Assessment of pan coefficient performance: A comparative study of empirical and model-driven approaches using a hill-climbing-based alternating model tree and MOORA

The Maritime Provinces of Canada play a significant role in the country's agricultural productivity, yet they face numerous changes due to climate change. Therefore, a reliable estimation of reference evapotranspiration (ET_o) requires accurate determination of the pan coefficient (K_pan). However, this is quite challenging due to variations in climate change and the deep non-linearity of meteorological data. Intensive experiments for pan evaporation (E_pan) were conducted to develop a model, which includes hill-climbing based BestFirst-ClassifierSubsetEval (BF), alternating model tree (AMT), and multi-objective optimization by ratio analysis (MOORA). The model was assessed by comparing its performance using Bidirectional long-short-term memory (Bi-LSTM), recurrent neural network (RNN), random forest (RF), elastic regression net (Elastic net), and Instance-based learner K-Nearest Neighbor (IBK). The model was further evaluated using five empirical equations of FAO-56. The input data included seven daily meteorological variables, including maximum, minimum, mean, relative humidity, Wind, and Slope, extracted from 2018 to 2023 datasets to compute ET_o and K_pan locally measured E_pan. Statistical indicators, including correlation coefficient (R), root mean square error (RMSE), Kling–Gupta efficiency (KGE), and Vulnerability, evaluated the model output. SHAP (Shapley Additive exPlanations) and Individual Conditional Expectation (ICE) were used to interpret the models' flexibility and visualize complex geographical phenomena and processes in an RF model. Overall, the outcomes revealed that the primary model (BF-AMT) outperformed all the data-driven and empirical models in terms of optimal metrics (RMSE=0.0143, Vulnerability=6.3260, and MOORA=0), followed by BF-Elastic net (RMSE=0.7891, Vulnerability=28.1081, and MOORA=0.073) and BF-Bi-LSTM (RMSE=0.0169, Vulnerability=64.8649, and MOORA=0.128), respectively. Finally, the SHAP results showed that wind and relative humidity were the most influential factors affecting the pan coefficient values.