Hierarchical Fuzzy Systems Integrated with Particle Swarm Optimization for Daily Reference Evapotranspiration Prediction: a Novel Approach

Reference evapotranspiration (ET 0 ) is a crucial element for deriving irrigation scheduling of major crops. Thus, precise projection of ET 0 is essential for better management of scarce water resources in many parts of the globe. This study evaluates the potential of a Hierarchical Fuzzy System (HFS) optimized by Particle Swarm Optimization (PSO) algorithm (PSO-HFS) to predict daily ET 0 . The meteorological variables and estimated ET 0 (using FAO-56 Penman–Monteith equation) were employed as inputs and outputs, respectively, for the PSO-HFS model. The prediction accuracy of PSO-HFS was compared with that of a Fuzzy Inference System (FIS), M5 Model Tree (M5Tree), and a Regression Tree (RT) model. Ranking of the models was performed using the concept of Shannon’s Entropy that accounts for a set of performance evaluation indices. Results revealed that the PSO-HFS model performed better (with Entropy weight = 0.93) than the benchmark models (Entropy weights of 0.77, 0.74, and 0.90 for the FIS, RT, and M5Tree, respectively). Furthermore, the generalization capabilities of the proposed models were evaluated using the dataset from a test station. Generalization performances revealed that the models performed equally well with the unseen test dataset and that the PSO-HFS model provided superior performance (with R = 0.93, RMSE = 0.59 mm d −1 and IOA = 0.94) while the RT model (with R = 0.82, RMSE = 0.90 mm d −1 , and IOA = 0.83) exhibited the worst performance for the test dataset. The overall results imply that the PSO-HFS model could effectively be utilized to model ET 0 quite efficiently and accurately.