A Multi-Criteria Framework for Evaluating Reference Evapotranspiration Models
DOI:
https://doi.org/10.52151/jae2025623.1950Keywords:
compromise programming index (CPI), empirical model, FAO-56 Penman-Monteith method, multi-criteria decision making, temperature-based evapotranspiration modelsAbstract
Accurate estimation of reference evapotranspiration (ETo) is essential for effective irrigation planning and water resource management. This study evaluated 10 temperature-based ETo models and compared with the Food and Agriculture Organization (FAO) Penman-Monteith method (FAO-56 PM) under the humid subtropical climate of Dehradun, India. Model performance was assessed using statistical indicators, including mean bias error (MBE), root mean square error (RMSE), normalized RMSE (NRMSE), percent bias (PBIAS), Kling-Gupta efficiency (KGE), index of agreement (d), and coefficient of determination (R²). As these statistical measures sometimes provide contradictory results; a structured decision-making tool was needed. To address this issue, compromise programming index (CPI) based on a multi-criteria decision-making (MCDM) approach, was employed in this study. CPI integrated multiple statistical indicators into a single composite index by quantifying the deviation of each model’s performance from an ideal solution. In this study, all indicators were weighted equally to avoid subjectivity and to ensure balanced evaluation across accuracy, bias, and efficiency measures. Results showed that the average ETo values from different ETo models ranged between 3.12 mm day-1 (Dorji model) and 5.97 mm day-1 (Baier and Robertson model), compared to 2.95 mm day-1 (FAO-56 PM method). The Dorji model outperformed other models, exhibiting the lowest errors (MBE = 0.17 mm day-1, RMSE = 0.35 mm day-1, NRMSE = 0.12, PBIAS = 5.79%) and strong agreement (KGE = 0.79, d = 0.98, R² = 0.99). CPI-based ranking confirmed the Dorji model as the most reliable (CPI = 0), followed by the Hargreaves-Samani models, while the Berti model ranked lowest, suggesting a need for recalibration. Overall, this study highlighted the value of integrating CPI with statistical indicators to identify locally suitable models for accurate ETo estimation under diverse climatic conditions.
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