Spatial analysis of seasonal precipitation using various interpolation methods in the Euphrates basin, Turkey

It is vital to accurately map the spatial distribution of precipitation, which is widely used in many fields such as hydrology, climatology, meteorology, ecology, and agriculture. This study aimed to reveal the spatial distribution of seasonal, long-term average precipitation in the Euphrates Basin with various interpolation methods. For this reason, Simple Kriging, Ordinary Kriging, Universal Kriging, Ordinary CoKriging, Empirical Bayesian Kriging, Radial Basis Functions (Completely Regularized Spline, Thin Plate Spline, Multiquadratic, Inverse Multiquadratic, Spline with Tensor), Local Polynomial Interpolation, Global Polynomial Interpolation, and Inverse Distance Weighting methods have been applied in the Geographical Information Systems environment. Long-term seasonal precipitation averages between 1966 and 2017 are presented as input for predicting precipitation maps. The accuracy of the precipitation prediction maps was based on linear regression analysis, root mean square error (RMSE), mean absolute error (MAE), correlation coefficient (R), and determination coefficient (R2) values obtained from the cross-validation tests. The most suitable method was chosen for the interpolation method that gives the lowest RMSE, MAE, and the largest R and R2. As a result of the study, Ordinary CoKriging in spring and winter precipitation, Local Polynomial Interpolation in summer precipitation, and Ordinary Kriging in autumn precipitation were the most appropriate estimation methods.


Introduction
Precipitation is one of the most significant driving forces in the hydrological cycle affecting hydrological processes (Caracciolo et al. 2014;Cheng et al. 2017). Precipitation data are mainly obtained from rain gauges, weather radars, and satellites (Price et al. 2014). Although there are various measurement methods, precipitation values measured by rain gauges are more reliable. Precipitation monitoring stations provide point precipitation, but studies related to hydrology, climate, agriculture, ecology, and environment require spatial precipitation data (Phillips et al. 1992). Analysis of time and space variability in precipitation is vital for the sustainable use of water resources, the management of droughts and floods, estimation of the surface and underground water resources, pollution of water resources, air pollution, landslides, extreme precipitation, and climate change (Adhikary et al. 2015;Yucel et al. 2014). In addition, detailed knowledge of the Spatio-temporal distribution of precipitation is needed to accurately model flood control using surface water storage or detention basins using rainwater harvesting systems (Bellu et al. 2016;Malik et al. 2019;Terêncio et al. 2018Terêncio et al. , 2017. Therefore, determining the spatial precipitation change using the best interpolation methods is vital. A sufficient number of observations are needed to characterize a particular variable's spatial distribution and map this distribution. However, it is not technically and economically possible to measure environmental variables everywhere in the world or a specific region (Aslantaş et al. 2016). Therefore, various spatial interpolation methods have been developed. Spatial interpolation is the process of using known values to estimate values at unknown points. For example, spatial interpolation can estimate the precipitation value at a location with no recorded data, using values from known 1 3 weather stations nearby. Spatial interpolation is based on Tobler's Law of Geography. This law expresses that points in space close to each other have more similar values than points that are very far from each other. Spatial interpolation is a tool based on spatial correlation logic to estimate the values of an environmental variable at unsampled points using data from point observations in the same region. This tool, widely used in geoinformatics, can be examined in two basic categories: deterministic and geostatistical techniques. While deterministic interpolation methods use sampled points and mathematical equations to produce surfaces, in geostatistical methods, estimations are made using the statistical properties of the data (Childs 2004). Spatial interpolation covers a variety of approaches, including trend surface models, Thiessen Polygons (TP), Natural Neighbor Interpolation (NNI), Polynomial Interpolation (PI), Inverse Distance Weighting (IDW), Splines, and Kriging.
It is known that there is no single interpolation method that can be used in all conditions. Some methods are more precise and useful than others but take longer to calculate. All of them have advantages and disadvantages (QGIS 2021). The method to be selected may vary depending on various parameters (precipitation, temperature, streamflow, groundwater, air humidity, soil moisture, air pollution, water pollution, etc.), data distribution (homogeneous or random), the level of accuracy required, and the time, computer resources available, tolerance of estimation errors and objectives of the study. Choosing a suitable spatial interpolation method is crucial in surface creation because different interpolation methods can create different results (Kamińska and Grzywna 2014). For these reasons, the interpolation methods that best fit the variable used should be compared, and the most effective one should be determined. Although this is a time-consuming process at first, as you gain experience and knowledge of different interpolation methods, the time required to find the most appropriate interpolation method will decrease (QGIS 2021). In this study, the interpolation method that best expresses the spatial distribution of seasonal precipitation data was investigated by trying geostatistical and deterministic methods.
There are various studies in the literature on determining the spatial distribution of precipitation. As an example to the prominent ones: Vicente-Serrano et al. (2003) analyze the validity of various rainfall and temperature maps obtained employing diverse interpolation methods (Global Interpolation (GI), Local Interpolation (LI), Ordinary Kriging (OK), Simple Kriging (SK), Co-Kriging (CK), Block Kriging (BK), Directional Kriging (DK), Universal Kriging (UK), and mixed methods) in the middle Ebro Valley. Lloyd (2010) applied various Kriging methods to evaluate the change in the spatial structure of precipitation. Bostan et al. (2012) created a spatial distribution map of Turkey's average annual precipitation change by using many variables such as altitude, aspect, surface roughness, distance to the shore, land use, and ecological regions. Keblouti et al. (2012) used OK, IDW, and spline to reveal spatial interpolation of annual rainfall in Annaba-Algeria. By comparing the error rates, the IDW method was chosen as the most representative method of interpolation to characterize the precipitation distribution. Yavuz and Erdogan (2012) applied OK, IDW, and Spline methods to determine the spatial variations of Turkey's monthly and annual precipitation trends. As a result, the OK method was chosen as the most suitable algorithm. Aslantaş et al. (2016) used OK and UK methods to determine the temporal and spatial variation of the annual precipitation values of the Euphrates Basin. Gupta et al. (2017) employed five geostatistical modeling techniques: Exponential Ordinary Kriging (EOK), Gaussian Ordinary Kriging (GOK), Circular Ordinary Kriging (COK), Spherical Ordinary Kriging (SOK), and Empirical Bayesian Kriging (EBK) to indicate spatial and temporal distributions of the annual rainfall in the north-west of India. Hadi and Tombul (2018) applied IDW, TP, OK, UK, SK, and Local Polynomial Interpolation (LPI) methods to interpolate precipitation and temperature in the Seyhan Basin, Turkey. Kale (2018) applied deterministic and stochastic methods to determine the spatial variation of long-term precipitation in the Yeşilırmak Basin, Turkey. Amini et al. (2019) compared the success of IDW, OK, UK, Natural Neighbor (NN), Regularized Spline (RS), and Tension Spline (TS) interpolation techniques in predicting precipitation, maximum and minimum temperatures in the Zayandeh-Rud River basin of Iran. According to the obtained error rates, OK provided the most effective results in the spatial distribution of minimum temperatures, and NN in the interpolation of maximum temperatures and precipitation. Agou et al. (2019) estimated spatial and temporal patterns of average annual rainfall in the Mediterranean island of Crete using regression kriging (RK) interpolation. Malik et al. (2019) applied the TP to interpolate spatial distribution of the trends in seasonal and annual precipitation in India. Khorrami and Gündüz (2019) compared different techniques such as IDW, CK, Kriging, and Radial Basis Function (RBF) to reveal the spatial distribution of precipitation in İzmir province and it was found that CK was the most successful. Rata et al. (2020) applied RK, OK, and Kriging with an External Drift (KED) methods to create maps of annual precipitation in the main watershed in Algeria. Ali et al. (2021) used 21 different deterministic and geostatistical interpolation methods to estimate spatial-temporal variations of precipitation of Pakistan. As a result, the EBK regression prediction method showed the most accurate predictions. Katipoglu (2021) used geostatistical interpolation methods to map annual precipitation. According to the analysis results, it was understood that the most suitable interpolation model was EBK. The most suitable EBK model used in estimating was obtained with the K-Bessel detrended semi-variogram function, the smooth circular neighbourhood type, and log empirical transformation without removing trends. When the available literature is examined, it appears that the spatial distribution of annual precipitation is generally estimated and a detailed comparison of all interpolation methods is lacking. For this reason, as the subject of the study, the interpolation method that best fits seasonal precipitation has been examined. Kumar and Jain (2010) stated that the change in precipitation distribution affects the temporal and spatial changes of surface flow, soil moisture, and groundwater reserves and can change the frequency of floods and droughts. Therefore, it is critical to interpolate the regional variations of precipitation. In addition, the spatial distribution of precipitation has high variability. Consequently, it is challenging to make an accurate prediction. Making the most accurate estimations depends on determining the lowest error rate by trying various methods. This study aims to compare the capability of 13 different spatial interpolation methods in precipitation prediction. For this purpose, seasonal precipitations of 21 meteorological observation stations in the Euphrates Basin were used, and various interpolation methods created

Study area and data
The Euphrates basin, which contains Turkey's significant water potential, is one of the important rivers in the Middle East region. The currents of the Euphrates are mainly due to snowmelt. The approximate area of the basin is 127,304 km 2 (Yilmaz and Muttil 2014). In the northern part of the basin, starting from the Malatya Plain, the winter is generally cold, snowy, and quite long. Frosts are also common. Although the summer season is usually calm, high temperatures are seen in the low areas. The summer season is generally very hot and dry in the basin's south, while the winter season is rarely cold. Most of the precipitation is in the winter and spring seasons, and the low relative humidity in the region increases the amount of evaporation. In addition, due to the low summer precipitation in the area, a severe and long drought prevails in the summer season (Sensoy et al. 2008).
In winter, the air mass in the northern parts of the study area is of Siberian origin. Since the autumn months, snowfall begins at high places due to this air mass that enters the region. Since the frontal activities are less in winter, the second dry period is winter. The winter season characterizes the cold anticyclonic weather conditions as the area is far from the sea, and the polar air masses affect the area for a long time. The areas in the south are under the influence of the continental tropical air mass, which is very dry and stagnant, primarily resulting from the Basra low pressure in the summer period. Therefore, this season is arid and hot for the field (Yurddaş 2008).
This study used monthly average precipitation  and topographic data collected from 21 meteorological stations in and around the Euphrates Basin. Data were obtained from the Turkish Meteorology General Directorate. The location map of the meteorological observation stations used in the study is shown in Fig. 1. The topographic data of the stations used are presented in Table 1.

Interpolation methods
Interpolation methods help to produce maps for large areas by detecting values for unknown points with the help of known points. Spatial interpolation techniques are gathered in two main groups: deterministic and geostatistical. Deterministic interpolation methods are used to construct a surface using the existing form of the sample points or to fit a mathematical function to the measured points. On the other hand, geostatistical techniques create a spatial correlation between the calculated and sample points. For geostatistical analysis to be carried out with a proximity relationship, there must be a spatial dependence, a spatial relationship, that is, autocorrelation. Since geostatistical techniques are based on statistics, they produce estimation maps and error maps that express the quality of the estimations (Johnston et al. 2001;Kamali et al. 2015). On the other hand, deterministic techniques use existing configurations of sample points to construct a surface or place a mathematical function on the measured points. In this study, seasonal precipitation maps were estimated with Simple Kriging, Ordinary Kriging, Universal Kriging, Ordinary CoKriging, Empirical Bayesian Kriging, Radial Basis Functions (Completely Regularized Spline, Thin Plate Spline, Multiquadratic, Inverse Multiquadratic, Spline with Tensor), Local Polynomial Interpolation, Global Polynomial Interpolation, Inverse Distance Weighting methods.

Inverse distance weighting (IDW)
It is a method for estimating cell values of unsampled points through the values of known sample points. The cell value is calculated considering various points moving away from the corresponding cell and depending on the distance increment.
The estimated values are a function of the distance and size of adjacent points, and the importance and effect on the cell to be estimated decreases as the distance increases. This method examines general distribution, tendency, anisotropy, and clustering properties. The data are only evaluated and compared locally (Doğan et al. 2013;Isaaks and Srivastava 1989).

Radial basis functions (RBF)
Radial basis functions are considered as the exact interpolation method. Exact interpolators estimate the identical values as measured at the same point, and the surface created requires passing through each measured point. Therefore, the estimated values may vary above the maximum or below the minimum of the measured values (Johnston et al. 2001;Nikolova and Vassilev 2006). There are five essential functions: Thin-Plate Spline (TPS), Spline with Tension (ST), Completely Regularized Spline (CRS), Multiquadric Function (MF), and Inverse Multiquadric Function (IMF). Each function has a different shape and results in a distinct interpolation surface. RBFs are used to estimate values that may vary above the maximum or below the minimum of the measured values. The estimated values of RBFs are based on a mathematical function that minimizes overall surface curvature and produces highly smooth surfaces (Karydas et al. 2009).

Global polynomial interpolation (GPI)
The GPI method is used to obtain a surface with a polynomial function covering the entire study area using sample points. This method allows creating different surfaces for each defined polynomial equation. First-order polynomial equations can generate linear surfaces, second-order polynomial equations can obtain curved surfaces, and third-order polynomial equations can generate cubic surfaces (Johnston et al. 2001).

Local polynomial interpolation (LPI)
The LPI method uses different polynomial equations for other study area locations, unlike the GPI method. This method uses sample points within a specified neighborhood search radius. The neighborhood search diameter is expressed as a circle or ellipse with a certain radius. With the polynomial equations created for each neighborhood search diameter obtained, an estimate is made from the values of the neighboring points for the point in the center of this neighborhood boundary (Johnston et al. 2001).

Kriging
The Kriging interpolation method is an interpolation method that estimates the optimum values of data at other points by using data from known close points. Kriging interpolation is a method that optimally estimates spatial changes at unsampled points using semi-variogram structural features. The most important feature distinguishing the Kriging method from other interpolation methods is that a variance value can be calculated for each predicted point or area (Isaaks and Srivastava 1989;Webster and Oliver 2000). The basic equation used in Kriging is as in Eq. 1.
n: the number of points forming the model, N i : geoid undulation values of the points used in the calculation of N p , N p : the sought undulation value, P i : the weight value corresponding to each N i value used in the calculation of N.

Empirical bayesian kriging (EBK)
EBK differs from conventional kriging methods by considering the error associated with the estimation of the semi-variogram model. This is accomplished by estimating and using multiple semi-variogram models instead of a single semivariogram. This process consists of the following stages: • A model of semi-variograms is estimated from the data. • This semi-variogram simulates a new value in each input data location. • Simulation data provide an estimate of a new semi-variogram model. Weight for this semi-variogram is computed using the Bayes rule, which indicates the probability of the observed data being created from the semi-variogram (Krivoruchko 2012).

Cross-validation test
The cross-validation method, one of the most frequently used methods to specify the accuracy of predictive models, examines the relationship between the predicted and measured values by using the available information in the sample data set. In this method, the value at a location is temporarily extracted from the data set, and an estimation process is done for this extracted location using the remaining values. This process is also repeated for all remaining samples (Isaaks and Srivastava 1989). Various error measurement methods can be used in the evaluation of estimation maps. In this study, the most preferred statistical criteria, root mean square errors (RMSE), mean absolute error (MAE), correlation coefficient (R), and determination coefficient (R 2 ) values and linear regression analysis, are used to evaluate model performance. These criteria are a frequently used measure of the differences between values predicted by a model. Linear regression lines interpret the success of the model through the scatter diagram between the measured and predicted values. The distribution of the data around the 45° line indicates the model's accuracy. The RMSE, MEA, R, and R 2 values are calculated as follows: Here x i : expected precipitation values, y i : the estimation values of precipitation, x avg : average of x values, y avg : average of y values, N: the number of data. The model with the lowest error rates (close to 0), and the largest R 2 value is evaluated as the best.

Results
This study compared various deterministic and geostatistical methods performances in mapping seasonal precipitation in the Euphrates Basin. Monthly total precipitation data of 21 meteorological observation stations covering 1966 to 2017 were used to establish the model. Cross-validation tests were used for the performance evaluation of the model. The model that gave the smallest error and largest R and R 2 values obtained due to the cross-validation test was selected as the most successful.

Spatial mapping in spring rainfall data series
In this part of the study, a spatial map of the long-term seasonal average precipitation was produced using 13 different interpolation methods (SK, OK, UK, OCK, EBK, RBF (CRS, TPS, MF, IMF, ST), LPI, GPI, and IDW). In the selection of the most appropriate interpolation method, various model parameters such as transform, trend, kernel function, semi-variogram, sector type, power parameter, order of the polynomial, and neighborhood type were tested by trial and error methods, and the parameters with the lowest error rate were applied. According to the comparison results, the most suitable estimator algorithm was OCK (Table 2). Also, the linear regression lines obtained by various crossvalidation tests of spring precipitation are shown in Fig. 6. When these lines are examined, it is seen that the measured and estimated values of the OCK method are closest to the 45° regression line. For this reason, the most successful method in the prediction of spring precipitation has been determined as OCK. The geostatistical model giving the lowest RMSE (34.93), and MAE (27.95) value in predicting spring precipitation was revealed as OCK with hole effect semi-variogram distribution. It is also noteworthy that UK interpolation has a high estimation success like OCK (Table 2). When the spring precipitation prediction success of the RBF models is compared, it is noteworthy that the spline with the tensor model is the most effective. It was also revealed that the prediction success of LPI, GPI, and IDW models is relatively low ( Table 2).
Simple interpolation methods do not consider the effects of topography on precipitation and can make significant mistakes in mountainous regions. For this reason, the OCK method in which altitude values are presented to the model as an auxiliary variable was also used in the study. When Fig. 2 Mapping of spring precipitation with the OCK method the interpolation methods of the first spring precipitation are compared, it is seen that the most effective predictions are obtained by the OCK method. The most suitable OCK model used in estimating was obtained with the Hole effect semi-variogram function and the standard neighborhood type, without transforming rainfall data or removing trends ( Table 2).
The spatial variation map of the long-term precipitation averages of the spring season is presented in Fig. 2. Based on the spatial variation map, it was noted that the least precipitation occurred in the Kangal, Tercan, Tortum, Erzurum, and Tercan precipitation stations located in the north and north-west of the Euphrates Basin, and this value was approximately between 148 and 183 mm. The precipitation amount has been determined to increase from the north to the south of the basin. The most precipitation falls in Bingöl and its surroundings, located in the inner parts of the basin.

Spatial mapping in summer rainfall data series
Various interpolation methods have been used for mapping summer precipitation. Interpolation parameters were tested to reveal the most successful predictive model. Figure 7 shows various linear regression lines obtained by cross-validation tests of summer precipitation. When these lines are examined, it is seen that the measured and estimated values of all models are scattered around the 45° regression lines. However, when the RMSE values are considered, the most successful method in estimating summer precipitation has been determined as LPI (Table 3). The geostatistical model indicating the lowest RMSE (11.06), MAE (8.15), the largest R (0.91), and R 2 (0.83) values in predicting summer precipitation were revealed as EBK with Exponential detrended semi-variogram distribution (Table 3). When the summer precipitation prediction success of the RBF models is analyzed, it is significant that the TPS model is the most effective according to statistical criteria. It was also seen that the LPI model is the most successful deterministic model (Table 3).
When the statistical criteria obtained as a result of the cross-validation test were compared, it was determined that the most accurate estimations for the summer rainfall estimation were obtained with the LPI method. The most suitable LPI model used in estimating was obtained with the Quartic semi-variogram function, the standard neighborhood type, and first-order polynomial ( Table 3).
The spatial variation map of the long-term precipitation averages of the summer season is given in Fig. 3. When the spatial variation map of summer precipitation is examined, it is seen that the least precipitation occurs in Adıyaman and Mardin precipitation observation stations located in the south of the Euphrates Basin, and this value is approximately between 11 and 21 mm. It has been determined that the precipitation increases from the south to the north of the basin, and the highest precipitation falls to the İspir, Tortum, Erzurum, and Horasan stations located in the north of the basin.

Spatial mapping in autumn rainfall data series
Various deterministic and geostatistical methods have been used to determine the spatial variation map of autumn precipitation. Various model parameters were tried to find the most successful estimator. As a result, the best model with the smallest error was chosen as the OK method (Table 4). In addition, the scatter plots of the values obtained according to the cross-validation tests of autumn precipitation are shown in Fig. 8. According to these graphs, it is seen that the measured and estimated values of the OK method are closer to the 45° regression line than other methods. Therefore, according to these graphs, it can be said that the most successful method in estimating autumn precipitation is OK.
It is seen that the geostatistical model with the lowest RMSE (24.65), MAE (20.19), the largest R (0.56), and R 2 (0.31) value in the prediction of autumn precipitation is OK with the J-Bessel semi-variogram model. On the other hand, when the autumn precipitation predicting the success of the RBF models is examined, the Spline with Tensor model was found to be the most effective according to statistical criteria. In addition, it was found that the prediction success of LPI, GPI, and IDW models is relatively low (Table 4).
When the RMSE statistics obtained as a result of the cross-validation test were compared, it was determined that the most accurate estimations for the autumn rainfall Fig. 3 Mapping of summer precipitation with the LPI estimation were obtained with the OK method. The most suitable OK model used in estimating was obtained with the J-Bessel semi-variogram function and the smooth neighborhood type without converting rainfall data or removing trends (Table 4).
The spatial variation map of the long-term precipitation averages of the autumn season is presented in Fig. 4. Based on the spatial variation map, it is seen that the least precipitation occurs in the Kangal, İspir, Tortum, and Erzurum precipitation stations located in the north and north-west of the Euphrates Basin, and this value is approximately between 82 and 103 mm. It has been determined that the precipitation amount generally increases from the north to the south of the basin. The most precipitation falls in Bingöl and its surroundings, located in the inner parts of the basin.

Spatial mapping in winter rainfall data series
Various interpolation methods have been used for mapping winter precipitation. Various model parameters were tested to reveal the most successful predictive model. As a result of model comparisons, it was seen that OCK was the most effective model (Table 5). Also, in Fig. 9, the results of the cross-validation test of winter precipitation are shown. According to these graphs, the OCK method best predicted the winter precipitation. It is concluded that the geostatistical model with the lowest RMSE (81.62), MAE (63.85), the largest R (0.66), and R 2 (0.43) value in the prediction of winter precipitation is OCK with the J-Bessel semi-variogram model. On the other hand, when the winter precipitation estimation success of the RBF models is compared, the CRS was the most forceful model. In addition, it was concluded that the prediction success of LPI and GPI models is relatively higher than RBF and IDW ( Table 5).
As a result of the cross-validation test being compared, it was determined that the most accurate estimations for the winter rainfall estimation were obtained with the OCK method. The most suitable OCK model used in estimating was obtained with the J-Bessel semi-variogram function and the smooth neighborhood type without converting rainfall data or removing trends (Table 5).
The spatial variation map of the long-term precipitation averages of the winter season is given in Fig. 5. According to the spatial variation map, it is seen that the least precipitation occurs in Kangal, İspir, Tortum, Erzurum, Horasan, Ağrı, Hınıs, and Malazgirt precipitation observation stations located in the northeast and north-west of the Euphrates Basin, and this value is approximately between 63 and 130 mm. It has been determined that the precipitation amount generally increases from the north to the south of the basin. The most precipitation falls around Bingöl, Tunceli, and Adıyaman.
Temperature decreases with increasing altitude. For this reason, most of the basin, which is generally at high altitudes, is dominated by snowfall in winter. As a result of the snowfall analysis with various interpolation methods, the most appropriate estimation method was OCK. This indicates that the OCK method increases the success of snowfall prediction, thanks to the fact that it also takes altitude values into account.
The spatial distribution of precipitation shows high variability. Therefore, it is challenging to make an accurate prediction. However, when the estimation success of the interpolation methods is evaluated according to seasonal precipitation, the RMSE values obtained by the cross-validation test show the lowest error level in summer precipitation while the highest error level in winter precipitation. It is thought that the region's topography and the variability in precipitation type affect this situation.

Discussion
In this study, the estimation performance of various spatial interpolation methods was compared to express the point precipitation data on a spatial basis. For this purpose, 21 meteorology stations located in the Euphrates basin, which has a mountainous structure, were used. As a result of the study, the successful predictions of the OCK interpolation method, whose altitude values are taken into account, especially in the spring and winter seasons, support the study of Fig. 4 Mapping of autumn precipitation with the OK method Lloyd (2005), Di Piazza et al. (2011), Khorrami and Gunduz (2019). Lloyd (2005) found that the success of precipitation estimation increased due to the use of altitude values as a secondary variable in the interpolation technique. Di Piazza et al. (2011) indicated that taking into account the altitude values in the precipitation estimation will increase the accuracy of the analysis. Khorrami and Gündüz (2019) stated that the geostatistical OCK method is the best interpolator to predict the spatial distribution of precipitation in and around İzmir. In addition, it is expected that the inclusion of the land topography as an auxiliary variable in the precipitation distribution estimations can significantly improve the prediction quality. According to the presented study and literature, it is seen that the OCK method is effective in the analysis of spatial precipitation. Keblouti et al. (2012) used OK, IDW, and spline methods to map annual rainfall in Annaba-Algeria, which contains a low rainfall network density. As a result, it has been determined that the most successful approach is IDW. Keblouti et al. (2012)'s study is inconsistent with the present study results. This situation is struck by the fact that the stations have a reasonably large number and homogeneous distribution in the study carried out. Ilker (2012) used IDW, Kriging, and Spline interpolation techniques to reveal the spatial distribution of precipitation in the Mediterranean Region. As a result of the analyzes, it was concluded that the IDW interpolation method gave appropriate results in precipitation estimation in general. However, the study of Ilker (2012) contradicts our study. The reason for this is that precipitation mapping is done using deterministic methods such as IDW since the land structure of the Mediterranean region is flat. However, since the Euphrates Basin has a mountainous structure, precipitation shows sudden spatial variability, and methods such as IDW are insufficient. For this reason, the Euphrates Basin has been mapped more successfully with geostatistical models. Aslantaş et al. (2016) applied space-time OK and space-time UK methods in the Euphrates Basin to total annual observations from 1970 to 2008. The OK method gave better RMSE and R 2 statistical indicators results than the UK method. When the results of the Aslantaş et al. (2016) study are compared with the presented study, they overlap in summer and autumn precipitation, but not in the spring and winter seasons. The difference can be explained by the difference in the time period used.
Kale (2018) used IDW and Kriging methods to reveal the spatial distribution of long-term precipitation in the Yeşilırmak Basin. It was noted that OK gave better results than the estimates made with IDW. It is seen that the existing literature overlaps with the study. When the results of OK and IDW interpolations used in the current study are compared, it is seen that OK is superior to IDW in all seasons. This result indicates that the current study overlaps with Kale (2018). Adhikary et al. (2017) compared the performances of various geostatistical and deterministic interpolation methods such as IDW, RBF, OK, OCK, and KED to estimate monthly rainfall in Australia, Middle Yarra and Ovens basins. The results show that geostatistical methods are more successful than deterministic methods, producing monthly precipitation forecasts with less error. In addition, the OCK method, which considers the altitude values, is the best estimator for estimating the spatial distribution of precipitation. In this respect, the results obtained are mainly in line with the presented study.
Javari and Education (2017) used IDW, OK, SK, UK, EBK, the indicator kriging (IK), the probability kriging (PK) and the disjunctive kriging (DK) methods to estimate the spatial variation of monthly precipitation in Iran. It has been proposed to use the EBK and OK methods Fig. 5 Mapping of winter precipitation with OCK method to estimate the spatial variation of monthly precipitation over Iran. This study supports the present study in terms of precipitation prediction success of the OK method.
Katipoğlu (2021) predicted the spatial change of average annual precipitation in the Euphrates Basin with geostatistical interpolation methods. As a result, it has been determined that the most successful model in annual precipitation forecasting is Empirical Bayesian Kriging. The result of the study does not agree with the presented research. The difference in the time period and methods used in the emergence of this situation comes to the fore.

Conclusions
This article presents a comprehensive review of determining the spatial distribution of seasonal, long-term precipitation averages using deterministic and geostatistical interpolation methods in Turkey's Euphrates Basin. The study was exhibited in the basin, which has a sparsely distributed meteorological observation network (a station in an area of 6062 km 2 ). The main results of the study can be presented as follows: • Geostatistical methods produce more accurate estimates than deterministic methods in creating precipitation maps in various periods. • The OCK, LPI, OK, and OCK methods are the most successful interpolation methods in modeling the spatial distribution of precipitation in the spring, summer, autumn, and winter seasons, respectively, since they have the smallest error and highest R and R 2 values. • Due to the mountainous nature of the basin, it was concluded that the OCK method, which included the height values as a secondary variable in the model, was more successful. • The OCK method produces more successful predictions in the seasons such as spring and winter, where the difference between the maximum and minimum precipitation values is greatest. • The OCK method has been the most successful in predicting snowfall because snowfall occurs in high altitude regions, and altitude values are presented as input to the OCK. • The J-Bessel, K-Bessel Detrended, and Hole effect semivariogram functions produced successful results in precipitation estimating.
• The precipitation in the basin varies between spring (148 and 323 mm), summer (11 and 118 mm), autumn (82 and 187 mm), and winter (63 and 396 mm). Therefore, widening the difference between the maximum and minimum precipitation values increases the prediction errors. • According to the statistical criteria and scatter plots obtained by the cross-validation test, the prediction success of summer precipitation is the highest, while the prediction success of winter precipitation is the lowest. • The predicted seasonal precipitation maps provide vital information in agriculture, water resources, industry, and energy. • Since the spatial interpolation techniques with the lowest performance in precipitation estimation are determined as TPS in spring, GPI in summer, GPI in autumn, and TPS in winter, It is recommended that these methods should not be preferred for seasonal precipitation interpolation.
It is seen that precipitation deficiencies are dominant in the northern and eastern parts of the basin in spring, the south of the basin in summer, the northeastern part of the basin in autumn, and the northeastern and northwestern parts of the basin in winter. For this reason, negative results will be encountered in the fields of water resources, agriculture, industry, energy, and health in these regions. For this reason, practices and initiatives such as the planning and management of water resources, increasing groundwater wells, the use of innovative methods and devices for water saving in irrigation and industrial sectors, the use of recyclable systems for water reuse, and water transfer to regions are required.
The creation of spatial maps depends on the number, distribution, and data diversity of meteorological stations in the study area. Therefore, to obtain better results, it is recommended to develop a meteorological observation network, get help from remote sensing techniques, and include different meteorological and topographic variables in the model.