Modeling soil organic carbon changes using signal-to-noise analysis: a case study using European soil survey datasets

Soil organic carbon (SOC) is a key indicator of soil health and a crucial component for assessing climate mitigation, making its reliable monitoring increasingly relevant. While digital soil mapping (DSM) using machine learning (ML) and Earth observation (EO) data enables time series of spatially explicit SOC predictions, detecting temporal soil carbon stock changes remains challenging and raises the question whether multi-temporal SOC measurements are sufficient to quantify changes with confidence. This study introduces a model-based signal-to-noise ratio (SNR) framework to assess the detectability of SOC change using both model-then-derive and derive-then-model approaches. We define SNR as the ratio of predicted SOC change to its modeled uncertainty. This enables the evaluation of change modeling reliability at both pixel and aggregated spatial levels. Applied to repeated SOC observations from the LUCAS soil survey at the European scale, the framework assesses the reliability of SOC change modeling across multiple land cover types using Random Forest (RF) and Quantile Regression Forests (QRF). At the site level prediction accuracy was poor, and SNR values were consistently low (<1). This highlights the limitations of current data for modeling SOC dynamics. However, spatial aggregation improved the SNR, supporting SOC change assessments at broader scales. SNR offers a practical diagnostic of model confidence, with a weak correlation to observation-based error, reflecting its role as an internal metric rather than a direct measure of accuracy. We advocate for routine SNR reporting to enhance the transparency and credibility of DSM-based SOC change monitoring while EO datasets enhance and ground-measurement surveys expand in time and quality.