Optimization of Hargreaves Equation Using Interval Type-2 Fuzzy Logic System for Predication of Reference Evapotranspiration : Case Study for Arid Climate Region of India

A reference evapotranspiration rate ( \(ET_0\) ) is critical for irrigation time scheduling and plant growth modeling. In comparison to direct measurement, estimating evapotranspiration using environmental factors is a more convenient approach. A variety of mathematical models have been proposed to estimate \(ET_0\) . The agricultural community has focused most of its attention on the Hargreaves (HG) equation, which requires the least amount of weather data. The HG equation, on the other hand, is a simple and practical model for estimating \(ET_0\) because it requires very little weather data. Because of the simplistic approach, the equation cannot accurately predict \(ET_0\) during severe weather scenarios. The calibration or adjustment of the HG equation parameters \(C_H\) and \(E_H\) for different climate conditions is a well-established method for obtaining error-free equation estimates. The existing calibration procedures are time-consuming and empirical. Furthermore, the results obtained using these methods are only valid for the specific location and season. The article presents a novel method for calibrating the HG equation using Interval Type-2 Fuzzy Inference Systems (IT2 FISs), an extension of Type-1 Fuzzy Inference Systems (T1 FISs), for precise evapotranspiration estimation in India’s arid climate region. The primary reason for this is that Fuzzy Inference Systems (FISs) can be designed with human knowledge, enabling intelligent dynamic adaptation of equation parameters. The proposed IT2 FIS calibrates two critical. The proposed modified HG equation using IT2 FIS is compared and validated against the benchmark Penman-Monteith FAO 56-PM equation, as well as experimentally calibrated values for various locations in India’s arid climate. Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE), and Correlation Coefficient (R) were used to assess the efficacy of the \(ET_0\) , MHG IT2 FIS model for reference evapotranspiration against the benchmark Penman-Monteith FAO 56-PM model. In conclusion, the \(ET_0\) , MHG IT2 FIS model outperformed the \(ET_0\) , MHG T1 FIS and \(ET_0\) , HG in predicting the ( \(ET_0\) ) from January to December for the entire research geographical area, with the highest correlation coefficient (R) value of 0.98. The calibrated values of \(C_H\) and \(E_H\) obtained using IT2 FIS were found to be more accurate than the conventional HG equation.