Optimization algorithms as training approaches for prediction of reference evapotranspiration using adaptive neuro fuzzy inference system

Reference evapotranspiration (ET0), widely used in efficient and meaningful scheduling of irrigation events, is an essential component of agricultural water management strategy for proper utilization of limited water resources. Accurate and early prediction of ET0 can provide the basis for designing effective irrigation scheduling and help in resourceful management of water in agriculture. This study aims to evaluate and compare the performances of different hybridized Adaptive Neuro Fuzzy Inference System (ANFIS) models with optimization algorithms for predicting daily ET0. The FAO-56 Penman-Monteith method was used to estimate daily ET0 values using historical weather data obtained from a weather station in Bangladesh. The obtained climatic variables and the estimated ET0 values form the input-output training patterns for the hybridized ANFIS models. The performances of these hybridized ANFIS models were compared with the classical ANFIS model tuned with combined Gradient Descent method and the Least Squares Estimate (GD-LSE) algorithm. Performance ranking of these ANFIS models was performed using Shannon's Entropy (SE), Variation Coefficient (VC), and Grey Relational Analysis (GRA) based decision theories supported by eight statistical indices. Results indicate that both SE and VC based decision theories provided the similar ranking though the numeric values of weights differed. On the other hand, GRA provided a slightly different sequence of ranking. Both SE and VC identified Firefly Algorithm-ANFIS (FA-ANFIS) as the best performing model followed by Particle Swarm Optimization-ANFIS. In contrast, FA-ANFIS was found to be the second-best performing model according to the ranking provided by GRA with a negligible difference in weight between FA-ANFIS and the classical ANFIS model (GD-LSE-ANFIS). Therefore, FA-ANFIS can be considered as the best model, which can be utilized to predict daily ET0 values for areas with similar climatic conditions. The findings of this research is of great importance for the planning of effective irrigation scheduling.