Modelling of daily reference evapotranspiration using deep neural network in different climates

Precise and reliable estimation of reference evapotranspiration (ETo) is an essential for the irrigation and water resources management. ETo is difficult to predict due to its complex processes. This complexity can be solved using machine learning methods. This study demonstrates the systematic application of deep neural networks (DNNs) for estimating reference evapotranspiration (ETo) across diverse climatic conditions. Previously proposed ANN and DNN methods have been realized, and their performances have been compared. By employing rigorous cross-validation over long-term datasets from 4 meteorological stations (Adana, Aksaray, Isparta and Niğde) during 1999–2018 in Türkiye, the analysis benchmarks DNN performance against established methods and evaluates input importance in hydrological terms. The results have shown that our proposed DNN models achieves satisfactory accuracy for daily ETo estimation compared to previous ANN and DNN models. The best performance has been observed with the proposed model of DNN with SeLU activation function (P-DNN-SeLU) in Aksaray with coefficient of determination (R2) of 0.9934, root mean square error (RMSE) of 0.2073 and mean absolute error (MAE) of 0.1590, respectively. While model sensitivity to activation functions and dropout is explored as part of robustness testing, the contribution primarily lies in showing that DNNs can provide reliable and understandable improvements for ETo estimation.