Effects of climate fluctuations on runoff in the headwater region of the Kaidu River in northwestern China

Abstract

The aim of this study was to analyze the effects of climate fluctuations on runoff in the headwater region of the Kaidu River in northwestern China. For this purpose, precipitation and potential evaporation (PET) data from 5 meteorological stations and the runoff depth data from the Dashankou hydrological station in the headwater region of the Kaidu River from 1960 to 2009 were collected, then the trends and abrupt changes of precipitation, PET and runoff depth were analyzed by means of Mann-Kendall test (M-K test) and Mann-Kendall-Sneyers test (M-K-S test), respectively. The runoff model driven by precipitation and PET was developed in this work and the sensitivity of runoff to climate fluctuation was simulated under different scenarios. Results showed that the annual precipitation and runoff depth both exhibited an increasing trend over the periods 1960–2009; however, this is not the case for the annual PET. The abrupt changes for annual precipitation, PET and runoff depth all occurred in the early 1990s. The established driving model could well reflect the complicated nonlinear relationship among runoff depth, precipitation and PET. The sensitivity analysis indicated that the precipitation had a positive effect on the runoff depth, opposite to what were observed between PET and runoff, and the runoff depth was more sensitive to precipitation than to PET in the headwater region of the Kaidu River.

Keywords

climate fluctuation / driving model / runoff depth / sensitivity analysis

Introduction

The hydrological cycle over a river basin ecosystem is a complex processes influenced by local climate, geographic feature and human activities. With the worsening of the water shortage and increase in the global water-related disasters the effects of climate change and human activities on water resources have long been a focus of global hydrology research (Ren et al., 2002; IPCC, 2007; Scanlon et al., 2007). Numerous studies have shown that climate change and human activities could significantly affect local and regional hydrological evolution processes (Rao, 1995; Ye et al., 2003; Milly et al., 2005; Liu et al., 2009). Climate change, especially global warming, has been affecting glacier and snow melt water generation processes and changing patterns of precipitation, thus accelerating the hydrological cycle (IPCC, 2007). Human activities have changed the temporal and spatial distribution of water resources mainly by the changes in land cover/use and agricultural irrigation (Piao et al., 2007; Milliman et al., 2008; Ling et al., 2011).

In arid and semi-arid regions, the effects of climate change and human activities on runoff seems more sensitive, these effects may increase (Brown et al., 2005) or decrease water yield (Ma et al., 2008; Jiang et al., 2011). Shi et al. (2007) noted that there had been a shift from a warm and dry climate to a warm and humid climate in northwestern China from the late 1980s, and the changes in precipitation and temperature had a significant effect on runoff. The Kaidu River, one of four headstreams of the Tarim River in southern Xinjiang, plays an important role in maintaining the ecological balance in the lower reaches of the Tarim River (Chen, 2010). In the headwater region of the Kaidu River where were characteristic by high elevation, water resources mainly come from the Tianshan Mountains, and runoff processes has not been affected by human activities owing to the small population size living in these mountainous area (Mupenzi and Li, 2011); Whereas the temperature and precipitation have been increasing since the late 1980s, and these changes have considerably affected the hydrological processes (Chen, 2010; Li et al., 2011). Consequently, a key question is how the climate fluctuations affect the runoff in the headwater region of the Kaidu River? Previous studies mainly focused on the linear relationship between runoff and climatic factors (i.e., precipitation and temperature)(Tao et al., 2007; Chen, 2010; Mupenzi and Li, 2011), whereas these two relationship mentioned above should be a nonlinear correlation in the Kaidu River Basin (Xu et al., 2008, 2013). On the other hand, the temperature is not only a hydrologic element, but a factor affecting the hydrologic situation by its impacts on PET and actual evaporation or other hydrologic elements (Zhang et al., 2011). Up until now, little is known about the relationship between runoff and climatic factors (i.e. precipitation and PET) in the headwater region of the Kaidu River. T For this purpose, the nonlinear runoff model driven by precipitation and PET were developed for the analysis of the sensitivity of runoff depth to precipitation and PET. The results of this study could serve as a reference for the regional water resources assessment and management.

Study area and data

Study area

The Kaidu River, a main tributary that discharges into the downstream of the Tarim River, is a river in the Xinjiang Uyghur Autonomous Region of China and an important source of water for the region. The sources of the Kaidu River are located on the central southern slopes of the Tianshan Mountains, and then the river flows through the Yulduz Basin and the Yanqi Basin into Lake Bosten. The headwater region of the Kaidu River is located at the upper region of Dashankou, which is situated within 41°47′N to 43°21′N latitudes and 82°58′E to 86°55′E longitudes with an area of 18,827 km². The elevation of intermountain basin is from 1,042 to 2,500 m, and the elevation of the mountainous area is 2,500 to 4,796 m (Fig. 1). The small population size living in the area affected the local environment only by low grazing. The average annual precipitation is less than 500 mm and pan evaporation is more than 1,100 mm. The average annual temperature is only -4.3°C and the extreme minimum temperature is -48.1°C. The frozen period lasts for 180 days approximately in the mountainous area and 140 days in the intermountain basin with a maximum frozen depth of 439 mm. The headwater region has a long snowfall period from November to the following March, and the annual snow-cover days could reach to 139.3 days with an average snow depth of 12 cm annual (Xu et al., 2008). Some areas of the mountains are covered with permanent glaciers. The stream in the headwater region is characterized by the snow melting in spring, the rainfall/snowfall and the perennial glacier melting in summer. The summer precipitation and the spring snow melting contribute 50% and 15% of the total runoff, respectively. However, the melting of glaciers in summer only contributes about 1% to 3% of the total runoff. The headwater region of the Kaidu River plays an important role in protecting Lake Bosten and its surrounding wetlands and maintaining the ecological balance and green corridor of the lower reaches of the Tarim River.

Data

There are 5 meteorological stations located in the study area that data are available from the National Meteorological Information Center (Fig. 1). The meteorological data had been proved to be unmistakable by means of the extreme value examination and time synchronization detection. The Dashankou hydrological station is the last station before the Kaidu River reaches the plain oases from the mountainous area (Fig. 1). The observed streamflow data in Dashankou were provided by the Xinjiang Tarim River Basin Management Bureau. To compare with the precipitation and potential evapotranspiration (PET), streamflow data were transformed into millimeter (runoff depth). In this paper, daily maximum and minimum air temperature, relative humidity, sunshine hours, wind speed were used to calculate PET via the Penman-Monteith equation recommended by FAO (Allen et al., 1998). Based on above work, the trend tests and abrupt changes tests for annual precipitation, PET and runoff depth in the period from 1960 to 2009 were carried out by means of M-K test and M-K-S test, respectively.

Methodology

Mann-Kendall nonparametric trend test

The M-K nonparametric trend test is commonly used to assess the significance of monotonic trends in meteorological and hydrologic series (Douglas et al., 2000; Zhang et al., 2009). For a time series X=﹛x₁, x₂, ... , x_n﹜, in which n>10, the standard normal statistic Z is estimated as follows:

(1)Z=\{\begin{array}{l}(S-\mathrm{1})/\sqrt{\mathrm{var}(S)S>\mathrm{0}}\\ (S+\mathrm{1})/\sqrt{\mathrm{var}(S)S>\mathrm{0}}\end{array},

where

(2)S={\displaystyle \sum _{i=\mathrm{1}}^{n-\mathrm{1}}{\displaystyle \sum _{j=i+\mathrm{1}}^n\mathrm{sgn}}(x_j-x_i)},

(3)

(4)\mathrm{var}(S)\left[n(n-\mathrm{1})(\mathrm{2}n+\mathrm{5})-{\displaystyle \sum _{t}t}(t-\mathrm{1})(\mathrm{2}t-\mathrm{5})\right]/\mathrm{18},

where t is the extent of any given tie, and \sum _tdenotes the summation of all ties.

The statistic Z follows the standard normal distribution. At a 5% or 1% significance level, the null hypothesis of no trend is rejected if︱Z︱>1.96 or ︱Z︱>2.58. A positive value of Z denotes an increasing trend, and the opposite corresponds to a decreasing trend.

Mann-Kendall-Sneyers test

The M-K-S nonparametric test is widely applied to determine the occurrence of abrupt change points of meteorological and hydrologic series, where it is simple and can identify the starting time and area of abrupt changes (Mann, 1945; Kendall, 1975; Sneyers, 1975). Let x₁, ... , x_n be the data points. For each element x_i, the numbers r_i of elements x_j preceding it (j<i) such that x_j<x_i are computed. Under the null hypothesis (no abrupt change point), the normally distributed statistic S_k can be calculated via the following formula:

(5)S_k={\displaystyle \sum _{i=\mathrm{1}}^k{r}_i}(\mathrm{2}\le k\le n).

Mean and variance of the normally distributed statistic S_k can be given by the following formulas:

(6){\overline{S}}_k=E(S_k)=k(k-\mathrm{1})/\mathrm{4},

(7)\mathrm{var}(S_k)=k(k-\mathrm{1})(\mathrm{2}k+\mathrm{5})/\mathrm{72}.

The normalized variable statistic UF_k is estimated as follows:

(8)U{F}_k=\left(S_k-{\overline{S}}_k\right)/\sqrt{\mathrm{var}(S_k)}.

The normalized variable statistic UF_k is the forward sequence, and the backward sequence UB_k is calculated using the same equation but with a reversed series of data. When the null hypothesis is rejected (i.e., if any of the points in the forward sequence is outside the confidence interval), the detection of an increasing (UF_k>0) or a decreasing (UF_k<0) trend is indicated. With the help of locating the intersection of the forward and backward curves of the test statistics, the sequential version of the test used here enables detection of the approximate time of abrupt changes occurring. If the intersection occurs within the confidence interval, then it indicates an abrupt change point.

Driving model

Liu and Fu (1993) put forward a general idea of developing the relationship between runoff depth (R) and precipitation (P) and PET, which can be expressed by the following equation:

(9)R=k{P}^{\alpha }PE{T}^{\beta }.

Eq. (9) provides us with a pattern between precipitation, PET and runoff depth. According to the related parameter fitting methods, we could obtain the parameters k, α and β. However, Zhang et al. (2011) found that the above three parameters have great intervals of variations, which make the physical meanings of three parameters become ambiguous. Consequently, the parameter k was adjusted and a new driving model was established based on the water balance equation: R = P·EXP (-PET/P) proposed by Schreiber (1904) and Eq. (9)

(10)R=EXP\left(-k{\displaystyle \frac{PET}{P}}\right)\cdot P\cdot PE{T}^{ϵ},

where k and ϵ are undetermined coefficients. ϵ represents the driving force of PET on runoff depth, and the smaller the ϵ is, the less runoff depth is, which means the less driving force of PET on runoff.

Three objective functions were adopted in order to optimize these parameters; they are relative error (RE), Nash-Sutcliffe efficiency coefficient (NSE) (Nash and Sutcliffe, 1970) and correlation coefficient (CC). RE represents systematic water balance error. NSE measures fraction of the variance of observed values explained by the model. CC indicates the strength of a linear relationship between observed and simulated discharge series. RE and NSE are estimated as follows:

(11)RE=\left({\overline{R}}_s-{\overline{R}}_o\right)/{\overline{R}}_o,

(12)NSE=\mathrm{1}-\left\{{\displaystyle \sum _{i=\mathrm{1}}^n{(R_{i,s}-R_{i,o})}^{\mathrm{2}}}/{\displaystyle \sum _{i=\mathrm{1}}^n{\left(R_{i,o}-{\overline{R}}_o\right)}^{\mathrm{2}}}\right\},

where {\overline{R}}_o and {\overline{R}}_s are mean values of the observed and simulated runoff depth, respectively, R_i,oand R_i,sare the observed and simulated runoff depth series, respectively.

Sensitivity analysis

Sensitivity analysis can provide crucial information about climate change and find out the difference in the degree of runoff in response to the assumed various climate change scenarios (Lan et al., 2010). In this paper, the responses degree of runoff depth to the various climate change scenarios is as follows:

(13)\mathrm{\Delta }{R}_{\mathrm{\Delta }P,\mathrm{\Delta }PET}={\displaystyle \frac{(R_{P+\mathrm{\Delta }P,PET+\mathrm{\Delta }PET}-R_{P,PET})}{R_{P,PET}}}\times \mathrm{100}\%,

where R_{P, PET} is the runoff depth under the combination of the current precipitation and PET, R_{P+ΔP,PET+ΔPET} is the runoff depth under the combination of the certain precipitation and PET variables, ΔR_ΔP,PET is the relative change rate of runoff depth between R_{P+ΔP,PET+ΔPET} and R_P,PET. Under the certain climate change scenario, the larger the responsive degree is, the more sensitive the response of runoff depth to climate change is. According to the sensitivity analysis of runoff to climate change, the dominant factor and secondary factor determining runoff variability can be identified (Lan et al., 2010).

Results and discussion

Trends and variations of precipitation, PET and runoff depth

Long-term trends in hydrological processes are potentially affected by climatic variabilities. The historical trends in these parameters can help to confirm the start of the climate-induced changes in these processes. Annual precipitation, PET, and runoff depth from 1960 to 2009 were analyzed using the M-K test to identify long-term trends. Figure 2 shows long-term trends and mean values of annual precipitation, PET, and runoff depth. PET exhibits a slightly decreasing trend, and annual PET value ranges from 745 mm to 709 mm with an average value of 734 mm during the period of 1960-2009. Precipitation and runoff depth, however, both exhibit a significant increasing trend (P<0.05) at a rate of 10.5 and 8.4 mm every 10 years, respectively. The average observed runoff depth from1960 to 2009 is 186 mm, which is smaller than average precipitation with a mean value of 334 mm.

Annual runoff depth and precipitation increased significantly in the past 50 years, this is not the case for the annual PET (Fig. 2). By locating the intersection of the forward and backward curves of the test statistics, the abrupt change points of annual runoff depth, precipitation and PET could be detected. Fig. 3 shows the abrupt change point of the runoff depth series. The intersection of the curves indicates that there are two abrupt changes in 1993 and 1995 for the runoff depth series (P<0.01). The tests for annual precipitation and PET showed that abrupt changes in annual precipitation and PET occurred in 1991 and 1994, respectively (P<0.01) (Table 1, figures not shown). Because the abrupt change points in annual runoff depth, precipitation and PET are basically uniform, it is reasonable to conclude that there is a correlation between the increase in annual runoff depth and annual precipitation and decrease in the annual PET in the headwater region of the Kaidu River.

Model establishment and parameter calibration and validation

The abrupt change points for annual runoff depth, precipitation and PET indicate that the characteristics of annual runoff depth, precipitation and PET all changed in the early 1990s. Based on the M-K-S test, the year 1993 could be identified as the first point that climate fluctuations began to obviously affect the runoff depth. Meanwhile the differences in the average runoff depth were detected before and after the year 1993, when an outset of a new complex process of runoff began later. If the 1993 is the demarcation point for calibration and validation, the driving model will be most effectively tested. Therefore, the period over1960-1992 could be taken as the calibration period, and the year 1993-2009 could be considered as the validation period. According to the modeling approach, the nonlinear runoff model driven by precipitation and PET was established as follows:

(14)R=EXP\left(-\mathrm{0.154}\times {\displaystyle \frac{PET}{P}}\right)\times P\times PE{T}^{-\mathrm{0.032}},

The CC and NSE were applied to validate the driving model. The CC between observed and simulated runoff depth are 0.8564 and 0.8575 in the calibration and validation period, respectively (Fig. 4), and the CC between observed and simulated runoff depth is 0.9041 during 1960-2009, which indicates that the trends of annual observed and simulated runoff depth are basically same over the whole study period. The NSE of the model is 0.62 and 0.71 in the calibration and validation period, respectively (Fig. 4), and the NSE of the model is 0.79 during 1960 to 2009. Over the whole study period, runoff depth was well simulated because the absolute value of RE is 0.037 lower than 0.1. The driving model suggests that the PET had a negative effect on the runoff depth in the past 50 years, when were characteristic by the increase in annual precipitation.

Runoff depth-precipitation-PET relations

To further analyze the driving effect of precipitation and PET on the runoff depth in the headwater region of the Kaidu River, the sensitivity of runoff depth to precipitation and PET was analyzed. Compared with the calibration period, precipitation and runoff depth increased by 13.8 and 26.4% respectively in the validation period; PET, however, decreased by 4.8%, which is lower than those in precipitation and runoff depth. According to the characteristics of regional climatic variabilities, the scenarios of changes in precipitation and PET were set to increase by -14%-14% and -5%-5%, respectively. The responses degree of runoff depth to the precipitation and PET change scenarios was calculated based on Eqs. (13) and (14).

The quantitative runoff depth-precipitation-PET relations plot drawn by Surfer 9.0 can intuitively reflect the responses degree of runoff depth to the precipitation and PET change scenarios. The general relationship between the runoff depth and the changes in precipitation and PET are different (Fig. 5). Runoff depth is positively related to precipitation, opposite to what were observed in PET. And the runoff depth is more sensitive to precipitation than that in PET. For example, a 14% higher precipitation results in a 21.49% increase in runoff depth if PET is maintained at the mean annual value before 1993, but only a 3.93% increase in runoff depth was observed when PET decrease by 5% and precipitation is maintained at the mean annual value before 1993 (Fig. 5). A 14% lower precipitation results in a 17.47% decrease in runoff depth, but a 0.14% decrease in runoff depth was detected if PET increases by 5% (Fig. 5). These results could be confirmed by simple linear regression analysis. The correlation coefficient is 0.7295 for the runoff depth-precipitation regression but -0.5237 for the runoff depth-PET regression (Fig. 6).

The change (%) in runoff depth as a function of changes (%) in precipitation and PET is not symmetric with reference to the change in the trend of precipitation (Fig. 5). These results suggest that the magnitude of the changes in runoff depth response to the changes in precipitation will be different from the changes in precipitation. As precipitation increases, the increase in runoff depth is proportionally greater than those changes in precipitation. However, when the decrease in precipitation is from -1% to -5%, the study area has a smaller percentage runoff depth decrease than the precipitation change; if the precipitation decreases more than -5%, the study area has a larger percentage runoff depth decrease than the precipitation change (Fig. 5).

In the headwater region of the Kaidu River, the runoff depth increase can be considered as the result of the synergistic effect of precipitation and PET (i.e. increase in precipitation and decrease in PET). Fig. 7 shows the relationship between the runoff depth and the humidity index (P/PET). The relationship indicates that a change in the humidity index has led to a greater change in runoff depth, which implies that a change in runoff depth will strongly respond to changes in precipitation and PET. However, the magnitude of the change in runoff depth depends on the synergistic effect of the changes in precipitation and PET.

The climate fluctuations have become a key factor affecting the runoff in the headwater region of the Kaidu River in the past 50 years. In recent years, numerous studies had been carried out with a focus on the linear relationship between runoff and precipitation, temperature (Yang and Cui, 2005; Tao et al., 2007; Li et al., 2011; Mupenzi and Li, 2011). However, the hydro-climatic processes are complex system with nonlinearity in the Kaidu River Basin (Xu et al., 2008; Xu et al., 2013). Consequently, a nonlinear driving model was established in this work which could well reflect the complicated nonlinear relationship between runoff depth and climatic factors (i.e. precipitation and PET), and then further analyzed the sensitivity of runoff depth to precipitation and PET. These could serve as a basis to understand and predict the mechanism of these nonlinear hydro-climatic processes under a specific climate change scenario in the headwater region of the Kaidu River.

Uncertainties of driving model and limitations of sensitivity analysis

Uncertainties of driving model

There are mainly two uncertainties regarding the evaluation of the effect of climate change on runoff depth using the established driving model. First, the input data in the driving model are from the observed hydro-meteorological data in the past 50 years, little attention is paid to the changes in the land use/cover, which increase at all the times and could influence the runoff generation processes by transforming the characteristics of infiltration, evapotranspiration, and so on.

Second, the effect of temperature on runoff depth is not considered in the driving model. Temperature is an important factor affecting watershed glacier and snow melt processes (Tanasienko and Chumbaev, 2008). In the headwater region of the Kaidu River, the snow pack lasts 5 months from November to the following March and there also exist glaciers with an area of 984.34 km² on the alpine area. When the temperature rise, water from glacier and snow melt may increase accompanied by the increase in the rainfall .The hydrologic processes is driven by snowmelt in spring, this is not the case for summer when water from glacier and snow melt plays an important role in the hydrologic processes (Dou et al., 2011). Due to the lack of weather stations in the high mountains, it is difficult to collect accurate and reliable data of temperatures for the simulation of water runoff from glacier and snow melt. .

Limitations of sensitivity analysis

The sensitivity analysis has been used widely to detect the response of runoff to climate change globally (Dooge, 1992; Jones et al., 2006; Lan et al., 2010). This method can provide important information about the effect of climate change on runoff and further analyze the mechanism about the differences in the response of hydrological elements to the climate change in the various river basins. The sensitivity analysis could further identified as a tool to identify the dominant factor and the secondary factor accounting for the changes in runoff. However, sensitivity analysis has its limitations. Firstly, the responsive degree of hydrological elements to the assumed climate change scenarios is not a forecast of runoff under the condition of future climate change. Secondly, a major limitation is the elasticity of runoff where is calculated by historical data and hydrological models, but its assumption is that the elasticity of runoff is fixed. Finally, when the sensitivity of runoff to climate change is analyzed, it is assumed that climate change does not change the spatial and temporal distribution of climatic factors, and the climate change scenarios only reproduce scaling sequences of precipitation, temperature and evaporation.

Conclusions

The climate conditions and runoff depth changed significantly in the headwater region of the Kaidu River during the period of 1960-2009. Thereinto, the annual precipitation and runoff depth exhibited an obvious upward trend over the past 50 years, the annual PET calculated by the Penman-Monteith equation, however, showed an unobvious downward trend. The abrupt change points for runoff depth, precipitation and PET were basically same, and the abrupt changes for annual runoff depth, precipitation and PET all occurred in the early 1990s. The increased in precipitation and the decrease in PET were two controlling factors to the increase of runoff depth in the headwater region of the Kaidu River over the past 50 years.

The driving model reflected the complicated nonlinear relationship among runoff depth and precipitation, PET, and so it could be used to estimate annual runoff depth depending on changes in both the precipitation and PET under different scenarios in the headwater region of the Kaidu River. This will provide a new idea of assessing the impact of climate change on runoff in continental river basin in the arid region of northwestern China.

The quantitative runoff depth-precipitation-PET relations plot drawn by Surfer 9.0 indicated that the runoff depth had various responses to the different scenarios of precipitation and PET and that precipitation was the dominant factor controlling the regional runoff processes in the headwater region of the Kaidu River. Contour plot was proved to be effective to quantify potential impacts of climate fluctuation on runoff in this study, as it provided a runoff depth-precipitation-PET relationship based on historical observed data. This method can be used to evaluate the effects of climate fluctuations on runoff in future study.

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