Spatio-temporal analysis of meteorological and hydrological droughts in the Euphrates Basin, Turkey

In this study, the aim was to measure changes in the spatio-temporal distribution of a potential drought hazard area and determine the risk status of various meteorological and hydrological droughts by using the kriging, radial basis function (RBF), and inverse distance weighting (IDW) interpolation methods. With that goal, in monthly, three-month, and 12-month time periods drought indices were calculated. Spatio-temporal distributions of the droughts were determined with each drought index for the years in which the most severe droughts were experienced. According to the results, the basin is under risk of meteorological drought due to the occurrence of severe and extreme droughts in most of the area, and especially in the north, during the monthly and three-month time periods. During the 12-month period, it was found that most of the basin is under risk of hydrological drought due to the occurrence of severe and extreme droughts, especially in the southern parts. The most effective interpolation method for the prediction of meteorological and hydrological droughts was determined as kriging according to the results of the cross-validation test. It was concluded that a drought management plan should be made, and early warnings and precautions should be applied in the study area.


GRAPHICAL ABSTRACT INTRODUCTION
Droughts, as recurrent natural disasters caused by long-term lack of precipitation, are hard to understand. The main parameters that trigger drought are low humidity and precipitation, high temperature, and wind (Okonkwo et  There are three types of drought: meteorological, agricultural and hydrological drought (Wilhite & Glantz ).
Drought begins as meteorological drought, which is directly affected by precipitation and is considered the most important parameter and progresses as agricultural drought and hydrological drought. In the case of lack of rainfall, meteorological drought is defined as hydrological drought in the case of lack of surface water or groundwater. Agricultural drought is expressed in terms of shortening of agricultural productivity by lack of rainfall, surface water and groundwater (Dai et al. ; Özcan ).
Drought is a natural phenomenon that can have devastating effects. In order to reduce these destructive effects, it should be determined how often drought occurs and in which regions it is more severe (Gümüş). Taking precautions against drought and being prepared will require determination of drought characteristics (Mishra & Nagarajan ). Information such as the area, severity, duration, and frequency of drought can be determined with the help of drought indices used as tools for drought monitoring. This information can be used to create a drought action plan by giving analysts and decision-makers ideas about the character of the drought. Estimating drought saves time for drought measures and helps reduce the negative effects.
Identifying regions at risk of meteorological and hydrological drought is of great importance in terms of management of water resources, agricultural production, hydroelectric energy production, the prosperity and livelihood of society, the economy of the country, and international relations. For these reasons, the drought situation of the study basin was evaluated and recommendations were made for measures to be taken against drought and mitigation policies.
For sustainable drought management, studies involving multiple measures on a basin basis should be undertaken with an integrated approach within the framework of a plan and program. In order to assess drought, the meteorological, agricultural, hydrological, and socio-economic aspects of drought should all be considered as a whole. In this way, sustainable solutions can be developed for every sector affected by drought disasters and economic and social benefits can be obtained. In this sense, it is necessary to implement multiple measures that do not entail structural elements, from public education to afforestation activities (Anonymous ).
In order to mitigate the negative effects of droughts and predict them, the spatio-temporal extent of a drought needs to be determined. For this reason, drought maps based on suitable drought indices should be created on a basin basis using various interpolation methods. The most preferred interpolation methods in drought mapping are the kriging, RBF, and IDW methods. The most effective of these methods can be determined by comparing various statistical parameters  In the Euphrates Basin, drought has a significant impact on agriculture, water resources and the ecosystem. Water scarcity and droughts increase the impact on water resources day by day. Water resources are very sensitive to climate change and variability. Therefore, changes in drought greatly affect the availability of water. Drought analysis is needed to determine the water potential and requirements in a region.
For this, in this study, extreme meteorological and drought characteristics belonging to various drought indices of the Euphrates Basin were investigated.
Assessing drought status and identifying risky areas with maps can provide a starting point for regional drought intervention and can help in the creation of a comprehensive drought management strategy to reduce the effects of drought. In this context, the objective of the present work is to evaluate several spatial interpolation techniques for predicting the spatial distribution of droughts in the Euphrates Basin. In this study, the most appropriate meteorological drought maps were created by comparing the ordinary kriging (OK), radial basis function (RBF), and inverse distance weighting (IDW) interpolation methods with cross-validation testing.

Study area and data
In this study, monthly total rainfall data and monthly average air temperature data from 1966 and 2017 belonging to 16 meteorological observation stations (MOSs) in the Euphrates Basin were chosen as meteorological observations. These data were used as input for the calculation of drought indices.
The location and spatial characteristics of the stations in the Euphrates Basin are shown in Figure 1 and Table 1. The main factors that trigger droughts are decrease in rainfall, and increase in temperature and evaporationtranspiration because of climate change in the region. In addition, drought is effective in the study area because it is away from the effects of the sea and the mountains that extend into the country parallel to the coast; in other words, the study area is in an inner part of the country receiving less effect of precipitation.

Drought indices
Drought indices are tools developed to detect, monitor and evaluate drought events. Over the last few decades, more than 150 drought indices have been developed for different locations, targets and applications (Zargar et al. ). In

Standard precipitation index (SPI)
In the calculation of the SPI index, the time series is deter- Here, T is the average temperature ( C) of the selected month, and K is a correlation factor that varies with latitude and month. I is the annual thermal index calculated as the when the value of PET is known, the difference (D) between precipitation (P) and PET in the relevant month is calculated as follows: where P i is the total precipitation of the i-th month (mm),

Z-score index (ZSI)
The ZSI is a dimensionless drought index that uses original data; in other words, it uses precipitation data that do not need to conform to the distribution. As can be seen in Equation (5), it is obtained by dividing the difference of precipitation data from the mean by the standard deviation within the specified time period (Wu et al. ).
The ZSI has standard deviation (1), standard mean (0), and values below the average are positive and those below are negative.
Here, P i : precipitation values, P: average of all precipitation data, σ: standard deviation of all precipitation data.

Rainfall anomaly index (RAI)
The basis of this index is the calculation of the deviation from the normal value of precipitation. For this, after finding the average ( P) in a long time-series, the average of the ten highest values ( M) and the average of the ten smallest values ( X) are obtained. The index value can be calculated using Equations (6) and (7). P > P is anomaly-positive and the index value is: If P < P, it is anomaly-negative and the index value is: Here, P i : precipitation values in monthly and annual time period.

Reconnaissance drought index (RDI)
The RDI is a general meteorological index for drought assessment. This index is widely accepted in arid and semi-arid regions. It is evaluated in three ways: initial value (α k ), normalized RDI (RDI n ), and standardized RDI (RDI st ). The initial value (α k ) is within a year for a reference period of k months. This value (α k ) can be obtained from the ratio of precipitation values to potential evapotranspiration on a monthly, seasonal, and annual basis. Equation (8) Here, P j is the precipitation value of month j and PET j is the evapotranspiration value of month j. Normalized RDI values (KKI n ) can be calculated by Equation (9). In this equation, a k is the average of the initial values.
Standardized RDI values (RDI st ) can be calculated by Equation (10). Here, y k ¼ Inα k : Moreover y k is the arithmetic mean of values of y k andσ k is the standard deviation (Tsakiris & Vangelis ).
Threshold values and corresponding categories of all drought indices used in the study are shown in Table 2.

Inverse distance weighting
Inverse distance weighting interpolation is the method that applies the assumption that the points close to each other are more similar than the distant ones. The general formula of the method: Here, x 0 : point to be estimated, Z (x 0 ): the value of the estimate at the point x 0 , Here, Z(x i ) represents the measured value at location i, W i , the unknown weight of measured values at location i, x 0 , the estimated location, and N is the number of measured values.
The sum of the weights must be equal to 1 to ensure the estimate is noncommittal: The difference between the estimated value of the estimated point and the random variable is expected to be 0: Each kriging prediction is associated with a kriging variance. There are weights for the kriging process that will then minimize the kriging variance, and the sum of the weights must be 1 as in Equation (15).
In the kriging method, the weighting process varies according to the size of the working area, the distribution of the stations, the distances and directions of each sample point according to the estimated regional variable, the distances between the sample points, the anisotropic or isotropic variation and the semivariogram model parameters (Oliver ; Sen ).

Semivariogram function
Kriging uses a semivariogram function to determine unknown values. The semivariogram provides information about the scale and structure of spatial change and is used to investigate the magnitude of spatial change and autocorelation of the study region in case the stationary hypothesis is valid. Semivariograms show the spatial variation of regional variables (random variables whose positions in time or space are known) (Curran ).
The function expressing the spatial relationship between regional variables is illustrated by Equation (17) (Matheron ). Using Equation (17), the semivariogram function is obtained in the form of Equation (18) Here, N is the number of sample pairs compared, h is the step range, and z(x i þ h) is the expected value of the regionalized variable at position x i þ h. The variogram function is expressed as the variance of the difference between two regional variables as far away as h from each other (Uyar ). Thus, spatial relationship and dependence between regional variables are expressed. While the variance between the sample pairs close to each other is expected to be low, it is likely that the variance will increase and the similarity will decrease with increasing distance (Uzunlar ).

Selection of the most suitable interpolation method
Spatio-temporal analysis of drought is of great importance in terms of assessing drought risk status. Drought index values depend on meteorological parameters such as precipitation, temperature, PET and hydrological parameters such as flow.
It is not possible to measure meteorological and hydrological data from all points in an area in terms of both cost and technique. For this, drought values in the whole area were estimated by using interpolation methods to determine the spatial distribution of droughts at various time intervals.
Thus, drought values at other points were estimated by making use of previously measured data. The geostatistical analysis tool of Arcmap 10.5 Software was used for spatial drought interpolation.
In this study, raster surfaces are estimated from the vector data defined on point geometries using kriging, RBF and IDW methods under geostatistical analysis.
There are different statistics parameters in the literature to determine the accuracy of the predicted surface. In general terms, the most widely used method is the root mean square error (RMSE) value obtained by crossvalidation test. Therefore, this method was used in model comparison.
The kriging model contains several model parameters such as semivariogram models, kernel functions, and neighborhood types (Table 3). In order to determine the best fit among these parameters, various variations were tried and the kriging model was applied, giving the smallest RMSE value by trial and error and cross-validation methods.
In the application of radial-based function interpolation, kernel functions, neighborhood and sector types were selected by trial and error, and the model with the lowest valuation method was applied with the cross-valuation method (Table 4)

Cross-validation
Cross-validation is an effective method used to estimate semivariogram model parameters. This method examines the relationship between predicted and actual values using the information available in the sample dataset. In this method, the value at one location is temporarily removed from the dataset and an estimate is made for that location, which is extracted using the remaining values (one-leaveout). This process is repeated for all the remaining samples (Isaaks & Srivastava ). For example, in Figure 2 below, ten randomly distributed data points are shown.
Cross-valuation ignores a point (red dot) and calculates the value of that location using the remaining nine dots

Evaluation of models
The performances of the established models have been tested with the help of different statistical criteria. In this study, Pearson correlation coefficient (R), determination coefficient (R 2 ) and root mean square error (RMSE) criteria were used. These statistical calculations can be made with the help of Equations (19) and (20), respectively. RMSE is a statistical measure that measures the predictive accuracy by determining the differences between the predicted values and the observed values. The determination coefficient (R 2 ) is a statistical measure that shows how close the data is to the fitted regression line.
Here, x i is the expected (observed) values of models, y i is the outputs (estimation values), and N is the number of data.
The models for which the R 2 value is the largest (close to 1)   and which have the lowest error rates (close to 0) are evaluated as the best.

Preliminary analysis of extreme drought characteristics
In this study, the aim was to obtain drought maps by the interpolation method. Accordingly, preliminary analysis of the years with the highest and most frequent droughts was made by analyzing the dry periods. Thus, it was chosen which year of drought should be mapped.
RAI is more sensitive to extreme droughts in the monthly and 12-month time periods, while SPEI is more effective in the three-month time period. RDI has been found to be almost as sensitive as RAI. In addition, it was found that SPI and ZSI were ineffective in the monitoring of extreme drought compared with other indices (Table 5).
When the results of the monthly, three-month and 12month meteorological drought indices outcome analyses were compared, it was found that the maximum drought was observed in the same years. However, the effect can be felt more since SPI, SPEI and RDI show maximum drought in a wider time period (Table 6). In addition, the years in which the most severe droughts were identified were taken as critical years in drawing drought risk maps in the later stages of the study.

Meteorological and hydrological drought interpolation
In this section, the spatial distributions of the drought classes on the basin were determined by kriging RBF and IDW methods according to the drought intensity determined by each drought index and drought risk maps were created. While one-and three-month indices show meteorological drought, 12-month indices give information about hydrological drought status. Note: '*' sign represents the maximum value.  1989, 2013-2014 1989 1989 1988, 1989, 2012- When using the RAI and IDW methods, some decrease in areal distribution intensity of droughts was encountered.

Monthly
This is due to the evaluation of the RAI according to different cut levels and to the IDW method being only a distancedependent deterministic method. In other words, the kriging  second-degree trend effects were removed. By removing the trend, the semivariogram will model spatial autocorrelation between data points without having to take into account the trend in the data. The trend is automatically added to the calculations before the final surface is produced.
The type of sector selected is determined by the number of neighboring points to be estimated and the proximity of the neighboring points to the forecast point. In this study, when the standard neighborhood type is used, four sectors with 45 offset is selected and the maximum number of neighborhoods is limited to 12.
In the radial basis function (RBF) method, it was determined that the most suitable estimation surface was obtained by using a multiquadric kernel function, sector    climatic factors, that evaporation/transpiration-based indices measure droughts more sensitively, and that the drought risk in the basin will gradually increase.

CONCLUSIONS
In this study, the aim was to determine drought levels according to various meteorological drought indices at the basin level, to compare the maps according to the drought indices, to determine the spatio-temporal variation of drought severity, to compare the kriging, RBF and IDW interpolation methods, to identify the risky areas in terms of drought in the basin and to manage the drought. The scope of the outputs obtained in the study basin drought management and planning of water resources in Turkey are qualities that would benefit decision makers and public institutions.
In this study, the kriging, RBF, and IDW methods were compared for the prediction of meteorological and hydrological droughts. The comparison process was performed according to the RMSE values obtained as a result of cross-validation testing. Since the meteorological stations in the basin are not distributed uniformly, they performed better than deterministic interpolation methods such as kriging, IDW, and RBF, which are geostatistical methods, for the prediction of meteorological droughts. In addition, in this study, risky areas were determined with drought maps and it was emphasized that the effects of droughts that might reoccur in the region should be reduced.
Risky areas were identified with drought maps and it was emphasized that the effects of droughts that are likely to repeat should be reduced by taking measures in these regions. It was determined that the meteorology stations of Kangal, Erzincan, Tunceli, Erzurum, Bingöl, Mus, Hınıs, Agȓı, and Malazgirt, especially in the northern parts of the basin, are under risk due to severe and extreme droughts in monthly and three-month time periods. In the 12-month period, it was determined that the southern parts of the basin were at risk, especially at the Adıyaman station, due to severe and extreme droughts.
In the Euphrates Basin, which is a mountainous basin, multiple quadratic kernel functions for interpolation of droughts with RTF and exponential or polynomial kernel functions for interpolation of droughts with kriging have been proposed.
As a result of the analysis run within the scope of this study, the maximum meteorological drought was observed in 1989 and between 2012 and 2017. This indicates that droughts have become more frequent in recent years. In addition, the occurrence of prolonged and very severe droughts in the basin reveals the need for more effective use of water resources and drought management plans.
As a continuation of this study, it is suggested to study the relationships between drought indices and atmospheric oscillations (NAO, SO, …), the relationships between meteorological droughts and hydrological droughts, and the recurrence intervals of meteorological and hydrological droughts. In addition, in this study, it is suggested that the models established can be improved by increasing the number of meteorological and hydrological measurement stations and their more homogeneous distribution.