The Application of Baseflow Separation and Master Recession Curves Methods in the Middle Yellow River Basins

Abstract

Baseflow is the part of the groundwater aquifer that replenishes surface streamflow and is one of the main components of studying the interaction between groundwater and surface water. It is a key factor in maintaining the healthy development of basin ecosystems and is of great significance for promoting the sustainable utilization and scientific management of water resources. However, the understanding of runoff and baseflow in the MYRB is still unclear, and the relationship between streamflow and baseflow has not been fully grasped. At the same time, there is currently no water balance function applicable to the MYRB. In order to solve the above problems, this article uses digital filtering methods to segment the baseflow and the MRC method to construct the main recession curve. The baseflow rate of MYRB was calculated, and the water balance function applicable to MYRB was found. The results obtained are as follows: the average annual baseflow index values for different basins were 0.81, 0.76, 0.81, 0.82, 0.79, and 0.79, respectively. The fitting of the Boussinesq function, the Maillet function, and the Brutsaert and Nieber function was significantly better than the other two functions.

1. Introduction

After atmospheric precipitation (including snowfall and rainfall) lands on the surface, it will eventually flow into rivers, lakes, and other open water bodies in different forms, and ultimately into the ocean, participating in the global water cycle and the land–sea cycle [1]. However, after the precipitation process ends, the streamflow process is not entirely a simple linear accumulation [2]. The streamflow flowing out from the outlet section can be simply added up. However, due to a series of constraints on surface and subsurface hydrogeological conditions, including surface vegetation and geological conditions, the evapotranspiration of surface vegetation and differences in geological conditions can retain a portion of streamflow, thereby having a profound impact on the basin [3]. This part of the water flow will continue to replenish the river for a week or even several months. The delayed outflow of recharge river streamflow generated by the upstream and surrounding areas of the river is called the baseflow [4]. Due to different opinions in the academic community on streamflow segmentation methods and baseflow sources, the accurate definition of baseflow cannot be completely unified until now, and there are several other opinions [5]. The first statement: Researchers believe that streamflow from groundwater is the baseflow rate of rivers, hence it is called baseflow. The second argument is that due to the very slow process of deep underground streamflow, rivers can maintain a stable flow during the dry season, and are therefore referred to as baseflow by relevant scholars. Based on this, scholars who hold this view often consider the average annual minimum flow as the basin baseflow when calculating it [6]. Baseflow plays an important role and position in the composition of water resources. It is the guarantee of river streamflow during dry and arid/semi-arid seasons, and also a concrete manifestation of water resource abundance. The baseflow is closely related to precipitation, climate [7], and basin size; therefore, calculating the baseflow reasonably is an urgent task at present [8]. For a long time in the past, many researchers have proposed different methods for this, such as the sliding minimum method [9], the hydrological model method [10], and the digital filtering method [11,12], among others. These methods have been tried, but their scope of application varies greatly, and the conditions of use also differ greatly [6,13].

Under arid and rainless climate conditions, water stored in basins is mainly transported through soil, groundwater, and vegetation transpiration [14]. Due to the differences in regional hydrological characteristics, this process has obvious spatiotemporal variations. Due to some shortcomings in existing experimental methods and theoretical assumptions, it is difficult to experimentally measure baseflow, and the simulated quantities obtained from different theories also vary greatly [15]. The process of streamflow recession refers to the continuous drainage and recession process during periods of little or no rainfall, and is an important component of hydrological processes. The recession curve is the relationship between water content θ and soil water potential φ. This curve is a characteristic of different types of soil, also known as soil moisture properties [16]. Analyzing the characteristics of groundwater withdrawal under drought and low rainfall conditions is helpful for studying the recharge rate of groundwater to surface streamflow and the changing characteristics of groundwater. Various methods are used to analyze the groundwater withdrawal process under these conditions, which is collectively referred to as withdrawal analysis [17]. Groundwater will continuously decrease due to insufficient recharge in the absence of precipitation and with very little precipitation, forming a gradual water withdrawal process. The rate of decline in this continuous drainage process is called the water withdrawal constant, which can be analyzed through the water withdrawal curve [18]. Understanding the process of water withdrawal is also an important aspect of studying basin water balance and hydrological response [4,19]. If the influence of factors such as rainfall infiltration, evaporation, and groundwater exploitation in the basin is not considered, the drawdown curve of the basin can be established based on the relationship between water storage and outflow. This relationship can then be combined with continuity functions to establish the relationship between outflow and time. This relationship can be used for dry season streamflow prediction, groundwater streamflow convergence calculation in hydrological models, water resource evaluation, and planning and management. Other applicable methods include short-term forecasting for irrigation, water supply, and groundwater resource estimation, among others [20,21].

In practical applications, the recession flow rate and aquifer storage capacity are usually represented as a linear relationship to derive the recession process of groundwater streamflow in a basin. However, the recession process of groundwater streamflow may not be the same in different basins, and analysis is needed from measured data. The most important aspect of recession analysis is recession curve analysis [22]. The drawdown curve is a simple and universal method for describing the feedback and replenishment of groundwater to rivers. The drawdown curve contains rich information on groundwater storage and aquifer characteristics, making drawdown analysis of significant value in water resource planning and management [5,23]. The main focus of baseflow prediction is on water supply, irrigation management, hydropower, and the treatment of river pollutants. Mathematical simulation mainly involves calibrating rainfall streamflow models and inputting parameters. In terms of process line analysis, the main focus is on dividing streamflow. Frequency analysis of baseflow. The study of regional baseflow is mainly applied to the research of water storage in basins [24,25]. Recession analysis is an objective and effective method for analyzing the flow rate of streamflow baseflow, and its conclusions often contain a wealth of valuable information [26,27]. The recession analysis method has always been the main analysis method for many hydrological researchers [28]. It can effectively perform automated analysis and can process unified data multiple times. In addition, it can reduce the uncertainty caused by the supervisor’s judgment during the analysis process and improve accuracy [29,30]. For example, using a simple exponential function for recession analysis depends on the choice of starting point and segment length. In some small basin recession analysis, it is difficult to obtain a reasonable baseflow. This is because the baseflow process has already been carried out for a period of time (usually a few days) before the selection of the baseflow starting point, which improves the accuracy of the analysis [31,32].

Baseflow plays an important role in the protection and development of water resources, and the process of streamflow retreat is an important aspect of baseflow research. In most cases, the process of streamflow retreat requires both qualitative and quantitative calculations [33,34]. Starting from this perspective, this article first comprehensively summarizes the baseflow and streamflow retreat process of typical tributaries of the Yellow River and important water systems in MYRB. Multiple calculation methods are used to systematically summarize the sources, influencing factors, and overall situation of the baseflow and streamflow retreat process [35,36]. At the same time, various technological means are used to study and explore the flow situation and mathematical models of the middle reaches of the Yellow River. The main research objective of this article is to investigate the magnitude and variation of base streamflow in the middle reaches of MYRB, and to find a suitable flow model for subsequent calculations in the region.

2. Principles and Methods

2.1. Study Area

The research area of this study is MYRB. The Yellow River is known as the “cradle” or “mother river” of Chinese civilization and is the largest water source in northern and northwestern China [3,25]. The Yellow River originates from the Qinghai Tibet Plateau and flows along a winding west-to-east direction before discharging into the Bohai Sea [22,37]. The middle reaches of the Yellow River refer to the section from Hekou Town to Longmen, with a drainage area of 111,600 square kilometers, accounting for 14.8% of the Yellow River drainage area. The mainstream of the Yellow River, also known as Jinshanxia, is 723 km long, with a drop of 607 m and a slope of 0.84‰. The valley has steep slopes and narrow river channels [38,39]. MYRB belongs to a temperate continental monsoon climate, with an average annual precipitation of 300–550 mm, decreasing from southeast to northwest. The annual precipitation is highly concentrated in July, August, and September, accounting for 61.6% of the annual precipitation [18,22]. MYRB has a shortage of groundwater resources and a high degree of development and utilization. At the same time, the situation of coal mining in MYRB is severe, and the duration of coal mining is relatively long (Figure 1) [14,40]. In response to the above issues, this article selects three typical tributaries in MYRB, the Fen River Basin, the Beiluo River Basin, and the Yihe River Basin for research [14,17].

The Hetao Plain and Fenwei Plain, which flow through the middle reaches of the Yellow River, are important agricultural irrigation areas [36]. The Yellow River provides abundant water sources for agricultural production in these areas. However, the relationship between baseflow and streamflow in the MYRB is still unclear, and the most suitable water balance function for the middle reaches of the MYRB is also unclear. This article aims to calculate the baseflow rate and baseflow index in the middle reaches of the Yellow River MYRB, and find a suitable water balance function for the MYRB. The current work is to segment the baseflow in the MYRB using various base flow segmentation methods, obtaining specific baseflow rates and baseflow indices. At the same time, the MRC method is used to fit the flow rate in the MYRB, observe the fitting situation, and select the most suitable water balance function for the region.

2.2. Method of Baseflow Separation

There are several mainstream methods for segmenting baseflow, including digital filtering, the time step method, the empirical formula method, the environmental isotope method, the hydrochemical method, and the hydrological model method, among others. Lyne et al. [41], Nathan and McMahon et al. [12], Chapman et al. [42], Arnold and Allen et al. [11,43], Eckhardt et al. [44] explored and improved digital filtering methods for segmenting base streams; they also proposed many digital filtering formulas suitable for segmenting base streams under different conditions and environments. This study mainly selected three non-chemical methods for baseflow segmentation: Digital Filtering Method 1 (DF1) [41], Digital Filtering Method 2 (DF2) [42], and Digital Filtering Method 4 (DF4) [44] (

Table 1. Baseflow index calculation functions.

Name	Functions	Source
Digital Filtering Method 1(DF1)	$B_i=\alpha B_{i-1}+(1-\alpha )/2\left(Q_i+Q_{i-1}\right)$ $q_i=Q_i-B_i$	[12,41]
Digital Filtering Method 2(DF2)	$B_i=\alpha /(2-\alpha )B_{i-1}+(1-\alpha )/(2-\alpha )Q_i$ $q_i=Q_i-B_i$	[42]
Digital Filtering Method 4(DF4)	$B_i=\left[\left(1-{BFI}_{max}\right)\alpha B_{i-1}+\left(1-\alpha \right){BFI}_{max}{Q}_i\right]/(1-\alpha {BFI}_{max})$ $q_i=Q_i-B_i$	[44]

).

2.3. Method of Construction of MRC

This article adopts some methods to construct and analyze the comprehensive drawdown curve. (1) Before constructing the comprehensive drawdown curve, it is necessary to determine the recession curve. To avoid the influence of noise on the flow data, a three-point moving average will be applied [45]. (2) The starting period of the recession curve should be known and considered to be when the ratio between continuous flows is less than zero (dQ/dt < 0) [46]. (3) The minimum duration of a recession should be clear and can be defined based on observations of streamflow sequence behavior and specific meteorological variables for each case studied [45,47]. If the start and duration can be confirmed, a recession curve will appear. (4) The matching strip method is used, which involves overlapping various recession curves to create a curve that represents the general behavior of the entire river flow data recession [46]. The matching strip method has the following steps: firstly, after confirming the recession curve, the point of the recession curve with the smallest Q value is considered as MRC data; secondly, keep the curve with the minimum Q value of MRC data static, and then move the curve horizontally from the minimum value to the maximum value based on the low Q value of MRC data. When moving, the position of the last curve with the same Q value as the MRC data of the curve to be moved should be found first. Then, the curve should be moved until its MRC data is the same as the point with the closest horizontal distance from that position to the previously mentioned position. If the position mentioned earlier cannot be found, the position of the curve point with the highest Q value will be considered as the position that should be found. (5) After all the movements, a common curve will be combined, which will be used to represent the Q-t function, called MRC (Figure 2). The functions in the table below (

Table 2. Q-t functions.

Conditions	Results	Source
Depuit–Boussinesq Aquifer model	$Q=Q_0{\left(1+kt\right)}^{-2}$	[48]
$S=kQ$ $ds/dt=-Q$ $Q=Q_0\left(t=0\right)$	$Q=Q_0{e}^{-kt}$	[49]
Depuit–Boussinesq Aquifer model	$Q=Q_0{\left(1+kt\right)}^{\mathrm{n}/(1-\mathrm{n})}$	[47]
Existing leakage situation	$Q+a=\left(Q_0+a\right)e^{-t/t\mathrm{*}}$	[50]
$S=k{Q}^{1/2}$ $ds/dt=-Q-Q_{et}$ $Q=Q_0\left(t=0\right)$	$Q=Q_{et}{tan}^2\left(arctan\sqrt{Q_0/Q_{et}}-\sqrt{Q_{et}}/kt\right)$	[34]

) will be used for matching and analyzing MRC.

2.4. Recession Analysis

Recession analysis is a statistical method used to study the relationship between variables. Its core purpose is to identify how independent variables affect the dependent variable and establish a mathematical model to predict or explain this relationship. Recession analysis can predict the value of Y based on known X, quantify the impact of each X on Y, and identify the true causal relationship among multiple variables. Correlation analysis studies whether phenomena are related, as well as the direction and degree of correlation; however, this generally does not distinguish between independent and dependent variables. Recession analysis requires analyzing the specific forms of correlation between phenomena, determining their causal relationships, and using mathematical models to represent their specific relationships.

2.5. Data

The daily streamflow data for the basins are from the measured streamflow data during the 1934–2020 period. These include the basin between Longmen hydrological station and Toudaoguai hydrological station, the basin between Huayuankou hydrological station and Longmen hydrological station, and the basin between Huayuankou hydrological station and Toudaoguai hydrological station. These are on the mainstream of the Yellow River and the Fen River Basin, Beiluo River Basin, and Yi River Basin. The data comes from National Earth System Science Data Center, National Science & Technology Infrastructure of China, whose URL is http://www.geodata.cn/ (accessed on 21 June 2024), the center arranges each year’s Hydrological Data of the Yellow River Basin compiled and printed by the Hydrological Bureau of the Ministry of Water Conservancy of the People’s Republic of China and uploaded by the Yellow River Water Conservancy Commission of the Ministry of Water Conservancy of the People’s Republic of China. The meteorological dataset is compiled from a combination of different data sources, the data from January 1951 to December 2010 was developed based on the “1951–2010 China 2474 National Ground Station Data Corrected Monthly Report Data File Basic Data Set” archived by the Ground Basic Meteorological Data Construction Project, the data from January 2011 to December 2014 was developed based on the ground monthly report data files reported by each province to the National Meteorological Information Center, the data for January 2015 to February 2015 was developed based on real-time database data of the National Meteorological Information Center, which was uploaded in real time from the hourly and daily data files of the ground automatic stations. At the same time, 90-m resolution digital elevation data from the Shuttle Radar Topography Mission (SRTM) products has been adopted (

Table 3. Base information of datasets.

Category	Dataset	Properties	Source
streamflow	Hydrological Data of the Yellow River Basin	Measured streamflow data during the period of 1934–2020	http://www.geodata.cn/ (accessed on 21 June 2024)
meteorological	(1) 1951–2010 China 2474 National Ground Station Data Corrected Monthly Report Data File Basic Data Set (2) Ground monthly report data files reported by each province to the National Meteorological Information Center (3) Real-time database data of the National Meteorological Information Center	January 1951 to December 2010 January 2011 to December 2014 January 2015 to February 2015	http://www.resdc.cn/ (accessed on 23 June 2024)
DEM	Shuttle Radar Topography Mission (SRTM) products	90-m resolution digital elevation	https://www.gscloud.cn/ (accessed on 25 June 2024)

).

3. Results

3.1. Situation of Baseflow in MYRB Temporal and Spatial Variations

From the figure (Figure 3), it can be seen that the flow rate of the main stream basins is relatively high, basically above 800 m³/s. In contrast, the baseflow and discharge in the Fen River Basin, Beiluo River Basin, and Yi River Basin are relatively small, only 20 m³/s. The calculation process of the seven digital filtering methods used to divide the baseflow of six basins is also roughly the same. The baseflow obtained after segmentation calculation is also reasonable, without any special or abnormal situations. The six basins involved in this article include three main Yellow River basins and three tributary basins. The three tributary basins are the three typical sub-basins of MYRB. Through the flow data of the six basins, the baseflow segmentation results of each basin at different time periods can be obtained. Therefore, multiple different baseflow segmentation methods were used to segment the streamflow data of six basins, and the segmentation effects of different methods were compared to accurately describe the characteristics of baseflow changes.

After parameter adjustment, the baseflow indicators calculated by the three digital filtering methods and the other four similar digital filtering methods for different basins are inconsistent. The multi-year average baseflow indicators obtained by multiple segmentation methods are between 0.50 and 0.80. The average annual baseflow index calculated by DF1 (ά = 0.925) method is about 0.70, the average annual baseflow index calculated by DF1 (ά = 0.95) method is about 0.65, the average annual baseflow index calculated by DF2 (ά = 0.925) method is about 0.51, the average annual baseflow index calculated by DF2 (ά = 0.95) method is about 0.52, the average annual baseflow index calculated by DF4 (ά = 0.925, BFI_max = 0.70) method is about 0.69, the average annual baseflow index calculated by DF4 (ά = 0.925, BFI_max = 0.80) method is about 0.72, and the average annual baseflow index calculated by DF4 (ά = 0.95, BFI_max = 0.80) method is about 0.72. The calculated annual average baseflow index is approximately 0.73. From the table, it can be seen that the annual average baseflow index calculated by the DF1 (ά = 0.925), DF4 (ά = 0.925, BFI_max = 0.80), and DF4 (ά =0.95, BFI_max = 0.80) methods is relatively large. The annual average baseflow index calculated by the DF1 (ά = 0.95) and DF4 (ά = 0.925, BFI_max = 0.70) methods is mostly in the middle. In comparison, the annual average baseflow index calculated by the DF2 (ά = 0.925) and DF2 (ά = 0.95) methods is relatively small.

From the figure (Figure 4), it can be seen that during the calculation period, the calculation results of the baseflow indicators in each basin of the Yellow River main stream were relatively stable, basically maintaining a flat and stable trend, without obvious downward or upward fluctuations. This may be because the Yellow River main stream is less affected by external factors. Compared with the calculation results of various basins in the mainstream of the Yellow River, there is a significant fluctuation trend in the baseflow index of the three sub-basins of the Yellow River. Among them, the baseflow index of the Fen River basin shows a downward trend over time and maintains this trend during the calculation period. The baseflow index of the Beiluo River Basin showed an upward trend before 1990, and then significantly decreased thereafter. The calculation results of the baseflow index in the Yi River Basin are unstable, showing an upward trend from 1981 to 1989 and a downward trend from 2011 to 2020, respectively.

It can be seen that the maximum, minimum, and average values of the characteristic values of the baseflow indicators for different basins calculated by the DF2 (α = 0.925) and DF2 (α = 0.95) methods are about 0.55, which is smaller than those of other methods. The extreme value ratio calculated by the DF1 (α = 0.925) method and the DF4 (α = 0.925, BFI_max = 0.70) method is higher than that of other methods. The standard deviation calculated by various methods is relatively small, all below 0.10. Based on the changes in numerical values, we know that the results obtained by using digital filtering methods to calculate the baseflow indicators of each basin have little variation. There are some internal mutations, which prove that there are also some changes in flow on the time scale. From the calculation results of the characteristic values of basic traffic indicators, it can be seen that the results of various methods are relatively good, and the differences in time scales are small. According to the sensitivity of this method, parameter adjustment indeed affects the calculation results of this method. For the DF1 method, the impact of alpha value changes is relatively small. The adjustment of the alpha value has a greater impact on the calculation results of the DF2 and DF4 methods than on the DF1 method. The change in BFI_max value has little impact on the calculation results.

3.2. Situation of Application to the Basins of the MRC

The data points in Figure 5a of the figure (Figure 5) exhibit a significant, abrupt downward trend at the tail end. Except for the Wangdingbao and Caiximing functions, which can fit the tail-end downward trend, all other functions can only match the front-end trend of the data. From the graph, it can be seen that the Boussinesq function, Maillet function, Brutsaert and Nieber function, and Chapman function all show a decreasing slope trend. In contrast, the Wangdingbao and Caiximing functions show an increasing slope trend. In terms of fitting degree, the Boussinesq function has a better fitting degree; the data points in Figure 5b show a significant, abrupt downward trend after time 40. From the graph, it can be seen that the Boussinesq function, Brutsaert and Nieber function, and Wangdingbao and Caiximing function all have a decreasing slope. In contrast, the Maillet function and Chapman function have an increasing slope. In terms of fitting degree, the Boussinesq function, Brutsaert and Nieber function, and Wangdingbao and Caiximing function fit better, while the Maillet function and Chapman function deviate far from the data points and fail to fit the data points well; the data points in Figure 5c show a significant, abrupt downward trend at the end. From the graph, except for the Chapman function, all other functions show a decreasing slope. In terms of fitting degree, the Boussinesq function, Maillet function, Brutsaert and Nieber function, and Wangdingbao and Caiximing function fit better, while the Chapman function can only fit a small number of data points. The data points in Figure 5d show a significant, abrupt downward trend at the end. From the graph, it can be seen that all functions have a decreasing slope. In terms of fitting degree, except for Chapman’s function, the fitting degree of other functions is very high, which can match the vast majority of data points. Except for the data with an abrupt downward trend at the end, the data can basically fall within the range of the fitting function. The data points in Figure 5e are different from those in other figures, and there is no abrupt decrease in the tail end. From the figure, all functions show a decreasing trend in slope. In terms of fitting degree, except for Chapman’s function, the other functions can basically fit all the data points and perfectly match all the experimental data. Currently, the fitting situation in this figure is the best among all the figures; the data points in Figure 5f exhibit a sudden decrease at time 60. From the graph, it can be seen that all functions show a decreasing slope trend. In terms of fitting degree, almost all functions have a certain degree of fitting difference, and there are cases of fitting mismatch. Relatively speaking, Brutsaert and Nieber function, Maillet function, and Wangdingbao and Caiximing function fit better.

Overall, in the early stage of the curve trend, all functions maintained a downward trend. As time passed, some functions, such as the Boussinesq function and the Brutsaert and Nieber function, showed a significant slowdown in their downward trend. In contrast, the downward trend of other functions became increasingly larger. The rate of decline in the later stage will become faster and faster. From the perspective of fitting, each function has a different fitting situation, with differences. Functions with good matching can basically fully fit the research data, while functions with poor matching can only partially fit the data points, that is, only fit the previous part of the data. From a global analysis, for this research period and basin, the Boussinesq function and Brutsaert and Nieber function have better fitting situations, significantly better than the other three functions. They are more suitable as comprehensive recession curve functions.

The data points in Figure 6a of the figure (Figure 6) exhibit a significant, abrupt downward trend at the tail end. Except for the Wangdingbao and Caiximing functions, which can fit the tail-end downward trend, all other functions can only match the front-end trend of the data. From the graph, it can be seen that the Boussinesq function, Maillet function, Brutsaert and Nieber function, and Chapman function all show a decreasing slope trend. In contrast, the Wangdingbao and Caiximing functions show an increasing slope trend. In terms of fitting degree, the Boussinesq function has a better fitting degree; the data points in Figure 6b show a significant, abrupt downward trend after time 20. From the graph, all functions show a decreasing slope. In terms of fitting degree, the Boussinesq function, Maillet function, Brutsaert and Nieber function, and Chapman function have a better fitting degree compared to the Wangdingbao and Caiximing functions, which better reflect the complementary advantages of data points and functions. The Wangdingbao and Caiximing functions did not fit the data points well; the data points in Figure 6c show a significant, abrupt downward trend at the end. From the graph, except for the Wangdingbao and Caiximing functions, all other functions show a decreasing slope. In terms of fitting degree, except for the Wangdingbao and Caiximing functions, all other functions fit well. Most of the data can be fitted appropriately or fall within the fitting range on both sides of the fitting function. The data points in Figure 6d show a significant, abrupt decrease trend after time 40. From the graph, all functions show a decreasing slope trend. In terms of fitting degree, almost all functions can fit the data, except for the data with an abrupt decrease at the end, and can match the vast majority of data points. The front-end data can basically fall within the range of the fitting function. The data points in Figure 6e are different from those in other figures, and there is no abrupt decrease at the tail end. From the figure, except for the Chapman function, all other functions show a decreasing trend in slope. From the fitting degree, the Chapman function and Maillet function can basically fit all the data points perfectly and match all the experimental data. However, the other three functions have a certain degree of deviation and can only fit the front-end data. The data points in Figure 6f exhibit a sudden decrease at time 50. From the graph, except for the Chapman function and Maillet function, all other functions show a decreasing slope trend. In terms of fitting degree, excluding the terminal mutation data, the fitting of other functions is relatively good and can basically fit the experimental data. Therefore, they can be used as fitting functions.

Overall, in the early stages of the curve trend, all functions maintained a downward trend. Over time, some functions, such as the Boussinesq function, the Maillet function, and the Brutsaert and Nieber function, showed a significant slowdown in their downward trend, while others showed an increasing downward trend. The rate of decline in the later stages will become faster and faster. From the perspective of fitting, each function has a different fitting situation, with differences. Functions with good matching can basically fully fit the research data, while functions with poor matching can only partially fit the data points, that is, only fit the previous part of the data. From a global analysis, for this research period and basin, the Boussinesq function and Maillet function have better fitting situations, significantly better than the other three functions. They are more suitable as comprehensive recession curve functions.

3.3. Situation of Application to Hydrologic Stations of MRC

The data points in Figure 7a of the figure (Figure 7) are smooth and continuous, with little decrease at the end. Except for the Maillet function, which can fit the downward trend at the end, all other functions can only match the front-end trend of the data. From the figure, the Boussinesq function, Maillet function, Brutsaert and Nieber function, and Chapman function all show a decreasing slope trend. In contrast, the Wangdingbao and Caiximing functions show an increasing slope trend. In terms of fitting degree, the Maillet function has a better fitting degree; the data points in Figure 7b show a significant, abrupt downward trend after time 25. From the graph, it can be seen that the Boussinesq function, Brutsaert and Nieber function, and Wangdingbao and Caiximing function all have a decreasing slope. In contrast, the Maillet function and Chapman function have an increasing slope. In terms of fitting degree, the Boussinesq function, Brutsaert and Nieber function, and Wangdingbao and Caiximing function fit better, while the Maillet function and Chapman function deviate far from the data points and fail to fit the data points well; the data points in Figure 7c show a significant, abrupt downward trend at the end. From the graph, except for the Chapman function, all other functions show a decreasing slope. In terms of fitting degree, the Boussinesq function, Maillet function, Brutsaert and Nieber function, and Wangdingbao and Caiximing function fit better. In contrast, the Chapman function can only fit a small number of data points. The data points in Figure 7d show a significant, abrupt downward trend at the end. From the graph, it can be seen that all functions have a decreasing slope. In terms of fitting degree, except for the Maillet function and Chapman function, the fitting degree of the other functions is very high, which can match the vast majority of data points. Except for the data with an abrupt downward trend at the end, the data can basically fall within the range of the fitting function. The data points in Figure 7e are different from those in other figures, and there is no abrupt decrease in the tail end. From the figure, all functions show a decreasing trend in slope. In terms of fitting degree, except for the Maillet function and Chapman function, the other functions can basically fit all the data points perfectly, matching all the experimental data. Currently, the fitting situation in this figure is the best among all the figures.

Overall, in the early stage of the curve trend, all functions maintained a downward trend. As time passed, some functions, such as the Boussinesq function and the Brutsaert and Nieber function, showed a significant slowdown in their downward trend, while the downward trend of other functions became larger and larger. The rate of decline in the later stage will become faster and faster. From the perspective of fitting, each function has a different fitting situation, with differences. Functions with good matching can basically fully fit the research data, while functions with poor matching can only partially fit the data points, that is, only fit the previous part of the data. From a global analysis, for this research period and basin, the Boussinesq function and Brutsaert and Nieber function have better fitting situations, significantly better than the other three functions, and are more suitable as comprehensive recession curve functions.

The data points in Figure 8a of the figure (Figure 8) show a significant, abrupt downward trend at the tail end, and all functions in the figure can only match the trend at the front end of the data. The fitting of data points with decreasing slopes at the tail end is not good. From the graph, it can be seen that all functions have a decreasing slope and may eventually tend to remain constant. In terms of fitting degree, except for the Wangdingbao and Caiximing functions, all other functions have a good fitting degree and can basically fit the data. The data points in Figure 8b exhibit a trend of a central data bulge. From the graph, it can be seen that all functions show a decreasing slope. In terms of fitting degree, all functions deviate far from the data points and fail to fit them well, especially the data points with abnormal upward deviation in the middle. The data points in Figure 8c show a significant downward trend at the end, starting to change abruptly around time 28. From the graph, it can be seen that all functions have a decreasing slope. In terms of fitting degree, almost all functions can roughly fit the experimental data points, but the fitting situation for the middle data is not good. The data points in Figure 8d show a significant, abrupt downward trend at the end, with an abnormal decrease starting around 30. From the graph, it can be seen that all functions show a decreasing slope trend. In terms of fitting degree, almost all functions have a high fitting degree, which can match the vast majority of data points. Except for the data with an abrupt downward trend at the end, the data can basically fall within the range of the fitting function. The data points in Figure 8e are different from those in other figures, and there is no abrupt decrease in the tail end. From the figure, all functions show a decreasing trend in slope. From the perspective of the fitting degree, the selected function can basically fit all the data points and perfectly match all the experimental data. Currently, the fitting situation in this figure is the best among all the figures.

Overall, in the early stages of the curve trend, all functions maintained a downward trend. Over time, some functions, such as the Boussinesq function, the Maillet function, and the Brutsaert and Nieber function, showed a significant slowdown in their downward trend, while others showed an increasing downward trend. The rate of decline in the later stages will become faster and faster. From the perspective of fitting, each function has a different fitting situation, with differences. Functions with good matching can basically fully fit the research data, while functions with poor matching can only partially fit the data points, that is, only fit the previous part of the data. From a global analysis, for this research period and basin, the Boussinesq function and Maillet function have better fitting situations, significantly better than the other three functions. They are more suitable as comprehensive recession curve functions.

4. Discussion

Prior to this study, scholars and researchers mainly focused on the independent changes of groundwater or surface water in MYRB. A large amount of work has been conducted in this area—establishing many models and empirical formulas with detailed and reliable content and sufficient evidence—to explain the changes and processes of key factors, such as groundwater baseflow in the middle reaches of the Yellow River, from various aspects and angles. The mechanism is rigorous, and the experimental results are convincing. The potential innovation of this article is reflected in the following aspects: the research area is located in MYRB, and few scholars in China have studied the changes in groundwater reserves through the study of baseflow changes in MYRB. At the same time, this article can study the changes in groundwater reserves under human influence and interference conditions, which lays a solid foundation for the study of key areas. The current problems in this study mainly include a certain gap in data volume and insufficient fitting accuracy. The current solution is to collect a certain amount of data from other units and individuals, while using other tools and software to improve the fitting accuracy. In order to better understand the hydrological mechanisms related to mining operations and predict the impact of future mining, it is necessary to use process-based hydrological modeling based on data-driven results and supported assumptions. In addition, there is no good explanation for the assessment and evaluation of groundwater resources and the coupling problem between groundwater and surface water. Therefore, the next step, which is also the focus of future work, is to further improve the practicality and application scope of the MRC method, such that it can be used for short time series traffic data, while improving its computing power to handle traffic data in abnormal years and annual data with outliers. Establish process-based hydrological modeling, increase data volume, find more convincing statistical methods to improve the reliability of calculations and statistics, and enhance its computing power to handle flow data in abnormal years and annual data with outliers, achieving more accurate calculations.

5. Summary and Conclusions

The baseflow index is the ratio of baseflow to total streamflow, used to reflect the contribution of baseflow to the total streamflow of a river. It can reflect the recharge characteristics of groundwater to rivers, as the baseflow mainly comes from groundwater recharge, which is relatively stable and not easily affected by seasons and rainfall events. The higher the baseflow index, the more significant the recharge of groundwater to the river. For example, the baseflow index of rivers mainly supplied by groundwater approaches 1, while the baseflow index of seasonal rivers approaches 0. At the same time, the baseflow index can provide a scientific basis for water resource management. By monitoring and analyzing changes in the baseflow index, the trend of river flow can be predicted, thereby helping decision-makers formulate reasonable water resource management strategies. For example, in arid and semi-arid regions, the baseflow index can help evaluate the reserves and utilization potential of groundwater resources. The baseflow index is an important hydrological parameter that can reflect the baseflow characteristics of rivers and has profound significance for water resource management, environmental protection, and ecosystem assessment. In addition, the baseflow index can help us understand the stability and variation characteristics of river flow. A higher baseflow index indicates that rivers can still maintain a certain flow rate during the dry season, which is of great significance for ensuring the stability of river ecosystems and the sustainable use of water resources. The main conclusions drawn from this article are as follows:

Calculate the changes in baseflow in MYRB and typical sub-basins. On a time scale, the ability to observe and explain the dynamic changes in groundwater reserves well on a multi-year average scale further enriches the evidence and basis for changes in groundwater reserves; at the spatial scale, updating the changes in groundwater storage within the basin is beneficial for further scientific research and can also provide direction for further progress. At the same time, it can identify the dynamic changes in groundwater reserves under human influence and interference, providing convenience for the calculation of groundwater resources. This article focuses on six basins in the middle reaches of the Yellow River, and through analysis and calculation, the values of their baseflow indices are 0.81, 0.81, 0.82, 0.79, 0.79, and 0.80, respectively. Overall, they are distributed around 0.80, which determines the overall situation of the Yellow River’s baseflow. Groundwater recharge accounts for a large proportion of it. If the groundwater situation in the middle reaches of the Yellow River is affected, it will inevitably affect the water volume of the Yellow River.

Overall, the flow and baseflow in MYRB and its main tributaries are relatively large, with the flow and baseflow in the main stream basin being greater than those in the main tributary basin, about 10 times that of the main tributary basin. The baseflow, divided by the digital filtering method, accounts for about 80% of the total flow (BFI = 0.80), and this value may vary under the influence of parameters. The flow and baseflow in the main river basin are about 300–1200 m³/d. The flow and baseflow of other tributary basins are mostly between 0 and 80 m³/d, with the Beiluo River basin having the smallest flow and baseflow between 0 and 40 m³/d. Through statistical analysis, it is found that the streamflow in MYRB is influenced by human activities. This article provides a systematic evaluation of three digital filtering methods—Lyne et al. [41], Nathan and McMahon et al. [12], Chapman et al. [42], Arnold and Allen et al. [11,43], Eckhardt et al. [44]—through the segmentation calculation of groundwater baseflow in MYRB. Utilizing a new parameterization method for water withdrawal constant-based automatic baseflow identification technology in water withdrawal analysis can make this parameter more physically meaningful, thereby reducing errors caused by subjective judgments in water withdrawal analysis.

This study mainly focuses on the flow and hydrological stations in MYRB. By analyzing previous theoretical research, standardized formulas and calculation methods applicable to MYRB can be proposed, filling the theoretical gap in the field of groundwater research in MYRB and providing guidance and assistance for others’ research and work, effectively saving time and energy. This study used recession analysis and classification comparison methods to mainly compare five different water balance functions. The fitting situation of different functions was visually displayed in the form of digital graphs; the comparison was clear, and the differences were obvious. Through the calculation of different basin flow and hydrological station flow, it was found that the Boussinesq function, Maillet function, Brutsaert and Nieber function fit well, significantly better than the other three functions, and are more suitable as water balance functions for the study area.