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

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.

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 ρ² 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.

LOTO-CV ρ² ranged from 0.408 (TFC) to 0.750 (carotenoids), with DPPH at 0.633 and TPC at 0.427. LOYO ρ² 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.

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.

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.