Detection of abrupt shift and non-parametric analyses of trends in runoff time series in the Dez river basin Open Access

Climate change and human activities have a significant influence on different components of the hydrology cycle (Milly et al. 2002; Ishak et al. 2013; Chen et al. 2019; Esha & Imteaz 2019; Ashrafi et al. 2020a, 2020b; Mohammadi et al. 2020, 2021; Lotfirad et al. 2021). In recent decades, about 31 percent of 145 main rivers in the world have shown significant statistical changes in their annual flow (Zhai & Tao 2017; Dinpashoh et al. 2019). In arid and semi-arid regions, water resources demand mostly relates to agriculture. Population increase in the future will result in higher demand for irrigation, industry, and drinking. It is expected that the hydrological system response to these changes may be regarded as a significant option for climate change (Mirza et al. 1998; Marofi et al. 2012; Lotfirad et al. 2019). Some researchers have concentrated on identifying nonstationary changes in hydrological long-term time series (Wang et al. 2015; Deng & Chen 2017; Zhai & Tao 2017). In addition, understanding the reasons for runoff change in a changing environment to confront drought or flood and also prevent unpredicted changes in the future is very important (Casse & Gosset 2015; Farajpanah et al. 2020). Many previous studies have addressed changes in runoff average or changes in hydrological trend (Zuo et al. 2012; Rougé et al. 2013; Feng et al. 2016; Gao et al. 2016; Biazar & Ferdosi 2020; Esmaeili-Gisavandani et al. 2021). Different techniques have been utilized to recognize possible changes including the Mann-Kendall test, Bayesian inference, and Pettit test (Reeves et al. 2007) in which significant changes in average values are defined as abrupt shifts for hydrological time series (Verbesselt et al. 2010; Rougé et al. 2013). Abrupt changes may be related to some anthropogenic activities including construction of reservoirs and dams, regulation of water flow, and a rapid increase in water consumption (Zhang et al. 2015; Cloern et al. 2016; Kam & Sheffield 2016; Wu et al. 2017). An abrupt change point is often considered a breakpoint. Usually, hydrological records have been influenced a little by human beings' activities before reaching breakpoint; but after that intense human activity affects them seriously. Furthermore, a significant gradual trend may occur in nonstationary hydrological time series. The most effective human interventions consist of a gradual increase in population, hydraulic engineering, and soil surface coverage (Zhang et al. 2015; Cloern et al. 2016; Kam & Sheffield 2016). Some human activities (such as hydrologic regulations in reservoirs) may change seasonal or annual characteristics of a flow (current) (White et al. 2005). Flow periodical changes derived from human activities don't attract much attention, although they play a significant role in providing regional water and hydropower generation (Koch et al. 2011; Stojković et al. 2014).

Villarini et al. (2011) suggested that the change point test should be applied on time series before evaluating hydrological time series trends. An abrupt shift in average and variance may be related to climate regime change (Potter 1976; Hare & Mantua 2000; Alley et al. 2003; Swanson & Tsonis 2009). The abrupt shift in average may also be related to anthropogenic factors such as dam and reservoir system construction, land coverage and use change, agricultural works, and river water displacement (Potter 1979; Villarini et al. 2009).

The Dez river basin, as a strategic basin, plays a key role in the development of the southwest of Iran through providing drinking and agricultural water. The largest rivers in this basin include the Dez, Sezar, Bakhtiari, Tiereh, Marbereh, Sabzan, and Sorkhab rivers (Adib & Tavancheh 2019). Height differences in the region and the Zagros mountains have influenced regional climate regimes and caused relative heterogeneity in the Dez river basin climate characteristics (Marofi et al. 2012).

The Dez dam has the most stable hydropower plant in Iran which, besides supplying the agricultural and drinking demands, contributes to power generation in Iran's cross country (national) network. Therefore the water level in reservoirs and its management is very important for the reservoir operators. Hence, estimating changes in the reservoir input and updating the rule curve of the Dez dam requires special attention. In this regard, it seemed necessary for this research to study the trend of the change in runoff entering the Dez reservoir. The last hydrometric station on the inflow into the Dez reservoir is Tale Zang station. This station is one of the best hydrometric stations considering the length of time for which statistics are available and the quality of the registered data and its data have been utilized in the present research.

The present research studies the following issues:

• 1.

  Do long-term time series (annual, seasonal, and monthly) in Tale Zang hydrometric station runoff have change points or not?

• 2.

  How large is the magnitude of this change point or trend (at the 95% level of confidence)?

• 3.

  Studying the existence or nonexistence of trends before and after the change point in runoff time series (at the 95% level of confidence).

• 4.

  Determining the upper and lower limits of Sen's slope in modes in which a trend exists and also specifying its additive or subtractive nature.

The present research used 61 years of daily runoff data of the Tale Zang hydrometric station located in the Dez basin. A total of 17 data sets including annual (1 data set), seasonal (4 data sets - 1 data set for each season), and monthly (12 data sets - one data set for each month) were generated. For each data set, the homogeneity test (Pettit test) was performed at a 95% level of confidence to recognize the existence or non-existence of a breakpoint. To study the existence or non-existence of trends in each time series (data sets), Mann-Kendall and auto-correlated Mann-Kendall tests were utilized. A trend study for all data sets in which a breakpoint is evident is performed in two stages (for data up until the breakpoint and for data after the breakpoint until the end). In data sets in which Mann-Kendall and auto-correlated Mann-Kendall tests of the trend are significant at the 95% level of confidence, Sen's slope certain upper and lower limits are calculated and presented, and according to them, it will be expressed if the trend is increasing or decreasing and their level of significance will be explained and results will be analyzed (Figure 1).

In the present research, daily rainfall volumes from the 1956–2016 period were used and from the annual, seasonal, and monthly time series the volume of runoff was calculated and tested. To determine change points and specify monotonic trends, the process was analyzed. Each time series includes 61 data sets. The data sets used in this research are complete and have no missing data. This data set is specific because there are not so many hydrometric stations in Iran with 61 years of complete data and most hydrometric stations in Iran include a much lower registered statistical period compared to Tale Zang station (the case study in this research).

Tale Zang station is considered one of the first-class stations located in the Dez river basin (Heidarnejad & Gholami 2012). This hydrometric station is situated at the inflow into Dez reservoir (Valipour et al. 2012). The geographical location of the Tale Zang hydrometric station in the Dez river basin is indicated in Figure 2.

The Dez river drainage basin, as a grade three basin, is considered a subset of the great Karun basin and in a larger classification it is located in the Persian Gulf and Oman Sea basin subsets. Of the main cities on this river, one may mention Dezful, Andimeshk, and Shush. The Dez river drainage basin is located in the central section of the Zagros mountains (in Iran). The total area of this basin is about 23,230 km² and the highest and lowest elevations of the basin relative to mean sea level are 4,065 m and −60 m respectively. The slope of the basin is from north to south (Figure 2). The Dez river includes the major rivers, Sezar and Bakhtiari, which join the Karun river in Band-e-Ghir and then lead to the formation of the Great Karun (Ashrafi et al. 2020a, 2020b).

The average annual temperature of the basin is 24.2 °C. The average annual rainfall of the Dez river basin at different stations varies so that the long-term average change interval for the basin's annual rainfall at different stations indicates values between 479 and 1,029 mm. The average basin slope is about 12.1% and upstream the slope becomes relatively steep (the slope in 10% of the basin is greater than 19.5%). The source of the basin's rainfall is the clouds deriving from Mediterranean sea currents. The dominant regime of the region is snowfall and major atmospheric falls in autumn and winter take the form of snow. Melting snow from the end of winter to the end of spring provides the greatest part of the annual volume of water derived from precipitation in the basin. The climate of the basin is classified in the cold and dry categories (Esmaeelzadeh et al. 2015; Adib & Tavancheh 2019).

Heterogeneity in time series may cause misinterpretation of limit events (Rahman et al. 2017) and mislead interpretation of trends. Abrupt shifts in average are one of the usual results of heterogeneity in time series' data (Rahman et al. 2017). The importance of the homogeneity test has been indicated by Buffoni et al. (1999) and also Reiter et al. (2012). Their results showed that the homogeneity test has better performance in recognizing heterogeneity in data sets and determining change points in time series, compared to other methods. There are different methods to indicate abrupt shifts of which the Pettit test is considered an expanded nonparametric method for recognizing heterogeneity in data sets and determining change points in time series (Arikan & Kahya 2019). The World Meteorological Organization suggests using Mann-Kendall's non-parametric trend test for identifying significant statistical biases in the environmental dataset (Irannezhad et al. 2016). Using the Mann-Kendall trend test, due to its simplicity and power, is common for analyzing climate and hydrologic time series and may distinguish the missed values (Gavrilov et al. 2016). The Mann-Kendall trend test, which is a non-parametric test, is usually used to diagnose monotonic trends in an environmental data set (Pohlert 2016). In the Mann-Kendall test, it is not required to assume data normality. Hamed & Rao (1998) developed a modified Mann-Kendall test for auto-correlated data. As an example, a function of this modified method has been developed by AmirAtaee et al. (2016). Yue et al. (2002) also studied the power of the Mann-Kendall test in hydrological time series.

In the present research, Pettit's test (Pettit 1979) was selected to distinguish heterogeneity in time series analysis. In Pettit (1979) a non-parametric approach was developed for analyzing change points which is still used extensively. This test calculates transferring data average at different significance levels of the hypothesis test (Liu et al. 2012; Lotfirad et al. 2018; Adib et al. 2021). The null hypothesis states that all data are homogenous, and there is an alternative hypothesis that opposes this hypothesis and indicates that there is one change in the data average. The present research was accomplished at a 5% (p-value) empirical level of significance.

In the above equation:

• g is the number of the tied groups in the data set;

• t_p is the data number in the tied group's p^th;

• n is the number of data in the time series.

The hypothesis test method was used at level of significance as a two-tailed test in which the null hypothesis indicates that there is no monotonic trend in time series (⁠⁠: ⁠) and the alternative hypothesis suggests the existence of a significant monotonic trend in time series (⁠⁠). The empirical level of significance for the p-value was determined.

In the above equation, ρ_s(i) is the autocorrelation among ranks of calculated observations after subtracting a non-parametric trend estimator such as Sens's slope, and is the number of the most effective number of observations to calculate autocorrelation in data; just ρ_s(i) ranked significant values are utilized for Var(S) which, in the case of positive autocorrelation, will be underestimated (Hamed & Rao 1998; Taxak et al. 2014).

values related to Q are classified from small to large and Q median amounts indicate trend slope. The advantage of this method is that it limits the effect of outliers on the slope (Shadmani et al. 2012) and is free from statistical limitations.

The two-tailed Pettit test was utilized in which the null hypothesis states that there is no shift (displacement) in the data average, and the alternative hypothesis states that a certain datum may be distinguished as a change point and the data set average is displaced in the breakpoint. The significance empirical level (p values) is indicated in Table 1. According to the results, from the statistical point of view, a significant change point may be distinguished at the 95% level of confidence for the annual, spring, summer, autumn, March, May, June, July, August, September, and October data sets respectively in 1997, 1997, 1999, 1997, 1999, 1999, 1999, 1997, 2000, 2007 and 2008. In all data sets with a change point, the average was downward and the most frequent year in which a breakpoint was recognized was 1997. Data sets relating to winter and January, February, April, November, and December were homogenous and no break point was distinguished (Table 1). In all other 11 data sets in which a change point was observed, the number of change points was just one case. After extensive research in the archive information about historical registered values of concern, no evident reason for these change points has been found and no displacement occurred during data measurement years. It seems that the main cause for the existence of the change points which have been found in this research is climate change which has resulted in displacement in the registered runoff average and has divided the data in each of these data sets into two sectors. Displacement in runoff average at the change point is shown in Figure 3.

As stated before, in 11 of the 17 data sets under study, a change point in runoff average trend was recognized. In each data set with a change point, just one change point existed. Table 2 presents the average of runoff values up to and after the change point (for data sets in which a change point has been recognized) and the runoff average for data sets in which a change point didn't exist. According to the results presented in Table 2, in heterogeneous modes, the greatest difference in the data set average is in May which is equal to 167.3 m³/sec and shows that until the change point, the runoff average is 452.1 m³/sec and after the change point, it drops to 284.8 m³/sec. Also, the smallest difference in the data set average occurs in October, when before the change point the runoff average is 74.9 m³/sec, and after the change point it drops to 59.9 m³/sec.

Table 3 presents non-parametric p-values of the Mann-Kendall trend test to distinguish monotonic trends. Trends are analyzed using the Mann-Kendall test and the modified Mann-Kendall test (Hamed & Rao 1998) to study the possibility of the presence of autocorrelation in hydrological data. In data sets in which a change point was found according to the Pettit test, Mann-Kendall and autocorrelated Mann-Kendall tests, both before and after the change points, were reviewed at a 95% level of confidence.

From a statistical aspect, the increasing trend of annual runoff is found to be significant based on Mann-Kendall and autocorrelated Mann-Kendall tests, both before the change point and after the change point. The increasing trend of runoff in spring is found to be significant according to both Mann-Kendall and autocorrelated Mann-Kendall tests until the change point but after the change point no significant trend was observed. Also, the increasing trend of runoff in March, September and October is significant before the change point, but after the change point, no significant trend change was observed. In other data sets, too, before and after the breakpoint no trend was observed (Table 3). The important point to note from the obtained results is that homogeneity and Mann-Kendall results support and overlap each other. For example, in the data sets in which no change point was found, no trend was recognized by the Man-Kendall test, either.

In Table 4, lower and upper limits of Sen's slope for significant trends (distinguished in past stages), have been presented at a 95% level of confidence. Sen's slope calculations for the annual data sets until the change point (2008), in both normal Mann-Kendall and autocorrelated Mann-Kendall tests (AMAU, MAU), show the 1.49–2.09 m³/sec increase of runoff for each year. But after the change point, in both Mann-Kendall and autocorrelated Mann-Kendall tests (AMAA, MAA), the 8.18–8.92 m³ increase of runoff is shown. In spring, in both normal Mann-Kendall and autocorrelated Mann-Kendall tests, before the change point, i.e. 2007 (AMSPU, MSPU), the values obtained for Sen's slope were similar. Between 1956–2007, a 3.75–2.15 m³/sec increase was recognized for each year in spring. Until the change point in the March data set, i.e. 1999, in both Mann-Kendall and autocorrelated Mann-Kendall trend tests (AMMU, MMU), between 1956–1999, a 5.82–8.27 m³/sec increase was recognized for that month. In September, in both Mann-Kendall and autocorrelated Mann-Kendall trend tests, before the change point, i.e. 1997, (AMSEU, MSEU) values obtained for Sen's slope were equal. Between 1956–1997, a 0.48–0.75 m³/sec increase of runoff has been identified. Until the change point in the October data set (i.e. 1997), in both Mann-Kendall and autocorrelated Mann-Kendall trend tests (AMOU, MOU), between 1956–1997, 0.52–0.68 m³/sec increase of runoff was identified for that month.

In Figure 4, Sen's slope change interval for each significant trend case (identified in the Mann-Kendall test) has been presented at a 95% level of confidence. Accordingly, the smallest change interval of Sen's slope relates to AMOU and MOU and the greatest change interval is found in AMMU and MMU, but the upper limit of Sen's slope, i.e. 8.92 m³/sec, is found in AMAA and MAA.

In the first phase of the present research, homogeneity of annual, seasonal, and monthly time series of the Tale Zang hydrometric station runoff (hydrometric station at the inflow into the Dez reservoir) was studied using Pettit's test. Results of the Pettit test indicated that from 17 data sets of different time series (annual, seasonal and monthly), 11 data sets are heterogeneous time series. In each time series with a change point, just one change point was recognized. In the second phase, the existence or nonexistence of trend in each time series was studied using Mann-Kendall and autocorrelated Mann-Kendall trend tests. In the cases with a change point time series, Mann-Kendall tests were calculated once before the change point and once after the change point. In the data sets where a trend existed, the upper and lower limits of Sen's slope were calculated and presented to clarify the changes in the runoff level in those cases and determine the additive or subtractive nature of the runoff.

Based on the results, a significant change point at a 95% confidence level was recognized in the annual, spring, summer, autumn, March, May, June, July, August, September, and October data sets in 1997, 1997, 1999, 1997, 1999, 1999, 1999, 1997, 2000, 2007, and 2008. In all modes with a change point, the average was lower and the most frequent year in which a break point was recognized was 2007. According to both Mann-Kendall and auto-correlated Mann-Kendall tests, until the change point and after that, the trend is significant and increasing. The trend at a 95% level of confidence, in spring and March, September and October under both the Mann-Kendall and the auto-correlated Mann-Kendall tests, is additive and significant until the change point. The important point to note in the obtained results is that homogeneity and the Mann-Kendall test results support and overlap each other. For example, in the models in which no change point was found in the data set, no trend was recognized by the Mann-Kendall test, either. The smallest change interval of Sen's slope relates to MOU and the greatest change interval of Sen's slope is found in MMU and AMMU, but the greatest upper limit of Sen's slope is found in both MAA and AMAA with 8.92 m³/sec.

All data, models, and code are available from the corresponding author by request.