ANFIS Modeling with ICA, BBO, TLBO, and IWO Optimization Algorithms and Sensitivity Analysis for Predicting Daily Reference Evapotranspiration

Evapotranspiration (ET) is an important factor in water resource management. This research investigated the performance of four optimization algorithms to hybridize adaptive network-based fuzzy inference systems (ANFIS) models as follow: ANFIS with imperialist competitive algorithm (ANFIS-ICA), ANFIS with biogeography-based optimization (ANFIS-BBO), ANFIS with teaching-learning–based optimization (ANFIS-TLBO), and ANFIS with invasive weed optimization algorithm (ANFIS-IWO). The hybridized algorithms were used to predict reference evapotranspiration (${\mathrm{ET}}_o$) values in Kerman synoptic station. Six observed variables, including mean air temperature ($T_{mean}$), bright sunshine hours ($SSH$), solar radiation ($R_s$), mean speed of the wind at 2-m height ($U_2$), pan evaporation ($E_{pan}$), and three estimated variables, including extraterrestrial radiation ($R_a$), saturation vapor pressure ($e_s$), and actual vapor pressure ($e_a$) were utilized to develop hybrid models. The results showed that the accuracy of hybrid models by using $T_{mean}$, $U_2$, $e_s$, and $e_a$ was better than those using all required variables for developing the FAO-Penman-Monteith (FAO-PM) equation. Among the hybrid models, the ANFIS-ICA with respect to $\mathrm{R}=0.99$, $\mathrm{RMSE}=0.5$, and $\mathrm{NSE}=0.98$ was considered the superior model. A sensitivity analysis has been done to assess the impact of inputs on the output of the superior model. $E_a$ and $T_{mean}$ had the highest and lowest effect on ${\mathrm{ET}}_o$ prediction, respectively. Finally, ${\mathrm{ET}}_o$ values were estimated by relatively new empirical equations and compared with FAO-PM equation. It was observed that the capability of hybrid models was more than the empirical equations in estimation of the ${\mathrm{ET}}_o$ values.