The headwater catchments of the Yellow River Basin are of great importance for the whole basin in terms of water resources, and streamflow from these catchments has decreased in the last decades. The concept of climate elasticity was used to assess the impacts of climate and land surface change on the streamflow. Results show that for the period 1960–2000 the elasticity of streamflow in relation to precipitation and potential evapotranspiration are 2.10 and −1.04, respectively, indicating that streamflow is more sensitive to precipitation than to potential evapotranspiration. However, land use change played a more important role than climate in reducing streamflow in the 1990s. It is estimated that land use change is responsible for more than 70% of the streamflow reduction in the 1990s, while climate change contributed to less than 30% of the reduction. The precipitation elasticity appears to have an inverse relationship with the runoff coefficient but a positive relationship with the aridity index, showing that the drier the catchment, the more sensitive the streamflow with respect to precipitation change.
 A number of studies have reported apparent trends in streamflow volume, both increases and decreases, in many parts of the world, and the changes in streamflow have intensified stresses on ecological and socioeconomic systems [Arnell et al., 2001; Liu and Xia, 2004], especially for regions with limited water resources such as the Yellow River Basin [Liu and Zheng, 2004; Zheng et al., 2007]. Both climate and land surface change are important factors expected to have widespread impacts on streamflow. Climate change, including changes in precipitation, temperature, vapor pressure, and wind speed, could lead to changes of streamflow directly or indirectly [Dam, 1999]. Land use and land cover change, on the other hand, is believed to have impacts on infiltration and evapotranspiration, which consequently results in changes of streamflow [Zhang et al., 2001].
 Using a nonparametric estimator of climate elasticity of streamflow, Vogel et al. [1999b] investigated the responses of streamflow to climate change for 1447 watersheds in the United States and reported that streamflow is more sensitive to precipitation changes rather than potential evapotranspiration changes. The nonparametric estimator of climate elasticity has been determined by Sankarasubramanian et al.  to be efficient and robust. More recently, Chiew  evaluated rainfall elasticity of streamflow in 219 catchments across Australia using the same nonparametric 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. To reflect the complicated nonlinear relationship among streamflow, precipitation, and temperature, Fu et al.  extended the nonparametric estimator to a two-parameter climate elasticity of streamflow to assess climate change effects on annual streamflow. The application of the modified method for two basins indicates that temperature is a critical factor controlling the regional runoff generation.
 With the intensifying human activities and climate change, the Yellow River has been confronting serious water resources problems. Attempts have been made to understand the long-term changes of water-energy balance [Yang et al., 2007] and the sensitivity of streamflow to climate change or variation in the Yellow River Basin [Fu et al., 2007]. However, it is still difficult to quantify the individual hydrological effects of climate change and land surface change.
 The purpose of this paper is to provide a framework assessing the relative contributions of climate and land surface change to changes of streamflow in the headwaters of the Yellow River Basin, which is called the “water tower” of the Yellow River Basin, contributing 35% of total water resources in the basin. The concept of climate elasticity is used with a new proposed nonparametric estimator. The estimator is evaluated in comparison to that proposed by Sankarasubramanian et al.  and that estimated on the basis of a simple water balance model with the Budyko hypothesis. The relationship between the streamflow elasticity and other hydrological indicators such as the aridity index and runoff coefficient will also be investigated.
2. Study Area and Data
 The headwaters of the Yellow River Basin (HYRB) are located in the region between 95°50′45″E and 103°28′9″E and between 32°12′11″ and 35°48′7″N with the Tangnaihai station as the outlet of the catchments (Figure 1). The catchments can be regarded as unimpaired with limited human activities. The combined drainage area of the catchments is about 121,972 km2 (15% of the whole Yellow River Basin), while the river length is about 1553 km. The altitude of most areas is between 3480 and 4680 m above sea level. Grassland covers almost 80% of the whole region, and the total area of lakes and swamps is about 2000 km2. The catchments belong to a semihumid region of the Tibetan Plateau subfrigid zone. Annual average daily temperature varies between −4 and 2°C from southeast to northwest. The annual average precipitation is about 534 mm. Of the total annual precipitation, 75–90% falls in the wet season (June–September) because of the southwest monsoon from the Bay of Bengal. Precipitation tends to decrease from southeast (∼800 mm) to northwest (∼300 mm). There are permanent snowpacks and glaciers in the southern Animaqing, Bayankala, and northern Qilian mountains. The annual average runoff is 20.5 × 109 m3 a−1 and contributes over 35% of water resources for the whole Yellow River Basin.
 The data used in this study includes annual streamflow series of Tangnaihai hydrologic stations obtained from the Yellow River Conservancy Commission (YRCC). The meteorological data from 13 stations with daily precipitation, temperature, wind speed, sunshine duration, and relative humidity were obtained from the China Meteorological Administration (CMA). All the data series are from 1960–2000. The long-term annual precipitation is obtained from the daily gauged records from 1960–2000, while potential evapotranspiration is estimated using the method proposed by Xu et al. . The method provides better definition and has been tested to provide good estimation of potential evapotranspiration in the HYRB [Sato et al., 2007]. The data set has been quality checked [Chen, 1996; Yellow River Conservancy Commission, 1997]. From the Institute of Geographic Sciences and Natural Resources Research (IGSNRR), two land use maps of 1986 and 1995 with resolution of 1 km × 1 km have been used to identify land use change in the study area. Figure 1 shows the locations of the catchment and hydrometeorological stations.
3.1. General Framework
 For unimpaired catchment with streamflow that is not subject to regulation or diversion, the streamflow can be modeled as a function of climatic variables and catchment characteristics:
where Q is streamflow; P and E0 are precipitation and potential evapotranspiration, respectively, representing dominant climate factors on hydrological cycle; and V is a factor that represents the integrated effects of catchment characteristics on streamflow. Following equation (1), changes in streamflow due to changing climate and catchment characteristics can be approximated as
where ΔQ, ΔP, ΔE0, and ΔV are changes in streamflow, precipitation, potential evapotranspiration, and catchment characteristics, respectively, with f′P = ∂Q/∂P, = ∂Q/∂E0 and f′V = ∂Q/∂V. In terms of climate change, the potential evapotranspiration instead of temperature is considered herein because potential evapotranspiration better represents effects of climate change on water balance and because it integrates the effects of temperature, wind speed, solar radiation, sunshine duration, and vapor pressure.
 On the assumption that the land surface factors are independent of the climate factors, equation (2) can be rearranged as
where ΔQC and ΔQV are changes in streamflow due to climate change and land use and land cover change, respectively. In equation (3a), ΔQ can be estimated from observed streamflow records; thus, if ΔQC or ΔQV is known, the framework can be used to separate the effect of climate change from that of land use and land cover change on streamflow.
 In this study, we first estimate the effect of climate change on streamflow (ΔQC) using the method of climate elasticity of streamflow proposed by Schaake . The climate elasticity of streamflow (ɛ) is defined by the proportional change in streamflow (Q) divided by the proportional change in a climatic variable such as precipitation or potential evapotranspiration (X) and is expressed as
where ɛP and are elasticity of streamflow with respect to precipitation and potential evapotranspiration. It is clear that ɛP = f′PP/Q and = If the relationship between streamflow and precipitation and potential evapotranspiration is known, the climate elasticity can be derived mathematically. For example, if we assume that Q = aPb, it can be shown that b is the precipitation elasticity of streamflow.
3.2. Nonparametric Estimator of Climate Elasticity
where ΔQi and ΔXi are changes of annual streamflow and the climatic variable (e.g., precipitation) with respect to long-term average of streamflow () and climate factors (), respectively. In equation (6), it should be noted that when X approaches , the denominator of the right-hand side of equation (6) approaches 0, causing a numerical problem in the estimation of ɛ. To overcome this numerical problem, the median descriptive statistics was used by Sankarasubramanian et al.  and was expressed as
where ɛ′ is the nonparametric estimator of climate elasticity of streamflow. The descriptive statistics of climate elasticity given in equation (7) were tested and were found to be robust via Monte Carlo experiments for three basins in the United States [Sankarasubramanian et al., 2001], but statistically they are weak when the sample size is small.
 In this study, an alternative nonparametric estimator of climate elasticity (ɛ) is derived to overcome the problem associated with small sample size. Rearranging equation (6), we have
Thus, the elasticity of streamflow ɛ can be regarded as the linear regression coefficient between ΔXi/ and ΔQi/. The elasticity of streamflow can then be estimated using the least squares estimator as
where ρX,Q is the correlation coefficient of X and Q and CX and CQ are coefficients of variation of X and Q, respectively. In comparison to the nonparametric estimator proposed by Sankarasubramanian et al. , the estimator defined by equation (9) shows a clear relationship with ρX,Q and CQ/CX, indicating that the higher ρX,Q and CQ/CX, the more sensitive the streamflow to the climate factors concerned.
3.3. Estimator of Climate Elasticity Based on the Budyko Hypothesis
 The climate elasticity of streamflow can also be estimated on the basis of the long-term water balance, expressed as
According to the Budyko hypothesis [Budyko, 1948], which assumes that actual evapotranspiration (Ea) is a function of aridity index (ϕ = E0/P),
As shown in equation (12), once the form of F(ϕ) is known, the climate elasticity of streamflow can be determined for any given value of the aridity index. Table 1 shows the six forms of F(ϕ) based on the Budyko hypothesis, while Figure 2 gives the relationship between precipitation elasticity of streamflow (ɛP) and aridity index (ϕ = E0/P). As shown in Figure 2, the value of ɛP increases as the aridity index increases, implying that streamflow is more sensitive to precipitation in arid regions. However, all the models show that when the aridity index is larger than 1.5, ɛP is almost unchanged except for the Schriber and Budyko models.
Table 1. Expressions for Annual Actual Evapotranspiration Estimation Based on the Budyko Hypothesis
The variables m and w are set to 2.5 and 1.0, respectively, in this study; w is plant available water coefficient.
Figure 3 shows long-term variations in annual precipitation (P), temperature (T), potential evapotranspiration (E0), and streamflow (Q) of the HYRB from 1960 to 2000. The long-term means (1960–2000) are 507 mm, −0.36°C, 768 mm, and 171 mm, respectively (Table 2). The aridity index (ϕ = E0/P) is around 1.5, representing a semihumid region.
Table 2. Climate and Streamflow Statistics of Different Periods in HYRB
T (deg C)
 For the annual streamflow in HYRB, a change point has been identified in 1990 [Zheng et al., 2007], while a change point of temperature is detected in 1986 by the moving t test method [Zheng et al., 2007]. Table 2 shows the difference of hydroclimate variables of the two periods before and after 1990. As shown in Table 2, precipitation, potential evapotranspiration, and observed streamflow of the HYRB in the 1990s is about 4.01, 3.01, and 20.19% less than that of the period 1960–1990, respectively, while temperature is 0.34°C higher. Concurrently, the variation coefficient of precipitation, potential evapotranspiration, and streamflow was reduced by 45, 44, and 17%, respectively. Although there is little change in the aridity index (0.66%), the runoff coefficient (Rc = Q/P) in the 1990s was 17% less than that in 1960–1990, indicating a large change in the rainfall-runoff relationship as a consequence of land use and land cover change.
 In terms of land use and land cover, grassland occupies the largest proportion of the HYRB area. The area of grassland, forest, and water bodies totals around 85% of the HYRB area. For the periods before and after 1990, it can be seen that there are significant changes in land use and land cover in the HYRB. As shown in Table 3, the grassland area decreased from 89.4 to 76%, while the sandy land area increased from 6.1 to 14.3%, and the forest area increased from 2.6 to 6.6%. Additionally, it has been reported that the significant increase of temperature in the last 50 years [Li et al., 2004] has resulted in permafrost degradation in the HYRB [Zhang et al., 2004]. For example, the lower limit of the permafrost retreated from 4320 m above the sea level in 1991 to 4370 m in 1998 on a north facing slope, with the maximum depth of the permafrost decreasing by 0.4 m [Zhang et al. 2004].
Table 3. Land Use Change in the Headwater Catchments of the Yellow River Basin
Change Rate (%)
4.2. Climate Elasticity of Streamflow
Table 4 shows the climate elasticity of streamflow estimated by the two nonparametric methods and six water balance models based on Budyko's hypothesis. As shown in Table 4, the precipitation elasticity of streamflow varies from 2.1 (equation (9)) to 2.7 [Ol'dekop, 1911], while potential evapotranspiration elasticity of streamflow ranges from −0.80 (equation (7)) to −1.7 [Ol'dekop, 1911]. For the two nonparametric methods, the one proposed by Sankarasubramanian et al.  (equation (7)) gives a larger ɛP but a smaller absolute value of than that estimated by equation (9). Compared to the six water balance models, climate elasticity estimated via equation (7) shows a smaller difference in ɛP but a rather bigger difference in than that estimated on the basis of equation (9).
Table 4. Proportional Impacts of Climate and Land Surface Change on Streamflow in the HYRB Estimated on the Basis of Different Climate Elasticity Estimators
Water Balance Model Based on the Budyko Hypothesis With Different F(ϕ)a
 Moreover, according to the methods based on Budyko's hypothesis, the sum of ɛP and used to be 1.0. However, it should also be noted that the complementary relationship between ɛP and may not hold to be true for most catchments and for all periods. One of the reasons is that the method based on Budyko's hypothesis is derived without consideration of changes in catchment water table and soil moisture. Using the two nonparametric methods for the period of 1960–2000 in the HYRB, ɛP and are estimated on the basis of equation (9) are 2.10 and −1.04, respectively, and are summed up close to unity, but ɛP and are estimated on the basis of equation (7) are summed up to be 1.79.
 It should also be noted that the climate elasticity may not be a constant, and it varies with climate. As shown in Figure 4, on the basis of the method proposed in equation (9), the precipitation elasticity of streamflow calculated with a moving window of 10 years increases from 1.55 in 1960–1969 to 2.23 in 1991–2000 (Figure 4a), but there is no monotonic trend in (Figure 4b). The result indicates that streamflow became more sensitive to changes in precipitation in the period 1991–2000.
 For the moving estimate of precipitation elasticity of streamflow with sample size n = 25 by the two nonparametric methods, Figure 5a shows that there is a good agreement between the two nonparametric estimators (ɛP and ɛ′P). However, the correlation coefficient (R) between ɛP and ɛ′P varies with the sample size. Figure 5b shows that R ranges from 0.5 to 0.7 when the sample size is less than 15 and is around 0.8 for a sample size larger than 15. It is noted that ɛ′P varies in a wider range than ɛP for different sample sizes, which is because the descriptive statistics median is weaker in representing statistical characteristics of all samples when the sample size is small. For example, for n = 50, ɛ′P tends to be a robust estimator of climate elasticity for a rather larger sample size as tested by Sankarasubramanian et al. .
4.3. Impacts of Climate Change and Land Use Change
 As the slope of the linear regression model between proportional change of streamflow and precipitation (equation (8)), the precipitation elasticity (ɛP) of streamflow in the HYRB is estimated to be 2.1 (Figure 6), indicating that a 10% change in precipitation will result in a 21% change in streamflow in the HYRB, which is larger than that of the whole Yellow River Basin, estimated by Fu et al.  to be 1.69. On the basis of equation (9), the potential evapotranspiration elasticity of streamflow is estimated to be −1.04, which means that 10% reduction in potential evapotranspiration will result in a 10.4% increase in streamflow. Considering the hydrologic effects of both precipitation and potential evapotranspiration, 10% increase (or decrease) of both precipitation and potential evapotranspiration may suggest 10% increase (or decrease) in streamflow.
 Following equation (5), with ɛP = 2.1, one can calculate that streamflow in 1991–2000 should be around 15.1 mm less than that of 1960–1990 because of a 20.5 mm decrease of precipitation (Table 4). On the other hand, since = −1.04, the 23.3 mm reduction of potential evapotranspiration in 1991–2000 may result in a 5.6 mm increase of streamflow (Table 4). Therefore, the comprehensive impacts of both precipitation and potential evapotranspiration sum up to a 9.5 mm decrease of annual streamflow in 1991–2000, which accounts for 26.2% of total streamflow reduction (36.2 mm). On the basis of equation (3a), meanwhile, land use and land cover change were then estimated to have resulted in a 26.7 mm decrease of annual streamflow, accounting for 73.8% of the streamflow change (Table 5). The result indicates that land use and land cover change play a more important role than climate change in the change of streamflow in the HYRB.
Table 5. Impacts of Climate and Land Surface Change on Streamflow in the HYRB
S1 and S2 represent climate and hydrological status of HYRB in 1960–1990 and 1991–2000, respectively. is long-term average of streamflow for the period 1960–1990.
S2 − S1
5.1. Climate Elasticity in Relation to Other Indicators
Chiew  reported a strong negative correlation between precipitation elasticity of streamflow (ɛP) and runoff coefficient (Rc) for 219 catchments in Australia. However, it is clear that precipitation elasticity of streamflow (ɛp) is inversely related to runoff coefficient (Rc) if we rearrange equation (9) as
This is found to be true in the HYRB as shown in Figure 7, where ɛP and Rc are both estimated in a moving window with size n = 25. The relationship indicates that streamflow is more sensitive to precipitation in catchments or periods with a low runoff coefficient.
 From equation (9), it is obvious that climate elasticity of streamflow depends on ρP,Q and CQ/CP. To investigate the relationship in the HYRB, the 10-year moving estimates of ɛ, ρP,Q, and CQ/CP were calculated. As shown in Figure 4a, the temporal variation in precipitation elasticity of streamflow (ɛp) is very similar to that of CQ/CP, but it is almost independent of ρP,Q. However, in contrast to precipitation elasticity, the 10-year moving estimates of potential evapotranspiration elasticity of streamflow (ɛE) showed stronger dependence on ρE,Q than on CQ/CE (Figure 4b).
 There are uncertainties associated with the estimates of climate change and land use and land cover change impacts on streamflow. As shown in Table 4, the effect of climate change on streamflow, calculated with different estimators, varies from 26.1 to 39.5%. Hence, the effect of land use and land cover change on streamflow ranges from 60.5 to 73.9% on the basis of equations (3a), (3b), and (3c). However, except for the nonparametric estimator in equation (7), all the other estimators show almost the same results that land use and land cover change contributes around 70% of streamflow change in the HYRB, indicating the dominant effect of land use and land cover change.
 The other uncertainty of the results exists in the assumption of the framework used in this study. It should be noted that the framework used to estimate proportional contribution of climate and land use and land cover change on streamflow is based on the assumption that land use and land cover change is independent of climate change. However, in fact, land surface and the climate system interact with each other. Especially in a catchment scale, climate change may play an important role in land use and land cover change and may consequently change streamflow. For example, the changes in the permafrost due to increasing temperature mean more available water for evaporation and hence decreased streamflow in the region. Although the change in permafrost is related to climate change, it is not considered as such in the present study. Further research is needed to explore the hydrologic impacts of changes of permafrost in the HYRB. Changes in other catchment characteristics such as increased forest cover in the catchment would increase evapotranspiration and would lead to streamflow reductions [Zhang et al., 2001].
 The HYRB are regarded as the “water tower” of the whole Yellow River Basin. Because of climate and land use change, the hydrological cycle of the catchments has been changing during the past 40 years. In this study, the concept of climate elasticity of streamflow has been applied to quantify sensitivity of streamflow to climate and land use and land cover change. Compared with the other estimators of climate elasticity, the nonparametric estimator proposed in this study shows good agreement with that based on the Budyko hypothesis and that introduced by Sankarasubramanian et al. . The climate elasticity of streamflow shows that it is a function of the aridity index and has a positive relationship with ρp,q and Cq/Cp but an inverse relationship between precipitation elasticity and the runoff coefficient.
 It was estimated that for the period 1960–2000 in HYRB, elasticity of streamflow with respect to precipitation and potential evapotranspiration is 2.10 and −1.04, respectively, which implies that streamflow is more sensitive to precipitation than to potential evapotranspiration. However, land use and land cover change play a more important role (>70%) than climate change (<30%) in streamflow change. It should be noted that uncertainties of the results exist because of two facets. One is because of the different estimators of climate elasticity, while the other is the assumption that the hydrologic impact of land use and land cover change is independent of that due to climate change. The hydrologic effects of permafrost change with increase in temperature need to be investigated in the future research.
 This research was supported by the Natural Science Foundation of China (40601015) and Key Projects in the National Science and Technology Pillar Program (2007BAC03A11) and was partially supported by the European Commission (FP7-ENV-2007-1 grant 212921) as part of the CEOP-AEGIS project. We are very appreciative of the constructive suggestions and comments of the anonymous reviewers and the editors.