The multi-time-scale correlations for drought–flood index to runoff and North Atlantic Oscillation in the headstreams of Tarim River, Xinjiang, China

According to the Fourth Intergovernmental Panel on Climate Change Report (2007), the global temperature has risen by 0.74 °C in the past 100 years (1906–2005), leading to accelerated global water circulation, an increase in precipitation, and the risk of more frequent flooding worldwide (Hu & Feng 2001; Zhang et al. 2008, 2015; Wang et al. 2013). One of the most significant potential consequences of changes in climate may be the alteration in regional hydrological cycles (Labat et al. 2004). The frequency of extreme events such as droughts and floods has been on the rise globally. As reported in the scientific literature, the changing patterns of drought–flood became a hot topic of research during 2001–2013 (Hu & Feng 2001; Gemmer et al. 2008; Zhang et al. 2008, 2010; Unami et al. 2010). Drought–flood variations are the result of several factors, with surface runoff and water resources being the main two factors. Considerable research has been carried out on the characteristics of drought–flood variation (Hu & Feng 2001; Gemmer et al. 2008; Zhang et al. 2008, 2010; Unami et al. 2010). The formation of surface runoff is closely related to climate factors (e.g., precipitation, temperature, and evaporation) and atmospheric circulation (Samaniego & Bardossy 2006; Brabets & Walvoord 2009; Karambiri et al. 2011). The response of runoff change to climate factors particularly results from the fluctuation in precipitation and temperature in arid and semi-arid regions (Gan 2000; Roger et al. 2006; Kamruzzaman et al. 2013; Dong et al. 2014). Therefore, discussing the effect of local climate change on runoff with a background of global change is important for sustainable social and economic development in a basin.

The Tarim River Basin is the largest inland river basin in China, and is characterized by abundant natural resources and a fragile environment (Xu et al. 2011). As a typical pure-dissipation inland river in the northwestern arid areas of China, the main stream of the Tarim River has no groundwater abstraction, and the runoff supply depends on precipitation and glacial meltwater in the headstream mountain areas. Previous research (Chen & Xu 2005; Chen et al. 2006; Xu et al. 2006, 2011, 2013; Yang et al. 2011) has demonstrated that there has been a substantial increase in precipitation in Xinjiang, and flooding has been a serious problem in the Tarim River Basin. Previous studies (Chen & Xu 2005; Xu et al. 2010a, 2010b, 2011) have mainly focused on runoff and climate change in the Tarim River Basin, which indicated rising trends in runoff, precipitation, and air temperature. The variations of the regional and global climate are related to changes in the North Atlantic Oscillation (NAO), and these changes have had a profound effect on regional and global distributions of surface temperature and precipitation (Hurrell & Loon 1997; Shorthouse & Arnell 1999; Ye et al. 2004; Fu & Zeng 2005). The Tarim River Basin, located in the hinterland of Eurasia, is a closed watershed. It is important to study the trends in local climate records in the Tarim River Basin and recognize the presence of strong regional patterns of change associated with phenomena like the NAO. Therefore, using precipitation and runoff data for the headstream mountain areas in the past 50 years, this paper analyzes the periodic significance of runoff and the drought–flood index through wavelet analysis, and investigates the correlation between the drought–flood index and the NAO index at multiple time-scales employing a cross-wavelet spectrum. It is hoped that these results can serve as a reference for the reasonable allocation and regulation of water resources in the Tarim River Basin.

Measurements of annual runoff (provided by the Administration of the Tarim River Basin) at five hydrological stations (Xiehela, Shaliguilanke, Wuluwati, Tongguziluoke, and Kaqun) in the headstream mountainous areas of the Tarim River from 1957 to 2008 were collected. The five stations are assumed to measure ‘natural’ runoff with negligible human disturbance. Precipitation data were recorded monthly at nine weather stations in the mountain areas (Xiehela, Shaliguilanke, Wuluwati, Heishan, Tongguziluoke, Aheqi, Turgat, Tashikurgan, and Kaqun) from 1957 to 2007, and these data have the characteristics of integrity and homogeneity according to a Standard Normal Homogeneity Test (Alexandersson 1986). An index of the NAO reveals its variability since 1846 (Hurrell 1995). The time series of NAO indexes used in this research are determined from the difference in monthly sea-level pressure between Gibraltar (36.1°N, 5.4°W) and Reykjavik (64.1°N, 22.5°W) from 1957 to 2007, reconstructed by the Climatic Research Unit at the University of East Anglia (UEA/CRU).

The length of the main stream of the Tarim River is 1,321 km, and the river basin has no runoff yield. The main stream has historically received water from the nine water systems of the Tarim River. Due to human activities and climate change, the Qarqan River, Keriya River, and Dina River separated from the main stream before the 1940s, and the Kashgar River, Kaidu River, Kongqi River, and Weigan River separated from the main stream after the 1940s. There are now only three headstreams – the Hotan River, Yarkand River, and Aksu River – flowing into the main stream by Alar, accounting for 23.2%, 3.6%, and 73.2% of the total water volume, respectively.

In the study, the Z index was employed to divide the drought and flood grades of precipitation in the three headstreams of the Tarim River. Wavelet analysis was chose to explore the periods of drought–flood index and runoff, and the multi-time-scale correlations for drought–flood index to runoff and NAO.

Four methods have been used to determine the drought–flood index in China: the anomaly percentage method, the Standardized Precipitation Index (SPI), the Z index method, and the humidity index method (Wu et al. 2001, 2011; Wang & Zhai 2003; Xue et al. 2015). Compared with the Z index method, the anomaly percentage method responds to drought and flood slowly and less sensitively, while the humidity index method responds quickly and is overly sensitive. The Z index can provide results similar to the SPI, but calculation of the Z index is relatively easy compared to the SPI (Wu et al. 2001). In addition, the coefficient of skew (c_s) is used in calculating the Z index, which means that Z relates to not only precipitation but also the regional precipitation distribution. When the coefficient of skew is larger, the analysis results of the Z index and its ability to reflect the degree of drought and flood improve (Zhang et al. 1998).

The China Z index has been used since 1995 by the National Climate Center of China as an operational real-time drought and flood monitoring tool (Wu et al. 2001; Zou et al. 2005). This paper analyzes the drought and flood conditions in the headstreams using the Z index method (Ju et al. 1998).

According to the normal distribution curve of variable Z (Zhang et al. 1998), seven grades of the Z index have been established for the drought–flood index as shown in Table 1.

Wavelet analysis is becoming a common tool for analyzing localized variations of power within a time series, which has been increasingly used in hydrology (Torrence & Compo 1998). Wavelet analysis has recently been widely used in determining the periodicities of precipitation and runoff time series (Farge 1992; Stuart 2007; Li et al. 2009, 2013; Liu et al. 2009). Not only does it detect significant periodic variations of drought–flood index and runoff at different time-scales, but it analyzes the phase changes at different time-scales in our study. In wavelet analysis, the Morlet wavelet represents a wave modulated by a Gaussian function. The continuous wavelet transform coefficient is calculated by using a discrete signal with a Morlet wavelet. The wavelet variance is acquired based on the integral equation of the wavelet transform coefficient. The peak values of wavelet variance correspond to the significant periods of different time-scales. The periodic significance of wavelet variance is determined by a chi-square test (Torrence & Compo 1998). The edge errors usually occur at the beginning and end of a time series with finite length, because the wavelet is not completely localized in time (Torrence & Compo 1998; Zhang et al. 2008). To avoid these effects, the time series of the drought–flood index and runoff were symmetrically extended before wavelet transformation. Therefore, the 1-year period was eliminated and the time series anomaly was used in the wavelet analysis (Torrence & Compo 1998; Zhang et al. 2008).

The cross-wavelet spectrum can describe in detail the correlations for the drought–flood index to runoff and NAO at different time-scales. A larger coefficient indicates better correlation. The significance of the wavelet spectrum is tested according to the red-noise standard spectrum (Torrence & Compo 1998). A ratio of wavelet spectrum to red-noise standard spectrum exceeding 1 indicates significant correlation (Torrence & Compo 1998).

Generally, regional climate change correlates closely with large-scale air circulation (João et al. 1998; Jaagus 2006; Fleming et al. 2016). There is a significant periodicity of approximately 3–8 years in the drought–flood index for the headstream mountain areas of the Tarim River, consistent with the periodicity of the El Niño/La Niña-Southern Oscillation (Trenberth et al. 2007).

Figure 4(a) reveals that the main periodicities in the annual runoff of the three headstreams were 6, 17, and 22 years and that the main periods were significant at a confidence level of 95% for a 2–6-year period, but not significant for periods longer than 6 years. According to Figure 4(b), an alternative high-frequency oscillation was apparent in the annual runoff for the 6-year period. The abrupt change points of the 17-year period were in 1969, 1983, 1995, and 2008, and the phases had four abrupt changes (positive–negative–positive–negative). In addition, the annual runoff of the Tarim River abruptly changed in 1987 in terms of the 22-year period. According to the wavelet coefficients of runoffs in the three significant periods, the fitting equations were acquired to predict the future runoff change (Figure 4(c) and Table 3). Figure 4(c) shows that there were significant shorter periods in 1957–1967, 1970–1981, and 1988–1997 for 2–6-year periods at a confidence level of 95%.

In the cross-wavelet spectrum, there was a positive correlation for periods over 20 years, but no significant correlation for the whole time series. The reason is that the original information loss becomes serious as the number of wavelet decompositions increases. The section of significant correlation encompasses the 2–10-year period from the early 1970s to the late 1990s. Specifically, the correlation is significantly negative in the 1970s for the 2–5-year period, the mid-1970s for the 7–8-year period, from the mid-1970s to the mid-1990s for the 9-year period, and in the early and mid-1990s for the 3–8-year period, and significantly positive in the early 1970s for the 8–9-year period, and the late 1970s and the early 1980s for the 7–8-year period.

Figure 6(a) reflects the multi-time-scale variation in the correlation between the drought–flood index and NAO index for the whole year, winter and summer. In the annual cross-wavelet spectrum, the correlation between the drought–flood index and NAO index was mainly negative, although it was significantly positive for periods longer than 21 years, and negative for the 15–21-year period. There was a positive correlation in the sections of significance in the 1970s in the 2–5-year period, and negative correlation from the mid-1990s to 2004. Furthermore, the correlation between the drought–flood index and NAO index was negative in 1985 to 1987 for the 4–5-year period, significantly negative in 1979 to 1986 for the 6–7-year period and from the late 1980s to the late 1990s, and negative for the 8–9-year period from the late 1970s to the late 1980s. The results demonstrate that the NAO index has affected the drought–flood index remarkably since the 1970s.

Figure 6(b) shows that there was a significant positive correlation between the NAO index and drought–flood index with the periods of 21–23 years, including the significant negative correlations of the 3–9-year period after 1985 in the winter. In Figure 6(c), there was a significant negative correlation between the NAO index and drought–flood index with the periods of 2–10 years in the summer. On the basis of this analysis, there is clearly a correlation between the drought–flood index and NAO index, especially for periods of less than 10 years. Therefore, we conclude that the NAO index affects drought and flood conditions by means of large-scale air circulation in the headstream mountain areas of the Tarim River. The Tarim River Basin is far from the sea, and vapor transport is thus restricted not only by vapor resources but also by the effect of terrain on air circulation. The southwest monsoon from the Indian Ocean is obstructed by the Himalaya Mountains and Tibet Plateau, which keep water from reaching Xinjiang. The southeast monsoon and tropical storms from the Pacific Ocean are meridional circulations and mainly affect the east of China because of the obstruction of the mountains and plateau. The Tarim River Basin is mid-latitude in the Northern Hemisphere and has prevailing westerlies. Therefore, the major resource of water vapor in the Tarim River Basin is westerly airflow from the Atlantic, followed by dry–cold airflow from the Arctic Ocean, and the water vapor quantity is 25–33% of west wind airflow (Zhou 1999).

It is found from the analysis of this paper that the drought–flood index has increased in the headstream mountain areas of the Tarim River in the past 50 years. Wavelet analysis showed that the drought–flood index had primary periodicity of 4, 8, and 22 years, with the periodicity of 4 and 8 years being significant. The period change during 1970–2001 was significant for the 3–8-year period.

The annual runoff of the headstreams in the Tarim River has had periodicity of 6, 17, and 22 years. Only the 6-year period is significant at a confidence level of 95%. A periodic zone of 2–6 years was significant during the periods 1957–1967, 1970–1981, and 1988–1997.

The correlation between the annual runoff and the drought–flood index at different time-scales was mainly negative. The significant time sections were the 2–10-year periods from the early 1970s and the late 1990s, which demonstrate that the drought–flood index is significantly correlated with annual runoff.

The NAO has been in positive and high phase since the 1970s. The changes in drought–flood are linked to the behavior of the NAO. There was a significant correlation between the drought–flood index and the NAO index for periods of less than 10 years, which was negative mainly for the whole year and summer, and positive in winter. This indicates that the influences of the NAO on the drought–flood in the headstream mountain areas of the Tarim River are linked with the changes in upper air circulation. However, the effect mechanism of the NAO on annual runoff has not been explored and should be given further attention.

We thank four anonymous reviewers who provided helpful comments and suggestions. The corresponding author gratefully acknowledges the research group at the Ecological Complexity and Modeling Laboratory, University of California at Riverside. This work was funded by the National Natural Science Foundation of China (41471099, 51479209, and 41401050), the West Light Foundation of The Chinese Academy of Sciences (XBBS-2014-13) and the Science & Technology Cooperation Program of the Tarim River Basin (0202192014).