Ranking and comparison of temperature-, mass transfer- and radiation based daily reference evapotranspiration models by using compromise programming index (CPI) and global performance indicator (GPI)

Accurate estimation of reference evapotranspiration (ETo) is crucial for irrigation planning and sustainable water resource management, particularly in regions with limited meteorological data. The widely recommended FAO56 Penman-Monteith (FAO56-PM) method often requires extensive climatic inputs, which are not always available in data-scarce areas. To address this challenge, empirical models have been developed, but their performance varies under different climatic conditions. Most previous studies relied solely on conventional statistical indices for model evaluation, such as the Kling-Gupta efficiency (KGE), index of agreement (IA), normalized root mean square error (NRMSE, mm/day), percent bias (PBIAS, %), mean bias error (MBE, mm/day), and coefficient of determination (R2). However, such single-criterion assessments may not adequately capture the trade-offs between error magnitude and efficiency measures. This study bridges this gap by employing advanced multi-criteria decision-making tools, namely the Compromise Programming Index (CPI) and the Global Performance Indicator (GPI), to integrate statistical indicators into a comprehensive ranking framework. 30 empirical ETo models-comprising temperature-based, radiation-based, and mass transfer-based equations-were evaluated against FAO56-PM across two contrasting agro-climatic zones in India: Dehradun (humid subtropical climate) and Ludhiana (semi-arid climate) on daily basis. Results showed that, based on CPI, the DORJ model performed best at Dehradun (KGE = 0.790, IA = 0.979, NRMSE = 0.117 mm/day, PBIAS = 5.788%, R2 = 0.986, MBE = 0.170 mm/day), while the JORI model (KGE = 0.721, IA = 0.905, NRMSE = 0.280 mm/day, PBIAS = 27.082%, R2 = 0.977, MBE = 0.798 mm/day) was ranked first using GPI. For Ludhiana, the HSM-3 model was the best according to CPI (KGE = 0.843, IA = 0.981, NRMSE = 0.121 mm/day, PBIAS = 5.965%, R2 = 0.968, MBE = 0.244 mm/day), whereas the HSM-1 model (KGE = 0.825, IA = 0.971, NRMSE = 0.156 mm/day, PBIAS = 13.308%, R2 = 0.982, MBE = 0.544 mm/day) achieved the highest GPI ranking. Temperature- and radiation-based models consistently outperformed mass transfer-based equations. This study highlights the necessity of localized calibration and multi-criteria evaluation in ETo modeling. The proposed framework offers practical, computationally efficient alternatives to FAO56-PM, supporting improved irrigation scheduling in data-sparse environments. Future research should expand spatial coverage, test different temporal scales, and integrate hybrid approaches with machine learning and remote sensing for enhanced ETo estimation accuracy.