Modelling the Spatial Distribution of Soil Organic Carbon Using Machine Learning and Remote Sensing in Nevado de Toluca, Mexico

Highlights

What are the main findings?

• The Quadratic Support Vector Machine using NDVI, elevation, and land use achieved high accuracy (R² = 0.84) for predicting soil organic carbon (SOC) in the volcanic landscape of Nevado de Toluca.
• Models using NDVI and BSI consistently outperformed those using MSAVI2 for SOC estimation, highlighting differences among vegetation indices in heterogeneous mountain terrains.

What is the implication of the main finding?

• Integrating multispectral remote sensing indices with machine learning enables accurate and cost-effective SOC mapping in ecologically complex areas.
• The approach supports scalable carbon monitoring and informs sustainable land management and conservation strategies in mountainous ecosystems.

Abstract

Accurate soil organic carbon (SOC) estimation is critical for assessing ecosystem services, carbon budgets, and informing sustainable land management, particularly in ecologically sensitive mountainous regions. This study focuses on modelling the spatial distribution of SOC within the heterogeneous volcanic landscape of the Nevado de Toluca (NdT), central Mexico, an area spanning 535.9 km² and characterised by diverse land uses, altitudinal gradients, and climatic regimes. Using 29 machine learning algorithms, we evaluated the predictive capacity of three key variables: land use, elevation, and the Normalised Difference Vegetation Index (NDVI) derived from satellite imagery. Complementary analyses were performed using the Bare Soil Index (BSI) and the Modified Soil-Adjusted Vegetation Index 2 (MSAVI2) to assess their relative performance. Among the tested models, the Quadratic Support Vector Machine (SVM) using NDVI, elevation, and land use emerged as the top-performing model, achieving a coefficient of determination (R²) of 0.84, indicating excellent predictive accuracy. Notably, 14 models surpassed the R² threshold of 0.80 when using NDVI and BSI as predictor variables, whereas MSAVI2-based models consistently underperformed (R² < 0.78). Validation plots demonstrated strong agreement between observed and predicted SOC values, confirming the robustness of the best-performing models. This research highlights the effectiveness of integrating multispectral remote sensing indices with advanced machine learning frameworks for SOC estimation in mountainous volcanic ecosystems

1. Introduction

Terrestrial ecosystems are crucial in the global carbon (C) cycle [1,2,3]; the natural environments can absorb or release consistent amounts of greenhouse gases such as carbon dioxide (CO₂) and methane (CH₄) [4,5]. Also, they can store a considerable quantity of C in biomass plants, litter, and soil pools [6,7]. In particular, the C stored in the earth’s soil, which ranges from 1500 to 2400 Pg [8], exceeds the combined total of C hoarded in the atmosphere and the biosphere [9]. The global pool of soil organic carbon (SOC) has been estimated at three times greater than the atmospheric C pool and about five times greater than the biotic C pool [10,11,12,13].

Storage of SOC is the result of different ecological dynamics, i.e., photosynthesis, organic matter decomposition, and soil respiration [14]. The SOC is an essential parameter of healthy soil; it contributes to multiple ecosystem services (i.e., nutrient cycles, water cycle, and food production) and multiple soil properties (i.e., aggregate stability, soil texture, porosity, and water-holding capacity) [15,16].

Several factors, such as geographic location, climate, soil moisture, soil texture, soil pH, leaching and land use, could determine or modify SOC in natural ecosystems [17,18,19]. The clay fraction in the soil accumulates more SOC than any other fraction (silt and sand) [20]. Acidic soil pH may depress the decomposition of freshly added organic material in humid forest soils [21,22]. The SOC in forest soils is generally negatively impacted by reduction/abatement in density, abundance, and biodiversity of vegetation (primary and shrubby), which involves a drop in litter input and changes in the distribution of plant roots [23,24].

Human activities such as agriculture, livestock husbandry, tourism, and urbanisation seriously compromise ecological services [25,26]. The SOC concentrations in the mountain soils show considerable spatial variability and, in many cases, can be profoundly altered by human activities and land use changes [24,27,28,29]. The conversion of virgin forests to croplands can reduce SOC stocks by an average of 40% [30]; furthermore, total C loss can reach 50% in the topsoil in agroforestry ecosystems due to land use change and constant agriculture [31,32].

Accurate SOC thematic maps based on a limited number of sample points and a few other data points about landscapes have always been challenging for researchers [33,34]. Readily accessible environmental variables, derived from digital elevation models (DEM) (altitude, slope), remote sensing systems (spectral indices) or thematic maps (land use, climate), are valuable inputs to improve the performance of GIS algorithms and the accuracy of SOC maps [35]. The remote sensing data could be acquired in different ways, i.e., unmanned aerial vehicle [36], airborne [37], and satellites [38,39].

Additionally, machine learning techniques, with remote sensing inputs (spectral indices) such as Normalized Difference Vegetation Index (NDVI), Enhanced Vegetation Index (EVI), Bare Soil Index (BSI) and Modified Soil-Adjusted Vegetation Index 2 (MSAVI2), are widely used for SOC geostatic analysis in different types of ecosystems and other geographic scales [21,40,41]. Multivariate analysis and machine learning methods for SOC mapping in natural ecosystems include generalised linear model (GLM), linear additive model (LAM), cubist, random forest (RF), and support vector machine (SVM) [42,43,44,45].

The “Área de Protección de Flora y Fauna del Nevado de Toluca” (NdT) [46] of 535.90 km² is located in central Mexico. As part of the Trans-Mexican Volcanic Belt, it reaches 4680 masl and is the fourth highest mountain of the country [47]. The NdT constitutes a nationally relevant biogeographic area that includes different types of landscapes, i.e., forest of pine, forest of fir, forest of oak, mixed forests of pine–oak and fir–pine, alpine pasture on the top of the mountain and agriculture on the lower slopes [47,48]. Illegal extraction of wood, land use change (conversion of forests into croplands), and forest fires are the leading causes of degradation and loss of SOC reserves in this region [47].

This research aimed to predict soil organic carbon (SOC) in the topsoil of the heterogeneous mountainous ecosystem of Nevado de Toluca (NdT) by applying twenty-nine machine learning (ML) techniques and linking the results to land use. Extensive sampling was conducted to ensure homogeneous coverage of the diverse landscapes within NdT, while model inputs included land use, elevation, and three widely used spectral indices—NDVI, BSI, and MSAVI2—derived from Sentinel-2 multispectral imagery. The novelty of this study lies in systematically benchmarking a large set of ML algorithms under complex volcanic mountain conditions, where steep altitudinal gradients, diverse land uses, and microclimatic variability pose significant challenges for SOC prediction. By integrating spectral indices with environmental variables, the proposed framework improves SOC prediction accuracy and demonstrates its applicability as a cost-effective and scalable monitoring tool. Beyond its local relevance, this approach can serve as a reference model for SOC analysis across the Trans-Mexican Volcanic Belt and, more broadly, in heterogeneous mountain ecosystems worldwide.

Study Area

The Área de Protección de Flora y Fauna del Nevado de Toluca, also known as Xinantécatl (Figure 1), is an eroded stratovolcano located in the central part of Mexico (18°51′31″–19°19′03″ N, 99°38′54″–100°09′58″ W). This heterogeneous high mountain ecosystem, part of the Trans-Mexican Volcanic Belt, stretches over about 535.90 km² and rises to 4680 masl. The region is characterised by diverse landscapes, including pine, fir, oak and mixed forests (≃257.23 km²), alpine grasslands at higher elevations (≃69.67 km²), and agricultural lands on lower slopes (≃209.00 km²). The soils in the NdT are classified into four main types, i.e., andosols, regosols, fluvisols, and cambisols. The region experiences three dominant climates, i.e., semi-cold, sub-humid, and cold, with an average annual precipitation of 1050 mm and temperatures ranging from −4 °C to 12 °C. The NdT is particularly sensitive to human impacts; in particular, the exploitation of natural resources (wood logging) and land use change (deforestation for agricultural expansion) have contributed to significant environmental degradation and loss of SOC reserves [49].

2. Materials and Methods

Integrating empirical field sampling with computational modelling, a hybrid approach was implemented to construct a predictive model for Soil Organic Carbon (SOC) (Figure 2). The Nevado de Toluca (NdT) region served as the study area, where SOC concentrations were quantified via established laboratory protocols utilising 281 georeferenced soil samples. Subsequently, machine learning methodologies were employed to model SOC content, with a comparative analysis of diverse regression algorithms to ascertain the optimal predictive paradigm. Rigorous statistical evaluation was conducted to validate model performance, yielding a quantitative framework for enhanced SOC estimation within ecological investigations.

2.1. Sampling and Laboratory Analysis

The topographic maps (scale 1:50,000) from the Istituto Nacional de Estadística y Geografía of Mexico (INEGI) were used as the primary cartographic reference, while the Continuo de Elevaciones Mexicano 3.0 (CEM 3.0), with a 15 m × 15 m resolution, was consulted for the altitudinal gradient [50].

Two hundred eighty-one (281) sampling locations, including 168 samples in forests, 48 samples in agriculture, and 65 samples in natural grasslands/moorlands, were selected to cover the area evenly and ensure a spatially representative sampling design (Figure 1).

At each sampling site, five individual soil samples (~1 kg each) were collected from the 0–15 cm top soil horizon following a rhomboidal sampling scheme (Figure 3). The central point coordinates were recorded using a portable global positioning system (GPS).

The five samples from each location were analysed separately, and their SOC values were averaged, obtaining a representative estimate for the rhomboidal site. For laboratory analysis, soil samples were air-dried and sieved through a 2 mm mesh [51]. The SOC concentrations were quantified using a Total Organic Carbon Analyser (TOC-VCSN) from Shimadzu, Canby, OR, USA.

2.2. Remote Sensing

This study examines the correlation between Soil Organic Carbon (SOC) content and vegetation indices in the Nevado de Toluca region. To ensure high spatial precision, sentinel-2 multispectral imagery was selected as the primary data source. While the MODIS sensor was initially considered for its extensive spectral coverage, its coarse spatial resolution (250–1000 m per pixel) limited its applicability for the fine-scale analysis required in this study.

The choice of Sentinel-2 was primarily driven by its higher spatial resolution (10 m for visible and near-infrared [NIR] bands), which is well-suited for computing vegetation indices in the heterogeneous landscapes of Nevado de Toluca. Although Landsat 9 provides similar multispectral capabilities, its coarser spatial resolution (30 m for multispectral data) was less aligned with the study’s precision requirements. Given that the analysis focused on vegetation indices derived from visible and NIR bands, Sentinel-2 was deemed the most appropriate dataset. The multispectral images were acquired from the Copernicus Sentinel-2 mission, operated by the European Space Agency (ESA), and downloaded via the Copernicus Browser platform. The Multi-Spectral Instrument (MSI) onboard Sentinel-2 features 13 spectral bands spanning the visible, near-infrared (VNIR), and shortwave infrared (SWIR) regions, with spatial resolutions of 10, 20, and 60 m and a swath width of 290 km [52]. This selection ensures an optimal balance between spectral richness and spatial detail, facilitating accurate assessment of SOC-vegetation relationships in the study area.

To ensure high-quality remote sensing data for analysing SOC and vegetation indices, a 1% cloud cover threshold was applied. This filter allowed for the selection of cloud-free Sentinel-2 images, minimising atmospheric interference in the study area. The Copernicus Browser platform provides two types of Sentinel-2 products: L1C (Level-1C): Radiometrically and geometrically corrected but retains the original sensor geometry, without atmospheric correction; and L2A (Level-2A): Includes atmospheric correction, producing surface reflectance data in a geometrically and radiometrically corrected format. For greater accuracy and control over the atmospheric correction process, L1C data were selected. Atmospheric correction was subsequently applied using ACOLITE software [53], developed by the Royal Belgian Institute of Natural Sciences (RBINS). Initially designed for coastal and inland water applications, ACOLITE has been successfully adapted for terrestrial environments, offering robust atmospheric correction and image processing capabilities.

After applying the search filters, a set of 10 images captured between 1 January 2024, and 22 November 2024, was obtained. These images were visually inspected to ensure the absence of residual cloud cover, making the 1 March 2024, image the most suitable for analysis. To optimise data processing, the study area was extracted using ACOLITE’s region-of-interest (ROI) clipping function, defined by the following geographic coordinates: North; 19.31310°; South: 19.00000°; West; −99.95396° and East: −99.64265°. This cropping process significantly reduced the file size, enhancing computational efficiency by focusing solely on the relevant portion of the scene.

The Sentinel Application Platform (SNAP) software was used to manage the information generated after the atmospheric correction performed with ACOLITE. The resulting ACOLITE product is in Network Common Data Form (NetCDF) format, which facilitates its handling in SNAP due to its compatibility and flexibility for multispectral data processing. The atmospherically corrected image was loaded into SNAP, where the Band Math function was used to apply the Normalised Difference Vegetation Index (NDVI) (1), Bare Soil Index (BSI) (2), and Modified Soil-Adjusted Vegetation Index 2 (MSAVI2) (3) spectral index algorithms. These indices were selected due to their widespread validation and robustness in differentiating vegetation, bare soil, and mixed land covers in heterogeneous landscapes. While more recent SOC-specific indices have been proposed in the literature [54,55,56], their application remains less standardized in operational remote sensing workflows. The use of NDVI, BSI, and MSAVI2 therefore ensures methodological comparability and reproducibility, while establishing a baseline for SOC prediction in mountainous environments.

$$NDVI={\displaystyle \frac{B8-B4}{B8+B4}}$$

(1)

$$BSI={\displaystyle \frac{\left(B11+B4\right)-(B8+B2)}{\left(B11+B4\right)+(B8+B2)}}$$

(2)

$$MSAV12={\displaystyle \frac{1}{2}}\left(2\left(B8+1\right)-\sqrt{{\left(2(B8)+1\right)}^2-8\left(B8-B4\right)}\right)$$

(3)

The calculated spectral indices provided critical insights into the study area’s terrain conditions and land cover characteristics. These indices optimised subsequent analytical processes by enhancing the differentiation of vegetation, bare soil, and mixed land covers. Following the computation of the raster datasets for these indices, the spectral values corresponding to the precise georeferenced locations of the field measurements were extracted. This step enabled a direct correlation between remotely sensed data and in situ observations, facilitating a more comprehensive and accurate assessment of the environmental conditions within the study area.

2.3. Machine Learning

This study employed a comprehensive suite of 29 Machine Learning (ML) regression models, encompassing nine distinct algorithmic families and their respective variants, to predict the target variable. These models included Linear Regression (LR) [57], Stepwise Linear Regression (SLR) [58], computationally Efficient Linear regression [59], Kernel-based Regression (KR) [60], Support Vector Machines (SVM) [61], Tree-based regression (TR) [62], Ensemble Methods (EM) [63], Gaussian Process Regression (GPR) [64], and Neural Networks (NN) [65]. Acknowledging the established body of literature detailing the theoretical underpinnings of machine learning algorithms,

Table 1. Machine learning model architecture.

Model Type	Preset
Tree	Fine Tree
Linear Regression	Linear
Linear Regression	Interactions Linear
Linear Regression	Robust Linear
Stepwise Linear Regression	Stepwise Linear
Tree	Fine Tree
Tree	Medium Tree
Tree	Coarse Tree
SVM	Linear SVM
SVM	Quadratic SVM
SVM	Cubic SVM
SVM	Fine Gaussian SVM
SVM	Medium Gaussian SVM
SVM	Coarse Gaussian SVM
Efficient Linear	Efficient Linear Least Squares
Efficient Linear	Efficient Linear SVM
Ensemble	Boosted Trees
Ensemble	Bagged Trees
Gaussian Process Regression	Squared Exponential GPR
Gaussian Process Regression	Matern 5/2 GPR
Gaussian Process Regression	Exponential GPR
Gaussian Process Regression	Rational Quadratic GPR
Neural Network	Narrow Neural Network
Neural Network	Medium Neural Network
Neural Network	Wide Neural Network
Neural Network	Bilayered Neural Network
Neural Network	Trilayered Neural Network
Kernel	SVM Kernel
Kernel	Least Squares Regression Kernel

summarises the critical hyperparameters for each model. All statistical analyses and model implementations were performed using MATLAB R2025 (The MathWorks Inc., Natick, MA, USA), utilising the Statistics and Machine Learning Toolbox. Statistical inferences were conducted at a 95% confidence level (α = 0.05) (Figure 4).

To rigorously evaluate model performance, the following metrics were computed: coefficient of determination (R²) [66,67], root mean squared error (RMSE) [68,69], mean squared error (MSE) [70], mean absolute error (MAE) [71], mean absolute percentage error (MAPE) [72,73], and training time. These metrics comprehensively assessed each model’s predictive accuracy and computational efficiency. To prevent overfitting, all models were validated using a k-fold cross-validation scheme (75% of data for training and 25% for validation), which partitioned the dataset into stratified folds to preserve sample representativeness. Model hyperparameters were optimized within the training folds exclusively, ensuring that evaluation metrics were computed on independent validation data. This procedure was repeated four times to minimize variability introduced by random partitioning. Furthermore, algorithm-specific mechanisms such as regularization (in LR and SVM), pruning (in decision trees), ensemble averaging (in bagged/boosted models), and Bayesian optimization (in Gaussian process regression) inherently reduced the risk of model overfitting. The final performance assessment was based on the average validation results rather than training accuracy, providing a robust estimate of each model’s generalization capacity. It is important to note that although the k-fold cross-validation strategy used here ensured statistical robustness, it did not explicitly account for spatial autocorrelation. Consequently, training and validation folds may contain spatially close samples, potentially leading to optimistic performance estimates. The authors acknowledge this limitation and recommend that future research incorporate spatial cross-validation schemes, such as spatial blocking or leave-location-out approaches, to further mitigate spatial dependence effects.

3. Results

Figure 5 shows that all three indices consistently highlighted the volcanic center as an area of sparse vegetation and exposed surfaces. However, beyond this shared feature, their spatial distributions diverged. NDVI strongly emphasized vegetation cover, BSI accentuated bare surfaces, and MSAVI2 provided a smoother representation of vegetation density. These complementary patterns reflect the distinct sensitivities of each index while reinforcing the central volcanic zone as a common feature of interest.

Table 2. Vegetation, elevation and SOC indices with their respective standard deviation.

Land Use	NDVI	MSAV12	BSI	Elevation	SOC
Agriculture	0.529 ± 0.241	0.722 ± 0.101	0.016 ± 0.201	3507.76 ± 282.673	18.85 ± 3.080
Forest	0.611 ± 0.249	0.746 ± 0.091	−0.053 ± 0.215	3349.449 ± 317.002	25.66 ± 8.820
Grasslands/Moorlands	0.615 ± 0.198	0.752 ± 0.084	−0.040 ± 0.178	3459.552 ± 292.939	12.12 ± 6.500

presents the descriptive statistics for the vegetation, elevation, and soil organic carbon (SOC) indices, including mean and standard deviation.

Table 3. Quantitative error metrics for each evaluated model. Columns labeled NDVI, MSAVI2, and BSI correspond to models where the respective index was combined with elevation and land use as predictors for SOC. In Gray the best R² models for each index.

Preset	RMSE			MSE			R2			MAE			MAPE %
	NDVI	MSAV12	BSI	NDVI	MSAV12	BSI	NDVI	MSAV12	BSI	NDVI	MSAV12	BSI	NDVI	MSAV12	BSI
Fine Tree	4.71	5.29	4.71	22.17	27.98	22.17	0.73	0.67	0.73	3.57	3.99	3.57	22.86	27.68	22.86
Linear	3.78	4.96	3.78	14.26	24.63	14.26	0.83	0.71	0.83	2.96	3.93	2.96	19.87	28.77	19.87
Interactions Linear	3.74	5.03	3.74	14.02	25.30	14.02	0.83	0.70	0.83	2.92	3.97	2.92	20.55	29.88	20.55
Robust Linear	3.78	4.98	3.78	14.26	24.80	14.26	0.83	0.71	0.83	2.96	3.92	2.96	19.79	28.12	19.79
Stepwise Linear	3.78	4.97	3.78	14.27	24.70	14.27	0.83	0.71	0.83	2.96	3.91	2.96	20.26	28.57	20.26
Fine Tree	4.71	5.29	4.71	22.17	27.98	22.17	0.73	0.67	0.73	3.57	3.99	3.57	22.86	27.68	22.86
Medium Tree	4.37	5.05	4.37	19.07	25.51	19.07	0.77	0.70	0.77	3.37	3.87	3.37	21.67	28.71	21.67
Coarse Tree	4.68	5.48	4.68	21.90	30.06	21.90	0.73	0.65	0.73	3.83	4.39	3.83	33.05	36.57	33.05
Linear SVM	3.79	4.98	3.79	14.34	24.78	14.34	0.83	0.71	0.83	2.97	3.91	2.97	19.86	27.45	19.86
Quadratic SVM	3.68	4.77	3.68	13.51	22.74	13.51	0.84	0.73	0.84	2.87	3.79	2.87	18.77	28.34	18.77
Cubic SVM	3.81	5.31	3.81	14.50	28.15	14.50	0.82	0.67	0.82	2.98	3.92	2.98	21.70	28.15	21.70
Fine Gaussian SVM	4.59	5.68	4.59	21.10	32.21	21.10	0.74	0.62	0.74	3.49	4.23	3.49	26.38	34.24	26.38
Medium Gaussian SVM	3.74	4.37	3.74	13.96	19.13	13.96	0.83	0.78	0.83	2.89	3.30	2.89	19.36	23.01	19.36
Coarse Gaussian SVM	3.76	4.89	3.76	14.17	23.91	14.17	0.83	0.72	0.83	2.96	3.86	2.96	20.30	28.35	20.30
Efficient Linear Least Squares	9.05	9.24	9.05	81.86	85.47	81.86	0.00	0.00	0.00	7.63	7.87	7.63	79.87	78.50	79.87
Efficient Linear SVM	9.05	9.24	9.05	81.92	85.38	81.92	0.00	0.00	0.00	7.63	7.88	7.63	81.24	77.63	81.24
Boosted Trees	4.38	4.86	4.38	19.15	23.63	19.15	0.77	0.72	0.77	3.33	3.67	3.33	21.19	25.06	21.19
Bagged Trees	4.17	4.72	4.17	17.36	22.27	17.36	0.79	0.74	0.79	3.28	3.58	3.28	22.04	26.60	22.04
Squared Exponential GPR	3.72	4.39	3.72	13.88	19.26	13.88	0.83	0.77	0.83	2.89	3.44	2.89	19.63	25.18	19.63
Matern 5/2 GPR	3.71	4.37	3.71	13.79	19.12	13.79	0.83	0.78	0.83	2.88	3.41	2.88	19.47	24.83	19.47
Exponential GPR	3.80	4.48	3.80	14.44	20.07	14.44	0.82	0.76	0.82	2.90	3.43	2.90	19.69	25.32	19.69
Rational Quadratic GPR	3.72	4.37	3.72	13.88	19.13	13.88	0.83	0.78	0.83	2.89	3.42	2.89	19.63	24.87	19.63
Narrow Neural Network	3.75	4.91	3.75	14.05	24.11	14.05	0.83	0.72	0.83	2.92	3.86	2.92	20.18	27.85	20.18
Medium Neural Network	4.20	5.00	4.20	17.61	25.01	17.61	0.79	0.71	0.79	3.23	3.70	3.23	22.06	27.40	22.06
Wide Neural Network	6.96	7.41	6.96	48.40	54.87	48.40	0.41	0.36	0.41	4.85	5.58	4.85	34.00	41.38	34.00
Bilayered Neural Network	4.72	6.03	4.72	22.30	36.33	22.30	0.73	0.57	0.73	3.37	4.36	3.37	23.33	31.30	23.33
Trilayered Neural Network	4.31	5.12	4.31	18.62	26.18	18.62	0.77	0.69	0.77	3.30	3.72	3.30	21.34	25.79	21.34
SVM Kernel	5.19	5.94	5.19	26.98	35.23	26.98	0.67	0.59	0.67	4.05	4.63	4.05	38.76	43.61	38.76
Least Squares Regression Kernel	4.11	5.07	4.11	16.92	25.67	16.92	0.79	0.70	0.79	3.21	3.96	3.21	24.79	33.63	24.79

reports the quantitative error metrics (e.g., R², RMSE, MAE) for all evaluated machine learning models.

Of the 29 tested models, 14 achieved a coefficient of determination (R²) greater than 0.80 when using NDVI, elevation, and land use as predictor variables, demonstrating strong predictive performance for SOC estimation. The model with the best performance was the Quadratic Support Vector Machine (SVM), which achieved an R² of 0.84, indicating excellent predictive accuracy (Figure 6). Similarly, 14 models exceeded an R² of 0.80 when using the Bare Soil Index (BSI) as input. In contrast, none of the models using MSAVI2 surpassed an R² value of 0.78, suggesting a lower predictive capacity of this index for SOC estimation.

Figure 7 also includes the validation plots comparing predicted versus actual SOC values for the top-performing models: (a) Quadratic SVM using NDVI, (b) Matern 5/2 Gaussian Process Regression (GPR) using MSAVI2, and (c) Rational Quadratic GPR using BSI. These plots highlight the strong agreement between observed and predicted values for the most accurate models under each index scenario.

The soil organic carbon prediction model results correspond well with the field-measured data (Figure 8). Both maps reveal similar spatial patterns, especially in the highest concentration range (21.01–35.00 g C kg⁻¹), which is predominantly distributed in the central and southern areas of the study region.

Table 4. MAE values for SOC ranges.

Range	SOC (g C kg−1)	MAE
		NDVI	MSAV12	BSI
1	0.00–12.00	1.9	11.8	4.9
2	12.01–21.00	3.0	7.3	2.7
3	21.01–35.00	3.3	12.8	5.2
All	0.00–35.00	2.9	11.1	4.4
MAE (Mean Absolute Error)

shows the Mean Absolute Error (MAE) values, revealing distinct performances of the vegetation indices across SOC ranges. NDVI consistently showed the lowest errors in both low (0–12 g C kg⁻¹; MAE = 1.9) and high (21.01–35 g C kg⁻¹; MAE = 3.3) SOC ranges, indicating its robustness in capturing extreme SOC conditions. In contrast, BSI performed best at intermediate SOC levels (12.01–21 g C kg⁻¹; MAE = 2.7), where it outperformed both NDVI and MSAVI2. MSAVI2, however, exhibited the highest MAE values across all SOC ranges, with errors exceeding 7.0, suggesting limited suitability for SOC prediction in this context. NDVI and BSI emerged as the most reliable indices, with their performance depending on the SOC interval considered.

NDVI performs better at low and high SOC ranges because it is highly sensitive to vegetation vigor and canopy density, which are strongly influenced by organic matter content. Areas with very low SOC often support sparse or stressed vegetation, making NDVI effective in detecting these conditions. Similarly, areas with high SOC generally sustain healthier vegetation, which again enhances NDVI’s response. However, NDVI tends to saturate in intermediate SOC levels where vegetation density is moderate, reducing its sensitivity.

BSI, on the other hand, is designed to capture bare soil conditions and responds better in intermediate SOC ranges, where the soil surface is partially exposed and vegetation does not dominate the spectral signal. This may explain why BSI produced the lowest MAE in the 12.01–21.00 g C kg⁻¹ range. MSAVI2 was expected to reduce vegetation saturation effects compared to NDVI, but in this study, it may have been affected by background soil reflectance and mixed pixels, leading to higher errors across all SOC ranges.

4. Discussion

Soil carbon sequestration, which consists of transferring carbon dioxide CO₂ from the atmosphere into the soil in the form of organic carbon, is influenced by various factors such as land use (forests, croplands, grasslands, moorlands) [74,75,76], land use change (conversion of forests to croplands or livestock pastures) [77,78], land management (mineral fertilisation) [79,80], climate (rainfall, temperature, humidity) [81,82], geography (altitude and slope soil) [83], physicochemical and microbiological parameters (soil depth, soil texture, microbiota) [84,85].

The SOC in the top soil in the NdT was highly varied and ranged from 0.39 g C kg⁻¹ (high moor zone) to 60.54 g C kg⁻¹ (forest). Our results indicate that SOC were significantly higher in the forest soil (mean: 25.66 g C kg⁻¹, ±8.82 g C kg⁻¹) than in the high moorland (mean: 12.12 g C kg⁻¹, ±6.50 g C kg⁻¹) and arable soil (mean: 7.42 g C kg⁻¹, ±3.08 g C kg⁻¹), which suggests that land use plays a key role in its spatial distribution. Other authors have reached the same conclusions as us.

Land use change, i.e., forest conversion to cropland in the NdT, has been linked with reduced SOC concentrations. Ref. [85] indicated that SOC, in the heterogeneous ecosystem of Coka watershed (Southern Ethiopia), decreased in the following order: bushland and forestland, grassland, cropland and bare land [86]. Those who focused their interest on the heterogeneous geographical area of Northeastern India reported that SOC was significantly higher in the topsoil of the forest than in the adjacent arable land and natural grassland. Ref. [87] indicated a mean SOC content of 44.70 g C kg⁻¹ in the top forest soil and only 14.70 g C kg⁻¹ in cropland top soil. Finally, ref. [51] stated that land use is the primary driver of SOC spatial distribution in a high mountain ecosystem of National Park La Malinche, an eroded stratovolcano, located approximately 250 km east of NdT.

The SOC concentrations registered in maise monoculture sites, in the lower altitude areas of NdT, varied from 0.85 to 18.85 g C kg⁻¹ and are comparable to those indicated by [88]. In the Song-Nen Plain maise croplands (Northeast China). The conventional agricultural practices, such as monoculture, tillage, and removal of crop residue, which are common among farmers in the NdT, most likely contributed to reducing SOC in the topsoil; furthermore, the legume-based rotation systems, where high SOC concentrations are generally recorded, have been largely abandoned in recent decades. According to [89], organic farming, which is characterised by periodically rotating crop fields in grass or legumes, has the potential to increase SOC concentrations and accumulation rates.

The SOC concentrations in the top forest soil were highly variable and ranged from 6.99 to 60.54 g C kg⁻¹; these results are comparable with those indicated by [51,90]. The organic matter (plant litter, plant roots, soil microorganisms and animal residues) is the primary source of SOC. The C soil inputs depend on the vegetation type and structure [91]; the forest sites where NDVI values ranged between 0.5 and 0.7, which are compatible with dense canopy cover and significant leaf litter accumulation, presented higher SOC concentrations [92]. According to [93], SOC showed a significantly high positive correlation with NDVI in the forest context, even refs. [94,95] indicated that NDVI was an effective SOC predictor in India.

At the top of the volcano (over 4000 masl) the vegetation was limited exclusively to grasses and high moor; the SOC varied between 0.39 and 29.31 g C kg⁻¹. It is likely that the soil erosion, caused by heavy rains and strong winds, and steep geography of the summit had impacted the SOC concentrations. Many authors pointed out soil erosion as the primary cause of the loss of SOC in alpine grassland landscapes [96,97,98].

A wide range of machine learning algorithms have been used to study SOC spatial distribution and its geoclimatic associated patterns [99,100,101,102]. The readily accessible environmental variables are often calculated through digital elevation models (DEMs) and satellite images (spectral indices). The twenty-nine (29) machine learning models used to predict the SOC in the NdT leveraged three key explanatory variables, i.e., land use, altitude, and satellite-derived vegetation indices (NDVI, BSI, and MSAVI2). Our results underscore the reliability of remote sensing data and topographic variables when integrated into advanced machine learning frameworks for predicting the SOC in this heterogeneous ecosystem. Fourteen (14) models—Linear, Interactions linear, Robust linear, Stepwise linear, Linear SVM, Quadratic SVM, Cubic SVM, Medium gaussian SVM, Coarse gaussian SVM, Squared exponential GPR, Matern 5/2 GPR, Exponential GPR, Rational quadratic GPR, and Narrow neural network—achieved determination coefficients (R2) greater than 0.80 when NDVI, elevation, and land use were used as complementary inputs; this indicates the robustness of these variables in estimating SOC at regional scales in a heterogeneous and multi-fragmented ecosystem. The Quadratic SVM emerged as the top-performing model, reaching an R² of 0.84 (MSE: 14.34 (g C kg⁻¹) and RMSE: 3.79 g C kg⁻¹). According to [100], the NDVI and precipitation were the most significant features/predictors for machine learning techniques explaining SOC variability in a heterogeneous area (Northern Iran). The NDVI is commonly used as an input for machine learning techniques in many studies, which indicate that SOC is highly dependent on vegetation cover [103,104,105,106].

Even when BSI inputs replaced NDVI data, the performances of fourteen (14) models—Linear, Interactions linear, Robust linear, Stepwise linear, Quadratic SVM, Cubic SVM, Medium gaussian SVM, Coarse gaussian SVM, Squared exponential GPR, Matern 5/2 GPR, Exponential GPR, Rational quadratic GPR,

The narrow neural network was satisfactory, with an R² threshold of 0.80. The Rational Quadratic GPR was the top-performing model, reaching an R² of 0.83 in predicting SOC (MSE: 3.72 (g C kg⁻¹) and RMSE: 13.88 g C kg⁻¹). Previous studies have demonstrated that BSI is a significant predictor of SOC variability in different types of ecosystems: agricultural land [107,108,109], floodplains [110], alpine wetlands [111], and forests [112,113].

Finally, when MSAVI2, elevation, and land use were chosen as inputs, the machine learning models exhibited weaker performance, with none exceeding an R² of 0.78.

The weaker performance of MSAVI2-based models in this study may be explained by the ecological and spectral characteristics of the Nevado de Toluca landscape. MSAVI2 was originally developed to minimize soil background effects in areas with low vegetation cover, improving over NDVI in sparse canopies. However, in the present study, the volcanic soils and heterogeneous vegetation cover (ranging from dense forest to open grassland and agricultural land) likely reduced its effectiveness. Specifically, in densely vegetated areas, MSAVI2 saturates similarly to NDVI and provides no clear advantage in sparsely vegetated volcanic terrains. On the other hand, where soil reflectance is highly variable due to lithological differences, the soil-adjustment term in MSAVI2 may amplify noise rather than reduce it.

In contrast, NDVI and BSI appear to better capture the vegetation and soil conditions that correlate with SOC across this heterogeneous volcanic environment. NDVI, despite its known saturation issue, performed more robustly because much of the study area is covered by moderately to highly vegetated land uses. BSI provided complementary information by enhancing the contrast between bare soil and vegetated surfaces, which was particularly relevant for sparsely covered agricultural or degraded lands.

Therefore, the underperformance of MSAVI2 does not necessarily reflect a weakness of the index itself, but rather its limited suitability to the specific biophysical conditions of Nevado de Toluca, where NDVI and BSI better captured SOC-related variability.

Validation plots further confirmed the consistency between predicted and observed SOC values. The Quadratic SVM models measured and predicted SOC values using NDVI and consistently displayed no significant difference across the study area.

Comparing the performances of machine learning techniques in predicting SOC across multiple ecosystems is challenging due to each study area’s local peculiarities (climate, geography, extension, heterogeneity, human activities). However, integrating freely available remote sensing products with machine learning techniques offers a cost-effective and scalable approach for SOC monitoring in a wide range of ecosystems.

5. Conclusions

This study aimed to model and predict soil organic carbon (SOC) across the complex mountainous landscape of the Nevado de Toluca (NdT) using a suite of 29 machine learning algorithms. The models leveraged three key explanatory variables—land use, elevation, and satellite-derived vegetation indices (NDVI, BSI, and MSAVI2)—to assess their effectiveness in capturing SOC spatial variability within this heterogeneous volcanic ecosystem.

The results underscore the predictive power of remote sensing and topographic variables when integrated into advanced machine learning frameworks. Of the 29 evaluated models, nearly half (14 models) achieved a coefficient of determination (R²) above 0.80 when NDVI, elevation, and land use were used as predictors. This highlights the robustness of these variables in estimating SOC at regional scales. The Quadratic Support Vector Machine (SVM) emerged as the top-performing model, reaching an R² of 0.84, demonstrating excellent accuracy in capturing SOC distribution patterns.

Comparable results were observed when using the Bare Soil Index (BSI) as a predictor, with 14 models surpassing the R² threshold of 0.80. However, MSAVI2-based models exhibited weaker performance, with none exceeding an R² of 0.78, suggesting limitations in this index for SOC prediction in sparsely vegetated volcanic terrains.

Validation plots further confirmed the consistency between predicted and observed SOC values, particularly for the best models associated with each index: Quadratic SVM for NDVI, Matern 5/2 Gaussian Process Regression (GPR) for MSAVI2, and Rational Quadratic GPR for BSI.

This work contributes significantly to the growing knowledge of SOC modelling in high-altitude and ecologically diverse regions. Integrating freely available remote sensing products with machine learning techniques offers a cost-effective and scalable approach for SOC monitoring, which is critical for carbon budgeting, ecosystem services assessment, and sustainable land management. Future studies may benefit from including hyperspectral data or higher-resolution imagery and temporal analysis to evaluate SOC dynamics over time.