Improving Reference Evapotranspiration Predictions with Hybrid Modeling Approach

Accurate prediction of Reference Evapotranspiration (ET0) is essential for determining crop water requirements, significantly contributing to the effective management and sustainable planning of the world's scarce water resources. Many statistical and Machine Learning (ML) models have been proposed for predicting ET0, but no universal algorithm has been found to be the best performance for all the diverse conditions. Therefore, this study introduces a novel hybrid modeling approach that integrates the Linear Mixed Effect (LME) model with Nonlinear Autoregressive Neural Network (NANN) and Support Vector Machine (SVM) ML models. By combining the strengths of LME for capturing linear patterns and NANN and SVM for modeling nonlinear residuals, this approach aims to minimize prediction errors and enhance accuracy under diverse conditions. For this purpose, climatic data from 1980 to 2021 from five meteorological stations located in Pakistan were utilized. Moreover, panel (i.e., Levin Lin Chu (LLC), Im, Pesaran, and Shin (IPS)) and Moving Block Bootstrap (MBB) unit root tests were applied to investigate the stationarity in the dataset. Correlation analysis showed that temperature had the highest correlation with ET0 among climatic variables. Both hybrid models and the LME model were evaluated across five meteorological stations in Pakistan. Results from the Statistical assessment indicated that although both proposed models exhibited commendable performance in the prediction of ET0, the hybrid model LME-SVM exhibited a comparative advantage over the hybrid model LME-NANN. The Taylor diagram confirmed a strong positive correlation between observed (estimated by modified Hargreaves-Samani equation) and predicted ET0 values for both hybrid models.