Quantitative Contribution of Climate Change and Human Activities to Runoff Changes in the Wei River Basin, China

Surface runoff from the Wei River basin, the largest tributary of the Yellow River in China, has dramatically decreased over last 51 years from 1958 to 2008. Climate change and human activities have been identified as the two main reasons for the decrease in runoff. The study period is split into two sub-periods (1958–1989 and 1990–2008) using the Mann–Kendall jump test. This study develops an improved climate elasticity method based on the original climate elasticity method, and conducts a quantitative assessment of the impact of climate change and human activities on the runoff decrease in the Wei River basin. The results from the original climate elasticity method show that climatic impacts contribute 37–40 % to the decrease in runoff, while human impacts contribute 60–63 %. In contrast, the results from the improved climate elasticity method yield a climatic contribution to runoff decrease of 22–29 % and a human contribution of 71–78 %. A discussion of the simulation reliability and uncertainty concludes that the improved climate elasticity method has a better mechanism and can provide more reasonable results.


Introduction
Climate change is expected to extensively alter global hydrological cycles (Legesse et al., 2003;Milly et al., 2005;Piao et al., 2007;Tang et al., 2013) by primarily changing the pattern of precipitation (IPCC, 2013;Sun et al., 2012).After the falling of precipitation into basins, human activities in-cluding land use change, dam construction, river diversion, and other engineering and management practices also modify hydrological cycles locally and therefore temporal and spatial distribution of water resources (Govinda, 1995;Milly et al., 2005).Quantitatively assessing the influence of climate change and human activities on surface runoff is vital for sustainable water resources management.
Quantitative evaluation of the effects of climate change and human activities on runoff has yielded significant results, but with complex regional patterns.For instance, Zhang et al. (2008) used the sensitivity of runoff to precipitation and potential evaporation to study the response of runoff to changes in climate and land use/cover in the Loess Plateau of China and pointed out that LUCC (land use and land cover change) accounted for over 50 % of the reduction in mean annual runoff in 8 out of 11 catchments.Bao et al. (2012) discussed the reasons for runoff changes in the Haihe River basin, analyzed the influence of human activities through the VIC model, and then proved human activities were the main driving force for the reduction of water resources.Wang et al. (2009) established a distributed monthly water balance model (DTVGM) to analyze the Chaobai River basin upstream of Miyun Reservoir in north China, and concluded that human activities were therefore the main cause of runoff changes.Ma et al. (2008) estimated that the effects of climate change accounted for over 64 % of the mean annual runoff reduction in the Shiyang River in the arid region of northwest China.For the same basin, human activities and climate change may have different influences on runoff for different periods.For example, Qiu et al. (2012) analyzed the influence of climate change and human activities on water resources in north China and found that in the 1970s-1980s the effects of climate change were dominant, but in the late 1980s and early 1990s the effects of the two factors were similar, and since the 1990s the influence of human activities has been slightly higher at around 55 %.Guo et al. (2008) employed the SWAT model to analyze the annual and seasonal runoff variability caused by climate change and human activities and found that the main influencing factor on annual runoff was climate change, but that changing land use was the main influence on seasonal runoff changes.
So far, there are many different methods used to evaluate and separate the effects of the two factors (Sun et al., 2014).One such method is based on physical processes or physical mechanisms.This method controls the evolution of the various elements and analyzes the changes in driving factors and contributions in a physical process simulation.The approach may be physically sound but requires major efforts on model calibration and can lead to remarkably different results because of uncertainty in model structure and parameter estimation (Nash and Gleick, 1991;Revelle and Waggoner, 1983;Schaake, 1990;Vogel et al., 1999).Other methods can be classified as statistical data analysis methods, such as the climate elasticity method used in this paper.The statistical data analysis methods are based on mean annual change trends in long time series, and provide generalized relationships which do not consider species differences.This approach incorporates measured or observed data via a variety of data validation techniques, and analyzes the contributions of different factors on different processes.The method is relatively simple, but requires a large volume of high-quality data (Risbey and Entekhabi, 1996).
Many studies have proven that the climate elasticity method is reasonable and credible (Chen et al., 2014).Chiew (2006) evaluated rainfall elasticity of streamflow in 219 catchments across Australia using the nonparametric climate elasticity estimator and compared the estimates with results obtained from the conceptual rainfall-runoff model SIMHYD, showing a consistent relationship between climate elasticity values estimated using the rainfall-runoff model and the nonparametric estimator.Ma et al. (2010) used a distributed hydrological model (GBHM) and a climate elasticity model to conduct a quantitative assessment of the impacts of climate change and human activities on inflow into a reservoir.The GBHM simulation and climate elasticity model showed that climate change accounts for about 55 and 51 % of the reservoir inflow reduction, respectively.Hu et al. (2012) analyzed the impacts of climate change and human activities on the Baiyangdian upstream runoff, using two assessment methodologies (climate elasticity and hydrological modeling).The climate elasticity method was implemented at the annual scale and was computationally relatively simple; it needed fewer data and parameters to calculate the impacts of climate change on an-nual runoff.The hydrological model was implemented at the daily scale, and therefore needed more data and parameters but yielded more detailed, high temporal resolution results.These two independent methods based on different timescales obtained consistent results.Thus, the climate elasticity method is considered to be an important indicator for quantifying the sensitivity of runoff to climate change and for separating the effects of natural and anthropogenic factors at catchment scale (Dooge et al., 1999;Fu et al., 2007;Milly and Dunne, 2002;Sankarasubramanian et al., 2001;Schaake, 1990;Zheng et al., 2009).However, the main point for the climate elasticity method's previous research indicates is that the method is used to separate the sensitivity of runoff to climate change without considering the human activities directly, and furthermore the accuracy of the original climate elasticity method should be improved.
In this paper we improve the climate elasticity approach by adding the influence of human activities to evaluate the hydrological consequences of climate change and human activities.To compare the original and improved climate elasticity approaches, we choose the Wei River basin as a case study.The application results have a great strategic meaning in the regional economic development and the development of west China (Song et al., 2007).The rest of the paper is structured as follows: Sect. 2 describes the study area and data; Sect. 3 presents the methodology; and results and discussion are in Sect. 4. The conclusions are presented in Sect. 5.

Study area
The Wei River is the largest tributary in the Yellow River.It originates from Niaoshu Mountain, and runs into the Yellow River at Tongguan.The basin is located between 104 • 00 E-110 • 20 E and 33 • 50 N-37 • 18 N, with a length of 818 km and a drainage area of 1.35 × 10 5 km 2 .
The Wei River basin is located in temperate continental monsoon climate region.The climate is cold, dry and rainless in winter controlled by the Mongolia high, while hot and rainy in summer affected by the western Pacific subtropical high.The mean air temperature is 7.8 to 13.5 • C, the mean annual precipitation is 400 to 800 mm, and the mean annual potential evapotranspiration is 800 to 1000 mm.The mean annual runoff in depth is 450 to 550 mm, with the coefficient of variation falling within 0.1 to 0.2 (He et al., 2009).

Data description
This study uses the continuous daily series data from 1958 to 2008 at seven national meteorological observatory stations in and around the Wei River basin.Observed daily mean air temperature, precipitation and solar shortwave radiation could largely reflect climatic change in the region (Fig. 1).In addition, observational runoff data for 1958-2008 comes from Hua County hydrological station, located in the river outlet downstream.
The potential evapotranspiration within the watershed can be calculated using the Hargreaves method, an empirical formula which was derived using the permeameter by Hargreaves and Samani (1982) to estimate potential evapotranspiration, and most appropriate in all radiation and temperature estimation methods in north China (Luo and Rong, 2007).The expression is as follows: where E 0 represents potential evapotranspiration, mm day −1 ; T represents mean air temperature, • ; R s represents solar shortwave radiation, MJ/(m 2 day −1 ); λ represents latency for vaporing water, λ = 2.45 MJ kg −1 .

Trend analysis
In this study, the Mann-Kendall trend test is used to test the long-term trends of precipitation, evaporation and runoff in the Wei River basin.The Mann-Kendall trend test is a nonparametric statistical test method.It does not need the sample to follow any particular distribution, and is not subject to interference from a small number of outliers.Moreover, the method is relatively simple (Mann, 1945;Kendall, 1975).For a time series X which has n samples, construct variable S: where x i and x j represent the values in years i and j , i > j , n is the record length of the series, and sgn(x i − x j ) is a characterization of the function.
The statistical test value Z c is calculated by the following formula: we accept the null hypothesis, which indicates the sequence does not have a trend.If |Z c | > Z 1−α/2 , we reject the null hypothesis and conclude that the sequence does have a significant trend.Z 1−α/2 is obtained from standard normal distribution function, and α is the significance level of the test.
To test the trend of the sequence in the Mann-Kendall test, it is usually necessary to estimate the slope of the monotonic trend, estimated as follows: A positive value of β indicates a rising trend (positive rate of change with time), and vice versa for negative β.

Change-point analysis
Identifying the change-point for runoff substantially influenced by human activities is significant.Depending upon the change-point, the hydrology series could be divided into two periods: before change-point, it was regarded as having no influence from human activities, and after change-point it was believed that human activities sharply affected runoff.Under the hypothesis that the time series is independent and stochastic, we can compute the following statistics: where E(S k ) and Var(S k ) represent the mean and variance of S k , respectively.Next, the time series order is reversed (i.e., x n , x n−1 , . . ., x 1 ), and the above process is repeated to yield the statistical variables UB k (k = n, n − 1, . . ., 1), such that Next, the curves of UB k and UF k are drawn, and if the two curves have an intersection point and if the value of U at this point satisfies |U | < 1.96, then that point is regarded as a change point, with a confidence level α of 0.05.Because the time series length in this study is 51 years, we use a significance test of t test.

Original climate elasticity method
Runoff (R) can be expressed as a function of climate variables (C) and other characteristics (H ) (Hu et al., 2012): where the parameter R represents the total runoff change; and R C , R H represent the runoff changes caused by climate change and human activities, respectively.The total runoff change can be obtained from the formula R = R obs1 − R obs2 , where R obs1 and R obs2 represent the measured runoff before and after the change point, respectively.Schaake (1990) first introduced the climate elasticity method to analyze the sensitivity of runoff to climate change.Climate elasticity of runoff (ε X ) can be defined as the proportional change in runoff (R) relative to the change in climatic variables (X) (such as changes in precipitation or potential evapotranspiration) (Fu et al., 2007): According to the long-term water balance equation (R = P − E), we assume that the runoff response to climate factors is mainly caused by the precipitation and potential evapotranspiration.According to the theory of total differential equations, the differential form is as follows: where R c represents runoff change caused by climate change, P and E 0 are the change of precipitation and potential evapotranspiration, and ε P and ε E 0 are the precipitation and potential evapotranspiration elasticities of runoff, respectively.
According to the Budyko hypothesis, actual evapotranspiration (E) is a function of the dryness indices (φ = E 0 /P ), specifically E = P * F (φ), and the precipitation and potential evapotranspiration elasticities of stream flow can be expressed as (11) The following formulae (one with a parameter and the others without) for the Budyko hypothesis are often used to estimate F (φ), as shown in Table 1.
According to Table 1, the precipitation elasticity (ε p ) and potential evapotranspiration elasticity (ε E 0 ) can be determined, allowing the runoff change caused by climate change ( R c ) to be calculated, and thus the contribution of climate change can be assessed.Calibration of Zhang's (2001) formula using land cover and land use conditions yielded a parameter value of 1.5.

Improved climate elasticity method
At the catchment scale, and over a long time period, the water balance equation can be simplified as P = E + R.Here the mean annual runoff R can be divided into observed runoff and changing runoff caused by human activities, i.e., R = R obs + R H , where R obs is observed runoff.R H refers mainly to water consumption or water intake by human activities which mainly include measures of water and soil conservation, river dam construction, water intake from rivers, water transfer and so on.So the water balance equation can be expressed as Meanwhile, according to the Budyko hypothesis E = P F (φ) , φ = E 0 /P , the total differential form can be expressed as When substituted into Eq.( 12), this leads to After dividing Eq. ( 14) by R obs , we obtain the following equation: − F (φ) The climate and anthropic elasticities are calculated as follows: 16) which satisfy From Table 1 and Eq. ( 16), the elastic coefficients ε P , ε E 0 , and ε H , which respectively represent the precipitation, evapotranspiration, and human activities elasticities, can be calculated.Next, the runoff change R H caused by human activities is computed.The contribution of human activities to runoff can be expressed by P H , where P H = R H / R, thus the contribution of climate change can also be calculated.

Detection of hydrologic changes
In this study, the Mann-Kendall trend test is adopted to determine the significance of the trends in runoff, precipitation Zhang ( 2001) According to the results of trend analysis and change-point analysis, the monthly runoff data in the periods of 1958-1990 and 1990-2008  the hydrological gauging station located the river basin outlet.Vogel and Fennessey (1994) provide the details of the FDC method, which represents the relationship between the magnitude and frequency of runoff, and provides an estimate of the percentage of time a given runoff that is equal to or exceeds an historical period.The relationship between the magnitude and frequency of monthly average runoff are shown in Fig. 4, which indicates that the percentage of time runoff exceeded in the period 1958-1990 is larger than that for 1990-2008, and the runoff relative change for the two periods only have large fluctuations at percentages less than 10 % and more than 90 %. Figure 4 also implies the decrease of runoff for 1990-2008 correlates with human activities.Furthermore, the influence on decreasing runoff is facilitated by the high-flow and low-flow periods at which the percentage time runoff exceeded is less than 10 % and more than 90 %.

Original climate elasticity method
In order to evaluate the influence on runoff caused by climate change, Eq. ( 11) is first used to calculate the elasticities of precipitation and potential evapotranspiration for 1958-2008, which can be expressed as ε P and ε E 0 , respectively, as shown in Table 2.These results reveal that if precipitation decreases by 10 %, runoff will decrease by 25.8-27.7 %, and if potential evapotranspiration decreases by 10 %, runoff will increase by 15.8-17.7 %.Then, according to the calculated ε P , ε E 0 and Eq. ( 10), the runoff decrease caused by climate change can be computed.The total contribution of precipitation and potential evapotranspiration to the runoff decrease is 32.1 mm.Therefore, the contribution of climate change to the runoff decrease is 37-40 %, and the contribution of human activities is 60-63 %.

Improved climate elasticity method
In order to evaluate the influence on runoff caused by human activities, Eq. ( 16) is first used to calculate the elasticities of precipitation, potential evapotranspiration and human activities for 1958-2008, which can be expressed as ε P , ε E 0 and ε H , as shown in Table 3.We realize that if annual runoff decreases by 32.1 mm, the decrease caused by human activities is 22.9-24.9mm.So the contribution of human activities to runoff decrease is 71-78 %, and the contribution of climate change is 22-29 %.

Comparison of the simulation results
In this paper, two methods are used to analyze the causes of the runoff decrease in the Wei River basin.One is the original climate elasticity method, and the other is the improved climate elasticity method.Each method adopts two formulas based on the Budyko hypothesis (noting that one formula includes parameters and the other does not).Results are compared with each other and with those calculated by other methods, and the precision of the two methods is analyzed.Both methods are implemented at the annual timescale, and require relatively simple computation.The contributions of climate change and human activities to runoff variability can thus be computed by fewer data and parameters compared with other methods.The results of the original climate elasticity method show that the contributions of climate change and human activities to runoff variability are 37-40 % and 60-63 %, respectively.Meanwhile, corresponding contributions calculated using the improved climate elasticity method are 22-29 % and 71-78 %, respectively.Early studies showed that during the 1970-1995 period, the contribution of human activities to runoff decrease was 58.3 % in the Wei River basin (Zhang and Wang, 2007).In recent years, human activities have intensified, so that by 2008 the contribution of human activities most likely increased, and may now exceed 60 %.Gao et al. (2013) found that the contribution of human activities to reduced stream flow in the Wei River basin was even as high as 82.80 %.Zhan et al. (2014) used the SIMHYD model to partition the effects of climate change and human activities on surface runoff in the Wei River basin and found that the contribution rate of human activities to stream flow change was more than 65 %.The results of the improved climate elasticity method are closer to the existing results than those of the original, suggesting that the improved climate elasticity method, which is more adaptable and easier to implement, is much more reliable and practical.Moreover, it is important to note that the improved climate elasticity method is the first to introduce human activities' elasticity ε H . Without the trend analysis and changepoint test, the strength of the influence of human activities on runoff changes can be calculated.When calculating the contribution of human activities to runoff changes, the changepoint test is needed so that the total runoff decrease can be calculated.
The improved climate elasticity method broadens the concept of climate elasticity, and provides a more intuitive and practical formula for calculating the contribution of human activities to runoff changes.Compared with the hydrological simulation method, the climate elasticity method not only needs fewer data and parameters, and is more reliable and easier to implement, but can also be easily extended.However, its temporal resolution is low and it lacks a physical basis.There is a trend towards coupling hydrological simulations with the more reliable hydrological and meteorological statistical methods, to quantitatively study hydrological responses to climate change and human activities.

Discussion
In this paper it is assumed that over a long period of time, change in catchment storage can be neglected, so that the water balance equation can be expressed as P = E + R. It is also assumed that the Budyko curve can comparably and precisely estimate mean annual evaporation.In fact the two assumptions are fundamental and commonly used in Budykotype elasticity studies for long-term averages (Gentine et al., 2012).We do not think there is an approach that can estimate the mean annual evaporation "precisely" but if any, the Budyko curve would be comparable at least for long-term means.
The maximum daily precipitation as well as the averaged top five maximum daily precipitation for each year are estimated as shown in Fig. 5.The results show that there is no steady decreasing trend in these two measures of extreme   rainfall and distribution, while the steady decrease in runoff investigated in this study would require a steady decrease in rainfall intensity if the change in distribution is the cause.Those results are consistent with our experience with this catchment in that precipitation and potential evapotranspiration are not the only influencing factors on runoff, but instead human activities have been the main influence on the decreasing runoff.
The impacts of human activities on runoff are reflected in land use and land cover changes.Land use and land cover change is a gradual process, and the impacts on runoff also accumulate gradually.We can decrease the uncertainty of quantitative predictions by analyzing the LUCC changes in the Wei River basin in 1980, 1990, 2000, 2005 and 2007, and then checking whether the results are reasonable.The main type of land cover in the Wei River basin is cultivated land, which covers more than 50 % of the total area, followed by woodland and grassland.
By analyzing the changing areas of cultivated land and woodland and grassland in the Wei River basin in 1980, 1990, 2000, 2005 and 2007, it can be concluded that the year 1990 is the turning point in cultivated land area, since the area decreases during the 1980-1990 period, and then begins to increase again after 1990.The year 1990 is also the turn-ing point in the area of woodland and grassland area, but the corresponding trends are opposite to those of the cultivated area.Because the area of cultivated land and woodland and grassland reaches 90 %, and considering the turning points of the three types of land, the year 1990 can be regarded as a more general turning point in surface characteristics (Song et al., 2012).This decreases the uncertainty regarding 1990 as the runoff change point.
Major sources of uncertainty in the simulation associated with the climate elasticity may arise from the input data, classification of the stages, and the parameter in the Zhang (2001) formula.Precipitation data used in the models are from seven rain gauges and meteorological stations in and around the study catchment.The flow data are measured during the 1958-2008 period from the Hua County hydrological station, which is located at the downstream end of the basin, but may not sufficiently represent the whole basin.Even though the breakpoint test is found to be reasonable, there remain some uncertainties, which may be caused by the test method and artifacts when reading the results in the chart.The parameter which is very sensitive in the Zhang (2001) formula is calibrated according to the land cover and land use conditions.
Furthermore, it is essential to point out that climate change and human activities are supposed to be two mutually independent variables when separating their impacts on runoff; however, we note that land use and land cover can be influenced by both climate change and by human activities.
In this study R is divided into R obs and R H because the water intake directly from rivers is a significant amount in almost all rivers in China.However, in the original Budykotype elasticity, this part is not considered directly and the main formulae are R = ε P Then that framework is extended by including the direct influence from water intake to adapt to catchments with intense water consumption and intake, and the main formula is R = ε P We believe this is a new contribution to the climate elasticity method reported in literatures.
Decreasing runoff in many rivers in China has been reported in recent years, and the Wei River basin is one of the most serious cases.This paper aims at developing a new approach to quantifying the impact of climate variations and human activities on this decreasing runoff in the Wei River basin.The man-made changes here include land use, vegetation, and other land surface conditions, while climate change and climate variability are reflected in precipitation and potential evapotranspiration.This study uses the Mann-Kendall test to assess the temporal trends in precipitation, potential evapotranspiration and runoff, and also analyzes the point of abrupt change.On this basis, the original climate elasticity method and improved climate elasticity method are used to analyze the quantitative hydrological effects of climate change and human activities; these findings are then compared to existing results from the hydrological simulation method.This study shows the following: In the last 50 years, the runoff from the Wei River basin has obviously decreased, but the precipitation and potential evapotranspiration have shown no clear trend.Therefore it can be seen that climate factors have not obviously contributed to the runoff decrease.
From 1958 to 2008, the runoff in the Wei River basin shows an abrupt change in 1990, effectively dividing the total runoff into natural runoff processes and runoff processes affected by human activities.At the same time, this change shows that human activities have significant effects on runoff.
Human activities resulted in a shift in land use and land cover in 1990, and the type of land use and land cover has a great influence on runoff.This illustrates that human activities, especially those causing land use and land cover change, are the main reason for the runoff decrease.
The original climate elasticity method shows that the contributions of climate change and human activities to runoff decrease are 37-40 % and 60-63 %, respectively, but the improved climate elasticity method indicated that the contributions of climate change and human activities to runoff decrease are 22-29 % and 71-78 %, respectively.The result of the improved climate elasticity method is closer to those results based on comprehensive hydrological models, thereby demonstrating that human activities are the main reason for the runoff decrease in the Wei River basin.

Figure 1 .
Figure 1.Location of the meteorological and hydrological stations used in this study.

Figure 2 .
Figure 2. Time series of annual precipitation, annual potential evapotranspiration and annual runoff in the Wei River basin from 1958 to 2008.

Figure 3 Figure 4 Figure 3 .
Figure 3 The result of the abrupt change point test in the Wei river basin 593 594

Figure 4 .
Figure 4. Flow duration curves under different periods in the Wei River basin.

600Figure 5 Figure 5 .
Figure 5 The top five maximum daily precipitation and the maximum daily precipitation curves 601 Figure 5.The top five maximum daily precipitation and the maximum daily precipitation curves.
represents the combined results of terrain, soil, land use/land cover and human activities (such as artificial water transfer).If the topography and soil in the study area remain constant during the study period, then H can represent human activities.So the runoff change can be expressed as www.hydrol-earth-syst-sci.net/18/3069/2014/ Hydrol.Earth Syst.Sci., 18, 3069-3077, 2014where the parameter H

Table 1 .
Different formulae for the Budyko hypothesis.

Table 2 .
Results of the original climate elasticity method.

Table 3 .
Results of the improved climate elasticity method.