Comparative analysis of Kernel-based versus BFGS-ANN and deep learning methods in monthly reference evaporation estimation

Proper estimation of the reference evapotranspiration (ET0) amount is an indispensable matter for agricultural water management in the efficient use of water. The aim of study is to estimate the amount of ET0 with a different machine and deep 20 learning methods by using minimum meteorological parameters in the Corum region which is an arid and semi-arid climate with an important agricultural center of Turkey. In this context, meteorological variables of average, maximum and minimum temperature, sunshine duration, wind speed, average, maximum, and minimum relative humidity are used as input data monthly. Two different kernel-based (Gaussian Process Regression (GPR) and Support Vector Regression (SVR)) methods, BFGS-ANN and Long short-term memory models were used to estimate ET0 amounts in 10 different combinations. According 25 to the results obtained, all four methods used predicted ET0 amounts in acceptable accuracy and error levels. BFGS-ANN model showed higher success than the others. In kernel-based GPR and SVR methods, Pearson VII function-based universal kernel was the most successful kernel function. Besides, the scenario that is related to temperature in all scenarios used, including average temperature, maximum and minimum temperature, and sunshine duration gave the best results. The secondbest scenario was the one that covers only the sunshine duration. In this case, the ANN (BFGS-ANN) model, which is 30 optimized with the BFGS method that uses only the sunshine duration, can be estimated with the 0.971 correlation coefficient of ET0 without the need for other meteorological parameters. https://doi.org/10.5194/hess-2020-224 Preprint. Discussion started: 22 July 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
It can be noted that water is one of the most important elements on earth that is used by every organism. Without water, it will become almost impossible to survive. It may easy to survive for a few days without getting enough meal but it is completely 35 unable to survive without drinking water. For plants, water is the main requirement for its growth. It means that it is not easy to grow plants without giving them proper water. Furthermore, one of the most important facts is that water is helping the living organisms to maintain their body temperature. The next fact is that water also helps to absorb the nutrients efficiently.
It is also used in dissolving nutrients. Another reason is that water is responsible for refraining from different kinds of diseases.
With the help of water, it will become easy to maintain the body shape more effectively without any sort of problem. 40 Accurate estimation of reference crop evapotranspiration (ET0) and crop water consumption (ET) is an important process for the management of water in agricultural sector in arid and semi-arid climatic conditions where water is scarce and valuable.
Although ET0 is a complex element of the hydrological cycle, it is also an important component of hydro-ecological applications and the water management in agricultural sector. ET0 is important in increasing irrigation efficiency, irrigation planning and reuse of water. ET0 estimation is an essential tool for the forcible management of irrigation and hydro-45 meteorological studies on the basin and national scale.
Many studies have been reported to introduce approaches for ET0 estimation and to test these methods. ET0 is considered a complex and nonlinear phenomenon that interacts with water, agriculture, and climate sciences. It is difficult to calculate such a phenomenon by experimental and classical mathematical methods. There are about twenty well-known methods for predicting ET0 based on different meteorological variables and assumptions. Many of these methods commonly require input 50 and output dataset. The Penman-Monteith (FAO56PM) method proposed by FAO is recommended to estimate ET0, as it usually gives the best results in different climatic conditions (Feng et al. 2016, Nema et al 2017. Today, it is seen that artificial intelligence techniques based on machine learning (ML) can successfully predict the processes showing a complex and nonlinear structure. It is witnessed that scientists frequently use artificial intelligence methods based on excess data in natural sciences, especially hydrology. Thus, methods such as ML, deep learning, and artificial intelligence 55 have gained popularity in calculating and predicting ET0, as can be seen from the literature search. Sattari et al. (2013) used the backpropagation algorithm of artificial neural network (ANN) and tree-based M5 model to estimate the monthly ET0 amount by employing climate dataset in the Ankara region. As the input parameter, the monthly air temperature, total sunshine duration, relative humidity, precipitation, wind speed and monthly time index were used, while the ET0 computed by FAO56PM was used as output for both approaches. The results revealed that the neural network approach gives better results 60 with this data set. Citakoglu et al. (2014) predicted the monthly average ET0 using the ANN and adaptive network-based fuzzy inference system (ANFIS) techniques. Different combinations of long-term average monthly climate data of wind speed, air temperature, relative humidity, and solar radiation recorded at the stations used as input data. According to the results of the study; Although ANFIS is slightly more successful than ANN, it has been found that both methods can be used in estimating the monthly mean ET0. Wen et al. (2015) predicted the daily ET0 amount by SVM method, using limited climate dataset in the 65 https://doi.org/10.5194/hess-2020-224 Preprint. Discussion started: 22 July 2020 c Author(s) 2020. CC BY 4.0 License. region of China's extremely arid Ejina basin. In the study, the highest and lowest air temperatures, daily solar radiation and wind speed values were used as model input and FAO56PM results as model output. Besides, the performance of the SVM method was compared to ANN and empirical techniques, including Hargreaves, Priestley-Taylor and Ritchie. The results indicated that among these models, the SVM provided the highest performance. Gocic et al. (2015) determined ET0 using the FAO56PM method using data from 1980-2010. They used four different computational intelligence methods: Genetic 70 programming (GP), SVM-Firefly algorithm (SVM-FFA), ANN, and SVM-Wavelet. While this study shows that the hybrid SVM-Wavelet provides the highest accuracy for the estimation of ET0; It is determined that SVM-Wavelet followed by the hybrid SVM-FFA provide the higher correlation coefficient compared to ANN and GP. Feng et al. (2016) used trained extremelearning machine (ELM), the integration of genetic algorithm-ANN (GA-ANN) and wavelet neural networks (WNN) to predict ET0 in a humid basin of Southeast China. The results were compared with empirical ET0 (temperature-based i.e. Hargreaves 75 and modified Hargreaves and radiation-based i.e. Makkink, Priestley-Taylor, and Ritchie). Results found that ELM and GANN are better than WNN models. It has been determined that temperature-based ELM and GANN have higher accuracy than Hargreaves and modified Hargreaves, and radiation-based ELM and GANN have higher performance than Makkink. Shamshirband et al. (2016) estimated ET0 with ANN and ANFIS models by employing the Cuckoo search algorithm (CSA).
In the study, the models of monthly climate data from the twelve meteorological stations in Serbia were used as input in the 80 1983-2010 period. For the study, they chose the FAO56PM equation as the ET0 equation. The results showed that the hybrid ANFIS-CSA can be employed for high-reliability ET0 estimation. Pandey et al. (2017) in their study, ML techniques for ET0 estimation using limited meteorological data; evaluated evolutionary regression (ER), ANN, multiple nonlinear regression (MLNR), and SVM. According to the results of the study, the ANN FAO56PM model performed better. In their study, Nema et al. (2017) studied the possibilities of using ANN to increase the performance of monthly evaporation prediction in the humid 85 area of Dehradun. They developed different ANN models including combinations of various educational functions and neuron numbers and compared them with ET0 calculated with FAO56PM. According to the results, the ANN trained by Levenberg-Marquardt algorithm with nine neurons in a single hidden layer made the best estimation performance. Feng et al. (2017) estimated the daily ET0 using temperature data, by employing ELM and generalized regression neural network (GRNN) at six meteorological stations in the southwestern Sichuan basin in China. In the study, ET0 determined by FAO56PM and 90 Hargreaves (HG) model for comparison. Two different scenarios were evaluated for ET0 estimation. ELM and GRNN models gave acceptable results. Fan et al. (2018) used four models based on SVM, ELM, and decision tree to predict daily reference evaporation, using a limited number of meteorological data in various climates of China. Considering the complexity level and estimation performance, Extreme Gradient Boosting (XGBoost) and Gradient Boosting Decision Tree (GBDT) models found to be suitable methods for the prediction of daily ET0. Banda et al. (2018) estimated the daily ET0 for the Bulawayo Goetz 95 region from climate data using neurocomputing methods and compared them with experimental methods. According to the results of the study, neurocomputing calculation techniques were found to be superior to empirical methods. data related to Iran to estimate evaporation (PE) and compare it with the measured values. The results showed that PE can be estimated using ML methods with a high performance and a small number of meteorological parameters that can be easily measured.
Corum region, with a total annual rainfall of 427 mm, can be classified as an arid and semi-arid region of Turkey. Proper prediction of reference evaporation is important to manage limited water resources for optimum agricultural production. ET0 120 is one of the most important elements in water, agriculture, hydrology, and meteorology studies, and its determination is a very important process. ET0 modeling is called as a complex and nonlinear phenomenon according to the interactions of climate factors. For this reason, ML, deep learning, and artificial intelligence methods have gained importance and popularity in this field.
This study has three important goals. In Corum conditions, which are arid and semi-arid climate, the amount of ET0 was 125 estimated by four machine and deep learning (GPR, SVR, hybrid ANN optimized with the Broyden -Fletcher -Goldfarb -Shanno approach (BFGS-ANN) and Long Short-Term Memory (LSTM)) method and the methods used were compared for the first time. Secondly, the effect of different kernel functions on SVR and GPR models results was investigated in ET0 estimation. Finally, determining the model that provides the highest performance with the least meteorological variable requirement for the study. 130 https://doi.org/10.5194/hess-2020-224 Preprint. Discussion started: 22 July 2020 c Author(s) 2020. CC BY 4.0 License.

Study area and dataset used
The surface area of Corum is 1 278 381 ha, of which 553 011 ha, or 43%, is agricultural land. Its population is 525 180 and 27% of it lives in rural areas. The water resource potential of the city is 4 916 hm 3 /year and 84 988 ha of agricultural land is being irrigated. The main agricultural products are wheat, paddy, chickpeas, onions, walnuts, and green lentils. This study was 135 conducted using the meteorological values measured from January 1993 -December 2018 in Corum province (Anonymous, 2017). Data used monthly are average, highest and lowest temperature, sunshine duration, wind speed, average, highest, and lowest relative humidity. 200 of the total 312 months of data were used for training and the remaining 112 were used for testing. Statistics of the data used are given in Table 1. The frequencies of meteorological data of the study area are given in  To determine the meteorological factors employed in the model and the formation of scenarios, the relationship between ET0 and other variables is given in Figure 2. As can be understood visually, the meteorological variables associated with temperature and especially the sunshine duration have a high correlation with ET0. Considering these relationships, 10 different 150 input scenarios were created and the effect of meteorological variables on ET0 estimation was evaluated. Table 2 gives the meteorological variables used in each scenario.

Calculation of ET0
The United Nations, Food and Agriculture Organization (FAO) have recommended Penman-Monteith (PM) equation (Eq.1) to calculate evapotranspiration of reference crop (Doorenbos and Pruitt, 1977). Although the PM equation is much more complex than the other equations, it has been formally explained by FAO. The equation has two main features: (1) It can be used in any weather conditions without local calibration, and (2) the performance of the equation is based on the lysimetric 170 data in an approved spherical range. Requirement for the many of meteorological factors can be defined as the main problem.
However, in many countries, there is still no equipment to record these parameters correctly, or data is not regularly recorded (Gavili et al., 2018

BFGS-ANN
In this study, the hybrid neural network method (BFGS-ANN) optimized with the Broyden -Fletcher -Goldfarb -Shanno approach was used to estimate ET0 amounts. In optimization studies, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method 190 is a repetitious approach for solving unlimited nonlinear optimization problems (Fletcher, 1987). The hybrid BFGS-ANN technique trains a multilayer perceptron ANN with one hidden layer by reducing the given cost function plus a quadratic penalty with the (BFGS) technique. The BFGS approach includes Quasi-Newton methods. For such problems, the required condition for reaching an optimal level accures when the gradient is zero. Newton and the BFGS methods cannot be guaranteed to converge unless the function has a quadratic Taylor expansion near an optimum. However, BFGS can have a high accuracy 195 even for non-smooth optimization instances (Curtis et al. 2015).
Quasi-Newton methods do not compute the Hessian matrix of second derivatives. Instead, the Hessian matrix is drawn by updates specified by gradient evaluations. Quasi-Newton methods are extensions of the secant method to reach the basis of the first derivative for multi-dimensional problems. In multi-dimensional problems, the secant equation does not specify a certain solution, and Quasi-Newton methods differ in how to limit the solution. The BFGS method is one of the frequently used 200 members of this class (Nocedal and Wright 2006). In the BFGS-ANN method application all attributes including the target attribute (meteorological variables and ET0) are standardized. In the output layer, the sigmoid function employed for classification. In approximation, the sigmoidal function can be specified for both hidden and output layers. For regression, the activation function can be employed as the identity function in the output layer.

SVR 205
The statistical learning theory is the basis of the SVM. The optimum hyperplane theory and kernel functions and nonlinear classifiers were added as linear classifiers (Vapnik 2013). Models of the SVM are separated into two main categories: (a) The classifier SVM and (b) the SVR model. An SVM is employed for the classification of data in various classes, and the SVR is employed for estimation problems. Regression is used to take a hyperplane suitable for the data used. The distance to any point in this hyperplane shows the error of that point. The best technique proposed for linear regression is the least-squares (LS) 210 method. However, it may be completely impossible to use LS estimator in the presence of outliers. In this case, a robust predictor have to be developed that will not be sensitive to minor changes, as the processor will perform poorly.

GPR
The Gauss process (GP) is defined by Rasmussen and Williams (2005) as follows: A GP is a complex of random variables, any limited number of which have a joint Gaussian distribution. Kernel-based methods such as SVM and GPs can work 215 together to solve flexible and applicable problems. The GP explained by two functions: Average and covariance functions (Eq. 2). The average function is a vector; the covariance function is a matrix. The GP model is a possibly nonparametric black box technique.
f ≈ GP (m, k) (Eq. 2) 220 Where f refers to Gauss distribution, m refers to a mean function and k refers to covariance function.
The value of covariance expresses the correlation between the individual outputs concerning the inputs. The covariance value determines the correlation between individual outputs and inputs. The covariance function produces a matrix of two parts Here Cf represents the functional part, but defines the unknown part of the modeling system, while Cn represents the noise part of the system. A Gaussian process (GP) is closely related to SVM and both are part of the kernel machine area in ML models.
Kernel methods are sample-based learners. Instead of learning a fixed parameter, the kernels memorize the training data sample 230 and assign a certain weight to it.

Long short-term memory (LSTM)
LSTM is a high-quality evolution of Recurrent Neural Networks (RNN). This neural network is presented for addressing the problems that were present in RNN and this had been done through adding more interactions per cell. These systems are also a special one because it contains remembering information from a long period. Moreover, it also contains four basic interacting 235 layers and all of them contain the different methods of communication. Its main structure can be explained with the help of  The next thing is that its complete network consists of a memory block. These blocks are also called as cells. The information is stored in one cell and then transferred into the next one with the help of gate controls. Through the help of these gates, it will become extremely easy to analyze the information accurately. All of these gates are extremely important and they are LSTM units or blocks are part of the repetitive neural network structure. Repetitive neural networks are made to use some artificial memory processes that can help these AI programs mimic human thinking more effectively. 250

Kernel functions
In this study, as given in Table 3, four different kernel functions that are frequently included in the literature were used. The polynomial, radial-based function, Pearson VII function (PUK), and normalized polynomial kernels used and their formulas and parameters are tabulated in Table 3. As is clear from Table 3, some parameters must be determined by the user for each kernel function. While the number of parameters to be determined for PUK kernel is two, it requires the determination of a 255 parameter in the model formation that will be the basis for classification for other functions. When kernel functions are compared, it is seen that polynomial and radial based kernels are more plain and understandable. Although it may seem mathematically simple, the increase in the degree of the polynomial makes the algorithm complex. This significantly increases processing time and decreases the classification accuracy after a point. In contrast, changes in the parameter (γ) of the radialbased function, expressed as the kernel size, were less effective on classification performance (Hsu et al., 2010). The 260 https://doi.org/10.5194/hess-2020-224 Preprint. Discussion started: 22 July 2020 c Author(s) 2020. CC BY 4.0 License. normalized polynomial function was proposed by Arnulf et al. (2001) in order to normalize the mathematical expression of the polynomial kernel instead of normalizing the data set.
It can be said that the normalized polynomial kernel is a generalized version of the polynomial kernel. On the other hand, PUK kernel has a more complex mathematical structure than other kernel functions with its two parameters (σ, ω) known as Pearson width. These two parameters affect classification accuracy and it is not known in advance which parameter pair will perform 265 best. For this reason, determining the most suitable parameter pair in the use of PUK kernel is an important step.
The editing parameter C must be determined by the user for all SVM during runtime. If values that are too small or too large 270 for this parameter are selected, the optimum hyperplane cannot be determined correctly, therefore there will be a serious decrease in classification accuracy. On the other hand, if C equal to infinity, the SVM model becomes suitable only for datasets that can be separated linearly. As can be seen from here, the selection of appropriate values for the parameters is a variable that directly affects the accuracy of the SVM classifier. Although a trial and error strategy is generally used, the cross-validation approach enables successful results. The purpose of the cross-validation approach is to determine the performance of the 275 classification model created. For this purpose, the data is separated into two categories. While the first part is used as training data in a model form that is the basis for classification, the second part is processed as test data to determine the performance of the model. As a result of applying the model created with the training set to the test data set, the number of samples classified correctly indicates the performance of the classifier. Therefore, by using the cross-validation method, the model that will be the basis for classification and determination of the kernel parameters, in which the best classification performance is obtained, 280 was created (Kavzoglu ve Golkesen, 2010). https://doi.org/10.5194/hess-2020-224 Preprint. Discussion started: 22 July 2020 c Author(s) 2020. CC BY 4.0 License.

Model Evaluation
Some common statistical parameters were used in the selection and comparison of the models used in the study. Differences between ET0 data determined by the root mean square error (RMSE), mean absolute error (MAE) and correlation fit (R) via Eq. 5-7. Here, Xi and Yi are the observed and predicted values, and N is the number of data. 285 Also, Taylor diagrams applied to check the performance of the used models. In this diagram, observed and statistical parameters can be detected simultaneously. Moreover, various points on the polar graph used to study the adaption between measured and predicted values in the Taylor diagrams. Besides, CC and normalized standard deviation are indicated by the 290 azimuth angle and radial distances from the base point, respectively (Taylor 2001).

Results
In this study, 10 different alternative scenarios were created by using monthly average, highest and lowest temperature, sunshine time, wind speed, average, highest, and lowest relative humidity data. ET0 amounts were estimated with the help of kernel-based GPR and SVR methods, BFGS-ANN, and one of the deep learning methods LSTM models. ET0 estimation 295 results obtained from different scenarios according to the GPR method are summarized in Table 4.
As can be seen from the chart, the 5th scenario including TMax, TMin, TMean and n containing four meteorological variables with the GPR method PUK function (R = 0.982, MAE = 9.947 mm/month, RMSE = 11.2109 mm/month) gave the best result. However, the 8th scenario with only one meteorological variable (sunshine duration) and an appropriate result (R = 0.9691, MAE = 11.8473 mm/month, RMSE = 15.8719 mm/month). Since the scenario with the least input parameters and with an 300 acceptable level of accuracy can be preferred, scenario 8 was chosen as the optimum scenario.   Within the SVR model, 3 different kernel functions were evaluated in scenarios under the same conditions, and the results obtained are given in Table 5.
As can be seen here, scenarios 5 and 8 have yielded the best and most appropriate results according to the PUK function.
According to the results, the 5th scenario including TMean, TMin, TMax and n meteorological variables gave the best result 315 (R = 0.9885, MAE = 7.07 mm/month, RMSE = 9.3259 mm/month). However, scenario 8 gave the most appropriate result (R = 0.9691, MAE = 11.2408 mm/month, RMSE = 15.5611 mm/month) only with the meteorological variable of sunshine duration (n). Although the accuracy rate of the 8th scenario is somewhat lower than the 5th scenario, it provides convenience and is preferred in terms of application and calculation since it requires a single parameter. The sunshine duration can be measured easily and without the need for excessive costs and personnel, so that with just one parameter, the amount of ET0 is 320 estimated within acceptable accuracy limits.
https://doi.org/10.5194/hess-2020-224 Preprint. Discussion started: 22 July 2020 c Author(s) 2020. CC BY 4.0 License. The scatter plot and time series graph drawn for the SVR model is given in Figure 6   In this study, ANN was optimized with the BFGS method and ET0 amounts were estimated for all scenarios and the results are given in Table 6. In the implementation of the BFGS-ANN method, all features, including target feature (meteorological variables and ET0), are standardized. In the hidden and output layer, the sigmoid function is f (x) = 1 / (1 + e ^ (-x)) used for classification.
As can be seen here, scenarios 5 and 8 have given the best and most appropriate results. According to the results, the 5th 335 scenario including TMean, TMin, TMax and n meteorological variables gave the best result (R = 0.989, MAE = 6.7885 mm/month RMSE = 8.8991 mm/month). However, Scenario 8 gave the most appropriate result (R = 0.971, MAE = 11.4761 mm/month, RMSE = 15.6399 mm/month) with only the sunshine duration (n) meteorological variable. Although the accuracy rate of the 8th scenario is less than the 5th scenario, it is easy and practical in terms of application and calculation since it consists of only one parameter. The scatter plot and time series graph drawn for the BFGS-ANN model is given in Figures 8  340 and 9. As can be seen, the BFGS-ANN method predicted ET0 amounts with a high success rate, and a high level of agreement was achieved between the estimates obtained from the model and FAO56PM-ET0 values.
https://doi.org/10.5194/hess-2020-224 Preprint. Discussion started: 22 July 2020 c Author(s) 2020. CC BY 4.0 License.  In this study, ET0 amounts were estimated with the LSTM method, which is included in deep learning techniques. In the LSTM model used in this study, two hidden layers with 200 and 150 neurons, relu activation function, and Adam optimization were used. Learning rate alternatives from 1e -1 to 1e -9 , Decay as 1e -1 to 1e -9 , and 500-750-1000 as epoch have been tried. The best results obtained for 10 different scenarios at the modeling stage according to the LSTM method are given in Table 7. 350 As in other methods, the 5th and 8th scenarios of the LSTM model gave the best and most appropriate results. According to 355 the results, the 5th scenario including TMean, TMin, TMax and n meteorological variables gave the best result (R = 0.9879, MAE = 6.2907 mm/month RMSE = 8.5897 mm/month). However, scenario 8 only gave the most appropriate result (R = 0.9687, MAE = 11.6711 mm/month, RMSE = 14.4864 mm/month) with the sunshine duration (n) meteorological variable.
Scatter plot and time series graphs are drawn for the LSTM model are given in Figures 10 and 11. As can be seen, the LSTM method predicted ET0 amounts with a high success rate, and a high level of agreement was achieved between the estimates 360 obtained from the model and FAO56PM-ET0 values.
https://doi.org/10.5194/hess-2020-224 Preprint. Discussion started: 22 July 2020 c Author(s) 2020. CC BY 4.0 License. In order to evaluate and compare the models used in this study, statistical values for the test phase are given in both FAO56PM-ET0 and the models in Table 8. 365 If the models are ranked according to the correlation coefficient, the best results were BFGS-ANN, SVR, LSTM, and GPR in the 5th scenario and BFGS-ANN, GPR, SVR, and LSTM in the 8th scenario. As can be seen from the table, all methods have estimated the ET0 amounts to be acceptable, all with little difference. 375 To evaluate the models with the help of diagrams besides the tables, Taylor diagram for the 5th and 8th scenarios is given in Figure 12. As can be understood from the figure, all four methods used follow one another with a slight difference, but BFGS-ANN seems to achieve higher success than others. When looking at the histogram graph (Figure 1.), it is seen that FAO56PM-ET0 values do not conform to normal distribution. This mismatch is considered to be the reason why the GPR method is relatively less successful than other methods. 380

Conclusion
The amount of ET0 can be calculated with many experimental equations. However, these equations can generally differ spatially and also contain many parameters. Since ET0 contains a complex and nonlinear structure, it can be easily estimated with the previously measured data without requiring a lot of parameters with ML methods. In this study, the estimation of the 385 amount of ET0 with a different machines and deep learning methods was made by using the least meteorological variable in the Corum region, which arid and semi-arid climate with Turkey has an important place in terms of agriculture. In this context, firstly, ET0 amounts were calculated with the Penman-Monteith method and taken into consideration as the output of the models used. Then, 10 different scenarios were created including the average, highest and lowest temperatures, sunshine duration, wind speed, average, highest, and lowest relative humidity meteorological variables. Kernel-based GPR and SVR 390 methods, BFGS-ANN, and LSTM models are used and ET0 amounts are estimated. According to the results obtained, the BFGS-ANN model performed better than others, although all four methods used predicted ET0 amounts in acceptable accuracy and error levels. In kernel-based methods (GPR and SVR), PUK was the most successful kernel function. Besides, the 5th scenario, which is related to temperature and includes four meteorological variables such as average, highest and lowest temperature, and sunshine duration, gave the best results in all the scenarios used. After the 5th scenario, the 8th scenario, 395 which includes only the duration of the sun, was determined as the most suitable scenario. In this case, the ET0 amount was estimated using only sunshine duration without the need for other meteorological parameters for the study area. The Corum region is described as arid and semi-arid as the rainfalls are low. In a sense, this means that the cloudiness is low and the sunshine duration is long. The reason for the models to give quite good results by using only n value is a long time in the work area. Continuous measurement of meteorological variables in large farmland is a costly process that requires expert personnel, 400 time, or good equipment. At the same time, some equations used for ET0 calculations are not preferred by specialists because they contain many parameters. In this case, it is very advantageous for water resources managers to estimate ET0 amounts only with the help of sunbathing time, which is easy to measure and requires no extra cost. (2221)

Conflicts Of Interest:
The authors declare no conflict of interest.