Introduction

Global environmental changes have significantly increased the frequency of natural disasters, with growing impacts on social and economic development. In this context, enhancing the ability of human society to respond to crises, maintain system stability, and adapt to future uncertainties has become a key focus and urgent need in international efforts to address climate change1. Within this context, resilience research has deepened and gradually evolved into a central concept in sustainable development. The term “Resilience” originates from the Latin word “Resilio”, meaning “to return to the original state”2,3. Unlike risk analysis, resilience research emphasizes a system’s ability to cope with external shocks. American scholar Holling4 introduced the concept of resilience into ecological studies, defining it as the capacity of a system to absorb disturbances, recover stability, adapt to changes, and transition to a new stable state. The resilience of water resources system emphasizes their capacity and functions to resist disturbances (whether natural or human-induced), adapt to resultant changes, and attain an improved state5,6. Given the growing pressures on water resources due to climate change, building resilient water governance systems is more important than ever7,8.

Regarding the research on the evaluation methods for water resources system resilience, domestic and international scholars have initially established an analytical framework, providing a theoretical foundation and reference for the in-depth study of water resources system resilience assessment9. Chaves and Alipaz10 proposed the Watershed Sustainability Index (WSI) to assess resilience in mid-sized Brazilian river basins, based on hydrology, environment, living conditions, and policy indicators. Lilian et al.11 proposed the Arctic Water Resources Vulnerability Index (AWRVI) to assess the resilience of water resources system based on changing physical and social indicators. Sandoval-Solis et al.12 established a water resource sustainability indicator system, based on a sustainable development index, incorporating reliability, restoration capacity, and vulnerability dimensions to assess the resilience of water resources in the United States and Mexico. Yang et al.13 indirectly characterized the resilience level of water resources system by assessing the vulnerability factors of watershed systems and used the recovery capacity of each factor as an important indicator of system sustainability. Liu et al.14 applied the WRSRI index in southern China to assess socio-economic drought under future climate and demographic scenarios. Lu et al.15 developed an agricultural water resilience evaluation system using the analytic hierarchy process (AHP) and entropy weight method (EVM) for weighting, combined with SBM-DEA and coordination models for the Yellow River Basin. Chen and Zhang16 combined an improved analytic hierarchy process with a variable fuzzy recognition model to quantitatively assess water environment resilience. Sun et al.17 considered cultural and systemic factors to construct a resilience indicator system. Yang et al.18 developed a three-dimensional system—resistance, recovery, and adaptability—and used the variable Pythagorean fuzzy VIKOR model for resilience evaluation and optimization. Overall, most studies focus on multidimensional indicators and comprehensive models, but insufficient attention has been paid to spatial differences in regional resilience. To address this gap, this paper focuses on nine provinces along the Yellow River and constructs a resilience evaluation system to support water resource management.

This study chooses nine provinces along the Yellow River selected as the research area, a multidimensional index system is constructed to evaluate the resilience of water resources system. Indicators are selected from five dimensions: hydrology, meteorology, socioeconomics, ecology, and engineering. Using the TOPSIS method, based on a game-theory-based combined weighting approach, the resilience of water resources system in the provinces along the Yellow River from 2009 to 2022 is evaluated. The ArcGIS spatial analysis tool is applied to examine the spatiotemporal evolution of resilience. Additionally, the paper investigates the underlying mechanisms driving resilience changes across these provinces, providing a theoretical basis for enhancing the resilience of water resources system.

Overview of the study area

Study area

The Yellow River, the second-longest river in China and the sixth-longest worldwide, originates in the Bayan Har Mountains on the Qinghai-Tibet Plateau. Flowing from west to east, it passes through nine provinces and autonomous regions—Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shanxi, Shaanxi, Henan, and Shandong—before emptying into the Bohai Sea at Kenli, Shandong Province. The basin extends from the Bayan Har Mountains in the west to the Bohai Sea in the east, reaching the Qinling Mountains in the south and the Yinshan Mountains in the north. The basin covers 78 prefecture-level administrative divisions and 657 county-level administrative units. The main course of the Yellow River stretches 5464 km, traversing the Qinghai-Tibet Plateau, the Inner Mongolia Plateau, the Loess Plateau, and the North China Plain, forming a distinctive “Ji”-shaped river course resembling the Chinese character “几”. The nine provinces along the Yellow River, holding a vital strategic position in China’s socio-economic development, are selected as the study area. these provinces collectively cover an an area of 3.57 million km2, accounting for 37.17% of China’s land area. In 2020, the total population in the region reached 421 million, representing 29.85% of the national population. The regional GDP amounted to 25.4 trillion CNY, contributing to 25% of the national economy19,20. This spatial and temporal imbalance in the distribution of water, population, and economic resourcespresents significant challenges to the sustainable and high-quality development of nine provinces along the Yellow River21,22,23.

The provinces along the Yellow River represent a typical region with significant regional economic disparities in China. Most of the areas falls within arid and semi-arid climatic zones, where long-term water scarcity continues to challenge the balance between water supply and demand. The region also suffers from frequent floods and droughts, high sedimentation, suspended river sections, intermittent flows, and complex environmental and ecological issues. Since the 1980s, rapid socioeconomic development and population growth have exacerbated regional water use conflicts. Therefore, the national strategy for ecological protection and high-quality development of the Yellow River Basin places higher demands on water resource security in the provinces along the Yellow River. The map of provinces along the Yellow River is shown in Fig. 1.

Fig. 1
figure 1

Location map of provinces along the Yellow River.

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Data sources

To investigate the spatial distribution characteristics of water resources system resilience in the provinces along the Yellow River, this paper integrates monitoring and statistical data, employing techniques such as data cleaning, data desensitization, data splitting, and interpolation-based extension. It systematically consolidates foundational data covering the entire Yellow River region, focusing on the collection of meteorological and hydrological observations, regional water supply and demand statistics, socioeconomic development indicators, ecological and environmental metrics, and water conservancy infrastructure data, as well as terrain and land surface features data derived from remote sensing technology. All data were classified according to temporal and spatial scales and used to establish a comprehensive database, providing a reliable basis for the quantitative evaluation of resilience indicators. The construction process of the water resources system resilience database is shown in Fig. 2. The main data collected from provinces along the Yellow River are shown in Table 1.

Fig. 2
figure 2

Construction of comprehensive database of water resources system resilience.

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Table 1 The data types and sources.
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Construction and evaluation of the water resources resilience index system for the provinces along the Yellow River

Construction of the resilience index system for the water resources system

The resilience of the water resources system is determined by the interactions among multiple subsystems, including the meteorological–hydrological–socio-economic–ecological–engineering dimensions. Based on the principles of scientific validity, comprehensiveness, and practicability, this paper establishes a scientific assessment framework for evaluating the resilience of the water resources system.

Under global climate warming and environmental change, the increasing frequency of drought disasters has resulted in reduced river runoff, flow interruptions, and the gradual shrinkage of lakes and wetlands. At the same time, with population growth, the increasing frequency of disaster events, industrial and agricultural development, and climate change have exacerbated the contradiction between water supply and demand. Based on the principles of scientific validity, comprehensiveness, and practicability, this study selects indicators from the meteorological–hydrological–socio-economic–ecological–engineering subsystems to construct an evaluation index system consisting of 34 indicators, These indicators are classified into positive and negative attributes based on their respective characteristics (“+” denotes a positive effect on the resilience of the water resources system; “−” denotes a negative effect).The resilience evaluation index system of the water resources system in the provinces along the Yellow River is shown in Table 2.

Table 2 Resilience evaluation index system of water resources system in the provinces along the Yellow River.
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A resilience evaluation model for the water resources system

Weight determination based on the game-theoretic combined weighting method

The index weight distribution is the core to determine the scientificity and accuracy of comprehensive evaluation. Current weighting approaches can be generally categorized into subjective and objective types. Subjective weighting method can integrate domain knowledge and reflect decision-making orientation, but its results are susceptible to the influence of knowledge structure and subjective bias, thus leading to some arbitrariness. The objective weighting method is completely based on the degree of correlation of the data itself. Its mathematical theory is rigorous, but excessive reliance on the quality and distribution of the data may lead to weight results contrary to the actual importance or physical meaning of the indicators. Therefore, to reconcile conflicts between subjective and objective weights and achieve consistency and compromise, this manuscript applied a game-theoretic combined weighting method for integration of weights. The subjective and objective weights were calculated using the Fuzzy Analytic Hierarchy Process (FAHP) and the Entropy Weight Method (EWM), respectively.

The game theory model establishes an equilibrium between subjective and objective weights, retaining the advantages of both while achieving an optimal compromise. This method fully considers the intrinsic correlations among indicators, effectively reduced the limitations of a single weighting method, and significantly enhanced the scientific validity and rationality of weight allocation24,25. The weight modification based on the game theory-based combined weighting method further optimizes the weight allocation in traditional approaches, compensates for the deficiencies caused by subjective and data bias, and provides a more scientific and reasonable basis for weight adjustment, thereby improving the reliability and fairness of decision-making outcomes26. The specific calculation process is as follows:

  1. (1)

    The weights of n indicators are determined using L methods:

    $$w_{l} = \left( {w_{l1} ,w_{l2} , \cdots w_{\ln } } \right),\;l = 1,2, \cdots ,L$$
    (1)

    The linear combination of the L weight vectors is given by:

    $$W* = \sum\limits_{l = 1}^{L} {\alpha_{l} w_{l}^{T} } \;\left( {\alpha_{l} > 0} \right)$$
    (2)

    W∗ is the combined weight vector, and \(\alpha_{l}\) is the linear combination coefficients.

  2. (2)

    Based on the combination principle of game theory, minimize the deviation between W* and \(\alpha_{l}\). The objective function is as follows:

    $$\min \left\| {\sum\limits_{l = 1}^{L} {\alpha_{l} w_{l}^{T} - w_{p}^{T} } } \right\|_{2} ,\quad p = 1,2, \cdots ,L$$
    (3)
  3. (3)

    According to the properties of matrix differentiation, the first—order derivative condition for the optimization of the above formula is as follows:

    $$\sum\limits_{l = 1}^{L} {\alpha_{l} w_{p} w_{l}^{T} } = w_{p} w_{p}^{T} ,\quad p = 1,2, \cdots ,L$$
    (4)

    The linear equation system equivalent to the above formula is as follows:

    $$\left[ {\begin{array}{*{20}c} {w_{1} w_{1}^{T} } & {w_{1} w_{2}^{T} } & \cdots & {w_{1} w_{L}^{T} } \\ {w_{2} w_{1}^{T} } & {w_{2} w_{2}^{T} } & \cdots & {w_{2} w_{L}^{T} } \\ \vdots & \vdots & \vdots & \vdots \\ {w_{L} w_{1}^{T} } & {w_{L} w_{2}^{T} } & \cdots & {w_{L} w_{L}^{T} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\alpha_{1} } \\ {\alpha_{2} } \\ \vdots \\ {\alpha_{L} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {w_{1} w_{1}^{T} } \\ {w_{2} w_{2}^{T} } \\ \vdots \\ {w_{L} w_{L}^{T} } \\ \end{array} } \right]$$
    (5)
  4. (4)

    Solve Eq. (5) to obtain the optimal combination coefficients \(\left( {\alpha_{1} ,\alpha_{2} , \cdots ,\alpha_{L} } \right)\), and normalize them. Considering that the optimal combination coefficients may include negative values, take the absolute values of the coefficients before normalization.

    $$\alpha_{l}^{*} = \frac{{\left| {\alpha_{l} } \right|}}{{\sum\nolimits_{l = 1}^{L} {\left| {\alpha_{l} } \right|} }}$$
    (6)
  5. (5)

    Calculate the combined subjective–objective weights W*.

    $$W^{*} = \sum\limits_{l = 1}^{L} {\alpha_{1}^{*} w_{l}^{T} } , \, l = 1,2, \cdots ,L$$
    (7)

Resilience evaluation model of the water resources system in the provinces along the Yellow River

Water resources system resilience evaluation refers to the systematic assessment of its capacity to recover and adapt under external pressures (such as climate change, extreme weather events, and human activities) and involves multiple dimensions. Therefore, resilience evaluation of water resources system in the provinces along the Yellow River represents a typical multi-criteria decision-making problem. In addition, the resilience of water resources system involves multiple complex and interrelated indicators. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is highly adaptable in handling multiple evaluation indicators, as it assigns different weights to reflect their relative importance, effectively integrates them, and provides a unified evaluation framework. By calculating the weighted values of indicators, it comprehensively assesses system resilience27,28,29. Therefore, this paper employs the entropy-weighted TOPSIS method for the comprehensive resilience evaluation of water resources system.

Building on the above theoretical analysis of the TOPSIS model, this paper analyzes its applicability and scientific validity in the resilience evaluation of water resources system. The specific calculation steps are as follows:

  1. (1)

    Perform standardization on the original data to obtain the standardized matrix \(S = \left( {x_{ij}^{\prime } } \right)_{m \times n}\).

  2. (2)

    Reconstruct the weighted normalized matrix X based on indicator weights:

    $$X = S \times W_{j}^{*} = \left( {X_{ij} } \right)_{m \times n}$$
    (8)

    where Wj* is the comprehensive weight of subjective and objective indicators, as shown in Formula (7).

  3. (3)

    Determine the positive ideal solution X+ and the negative ideal solution X−

    The positive ideal solution X+ is composed of the maximum value in each column of X.

    $$\begin{aligned} X^{ + } & = \left( {\max \left\{ {X_{11} ,X_{21} , \cdots ,X_{m1} } \right\},\max \left\{ {X_{12} ,X_{22} , \cdots ,X_{m2} } \right\}, \cdots ,\max \left\{ {X_{1n} ,X_{2n} , \cdots ,X_{mn} } \right\}} \right) \\ & = \left( {X_{1}^{ + } ,X_{2}^{ + } , \cdots ,X_{n}^{ + } } \right) \\ \end{aligned}$$
    (9)

    The negative ideal solution X- is composed of the minimum value in each column of X.

    $$\begin{aligned} X^{ - } & = \left( {\min \left\{ {X_{11} ,X_{21} , \cdots ,X_{m1} } \right\},\min \left\{ {X_{12} ,X_{22} , \cdots ,X_{m2} } \right\}, \cdots ,\min \left\{ {X_{1n} ,X_{2n} , \cdots ,X_{mn} } \right\}} \right) \\ & = \left( {X_{1}^{ - } ,X_{2}^{ - } , \cdots ,X_{n}^{ - } } \right) \\ \end{aligned}$$
    (10)
  4. (4)

    Calculate the Euclidean distances between each evaluation object and the positive and negative ideal solutions:

    Euclidean distance from the positive ideal solution:

    $$D_{i}^{ + } = \sqrt {\sum\limits_{j = 1}^{n} {\left( {X_{j}^{ + } - X_{ij} } \right)^{2} } }$$
    (11)

    Euclidean distance from the negative ideal solution:

    $$D_{i}^{ - } = \sqrt {\sum\limits_{j = 1}^{n} {\left( {X_{j}^{ - } - X_{ij} } \right)^{2} } }$$
    (12)
  5. (5)

    Calculate the closeness between the evaluation object and the ideal solution, denoted as the water resources system resilience evaluation value Ci:

    $$C_{i} = \frac{{D^{ - } }}{{D^{ + } + D^{ - } }},0 < C_{i} \le 1$$
    (13)

Results and discussion

Results of the resilience evaluation of the water resources system

This study calculates the resilience level of the water resources system in the provinces along the Yellow River from 2009 to 2022 using the game-theoretic combined weighting TOPSIS method, analyzes its spatial and temporal evolution characteristics, and explores in depth the principal causes and differences in resilience levels among these provinces. The degree of closeness (Ci) is used to quantify the proximity of each alternative to the ideal optimal solution, with a value range of 0–1, and the higher the value, the greater the resilience level of the water resources system; conversely, the lower the value, the lower the resilience level. Based on the research findings of various experts and scholars, combined with the natural breaks classification method in ArcGIS, this study divides the Ci values representing the resilience level of the water resources system in the provinces along the Yellow River during 2009–2022 into four grades: high resilience, higher resilience, medium resilience, and low resilience. The classification criteria are shown in Table 3.

Table 3 Classification criteria of resilience level of water resources system.
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Equations (8)–(13) are applied to calculate the resilience level of the water resources system from 2009 to 2022, and the results are shown in Table 4.

Table 4 Yellow River Basin water resources system resilience evaluation results.
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Temporal evolution patterns of the water resources system resilience

Based on the TOPSIS results, the changes in water resources system resilience in nine provinces along the Yellow River from 2009 to 2022 are shown in Fig. 3.

Fig. 3
figure 3

Resilience level of water resources system in the nine provinces of the Yellow River Basin from 2009 to 2022.

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As shown in Fig. 3, the resilience of water resources system in the nine provinces along the Yellow River exhibited a fluctuating upward trend from 2009 to 2022. Provinces such as Shanxi, Gansu, and Qinghai experienced significant fluctuations due to climatic factors, environmental changes, and local policy implementation. In contrast, Shaanxi and Shandong demonstrated relatively stable resilience levels.

The improvement of resilience in the upstream provinces along the Yellow River is primarily attributable to the implementation of major ecological restoration and water conservancy projects. The resilience level of Qinghai Province showed a trend of ‘decrease-then-increase’. After decreasing from 0.38 in 2009 to 0.29 in 2013, with the improvement of the ecological conservation system in Sanjiangyuan National Park and the enhancement of water conservation capacity, the resilience value rebounded to 0.61 by 2020. The resilience level of Sichuan fluctuates slightly, generally remaining within the range of 0.36–0.63. Although there are large fluctuations in a few years (such as 2012–2015), the overall trend is relatively stable. In 2022, Sichuan Province suffered floods, droughts, geological disasters, etc., and the resilience level declined to 0.41. After the key node of Yintao Project in Gansu Province in 2015, the resolution of drought and drinking water safety issues in central Gansu significantly promoted a continuous increase in resilience from the early low level (0.26–0.37) to a peak of 0.64 in 2020. Ningxia has effectively improved agricultural water-use efficiency through the implementation of the water rights trading system in 2016, and the resilience level has gradually increased from the previous low value (0.27–0.32 ) to 0.62 in 2022. Inner Mongolia showed a “stepwise upward” pattern. The grassland ecological compensation policy in 2011 prompted the water consumption in pastoral areas to decrease by 19%, and the resilience value increased steadily from 0.30 in 2009 to 0.64 in 2021.

The resilience recovery of the middle reaches provinces along the Yellow River benefited from the support of water diversion projects. Shaanxi Province demonstrated a ‘U-shaped’ trend in water resources system resilience from 2009 to 2022. Resilience decreased from 0.40 to a low of 0.36 between 2009 and 2015, followed by recovery from 2016 onward, reaching a peak of 0.58 in 2021. This improvement was attributed to the effective water allocation enabled by the Hanjiang-Weihe Water Diversion Project. Shanxi Province’s resilience fluctuated between 0.30 and 0.46 from 2009 to 2016 and steadily increased after 2017, reaching a peak of 0.53 in 2021.

The steady improvement in the resilience of the downstream provinces along the Yellow River is attributed to the enhancement of major national water conservancy infrastructure. Shandong Province’s resilience evolution showed a “fluctuating upward trend”. It achieved a significant leap following the completion of the Jiaodong Water Diversion Project and the eastern route of the South-to-North Water Diversion Project in 2013. (adding 140 million m3 of annual water supply). Although resilience fluctuated due to drought and flood disasters in 2014–2015, with the completion of provincial-level backbone water network projects, reaching a resilience value of 0.56 in 2021. Henan Province’s resilience level fluctuated at a low range (0.33–0.38) between 2009 and 2015. Subsequently, with the continuous improvement of supporting projects for the Central Route of the South-to-North Water Diversion Project, the resilience level gradually increased, reaching a peak value of 0.63 in 2021.

In summary, the water resources system resilience of the nine provinces along the Yellow River generally exhibited an upward trend from 2009 to 2022, with widespread improvements especially after 2019. This indicates that the implementation of water resources management policies, growing awareness of ecological protection, and continuous improvements in regional water infrastructure have collectively enhanced the adaptive capacity to climate change, leading to significant improvement in the resilience of water resources system in the Yellow River Basin.

The average resilience levels of the water resources system in the Yellow River Basin from 2009 to 2022 , and the average resilience levels of the nine provinces are shown in Fig. 4.

Fig. 4
figure 4

Resilience level of water resources system in the provinces along the Yellow River from 2009 to 2022.

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At the basin scale, the temporal evolution of water resource system resilience in the Yellow River Basin exhibits a clear stage-wise fluctuating upward trend (Fig. 4a). The period from 2009 to 2013 represented a low-level fluctuation phase, with the average resilience value ranging between 0.34 and 0.41, reflecting the incomplete development of the early water resource management system. In 2015, affected by an extreme drought event, the Yellow River’s runoff decreased significantly, causing the basin’s resilience level to plummet to 0.35, highlighting the impact of extreme climate events on system stability. After 2015, with the deepening implementation of the Ecological Protection and High-Quality Development Strategy of the Yellow River Basin, a series of comprehensive measures—such as water conservation, water diversion, and ecological restoration—were jointly promoted, leading the basin into a phase of rapid resilience enhancement and resulting in a peak value of 0.59 by 2021.

As shown in Fig. 4b, the average resilience levels of water resources system in the provinces along the Yellow River from 2009 to 2022, in desceending order, were: Sichuan > Henan > Shaanxi > Inner Mongolia > Qinghai > Shandong > Ningxia > Gansu > Shanxi. Sichuan Province consistently ranks first in resilience due to its superior baseline water resources. Henan Province has risen to second place by optimizing the Yellow River water resource allocation mechanism. Shanxi Province, with an annual precipitation of 380–550 mm, has relatively low average resilience due to scarce water resources and relatively high development and utilization pressures.Sichuan recorded the highest average resilience at 0.49, followed by Henan at 0.46. Henan’s optimization of the Yellow River’s water dispatch system has notably ensured the ecological base flow. In contrast, Shanxi exhibited the lowest resilience level at 0.39. Located on the Loess Plateau, the province suffers from low and unevenly distributed precipitation, with an annual average ranging only 380–550 mm. Its natural endowment of water resources is poor, with both surface and groundwater resources being scarce. As a result, per capita water supply and water availability per unit of cultivated land are significantly lower than the national average.

Spatial evolution characteristics of water resources system resilience

To comprehensively understand the long-term evolution of water resources system resilience in the provinces along the Yellow River, selecting representative years as study samples is crucial. Five representative years—2009, 2012, 2015, 2018, and 2022—were selected from the period 2009–2022 for analysis. These years not only span a substantial time period but also reflect differences in economic development stages, basin water resource endowments, and social conditions, providing strong support for obtaining a comprehensive assessment of the long-term evolution of resilience.

In order to describe the difference and evolution of the resilience level of water resources system in provinces along the Yellow River more clearly and intuitively, the spatial analysis tool in ArcGIS 10.2 was employed to visualize the resilience level of the water resources system in the Yellow River Basin. Based on the classification criteria presented in Table 3 and using the natural breaks classification method, the spatial distribution characteristics of water resources system resilience were analyzed, as shown in Fig. 5.

Fig. 5
figure 5

Temporal and spatial evolution characteristics of resilience level of water resources system in nine provinces of the Yellow River Basin.

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As shown in Fig. 5, in 2009 (Fig. 5a), except for Gansu Province, which had level IV low resilience, the other provinces along the Yellow River had level III moderate resilience. The overall resilience level of the watershed’s water resources system was relatively low. The main reason was that in 2009, water conservancy infrastructure across the region was incomplete. Flood control and disaster reduction capacities needed improvement. The efficiency of comprehensive water resource management was low. By 2012 (Fig. 5b), the overall resilience of the basin’s water resources system had improved. Especially, Inner Mongolia and Sichuan provinces had upgraded to level II resilience. In 2015 (Fig. 5c), the provinces along the Yellow River experienced a severe drought event. The drought covered 60.7% of the area and caused serious negative impacts on agriculture, ecosystems, and the socio-economy. As a result, the overall resilience of the basin declined. Since 2017, resilience levels have increased significantly. The main reason was that a policy system emphasizing both ecological protection and high-quality development was implemented in the Yellow River Basin. Rigid constraints on water use were strengthened. The “Four Waters and Four Determinations” principle was enforced, which further improved the precision of water resources management and provided institutional support for the resilience of the water resources system in the provinces along the Yellow River. In 2018 (Fig. 5d), only Shaanxi, Shanxi, and Shandong remained at level III moderate resilience. By 2022 (Fig. 5e), resilience declined only in Sichuan Province, while the upper reaches of the Yellow River (including Qinghai, Gansu, and Ningxia) achieved Level I high resilience, and the middle and lower reaches reached Level II relatively high resilience.

The average resilience distribution of the provinces along the Yellow River and its trend from 2009 to 2022 are shown in Fig. 6. Except for Sichuan and Henan, which were at Level II higher resilience, other provinces wereat Level III moderate resilience. Resilience levels generally increased with fluctuations from 2009 to 2022.

Fig. 6
figure 6

The average resilience distribution and change trend of water resources system in the Yellow River Basin.

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Conclusions

The resilience levels of water resources system in the provinces along the Yellow River Basin from 2009 to 2022 were calculated using the TOPSIS method based on game-theoretic weighting, and the spatiotemporal characteristics and regional differences in resilience across the basin were analyzed. The results indicate that: (1) The resilience levels of water resources system in the nine provinces along the Yellow River exhibited a fluctuating upward trend influenced by climatic and environmental factors. Provinces such as Shanxi, Gansu, and Qinghai showed significant fluctuations, whereas Shaanxi and Shandong maintained relatively stable resilience levels. (2) Overall, the resilience of water resources system along the Yellow River showed an increasing trend from 2009 to 2022, with the lowest value of 0.36 in 2009 and 2010 and the highest value of 0.59 in 2021. (3) The nine provinces were ranked in descending order of resilience levels as follows: Sichuan > Henan > Shaanxi > Inner Mongolia > Qinghai > Shandong > Ningxia > Gansu > Shanxi. (4) Among the provinces along the Yellow River, only Sichuan and Henan showed level II higher resilience, while the remaining provinces exhibited level III a medium resilience. From 2009 to 2022, the resilience of water resources system in all provinces exhibited a fluctuations upward trend.