Hybrid particle swarm optimization with extreme learning machine for daily reference evapotranspiration prediction from limited climatic data

Abstract Accurate prediction of reference evapotranspiration (ETo) is pivotal to the determination of crop water requirement and irrigation scheduling in agriculture as well as water resources management in hydrology. In the present study, the particle swarm optimization (PSO) algorithm was utilized to optimally determine the parameters of the extreme learning machine (ELM) model, and a novel hybrid PSO-ELM model was thus proposed for estimating daily ETo in the arid region of Northwest China with limited input data. The PSO-ELM model was compared with the original ELM, artificial neural networks (ANN) and random forests (RF) models as along with six empirical models (including radiation-, temperature- and mass transfer-based empirical models). Three input combinations were utilized to develop the data-driven models, which corresponded to the radiation-, temperature- and mass transfer-based models, respectively. The results indicated that machine learning models provided more accurate ETo estimates, compared with the corresponding empirical models with the same inputs. The hybrid PSO-ELM model exhibited better performance than the other models for daily ETo estimation as indicated by the statistical results. Although radiation-based machine learning models outperformed temperature- and mass transfer-based machine learning models, the temperature-based PSO-ELM model obtained reasonable results when only air temperature data were available, which was considered as a promising model for forecasting future ETo with temperature data. Overall, the PSO-ELM model was superior to the other machine learning and empirical models, which was thus recommended to predict daily ETo with limited inputs in the arid region of Northwest China.