Gaussian Process Modelling for Precision Olive Irrigation-Fertilization Management: Continuous Prediction and Uncertainty Quantification of Olive Oil Quality

Introduction Olive oil quality is influenced by irrigation, fertilization, and seasonal climate variability. This study aimed to predict quality at unobserved water-fertilizer combinations while quantifying predictive uncertainty for risk-informed management. Methods A two-year (2023-2024) split-plot 3×3 factorial trial at INRA Meknès, Morocco, generated 54 biological olive-oil samples of Olea europaea L. cv. Picholine Marocaine across nine water-fertilizer combinations (50-100% ETc × 50-100% NPK), yielding 324 FTIR-ATR acquisitions. Matérn-5/2 Gaussian Process models with Automatic Relevance Determination were trained on 18 treatment-year means. Performance was assessed using Spearman ρ 2 under leave-one-treatment-out and leave-one-year-out cross-validation. Uncertainty was partitioned into aleatoric, temporal, and epistemic components, and Pareto optimisation identified resource-efficient regimes. Results LOTO-CV ρ 2 ranged from 0.408 (TFC) to 0.750 (carotenoids), with DPPH at 0.633 and TPC at 0.427. LOYO ρ 2 reached 0.790 for carotenoids and 0.494 for TPC. Temporal uncertainty accounted for ~58% of total uncertainty, versus 36% aleatoric and 6% epistemic. TPC was more sensitive to irrigation than fertilization (W/F = 0.22). The Pareto-optimal regime (≈50% ETc × ≈56% NPK) achieved 91% of maximum composite quality with 28% lower fertilisation cost. Discussion Seasonal variability was the dominant uncertainty source, highlighting the importance of multi-year data. Carotenoid and TPC patterns transferred across seasons, whereas DPPH required seasonal recalibration. Conclusion FTIR-GP modelling with Pareto optimisation offers a promising framework for uncertainty-aware olive management, but broader validation across seasons, sites, and cultivars is needed.