In this study, the temporal variability of monthly total precipitation and monthly average temperature data of Palu station were analyzed. In addition to statistical analysis such as Mann–Kendall (MK) and SR, innovative polygon trend analysis (IPTA), innovative trend analysis (ITA), and combination of Wilcoxon test and scatter diagram (CWTSD) methods were used in the study. A total of 24 trend analyses (for 12 months of precipitation and temperature data) were conducted for each method used for temperature and precipitation parameters in the study. Looking at the results of these methods, a decreasing trend was detected only in December for precipitation data, common to all methods. For temperature data, an increasing trend was detected only in February and March. With the application of the IPTA, an increasing trend in some months and a decreasing trend in other months were detected for the two parameters. The Wilcoxon test exhibits significant consistency with the MK and Spearman's Rho (SR) in terms of the statistical trend, according to the examination of temperature and precipitation data using the CWTSD approach, which is relatively recent. Furthermore, the visual trend analysis demonstrates high consistency between the NO-ITA and Şen-ITA approaches.

  • This article provides a comparison of different trend analysis methods.

  • It sets the trends for the province of Elazığ, which is located in eastern Turkey.

  • The management of water resources includes methods that can be used to detect future changes in hydro-meteorological parameters significantly affecting ecosystems and agricultural activities.

Today, with the rapid increase in the population and hence the efforts to develop agricultural foods, the developments in the industrialization sector such as industrial growth increase the need for water and make water resources important (Saplıoğlu et al. 2014). In addition, it is very important to both evaluate data and make predictions for the future in the design of water structures such as dams and moorings (Keskin et al. 2018). Climate change is a globally recognized phenomenon that has gained widespread acceptance within the scientific community (Verma et al. 2023a, 2023b, 2023c). Determining the trend of hydro-meteorological parameters is one of the best methods for both observing the effects of climate change and making predictions for the future. For this reason, trend analysis methods can be used to detect the change in climate over a long period of time (Mishra & Coulibaly 2014; Ceyhunlu & Aydın 2020).

Many methods have been developed to determine the trends of hydro-meteorological data, and these methods have been used in many studies. The Mann–Kendall (MK) test (Mann 1945; Kendall 1975; Mehta & Yadav 2021a, 2021b; Verma et al. 2022a, 2022b) and the Spearman Rho test (Lehmann & D'Abrera 1975; Dahmen & Hall 1990) were the most common trend analysis methods used in the literature (Güner Bacanlı 2017; Zakwan et al. 2019; Ceyhunlu et al. 2021; Verma et al. 2021; Wang & Wan 2023). In addition, today, trend testing has become easier to interpret with innovative approaches. Şen innovative trend analysis (ITA) (Şen 2012, 2014; Pastagia & Mehta 2023), innovative polygon trend analysis (IPTA) (Şen et al. 2019), and the combination of Wilcoxon test and scatter diagram (CWTSD) (Saplıoğlu & Güçlü 2022) are most important innovative approaches. These methods have also been used in many studies (Caloiero 2018; Nissansala et al. 2020; Achite et al. 2021; Bora et al. 2022; Ahmed et al. 2022; Umar et al. 2022). Long-term historical data and their interpretation are important aspects of understanding any changes that occur as a result of changing environmental behaviors (Verma et al. 2022a, 2022b; Sahu et al. 2023). Many scientists have carried out trend analyses for meteorological and hydrological measurements using these classical methods (Güçlü Bacanlı 2018; Verma et al. 2023a, 2023b, 2023c). It should be noted that these methods, strictly applied to time series, make some assumptions. The ITA method, in other words, the 1:1 correct approach, discovered by Şen in 2012, does not require any assumptions and therefore can be applied to all time series. Şen et al. (2019) found that it is possible to detect changes in successive time periods in the time series. In addition to determining the trend of a time series, information can be obtained about the magnitude and slope of trend transitions between months. In addition to statistical methods (MK, SR, etc.), it is preferred by different researchers as a supporting method in determining the trends of meteorological time series (Mehta et al. 2022). Unlike ITA, the CWTSD method developed by Saplıoğlu & Güçlü (2022) does not list the data used to avoid any changes when comparing the two halves of the time series. The hydro-meteorological parameters determining the trends such as precipitation (Chaouche et al. 2010; Li et al. 2011; Sahu et al. 2022; Verma et al. 2024), temperature (Dawood 2017; Gavrilov et al. 2018; Mehta & Yadav 2022a, 2022b), evaporation (Tabari et al. 2011; Makwana et al. 2020), drought (Mehta & Yadav 2021a, 2021b, 2022a, 2022b; Patel et al. 2021), and relative humidity (Salami et al. 2016; Fallah Ghalhar et al. 2022) play an important role in climate change and in the planning, construction, and management of water resources.

Saplıoğlu (2015) proposed a new method based on the graphic method developed by Şen in his study. The proposed method was compared with the MK method, the regression model, and Şen's graphical method. Precipitation data from the provinces of Burdur and Isparta in Turkey have been used for this process. He made monthly and annual trend analyses of these data. As a result, he said that the new method that Şen suggested with the graphic test gave similar results and that the results of the regression test supported both tests. He said that the results of the MK test were partially similar to the results of this study. Mondal et al. (2012) conducted a study on the changing precipitation trend of a river basin close to the coastal region of Orissa. They used the MK test, modified MK test, and Şen's slope estimation method to determine the monthly variability of 40-year daily precipitation data between 1971 and 2010. As a result, they said that precipitation data showed an increasing trend in some months and a decreasing trend in other months. Yue et al. (2002) used the MK and Spearman Rho tests to evaluate trends in annual maximum streamflow data for 20 watersheds in Ontario, Canada. They said that P values determined using the two methods were almost the same. They evaluated the trends at the 0.05 significance level. As a result, they said that the number of regions with a decreasing trend is higher. Yıldız et al. (2022) examined the severity, trend, and results of drought by applying the standard precipitation index (SPI) method in the Susurluk Basin of Turkey, taking into account the 48-year period between 1972 and 2019 and the 12-month timescale. ITA and MK test methods were used to determine the trends of SPI values. As a result of the MK trend analysis, they determined that there is an increasing trend at 50 and 85% confidence levels across the basin, excluding Uludağ and Keles. In Uludağ and Keles stations in Turkey, it has been found that there has been a decreasing trend in many months of the year. According to the ITA results, they determined that there was an increasing trend across the basin in the drought and rainy groups. Kizilelma et al. (2015) examined the trends of annual, seasonal, and monthly average values of temperature and precipitation data of meteorological stations in the Central Anatolia Region. The MK test analyzed trends using Şen's slope method and linear regression methods. They stated that there were significant increases in the trends of the maximum and minimum temperature values throughout the study area and that there were increases in the average temperature value at the 95% confidence interval at all stations except the Ürgüp station. Kankal & Akçay (2019) used MK and Şen's innovative trend methods to determine the trend of precipitation in Trabzon province in the Eastern Black Sea region. They used annual, seasonal, and monthly total precipitation data from two stations in Trabzon (Trabzon-Akçaabat). Finally, they said that there is a general increasing trend in both stations in autumn and spring. They said that no trend was detected in Trabzon station in the summer season and that there was a decreasing trend in the Akçaabat station.

Summary information about the studies mentioned earlier and the current study are presented in Table 1. For effective trend analysis, periods of sufficient and reliable precipitation data need to be taken into account. Shorter term precipitation records may not provide reliable results. The longer the recording period, the better, more reliable, and more accurate the trend analysis can provide results (Patel & Mehta 2023). Therefore, having the water year close to the present day and having a long interval may provide more accurate information about the study areas. In addition, it is understood that only statistical trend analysis methods (MK, SR) were used among the studies given in the table. In addition to the methods used in these studies, innovative trend methods such as IPTA, ITA, and CWTSD, which can be interpreted both statistically and visually, were used. Performance comparisons can be made in studies using different methods.

Table 1

Summary about past studies

StudyExamined stationsWater yearMethodData usedTemporal resolution
Saplıoğlu (2015)  Burdur-Isparta (Turkey) 1975–2006 Saplıoğlu method, ITA, MK, Regression Precipitation Monthly–annual 
Mondal et al. (2012)  Orissa-Cuttack (India) 1971–2010 MK, modified MK, Sen's slope estimator Precipitation Monthly 
Yue et al. (2002)  Ontario (20 basins) (Canada) 75 years MK, SR Streamflow Annual 
Yıldız et al. (2022)  Susurluk Basin (Turkey) 1972–2019 ITA, MK SPI Monthly 
Kızılelma et al. (2015)  Central Anatolia (Turkey) 1970–2010 MK-Sen's slope estimator-linear regression Precipitation–temperature Monthly–seasonal–annual 
Kankal & Akçay (2019)  Trabzon-Akçaabat (Turkey) 1948–2017 (Trabzon); 1964–2017 (Akçaabat) ITA, MK Precipitation Monthly–seasonal–annual 
This study Elazığ – Palu (Turkey) 1965–2020 (T); 1965–2012 (P) MK, SR, CWTSD, ITA, IPTA Precipitation–temperature Monthly 
StudyExamined stationsWater yearMethodData usedTemporal resolution
Saplıoğlu (2015)  Burdur-Isparta (Turkey) 1975–2006 Saplıoğlu method, ITA, MK, Regression Precipitation Monthly–annual 
Mondal et al. (2012)  Orissa-Cuttack (India) 1971–2010 MK, modified MK, Sen's slope estimator Precipitation Monthly 
Yue et al. (2002)  Ontario (20 basins) (Canada) 75 years MK, SR Streamflow Annual 
Yıldız et al. (2022)  Susurluk Basin (Turkey) 1972–2019 ITA, MK SPI Monthly 
Kızılelma et al. (2015)  Central Anatolia (Turkey) 1970–2010 MK-Sen's slope estimator-linear regression Precipitation–temperature Monthly–seasonal–annual 
Kankal & Akçay (2019)  Trabzon-Akçaabat (Turkey) 1948–2017 (Trabzon); 1964–2017 (Akçaabat) ITA, MK Precipitation Monthly–seasonal–annual 
This study Elazığ – Palu (Turkey) 1965–2020 (T); 1965–2012 (P) MK, SR, CWTSD, ITA, IPTA Precipitation–temperature Monthly 

In this study, temperature and precipitation data of the Palu station, located within the borders of Elazığ province in Turkey, between 1965–2020 and 1965–2012, respectively, were obtained from the General Directorate of Meteorological Affairs. The study aimed to determine the trends of precipitation and temperature data in this region and to determine the performance analysis of the trend methods (MK, SR, Wilcoxon, Şen-ITA, NO-ITA, and IPTA), which were used to determine these trends. It is also aimed to compare the performance results of MK, SR, Wilcoxon, Şen-ITA, NO-ITA, and IPTA methods, which have different characteristics compared to each other in determining trends.

Study area

The Upper Euphrates Basin was chosen as the study area (Figure 1). This basin covers approximately 8.1% of Turkey’s surface area. It has a drainage area of approximately 6,310.8 km2 and an altitude varying between 835 and 4,040 m (Ergüven 2022). Palu station numbered 17806, located within the borders of the basin, was chosen to be used in the study. The location map of this station is given in Figure 2. For Palu station with 38°41′26.52″ N, 39°55′33.60″E coordinates, precipitation and temperature data for the years 1965–2012 and 1965–2020 were obtained from the General Directorate of Meteorology Affairs. The average precipitation and temperature values observed by months and the smallest and largest monthly average precipitation and temperature values observed are summarized in Table 3. The temperature and precipitation data used in the study were subjected to the prewhitening procedure after homogeneity analysis was performed with the run test. The purpose here is to determine whether temperature and precipitation data have autocorrelation. Since the presence of autocorrelation can cause errors in determining the trend in nonparametric methods such as the MK test and the SR test, the autocorrelation effect must be eliminated by subjecting the time series in which the presence of autocorrelation is detected by the prewhitening procedure. The correlation coefficients calculated for the precipitation and temperature data used in the study and the lower and upper limit values calculated for the 95% significance level are presented in Table 2.
Table 2

Autocorrelation values and lower and upper limit values calculated for precipitation and temperature data

Precipitation
Temperature
MonthUpper limitCorrelation coefficientLower limitCorrelation statusUpper limitCorrelation coefficientLower limitCorrelation status
January 0.3123 −0.4287 −0.3123 (+) 0.2781 0.1159 −0.2781 (–) 
February 0.3123 −0.3016 −0.3123 (–) 0.2781 0.0633 −0.2781 (–) 
March 0.3123 −0.0903 −0.3123 (–) 0.2781 −0.0673 −0.2781 (–) 
April 0.3123 −0.3221 −0.3123 (+) 0.2781 −0.2544 −0.2781 (–) 
May 0.3123 0.1654 −0.3123 (–) 0.2781 0.1014 −0.2781 (–) 
June 0.3123 −0.4192 −0.3123 (+) 0.2781 0.0942 −0.2781 (–) 
July 0.3123 −0.0120 −0.3123 (–) 0.2781 −0.0423 −0.2781 (–) 
August 0.3123 −0.1428 −0.3123 (–) 0.2781 0.1376 −0.2781 (–) 
September 0.3123 0.0164 −0.3123 (–) 0.2781 −0.3039 −0.2781 (+) 
October 0.3123 0.4923 −0.3123 (+) 0.2781 0.2460 −0.2781 (–) 
November 0.3123 0.1690 −0.3123 (–) 0.2781 0.0031 −0.2781 (–) 
December 0.3123 −0.0048 −0.3123 (–) 0.2781 −0.1523 −0.2781 (–) 
Precipitation
Temperature
MonthUpper limitCorrelation coefficientLower limitCorrelation statusUpper limitCorrelation coefficientLower limitCorrelation status
January 0.3123 −0.4287 −0.3123 (+) 0.2781 0.1159 −0.2781 (–) 
February 0.3123 −0.3016 −0.3123 (–) 0.2781 0.0633 −0.2781 (–) 
March 0.3123 −0.0903 −0.3123 (–) 0.2781 −0.0673 −0.2781 (–) 
April 0.3123 −0.3221 −0.3123 (+) 0.2781 −0.2544 −0.2781 (–) 
May 0.3123 0.1654 −0.3123 (–) 0.2781 0.1014 −0.2781 (–) 
June 0.3123 −0.4192 −0.3123 (+) 0.2781 0.0942 −0.2781 (–) 
July 0.3123 −0.0120 −0.3123 (–) 0.2781 −0.0423 −0.2781 (–) 
August 0.3123 −0.1428 −0.3123 (–) 0.2781 0.1376 −0.2781 (–) 
September 0.3123 0.0164 −0.3123 (–) 0.2781 −0.3039 −0.2781 (+) 
October 0.3123 0.4923 −0.3123 (+) 0.2781 0.2460 −0.2781 (–) 
November 0.3123 0.1690 −0.3123 (–) 0.2781 0.0031 −0.2781 (–) 
December 0.3123 −0.0048 −0.3123 (–) 0.2781 −0.1523 −0.2781 (–) 
Table 3

Monthly precipitation (1965–2012) and temperature (1965–2020) data for Palu station

MonthsJan.Feb.Mar.Apr.MayJuneJulyAug.Sept.Oct.Nov.Dec.
Precipitation (mm) Average 62.6 60.1 75.4 83.7 51.8 14.2 2.9 2.9 7.2 51.1 60.5 66.0 
Standard deviation 45.77 31.93 39.71 43.32 38.62 11.2 4.33 5.41 9.30 38.79 33.47 41.64 
Kurtosis 0.72 0.10 −0.69 −0.03 −0.26 −0.4 7.21 5.90 1.28 −0.84 −0.51 3.17 
Skewness 1.06 0.37 0.23 0.47 0.69 0.73 2.47 2.36 1.42 0.68 −0.11 1.23 
Maximum 190.4 139.4 166.2 199.0 146.0 38.6 21.3 24.8 34.6 132.6 122.2 223.9 
Minimum 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 
Run homogeneity test Z (±1.96) 0.00 1.57 0.87 0.00 0.00 1.22 0.00 0.00 0.87 −1.22 0.00 0.00 
Temperature (°C) Average −0.1 1.2 7.0 12.9 17.8 23.2 27.6 27.3 22.3 15.5 7.7 2.4 
Standard deviation 3.03 3.38 2.61 1.72 1.29 1.16 1.20 1.33 1.39 1.56 1.70 2.37 
Kurtosis −0.24 −0.69 0.64 −0.01 −0.17 0.06 0.63 −0.4 0.31 0.12 0.05 −0.80 
Skewness −0.64 −0.51 −0.75 0.41 −0.39 0.07 −0.7 −0.3 0.48 −0.04 −0.25 −0.29 
Maximum 5.4 6.9 12.1 17.7 20.2 26.1 29.6 29.8 26.0 19.1 11.5 7.0 
Minimum −8.3 −5.6 −0.7 9.2 14.6 20.7 23.7 24.4 19.4 11.6 3.5 −2.5 
Run homogeneity test Z (±1.96) −0.78 −0.16 1.42 1.41 −0.41 1.41 0.47 −0.78 1.42 −1.09 −0.10 1.09 
MonthsJan.Feb.Mar.Apr.MayJuneJulyAug.Sept.Oct.Nov.Dec.
Precipitation (mm) Average 62.6 60.1 75.4 83.7 51.8 14.2 2.9 2.9 7.2 51.1 60.5 66.0 
Standard deviation 45.77 31.93 39.71 43.32 38.62 11.2 4.33 5.41 9.30 38.79 33.47 41.64 
Kurtosis 0.72 0.10 −0.69 −0.03 −0.26 −0.4 7.21 5.90 1.28 −0.84 −0.51 3.17 
Skewness 1.06 0.37 0.23 0.47 0.69 0.73 2.47 2.36 1.42 0.68 −0.11 1.23 
Maximum 190.4 139.4 166.2 199.0 146.0 38.6 21.3 24.8 34.6 132.6 122.2 223.9 
Minimum 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 
Run homogeneity test Z (±1.96) 0.00 1.57 0.87 0.00 0.00 1.22 0.00 0.00 0.87 −1.22 0.00 0.00 
Temperature (°C) Average −0.1 1.2 7.0 12.9 17.8 23.2 27.6 27.3 22.3 15.5 7.7 2.4 
Standard deviation 3.03 3.38 2.61 1.72 1.29 1.16 1.20 1.33 1.39 1.56 1.70 2.37 
Kurtosis −0.24 −0.69 0.64 −0.01 −0.17 0.06 0.63 −0.4 0.31 0.12 0.05 −0.80 
Skewness −0.64 −0.51 −0.75 0.41 −0.39 0.07 −0.7 −0.3 0.48 −0.04 −0.25 −0.29 
Maximum 5.4 6.9 12.1 17.7 20.2 26.1 29.6 29.8 26.0 19.1 11.5 7.0 
Minimum −8.3 −5.6 −0.7 9.2 14.6 20.7 23.7 24.4 19.4 11.6 3.5 −2.5 
Run homogeneity test Z (±1.96) −0.78 −0.16 1.42 1.41 −0.41 1.41 0.47 −0.78 1.42 −1.09 −0.10 1.09 
Figure 1

The Upper Euphrates Basin map (Yıldız et al. 2019).

Figure 1

The Upper Euphrates Basin map (Yıldız et al. 2019).

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Figure 2

The location of the station where the data were obtained (Google, Google Maps (Access: 3 Aug. 2023)).

Figure 2

The location of the station where the data were obtained (Google, Google Maps (Access: 3 Aug. 2023)).

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When we look at the run (Z) test values of the parameters examined in Table 3, it is seen that the value obtained for each month is between ±1.96. Therefore, it can be said that the data are randomly distributed (homogeneous) within the 95% confidence interval. Looking at the standard deviation values of the parameters examined in Table 3, it is seen that the precipitation parameter is above the average only in July, August, and September, and therefore, it can be interpreted that the data are distributed in places far from the average. In the temperature parameter, it is seen that the standard deviation values are above the average only in January and February, and it can be interpreted that the data are distributed in places far from the average. The skewness values of the parameters in the table vary between −0.11 and 2.47 in the precipitation parameter and −0.75 and 0.48 in the temperature parameter for all months. In the precipitation parameter, the skewness coefficient in January, July, August, September, and December is 1.06, 2.47, 2.36, 1.42, and 1.23, respectively, and is very skewed (>1). Other months have moderate skewness in precipitation and temperature parameters. Moreover, in the precipitation parameter, only November is skewed to the left, while the other months are skewed to the right. In the temperature parameter, April, June, and September are skewed to the right, while all other months are skewed to the left. In the precipitation parameter, kurtosis values are negative in March, April, May, June, October, and November, and there is a Platykurtic distribution. In other months, kurtosis values are positive, and there is a Leptokurtic distribution. In the temperature parameter, kurtosis values are negative in January, February, April, May, August, and December, and there is a Platykurtic distribution. In other months, kurtosis values are positive, and there is a Leptokurtic distribution. In addition, in the precipitation parameter, the kurtosis values of July, August, and December are 7.21, 5.90, and 3.17, respectively, so that they have very thick tails and many outliers.

Trend analysis with combination of Wilcoxon test and scatter diagram

This method was suggested by Saplıoğlu & Güçlü (2022). It offers statistical trend analysis graphically and within a certain confidence interval. In the graphical study, the time series data are divided into two equal parts, as in the basic principle of the ITA method. Unlike the ITA method, no sorting is done among the data to prevent any changes in the divided time series. Then, the first subseries are marked mutually in the Cartesian coordinate system, with the second subseries on the horizontal axis and the second subseries on the vertical axis. Finally, the assessment of increasing or decreasing trend is made visually. If the points representing the data are equally distributed in both triangle regions, it is interpreted that there is no trend (Köyceğiz & Büyükyıldız 2023). Figures showing the differences between the Sen-ITA method (ordered data) and the NO-ITA method (unordered data) are available in various studies in the literature and are not included here (Saplıoğlu & Güçlü 2022; Buyukyildiz 2023).

According to this method, statistical trend evaluation is done by the Wilcoxon test. Wilcoxon attempts to test whether the distribution of two variables is the same by taking into account the differences in the two halves of data. For this purpose, absolute values are calculated as shown in Equation (2), and the differences between quasi-observations are calculated according to Equation (1) (Lee & Kang 2015). These absolute values are sorted from smallest to largest with the given sequence numbers. The sum of marked rows is taken as T+, which is the sum of rows with plus signs, and T, which is the sum of rows with minus signs. The total is given as shown in Equation (3) according to Karagöz (2019).
formula
(1)
formula
(2)
formula
(3)
Here, Di is the difference between the first half data Xi and the second half data Yi. According to the Zw Za/2 value in Equation (4) (for two tails), it is the test statistic value for Wilcoxon that helps define the trend conditions. The distribution standard deviation value is σT, and the arithmetic mean value is denoted by μT. Since the hypothesis is based on the μT value being zero, it is taken as zero (Wilcoxon 1992). H0: T+ = T, and the sum of the positive and negative differences between the trial results is equal (Ramazan & Saplıoğlu 2022; Saplıoğlu & Güçlü 2022).
formula
(4)
formula
(5)

According to the obtained Zw value, trend evaluation is made by comparing the Zcritic value at the α significance level obtained from the standard normal distribution table, as in the MK test statistic method (Buyukyildiz 2023).

Innovative polygon trend analysis test

IPTA was first reported by Şen et al. (2019) and Gümüş et al. (2022). The IPTA method can be adapted to timescales such as annual, monthly, weekly, and daily. In the case of a monthly time frame, a matrix is created using 12-month sets of each parameter from the first half of the series and each parameter of the second half of the series. While creating this matrix, arithmetic mean and standard deviation statistical techniques are generally used. Parameters such as the maximum or minimum skewness coefficient can also be used, which provide more detailed information on the data. The matrix of the meteorological monthly data set is created as shown in Equation (6):
formula
(6)

Here, j represents months and k represents years (Sharma & Ghosh 2022).

These monthly data represented in the matrix are then j = 1,2,3 … ., upper (first) half of k/2 and j = k/2 + 1, k/2 + 2, … , and lower (the second) is divided into two equal halves. Now the ‘arithmetic mean’ and ‘standard deviation’ can be evaluated separately for both halves. Then, in the Cartesian coordinate system, the arithmetic mean or standard deviation of the upper series is placed on the X-axis, and the arithmetic mean or standard deviation of the lower series is placed on the Y-axis. If a 1:1(45◦) ideal line without a trend is drawn and the point is drawn in the upper triangle area, the increasing trend is emphasized, and if the ideal line is drawn in the lower triangle area, there is a decreasing trend (Achite et al. 2021; Ergüven 2022). Figures showing the graphical representation of the IPTA method for monthly data are available in various studies in the literature and are not included here (Ceribasi et al. 2021; Sharma & Ghosh 2022).

Each consecutive month point shown in Figure 4 is connected by a straight line that shows trend information and also shows the transition from 1 month to the next. The points scattered on the graph depend on the yield of many meteorological activities that occur throughout the seasons. For example, in Figure 4, while a downward trend is seen between February and May, an upward trend is observed between July and January. Looking at the data, it can be concluded that there is an increase in data trend lines from July to mid-January. The template given in the example shows a systematic polygon with one loop due to data homogeneity, but there may be more than one polygon depending on data complexity and dynamics. For example, precipitation data may have multiple polygon loops causing runoff (Sharma & Ghosh 2022).

In Figure 4, 12 different vertices (ays) are joined by a straight line with different lengths and slopes. In general, the length and slope of the straight line between successive points can be calculated as (Equations (7) and (8)) follows:
formula
(7)
formula
(8)

Here, |XY| is the trend length and s represents the trend slope. u1 and u2 represent the values of two consecutive points in the first half of the series, and l1 and l2 represent the values of two consecutive points in the second half of the series (Sharma & Ghosh 2022).

MK trend test

The MK test detects trends and sudden changes in meteorological and hydrological time series (Gao et al. 2015). Numerous scholars have examined the existence of statistically significant patterns in hydroclimatic variables including precipitation, streamflow, and temperature in the past using nonparametric MK tests (Kumar et al. 2023; Verma et al. 2023a, 2023b, 2023c). This method is also used to examine and process temporal changes in climate data. Its advantage is that it is a nonparametric test statistic method, so it is independent of the distribution of the random variable (it does not require that the sample data follow a certain distribution). In addition, the MK test performs better than the parameter test (Mallick et al. 2021; Alifujiang et al. 2023). During the analysis process, the time series is divided into two groups as x1, x2, … ., xn, xi, and xj. Then the P value is increased by one for each case xi < xj and i < j. For xi > xj and i > j, the M value is increased by 1. Then, the MK trend test statistic S is defined as (Equation (9)) follows:
formula
(9)
If n > 10, the Kendall correlation coefficient is calculated as shown in Equation (10):
formula
(10)
formula
(11)

As shown in Equation (11), if the calculated z value is less than the (α) significance value corresponding to the z/2 value in the normal distribution, it is accepted as the null hypothesis (H0) and it is determined that there is no trend. If the z value is greater than the significance value (α) corresponding to the z/2 value, the null hypothesis (H0) is rejected and it is accepted as a trend. In cases where the S value obtained in Equation (1) is positive, it is determined that the trend tends to increase, and if it is negative, the trend is in the direction of decreasing (Yu et al. 1993; Saplıoğlu & Murat 2012).

Spearman's Rho trend test

The SR test is similar to the MK method and is a nonparametric method (Gümüş et al. 2022). The SR test is used to determine whether there is a correlation between two parameter series. It is also a fast, convenient, and simple test for detecting the presence of the linear trend. Therefore, it is one of the most preferred trend analysis methods for determining existing trends (Ergüven 2022). In this test, the hypothesis (H0) is that all the data in the time series are independently and similarly distributed, while the alternative hypothesis (H1) is that there is an increasing trend or a decreasing trend (Shadmani et al. 2012). In this method, test statistic D and standardized test statistic Z are expressed as shown in Equations (12) and (13), respectively:
formula
(12)
formula
(13)

Here, Ri is the order of the observation of Xi in the time series. n represents the length of the time series. If the absolute value of the detected Z is less than the significance value (α) corresponding to the Zα/2 value in the normal distribution, the null hypothesis (H0) is accepted and it is determined that there is no trend. If the Z value is greater than the significance value (α) corresponding to the Zα/2 value, the null hypothesis (H0) is rejected and the trend is accepted. It is concluded that if the Z value is positive, there is an increasing trend, and if the Z value is negative, there is a decreasing trend (Çeribaşı & Doğan 2015).

Şen trend test (ITA)

Şen (2012, 2014) presented a new graphical method for trend, which has the advantages of being independent of the restrictive assumptions of MK and Spearman's Rho tests. The method is based on dividing the time series into two equal-length subsections called sequences. Both arrays are sorted first in the ascending order. A scatter diagram is then generated so that the first and second series are considered as examples of the x and y axes, respectively. Finally, the 1:1 (45̊) straight line is passed through the square area defined by the variation area of the given variable. In such a scatterplot, subsets for which the trend is not present are ranked along the 1:1 line. Uptrends occupy the upper triangular area of the 1:1 line, while downtrends occupy the lower triangular area of the 1:1 line (Figure 3) (Nourani et al. 2018).
Figure 3

Trend states according to the 1:1 line (Saplıoğlu & Güçlü 2022).

Figure 3

Trend states according to the 1:1 line (Saplıoğlu & Güçlü 2022).

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Figure 4

Palu (station no. 17806) district Şen-ITA and NO-ITA test monthly total precipitation trends.

Figure 4

Palu (station no. 17806) district Şen-ITA and NO-ITA test monthly total precipitation trends.

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Implementation steps of the study

  • -

    A descriptive statistics table of the data has been created, and its suitability has been checked.

  • -

    Precipitation and temperature data, which have been determined to be appropriate, have been compiled into a table suitable for analysis for each month.

  • -

    Then, for MK and SR test statistics, which are statistical methods, monthly total precipitation and monthly average temperature data have been analyzed separately for each month with coding provided via Matlab. In addition, the data have been analyzed with IPTA, innovative Şen test (Şen-ITA), and CWTSD methods, which are capable of interpreting both statistically and visually.

  • -

    The CWTSD method has been statistically carried out by using the SPSS program to analyze the data in an unordered manner using the Wilcoxon test statistics method. Visually, the NO-ITA method (visual trend analysis of unordered data) has been used. In the ITA method, the data have been sequentially divided into two equal parts, and visual trend analysis has been performed. In the IPTA method, trend analysis has been carried out separately for each month, using both the standard deviation values and mean values of the data, thanks to the program prepared in the Excel program. Again, thanks to the program prepared in Excel, trend slope and trend length values have been determined regarding the transitions of these data between months.

  • -

    These methods have been compared with each other by looking at the findings obtained.

In the study, the trends of monthly total precipitation values between 1965 and 2012 and monthly average temperature values between 1965 and 2020 in the Palu district of Elazığ province, located in the east of Turkey, were analyzed graphically in the first step. For this purpose, Şen-ITA, NO-ITA, and IPTA tests were used. Of these three methods that provide visual trend evaluation, the Şen-ITA method (based on the ranking of each subdata series in a time series divided into two) and the NO-ITA method (which does not require the ranking of data within the same subseries) are used in the same coordinate system for the station where the precipitation and temperature data are provided. MK test and SR test methods were applied for numerical trend evaluation and trends were determined accordingly. Thus, thanks to this study, information has been provided to the literature regarding the region that will help future climate studies. The analyzed data were attempted to be summarized in the form of tables and graphs.

Trend analysis results of precipitation data

For visual trend evaluation, monthly total precipitation data between 1965 and 2012 (48 years) were divided into two subseries: 1965–1988 period (first half) and 1989–2012 period (second half). The graphic results obtained by applying the Şen-ITA and NO-ITA procedures to the two subseries obtained for the Palu station are presented in Figure 7. According to both the Şen-ITA method and the NO-ITA method, it is seen that most of the data are located in the triangular region below the straight line, especially in March, November, December, and January. Therefore, as a result of the visual examination made in the mentioned months, it can be said that there is a decreasing trend in the monthly total precipitation values according to both methods. From the graphs of August, September, and February, it can be said that the points in the upper triangle region are slightly denser than the lower triangle region, according to both methods, so that there is an increasing trend in these months. In all other months, according to both Şen-ITA and NO-ITA, the points are approximately equally distributed in two triangular regions and the 1:1 straight line, so it can be interpreted that there is no trend in the mentioned months.

Statistical evaluation of trends cannot be made according to both methods from the graphs given in Figure 4. The Wilcoxon test applied to unordered data was used to statistically evaluate trends at the α = 0.05 significance level in NO-ITA. Trend analysis results of monthly total precipitation data at this station are presented in Table 4. Accordingly, it is seen that similar results were obtained as a result of the analyzed data of MK test, SR test, and Wilcoxon test statistics methods. Considering the results of the MK test, SR test, and Wilcoxon test statistics, the null hypothesis "H0: no trend" is rejected because the absolute value of Z in December is greater than the Zα/2 = 1.96 value of the standard normal distribution, which corresponds to the selected α = 0.05 level, and the time period examined. It is concluded that there is a decreasing trend in the series. In other months, since the absolute value of Z is less than the Zα/2 = 1.96 value of the standard normal distribution, which corresponds to the selected α = 0.05 level, the null hypothesis "H0: no trend" is accepted, and it is concluded that there is no trend in the time series examined. The results obtained from MK test, SR test, and Wilcoxon test statistics methods are generally compatible with each other in terms of the direction of the trend.

Table 4

Outcome of monthly total precipitation data of Palu station

Mann–Kendall
Spearman Rho
Wilcoxon
MonthZMKTrend Z (0.95)ZSRTrend Z (0.95)ZWİLTrend Z (0.95)ITANO-ITA
January 0.4447 ↔ 0.5041 ↔ −0.8570 ↔ ↓ ↓ 
February 0.4444 ↔ 0.6263 ↔ −0.6000 ↔ ↑ ↑ 
March −0.3644 ↔ −0.4071 ↔ −0.3710 ↔ ↓ ↓ 
April −1.2749 ↔ −1.1418 ↔ −0.1710 ↔ ↔ ↔ 
May −1.0843 ↔ −1.0772 ↔ −0.4570 ↔ ↔ ↔ 
June −0.9191 ↔ −0.8058 ↔ −0.5430 ↔ ↔ ↔ 
July −0.3555 ↔ 0.7219 ↔ −0.2050 ↔ ↔ ↔ 
August −0.0978 ↔ 1.7593 ↔ −0.8060 ↔ ↑ ↑ 
September 0.0356 ↔ 0.4012 ↔ −0.9430 ↔ ↑ ↑ 
October −0.6819 ↔ −0.7099 ↔ −0.1430 ↔ ↔ ↔ 
November −1.9109 ↔ −1.8237 ↔ −1.1710 ↔ ↓ ↓ 
December −2.7820 ↓ −3.0227 ↓ −2.2000 ↓ ↓ ↓ 
Mann–Kendall
Spearman Rho
Wilcoxon
MonthZMKTrend Z (0.95)ZSRTrend Z (0.95)ZWİLTrend Z (0.95)ITANO-ITA
January 0.4447 ↔ 0.5041 ↔ −0.8570 ↔ ↓ ↓ 
February 0.4444 ↔ 0.6263 ↔ −0.6000 ↔ ↑ ↑ 
March −0.3644 ↔ −0.4071 ↔ −0.3710 ↔ ↓ ↓ 
April −1.2749 ↔ −1.1418 ↔ −0.1710 ↔ ↔ ↔ 
May −1.0843 ↔ −1.0772 ↔ −0.4570 ↔ ↔ ↔ 
June −0.9191 ↔ −0.8058 ↔ −0.5430 ↔ ↔ ↔ 
July −0.3555 ↔ 0.7219 ↔ −0.2050 ↔ ↔ ↔ 
August −0.0978 ↔ 1.7593 ↔ −0.8060 ↔ ↑ ↑ 
September 0.0356 ↔ 0.4012 ↔ −0.9430 ↔ ↑ ↑ 
October −0.6819 ↔ −0.7099 ↔ −0.1430 ↔ ↔ ↔ 
November −1.9109 ↔ −1.8237 ↔ −1.1710 ↔ ↓ ↓ 
December −2.7820 ↓ −3.0227 ↓ −2.2000 ↓ ↓ ↓ 

Note: ↔, no trend; ↑, increasing trend; ↓, decreasing trend.

In the study by Serinaldi et al. (2020), the weak points of the ITA method have been shown by the researchers. Therefore, examining the ITA method alone may lead to erroneous results. Therefore, in this study, the IPTA method and CWTSD, which provide a statistical representation of the ITA method, are discussed together.

The IPTA technique was applied to the monthly total precipitation data for the 48-year period (1965–2012) of the Palu station. The findings obtained as a result of the application of the IPTA method to the precipitation data are given in Table 5. In Figure 5, IPTA graphs are shown separately as arithmetic mean and standard deviation. The slope and length values of these graphs are presented in Table 6. The results given in the table show the passage of months between each other. The calculated maximum values are considered as a sudden transition between 2 months. The evaluation of the results shown in Figure 5 and Table 5 can be summarized as follows.
Table 5

Outcome of monthly total precipitation arithmetic mean and standard deviation

MonthsJan.Feb.Mar.Apr.MayJuneJulyAug.Sept.Oct.Nov.Dec.
Pmm AM ↓ ↑ ↓ ↓ ↓ ↓ ↓ ↑ ↑ ↑ ↓ ↓ 
SD ↓ ↑ ↑ ↑ ↑ ↓ ↑ ↑ ↑ ↓ ↑ ↓ 
MonthsJan.Feb.Mar.Apr.MayJuneJulyAug.Sept.Oct.Nov.Dec.
Pmm AM ↓ ↑ ↓ ↓ ↓ ↓ ↓ ↑ ↑ ↑ ↓ ↓ 
SD ↓ ↑ ↑ ↑ ↑ ↓ ↑ ↑ ↑ ↓ ↑ ↓ 

Note: ↔, no trend; ↑, increasing trend; ↓, decreasing trend; AM, arithmetic mean; SD, standard deviation.

Table 6

Statistical values of arithmetic mean and standard deviation for Palu station

Palu stationMonths
Jan.–Feb.Feb.–Mar.Mar.–Apr.Apr.–MayMay–JuneJune–JulyJuly–Aug.Aug.–Sept.Sept.–Oct.Oct.–Nov.Nov.–Dec.Dec.–Jan.
Arithmetic mean Trend length (mm) 11.81 23.26 11.84 45.19 53.29 16.02 0.63 6.16 62.00 15.98 14.36 12.66 
Trend slope − 27.13 23.38 47.30 45.20 41.56 39.98 − 49.32 53.75 44.95 12.02 − 12.65 − 23.15 
Standard deviation Trend length (mm) 20.79 11.11 5.31 6.79 39.19 10.09 1.55 5.50 42.38 9.26 13.95 11.31 
Trend slope 25.04 44.43 37.28 53.18 49.53 31.71 39.14 46.61 39.88 15.93 − 9.49 77.71 
Palu stationMonths
Jan.–Feb.Feb.–Mar.Mar.–Apr.Apr.–MayMay–JuneJune–JulyJuly–Aug.Aug.–Sept.Sept.–Oct.Oct.–Nov.Nov.–Dec.Dec.–Jan.
Arithmetic mean Trend length (mm) 11.81 23.26 11.84 45.19 53.29 16.02 0.63 6.16 62.00 15.98 14.36 12.66 
Trend slope − 27.13 23.38 47.30 45.20 41.56 39.98 − 49.32 53.75 44.95 12.02 − 12.65 − 23.15 
Standard deviation Trend length (mm) 20.79 11.11 5.31 6.79 39.19 10.09 1.55 5.50 42.38 9.26 13.95 11.31 
Trend slope 25.04 44.43 37.28 53.18 49.53 31.71 39.14 46.61 39.88 15.93 − 9.49 77.71 
Figure 5

IPTA analytics of arithmetic mean and standard deviation for monthly total precipitation.

Figure 5

IPTA analytics of arithmetic mean and standard deviation for monthly total precipitation.

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The standard deviation and arithmetic mean graphs for precipitation data have a similar structure and a stationary structure since there is no systematic change in the transitions between the months. In the arithmetic mean results, it can be deduced that the months of January, March, April, May, June, July, November, and December are in the decreasing region (declining trend), while the other months are in the increasing region (increasing trend). While the dots representing January, March, April, May, November, and December show a strong downward trend since they seem far from the nontrend (1:1) line, it can be deduced that the dot representing February also shows a strong upward trend. In the arithmetic average graph, there is a transition from the decreasing trend to the increasing trend and from the increasing trend to the decreasing trend in the transition period between January and February, and February and March, respectively, and the downward trend continued until June. In addition, the precipitation data started to decline from October to November, which had an increasing trend, and this downward trend continued throughout December. In the standard deviation results, it can be deduced that January, June, October, and December are in a downward trend, while all other months are in an upward trend. In the standard deviation graph, there is a transition from a downward trend to an upward trend between January and February and the upward trend continued until May. Then, between May and June and June and July, there is a transition from the increasing trend to the decreasing trend and from the decreasing trend to the increasing trend, respectively, and the upward trend continued until September. Then, a transition from the increasing trend to the decreasing trend was observed between September and October, from the decreasing trend to the increasing trend between October and November and from the increasing trend to the decreasing trend between November and December. Finally, from Table 6, the maximum value of the trend length for the arithmetic mean of the precipitation data was as 62.00 mm between September and October and the maximum value of the trend slope was 53.75 between August and September. For the standard deviation, the maximum trend length was 42.38 mm in September and October, and the maximum trend slope value was 77.71 mm between December and January.

Trend analysis results of temperature data

Monthly average temperature data between 1965 and 2020 (56 years) at this station is divided into two subseries: 1965–1992 period (first half) and 1993–2020 (second half). Then, the graphic results obtained by applying Şen-ITA and NO-ITA procedures to these two subseries are presented in Figure 6. According to both methods, it is seen that most of the data in January, February, March, and December are located in the triangular region above the straight line. Therefore, as a result of the visual examination made in the mentioned months, it can be said that there is an increasing trend in monthly average temperature values according to both methods. In all other months, according to both methods, the points are distributed approximately equally in two triangular regions and a 1:1 straight line. Therefore, it can be interpreted that there is no trend in the mentioned months. Since statistical evaluation of trends could not be made from the graphs shown in Figure 6, the Wilcoxon test applied to unordered data was used to statistically evaluate trends at the α = 0.05 significance level in the NO-ITA method. Trend analysis results of monthly average temperature data at this station are given in Table 7. Accordingly, it is seen that similar results were obtained as a result of the analyzed data of MK test, SR test, and Wilcoxon test statistics methods. Considering the results of MK test, SR test and Wilcoxon test statistics, it is concluded that there is an increasing trend in February, March, June, July, August, and October. The results obtained from MK test, SR test, and Wilcoxon test statistics methods are generally compatible with each other in terms of the direction of the trend. The IPTA technique was applied to the monthly average temperature data for the 56-year period (1965–2020) of the Palu station. The findings obtained as a result of the application of the IPTA method to the temperature data are given in Table 8. In Figure 7, IPTA graphs are shown separately as arithmetic mean and standard deviation. The slope and length values of these graphs are shown in Table 9. The results given in the table show the passage of months between each other. The calculated maximum values are considered as a sudden transition between 2 months. The evaluation of the results shown in Figure 7 and Table 8, respectively, can be summarized as follows.
Table 7

Outcome of monthly mean temperature data of Palu station

MonthMann–Kendall
Spearman Rho
Wilcoxon
ITANO-ITA
ZMKTrend Z (0.95)ZSRTrend Z (0.95)ZWİLTrend Z (0.95)
January 1.3923 ↔ 1.3952 ↔ 1.8670 ↔ ↑ ↑ 
February 2.4595 ↑ 2.5923 ↑ 2.0950 ↑ ↑ ↑ 
March 2.4736 ↑ 2.8928 ↑ 1.9980 ↑ ↑ ↑ 
April 1.5831 ↔ 1.6445 ↔ 1.1560 ↔ ↔ ↔ 
May 0.7421 ↔ 0.9919 ↔ −1.0700 ↔ ↔ ↔ 
June 3.3359 ↑ 3.8395 ↑ 2.8250 ↑ ↔ ↔ 
July 2.4948 ↑ 2.8165 ↑ 2.3470 ↑ ↔ ↔ 
August 3.3783 ↑ 3.9945 ↑ 2.4150 ↑ ↔ ↔ 
September 0.7039 ↔ 0.7369 ↔ −1.0940 ↔ ↔ ↔ 
October 2.3323 ↑ 2.5030 ↑ 2.4150 ↑ ↔ ↔ 
November 0.6078 ↔ 0.6769 ↔ −1.1280 ↔ ↑ ↑ 
December 1.1520 ↔ 1.2309 ↔ 0.8430 ↔ ↑ ↑ 
MonthMann–Kendall
Spearman Rho
Wilcoxon
ITANO-ITA
ZMKTrend Z (0.95)ZSRTrend Z (0.95)ZWİLTrend Z (0.95)
January 1.3923 ↔ 1.3952 ↔ 1.8670 ↔ ↑ ↑ 
February 2.4595 ↑ 2.5923 ↑ 2.0950 ↑ ↑ ↑ 
March 2.4736 ↑ 2.8928 ↑ 1.9980 ↑ ↑ ↑ 
April 1.5831 ↔ 1.6445 ↔ 1.1560 ↔ ↔ ↔ 
May 0.7421 ↔ 0.9919 ↔ −1.0700 ↔ ↔ ↔ 
June 3.3359 ↑ 3.8395 ↑ 2.8250 ↑ ↔ ↔ 
July 2.4948 ↑ 2.8165 ↑ 2.3470 ↑ ↔ ↔ 
August 3.3783 ↑ 3.9945 ↑ 2.4150 ↑ ↔ ↔ 
September 0.7039 ↔ 0.7369 ↔ −1.0940 ↔ ↔ ↔ 
October 2.3323 ↑ 2.5030 ↑ 2.4150 ↑ ↔ ↔ 
November 0.6078 ↔ 0.6769 ↔ −1.1280 ↔ ↑ ↑ 
December 1.1520 ↔ 1.2309 ↔ 0.8430 ↔ ↑ ↑ 

Note: ↔, no trend; ↑, increasing trend; ↓, denotes decreasing trend.

Table 8

Outcome of monthly mean temperature arithmetic mean and standard deviation

MonthsJan.Feb.Mar.Apr.MayJuneJulyAug.Sept.Oct.Nov.Dec.
Tmean AM ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ 
SD ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↑ ↓ ↓ ↑ 
MonthsJan.Feb.Mar.Apr.MayJuneJulyAug.Sept.Oct.Nov.Dec.
Tmean AM ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ 
SD ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↑ ↓ ↓ ↑ 

Note: ↔, no trend; ↑, increasing trend; ↓, decreasing trend; AM, arithmetic mean; SD, standard deviation.

Table 9

Statistical values of arithmetic mean and standard deviation for Palu station

Palu stationMonths
Jan.–Feb.Feb.–Mar.Mar.–Apr.Apr.–MayMay–JuneJune–JulyJuly–Aug.Aug.–Sept.Sept.–Oct.Oct.–Nov.Nov.–Dec.Dec.–Jan.
Arithmetic mean Trend length (mm) 1.97 8.11 8.38 6.97 7.61 6.25 0.49 7.00 9.67 10.99 7.50 3.67 
Trend slope 54.98 42.37 38.93 45.27 47.96 43.31 24.69 47.23 43.25 47.92 42.22 34.34 
Standard deviation Trend length (mm) 0.43 1.16 1.10 0.64 0.32 0.20 0.24 0.30 0.41 0.30 1.04 1.31 
Trend slope 56.62 12.48 42.31 54.07 34.42 − 6.10 − 84.71 − 76.27 − 19.80 37.68 71.66 − 9.88 
Palu stationMonths
Jan.–Feb.Feb.–Mar.Mar.–Apr.Apr.–MayMay–JuneJune–JulyJuly–Aug.Aug.–Sept.Sept.–Oct.Oct.–Nov.Nov.–Dec.Dec.–Jan.
Arithmetic mean Trend length (mm) 1.97 8.11 8.38 6.97 7.61 6.25 0.49 7.00 9.67 10.99 7.50 3.67 
Trend slope 54.98 42.37 38.93 45.27 47.96 43.31 24.69 47.23 43.25 47.92 42.22 34.34 
Standard deviation Trend length (mm) 0.43 1.16 1.10 0.64 0.32 0.20 0.24 0.30 0.41 0.30 1.04 1.31 
Trend slope 56.62 12.48 42.31 54.07 34.42 − 6.10 − 84.71 − 76.27 − 19.80 37.68 71.66 − 9.88 
Figure 6

Palu (station no. 17806) district Şen-ITA and NO-ITA test monthly mean temperature trends graphs.

Figure 6

Palu (station no. 17806) district Şen-ITA and NO-ITA test monthly mean temperature trends graphs.

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Figure 7

IPTA analytics of arithmetic mean and standard deviation for monthly mean temperature.

Figure 7

IPTA analytics of arithmetic mean and standard deviation for monthly mean temperature.

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Figure 7 shows that the standard deviation graph for temperature data contains more complex polygons than the arithmetic mean graph. While an increasing trend is observed at almost all points in the arithmetic average graph, November is close to the nontrend (1:1) line, but it can still be interpreted that it has an increasing trend. In the standard deviation results, it can be deduced that September and December are in an increasing trend and all other months are in a decreasing trend. The August point is close to the (1:1) line, but it can still be interpreted as having a decreasing trend. In the standard deviation graph, there is a transition from a downward to an upward trend between August and September. Then, between September and October, and November and December, there is a transition from the increasing trend to the decreasing trend and from the decreasing trend to the increasing trend, respectively. The upward trend ends with a sharp transition from December to January. Finally, for the arithmetic mean of the temperature data from Table 9, the maximum value of the trend length was 54.98 mm between January and February and the maximum value of the trend slope was 10.99 between October and November. For the standard deviation, the maximum trend length was 1.31 mm between December and January, and the maximum trend slope value was calculated as −84.71 between July and August.

In this study, the trends of precipitation and temperature data of Palu station, located within the borders of Elazığ province in the east of Turkey, were statistically examined using MK, SR, and Wilcoxon test methods. As a visual trend evaluation, it was examined with the Şen Trend Test (ITA), NO-ITA, and IPTA test methods, and the detected changes were summarized in tables and graphs. Following the analysis, the following evaluations were made:

  • In the IPTA method, 48-year data for precipitation and 56-year data for temperature were separated monthly and polygons were obtained using these data. Thanks to these polygons, it was determined in which months the trends would occur during the year. In addition, the transitions between the increasing and decreasing regions of the trends on a monthly basis were determined. Then, the slopes and lengths of the trends resulting from the transitions between months were calculated.

  • The size of trend lengths and trend slopes indicate the variability that occurred between months. For example, while the maximum trend lengths for the arithmetic mean and standard deviation in temperature data were 10.99 mm and 1.31 mm, respectively; values of 54.98 and −84.71 were calculated for maximum trend slopes, respectively. These values show that the transition between the 2 months was severe, and the change was the effect of climate change.

  • When looking at the IPTA graphs of monthly total precipitation and monthly average temperature, it was seen that it is not a single or regular polygon. This could be interpreted as precipitation and temperature data varying from year to year and not exhibiting a homogeneous behavior.

  • It was observed that MK test, SR test, and Wilcoxon test statistics methods gave similar results for two parameters (precipitation and temperature). In both methods, the direction of the trend was the same in all months.

  • The most striking aspect of the results obtained from the analyses is that trends that could not be detected on a monthly basis in the MK test statistics, SR test statistics, and Wilcoxon test statistics, Şen-ITA and NO-ITA methods were detected in the analyses made with the IPTA method. The main reason for this could be said to be that the size of the differences did not have a weighting effect, especially in the MK test, SR test, and Wilcoxon test statistics methods.

  • Due to the advantages such as performing numerical and visual trend analysis with the CWTSD method and determining the trends of data with low-medium-high values, it could be interpreted that this method could be used as an alternative to the MK test, SR test, and Şen-ITA methods that were widely used in the literature.

  • In future studies, the IPTA method could be used to quantitatively analyze and detect trends of other hydro-meteorological parameters that could be helpful in many areas related to agricultural activities and water supply.

The authors declare that no funds, grants, or other support was received during the preparation of this manuscript.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

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