Understanding the influencing factors and evolving trends of the Yellow River Water-Sediment Regulation System from a system perspective

Abstract

Understanding the influencing factors and the evolving trends of the Water-Sediment Regulation System (WSRS) is vital for the protection and management of the Yellow River. Past studies on WSRS have been limited in focus and have not fully addressed the complete engineering control system of the basin. This study takes a holistic view, treating sediment management in the Yellow River as a dynamic and ever-evolving complex system. It merges concepts from system science, information theory, and dissipative structure with practical efforts in sediment engineering control. The key findings of this study are as follows: between 1990 and 2019, the average Yellow River Sediment Regulation Index (YSRI) was 55.99, with the lowest being 50.26 in 1990 and the highest being 61.48 in 2019; the result indicates that the WSRS activity decreased, yet it fluctuated, gradually approaching the critical threshold of a dissipative structure.

Graphical abstract

Keywords

Yellow River / Water-Sediment Regulation System / Yellow River Sediment Regulation Index / system perspective / sustainable management.

1 Introduction

The regulation of water-sediment interactions is a complex and multidisciplinary research field. In recent years, the focus of water and sediment regulation has shifted from studying individual relationships to considering multiple objectives (Bai et al., 2023). Scholars have increasingly recognized the comprehensive influence of various factors, such as climate variations (Hansford et al., 2020), river channel morphology (Kemper et al., 2023; Vázquez-Tarrío et al., 2020; Kayitesi et al., 2022; Chong et al., 2021), the dynamics of suspended sediment transport (Vercruysse et al., 2017), sedimentary architectures (Colombera et al., 2019), and the impacts of dams (Habets et al., 2018; Wang et al., 2017). The Yellow River, known as one of China’s major rivers, plays a vital role in the country’s agriculture and industry. However, the basin has long faced serious soil erosion, leading to significant sediment-related issues. The influx of large amounts of sediment into the river has resulted in harmful effects, presenting substantial challenges for the management and engineering of the Yellow River. Sediment accumulation has increased the risk of flooding and decreased the lifespan of reservoirs, emphasizing the need to understand the underlying forces driving sediment evolution for sustainable river management and ecological preservation (Wasson et al., 2022; Liu et al., 2018a; Habersack et al., 2016; Guo et al., 2018). The sediment-related issues within the Yellow River Basin are characterized by complexity, nonlinearity, and uncertainty. First, these problems arise from the interaction of multiple factors, including geographical conditions, climate change, and human activities, which contribute to the overall complexity of sediment-related issues (Qian et al., 1987; Song and Chiew, 1997; Zhang et al., 2006; Mu et al., 2014). Second, there is a nonlinear relationship between sediment generation and transport processes. For example, an increase in rainfall does not necessarily result in a linear increase in sediment inflow due to the involvement of thresholds and sudden changes (Wang et al., 2019; Qian and Wan, 1991). Additionally, sediment erosion and accumulation in rivers exhibit nonlinear characteristics due to the interplay between channel morphology, water-sediment conditions, and other factors, leading to complex and nonlinear response relationships (Li et al., 2015; Xia et al., 2014; Cheng et al., 2020). Finally, the generation and transport of sediment are influenced by numerous uncertain factors, including human activities, rainfall, land use and cover changes, and surface and groundwater flow, with significant temporal and spatial variations, further contributing to the prevailing uncertainty (Hu et al., 2020; Wang et al., 2020; Sun et al., 2019; Zhang et al., 2021a). In summary, the sediment-related issues in the Yellow River Basin display complexity, nonlinearity, and uncertainty.

The following specific research objectives are identified:

i. To investigate the influencing factors and evolution trends of the Yellow River Water-Sediment Regulation System (WSRS) from a system perspective using a holistic approach that integrates theories from systems science, information theory, dissipative structures, and practical sediment control efforts.

ii. To establish the Yellow River Sediment Regulation Index (YSRI), a macro-meso-micro evaluation system, for comprehensively assessing the evolutionary status and development quality of the WSRS.

This research contributes to a better understanding of river system dynamics and helps in formulating effective policies and strategies for sustainable river management and environmental conservation.

2 The Yellow River Water-Sediment Regulation System

The Yellow River Basin is the second largest river basin in northern China, covering approximately 795,000 km² in a continental climate. The average annual temperature in the basin ranges from −4°C to 14°C. Except for the southern Qinling Mountains bordering Gansu and Sichuan, which are within a humid climate zone, the eastern part of the basin is primarily a semihumid climate zone, the central part is a semiarid climate zone, and the north-west part is an arid climate zone. The normal annual runoff is 58 billion m², accounting for 2% of the country’s total runoff. Stretching approximately 5,464 km, the terrain in the Yellow River basin varies greatly, featuring diverse landforms and complex habitats that foster the development of various vegetation types. It includes four vegetation zones from east to west: the deciduous broad-leaved forest zone, grassland zone, desert zone, and Qinghai‒Xizang Plateau vegetation zone (Zhang, 2023). The middle and upper reaches of the Yellow River are predominantly mountainous, while the middle and lower reaches consist mainly of plains and hills. The upstream geological structure primarily consists of metamorphic rocks and granite, while the middle reaches are characterized by deeply buried sand, gravel, and sandy riverbeds. The downstream geological structure is primarily composed of sandy shale formations and deep alluvial soil layers.

To address sedimentation issues in the Yellow River, extensive research has been conducted on a comprehensive management system called the Yellow River’s WSRS (Hu et al., 2022; Hu, 2016; Wang et al., 2013; Hu and Zhang, 2020). The key components of the Yellow River’s WSRS include the construction of a network of reservoirs along the river, sedimentation measurement and forecasting techniques, regular channel maintenance and dredging, ecological restoration efforts, flood control structures, and water diversion projects.

The reservoirs in the system serve as crucial tools for regulating water and sediment flow. Heavy metals store excess water and sediment during flood seasons and release it during drought periods, ensuring balanced water resource management (Ran et al., 2013; Zhang, 2022a). Sedimentation measurement and forecasting techniques are utilized to effectively manage sedimentation. These techniques aid in predicting sediment load and enable timely release or storage of sediment as required (Xia et al., 2016; Chen et al., 2010). To prevent excessive sedimentation, regular maintenance and dredging of the river channel are conducted. This essential practice involves the removal of sediment deposits from the riverbed to ensure a smooth flow of water. Additionally, efforts are being made to protect and restore the natural ecosystem along the river, which includes initiatives such as reforestation projects, wetland conservation, and the implementation of sustainable land management practices (Wang et al., 2006; Xiao et al., 2020; Zhu et al., 2019).

The construction of flood control structures, such as embankments and levees, is crucial for preventing overflow during periods of heavy rainfall (Liu et al., 2018b; Zhang, 2022b). These structures serve to minimize the impact of floods on nearby communities and agricultural lands. Furthermore, water diversion projects are included in the WSRS to redistribute water resources and alleviate water shortages in regions facing water scarcity (Jia and Liang, 2020; Deng, 2018; Cheng and Wang, 2006; Wang and Yang, 2005; Zhu et al., 2016). These projects involve the transfer of water from surplus areas to regions with limited water resources.

Overall, research on WSRS has focused primarily on specific aspects, such as watershed governance (Jiang and Li, 2020; Xu et al., 2012; Zheng et al., 2021), reservoir regulation (Guo et al., 2015; Hu et al., 2010; Tao and Zhou, 2016), and river channel regulation (Bi et al., 2019; Ma et al., 2012; Cai et al., 2022). As a result, there is a lack of analysis and exploration of multilevel, multilink, and whole basin engineering systems. To comprehend and address this issue comprehensively, it is necessary to consider the impact of these factors holistically, which can be achieved through the establishment of integrated models and precise observations to enable scientific analysis and prediction. It is important to note that, unlike previous studies, this article will examine the entire lifecycle of sediment in the Yellow River, including the generation of sediment, its transport and accumulation in reservoirs and river channels, and the discharge of sediment into the sea (Section 3.1). Qian (2011) emphasized that a system is composed of many interconnected and interdependent parts with specific functions.

3 Methodology

In recent years, there has been increased interest in system governance among researchers due to the implementation of the national strategy for the Yellow River Basin. For instance, Zhang et al. (2021a) proposed a comprehensive assessment method and a giant system framework for the Yellow River Basin based on system science. Additionally, Zhang et al. (2021b) utilized system thinking and information entropy models to evaluate the impact of comprehensive scheduling of the Longyangxia–Liujiaxia Reservoir on the Ningxia–Inner Mongolia section of the Yellow River (Zhang et al., 2021c). Furthermore, Cao et al. (2023) proposed an assessment method for the quality and stability of the ecological system in the Yellow River Basin. These research achievements provide the necessary theoretical support for system-based research on the WSRS of the Yellow River.

3.1 Lifecycle of sediment

This research begins by understanding the lifecycle of sediment in the Yellow River. Based on the attributes of sediment sources and generation, sediment transport, reservoir sediment deposition, river channel deposition, and erosion, the lifecycle of Yellow River sediment can be divided into four stages or subsystems (Fig.1).

i. The first subsystem focuses on controlling the influx of sediment into the Yellow River, primarily through water conservation measures, silt detention dams, and small watershed management. The main objective is to reduce sediment production and control sediment inflow into the Yellow River by employing comprehensive soil and water conservation measures within the watershed.

ii. The second subsystem concentrates on sediment control in tributaries and reservoirs such as Wanjiazhai, Sanmenxia, and Xiaolangdi. It relies on sediment interception and the coordinated operation and management of reservoirs to establish favorable water-sediment processes for sediment transport and maintain a stable river channel.

iii. The third subsystem emphasizes sediment control within river channels. It primarily considers the functions of flood retention, peak reduction, sedimentation, and coordination of water-sediment relationships in the middle and lower reaches of wide floodplain river sections.

iv. The fourth subsystem focuses on sediment control at the river mouth. The sediment control function of the river mouth subsystem was analyzed primarily by considering the downstream response to river mouth flow adjustments. Sedimentation in the river mouth, along with upstream sedimentation, extends the river channel and increases the erosional base level downstream of the Yellow River, resulting in downstream flood control issues.

Overall, understanding the lifecycle of sediment provides a systematic viewpoint for understanding sediment issues in the Yellow River. Subsequently, a macromeso-micro evaluation approach, known as YSRI, is proposed to explore the evolutionary status and developmental quality of the Yellow River WSRS.

3.2 Yellow River Sediment Regulation Index (YSRI)

The YSRI is proposed to investigate the factors influencing and the evolutionary pattern of the Yellow River’s WSRS across the macro, meso, and micro levels (Fig.2). This study adopts a systematic and holistic perspective by integrating theories such as systems science, information theory, and dissipative structures with practical sediment engineering control work.

i. Macrolevel: The Yellow River sediment regulation system constitutes a vast and intricate mega-system. Achieving effective sediment control across its lifecycle necessitates a systemic approach. This entails formulating a comprehensive strategy, devising implementation plans, establishing governance frameworks, designing engineering layouts tailored to different river segments, and implementing specific operational management protocols for individual projects. It is crucial to perceive the research objectives as components of an organic compound system and to afford thorough consideration to all facets. At the macro level, elucidating the overarching developmental patterns of the WSRS is predicated on the principles of entropy increase and the dissipative structure model. The YSRI value serves as a barometer of the developmental quality of the WSRS, with higher values indicating superior development quality.

ii. Meso level: The Yellow River sediment regulation system can be segmented into four components. The initial subsystem focuses on curtailing sediment influx into the Yellow River via water conservation measures, silt retention dams, and small watershed management. The subsequent subsystem centers on sediment management in the primary and ancillary rivers, including reservoirs such as Wanjiacun, Sanmenxia, and Xiaolangdi. The third subsystem emphasizes sediment regulation within the river channels, addressing functions such as flood retention, peak flow reduction, sediment deposition, and harmonization of the water-sediment dynamics in the expansive sandbars of the middle and lower reaches. The final subsystem primarily addresses sediment control at the river mouth, commencing with modifications to the flow route at the river mouth and examining the role of sediment control within the estuarine subsystem vis-à-vis the downstream regions of the Yellow River. At the meso level, information entropy and entropy weight calculations for indicators and subsystems serve to discern evolving patterns within subsystems and identify pivotal influencing factors.

iii. Micro level: To underpin data analysis at the macro and meso levels, the micro level focuses on constructing a corresponding indicator system. Key functions entail mining data pertaining to each indicator and scrutinizing the interactional dynamics among them. This level facilitates a granular examination of the influencing factors and their ramifications on the Yellow River’s WSRS.

3.2.1 Micro level

The Yellow River sediment regulation system has various implications, such as managing sediment entry into the Yellow River, controlling sediment in main and tributary reservoirs, regulating sediment in river channels, and managing sediment at the river mouth. To ensure ecological protection and promote the high-quality development of the Yellow River Basin, we developed a comprehensive and user-friendly indicator system based on relevant practices and expert opinions on river development evaluation from both domestic and international sources. For more detailed information on the specific indicator framework, please refer to Tab.1.

The types of indicator data mainly include basic data and industry-specific (professional) data. Basic data primarily consist of remote sensing, surveying, and geographic information data. Industry-specific (professional) data, which are selected from daily operations and research in the Yellow River Basin, are widely applied to relatively mature spatiotemporal sequence data. These data serve as a historical and current depiction of crucial indicators in the research system, monitoring their dynamic changes and providing fundamental objective information. The collected data are organized in terms of spatial and temporal dimensions. For historical reasons, a small portion of the data are missing. In this study, for missing data, various methods, such as linear interpolation, spline interpolation, Lagrange interpolation, and gray forecasting, are flexibly employed based on different circumstances. After a reasonable analysis, they are used in this research.

3.2.2 Meso level

The meso level aims to identify the changing trends of subsystems and key influencing factors. In this study, the concept of entropy is introduced to quantify the information of the indicator elements, the degree of order (chaos) of the system, and the development trend of WSRS (Gu et al., 2020; Huang et al., 2017; Li et al., 2012). Information entropy is a measure of uncertainty. The higher the entropy value of the indicators is, the more chaotic the system, and the lower the degree of order. The greater the uncertainty of the development factors is, the lower the development quality. The information entropy not only represents the order of the WSRS, but also assesses the development trend of the WSRS through the annual change in the entropy value. The entropy value of the basin WSRS index is calculated as follows (Zhang et al., 2021d):

(1)p_{ij}=\frac{f_{ij}}{\sum _{j=1}^n{f}_{ij}} ,

(2)S_i=\frac{1}{\ln n} \sum _{j=1}^n\left(p_{ij}\ln p_{ij}\right),

where f_{ij} is the whitening function value of indicator i and standard j, p_{ij} is the proportion of each standard whitening function value in all values, n is the number of indicator standard intervals, and S_i is the entropy value of indicator i.

To identify the key indicators of the WSRS, the entropy weight method is used to calculate the weight of each indicator in the system. The entropy weight method quantitatively determines the change in each index’s weight in the system based on the change in each index’s entropy value. This allows for a more scientific simulation of the mutual dynamic influence of each index and avoids subjective weight judgment.

The entropy weight of an index w_i is calculated by using the proportion of the entropy value of an index S_i in all indices. The information entropy value of each index i (i=1,2,\dots , N) is S_i, with the weight w_i as follows (Zhang et al., 2021e):

(3)w_i=\frac{1-S_i}{N-\sum _{i=1}^N{S}_i}.

3.2.3 Macro level

The macro level aims to explore the overarching developmental patterns of the WSRS. According to the principle of entropy increase, the changes in the WSRS in the Yellow River Basin depend on two key factors. One is the positive entropy generated by the irreversible process of the survival and development of the WSRS. The other factor is that the WSRS in the Yellow River Basin is similar to an organism. To maintain a healthy and sustainable orderly development trend, an effective negative entropy flow from the external environment must be obtained. This means that information, materials, and energy are constantly exchanged between the WSRS and the external environment.

Applying the principle of dissipative structure, the basin WSRS indicators are divided into positive and negative entropy indicators. The entropy values e_{A_i} and w_{A_i} of the positive entropy indicators and e_{B_i} and w_{B_i} of the negative entropy indicators are calculated. After weighted summation, the total positive entropy A and total negative entropy B of the WSRS in each time period are calculated. The formula is as follows:

(4)A=\sum _{i=1}^{n_A}{w}_{A_i}{e}_{A_i},\left(i=1,2,\dots n_A\right),

(5)B=\sum _{i=1}^{n_B}{w}_{B_i}{e}_{B_i},\left(i=1,2,\dots n_B\right),

where n_A and n_B represent the number of positive and negative entropy indices, respectively, of the WSRS.

Calculate the criteria for steady-state transformation:

(6){Index}_{DS}=|B|-\left(1+A^2\right),

where {Index}_{DS} is a discriminant index calculated based on the Brussels model. Considering the need for easy popularization, this study used a percentile system to score the YSRI. When calculating the score, the value range of the dissipative structure index is linearly converted to the [0,100] interval, and the conversion formula of the YSRI value is as follows:

(7)\mathrm{Y}\mathrm{S}\mathrm{R}\mathrm{I}=100\times \frac{\left({Index}_{DS}+2\right)}{3}.

When {Index}_{DS} is 0, that is, when the basin WSRS reaches the threshold of dissipative structure, the YSRI score is 66.7.

4 Results and discussion

4.1 YSRI

The YSRI value, which represents the overall development trend of the WSRS, ranged from 50.26 to 61.48 from 1990 to 2019. Fig.3 illustrates the fluctuating increase in YSRI development. The development can be categorized into three distinct stages:

i. From 1990 to 1998, the YSRI showed an increasing but fluctuating trend, largely attributed to significant natural disasters. In 1993, there was a breach in the Inner Mongolia section of the Yellow River during the river closure period. This breach caused a massive flood in August 1996, resulting in major disasters that affected the communities along the river. Additionally, the cutoff length of the Yellow River reached a historical maximum of 704 km in 1997. Despite some improvements, the YSRI remained at historically low levels during this period. However, by 1998, the YSRI had made significant advancements.

ii. Between 1999 and 2011, the YSRI experienced slow fluctuations with an overall stable trend and slight increase. During this stage, the economic development of the basin gradually improved, which led to increased attention being given to ecological environmental protection and maintaining the basin’s carrying capacity. As a result, all elements of basin development were simultaneously competing and coordinating, causing fluctuations in the YSRI. From 2006 to 2008, the YSRI experienced a slight decrease, impacting downstream riverbed morphology and the ecological environment due to reduced coordination of water and sediment, among other factors.

iii. From 2012 to 2019, the YSRI displayed a significant positive development trend. Although there was some initial volatility, the YSRI showed a clear linear increase. This positive development can be attributed to the combined effects of scientific decision-making, systematic management, and major projects in the basin. The comprehensive control project of the Loess Plateau and the coordinated water and sediment regulation with downstream projects, such as Xiaolangdi, effectively controlled sediment inflow in the middle and lower reaches of the Yellow River. This continuous improvement in sediment system development in the Yellow River Basin contributed to the positive trend in the YSRI.

To further analyze the changes in the indicators within the YSRI over time, principal component analysis (PCA) was conducted using the indicator variables examined in this study. PCA revealed that the first principal component (PC1) accounted for 35.37% of the total variance, while the second principal component (PC2) accounted for 23.04% of the total variance. The cumulative contribution rate of the PCA reached 58.41%. Based on Fig.3 it can be inferred that there were significant differences in the 16 indicators across the three time periods: 1990–1998, 1999–2011, and 2012–2019 (Adonis test: P < 0.001; Fig.3). Compared with those during the 1990–1998 and 1999–2011 periods, the indices during the 2012–2019 period were more tightly grouped (represented by triangles in Fig.3), indicating greater stability of the WSRS during the 2012–2019 period. Moreover, the points representing the three stages progressively became more tightly clustered over time, suggesting increasing system stability.

4.2 Subsystem analysis

To identify the changing trends of subsystems and key influencing factors, we initially calculated the entropy values of the subsystems. A smaller entropy corresponds to a higher degree of order or chaos. For example, when analyzing the first subsystem, we observed that the entropy value was 0.51 in 1990 and 0.26 in 2019. These values clearly indicate that the system exhibited greater chaos in 1990 than in 2019.

4.2.1 First subsystem

From Fig.4, it is evident that the entropy of the first subsystem decreased with fluctuations over the past 30 years, indicating an overall improvement in orderliness. This suggests that effective soil and water loss management on the Loess Plateau has successfully controlled the flow of sediment into the Yellow River, leading to increased stability in the first subsystem.

To evaluate the contribution of each indicator to the system order, the weight of each indicator in the subsystem was calculated, as shown in Fig.4, which shows that between 1990 and 2001, the weights of four indicators, namely, the vegetation coverage of the Loess Plateau (Indicator 1), the area of terraced fields (Indicator 2), the area of forest and grass (Indicator 3), and the area growth rate of warping dams on the Loess Plateau (Indicator 4), exhibited significant fluctuations. In addition, the comprehensive weights of these four indicators initially increased and then decreased. From 2002 to 2010, the weights of the first four indicators remained relatively stable, with minimal volatility. However, between 2011 and 2019, the weights of these indicators experienced notable fluctuations, with the comprehensive weight showing an upward trend. This indicates that the implementation of various measures for comprehensive control on the Loess Plateau has increasingly evident effects on the first subsystem. Therefore, it is crucial to emphasize the importance of forests, grasses, terraces, and dams on the Loess Plateau while continuing to implement comprehensive control measures to effectively manage sediment inflow into the Yellow River in the first subsystem.

4.2.2 Second subsystem

Fig.5 presents the trend of the entropy value for the second subsystem. The figure illustrates a general decline in the entropy value from 1990 to 2019. However, an increase in entropy was observed during the period of 1990–1997, with the maximum entropy occurring in 1997. This suggests that the second subsystem experienced unstable development before 1997. The analysis indicates that only the Sanmenxia Reservoir played a minor role in secondary control before 1997. Due to inadequate reservoir regulation, the downstream Yellow River basin experienced a 226-day water cutoff. The Wanjiazhai and Xiaolangdi reservoirs in the middle reaches became operational in 1998 and 1999, respectively, leading to improved development of the system after 1997. Significant system development occurred after 2002, attributed to continuous water and sediment regulation practices. However, the current reservoir project’s capacity to regulate runoff and sediments is limited. Therefore, the optimization of the application mode alone is insufficient to foster the continuous development of the system. From a system stability perspective, the current subsystem faces the issue of insufficient follow-up power.

Fig.5 presents the weight distributions of the indicators in the second subsystem. The weight of the sediment-holding capacity (Indicator 6) decreases in large reservoirs in increments, while the weight of comprehensive control indicators increases incrementally. The weights of the water regulation degree (middle and lower reaches, indicator 7) and sediment regulation degree (middle and lower reaches, indicator 8) for the mainstream reservoirs initially decrease and then increase. The weight of the water and sediment coordination degree at Huayuankou (Indicator 9) first increases and then decreases.

4.2.3 Third subsystem

Fig.6 illustrates the development trend of the entropy value in the third subsystem. The entropy value exhibited a volatile downward trend, with increasing fluctuations from 1990 to 1998. Subsequently, the entropy generally decreased. During this period, the minimum flat discharge of the downstream river channel decreased, the swing of the mainstream river channel became significant, and frequent cutoffs occurred, resulting in poor system stability. From 1999 to 2002, despite the continued decrease in minimum flat discharge, the swing amplitude of the mainstream line of the river decreased compared to that in previous years. Additionally, the reach above Gaocun transitioned from continuous siltation to scouring, enabling better system development. Since 2003, with the advancement of water and sediment regulation technology, the river section has maintained a scouring trend, and the flat discharge has continued to increase. However, the swing of the river’s mainstream has persisted, causing fluctuations in the stability of the third subsystem. Hence, the swing of the river channel significantly impacts sediment control in the third subsystem of the basin.

Fig.6 presents the weight distribution of the indicators in this subsystem. The figure illustrates that the weight of the minimum flat discharge (Indicator 10) initially decreased and then increased. Similarly, the weight of the swing amplitude (indicator 11) of the wandering river reach first increased and then decreased. The weight of the river facies coefficient (Indicator 13) of Jiahe beach decreased and then increased, while the weight of the media indicator Tiexie-Gaocun full section scouring and silting volume (Indicator 12) changed in accordance with the comprehensive weight of the control indicators.

From 1990 to 2001, no effective sediment project control measures were implemented in the downstream river channel. Consequently, the wandering river section experienced significant swings, and channel erosion and deposition fluctuated considerably. The flat discharge and river facies coefficient also displayed relative instability. As a result, the weight of each index fluctuated greatly, with Indicator 11 exhibiting the most intense variation.

After 2001, with the operation of the Xiaolangdi Reservoir and the implementation of water and sediment regulation in 2002, the minimum flat discharge in the lower Yellow River steadily increased, along with its weight. The other three indicators also demonstrated positive development. During this period, the weight variation of the indicators remained relatively stable with minimal volatility. The weights of the four indicators in the third subsystem were similar.

The weight variation process indicated that the swing of the wandering river reach (Indicator 11) played a crucial role in the third subsystem. Consequently, after 2002, when the section shape of the downstream river channel and the flow remained relatively stable, the river channel dynamically adjusted itself through the swing of the river regime to accommodate different water and sediment conditions. This adjustment led to a state of stability and eventually balanced the various influencing factors in the third subsystem.

4.2.4 Fourth subsystem

Fig.7 illustrates the temporal evolution of the entropy value of the fourth subsystem. Throughout the observed period, there was a consistent decrease in the entropy value of the fourth subsystem. Initially, before 1996, the original river course served as the flow path in the estuary area, resulting in a generally high entropy value. However, after 1996, the flow route in the estuary area changed to the eight branches of Qingshuigou, leading to a substantial reduction in the entropy value and an overall improvement in the fourth subsystem. Between 2000 and 2008, the relationship between water and sediments in the estuary area experienced significant changes due to diverted flow paths and the operation of the Xiaolangdi Reservoir, resulting in notable fluctuations in the overall system. Nonetheless, effective water and sediment regulation measures improved control over the estuary area, and continuous enhancement of ecological control measures contributed to the steady development of the fourth subsystem.

Fig.7 visually presents the weight distributions of indicators within the subsystem. The length of the river channel below the West River Estuary (Indicator 15) displayed a fluctuating trend characterized by an alternating increase and decrease, while the swing of the river flow path (Indicator 16) exhibited an opposite fluctuation trend compared to that of Indicator 15. Furthermore, the sediment volume at Lijin Station corresponded to the comprehensive weights of the control indicators.

Examining Fig.7, it becomes evident that the Yellow River in the estuary area underwent multiple cutoffs from 1990 to 2000, resulting in significant fluctuations in sediment inflow from Lijin. Both the length and swing amplitude of the river channel below the western estuary exhibited notable fluctuations. During this time frame, the sediment amount at Lijin mainly correlated with the length of the river channel. In 1996, changes in the estuary flow path led to further siltation and extension. Between 2000 and 2007, the implementation of the Xiaolangdi Reservoir improved control over water and sediments entering the estuary area, thereby reducing the amount of sediment at Lijin, which remained stable. The weight of the feedback response between the channel swing and the Lijin sediment gradually increased. In 2007, the Qingbacha section bifurcated, causing a certain amount of siltation. Consequently, a short-term significant feedback response between the channel length and the amount of Lijin sediment was observed. After 2008, advancements in water and sediment diversion technology further improved and matured the system. As a result, the sediment volume at Lijin exhibited steady changes, the river branches remained relatively stable, and the extent of siltation decelerated. This phase primarily depicted the feedback response between the river swing and the Lijin sediment.

4.3 Response relationship analysis

The gray correlation analysis method was utilized to analyze and calculate the correlations of 16 indicators of the basin WSRS from 1990 to 2019. The resulting thermodynamic diagram of the indicators is presented in Fig.8. Throughout the system development process, indicators that exhibited consistent variation trends, indicating high synchronous change and correlation, are represented by a dark blue color in the thermodynamic diagram. Conversely, indicators that showed low correlation are represented by a light blue color.

From the heatmap in Fig.8, it is evident that the development trends of vegetation coverage on the Loess Plateau, terrace control area, and forest and grass control area (Indicators 1–3) were strongly correlated. This suggests a consistent impact of the comprehensive management measures implemented on the Loess Plateau on these indicators. Furthermore, the first subsystem indirectly influenced the sediment-retaining capacities of large reservoirs through the mediating effect of the sediment volume at Tongguan Station (i.e., Indicators 1–3 showed good correlations with Indicator 6). Similarly, there was a feedback effect of the second subsystem, which transmitted information to the first subsystem.

The correlation analysis between subsystems in the upper right section of Fig.8 revealed positive correlations between the first and second subsystems (p < 0.0001), the second and third subsystems (p < 0.0001), and the third and fourth subsystems (p = 0.0005). This indicates that each subsystem regulates its own sediments through corresponding measures and positively influences the next subsystem in a bottom-up manner. Moreover, there were significant positive correlations between the first and third subsystems (p < 0.0001), the first and fourth subsystems (p < 0.0001), and the second and fourth subsystems (p < 0.0001). These results suggest that the first subsystem focuses on the control of incoming sediments, and the second subsystem focuses on the control of main and tributary reservoirs. These subsystems play important roles in the WSRS, with engineering measures having significant effects on subsequent subsystems through top-down transmission. Collectively, these findings demonstrate that the WSRS has been a coupled organic system with high cooperativity between subsystems over the past 30 years.

4.4 Discussion

The trends in the YSRI of the Yellow River Basin were analyzed across three periods: 1990–1998, 1999–2011, and 2012–2019. However, fluctuating yet increasing YSRI values were observed from 1990 to 1998 due to natural disasters such as breaches and floods along the Yellow River. Substantial advancements occurred by 1998. Between 1999 and 2011, the YSRI showed minor fluctuations with an overall stable trend and a slight increase. Economic development has led to increased attention being given to ecological environmental protection. From 2012 to 2019, the YSRI demonstrated significant positive development due to scientific decision-making, systematic management, and major projects in the basin. Continuous monitoring and management are crucial for sustainable development.

An analysis was conducted on the change trends and key influencing factors of different subsystems in the sediment regulation system. The entropy value and weight distributions of the indicators were examined to determine the orderliness and relationship between coordination and competition. For each subsystem, detailed observations were made regarding the changes in entropy values and weight distributions over time. Emphasizing effective control measures, comprehensive management, and ecological control are important for the balanced functioning and continuous development of each subsystem.

Using gray correlation analysis, correlations among 16 indicators were calculated for the basin’s WSRS from 1990 to 2019. The analysis revealed strong correlations between vegetation coverage on the Loess Plateau, terrace control area, and forest and grass control area. This suggests that comprehensive management measures on the Loess Plateau consistently impact these indicators. Correlation analysis also revealed positive correlations between different subsystems, indicating bottom-up and top-down transmission of information and influence among the subsystems. These results highlight the high cooperativity within the WSRS over the past 30 years.

5 Conclusion

This study investigated the characteristics of the Yellow River WSRS using the YSRI evaluation approach. It also examines the influencing factors and evolving trends. The main findings can be summarized as follows:

i. From 1990 to 2019, the WSRS of the Yellow River basin exhibited a stable and positive development trend, with the lowest score of 50.26 in 1990 and the highest score of 61.48 in 2019. However, there were fluctuations in the stability of the subsystems. Therefore, it is necessary to implement appropriate project control to maintain system stability and ensure orderly development.

ii. The entropy values of the four subsystems generally decreased, indicating that through negative entropy inflow from human control, the order and quality of the WSRS in the Yellow River gradually improved.

iii. A study conducted on the state of the Yellow River WSRS through the framework of dissipative structure theory indicated that the WSRS exhibited a less active state but demonstrated an overall oscillatory trend. Over time, it gradually approached the critical conditions necessary for the emergence of a dissipative structure.

This study has two limitations. First, the WSRS of the Yellow River is a highly dynamic and complex system that is influenced by multiple factors, including climate change, precipitation, evaporation, and soil moisture. The relative importance of different indicators may vary based on the environmental conditions prevailing in the Yellow River Basin, necessitating further comprehensive research to enhance the evaluation system. Second, the ongoing adjustments and enhancements made to the Yellow River’s WSRS pose challenges in terms of data collection and updates.

Despite these limitations, this study offers a fresh perspective on addressing sediment-related issues in the Yellow River and serves as a key technical resource for ensuring the long-term stability of the river. The research carried out by the YSRI sheds light on the historical evolution and interaction mechanisms of the WSRS in the Yellow River Basin, establishing a system model with evaluation and decision support functionalities. This provides crucial technical assistance in the unified implementation of engineering measures and systematic resolution of sediment-related issues, as well as serving as the basis for decision-making in water resource management and the preplanning of major projects within the Yellow River Basin.

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