Estimating reference evapotranspiration in three arid, semi-arid and humid climates using gradient boosted tree, generalized linear model and random forest

Background and Objectives
Evapotranspiration is one of the main components of water balance in agriculture and is one of the effective and efficient factors for accurate irrigation planning and management. Direct measurement of evapotranspiration values is time consuming and costly. On the other hand, modeling such a complex process in which many parameters interact with each other is so difficult that it is not possible to simplify the issue without multiple assumptions. Therefore, accurate estimation of this parameter has always been considered by the researchers. In the other point of view, the FAO-56 method was used as the accurate and accepted method for calculating reference evapotranspiration. One of the weaknesses of this model is its dependence on various meteorological variables. Therefore, it is necessary to use methods which need low number of meteorological variables and estimate the reference evapotranspiration with high accuracy. Additionally, due to the use of many meteorological variables and the complexity of the calculations, it is difficult to use FAO-56 method in all regions. Therefore, in the recent years, many researchers implemented machine learning methods to estimate reference evapotranspiration. Most studies in the field of reference evapotranspiration estimation use experimental models that require all the effective reference evapotranspiration parameters to provide an acceptable estimate. Hence, the aim of the current study was to present a superior model from three machine learning models, including random forest (RF), gradient boosted tree (GBT) and generalized linear model (GLM) for estimating reference evapotranspiration in three synoptic stations located at arid, semi-arid and wet climates of Iran. To the best of our knowledge, the proposed GBT and GLM methods have not been used for estimating reference evapotranspiration in the mentioned stations.
Methodology
In this research, the FAO-56 method was used to estimate the reference evapotranspiration. Also, three machine learning methods including GBT, GLM and RF were implemented to estimate the amount of reference evapotranspiration. Daily parameters of some fundamental and effective meteorological variables on evapotranspiration during 21-years statistical period (2000-2020) were collected in three stations located at different climates including Yazd station (arid), Birjand station (semi-arid) and Sari station (wet). In order to investigate the possibility of using different
 
combinations of meteorological parameters to estimate the reference evapotranspiration as accurately as possible, seven different combinations of meteorological parameters were defined. The accuracy of the utilized methods was evaluated using three criteria such as correlation coefficient, scattering index and Nash-Sutcliffe coefficient. Additionally, Taylor diagrams were implemented for evaluating the accuracy of the used methods. It should be noted that the Taylor diagram shows the three parameters of root mean square error, correlation coefficient and standard deviation simultaneously in one figure. Also, the most suitable combination of meteorological parameters that had good accuracy for estimating reference evapotranspiration, was suggested.
Findings
The results showed that in the best model at Birjand Station, and Yazd stations scenario number three by two meteorological variables of temperature and wind speed and in Sari station the scenario number two with temperature and relative humidity, the gradient boosted tree model was reinforced with Nash-Sutcliffe coefficient of 0.804, 0.826 and 0.733, with correlation coefficient of 0.997, 0.997 and 919 and scatter index of 0.249, 0.218 and 0.361 and the generalized linear model with Nash-Sutcliffe coefficient of 0.892, 0.931 and 0.869 correlation coefficient of 0.952, 0.966 and 0.933 and scatter index of 0.185, 0.137 and 0.252, respectively. Finally, the RF method with Nash-Sutcliffe coefficient of 0.954, 0.956 and 0.929, correlation coefficient of 0.978, 0.978 and 0.965 and scatter index of 0.121, 0.110 and 0.186 had good performance for estimating the reference evapotranspiration. On the other hand, in all methods, the scenario number seven using the meteorological parameters of temperature, relative humidity of sunny hours and wind speed in all three stations, presented the most accurate performance. Therefore, all three methods may be proposed as models with high degree of accuracy for estimating reference evapotranspiration.
Conclusion
Reference evapotranspiration is one of the main components of water balance in agriculture and is one of the effective and influential factors for accurate irrigation planning. Therefore, accurate estimation of this parameter has a significant role on reducing excessive water consumption. In this study, three data-driven models of RF, GBT and GLM were used in three stations of Yazd, Birjand and Sari stations. The obtained results indicated that the seventh scenario using all four meteorological parameters in all stations with the highest correlation coefficient, the lowest scatter index and the highest Nash-Sutcliffe coefficient provided most accurate estimates of the reference evapotranspiration and may be recommended for proper estimation of reference evapotranspiration.