ABSTRACT
In climate change research, it is vital to have knowledge about future changes in the trends of climatological time series. The purpose of this study is to look at the effect of seasonality on the trend and long-term persistence of precipitation and temperature time series in the Konya Endorheic Basin, a semi-arid basin in central Anatolia, Turkey. Seasonal-trend decomposition by locally estimated scatterplot smoothing was used to obtain a seasonality adjusted time series, and a comparative analysis with the original series was performed. The Mann–Kendall test and simple linear slope were used to determine monotonic trends. To observe long-term persistence, Hurst exponents were computed using the rescaled range analysis approach. The Onyutha trend test was then used to investigate the sub-trends. As a result, there is a significant increase in temperature. Precipitation is increasing in the west and east of the basin while decreasing in the north and south. The magnitude of the monotonic and sub-trend is enhanced by seasonal adjustment. Meanwhile, in the seasonally adjusted dataset, the Hurst exponent grew dramatically, reinforcing the long-term persistence. Seasonality has less of an impact on precipitation, which is more affected by local variability, than temperature.
HIGHLIGHTS
The precipitation and temperature seasonality effect on trend and long-term persistence in the Konya Endorheic basin has been explored.
Seasonality adjustment has enhanced the Hurst exponent of the precipitation and temperature series substantially.
The seasonality adjusted series exhibits a higher trend magnitude than the original.
Local variability affects precipitation seasonality more than temperature.
INTRODUCTION
Seasons are defined as the physical climate system's non-linear response to annual solar forcing (Pezzulli et al. 2005). When considering the annual cycle, this response does not have to be consistent. All hydroclimatological series, especially precipitation and temperature with seasonal periodicity, contain sinusoidal functions. Therefore, complex seasonal periodicities including minimum, maximum, amount, timing, and duration occur. The structure of this annually repeated periodicity is complicated. Seasonal variability is driven by changes in the Earth's annual and daily movements, as well as internal and external forcings (continentality, land cover, altitude, atmospheric circulation patterns, and volcanic activity) (Kwiecien et al. 2022). There are studies examining wet/dry seasons of precipitation (Marani & Zanetti 2015), extreme precipitation (Iliopoulou et al. 2018), temperature in heat waves (Schliep et al. 2021), and temperature minima and maxima (Glynis et al. 2021). In analyzing the variability of precipitation and temperature, prioritizing the effect of seasonality is also of great importance in better understanding repetitive disasters.
Studies on the analysis of hydrometeorological time series in the literature focus on the spatial and temporal variability of parameters, especially precipitation and temperature, and the effects that cause this variability (Akter et al. 2023). The goal of studies on spatial variability is to better understand the physics of local (land use/cover change, building of water resource structures, etc.) and global (climate change, etc.) effects as well as to predict the possible risks of future trends (Madane & Waghaye 2023). In examining temporal variability, the aim is to understand disasters that have occurred in the past to prevent them from occurring in the future and (or) to minimize their possible impacts (Buyukyildiz 2023). In this respect, it should be noted that trend studies have an important position in the analysis of hydrometeorological time series. Studies on the seasonality of precipitation and temperature are commonly concerned with the determination of spatial or temporal variability and monotonic trends (Tao et al. 2018). However, recently, trend analysis studies have been carried out by considering different properties of hydroclimatological time series such as long-term persistence (LTP). Hamed (2008) proposed the Mann–Kendall (MK) test adjusted for LTP. Bayazit (2015) investigated trend analysis of non-stationary hydrological records. Iliopoulou & Koutsoyiannis (2020), who analyzed future rainfall extremes using non-stationary approaches, brought a deeper perspective to the concept of trend. Many innovative studies are needed in the observation of hydrological and atmospheric components subject to significant variability under the influence of a changing climate.
Hurst exponent is quite useful in analyzing the LTP of precipitation and temperature series. It also provides important information about climate change. Kumar et al. (2013) examined the spatial and temporal variation of the Hurst exponent across the world, using precipitation and temperature data from Phase 5 of the Coupled Model Intercomparison Project (CMIP5). The increasing trend in temperature has LTP. However, due to the high local variability of precipitation, LTP is 60% less than that of temperature. Hu et al. (2016) examined the variability of precipitation and temperature in alpine grasslands of Central Asia. The rising temperature trend indicated significant LTP. Although not as significant as temperature, the increase in precipitation series has been determined to have LTP. O'Connell et al. (2023) examined the relationship between spatial scale and LTP in global annual precipitation data. At the regional scale, LTP is associated with large-scale fluctuation patterns in the climate system. Zhou et al. (2023) found that there is no LTP in the increasing trend of precipitation and temperatures in Xinjiang, one of the arid regions of Central Asia. In this case, it is concluded that temperature and precipitation will decrease in the future. There are quite limited studies in the literature investigating the Hurst phenomenon in hydrometeorological series.
The Konya Endorheic Basin (KEB), the study area, has a semi-arid climate and is subject to high groundwater depletion (Duygu et al. 2017). The intense effects of climate change in the basin can be expressed as the main reason for global variability, and exposure to human impacts can be expressed as the main reason for local variability. Being an endorheic basin, it has a sensitive hydrological balance. While temperature increases throughout the basin, precipitation increases in some parts and decreases in others. However, the slight increasing trend in precipitation is suppressed by the strong rising trend of evapotranspiration (Koycegiz et al. 2023). The lack of a study analyzing the trends of precipitation and temperature series of the KEB by taking into account the seasonality effect reveals the local significance of this study.
Previous trend studies have been fairly limited in terms of evaluating the seasonality effect on climatological time series. The few studies examining the Hurst phenomenon in hydrometeorological time series include research on the LTP of the trend. It is thought that revealing the relationship between seasonality, which is an important component in precipitation and temperature series, and the Hurst phenomenon will make important contributions to the science. To the best of the knowledge available in the literature, the relationship between the LTP of the trends of precipitation and temperature series and the seasonality effect has not yet been examined. To fill this gap, this study investigates the effect of seasonality on the LTP of precipitation and temperature series. The variability of precipitation and temperature series at 11 stations in the KEB was analyzed by separating them into their components (seasonal, trend, and residual). Monotonic trends of seasonality adjusted and original time series were determined. Then, the variation of the Hurst exponent with seasonality effect was investigated. The variability of the seasonality effect on the sub-trend was analyzed.
STUDY AREA AND DATA
The location of the stations used in the study and the KEB within Turkey.
Spatial maps of long-term average annual total precipitation and annual mean temperature of the KEB for 1971–2019.
Spatial maps of long-term average annual total precipitation and annual mean temperature of the KEB for 1971–2019.
In the study, monthly total precipitation and monthly mean temperature data of 11 stations located in the KEB were used. Data for the period 1971–2019 were obtained from the Turkish State Meteorological Service. The study period was determined as the common period with no missing data at all stations. To save space, basic statistics of the data used in the study are given in the supplementary materials (see Supplementary Materials Table S1). For more information on the KEB and the stations, the references can be consulted (Koycegiz & Buyukyildiz 2024).
The time interval with no missing data from the data obtained from automatic meteorological observation stations calibrated by TSMS was determined as the study period. During the pre-processing of the data, no outliers were found in the 1971–2019 time span, which was determined as the study period. When the basic statistics are analyzed, it is consistent with the information expressed in the literature. The stations, from which data were obtained, were selected to consistently reflect the spatial heterogeneity of the climatology of the study area.
METHODOLOGY
Seasonal-trend decomposition by LOESS

Trend analysis methods
Simple linear slopes were calculated for all the series in this study to get first-hand and knowledge regarding the monotonic trend. Outliers have a considerable impact on the simple linear slope (You et al. 2019). Therefore, the non-parametric MK test (Kendall 1975; Mann 1945) was applied to examine monotonic trends. Serial dependence leads to bias in obtaining long-term trend information. For this reason, the version of Yue & Wang (2002), which includes a pre-whitening procedure that considers serial dependence, is preferred.
An increase or decrease in a certain part of the time series cannot be observed in monotonic trend analysis. Therefore, Onyutha (2021) introduced the Onyutha trend test (OTT) to examine sub-trends. This method is based on rescaled, non-parametric time series. The statistic obtained as a result of the test is shifted within the time window determined by the researcher, allowing the sub-trends throughout the entire time series to be examined by considering the significance level. In this study, the time window was set as 12 months to observe climatic variability. The cumulative sum of difference variability analysis tool (CSD-VAT) was used in the application of OTT (Onyutha 2022). In recent years, it has been widely used in the study of sub-trends of hydrometeorological time series (Koycegiz & Buyukyildiz 2023). Please see references for more information on the theoretical background (Onyutha 2021, 2016a, 2016b).
Calculating Hurst exponent (H)
Hurst exponent (H) is defined as a measure of the long-term memory of time series (Hurst 1951). In fractal geometry, it is directly related to fractal dimension (D), a measure of randomness (Porrà 2006). Hurst exponent is used in many fields such as health, finance, and natural sciences, especially in hydrology to observe the LTP of time series. H varies between 0 and 1. If H = 0.5, it is defined as a Brownian time series, that is, the present observation has no correlation with future observations. If H < 0.5, the time series is anti-persistent, and an increase (decrease) is followed by a decrease (increase). If H > 0.5, it is a persistent time series. In this situation, increases are followed by increases and decreases by decreases. LTP is of great importance in observing the effects of climate change, especially in meteorological time series. In this study, the rescaled range analysis (R/S) method was used to determine H. The theoretical background of the R/S method is described in detail in the literature. For more information, please see the references Byakatonda et al. (2018) and Kumanlioglu (2020).
Inverse distance weighting
In this study, Inverse distance weighting (IDW) was used to investigate the spatial variability of point data. IDW is a method for obtaining more observations from the closest points. The value in a given cell is determined by a linear function in relation to the distances of the surrounding point data. The weight of each observation is inversely proportional to the distance. Distant observations have less influence on the reference point, while close observations have a greater influence. IDW is recommended for analyzing the spatial variability of meteorological variables when there are less than 30 observation points (Chen et al. 2017; Sluiter 2009).
RESULTS
Variation of seasonality component
The seasonality component of the precipitation and temperature time series (1971–2019) of 11 meteorological stations in the KEB was obtained with STL. The basic statistics of the obtained seasonality component are given in Table 1. The fundamental statistics of the other components (trend and residual) are given in Tables S5 and S6 (see Supplementary Materials). Table 1 shows that the seasonality of precipitation at St-3 (Min: −47.893 mm; Max: 99.315 mm) and St-9 (Min: −69.462 mm; Max: 159.843 mm) in the west of the basin has a larger amplitude than the other stations. While the minimum values are close to each other at other stations, the maximum value (Max: 110.352 mm) is higher at St-11. Standard deviation values are also high at St-3 (Std dev: 24.677 mm) and St-9 (Std dev: 43.6 mm), while they vary between 13 and 17 mm at other stations. All stations in the basin have similar patterns in temperature. In the seasonal component of temperature, the minimum varies between −14 and −17.5 °C, while the maximum varies between 12.5 and 13.5 °C. The skewness coefficients of precipitation are all less than one except for one station (St-11). In excess kurtosis, it generally varies around zero, while St-11 has a value considerably larger than the others. The skewness of temperature varies around zero and excess kurtosis around −1.35. The 1-month, 1-year, and 30-year lagged autocovariance values (Table S3) and basic statistics for the four seasons (Table S4) are given in the Supplementary Materials.
Descriptive statistics of the seasonality component for precipitation and temperature
St No . | ID . | Precipitation (mm) . | Temperature (°C) . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Min . | Mean . | Max . | Std dev . | Skew . | Excess kurt . | Min . | Mean . | Max . | Std dev . | Skew . | Excess kurt . | ||
St-1 | 17191 | −30.20 | 0.03 | 49.91 | 14.24 | 0.31 | −0.34 | −17.51 | 0.00 | 13.45 | 8.25 | 0.00 | −1.36 |
St-2 | 17192 | −29.46 | −0.02 | 41.77 | 16.63 | 0.31 | −0.72 | −15.83 | 0.00 | 13.02 | 7.98 | −0.01 | −1.34 |
St-3 | 17242 | −47.89 | −0.01 | 99.31 | 24.68 | 0.80 | 0.82 | −14.59 | 0.00 | 12.80 | 7.73 | 0.02 | −1.38 |
St-4 | 17244 | −31.10 | 0.03 | 50.80 | 15.03 | 0.36 | −0.23 | −14.02 | 0.01 | 13.16 | 8.22 | 0.02 | −1.39 |
St-5 | 17246 | −29.48 | 0.07 | 58.64 | 15.62 | 0.28 | −0.37 | −14.11 | 0.00 | 12.87 | 7.90 | 0.02 | −1.41 |
St-6 | 17248 | −27.58 | −0.01 | 50.74 | 14.52 | 0.43 | −0.04 | −16.81 | 0.00 | 12.77 | 8.02 | −0.03 | −1.36 |
St-7 | 17250 | −33.60 | −0.03 | 64.44 | 16.67 | 0.43 | 0.04 | −15.81 | 0.01 | 12.66 | 7.86 | −0.01 | −1.35 |
St-8 | 17754 | −33.99 | −0.04 | 52.68 | 17.07 | 0.44 | −0.25 | −14.36 | 0.00 | 13.21 | 8.17 | 0.03 | −1.40 |
St-9 | 17898 | −69.46 | −0.07 | 159.84 | 43.60 | 0.84 | 0.32 | −14.76 | 0.00 | 13.11 | 8.05 | 0.02 | −1.37 |
St-10 | 17900 | −32.47 | 0.06 | 73.57 | 14.55 | 0.44 | 0.67 | −14.05 | 0.00 | 12.79 | 7.85 | −0.01 | −1.39 |
St-11 | 17902 | −32.41 | 0.09 | 110.35 | 13.72 | 1.31 | 8.20 | −14.41 | 0.00 | 12.90 | 7.98 | 0.03 | −1.39 |
St No . | ID . | Precipitation (mm) . | Temperature (°C) . | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Min . | Mean . | Max . | Std dev . | Skew . | Excess kurt . | Min . | Mean . | Max . | Std dev . | Skew . | Excess kurt . | ||
St-1 | 17191 | −30.20 | 0.03 | 49.91 | 14.24 | 0.31 | −0.34 | −17.51 | 0.00 | 13.45 | 8.25 | 0.00 | −1.36 |
St-2 | 17192 | −29.46 | −0.02 | 41.77 | 16.63 | 0.31 | −0.72 | −15.83 | 0.00 | 13.02 | 7.98 | −0.01 | −1.34 |
St-3 | 17242 | −47.89 | −0.01 | 99.31 | 24.68 | 0.80 | 0.82 | −14.59 | 0.00 | 12.80 | 7.73 | 0.02 | −1.38 |
St-4 | 17244 | −31.10 | 0.03 | 50.80 | 15.03 | 0.36 | −0.23 | −14.02 | 0.01 | 13.16 | 8.22 | 0.02 | −1.39 |
St-5 | 17246 | −29.48 | 0.07 | 58.64 | 15.62 | 0.28 | −0.37 | −14.11 | 0.00 | 12.87 | 7.90 | 0.02 | −1.41 |
St-6 | 17248 | −27.58 | −0.01 | 50.74 | 14.52 | 0.43 | −0.04 | −16.81 | 0.00 | 12.77 | 8.02 | −0.03 | −1.36 |
St-7 | 17250 | −33.60 | −0.03 | 64.44 | 16.67 | 0.43 | 0.04 | −15.81 | 0.01 | 12.66 | 7.86 | −0.01 | −1.35 |
St-8 | 17754 | −33.99 | −0.04 | 52.68 | 17.07 | 0.44 | −0.25 | −14.36 | 0.00 | 13.21 | 8.17 | 0.03 | −1.40 |
St-9 | 17898 | −69.46 | −0.07 | 159.84 | 43.60 | 0.84 | 0.32 | −14.76 | 0.00 | 13.11 | 8.05 | 0.02 | −1.37 |
St-10 | 17900 | −32.47 | 0.06 | 73.57 | 14.55 | 0.44 | 0.67 | −14.05 | 0.00 | 12.79 | 7.85 | −0.01 | −1.39 |
St-11 | 17902 | −32.41 | 0.09 | 110.35 | 13.72 | 1.31 | 8.20 | −14.41 | 0.00 | 12.90 | 7.98 | 0.03 | −1.39 |
Long-term (1971–2019) average of the seasonality component of precipitation and temperature.
Long-term (1971–2019) average of the seasonality component of precipitation and temperature.
Monotonic trends of precipitation and temperature
The monotonic trend has an important place in obtaining important information about the entire time series of meteorological parameters. For this reason, the linear slope and the Mann–Kendall (ZMK) statistics of the original and seasonality adjusted time series of precipitation and temperature data for the period 1971–2019 in the KEB are given in Table 2 for 11 stations. Accordingly, in the precipitation original series, the linear slopes of three stations (St-5, St-8, and St-10) are negative and the other stations are positive. According to the ZMK values, although not meaningful at a 95% significance level, almost half of the stations are negative, and the other half are positive. In the original temperature series, the linear slopes are all positive. According to the ZMK, there is an insignificant increasing trend in all stations except for one station (St-3). The linear slopes of precipitation generally increased after seasonality adjustment. At two stations (St-3 and St-9) the linear slopes remained the same, while at one station (St-11) it decreased. According to the ZMK statistics, the insignificant rising trend changed to a significant increasing trend at St-3, St-7, and St-9, where the amplitude of the seasonality component is relatively larger compared to other stations. At the other stations, insignificant statistical changes were observed after adjusting for the seasonality effect. For the temperature, which has a homogeneous seasonal pattern, the linear slopes did not vary significantly after the seasonal effect was removed, while the ZMK statistics showed strong significant increases.
Monotonic trend statistics in original and seasonality adjusted time series of precipitation and temperature*
St No . | ID . | Precipitation . | Temperature . | ||||||
---|---|---|---|---|---|---|---|---|---|
Original . | Seasonality adjusted . | Original . | Seasonality adjusted . | ||||||
LS (mm/year) . | ZMK . | LS (mm/year) . | ZMK . | LS (°C/year) . | ZMK . | LS (°C/year) . | ZMK . | ||
St-1 | 17191 | 0.042 | −0.153 | 0.049 | −0.494 | 0.056 | 0.273 | 0.052 | 8.707 |
St-2 | 17192 | 0.007 | −0.298 | 0.012 | −0.867 | 0.058 | 0.341 | 0.055 | 7.982 |
St-3 | 17242 | 0.175 | 0.931 | 0.175 | 4.575 | 0.023 | −0.109 | 0.020 | 3.723 |
St-4 | 17244 | 0.022 | −0.474 | 0.028 | −0.152 | 0.036 | 0.042 | 0.034 | 4.953 |
St-5 | 17246 | −0.031 | 0.007 | −0.027 | −1.677 | 0.044 | 0.115 | 0.042 | 6.036 |
St-6 | 17248 | 0.019 | −0.474 | 0.030 | 0.568 | 0.062 | 0.430 | 0.059 | 8.429 |
St-7 | 17250 | 0.119 | 1.326 | 0.123 | 2.465 | 0.055 | 0.236 | 0.052 | 7.503 |
St-8 | 17754 | −0.038 | −0.950 | −0.026 | −1.574 | 0.054 | 0.191 | 0.051 | 7.639 |
St-9 | 17898 | 0.223 | 0.417 | 0.233 | 4.166 | 0.039 | 0.044 | 0.036 | 6.485 |
St-10 | 17900 | −0.011 | −0.458 | −0.008 | −1.028 | 0.048 | 0.036 | 0.046 | 6.918 |
St-11 | 17902 | 0.034 | 0.409 | 0.028 | 0.337 | 0.040 | 0.057 | 0.037 | 5.653 |
St No . | ID . | Precipitation . | Temperature . | ||||||
---|---|---|---|---|---|---|---|---|---|
Original . | Seasonality adjusted . | Original . | Seasonality adjusted . | ||||||
LS (mm/year) . | ZMK . | LS (mm/year) . | ZMK . | LS (°C/year) . | ZMK . | LS (°C/year) . | ZMK . | ||
St-1 | 17191 | 0.042 | −0.153 | 0.049 | −0.494 | 0.056 | 0.273 | 0.052 | 8.707 |
St-2 | 17192 | 0.007 | −0.298 | 0.012 | −0.867 | 0.058 | 0.341 | 0.055 | 7.982 |
St-3 | 17242 | 0.175 | 0.931 | 0.175 | 4.575 | 0.023 | −0.109 | 0.020 | 3.723 |
St-4 | 17244 | 0.022 | −0.474 | 0.028 | −0.152 | 0.036 | 0.042 | 0.034 | 4.953 |
St-5 | 17246 | −0.031 | 0.007 | −0.027 | −1.677 | 0.044 | 0.115 | 0.042 | 6.036 |
St-6 | 17248 | 0.019 | −0.474 | 0.030 | 0.568 | 0.062 | 0.430 | 0.059 | 8.429 |
St-7 | 17250 | 0.119 | 1.326 | 0.123 | 2.465 | 0.055 | 0.236 | 0.052 | 7.503 |
St-8 | 17754 | −0.038 | −0.950 | −0.026 | −1.574 | 0.054 | 0.191 | 0.051 | 7.639 |
St-9 | 17898 | 0.223 | 0.417 | 0.233 | 4.166 | 0.039 | 0.044 | 0.036 | 6.485 |
St-10 | 17900 | −0.011 | −0.458 | −0.008 | −1.028 | 0.048 | 0.036 | 0.046 | 6.918 |
St-11 | 17902 | 0.034 | 0.409 | 0.028 | 0.337 | 0.040 | 0.057 | 0.037 | 5.653 |
*Statistically significant Z values are in bold.
Spatially distributed maps of the differences between the seasonality adjusted and original linear slopes of precipitation and temperature.
Spatially distributed maps of the differences between the seasonality adjusted and original linear slopes of precipitation and temperature.
Spatially distributed maps of ZMK statistics of original and seasonality adjusted time series of precipitation and temperature in the KEB.
Spatially distributed maps of ZMK statistics of original and seasonality adjusted time series of precipitation and temperature in the KEB.
Sub-trends of precipitation and temperature
Sub-trend (CSDZ) plots of original and seasonality adjusted time series of precipitation and temperature for 11 stations with OTT.
Sub-trend (CSDZ) plots of original and seasonality adjusted time series of precipitation and temperature for 11 stations with OTT.
Changes in Hurst exponent
The Hurst exponent (H) is commonly used to observe the LTP of a time series. Table 3 shows the variability of H of seasonality for precipitation and temperature in the KEB. The H values of precipitation (0.429–0.490) and temperature (0.267–0.308) are consistent within the basin. Spatial variability within the basin did not significantly affect the LTP of precipitation and temperature time series.
Hurst exponents in original and seasonality adjusted time series of precipitation and temperature
St no . | ID . | Precipitation . | Temperature . | ||
---|---|---|---|---|---|
Original . | Seasonality adjusted . | Original . | Seasonality adjusted . | ||
St-1 | 17191 | 0.476 | 0.603 | 0.290 | 0.794 |
St-2 | 17192 | 0.430 | 0.595 | 0.300 | 0.775 |
St-3 | 17242 | 0.436 | 0.554 | 0.272 | 0.752 |
St-4 | 17244 | 0.490 | 0.649 | 0.282 | 0.775 |
St-5 | 17246 | 0.451 | 0.591 | 0.287 | 0.746 |
St-6 | 17248 | 0.439 | 0.595 | 0.308 | 0.797 |
St-7 | 17250 | 0.454 | 0.601 | 0.299 | 0.776 |
St-8 | 17754 | 0.439 | 0.576 | 0.292 | 0.785 |
St-9 | 17898 | 0.429 | 0.573 | 0.267 | 0.746 |
St-10 | 17900 | 0.457 | 0.590 | 0.292 | 0.770 |
St-11 | 17902 | 0.449 | 0.569 | 0.287 | 0.739 |
Mean | 0.450 | 0.591 | 0.289 | 0.769 |
St no . | ID . | Precipitation . | Temperature . | ||
---|---|---|---|---|---|
Original . | Seasonality adjusted . | Original . | Seasonality adjusted . | ||
St-1 | 17191 | 0.476 | 0.603 | 0.290 | 0.794 |
St-2 | 17192 | 0.430 | 0.595 | 0.300 | 0.775 |
St-3 | 17242 | 0.436 | 0.554 | 0.272 | 0.752 |
St-4 | 17244 | 0.490 | 0.649 | 0.282 | 0.775 |
St-5 | 17246 | 0.451 | 0.591 | 0.287 | 0.746 |
St-6 | 17248 | 0.439 | 0.595 | 0.308 | 0.797 |
St-7 | 17250 | 0.454 | 0.601 | 0.299 | 0.776 |
St-8 | 17754 | 0.439 | 0.576 | 0.292 | 0.785 |
St-9 | 17898 | 0.429 | 0.573 | 0.267 | 0.746 |
St-10 | 17900 | 0.457 | 0.590 | 0.292 | 0.770 |
St-11 | 17902 | 0.449 | 0.569 | 0.287 | 0.739 |
Mean | 0.450 | 0.591 | 0.289 | 0.769 |
After adjusting for seasonality, the time series of 11 stations showed persistent (>0.5) behavior in precipitation and temperature parameters. Accordingly, the seasonal component is crucial for the LTP of the time series of precipitation and temperature parameters. In the temperature parameter, where seasonality adjusted series is more persistent than in the original time series, the H coefficient increases considerably.
DISCUSSION
The seasonality effect on the trend and LTP of the KEB precipitation and temperature parameters were investigated in this study. Based on the results obtained, the KEB has a strong increasing trend in temperature and slight increases in precipitation, although there are some regional differences. Koycegiz et al. (2023) stated that the sensitive hydrology of the KEB is under intense stress. As observed at all stations, the dry period in the 2000s followed by a wet period is in agreement with the findings of Koycegiz et al. (2023). According to the findings of this study, the significant increase in temperature is in line with the findings of Koycegiz & Buyukyildiz (2020). Based on this, it can be concluded that the findings obtained are consistent with the studies conducted in the literature related to the field of study.
Machiwal et al. (2017) examined long-term precipitation trends and change points in hot and cold arid regions in India. In this study, 32 stations were grouped into two categories (Cluster I, partly arid; Cluster II, entirely arid). Significant LTP was found in partially arid (Cluster I) regions. This is considered as a sign of the consistency of the increasing trend in precipitation. In the KEB, which is a semi-arid basin, the consistency of the strengthening trends in the tendency results, adjusted for seasonality, is parallel. It is possible to associate the strong consistency in increasing temperature with the strong impact of climate change. However, the local variability in precipitation may be linked to the rapid change in land cover. In areas where agricultural activities are intensive, groundwater is brought to the surface for irrigation purposes, which may have caused local precipitation with a convective movement. Increasing temperature causes an increase in evapotranspiration in the basin (Duygu et al. 2017). This makes hydrological production (precipitation–evapotranspiration) negative (Gokmen 2013). These signals indicating strong drought are supported by the findings of this study. It should also be kept in mind that the consistency detected is a sign that the drought in the KEB may not reverse in the near future. Since a significant portion of water consumption occurs in agriculture (Yazicis & Taner 2023), it is thought that it would be useful for decision makers to consider the findings of this study in determining the long-term agricultural pattern of the KEB, allocating water resources, and carrying out climate change adaptation processes.
The findings of Kumar et al. (2013), where the Hurst phenomenon is examined in precipitation and temperature series around the world, show that the Hurst exponent for both parameters for the KEB is about 0.5. The Hurst exponents of precipitation and temperature series in this study are in the ranges of 0.429–0.490 and 0.267–0.308, respectively. Although similar findings are generally found in the LTP of the series, there is a quantitative difference. The first reason for this is thought to be the resolution of the data sets used. As in O'Connell et al. (2023), increasing the spatial resolution of the data increases the effect of local variability on time series. This leads to a decrease in the H of the series. Kumar et al. (2013) used a dataset with a resolution of approximately 250 km, while point data were used in this study. Dimitriadis et al. (2021) investigated stochastic analogies for different processes of the hydrological cycle and found a Hurst exponent of 0.61 and 0.81 for precipitation and temperature, respectively. These values are close to the average Hurst exponent of precipitation (0.59) and temperature (0.77) found in this study.
Seasonality is found to have a significant impact on the Hurst phenomenon. The seasonality adjusted series has strong LTP, especially for temperature. Hu et al. (2016) used anomaly series for precipitation and temperature in their study. Thus, the seasonality effect is minimized in the all-time series. It is observed that the series for temperature and precipitation have LTP. In this study, it is stated in the findings that adjusting the seasonality effect is a factor that increases the H. Thus, it was observed that the findings were similar to Hu et al. (2016). The significant impact of seasonality on LTP has been observed in this study. There are methods suggested in the literature to overcome this issue. Among these, the variance and scale method, as an extension of the R/S method, stands out prominently (Beran et al. 2013). Additionally, the bias-adjusted climacogram method is also recommended (Dimitriadis & Koutsoyiannis 2015). The climacogram is used to obtain information about the long-term consistency, persistence, or clustering of a time series. The functions proposed for different situations, including continuous and discrete-time processes, are important advantages of the climatogram method.
Although temperature and precipitation are highly correlated parameters, they are climatological phenomena with complex physics. Koskinas et al. (2022) stated that it is quite important to examine cross-correlation effects in LTP analyses. For this reason, the lagged correlation analysis of the precipitation and temperature parameters used in the study for 11 stations is included in the supplementary materials (Table S2). The global and local forcings are affected by increasing the uncertainty of this complex physics. Therefore, it is vital to know how much time series are affected by local forcings in their LTP. For the study area, temperature has a more homogeneous distribution than precipitation (Figure 3). It is thought that local variability may relatively differentiate the effect of time series seasonality on the Hurst phenomenon. According to the findings of this study, seasonality affects the LTP of temperature more than precipitation.
CONCLUSION
This study aims to investigate the effect of the seasonality of temperature and precipitation series on the Hurst phenomenon. Monthly total precipitation and monthly mean temperature data between 1971 and 2019 from 11 stations of the KEB in Turkey were used in the study. First, the time series were separated into components (seasonal, trend, and residual). The variability of the seasonal component is analyzed. Then, a seasonality adjusted series of precipitation and temperature were obtained. The monotonic trend of the original and seasonality adjusted series was determined. Hurst exponents were calculated to investigate the LTP of the monotonic trends. Sub-trend analysis was conducted to examine the sub-trends of the original and seasonality adjusted series of precipitation and temperature and to investigate their relationship with LTP. The major findings are given below:
In the KEB, temperature has a more homogeneous seasonal component compared to precipitation. It is observed that precipitation is more affected by local forcings than temperature.
The temperature in the basin has an ascending strong monotonic trend. Precipitation has an increasing trend in the west and east of the basin and a decreasing trend in the north and south. The magnitude of the monotonic trends increased with the seasonal adjustment. It allowed the existing trends to be observed more clearly. While the study's period (1971–2019) may provide an overview of long-term climate patterns, it may be insufficient to capture substantial changes in climate over longer time scales, particularly in the context of climate change. Therefore, it is recommended to work with longer periods of data when it is aimed to observe the effects of climate change.
The seasonality of temperature and precipitation negatively affects LTP. Significant increases in the Hurst exponent were found in the seasonality adjusted time series.
For the temperature parameter, which is less affected by local variability, seasonality has a stronger effect on LTP. High local variability in precipitation reduces the effect of seasonality on LTP.
Precipitation and temperature sub-trends, which may have caused drought in the basin in 1980–1990 and 2000s, have been observed. Seasonality effect does not cause significant effects on the general behavior of the sub-trends. However, it is observed that it affects the magnitude of the sub-trends enough to change the level of significance.
The results obtained on the impact of precipitation and temperature seasonality on LTP may be useful in overcoming drought and periodic climatic challenges. It is suggested that the effect of seasonality should be taken into account in trend and LTP studies of hydrometeorological parameters. In future studies, it is planned to examine the LTP of other important components of the hydrological cycle (snowfall, surface water storage, soil moisture, etc.). It is also believed that investigating the factors affecting the Hurst phenomenon in the hydrological cycle will reveal important information.
One of the limitations of the study is the limited number of long-period measurement stations. In the basin where agricultural activities are intensively carried out, driving factors have significant spatial variability. In addition, different microclimate effects can be observed in regions with rapidly changing land cover. It should be noted that the trends of the hydroclimatological parameters of the KEB are not only subject to local variability. The effects of global climate phenomena on the hydroclimatology of the KEB and the country in which it is located, Turkey, should not be ignored. The investigation of the long-term effects through seasonal decomposition, taking into account the lagged effects of the data used in the study, is planned as a future research direction. Such an analysis is suggested by Koutsoyiannis (2023) to be a more successful method in examining long-term autocovariance series. It is believed that examining the structure of long-term autocovariance and exploring the relationship between time series stochastic structures and LTP will make significant contributions to the field of hydrology.
ACKNOWLEDGEMENTS
We would like to thank the Turkish State Meteorological Service for the data used in the study.
FUNDING
There was no specific grant from any funding agency in the public, private, or non-profit sectors for this research.
DATA AVAILABILITY STATEMENT
Data cannot be made publicly available; readers should contact the corresponding author for details.
CONFLICT OF INTEREST
The authors declare there is no conflict.