Graph neural networks for Soil Organic Carbon Estimation: Data-efficient modeling of multimodal spatial dependencies

Soil Organic Carbon (SOC) is a key indicator of soil fertility and a component of the carbon cycle, yet its direct measurement remains costly, time-consuming, and spatially sparse. In this work, we investigate the potential and limitations of Graph Neural Networks (GNNs) for SOC estimation under data-constrained conditions, with a particular focus on methodological aspects of graph-based learning. Using a 2018 georeferenced dataset from the Beja district (southern Portugal), we integrate heterogeneous covariates derived from multispectral satellite imagery (Sentinel-1, -2, and -3), topography (Copernicus DEM), and meteorological records (Climatic Research Unit) into a spatial graph constructed from pairwise Haversine distances. The study adopts a dual evaluation strategy, contrasting a transductive learning paradigm (based on repeated random node partitions within a fixed graph) with a more stringent inductive setting implemented through a leave-one-cluster-out protocol. While the GNN is able to converge and generalize in the transductive context, inductive learning reveals substantial challenges associated with graph fragmentation and structural distributional shifts in small spatial graphs. To further interrogate model behavior beyond predictive accuracy, we conduct a feature relevance and stability analysis leveraging intrinsic mechanisms of conventional machine learning approaches (Random Forest, XGBoosting). Rather than supporting aggressive feature selection, the results highlight distributed, context-dependent relevance patterns and underscore the importance of aligning evaluation protocols with the structural assumptions of graph-based models. Overall, the study provides methodological insights into the use, interpretation, and limitations of GNNs for SOC estimation in low-sample, heterogeneous geospatial settings, informing future applications in soil monitoring and environmental modeling. • First application of Graph Neural Networks (GNNs) for Soil Organic Carbon (SOC) estimation. • GNNs capture spatial dependencies from limited, multimodal soil data. • Benchmarking shows GNNs outperform RF, MLP, and XGBoost models in a transductive learning. • Systematic comparison of transductive and inductive learning paradigms for SOC estimation with GNNs. • Methodological guidance for future graph-based environmental modeling studies.