Introduction

Along with the expansion of modern economy and the continuous development of global economy, the exploitation of resources is increasing, which leads to the huge problem of resource depletion1,2,3. It is noteworthy that a large number of uncontrolled exploitation of resources are not fully utilized in the process of use and are discarded when they fail to achieve maximum performance, which leads to a large number of solid waste disposal problems4,5. Currently, the main solid waste disposal methods are either stockpiling or landfilling, both of which require large amounts of land and therefore pose ecological hazard6,7 Along with the dense population development of large and medium-sized cities around the world, land resources are becoming increasingly scarce. Traditional solid waste disposal methods have encroached on all the resources needed for population development, and the traditional urban development model needs to be reshaped urgently. In this context, some developed countries and regions have proposed the concept of “circular economy” and “zero waste” for sustainable development since the 1990s, and have been practicing and exploring urban governance and resource recycling8,9,10.

For all types of pollution sources and pollutants generated in cities, one of the most significant is industrial solid waste11. Many of the cities that depended on heavy industrial production in the last century caused a large amount of industrial solid waste problems for cities due to the production of heavy industries such as steel, coal mining, and machinery12. Industrial solid waste is generated along with industrial production activities and causes pollution in and around cities for a longer period of time, so it has been an important part of urban pollution management13,14. By establishing “Zero waste cities” and exploring the ways of solid waste management at the city level from the point to the surface, it will have an impact on the original industrial structure that has been formed in the city for a long period of time. In particular, the fixed production patterns that have been formed by traditional industries will have a greater impact15 and create a greater impetus for industrial transformation, promoting the reform of traditional industries and the generation of new industries16,17. In particular, some heavy industrial cities that strongly rely on natural resources form an inseparable relationship with natural resources in the original urban economic development. The economy of their cities also relies mainly on natural resource production chains, and the industries of these cities are subject to greater impact of industrial transformation18,19,20,21. For these cities, the difficulty of building “Zero waste cities” is self-evident, and will certainly pose a great challenge to the adjustment of production patterns and ecological transformation of traditional industrial structures22,23. It is necessary to use scientific methods to analyze and combine various measures to guarantee the smooth transition of the economy and realize the ecological upgrading of traditional industries. And make it possible to form self-adaptation in a certain period of time to meet the sustainable goals of urban development.

Literature review

The concept of “zero waste city” originated from the concept of “zero waste” in the 1970s24. At present, there are some differences in the definition and scope of zero waste among advanced countries in the world, and there is no clear general conclusion on the concept of “zero waste city”. According to the definition of similar concepts in existing mainstream positions such as the European Union and Singapore, “zero waste” refers to the repeated use of the same materials until the optimal level of consumption is reached25. This urban industrial development model of production cycle can solve the bottleneck problems of resource consumption and resource depletion that have arisen in the development of many cities. It can also form a new type of industrial chain, thereby promoting the continuous optimisation of the circular economy and gradually expanding it to all aspects of urban construction26. Based on the needs of urban development, China has drawn on and learnt from similar international models of urban development and put forward the concept of building “zero waste cities” from the perspective of top-level design. In the course of its urban construction activities, it has been summing up its experience and updating its new urban management model. Innovative safeguard mechanisms and measures have been proposed to promote the construction of zero waste cities on a pilot basis.

The concept of “zero waste” was proposed by developed countries in the early stage, but now it has gradually reached international consensus and expanded to developing countries27, and many countries have explored the final form of “zero waste” and “sustainable” through urban construction practices. Many countries with “zero waste” and “sustainable” development strategies have been exploring the final form of “zero waste” through urban construction practices. zero waste cities in the international pilot practice material is also unique, for the realisation of zero waste globalization, zero-waste society development vision of the future to provide ideas and paths28.

Zero waste is the development direction of new sustainable cities, especially for some resource-based cities with deep traditional industrial foundation, carrying out “zero waste cities” construction is a necessary trend of urban transformation. In the past economic development, resource endowment provided the foundation for traditional industries, which played an important supporting role in the development of national economy for a long period of time29,31. Abundant natural resources (such as minerals and energy) provided raw materials and energy support for traditional industries (such as mining and metallurgy)32. In addition, resource-rich areas often formed industrial clusters of traditional industries, which further promoted the rapid economic development of urban agglomeration at that time33. However, with the gradual depletion of non-renewable resources, while resource exploitation and industrial activities are often accompanied by environmental pollution and ecological destruction, bringing new problems to modern cities, so the pressure of “waste free” construction is greater at this stage.At the same time, some relevant studies on resource-dependent cities also reflect the relationship between resource-rich areas and economic development level34,35,36,37. Therefore, before conducting research on the ecological transformation of traditional industries in the context of “Zero waste cities”, the economic relationship between the construction of “Zero waste cities” and “traditional industries” should be clarified first. The economic relationship between the construction of “Zero waste cities” and “traditional industries” should be clarified. The economic relationship between industrial construction and urban construction has been studied by many international scholars38,39. Zero waste cities are mainly examined in terms of economic level, waste emission level, governance level, etc., and the impact of traditional industrial production on the above three dimensions is very high. Is there a long-term stable relationship between the effects of industrial production on these three dimensions? In this study, a co-integration model is used to analyze the economic variables and waste and governance related indicators of the pilot cities of zero waste cities in China.

The future direction of urban development aims to make a breakthrough in urban resource circulation and metabolism. The key issue is to break through the current bottleneck of low comprehensive utilisation of resources, especially need to focus on the representative traditional industry to improve eco-efficiency and resource utilisation, embodied in the production chain to improve the efficiency of material flow40,41,42. It can be foreseen that the relevant technical issues for realising sustainable urban development in the future are based on this goal. On the one hand, exploring the application of new technologies to reduce energy consumption from a technical perspective. On the other hand, from the non-technical point of view to construct the relevant management mode, to achieve the policy guarantee, and finally to form a systematic integrated programme. Different cities strengthen regional and industrial linkages and synergies, and promote related scientific and technological innovation and policy implementation.

This study is based on 10 years of panel data from China’s first batch of “zero waste city” pilot cities, providing a new perspective on the intersection of “waste-free city” construction and traditional industrial transformation. Theoretically, the study constructs a framework of dynamic correlation between urban economy, emissions and governance, and verifies the long-term equilibrium relationship between the two through a cointegration model, revealing their non-linear feedback mechanism and making up for the lack of dynamic measurement support in existing studies. Methodologically, it innovatively integrates dynamic econometrics with a coupling coordination model, overcoming the limitations of single-index evaluations. The study assigns weights using the entropy method and employs a VAR model to quantitatively assess the synergy effects of pilot city transformations. By studying the practice cases of waste-free cities in developing countries, this study provides scientific basis for policy makers to optimise the path of industrial transformation and enhance the effectiveness of sustainable urban governance.

Methods and data

Dynamic measurement research

Cointegration model

In management science and economic problems, because of the “random wandering” nature of the variables selected43, mathematical analysis and data empirical evidence are usually analyzed using cointegration techniques to facilitate the determination of The cointegration technique is used to determine whether there is a stable relationship between the variables themselves and between the variables44,45. Avoiding the problem of negating the linear stability between variables due to their own instability, the cointegration model can be used to analyze whether there is a stable relationship between variables over time, thus facilitating the next step of research analysis. In the application of cointegration models, many scholars of economic management have used this method to conduct studies between different variables, for example, Atakhanova conducted a cointegration study on the relationship between economic growth and the growth of electricity demand in Kazakhstan46 Patterson M used the cointegration method to measure the effect of energy efficiency factors of energy efficiency using cointegration method47.

Since some of the observed economic variables are dynamic in practice, the corresponding mean and variance data may also fluctuate. However, there may be a stable linear relationship between different economic variables, and such a stable linear relationship between multiple factors is called cointegration relationship. The system of linear equations formed is collectively called the covariance equation48, and its specific expressions and meanings are as follows:

The combination of linear relations consisting of multidimensional vectors is denoted as \(X_{t} = \left( {X_{1t} ,X_{2t} , \ldots ,X_{kt} } \right)\), which should satisfy the following conditions assuming the existence of multi-order cointegration relations and that X1t, X2t…Xkt are all single integers of order d.:

  1. 1.

    If \(Xt \to I(d)\), then \(X_{1t} ,X_{2t} , \ldots ,X_{kt} \sim I(d)\). That is, each component is a d-order integer;

  2. 2.

    There is a vector \(\alpha (\alpha \ne 0)\) , and \(\alpha^{\prime } X_{t} \to I(d - b),0 < b \le d\).

It should be noted that cointegration is possible only when the time series of both variables are of the same order and are single integer series. And cointegration does not determine all non-stationary series. Before determining whether there is a cointegration relationship between two variables, a stationarity test is also required, which has the following procedure.

Unit root test

Unit root test is the process of determining whether a series is single integer or not. The difference operation is used to convert a smooth series into a non-smooth series. Since the order of a single integer series is equal to the number of unit roots of the series, a non-smooth series is formed by d times of difference and the smooth series is called \(Xt \to I(d)\).

According to the literature search and review, the unit root tests commonly used in economic research are ADF test, PP test, etc. In this paper, the ADF (Augment Dickey–Fuller Test) test is used for variable stability determination. The ADF stability test is based on three OLS regression equations:

$$X_{k} = \theta_{0} X_{k - 1} + \sum\limits_{i = 1}^{p} {\theta_{i} } X_{k - i} + \mu_{k}$$
(1)

where μk is the i.i.d sample. (independent and identically distributed) \(\mu_{k} \sim N(0,\sigma^{2} )\), k = 1,2,…,K

$$X_{k} = \theta_{0} X_{k - 1} + \sum\limits_{i = 1}^{p} {\theta_{i} } X_{k - i} + C + \mu_{k}$$
(2)

where C is a constant, \(k = 1,2, \ldots ,K\);

$$X_{k} = \theta_{0} X_{k - 1} + \sum\limits_{i = 1}^{p} {\theta_{i} } X_{k - i} + C + \delta_{t} + \mu_{k}$$
(3)

where \(\delta_{t}\) is the linear trend function,\(k = 1,2, \ldots ,K\).

Subtract the first order Xt-1 from both sides of the above formula, and the formula is as follows:

$$\Delta X_{k} = \alpha X_{k - 1} + \sum\limits_{i = 1}^{p} {\beta_{i} } \Delta X_{k - i} + \mu_{k}$$
(4)
$$\Delta X_{k} = \alpha X_{k - 1} + \sum\limits_{i = 1}^{p} {\beta_{i} } \Delta X_{k - i} + C + \mu_{k}$$
(5)
$$\Delta X_{k} = \alpha X_{k - 1} + \sum\limits_{i = 1}^{p} {\beta_{i} } \Delta X_{k - i} + C + \delta_{t} + \mu_{k}$$
(6)

The ADF test criterion, i.e., to determine whether α in Eqs. (4–6) is equal to 0, can be made with the following assumptions:

H0:α = 0, the alternative hypothesis is H1:α < 0. If H0 holds, i.e., Xt is a first-order single-integer sequence when α = 0. If H1 holds, it is judged to be a non-first-order single-integer sequence.

Cointegration test

After the series is determined to be a single integer series by unit root test, it is further determined whether there is cointegration relationship between the series. The common methods of cointegration testing include unit root test on the residuals of the regression equation, and another method is Johansen’s VAR model for regression testing. When there is a multivariate set of equations, Johansen is more advantageous for cointegration testing, so Johansen method is used in this study.

The Johansen method test idea first needs to establish the VAR model, and the calculation formula is as follows:

$$X_{k} = A_{1} X_{k - 1} + \cdots + A_{p} X_{k - p} + BY_{k} + \varepsilon_{k}$$
(7)

where Xk is a non-smooth variable and Yt is a deterministic multi-order nepheline variable, which also contains explicit terms such as constant and trend terms). is the perturbation vector, which is transformed by difference as follows:

$$\Delta X_{k} = \prod X_{k - 1} + \sum\limits_{i = 1}^{p - 1} {\Gamma_{i} \Delta X_{k - i} + BY_{t} } + \varepsilon_{t}$$
(8)

Among,

$$\prod = \sum\limits_{i = 1}^{p} {A_{i} - 1} ,\Gamma_{i} = - \sum\limits_{j = i + 1}^{p} {A_{j} }$$
(9)

The rank of the matrix is equal to the number of non-zero eigenroots, so let the eigenroots of the matrix \(\prod\) be \(\lambda_{1} ,\lambda_{2} \ldots \lambda_{k}\) and \(\lambda_{1} > \lambda_{2} > \cdots > \lambda_{k}\). For the eigenroot trace test, make the following assumptions.:

Original assumption Hr0: there are r cointegration relationships.

Alternative hypothesis Hr1: there are r + 1 cointegration relationships.

The test trace statistic is calculated as \(\eta_{r} = - n\sum\limits_{i = r + 1}^{k} {\ln (1 - \lambda_{i} )}\), where \(\eta_{r}\) is the characteristic root trace statistic, r is the number of cointegration relationships (number of through cointegration vectors), n is the sample size, and the judgment criterion is:

  1. 1.

    When \(\eta_{0}\) is less than the critical value, the original hypothesis H00 is accepted, no cointegrating vector exists and there is no cointegration relationship.

  2. 2.

    Reject the original hypothesis H10 when \(\eta_{0}\) s greater than the critical value and there is at least one cointegration relationship.

  3. 3.

    When \(\eta_{r}\) is less than the critical value, Hr0 is accepted and there are r cointegration relations.

The maximum eigenvalue test was then performed with the original hypothesis Hr0:\(\lambda_{r + 1} = 0\); the alternative hypothesis Hr1:\(\lambda_{r + 1} > 0\), and the maximum eigenvalue test statistic was calculated as \(\varepsilon_{r} = - n \cdot \ln (1 + \lambda_{r + 1} )\);

  1. (1)

    When \(\varepsilon_{r}\) is less than the critical value, the original hypothesis H00 is accepted and the judgment is that there is no cointegration relationship.

  2. (2)

    When \(\varepsilon_{r}\) is greater than the critical value, the original hypothesis H00 is rejected and there is at least one cointegration relationship.

  3. (3)

    When \(\varepsilon_{r}\) is smaller than the critical value, accepting the original hypothesis Hr0, with r cointegration relations.

Granger causality test

Significant correlations between variables can be found from the variable observations. However, whether it is economically significant needs to be judged by causality test, Granger causality test can be understood as whether variable A will cause changes in variable B. It can be explained from the present B can be explained by variable A, considering the time relationship, after adding whether the backward can make the degree of explanation. After calculating that indeed variable A and variable B have a significant relationship in the statistical correlation coefficient, it can be determined that variable B is caused by variable A.

The calculation process includes first calculating the mean square error of the S-period forecast of variable B, and the calculation formula is as follows:

$$MSE = \frac{1}{s}\sum\limits_{i = 1}^{s} {\left( {\hat{B}_{t + i} - B_{t + i} } \right)}^{2}$$
(10)

If \(MSE\left[ {\hat{E}\left( {B_{k + s} \left| {B_{k} ,B_{k + 1} } \right.} \right)} \right] = MSE\left[ {\hat{E}\left( {B_{k + s} \left| {B_{k} ,B_{k + 1} , \ldots ,A_{k} ,A_{k + 1} } \right.} \right)} \right]\), then it is considered that A cannot Granger cause B.

The following assumptions are made for a binary P-order VAR model:

H0: \(b_{11}^{(p)} = 0,q = 1,2, \ldots ,p\)

H1: There exists at least one q such that \(b_{11}^{(p)} \ne 0\).

If the above requirements meet the definition of Gaussian distribution, the test statistics are:

\(S_{1} = \frac{{\left( {RSS_{0} - RSS_{1} } \right)}}{{RSS_{1} /\left( {T - 2p - 1} \right)}}\sim F(p,T - 2p - 1)\), where \(RSS_{1} = \sum\limits_{t = 1}^{T} {\hat{\varepsilon }_{1t}^{2} }\), if S1 is greater than the critical value of F, rejects the original hypothesis that A can Granger cause B; conversely, accepts the original hypothesis that A cannot Granger cause B.

Each of the 11 pilot zero waste cities has its own characteristics in terms of economic base and industrial structure. Especially for the traditional heavy industry cities, when observing their economic data, it is found that the economic growth has been gradually showing its weakness in recent years. This means that traditional industries cannot be transformed in time and their pulling effect on urban economic development has been gradually slowing down, which may even bring a series of urban ecological problems. Therefore, the relationship between urban economic development and ecological environment should also be studied in depth, so as to explore the path of sustainable industrial development, which can contribute to the construction of new cities49.

In order to further observe the basic situation of “Zero waste cities” pilot cities in China, this study collects three major indicators of comprehensive economy, pollution indicators and governance indicators from 2010 to 2019 for 11 cities. Three specific indicators were set, including the comprehensive economy, including regional GDP, per capita regional GDP, and regional GDP growth rate; pollution indicators, including industrial waste water, industrial waste, and industrial solid waste emission indicators; governance indicators, including the harmless treatment rate of domestic waste, the comprehensive utilization rate of general industrial solid waste, and the centralized treatment rate of sewage, for a total of nine items, as shown in Table 1.

Table 1 The first batch of "zero waste city" pilot city dynamic measurement index system.
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In order to analyze the economic base and waste base of different “Zero waste cities” pilot cities in the transition, we first analyze the dynamic relationship between the economic level and waste level of the above zero waste cities from a macro perspective50.

In order to analyze the relationship between urban economic development and waste and governance in the pilot cities of zero waste cities in China, a Vector Autoregression Model (VAR) can be established to conduct dynamic econometric analysis. Firstly, the unit root test is used to determine whether the economic level indicators of the pilot cities and the emission and governance indicators are smooth series; then the co-integration test is used to analyze whether there is a stable relationship between the economic level indicators of the pilot cities and the emission and governance; Secondly, Granger causality analysis is used to determine the causal relationship between the two composite indices; finally, impulse response and variance decomposition are used to analyze the relationship between the economic level indicators of the pilot cities and the emission and governance. Finally, impulse response and variance decomposition were used to analyze the intensity of the impact between the pilot cities’ economic level indicators and the emission and governance. (Specific data shown in Appendix 1).

Data calculation

Unit root test

This study begins with an ADF unit root test, where H0 assumes the existence of a unit root, and if the significance test statistic obtained is less than three confidence levels (10%, 5%, 1%), it corresponds to having (90%, 95, 99%) certainty to reject the original hypothesis. The specific formula is as follows:

$$\Delta Y_{t} = \beta_{0} + \beta_{1} t + \delta Y_{t - 1} + \xi_{1} \Delta Y_{t - 1} + \cdots + \xi_{p - 1} \Delta Y_{t - p + 1} + u_{t}$$
(11)

where Yt is the time series to be tested.

A unit root test was conducted to determine whether the economic development level and the emission and treatment situation of the pilot cities of zero waste cities were stationary series. The results were calculated using Eviews software, following the SIC criterion of automatic order selection, as shown in Table 2:

Table 2 ADF test results of urban economic indicators and urban waste control indicators.
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The results of the above unit root tests show that among the 11 pilot cities of zero waste cities, the series of urban waste management indicators is stable, while the series of urban economic indicators and urban waste management indicators are not stable at 1%, 5%, and 10% significance levels. The series of urban economic indicators and urban waste indicators are not stable at 1%, 5% and 10% significance levels. Therefore, the first-order differential series smoothness test was conducted. In the first-order difference series test, the urban economic level series and the urban waste and urban pollution control series are all smooth, which is a first-order single integer series and satisfies the prerequisite of cointegration test.

Johansen cointegration test

The Johansen cointegration test was used to test whether there is a long-term stable relationship between the level of urban economy and the level of urban waste emission and urban pollution control. Calculations were performed by Eviews software, and the test results are shown in Tables 3, 4 and 5:

Table 3 Johansen cointegration test results of urban economic level and urban waste discharge level.
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Table 4 Johansen cointegration test results of urban economic level and urban governance level.
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Table 5 Johansen cointegration test results of urban waste discharge level and urban governance level.
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  1. (1)

    Urban Economic Level and Urban Waste Discharge Level (urban,pollute)

According to the calculation results in Table 3, there are 2 cointegration relationships between urban economic level and urban waste discharge at 5% significance level, indicating that there is a long-term dynamic equilibrium relationship between urban economic level and urban waste discharge.

  1. (2)

    Urban economic level and urban governance level(urban,control).

According to the calculation results in Table 4, there is no co-integration relationship between the level of urban economy and the level of urban governance at the 5% significance level, indicating that there is no long-term dynamic equilibrium relationship between the level of urban economy and the level of urban governance, i.e., there is no necessary correlation and mutual influence between the high level of urban economy and the level of urban governance.

  1. (3)

    Urban Waste Discharge Level and Urban Governance Level (pollute,control)

According to the calculation results in Table 5, there is at least 1 cointegration relationship between urban waste level and urban governance at 5% significance level, indicating that there is a long-term dynamic equilibrium relationship between urban waste level and urban governance level.

Granger causality test

Granger Causality Test is mainly used to analyze the causal relationship between variables in time series data. Its central role is to determine whether a variable has predictive power for another variable, that is, whether the historical value of one variable helps to predict the future value of another variable. If the past value of X significantly improves the prediction of Y, then X Granger is said to cause Y.

Johansen cointegration test argues that there is a long-run dynamic equilibrium relationship between the level of urban waste discharge and the level of urban economy and urban governance. The Granger Causality Test44 can be performed on the variables separately when it is clear that there is an equilibrium relationship between the factors. The results of this study using Eviews software are calculated in Table 6:

Table 6 Granger causality test results.
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The Granger causality test results between the above factors are shown in Fig. 1:

Fig. 1
figure 1

Result of Granger causality test between Control and pollute: (a) Urban emission level (Pollute) and Granger causality test for the level of urban governance (Control); (b) Urban emission level (Pollute) and Urban economic level (Urban) Granger causality test.

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Through the above calculation, it can be seen that there is no Granger causality among the three dimensions of the Pollute, Control and Urban, which further explains the independence of the three dimensions, which means that the historical value of a single indicator cannot be used to predict the future value of another indicator, providing support for the subsequent coupling coordination research.

Impulse response analysis

Impulse Response Analysis is used to evaluate the dynamic effects of an external shock on one variable in a time series model. Its core role is to reveal the dynamic interaction between variables in the system and help understand the transmission mechanism of shock.

Impulse response analysis of urban innovation level and eco-efficiency over 10 periods was performed by Eviews software, and the images shown in Fig. 5 and Fig. 6 were obtained. The solid line indicates the impulse response coefficient, and the dashed line indicates the positive and negative two times standard deviation deviation bands, which are analyzed as Fig. 2:

Fig. 2
figure 2

Impulse response of urban economic level and urban waste discharge level.

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  1. (1)

    In Fig. 2, it can be seen that the urban economic level (Urban) and the urban emission level (Pollute) are relatively smooth and small shocks in the first 5 periods. From the fifth period onward, the level of urban waste has a negative impact on the level of urban economy, which means that the level of urban waste decreases while the level of urban economy increases; from the sixth period onward to the tenth period, there is a fluctuating shock, which means that the level of urban economy and the level of urban waste fluctuate repeatedly before the ninth period, with positive or negative shocks alternating. After the ninth period, there is a strong negative shock, which means that the increase of urban economic level will lead to the decrease of urban waste level. It indicates that when the urbanization process is passed for a period of time, with the continuous improvement of urban economic level, the urban waste management of all kinds of waste has certain effect and can reduce the emission of urban polluting waste.

  2. (2)

    As shown in Fig. 3, the level of urban exhaustion (Pollute) and the level of urban governance (Control) fluctuate in the first period, with urban governance first having a positive effect on urban exhaustion until the second period. From the second period to the third period, a negative effect starts to appear, specifically referring to the failure of urban governance to show its effectiveness in the initial period. And after the second period, as the level of urban governance increases, then the level of urban emission decreases and urban governance has a positive effect; then it enters a stable state after the third period, indicating that urban governance and urban emission maintain a balanced and stable state.

    Fig. 3
    figure 3

    Impulse response of urban waste discharge level and urban governance level.

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  3. (3)

    In contrast, the pulse effect of urban waste on urban governance is found to be negative in the first three periods, implying that more urban waste will make urban governance lower. After some fluctuations from the third to the seventh period, the equilibrium state is stable from the seventh period onward.

Variance decomposition

The function of variable disposition is to further reflect the contribution rate of self impact and impact of other variables on the basis of impulse response analysis, so as to understand the relative importance of impact of each variable to endogenous variables of the model. The result of variance disposition is shown in Table 7:

Table 7 Results of variance decomposition.
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From the data of variance decomposition, we can see that for the urban economic level, it is mainly influenced by its own factors, and it is stable in the probability range above 99% from the second period to the tenth period, and the impact of urban governance level and urban waste level on the urban economic level is not significant; the urban waste level is also mainly influenced by its own factors, and it is stable in the probability range above 99% from the first period to the tenth period. The other two factors have little impact on its impact; as for the level of urban governance, it is mainly influenced by itself, with a stable probability of more than 75%, followed by the impact of urban waste, with an average probability of more than 21%, and finally, it is also related to the level of urban economy, with a probability level of about 3%.

In summary, the level of urban economy as well as the level of urban waste discharge are more independent factors with the ability to explain themselves mainly, while the level of urban governance has a greater influence with urban waste discharge in addition to its own influence with the level of urban economy.

Research on coupling coordination

Coupling denotes the relationship of interdependence and interaction between different systems, where a change in one element can cause changes in other elements51. In the real world, there are complex connections between various urban construction activities, socioeconomic development and natural environment elements, which constituting a complex system52. Coupling degree quantitatively represents the coupling effect, indicating the extent of interaction between two or more systems, with its value reflecting the degree of correlation among the systems. Coupling degree primarily focuses on quantifying the interrelation between systems, lacking in depicting the merits and demerits of system development trends53.

The degree of coupling coordination on the basis of the degree of coupling, emphasizing the elements of the system through collaboration, synergy and regulation to achieve a state of equilibrium between the system, focusing on the description of the coordination of the system54. If the rank of coupling coordination degree is high, it represents a higher degree of coordinated development between systems. Coupled coordination seeks balanced and coordinated solutions in complex systems by applying it to environmental protection, economic development, and social management55.

The entropy weight method is used to determine the weight of the indicators, according to the principle of information entropy, the weight depends on the amount of information of the indicators, reflecting the intrinsic connection and variability of the indicators. The smaller the information entropy is, the greater its influence on the results and the higher the weight. Conversely the greater the information entropy is, the smaller its influence on the results and the lower the weight.

Compared with other methods, the entropy method is relatively objective in determining weights. It can avoid the influence of human factors and improve the objectivity and accuracy of the calculation results.

The weight of the indicator Zij is calculated from Eq. 12:

$$Z_{ij} = \frac{{Y_{ij} }}{{\sum\nolimits_{j}^{i} {Y_{ij} } }}$$
(12)

The entropy Ei is calculated as follows Eq. 13:

$$E_{i} = \frac{ - 1}{{\ln (i \times t) \times \sum\nolimits_{j}^{i} {p_{ij} \ln (p_{ij} )} }}$$
(13)

The coefficient of variation \(\xi_{i}\) is as follows Eq. 14:

$$\xi_{i} = 1 - E_{i}$$
(14)

The indicator weight wi is calculated from Eq. 15:

$$\omega_{i} = \frac{{\xi_{i} }}{{\sum\nolimits_{1}^{n} {\xi_{i} } }}$$
(15)

In the above formulas, Ei ∈ [0,1], wi ∈ [0,1].

This paper refers to Qian56 and Shujia57 for the derivation and calculation of the ternary coupling model, the coupling level is shown in Formula 16:

$$C = \left[ {\frac{{\prod\limits_{k = 1}^{k} {u_{k} } }}{{\frac{1}{k}\sum\limits_{k = 1}^{k} {u_{k} } }}} \right]^{\frac{1}{k}}$$
(16)

Evaluation of coupling degree

The weight values of each indicator of the three subsystems of integrated economy, urban waste discharge and pollution control in the low-carbon transformation of traditional industries in the first batch of pilot cities without waste are shown in Table 8:

Table 8 Coupled coordination evaluation indicators and weights for zero waste cities.
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The evaluation value of the coupling degree of low-carbon transformation of traditional industries in zero waste pilot cities is further calculated according to Eq. 15, as shown in Table 9. During the period 2012–2021, the highest level of coupling evaluation in the low-carbon transformation of traditional industries in the first batch of zero waste city pilots is Chongqing, and the lowest is Sanya. The coupling level with the largest improvement is Weihai, with a mean growth rate of 11.13%. While the lowest coupling growth rate is Panjin, with a mean growth rate of − 0.29%.

Table 9 Evaluation of the coupling degree of low-carbon transformation of traditional industries in zero waste cities.
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Figure 4 shows that the coupling in the low-carbon transition of traditional industries in the first batch of pilot cities without waste shows small fluctuations but is generally balanced and maintains a slight upward trend during the period 2012–2021.

Fig. 4
figure 4

Evaluation of coupling degree of low-carbon transformation of traditional industries in the first batch of zero waste cities pilot cities.

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Figure 5 indicates that the mean value of coupling in the low-carbon transition of traditional industries in the first pilot cities of zero waste cities is relatively stable over the period 2012–2021. Among them, only Chongqing has a value higher than 0.2, while all other cities fluctuate between 0.1 and 0.2.

Fig. 5
figure 5

Mean value of coupling for low-carbon transformation of traditional industries of zero waste cities pilot cities.

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Evaluation of the degree of coupling coordination

The coupling coordination model comprehensively considers the interactions among different factors and subsystems. It is applicable for studying the coordinated coupling states among various subsystems involved in the traditional industrial low-carbon transformation of the first batch of zero waste city pilot projects, which include urban comprehensive economy, urban wastewater discharge level, and urban pollution control. Through the coupling coordination model, it becomes possible to quantify more clearly the degree of balanced coordination among multiple subsystems. The simplified general form of the coupling coordination model is as follows formula 17:

$$R = f(X,Y,Z)$$
(17)

where R represents the comprehensive evaluation index of coupling coordination. The function f represents the relationship between the three systems and the state of coupling coordination, X represents the level of comprehensive economic evaluation of the city, and Y is the level of evaluation of urban waste discharge, and Z represents the level of evaluation of urban pollution control. Coupling coordination refers to the formation of a good mechanism of interaction and mutual constraints between the systems. In order to more accurately measure the coupling coordination status in the low-carbon transformation of traditional industries in the first pilot batch of zero waste cities, the following coupling coordination formula is constructed based on the coupling model of physics:

  1. (1)

    Systems development model

The systems development model as shown in formula 18:

$$T = \alpha \times Q + \beta \times E + \delta \times K$$
(18)

where T is the comprehensive evaluation level, Q is the comprehensive economic evaluation level of the city, E is the evaluation level of urban wastewater discharge, and K denotes the evaluation level of urban pollution control. \(\alpha ,\beta ,\delta\) are the weight coefficients, which denote the proportion of the three sub-systems contributing to the comprehensive evaluation level, and take the value of 1/3.

  1. (2)

    System coordination model

The systems coordination model as shown in formula 19:

$$C = \sqrt {\frac{9Q \times E \times K}{{\left( {Q + E + K} \right)^{2} }}}$$
(19)

In order to compare the stability of the system coordination model, this paper referred to Shujia Wang’s revision method of the model2, and used formula 20 for comparison reference:

$$C = \sqrt {\left[ {1 - \frac{{\sqrt {(K - Q)^{2} } + \sqrt {(E - Q)^{2} } + \sqrt {\left( {K - E} \right)^{2} } }}{3}} \right] \times \sqrt {\frac{Q}{K} \times \frac{E}{K}} }$$
(20)
  1. (3)

    System coupling model

The systems coupling model as shown in formula 21:

$$D = \sqrt {C \times T}$$
(21)

The system development model expresses the relationship between the three subsystems. The system coordination model describes the degree of coordination of the system, which is used to assess the coupling and coordination status of the construction industry development and the urban ecological environment, and the closer the C value is to 1, the higher the degree of coupling between the systems. The system coupling model obtains the coupling degree (D) of the system by multiplying the coordination degree (C) of the system by the comprehensive evaluation level (T).

The evaluation value of the coupled coordination degree of low-carbon transformation of traditional industries in the first batch of zero waste cities pilot cities which combining Formulas 18, 19 and 21 is shown in Table 10.

Table 10 Evaluation of the coupled coordination degree of low-carbon transformation of traditional industries of zero waste cities pilot cities.
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Table 10 shows that all the cities show a balanced and stable trend with a small increase during the 10-year period. The line graph of the evaluation of the coupling degree of coordination between the first batch of zero waste cities and the low-carbon transformation of traditional industries is shown in Fig. 6, which shows that the development trend of the coupling degree of each city is relatively stable during the period of 2012–2021. In addition, Baotou, Weihai and Sanya have certain fluctuations in individual years, and the coupling coordination degree of other cities fluctuates slightly within 0.250–0.350.

Fig. 6
figure 6

Evaluation of the coupled coordination degree of low-carbon transformation of traditional industries of zero waste cities pilot cities.

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By combining Formulas 18, 20 and 21, the evaluation value of coupling coordination degree of traditional industrial low-carbon transformation in the first batch of waste free cities pilot cities is calculated, as shown in Table 11.

Table 11 Evaluation of the coupled coordination degree of low-carbon transformation of traditional industries of zero waste cities pilot cities (Modified).
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Through the calculation of the modified model, it is found that the distribution of the coupling coordination degree of the low-carbon transformation of traditional industries in the first batch of zero waste cities is basically consistent with that before the modification, fluctuating within the range of 0–0.4, and the overall situation is relatively balanced, with the peak value of Chongqing and the valley value of Sanya, which further explains the stability of the coordination model in this study.

Figure 7 illustrates the mean value of the evaluation of the first batch of zero waste cities and the low-carbon transition of traditional industries. Chongqing has the highest mean value of coupled coordination evaluation during the 10-year period, and Sanya has the lowest, which is overall more stable and belongs to the budding stage.

Fig. 7
figure 7

Mean value of coupled coordination evaluation of low-carbon transformation of traditional industries of zero waste cities pilot cities.

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Discussion and results

This paper focuses on the social and economic connections between zero waste cities pilot cities construction and the transformation of traditional industrial ecology. Dynamic econometric research indicates dynamic connections among the economic level of zero waste cities, urban waste discharge levels, and urban pollutant treatment levels. Traditional industries exert significant influence on urban waste discharge and urban pollutant treatment, necessitating an understanding of the dialectical relationship between zero waste city construction and the transformation of traditional industrial ecology. Simultaneously, coupling coordination analysis is conducted, incorporating relevant data from the first batch of zero waste city pilot projects from 2012 to 2021.

Analysis of the overall trend of coupling degree

The coupling degree of the first batch of zero waste cities pilot cities showed different trends and gradient characteristics during the past decade, as shown in Fig. 8. In terms of the overall coupling change of each city, Baotou, Shenzhen, Weihai, Shaoxing and Xuchang all show a gradual growth trend, which indicates that in the process of transformation of the traditional industry in Baotou, the connection between the various industries has been gradually strengthened, and the coordinated development has been gradually revealed. Among them, Shenzhen, as a representative economic powerhouse, has seen its coupling degree grow from 0.17 to 0.22, indicating that in its economic restructuring, the linkages among industries have also been gradually strengthened, resulting in a closer pattern of synergistic industrial development. In contrast, the fluctuation of the coupling degree of cities such as Panjin and Weihai is relatively smooth, but the overall trend is still characterized by a gradual increase, indicating that these cities are also strengthening the synergistic development among industries in the transformation of traditional industries.

Fig. 8
figure 8

Trends in the evolution of coupling degree of zero waste cities pilot cities.

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In addition, there are fluctuations in the change in coupling between the cities of Chongqing, Sanya and Xining. Chongqing has fluctuated more over the past decade, but the overall trend is still characterized by a slight increase, which is related to the uncertainty of economic restructuring in the Chongqing regional district. However, its inter industry synergy is still gradually strengthening. Sanya and Xining show a fluctuating and decreasing state of development, indicating that the industrial restructuring in these regions is slightly slower, and there are problems such as unstable economic development.

Analysis of coupling degree gradient

Based on the changes in the coupling degree of each city, they can be categorized into three gradients, namely, the high coupling gradient, the medium coupling gradient and the low coupling gradient. Cities in the high coupling gradient include Shenzhen, Chongqing and Shaoxing, whose coupling degree is continuously maintained at a high level and shows a trend of steady growth. These cities have a relatively complete industrial structure, with close links between industries, forming a good pattern of industrial synergistic development.

Cities with medium coupling degree gradient are Baotou, Xuzhou, Weihai, Xuchang and Tongling, which have already achieved certain development results in the transformation of traditional industries. However, there is still a need to strengthen the links between industries and promote synergistic development of industries, which can be achieved by strengthening cross-border cooperation and promoting industrial integration to further enhance the coupling gradient between industries and realize the optimization and upgrading of industrial structure.

Xining, Panjin and Sanya belong to the low-coupling gradient and show a downward trend, indicating that they face greater challenges in the transformation of traditional industries. Due to the industrial structure is relatively lagging behind and the links between industries are weak, it is necessary to increase the efforts of industrial restructuring, promote the integration and development of different industries, and enhance the synergies between industries in order to realize the sustained and healthy development of the economy.

Analysis of coupling coordination degree

The results of the coupling coordination degree reflect the level of coordinated development between the subsystems of cities in the process of traditional industrial transformation (Fig. 9). From the overall trend, the coupling coordination degree of each city shows a yearly increase, which indicates that the coordination among the three subsystems, namely, the comprehensive economy of the city, the level of urban waste elimination, and the urban pollution control, has gradually increased during the past decade. This is consistent with the policy orientation of traditional industrial transformation in the context of zero waste cities pilot cities, where cities are paying more attention to environmental protection and the sustainability of resource utilization along with economic development, thus promoting the synergistic development among the subsystems.

Fig. 9
figure 9

Trends in the evolution of the degree of coupled coordination of zero waste cities pilot cities.

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There are differences in the coupling coordination degree of each city in different years. The coupling coordination degree of Shenzhen gradually increases from 0.289 in 2012 to 0.331 in 2021, indicating that Shenzhen has a high degree of coordination in the three aspects of comprehensive urban economy, emission level and pollution control. The coupling coordination degree of Tongling, Sanya and other cities is relatively low and fluctuates greatly, which may be related to its economic development level, environmental governance capacity and other factors, and it is necessary to further strengthen the relevant policies and measures to promote the synergistic development of the subsystems.

In summary, there still exist contradictions between the development of traditional industries and the ecological environment under the zero waste city construction. Firstly, the industrial structure is less optimized compared to developed countries and developed coastal provinces and cities in China. Secondly, during the transition process, there is a relatively insufficient intensity of research and development investment and stronger constraints from resource and environmental factors. Additionally, there is a lack of incentive policies supporting large-scale, high-quality investment capacity and effective release of value-added and value creation capacity. Lastly, there are issues such as inadequate implementation of ecological environmental protection responsibilities in a few sectors.

The role of traditional industrial upgrading on the construction of zero waste cities

Through the dynamic measurement study of economic level and urban waste discharge level and urban pollutant treatment level, this study found that urban waste discharge level is one of the important mechanisms affecting urban economic level, and the improvement of urban economic level also drives the treatment level of urban pollutants, especially for resource-dependent cities. Emission reduction and treatment of pollutants are important indicators affecting the effectiveness of the construction of “zero waste cities”, which is consistent with the conclusions of relevant studies on industrial structure adjustment in innovative pilot cities58,59,60. Therefore, this study further confirms that at the technical and industrial levels, the active industrial professional upgrading of enterprises can promote the green transformation of traditional industries, thus further promoting the sustainable development of innovative cities (including zero waste cities). But it should also be noted that the phenomenon of “resource curse” is more common in resource-based cities than in non-resource-based cities. Therefore, according to the resource-dependent economic development mode, the transformation of traditional industries in resource-based cities faces more difficulties and challenges.

Conclusion

Based on the background of building zero waste cities in China, this paper selects 11 cities in the first batch of zero waste city pilots to carry out a study on the dynamic measurement and coupling coordination degree of the evolution and development of zero waste cities in the low-carbon transformation of traditional industries. The study finds that there is a long-term equilibrium relationship between the level of urban pollution control, the level of comprehensive economy and the level of urban waste discharge, and there is a correlation between the three subsystems. From the time dimension of 2012–2021, the evolution and development of these pilot cities share commonalities as well as imbalances based on the differences in their industrial structures. Specifically, the degree of coupling coordination fluctuates within a certain range, but generally shows a trend toward coordinated development.

Considering that the pilot work of zero waste cities in China has not been carried out for a long time, the city objects selected for this study are the first batch of pilot cities, which cannot fully reflect the current situation of all the current pilot cities of zero waste cities in China. In addition, the time span from the pre-pilot establishment to the post-pilot implementation stage, the endogeneity of data evolution is not considered in this study for the time being.

Therefore, future research can be carried out by combining more sample data in the pilot cities of zero waste cities in China at this stage. The establishment of more multi-dimensional evaluation indicators to observe the impact of the low-carbon transformation of traditional industries on the construction of pilot cities without waste, and to reflect more comprehensively the development of China’s industrial eco-transformation process and urban governance.

In the new development stage, comprehensively advancing towards an ecological civilization requires deepening ecological industrialization and industrial eco-transformation, promoting a shift in industrial development mode, driving changes in motivation, and pursuing green growth. Industrial eco-transformation refers to following the organic circulation mechanisms of natural ecology, taking the carrying capacity of natural systems as the criterion, and coordinating and optimizing industrial systems, natural systems, and social systems within a region. It involves innovatively transforming traditional industrial structures with information technology, continuously promoting the orderly elimination of traditional industries, conditional transformation, and integration with emerging industries. This process is essential for building a high-quality industrial system, transforming economic growth patterns, and embarking on a new path of industrialization.