Introduction

Water resource, energy resource and food resource are crucial material bases for human production and life, and key driving forces for social and ecological development1,2. Since the concept of WEF nexus was introduced at the Bonn2011 Conference: The Water, Energy and Food Security Nexus, resource linkage management had gradually become a research focus on sustainable development3,4. With rapid urbanization and rising economic level, the challenge of ensuring the adequate supply of water resources, energy resources and food resources, and the stable operation of WEF nexus, has increased significantly5,6. Meanwhile, the spatial misallocation of water, energy and food resources leads to unreasonable regional multi-resource program and management, which seriously threatens the security of WEF nexus7. Hence, it is very important to search the spatial conflict of water, energy and food resources and optimize the allocation of resources for regional sustainable development8,9.

WEF nexus operate stably by interacting with the external environment10,11. The natural environment provides the basic material conditions and geographical space for resource development and human survival, while the water resources, energy resources and food resources, as the boosters of regional development, provide the necessary resource carrying capacity for human production and life12,13. Global climate change, rapid urbanization and the transformation of dietary structure lead to the intensification of resource demand and the deterioration of eco-environment14,15, making the relation between water resource, energy resource and food resource more complex and fragile, and bringing more uncertainties to multi-resource management16,17. With the increasingly prominent characteristics of the synergetic development among the social-economic-natural environment system and the WEF nexus, it is essential to clarify the intricate linkage mechanism between the WEF nexus and the resource and the external environment from the perspective of the multi-resource complex system. It is vital to objectively evaluate the development trend of multi-resource complex system, analyze the internal resource allocation situation and clarify the coordinated development mechanism of the complex system for strengthening the comprehensive management of multi-resource and ensuring the security of resource supply and demand.

The previous research on the spatial relationship of WEF nexus mainly focuses on the quantitative analysis of resource coupling relationship and resource matching relationship18,19. By exploring the cross-sectoral pressure in connected with water resource, energy resource and food resource, Qin et al. pointed out that the spatial mismatch of resources was an important reason for the pressure transfer within and between countries7. White et al. showed that due to lack of attention to the external environment, there was not match between regional water, energy and food supply with endmost resource consumption20. Although these researches had analyzed the spatial mismatch of WEF nexus, they lacked the spatial adaptation of multi-resource systems from the dimension scale, which made it difficult to obtain theoretical support for cross-sectoral collaboration and policy planning of Water-Energy-Food system.

The YRB is a key zone for rapid economic development and ecological security, and has major national strategies to promote ecological protection and high-quality development21. Water resources, energy resources and food resources are the three core elements of the society-economic-ecosystem system. Whether they can realize the coordination among the elements and enhance the sustainable development ability of the system is vital to promoting high-quality development in the YRB. At present, most studies on the correlation among water, energy and food in the YRB focus on the overall comprehensive evaluation of the basin, and lack of detailed research on zoning and reaches, which is not conductive to finding the key areas that hinder the coordination development of water, energy and food, resulting in the lack of operability of the research results22,23.

Changes in a single dimension can be cascaded to other dimensions by the coupling effect in a complex system, eventually triggering a comprehensive change in the entire WEF CS. Therefore, in order to achieve regional coordinated development, it is particularly crucial to deeply analyse the spatial adaptation pattern and coordinated development mechanism of key regions in the YRB from regional and dimensional scales. Although previous studies have begun to explore the role of the external environment in WEF nexus connection, they have failed to effectively establish the correlation with external environment, resulting in a comprehensive and in-depth analysis of the feedback mechanism of this complex system, thus limiting the depth and breadth of resource correlation analysis. Furthermore, these studies lack the necessary organic link between spatial adaptation and coordination development, and the analysis of key zones in the YRB is not deep enough.

The existing knowledge gap needs to be solved by a comprehensive evaluation system of WEF CS. On the one hand, the WEF nexus reflects the dimension of regional resource security and provides the necessary material basis for human development. On the other hand, the external environment reflects the dimension of regional social and economic development and provides bearing space for the circulation and utilization of natural resources. The spatial adaptation and coordinated development of water, energy and food resources provide solutions for the sustainable development of regional natural resources and human well-being. In this context, this study attempts to answer: (1) What is the index framework of the WEF CS? (2) What is the internal correlation mechanism of the spatial adaptation pattern and coordinated development of the WEF CS at the basin scale? (3) Which indicators are key factors to drive the weak areas of the WEF CS in the YRB? To fill the gaps, based on the three-level logic of “unit-nexus-external environment”, a new theoretical framework is proposed to consider the mutual effects between the WEF nexus and the “society-economic-nature” external environment. Under the framework, the development level of WEF CS in nine provinces and regions of YRB was analyzed, the key zones that hindered the collaborative development of WEF were found, and the correlation factors of regional scale and dimensional scale of complex system were explored. The purpose of this research is to classify the development trend and improvement mechanism of the WEF CS in nine provinces and regions of YRB, and to propose a path suggestion for facilitating the sustainable development of the WEF CS.

Methodology

Study region

As the second longest river in China, the Yellow River has a length of 5464 km. It originates from the Bayankala Mountains in Qinghai and flows through the Loess Plateau, then the North China Plain and the coastal plain of Bohai Bay. There are nine provinces and regions along the Yellow River, namely Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shaanxi, Shanxi, Henan and Shandong (Fig. 1). It reaches Yinshan Mountain in the north, Qinling Mountains in the south, Bayankhara Mountain in the west, and Bohai Sea in the east.

Fig. 1
figure 1

Provinces along the YRB. (Note the map was created using ArcGIS Pro software, developed by Esri. URL link: https://www.esri.com/en-us/arcgis/products/arcgis-pro/overview)

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Theoretical framework

The research of trade-offs and synergy between water, energy and food resources contributes to regional sustainable development24,25. However, this single linear study focusing on the WEF nexus is not conductive to the development of multi-scale and multi-dimensional regional planning. The complex ecosystem is composed of natural resources and human social and economic activities, which provides a comprehensive perspective for the research of water, energy and food. Based on the cascading relationship between water, energy and food resources and social, economic and eco-environment, we build a comprehensive composite system from point to line and from line to surface. Specifically, based on of WEF nexus and the external environment of society-economy-eco-environment, it constructs the WEF CS from the logical framework of “unit-nexus-external environment”. The complex system takes water system, energy system and food system as the system unit, water-energy nexus, water-food nexus and energy-food nexus as the link, and realizes the material circulation, energy flow and information transmission among water system, energy system and food system under the natural environment background of society-economy-eco-environment. It shows that the water, energy and food system units are connected by water-energy nexus, water-food nexus and energy-food nexus, and the units and nexus are nested in the natural environment. The theoretical framework of WEF CS is displayed in Fig. 2.

Fig. 2
figure 2

Theoretical framework of WEF CS.

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The WEF CS consists of three levels.

  1. 1.

    As a system unit, water, energy and food systems are the main body of the complex system and the basic unit of material circulation, energy flow and information transmission. The quantity, quality, structure and load-bearing capacity of resources inside the system unit determine the upper limit of balanced development of the complex system.

  2. 2.

    Nexus refers to the close relationship between the correlative dependence and conversion of water, energy and food. Concretely, energy provides power for agricultural production, transportation and water resources exploitation and utilization26. Water resource is demanded in agricultural irrigation and energy processing, and groundwater development is crucial for improving agricultural growth and guaranteeing food security in climate crisis27. Waste and energy plants in agricultural production and processing can be converted into biomass energy under certain conditions. Nexus is a crucial basis for the evolution of complex systems.

  3. 3.

    The society-economy-eco-environment belongs to the external environment, which is used to carry the system units and nexus relationships, and ensure the stable operation of the complex system. The natural environment provides the necessary operating conditions and a certain capacity for the complex system. While ensuring the normal operation of the system units and nexus relationships, it absorbs some of the pollutants generated by production and life, resource exploitation and processing. Therefore, the sustainable development of the natural environment is essential to maintain the balance and stability of the WEF CS.

Indicator system

Select indicators according to the principles of systematic, typical, operability and accessibility, refer to the relevant indicators used on the existing research on water, energy and food systems, and consider the transfer of material, energy and information by resource elements in the composite system based on the logical framework of “unit-nexus-external environment”. The index system of WEF CS is divided into three dimensions: system unit, nexus and natural environment. The system unit dimension includes three factors: water system, energy system and food system, and six indicators are set from the perspective of resource supply and consumption, namely the total water supply and the total water use, the production of main energy products and the consumption of main energy products, as well as the grain production and the grain consumption. The nexus dimension has three factors: Water-Energy nexus, Water-Food nexus and Energy-Food nexus, and the representative indicators are adopted based on large correlation proportion in these dimensions, which are respectively the proportion of industrial water use, the hydroelectric power generation and the industrial added value water consumption in Water-Energy nexus, the proportion of agricultural water use, the agricultural water consumption per 10,000 yuan of output value and the effective irrigation area in Water-Food nexus, as well as the total power of agricultural machinery, the waterlogging control area and the agricultural diesel use in Energy-Food nexus. The natural environment dimension includes three factors: society, economy and eco-environment. In order to establish the connection between water, energy and food resources and human social and economic activities, the urbanization rate, the per capita energy consumption, the per capita water consumption and the per capita grain consumption are adopted in society; the GDP per capita, the water resources consumption per GDP, the energy consumption per GDP and the total value of agricultural output are adopted in economy; the crop affected area, the total wastewater discharge, the forest coverage rate and the water and soil loss control area are adopted in eco-environment.

The data came from the statistical yearbook, survey yearbook, urban statistical yearbook, rural statistical yearbook, market statistical yearbook, energy statistical yearbook and regional economic statistical yearbook of provinces along Yellow River from 2005 to 2021, and the National Bureau of Statistics in China (www.stats.gov.cn). Based on the theoretical framework, the indicator system was constructed (Table 1), with 27 indicators.

Table 1 WEF CS index system.
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Research method

Entropy evaluation method

The entropy evaluation method is an objective weighting method based on the principle of information entropy, which is mainly used to determine the weight of each index in a comprehensive evaluation system28. The basic principle is to use information entropy to measure the degree of dispersion of an indicator. The greater the degree of dispersion, the greater the impact of the indicator on the comprehensive evaluation, and the higher the weight. Entropy evaluation method takes advantage of the data information contained in each index data to determine the weight, which effectively guarantees the authenticity and rationality of the index weight, and is a popular objective weighting methods in current research. The comprehensive evaluation model of entropy method is served as measuring the development level of WEF CS in nine provinces along YRB from 2004 to 2020.

  1. 1.

    Data standardization.

It takes advantage of the range method to standardize the data.

$${x_{ij}}=\left\{ {\begin{array}{*{20}{c}} {\frac{{{x_{ij}} - min\left\{ {{x_{1j}}, \ldots ,{x_{mj}}} \right\}}}{{max\left\{ {{x_{1j}}, \ldots ,{x_{mj}}} \right\} - min\left\{ {{x_{1j}}, \ldots ,{x_{mj}}} \right\}}}~~~~\left( + \right)} \\ {\frac{{max\left\{ {{x_{1j}}, \ldots ,{x_{mj}}} \right\} - {x_{ij}}}}{{max\left\{ {{x_{1j}}, \ldots ,{x_{mj}}} \right\} - min\left\{ {{x_{1j}}, \ldots ,{x_{mj}}} \right\}}}~~~~\left( - \right)} \end{array}} \right.$$
(1)

Where, \({x_{ij}}\) is the raw data of the jth indicator of the ith evaluation target, m indicates the number of evaluation targets.

  1. 2.

    Calculating the ratio of the jth indicator of the ith evaluation target.

$${F_{ij}}={f_{ij}}/\mathop \sum \limits_{{i=1}}^{m} {f_{ij}}$$
(2)
  1. 3.

    Calculate index entropy.

$${e_j}= - \frac{1}{{lnm}}\mathop \sum \limits_{{i=1}}^{m} {F_{ij}}ln{F_{ij}}$$
(3)
  1. 4.

    Calculate entropy backwards.

$${h_j}=1 - {e_j}$$
(4)
  1. 5.

    Calculate index weight.

$${w_j}=\frac{{{h_j}}}{{\mathop \sum \nolimits_{{j=1}}^{n} {h_j}}}$$
(5)
  1. 6.

    Comprehensive evaluation value determination.

According to the comprehensive evaluation model, the comprehensive development level of the WEF CS was obtained.

$$E=\mathop \sum \limits_{{j=1}}^{n} {w_j}{f_{ij}}$$
(6)

Where, \(\:E\) is the comprehensive development level index of the WEF CS.

Dagum Gini Coefficient

The Dagum Gini Coefficient is a statistical indicator used for measuring regional income disparities. It provides more detailed disaggregated information than the traditional Gini Coefficients, including the intra-group Gini coefficient (Gw), the inter-group Gini coefficient (Gb), and the super-variable density Gini coefficient (Gt)29. Gw reflects the difference in level within each region. Gb indicates the level difference between regions. Gt reflects the overlapping phenomenon of various regions and the relative gap. Dagum Gini Coefficient can make up for the drawback of other methods to measure regional discrepancy, which can not only solve the overlapping phenomenon of the investigated data, but also better recognize the sources of regional discrepancy. Dagum Gini Coefficient has the characteristics of flexibility, strong analytical ability and can solve the problem of cross-overlapping samples between regions, so it is suitable for exploring the spatial adaptation in the YRB.

$$G=\frac{1}{{2{n^2}y}}\mathop \sum \limits_{{j=1}}^{k} \mathop \sum \limits_{{h=1}}^{k} \mathop \sum \limits_{{i=1}}^{{nj}} \mathop \sum \limits_{{r=1}}^{{nh}} \left| {{y_{ji}} - {y_{hr}}} \right|$$
(7)

In the formula, \({y_{ji}}\) and \({y_{hr}}\) are the development level indexes of the WEF CS in each province in the j and h zones, respectively. \(\:y\) is the average development level of WEF CS in nine provinces of the YRB. n is the number of provinces; k is the number of subdivisions in the YRB. In this study, the YRB is divided into the upstream, the midstream and the downstream. The upstream includes Qinghai, Sichuan, Gansu and Ningxia; the midstream includes Inner Mongolia, Shaanxi and Shanxi, and the downstream includes Henan and Shandong. \(nj\) is the number of provinces in the YRB; G is the overall Gini coefficient; h is a different partition of k YRB partitions, and j = 1, 2, …, k; r is the number of different provinces in a zone.

The Dagum Gini Coefficient decomposition method decomposed the total Gini coefficient G into Gw of intra-regional difference contribution, Gb of inter-regional net difference contribution and Gt of super-variable density contribution.

$$G={G_W}+{G_b}+{G_t}$$
(8)

The formula for calculating intra-regional differential contribution is as follows:

$${G_{jj}}=\frac{1}{{2n_{j}^{2}{y_j}}}\mathop \sum \limits_{{i=1}}^{{nj}} \mathop \sum \limits_{{r=1}}^{{nj}} \left| {{y_{ji}} - {y_{jr}}} \right|$$
(9)
$${G_W}=\mathop \sum \limits_{{j=1}}^{k} {G_{jj}}{p_j}{s_j}$$
(10)
$${G_b}=\mathop \sum \limits_{{j=2}}^{k} \mathop \sum \limits_{{h=1}}^{{j - 1}} {G_{jh}}\left( {{p_j}{s_h}+{p_h}{s_j}} \right){D_{jh}}$$
(11)
$${G_{jh}}=\mathop \sum \limits_{{i=1}}^{{nj}} \mathop \sum \limits_{{r=1}}^{{nh}} \left| {{y_{ji}} - {y_{hr}}} \right|/{n_j}{n_h}\left( {{y_j}+{y_h}} \right)$$
(12)
$${G_t}=\mathop \sum \limits_{{j=2}}^{k} \mathop \sum \limits_{{h=1}}^{{j - 1}} {G_{jh}}\left( {{p_j}{s_h}+{p_h}{s_j}} \right)\left( {1 - {D_{jh}}} \right)$$
(13)
$${D_{jh}}=\frac{{{d_{jh}} - {p_{jh}}}}{{{d_{jh}}+{p_{jh}}}}$$
(14)

Where, \({p_j}={n_j}/n\) is the ratio of the number of provinces in j region to the nine provinces of the YRB;

\({s_i}={n_i}{y_i}/ny,j=1,2, \ldots ,k;\)

\({D_{jh}}\) is the relative impact on the development level of WEF CS between j and h zones.

\({d_{jh}}\) is defined as the discrepancy of the development level of the WEF CS between subregions, that is, the mathematical expectation of the sample sum satisfying the condition of \({y_{ji}} - {y_{hr}}>0\) in the partition and the h partition. \({p_{jh}}\) is defined as a hypervariable matrix, showing the mathematical expectation of the sum of all \({y_{hr}} - {y_{ji}}>0\) sample values in the j and h partition. \({F_j}\), \({F_h}\) are the cumulative density distribution functions of the j and h partitions, respectively.

$${d_{jh}}=\mathop \smallint \limits_{0}^{\infty } d{F_j}\left( y \right)\mathop \smallint \limits_{0}^{y} \left( {y - x} \right)d{F_h}\left( x \right)$$
(15)
$${p_{jh}}=\mathop \smallint \limits_{0}^{\infty } d{F_h}\left( y \right)\mathop \smallint \limits_{0}^{y} \left( {y - x} \right)d{F_j}\left( x \right)$$
(16)

Traditionally, a Gini coefficient of less than 0.2 is high average, 0.2–0.29 is relatively average, 0.3–0.39 is relatively reasonable, 0.4–0.59 is large difference, as well as a coefficient greater than 0.6 indicates huge difference.

Coupling coordination degree

The coupling coordination degree (CCD) model measures the degree of coordination between multiple systems30.

$$C=3 \times {\left[ {\frac{{f\left( x \right) \times g\left( y \right) \times h\left( z \right)}}{{f\left( x \right)+g\left( y \right)+h\left( z \right)}}} \right]^{1/3}}$$
(17)
$$D=\sqrt {C \times T} ,{\text{~}}T=\alpha f\left( x \right)+\beta g\left( y \right)+\delta h\left( z \right)$$
(18)

C: the coupling degree between \(f\left( x \right)\), \(g\left( y \right)\) and \(h\left( z \right)\);

\(f\left( x \right)\): the system unit; \(g\left( y \right)\): the nexus; \(h\left( z \right)\): the natural environment; D: the CCD; T: the comprehensive development index of research objectives; α, β and δ: indeterminate coefficients, which express the contribution of the three research objectives to the coordination development. Hereon, α = β = δ = 1/3 is assigned.

Table 2 Coupling degree C and coordination degree D classification criteria.
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The grey prediction model

The grey prediction model uses differential equation to fully explore the essence of data, and has the advantages of less information required for modeling, high precision, simple operation and easy verification.

Raw data series \({{\text{Z}}^{\left( 0 \right)}}\):

$${Z^{\left( 0 \right)}}=\left( {{Z^{\left( 0 \right)}}\left( 1 \right),{Z^{\left( 0 \right)}}\left( 2 \right), \ldots ,{Z^{\left( 0 \right)}}\left( M \right)} \right)$$
(19)

Build the GM (1,1) model for the sequence \({{\text{Z}}^{\left( 1 \right)}}\).

$${Z^{\left( 1 \right)}}\left( {t+1} \right)=\left[ {{Z^0}\left( 1 \right) - \frac{b}{a}} \right]{e^{ - at}}+\frac{b}{a}$$
(20)

In the formula, a and b are identification parameters.

Matrix establishment:

$$\bar {a}={\left( {{B^T}B} \right)^{ - 1}}{B^T}X={\left[ {a,b} \right]^T}$$
(21)

The forecast model:

$$\widehat {{{Z^{\left( 0 \right)}}}}\left( {t+1} \right)= - a\left[ {{Z^{\left( 0 \right)}}\left( 1 \right) - \frac{b}{a}} \right]{e^{ - at}}$$
(22)

The accuracy of the research results is examined by variance ratio C, small error probability P and root-mean-square error RMSE (Table 3). The range of root-mean-square error RMSE is non-negative real numbers, and generally the smaller the value, the better the fitting effect of the model.

Table 3 Precision test criterion.
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The grey correlation model

Grey correlation model is a method to quantitatively describe the development and change of the system based on grey system theory. It is mainly based on the evaluation of the geometric proximity between the driving factors to determine the degree of correlation. It has the advantages of convenient calculation and wide applicability. It has no limit on the number of samples and does not require samples to obey any probability distribution.

Construct reference sequence \({X_0}\) and comparison sequence \({X_1}\)

$${X_0}=\left\{ {{X_0}\left( 1 \right),{X_0}\left( 2 \right), \cdots ,{X_0}\left( n \right)} \right\}$$
(23)
$${X_1}=\left\{ {{X_1}\left( 1 \right),{X_1}\left( 2 \right), \cdots ,{X_1}\left( n \right)} \right\}$$
(24)

Correlation coefficient

$${\xi _i}\left( k \right)=\frac{{mi{n_i}mi{n_k}\left| {{X_0}\left( k \right) - {X_i}\left( k \right)} \right|+\delta ma{x_i}ma{x_k}\left| {{X_0}\left( k \right) - {X_i}\left( k \right)} \right|}}{{\left| {{X_0}\left( k \right) - {X_i}\left( k \right)} \right|+\delta ma{x_i}ma{x_k}\left| {{X_0}\left( k \right) - {X_i}\left( k \right)} \right|}}$$
(25)

Where, \(\delta \in \left( {0,~\infty } \right)\), \(\delta =0\) is usually taken.

Correlation degree

$$\:{y}_{i}=\frac{1}{n}\sum\:_{k=1}^{n}{\xi\:}_{i}\left(k\right)$$
(26)

Results

Spatiotemporal evolution of WEF CS

There was obvious spatial difference in the development trend of the WEF CS in the YRB (Fig. 3). In 2020, on the whole, the upstream development level was higher than that of the downstream, and the downstream development level was higher than that of the midstream. From 2004 to 2020, except for Shaanxi and Henan, the development index of WEF CS in other seven provinces showed an increasing trend, and the average annual growth rate of Gansu’s development index was the highest, which was 6.77%. The development status of the WEF CS in Shaanxi showed a downward tendency on the whole, while that in Henan showed an inverted U-shaped trend. In addition, the average annual growth rates of development indexes in Shaanxi and Henan were negative value, at − 1.73% and − 0.31% respectively.

Fig. 3
figure 3

Spatiotemporal evolution of the development level of WEF CS in the YRB from 2004 to 2020.

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Spatial adaptation pattern of WEF CS

In Fig. 4, the overall Gini coefficient of the WEF CS in the YRB showed a decreasing trend, from 0.123 in 2004 to 0.084 in 2020, with a decrease of 31.71%. Moreover, the overall difference of the development level in the WEF CS showed a significant stage. From 2004 to 2008, the overall difference declined significantly, and the overall Gini coefficient reduced from 0.123 in 2004 to 0.059 in 2008, declining 52.03%; from 2009 to 2017, it showed a fluctuating state, with the maximum being 0.77 in 2015 and the minimum being 0.56 in 2009; it was a brief increase from 2018 to 2020, from 0.072 in 2018 to 0.084 in 2020.

During 2004–2020, the average annual contribution rates of intra-regional differences, inter-regional differences and super-variable density difference were 26.66%, 48.66% and 24.68%, respectively, indicating that the differences in the development status of the WEF CS in the YRB come from inter-region (Fig. 4). Among them, about inter-regional differences, the largest value was between in 2004–2013 and 2016–2020. At the same time, the differences between super-variable density in 2014 and 2015 were the largest. The trend of the super-variable density was opposite to the inter-regional differences, which indicated that the interaction between the intra-regional difference and the inter-regional difference of the WEF CS in the YRB hindered the spatial adaptation of water, energy and food in the upstream, midstream and downstream. The contribution rate decreased by 0.85% in intra-region, and the contribution rate reduced by 72.31% in super-variable density. It was worth that the contribution rate in inter-region changed from 51.25% in 2004 to 66.75% in 2020, increasing by 30.25%, which showed that the development status of the WEF CS in the upstream, midstream and downstream was significantly different, and the development was unbalanced in the YRB.

Fig. 4
figure 4

Gini coefficient and contribution rate.

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From the variation trend of intra-basin differences, the upstream, midstream and downstream all showed a trend of fluctuation decline (Fig. 5). Among them, the upstream reduced from 0.092 in 2004 to 0.071 in 2020, a decrease of 22.83%; the midstream reduced from 0.103 in 2004 to 0.022 in 2020, a decrease of 78.64%; downstream was from 0.103 in 2004 to 0.066 in 2020, the decline was 35.92%. The differences within three reaches generally showed a downward trend, which might be related to the promotion of ecological protecting and high-equality development in the YRB.

From the perspective of the variation trend of differences among reaches, the upstream and downstream, the midstream and downstream all showed a trend of fluctuation reduction, among which, the discrepancy between the upstream and downstream decreased from 0.161 in 2004 to 0.075 in 2020, a decrease of 53.42%; the discrepancy between midstream and downstream from 0.116 in 2004 to 0.065 in 2020, the decline of 43.97%. The difference among the upstream and midstream showed a U-shaped trend, from 0.131 in 2004 to 0.124 in 2020, a decrease of 5.34%. In summary, the intra differences reduced in the upper, middle and lower reaches respectively, indicating that the WEF CS of provinces in the intra- reaches presented a trend of coordinated development. Although there were differences among inter-reaches, the differences had been decreasing, and it was necessary for all regions to actively promote the measures for the stable operation of the WEF CS and accelerated the coordinated development of the YRB.

Fig. 5
figure 5

Intra-group and inter-group differences.

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Coupling and coordination development

After analyzing whether the development level of the WEF CS was balanced among reaches and within reaches in the YRB, this part explored the coordination among various dimensions within the complex system. In the coupling relationship between system unit dimension, nexus dimension and natural environment dimension (Fig. 6), the coupling degree of Qinghai, Sichuan, Gansu, Ningxia, Shanxi and Shandong all showed a fluctuating upward trend. The WEF CS of Qinghai, Sichuan, Gansu, Ningxia and Shanxi would reach extreme coupling in 2020, while that of Shandong would reach moderate coupling in 2020. From 2004 to 2020, the coupling degree of Inner Mongolia, Shaanxi and Henan showed a fluctuating downward trend, among which Inner Mongolia and Shaanxi were still in a state of extreme coupling in 2020, and Henan was in the slight coupling state. In the coordination relationship between system unit dimension, nexus dimension and natural environment dimension, Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shanxi and Shandong showed an overall upward trend, among which Qinghai, Sichuan, Gansu, Ningxia and Shanxi reached extreme coordination in 2020, and Inner Mongolia and Shandong reached moderate coordination in 2020. However, Shaanxi and Henan showed a downward trend, with Shaanxi dropping from 0.93 (extremely coordination) in 2004 to 0.59 (slightly coordination) in 2020, and Henan from 0.81 (extremely coordination) in 2004 to 0.58 (slightly coordination) in 2020.

Fig. 6
figure 6

CCD of WEF CS along the YRB.

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Moreover, the internal coupling coordination of each dimension in the WEF CS was discussed (Fig. 7). The results showed that the CD and CCD of each dimension in Qinghai, Sichuan, Gansu and Ningxia showed an overall upward trend. Among the coupling relations within each dimension of the complex system, the nexus dimension and natural environment dimension of Inner Mongolia, the system unit dimension of Shaanxi, the system unit dimension of Shanxi and the system unit dimension of Shandong were downward trends, and the CD of the system unit dimension of Shandong was the most obvious decline. It had reduced from 0.96 (extremely coupling) in 2004 to 0.23 (moderate decoupling) in 2020. In the internal coordination relationship of each dimension, the system unit dimension of Inner Mongolia, Shaanxi, Shanxi, Henan and Shandong showed a downward trend. Among them, the CCD of system unit in Shaanxi and Shandong had the most obvious decline, from 0.84 (extremely coordination) in 2004 to 0.45 (slightly coordination) in 2020, and from 0.84 (extremely coordination) in 2004 to 0.19 (extremely unbalanced) in 2020 in Shandong.

Fig. 7
figure 7

The CCD of WEF CS in various dimensions.

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To explore the relationship between external representation and internal coordination of WEF CS in nine provinces of YRB, a spatial adaptation and coordination diagram was constructed (Fig. 8). It was found that Gansu and Shanxi were in high average and extreme coordination state, indicating that the dimensions of the WEF CS in Gansu and Shanxi were both spatial compatible and internally coordinated. Qinghai, Sichuan and Ningxia were in relatively average and extreme coordination state, which indicated that the WEF CS of the three provinces was relatively coordinated and spatially compatible in all dimensions. Inner Mongolia and Shandong were in a relatively average and moderately coordination state, which showed that the WEF CS in the two regions was moderately coordinated in all dimensions and relatively compatible in space. Shaanxi was in a highly average and slightly coordination state, and Henan was in the relatively average and slightly coordination state, indicating that these two provinces were compatible in each dimension space, but the coordination between the dimensions was not strong.

Fig. 8
figure 8

The relationship between internal coordination and spatial adaptation of WEF CS.

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Grey prediction

So as to predict whether the WEF CS in the nine provinces of the YRB can achieve the goals of the Outline of the Plan for Ecological Protecting and High-quality Development of the YRB in 2030, a grey prediction model was used to infer the development trend (Table 4; Fig. 9). The results showed that the WEF CS in Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shanxi and Shandong would double the development level of 2004 in 2030 under the coordinated development of system unit dimension, nexus dimension and natural environment dimension; however, the development status of the WEF CS in Shaanxi showed an obvious downward trend, which was expected to drop to 0.029 by 2030; the development level of Henan’s WEF CS showed a stagnant trend, and was expected to remain stagnant at about 0.070 by 2030.

Table 4 Test of gray prediction model from 2004 to 2020.
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Fig. 9
figure 9

Prediction of the development level of WEF CS in nine provinces of the YRB.

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Discussions

Correlation factor

Based on the above research and prediction findings, it was found that the CD of the WEF CS decreased in the regional scale in Shaanxi and Henan, and the CD of the system unit dimension in Shaanxi and Shandong significantly reduced in the dimensional scale. Therefore, in order to realize the sustainable development of the WEF CS in the YRB, the correlation factors between the coordination degree of regional scale and dimension scale and the index system were explored (Fig. 10).

Fig. 10
figure 10

Correlation degree.

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At the regional scale, the coordination of WEF CS in Henan was greatly affected by grain consumption, per capita grain consumption, energy consumption per GDP, total water supply and crop affected area (Fig. 10A). The results showed that most of the important factors affecting the WEF CS in Henan province were related to food resources, which was consistent with the results of Wang et al.31. The coordination of WEF CS in Shaanxi was greatly affected by energy consumption per GDP, agricultural water consumption per 10,000 yuan of output value, water resources consumption per GDP, crop affected area and proportion of industrial water use (Fig. 10B). It proved Chen et al.’s point of view that water resources is the main contradiction in the coordinated development of water, energy and food resources in Shaanxi province32.

At the dimensional scale, the coordination of system unit dimension in Shandong was greatly affected by proportion of agricultural water use, total water supply, per capita water consumption, energy consumption per GDP and agricultural diesel use (Fig. 10C). It was proved that water resource is an important factor affecting the security of water-energy-food system in Shandong region33. The coordination of system unit dimension in Shaanxi was greatly affected by energy consumption per GDP, proportion of industrial water use, crop affected area, water and soil loss control area and agricultural water consumption per 10,000 yuan of output value (Fig. 10D). The results showed that the influence of water resources on the WEF CS in Shaanxi province was vital both from the perspective of regional scale and dimension scale. In addition, the research on the weak area of coordinated development of WEF CS in the YRB that the indicators of natural environment dimension had an important impact on the coordinated development of water, energy and food resources. Therefore, it is necessary to construct the index system of WEF CS based on the logic framework of “unit-nexus-external environment” to explore the sustainable development of water, energy and food.

Innovation and policy suggestion

As a hot spot of resource correlation research, the existing research on water, energy and food not only discusses the integrated resource management from multi-regional scale (provincial, watershed and national scale), but also gradually develops from describing the spatio-temporal evolution to the operation mechanism34,35,36,37. However, the existing studies still lack a more detailed exploration of correlation adaptation and focus more on simple characterization of the synergistic development of water, energy and food resources. Although existing research has begun to pay attention to the influence of external factors such as society, economy and nature on WEF nexus, the lack of establishing the correlation relationship between WEF nexus and social-economic-natural external environment has failed to comprehensively analyze the complex feedback mechanism, which has weakened the depth and breadth of the analysis of resource linkages38,39. Based on the logical framework of “unit-nexus-external environment”, the theoretical framework of WEF CS can better explain the complex adaptive relationship between various dimensions, and provide a new way to study the relationship between water resources, energy resources and food resources. In view of the single and linear of the existing studies, the WEF CS was analyzed from the perspectives of external adaptability and internal coordination, filling the gap in the comparative study of spatial suitability and internal coordination, and providing a reference path of “internal synergy-external adaptation” for realizing the sustainable development of water, energy and food in nine provinces of the YRB.

Based on the research results, the following suggestions are put forward for the sustainable development of the WEF CS in the YRB.

  1. 1.

    Make reasonable planning and improve resource utilization. The main factors hindering the spatial adaptation of the WEF CS are the regional differences in the YRB, among which the differences between the upper and middle reaches are the most obvious. The upstream water resources are abundant, energy development and food production are insufficient; the midstream are short of water resources and rich in energy resources, but affected by the constraints of water resources, agricultural development has aggravated soil erosion and non-point source pollution to a certain extent. Therefore, it is necessary to improve the efficiency of water resources utilization through scientific and technological innovation, and build a high-standard and high-efficiency energy system, agricultural production system and water resources allocation and management system. Under the constraints of national energy security and “dual carbon” goals in China, rationally optimize the industrial layout, promote the construction of low-consumption water, clean and low-carbon energy, and promote the green transformation and development of the energy industry. Through the establishment of cross-departmental and cross-regional comprehensive coordination mechanisms, exchanges and cooperation between competent departments of natural resources, energy and agriculture should be strengthened to promote the cross-regional flow of resources.

  2. 2.

    Planning the weak area of WEF CS in the YRB. Henan province needs to strengthen the cultivated land protection system, promote the construction of high-standard farmland and the protection of cultivated land quality, and improve the integrated development of the grain industry. The stable operation of the WEF CS in Shaanxi and Shandong needs to strictly implement the requirements of “determining the city by water, determining the land by water, determining the people by water, and determining the production by water”, optimize the allocation of water resources, and improve the allocation system of water resources.

Limitations and further research

There are some limitations in the study. Firstly, the relationship is intricate between the water, energy and food resources and the external environment in the WEF CS. The construction of the index system still needs to be further improved. Secondly, due to the lack of quantitative research on energy generation, flow and feedback in the complex system, the conduction mechanism of energy between different dimensions in the WEF CS had not been further explored. Thirdly, the assumption of the grey prediction model is that all variables are linear, which is obviously impossible to achieve in reality. Therefore, we will explore the coordinated development of WEF CS based on nonlinear relationship between variables in future studies.

Conclusions

Based on the logical framework of “unit-nexus-external environment”, a theoretical framework of “system unit-nexus-natural environment” was established to quantify the development level of the WEF CS. It analyzed the WEF nexus from three levels: unit, correlation and external environment, and discussed the spatial adaptation and coordinated development mechanism of the upper, middle and lower reaches of the YRB. The findings showed that the overall development level of WEF CS showed significant differences in stages, and the development status of the upstream was better than that of the downstream, and the downstream was better than that of the midstream. The overall Gini coefficient of WEF CS in the YRB was decreasing from 0.123 in 2004 to 0.084 in 2020. The discrepancy of the development level of complex system mainly came from inter-region. At the regional scale, Shaanxi and Henan are the weak regions of the WEF CS in the YRB, and the main related factors are water and food resources, respectively. at the dimensional scale, Shaanxi and Shandong are the weak regions of the WEF CS, and the main correlation factors are related to water resources. In addition, it is found that the natural environment dimension has an important influence on the coordinated development of the WEF CS. Therefore, the construction of WEF CS based on the logical framework of “unit-nexus-external environment” is of theoretical significance and practical demand.

Water, energy and food are the basic strategic resources for the development of human society, and there are close relations and mutual feed-back relations among them. A comprehensive study of WEF CS is helpful to reveal the internal relationship between various resources, so as to formulate more scientific resource management and allocation strategies to ensure resource security. The research shows that the theoretical framework of the WEF CS of “system unit-nexus-natural environment” is an effective evaluation system. Here, we hope to provide a useful template to illustrate the complex interrelationships between water, energy, and food. In the future, with the change of the research area and the improvement of the data, the evaluation system can be further improved.