Comparison of the performances of six empirical mass transfer-based reference evapotranspiration estimation models in...

Accurately measured or estimated reference evapotranspiration (ET_o) data are needed to properly manage water resources and prioritise their future uses. ET_o can be most accurately measured using lysimeter systems. However, high installation and operating costs, as well as difficult and time-consuming measurement processes limit the use of these systems. Therefore, the approach of estimating ET_o by empirical models is more preferred and widely used. However, since those models are well in accordance with the climatic and environmental traits of the region in which they were developed, their reliability must be examined if they are utilised in distinctive regions. This study aims to test the usability of mass transfer-based Dalton, Rohwer, Penman, Romanenko, WMO and Mahringer models in Van Lake microclimate conditions and to calibrate them in compatible with local conditions.

Firstly, the original equations of these models were tested using 9 years of daily climate data measured between 2012 and 2020. Then, the models were calibrated using the same data and their modified equations were created. The original and modified equations of the models were also tested with the 2021 and 2022 current climate data. Modified equations have been created using the Microsoft Excel program solver add-on, which is based on linear regression. The daily average ET_o values estimated using the six mass transfer-based models were compared with the daily average ET_o values calculated using the standard FAO-56 PM equation. The statistical approaches of the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), Nash-Sutcliffe Efficiency (NSE), and determination coefficient (R²) were used as comparison criterion.

The best and worst performing models in the original equations were Mahringer (MAE = 0.70 mm day^-1, MAPE = 15.86%, RMSE = 0.87 mm day^-1, NSE = 0.81, R² = 0.94) and Penman (MAE = 1.84 mm day^-1, MAPE = 33.68%, RMSE = 2.39 mm day^-1, NSE = -0.49, R² = 0.91), respectively, whereas in the modified equations Dalton (MAE = 0.29 mm day^-1, MAPE = 7.51%, RMSE = 0.33 mm day^-1, NSE = 0.97, R² = 0.97) and WMO (MAE = 0.36 mm day^-1, MAPE = 8.89%, RMSE = 0.43 mm day^-1, NSE = 0.95, R² = 0.97). The RMSE errors of the daily average ET_o values estimated using the modified equations were generally below the acceptable error limit (RMSE < 0.50 mm day^-1). It has been concluded that the modified equations of the six mass transfer-based models can be used as alternatives to the FAO-56 PM equation under the Van Lake microclimate conditions (NSE > 0.75), while the original equations-except for those of Mahringer (NSE = 0.81), WMO (NSE = 0.79), and Romanenko (NSE = 0.76)-cannot be used.