A Stochastic Approach to Quantifying Uncertainty in Soil Organic Carbon

Soil organic carbon (SOC) is a key driver of soil hydraulic properties like, field capacity and wilting point, necessary for in-field scale yield prediction using tipping bucket models. However, the labor-intensive nature of obtaining spatially distributed SOC often leads to its extrapolation using satellite imagery, resulting in significant inaccuracies in SOC prediction. In this study, we propose a Monte Carlo-based (MC) procedure to quantify the propagation of SOC error to simulated yield estimates. This procedure stochastically generates data, considering both uncorrelated and correlated data. For uncorrelated data, each SOC value is generated following an independent normal distribution. For correlated data, covariances are considered, accounting for the spatial correlation of in-field SOC variability. The autocorrelation between each pair of pixels is calculated, building a correlation matrix, which is submitted to the Cholesky decomposition, resulting in a lower triangular matrix. This matrix is then used to generate correlated SOC values for each pixel, maintaining the shape of the SOC clusters while varying the SOC value in each pixel according to its error. We validated our methodology using synthetic data, then used the methodology to assist error propagation of SOC with true data in a field located in Booßen, Germany. We generated 5000 SOC images, each with approximately 6000 pixels, and simulated the yield for each pixel. The results were analyzed by the field as a whole and each pixel across different images, by generating probability distributions for both. Another comparison was made by direct measurement between measured and simulated yields. Our results confirm the consistency of our method. In the specific scenario analyzed, preliminary results show that the SOC uncertainty was sufficient to explain the entire difference between the true and estimated crop yield, highlighting the importance of accurately assessing SOC uncertainty in yield prediction models.