Water balance changes in response to climate change in the upper Hailar River Basin, China

Projected climate change will have a profound effect on the hydrological balance of river basins globally. Studying water balance modi ﬁ cation under changing climate conditions is signi ﬁ cant for future river basin management, especially in certain arid and semiarid areas. In this study, we evaluated water balance changes (1981 – 2011) in the upper Hailar River Basin on the Mongolian Plateau. To evaluate the hydrological resilience of the basin to climate change, we calculated two Budyko metrics, i.e. dynamic deviation ( d ) and elasticity ( e ). The absolute magnitude of d re ﬂ ects the ability of a basin to resist the in ﬂ uence of climate change and maintain its stable ecological function, whereas parameter e is used to assess whether a basin is hydrologically elastic. Results revealed modi ﬁ cation of the hydrological balance during the study period has manifested as a decreasing trend of runoff and runoff-precipitation ratio. Correspondingly, basin-averaged evapotranspiration has also shown a decreasing trend, attributable mainly to precipitation. Furthermore, the calculated elasticity ( e ¼ 8.03) suggests the basin has high hydrological resilience, which indicates the basin ecosystem may maintain its hydrological function to a certain extent under a changing climate. The results of this study could assist water resource management in the study area and the prediction of ecosystem response to future climate change.


INTRODUCTION
The arid and semiarid areas that cover >50% of China's national mainland territory are distributed primarily on the Tibetan Plateau and in northern China. Grassland is the main vegetation type in such regions that are usually subjected to water limitations and intense effects associated with climate warming (Fang et al. a; Han et al. a; Aa et al. b). Therefore, arid and semiarid areas are ecologically vulnerable and sensitive to climate extremes (Miao et al. ; Fang et al. b). Moreover, vegetation transpiration accounts for a large proportion of the total evapotranspiration in arid and semiarid regions and thus it plays an essential role in the regional hydrological balance (Han et al. a; Wang et al. a; Aa et al. a).
Research has shown that drought in arid and semiarid areas is projected to become intensified in the future, which could trigger considerable change in the processes of the hydrological balance and affect regional water resources (Dai ; Wang et al. a). Therefore, it is of critical importance to study the modification of the water balance under the effects of climate change in arid and semiarid regions to ensure sustainable water resources management. showed that streamflow has decreased during recent decades. In the Kuye River Basin in Northwest China, Yang & Yang () found annual runoff has declined significantly during the past 60 years. Generally, streamflow has tended to diminish and evaporation has tended to increase in many basins of northern China owing to climate change (Wang & Hejazi ; Wang et al. a, b, b; Shen et al. ). However, the extent to which these basins may be resistant to climatic perturbations should be explored further with regard to the prediction of basin responses to future climate change (Xue et al. ).
In hydrology, the concepts of resistance and resilience, which are taken from the field of ecology, are two metrics used to quantify basin response to climate change (Zhang et al. ; Williams et al. ). In ecological studies, a resilient ecosystem is defined as one that has the ability to absorb change induced by external factors and retain its ecological function (Creed et al. ). In recent years, this concept has been applied in hydrological sciences (Trenbath ; Gerten et al. ). The concept of hydrological resilience is described as the capability of a basin to maintain stability in multiple hydrological equilibrium states (Brand et al. 2007). Creed et al. () found that climate warming was projected to change forest runoff, so he calculated the resilience and resistance of 12 watersheds across North America and concluded that the forest type is the dominant factor affecting the elasticity of a specific watershed.
Helman et al. () calculated these two metrics of forests in the Eastern Mediterranean and found that a drier climate may induce higher resilience compared with a more humid climate. Therefore, these two metrics have been applied and to some extent it can reflect the characteristics of the river basin following the climate change. In this study, we used the Budyko theoretical curve to describe the relationship between basin resilience and climate change (Shen et al. the Budyko curve, we calculated two metrics, i.e. dynamic deviation (d ) and elasticity (e), which can be used to quantify the resilience and resistance of a basin to the effects of climate change (Creed et al. ; Helman et al. ).
Dynamic deviation, which is described as the vertical departure of the EI from the corresponding value calculated using the theoretical Budyko curve, represents the resistance of a basin in terms of the runoff change caused by climate Moreover, its location belongs to the ecologically vulnerable area. So it is meaningful to detect the water balance changes following the climate change and quantify its hydrological resilience and resistance to climate change for future water resource management. In this study, we employed the Mann-Kendall test to analyze the changing hydrological balance of the study basin and adopted two metrics to determine the basin's hydrological resilience, which is used as a supplement. The objective was to investigate the following: (1) the changes of hydroclimatic variables/climate in the study basin over the previous 30 years, (2) the basin response to the changes in climate and water balances variables, and (3) the resilience of the basin to climate change. The findings of this study will assist water resources management in the basin.

Study area
The study area comprised the upper reaches of the Hailar River Basin that drains a watershed of 43,345 km 2 (Fang et al. ). This area is located in northeastern Inner Mon- cn). The study area is 510-1,622 m above sea level and its topography is predominantly mountains, hills, and wetlands.

Standardized precipitation and evapotranspiration index
In this study, the standardized precipitation and evapotranspiration index (SPEI) was selected as the drought monitoring index. This index considers the statistical distribution of precipitation and the potential evapotranspiration at the same time and it can reflect the regional drought more comprehensively. According to Abbasi et al. (), the SPEI can be calculated as described in the following.
First, the water-year potential evapotranspiration (ET 0 ) is calculated using the radiation-based formulation of Priestley and Taylor (Dewes et al. ), as shown below: where R N is net radiation, Δ is the gradient of saturated vapor pressure, G is soil heat flux, and γ is the psychrometric constant. The unit of the variable PET is mm/d. Second, the difference between monthly precipitation and evapotranspiration is calculated as D i ¼ P i À PET i , where i is the month counter. Third, the accumulation sequence of water profit and loss over different timescales is established using Equation (2), where k is the timescale (here, k ¼ 12): Fourth, the D k n data series should be fitted and normalized to calculate the SPEI. Vicente-Serrano et al. () showed that the log-logistic density function is the best fitting function to fit the D k n data series through contrasting the different types of parameter function. The expression of the log-logistic probability density function including three parameters is as follows: where α, β, and γ are the parameters of scale, shape, and beginning, respectively. The linear moment method is adopted to estimate the fitting parameters of this function according to the following formulas: where w s is the probability weighted moment, s is taken as 0, 1, or 2, l is the sequence of accumulated water deficit X in ascending order (X 1 X 2 ,…, X n ), and Γ(β) is the gamma function. Through the three-parameter log-logistic probability distribution function, the cumulative probability on a given timescale can be calculated using Equation (7) (Polong et al. ). Then, the SPEI is calculated using Equation (9): Finally, W is calculated using Equation (11): Having obtained the SPEI, a criterion was required to determine the occurrence of drought (Table 1). In this study, if the value of the SPEI was less than -0.5, we considered a drought phenomenon happened; if the value of the SPEI was positive, we considered the drought period over (Begueria et al. ).

Calculation of Budyko metrics
Based on the Budyko hypothesis, the annual water balance can be described using the function of water (precipitation) and energy (potential evaporation). Among the various forms of equations for Budyko curves, we selected the following (Zhang et al. ): where P, ET, and ET 0 are mean annual precipitation, mean annual actual evaporation, and potential evapotranspiration, respectively. Parameter w is a constant determined by the characteristics of the watershed, e.g. vegetation type and soil type (Qiu et al. ). In this study, we used the adjusted equation assuming w ¼ 2 to describe the theoretical relationship between the dryness index DI ¼ ET 0 P and the The parameters of deviation (d) and elasticity (e) were calculated for the studied basin to represent the potential departure from the Budyko theoretical curve of the DI and EI points (Creed et al. ). Deviation is described as the vertical departure of the EI from the corresponding B value calculated from the theoretical Budyko curve, which is composed of two parts: static and dynamic deviation.
Static deviation is calculated as the mean annual EI minus its theoretical B value obtained from the mean annual DI, which is the inherent deviation with average normal climate Figure 3). Dynamic deviation where P is precipitation, R is streamflow, E is evapotranspiration, and ΔS is the change of water storage volume (Bao et al. ). We considered water storage negligible, assuming a steady state for the study period .

The Mann-Kendall test
The For an assumed data series X (x 1 , x 2 , Á Á Á x n ), n is the length of the data series. First, the cumulative statistic S should be calculated as follows: where statistic S is the cumulative number of values at time i larger than at time j. Under the assumption of random independence of the time series, the statistic UF k can be defined by the following formula: In Equation (16), UF 1 ¼ 0, and E(S k ) and Var(S k ) represent the expected value and the variance, respectively, of the cumulative value S k , which can be obtained as follows: UF i is a standard normal distribution, which is a sequence of statistics calculated from the order of time series X. Given significance level α, a condition of jUF i j > U α indicates an obvious trend change in the sequence. Using the inverse time series, we calculated the UF i again using the above calculation process, where UB i ¼ ÀUF i and i ¼ n, n À 1, Á Á Á , 1 for the same test method as described above.

Data sources
We used daily Q data from the hydrological station at the  (Figure 4(a)). Moreover, the results of the Mann-Kendall test revealed an oscillation in mean annual precipitation before 1998 and after 1998, indicating that the trend of decrease of mean annual precipitation became slightly more evident (Figure 4(b)). Therefore, although the trend of decrease of mean annual precipitation was mild, the scale of the trend intensified.
During 1981-2011, average annual temperature in the study area was -1.81 C, with the lowest (highest) average annual temperature of -3.53 C (-0.19 C) in 1984 (2007).
There has been a trend of increase in average annual temperature over the 30-year study period (Figure 4(c)). The multiyear annual mean temperature was -2.4, -1.56 and -1. 51 C in 1981-1990, 1991-2000, and 2001-2011, respect-ively. The multiyear mean annual temperature during 1991-2000 was 0.84 C higher than in 1981-1990 but 0.04 C lower than in 2001-2011, which indicates that the rate of increase in temperature has decreased slightly in comparison with earlier years. Statistically, the P value (P ¼ 0.4835) calculated from the linear regression indicates that this trend of increase was not significant and that its process of change was uncertain (Figure 4(c)). In addition, according to the results of the Mann-Kendall test, the trend of increase in annual mean temperature was significant after 1993 at the α ¼ 0:05 level. Generally, despite the uncertain trend of change of temperature, it was clearer than that of precipitation (Figure 4(d)).
We also analyzed the change of humid/dry climate in the Hailar River Basin based on the SPEI. It was found that drought intensified during the study period, especially

Water balance change in the Hailar River Basin
The water balance of the Hailar River Basin has changed during the study period ( Figure 6). During 1981-2011, annual mean runoff at the outlet hydrological station has decreased at the rate of 1.46 mm/year (Figure 6(a)). The change trend of annual mean runoff was similar to that of precipitation (Figure 4(a)). During 1981During -1990During , 1991During -2000During , and 2001During -2011  study period with a change trend similar to but more evident than that of annual mean runoff (Figure 6(b)). However, the rate of decrease of annual mean evaporation has been smaller than the change trend of precipitation.
The proportions of precipitation allocated to runoff and evaporation have also changed during the study period, i.e. a smaller proportion of precipitation has generated runoff, while a greater proportion has been evaporated. As shown in Figure 7, there has been a general trend of decrease in the runoff-precipitation ratio and a trend of increase in the evaporation-precipitation ratio. The multiyear mean runoffprecipitation ratio was 0. 206, 0.194, and 0.143 during 1981-1990, 1991-2000, and 2001-2011, respectively. It is evident that there was no change in the relationship between precipitation and runoff during 1981-2000, i.e. the

DISCUSSION
During 1981-2011 in the Hailar River Basin, there was a trend of decrease in annual mean precipitation and a trend of increase in annual mean temperature ( Figure 4).
As the calculated results showed, the rate of decrease of precipitation and the rate of increase of temperature both increased gradually to some degree, indicating that the climate of the upper Hailar River Basin during the studied 30-year period has changed and that this change might become intensified in the future (Figure 4). Moreover, the observed decreased precipitation and increased temperature are projected to lead to intensification of drought, consistent with the results of Wang et al. (a, b). This type of phenomenon is consistent with that observed in the region

CONCLUSIONS
In the Hailar River Basin, the major features of climate change during the 30-year study period  are represented by increased temperature, decreased precipitation, and intensified drought. We used the Mann-Kendall test to investigate the water balance changes in this basin based on certain hydrological variables, e.g. precipitation and runoff.
Based on hydrological data obtained during the study period, it was determined that the water balance change has been manifest as trends of decrease of runoff and evaporation. In addition, we used two Budyko metrics to quantify the resistance and resilience of runoff in this basin to the effects of climate change. The results showed the basin has high hydrological resilience and resistance and that it could retain its ecological function in a changing climate.