Deep Learning for Hourly FAO-56 PM-Derived Crop Evapotranspiration Estimation Using a Transformer Encoder Approach for Data-Driven Irrigation Management in Tropical Horticulture

Accurate hourly crop evapotranspiration (ETc) estimation is important for data-driven irrigation management support in tropical horticulture, yet existing approaches are constrained by data requirements and an inability to capture multi-scale temporal dynamics. This study proposes a Transformer encoder model for one-step-ahead hourly FAO-56 PM-derived ETc estimation in a durian orchard in Chanthaburi Province, Eastern Thailand, using 36,528 hourly meteorological observations obtained from the Visual Crossing Weather API for the orchard location over four years, with ETc computed from these inputs using the FAO-56 Penman–Monteith equation. The model employs a 168-h (7-day) look-back window, three stacked encoder blocks with multi-head self-attention (h=8, dmodel=128), and five meteorological input features (air temperature, relative humidity, solar radiation, wind speed, and ETc). A SARIMA(2,1,2)(1,0,0)24 model trained on the same dataset served as the statistical baseline. The Transformer achieved an RMSE of 0.0308 mm/h, MAE of 0.0188 mm/h, and R2 of 0.9018 on the 168-h test set, outperforming SARIMA (RMSE = 0.0717, MAE = 0.0593, R2 = 0.4688), representing a 57.0% reduction in RMSE, a 68.3% reduction in MAE, and a 92.4% improvement in R2. The Transformer also achieved a daytime-only RMSE of 0.0414 mm/h vs. 0.0791 mm/h for SARIMA, and a daily cumulative ETc MAE of 0.1599 mm/day vs. 0.5901 mm/day, demonstrating superior accuracy during agronomically critical periods. The Transformer accurately reproduced both the 24-h diurnal cycle and the 7-day weekly pattern of ETc, whereas SARIMA exhibited a damped amplitude response. A recursive 168-h heuristic simulation demonstrated that the model generates physically plausible ETc patterns under an approximated meteorological scenario, suggesting the approach warrants further investigation as a component of future irrigation decision-support research. These results highlight the potential of Transformer-based deep learning for site-specific, proof-of-concept ETc estimation from meteorological inputs in tropical fruit production, pending validation across diverse sites and seasons.