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Abstract:  
Introduction: Measuring the amount of evapotranspiration is one of the most important parameters required for the proper implementation of water resources management, irrigation planning and optimization of water structures and water allocation and distribution, and there are several methods for measuring. These methods are generally time consuming, costly or require a lot of meteorological data. In recent years, innovative methods to solve some problems have been introduced and widely used. In addition to high accuracy and speed of estimation, ultra-innovative algorithms require less data. The purpose of this study is to identify the effective parameters in calculating daily reference evapotranspiration in the Sistan plain and to extract the best patterns by gene expression programming models and deep learning based on evaluation.
Material and methods: Sistan plain in the north of Sistan and Baluchestan province in the northern latitude to and the eastern longitude to  is located. Sistan plain with an average annual rainfall of 50 mm and an annual evaporation rate of 5000-4000 mm does not have suitable cultivation environmental conditions and is considered as one of the super-arid regions based on the dormitory drought index.The data used in this study were obtained from Zabol Synoptic Station. These climatic statistics include maximum temperature, minimum temperature, average temperature, maximum relative humidity, minimum relative humidity, average relative humidity, sunny hours, wind speed, precipitation and evaporation from the basin on a daily basis brought during the statistical period of 2009-2017. In this study, the accuracy of the two methods of gene expression programming and deep-learning was compared to FAO-Penman-Montith method. GeneXproTools software (4.0) was used to run the gene expression programming model and MATLAB was used to run the deep learning model. In order to train and validate the model, the data were divided into two categories and 80% of the data were used for training and 20% for model validation. Because in smart models, choosing the right and effective primary inputs will improve performance, various combinations of meteorological data were considered as input to the models and by evaluating the results of different scenarios and combinations, the best scenario for predicting the amount of evapotranspiration was selected. Explanation coefficient () to determine the correlation between predicted and measured values, mean absolute error value (MAE) to show the degree of consistency between the data sets of observed and modeled values and also The root mean square error (RMSE) (expressing the error rate) was used as the evaluation criteria.
Results: The results showed that gene expression and deep learning programming models is highly accurate in estimating evapotranspiration in all scenarios, the deep learning model has a higher accuracy than the gene expression model. In deep learning model, M5 scenario with the variables of maximum temperature, minimum temperature, average temperature, maximum humidity, minimum humidity, average humidity, wind speed and evaporation from the pan with the lowest error (RMSE = 0.517) and the highest coefficient explanation () and in the programming model of M1 scenario gene expression with the variables of mean temperature, minimum temperature, maximum temperature and maximum humidity with the highest explanation coefficient R2 = 0.985 and the lowest error RMSE = 0.985 were the most accurate. In the deep learning model, the lowest accuracy is related to M15, M18, M14 and M16 scenarios with MAE‌ values equal to 4.213, 3.131, 2.656 and 2.298, respectively, and the highest accuracy is related to the model. M5, M6, M1 and M3 with MAE values are 0.399, 0.402, 0.422 and 0.422, respectively, in this model, all scenarios are overestimated. In gene expression model, the lowest accuracy is related to M24, M15, M14 and M16 models with MAE‌ values equal to 4.621, 4.438, 3.198 and 2.355, respectively, and the highest accuracy is also related ti models M1, M3, M13 and M7 with MAE values are equal to 0.683, 0.733, 0.780 and 0.991, respectively. In this model, all scenarios are overestimated. According to the outputs of the GEP model, the variables of mean temperature, minimum temperature, maximum temperature and maximum humidity are the most important parameters, which have a greater effect on predicting ET0 values. In the gene expression programming model, scenario M1 with the highest coefficient of explanation R2 = 0.985 and the lowest error RMSE = 0.985 and MAE = 0.683 was selected as the best scenario. In the gene expression programming model, among all scenarios, M1 scenario with the highest correlation coefficient (R2 = 0.985) and the lowest error (RMSE = 0.953) was selected as the best model. After this pattern, the M3 and M7 patterns were ranked second and third. In the deep learning model, M5 scenario had the most impact and M1 and M3 scenarios were in the next ranks. There is a high correlation between the evapotranspiration estimated from these models and the Fao-penman-montith method, and these computational models can be used to estimate daily evapotranspiration when more limited data are available.
Discussion and Conclusion: The results showed that the amount of evapotranspiration of the reference plant in Sistan region can be determined using less parameters (compared to FAO method), in the shortest possible time (deep learning of 3 minutes and 26 seconds) and with accuracy acceptable estimates. The general result is to recommend the application of deep learning model in Sistan region.
     
Type of Study: Applicable | Subject: water resource management
Received: 2020/12/21 | Accepted: 2021/05/11

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