Temperature Contributes More than Precipitation to Runoff in the High Mountains of Northwest China

Abstract

In alpine areas in Northwest China, such as the Tianshan Mountains, the lack of climate data (because of scarce meteorological stations) makes it difficult to assess the impact of climate change on runoff. The main contribution of this study was to develop an integrated method to assess the impact of climate change on runoff in data-scarce high mountains. Based on reanalysis products, this study firstly downscaled climate data using machine learning algorithms, then developed a Batch Gradient Descent Linear Regression to calculate the contributions of temperature and precipitation to runoff. Applying this method to six mountainous basins originating from the Tianshan Mountains, we found that climate changes in high mountains are more significant than in lowlands. In high mountains, the runoff changes are mainly affected by temperature, whereas in lowlands, precipitation contributes more than temperature to runoff. The contributions of precipitation and temperature to runoff changes were 20% and 80%, respectively, in the Kumarik River. The insights gained in this study can guide other studies on climate and hydrology in high mountain basins.

1. Introduction

Global warming has exacerbated the uncertainty of runoff in mountainous rivers [1,2]. Mountainous rivers provide water for people and support lowland industries and agriculture [3,4,5]. However, in the alpine areas of Northwest China, such as the Tianshan mountains, limited climate data is available (because of the scarcity of meteorological stations), which makes it difficult to calculate the contribution of climate change to runoff [6,7]. New methods need to be developed in order to address this knowledge gap [8].

In recent years, various methods have been applied to calculate the contribution of climate change to runoff, including correlation analysis [9], sensitivity analysis [10], nonparametric Mann–Kendall tests [11], water–energy balance equations [12,13], two-parameter climate elasticity [14], weight connections [15], multiple linear regression (MLR) [16], Budyko curves [17], intelligent water drop algorithms [18], and hydrological models, such as VIC [19] and SWAT [20,21]. Using weight connections and artificial neural networks, Wang et al. [15] calculated the contributions of precipitation and temperature to runoff, which were 48% and 52% in the Toshkan River and 36% and 64% in the Kumarik River. Climate and streamflow processes have non-linear characteristics [22]. Improved, complete ensemble empirical mode decomposition, with adaptive noise (ICEEMDAN), can effectively decompose signals [23], and can be applied to analyze the impacts of climate change on runoff at different scales [14]. However, existing methods are mostly based on observed data [24], so they cannot be easily applied to data-scarce mountainous basins.

Precipitation and temperature are the main variables affecting runoff changes in mountainous basins [25,26]. Various studies have shown that precipitation changes have led to runoff changes in many rivers around the world [27,28]. Increasing temperatures can accelerate the melting of snow and glaciers [29], providing large amounts of runoff to mountainous rivers [30]. For data-scarce areas, reanalysis products spatially distributed climate data [31]. The ERA5 precipitation (ERAP) and ERA-interim temperature (ERAT) show climate change at the regional scale and are strongly correlated with empirical observations in China [32,33,34,35,36]. However, when applied to basins, the reanalysis products need to be downscaled, in order to improve spatial resolution [37,38].

The purpose of this study is to develop a method to calculate the contributions of temperature and precipitation to runoff in data-scarce mountainous rivers. Selecting six mountainous basins originating from the Tianshan Mountains, we first downscaled temperature and precipitation using machine learning algorithms, and we then developed a Batch Gradient Descent Linear Regression (BGDLR) model to calculate the contributions of temperature and precipitation to runoff. This research can provide references for hydrological forecasts in mountainous areas.

2. Materials and Methods

2.1. Study Area

To calculate the contributions of temperature and precipitation to runoff changes in mountainous rivers, we selected as study areas the Manas River basin (MRB) (84°96′E–86°31′E; 43°07′N–43°98′N) and Urumqi River basin (URB) (86°80′E–87°29′E; 43°02′N–43°38′N) originating from the northern slope of the Tianshan Mountains, and Kashgar River basin (KaRB) (83°00′E–85°00′E; 43°21′N–44°06′N), Toxkan River basin (TRB) (75°54′E–78°62′E; 40°28′N–41°50′N), Kumaric River basin (KuRB) (78°07′E–80°33′E; 41°39′N–42°48′N), and Kaidu River basin (KRB) (82°57′E–86°06′E; 42°06′N–43°21′N), originating from the southern slope of the Tianshan Mountains (Figure 1). There is only one meteorological station in the KRB and TRB, and no meteorological station in the KuRB, KaRB, MRB, or URB (Figure 1). Therefore, the above basins are typical data-scarce mountainous areas.

The Kashgar River is the main tributary of the Yili River, with a mean elevation of 3100 m [39]. In KaRB, the terrain is open to the west, and the westerly airflow brings abundant water vapor [40]. Among the rivers on the northern slope of the Tianshan Mountains, the Manas River has the most abundant runoff [41]. The Aksu River and KRB provide more than 80% of runoff for the Tarim River in Northwestern China [42]. The Toshkan River and Kumarik River are the main sources of the Aksu River [43]. The mean elevations are 3737 m and 3550 m, respectively, and the basin areas in the KuRB and TRB are 13,557 km and 18,835 km², respectively. The Kaidu River originates in the Sarming Mountains, with an average elevation of 2990 m and an area of 18,727 km². Snow and glaciers are widely distributed above the mountainous basins, which are an important supply of runoff [44]. There is a hydrological station in the mountain pass of each basin, the observed data of which can reflect runoff changes.

2.2. Datasets

The data used in this study included observed data and reanalysis data. We first downscaled temperature and precipitation based on reanalysis products and verified the accuracy of the downscaled results by observed data from meteorological stations. Then, based on the downscaled climate data and observed runoff, we calculated the contributions of temperature and precipitation to runoff change.

The reanalysis products include ERAP, ERAT, and the Digital Elevation Model (DEM). The United States Geological Survey provided the DEM (http://srtm.csi.cgiar.org, accessed on 4 July 2022), with a resolution of 90 m × 90 m. The ERAT and ERAP are the third- and fifth-generation products of ECMWF, respectively. The spatial resolution of ERAT is 0.125° × 0.125°, and that of ERAP is 0.25° × 0.25° (https://apps.ecmwf.int/datasets/data/, accessed on 4 July 2022). The period of ERAT is from January 1979 to August 2019, and that of ERAP is from January 1979 to December 2020. To analyze the mechanism of climate change driving runoff, this study used a long-time series data set of snow depth in China, with a time resolution of one day, and a spatial resolution of 25 km. The data were provided by the National Glacier-Permafrost Desert Science Data Center (http://www.ncdc.ac.cn/portal/, accessed on 10 July 2022), from 1979 to 2016 [45].

To verify the accuracy of downscaled results, we used the observed monthly temperature and precipitation from 17 meteorological stations located near the six basins (http://data.cma.cn/, accessed on 17 June 2022). The data were downloaded from the National Meteorological Information Center, from 1979 to 2020. The monthly runoff was provided by the Hydrological Bureau of Xinjiang Uygur Autonomous Region. The runoff data for URB, MRB, and KaRB are from 1980 to 1987 and 2006 to 2011, and for KRB, TRB, and KuRB are from 1979 to 2015.

2.3. Methods

To calculate the contribution of climate change to runoff in data-scarce mountainous rivers, we integrated climate downscaling, the Mann–Kendall test, ICEEMDAN, and BGDLR. We first downscaled temperature and precipitation using machine learning algorithms, then developed a BGDLR model to calculate the contributions of temperature and precipitation to runoff change.

2.3.1. Climate Downscaling

Topography and geographical location are the main factors affecting precipitation and temperature distribution in mountainous areas [46,47]. Introducing terrain and geographic location to the downscaling of precipitation and temperature is useful [48]. This research fitted nonlinear models for temperature and precipitation, then trained the models using a gradient descent algorithm [49]. The downscaling models can be expressed as follows:

$$\mathrm{T}={\mathrm{F}}_1\left(\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D},\mathrm{E}\right)+\Delta \mathrm{T},$$

(1)

$$\mathrm{P}={\mathrm{F}}_2\left(\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D},\mathrm{E}\right)+\Delta \mathrm{P},$$

(2)

where ∆T and ∆P are residuals; A, B, C, D, and E are elevation, latitude, longitude, aspect, and slope, respectively. The steps build on Fan et al. [50,51].

2.3.2. Climate and Hydrological Process Analysis

The Mann–Kendall test [52,53] is an effective tool for analyzing trends in time series [22,54]. We applied this method to explore the changes in climate and runoff. In addition, we used Sen’s slope [55] to verify trends in the Mann–Kendall test. For the steps of the Mann–Kendall test and Sen’s slope, please see Wang et al. [15].

Runoff and climate have non-linear changes [56,57]. ICEEMDAN can effectively decompose signals [58,59,60]. In this research, ICEEMDAN was used to extract the multi-scale changes in runoff and climate. For the steps of ICEEMDAN, please see Ali and Prasad [61].

2.3.3. Contributions of Climate Change to Runoff

Precipitation and temperature are the main climatic variables affecting runoff changes in mountainous basins. Affected by factors such as geographic environment and altitude, the contribution of climate change to runoff varies in different basins and seasons. Linear regressions can clarify the relationship between dependent and independent variables [62,63]; the regression may be applied to calculate the contributions of independent variables to a dependent variable [64]. In this study, we developed a multi-linear model of runoff with temperature and precipitation and solved the model using a batch gradient descent (BGD) algorithm [49]. Before applying this method, normalization of temperature, precipitation, and runoff was performed with the equation as follows:

$${\mathrm{X}}_{\mathrm{is}}=\left({\mathrm{x}}_{\mathrm{i}}-{\mathrm{x}}_{\min }\right)/\left({\mathrm{x}}_{\max }-{\mathrm{x}}_{\min }\right),$$

(3)

where ${\mathrm{x}}_{\mathrm{i}}$ is the sequential data and ${\mathrm{X}}_{\mathrm{is}}$ is the normalized variable.

To avoid collinearity in the model, multicollinearity among the explanatory variables was evaluated, using the tolerance and variance inflation factor [65]. We also used partial correlation analysis to remove the effect between explanatory variables. According to Hair et al. [65], when the tolerance of independent variables is >0.1, the variance inflation coefficient is <10, indicating that there is no collinearity between independent variables. The resulting beta coefficients (partial regression coefficients) for the explanatory variables represent the independent contributions of each explanatory variable [66]. The regression model was as follows:

$$\mathrm{R}={\mathrm{c}}_1\mathrm{T}+{\mathrm{c}}_2\mathrm{P}+\mathrm{a},$$

(4)

where R, T, and P, are normalized runoff, temperature, and precipitation, respectively; ${\mathrm{c}}_1$ is the regression coefficient of T; ${\mathrm{c}}_2$ is the regression coefficient of P; and a is the regression constant.

In the model, the cost function for regression is:

$$\mathrm{J}\left(\mathsf{\theta }\right)=\frac{1}{2\mathrm{m}}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{m}}{\left({\mathrm{h}}_{\mathsf{\theta }}\left({\mathrm{x}}^{\left(\mathrm{i}\right)}\right)-{\mathrm{y}}^{\left(\mathrm{i}\right)}\right)}^2,$$

(5)

where $\mathrm{m}$ is the number of samples; ${\mathrm{x}}^{\left(\mathrm{i}\right)}$ represents the characteristics of the sample; and ${\mathrm{y}}^{\left(\mathrm{i}\right)}$ is the target.

Then, we used the BGD algorithm to train the dataset to minimize $\mathrm{J}\left(\mathsf{\theta }\right)$ and find the optimal solution of $\mathsf{\theta }$, which are as follows:

$$\frac{\partial }{\partial {\mathsf{\theta }}_{\mathrm{j}}}\mathrm{J}\left(\mathsf{\theta }\right)=\frac{1}{\mathrm{m}}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{m}}\left({\mathrm{h}}_{\mathsf{\theta }}\left({\mathrm{x}}^{\left(\mathrm{i}\right)}\right)-{\mathrm{y}}^{\left(\mathrm{i}\right)}\right){\mathrm{x}}_{\mathrm{j}}^{\left(\mathrm{i}\right)},$$

(6)

The correction function for θ is:

$${\mathsf{\theta }}_{\mathrm{j}}={\mathsf{\theta }}_{\mathrm{j}}-\mathsf{\alpha }\frac{1}{\mathrm{m}}{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{m}}\left({\mathrm{h}}_{\mathsf{\theta }}\left({\mathrm{x}}^{\left(\mathrm{i}\right)}\right)-{\mathrm{y}}^{\left(\mathrm{i}\right)}\right){\mathrm{x}}_{\mathrm{j}}^{\left(\mathrm{i}\right)},$$

(7)

where $\mathsf{\alpha }\mathrm{is}\mathrm{the}\mathrm{learning}\mathrm{rate}.$

Based on the regression coefficients, the contributions of precipitation and temperature to runoff are calculated as:

$${\mathsf{\eta }}_1=\left|{\mathrm{c}}_1\right|/\left(\left|{\mathrm{c}}_1\right|+\left|{\mathrm{c}}_2\right|\right),$$

(8)

$${\mathsf{\eta }}_2=\left|{\mathrm{c}}_2\right|/\left(\left|{\mathrm{c}}_1\right|+\left|{\mathrm{c}}_2\right|\right),$$

(9)

where ${\mathsf{\eta }}_1$ is the contribution of temperature to runoff and ${\mathsf{\eta }}_2$ is the contribution of precipitation to runoff.

3. Results

3.1. Accuracy of Downscaled Climate Data

After climate downscaling, we spatially distributed precipitation and temperature in six basins. The resolution of downscaled data is 90 m × 90 m. The observations from 17 meteorological stations distributed in and near the basins were used to verify the accuracy of the downscaling results. Tables S1 and S2 indicated the robust performance of the developed method. At 17 meteorological stations, the slope between the downscaled and observed data was close to 1, and the NSE was higher than 0.5. At most stations, the MAE and RMSE between downscaled temperature and observations were <3 °C (Table S1), and that between downscaled precipitation and observations were <10 mm (Table S2). At 11 stations, the NSE of downscaled temperature and the observed temperature was >0.9 (Table S1). The downscaled data accounted for scarce observations and reveal climate change in mountainous basins.

3.2. Climate Change

The mean and slope of downscaled grid data showed the characteristics of temperature and precipitation change. According to Figure 2, the temperature is <0 °C and annual precipitation is <600 mm in six basins. In valleys and plains, the annual precipitation is <300 mm, and the temperature is >0 °C. In mountainous areas, the annual precipitation is >300 mm, and the temperature is <0 °C.

There are significant differences in the temperature and precipitation changes in different basins (Figure 2). In the past 40 years, KRB has experienced wetting, with a humidification rate of 9 mm/10a (Figure 2b,d). At the same time, KaRB became increasingly dry at 40 mm/10a (Figure 2l). Different from the above basins, TRB, KuRB, MRB, and URB have experienced warming and wetting. In TRB and KuRB, the rate of warming and humidification gradually slowed from west to east. In TRB, the temperature increased 0.29 °C/10a in the west and 0.20 °C/10a in the east (Figure 2n); the precipitation increased 50 mm/10a in the west and 7.42 mm/10a in the east (Figure 2p). In KuRB, the temperature increased 0.21 °C/10a in the west and 0.18 °C/10a in the east (Figure 2f); the precipitation increased 30 mm/10a in the west and 27 mm/10a in the east (Figure 2h). On the whole, compared with valleys and plains, the high mountains have more dramatic changes in temperature and precipitation.

3.3. Impact of Climatic Variables on Runoff

3.3.1. Correlation of Runoff with Temperature and Precipitation

Figure 3 displays the correlation coefficients of runoff with climate on a monthly scale. In KaRB, the runoff has a stronger correlation with temperature, whereas in MRB, URB, KuRB, and KRB, the runoff has a stronger correlation with precipitation (Figure 3). Studies have shown that the correlations between runoff and climate varies in different seasons. Therefore, on a monthly scale, temperature and precipitation are the main driving factors for the runoff changes in mountainous watersheds. The difference is that, in KaRB, the temperature has a greater effect on runoff than precipitation, whereas, in MRB, URB, KuRB, and KRB, precipitation dominates the monthly runoff changes.

The seasonal correlation coefficients between runoff and climate are shown in

Table 1. Seasonal correlation coefficients between climate and runoff.

Basin	Season	Streamflow vs. Temperature	Streamflow vs. Precipitation
MRB	Spring	0.05	0.37 *
	Summer	0.69 *	0.54 *
	Autumn	0.32	0.21
	Winter	0.22	0.37 *
URB	Spring	−0.29 *	0.08
	Summer	−0.13	0.65 **
	Autumn	−0.12	−0.09
	Winter	0.14	0.12
KaRB	Spring	0.09	0.54 *
	Summer	−0.02	0.74 *
	Autumn	−0.02	0.07
	Winter	0.28	0.12
TRB	Spring	−0.17	0.46 *
	Summer	0.02	0.24
	Autumn	0.30	0.44 *
	Winter	0.13	0.09
KuRB	Spring	0.38 *	0.05
	Summer	0.67 *	0.09
	Autumn	0.58 *	0.12
	Winter	−0.01	0.02
KRB	Spring	−0.02	0.32 *
	Summer	0.06	0.55 *
	Autumn	−0.01	0.24
	Winter	−0.06	0.10

Table note: * indicates the significance of a < 0.05 and ** indicates the significance of a ≤ 0.01.

. In URB, a positive correlation between runoff and precipitation is only shown in summer, which indicates that the runoff in URB is mainly supplied by summer precipitation. In MRB, the runoff has significant positive correlations with both temperature and precipitation in summer, indicating that the runoff is mainly replenished by summer precipitation and glacier meltwater. In KaRB and KRB, a significant positive correlation is shown between runoff and precipitation in spring and summer, so the runoff in KaRB and KRB is mainly replenished by spring and summer precipitation. In TRB, the correlation is positive between precipitation and runoff in spring and autumn, indicating that the runoff in TRB is mainly replenished by spring and autumn precipitation. In KuRB, the correlation between runoff and temperature is significant and positive in spring, summer, and autumn, which indicates that the snowmelt water in spring and autumn, and melted ice water in summer, are the main replenishments for the runoff in KuRB (Table 1). There are obvious differences in the correlations between runoff and climate in different seasons. Overall, the changes in spring and autumn temperature, and summer precipitation, have an important impact on runoff.

ICEEMDAN was used to explore the multi-scale variations of climate and runoff. Table S3 shows that the runoff has similar cycles with temperature and precipitation. In MRB, URB, and KaRB, five intrinsic mode functions (IMF) and one residual component (RES) were obtained after the decomposition of runoff, temperature, and precipitation. While in other basins, six IMF and one RES were obtained after the decompositions. We reconstructed the precipitation, temperature, and runoff on inter-seasonal, inter-annual, and inter-decadal scales [67], then calculated the correlation coefficients between runoff and climate on different scales (

Table 2. Multi-scale correlation coefficients between runoff and climate.

Basin	Scale	Streamflow vs. Temperature	Streamflow vs. Precipitation
MRB	Seasonal	0.7548 *	0.1586 *
	Inter-annual	0.4392 *	0.7284 *
URB	Seasonal	0.7915 *	0.1678 *
	Inter-annual	0.1214 *	0.6550 *
KaRB	Seasonal	0.0156	0.1681 *
	Inter-annual	0.2283 *	0.5309 *
TRB	Seasonal	0.7467 *	0.3494 *
	Inter-annual	0.2812 *	0.3866 *
	Inter-decadal	0.1837 *	0.9174 *
KuRB	Seasonal	0.1431 *	0.2772 *
	Inter-annual	0.6746 *	0.7185 *
	Inter-decadal	0.3832 *	0.2023 *
KRB	Seasonal	0.1458 *	−0.0136
	Inter-annual	0.2524 *	0.8536 *
	Inter-decadal	0.2008 *	−0.2041 *

Table note: * indicates the significance of a < 0.05.

). In MRB, URB, and KaRB, the inter-decadal variations of runoff are not shown because of the short period of runoff data. On the seasonal scale, the runoff has a stronger correlation with temperature in the KaRB and KuRB, and has a stronger correlation with precipitation in other basins; on the inter-annual scale, the correlation between runoff and temperature is stronger than that of precipitation; on the inter-decadal scale, the runoff has a stronger correlation with temperature in TRB and KRB, and has a stronger correlation with precipitation in KuRB (Table 2). It is worth noting that the runoff and temperature in KRB are significantly negatively correlated on the inter-decadal scale, and the specific mechanism(s) needs to be further studied.

3.3.2. Contributions of Climate Change to Runoff

Table S4 shows the collinearity tests for regression models. In the six basins, the tolerances were all > 0.8, and VIF were all < 2, indicating that the models did not have collinearity. According to partial regression coefficients, the contributions of temperature and precipitation to runoff can be calculated (Figure 4). Statistical results indicate significant differences in the contribution ratios among different basins. In KuRB, the temperature dominates annual runoff changes, whereas precipitation contributes more than temperature to runoff changes in other basins. Among the six watersheds, the KuRB has the highest elevation, and glaciers and permanent snow are widely distributed. Therefore, in high mountainous areas, the temperature contributed more than precipitation to runoff changes.

Across the seasons, there are obvious differences in the contribution of temperature and precipitation change to runoff (Figure 4). Generally, summer runoff accounts for the highest proportion of annual runoff in alpine basins [68]. Therefore, the relative contribution of temperature and precipitation to summer runoff changes can reflect the replenishment of runoff. In MRB, the contribution of precipitation change to runoff is 97% in spring, whereas the temperature change has a higher contribution than precipitation to runoff in summer and autumn, indicating that the glacier and snow melt water in summer is the main replenishment for runoff in MRB, followed by spring and summer precipitation. In URB, in spring, the contribution of temperature changes to runoff is higher than precipitation, indicating that glacier and snowmelt water are important replenishments for runoff; in summer, the runoff is mainly affected by precipitation change, and in autumn and winter, temperature and precipitation contribute equally to runoff. In KaRB, the relative contribution of precipitation changes to runoff is 72%, 88%, and 99% in spring, summer, and winter, respectively. Located in the Ili River Valley, KaRB is affected by warm and humid water vapor from the Atlantic Ocean; therefore, the runoff changes in KaRB are mainly affected by precipitation.

In TRB, precipitation contributed more than temperature to runoff in spring, summer, and autumn, whereas temperature has a higher contribution than precipitation to runoff in winter. This indicates that summer precipitation is the main replenishment of runoff in TRB, followed by spring and autumn precipitation. Different from other basins, in KuRB the temperature changes have a higher contribution than precipitation to runoff; therefore, glacier and snow melt water in summer is the main recharge of the runoff. In KRB, the contribution of precipitation changes to runoff is higher than temperature in each season, indicating that summer precipitation is the most important replenishment for runoff in KRB. In MRB and KuRB, glacier and snow melt water in summer is the main recharge of runoff, and runoff is mainly affected by temperature changes, whereas in other watersheds, summer precipitation is the main recharge of runoff, and runoff is mainly affected by precipitation changes.

4. Discussion

4.1. Climate Downscaling

Almost all previous studies have calculated the contribution of climate change to runoff using observed precipitation and temperature [11,16]. Generally, observed data only reflect climate change at immediate locations [51]. For data scarce areas, reanalysis products spatially distributed temperature and precipitation [31,32], whereas the low resolution eliminates the climate heterogeneity in basins [69]. Based on climate downscaling, this research obtained high-resolution temperature and precipitation data. We extracted the downscaled temperature (September 2017) and compared it with ERAT and observations at the corresponding time (Figure 5). There is only one meteorological station in KRB and TRB, and there is no meteorological station in KuRB, KaRB, MRB, and URB. Compared with observations and ERAT, downscaled data more accurately showed temperature changes in data-scarce mountain basins (Figure 5).

4.2. Climate and Runoff Processes in Mountainous Rivers

In high mountainous watersheds, runoff is mainly supplied by precipitation and glacial snowmelt water, among which precipitation mainly supplies runoff in the form of rainfall and snowfall [44,70]. Above the snow line, snow transforms into glaciers and snow, which melts as temperatures increase, thereby replenishing runoff [71]. Studies have shown that glacier meltwater accounts for about 20% to 40% of total runoff in the Tianshan Mountains [72]. In the context of climate warming, the precipitation form in mountainous areas has changed, which has caused changes in the runoff process [73,74]. In rivers dominated by snowmelt runoff, a decrease in snowfall rates will lead to a shift to precipitation [75], thereby altering the seasonal distribution of runoff and leading to earlier flood peaks [76]. Studies have shown that the contributions of precipitation and temperature to runoff were 36% and 64% in KuRB, 52% and 48% in TRB [70], and 56% and 44% in KRB [15], which is consistent with our results.

To further understand the mechanisms of climate change driving runoff in the Tianshan Mountains, selecting KRB as an example, this section first compared the changes of temperature, precipitation, and runoff, then analyzed glacier and snow changes. Figure 6a shows that runoff has an annual distribution consistent with temperature and precipitation. In summer, temperature is the highest, precipitation is abundant, and runoff is the most abundant. Interannual variation shows that runoff is consistent with the changes in temperature and precipitation, and runoff increases (decreases) when the temperature and precipitation increase (decrease) (Figure 6).

In the context of global warming, glacier and snow areas in KRB have changed. Bai [77] extracted the glacier area of KRB based on the cataloging data of two glaciers periods. Compared with the first statistical period (1956–1983), the glacier area in the second statistical period (2005–2010) decreased by 45.27% (Figure 7a). Warming is not only causing glaciers to retreat, but also accelerating snow melt. In the past few decades, the snow depth of KRB decreased; downward trends were most obvious in central and eastern regions. Relative to January 1980, snow depth in the northeastern mountains decreased by 10 cm (Figure 7b). Previous studies have shown that the correlation coefficients between temperature and snow cover in KRB are −0.81, −0.48, −0.80, and −0.82 in spring, summer, autumn, and winter, respectively. The above results confirmed that temperature has an important impact on the runoff change in high mountainous areas.

This research indicates that high mountains have more sensitive responses than plains to global climate changes. In mountainous areas, glaciers and snow are widely distributed, and plant diversity is abundant [78]. In valleys and plains, topography, latitude, and ecosystem stability may cause a buffering effect [79], with slower increases in temperature and precipitation than in mountains. The increase of precipitation is faster in mountainous areas than in plains, which is consistent with results from other studies [80]. In mountainous areas, increasing temperature accelerated the melting of snow and glaciers, leading to increased water vapor. Moreover, low saturated water vapor pressure in mountainous areas is conducive to the formation of precipitation [81].

Driven by climate change, runoff decreased in the KaRB in the past 40 years, which was mainly caused by decreasing precipitation. The KaRB is located near the Ili River Valley, and the decrease in precipitation may be related to the North Atlantic Drift [82]. At the same time, runoff increased in MRB, URB, KuRB, TRB, and KRB, but there are significant differences in the increase rate among different basins, and previous studies [70] have supported this.

4.3. Limitations

This study simulated high-resolution temperature and precipitation by downscaling reanalysis products. For alpine mountain areas, reanalysis products spatially distributed climate data. However, there is a deviation between the simulations of reanalyzed products and observed data, and the accuracy of products needs to be further improved. In addition, vegetation impacts climate change in mountainous areas, especially precipitation [83]. Due to the short time series and low spatial resolution of existing vegetation data, this study only introduced geographical and terrain factors in climate downscaling. In future research, the accuracy of downscaling results can be further improved if vegetation data with high temporal and spatial resolution are obtained.

This study mainly analyzed the impact on runoff of two main climate variables, temperature, and precipitation. In high mountainous basins, glaciers and snow melt are the main supplies of runoff. In future research, it is necessary to quantify the contributions of glaciers and snow to runoff change, to more clearly understand the mechanisms of climate change driving runoff. In addition, this study did not analyze the impact of alpine permafrost thawing on runoff change.

This study used beta coefficients (partial regression coefficients) of regression models to calculate the contributions of temperature and precipitation to runoff change. The bias of precipitation and temperature will lead to uncertainty in the calculation results of contribution ratio. In addition, as a component of the regression model, the contribution of regression constants to runoff were not calculated in this study. In future research, we will make improvements to the model to enhance its applicability.

5. Conclusions

Based on reanalysis products, this study developed an integrated method to calculate the contributions of climate change on runoff, in data scarce high mountains. Applying this method to six mountainous basins originating from the high Tianshan Mountains, this study found that, in high mountains, runoff changes are mainly affected by temperature, whereas in lowlands, precipitation contributes more than temperature to runoff changes. The contributions of precipitation and temperature change to runoff were 20% and 80%, respectively, in the Kumarik River. This study also found that climate changes are more significant in high mountains than in lowlands.

The present study lays the groundwork for future research using runoff simulations, which is of great significance to hydrological forecasting and water resource management in mountainous basins. This study highlights the impact of glaciers and snow on mountainous runoff. Thus, introducing the distribution of glaciers and snow into a hydrological modeling framework could better characterize runoff. Based on future climate scenarios, water management planning should be oriented to generate new strategies to cope with possible future changes in the strength of seasonality, and other variables.