

where k is the number of parameters in the model, and L is the model’s maximum likelihood estimate.

In this process, highly correlated variables with redundant information were indirectly reduced, as SHAP prioritizes features with independent contributions to prediction, and AIC penalizes unnecessary model complexity. Although our primary goal was to enhance predictive performance, this feature selection process also mitigates potential multicollinearity among covariates.

2.2.2. Machine Learning with Bayesian Model Averaging (ML-BMA)

To enhance the stability and accuracy of multi-model predictions, the Bayesian model averaging (BMA) method is used to integrate four ML models (RF, XGBoost, SVR, and Cubist), forming the ML-BMA model. ML-BMA leverages the strengths of multiple models [46,47], avoiding the bias of a single model and improving the stability and accuracy of predictions. In practical applications, BMA is typically combined with cross-validation to further enhance the model’s generalization ability. Compared to other ensemble methods (such as simple weighted averaging, voting, Bagging, and Boosting), BMA assigns weights based on posterior probabilities, thereby more accurately reflecting model uncertainty. As a result, ML-BMA can adaptively select the best model combination, improving prediction reliability. The prediction result of ML-BMA is shown in Equation (2).

$${\widehat{y}}_{BMA}=\sum _{i=1}^{k}P\left(M_i\left|D\right.\right)·{\widehat{y}}_{M_i}$$

(2)

where ${\widehat{y}}_{M_i}$ is the prediction of model $M_i$, and $P\left(M_i\left|D\right.\right)$ is the posterior probability of model $M_i$, representing the model’s relative confidence given the data D.

2.2.3. Spatial Attention Coupled Bayesian Aggregator (SAC-BA)

To further enhance the robustness and local adaptability of the model under complex spatial structures, this study proposes a Spatial Attention Coupled Bayesian Model (SAC-BA), which integrates spatial attention mechanisms and spatial aggregation penalty factors. Building upon Bayesian weighted fusion, the method introduces two core improvement modules: neighborhood spatial attention and LISA penalty factors, to improve the model’s ability to perceive and respond to spatial heterogeneity.

• Spatial Autocorrelation Analysis:
  To characterize the spatial clustering and structural stability of AGB, spatial autocorrelation analysis was employed to construct structural penalty factors in the model fusion process. Global Moran’s I [23], defined in Equation (3), quantifies overall spatial autocorrelation, with values ranging from –1 (dispersion) to 1 (clustering), and values near 0 indicating randomness. To mitigate uncertainty diffusion in spatial transition zones, a local spatial penalty was further introduced based on LISA. Each pixel was classified into five types based on local and neighboring values: high–high (HH) for high-value pixels surrounded by high-value neighbors, low–low (LL) for low-value pixels surrounded by low-value neighbors, high–low (HL) for high-value pixels surrounded by low values, low–high (LH) for low-value pixels surrounded by high values, and Not Significant (NS) where no significant local spatial association was detected.

  $$I={\displaystyle \frac{N}{\sum \sum W_{ij}}}·{\displaystyle \frac{\sum \sum (X_i-\overline{X})(X_j-\overline{X})}{\sum {(X_i-\overline{X})}^2}}$$

  (3)

  where, $X_i$ and $X_j$ represent the $i^{th}$ and $j^{th}$ variable values, and $\overline{X}$ is the mean of all X. $W_{ij}$ represents the spatial weight or relationship between the $i^{th}$ and $j^{th}$ variables. $\sum \sum W_{ij}$ represents the sum of all weights, and N represents.
• Spatial Attention Weight Construction:
  The attention mechanism, originally used in natural language processing and image recognition, is a key component in the efficient allocation of resources during information processing [48]. The attention mechanism assigns sufficient focus to critical information by means of a probability distribution. In spatial modeling, it is used to measure the similarity between the target pixel and its neighboring pixels, and based on this, different weighted contributions are allocated. In this study, we first construct a 3 × 3 sliding window centered on each target pixel and extract the 8 neighboring pixels within its neighborhood. For each neighboring pixel j, we calculate the difference between it and the center pixel c in three aspects: first, the difference between the AGB prediction values; second, whether the LISA clustering categories are consistent; and third, the difference in terrain factors, specifically the slope.
  The AGB value difference is calculated through the absolute value difference and adjusted by the coefficient $\gamma$, as shown in Equation (4):

  $$S_j=-\gamma ·|x_j-x_c|$$

  (4)
  The LISA classification difference is represented by an indicator function, where if the two classifiers are different, it takes the value 1, otherwise, it is 0. This is adjusted by the coefficient $\lambda$, as shown in Equation (5):

  $$P_j=-\lambda ·\mathbb{I}(L_j\ne L_c)$$

  (5)
  The terrain difference is calculated through slope difference and adjusted by the weight coefficient $\eta$, as shown in Equation (6):

  $$H_j=-\eta ·|T_j-T_c|$$

  (6)
  The above three items are summed up as an index, used as the unified attention weight for the region around pixel j, as shown in Equation (7):

  $$q_j=exp(S_j+P_j+H_j)$$

  (7)
  Finally, the attention coefficient $A_i$ for the center pixel i is obtained as in Equation (8):

  $$A_i={\displaystyle \frac{q_c}{{\sum }_{j\in N\left(e\right)}{q}_j}}$$

  (8)
• Fusion Weight Calculation Method:
  This study designs a fusion method based on uncertain prediction, where the uncertainty of spatial and terrain heterogeneity is introduced into the modeling process. The method improves the model’s prediction uncertainty and stability. This paper, based on the ML-BMA framework, proposes a SAC-BA model to handle fusion uncertainty. LISA aggregation and spatial attention based on three factors are incorporated.
  The specific fusion formula is shown in Equation (9):

  $$w_m\left(i\right)={\displaystyle \frac{exp(-\alpha ·u_m\left(i\right)-\beta ·p\left(i\right))·A_i}{{\sum }_{m}exp(-\alpha ·u_m\left(i\right)-\beta ·p\left(i\right))·A_i}}$$

  (9)

  where
  • $\alpha$ represents the impact weight of uncertainty factors;
  • $\beta$ represents the impact weight of structural factors;
  • $u_m\left(i\right)$ is the predicted uncertainty of model m at pixel i; the uncertainty is treated as a model difference in our study;
  • $p\left(i\right)$ is the LISA cluster type of pixel i, which indicates different spatial distribution of cluster stability. It is set as follows in Equation (10):
  $$p\left(i\right)=\left\{\begin{array}{cc}0.2,\hfill & \mathrm{if}\mathrm{pixel}i\mathrm{belongs}\mathrm{to}HH\mathrm{or}LL\hfill \\ 0.8,\hfill & \mathrm{if}\mathrm{pixel}i\mathrm{belongs}\mathrm{to}HL\mathrm{or}LH\hfill \\ 0.4,\hfill & \mathrm{if}\mathrm{pixel}i\mathrm{belongs}\mathrm{to}NS\hfill \end{array}\right.$$

  (10)
  The final fused prediction value is expressed as Equation (11):

  $${\widehat{y}}_{\mathrm{fused}}\left(i\right)=\sum _m{w}_m\left(i\right)·{\widehat{y}}_m\left(i\right)$$

  (11)

  where ${\widehat{y}}_{\mathrm{fused}}\left(i\right)$ denotes the fused prediction at pixel i, $w_m\left(i\right)$ is the fusion weight of model m at pixel i, and ${\widehat{y}}_m\left(i\right)$ is the prediction result of model m at pixel i.

3. Results

3.1. Variable Characteristics and Contributions to AGB Prediction

Understanding the statistical properties and predictive contributions of input variables is essential for reliable AGB estimation. Appendix

Table A2. Statistical analysis of AGB and predictive variables was conducted based on the 89 sample points.

	Mean	Maximum	Minimum	Median	SD	CV (%)	Range
AGB	109.66	329.36	1.70	108.51	71.27	64.99	327.66
AP	2518.40	3937.10	1302.00	2631.70	585.92	23.27	2635.10
BSI	−0.25	−0.07	−0.55	−0.24	0.09	-	0.48
EVI	0.34	0.55	0.08	0.35	0.10	30.05	0.47
MAT	26.98	28.68	24.83	26.87	0.78	2.89	3.842
MNDWI	−0.10	0.20	−0.47	−0.11	0.16	-	0.67
NDBI	−0.41	−0.19	−0.60	−0.42	0.08	-	0.37
NDVI	0.47	0.87	0.11	0.43	0.21	44.27	0.76
SR_B1	0.07	0.27	0.00	0.04	0.07	98.32	0.27
SR_B2	0.08	0.27	0.01	0.05	0.07	83.96	0.26
SR_B3	0.12	0.30	0.04	0.01	0.06	55.42	0.26
SR_B4	0.10	0.30	0.01	0.09	0.07	64.47	0.28
SR_B5	0.31	0.45	0.12	0.32	0.07	20.88	0.33
SR_B6	0.13	0.21	0.06	0.13	0.03	24.48	0.15
SR_B7	0.10	0.19	0.04	0.09	0.04	38.51	0.15
ST_B10	0.87	1.08	0.28	0.94	0.18	21.08	0.80
VH	−16.14	−13.22	−22.66	−15.41	2.32	-	9.44
VV	−10.20	−7.23	−17.27	−9.44	2.45	-	10.05
VV/VH	0.61	0.77	0.52	0.60	0.06	9.18	0.25
DEM	9.47	26.82	0.50	8.51	5.57	58.80	26.32
slope	4.39	12.19	0.75	3.73	2.65	60.35	11.45

presents the descriptive statistics of the field-observed AGB values and related environmental predictors. The average AGB across Indonesian mangrove plots is 109.66 Mg/ha, with values ranging from 1.70 to 329.36 Mg/ha. The high SD (71.27 Mg/ha) and CV (64.99%) reflect the considerable ecological heterogeneity of mangrove ecosystems in the region. These metrics suggest wide variation in vegetation growth and carbon accumulation. Although the mean and median AGB values are relatively close, indicating a roughly symmetric distribution, the Shapiro–Wilk test confirms a statistically significant deviation from normality.

To model AGB, we trained four ML models (RF, SVR, XGBoost, and Cubist), using remote sensing-derived spectral indices, climate variables, and terrain features. Feature selection and integration of multi-dimensional environmental inputs improved model performance in capturing spatial biomass variation. To quantify each variable’s influence on model predictions, we employed SHAP values. Figure 3 shows the relative importance of predictors across models. AP consistently emerged as the most influential variable, particularly in RF and SVR, underscoring the role of macroclimate in mangrove productivity. MAT followed, while spectral indices such as NDVI, EVI, and MNDWI contributed significantly across models. DEM and slope also played notable roles, particularly in XGBoost and Cubist models. These findings are consistent with previous research on the environmental drivers of mangrove biomass [49,50,51].

3.2. Performance of Different AGB Estimation Models

Table 1. Performance of the AGB estimation models.

Model	Input Variables	Training		Validation		AIC
		${\mathbf{R}}^{\mathbf{2}}$	RMSE	${\mathbf{R}}^{\mathbf{2}}$	RMSE
RF	All features	0.88	28.61	0.79	33.13	129.27
	Optimized features	0.89	27.86	0.79	32.64	129.02
Cubist	All features	0.89	26.07	0.73	36.86	124.67
	Optimized features	0.90	25.06	0.73	36.85	123.01
SVR	All features	0.86	23.03	0.78	33.34	126.66
	Optimized features	–	–	–	–	–
XGBoost	All features	0.87	21.52	0.78	33.08	132.77
	Optimized features	0.88	26.07	0.80	31.81	132.22
ML-BMA	–	0.89	25.38	0.80	31.47	–
SAC-BA	–	0.90	21.08	0.82	29.90	–

presents the performance comparison of various AGB estimation models. When using all input variables, all four baseline ML models (RF, Cubist, SVR, and XGBoost) achieved comparable results, with ${\mathrm{R}}^2$ values ranging from 0.73 to 0.80. Feature optimization based on SHAP values and AIC yielded modest improvements in most cases. For the RF and Cubist models, optimization led to slight reductions in RMSE and AIC, while ${\mathrm{R}}^2$ remained unchanged. Notably, SVR performed best with all variables, while XGBoost benefited more notably from feature selection, with ${\mathrm{R}}^2$ increasing from 0.78 to 0.80 and RMSE decreasing from 33.08 to 31.47 Mg/ha.

Building on the outputs of individual models, the ensemble-based ML-BMA method further improved prediction accuracy. It achieved an ${\mathrm{R}}^2$ of 0.80 and an RMSE of 31.47 Mg/ha, outperforming all individual models. This demonstrates the effectiveness of BMA in leveraging the strengths of multiple learners. The proposed SAC-BA model exhibited the highest overall accuracy, as evidenced by an ${\mathrm{R}}^2$ of 0.82 and RMSE of 29.90 Mg/ha (Figure 4), representing substantial improvements over both individual models and the ML-BMA ensemble. These results indicate that integrating spatial attention and spatial heterogeneity factors can significantly enhance the accuracy of AGB estimation.

3.3. Spatial Pattern Analysis

This study investigated the spatial heterogeneity of mangrove AGB estimation through spatial attention weights, LISA clustering, and uncertainty analysis.

Figure 5 illustrates the spatial distribution of attention weights generated by the SAC-BA model during the AGB fusion prediction process. The color gradient from red to blue indicates the importance of each pixel, from low to high, reflecting the model’s perception and focus across different spatial regions. Overall, the attention weights display clear spatial heterogeneity across geographical areas, suggesting that the model effectively responds to variations in local representativeness and structural stability. Higher attention weights are primarily concentrated in the core mangrove zones along the coastlines, such as southern Kalimantan, western Papua, and northeastern Sumatra. These regions typically feature extensive, continuous mangrove coverage, strong structural integrity, and stable remote sensing characteristics, leading the model to assign them greater importance in the fusion process.

To further evaluate the ecological consistency of the attention mechanism in SAC-BA, we compared the spatial distribution of attention weights (Figure 5) with the Global Mangrove Soil Organic Carbon Stocks dataset, which was developed using a spatiotemporal machine learning framework [52]. Notably, high attention weights in our model were concentrated in Java, Papua Barat, Kalimantan, and the Riau region, which also exhibit higher soil organic carbon density in the global dataset. This spatial correspondence suggests that SAC-BA’s attention mechanism effectively prioritizes ecologically significant regions with high carbon storage potential. It reinforces the model’s ability to identify zones of greater ecological relevance, thus enhancing both prediction accuracy and interpretability.

In this study, the LISA clustering results used to construct the SAC-BA model were derived from the AGB predictions of the ML-BMA model. The HH and LL clusters indicate the spatial aggregation of high and low AGB values, respectively, rather than a random distribution, suggesting a strong spatial autocorrelation of mangrove AGB in the study area. In contrast, HL and LH clusters typically represent spatial edge zones or local anomalies. Compared to ML-BMA, the improved SAC-BA model showed a substantial increase in the number of HH and LL clusters, accompanied by a reduction in NS, HL, and LH clusters (as shown in Figure 6). This indicates that the SAC-BA model has a stronger capability in capturing structurally stable areas and is more effective in suppressing spatial randomness and unstable boundary regions.

Figure 7 compares the spatial details of LISA classifications across three representative regions. In Site A, both SAC-BA and ML-BMA identified extensive LL-type areas, but SAC-BA demonstrated better continuity and boundary integrity, with a notable reduction in NS zones. In Site B, ML-BMA produced a large number of HL and LH edge-type patches with mixed cluster patterns, while SAC-BA effectively reassigned many of these fragmented zones into coherent HH regions, thereby improving spatial consistency. In Site C, SAC-BA significantly reduced the extent of NS areas and enhanced the identification of HH and LL clusters, resulting in more stable and structurally coherent prediction outcomes.

Figure 8 presents the normalized uncertainty map generated by the SAC-BA model during the mangrove AGB prediction process. This map reflects the model’s confidence levels across different regions, as well as its sensitivity to spatial factors such as sample sparsity, terrain complexity, and structural boundaries. Across the Indonesian region, uncertainty exhibits clear spatial heterogeneity. The overall trend shows lower uncertainty in core mangrove zones and large continuous areas, while higher uncertainty is observed in edge regions, fragmented island zones, estuarine intersections, and areas with frequent disturbances. This spatial pattern demonstrates that the fusion process in the SAC-BA model effectively distinguishes between high-confidence and high-risk areas, providing a solid basis for subsequent weighted optimization. Although spatial autocorrelation of residuals was not explicitly modeled during area-level aggregation, SAC-BA’s integration of LISA-based structural constraints and spatial attention mechanisms helps suppress noise propagation and over-smoothing, particularly along ecological boundaries and high-variance zones.

3.4. The Spatial Distribution of AGB

To assess model performance in mangrove AGB estimation, this study compared four traditional ML models (RF, SVR, XGBoost, Cubist) and two ensemble models (ML-BMA, SAC-BA). RF and Cubist produced smooth spatial outputs (9.56–290.96 and 5.12–299.71 Mg/ha, respectively), but showed fragmentation in edge and complex terrain regions. SVR (10.46–282.46 Mg/ha) was stable but conservative, underestimating high-AGB zones. XGBoost (3.62–273.33 Mg/ha) captured some extremes but displayed localized anomalies and lower average predictions.

ML-BMA incorporated uncertainty in its ensemble process, producing a wider AGB range (5.12–299.65 Mg/ha) but remained conservative in structure. The proposed SAC-BA model integrated uncertainty, spatial attention, and LISA-based constraints, yielding more balanced and realistic spatial patterns (11.38–291.65 Mg/ha, mean = 103.20 Mg/ha, total = 217.17 × ${10}^6$ Mg) (Figure 9). It effectively responded to high-value zones and edge transitions while avoiding over-smoothing or noise amplification. To quantify national-scale uncertainty, we aggregated the standard deviation outputs from the ensemble predictions of SAC-BA. The resulting uncertainty was ±1.17 × ${10}^7$ Mg, equivalent to 5.4% of the total AGB. While the pixel-level uncertainty map is visualized as a relative percentage in Figure 8, the area-level estimate was derived from the absolute uncertainty values.

Regionally, Papua exhibited the highest AGB (68.81 × ${10}^5$ Mg), followed by Kalimantan (68.13 × ${10}^5$ Mg). Despite their smaller, fragmented patches, Java and Sumatra also contributed meaningfully, highlighting the ecological value of conserving even minor mangrove areas.

In addition, three representative regions in Indonesia were selected for comparative analysis, as illustrated in Figure 10. The AGB distribution maps generated by the SAC-BA method reveal clearer spatial variation patterns that align more closely with the actual mangrove distribution. Across all three selected sites, the SAC-BA model effectively balances spatial smoothness and sensitivity to extreme values, successfully identifying continuous high-AGB zones. In peripheral areas, the model demonstrates distinct transitional gradients, and the prediction results exhibit strong spatial coherence.

4. Discussion

4.1. Comparison with Historical AGB Maps

To further assess the ecological plausibility of our model results, we compared the 2017 AGB map based on SAC-BA with the global mangrove AGB products published by Simard et al. [53] in 2000 and Hu et al. [31] in 2004. Figure 11 illustrates the spatial differences among four representative sites in Indonesia. Red areas indicate increased AGB, while blue areas indicate decreased AGB. In regions such as Kalimantan (Site B) and Sumatra (Site C), our results align with historically high biomass areas, indicating that SAC-BA can accurately capture spatial biomass patterns over time. Although this comparison is not based on direct ground observations, the consistency in temporal trends provides valuable validation and further reinforces the spatial credibility of our predictions.

Variations in AGB estimates across previous studies can be largely attributed to differences in data sources, modeling strategies, and spatial resolutions. For example, Mitchard et al. [54] compared two pan-tropical biomass maps based on LiDAR-derived canopy height, but calibrated with different field data and modeling approaches, revealing substantial spatial discrepancies despite similar global totals. Baccini et al. [55] used LiDAR, optical imagery, and climate data to build a linear regression model for tropical forest carbon estimation and Avitabile et al. [56] fused multiple existing products to reduce bias. These methodological differences result in inconsistencies in biomass magnitude and spatial patterns. Bouvet et al. [57] utilized ALOS PALSAR L-band SAR data and Bayesian inversion to produce a 25 m resolution biomass map of African savannas.

Compared with these datasets, our SAC-BA model leverages spatial autocorrelation, model uncertainty, and multi-source predictors to produce more balanced and ecologically coherent outputs. While minor differences in absolute values remain, the predicted spatial distribution patterns align well with known mangrove zones, especially in Sumatra, Borneo, and Papua.

4.2. Novelty and Advantages of the SAC-BA Method

The proposed SAC-BA framework provides a novel and robust approach for estimating AGB in mangrove ecosystems by integrating spatial attention mechanisms with Bayesian model averaging. Compared with conventional ensemble methods, such as simple averaging or traditional BMA [47], SAC-BA explicitly incorporates spatial structure information into the fusion process through LISA-based spatial autocorrelation and local attention mechanisms. This design addresses the common challenge of spatial fragmentation in AGB mapping and enhances prediction consistency across heterogeneous landscapes.

Recent studies have employed BMA for biomass estimation in terrestrial ecosystems. For example, Zeng et al. [58] applied BMA combined with machine learning to estimate grassland AGB in the Three-River Headwater Region of China. However, their framework did not explicitly consider spatial heterogeneity or spatial dependence in model fusion, limiting its effectiveness in complex landscapes. In contrast, SAC-BA integrates both spatial autocorrelation and uncertainty-aware weighting, offering a more spatially coherent and ecologically interpretable mapping framework, particularly suited to fragmented coastal ecosystems like mangroves.

SAC-BA offers distinct advantages over machine learning-based approaches commonly applied in mangrove AGB estimation. Pham et al. [59] utilized XGBoost with Sentinel-2 and ALOS-2 PALSAR-2 datasets to estimate mangrove AGB but did not explicitly model spatial relationships, which can lead to boundary artifacts and spatial inconsistency in heterogeneous regions. Similarly, Basyuni et al. [60] focused on UAV-based regression models at the local scale, achieving fine resolution but lacking scalability and transferability for national-scale AGB monitoring. Compared with these approaches, SAC-BA combines spatial attention, spatial autocorrelation, and probabilistic fusion to enhance prediction accuracy and spatial generalization across large and complex mangrove landscapes.

In addition, the spatial attention mechanism embedded within SAC-BA prioritizes ecologically significant areas, such as dense mangrove cores, ensuring that these regions receive greater modeling focus during prediction. This spatially adaptive mechanism is consistent with the insights presented by Hu [31] and Twomey [61], which underscore spatial heterogeneity as a key factor in global mangrove biomass estimation. However, SAC-BA further advances these ideas by offering higher spatial resolution outputs with reduced uncertainty and enhanced boundary consistency. Collectively, SAC-BA provides a scalable, robust, and interpretable framework for regional to national-scale mangrove AGB estimation and blue carbon monitoring.

4.3. Limitations of the Current Study

Although our mangrove AGB map for Indonesia demonstrates improved accuracy over previous maps, it still shares limitations common to earlier studies, both in terms of data and methodology.

The primary limitation lies in the inherent uncertainty of ground-based AGB measurements, which arises from errors in estimation methods, such as inaccuracies in measurement techniques and allometric models, as well as geographic location errors. These sources of uncertainty cannot be fully eliminated, and their impact on results is difficult to assess. This is particularly problematic when using generalized allometric models or conversion factors, which overlook variations in species composition, environmental factors, or climate. To mitigate this uncertainty, adopting localized or species-specific AGB estimation methods and enhancing the integration of remote sensing data during mapping can help reduce errors from ground-based measurements.

The second limitation arises from the time mismatch between ground measurements and remote sensing data, which can introduce uncertainty into the predictive models. The ground-based data we gathered was collected between 2016 and 2019, with a concentration in 2017, while the Landsat 8 and Sentinel-1 data employed in our study were also from 2017. However, the exact sampling year for many plots is not recorded, making it difficult to align the ground data with the satellite data used for model fitting. If we had restricted the analysis to data from 2017, the sample size would have been insufficient for effective model training.

In addition, although we aggregated pixel-level uncertainties derived from the ensemble predictions of SAC-BA to estimate national-scale uncertainty (±1.966 × ${10}^7$ Mg, equivalent to 8.3% of the total AGB), this approach assumes pixel-level uncertainties are independent and does not explicitly account for the spatial autocorrelation of errors. Consequently, the aggregated uncertainty may be underestimated, as spatially correlated residuals can lead to compounded uncertainty when scaling up. Future studies could incorporate geostatistical methods or spatial hierarchical models to more rigorously account for spatial dependence in uncertainty propagation.

4.4. Further Improvement of Mangrove AGB Estimation

One potential approach to enhance AGB estimation is the development of stratified models tailored to different mangrove species groups. Mangrove ecosystems consist of several species, such as Aegialitis, Rhizophora, and Avicennia, each of which exhibits distinct growth characteristics, ecological requirements, and biomass accumulation patterns. As a result, using a single model for AGB estimation may fail to fully account for the variations between species. By creating stratified models that are specific to the characteristics of each mangrove species, we can obtain more accurate AGB estimates that reflect the unique traits and ecological dynamics of each species.

It is important to note that Twomey et al. [61] have developed a global dataset on mangrove species distribution, which significantly aids in improving AGB estimation. This dataset provides spatial information on the distribution of mangrove species worldwide, helping to identify the areas where different species are found and their ecological characteristics. By integrating this dataset, we can develop more accurate stratified models based on the distribution and ecological adaptability of each species, thereby enhancing the precision of AGB estimation.

Moreover, considering the ecological diversity of mangrove species across different regions, adaptive models could enhance AGB predictions by incorporating regional factors such as climate, soil types, and hydrological conditions. This approach would not only improve biomass estimation for local mangrove areas but also provide more reliable data for global assessments of mangrove carbon stocks. Ultimately, these models would deepen our understanding of the carbon storage potential of mangrove ecosystems and their responses to climate change.

5. Conclusions

Spatial quantification of mangrove AGB is essential for understanding blue carbon dynamics and informing conservation and climate mitigation strategies. In this study, we developed SAC-BA, a novel ensemble framework that integrates field-observed AGB data with multi-source remote sensing, meteorological, and topographic variables through a spatially structured and uncertainty-aware Bayesian fusion process. Unlike conventional ensemble methods, SAC-BA incorporates spatial attention weights and LISA-based constraints into Bayesian model averaging, explicitly addressing the spatial autocorrelation often observed in biomass distribution and model residuals. This integration improves both the numerical accuracy and spatial consistency of AGB predictions, particularly in heterogeneous and fragmented mangrove landscapes. The findings highlight the advantages of combining probabilistic reasoning with spatial structure modeling in ecological applications. SAC-BA offers a scalable and transferable approach for regional biomass estimation, capable of preserving fine-scale ecological patterns while minimizing uncertainty in high-risk zones.