Comparative analysis of 12 reference evapotranspiration methods for semi-arid regions (Spain)

Evapotranspiration and precipitation are the most influential variables for runoff determination (Licciardello et al. 2011; Hernández Bedolla et al. 2019), irrigation studies (Srivastava et al. 2018; Rodrigues & Braga 2021), and generation of climate change scenarios (Djaman et al. 2015; Pandey et al. 2016; Flores-Fernández et al. 2022; Hadri et al. 2022; Zhao & Dai 2022). Based on the available information (Vanderlinden et al. 2004), various methods are applied for regional analysis to define the reference evapotranspiration (ET_o). The Penman-Monteith method modified by FAO (PMFAO56) (Allen et al. 1998) is widely used to determine evapotranspiration and to compare with other approaches (Valiantzas 2012, 2018; Pandey et al. 2016; Shashidhar & Krishnamurthy 2017; Paredes et al. 2018; Lu et al. 2022; Vishwakarma et al. 2022). Evapotranspiration (PMFAO56) depends on temperature, relative humidity, radiation, and wind speed (Allen et al. 1998). This climate weather information is not always available for all study zones. Therefore, it is necessary to apply methods with fewer climate variables obtainable for these areas.

Alternative approaches can be classified into radiation-based methods, temperature-based methods, combination methods, mass transfer-based methods, genetic algorithms (Valle Júnior et al. 2020), Adaptive Neuro-Fuzzy Inference System (ANFIS) (Güçlü et al. 2017; Roy et al. 2020; Gonzalez del Cerro et al. 2021; Roy et al. 2021), machine learning models (Jing et al. 2019; Kadkhodazadeh et al. 2022; Manikumari et al. 2022; Tejada et al. 2022), and gene-expression models (Traore & Guven 2012, 2013; Mattar & Alazba 2019; Sanikhani et al. 2019; Wang et al. 2019).

Alternative methods based on available information were compared to PMFAO56: (a) temperature-based methods and (b) radiation-based methods. Within the temperature-based methods are Hargreaves (Hargreaves & Samani 1985), and Modified Hargreaves (Thornthwaite 1948; Baier & Robertson 1965; Droogers & Allen 2002). Examples of common radiation-based methods are: Caprio (Caprio 1974), Irmark (Tabari et al. 2013), Makkink (Makkink 1957), Priestley-Taylor (Priestley & Taylor 1972), and Hasen (Hansen 1984).

Various alternative methods are applied to different climates. For humid and subtropical conditions, 30 techniques have been tested, in which Turc and Hargreaves have the best performance (Vishwakarma et al. 2022). For humid climates, Huang (Huang et al. 2019) found that categorical boosting is more efficient. The Turc method provides better results among the five approaches for humidity climate conditions (Trajkovic & Kolakovic 2009). For humid to semi-arid climates, Baier and Robertson, Jensen and Haise, and the Penman equation are highly effective (Sharafi & Mohammadi Ghaleni 2021). Penman is more appropriate than the four empirical methods for semi-arid conditions. However, artificial intelligence methods have the best overall performance (Yurtseven & Serengil 2021). Recently, reanalysis products have been used to estimate reference evapotranspiration (Nouri & Homaee 2022), including soil moisture variations (Nouri & Homaee 2021), soil moisture deficits (Herold, et al. 2016), spatially interpolated observations (Pelosi et al. 2020), and satellite-based radiation data (Pelosi & Chirico 2021). The different methods for ET_o calculation are subject to the area where they were developed and applied. Additionally, they depend on the information available for different climatic conditions and latitudes. Therefore, a method developed for arid zones presents errors for tropical or humid regions and vice versa.

Evapotranspiration is of significant importance in Spain due to its influence on various aspects of the environment, agriculture, and water resource management. The climate information available for Spain is precipitation and maximum and minimum temperatures from 1950 to date. In 2000, the Ministry of Agriculture, Fisheries and Food created the Agroclimatic Information System for Irrigation. The climatic variables available in addition to temperatures and precipitation are: maximum and minimum relative humidity, solar radiation, and wind speed. With this available data, it is possible to use the PMFAO56 method and analyze alternative methods with limited information. In Spain, different studies have been carried out to analyze reference evapotranspiration. Vanderlinden (Vanderlinden et al. 2004) evaluated the Hargreaves method for southern Spain and found adequate performance. Espadafor (Espadafor et al. 2011) tested eight stations in Andalusia from 1960 to 2005 by the PMFAO56 method and four alternative approaches: Hargreaves, Blaney-Criddle, Radiation, and Priestley-Taylor. For the Duero Basin, seven empirical methods were calibrated with monthly climate variables and found acceptable results (Moratiel et al. 2020). The Hargreaves method has the best performance with calibration for Catalonia and Navarre in northeastern Spain (Senatore et al. 2020).

In the present work, several approaches to determine reference evapotranspiration by the PMFAO56 method were analyzed and compared with 12 others, including temperature-based and radiation-based methods, in order to see which ones can be applied. In the absence of climate variables, daily temperature-based models can be used. Moreover, we use linear regression to calibrate daily equations and improve the models' performance.

We proposed comparative methods when different climate data is unavailable, for example, wind speed, maximum and minimum relative humidity, and solar radiation. Alternative methods can be used to estimate evapotranspiration for semi-arid regions. Other methods were evaluated on a daily scale and compared with the PMFAO56. We applied two comparative methods: (1) temperature-based and (2) radiation-based.

The temperature-based methods are the following:

The radiation-based methods are the following:

Different regional calibrations have been proposed, including monthly climate predictors (Sharafi & Mohammadi Ghaleni 2021). We use the linear regression calibration at daily data for all the standardized PMFAO56 versus alternative methods. This calibration consists of performing a linear regression and recalculating the evapotranspiration alternative method according to the obtained coefficients.

The Jucar River Basin is located east of Spain. The basin covers an area of approximately 22,291 km². Basin and sub-basins information was downloaded from the official site of the Jucar Hydrographic Confederation (www.chj.es). The Jucar River is the most significant in the basin, which captures the surface runoff of all sub-basins (Pedro-Monzonís et al. 2015). The Jucar River Basin is semi-arid based on different standardized indicators (Marcos-Garcia et al. 2017; Ortega-Gómez et al. 2018).

Meteorological data was obtained from the Sistema de Información Agroclimática para el Regadío (SIAR) database at http://eportal.mapama.gob.es/websia. Although this database is of recent creation, records are available for 2000–2022. Information was extracted for climate variables such as maximum, minimum, and average temperatures, maximum and minimum relative humidity, solar radiation, and wind speed. For the present paper, we applied the available information in the same period for all stations and completed the years 2005–2021.

For the header sub-basin Alarcon, the method that provided the best correlation coefficient is Hargreaves 2 (0.97). Moreover, the RMSE, MAE, and PE are 0.432 mm/day, 0.326 mm/day, and 0.14%, respectively. The best performance of mean error was 0.004 mm/day (Hargreaves 1) and the best standard deviation was provided for the Hargreaves 2 method (1.714 mm/day).

In the case of header sub-basin Contreras, the results are similar to Alarcon. The best performance was provided for Hargreaves 2. The mean error is 0.022 mm/day, the standard deviation error was 0.070 mm/day, and the correlation coefficient was 0.963. For the RMSE, the best results were provided for the Hargreaves 1 method (0.388 mm/day). PE is 0.54% for the Hargreaves method.

For the middle sub-basin Molinar, the method that provided the best result was Hargraves 1 for four of the six parameters. The standard deviation error was 0.084 mm/day, the R was 0.963, The RMSE error was 0.62 mm/day, and the MAE error was 0.471 mm/day. The best mean error was 0.007 mm/day and PE is 0.2% for the Hargreaves method.

For the middle sub-basin Tous the Hargreaves and Hargreaves 1 methods had the best performance, both with the three best parameters. The mean error was 0.003 mm/day, R was 0.954, and PE was 0.071% for the Hargreaves method. The standard deviation error was 0.107 mm/day, RMSE was 0.682 mm/day, and MAE was 0.513 mm/day for the Hargreaves 1 method.

Finally, for the lower basin Huerto Mulet, the best performance was for the Hargreaves 1 method with the three best parameters. The standard deviation error was 0.064 mm/day, the R was 0.966, and the RMSE was 0.499 mm/day (Hargreaves 1). The minimum mean error was 0.018 mm/day and PE was 0.6% for the Hargreaves method. The best MAE was 0.347 mm/day for the Hargreaves 2 method.

For the present study, several alternative methods were analyzed. The best performance for the Jucar River Basin was through the Hargreaves methods, similar to other studies realized in Spain (Senatore et al. 2020). Moreover, Hargreaves, Hargreaves 1, and Hargreaves 2 are suitable for semi-arid regions. Regional calibration for the Hargreaves methods is strongly recommended due to the estimation improvement.

For the three Hargreaves approaches, the mean is similar to the PMFAO56 method. Hargreaves 3 method has been demonstrated to be more efficient in header sub-basin, elevation values of stations are near 1,000 msnm. For Molinar and Tous sub-basins, Hargreaves and Hargreaves 1 have similar performance, better than Hargreaves 3. Elevation values for these sub-basins are near 700 msnm. In the case of Huerto Mulet sub-basin, the Hargreaves 1 method provides the best results. The station is located at 22 msnm.

For semi-arid regions, we advise the use of calibration techniques based on Hargreaves methods. These can estimate evapotranspiration by applying only a few climate variables (maximum temperature, minimum temperature).

The motivation for this work is the absence of data from the climate stations on variables such as solar radiation, wind speed, maximum humidity, and minimum humidity. In the absence of this information, it is required to determine the reference evapotranspiration. This module will be incorporated into a stochastic model of temperatures in order to analyze climate change scenarios and evapotranspiration.

In the present work, 12 methods were used to obtain evapotranspiration, the first of which is the most common, the PMFAO56 method. Comparisons were made with ten other approaches based on temperatures and radiation. Of these, it was found that the ones based on Hargreaves temperature and modifications of Hargreaves 2 and Hargreaves 3 show the best results with regard to radiation-based methods. These discrepancies are mainly due to the study areas where the methods based on both temperature and radiation have been proposed.

On the other hand, the Hargreaves method and its respective modifications were calibrated to have a more accurate representation of the study area, which can also be calibrated to different stations in the basin, data commonly available in climate basins or extrapolated from regular grid information.

We thank the anonymous reviewers and the editor for their constructive comments on the manuscript. We also value the support provided by the Hydraulics Department of the Michoacana University of San Nicolás de Hidalgo and the Department of Hydraulic Engineering and Environment of the Polytechnic University of Valencia.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.