Uncertainty Quantification in Soil Fertility Prediction

Abstract

This study addresses the need for soil fertility prediction methods that combine high accuracy with calibrated uncertainty to support risk-aware management in heterogeneous agroecosystems. Using soil chemistry data from UNIZIK Awka, including pH, organic carbon, available phosphorus, exchangeable bases, and acidity indices, the soil was found to be moderately acidic overall (mean pH 5.85) but characterized by high variability in key fertility drivers, particularly Na⁺, H⁺, and organic carbon. This instability demonstrates the limitations of point-only prediction approaches. Bayesian Neural Networks and Monte Carlo Dropout were applied to generate full predictive distributions and adaptive uncertainty intervals. Uncertainty decomposition revealed that predictive risk is dominated by aleatoric, or irreducible, variability rather than epistemic model uncertainty, especially for pH and Na⁺, indicating that inherent soil process noise governs prediction reliability. While Random Forests remained competitive for point-prediction accuracy, Bayesian models were specifically evaluated for probabilistic calibration and decision-relevant predictive uncertainty. The Bayesian neural network achieved strong calibration for available phosphorus, whereas Monte Carlo Dropout showed severe overconfidence for calcium. Linking predictive intervals to agronomic thresholds showed that uncertainty directly affects management decisions, with many cases requiring confirmation sampling. Overall, the results demonstrate that calibrated Bayesian uncertainty enables more robust, decision-relevant soil fertility prediction for precision agriculture.