A Three-Dimensional Evaluation Method for the Metabolic Interaction System of Industrial CO₂ and Water Pollution

Abstract

The inherent complexity of modern supply chains obscures significant hidden CO₂ and Water Pollution Equivalent (WPE) emissions, presenting mounting challenges for integrated environmental governance. While prior research has largely treated carbon and water pollution metabolic systems in isolation, this study addresses the critical gap in understanding their bidirectional interactions under socioeconomic dynamics. We develop a novel Three-Dimensional Evaluation Method for the Metabolic Interaction System of Industrial CO₂ and Water Pollution (TDE-ISCW). This framework integrates Environmental Input–Output Analysis and Ecological Network Analysis to: (1) identify key industrial sectors and utility relationships within individual CO₂ and WPE systems; (2) quantify the mutual disturbance responses between the CO₂ and WPE metabolic systems through changes in sectoral emissions/output, inter-sectoral relationships, and sector–system linkages; and (3) propose optimized industrial restructuring strategies for synergistic pollution and carbon reduction. Applied to the highly industrialized Yangtze River Economic Belt, key findings reveal: (i) substantial upstream dependency, exemplified by Advanced Equipment Manufacturing’s 95.7% indirect CO₂ emissions; (ii) distinct key sectors for CO₂ (e.g., MOO, FTO, MNM) and WPE (e.g., MPM, OTH, FTO) reduction based on competitive relationships; and (iii) complex trade-offs, where emission reductions in one system (e.g., CO₂ via FTO restructuring) can trigger heterogeneous responses in the other (e.g., altered WPE influence or downstream CO₂/economic shifts). The TDE-ISCW framework provides actionable insights for designing coordinated, adaptive emission reduction policies that account for cascading cross-system effects, ultimately supporting regional industrial upgrading and resource efficiency goals. Future research should incorporate temporal dynamics and full industrial–metabolic cycles.

1. Introduction

The structural complexity of modern economic systems amplifies the hidden CO₂ and Water Pollution Equivalent (WPE) emissions embedded within interlinked supply chain networks [1,2,3]. For example, industrial manufacturing—especially in the metallurgical and chemical sectors—relies heavily on fossil fuel consumption, resulting in significant CO₂ emissions and water pollution [4,5,6]. The interdependence between carbon and water pollution emissions, combined with the complexity of supply chains, presents mounting challenges for environmental governance [7,8]. In the context of trade, the interconnectedness and mutual interactions among industrial sectors are critical to achieving effective CO₂ and water pollution control. Through supply chain interdependencies, industrial sectors influence one another’s environmental responses [9,10]. For instance, excessive emissions in one sector can compel other sectors to implement more stringent mitigation strategies, generating system-wide environmental ripple effects [11].

Prior research has predominantly treated carbon and water pollution metabolic systems as separate domains, emphasizing enhanced pollutant accounting accuracy, analysis of driving forces, and identification of critical nodes within their respective networks [12,13,14,15,16,17]. In trade-related contexts, a growing body of research has examined transboundary flows of embodied pollutants across both systems, with the goal of achieving more equitable environmental responsibility allocation and attribution [18,19]. For example, Gao et al. [20] utilize ecological network analysis to assess urban water metabolism with a focus on water pollutant dynamics, examining six sub-basins in Fuzhou, China. Key findings include improved pollutant metabolism efficiency, identification of critical sub-basins for pollutant control, and the proposal of five ENA indicators for evaluating water quality and pollutant management in urban environments. Liddle [21] uses a consumption-based carbon emissions database to assess the impact of trade on national emissions, comparing it with territory-based emissions data. The findings highlight that most countries are net importers of carbon emissions, with consumption-based emissions typically higher than territory-based emissions. One research stream focuses on quantitatively decomposing the driving mechanisms to clarify the contribution of individual factors to system operation [22,23]. For example, Chen and Chen [24] develop a system-based framework to model urban carbon metabolism, integrating metabolic flow inventory, input–output analysis, and network analysis, using Beijing as a case study. The findings reveal that while direct carbon emissions have continued to rise, the consumption-based carbon footprint may have peaked around 2010, with efficiency gains and increasing consumption playing key roles in shaping the city’s carbon trajectory. Sun et al. [25] analyze the transfer and driving factors of industrial embodied wastewater in interprovincial trade in China, using the multiregional input–output model and structural decomposition analysis. The study finds that the transfer of industrial embodied wastewater increased significantly from 2012 to 2015, with net outflows from eastern provinces and inflows to central and western regions. Additionally, another stream centers on the identification of critical nodes, aiming to locate strategic intervention points for targeted pollution and carbon mitigation [26,27,28]. A framework is developed to analyze regional water metabolism from the perspective of quantity–quality collaborative control, utilizing the Grey Model–Biproportional Scaling Method, Input–Output Analysis, and Ecological Network Analysis. Applied to Zhejiang Province, China, the results identify key industrial sectors—agriculture, manufacturing, gas, and others—as crucial for improving both water conservation and environmental quality [29]. Input–output and ecological network analyses are applied to examine urban metabolism in four cities—Vienna, Malmö, Beijing, and Shanghai—comparing both methods to analyze carbon emissions at the city scale. The results identify transportation, manufacturing, and electricity production as the key sectors driving both direct and indirect carbon emissions, with final demand for domestic exports being the highest contributor in each city, highlighting their role as carbon producers in the broader national economy [30].

Prior research has predominantly examined the influence of socioeconomic activities on either industrial CO₂ or water pollution emissions in isolation, while largely neglecting their combined and interrelated impacts on both systems [31,32]. Moreover, there is a notable gap in the literature concerning the bidirectional interactions between industrial CO₂ and water pollution systems under the influence of socioeconomic drivers. For instance, restructuring the trade network of one emission system inevitably affects the other, potentially resulting in unintended and adverse consequences—either directly or indirectly. To address this gap, there is an urgent need to investigate the bidirectional disturbance mechanisms linking CO₂ and water pollution emission systems under socioeconomic dynamics. Systematic evaluation and quantification of the mutual responses between these two systems are essential for informing more effective and integrated emission reduction strategies.

Accordingly, this study develops a Three-Dimensional Evaluation Method for the Metabolic Interaction System of Industrial CO₂ and Water Pollution (TDE-ISCW), with the goal of investigating the bidirectional disturbance mechanisms between CO₂ and water pollution metabolic systems in industrial sectors. Using the Yangtze River Economic Belt (YREB), a region characterized by intensive CO₂ and water pollution emissions, as the empirical case, the objectives of this method are to: (a) identify utility relationships among key industrial sectors within the CO₂ and water pollution metabolic systems; (b) quantify the mutual disturbance responses between CO₂ and water pollution metabolic systems; (c) optimize industrial structures to devise coordinated emission reduction strategies for CO₂ and water pollution, thereby supporting regional objectives of pollution and carbon mitigation while offering actionable insights for industrial upgrading and enhanced resource efficiency.

2. Development of TDE-ISCW

The Three-Dimensional Evaluation Method for the Metabolic Interaction System of Industrial CO₂ and Water Pollution (TDE-ISCW) is designed to clarify how CO₂ and water pollution metabolic systems influence each other within industrial sectors (see Figure 1). This method provides several advantages for reducing pollution and carbon emissions in industrial metabolic systems: (i) It identifies key sectors for emission reduction in individual CO₂ or Water Pollution Equivalent (WPE) emission systems based on the utility relationships among industrial sectors. (ii) It evaluates how one system (CO₂ or WPE) responds to changes in the other by considering shifts in emissions, economic output, inter-sectoral relationships, and connections between sectors and the overall system. This integrated approach helps quantify their mutual interactions. The method involves two steps (see Figure 1). First, it applies environmental input–output analysis and ecological network analysis to identify key industrial sectors that need structural adjustment in the CO₂/WPE systems. Second, emission reduction plans are designed for the key sectors identified. The bidirectional responses of the CO₂ and WPE systems are then assessed using three indicators: (i) changes in sectoral emissions and output, (ii) changes in inter-sectoral relationships, and (iii) changes in sector–system linkages. These assessments inform targeted strategies for pollution and carbon reduction.

Input–Output Analysis (IOA) is a robust method for quantifying the input–output relationships between economic sectors [33,34,35]. In this study, IOA is used to track changes in monetary flows across sectors over time [36,37]. The total output of sector i is the sum of intermediate consumption and final demand. Columns represent primary and intermediate inputs into production, whereas rows indicate intermediate outputs and final demand. To capture complex inter-sectoral linkages, the concept of environmental intensity is introduced, allowing the monetary input–output model to be transformed into an urban emissions network [38]. Equations (1)–(6) are sourced from the environmental input–output model [39].

$$x_i={\displaystyle \sum _{j=1}^n{H}_{ij}+f_i}$$

(1)

$${\mathbf{DE}}_{(1\times 13)}^{C{O}_2,WPE}+{\mathsf{\epsilon }}_{(1\times 13)}^{C{O}_2,WPE}{\mathbf{H}}_{(13\times 13)}={\mathsf{\epsilon }}_{(1\times 13)}^{C{O}_2,WPE} diag{\mathbf{X}}_{(13\times 13)}$$

(2)

$$diag {\mathsf{\epsilon }}_{(1\times 13)}^{C{O}_2,WPE}=diag D{\mathbf{E}}_{(1\times 13)}^{C{O}_2,WPE}· {[ diag\mathbf{X}-\mathbf{H}]}^{-1}$$

(3)

$$\mathbf{E}{\mathbf{F}}_{(13\times 13)}^{C{O}_2,WPE}=diag{\mathsf{\epsilon }}_{(1\times 13)}^{C{O}_2,WPE} ·\mathbf{H}$$

(4)

$$I{E}_j^{C{O}_2,WPE}={\displaystyle \sum _{i=1}^{13}E{F}_{ij}^{C{O}_2,WPE}}$$

(5)

$$T{E}_i^{C{O}_2,WPE}={\displaystyle \sum _{j=1}^{13}E{F}_{ij}^{C{O}_2,WPE}+D{E}_i^{C{O}_2,WPE}}$$

(6)

Let xᵢ be the total output of sector i, Hᵢⱼ the amount of input from sector i used by sector j, and fᵢ the final demand for the output of sector i. ${\mathbf{DE}}_{(1\times 13)}^{C{O}_2,WPE}$ is the emission matrix for CO₂ or water pollution, ${\mathsf{\epsilon }}_{(1\times 13)}^{C{O}_2,WPE}$ denotes the matrix of embodied CO₂ or water pollution intensities, and $\mathbf{E}{\mathbf{F}}_{(13\times 13)}^{C{O}_2,WPE}$ represents the matrix of indirect emissions between industrial sectors. $I{E}_j^{C{O}_2,WPE}$ refers to the indirect CO₂ or water pollution emissions associated with sector j. $T{E}_i^{C{O}_2,WPE}$ denotes the total CO₂ or water pollution emissions of sector i, which equal the sum of its direct and indirect emissions.

$${\mathbf{D}}_{(13\times 13)}^{C{O}_2,WPE}=[d_{ij}^{C{O}_2,WPE}]={\displaystyle \frac{E{F}_{ij}^{C{O}_2,WPE}-E{F}_{ji}^{C{O}_2,WPE}}{T{E}_i^{C{O}_2,WPE}}}$$

(7)

$${\mathbf{U}}_{(13\times 13)}^{C{O}_2,WPE}=[u_{ij}^{C{O}_2,WPE}]={\mathbf{D}}_{(13\times 13)}^0+{\mathbf{D}}_{(13\times 13)}^1+\dots +{\mathbf{D}}_{(13\times 13)}^{\infty }={\left({\mathbf{I}}_{(13\times 13)}-{\mathbf{D}}_{(13\times 13)}^{C{O}_2,WPE}\right)}^{-1}$$

(8)

$$\mathbf{Sign}{\mathbf{U}}_{(13\times 13)}^{C{O}_2,WPE}=[sign(u_{ij}^{C{O}_2,WPE})]$$

(9)

Understanding how CO₂ and water pollution are transferred between sectors offers important insights for system-wide emission reduction strategies [40]. Equations (7)–(9) are based on the utility analysis of the industrial emissions network [41]. The dimensionless utility intensity matrix ${\mathbf{D}}_{(13\times 13)}^{C{O}_2,WPE}$ (Equation (8)) is derived from the direct utility intensity matrix $d_{ij}^{C{O}_2,WPE}$ (Equation (7)), which characterizes interactions within the CO₂ and water pollution systems. Here, ${\mathbf{U}}_{(13\times 13)}^{C{O}_2,WPE}$ represents a matrix corresponding to a specific path length, with its superscript denoting the length of the path. The sign (positive or negative) of the elements in the integrated utility matrix (Equation (9)) reveals the nature of emission reduction relationships between sectors. Inter-sectoral emission reduction relationships can be classified into four types: (1) Reciprocal (+ +): Emission reduction in one sector results in reduced emissions in another. (2) Exploitative (+ −): One sector transfers more pollution than it receives, benefiting at the cost of another. (3) Controlling (− +): Pollution transfer from one sector is governed or influenced by another. (4) Competitive (− −): Simultaneous emission reductions in both sectors intensify system interactions, potentially exacerbating overall environmental impacts [42]. As controlling and exploitative relationships are mutually linked, they are combined into one category. Competitive relationships are unfavorable to the performance of both CO₂ and water pollution systems [43,44]. Therefore, sectors engaged in competitive relationships are identified and their occurrences are quantified. The three industrial sectors with the highest number of competitive relationships in each system are designated as key sectors [45]. By modifying the trade structure among sectors, competitive relationships involving key sectors are transformed into reciprocal ones. These yield updated matrices: $u_{ij}^{C{O_2}^{\prime }}$, $u_{ij}^{WP{E}^{\prime }}$, and ${\mathbf{U}}^{C{O_2}^{\prime },WP{E}^{\prime }}=[u_{ij}^{C{O_2}^{\prime },WP{E}^{\prime }}]$. Based on Equations (4)–(10), the adjusted $d_{ij}^{C{O_2}^{\prime }}$ or $d_{ij}^{WP{E}^{\prime }}$ matrices are calculated for the CO₂ or water pollution systems under the new sectoral configuration. According to Equation (7), the adjusted matrix $E{F}_{ji}^{C{O_2}^{\prime },WP{E}^{\prime }}$ for key sectors is determined. Assuming that embodied emission intensity ${\mathsf{\epsilon }}^{C{O}_2,WPE}$ and unit output intensity $e^{C{O}_2,WPE}$ remain constant (per Equation (4)), the revised ${\mathbf{H}}^{C{O_2}^{\prime },WPE}$ is calculated. From Equations (11) and (12), the updated ${\mathbf{X}}^{C{O}_2,WP{E}^{\prime }}$ and direct emissions ${\mathbf{DE}}^{C{O}_2,WP{E}^{\prime }}$ for each sector are computed. Consequently, a new environmental input–output table is developed for the CO₂ or water pollution systems, reflecting the structural adjustments in key sectors. The prime symbol (′) indicates parameters derived from the restructured environmental input–output table.

$${\mathbf{D}}^{C{O_2}^{\prime },WP{E}^{\prime }}=\mathbf{I}-{\left({\mathbf{U}}^{C{O_2}^{\prime },WP{E}^{\prime }}\right)}^{-1}$$

(10)

$$diag{\mathbf{X}}^{C{O}_2,WP{E}^{\prime }}=-{({\mathbf{e}}^{C{O}_2,WPE}\mathbf{I}-diag{\mathsf{\epsilon }}^{C{O}_2,WPE})}^{-1}\times diag{\mathsf{\epsilon }}^{C{O}_2,WPE}\times {\mathbf{H}}^{C{O}_2,WP{E}^{\prime }}$$

(11)

$${\mathbf{DE}}^{C{O}_2,WP{E}^{\prime }}={\mathbf{e}}^{C{O}_2,WPE}\times diag{\mathbf{X}}^{C{O}_2,WP{E}^{\prime }}$$

(12)

Scenario setting: In both the CO₂ and WPE metabolic systems, all industrial sectors are aggregated into 13 composite sectors (see

Table 1. Abbreviations and descriptions of industrial sectors in dual-system aggregation classification.

Sector Abbreviation	Sector Description
MWC	Coal mining and selection products; oil and gas extraction and processing
MPM	Metal ore mining, selection, and processing
MOO	Mining and selection of non-metallic minerals and other minerals
FTO	Food and tobacco
TEI	Textile industry
PTP	Wood processing products and furniture/paper printing and cultural, educational, and sports
PPC	Petroleum, coking products, and nuclear fuel processing
CHE	Chemical products
MNM	Processing of non-metallic mineral products
MEI	Metal smelting and rolling processing
ADM	Advanced equipment manufacturing
OTM	Other manufacturing industries
MET	Materials and energy transformation and conversion supply

). Structural adjustments in the key sectors of one system inevitably induce a disturbance response in the other. Therefore, it is essential to examine how structural improvements in the CO₂ system’s key sectors impact the WPE system and to quantify the extent of such disturbances. Likewise, assessing the impact of structural changes in the WPE system’s key sectors on the CO₂ system is equally important, as shown in

Table 2. Scenario settings for mutual disturbance of dual-system emission reduction schemes.

	CO2 System Emission Reduction Plan	WPE System Emission Reduction Plan
Key sectors	MOOCO2→WPE	MPMWPE→CO2
	FTOCO2→WPE	FTOWPE→CO2
	MNMCO2→WPE	OTHWPE→CO2

Notes: The subscript _CO2→WPE refers to the response of the WPE system to emission reduction measures implemented in the CO₂ system, whereas _WPE→CO2 denotes the response of the CO₂ system to emission reduction measures applied in the WPE system.

. MATLAB 2024 offers robust matrix computation capabilities (for environmental input–output analysis) and numerical computing functions (for ecological network analysis), enabling the efficient processing of large-scale datasets and multidimensional model analysis and simulation across all scenarios.

2.1. Disturbance Model of CO₂ Metabolic System on WPE System

By optimizing the utility relationships between key CO₂ sectors and other sectors, changes in the WPE system’s three-dimensional indicators can be mapped. These indicators include: (1) changes in water pollution emissions and economic output across WPE sectors; (2) changes in inter-sectoral water pollution relationships; and (3) changes in the linkages between individual sectors and the overall WPE system. The WPE system’s three-dimensional indicators are then calculated iteratively based on the predefined CO₂ emission reduction scenarios in key sectors.

$$T{E}_i^{WP{E}^{\prime }}={\displaystyle \sum _{j=1}^{13}E{F}_{ij}^{WP{E}^{\prime }}+D{E}_i^{WP{E}^{\prime }}}$$

(13)

$$\begin{array}{l}\mathrm{\Delta }T{E}_i^{WPE}=T{E}_i^{WP{E}^{\prime }}-T{E}_i^{WPE}\\ \mathrm{\Delta }{X}_i^{WPE}={\mathrm{X}}_i^{WP{E}^{\prime }}-{\mathrm{X}}_i^{WPE}\end{array}$$

(14)

The impacts of emission reduction strategies in key CO₂ sectors on water pollution emissions and economic output in the WPE system are captured by Equations (13) and (14). $T{E}_i^{WP{E}^{\prime }}$ represents the combined total of inter-sectoral water pollution transfers and direct emissions. $\mathrm{\Delta }T{E}_i$ and $\mathrm{\Delta }{X}_i$ denote the changes in total water pollution emissions and economic output, respectively, for each WPE sector—relative to the baseline WPE system—resulting from CO₂ emission reductions in key sectors.

$${\mathbf{D}}^{WP{E}^{\prime }}=[d_{ij}^{WP{E}^{\prime }}]={\displaystyle \frac{E{F}_{ij}^{WP{E}^{\prime }}-E{F}_{ji}^{WP{E}^{\prime }}}{T{E}_i^{WP{E}^{\prime }}}}$$

(15)

$${\mathbf{U}}^{WP{E}^{\prime }}=[u_{ij}^{WP{E}^{\prime }}]={\mathbf{D}}^0+{\mathbf{D}}^1+\dots +{\mathbf{D}}^{\infty }={\left({\mathbf{I}}_{(13\times 13)}-{\mathbf{D}}_{(13\times 13)}^{WP{E}^{\prime }}\right)}^{-1}$$

(16)

$$Sign{\mathbf{U}}_{(13\times 13)}^{WP{E}^{\prime }}=[sign(u_{ij}^{WP{E}^{\prime }})]$$

(17)

The response of inter-sectoral water pollution emission relationships within the WPE system to emission reduction measures in key CO₂ sectors is presented in Equations (15)–(17). ${\mathbf{D}}^{WP{E}^{\prime }}$ and ${\mathbf{U}}^{WP{E}^{\prime }}$ denote the direct utility intensity matrix and the integrated utility intensity matrix of the WPE system under the CO₂ emission reduction scenario, respectively.

$$g_{ij}^{WP{E}^{\prime }}=E{F}_{ij}^{WP{E}^{\prime }}/T{E}_i^{WP{E}^{\prime }}$$

(18)

$${\mathbf{N}}_{(13\times 13)}^{WP{E}^{\prime }}=[n_{ij}^{WP{E}^{\prime }}]={({\mathbf{G}}_{\left(13\times 13\right)}^{WP{E}^{\prime }})}^0+{({\mathbf{G}}_{\left(13\times 13\right)}^{WP{E}^{\prime }})}^1+{({\mathbf{G}}_{\left(13\times 13\right)}^{WP{E}^{\prime }})}^2+\dots +{({\mathbf{G}}_{\left(13\times 13\right)}^{WP{E}^{\prime }})}^{\infty }={\left(\mathbf{I}-{\mathbf{G}}_{\left(13\times 13\right)}^{WP{E}^{\prime }}\right)}^{-1}$$

(19)

$${\mathbf{Y}}_{\left(13\times 13\right)}^{WP{E}^{\prime }}=diag{(\mathbf{T}{\mathbf{E}}_j^{WP{E}^{\prime }})}_{\left(13\times 13\right)} {\mathbf{N}}_{\left(13\times 13\right)}^{WP{E}^{\prime }}$$

(20)

$$C{W}_i^{WP{E}^{\prime }}={\displaystyle \sum _{j=1}^n{y}_{ij}^{WP{E}^{\prime }}}/{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{y}_{ij}^{WP{E}^{\prime }}}}$$

(21)

$$C{W}_j^{WP{E}^{\prime }}={\displaystyle \sum _{i=1}^n{y}_{ij}^{WP{E}^{\prime }}}/{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{y_{ij}}^{WP{E}^{\prime }}}}$$

(22)

$$C{F}_i^{WP{E}^{\prime }}=C{W}_i^{WP{E}^{\prime }}+C{W}_j^{WP{E}^{\prime }}$$

(23)

The response of water pollution transfer relationships between industrial sectors and the overall WPE system, under the CO₂ key sector emission reduction scenario, is described by Equations (18)–(23) [46]. $g_{ij}^{WP{E}^{\prime }}$ denotes the dimensionless, input-oriented water pollution transfer from sector j to sector i. ${\mathbf{N}}_{(13\times 13)}^{WP{E}^{\prime }}$ refers to the dimensionless matrix of integrated water pollution emission intensity. ${\mathbf{Y}}_{\left(13\times 13\right)}^{WP{E}^{\prime }}$ indicates the integrated water pollution flows transmitted across different path lengths. $C{W}_i^{WP{E}^{\prime }}$ measures the cumulative flow intensity received by sector i from the system, indicating its capacity to absorb water pollution transfers from other sectors. It also reflects the sector’s “pulling power,” defined as its influence on other sectors through forward (demand-side) linkages, as shown in Equation (21). $C{W}_j^{WP{E}^{\prime }}$ represents the sector’s “driving power,” or its capacity to stimulate water pollution transfers through backward (supply-side) linkages, as defined in Equation (22). $C{F}_i^{WP{E}^{\prime }}$ combines both pulling and driving power to indicate a sector’s total influence on the water pollution emission system.

Edge centrality reflects the influence of inter-sectoral pathways on the overall system, as defined in Equations (24)–(27) [46]. The network consists of nodes and edges: industrial sectors in the Yangtze River Economic Belt’s water pollution system are treated as nodes, while pollutant transfers between sectors serve as edges. These pollutant-carrying edges are defined as transfer centers in the urban emission network. The concept of centrality is derived from network theory. Edge centrality is quantified based on the volume of water pollution flow it carries, indicating the edge’s importance in transmitting emissions within the network. Central pathways serve as network hubs, contributing substantially to emission flow and directly influencing the stability of the system. A generic emission path in the system begins at sector i, ends at sector j, and passes through k nodes and the k − 1 edge. The volume of pollutant flow transmitted along this path is given in Equation (24).

$$\begin{array}{l}EF{P}_{ij,k}^{WP{E}^{\prime }}={\displaystyle \frac{E{F}_{i{s}_1}^{WP{E}^{\prime }}}{T{E}_{s_1}^{WP{E}^{\prime }}}}\times {\displaystyle \frac{E{F}_{s_1{s}_2}^{WP{E}^{\prime }}}{T{E}_{s_2}^{WP{E}^{\prime }}}}\times {\displaystyle \frac{E{F}_{s_2{s}_3}^{WP{E}^{\prime }}}{T{E}_{s_3}^{WP{E}^{\prime }}}}\times \dots \times {\displaystyle \frac{E{F}_{s_{k-2}{s}_{k-1}}^{WP{E}^{\prime }}}{T{E}_{s_{k-1}}^{WP{E}^{\prime }}}}\times {\displaystyle \frac{E{F}_{s_{k-1}{s}_k}^{WP{E}^{\prime }}}{T{E}_{s_k}^{WP{E}^{\prime }}}}\times {\displaystyle \frac{E{F}_{s_{k}j}^{WP{E}^{\prime }}}{T{E}_j^{WP{E}^{\prime }}}}\times T{E}_j^{WP{E}^{\prime }}\\ \hspace{1em}\hspace{1em}\hspace{1em}=g_{i{s}_1}^{WP{E}^{\prime }}\times g_{s_1{s}_2}^{WP{E}^{\prime }}\times \dots \times g_{s_{k-2}{s}_{k-1}}^{WP{E}^{\prime }}\times g_{s_{k-1}{s}_k}^{WP{E}^{\prime }}\times T{E}_j^{WP{E}^{\prime }}\end{array}$$

(24)

Assume that sectors a and b are two adjacent nodes along a water pollution emission path, denoted as $i\to j(a\ne i,b\ne j)$. The centrality $C_{a\to b}$ of inter-sectoral trade is defined as the volume of water pollution flow transmitted through edge $a\to b$, as specified in Equation (25).

$$C_{a\to b}^{WP{E}^{\prime }}=g_{i{s}_1}^{WP{E}^{\prime }}\times \dots \times g_{s_{N_a}a}^{WP{E}^{\prime }}\times g_{ab}^{WP{E}^{\prime }}\times g_{b{s}_{k-N_b+1}}^{WP{E}^{\prime }}\times \dots \times g_{s_{k}j}^{WP{E}^{\prime }}\times T{E}_j^{WP{E}^{\prime }}$$

(25)

Let $C_{a\to b,N_a,N_b}^{C{O}_2\to WPE}$ represent the total volume of WPE (Water Pollution Equivalent) emissions transferred along all emission paths that pass through edge $a\to b$, with node $N_a$ located upstream of $a\to b$, and node $N_b$ downstream of $a\to b$. This relationship is formalized in Equation (26).

$$\begin{array}{l}{C}_{a\to b,N_a,N_b}^{WP{E}^{\prime }}={\displaystyle \sum _{1\le i,s_1,\dots ,s_{N_a}\le n1\le }{\displaystyle \sum _{s_{k-N_b+1},j\le n}{g}_{i{s}_1}^{WP{E}^{\prime }}\times \dots \times g_{s_{N_a}a}^{WP{E}^{\prime }}\times g_{ab}^{WP{E}^{\prime }}\times g_{b{s}_{k-N_b+1}}^{WP{E}^{\prime }}\times \dots \times g_{s_{k}j}^{WP{E}^{\prime }}\times T{E}_j^{WP{E}^{\prime }}}}\\ ={\displaystyle \sum _{1\le i,s_1,\dots ,s_{N_a}\le n1\le }{\displaystyle \sum _{s_{k-N_b+1},j\le n}(g_{i{s}_1}^{WP{E}^{\prime }}\times \dots \times g_{s_{N_a}a}^{WP{E}^{\prime }})\times g_{ab}^{WP{E}^{\prime }}\times (g_{b{s}_{k-N_b+1}}^{WP{E}^{\prime }}\times \dots \times g_{s_{k}j}^{WP{E}^{\prime }}\times T{E}_j^{WP{E}^{\prime }})}}\\ ={{\displaystyle \sum g_{ab}^{WP{E}^{\prime }}(G^{N_a})}}_{[a]}{(G^{N_b})}^{[b]}diag(T{E}^{WP{E}^{\prime }})\end{array}$$

(26)

Here, $N_a$ and $N_b$ are positive integers. The inflow vector ${(G^{N_a})}_{[a]}$ corresponds to column a of matrix $G^{N_a}$, while the outflow vector ${(G^{N_b})}_{[b]}$ corresponds to row b of matrix $G^{N_b}$. Considering all emission paths of different lengths that pass through edge $a\to b$, the edge centrality is calculated using Equation (27).

$$\begin{array}{l}{c}_{ij}^{WP{E}^{\prime }}={\displaystyle \sum _{N_a=1}^{\infty }{\displaystyle \sum _{N_b=1}^{\infty }{C}_{a\to b}^{WP{E}^{\prime }}(N_a,N_b)}}\\ ={\displaystyle \sum _{N_a=1}^{\infty }{\displaystyle \sum _{N_b=1}^{\infty }({{\displaystyle \sum g_{ab}^{WP{E}^{\prime }}(G^{N_a})}}_{[a]}\times {(G^{N_b})}^{[b]}diag(T{E}^{WP{E}^{\prime }}))}}\\ ={\displaystyle \sum g_{ab}^{WP{E}^{\prime }}\times ({\displaystyle \sum _{N_a=1}^{\infty }{G}^{N_a}{)}_{[a]}}}\times ({\displaystyle \sum _{N_b=1}^{\infty }{G}^{N_b}}{)}^{[b]}diag(T{E}^{WP{E}^{\prime }})\\ ={\displaystyle \sum g_{ab}^{WP{E}^{\prime }}\times (N^{WP{E}^{\prime }}-I)}(N^{WP{E}^{\prime }}-I)diag(T{E}^{WP{E}^{\prime }})\end{array}$$

(27)

$C=[c_{ij}],i\ne j$ denotes the cumulative volume of water pollution emissions transferred via edge $a\to b$ throughout the entire network process.

2.2. Disturbance Model of WPE Metabolic System on CO₂ System

By optimizing the utility relationships between key sectors in the WPE system and other sectors, changes in the CO₂ system’s three-dimensional indicators can be systematically mapped. These indicators include: (1) changes in water pollution emissions and economic output of each sector in the CO₂ system; (2) changes in inter-sectoral water pollution relationships; and (3) changes in sector-to-system water pollution transfer dynamics. Based on the predefined emission reduction scenarios for key sectors in the WPE system, the CO₂ system’s three-dimensional indicators are calculated iteratively.

$$T{E}_i^{C{O_2}^{\prime }}={\displaystyle \sum _{j=1}^{13}E{F}_{ij}^{C{O_2}^{\prime }}+D{E}_i^{C{O_2}^{\prime }}}$$

(28)

$$\begin{array}{l}\mathrm{\Delta }T{E}_i^{C{O}_2}=T{E}_i^{C{O_2}^{\prime }}-T{E}_i^{C{O_2}^{\prime }}\\ \mathrm{\Delta }{X}_i^{C{O}_2}={\mathrm{X}}_i^{C{O_2}^{\prime }}-{\mathrm{X}}_i^{C{O}_2}\end{array}$$

(29)

The impact of emission reduction in key WPE sectors on water pollution emissions and economic output within the CO₂ system is described by Equations (28) and (29). $T{E}_i^{WP{E}^{\prime }}$ denotes the total of inter-sectoral CO₂ transfers and direct CO₂ emissions. $\mathrm{\Delta }T{E}_i$ and $\mathrm{\Delta }{X}_i$ denote, respectively, the changes in total water pollution emissions and economic output in each CO₂ sector—relative to the baseline CO₂ system—resulting from emission reductions in key WPE sectors.

$${\mathbf{D}}^{C{O_2}^{\prime }}=[d_{ij}^{C{O_2}^{\prime }}]={\displaystyle \frac{E{F}_{ij}^{C{O_2}^{\prime }}-E{F}_{ji}^{C{O_2}^{\prime }}}{T{E}_i^{C{O_2}^{\prime }}}}$$

(30)

$${\mathbf{U}}^{C{O_2}^{\prime }}=[u_{ij}^{C{O_2}^{\prime }}]={\mathbf{D}}^0+{\mathbf{D}}^1+\dots +{\mathbf{D}}^{\infty }={\left({\mathbf{I}}_{(13\times 13)}-{\mathbf{D}}_{(13\times 13)}^{C{O_2}^{\prime }}\right)}^{-1}$$

(31)

$$Sign{\mathbf{U}}_{(13\times 13)}^{C{O_2}^{\prime }}=[sign(u_{ij}^{C{O_2}^{\prime }})]$$

(32)

The response of inter-sectoral water pollution transfer relationships within the CO₂ system to emission reduction in key WPE sectors is presented in Equations (30)–(32). ${\mathbf{D}}^{C{O_2}^{\prime }}$ and ${\mathbf{D}}^{C{O_2}^{\prime }}$ denote the direct and integrated utility intensity matrices, respectively, of the CO₂ system under the WPE emission reduction scenario.

$$g_{ij}^{C{O_2}^{\prime }}=E{F}_{ij}^{C{O_2}^{\prime }}/T{E}_i^{C{O_2}^{\prime }}$$

(33)

$${\mathbf{N}}_{(13\times 13)}^{C{O_2}^{\prime }}=[n_{ij}^{C{O_2}^{\prime }}]={({\mathbf{G}}_{\left(13\times 13\right)}^{C{O_2}^{\prime }})}^0+{({\mathbf{G}}_{\left(13\times 13\right)}^{C{O_2}^{\prime }})}^1+{({\mathbf{G}}_{\left(13\times 13\right)}^{C{O_2}^{\prime }})}^2+\dots +{({\mathbf{G}}_{\left(13\times 13\right)}^{C{O_2}^{\prime }})}^{\infty }={\left(\mathbf{I}-{\mathbf{G}}_{\left(13\times 13\right)}^{C{O_2}^{\prime }}\right)}^{-1}$$

(34)

$${\mathbf{Y}}_{\left(13\times 13\right)}^{C{O_2}^{\prime }}=diag{(\mathbf{T}{\mathbf{E}}_j^{C{O_2}^{\prime }})}_{\left(13\times 13\right)} {\mathbf{N}}_{\left(13\times 13\right)}^{C{O_2}^{\prime }}$$

(35)

$$C{W}_i^{C{O_2}^{\prime }}={\displaystyle \sum _{j=1}^n{y}_{ij}^{C{O_2}^{\prime }}}/{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{y}_{ij}^{C{O_2}^{\prime }}}}$$

(36)

$$C{W}_j^{C{O_2}^{\prime }}={\displaystyle \sum _{i=1}^n{y}_{ij}^{C{O_2}^{\prime }}}/{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{y_{ij}}^{C{O_2}^{\prime }}}}$$

(37)

$$C{F}_i^{C{O_2}^{\prime }}=C{W}_i^{C{O_2}^{\prime }}+C{W}_j^{C{O_2}^{\prime }}$$

(38)

The response of sector-to-system CO₂ emission relationships under the WPE key sector emission reduction scenario is described by Equations (33)–(38). $g_{ij}^{WP{E}^{\prime }}$ denotes the dimensionless, input-oriented CO₂ transfer from sector j to sector i. ${\mathbf{N}}_{(13\times 13)}^{WP{E}^{\prime }}$ refers to the dimensionless integrated intensity matrix of CO₂ emissions. ${\mathbf{Y}}_{\left(13\times 13\right)}^{WP{E}^{\prime }}$ indicates the cumulative CO₂ flow transferred along all path lengths. $C{W}_i^{WP{E}^{\prime }}$ measures the extent to which sector i receives CO₂ transfers from other sectors, known as its “pulling power” (Equation (36)). $C{W}_j^{WP{E}^{\prime }}$ captures the ability of a sector to transfer CO₂ to others, defined as its “driving power” (Equation (37)). $C{F}_i^{WP{E}^{\prime }}$ is the sum of a sector’s pulling and driving power, denoting its overall influence on the CO₂ emission system.

$$\begin{array}{l}{c}_{ij}^{C{O_2}^{\prime }}={\displaystyle \sum _{N_a=1}^{\infty }{\displaystyle \sum _{N_b=1}^{\infty }{C}_{a\to b}^{C{O_2}^{\prime }}(N_a,N_b)}}\\ ={\displaystyle \sum _{N_a=1}^{\infty }{\displaystyle \sum _{N_b=1}^{\infty }({{\displaystyle \sum g_{ab}^{C{O_2}^{\prime }}(G^{N_a})}}_{[a]}\times {(G^{N_b})}^{[b]}diag(T{E}^{C{O_2}^{\prime }}))}}\\ ={\displaystyle \sum g_{ab}^{C{O_2}^{\prime }}\times ({\displaystyle \sum _{N_a=1}^{\infty }{G}^{N_a}{)}_{[a]}}}\times ({\displaystyle \sum _{N_b=1}^{\infty }{G}^{N_b}}{)}^{[b]}diag(T{E}^{C{O_2}^{\prime }})\\ ={\displaystyle \sum g_{ab}^{C{O_2}^{\prime }}\times (N^{C{O_2}^{\prime }}-I)}(N^{WP{E}^{\prime }}-I)diag(T{E}^{C{O_2}^{\prime }})\end{array}$$

(39)

Based on Equations (24)–(27), Equation (39) defines the total volume of CO₂ emissions cumulatively transferred through edge $a\to b$ across the entire network emission process.

3. Case Study and Data Source

The Yangtze River Economic Belt (YREB) is a core region of China’s economic development and a significant source of both CO₂ and water pollution emissions. The emission systems for CO₂ and water pollution in the YREB’s industrial sectors display distinct characteristics, highlighting the inherent tension between regional economic development and environmental sustainability. The industrial structure of the YREB is dominated by energy-intensive sectors—such as steel, cement, chemicals, and electricity—which are characterized by high energy consumption and elevated CO₂ emission intensities. Significant technological disparities exist across regions and sectors. The adoption of energy-efficient and low-carbon technologies remains limited in several industries, leading to overall low carbon efficiency. The YREB’s industrial sectors are also major contributors to China’s water pollution, with emissions of COD, NH₃-N, and TP consistently exceeding the national average. Different industries emit distinct types of pollutants—for instance, organic pollutants dominate in paper and textile sectors, whereas the chemical industry primarily releases inorganic salts. This paper adopts the Water Pollution Equivalent (WPE) as a composite index to assess the combined impact of COD, NH₃-N, and TP ($WP{E}_i = E_{i,\mathrm{COD}}/{\eta }_{\mathrm{COD}}+E_{i,{\mathrm{NH}}_3-\mathrm{N}}/{\eta }_{{\mathrm{NH}}_3-\mathrm{N}}+E_{i,\mathrm{TP}}/{\eta }_{\mathrm{TP}}$).

Additionally, supply–demand relationships among the YREB’s industrial sectors play a critical role in shaping both CO₂ and water pollution metabolic dynamics. Upstream–downstream industrial linkages, resource complementarity, and joint production mechanisms collectively shape the inter-sectoral pollution profiles and intensities. Upstream sectors (e.g., steel, chemicals) provide raw materials to downstream industries (e.g., manufacturing, electronics), while downstream activities amplify upstream production demands. This interdependence leads to the mutual transfer and accumulation of CO₂ and water pollutants across sectors, forming a cascading effect. Due to sectoral variation in emission characteristics, pollution from high-energy, high-emission upstream sectors is transmitted along the value chain, amplifying downstream environmental burdens. For example, CO₂ and water pollutants produced by the chemical industry may be transferred through material supply chains to sectors such as electronics and automotive manufacturing, elevating their environmental loads. CO₂ and water pollution flows among sectors are intricately embedded within inter-sectoral trade and production systems. Under carbon reduction policy pressures, there is a risk of disproportionate focus on CO₂ transfer reduction, while integrated water pollution control is neglected. The absence of a coordinated environmental policy may result in structural adjustments that reduce carbon emissions but fail to control pollution—further intensifying pollutant transfer and diffusion. Against this backdrop, clarifying the bidirectional disturbance mechanisms between CO₂ and water pollution metabolic systems in the YREB’s industrial sectors is essential. Doing so will support integrated pollution and carbon reduction strategies, enabling green transition and long-term sustainability.

The analysis is supported by: (a) the 2017 national input–output table of China; (b) CO₂ emissions data from 40 industrial sectors across 11 provinces of the YREB; and (c) water pollution data (COD, NH₃-N, TP) for 25 industrial sectors in the same region. Based on the economic and emission characteristics of sub-sectors, both the CO₂ and water pollution systems are consolidated into 13 aggregated industrial sectors.

4. Results and Discussion

4.1. Identifying Key Industrial Sectors in CO₂ and WPE Metabolic Systems

Figure 2 illustrates the CO₂ and Water Pollution Equivalent (WPE) emission levels across 13 aggregated industrial sectors in the Yangtze River Economic Belt (YREB). The x-axis denotes the sectors, while the left y-axis indicates the emission volumes. Blue bars indicate direct emissions, and pink bars indicate indirect emissions. Figure 2 reveals substantial variation in CO₂ and WPE emissions across different industrial sectors. As shown in Figure 2a, the MET sector reports the highest total CO₂ emissions at 2126.48 Mt, primarily driven by direct emissions of 1551.34 Mt. This suggests that the sector generates substantial emissions through energy transformation and material provision activities. With a CO₂ emission intensity of 8.40 tonnes/10⁴ ¥, the MET sector has the highest carbon intensity, suggesting a heavy emission load per unit of output. This underscores the need to improve energy efficiency and reduce emissions. In the ADM sector, indirect CO₂ emissions amount to 855.19 Mt—approximately 95.7% of total emissions—indicating that high-end equipment manufacturing relies heavily on upstream sectors for emissions. With an emission intensity of 1.85 tonnes/10⁴ ¥, the ADM sector exhibits relatively high production efficiency. While total emissions are significant, the sector’s carbon intensity is comparatively low. Sectors including FTO, TEI, and CHE exhibit similar emission profiles, where indirect emissions constitute the major share. Figure 2b indicates that the FTO sector has the highest total WPE emissions, reaching 6.94 × 10⁸ ep, mainly attributed to direct emissions of 5.3 × 10⁸ ep, which reflects substantial water pollution discharge in food processing. Its WPE intensity reaches 1.38 ep/10⁴ ¥—the highest among all sectors—implying the greatest water pollution pressure per unit of economic output. It is imperative for the FTO sector to prioritize water conservation and invest in efficient wastewater treatment technologies to mitigate its environmental burden.

Owing to interdependencies among industrial sectors, Ecological Network Analysis (ENA) unveils the intricate interactions between CO₂ and water pollution emissions. Figure 3 depicts the utility relationships among industrial sector pairs within the CO₂ and Water Pollution Equivalent (WPE) emission networks. Blue, yellow, and red squares represent symbiotic, exploitative, and competitive relationships, respectively. In symbiotic relationships, reducing emissions in one sector induces emission reductions in others, indicating promising paths for collaborative pollution mitigation. In exploitative relationships, where a sector simultaneously acts as both the exploiter and the exploited, emission reductions in one may inadvertently cause increases in another. In competitive relationships, simultaneous emission reductions in both sectors can disrupt supply chains and inter-sectoral dynamics, ultimately increasing system-wide CO₂ and WPE emissions. Competitive relationships pose significant barriers to emission mitigation in both CO₂ and WPE metabolic systems and warrant targeted structural interventions.

Table 3. The number of CO₂ and WPE emissions utility relationships for each industrial sector.

	CO2 Metabolic System			WPE Metabolic System
	Symbiotic Relationship	Exploitative Relationship	Competitive Relationship	Symbiotic Relationship	Exploitative Relationship	Competitive Relationship
MWC	5	8	0	3	7	3
MPM	3	5	5	2	6	5
MOO	1	5	7	1	9	3
FTO	1	5	7	1	8	4
TEI	2	5	6	2	9	2
PTP	1	8	4	1	10	2
PPC	2	6	5	2	8	3
CHE	1	8	4	1	12	0
MNM	1	5	7	1	11	1
MEI	1	6	6	1	10	2
ADM	4	5	4	6	7	0
OTM	2	5	6	2	7	4
MET	1	11	1	2	9	2

summarizes the distribution of symbiotic, exploitative, and competitive relationships among sectors in the CO₂ and WPE metabolic systems. Specifically, each system contains 91 emission relationships among the 13 aggregated industrial sectors. In the industrial CO₂ metabolic system (Figure 3a), 20.88% are symbiotic, 45.10% exploitative, and 34.02% competitive—indicating that exploitative relationships are predominant. Sectors like MOO, FTO, MNM, TEI, MEI, and OTH demonstrate numerous competitive ties, with MOO, FTO, and MNM each involved in seven. In the WPE metabolic system (Figure 3b), symbiotic, exploitative, and competitive relationships constitute 20.88%, 62.64%, and 16.48% of all sectoral interactions, respectively. Sectors including MPM, OTH, MWC, MOO, FTO, and PPC are characterized by relatively highly competitive interactions; MPM, OTH, and FTO are involved in five, four, and four relationships, respectively.

As the CO₂ and WPE metabolic systems share the same 13 industrial sectors, complex interdependencies exist between them. Any structural adjustment in one system is bound to induce a response in the other. Based on the analysis of sectors exhibiting a high frequency of competitive relationships, MOO, FTO, and MNM are identified as key emission reduction sectors in the CO₂ metabolic system, while MPM, OTH, and FTO are identified as counterparts in the WPE metabolic system. For the CO₂ system, structural optimization involves transforming competitive relationships between MOO, FTO, and MNM and other sectors into symbiotic relationships. This allows examination of how structural changes in the CO₂ system affect sectoral economic performance, WPE emissions, and inter-sectoral dynamics in the WPE system. Similarly, in the WPE system, competitive ties between MPM, FTO, and OTH and other sectors are modified into symbiotic relationships. This enables the assessment of how structural adjustments in the WPE system affect sectoral economic activity, CO₂ emissions, and inter-sectoral interactions within the CO₂ metabolic framework.

4.2. Analysis of Disturbance Induced by CO₂ System on WPE System

To explore how structural improvements in key sectors of the CO₂ metabolic system influence the WPE metabolic system, this section evaluates a set of three-dimensional indicators for the WPE system. These indicators encompass: (1) sector-level water pollution emissions, (2) inter-sectoral relationships, and (3) linkages between sectors and the overall system.

Figure 4 presents the emission and economic responses of industrial sectors within the WPE metabolic system resulting from emission reductions in key sectors of the CO₂ metabolic system. Each dot’s color indicates the industrial sector category, while its size reflects the total WPE emission intensity. The x-axis represents changes in sectoral WPE emissions: positive values indicate increases, and negative values indicate reductions. The y-axis represents changes in sectoral economic output relative to the original WPE metabolic system. Positive values reflect output gains, while negative values reflect losses.

Figure 4a demonstrates that under the MOO_CO2 scenario, most sectors in the WPE metabolic system respond noticeably in terms of both water pollution emissions and economic output. While the majority of sectors achieved WPE reductions, these were generally accompanied by decreases in economic output. Sectors such as MET, CHE, and MOO showed clear downward trends in WPE emissions. The MET sector (Materials and Energy Transformation) demonstrated the most substantial reduction, with emissions decreasing by 1.6 × 10⁸. Economic output declined across most sectors, notably in ADM, MEI, and CHE. The ADM (Advanced Equipment Manufacturing) sector experienced the sharpest contraction, with a reduction of 5 × 10⁸ RMB. This outcome may be attributed to increased production costs or declining production efficiency in the ADM sector. Figure 4b illustrates the WPE system’s response to emission reduction actions in the FTO (Food and Tobacco) sector of the CO₂ metabolic system. This scenario reflects adjustments across the food and tobacco industry’s upstream and downstream supply chains. The CHE (Chemical Products) and MET sectors achieved significant WPE reductions of 5.7 × 10⁷ and 1.5 × 10⁸, respectively. These reductions likely result from supply chain shifts triggered by FTO’s emission reduction efforts, which indirectly reduced pollution in related sectors. Figure 4c shows that under the MNM_CO2 scenario, the MNM sector (Non-metallic Mineral Products) experienced a 3.51 × 10⁶ increase in WPE emissions, accompanied by a 1.5 × 10⁷ RMB increase in economic output. This suggests that emission reductions in the CO₂ metabolic system’s MNM sector imposed both environmental and economic burdens on its WPE counterpart.

Figure 5a–c illustrate the pairwise utility relationships among industrial sectors in the WPE metabolic system under the MOO_CO2, FTO_CO2, and MNM_CO2 emission reduction scenarios. Under the MOO_CO2 scenario (Figure 5a), symbiotic, exploitative, and competitive relationships represent 15.38%, 57.14%, and 27.48% of all inter-sectoral connections, respectively. Under the FTO_CO2 scenario (Figure 5b), the respective proportions are 15.38%, 54.95%, and 29.67%. Under the MNM_CO2 scenario (Figure 5c), the corresponding shares are 19.78%, 59.34%, and 29.68%. In terms of symbiotic relationships, the ADM and MET sectors maintain a symbiotic relationship under both the MOO_CO2 and FTO_CO2 scenarios. Under the MNM_CO2 scenario, the MNM sector develops new symbiotic relationships with TEI, PTP, and MEI, which were absent in the original WPE system—indicating a notable improvement. This suggests that emission reductions in the MNM sector of the CO₂ system positively influence its interaction with other sectors in the WPE system. Regarding exploitative relationships, under the MOO_CO2 scenario, the MPM sector in the WPE system forms only three such connections—with PPC, MNM, and MEI. In terms of competitive relationships, both the MOO_CO2 and FTO_CO2 scenarios lead to a significant increase in competitive ties for sectors such as MPM, TEI, ADM, and OTH. This reflects that CO₂ emission reductions in the MOO and FTO sectors adversely affect MPM, TEI, ADM, and OTH within the WPE system, exacerbating competitive tensions.

Figure 6a–c illustrate the sectoral pulling power, driving power, and integrated influence within the WPE metabolic system under various CO₂ key sector emission reduction scenarios. The blue line represents pulling power (sectoral dependence on the system), the orange line denotes driving power (contribution to system support), and the grey line indicates the integrated influence (overall impact on the system). In the baseline WPE system, FTO, CHE, and TEI demonstrate high levels of both pulling and driving power—indicating strong dependence on and significant contributions to the system. Their integrated influence ranks among the top three across all sectors. Under the MOO_CO2 scenario, pulling power increases significantly for sectors such as MET, MEI, and MWC. For instance, MET’s pulling power rises from 1.38% to 12.91%, reflecting greater reliance on the system as a result of emission reductions in the MOO (Mining of Non-metallic Minerals) sector. Conversely, ADM, CHE, and TEI experience a substantial decline in pulling power—from 13.8%, 20%, and 14.75% to 4.14%, 19.6%, and 11.78%, respectively. In most sectors, driving power follows the same trend as pulling power; however, exceptions exist—for instance, MEI exhibits a slight decrease in driving power despite a notable increase in pulling power. FTO displays the opposite pattern, with enhanced driving power and marginally reduced pulling power. Although changes in integrated influence for FTO, CHE, and TEI are minimal, their high pulling and driving powers ensure they continue to exert dominant influence within the system. A comparison across the MOO_CO2, FTO_CO2, and MNM_CO2 scenarios reveals slight differences in integrated influence values, while the overall trends remain largely consistent. In most sectors, integrated influence under the three emission reduction scenarios is either greater or less than in the baseline WPE system. FTO’s integrated influence increases under the MOO_CO2 and MNM_CO2 scenarios but declines under its own FTO_CO2 scenario. This outcome reflects how structural adjustments in the CO₂ system—particularly in the FTO sector—reshape its overall influence within the WPE metabolic framework.

4.3. Analysis of Disturbance Induced by WPE System on CO₂ System

Figure 7 illustrates the CO₂ emission and economic responses of industrial sectors in the CO₂ metabolic system to emission reduction measures targeting key sectors in the WPE system. The color and size of each dot represent the industrial sector category and the total CO₂ emission intensity, respectively. The x-axis denotes changes in CO₂ emissions: positive values represent increases, while negative values indicate reductions. The y-axis represents changes in economic output relative to the baseline CO₂ metabolic system—positive values imply output growth, and negative values reflect output losses. Figure 7a shows that under the MPM_WPE scenario, CO₂ system sectors respond to varying degrees in both emissions and economic output. For instance, the CHE (Chemical Products) sector exhibits a 15.84 Mt increase in CO₂ emissions—possibly due to increased demand or production of chemical inputs following reductions in the MPM sector—while its economic output drops by 1.82 × 10⁸ RMB. This suggests that the MPM_WPE reduction scenario imposes simultaneous environmental and economic burdens on the CHE sector. The MET and MNM sectors similarly exhibit increased CO₂ emissions (293 Mt and 116 Mt, respectively), yet achieve economic output gains of 5.76 × 10⁷ and 9.08 × 10⁷ RMB. The ADM (Advanced Equipment Manufacturing) sector benefits most under the MPM_WPE scenario, achieving a 552 Mt reduction in CO₂ emissions and a 7.46 × 10⁸ RMB increase in economic output. This implies that emission reductions in the MPM sector may enhance material efficiency and productivity in the ADM sector—achieving both mitigation and performance gains. Figure 7b,c reveal similar emission and output patterns under the FTO_WPE and OTH_WPE reduction scenarios. Compared with the MPM_WPE scenario, the FTO_WPE and OTH_WPE scenarios lead to substantial CO₂ reductions in the MWC (Coal Mining) and CHE sectors but a significant increase in ADM sector emissions. Specifically, under the FTO_WPE and OTH_WPE scenarios, MWC and CHE emissions fall by 188.63 and 140.66 Mt and by 180.37 and 148.35 Mt, respectively; ADM emissions increase by 366.58 and 384.91 Mt. In terms of CO₂ emission intensity, the MET sector worsens under all three scenarios, rising from 8.40 t/10⁴ RMB (baseline) to 9.37, 9.45, and 9.68 t/10⁴ RMB, respectively. The ADM sector shows divergent trends: emission intensity drops to 0.55 t/10⁴ RMB under MPM_WPE, but rises to 0.85 and 0.98 t/10⁴ RMB under the FTO_WPE and OTH_WPE scenarios. These results highlight that WPE key sector emission reductions can trigger cascading supply chain reactions in the CO₂ system, leading to emission increases or shifts in sectoral economic performance. Policymakers should account for these chain effects and develop targeted, adaptive strategies for integrated pollution and carbon reduction.

Figure 8 illustrates the pairwise utility relationships among industrial sectors in the CO₂ metabolic system under the MPM_WPE, FTO_WPE, and OTH_WPE emission reduction scenarios. Under the MPM_WPE scenario (Figure 8a), symbiotic, exploitative, and competitive relationships account for 21.98%, 41.76%, and 36.26%, respectively. Under the FTO_WPE scenario (Figure 8b), the proportions are 15.38%, 46.15%, and 38.47% for symbiotic, exploitative, and competitive relationships, respectively. Under the OTH_WPE scenario (Figure 8c), the shares are 15.38%, 47.25%, and 37.37%, respectively. From the perspective of symbiotic relationships, the MPM_WPE scenario leads to an increase in symbiotic connections between the MWC sector and other sectors, relative to the baseline CO₂ system. MWC forms symbiotic relationships with MPM, TEI, ADM, and OTH sectors. This indicates that emission reductions in the WPE system’s MPM sector have a positive impact on the MWC sector within the CO₂ system. In contrast, the number of symbiotic relationships involving the MWC sector decreases under the FTO_WPE and OTH_WPE scenarios, relative to the original CO₂ system. This suggests that emission reductions in the FTO and OTH sectors of the WPE system have a negative effect on the MWC sector in the CO₂ system. Additionally, the ADM sector develops more symbiotic relationships with other sectors compared with the baseline CO₂ system. This indicates that FTO and OTH emission reductions in the WPE system positively influence the ADM sector’s role within the CO₂ metabolic system.

Figure 9a–c display the pulling power, driving power, and integrated influence between industrial sectors and the CO₂ system under three different WPE key sector emission reduction scenarios. In the baseline CO₂ system, the MET, MEI, ADM, and CHE sectors exhibit high values across all three dimensions—indicating both strong systemic dependence and contribution. Under the MPM_WPE scenario, ADM’s pulling power rises sharply to 40.59%, up from 22.54% in the baseline. In contrast, MET, CHE, and MEI show clear declines in pulling power. This suggests that emission reductions in the MPM (Metal Mining and Processing) sector of the WPE system enhance ADM’s systemic reliance within the CO₂ network. MET retains the highest share of driving power at 34.82%, with ADM at 25.6%; however, ADM leads in integrated influence, followed closely by MET. In the FTO_WPE and OTH_WPE scenarios, the CHE and MWC sectors experience notable increases in pulling power and integrated influence, accompanied by slight decreases in driving power. This suggests that, for the CHE sector, pulling power outweighs driving power under these scenarios. When comparing scenarios, ADM’s integrated influence peaks under MPM_WPE—highlighting that reductions in the WPE system’s MPM sector reinforce ADM’s core position in the CO₂ system. However, the majority of sectors exhibit greater integrated influence under FTO_WPE and OTH_WPE compared with MPM_WPE. This discrepancy is likely attributable to ADM’s disproportionately dominant influence under the MPM_WPE scenario.

4.4. Policy Recommendations

The CO₂ and WPE systems exhibit a complex interdependence. In certain scenarios, reductions in CO₂ emissions directly or indirectly drive reductions in WPE, as seen in the MOO_CO2 and FTO_CO2 scenarios, where CO₂ reduction significantly impacted the WPE system. However, in some instances, CO₂ reduction may result in an increase in WPE, especially in industries with strong competitive dynamics, such as MOO, FTO, and MNM.

Economic and environmental responses differ across multiple scenarios. By analyzing various emission reduction scenarios, we uncover the economic responses of different sectors to CO₂ and WPE reduction strategies. For instance, in the MOO_CO2 scenario, most sectors achieved WPE reductions through structural adjustments, but this was accompanied by a decrease in economic output, reflecting the economic trade-offs that may arise during emission reductions, particularly in high-pollution and high-energy-consuming sectors. In the FTO_CO2 and MNM_CO2 scenarios, certain sectors (such as CHE and MET) achieved dual reductions in both WPE and CO₂, illustrating that optimizing supply chain interactions and enhancing technological efficiency can lead to synergistic reductions across different pollutants.

These results offer valuable insights for policymakers. When implementing regional pollution control and carbon reduction policies, it is crucial to consider the complex interactions between industries. Single emission reduction measures may produce unintended side effects, particularly in competitive sectors. Therefore, policies should focus more on structural adjustments in key sectors, encouraging cross-sector cooperation, particularly in the synergistic reduction of pollution and carbon emissions in high-pollution and high-energy-consuming industries. Furthermore, economic trade-offs and industry chain reactions should also be considered to ensure the effectiveness and sustainability of the policies.

5. Conclusions

To explore the bidirectional interaction mechanisms between industrial CO₂ and water pollution metabolic systems, this study proposes a TDE-ISCW method. This method identifies critical utility relationships, quantifies the mutual perturbation responses between the two systems, and proposes sectoral restructuring strategies to achieve synergistic regional pollution and carbon reduction goals. The findings are as follows: (1) The Advanced Equipment Manufacturing (ADM) sector records total CO₂ emissions of 893.44 Mt, of which 855.19 Mt (95.7%) are indirect—highlighting substantial upstream dependency. Nevertheless, ADM has the lowest water pollution intensity per unit of output, likely reflecting its relatively advanced technologies and reduced COD, NH₃–N, and TP discharges. (2) Sectors exhibiting high levels of competitive relationships—MOO, FTO, and MNM—are identified as key to CO₂ emission reduction, while MPM, OTH, and FTO are designated as critical for WPE control. (3) In the MOO_CO2, FTO_CO2, and MNM_CO2 scenarios, most sectors achieve WPE reductions by restructuring interactions with key emitters; however, such gains frequently involve economic trade-offs, especially among high-polluting, energy-intensive industries. Emission reductions in WPE key sectors may trigger heterogeneous supply chain reactions, leading to CO₂ increases or shifts in economic output in downstream industries.

Future studies should: (1) develop temporal models to simulate supply chain cascades from sectoral restructuring, integrating real-time economic feedback with heterogeneous pollution transfers. This quantifies dynamic thresholds where emission cuts disproportionately reduce industrial output; (2) explore the effects of varying levels of conversion efficiency on the structure and function of ecological networks. Models that more realistically reflect real-world barriers to relationship transformation are also aimed to be developed, enabling the impacts of partial conversion on system resilience and sustainability to be assessed; (3) incorporate an economic/emission forecasting model to project parameters for the most recent and upcoming years, thereby addressing the timeliness issue of the model; and (4) refine and expand the model by incorporating sub-industrial emission intensities, technological pathways, and regional differences to provide more targeted and precise policy recommendations.