Uncertainty-aware sensor-adaptive ET0 prediction under sparse weather sensing via Bayesian-calibrated FAO-56 Penman–Monteith and a masked neural network

Reliable estimation of reference evapotranspiration (ET0) is essential for irrigation scheduling and agricultural water-resources management. Although the FAO-56 Penman–Monteith equation is widely accepted as the standard method for ET0 estimation, its practical application requires a complete set of meteorological variables that many low-cost, legacy, or sparsely instrumented weather stations cannot continuously provide. Existing data-driven approaches partly alleviate this limitation, but they often either neglect the physical constraints of the FAO-56 Penman–Monteith formulation or rely on separate models for fixed input subsets, which limits adaptability across heterogeneous sensor networks. This study proposes a hybrid framework for daily ET0 estimation under sparse and variable meteorological sensing by coupling Bayesian calibration of the FAO-56 Penman–Monteith equation with a sensor-adaptive masked artificial neural network (ANN). In the Bayesian stage, the least directly observed energy-balance terms, net radiation and soil heat flux, are parameterized and inferred using Hamiltonian Monte Carlo to generate uncertainty-aware, physically constrained ET0 targets. A combined feature-selection strategy based on Sobol indices, SHAP values, and Pearson correlation then identifies four dominant drivers: solar radiation, maximum air temperature, mean wind speed, and mean relative humidity. These variables, together with binary sensor-availability masks, are used to train a single masked ANN capable of operating under all 15 non-empty input combinations without retraining separate models. The framework was evaluated using 15 min IoT weather-station data from the Fès–Meknès region of Morocco (January 2023 to October 2025) under leakage-safe balanced 10-fold cross-validation. Under full-driver availability (k = 4), the masked ANN reproduced the Bayesian-calibrated FAO-56 reference with RMSE = 0.226 mm day−1, MAE = 0.166 mm day−1, MAPE = 4.32%, and R2 = 0.996. Performance degraded smoothly as sensors were removed, while the model remained operational under single-sensor scenarios. These results show that the proposed Bayesian–masked-ANN framework provides physically consistent, uncertainty-aware, and deployment-ready ET0 estimation for heterogeneous smart-irrigation networks with incomplete meteorological observations.