1 Introduction

In recent years, climate change combined with human activities resulted in large changes in hydrological processes and water availability in many regions of the world (e.g., Milly et al. 2008; Xu et al. 2010; Immerzeel et al. 2010). Increased evaporation, combined with changes in precipitation, has the potential to affect streamflow. Human activities such as land use/cover change can also alter hydrological processes and impact the generation of streamflow (e.g., Zhang and Schilling 2006; Raymond et al. 2008; Tomer and Schilling 2009). Different methods were used to quantitatively separate the impacts of climatic variation and human activities on streamflow. Among these methods, the climate elasticity method (e.g., Schaake and Waggoner 1990; Dooge et al. 1999) was widely used in different regions of the world (e.g., Sankarasubramanian et al. 2001; Arora 2002; Li et al. 2007; Liu et al. 2012).

The climate elasticity method measures the contribution of climatic variation on streamflow change and assumes that the remaining change of streamflow would come from human influence or other unidentified factors. Generally, the streamflow record is divided into two periods and the change in streamflow between the two periods (ΔQ) is estimated as:

$$ \Delta Q = \Delta {Q_{\text{C}}} + \Delta {Q_{\text{H}}} $$
(1)

where ΔQ C and ΔQ H are changes in streamflow due to climatic variation and human activities, respectively. ΔQ C is approximately estimated as follows (e.g., Dooge et al. 1999; Milly and Dunne 2002):

$$ \Delta {Q_{\text{C}}} = \Delta {Q_P} + \Delta {Q_{{{\text{E}}{{\text{T}}_0}}}} = \left( {{{{{\varepsilon_{\text{P}}}\Delta P}} \left/ {P} \right.} + {{{{\varepsilon_{{{\text{E}}{{\text{T}}_0}}}}\Delta {\text{E}}{{\text{T}}_0}}} \left/ {{{\text{E}}{{\text{T}}_0}}} \right.}} \right)Q $$
(2)

where Q is streamflow, P is precipitation, ET0 is potential evapotranspiration. ΔQ P and \( \Delta {Q_{{{E_0}}}} \) are the contributions of change in P and ET0 to change in streamflow, respectively. ΔP and ΔET0 are the change in P and ET0 between the two periods, respectively. ε P and \( {\varepsilon_{{{\text{E}}{{\text{T}}_{{0}}}}}} \) are climate elasticity of streamflow to P and ET0, respectively.

The climate elasticity method considers the precipitation and potential evapotranspiration as the representative indicators to estimate the impacts of climatic variation on streamflow. One of the uncertainties is that the impacts of changes in precipitation and potential evapotranspiration on streamflow are separated with the assumption that they are independent in Eq. 2. However, precipitation and potential evapotranspiration are not totally independent. For example, increase in precipitation could lead to an increase in vapor pressure, thus leading to a decrease in potential evapotranspiration (Liu et al. 2011). The aridity index, as the function of precipitation and potential evaporation, could be used as the representative indicator to estimate the impacts of climatic variation on streamflow in the climate elasticity method.

The Danjiangkou Reservoir basin (DRB) is the water source of the central route of China’s South-to-North Water Diversion Project (SNWDP) while Beijing is one of the water destinations of the Project (Fig. 1). The Miyun Reservoir basin (MRB) is the current main surface water source for Beijing, providing nearly half of the water supply for the city (Xu et al. 2009). The impacts of climatic variation on streamflow in the two basins would inevitably have impacts on the implementation of the SNWDP. The objectives of this study are: (1) to characterize the change in annual streamflow and aridity index in the DRB and MRB from 1960 to 2005, (2) to assess and compare the sensitivity of streamflow to aridity index in the two basins, and (3) to estimate the impacts of climatic variation on streamflow using the indicator of aridity index in the two basins.

Fig. 1
figure 1

The locations of the Hanjiang River Basin, MRB and the central route of China’s SNWDP

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2 Study area and data

The DRB (111.5 E, 32.7 N) is located on the middle reaches of the Hanjiang River, the largest tributary of the Yangtze River (Fig. 2a). The Reservoir has a drainage area of 96,000 km2 with the average elevation of 656 m. The DRB is located in the sub-tropical monsoon climate zone. The average annual temperature ranges from 13.5 to 15.5 °C. The annual precipitation varies from 700 to 1100 mm, and 70–80 % of the precipitation occurs in the wet months from May to October. The runoff between July and October accounts for about 65 % of the total annual runoff.

Fig. 2
figure 2

The meteorological stations in the DRB (a) and MRB (b)

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The Miyun Reservoir (116.9 E, 40.5 N) is about 100 km north of Beijing. The Reservoir has a drainage area of 15,800 km2 with the average elevation of 89 m (Fig. 2b). The MRB is also located in the monsoon climate zone and is a semi-arid region. The average annual temperature ranges from 9 to 10 °C, and the annual rainfall varies between 300 and 700 mm. The monsoon season (June to September) contributes more than 80 % of annual rainfall.

Daily meteorological records of 18 national meteorological stations from 1960 to 2005 from the National Climatic Centre of China Meteorological Administration were used in the study (Fig. 2). There are 11 stations located in the DRB and 7 stations located in or around the MRB. The meteorological data include daily P, air temperatures (T), wind speed, vapor pressure, and sunshine duration. ET0 was calculated by the Penman–Monteith method (Allen et al. 1998). The monthly streamflow (1960–2005) into the DRB and MRB was provided by the Bureau of Hydrology of the Yangtze Water Resources Commission and Beijing Water Authority, respectively. The land use maps of the year 1980 and 1995 used to identify the land use change were provided by the Chinese Academy of Sciences. The maps have a resolution of 1 × 1 km and were also used in other hydro-climatic studies (e.g., Wang et al. 2009).

3 Methodology

3.1 Statistical analysis

The non-parametric Mann–Kendall method (Mann 1945; Kendall 1975) has been widely used to analyze the abrupt change of the hydro-climatic time series (e.g., Douglas et al. 2000). The Mann–Kendall method presumes a steady time series. Given a data series composed of x 1, x 2… x n , for each element, the Mann–Kendall rank statistic (d k ) is calculated as the summation of m i , which is the number of later terms in the series whose values exceed x i:

$$ \matrix{ {{d_k} = \sum\limits_{{i = 1}}^k {{m_i}} } &{\left( {2 \leqslant k \leqslant n} \right)} \\ }<!end array> $$
(3)

The mean and variance of the test statistic d k are:

$$ \left\{ {\begin{array}{*{20}{c}} {E\left[ {{{d}_{k}}} \right] = k\left( {k - 1} \right)/4} \hfill \\ {{\text{var}}\left[ {{{d}_{k}}} \right] = k\left( {k - 1} \right)\left( {2k + 5} \right)/72\quad \left( {2 \leqslant k \leqslant n} \right)} \hfill \\ \end{array} } \right. $$
(4)

The sequential values of the statistic u(d k ) are then calculated as:

$$ u\left( {{d_k}} \right) = {{{\left( {{d_k} - E\left[ {{d_k}} \right]} \right)}} \left/ {{\sqrt {{{\text var} \left[ {{d_k}} \right]}} }} \right.} $$
(5)

The terms of the u(d k ) (1 ≤ k ≤ n) constitute a forward sequence curve (C1). The same method is then applied to the inversed series and to get a backward sequence (C2). The intersection point of C1 and C2 located between the confidence interval is the time when a climate jump occurred.

3.2 Sensitivity coefficient

The sensitivity coefficient, defined as the ratio of change rate of dependent variable to change rate of independent variable, is an indicator of sensitivity to a factor (McCuen 1974). The sensitivity of streamflow to aridity index (S ϕ ) can be evaluated as:

$$ {S_{\phi }} = \mathop{{\lim }}\limits_{{{{{\Delta \phi }} \left/ {\phi } \right.}}} \left( {\frac{{\Delta Q/Q}}{{\Delta \phi /\phi }}} \right) = \frac{{\partial Q}}{{\partial \phi }} \times \frac{\phi }{Q} $$
(6)

where ϕ is the aridity index and expressed as ϕ = ET0 /P. Q is the streamflow (in millimeters). Essentially, a positive or negative sensitivity coefficient indicates that Q will increase or decrease as ϕ increases, respectively. A sensitivity coefficient of −0.1 would mean that a 10 % increase of aridity would lead to a decrease in streamflow by 1 %. This sensitivity analysis has been widely used in the hydro-climatic studies (e.g., Hupet and Vanclooster 2001; Gong et al. 2006).

The streamflow records into DRB and MRB from 1960 to 2005 were divided into two periods by the Mann–Kendall method (periods I and II). The contribution of change in aridity index to streamflow between the two periods is the product of streamflow sensitivity to aridity index and the change rate of aridity index. Thus, the contribution of change in aridity index to streamflow can be calculated as:

$$ {C_{\phi }} = {S_{\phi }} \times \frac{{{\phi_2} - {\phi_1}}}{{{\phi_1}}} $$
(7a)

and the contribution rate can be estimated as

$$ {\rho_{\phi }} = {{{{C_{\phi }}}} \left/ {{\left( {\frac{{{Q_2} - {Q_1}}}{{{Q_1}}}} \right)}} \right.} = {S_{\phi }} \times {{{\frac{{{\phi_2} - {\phi_1}}}{{{\phi_1}}}}} \left/ {{\left( {\frac{{{Q_2} - {Q_1}}}{{{Q_1}}}} \right)}} \right.} $$
(7b)

where C ϕ is the contribution of change in aridity index to change in streamflow (unit, in percent). ϕ 1 and ϕ 2 is the average aridity index in periods I and II, respectively. ρ ϕ is the contribution rate of change in aridity index to change in streamflow. Q 1 and Q 2 is the average streamflow in the two periods, respectively.

The water balance for a catchment can be written as:

$$ P = Q + {E_{\text{a}}} + \Delta S $$
(8)

where P is precipitation, E a is evapotranspiration, Q is the streamflow, and ΔS is change in catchment water storage. Over a long period of time (i.e., 10 years), it is reasonable to assume ΔS is zero. According to the Budyko hypothesis (Budyko 1963), E a can be calculated as:

$$ {E_{\text{a}}} = P \times F\left( \phi \right) $$
(9)

where F(ϕ) is the function of ϕ and the detailed expressions of F(ϕ) are listed in Table 1. Based on Eqs. 8 and 9, Q can be written as:

Table 1 Expressions for estimating annual evapotranspiration based on the Budyko hypothesis and the mathematical expressions of F′(ϕ) for all the five formulas
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$$ {\text{Q}} = P - PF\left( \phi \right) $$
(10)

Following Eq. 10, the partial derivative of Q to ϕ can be calculated as:

$$ \frac{{\partial Q}}{{\partial \phi }} = \frac{{\partial P}}{{\partial \phi }} \times \left( {1 - F\left( \phi \right)} \right) - PF\prime \left( \phi \right) $$
(11)

Considering ϕ is the function of P and ET0, the partial derivative of P to ϕ can be calculated as:

$$ \frac{{\partial P}}{{\partial \phi }} = {{{ - {\text{E}}{{\text{T}}_0}}} \left/ {{{\phi^2}}} \right.} = {{{ - {P^2}}} \left/ {{{\text{E}}{{\text{T}}_0}}} \right.} $$
(12)

Thus, based on Eqs. 11 and 12, the partial derivative of Q to ϕ can be rewritten as:

$$ \frac{{\partial Q}}{{\partial \phi }} = - \frac{{{P^2}}}{{{\text{E}}{{\text{T}}_0}}}\left( {1 - F\left( \phi \right)} \right) - PF\prime \left( \phi \right) $$
(13)

Therefore, based on Eqs. 6 and 13, the sensitivity coefficient of streamflow to aridity index can be calculated as:

$$ {S_{\phi }} = - \frac{P}{Q}\left( {1 - F\left( \phi \right)} \right) - \frac{{{\text{E}}{{\text{T}}_{{0}}}}}{Q}F\prime \left( \phi \right) $$
(14)

4 Results

4.1 Changes in streamflow and aridity index

Figure 3a, b shows the variation of annual streamflow of the DRB and MRB from 1960 to 2005, respectively. The average annual streamflow of the DRB was 394.06 mm. The wettest year was observed in 1964 with annual streamflow of 828.25 mm while the driest year was in 1999 with annual streamflow of 275.75 mm in the DRB. The average annual streamflow of the MRB was 50.58 mm. The wettest year was observed in 1974 with annual streamflow of 135.91 mm while the driest year was in 2002 with annual streamflow of 8.75 mm in the MRB. The average streamflow of the DRB was about 7.8 times of the MRB, which is partially the reason why the SNWDP is necessary. Figure 3c, d shows the Mann–Kendall test of the changes of the streamflow records in the two basins. Abrupt change points for annual streamflow records of the DRB and MRB were identified around the year 1990 and 1980, respectively (α = 0.05). In the DRB, the average annual streamflow was 426.85 mm from 1951 to 1989 (period I) and decreased to 332.58 mm from 1990 to 2005 (period II). The average annual streamflow in period II decreased by 94.27 mm with a relative change of −22.1 % in the DRB (Table 2). In the MRB, the average annual streamflow was 69.70 mm from 1951 to 1979 (period I), and decreased to 35.87 mm from 1980 to 2005 (period II). The average annual streamflow in the period II decreased by 33.82 mm with a relative change of −48.5 % compared with period I in the MRB. The relative decrease of streamflow in the MRB was much larger than that in the DMB. Figure 3e, f shows the variations of aridity index in the DRB and MRB from 1960 to 2005. There were general increasing trends of the aridity index in the DRB and MRB (i.e., both basins became drier), with relative changes of 7.6 and 5.1 % between the two periods, respectively.

Fig. 3
figure 3

Variations of annual streamflow in the DRB (a) and the MRB (b) from 1960 to 2005. The Mann–Kendall analysis of annual streamflow in the DRB (c) and the MRB (d). The black horizontal dotted lines represent the critical values corresponding to the 5 % significance level. The cross points of C1 and C2 at 1990 and 1980 were the start point of abrupt change in streamflow for the DRB and the MRB, respectively. Variations of annual aridity index in the DRB (e) and the MRB (f) from 1960 to 2005. The red horizontal dotted lines represent the averages of the corresponding periods

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Table 2 Hydro-climatic statistics of the two periods in the Danjiangkou Reservoir basin (DRB) and Miyun Reservoir basin (MRB)
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4.2 Sensitivity of streamflow to aridity index

Figure 4a and b show the variation of annual sensitivity coefficient of streamflow to aridity index calculated by the five forms of F(ϕ) based on the Budyko hypothesis in the DRB and MRB from 1960 to 2005, respectively. The average value of the sensitivity coefficient varied from −2.22 to −1.91 in the DRB and from −3.45 to −2.47 in the MRB by the five formulas (Table 3). The sensitivity coefficients calculated by different formulas based on the Budyko hypothesis have slight differences because the basic principle of the formulas is the same. The sensitivity coefficient calculated by Zhang et al. (2001) formula was taken as an example to describe the result. The average values of the sensitivity coefficient in the two basins were −2.00 and −3.01, respectively. It indicated that streamflow would decrease by 20.0 % in the DRB and 30.1 % in the MRB if the aridity index increased by 10 %. In addition, the absolute value of the sensitivity coefficient in the MRB was larger than that in the DRB, indicating that streamflow in the MRB was more sensitive to aridity index than that in the DRB. It is noteworthy that the sensitivity coefficients were not constant, and the absolute value of the sensitivity coefficient increased at the rate of 0.08 and 0.13 year−1 in the DRB and MRB from 1960 to 2005, respectively. This finding suggests that the streamflows in the two basins have been more and more sensitive to the change in aridity index in the study period.

Fig. 4
figure 4

Variation of annual sensitivity coefficient of streamflow to aridity index calculated by the five forms of F(ϕ) based on the Budyko hypothesis in the DRB (a) and the MRB (b) from 1960 to 2005. The red dotted lines represent the linear trends fitted to the period

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Table 3 The sensitivity coefficient of streamflow to aridity index in the Danjiangkou Reservoir basin (DRB) and Miyun Reservoir basin (MRB) and the contributions of change in aridity index on streamflow in the two basins
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4.3 Impacts of climatic variation and human activities on streamflow

The contribution and contribution rate of change in aridity index to the change in streamflow were calculated according to Eqs. 7a and 7b with the results shown in Table 3. Following the formula of Zhang et al. (2001), the 7.6 and 5.1 % increase of aridity index in period II led to streamflow decreasing by 15.2 and 15.3 % in the DRB and MRB, respectively. Table 2 shows that the relative decrease of streamflow in period II compared with period I was −22.1 and −48.5 % in the DRB and MRB, respectively. Therefore, the increase in the aridity index contributed 68.8 and 31.5 % of the total decrease in streamflow in the two basins, respectively. Increase in aridity index associated with climatic variation was the main reason of the decrease in streamflow in the DRB, while it was not the main reason of decreasing streamflow in the MRB. Other factors such as human activities could lead to the decrease in streamflow in the MRB.

In the MRB, human activities mainly included the soil and water conservation program, land use/cover change and increasing water demands (Chaobai River Management Bureau of Beijing 2004). A soil water conservation program including reforestation has been implemented in the MRB since the 1980s. Table 4 shows the land use in the MRB in the year of 1980 and 1995. The coverage of forest increased from 48.2 % in 1980 to 65.0 % in 1995 while grassland and cultivated land decreased from 27.5 and 21.9 to 15.7 and 16.9 %, respectively. In addition, the water demands in the MRB also increased substantially since the 1980s. The annual average “direct withdrawal of water” from the upstream of the Miyun Reservoir increased from 0.03 km3 in 1970s to 0.18 km3 in 1990s according to the result of the “Second National Water Resources Assessment Project” (Ren 2007). Therefore, the impacts of human activities on streamflow were significant in the MRB. Wang et al. (2009) also found that human activities such as land use/cover change and increasing water demands contributed most of the decrease in streamflow in the MRB based on a monthly water balance model.

Table 4 The proportion of land use in the Danjiangkou Reservoir basin (DRB) and Miyun Reservoir basin (MRB) between 1980 and 1995
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The DRB is located in mountainous areas and has low population density. The water demands in the DRB did not change significantly. In addition, the land use and land cover in the DRB nearly remained the same between 1980 and 1995. Table 4 shows that largest change rate in land use/cover was observed for forest, which increased by only 0.97 % between 1980 and 1995. Therefore, the impacts of human activities on streamflow were relatively small compared with the impacts of climatic variation. As a result, climatic variation was the main reason of the decrease in streamflow in the DRB.

5 Discussion

5.1 Uncertainties

The uncertainties of evaluating the climatic variation effects on streamflow using aridity index existed in this study. The empirical formulas based on Budyko hypothesis (Table 1) express the relationship between evapotranspiration and precipitation at the annual timescale. Therefore, Eqs. 8 and 10 can only be applied to the annual streamflow responding to climatic variation. In addition, the sensitivity coefficients calculated by different formulas based on the Budyko hypothesis had slight differences. For example, the average sensitivity coefficient calculated by the equation of Budyko (1963) was −2.69 in MRB while it was −2.47 by the equation of Turc (1953) and Pike (1964). Accordingly, the contribution rate of change in aridity index to the change in streamflow calculated by the two formulas was 28.3 and 26.0 %, respectively (Table 3).

5.2 Sensitivity coefficient of streamflow to aridity index and change in aridity index

In this study, the sensitivity coefficient of streamflow to aridity index was considered as the streamflow sensitivity to climatic variation. The larger absolute value of the sensitivity coefficient indicates that the basin is more sensitive to climatic variation. According to Eq. 14, the sensitivity coefficient of streamflow to aridity index is the function of precipitation, potential evapotranspiration and streamflow. In addition, the absolute value of the sensitivity coefficient is proportional to precipitation and potential evapotranspiration while it is inversely proportional to streamflow. This indicates that basins that have small values of streamflow are more sensitive to climatic variation than basins with large values of streamflow. Table 2 shows that the annual average streamflow in the DRB was much larger than that in the MRB. Therefore, the sensitivity coefficient of streamflow to aridity index in MRB is larger than that in the DRB, and the MRB is more sensitive to climatic variation than the DRB.

Decrease in potential evapotranspiration could lead to decrease in aridity index, while decrease in precipitation could lead to increase in aridity index. Table 2 shows that average annual precipitation decreased from 848.83 mm in period I to 782.13 mm in period II while potential evapotranspiration almost remained unchanged between the two periods in the DRB. Therefore, aridity index increased in the DRB, and the DRB became drier in period II. In the MRB, both potential evapotranspiration and precipitation decreased in period II, and the amplitude of decrease in precipitation was larger than that in potential evapotranspiration. Therefore, aridity index also increased in the MRB.

5.3 Impacts of decreasing streamflows on the central route of the SNWDP

The DRB is the headwater source of the central route of China’s SNWDP. Water diversion would inevitably have negative influence on the downstream of the Hanjiang River. The dramatic decrease in streamflow in the DRB would aggravate the negative influence. The SNWDP should have appropriate management guidance to mitigate the negative impact under the background of decreasing streamflow in the DRB. In addition, it is noticeable that annual streamflow into the DRB was only 275.75 mm (17.1 billion m3) in the driest year of 1999. Thus, consistently diverting 13.0 billion m3 of water is at great risk in certain years. Therefore, the water managers in the MRB should have adaptive measures when water resources in the DRB may not be sufficient for diversion in certain years. In the MRB, there is room to improve water conservation and increase irrigation efficiency. Irrigation efficiency was only about 48 % in MRB in 2009 (Ren 2007) compared to nearly 60 % in Israel and Japan (Postel and Vickers 2004). Conserving water and improving irrigation efficiencies would alleviate the water pressure in the MRB.

6 Conclusions

The changes in streamflow were analyzed and the sensitivity of streamflow to aridity index was evaluated in the DRB and MRB in this study. The Mann-Kendall test indicated that abrupt change points for annual streamflow series were identified around the year 1990 and 1980 in the DRB and MRB, respectively. The average annual streamflow decreased 22.1 % in the DRB since 1990, while it decreased 48.5 % in the MRB since 1980. The 7.6 % of increase in aridity index led to streamflow decreasing by 15.2 % since 1990 in the DRB while the 5.1 % increase in aridity index led to streamflow decreasing by 15.3 % since 1980 in the MRB. The increase in aridity index contributed 68.8 and 31.5 % of the total decrease in streamflow in the two basins, respectively. In the MRB, large change rate of land use was observed and the impacts of human activities on streamflow were significant. However, the DRB is located in mountainous areas with low population density, and the impacts of human activities on streamflow were not significant. Therefore, climatic variation was the main reason of the decrease in streamflow in the DRB while the decreasing streamflow was more associated with human activities such as increased forest area and water demands in the MRB.