Hybrid heuristic algorithm (HA), an innovative technique in the machine learning field, enhances the accuracy of reference evapotranspiration (ETo) prediction, which is of paramount significance for regional water management, agricultural planning, and irrigation designing. However, the new hybrid HA techniques, namely Moth-Flame Optimization Algorithm (MFO) and Water Cycle Optimization Algorithm (WCA) are rarely applied to estimate ETo in the earlier literature. Therefore, this study assessed prediction and the estimation abilities of a novel hybrid adaptive neuro-fuzzy inference system (ANFIS-WCAMFO) for monthly ETo of Dhaka and Mymensing stations with data-limited humid regions of south-central Bangladesh. Prediction precision of the ANFIS-WCAMFO model is compared with other state-of-art models, i.e., ANFIS-WCA and ANFIS-MFO using a 4-fold cross-validation method including root-mean-square-error (RMSE), mean absolute error (MAE), and Nash-Sutcliffe efficiency (NSE), and coefficient of determination (R2). Nine input combinations of meteorological datasets, including extraterrestrial radiation (Ra), solar radiation (Rs), maximum and minimum temperatures (Tmax and Tmin), relative humidity (RH), and wind speed (U2), were employed for model training and testing purposes. The ANFIS-WCAMFO performed superior to the other state-of-arts methods in estimating monthly ETo in all input combinations. The ANFIS-WCA, ANFIS-MFO, and ANFIS-WCAMFO hybrid models for estimating ETo improved RMSE as 2.7%, 6.9%, and 15.1% for Dhaka station and 0.6%, 7.3%, 12.4% for Mymensingh station, respectively. The use of the Ra variable with the temperature inputs considerably improved the models’ accuracy in ETo; improvements in RMSE, MAE, NSE, and R2 of the hybrid ANFIS-WCMFO models were 26.6%, 30.9%, 17.6%, and 8.2% for Dhaka station and by 28.8%, 34.2%, 18.8% and 22.1% for Mymensingh station, respectively. The proposed hybrid neuro-fuzzy model has been suggested as a promising technique due to high predictive accuracy and less error for monthly ETo prediction in a data-limited tropical humid region.
