Predicting transpiration of tomato in greenhouse using quantile regression with the Penman–Monteith equation and neural networks

Estimation of plant transpiration is essential for developing efficient irrigation strategies and improving crop management. However, delineating water flow within complex crop production systems is challenging. Neural networks can model complicated relationships without manual feature extraction; therefore, they can help in extracting transpiration rates from greenhouse data. This study introduces a quantile regression approach to predict transpiration rates using the Penman–Monteith (PM) equation in conjunction with long short-term memory (LSTM) networks. Data from load cell scales were used to collect the weight measurements, and weight-based transpiration rates were calculated to calibrate the PM equation. The quantile regressor was applied at various quantiles (0.1, 0.3, 0.5, 0.7, and 0.9) using the LSTM model and demonstrated acceptable accuracy with an R² of 0.56 and root mean square error (RMSE) of 0.15 g m^{− 2} min^{− 1}, which was slightly better than those of multivariate regression (R²= 0.53, RMSE = 0. 16 g m^{− 2} min^{− 1}). The proposed model provided highly robust transpiration rate predictions than multivariate regression. Utilizing quantile regression with neural networks can improve water management and optimize resource use in controlled environments.