Accurate estimation of reference evapotranspiration is essential in many studies such as water hydrological balance, design and management of irrigation systems, simulation of plant growth stages and yield, and planning and management of water resources. Accurate estimation of this parameter can lead to proper management and planning of water resources. The aim of this study was to estimate the values of reference evapotranspiration in synoptic stations of Kermanshah province during the statistical period of 2010-2020, evaluation of HARGREAVES Samani and modified HARGREAVES Samani methods and zoning of reference evapotranspiration in the province. The standard Penman Monteith-FAO method resulting from the water requirement system of plants was used to determine the reference evapotranspiration. The results showed that the highest and lowest annual reference evapotranspiration among the meteorological stations in the amount of 1770 and 1341 mm per year belonged to Qasr-e-Shirin and Sararood stations, respectively. The most important effective parameter in the higher reference evapotranspiration in Qasr-e-Shirin station was high temperature and wind speed compared to other stations. The results of zoning of reference evapotranspiration showed that the western regions of the province have a higher intensity than the eastern regions. Evaluation of HARGREAVES Samani and modified HARGREAVES Samani methods showed that the mean of R2, RMSE and NRMSE statistics in HARGREAVES Samani method were 0.9, 0.78 mm day-1 and 0.19, respectively. The mean values of these statistics in the modified HARGREAVES Samani method were 0.71, 2.59 mm day-1 and 0.65, respectively. Therefore, the application of HARGREAVES Samani method to calculate the reference evapotranspiration in this province is recommended.

The Food and Agriculture Organization (FAO) has proposed the FAO 56 Penman-Monteith model as a standard method for estimating reference evapotranspiration (ETo). However, using this model for the high-altitude regions mostly faces uncertainty due to the lack of meteorological stations, observation problems, and incomplete meteorological data. Therefore, in these regions models should be used that require fewer meteorological variables and can also be considered as a function of altitude. In the present study, the data from 28 synoptic stations in Iran with an altitude of more than 2000 meters above sea level in the period of 1989-2019 were used to modify the HARGREAVES-Samani model based on the altitude and also correct the temperature factor coefficients. The comparison of the results of the FAO 56 Penman-Monteith model as a standard method, the original HARGREAVES-Samani, and the modified HARGREAVES-Samani models showed that the modified model offers better results than the original model and is able to estimate the ETo more accurately in the highaltitude regions of Iran. Based on the results of MBE, MAE, RMSE, PVC, LVC, d, r, and PI statistical indices, the highest agreement in estimating ETo with modified HARGREAVES-Samani and FAO 56 Penman-Monteith models was observed at Firuzkuh, Baft, Baladeh, Sisakht, Avaj, Khansar, Abali, Daran, Fereidunshahr, Borujen, Samirom, Aligudarz, Farokhshahr, Damavand, Sepidan and Saman stations, which had an average error reduction of 14% compared to the values obtained from the original HARGREAVES-Samani model.

The evapotranspiration (ET) is the one of the most important component of hydrological cycle. Nowadays many researchers presented the valuable relations involving climatic parameters for estimating the potential evapotranspiration of reference plant (ETo), prevent from water stress and water loss. Among them the HARGREAVES-Samani (H-S) method is common in the regionS that the measuring of meteorological parameters are limited. This study aims to determine the most accurate correction factor for H-S method to estimate ETo according to the FAOPenman- Monteith (F-P-M) method in Gorgan synoptic station. This coefficient is related to climatic parameters which are available in climatology stations. At first equations were optimized using all parameters in excels environment, then some less effective parameters were omitted and again more equations optimized using the others. For verification of results, the meteorological data were divided to 2 groups namely 80 and 20 percent for calibrating and testing the model respectively.The results showed that the equation which included the maximum and average of daily temperature and max, min and average of relative humidity (RH) data, had the maximum ranking due to statistical investigation (R=0.93, RMSE=0.29). Using the mentioned equation the mean annual evapotranspiration of 1165mm (using H-S method) reduced to 925mm. Moreover there was lower error compared to the F-PM- method which estimated 853 mm of wapo=transpiration.

Due to the water scarcity in areas with hot climates, an accurate estimation of evapotranspiration has a significant impact on water resources management and planning. In this paper, the gene expression programming (GEP) approach was used to estimate the daily evapotranspiration in Yazd (hot and dry climate) and Jiroft (warm and humid climate) synoptic stations. The results of this method along with the results of empirical relation of HARGREAVES-Samani were validated with those of the empirical relation of Penman Mantis FAO-56. Statistical indices of coefficient of determination (R2), root-mean-square error (RMSE) and mean absolute error (MAE) were employed to evaluate the efficiency of the utilized methods. The results indicated that GEP model (with R2 = 0.951 and RMSE = 0.66 mm/day for Yazd and R2 = 0.958 and RMSE = 0.65 mm/day for Jiroft) had higher performance compared to HARGREAVES-Samani relation. Therefore, the use of GEP as a model with high capabilities is recommended for estimation of evapotranspiration in areas with hot-dry and warm-humid climates

Different equations have been introduced for estimating grass reference evapotranspiration (ETo) that are in the range of easy to very complex equation of energy balance. Empirical ETo equations have remained in popular use because of simplicity and the smaller number of input parameters needed for computation. The HARGREAVES−Samani (1985) equation is one of the empirical equations which widely used by researchers for estimating the ETo. The most important parameters in estimating ETo are temperature and solar radiation (Rs). The RS has a key role in energy balance in the ground-atmosphere system and is a key parameter in calculating ETo. HARGREAVES and Samani (1982) recommended a simple equation to estimate solar radiation (Rs): R_S=(KT) (R_a)[(TD)]Ù0.5 (1) Combining equation 1 with the original HARGREAVES equation (Hansen et al, 1979) resulted in a simplified equation which requires only temperature and latitude (HARGREAVES and Samani, 1982, 1985). The simplified equation is as: ET_o=0.0135 (KT) (R_a) (TD)Ù0.5 (T+17.8) (2)In the above equations, TD is the difference between maximum and minimum daily air temperature (Tmax-Tmin) (oC) for weekly or monthly periods; Ra is extraterrestrial radiation (mm/day); KT is empirical coefficient and T is the average daily air temperature (oC). The equation 2 and its empirical coefficient (KT) were investigated in various studies and its application in ETo proper estimation was validated. Ever now it was not done any study about the effect of solar radiation estimation methods on the results of HARGREAVES-Samani ETo equation in Shahrekord plain. In the present study, the effect of 8 radiation estimation models on estimating ETo by HARGREAVES-Samani model based on lysimeter measurements was investigated. This study was carried out in the agricultural station of Shahrekord in Charmahal-va-Bakhtiari province in Karoon basin, Iran. The experimental site is characterized with cold semi humid climate, altitude 2070 m above sea level, mean annual air temperature equals to 12.02oC and average annual precipitation of 321.5 mm (Mahdavi et al, 2011). The present study was done by using a volumetric lysimeter planted with alfalfa in the Agricultural Research Center of Charmahal-va-Bakhtiari province in 2011. The date of the beginning and end of the measurement was on 21 April and 22 October 2011, respectively. In the next of the lysimeter, a drainage water measuring hole was constructed. The time of irrigation was based on 50% of maximum allowable depletion (MAD) of soil moisture and this amount was applied based on measuring the soil moisture in depth of 180 centimeters of the lysimeter. Meteorological data used in this study were collected from the weather station of Agricultural Research Center of Shahrekord in 2011. The used meteorological variables were maximum, minimum and average daily air temperature, solar radiation (RS), precipitation, wind speed, soil temperature, dew point temperature, sunshine hours, relative humidity, cloudiness ratio and evaporation from pan. The amount of Rs was calculated from 8 estimation models including HARGREAVES-Samani (HS), Doorenbos- Pruitt, Annandale et al, Allen, Ertekin-Yaldiz, Samani, Goodin et al and Mahmood-Hubbard. Then ETo calculated from HS equation based on the Rs resulted from the radiation models was compared with ETo measured by lysimeter. For evaluating model accuracy, some indices include mean bias error (MBE), root mean square error (RMSE), relative error (RE), coefficient of determination (R2), index of agreement (d) and model efficiency (ME) were used.The results showed that the HARGREAVES-Samani equation had underestimation based on more Rs models. With respect to differences related to lysimeter data, the Goodin et al and Ertekin-Yaldiz models had the poorest results. Also ETo calculated from Mahmood-Hubbard and Annandale et al models had the best results with 8% and 10% underestimation, respectively. With respect to all the evaluation criteria, it can be concluded that the Mahmood-Hubbard is the best solar radiation model with respect to effecting on calculating ETo in the climate of the present study and the Annandale et al model is in the next order. Also the Goodin et al and Samani are the poorest models in the solar radiation estimation.The Mahmood-Hubbard model generally has more physically base and obtained under various conditions and 9 years data. For this reason, probably the model had the best results in calculating ETo. Also the Annandale et al model takes into account the effect of elevation and reduced thickness of the atmosphere on the primary HARGREAVES-Samani model and because the area of study (Shahrekord plain) is a region of high elevation, therefore the Annandale et al model has been a proper model in second order in estimating ETo. The poor result of the Goodin et al model was probably because of obtaining the coefficients of this model under limited conditions.

AbstractBackground and Objectives: The constant need to increase agricultural production, along with more and more frequent drought events in the country, requires a more accurate assessment of irrigation needs and thus a more accurate estimate of actual evapotranspiration. Prediction of water consumption over agricultural areas is important for agricultural water resources planning, management, and regulation. It leads to the establishment of a sustainable water balance, mitigates the impacts of water scarcity, as well as prevents the overusing and wasting of precious water resources. As evapotranspiration is a major consumptive use of irrigation water and rainwater on agricultural lands, improvements of water use efficiency and sustainable water management in agriculture must be based on the accurate estimation of ET. Irrigated agriculture is expected to produce more crops with less water consumption in the future. Therefore, accurate forecasting of water demand along with sustainable management and more efficient methods to meet the growing demand under scarce water resources is necessary. The models used to predict evapotranspiration should be used in different regions with different climates to evaluate their performance. Therefore, in this research, tree models and HARGREAVES were used in Yazd and West Azerbaijan provinces, which have different climates, in order to evaluate the performance of the models used.Methodology: In recent years, water management issues have been addressed using models derived from artificial intelligence research. In recent years, water management issues have been addressed using models obtained from multiple types of research. The use of combined models has made significant progress in recent years. combined models are able to perform processing in a short period of time and at the same time with high accuracy. Using these models, the main challenging aspects are represented by the selection of the best possible algorithm, the selection of suitable representative variables and the availability of suitable data sets. Therefore, in this study, the ability of tree models (M5P and RF) with HARGREAVES model (Hs) in estimating daily evapotranspiration in Urmia and Yazd stations during the period of 2000-2021. The noteworthy point is that in the combined tree-HARGREAVES model, the used tree models were used as input to the HARGREAVES model. The combined model has been used for the first time in this research and the use of this model can predict daily evapotranspiration as well as possible.Findings: The results of the model are performed using 5 evaluation criteria of Coefficient of determination, Root mean square error, Nash-Sutcliffe coefficient, and Wilmot’s index of agreement. In all the used models, the best scenario was the model whose input included parameters of minimum temperature, maximum temperature, relative humidity, wind speed, and sunshine hours. Comparison and evaluation of standalone tree models showed that in the Urmia station two models RF-5 and M5P-5 had less error (0.4 and 0.38-mm day-1, respectively) than other standalone models. Similarly, in the Yazd station, RF-5 and M5P-5 models have higher accuracy (0.36 and 0.35 mm day-1(, respectively) than other standalone models. For combined models, the obtained results showed that the fifth scenario of the M5P-Hs model provided the best performance in Urmia and Yazd stations with the lowest error (0.33 and 0.24 mm day-1) respectively. It was also concluded that the fifth scenario of the RF-Hs model in Urmia and Yazd stations had a lower error (0.36 and 0.26 mm day-1) than other models, respectively. Finally, tree models have increased the accuracy of the HARGREAVES model in this research.Conclusion: Finally, the RF, M5P, RF-Hs and M5P-Hs models were able to predict daily evapotranspiration values in the shortest time and with the highest accuracy. However, the results showed that the lower the model inputs, the weaker the model prediction. The results of this research showed that the combination of tree models with HARGREAVES model is able to predict daily evapotranspiration values with high accuracy compared to individual models. The results of this research showed that the wind speed parameter is one of the most important meteorological parameters needed in estimating daily evapotranspiration, so adding this parameter results in the highest accuracy in all models. Also, due to the important role of wind speed in predicting daily evapotranspiration values and the unavailability of the maximum wind speed parameter in this research, it is recommended to use the maximum wind speed parameter as one of the model inputs for further studies.

Reference Evapotranspiration (ETo) counted as the main factor for assessing the amount of water, needed for crops as well as for the planning of water resources management. Several techniques, methods, and equations have been used for computing ETo. Thus, required weather data sets are the main challenge for evaluating this factor. FAO Penman-Monteith is the most popular technique to determine the ETo. The FAO 56-PM equation requires accurate weather data like air temperature, humidity, solar radiations, and wind speed. Unfortunately, not all these data are possible to reach easily on the station's side. Therefore, FAO 56 recommended another equation namely HARGREAVES-Samani (HS) equation when sufficient weather data may not be available to estimate ETo by FAO56-PM. In the context of this, this study aimed to estimate ETo using the HS equation. For this purpose, historical annual, seasonal, and monthly temperature and wind data were collected from 1981 to 2020 using ‘, The Prediction of Worldwide Energy Resources (POWER)’,web portal. It is concluded that the HS method in conjunction with the POWER datasets and spatially mapping with IDW interpolation gave reliable and accurate results of ETo. This technique gives an idea of water losses in a district and demonstrates a trend of historical annual, seasonal, and monthly ETo.

Evapotranspiration is one of the most important components of the hydrological cycle, which has an important role in water resource management. In the present study, the accuracy of the HARGREAVES method for estimating evapotranspiration with the help of Adjusted coefficient K was investigated using artificial neural network model and M5 decision tree model. The weather data used in this study during the period of 2013-2004 from Farakhshahr station and Shahrekord airport in Chaharmahal and Bakhtiari province included minimum temperature, maximum temperature and relative humidity with cold and arid climate. Data were divided into 75% for training and validation and 25% for testing. The results show that neural network and decision tree model have good correlation modeling. Before using the Adjusted coefficient for Farkhshahr station, the root mean square of the HARGREAVES strain was RMSE = 0. 90 according to the Penman-Monteith-FAO method, which after applying the Adjusted coefficient using the neural network to RMSE = 0. 69 and using The Adjusted coefficient for the decision tree was RMSE = 0 72. In general, the results showed that the HARGREAVES model improved after using the Adjusted coefficient. Neutbay showed that the performance of the artificial neural network is more accurate, but the tree model offers linear, easier, and more intelligible relationships.

Due to the long distance from moisture sources and having more radiation exposure, the rate of evapotranspiration in dry regions is more than the annual precipitation. Evapotranspiration rates have proved to be good indicators in estimating the severity of aridity in a region. Because of the lesser errors of this method and the lack of recorded climatic parameters in many synoptic stations in Iran, In this study the HARGREAVES – Samani method has been used to evaluate the evapotranspiration for 48 synoptic stations in Iran to calculate the evapotranspiration. Then, the spatial analysis was done based on DEM in GIS environment to produce the evapotranspiration maps. Finally, the results integrated to produce the zonation map of intensity aridity in Iran. The results in seasonal and monthly scale showed that the intensity of evapotranspiration was acceptable in conformity with dominated air masses during different seasons in Iran. The Combination of the produced evapotranspiration maps for mean scale of 12 months in 30 years time period revealed that all of the different regions of iran are located in the dry climatic condition since in all of these regions evapotranspiration rate is more than rainfall at least in three months of a year. The accuracy of the results with more intensity is confirmed in the northern and southern coasts of the country and for the central plateau of Iran.

Determination of reference evapotranspiration is the basis of all calculations of water requirement and is considered as the main foundation in determining water requirement, therefore, proper estimation of reference evapotranspiration is of great importance. Globally, systems have been developed that provide users with this information in a location-based manner. In this study, using the database of the country's water requirement system, the evapotranspiration rates of the reference plant were evaluated using meteorological data at Karaj station as a combination regression function. In this study, using SPSS software, the values ​​of different curves based on the parameters of relative humidity, temperature and sunshine were calibrated. The results showed that there is a significant relationship between transpiration evaporation and parameters of relative humidity, temperature, and sunshine. Therefore, two combined and multivariate regression models were calibrated using 7300 data of Karaj station and for evaluation using 15432 data in Alborz province. The evaluation results showed that the combined regression model with normal error of 29% and root mean square error index of about 0.5 mm, agreement index of 0.98 and efficiency index of model 0.94 had better performance. Therefore, this method can be used to determine the reference evapotranspiration in the stations of IRAN.