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Increasing precipitation and baseflow in Aksu River since the 1950s
Quaternary International xxx (2013) 1e9
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Increasing precipitation and baseflow in Aksu River since the 1950s Yuting Fan a, b, Yaning Chen a, *, Weihong Li a a State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, CAS, South Beijing Road 40-3#, Urumqi, Xinjiang 830011, China b Graduate University of Chinese Academy of Science, Beijing 100039, China
a r t i c l e i n f o
a b s t r a c t
Article history: Available online xxx
The Aksu River is the most important recharge source of the Tarim River in northwest China, representing 73.2% of the total volume to the Tarim River in the dry season. There are three types of recharge: glacier-snow melt water, precipitation, and groundwater. Precipitation and baseflow in the basin play a decisive role. The dynamics of precipitation in the last past 50 years were investigated. The digital filtering method was used to separate baseflow from surface flow. Relationships between precipitation and baseflow were identified by correlation analysis and wavelet analysis. The major findings of this study include: 1) In the past 50 years, step changes of both precipitation and baseflow in the drainage basin occurred, and both precipitation and baseflow performed a significant increase trend since the 1960s. The 1990s was the wettest decade of precipitation, and baseflow in the late 1990s was the wettest. 2) The time scale of the annual precipitation time series in the Aksu River Basin are 3, 6, 12, and 27 years, of which the six-year cycle oscillation is the strongest and a main cycle. Aksu River basin annual precipitation is manifested in the smaller time scales, as the time scale increases, the smaller its role is. 3) The baseflow showed an increasing trend in all seasons, and precipitation exhibits a monotonic increasing trend in summer and autumn, and decreasing trend in spring and winter. 4) The responses of baseflow to precipitation were different by season. Precipitation and baseflow have significant common power in the 4e6 year band from 1980 to 1998, and the baseflow has a 0e3 months lag from precipitation. Ó 2013 Elsevier Ltd and INQUA. All rights reserved.
1. Introduction
River is mainly recharged by alpine glacier-snow melt water and precipitation, and the mean annual discharge is nearly 2 102 m3/s (Fu et al., 2010). Among these three headstream flows into Tarim River, Aksu River is not only the main source for supplying water to the mainstream of Tarim River, but also the only one tributary supplying the Tarim River during dry seasons, accounting for 73.2% of the volume, while the supplies from Hotan River and Yarkand River account for 23.2% and 3.6%, respectively (Zhang et al., 2008). Therefore, the changes of Aksu River runoff play a decisive role in the formation, development, and evolution of the Tarim River. Temperature and precipitation have significant effects on maintaining discharge in the inland river area (Zhou et al., 2010). For the Aksu River, there are three types of recharge: glacier-snow melt water accounted for 45.0%, precipitation 33.1%, and groundwater 21.9% (Fu et al., 2010). Precipitation and baseflow in the basin play a decisive role. Recently, the trend of regional climate change and its impact on water resources have been investigated, but most studies mainly focused on runoff and its influencing factors in rivers (i.e. Chen and Xu, 2005, 2010; Ye et al., 2006; Xu et al., 2010, 2011; Li et al., 2012). There have been few studies on the characteristics and tendency of the precipitation sequence of the Aksu River Basin
Climate change and its consequent impacts on hydrology and water resources are hot topics for scholars and researchers around the world. During the past 50 years, rising global temperatures have accelerated the water cycle, causing a redistribution of water resources that ranges from minor to extreme. Arid areas are especially affected by this process due to the fragile nature of their ecohydrology, which is more sensitive to climatic changes. The Tarim River Basin, the largest inland river basin in China, is located in south Xinjiang and covers about two thirds of the total area of Xinjiang. The change of runoff and the utilization of water resources in Tarim River determine the amount of water resources, and deeply affect the water quality and ecological environment in the lower reaches of Tarim River (Chen and Xu, 2005). Now only three water systems have a natural hydraulic relationship with the mainstream: Aksu River, Hotan River, and Yarkand River. The Aksu
* Corresponding author. E-mail address: [email protected] (Y. Chen). 1040-6182/$ e see front matter Ó 2013 Elsevier Ltd and INQUA. All rights reserved. http://dx.doi.org/10.1016/j.quaint.2013.09.037
Please cite this article in press as: Fan, Y., et al., Increasing precipitation and baseflow in Aksu River since the 1950s, Quaternary International (2013), http://dx.doi.org/10.1016/j.quaint.2013.09.037
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Y. Fan et al. / Quaternary International xxx (2013) 1e9
Fig. 1. Map of Aksu River showing observation sites.
and the impact of precipitation on baseflow has received little attention. As precipitation is a primary factor in the generation of river runoffs, the relationship between river baseflow in the basin needs further investigation. It was hypothesized that the precipitation in the Aksu River had been experiencing considerable variation and would have some impact on the baseflow. This study chose the Aksu River Basin in Xinjiang to give its precipitation and baseflow variation in the past 50 years a close inspection. There are three aims of this study: (i) to detect trend of precipitation time series by a ManneKendall test, and to analysis the cycles of the precipitation time series by wavelet; (ii) to assess the temporal variability in the quantity of the baseflow for the Aksu
River by using hydrometric data and RDF; and (iii) to determine the correlation between the baseflow and precipitation, by correlation analysis and wavelet analysis. This study synthesizes time analysis with insights from correlation analysis to assess the variation in precipitation and baseflow characteristics in the Aksu River. This study will add to understanding of the relationship between discharge and precipitation. 2. Study area and data Located in the northern margin of the Tarim Basin, the Aksu River has two mainstreams originating from Kyrgyzstan. The
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Kunmalake River originates from the Hantengri Mts., and the Toxkan River originates from the Artbash Mts. The Aksu River is formed by the confluence of the two rivers, and at Eressea, the Aksu River divides into two branches: Xinda River and Laoda River. The two branches join at Awati and finally join the Tarim River at Xiaoxiake (Fig. 1). The Aksu River has varied landforms, and the geography is complicated. The basin area is 5.0 104 km2, 457 km long (Liu et al., 2007). Regional climate differences are significant. The high mountain area has low temperature and sufficient precipitation, and there is snow cover over the whole year. The middle mountain area has clear demarcation between cold and warm, and has the largest precipitation. The lower mountains are extremely dry, and with large differences in climate in different seasons. The plain area in the southeast is surrounded by high mountains in the north and Taklimakan Desert in the south, so that a typical continental climate in arid environments was formed. It has an extremely dry desert climate with infrequent and low precipitation and strong potential evaporation, large temperature difference, long hours of sunshine and abundant light and heat resources. The study area is the region that the Aksu River flows through (from Aheqi station to Alar station). Observed annual time series of precipitation in the Aksu River were used to estimate monotonic trends. Seven stations with continuous data series from 1956 to 2006 were selected in this study. The locations of the selected stations in the basin are shown in Fig. 1. Two hydrological stations and five meteorological stations (Fig. 1), six around the Aksu River and another in the mainstream, were used in this study. In the head water catchment region, Shaliguilanke station is located along the Toxkan River, and Xiehela station along the Kunmalake River. Aksu station, Awati station and Xidaqiao station are along the mainstream of Aksu River. Alar station is the first gauge in the mainstream region of the Tarim River. 3. Methodology 3.1. Baseflow separation The recursive digital filtering (RDF) technique was investigated to approximate well the baseflow sequence calculated by the matching strips manual separation technique (Eckhardt, 2005). The RDF technique, which was originally used for signal analysis and processing, became popular in hydrology literature for baseflow separation (e.g., Eckhardt, 2008). The RDF technique was selected for its less parameters and simple accurate advantages. RDF smooths the sharp peaks in the fast component of the streamflow so that the separated flow represents the delayed component of the streamflow, i.e., the baseflow. The output of the filter is constrained so that the separated flow cannot take negative values and is not greater than the total flow (Lyne and Hollick, 1979). The RDF process can be represented as (Hafzullah et al., 2009),
Qd ðtÞ ¼ bQd ðt 1Þ þ ð1 þ bÞ=2½Q ðtÞ Q ðt 1Þ
(1)
where Qd (m3/s) is the filtered quick streamflow, Q (m3/s) is the total streamflow, t is the time step (day), and b is a filter parameter. The filtered baseflow Qb can then be obtained by:
3
series estimates of baseflow, with the last being the projected baseflow time series. The justification for the use of this method rests on the fact that filtering out high-frequency signals is intuitively analogous to the separation of low frequency baseflow from the higher frequencies of quickflow (Nathan and McMahon, 1990). The output of the filter is constrained, such that the separated flow cannot take negative values and is not greater than the total flow. 3.2. Time series analysis Hypothesis testing to estimate long-term climate change trends is helpful to understand the inherent mechanism of hydrological process. In this study, two types of general trends are investigated: the monotonic trend and step change (Zhao et al., 2008). While it is difficult to gain a thorough understanding of the non-linear mechanism of any individual hydroclimatic process (Xu et al., 2009, 2011), such processes can be evaluated theoretically to determine if they comprise an ordered deterministic system, an unordered random system, and whether change patterns of periodicity exist. Specific to the series of climate changes that have occurred in the arid/semi-arid regions of western China, such inquiries may be designed to determine if these changes represent a localized transition to a warm and wet climate in response to climate change, or merely reflect a centennial periodicity in hydrological dynamics. 3.2.1. ManneKendall test Considering the power of the test, i.e. the ability to distinguish between H0 and H1, nonparametric tests are more robust compared to their parametric counterparts. The nonparametric ManneKendall test was used to detect the monotonic trend of precipitation and baseflow. The ManneKendall test statistic is given as follows (Mann, 1945; Kendall, 1975; Chen et al., 2009),
8 pS1 ffiffiffiffiffiffiffiffiffiffi; S > 0 > > > varðSÞ > < Zc ¼ 0; S ¼ 0 > > > > ffiffiffiffiffiffiffiffiffiffi; S < 0 : pSþ1
In which S ¼
n 1 X
n X
sgnðxk xi Þ
(3)
i ¼ 1 k ¼ iþ1
varðSÞ
where the xk, xi are the sequential data values, n is the length of the data set, and sgn(q) is equal to 1,0,1 if q is greater than, equal to, or less than zero, respectively. The null hypothesis H0 is accepted if Z1-a/2 Zc Z1-a/2 3.2.2. ManneWhitney test Given the data vector X ¼ (x1,x2,..,xn) partition X such that Y ¼ (x1,x2,..,xn) and Z ¼ (xn1þ1,xn2þ2,..,xn1þn2). The Manne Whitney test Statistic is given as (Mann and Whitney, 1947),
Pn1 Zc ¼
t¼1
rðx1 Þ n1 ðn1 þ n2 þ 1Þ=2
½n1 n1 ðn1 þ n2 þ 1Þ=121=2
(4)
(2)
In which r(x1) is the rank of the observations. The null hypothesis H0 is accepted if Z1-a/2 Zc Z1-a/2 where Z1-a/2 are the 1-a/2 quartiles of the standard normal distribution corresponding to the given significance level for the test (Xu et al., 2003).
The best results were obtained when b was in the range 0.90e0.95, with an optimal value of 0.925 (Nathan and McMahon, 1990). The algorithm separates baseflow from total stream flow by passing the filter over the streamflow record three consecutive times (forwards, backwards, and forwards again). Each filter pass produces three time
3.2.3. Correlation analysis Correlation analysis is a method to study the linear correlation between two variables. This study used correlation analysis to evaluate the relationships between baseflow and precipitation. The correlation coefficient is defined as:
Qb ðtÞ ¼ Q ðtÞ Qd ðtÞ
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Y. Fan et al. / Quaternary International xxx (2013) 1e9
Pn i ¼ 1 ðxi xÞðyi yÞ r ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 Pn 2 i ¼ 1 ðxi xÞ i ¼ 1 ðyi yÞ
(5)
The physical meaning of r is the correlation between the parts of xi and yi. The correlation coefficient ranges from 1 to þ1. A positive r indicates a positive linear relationship between the two variables, and a negative r indicates a negative linear correlation between the two variables (Fuente et al., 2004). 3.2.4. Wavelet analysis The cross wavelet transform (XWT) of two time series xn and yn is defined as WxY ¼ WxWY*, where * denotes complex conjugation. The cross wavelet power is defined as jWxYj. The complex argument arg(Wxy) can be interpreted as the local relative phase between xn and yn in time frequency space. The theoretical distribution of the cross wavelet power of two time series with background power spectra PkX and PkY is given in Torrence and Compo (1998) as
D
X Wn ðsÞWnY* ðsÞ sXsY
!
¼
Zv ðpÞ v
qffiffiffiffiffiffiffiffiffiffiffi PkX PkY
(6)
where Zv(p) is the confidence level associated with the probability p for a pdf defined by the square root of the product of two 2 distributions. Cross wavelet power reveals areas with high common power (Grinsted et al., 2004; Maraun and Kurths, 2004). Another useful measure is how coherent the cross wavelet transform is in time frequency space. Following Torrence and Webster (1999) the wavelet coherence (WTC) of two time series is
2 S s1 WnXY ðsÞ 2 Rn ðsÞ ¼ S s1 WnX ðsÞ S s1 WnY ðsÞ
(7)
where S is a smoothing operator. This definition closely resembles that of a traditional correlation coefficient, and it is useful to think of the wavelet coherence as a localized correlation coefficient in time frequency space. The smoothing operator S is
SðWÞ ¼ Sscale ðStime ðWn ðsÞÞÞ
(8)
where Sscale denotes smoothing along the wavelet scale axis and Stime denotes smoothing in time. It is natural to design the smoothing operator so that it has a similar footprint as the wavelet used. For the Morlet wavelet a suitable smoothing operator is given as
Stime ðwÞjs ¼
t 2 Y Wn ðsÞc12s2 ; Stime ðWÞjs ¼ Wn ðsÞc2 ð0:6sÞ s
n
(9)
Fig. 2. Temporal series of precipitation and baseflow in the Aksu River Basin.
Q where c1 and c2 are normalization constants and is the rectangle function. The factor of 0.6 is the empirically determined scale decorrelation length for the Morlet wavelet. 4. Results and analysis 4.1. Time series analysis of the precipitation 4.1.1. Precipitation trend Fig. 2(a) shows the temporal series of precipitation in the Aksu River Basin from 1957 to 2006. The figure reveals that the precipitation in the basin has significantly increased since the lowest precipitation in 1985, and the precipitation fluctuated in the decade of the 1970s. For the visualization purposes, the 5-year moving averages (MA) are also given in the graph. Scrutiny of the time series in Fig. 2 (a) reveals that precipitation peaked in the early 1980s and has been increasing since then. The formula e (average annual precipitation e this year precipitation)/average annual precipitation was used to calculate the results. Values less than 25% indicate dry years, and less than 10% indicate approximate dry years; 10 to 10% indicate normal years; greater than 10% indicate approximate wet years; and greater than 25% indicate wet years. A significantly higher precipitation regime marked 1970e1973, 1986e1989, 1992e2005, and 1982 and 1996 were the wettest on the record. The period from 1956 to 1970 was one of the driest periods during the study period. Three years: 1961, 1979, and 1985, were the three driest on record. Sixteen years since the year 1990 had above-average precipitation over this 50-year period. The precipitation time series exhibit a monotonic step change (Table 1).
Table 1 Partitions of the precipitation time series Monotonic trend test for precipitation time series. Item
No.
Time series
Length of record
Mean value
Standard dev.
Coeff.of variation
ManneKendall Z0
H0
Precipitation
1 2 3 1 2 3
1956e1970 1971e1986 1987e2010 1960e1976 1977e1994 1995e2006
15 16 24 17 18 12
48.67 55.30 135.02 11.81 10.58 17.02
8.41 21.79 36.07 1.72 1.83 2.68
0.17 0.39 0.27 0.15 0.17 0.16
2.77
R
3.50
R
Baseflow
R: Reject H0; Significance level p ¼ 95%; Z0 is statistics of ManneKendall test.
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4.1.2. Precipitation step trend Fig. 3(a) shows the temporal series of precipitation in the Aksu River Basin from 1956 to 2006. The possible partition points are identified by visual observation, the national precipitation time series is divided into three sub-series (Table 1), and through the ManneWhitney test, the precipitation contradicts the null hypothesis. The time series exhibits an obvious step change. Table 2 presents the ManneWhitney test result on the assessment of step changes for the Aksu River Basin precipitation. The results suggest that there was no significant precipitation increase from 1956 to 1970 and from 1971 to 1986, but significant step changes from 1971 to 1986, and 1987 to 2006. Combining the results of Kendall diagnosis on step trends for the Aksu River Basin precipitation, the year 1987 was the cut-off point when a significant step change appeared (Table 2). Thus, a significant phasic precipitation increase occurred around 1987. Table 2 ManneWhitney test results of step trend for precipitation time series. Item
Precipitation Baseflow
No.
1 2 1 2
and and and and
Series
2 3 2 3
ManneWhitney
N1
N2
Zc
H0
15 16 17 18
16 24 18 12
0.493 2.012 2.812 2.973
A R R R
Step points
1987(þ) 1977(þ) 1995(þ)
A: Accept H0; R: Reject H0; Significance level p ¼ 95%; Zc is statistics of Manne Whitney test; the þ means jump or trend is significantly, and the e means jump or trend is not significantly, Significance level a ¼ 0.01.
4.1.3. Precipitation cycle Fig. 6 is the wavelet analysis results of the annual precipitation time series of Aksu River Basin in the past 50 years, showing characteristics of precipitation variation by time scale and its distribution in the time domain. The vertical axis points correspond to different cycles, and varies scales of oscillation center (positive and negative) show that the precipitation contains a number of different scales of the cycle. The strength of the signal is represented by the wavelet coefficients. Zero corresponds to the step points. Different time scales correspond to different precipitation structure. Aksu River Basin annual precipitation fluctuations have three main frequencies: 2e4 years, 6 years, 12 years, and 27 years cycle. Centred at about 12 years, 11e13 year time scales were obvious in 1956 and 1970. Small-scale cycles less than 12 years indicate more rain and dry periods alternating, with more step points. A 3 year time scale was also evident, and positive and negative changed
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alternated. Among them, there are 11 six-year time scales: the late 1950s, late 1960s, late 1970s, the mid-1980s, early 1990s and after 2005 represent the positive phase of the rainy period. The early 1960s, early 1970s, early 1980s, the mid-1990s and year before 2005 show the negative phase of the dry period. In addition, the 24e30 year cycle was apparent, centred about 27 years. The phase structure of the cycle in the 1960s, mid-1970s and after 1990s are positive rainy periods; the late 1970s and late 1980s are negative phase dry periods. 4.2. Time series analysis of the baseflow 4.2.1. Baseflow trend Fig. 4 shows the yearly baseflow result and daily baseflow varies situation, In the study area, winter baseflow is less related to winter precipitation. Snowfall is accumulated from December to February and supplies baseflow during the spring snowmelt season. Three months’ baseflow are the basic flow for a whole year, and there is a comparison between baseflow and streamflow. Fig. 2(b) shows the temporal series of baseflow anomaly in the Aksu River Basin from 1960 to 2006. The baseflow has significantly increased since the minimum in 1985, and the baseflow has significantly decreased in the decade of the 1970s. Scrutiny of the time series in Fig. 2(b) reveals that baseflow peaked in the late 1990s. Significantly higher baseflow regimes existed from 1965 to 1971, 1993 to 1994, 1997 to 2006, and 1999 and 2003 were the wettest on the record. The period from 1978 to 1986 was one of the driest periods during the study period. Three years: 1962, 1980, and 1985, were the three driest on record. Ten years since 1997 had above-average precipitation over this 50-year period. Because of the limited storage in superficial deposits and thin soils, precipitation becomes surface run-off and enters streams directly instead of via deep percolation. 4.2.2. Baseflow step trend Fig. 3(b) shows the temporal series of baseflow in the Aksu River Basin from 1960 to 2006. The possible partition points were identified by visual observation. The national baseflow time series is divided into three sub-series (Table 1). The ManneWhitney test indicates that the baseflow contradicts the null hypothesis, and the time series exhibits a step change. Table 2 presents the Manne Whitney test result on the assessment of step changes for the Aksu River Basin baseflow. Step change points in runoff are affected by not only climate factors (Liu et al., 2011) but also human activities (Xu et al., 2011). The results suggest that there was significant baseflow decrease from 1960 to 1976 and from 1977 to 1994, and significant increases from 1977 to 1994 and 1995 to 2006.
Fig. 3. Average annual precipitation showing the possible step trends.
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climate variables (such as temperature, precipitation, etc.) causing changes in the baseflow. If the magnifying effect of only a minor climate change is large, then the hydrology and water resources systems are highly sensitive to climate change.
Fig. 4. Yearly streamflow and baseflow, daily streamflow and baseflow.
Combining the results of step trends for the Aksu River Basin baseflow, the year 1977 and 1995 were cut-off points, when a significant step change appeared (Table 2). The sensitivity of baseflow to climate change refers to the magnifying effect of one or more
4.2.3. Seasonal effect of precipitation on baseflow The precipitation and the baseflow in all seasons show an upward trend (Fig. 5). Precipitation in the summer and autumn and of baseflow indicates that the trend of baseflow is somewhat coincident with precipitation trend, but the changing characteristics of spring and winter are different. The trend of baseflow in spring and winter are opposite to the precipitation trend. Both significant increasing trends were tested in the summer precipitation and summer baseflow from the 1990s, and both significant increasing trends were tested in the autumn precipitation and autumn baseflow since 2000. In spring and winter, several years with high precipitation correspond to low baseflow, and low precipitation to high baseflow. The glacial ablation areas in the northwest are generally located at higher altitudes, where melting mainly occurs in summer and most river baseflow is directly related to glacial melt water (Yang and Zeng, 2001). Table 3 presents the results of the trend analysis on seasonal baseflow for the Aksu River. The baseflow exhibits a monotonic increasing trend. The baseflow in spring, summer, autumn, and winter exhibit a monotonic increasing trend, and precipitation exhibits a monotonic increasing trend in summer and autumn. Baseflow was affected by temperature, precipitation, elevation, and subsurface conditions. The large increase in baseflow in the melt season was possibly caused by temperature. The role of precipitation on baseflow is not clear. Huge regional differences exist in the correlation of baseflow and precipitation in different seasons. The differences may be related to the recharge types of baseflow. The correlation of baseflow and precipitation is higher in the rivers where the proportion of glacier-melt run-off is low. However, in glacial-melt dominant rivers, the correlation of baseflow and
Fig. 5. Seasonal precipitation and baseflow time series. (a) spring (b) summer (c) autumn (d) winter.
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Fig. 6. Wavelet coefficients of annual precipitation.
temperature is higher (Fan et al., 2013). The correlation of baseflow and precipitation and of baseflow and temperature is high in the rivers which are fed equally by glacier-melt and precipitation. This deep-seated mechanism needs further study. Table 3 Monotonic trend test for Precipitation and Baseflow time series ManneKendall Precipitation Baseflow
Z0 H0 Z0 H0
Spring
Summer
Autumn
Winter
0.769 A 2.613 R
2.185 R 2.443 R
2.948 R 3.068 R
1.673 R 3.503 R
R: Reject H0; Significance level p ¼ 95%; Z0 is statistics of ManneKendall test.
4.3. Increasing precipitation impact on baseflow trend 4.3.1. Correlation between precipitation and baseflow Water resources mainly come from natural precipitation in mountains and mountain snowmelt water that is greatly affected by temperature. Climate change leads to increases in heavy precipitation days and flood frequency. In high latitudes and snowmelt recharge basins, increases in temperature cause increases in the rain/snow ratio. The correlation between precipitation and runoff is statistically significant at p < 0.05 or 0.01 levels according to the above results. Table 4 shows the results of the correlation analysis. According to the results, the precipitation had different impacts on the baseflows of the Aksu River in different seasons. Significant correlations were only found between February precipitation and February baseflow, February precipitation and March baseflow, April precipitation and May baseflow, and September precipitation and October baseflow. Table 4 Correlation between Precipitation and Baseflow in different seasons/months Correlation
Baseflow
Precipitation Baseflow Correlation
Precipitation
Spring Summer Autumn Winter Month average Month average 0.527**
Spring
Summer
Autumn
Winter
0.077 0.095 0.027 0.107 February February 0.361*
0.164 0.292 0.327* February March 0.372*
0.509** 0.509** April May 0.311*
0.037 September October 0.408**
Note: * and ** indicate the significance at the levels of p < 0.05, p < 0.01 (2-tailed), respectively.
The spring precipitation has a small positive impact on summer baseflows, but has a small negative impact on spring and autumn and winter baseflow. When temperature rises from spring to summer, the underlying surface become more susceptible to infiltration. Before significant ablation of the glaciers, precipitation was delayed, supplying baseflow until summer, and thus the summer precipitation has a weak positive correlation with summer baseflow. The summer precipitation has a positive impact on summer and autumn baseflow, and a significant positive impact on winter baseflow. As one component of streamflow, summer rainfall recharges surface flow and is transformed to groundwater in dry seasons. The autumn precipitation has a significant positive impact on autumn and winter baseflow. The winter precipitation has a small negative impact on winter baseflow, because the winter precipitation is stored as a solid form before melting. The winter flows influence the annual baseflow. The results show that the correlations between baseflow and precipitation are dissimilar in different temperature conditions, which may be related to the baseflow recharge from snow and glacier melt. The average temperature in the Aksu River Basin has an increasing trend over the past 50 years (Fan et al., 2011), and in spring and summer, glaciers contribute 40% water of the total streamflow to the Tarim River (Shen et al., 2006). Melt water may recharge baseflow synchronously. 4.3.2. Cross wavelet and wavelet coherence Cross wavelet analysis and wavelet coherence are powerful methods for testing proposed linkages between two time series. The XWT of precipitation and baseflow is shown in Fig. 7a. The common features visible from the individual wavelet transforms stand out as being significant at the 5% level. There also is significant common power in the 4e6 year band from 1980 to 1998. The XWT shows that precipitation and baseflow are in anti-phase in some sectors and in-phase in other sectors with significant common power. Baseflow to a large extent simply mirrors the precipitation. Outside the areas with significant power, the phase relationship is also predominantly anti phase. There appears to be a stronger link between precipitation and baseflow than that implied by the cross wavelet power. This basically confirms the conclusion that precipitation and baseflow are in anti-phase, and the time series have a 0e3 months lag. The wavelet coherence between the precipitation and baseflow is shown in Fig. 7b. Oscillations in precipitation are manifested in the baseflow on wavelengths varying from 3 to 6 years, suggesting that baseflow passively mirrors precipitation. Regions with low
Please cite this article in press as: Fan, Y., et al., Increasing precipitation and baseflow in Aksu River since the 1950s, Quaternary International (2013), http://dx.doi.org/10.1016/j.quaint.2013.09.037
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Y. Fan et al. / Quaternary International xxx (2013) 1e9
Fig. 7. Cross wavelet transform and wavelet coherence of the precipitation and baseflow time series. The 5% significance level against yellow or red noise is shown as a thick contour. The relative phase relationship is shown as arrows, All significant sections show anti-phase behavior. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
coherence coincide with low wavelet power in the precipitation and are therefore expected. The mean phase angle over the regions with significant wavelet coherence is 90 to 45. The precipitation has positive impact on baseflow at sometimes, but negative impact on baseflow in other situations. According to the correlation analysis results, the baseflow has a 0e3 months lag from precipitation. Baseflow in the Aksu River is increasing with rising precipitation. Precipitation recharges baseflow to some degree, but the precipitation is usually accompanied by cooling, and the temperature decrease leads to glacial melt water reduction. When precipitation is less than glacial melt water reduction, the correlation between baseflow and precipitation exhibits a negative significance. 5. Conclusion and discussion This study synthesized time analysis with insights from precipitation to assess the variation in baseflow characteristics of the Aksu River, the main tributary of the Tarim River, a major water resource of the vast arid area in south Xinjiang, China. The time series analysis techniques were used to address two aspects: Application of the ManneKendall and ManneWhitney tests for precipitation time series over the Aksu River Basin showed both monotonic trends and step changes in precipitation. A step change occurred in precipitation time series around 1986. The test results for the long-term trend of the precipitation showed that there is an increasing tendency in annual precipitation during the past 50 years, and the increasing trend is significant at the 5% level of significance. During the last five decades, the precipitation has increased by 30.7% per decade. The wetting trend in the Aksu River Basin could be a local response to global climate change. The time scale of the annual precipitation time series in the Aksu River Basin are 3, 6, 12 and 27 years, of which the six-year cycle oscillation is the strongest and a main cycle. The Aksu River basin annual precipitation is manifested in the smaller time scales: as the time scale increases, the smaller its role is. Step changes of baseflow in the drainage basin occurred in 1977 and 1995, and baseflow showed a significant increase trend since the 1960s. The late 1990s baseflow was the wettest in the past 50 years. The baseflow time series exhibit monotonic increasing trends in spring, summer, autumn, and winter. During the last five decades, the global temperature has increased by 0.2e0.3 C / decade, and the temperature has increased by 0.2 C /decade in west China (Li et al., 2012). The increasing trend in the baseflow should be a local response to global temperature change, and thus the response of baseflow to precipitation exhibited a complex
mechanism. The trend of baseflow is somewhat coincident with the precipitation trend in summer and autumn, but opposite to the precipitation trend in spring and winter. Precipitation has both significant positive and negative impact on baseflow in different seasons. The summer precipitation has a positive impact on winter baseflow. The autumn precipitation has significant positive impact on both autumn and winter baseflow. There are significant negative correlation between February precipitation and February baseflow, February precipitation and March baseflow, and April precipitation and May baseflow; and there is a significant positive correlation between September precipitation and October baseflow. The baseflow has significantly increased since the minimum in 1985. Chen et al. (2009) found the warminge wetting trend in the Tarim River Basin was a local response to global climate change. The highest annual temperature in 1990s may have impacted the baseflow by the melt water in summer, which led to the high precipitation in summer having a small positive correlation with baseflow. The correlations between baseflow and precipitation are dissimilar in different months, which may be related to baseflow recharge characters. The precipitation in winter and spring show negative correlations with baseflow, because the stable part of the streamflow is mainly recharged by baseflow. In summer, runoff and baseflow are recharged from both rainfall and glacier melt water, so the correlation between summer precipitation and summer baseflow shows positive correlation. The significant positive correlation between autumn precipitation and autumn baseflow reflects that the recharge proportion from precipitation in autumn is large than other seasons, because the impact of temperature on glaciers in autumn becomes weaker. Precipitation recharges baseflow mainly in autumn and winter, and in spring and summer, baseflow recharges proportion from glaciers (Shen et al., 2006) affect precipitation’s role in baseflow. Cross wavelet analysis indicates significant common power in the 4e6 year band from 1980 to 1998 between precipitation and baseflow. The precipitation has both positive and negative impacts on baseflow in different seasons. According to the correlation analysis results, the baseflow has a 0e 3 months lag from precipitation. The baseflow resource is an important part of water resources in the northwest arid area. Typically, baseflow is not very sensitive to rainfall but is more associated with discharge from groundwater. The baseflow thus does not only supply the river’s run-off during the rainless season, but also recharges groundwater during the wet season. Baseflow recharge is a universal form in arid zone river supplies. Basin groundwater recharge and surface water sources
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have a close hydraulic connection. baseflow changes with the size of surface runoff and exploitation conditions. In wet periods, the baseflow is high; in dry seasons, the baseflow is low. In the past 50 years, the expansion of the oasis and irrigated area and exploitation intensity of riverwater increased, and in many parts of the northwest arid area groundwater levels declined. The river dominated by baseflow recharge in dry season has very uniform runoff distribution: spring and summer water are similar, and there is no obvious flood season and dry season. As a result, change of baseflow would greatly affect the quantity and quality of the water resources of the Tarim River, and considerably impact the human society and natural ecological environment in the region. Acknowledgements This research is supported by the National Basic Research Program of China (973 Program), No. 2010CB951003. References Chen, Y.N., Xu, Z.X., 2005. Plausible impact of global climate change on water resources in the Tarim River Basin, China. Science in China: Series D 48, 65e73. Chen, Y.N., Xu, C.C., Hao, X.M., Li, W.H., Chen, Y.P., Zhu, C.G., Ye, Z.X., 2009. Fifty-year climate change and its effect on annual runoff in the Tarim River Basin, China. Quaternary International 208, 53e61. Chen, Y.N., Xu, C.C., Chen, Y.P., Li, W.H., Liu, J.S., 2010. Response of glacial-lake outburst floods to climate change in the Yarkant River basin on northern slope of Karakoram Mountains, China. Quaternary International 226, 75e81. Eckhardt, K., 2005. How to construct recursive digital filters for baseflow separation. Hydrological Processes 19, 507e515. Eckhardt, K., 2008. A comparison of baseflow indices, which were calculated with seven different baseflow separation methods. Journal of Hydrology 352, 168e 173. Fan, Y.T., Chen, Y.N., Li, W.H., Wang, H.J., 2011. Response of runoff to temperature and precipitation changes in Tarim River during the past 50 years. Journal of Arid Lands 3, 220e230. Fan, Yuting, Chen, Yaning, Liu, Yongbo, 2013. Variation of baseflows in the headstreams of the Tarim River Basin during 1960e2007. Journal of Hydrology 487, 98e108. Fu, L.X., Chen, Y.N., Li, W.H., He, B., Xu, C.C., 2010. Relation between climate change and runoff volume in the headwaters of the Tarim River during the last 50 years. Journal of Desert Research 30, 204e209. Fuente, A.D., Bing, N., Hoeschele, I., 2004. Discovery of meaningful associations in genomic data using partial correlation coefficients. Bioinformatics 20, 3565e 3574. Grinsted, A., Moore, J.C., Jevrejeva, S., 2004. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics 11, 561e566.
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Hafzullah, A., Ilker, K., Ebru, E., 2009. Filtered smoothed minima baseflow separation method. Journal of Hydrology 372, 94e101. Kendall, M.G., 1975. Rank Correlation Methods. Griffin, London. Lyne, V., Hollick, M., 1979. Stochastic time variable rainfall runoff modeling. In: Hydrology and Water Resources Symposium Perth Proceedings. National Committee on Hydrology and Water Resources of the Institution of Engineers, Australia, pp. 89e92. Liu, W.P., Wer, W.S., Yang, Q., 2007. Study on climate change in the Aksu River Basin since Recent 40 Years. Arid Zone Research 30, 204e209. Liu, L.L., Liu, Z.F., Ren, X.Y., Fischer, T., Xu, Y., 2011. Hydrological impacts of climate change in the Yellow River Basin for the 21st century using hydrological model and statistical downscaling model. Quaternary International 244, 211e220. Li, B.F., Chen, Y.N., Chen, Z.S., Li, W.H., 2012. Trends in runoff versus climate change in typical rivers in the arid region of northwest China. Quaternary International. http://dx.doi.org/10.1016/j.quaint.2012.06.005. Maraun, D., Kurths, J., 2004. Cross wavelet analysis: significance testing and pitfalls. Nonlinear Processes in Geophysics 11, 505e514. Mann, H.B., 1945. Nonparametric tests against trend. Econometrica 13, 245e259. Mann, H.B., Whitney, D.R., 1947. On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics 18, 50e 60. Nathan, R.J., McMahon, T.A., 1990. Evaluation of automated techniques for base flow and recession analyses. Water Resources Research 26, 1465e1473. Shen, Y.P., Wang, S.P., Wang, G.Y., 2006. Response of glacier flash flood to global warming in Tarim River Basin. Advances in Climate Change Research 2, 32e35. Torrence, C., Webster, P.J., 1999. Interdecadal changes in the enso–monsoon system. Journal of Climate 12, 2679e2690. Torrence, C., Compo, G.P., 1998. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society 79, 61e78. Xu, Z.X., Takeuchi, K., Ishidaira, H., 2003. Monotonic trend and step changes in Japanese precipitation. Journal of Hydrology 279, 144e150. Xu, C.C., Chen, Y.N., Yang, Y.H.I., Hao, X.M., Shen, Y.P., 2010. Hydrology and water resources variation and its response to regional climate change in Xinjiang. Journal of Geographical Sciences 20, 599e612. Xu, J.H., Chen, Y.N., Lu, F., Li, W.H., Zhang, L.J., Hong, Y.L., 2011. The nonlinear trend of runoff and its response to climate change in the Aksu River, western China. International Journal of Climatology 31, 687e695. Xu, J.H., Chen, Y.N., Li, W.H., Ji, M.H., Dong, S., 2009. The complex nonlinear systems with fractal as well as chaotic dynamics of annual runoff processes in the three headwaters of the Tarim River. Journal of Geographical Sciences 19, 25e35. Ye, B.S., Ding, Y.J., Yang, D.Q., 2006. Regional patterns of climate change in Northwest China during the last 50 years viewed from annual discharge change. Journal of Glaciology and Geocryology 28 (3), 307e311. Yang, Z.N., Zeng, Q.Z., 2001. Glacier Hydrology. Chongqing Press, Chongqing. Zhao, F.F., Xu, Z.X., Huang, J.X., Li, J.Y., 2008. Monotonic trend and abrupt changes for major climate variables in the headwater catchment of the Yellow River basin. Hydrological Processes 22, 4587e4599. Zhou, S.Q., Kang, S.C., Gao, T.G., Zhang, G.S., 2010. Response of Zhadang Glacier runoff in Nam Co Basin, Tibet, to changes in air temperature and precipitation form. Chinese Science Bulletin 55, 2103e2110. Zhang, J., Liu, G.X., Shen, Y.P., 2008. Changes in runoff and climate and the human activity impacts in the Aksu River outside the mountains since the second half of 20th Century. Journal of Glaciology and Geocryology 30, 218e 223.
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Increasing precipitation and baseflow in Aksu River since the 1950s Yuting Fan a, b, Yaning Chen a, *, Weihong Li a a State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, CAS, South Beijing Road 40-3#, Urumqi, Xinjiang 830011, China b Graduate University of Chinese Academy of Science, Beijing 100039, China
a r t i c l e i n f o
a b s t r a c t
Article history: Available online xxx
The Aksu River is the most important recharge source of the Tarim River in northwest China, representing 73.2% of the total volume to the Tarim River in the dry season. There are three types of recharge: glacier-snow melt water, precipitation, and groundwater. Precipitation and baseflow in the basin play a decisive role. The dynamics of precipitation in the last past 50 years were investigated. The digital filtering method was used to separate baseflow from surface flow. Relationships between precipitation and baseflow were identified by correlation analysis and wavelet analysis. The major findings of this study include: 1) In the past 50 years, step changes of both precipitation and baseflow in the drainage basin occurred, and both precipitation and baseflow performed a significant increase trend since the 1960s. The 1990s was the wettest decade of precipitation, and baseflow in the late 1990s was the wettest. 2) The time scale of the annual precipitation time series in the Aksu River Basin are 3, 6, 12, and 27 years, of which the six-year cycle oscillation is the strongest and a main cycle. Aksu River basin annual precipitation is manifested in the smaller time scales, as the time scale increases, the smaller its role is. 3) The baseflow showed an increasing trend in all seasons, and precipitation exhibits a monotonic increasing trend in summer and autumn, and decreasing trend in spring and winter. 4) The responses of baseflow to precipitation were different by season. Precipitation and baseflow have significant common power in the 4e6 year band from 1980 to 1998, and the baseflow has a 0e3 months lag from precipitation. Ó 2013 Elsevier Ltd and INQUA. All rights reserved.
1. Introduction
River is mainly recharged by alpine glacier-snow melt water and precipitation, and the mean annual discharge is nearly 2 102 m3/s (Fu et al., 2010). Among these three headstream flows into Tarim River, Aksu River is not only the main source for supplying water to the mainstream of Tarim River, but also the only one tributary supplying the Tarim River during dry seasons, accounting for 73.2% of the volume, while the supplies from Hotan River and Yarkand River account for 23.2% and 3.6%, respectively (Zhang et al., 2008). Therefore, the changes of Aksu River runoff play a decisive role in the formation, development, and evolution of the Tarim River. Temperature and precipitation have significant effects on maintaining discharge in the inland river area (Zhou et al., 2010). For the Aksu River, there are three types of recharge: glacier-snow melt water accounted for 45.0%, precipitation 33.1%, and groundwater 21.9% (Fu et al., 2010). Precipitation and baseflow in the basin play a decisive role. Recently, the trend of regional climate change and its impact on water resources have been investigated, but most studies mainly focused on runoff and its influencing factors in rivers (i.e. Chen and Xu, 2005, 2010; Ye et al., 2006; Xu et al., 2010, 2011; Li et al., 2012). There have been few studies on the characteristics and tendency of the precipitation sequence of the Aksu River Basin
Climate change and its consequent impacts on hydrology and water resources are hot topics for scholars and researchers around the world. During the past 50 years, rising global temperatures have accelerated the water cycle, causing a redistribution of water resources that ranges from minor to extreme. Arid areas are especially affected by this process due to the fragile nature of their ecohydrology, which is more sensitive to climatic changes. The Tarim River Basin, the largest inland river basin in China, is located in south Xinjiang and covers about two thirds of the total area of Xinjiang. The change of runoff and the utilization of water resources in Tarim River determine the amount of water resources, and deeply affect the water quality and ecological environment in the lower reaches of Tarim River (Chen and Xu, 2005). Now only three water systems have a natural hydraulic relationship with the mainstream: Aksu River, Hotan River, and Yarkand River. The Aksu
* Corresponding author. E-mail address: [email protected] (Y. Chen). 1040-6182/$ e see front matter Ó 2013 Elsevier Ltd and INQUA. All rights reserved. http://dx.doi.org/10.1016/j.quaint.2013.09.037
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2
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Fig. 1. Map of Aksu River showing observation sites.
and the impact of precipitation on baseflow has received little attention. As precipitation is a primary factor in the generation of river runoffs, the relationship between river baseflow in the basin needs further investigation. It was hypothesized that the precipitation in the Aksu River had been experiencing considerable variation and would have some impact on the baseflow. This study chose the Aksu River Basin in Xinjiang to give its precipitation and baseflow variation in the past 50 years a close inspection. There are three aims of this study: (i) to detect trend of precipitation time series by a ManneKendall test, and to analysis the cycles of the precipitation time series by wavelet; (ii) to assess the temporal variability in the quantity of the baseflow for the Aksu
River by using hydrometric data and RDF; and (iii) to determine the correlation between the baseflow and precipitation, by correlation analysis and wavelet analysis. This study synthesizes time analysis with insights from correlation analysis to assess the variation in precipitation and baseflow characteristics in the Aksu River. This study will add to understanding of the relationship between discharge and precipitation. 2. Study area and data Located in the northern margin of the Tarim Basin, the Aksu River has two mainstreams originating from Kyrgyzstan. The
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Kunmalake River originates from the Hantengri Mts., and the Toxkan River originates from the Artbash Mts. The Aksu River is formed by the confluence of the two rivers, and at Eressea, the Aksu River divides into two branches: Xinda River and Laoda River. The two branches join at Awati and finally join the Tarim River at Xiaoxiake (Fig. 1). The Aksu River has varied landforms, and the geography is complicated. The basin area is 5.0 104 km2, 457 km long (Liu et al., 2007). Regional climate differences are significant. The high mountain area has low temperature and sufficient precipitation, and there is snow cover over the whole year. The middle mountain area has clear demarcation between cold and warm, and has the largest precipitation. The lower mountains are extremely dry, and with large differences in climate in different seasons. The plain area in the southeast is surrounded by high mountains in the north and Taklimakan Desert in the south, so that a typical continental climate in arid environments was formed. It has an extremely dry desert climate with infrequent and low precipitation and strong potential evaporation, large temperature difference, long hours of sunshine and abundant light and heat resources. The study area is the region that the Aksu River flows through (from Aheqi station to Alar station). Observed annual time series of precipitation in the Aksu River were used to estimate monotonic trends. Seven stations with continuous data series from 1956 to 2006 were selected in this study. The locations of the selected stations in the basin are shown in Fig. 1. Two hydrological stations and five meteorological stations (Fig. 1), six around the Aksu River and another in the mainstream, were used in this study. In the head water catchment region, Shaliguilanke station is located along the Toxkan River, and Xiehela station along the Kunmalake River. Aksu station, Awati station and Xidaqiao station are along the mainstream of Aksu River. Alar station is the first gauge in the mainstream region of the Tarim River. 3. Methodology 3.1. Baseflow separation The recursive digital filtering (RDF) technique was investigated to approximate well the baseflow sequence calculated by the matching strips manual separation technique (Eckhardt, 2005). The RDF technique, which was originally used for signal analysis and processing, became popular in hydrology literature for baseflow separation (e.g., Eckhardt, 2008). The RDF technique was selected for its less parameters and simple accurate advantages. RDF smooths the sharp peaks in the fast component of the streamflow so that the separated flow represents the delayed component of the streamflow, i.e., the baseflow. The output of the filter is constrained so that the separated flow cannot take negative values and is not greater than the total flow (Lyne and Hollick, 1979). The RDF process can be represented as (Hafzullah et al., 2009),
Qd ðtÞ ¼ bQd ðt 1Þ þ ð1 þ bÞ=2½Q ðtÞ Q ðt 1Þ
(1)
where Qd (m3/s) is the filtered quick streamflow, Q (m3/s) is the total streamflow, t is the time step (day), and b is a filter parameter. The filtered baseflow Qb can then be obtained by:
3
series estimates of baseflow, with the last being the projected baseflow time series. The justification for the use of this method rests on the fact that filtering out high-frequency signals is intuitively analogous to the separation of low frequency baseflow from the higher frequencies of quickflow (Nathan and McMahon, 1990). The output of the filter is constrained, such that the separated flow cannot take negative values and is not greater than the total flow. 3.2. Time series analysis Hypothesis testing to estimate long-term climate change trends is helpful to understand the inherent mechanism of hydrological process. In this study, two types of general trends are investigated: the monotonic trend and step change (Zhao et al., 2008). While it is difficult to gain a thorough understanding of the non-linear mechanism of any individual hydroclimatic process (Xu et al., 2009, 2011), such processes can be evaluated theoretically to determine if they comprise an ordered deterministic system, an unordered random system, and whether change patterns of periodicity exist. Specific to the series of climate changes that have occurred in the arid/semi-arid regions of western China, such inquiries may be designed to determine if these changes represent a localized transition to a warm and wet climate in response to climate change, or merely reflect a centennial periodicity in hydrological dynamics. 3.2.1. ManneKendall test Considering the power of the test, i.e. the ability to distinguish between H0 and H1, nonparametric tests are more robust compared to their parametric counterparts. The nonparametric ManneKendall test was used to detect the monotonic trend of precipitation and baseflow. The ManneKendall test statistic is given as follows (Mann, 1945; Kendall, 1975; Chen et al., 2009),
8 pS1 ffiffiffiffiffiffiffiffiffiffi; S > 0 > > > varðSÞ > < Zc ¼ 0; S ¼ 0 > > > > ffiffiffiffiffiffiffiffiffiffi; S < 0 : pSþ1
In which S ¼
n 1 X
n X
sgnðxk xi Þ
(3)
i ¼ 1 k ¼ iþ1
varðSÞ
where the xk, xi are the sequential data values, n is the length of the data set, and sgn(q) is equal to 1,0,1 if q is greater than, equal to, or less than zero, respectively. The null hypothesis H0 is accepted if Z1-a/2 Zc Z1-a/2 3.2.2. ManneWhitney test Given the data vector X ¼ (x1,x2,..,xn) partition X such that Y ¼ (x1,x2,..,xn) and Z ¼ (xn1þ1,xn2þ2,..,xn1þn2). The Manne Whitney test Statistic is given as (Mann and Whitney, 1947),
Pn1 Zc ¼
t¼1
rðx1 Þ n1 ðn1 þ n2 þ 1Þ=2
½n1 n1 ðn1 þ n2 þ 1Þ=121=2
(4)
(2)
In which r(x1) is the rank of the observations. The null hypothesis H0 is accepted if Z1-a/2 Zc Z1-a/2 where Z1-a/2 are the 1-a/2 quartiles of the standard normal distribution corresponding to the given significance level for the test (Xu et al., 2003).
The best results were obtained when b was in the range 0.90e0.95, with an optimal value of 0.925 (Nathan and McMahon, 1990). The algorithm separates baseflow from total stream flow by passing the filter over the streamflow record three consecutive times (forwards, backwards, and forwards again). Each filter pass produces three time
3.2.3. Correlation analysis Correlation analysis is a method to study the linear correlation between two variables. This study used correlation analysis to evaluate the relationships between baseflow and precipitation. The correlation coefficient is defined as:
Qb ðtÞ ¼ Q ðtÞ Qd ðtÞ
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Y. Fan et al. / Quaternary International xxx (2013) 1e9
Pn i ¼ 1 ðxi xÞðyi yÞ r ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 Pn 2 i ¼ 1 ðxi xÞ i ¼ 1 ðyi yÞ
(5)
The physical meaning of r is the correlation between the parts of xi and yi. The correlation coefficient ranges from 1 to þ1. A positive r indicates a positive linear relationship between the two variables, and a negative r indicates a negative linear correlation between the two variables (Fuente et al., 2004). 3.2.4. Wavelet analysis The cross wavelet transform (XWT) of two time series xn and yn is defined as WxY ¼ WxWY*, where * denotes complex conjugation. The cross wavelet power is defined as jWxYj. The complex argument arg(Wxy) can be interpreted as the local relative phase between xn and yn in time frequency space. The theoretical distribution of the cross wavelet power of two time series with background power spectra PkX and PkY is given in Torrence and Compo (1998) as
D
X Wn ðsÞWnY* ðsÞ sXsY
!
¼
Zv ðpÞ v
qffiffiffiffiffiffiffiffiffiffiffi PkX PkY
(6)
where Zv(p) is the confidence level associated with the probability p for a pdf defined by the square root of the product of two 2 distributions. Cross wavelet power reveals areas with high common power (Grinsted et al., 2004; Maraun and Kurths, 2004). Another useful measure is how coherent the cross wavelet transform is in time frequency space. Following Torrence and Webster (1999) the wavelet coherence (WTC) of two time series is
2 S s1 WnXY ðsÞ 2 Rn ðsÞ ¼ S s1 WnX ðsÞ S s1 WnY ðsÞ
(7)
where S is a smoothing operator. This definition closely resembles that of a traditional correlation coefficient, and it is useful to think of the wavelet coherence as a localized correlation coefficient in time frequency space. The smoothing operator S is
SðWÞ ¼ Sscale ðStime ðWn ðsÞÞÞ
(8)
where Sscale denotes smoothing along the wavelet scale axis and Stime denotes smoothing in time. It is natural to design the smoothing operator so that it has a similar footprint as the wavelet used. For the Morlet wavelet a suitable smoothing operator is given as
Stime ðwÞjs ¼
t 2 Y Wn ðsÞc12s2 ; Stime ðWÞjs ¼ Wn ðsÞc2 ð0:6sÞ s
n
(9)
Fig. 2. Temporal series of precipitation and baseflow in the Aksu River Basin.
Q where c1 and c2 are normalization constants and is the rectangle function. The factor of 0.6 is the empirically determined scale decorrelation length for the Morlet wavelet. 4. Results and analysis 4.1. Time series analysis of the precipitation 4.1.1. Precipitation trend Fig. 2(a) shows the temporal series of precipitation in the Aksu River Basin from 1957 to 2006. The figure reveals that the precipitation in the basin has significantly increased since the lowest precipitation in 1985, and the precipitation fluctuated in the decade of the 1970s. For the visualization purposes, the 5-year moving averages (MA) are also given in the graph. Scrutiny of the time series in Fig. 2 (a) reveals that precipitation peaked in the early 1980s and has been increasing since then. The formula e (average annual precipitation e this year precipitation)/average annual precipitation was used to calculate the results. Values less than 25% indicate dry years, and less than 10% indicate approximate dry years; 10 to 10% indicate normal years; greater than 10% indicate approximate wet years; and greater than 25% indicate wet years. A significantly higher precipitation regime marked 1970e1973, 1986e1989, 1992e2005, and 1982 and 1996 were the wettest on the record. The period from 1956 to 1970 was one of the driest periods during the study period. Three years: 1961, 1979, and 1985, were the three driest on record. Sixteen years since the year 1990 had above-average precipitation over this 50-year period. The precipitation time series exhibit a monotonic step change (Table 1).
Table 1 Partitions of the precipitation time series Monotonic trend test for precipitation time series. Item
No.
Time series
Length of record
Mean value
Standard dev.
Coeff.of variation
ManneKendall Z0
H0
Precipitation
1 2 3 1 2 3
1956e1970 1971e1986 1987e2010 1960e1976 1977e1994 1995e2006
15 16 24 17 18 12
48.67 55.30 135.02 11.81 10.58 17.02
8.41 21.79 36.07 1.72 1.83 2.68
0.17 0.39 0.27 0.15 0.17 0.16
2.77
R
3.50
R
Baseflow
R: Reject H0; Significance level p ¼ 95%; Z0 is statistics of ManneKendall test.
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4.1.2. Precipitation step trend Fig. 3(a) shows the temporal series of precipitation in the Aksu River Basin from 1956 to 2006. The possible partition points are identified by visual observation, the national precipitation time series is divided into three sub-series (Table 1), and through the ManneWhitney test, the precipitation contradicts the null hypothesis. The time series exhibits an obvious step change. Table 2 presents the ManneWhitney test result on the assessment of step changes for the Aksu River Basin precipitation. The results suggest that there was no significant precipitation increase from 1956 to 1970 and from 1971 to 1986, but significant step changes from 1971 to 1986, and 1987 to 2006. Combining the results of Kendall diagnosis on step trends for the Aksu River Basin precipitation, the year 1987 was the cut-off point when a significant step change appeared (Table 2). Thus, a significant phasic precipitation increase occurred around 1987. Table 2 ManneWhitney test results of step trend for precipitation time series. Item
Precipitation Baseflow
No.
1 2 1 2
and and and and
Series
2 3 2 3
ManneWhitney
N1
N2
Zc
H0
15 16 17 18
16 24 18 12
0.493 2.012 2.812 2.973
A R R R
Step points
1987(þ) 1977(þ) 1995(þ)
A: Accept H0; R: Reject H0; Significance level p ¼ 95%; Zc is statistics of Manne Whitney test; the þ means jump or trend is significantly, and the e means jump or trend is not significantly, Significance level a ¼ 0.01.
4.1.3. Precipitation cycle Fig. 6 is the wavelet analysis results of the annual precipitation time series of Aksu River Basin in the past 50 years, showing characteristics of precipitation variation by time scale and its distribution in the time domain. The vertical axis points correspond to different cycles, and varies scales of oscillation center (positive and negative) show that the precipitation contains a number of different scales of the cycle. The strength of the signal is represented by the wavelet coefficients. Zero corresponds to the step points. Different time scales correspond to different precipitation structure. Aksu River Basin annual precipitation fluctuations have three main frequencies: 2e4 years, 6 years, 12 years, and 27 years cycle. Centred at about 12 years, 11e13 year time scales were obvious in 1956 and 1970. Small-scale cycles less than 12 years indicate more rain and dry periods alternating, with more step points. A 3 year time scale was also evident, and positive and negative changed
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alternated. Among them, there are 11 six-year time scales: the late 1950s, late 1960s, late 1970s, the mid-1980s, early 1990s and after 2005 represent the positive phase of the rainy period. The early 1960s, early 1970s, early 1980s, the mid-1990s and year before 2005 show the negative phase of the dry period. In addition, the 24e30 year cycle was apparent, centred about 27 years. The phase structure of the cycle in the 1960s, mid-1970s and after 1990s are positive rainy periods; the late 1970s and late 1980s are negative phase dry periods. 4.2. Time series analysis of the baseflow 4.2.1. Baseflow trend Fig. 4 shows the yearly baseflow result and daily baseflow varies situation, In the study area, winter baseflow is less related to winter precipitation. Snowfall is accumulated from December to February and supplies baseflow during the spring snowmelt season. Three months’ baseflow are the basic flow for a whole year, and there is a comparison between baseflow and streamflow. Fig. 2(b) shows the temporal series of baseflow anomaly in the Aksu River Basin from 1960 to 2006. The baseflow has significantly increased since the minimum in 1985, and the baseflow has significantly decreased in the decade of the 1970s. Scrutiny of the time series in Fig. 2(b) reveals that baseflow peaked in the late 1990s. Significantly higher baseflow regimes existed from 1965 to 1971, 1993 to 1994, 1997 to 2006, and 1999 and 2003 were the wettest on the record. The period from 1978 to 1986 was one of the driest periods during the study period. Three years: 1962, 1980, and 1985, were the three driest on record. Ten years since 1997 had above-average precipitation over this 50-year period. Because of the limited storage in superficial deposits and thin soils, precipitation becomes surface run-off and enters streams directly instead of via deep percolation. 4.2.2. Baseflow step trend Fig. 3(b) shows the temporal series of baseflow in the Aksu River Basin from 1960 to 2006. The possible partition points were identified by visual observation. The national baseflow time series is divided into three sub-series (Table 1). The ManneWhitney test indicates that the baseflow contradicts the null hypothesis, and the time series exhibits a step change. Table 2 presents the Manne Whitney test result on the assessment of step changes for the Aksu River Basin baseflow. Step change points in runoff are affected by not only climate factors (Liu et al., 2011) but also human activities (Xu et al., 2011). The results suggest that there was significant baseflow decrease from 1960 to 1976 and from 1977 to 1994, and significant increases from 1977 to 1994 and 1995 to 2006.
Fig. 3. Average annual precipitation showing the possible step trends.
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climate variables (such as temperature, precipitation, etc.) causing changes in the baseflow. If the magnifying effect of only a minor climate change is large, then the hydrology and water resources systems are highly sensitive to climate change.
Fig. 4. Yearly streamflow and baseflow, daily streamflow and baseflow.
Combining the results of step trends for the Aksu River Basin baseflow, the year 1977 and 1995 were cut-off points, when a significant step change appeared (Table 2). The sensitivity of baseflow to climate change refers to the magnifying effect of one or more
4.2.3. Seasonal effect of precipitation on baseflow The precipitation and the baseflow in all seasons show an upward trend (Fig. 5). Precipitation in the summer and autumn and of baseflow indicates that the trend of baseflow is somewhat coincident with precipitation trend, but the changing characteristics of spring and winter are different. The trend of baseflow in spring and winter are opposite to the precipitation trend. Both significant increasing trends were tested in the summer precipitation and summer baseflow from the 1990s, and both significant increasing trends were tested in the autumn precipitation and autumn baseflow since 2000. In spring and winter, several years with high precipitation correspond to low baseflow, and low precipitation to high baseflow. The glacial ablation areas in the northwest are generally located at higher altitudes, where melting mainly occurs in summer and most river baseflow is directly related to glacial melt water (Yang and Zeng, 2001). Table 3 presents the results of the trend analysis on seasonal baseflow for the Aksu River. The baseflow exhibits a monotonic increasing trend. The baseflow in spring, summer, autumn, and winter exhibit a monotonic increasing trend, and precipitation exhibits a monotonic increasing trend in summer and autumn. Baseflow was affected by temperature, precipitation, elevation, and subsurface conditions. The large increase in baseflow in the melt season was possibly caused by temperature. The role of precipitation on baseflow is not clear. Huge regional differences exist in the correlation of baseflow and precipitation in different seasons. The differences may be related to the recharge types of baseflow. The correlation of baseflow and precipitation is higher in the rivers where the proportion of glacier-melt run-off is low. However, in glacial-melt dominant rivers, the correlation of baseflow and
Fig. 5. Seasonal precipitation and baseflow time series. (a) spring (b) summer (c) autumn (d) winter.
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Fig. 6. Wavelet coefficients of annual precipitation.
temperature is higher (Fan et al., 2013). The correlation of baseflow and precipitation and of baseflow and temperature is high in the rivers which are fed equally by glacier-melt and precipitation. This deep-seated mechanism needs further study. Table 3 Monotonic trend test for Precipitation and Baseflow time series ManneKendall Precipitation Baseflow
Z0 H0 Z0 H0
Spring
Summer
Autumn
Winter
0.769 A 2.613 R
2.185 R 2.443 R
2.948 R 3.068 R
1.673 R 3.503 R
R: Reject H0; Significance level p ¼ 95%; Z0 is statistics of ManneKendall test.
4.3. Increasing precipitation impact on baseflow trend 4.3.1. Correlation between precipitation and baseflow Water resources mainly come from natural precipitation in mountains and mountain snowmelt water that is greatly affected by temperature. Climate change leads to increases in heavy precipitation days and flood frequency. In high latitudes and snowmelt recharge basins, increases in temperature cause increases in the rain/snow ratio. The correlation between precipitation and runoff is statistically significant at p < 0.05 or 0.01 levels according to the above results. Table 4 shows the results of the correlation analysis. According to the results, the precipitation had different impacts on the baseflows of the Aksu River in different seasons. Significant correlations were only found between February precipitation and February baseflow, February precipitation and March baseflow, April precipitation and May baseflow, and September precipitation and October baseflow. Table 4 Correlation between Precipitation and Baseflow in different seasons/months Correlation
Baseflow
Precipitation Baseflow Correlation
Precipitation
Spring Summer Autumn Winter Month average Month average 0.527**
Spring
Summer
Autumn
Winter
0.077 0.095 0.027 0.107 February February 0.361*
0.164 0.292 0.327* February March 0.372*
0.509** 0.509** April May 0.311*
0.037 September October 0.408**
Note: * and ** indicate the significance at the levels of p < 0.05, p < 0.01 (2-tailed), respectively.
The spring precipitation has a small positive impact on summer baseflows, but has a small negative impact on spring and autumn and winter baseflow. When temperature rises from spring to summer, the underlying surface become more susceptible to infiltration. Before significant ablation of the glaciers, precipitation was delayed, supplying baseflow until summer, and thus the summer precipitation has a weak positive correlation with summer baseflow. The summer precipitation has a positive impact on summer and autumn baseflow, and a significant positive impact on winter baseflow. As one component of streamflow, summer rainfall recharges surface flow and is transformed to groundwater in dry seasons. The autumn precipitation has a significant positive impact on autumn and winter baseflow. The winter precipitation has a small negative impact on winter baseflow, because the winter precipitation is stored as a solid form before melting. The winter flows influence the annual baseflow. The results show that the correlations between baseflow and precipitation are dissimilar in different temperature conditions, which may be related to the baseflow recharge from snow and glacier melt. The average temperature in the Aksu River Basin has an increasing trend over the past 50 years (Fan et al., 2011), and in spring and summer, glaciers contribute 40% water of the total streamflow to the Tarim River (Shen et al., 2006). Melt water may recharge baseflow synchronously. 4.3.2. Cross wavelet and wavelet coherence Cross wavelet analysis and wavelet coherence are powerful methods for testing proposed linkages between two time series. The XWT of precipitation and baseflow is shown in Fig. 7a. The common features visible from the individual wavelet transforms stand out as being significant at the 5% level. There also is significant common power in the 4e6 year band from 1980 to 1998. The XWT shows that precipitation and baseflow are in anti-phase in some sectors and in-phase in other sectors with significant common power. Baseflow to a large extent simply mirrors the precipitation. Outside the areas with significant power, the phase relationship is also predominantly anti phase. There appears to be a stronger link between precipitation and baseflow than that implied by the cross wavelet power. This basically confirms the conclusion that precipitation and baseflow are in anti-phase, and the time series have a 0e3 months lag. The wavelet coherence between the precipitation and baseflow is shown in Fig. 7b. Oscillations in precipitation are manifested in the baseflow on wavelengths varying from 3 to 6 years, suggesting that baseflow passively mirrors precipitation. Regions with low
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Fig. 7. Cross wavelet transform and wavelet coherence of the precipitation and baseflow time series. The 5% significance level against yellow or red noise is shown as a thick contour. The relative phase relationship is shown as arrows, All significant sections show anti-phase behavior. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
coherence coincide with low wavelet power in the precipitation and are therefore expected. The mean phase angle over the regions with significant wavelet coherence is 90 to 45. The precipitation has positive impact on baseflow at sometimes, but negative impact on baseflow in other situations. According to the correlation analysis results, the baseflow has a 0e3 months lag from precipitation. Baseflow in the Aksu River is increasing with rising precipitation. Precipitation recharges baseflow to some degree, but the precipitation is usually accompanied by cooling, and the temperature decrease leads to glacial melt water reduction. When precipitation is less than glacial melt water reduction, the correlation between baseflow and precipitation exhibits a negative significance. 5. Conclusion and discussion This study synthesized time analysis with insights from precipitation to assess the variation in baseflow characteristics of the Aksu River, the main tributary of the Tarim River, a major water resource of the vast arid area in south Xinjiang, China. The time series analysis techniques were used to address two aspects: Application of the ManneKendall and ManneWhitney tests for precipitation time series over the Aksu River Basin showed both monotonic trends and step changes in precipitation. A step change occurred in precipitation time series around 1986. The test results for the long-term trend of the precipitation showed that there is an increasing tendency in annual precipitation during the past 50 years, and the increasing trend is significant at the 5% level of significance. During the last five decades, the precipitation has increased by 30.7% per decade. The wetting trend in the Aksu River Basin could be a local response to global climate change. The time scale of the annual precipitation time series in the Aksu River Basin are 3, 6, 12 and 27 years, of which the six-year cycle oscillation is the strongest and a main cycle. The Aksu River basin annual precipitation is manifested in the smaller time scales: as the time scale increases, the smaller its role is. Step changes of baseflow in the drainage basin occurred in 1977 and 1995, and baseflow showed a significant increase trend since the 1960s. The late 1990s baseflow was the wettest in the past 50 years. The baseflow time series exhibit monotonic increasing trends in spring, summer, autumn, and winter. During the last five decades, the global temperature has increased by 0.2e0.3 C / decade, and the temperature has increased by 0.2 C /decade in west China (Li et al., 2012). The increasing trend in the baseflow should be a local response to global temperature change, and thus the response of baseflow to precipitation exhibited a complex
mechanism. The trend of baseflow is somewhat coincident with the precipitation trend in summer and autumn, but opposite to the precipitation trend in spring and winter. Precipitation has both significant positive and negative impact on baseflow in different seasons. The summer precipitation has a positive impact on winter baseflow. The autumn precipitation has significant positive impact on both autumn and winter baseflow. There are significant negative correlation between February precipitation and February baseflow, February precipitation and March baseflow, and April precipitation and May baseflow; and there is a significant positive correlation between September precipitation and October baseflow. The baseflow has significantly increased since the minimum in 1985. Chen et al. (2009) found the warminge wetting trend in the Tarim River Basin was a local response to global climate change. The highest annual temperature in 1990s may have impacted the baseflow by the melt water in summer, which led to the high precipitation in summer having a small positive correlation with baseflow. The correlations between baseflow and precipitation are dissimilar in different months, which may be related to baseflow recharge characters. The precipitation in winter and spring show negative correlations with baseflow, because the stable part of the streamflow is mainly recharged by baseflow. In summer, runoff and baseflow are recharged from both rainfall and glacier melt water, so the correlation between summer precipitation and summer baseflow shows positive correlation. The significant positive correlation between autumn precipitation and autumn baseflow reflects that the recharge proportion from precipitation in autumn is large than other seasons, because the impact of temperature on glaciers in autumn becomes weaker. Precipitation recharges baseflow mainly in autumn and winter, and in spring and summer, baseflow recharges proportion from glaciers (Shen et al., 2006) affect precipitation’s role in baseflow. Cross wavelet analysis indicates significant common power in the 4e6 year band from 1980 to 1998 between precipitation and baseflow. The precipitation has both positive and negative impacts on baseflow in different seasons. According to the correlation analysis results, the baseflow has a 0e 3 months lag from precipitation. The baseflow resource is an important part of water resources in the northwest arid area. Typically, baseflow is not very sensitive to rainfall but is more associated with discharge from groundwater. The baseflow thus does not only supply the river’s run-off during the rainless season, but also recharges groundwater during the wet season. Baseflow recharge is a universal form in arid zone river supplies. Basin groundwater recharge and surface water sources
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have a close hydraulic connection. baseflow changes with the size of surface runoff and exploitation conditions. In wet periods, the baseflow is high; in dry seasons, the baseflow is low. In the past 50 years, the expansion of the oasis and irrigated area and exploitation intensity of riverwater increased, and in many parts of the northwest arid area groundwater levels declined. The river dominated by baseflow recharge in dry season has very uniform runoff distribution: spring and summer water are similar, and there is no obvious flood season and dry season. As a result, change of baseflow would greatly affect the quantity and quality of the water resources of the Tarim River, and considerably impact the human society and natural ecological environment in the region. Acknowledgements This research is supported by the National Basic Research Program of China (973 Program), No. 2010CB951003. References Chen, Y.N., Xu, Z.X., 2005. Plausible impact of global climate change on water resources in the Tarim River Basin, China. Science in China: Series D 48, 65e73. Chen, Y.N., Xu, C.C., Hao, X.M., Li, W.H., Chen, Y.P., Zhu, C.G., Ye, Z.X., 2009. Fifty-year climate change and its effect on annual runoff in the Tarim River Basin, China. Quaternary International 208, 53e61. Chen, Y.N., Xu, C.C., Chen, Y.P., Li, W.H., Liu, J.S., 2010. Response of glacial-lake outburst floods to climate change in the Yarkant River basin on northern slope of Karakoram Mountains, China. Quaternary International 226, 75e81. Eckhardt, K., 2005. How to construct recursive digital filters for baseflow separation. Hydrological Processes 19, 507e515. Eckhardt, K., 2008. A comparison of baseflow indices, which were calculated with seven different baseflow separation methods. Journal of Hydrology 352, 168e 173. Fan, Y.T., Chen, Y.N., Li, W.H., Wang, H.J., 2011. Response of runoff to temperature and precipitation changes in Tarim River during the past 50 years. Journal of Arid Lands 3, 220e230. Fan, Yuting, Chen, Yaning, Liu, Yongbo, 2013. Variation of baseflows in the headstreams of the Tarim River Basin during 1960e2007. Journal of Hydrology 487, 98e108. Fu, L.X., Chen, Y.N., Li, W.H., He, B., Xu, C.C., 2010. Relation between climate change and runoff volume in the headwaters of the Tarim River during the last 50 years. Journal of Desert Research 30, 204e209. Fuente, A.D., Bing, N., Hoeschele, I., 2004. Discovery of meaningful associations in genomic data using partial correlation coefficients. Bioinformatics 20, 3565e 3574. Grinsted, A., Moore, J.C., Jevrejeva, S., 2004. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics 11, 561e566.
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