The historic streamflow series can be split into subseries from a year before which human activity is negligible. The record years prior to this break year are defined as baseline period, while the record years after this break year are defined as changed period. The difference between the mean annual streamflow during changed period (Q2) and the mean annual streamflow during baseline period (Q1) can represent the total change of streamflow (ΔQ) after the break year. The ΔQ can be regarded as a function of climatic variables and integrated effects of topography, soil, land use/land cover and human activities like water withdrawing. Under the assumption that topography and soil of the study area did not vary during the study period, ΔQ could be referred to a combination of climate variability and human activity, and can be estimated as formulation (Eq. ): ΔQ=Q2-Q1, where ΔQ is the total change in the mean annual streamflow, Q1 and Q2 are the average annual streamflows before and after an abrupt change, respectively.

The total change in mean annual streamflow can be estimated as ΔQ=ΔQC+ΔQH, where ΔQC and ΔQH are the changes in the mean annual streamflow due to climate and human activities, respectively.

The concept of streamflow elasticity was firstly introduced by Schaake (1990) to evaluate the sensitivity of streamflow to climate changes. It represents the proportional change in streamflow divided by the proportional change in a climatic variable (X) such as precipitation or potential evapotranspiration and is expressed as ε=∂Q/Q∂X/X. Thus, precipitation elasticity and evapotranspiration elasticity of streamflow were defined by Schaake (1990) as εP(P,Q)=dQ/QdP/P=dQdPPQ,εE0=dQ/QdE0/E0, where P, E0 and Q were precipitation, potential evapotranspiration and streamflow, respectively. εP and εE0 are the elasticity of streamflow with respect to P and E0. Changes of these factors could lead to streamflow variation and the relationship can be estimated as (Milly and Dunne, 2002): ΔQC=εPΔP/P+εE0ΔE0/E0Q, where ΔP and ΔE0 are the changes in precipitation and potential evapotranspiration, and εP+εE0=1. To estimate ΔQC using Eq. (), one needs to estimate precipitation elasticity of streamflow εP. In this paper, Budyko hypothesis was used to estimate εP.

The Budyko hypothesis (Yang et al., 2008; Teng et al., 2012) produces a simplified but powerful coupled water–energy balance method to partition the precipitation into evapotranspiration and streamflow. It is a holistic approach that assumes the equilibrium water balance is controlled by water availability and atmospheric demand. The water availability can be approximated by precipitation, the atmospheric demand represents the maximum possible evapotranspiration and is often equated with potential evapotranspiration. According to the long-term water balance equation (Q=P-Ea) and the Budyko hypothesis, the actual evapotranspiration (Ea) is a function of aridity index (Φ=E0/P), and the precipitation and potential evapotranspiration elasticity of streamflow can be expressed as (Arora, 2002; Dooge et al., 1999): εP=1+∅F′(∅)/(1-F(∅))andεP+εE0=1. A couple of mathematical functions were proposed to represent the Budyko hypothesis (e.g., Fu, 1996; Milly, 1993). We use the Budyko formulation of Fu. Fu (1981) combined dimensional analysis with mathematical reasoning and developed analytical solutions for mean annual actual evapotranspiration: F(∅)=1+∅-(1+∅w)1/w, where w is a model parameter related to vegetation type, soil hydraulic property, and topography (Fu, 1996). w was set to 2.0 according to the land use and land cover status in the study area.

Hydrological models can also be used to assess the impacts of climate change on streamflow. A hydrologic model was calibrated and validated using data during baseline period, to estimate ΔQC or ΔQH. The model was run using climate (e.g., precipitation and temperature) during changed period with human activity (i.e., land use and management) and during the baseline period. ΔQC is estimated as the difference of the mean annual average of simulated streamflow during changed period than the mean annual average of simulated streamflow during baseline period, whereas, ΔQH is estimated as the difference of the mean annual average of simulated streamflow during changed period than the mean annual average of observed streamflow during changed period.

TOPMODEL (Beven and Kirkby, 1979) is a semi-distributed variable contributing area hydrological model. It is based on simple physical reasoning and assumes that there is a steady transfer of water in the saturated zone along hillslopes, with a water table nearly parallel to the ground surface. It considers two stream flow sources: (shallow) groundwater and saturation overland flow. The model assumes an exponential decay of soil transmissivity with increasing water table depth and considers two main parameters for the dynamics of the saturated store: the recession parameter m [L] and the average soil transmissivity at saturation T [LT-1]. The classical form for the topographic index that follows from the exponential assumption, λi=ln⁡(a/tan⁡b) was used, where a is the drained area per unit length of contour curve, and b is the topographic gradient. All points in the catchment with the same topographic index are predicted as having the same deficit, i.e. they are considered as hydrologically similar. Since the early 1990s, TOPMODEL has been widely applied to watersheds all over the world because it can provide spatially distributed hydrologic information with available input requirements (e.g., Digital Elevation Model (DEM) data) (Seibert et al.,1997; Chen and Wu, 2012; Furusho et al., 2013). Also, some papers have applied the TOPMODEL in semi-arid area basin, such as the Yellow River in China, and the results show that this model is applicable in a wide range of environments (Xiong et al., 2004; Boston et al., 2004; Gumindoga et al., 2015).

The VIC model is a large-scale hydrologic model, originally developed at the University of Washington (Liang et al., 1994; Grimson et al., 2013; Gao et al., 2011). The hydrological processes of the model includes interaction of the atmosphere with underlying vegetation and soils, where the dynamic water and energy fluxes are considered. One distinguishing characteristic of the VIC model is that it represents the sub-grid spatial heterogeneity of precipitation with sub-grid spatial variability of soil infiltration capacity. A variable infiltration curve (Xinanjiang model citation) is used to represent the sub-grid variability of soil infiltration capability under different land cover and soil types. Three types of evaporation are considered in the model: evaporation from the canopy layer of each vegetation class, transpiration from each of the vegetation classes, and bare soil evaporation. VIC model has been successfully applied to assess the impact of climate change on hydrology and water resources in China (Wang et al., 2010; Bao et al., 2012; Su and Xie, 2003).

The regional average precipitation, potential evaporation and temperature in the JRB during 1960–2010 was calculated by using the Tyson polygon method of the ArcGIS 9.3 according to the corresponding data of ten hydrometeorology stations.

Both the annual observed precipitation in the JRB and streamflow at Zhangjiashan station showed a statistically decreasing trend (Fig. 3), while the streamflow had a larger decrease. The values of the regression slope were respectively -1.44 and -0.58. The annual mean value of runoff was 43.47 mm from 1960 to 1990, and reduced by 17.39 % compared with the multi-year average streamflow. The average annual streamflow was 27.05 mm during 1991–2010 reduced by -26.96 %, therefore, the speed of streamflow decrease was higher since 1990. The three-year moving curve showed that precipitation and streamflow fluctuation was similar, which indicated that precipitation was the main source of streamflow. The statistical results of precipitation, streamflow and runoff coefficient in JRB were listed in Table 1. The maximum of precipitation and streamflow appeared in the same time of 1964, however the minimum occurred in different years which resulted from water withdrawl and other reasons such as changes in underground water. The precipitation and streamflow during flood season (from July to October) accounted for 64.21 and 59.17 %, respectively, and the proportion of dry period (from November to March of next year) was 6.15 and 17.57 %, respectively. The proportion of rainfall that becomes runoff is low, with a mean annual runoff ratio of 0.07, but increases during wet years.

The result of Mann–Kendall's test showed the same decreasing trend for annual precipitation and streamflow in JRB from 1960 to 2010. The Z value of streamflow and precipitation was respectively -4.26 and -1.39 at confident level of 99 and 90 %, which means the significant decreasing trend for streamflow and insignificant for precipitation at a=0.05 level.

Table 2 showed the monthly and seasonaly potential evaporation and temperature in the JRB, which indicated that the evaporation (122 mm) and temperature (20.7 ∘C) in summer are much higher than other three seasons, and the maximum value of evaporation and temperature appeared in June and July respectively. The inter-annual variation and characteristic values of evaporation and temperature were shown in Fig. 4 and Table 3. The mean annual evaporation in 80s (822 mm) has decreased compared with 60s values (861 mm), and started to grow slowly in 90s (973 mm). Temperature value showed a slight upward trend in the 70s, 80s, and had a sharp upward trend in the 90s era. The Z value of evaporation and temperature for Mann–Kendall's test were 0.4 and 4.12 respectively, which means evaporation presents an insignificant increasing trend, but the temperature has a significant increasing trend.

In this study, two hydrological models, TOPMODEL and VIC model, are used to investigate the effects of climate variability and human activity on streamflow. The original TOPMODEL has four parameters, i.e. the maximum allowable root storage deficit (SRmax), the transmissivity of the soil in saturated state (T), the maximum moisture max deficit (Szm), and the recharger delay parameter (Td). There are six parameters we used in the calibration of the VIC model. These include three baseflow parameters: Dm, Ws, and Ds; the variable soil moisture capacity curve parameter: b; and two parameters, d2 and d3, that controls the thickness of the second and third soil layer, respectively. There was little human activity in the JRB prior to 1970, so we have taken 1960–1970 as the baseline period for this study. The models were calibrated using the historical data from 1960 to 1966 and validated against the observation during the period of 1967–1970. During the calibration, adjustments were made to minimize the sum of squares of the difference between the modelled and recorded monthly streamflows. Nash–Sutcliffe efficiency coefficients (NSE) and relative Water Balance Error percentage (WBE) were used for the model assessment using observed data and model estimates.

During model simulation, the digital elevation quadrangles at 40 m resolution with study area was used (Fig. 5). In the TOPMODEL, several sub-basins were divided according to the flow accumulation by means of ArcGIS, and the flow direction, flow accumulation were extracted in ARCGIS to calculate the topographic index-area ratio of sub-basin. Monthly precipitation, potential evapotranspiration and observed streamflow acted as input data. Figure 6 shows simulated and recorded streamflow for the calibration and validation period. A calibrated VIC model was also employed to separate hydrological impacts of land use change and climate change. The VIC model was used for streamflow simulation at a 0.5∘ spatial and daily temporal resolution in the JRB (Fig. 5). Figure 6 shows simulated and observed streamflow for the calibration and validation period with outputs computed on a monthly basis.

In the scatter plots in Fig. 7 the observed monthly streamflow was plotted along the x axis and the model simulated streamflow (calibration and validation) were plotted along the y axis. The scatter plots in Fig. 7 showed that both the hydrological models performed reasonably well in model calibration with high NSE values and low WBE values. The correlation of simulated streamflow and measured streamflow was higher in calibration period, R value exceeds 0.8.The observed and simulated streamflow over the non-calibration period was compared to determine the suitability of the model for this study. The validation NSE and WBE values (see Fig. 7) suggested that both the rainfall–runoff models and the calibration method used in this study are robust for the calibrated model to be used over an independent simulation period adequately. Also, the results justified the suitability of the models applied for assessing the change in streamflow due to climate variability and human activity.

The calibrated model parameters for both the models from baseline periods of 1960 to 1970 were used with the meteorological time series to simulate streamflow for the changed period of 1971–2010, and to investigate the effects of climate variability and human activity. The scatter plots in Figs. 8 and 9 showed the comparison of the simulated and observed monthly and annual streamflows time series for the JRB for the entire modelling period (1971–2010) for the TOPMODEL and VIC model respectively.

The model simulation results showed that streamflow had a strong response to the environment change after 1970. In the scatter plots in Fig. 8, the simulated monthly streamflow values were mostly above the 1:1 line indicating that the simulated streamflow was much higher than the observed streamflow for most of the months. The time series plots in Fig. 9 showed that the simulated annual runoff values were always higher than the observed streamflow. The effect of climate variability has been eliminated from the simulations for the changed periods by using the actual observed climate to drive the calibrated models. The difference in observed and simulated streamflow during the changed period is due to the difference in land cover and other human activities. The results indicated that human activity has caused significant reduction in streamflow, and these results were consistent with the finding (Chang et al., 2014; Tang et al., 2013; Zhan et al., 2014).

To separate and quantify the effects of human activity on streamflow after 1970, the simulated streamflow for the two models were compared against the observed values during baseline and changed period (methodology details in Sect. 3.1). The differences in observed streamflow values during baseline period and changed periods are caused by the differences in climatic conditions and human activity. Tables 4 and 5 summarized the mean annual statistics of observed and simulated streamflows for different periods of 1970s, 1980s 1990s and 2000s. The third column provided the values for ΔQ which was the difference between observed streamflow (QB) during changed periods and baseline. The fourth column showed the simulated streamflow (QS) for the changed periods when using climate and calibrated parameter values from the baseline period. ΔQH was the difference between QB and QS for changed periods, and ΔQC was the difference between QS for changed period and QB of baseline.

The results showed that the average annual streamflow for 1971–2010 (12.3×108 m3) was less than that of the baseline period (18.3×108 m3), which means the recorded streamflow in the JRB markedly decreased over the past few decades. The total reduction ΔQ in streamflow for the changed period of 1971–2010 (when compared to the baseline period) due to human activity and climate variability for JRB were 4.6×108 and 1.4×108 m3 for the TOPMODEL respectively, which was about 76.7 and 23.3 % of the total reduction. The corresponding reductions were 4.7×108 m3 (78.3 %) and 1.3×108 m3 (21.7 %) for the VIC model.

For the different periods of 1970s, 1980s,1990s and 2000s, the reductions in streamflow due to human activity were 5.6×108 m3 (81.2 % of the total change), 3.8×108 m3 (95 % of the total change), 3.0×108 m3 (52.6 % of the total change) and 6.1×108 m3 (82.4 % of the total change) for TOPMODEL model and 5.7×108 m3 (82.6 % of the total change), 4.5×108 m3 mm (112.5 % of the total change), 3.2×108 m3 mm (56.1 % of the total change) and 5.8×108 m3 mm (78.4 % of the total change) for VIC model respectively. Compared with the baseline period of 1960–1970, streamflow greatly decreased during 2001–2010. The change impacts (i.e., ΔQH and ΔQC) in 2001–2010 were about 77.4 and 22.6 % of the total reduction when averaged over the two methods.

To assess the impacts of climate variability on streamflow, the climate elasticity of streamflow was calculated using Eqs. ()–() based on the annual precipitation and annual potential evapotranspiration of the period 1971–2010. Table 6 summarized the annual precipitation (P), potential evapotranspiration (E0), precipitation elasticity (εP), evapotranspiration elasticity (εE0) of streamflow for different periods, and percentage change in streamflow results for different periods when using the elasticity-based approaches. The variation of εP was between 1.45 and 1.52, whilst the variation of εE0 was between -0.45 and -0.52. As shown in Table 6, for the period of 1971–2010, the value of εP and εE0 obtained were 1.48 and -0.48, respectively. The results indicated that a 10 % decrease in precipitation would result in 14.8 % drop in streamflow, while a 10 % decrease in potential evapotranspiration would induce 4.8 % increase of streamflow. According to Eq. (3), with the calculated εP and εE0, it can be estimated that the 6.1 mm decrease of precipitation in 1971–2010 may lessen the streamflow by 4.9 mm, meanwhile, the 7.3 mm increase in potential evapotranspiration may cause 5.1 mm decrease of streamflow.

The reductions in streamflow during 1971–2010 due to climate variability when using the Budyko framework method ranged between 7.5 and 29.9 % with a median of 19.3 % for the JRB. The maximum and minmum value of the aridity index (E0/P, Willmott and Feddema, 1992) was 1.91 and 1.53 appeared in 1991–2000 and 1981–1990 respectively. Compared with 1960–1970 baseline period, reduction in ΔQ for 1991–2000 and 1981–1990 was 5.7×108 and 4.0×108 m3, with climate variability making the greatest and smallest contributions (i.e., 29.9 and 7.5 % see Table 6).

In this paper, we used an elasticity-based analysis, TOPMODEL and VIC model to isolate hydrological impacts of human activity from that of climate variability. The climate elasticity method is relatively more simple and can be easily transplanted to other areas, and it gives a general streamflow change with less data and parameters (Ma et al., 2010). The hydrological modeling method, on the other hand, distinguishes more precisely streamflow change, such as monthly change or daily change. In this paper, the three methods were implemented independently at different time scales (climate elasticity method based on yearly scale, TOPMODEL based on monthly scale and Vic model hydrological simulation based on daily scale). For the whole JRB, the contribution ratios of climate variability in 1971–2010 were 23.3, 21.7 and 20 % from TOPMODEL, VIC hydrological modeling method and elasticity method respectively, and the mean contribution ratio is 21.7 %. The most significant climate variability impact was 2.7×108 m3 (47.4 %), 2.5×108 m3 (43.9 %) and 1.7×108 m3 (29.9 %) for the TOMODEL, VIC model and elasticity based model, appearing in the 1990s. The most significant human activity impact was 3.8×108 m3 (95 %), 4.5×108 m3 (112.5 %) and 3.7×108 m3 (92.4 %) for the TOMODEL, VIC model and elasticity based model, appearing in the 1980s. The analysis showed that the results from the two hydrological models were similar to those from the commonly used elasticity-based approach. We conclude that the three methods are in good agreement in terms of dominant contributor, i.e., human activity plays a more important role in the streamflow decrease than change in climate in the JRB. The main result of this research agrees with the findings of some other studies in Northwest China. Tang et al. (2013) used the climate elasticity method and the Soil and Water Assessment Tool (SWAT) model to evaluate the impact of climate variability on runoff in the Yellow River basin. The two methods gave consistent results. Zhan et al. (2014) developed an improved climate elasticity method based on the original climate elasticity method, and conducted a quantitative assessment of the impact of climate change and human activity on the runoff decrease in the Wei River basin. 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 %.

There are still differences in terms of the magnitude of each attributor. Compared to the results of hydrological model, TOPMODEL and VIC model, the streamflow variation caused by climate variability estimated from the elasticity-based methods was smaller and that caused by human activity was larger, which agree with the results of Li et al. (2012), Yu et al. (2013). Except for the annual precipitation change which was the most important impact on the streamflow change, the inter-annual and intra-annual precipitation variability as the second order climate effects can lead to significant change in streamflow. However, these second order climate effects cannot be taken into account in the elasticity-based methods, while can be considered in the dynamic hydrological modeling method, which may partly explain the difference of the results (Potter and Chiew, 2011).

The elasticity-based assessment of environment change on streamflow has more advantages to the hydrological modeling approach because it does not require detailed spatial input data. In this paper, the elasticity coefficient (i.e. the sensitivity coefficient of streamflow to climatic variable changes) was estimated. Whilst it was commonly suggested that catchment properties were spatially and temporally varied and were influential on streamflow of watershed (Roderick and Farquhar, 2011; Donohue et al., 2011), the errors with both model structure (Budyko equations) and the model parameter in Fu's model (w) which we have assumed to be temporally consistent caused the elasticity-based analysis to not be error-free.

For hydrological model of TOPMODEL and VIC model, due to the errors of model structure, input time series, and initial and boundary conditions, predictions of physically-based distributed models commonly contain a certain degree of uncertainty.

The result indicated that human activity was the dominant factors (about 80 %) for streamflow decrease in 1971–2010 in the study area. There were several kinds of human activities which influenced streamflow, including water conservancy projects, land use and land cover change, and development and utilization of water. The human-induced reduction in runoff in the JRB is primarily caused by soil and water conservation measures. From Table 7, it can be seen that the large-scale soil conservation area has expanded with time to prevent soil and water loss since the 1970s. As shown in Fig. 2, the amount of afforestation and level terrace land have steadily increased since 1970, and the amount of grass-planting land has been markedly increasing since 1990. As of 2000s, newly increased soil and water conservation area in the basin was comprised of 2907 km2 of terrace land, 4773 km2 of afforestation land, 1146 km2 of grassland and 52 km2 of dammed land. These soil conservation practices intercept precipitation, change local characteristics, improve the infiltration rate of water flow, slow down or retain the streamflow, and consequently delay or even reduce streamflow. Also, during the past decades, there were dramatically increase of population and irrigated area in the study area, which could have resulted in increased water withdrawal from the river. In addition, although the total comprehensive effect of soil and water conservation measures and irrigation water withdrawal was assessed in the study, evaluation of the individual effects on the hydrological regime still poses a challenge for hydrologists.