recent years, remote sensing has emerged as a particularly effective method for tracking agricultural and environmental changes [23,24,25,26]. The technology relies on diverse sensors and platforms, such as satellite constellations and Unmanned Aerial Systems (UAS) to gather data, which are then typically processed using advanced algorithms, often in the realm of machine learning (ML) and deep learning (DL) [27].

Deep learning represents a specialized subset of machine learning that excels at learning from large, unstructured datasets using complex, layered neural networks. While traditional ML algorithms work well with smaller, structured datasets and often require manual feature selection, DL algorithms automatically extract features and patterns, especially from data like images and speech. This makes deep learning more powerful for certain applications, but it requires more computational resources and is often less interpretable than conventional machine learning techniques.

The ongoing advancements in remote sensing represent a promising alternative to traditional SOC monitoring. Toth and Jóžków provide a fairly recent review of different remote sensing platforms and sensors available today [28].

In the study presented here, the focus is on inferring SOC content from satellite data only. Most studies focused on determining SOC, however, rely on data (spectrograms) collected from hand-held sensors. While the accuracy achieved in this way is typically higher than using satellite imagery, such approaches can hardly be scaled to enable continuous monitoring of carbon stocks on a global level.

Gomez et al. [29] presented an early, albeit limited study (based on just 146 soil samples), which compared the results that can be achieved applying ML methods to in-the-field Vis–NIR measurements vs. applying them to hyperspectral satellite imagery. The images were obtained from the Hyperion sensor on the EO-1 satellite, which is, unfortunately, no longer functional, and there is no longer an active hyperspectral satellite that captures images in the VNIR–SWIR region, making it hard to replicate their work. In addition to trying to model the whole dataset used in the study, the authors tried focusing on specific land cover classes (cropping soils, pasture soils) and opted for a partial least-squares regression as their SOC predictor. Gomez et al. observed that the SOC in their cropping soils ranged between 0.54% and 1% and was lower than in the pastures, where SOC was in the 1.08% to 5.1% range. They evaluated their methodology based on R² and the Root-Mean-Squared Error (RMSE). The models based on satellite imagery did not perform well for cropping soils (R² of 0.04 and RMSE of 0.11) and lagged significantly behind the hand-held-sensor-based models in terms of R² (R² of 0.16 and RMSE of 0.1). However, when evaluated on pastures and the whole dataset, the two approaches achieved comparable and much better performance. The approach based solely on satellite data at their native resolution achieved an R² of 0.51, but the RMSE was quite high (0.73% SOC). Thus, the study showed that land cover is very important, when it comes to modeling and estimating SOC remotely.

More recently, Wang et al. [30] tried to use ML techniques to estimate SOC stock in the semi-arid rangelands of eastern Australia through the application of different machine learning techniques, with a focus on evaluating the impact of considering seasonal fractional cover on model performance. These features were used to extend other hand-crafted features derived from satellite imagery, as well as other remotely sensed climate features such as rainfall and temperature and data about lithology. They trained and evaluated their models using a limited amount of soil samples (705). They used random forests (RF) [31], Boosted Regression Trees (BRT) [32], and support vector machines (SVM) [33] to model their data. The RF approach performed the best and achieved an R² of 0.47 on their dataset.

Several studies tried to evaluate the effectiveness of hyperspectral data obtained from airborne sensors and extended their findings to evaluate the expected performance of sensors expected to be deployed in the future [34,35]. While we focus on multispectral data in the study presented here, it is worth noting that, albeit relying on a very limited set of soil samples (81) obtained for a 7 km² area in Luxembourg, 40% of which were used as a test set, Steinberg et al. achieved a relatively high R² (0.74) and an RMSE of 0.22% for SOC using autoPSLR applied to hyperspectral data from an airborne sensor [35]. Once sufficient hyperspectral data are available, the methodology we propose can easily be adapted to that domain, leading to even better performance.

Over the last decade, deep learning has revolutionized the area of machine learning and artificial intelligence and has become the dominant paradigm in the domain. The crucial advance over previously used methods is that the approach relies on end-to-end learning, which allows the ML models to learn the features on which to make their decisions and estimated directly from the raw input data, instead of relying on human-engineered features [36].

Yuan et al. provided an overview of the applications of both classical neural networks and DL models to the monitoring of environmental parameters using remote sensing data [37]. They showed that DL outperformed traditional ML models and has led to significant improvements in many applications, including land cover mapping, vegetation parameter, soil moisture, evapotranspiration, agricultural yield prediction, etc. The authors correctly highlighted the limitation of the DL approaches, which is related to the relatively limited amounts of training data available, as well as the potential to apply transfer learning to circumvent this problem. They mentioned two types of transfer learning: region-based and data-based. The first relates to pretraining on a geographical region for which ample data are available and adjusting the model to a different region with limited data available. In the ML community, this is usually referred to as fine-tuning. The latter is more in line with what the meaning of transfer learning is in the ML domain and relates to transferring the models trained on data obtained from a sensor or a group of sensors to other sensors. In the study presented here, we use a third kind of transfer learning, common in the computer vision community [38], where the initial model is trained on the same type of input data (Sentinel-2), but for a different visual task (land cover classification), and is used as a feature extractor for the final model (which performs SOC estimation in our case).

While the first application that Yuan et al. discussed was land cover, no approaches to estimating SOC were mentioned in this study. In addition, while approaches based on different DNN architectures were discussed (most relying on convolutional neural networks), none were identified in the study that use the U-Net model.

Rakhlin et al., however, successfully applied U-Net with Lovász softmax loss for land cover classification using RGB data made available as part of the DeepGlobe Challenge [39].

Yang et al. used a CNN to try to infer SOC for a central location based on input data that covered the surrounding region [40]. The input of their model was environmental variables combined with MODIS MCD12Q2 phenology variables. They trained and evaluated their approach on a limited set of 733 samples, collected in Anhui Province of China. This limited the complexity of the CNN they could use, since no transfer learning was used in the study, but the CNN fared better than a random forest model, achieving a modest R² of 0.26.

Emadi et al. [41] focused on Northern Iran and used a large number of input features (105). Most were human-crafted indices extracted from Landsat-8 and MODIS satellite imagery, but their input also included topology-related parameters, such as curvature, slope, etc. Using a dataset of 1879 composite soil samples and relying on 10-fold cross-validation, they compared the performance of several traditional ML algorithms (support vector machines, multi-layer-perceptron, regression decision trees, random forests, and extreme gradient boosting) with a DL model when predicting SOC. The DL model that showed the best results in the study was a fairly simple fully connected neural net, with seven hidden layers and 50 neurons in each of them, but it still outperformed the other methods tested. The authors reported a comparatively large R² value of 0.65, with an RMSE of 0.75% SOC.

In a recent study, Castaldi et al. [42] evaluated the capability of Sentinel-2 time series to estimate soil organic carbon and clay content at local scale in croplands. The pipeline they proposed relies heavily on human engineering, both in terms of the features they derived from Sentinel-2 imagery (NDVI, NBR2, BSI, S2WI), as well as in terms of how they were used to create the input to their machine learning models. In terms of modeling, they did not opt for deep neural networks, but the Quantile Regression Forest (QRF) algorithm, QRF with added longitude and latitude as covariates, and a hybrid approach, the Linear Mixed-Effect Model (LMEM), which included the spatial autocorrelation of the soil properties. While the latter takes spatial information into account up to a point, their approach is essentially pixel based, which differs from the one proposed here. In addition, the authors of the study aimed to assess the capability of their approach in a very limited scenario, by creating and evaluating models for each of their test sites separately. No attempt was made to create a single model that could be applied globally, or at least for a large part of the Earth’s surface. Thus, the results they achieved could be viewed as a sort of “blue-sky-performance”, which could be reached by a global model using Sentinel-2 images as the input. The R² of the best of Castaldi et al.’s models ranged from 0.26 to an impressive 0.96 for different locations, with an average R² of 0.67. The RMSE (in % SOC) ranged from 0.09 to 0.22 and was 0.152 on average.