The Weihe River Basin (104°00′∼110°20′E, 33°50′∼37°18′N) is located south of the Yellow River. The river system is distributed in a fan shape, with an area of approximately 13.48 × 104 square kilometers (Figure 1). The northwestern edge is relatively high and belongs to the Loess Plateau, and the southeastern part is relatively low and belongs to the plains. The basin belongs to the arid and semi-arid region. It is in the continental monsoon climate zone. Affected by the monsoon climate, the precipitation decreases from southeast to northwest, and the average annual precipitation in the basin is approximately 573 mm (Du and Shi, 2012). The average annual temperature is 7.8∼13.5 °C, and the average annual temperature shows a decreasing trend from east to west and from south to north. The Wei River basin is located in a transitional zone between the Guanzhong Plain and the Loess Plateau, making it an ecologically fragile area that is highly susceptible to the severe impacts of climate change and human activities. The Wei River basin is located in the transitional zone between the Guanzhong Plain and the Loess Plateau, and its ecosystem is relatively fragile. It is easily and severely affected by climate change and human activities (Li et al., 2019). The Wei River basin faces water scarcity, sediment deposition, and water quality problems, prompting the development of integrated management strategies (Gao et al., 2013). In this paper, the area north of the Weihe River channel is the north bank and the area south of it is the south bank. The north bank is mostly the Loess Plateau area, and the south bank is the Qinling Mountains area. The area of the north bank is significantly larger than that of the south bank. Due to the increase of population, agricultural production and industrial activities, the rapid decrease of river flow and groundwater (Chang et al., 2015) has led to the increasingly serious problem of river ecological drought in the basin (Gai et al., 2019).

There are 11 hydrological stations on the north bank, including Jingning Station, Qin’an Station, Longde Station, Shetang Station, Fenggeling Station, Zhuyuan Station, Qianyang Station, Antou Station, Liulin Station, Yaoxian Station, and Chunhua Station; and 7 hydrological stations on the south bank, including Gangu Station, Tianshui Station, Laoyukou Station, Dayu Station, Qinduzhen Station, Luolicun Station, and Luofubao Station. The hydrological data used in this study were obtained from the Annual Hydrological Report of the People’s Republic of China: Hydrological Data of the Yellow River Basin, with a time series from 2006 to 2020. Meteorological data are from the China Meteorological Science Data Sharing Service Network (http://data.cma.cn). The geographical locations of the hydrological and meteorological stations are shown in Tables 1, 2. Land use data are provided by the Resources and Environmental Sciences Data Center (RESDC) of the Chinese Academy of Sciences (http://www.resdc.cn).

In studies, the low flow index is often used to reflect the characteristics of groundwater recharge of river runoff in each tributary. The product of the low flow index and the total annual runoff is used as the observed value of the annual base flow (Smakhtin, 2001). Q o i = Q 90 Q 50 Q i (8)

In the formula, Q _oi represents the observed annual base flow. Q ₉₀ and Q ₅₀ represent the annual daily runoff when it is below 90% and 50%, respectively. Q _i is the annual runoff. Q ₉₀ represents high-probability flow and reflects the groundwater recharge maintenance status during periods of insufficient supply (Nicolle et al., 2014). Q ₉₀ /Q ₅₀ is interpreted as an indicator to measure the relative contribution of base flow, while also reducing the influence of drainage area (Kissel and Schmalz, 2020).

To evaluate the effectiveness of baseflow separation, we used the Nash-Sutcliffe efficiency coefficient (NSE) and the Kling-Gupta efficiency coefficient (KGE). These two coefficients are widely used in hydrological modeling and provide different diagnostic information (Gupta et al., 2009; Moriasi et al., 2015). The NSE is used to evaluate the drought index estimate and the baseflow separation estimate (Nash and Sutcliffe, 1970): NSE = 1 − ∑ i = 1 n Q m i − Q o i 2 ∑ i = 1 n Q o i − Q ¯ o 2 (9)

In the formula, Q _mi is the base flow rate for the ith year calculated by the base flow segmentation method, and Q _o is the average annual base flow rate estimated by the drought index. The value of NSE is generally between 0 and 1. The closer the NSE value is to 1, the better the estimation effect; the closer the NSE is to 0, the worse the estimation effect.

KGE was used to evaluate the accuracy of nine base current separation methods (Knoben et al., 2019): KGE = 1 − r − 1 2 + σ m σ o − 1 2 + Q m Q o − 1 2 (10)

In the formula, r is the Pearson correlation coefficient between the observed baseflow and the baseflow calculated by the baseflow separation method. σ m is the standard deviation of the baseflow calculated by the baseflow separation method. σ o is the standard deviation of the observed baseflow. Q _m is the average value of the baseflow calculated by the baseflow separation method.

In this study, we employed a sliding T-test with a significance level set at P = 0.05 (Rougé et al., 2013). The sliding T-test examines whether the difference between the means of two groups of samples is significant. This method treats two subsequences in a hydrological sequence as questions of whether there is a significant difference between the means of two populations. If the difference between the means of the two subsequences exceeds a certain significance level, it can be considered that the means have undergone a qualitative change and that variation has occurred (Menghui et al., 2021). The sliding t-test, which identifies statistically significant breakpoints, is widely recommended for hydroclimatic and hydrological time series analysis and was used in this study for variability and attribution analysis (Reeves et al., 2007; Rougé et al., 2013). The sliding t-test has advantages in diagnosing contrasts between multiple stations and sub-basins (Xie et al., 2019). Since sliding window testing is sensitive to the window length, we conducted tests using different window sizes. This was done to ensure that the results remained consistent within a reasonable range of window sizes, thereby reducing errors caused by window selection. (Aminikhanghahi and Cook, 2017).

For a time series x with n samples, a certain time point is arbitrarily set as the baseline. The sample sizes of the two subsequences x ₁ and x ₂ before and after the baseline are n ₁ and n ₂, respectively. The average values of the two subsequences are x1 and x2, respectively. Define the following statistics: t = x ¯ 1 − x ¯ 2 s 1 n 1 + 1 n 2 (11)

In the formula, S = n 1 s 1 2 + n 2 s 2 2 n 1 + n 2 − 2 (12)

Equation 12 follows a t-distribution with degrees of freedom V = n 1 + n 2 − 2 .

The Slope Change in Cumulative Baseflow (SCRCQ) method is used to quantify the impact of climate change and human activities on baseflow changes. Specifically, we use precipitation (P), potential evapotranspiration (PET), and air temperature (T) to characterize climate drivers. This is because P, PET, and T effectively represent water supply and atmospheric water demand (Wang and Hejazi, 2011). This provides a concise and physically meaningful basis for distinguishing between climate-driven changes and anthropogenic influences, and the PET variable incorporates the effects of variables such as solar radiation (Yang and Yang, 2011). On the cumulative baseflow curve, the fitted linear slope represents the average annual rate of baseflow change. Within the SCRCQ framework, the contribution rate of a driving factor can be estimated by the ratio of its slope change to the change in the cumulative baseflow slope (Zhou et al., 2023). The slopes of the linear relationship between cumulative baseflow and time for the two periods before and after the change point are S _Ba and S _Bb , respectively. The slopes of the linear relationship between cumulative precipitation and time for the two periods before and after the change point are SPa and S _Pb , respectively. The slopes of the linear relationship between cumulative potential evaporation and time are SPETa and S _PETb , respectively. The slopes of the linear relationship between cumulative actual evaporation and time are STEMA and S _TEMAb , respectively. The calculation process of the SCRCQ method is as follows: S B = S B b − S B a S B a (13) S P = S P b − S P a S P a (14) S P E T = S P E T b − S P E T a S P E T a (15) S T E M = S T E M b − S T E M a S T E M a (16) C P = 100 × S P S B (17) C P E T = − 100 × S P E T S B (18) C T E M = − 100 × S T E M S B (19) C H = 100 − C P − C P E T − C T E M (20)

In the formula, S _B , S _P , S _PET , and S _TEM represent the cumulative slopes of baseflow, precipitation, potential evapotranspiration, and temperature, respectively. C _P , C _PET , C _TEM , and C _H represent the contribution rates of precipitation, potential evapotranspiration, temperature, and human activities to baseflow variation, respectively.

Tables 3, 4 show the baseflow characteristics and BFI values for different segmentation methods in the Wei River Basin, respectively. The baseflow of the rivers (11 tributaries) on the north bank of the Wei River ranges from 1.44 to 188.01 × 10⁶, with BFI values ranging from 0.39 to 0.79. The baseflow of the rivers (7 tributaries) on the south bank of the Wei River ranges from 5.79 to 131.29 × 10⁶, with BFI values ranging from 0.29 to 0.70.

The results from the nine baseflow separation methods show significant differences. Table 4 shows that the BFI values of the five digital filtering methods differ significantly. The results obtained by the local minimum method (F6) and the smoothed minimum method (F7) show smaller differences, and the differences between the two BFI methods are also relatively small. On the north bank of the Wei River, the F8 method calculates the largest BFI value, while the F5 method calculates the smallest. However, on the south bank of the Wei River, the F4 method calculates the largest BFI value, while the F5 method calculates the smallest.

9 baseflow separation methods were used to segment the baseflow at 18 hydrological stations on both banks of the Wei River from 2006 to 2020. The evaluation results are shown in Figure 2. Each box in the figure represents the NSE and KGE distributions for the corresponding baseflow separation method at the 18 hydrological stations. In Figure 2a, the black horizontal line in each box represents the median NSE for the corresponding method, from left to right: 0.41, 0.73, 0.72, 0.43, 0.72, 0.40, 0.54, 0.44, and 0.53. The median KGE for each method is shown in Figure 2b, from left to right: 0.52, 0.76, 0.75, 0.45, 0.76, 0.35, 0.63, 0.47, and 0.49. Method F2 showed the highest NSE coefficient and KGE value, indicating the best performance.

Furthermore, we conducted a hydrological rationality analysis of the results from nine baseflow separation methods. Figure 3 shows the separation results of the nine methods. Among the digital filtering methods, the baseflow process lines of methods F1, F2, and F3 exhibited smaller fluctuations, smoother curves, and similar segmentation results. Compared to the baseflow process lines of other methods, these methods showed baseflow processes that better conformed to general laws and demonstrated better stability. The baseflow process line of method F4 was characterized by high and sharp peaks and relatively steep fluctuations. The baseflow process line of method F5 showed minimal fluctuations, significantly differing from the dynamic changes of the runoff process line. Methods F6, F7, and F8 showed obvious limitations when the flow process line suddenly and sharply increased. When the flow process line increased sharply, the baseflow process lines of these three methods remained stable, failing to reflect the dynamic characteristics of flow changes in a timely manner. In short-term events of rapid runoff increase, method F9 did not show corresponding fluctuations in the baseflow obtained. It was unable to accurately capture the interaction process between baseflow and surface runoff.

The results of climate change trend analysis provide a basis for studying the degree and manner (positive or negative) of baseflow impact. Based on precipitation, potential evapotranspiration, annual mean temperature, runoff, and optimal baseflow separation results on both banks of the Wei River basin, the changing trends of hydrometeorological variables were analyzed (Figure 4). The maximum annual precipitation and annual mean temperature in the Wei River basin occurred on the south bank in 2011 (811.71 mm) and 2006 (10.4 °C), respectively. Meanwhile, the maximum potential evapotranspiration occurred on the north bank in 2006 (1047.71 mm). Precipitation on both banks of the Wei River basin showed an increasing trend, while potential evapotranspiration and temperature showed a decreasing trend. Specifically, the increase in precipitation was greater on the north bank than on the south bank, while the decrease in potential evapotranspiration and temperature was greater on the south bank than on the north bank.

As shown in Figure 4, the base flow and runoff on the north bank of the Wei River reached their maximum in 2020, at 69.64 × 10⁶ m³ and 149.79 × 10⁶ m³, respectively. The maximum base flow and runoff on the south bank occurred in 2014 and 2011, at 61.22 × 10⁶ m³and 124.29 × 10⁶ m³, respectively. Figures 4c,d show the process lines and trend lines for runoff, base flow, and BFI values on both the north and south banks of the Wei River basin. The slopes of runoff, base flow, and BFI values on both banks are positive, indicating an upward trend. The upward trend of runoff and base flow on the north bank is greater than that on the south bank. The annual increase in runoff and base flow on the north bank is approximately 3.71 × 10⁶ m³ (approximately 1.05 × 10⁶ m³ on the south bank) and 1.82 × 10⁶ m³ (approximately 0.83 × 10⁶ m³on the south bank), respectively, while the upward trend of BFI values on the south bank is greater than that on the north bank. The Mann-Kendall method was used to further analyze the trend significance of hydrometeorological variables in the study area, and the results are shown in Table 5. During the study period, precipitation, potential evapotranspiration, annual mean temperature, base discharge, runoff, and BFI values on both the north and south banks of the Wei River Basin did not show significant trends.

The determination of abrupt change points is closely related to the division of the baseline period and the variation period. This study uses the sliding T-test for analysis and comprehensively considers abrupt change points under three step sizes, selecting the year with the highest frequency as the abrupt change point. The identified variation points for all hydrological stations are summarized in Table 6. The variation point is determined based on the baseflow time series calculated using the F2 baseflow method, and the results are shown in Table 4. The variation years differ for different hydrological stations. The period before the first abrupt change point is defined as the baseline period, and the period after is defined as the variation period.

The SCRCQ method was used to estimate the contribution rates of climate change and human activities to baseflow changes at 18 hydrological stations on both banks of the Wei River. No contribution rate analysis was performed at the Antou station because no variation point was detected. According to Figure 5, the contributions of climate change and human activities to baseflow values at hydrological stations on the north bank of the Wei River ranged from −26.17% to 72.92% and 27.08%–126.17%, respectively. At hydrological stations on the south bank, the contributions ranged from 9.39% to 74.55% and 25.45%–90.61%, respectively. Baseflow changes at the Laoyukou, Dayu, and Luolicun stations on the south bank were mainly influenced by climate change. Meanwhile, on the north bank, only the Fenggeling and Qianyang stations showed baseflow changes primarily driven by climate change. However, the baseflow changes at the remaining 12 hydrological stations were mainly driven by human activities.

Based on current research, two main baseflow separation methods are widely recognized: tracer-based and baseflow separation methods, which are often considered the dividing line between other non-tracer methods. However, due to the lack of tracer observation data, this method is not suitable for long-term, large-scale watershed studies (Zhang et al., 2017). Given this, there is an urgent need to enrich the baseflow separation algorithm system in scenarios involving large-scale, long-term studies or when tracer data is lacking. Therefore, this study combines five digital filtering methods with four graphical methods to reduce the uncertainty of the research results. As can be seen from Figure 3, the four graphical methods performed poorly in the baseflow separation process. Parameter estimation may be the main reason for their poor applicability in the Weihe River Basin. For example, the local minimum method (F7) only considers the catchment area when estimating the parameter N value, without taking into account the influence of climate and topography on direct runoff. This may lead to an overestimation of the N value, thus affecting the accuracy of the baseflow calculation. In particular, the smoothing minimum method (F6) directly uses the empirical coefficient 5 as the direct runoff duration, ignoring other key factors, which may also be the reason for its poor performance. In the digital filtering method, although F1 to F4 all use fixed filtering parameters, their baseflow calculation results are still different, which shows that the internal mechanism of the method has a greater impact on the baseflow separation results than the parameters. The F5 method is based on calculations using the maximum base flow index and the recession constant. However, precipitation in the Wei River basin is highly concentrated during the flood season, and frequent heavy rainfall easily generates short-term flood runoff. This significantly interferes with the parameter estimation of the maximum base flow index, ultimately leading to lower accuracy in the base flow calculation results of this method. Similar conclusions were also verified by Xie et al. (2020) when studying the baseflow separation results of 1815 adjacent watersheds in the United States.

The results show (Figure 4) that the trends of baseflow, runoff and precipitation on both sides of the Wei River are consistent, while they are opposite to the trends of potential evapotranspiration and annual average temperature. Figure 6 shows the correlation between baseflow, runoff, precipitation, potential evapotranspiration and temperature on both sides of the Wei River. It can be seen from the figure that the correlation between baseflow and runoff and precipitation on the north bank of the Wei River is significantly stronger than that with potential evapotranspiration. Both baseflow and runoff on both the north and south banks are significantly positively correlated with precipitation. At the same time, they are negatively correlated with potential evapotranspiration and temperature, with the weakest correlation with temperature. The relationship between runoff and precipitation and potential evapotranspiration is closer than that between baseflow and precipitation, indicating that precipitation is the main source of runoff in the Wei River Basin. The infiltration process of precipitation is affected by vegetation and soil, while potential evapotranspiration will lead to soil moisture evaporation, thereby reducing the amount of soil water supplied by precipitation and indirectly reducing the generation of baseflow (Li-qun et al., 2006; Shi et al., 2023). Therefore, the impact of precipitation on baseflow is relatively small. In addition, many scholars have also found that precipitation and potential evapotranspiration have a greater impact on runoff and baseflow when studying the impact of climate change on runoff and baseflow. Precipitation is positively correlated with baseflow and runoff, while potential evapotranspiration and temperature are negatively correlated, which is consistent with the results of this study (Tan et al., 2020; Wu et al., 2020; Li et al., 2021).

The results of the study indicate that human activities are the main cause of changes in baseflow, which is consistent with the findings of Mo et al. (2021) and Shi et al. (2023). Figure 7 shows the spatial distribution of land use in the Weihe River Basin in 2005 and 2020. As can be seen from the figure, the main land types in the Weihe River Basin are cultivated land, forest land and grassland. Among them, cultivated land has the widest distribution area, mainly concentrated in the southeast of the Weihe River. Forest land is mainly distributed in the Qinling Mountains in the south of the Weihe River and the plateau area in the central and eastern parts. From 2005 to 2020, the cultivated land area decreased by 3171.31 km², the grassland area increased by 1512.11 km², the water area decreased by 3598.72 km², while the construction land area increased by 5123.22 km². The expansion of construction land has led to an increase in the demand for industrial and domestic water. With the development of the economy and society and the improvement of water conservation awareness, the efficiency of industrial and domestic water use may be improved. In addition, the “Hanjiang-to-Weihe River Diversion Project” has also increased the runoff and baseflow of the Weihe River. After the implementation of the policy of returning farmland to forest and grassland, the cultivated land area in the Weihe River Basin gradually decreased, and at the same time, the agricultural irrigation method changed, and the demand for irrigation water decreased accordingly (Xue et al., 2021). This is also one of the important reasons for the corresponding increase in runoff and baseflow. The increase in grassland area has improved the soil’s water holding capacity and improved the groundwater recharge conditions, thereby further promoting the increase in baseflow.

To select the optimal baseflow separation method, nine baseflow separation methods were compared. Among them, the digital filtering method exhibits certain uncertainties. In quantifying the impact of climate change and human activities on baseflow, this study adopted the SCRCQ method, but this method also has certain uncertainties.

When using the digital filtering method for baseflow separation, the selection of parameters has a significant impact on the baseflow calculation results. Therefore, the uncertainty of parameter selection is one of the key factors affecting the accuracy of the analysis. However, this study did not conduct a specific optimization analysis of the digital filtering parameters for the study area, but directly adopted the default parameters of the method without calibrating the optimal parameters for the study area. Although the default parameters have been widely used under similar hydrological conditions and their applicability has been verified to some extent, the hydrological, meteorological, and underlying surface conditions of the study area may differ from the applicable range of the default parameters. Unoptimized parameter settings may introduce certain uncertainties. Therefore, it is recommended that future studies fully consider the uncertainties brought about by parameter selection and conduct optimization analysis.