Artificial intelligence models versus empirical equations for modeling monthly reference evapotranspiration

Accurate estimation of reference evapotranspiration (ETₒ) is profoundly crucial in crop modeling, sustainable management, hydrological water simulation, and irrigation scheduling, since it accounts for more than two-thirds of global precipitation losses. Therefore, ETₒ-based estimation is a major concern in the hydrological cycle. The estimation of ETₒ can be determined using various methods, including field measurement (the scale of the lysimeter), experimental methods, and mathematical equations. The Food and Agriculture Organization recommended the Penman-Monteith (FAO-56 PM) method which was identified as the standard method of ETₒ estimation. However, this equation requires a large number of measured climatic data (maximum and minimum air temperature, relative humidity, solar radiation, and wind speed) that are not always available on meteorological stations. Over the decade, the artificial intelligence (AI) models have received more attention for estimating ETₒ on multi-time scales. This research explores the potential of new hybrid AI model, i.e., support vector regression (SVR) integrated with grey wolf optimizer (SVR-GWO) for estimating monthly ETₒ at Algiers, Tlemcen, and Annaba stations located in the north of Algeria. Five climatic variables namely relative humidity (RH), maximum and minimum air temperatures (Tₘₐₓ and Tₘᵢₙ), solar radiation (Rₛ), and wind speed (Uₛ) were used for model construction and evaluation. The proposed hybrid SVR-GWO model was compared against hybrid SVR-genetic algorithm (SVR-GA), SVR-particle swarm optimizer (SVR-PSO), conventional artificial neural network (ANN), and empirical (Turc, Ritchie, Thornthwaite, and three versions of Valiantzas methods) models by using root mean squared error (RMSE), Nash-Sutcliffe efficiency (NSE), Pearson correlation coefficient (PCC), and Willmott index (WI), and through graphical interpretation. Through the results obtained, the performance of the SVR-GWO provides very promising and occasionally competitive results compared to other data-driven and empirical methods at study stations. Thus, the proposed SVR-GWO model with five climatic input variables outperformed the other models (RMSE = 0.0776/0.0613/0.0374 mm, NSE = 0.9953/ 0.9990/0.9995, PCC = 0.9978/0.9995/0.9998 and WI = 0.9988/0.9997/0.9999) for estimating ETₒ at Algiers, Tlemcen, and Annaba stations, respectively. In conclusion, the results of this research indicate the suitability of the proposed hybrid artificial intelligence model (SVR-GWO) at the study stations. Besides, promising results encourage researchers to transfer and test these models in other locations in the world in future works.