EVAPORATION is an essential component of hydrological cycle. Several meteorological factors play role in the amount of PAN EVAPORATION. These factors are often related to each other. In this study, a multiple linear regression (MLR) in conjunction with Principal Component Analysis (PCA) was used for modeling of PAN EVAPORATION. After the standardization of the variables, independent components were obtained using the (PCA). The series of principal component scores were used as input in multiple linear regression models. This method was applied to four stations in East Azerbaijan Province in the North West of Iran. Mathematical models of PAN EVAPORATION were derived for each station. The results showed that the first three components in all four stations account for more than 90% of the data variance. Performance criteria, namely coefficient of determination (R2) and root mean square error (RMSE), were calculated for models in each station. The results showed that in all the PCA-MLR models, the R2 value was greater than 0. 74 (significant at the 5% level) and the RMSE was less than 0. 52 mm per day. In general, the results showed an improvement in the results using combination of PCA and MLR models for PAN EVAPORATION estimation.

The PAN EVAPORATION is one of the major components of hydrological cycle. It is quite important in agricultural water management and water balance estimations. The current research was performed with two main goals. First, to study the trend of PAN coefficient during baseline period of 1993-2018 and second, projection of PAN EVAPORATION during three future periods under RCP climate change scenarios in 5 selected stations across Iran, namely Mashhad, Bushehr, Ahvaz, Kerman. In part one; the monthly trend of Kp values were studied using Man-Kendal and Sen’s slope estimator in warm season (Spring and Summer).During baseline period a significant decreasing trend in PAN EVAPORATION was observed Mashhad,Bushehr and Ahvaz stations.In second part, for projection of PAN EVAPORATION under RCP scenarios, the PenPAN model, a modified form of P-M equation, was used. The required projected climate data were retrieved from CNRM-C5 model outputs under RCP 4.5 and RCP 8.5 scenarios. The trend analysis of Kp values using Man-Kendal test during the baseline period showed a significant decreasing trend except for the Yazd station with the least coefficient of -1.88 mm. The greatest decreasing value based on Sen’slope estimator was observed in Bushehr station. The results of Man-Kendal test revealed a decreasing trend in PAN EVAPORATION in Ahvaz, Mashhad, Bushehr and increasing trend in Kerman stations. For future periods of 2020-2049, 2050 to 2079 and 2080 to 2100, an increasing trend of PAN EVAPORATION in Kerman station and decreasing trend in 3 other stations was detected. According to Sens’s slope estimator test, during the baseline period the most increasing trend was observed in Kerman station. For future period the most increasing trend was observed in Mashhad station (+0.64). It is projected that mean PAN EVAPORATION values during near, middle and far future periods would decrease 4.7, 6.2 and 8.8%, respectively. Despite of projected increase of air temperature in Mashhad, Bushehr and Ahvaz stations, a reduction in PAN EVAPORATION was observed which might be attributed to reduced received radiation, confirmed in previous studies as EVAPORATION paradox.

EVAPORATION is one of the main elements of hydrologic cycle. Accurate estimation of PAN EVAPORATION is very important in many water-related activities such as irrigation and drainage projects, water balance studies, reservoir operation, and the like. The class A PAN is one of the main PAN EVAPORATION instruments, which is used in standard synoptic weather stations in Iran. Direct measurement of EVAPORATION is expensive and time-consuming. Therefore, different empirical models, which use different meteorological variables, can be used to estimate PAN EVAPORATION. This is so crucial in arid and semi-arid countries such as Iran, where the climate is mostly hyper-arid and it is not easy to measure EVAPORATION directly. In the recent decades, by the development of computers many data driven models have been created for estimating EVAPORATION. One of the intelligent models widely used to hydrologic processes is Bayesian Network Model, which was introduced by Bentin in 1990, and then applied for neural networks by MacKey (1992). Bayesian networks (BNs), also known as belief networks (or Bayes nets for short), belong to the family of probabilistic graphical models (GMs). These graphical structures are used to represent knowledge about an uncertain domain. In particular, each node in the graph represents a random variable, while the edges between the nodes represent probabilistic dependencies among the corresponding random variables. These conditional dependencies in the graph are often estimated by using known statistical and computational methods. Hence, BNs combine principles from graph theory, probability theory, computer science, and statistics. GMs with undirected edges are generally called Markov random fields or Markov networks. These networks provide a simple definition of independence between any two distinct nodes based on the concept of a Markov blanket. Markov networks are popular in fields such as statistical physics and computer vision. BNs correspond to another GM structure known as a directed acyclic graph (DAG) that is popular in statistics, machine learning, and artificial intelligence societies. They enable an effective representation and computation of the joint probability distribution (JPD) over a set of random variables (Reggiani and Weerts, 2008). In addition, BNs model the quantitative strength of the connections between variables, allowing probabilistic beliefs about them to be updated automatically as new information becomes available. In this model, the unknown relationships between parameters in processes can be shown by a diagram. This diagram is non-circular, and has directions composed of nodes and curves for showing the possible relationships in parameters (Money et al, 2012). Therefore, the main objective of this study is modeling of daily class A PAN EVAPORATION using the Bayesian Network model in six stations of East Azerbaijan Province.

The purpose of this study was to assess changes in PAN EVAPORATION over the period 1985-2005 in a network consisting of 14 synoptic stations of Iran using parametric and non-parametric methods. All seasonal and annual series have been checked for normality with the Kolmogorov-Smirnov test. Time trends of this variable were analyzed using parametric and non-parametric techniques (Pearson correlation coefficient, least square linear regression, Mann-Kendall and rho-Spearman correlation coefficient). The results showed that based on the Mann-Kendall test, 21.5% of annual series, 7% of Summer and Spring series had an increasing trend. Besides, 50% of Summer series, 43% of Spring series, 14% of autumn series and 21.5% of annual series showed a decreasing trend. Based on Pearson correlation coefficient, 28.5% of annual series, 7% of Summer and Spring series had an increasing trend. Similarly, in 21.5% of annual series, 43% of Spring series, 50% of Summer series and 14 % of annual series a decreasing trend was observed. The study indicated, 57% of summer series have significant series using Mann-Kendall, rho-Spearman correlation coefficient and Pearson correlation coefficient. In general, decreasing series were more than increasing ones. Despite of slightly increasing temperature trend previously reported in different regions of the country, results of this study showed that EVAPORATION paradox does exist in different climates of Iran also. These reduced values of PAN EVAPORATION, as a key element in arid and semi arid climates of Iran, would have a significant effect in hydro-meteorological studies.

Evapotranspiration is one of the most important parameters in the Planning and operation of reservoirs, designing of irrigation systems. The practical importance of accurate estimates of EVAPORATION and the complexity of effect phenomenon, shows the use of new methods of data mining. In this study, the simulation of PAN EVAPORATION in Tabriz station using multiple regression models were investigated. Meteorological data, including maximum and minimum air temperature, dew point, maximum and minimum air relative humidity, number of sunshine hours and Daily wind speed during (1992-2012) were used in synoptic Tabriz stations. Various models of multiple linear regression and nonlinear one were derived for Tabriz station. The selected multiple linear regression model were tested by Ridge Regression method to be considered multi-collinearity among inputs in the model. Variance inflation factor, values for each variable were calculated. The results showed that all Variance inflation factor, s had the value less than 10. In addition, the ratio lmax/lmax for two- variable selected model was 3.34. Therefore, there was no multi-collinearity in the selected multiple linear regression model f (Tmin, n). Durbin-Watson statistic for the selected model was 1.45 that shows the reliability of the selected multiple linear regression model. RMSE and R2 values of the selected models (multiple linear regression and Non- Linear Regression) was calculated as 2.45 and 0.67 and 2.58 and 0.65, respectively. This results demonstrate the ability of regression techniques to estimate PAN EVAPORATION in Tabriz station.

AbstractBackground and Objectives: EVAPORATION is one of the most complex and important processes in studying hydrological and meteorological factors and plays a major role in determining the energy balance equations on the earth's surface. So, knowing the exact amount of EVAPORATION volume is important for monitoring and correct management of water resources, irrigation planning, determining the irrigation needs, estimating EVAPORATION from the reservoir of dams and modeling hydrological projects, especially in arid and semi-arid regions. 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 this issue without multiple assumptions. Therefore, accurate estimation of EVAPORATION has always been of great importance. Many experimental methods have been presented in estimating EVAPORATION, but since these methods require a lot of input data or it is not possible to measure the variables in all areas, many of these methods have lost their effectiveness. Therefore, it is necessary to use methods which need fewer number of meteorological variables and estimate the EVAPORATION with high accuracy. Therefore, the aim of the current research is to evaluate and present the most accurate model of EVAPORATION estimation using three data-driven models in six synoptic stations in arid, semi-arid and humid climates of Iran, so that the proposed model, in addition to having sufficient accuracy, requires fewer input parameters to estimate EVAPORATION even when there is no sufficient data.Methodology: In this regard, the ability of three machine-learning methods of gradient boosted tree (GBT), generalized linear model (GLM) and artificial neural network-multi layer perceptron (MLP) in estimating the amount of PAN EVAPORATION in dry (Yazd and Bafq stations), semi-arid (Birjand and Siah-Bisheh stations) and humid climates (Sari and Ferdous stations) were investigated. Daily parameters of some fundamental and effective meteorological variables on EVAPORATION during the time period of 2001-2020 were collected. In order to investigate the possibility of using different combinations of meteorological parameters to estimate the EVAPORATION as accurately as possible, six different combinations of meteorological parameters (average temperature, relative humidity, and wind speed and sunshine hours) were considered. Also, to evaluate the accuracy of the mentioned models, four assessment criteria were used including root mean square error (RMSE), mean absolute error (MAE), correlation coefficient (R) and scatter index (SI). Furthermore, diagrams of time series of the best models and the distribution diagram of observed and predicted PAN EVAPORATION by the models were presented and the most suitable combination of meteorological parameters that had suitable accuracy for estimating PAN EVAPORATION was suggested.Findings: The results showed that in Birjand, Yazd, Ferdos, and Siah-Bisheh stations, MLP-VI with RMSE of 1.97, 1.95, 1.97, 2.91, respectively, performed more accurate than other studied models. Moreover, In Sari station MLP-IV and in Bafq station, MLP-V, with RMSE of 1.41 and 1.92, respectively, provided the most precise estimates of EVAPORATION values. Finally, it can be comprehended that in all three studied stations, MLP provided the most accurate estimations of the amount of PAN EVAPORATION and it is suggested as a method with high degree of accuracy. Furthermore, GBT presented the weakest performance in comparison with other studied models. The mentioned trend about the high accuracy of the mentioned models for all studied stations can also be concluded from presented Figures. So, it can be inferred that the accurate models mentioned in each station had the least distribution around the bisector line and had the most accuracy and the least error. In other words, it is possible to estimate the EVAPORATION values in all stations with the meteorological data of temperature, relative humidity, sunshine hours and wind speed with acceptable accuracy.Conclusion: EVAPORATION is one of the main components of water balance in agriculture and is one of the effective and influential factors for suitable irrigation planning. Therefore, accurate estimation of this parameter has a significant role on reducing excessive water consumption. So, in this study, three data-driven models of MLP, GBT and GLM were implemented in six stations including Yazd, Birjand, Sari, Bafq, Siah-Bisheh and Ferdous. The obtained results indicated that the sixth scenario using all utilized meteorological parameters in Yazd, Birjand, Siah-Bisheh, and Ferdous stations, forth scenario in Sari and fifth scenario in Bafq station with the lowest error provided the most accurate estimates of the EVAPORATION and may be recommended for proper estimation of PAN EVAPORATION values.

Estimation the exact amount of water that is used for evapotranspiration, is the major factor in planning for achieving higher production and its most important parameter of management of water in plants. In terms of lack of access to accurate data lysimeters may use the FAO- Penman-Monteith method as the standard method to evaluate the experimental results. In this study using 15 years of weather data of Ahvaz (1998-2012) EVAPORATION PAN coefficient has been calculated with the equations of Orang, Snyder, Cuenca, Allen and Pruitt and their results were compared with the FAO Penman-Monteith. Also for choosing the best model, between five coefficient of determination parameters, Root mean square error, the mean absolute error, the slope and width of the source rank test was performed and the results showed for daily and seasonal PAN coefficient calculation is better to use Allen and Pruitt and in ten-day use Snyder in Ahvaz climate.

EVAPORATION is a physical phenomenon by which water particles enter the atmosphere in the form of vapor from the surface of water or the surface of wet soil through receiving solar energy. EVAPORATION process is an essential part of the hydrological cycle and it takes place continuously in nature. The importance of EVAPORATION estimation in water resources and agriculture studies is undeniable. The EVAPORATION PAN is used as an indicator to determine the EVAPORATION from the water level of lakes and reservoirs all over the world due to the ease of interpreting its data. EVAPORATION prediction is one of the important variables in planning and managing water resources. Various models are used to predict EVAPORATION, such as stochastic time series models, experimental models, data mining models. Due to the fact that EVAPORATION is affected by many parameters that are non-linear, non-stationary and random and occurs in a dynamic and complex manner, the use of experimental methods to predict EVAPORATION that is based only on weather information such as temperature, relative humidity, wind speed and solar radiation are used, the accuracy is not enough. So far, various methods have been presented to calculate and estimate EVAPORATION, such as the water balance method and experimental methods. These methods have flaws such as the inability to generalize to other places and different climatic conditions. Therefore, researchers tried to find a way to reduce the error as much as possible. The use of machine learning models are among these methods. Materials and Methods In this research, two techniques of support vector machine and network with long short-term memory will be used to estimate the amount of EVAPORATION from the PAN in Kohgiluyeh and Boyer-Ahmad Province, and the results will be compared with the actual EVAPORATION values recorded in evapotranspiration stations and some experimental methods of EVAPORATION estimation. In order to model and estimate the amount of EVAPORATION, daily data of parameters of PAN EVAPORATION, rainfall, wind speed, maximum and minimum temperature, cloudiness, soil temperature, maximum and minimum relative humidity, average dew point temperature, sea level pressure and actual vapor pressure has been prepared from the regional water organization for 6 stations including Yasouj, Imamzadeh Jafar, Dehdasht, Dogonbadan, Siskhet and Likk. The length of the statistical data period varies from 39 years in Dogonbadan to 14 years in Likk. In this research, two SVM and LSTM models, as well as three experimental methods of Mayer, US Civil Engineering Organization (USBR) and Ivanov were used to estimate EVAPORATION from PANs. To use the models to estimate EVAPORATION, first the data were randomly divided into training and testing stage. 70% of the data were considered as training data and 30% of the data were considered as test data. Finally, in order to evaluate the models, the statistical indices of explanation coefficient (R2), root mean square error (RMSE) and mean absolute value of error (MAE), model efficiency index or Nash Sutcliffe coefficient (N.S) and residual mass index (CRM) were used. Results and Discussion The results of the SVM model show that the error values of daily PAN EVAPORATION estimation in the SVM model in the training stage vary between 1.6 and 1.2 mm per day. The efficiency coefficient also shows that the model is in a satisfactory condition in terms of estimation and forecasting ability in the Siskhet station, in a good condition in the Yasouj station, and in a very good condition in other stations. LSTM model has weaker results than SVM model. The error values in this model are higher than the SVM model and vary between 2.2 and 3 mm per day. Also, the results of the efficiency coefficient of the model (N.S) also show that this model has not provided acceptable results for estimating PAN EVAPORATION in the two stations of Sisakht and Yasouj. In part of the models test, the LSTM model also showed a weaker ability than the SVM model in most of the stations. The LSTM model has provided better results than the SVM model only in Imamzadeh Jafar station. The best result among all the stations and the two investigated models was obtained at the Dehdasht station with an error of 1.6 mm per day and a Nash coefficient of 0.87 for the SVM model. Comparison of the results of the models with 3 experimental methods of Mayer, Ivanov and USBR also showed that, except for Ivanov's method and at Doganbadan station, none of the experimental methods could simulate the daily EVAPORATION values well. Conclusion In summary, the results of this research show that the SVM model has estimated the northern and central regions of the province with an error between 15 and 18 percent, while the LSTM model estimates the same regions with a greater error and about 22 to 26 percent. In the south of the province, the results is almost reversed and the SVM model has an error of about 19 to 21 percent and the LSTM model has an error of between 13 to 21 percent. In the east of the province, the amount of error in the estimation of PAN EVAPORATION in the LSTM model is also higher than in the SVM model. In total, the comparison of the results of two models and three experimental methods of estimating EVAPORATION from PANs in Kohgiluyeh and Boyer-Ahmad provinces showed that LSTM model is the best model for Imamzadeh Jafar station and SVM model is the best model for the other 5 investigated stations. None of the three experimental models, provided acceptable results for the province. The results of this research show that, despite the emergence of powerful models that are capable of detecting complex and non-linear behaviors of variables based on mathematical relationships that can well recognize and simulate the pattern of data variability, the use of experimental methods to estimate PANs EVAPORATION is not recommended.

EVAPORATION is one of most important parameters which are affected by many variables such as rainfall, wind velocity, sunny hours, and relative humidity etc. EVAPORATION estimation is important for any area with surface water resources because of its effect on dam lakes, precipitation-runoff modelling, river area performance, water management – calculating amount of water that plants need and planning for watering and so on. EVAPORATION can have significant effect on water balance of a river or a reservoir and it may be cause water level to decrease. Due to hydraulic system complications caused by statistical information imperfection and determining all parameters involved, complete hydraulic system modelling is impossible. At such circumstances using al mathematical modelling system will be considered. Matherials & Method In this study we tried to estimate PAN EVAPORATION using two models including Artificial Neural Network (ANN) and Support Vector Machine (SVM) with data preprocessing (gamma test and principal component analysis) to determine affective inputs into two models. For this matter data gatherd from three synoptic stations at Astara, Kiashahr and Talesh at Guilan province has been used. Synoptic stations data includes EVAPORATION, wind velocity at two meter altitude, temperature (minimum, average and maximum), humidity (minimum, average and maximum), sunny and rainy hours. Statistical period of data for Astara and Talesh synoptic stations were 1384 to 1393 and for Kiashahr were 1385 to 1393. 80 percent of meteorology data were used for calibration and other 20 percent were used for model validation. In this study we used multilayer perceptron artificial neural network with sigmoid tangent function and 1 to 20 neurons for hidden layer and support vector machine with radial based kernel function. Calculations has been made in to section with two data preprocess methods. At first section input variable has been selected by gamma test and PAN EVAPORATION estimation was made by both models. At second section modelling has been pulled out by input variables selected by principal component analysis. Discussion of results At gamma test section PAN EVAPORATION estimation parameters were as follows: minimum temperature, maximum humidity, minimum humidity, rainfall and sunny hours for Astara station; maximum temperature, minimum temperature, minimum humidity, rainfall and sunny hours for Kiashahr station and maximum temperature, minimum temperature, maximum humidity, average humidity, rainfall and sunny hours for Talesh station. According to principal component analysis results on Astara, Kiashahr and Talesh stations, five, five and four principal component were used in modeling these stations respectively. At first section input compound determined by gamma test to estimate PAN EVAPORATION of the selected stations were used. PAN EVAPORATION estimation results shows that at Astara station GT-ANN model has less root mean square error than GT-SVM model and beter performance. PAN EVAPORATION estimation at Kiashahr station was done suitably with both models. At this station GT-SVM had a better performance with root mean square error of 1. 295 compared to GT-ANN model with 1. 356. At Talesh station both models had close results but results for GT-SVM were more accurate compared to GT-ANN. Nash Sutcliffe coefficient attained for Astara and talesh stations acknowledges their excellent results and for Kiashahr station shows the satisfactory results. At second section modelling were done by using selected inputs by PCA preprocess method. Accordint to results, PCA-ANN model had better performance estimating PAN EVAPORATION at Astara and talesh stations than PCA-SVM model as its root mean square error was lower. Value of Nash Sutcliffe coefficient shows the suitable performance of both models at both stations. PCA-SVM model had better performance estimation PAN EVAPORATION than PCA-ANN with lower root mean square error at Kiashahr station. Nash Sutcliffe coefficient of PCA-SVM model was 0. 666 and for PCA-ANN model was 0. 634 which shows the satisfactory performance of both models. Conclusions Results shows the good performance of preprocessing methods (principal component analysis and gamma test). Actually performance of GT-ANN, PCA-ANN, GT-SVM and PCA-SVM models performance estimating PAN EVAPORATION of each one of the stations are very close to each other. This similarity is caused by performance of gamma test and principal component analysis preprocessing methods. Principal component analysis converts input variables to independent principal component using linear relation between input variables. Actually this method reduces the effect of the variables with similar information by giving them lower factor. But in gamma test method consider to gamma factor attained from various input compounds, variable that has a negative effect on output will be determined and eliminated from final input compound. As we said before, nature of none linear Gamma and linear PCA methods are different but when PCA method decreases the factor that is eliminated in gamma test to a small value, inputs determined by both methods will be close to each other. This can be one of the reasons that close the estimating models results to each other. So we cannot recommend one preprocessing methods better than the other. We can conclude that for estimating PAN EVAPORATION at these stations both preprocessing methods are suitable. According to results PCA-ANN for Astara and Talesh and GT-SVM model for Kiashahr station had better performance than others. Although both models had acceptable performance estimating PAN EVAPORATION of stations but SVM model results were better than ANN model.