Multi-Dimensional Method Innovation and System Construction for Synergistic Damage Assessment of Multi-Media Pollution

Abstract

To address issues existing in current multi-media pollution assessment, such as data mismatch, parameter conflicts, and inadequate characterization of nonlinear effects, this study developed a multi-factor synergistic assessment methodological system encompassing “data preprocessing-parameter calibration-damage quantification-model coupling”. A three-stage parameter calibration system of “inheritance-linkage-sensitivity screening” was established to achieve cross-media parameter synergy; an Environmental Damage Entropy (EDE) model was constructed based on information entropy to quantify the nonlinear coupled damage of multiple factors; and the optimal governance threshold was determined by combining the coupling theory of marginal damage and governance cost. Taking a multi-media pollution incident (atmosphere-soil-surface water-groundwater) caused by a chemical plant explosion as a case study, pollution chain identification, damage quantification, ecological risk cascading effect analysis, and health risk assessment were conducted. The results show that this method can accurately identify key pollution pathways. Based on the calculation of Environmental Damage Entropy (EDE = 0.604) and the synergy coefficient (δ = 1.32), the comprehensive damage value was quantified as 8.21 million yuan. Additionally, the threshold exceedance characteristics of various media were identified, reflecting the cumulative and lagging nature of ecological risk cascading effects. The method proposed in this study can accurately identify key pollution pathways and quantify comprehensive damage as well as ecological risks, providing scientific support for the allocation of multi-media pollution governance responsibilities and precise prevention and control.

1. Introduction

Environmental pollution is inherently a multi-media problem [1]. Contaminants do not remain confined to a single medium; they migrate and transform across the atmosphere, water, soil, and biota [2]. This cross-media movement complicates impact assessment, as interactions among different environmental elements can produce synergistic, additive, or antagonistic effects, which are often missed in single-medium evaluations [3,4]. The inherent complexity of these pathways, governed by diverse physicochemical and biological processes, necessitates an assessment approach that moves beyond compartmentalized analysis to capture the system’s emergent behaviors and cascading risks [5].

In recent decades, industrial expansion, urbanization, and intensive agriculture have increased the frequency and severity of multi-media pollution incidents [6]. These events involve complex pathways—such as atmospheric deposition to soil, leaching to groundwater, and bioaccumulation through food webs—posing serious threats to ecosystem integrity, human health, and socio-economic stability [7,8]. Consequently, there is an urgent need to develop robust methodological frameworks capable of quantifying the integrated damage from multi-media pollution [9,10].

Conventional assessment approaches have traditionally treated environmental compartments in isolation [11]. While these methods have advanced our understanding of pollution dynamics within individual compartments, they exhibit critical and systemic shortcomings when applied to interconnected multi-media systems, where the whole impact is greater than the sum of its parts [12,13]. A primary challenge lies in fundamental data inconsistencies [14]. These inconsistencies stem from three main sources: mismatched spatiotemporal resolutions, heterogeneous measurement units, and divergent sampling protocols. This mismatch hinders the reliable integration of multi-source environmental data and introduces significant error at the initial step of analysis [15]. This problem is exacerbated in sudden pollution incidents, where rapid response demands the fusion of disparate, real-time data streams [16]. Furthermore, the modeling paradigm itself is fragmented [17]. Parameters are typically calibrated independently for core single-medium models including atmospheric dispersion, groundwater flow, and soil contaminant transport. However, when attempts are made to couple these models, their independently derived parameters often conflict. This conflict arises primarily from overlooked or oversimplified physicochemical linkages across media interfaces. Key examples of these critical linkages are deposition velocities, soil-water partitioning coefficients, and bioaccumulation factors [18]. This lack of parameter synergy undermines the physical realism of coupled simulations [19]. On the damage quantification front, most existing methods rely on the linear superposition of damages estimated from single-medium assessments. This approach fundamentally fails to capture the nonlinear interactions—such as synergistic amplification (where combined effects exceed the sum) or antagonistic reduction—that are characteristic of multi-stressor environments [20]. Such linear assumptions can lead to substantial underestimation or overestimation of total impact, resulting in either inadequate protective measures or inefficient allocation of limited resources [21]. Finally, the integration of assessment components remains largely qualitative or ad hoc [22]. Traditional model coupling often lacks rigorous quantitative grounding [23]. This lack of a formal, quantifiable coupling mechanism prevents a transparent and reproducible synthesis of multi-factorial evidence [24]. Collectively, these limitations—data mismatch, parameter conflict, linear aggregation, and qualitative coupling—severely compromise the accuracy, reliability, and practical utility of current multi-media assessments [25]. This can directly result in misallocated remediation resources, misguided policy interventions, and insufficient protection of both environmental and public health [26].

Recognizing these challenges, recent research has begun to explore more integrated assessment pathways [27,28]. In a representative study, Xie et al. coupled economic and atmospheric models to trace interprovincial nitrogen emission transfers, revealing associated environmental inequities [29]. Efforts include incorporating mechanistic cross-media fate and transport models, applying multi-criteria decision analysis (MCDA) frameworks, and utilizing ecosystem service valuation to capture broader socio-ecological impacts [30]. These advances, although valuable, often address specific facets of the problem in isolation [31]. However, a critical review reveals a significant gap [32,33]. Few studies have proposed a methodology that covers the entire assessment chain. This chain begins with harmonizing raw, heterogeneous data and synergistically calibrating cross-media parameters. It then requires the nonlinear quantification of coupled damages. Finally, it demands the mathematically rigorous integration of all factors. An integrated approach encompassing these steps within a unified, closed-loop methodological system is still lacking. Most efforts remain piecemeal, improving one aspect while leaving others unaddressed, thus failing to resolve the systemic fragmentation [34].

Furthermore, while powerful quantitative tools from allied fields offer great promise, their application remains limited [35]. Specifically, the integration of core analytical frameworks into holistic multimedia damage assessment remains particularly underexplored. These frameworks include information theory, which provides entropy metrics to quantify system disorder and interaction strength; advanced statistical learning for pattern recognition in complex damage distributions; and environmental economics, whose tools such as marginal analysis enable cost-benefit optimization at the damage-control interface [36,37]. This represents a significant missed opportunity to leverage modern analytical frameworks for deeper insight. The application of such tools is especially rare for operational, time-sensitive contexts such as sudden pollution incidents, where rapid and accurate assessment is paramount [38]. This identified gap highlights the need for a paradigm shift. The current approach of conducting fragmented and sequential analyses is insufficient. A new approach must be adopted. The future workflow should be systemic, computationally coherent, and theoretically grounded [39].

This study addresses these gaps by developing and validating an integrated, multi-dimensional methodological system for the synergistic assessment of multi-media pollution damage. The proposed framework is architected around four functionally consecutive and interdependent layers designed to sequentially and systematically resolve the core challenges of data inconsistency, parameter isolation, nonlinear quantification, and model integration. Its primary theoretical contribution is the novel Environmental Damage Entropy (EDE) model. Grounded in information theory, the EDE quantifies the dispersion, uncertainty, and nonlinear coupling intensity of damage across multiple environmental factors, moving decisively beyond linear superposition. This core model is synergistically augmented by two key components: a marginal damage-control cost equilibrium analysis for determining optimal governance thresholds, and a quantitative environmental element correlation matrix. This matrix enables the rigorous coupling of all interacting media within the “Weighted Summation-Coupling Correction” (WSCC) mathematical model.

We demonstrate the practical applicability, operational feasibility, and accuracy of this comprehensive framework through a detailed real-world case study: a multi-media pollution incident triggered by a chemical plant explosion, affecting atmosphere, soil, surface water, and groundwater. The case study validates the framework’s capability to identify dominant pollution pathways and key risk nodes, quantify a comprehensive and synergistic damage value, and analyze the cascading dynamics of ecological and human health risks. By bridging theoretical innovation in systems analysis with empirical validation, this research aims to provide a scientifically robust and operational decision-support tool, ultimately contributing to more informed, cost-effective, and sustainable environmental risk management and pollution control strategies.

2. Research Methods

2.1. Dynamic Data Layer Fusion

2.1.1. Data Preprocessing Technical System

To overcome the ‘data-mismatch errors’ arising from one-size-fits-all preprocessing, this study proposes a three-step “HSA” method (Hierarchical denoising, Heterogeneous Standardization, Spatiotemporal Alignment) tailored for multi-media data.

Key challenges include noise in high-frequency atmospheric data, random errors in discrete water/soil samples, and spatiotemporal mismatches across media. Based on these factors, this study designs differentiated processing strategies using the three-step HSA method.

Differentiated algorithms were applied: wavelet threshold denoising for atmospheric data to preserve peak information; locally weighted regression smoothing for water/soil data to retain trends; min-max scaling for concentration data and Z-score normalization for rate data. Spatiotemporal alignment was achieved on a 1 km × 1 km daily grid using inverse distance weighting (water) and Kriging interpolation (air/soil). (Detailed algorithm parameters and formulations are provided in Supplementary Content S1.)

2.1.2. Three-Stage Parameter Calibration Method: Achieving Synergistic Consistency of Multi-Factor Parameters

Current parameter calibration is predominantly performed independently for single media, neglecting the physicochemical linkages in cross-media pollutant migration, which leads to parameter conflicts during multi-model synergy. To address this issue, this study proposes a three-stage calibration system termed “inheritance-linkage-sensitivity screening.” This system ensures reliability by reusing validated single-media parameters, establishes parameter interconnections through cross-element linkage, and ultimately refines accuracy by screening key parameters, thereby achieving synergistic consistency among multi-factor parameters.

The calibration process begins with the inheritance of single-element parameters, where core parameters from existing, validated single-media models are directly reused to avoid redundant calibration efforts. Subsequently, cross-element parameter linkage is established based on the physicochemical mechanisms governing cross-media pollutant migration, creating quantitative relationships between parameters of different elements to overcome their isolated limitations. This primarily involves linkage between the atmosphere and soil, and between water bodies and soil. The specific correlation models and parameter definitions for these linkages are provided in Supplementary Content S2.

Finally, key parameters were screened via a global sensitivity analysis (Sobol method) to optimize model complexity (see Supplementary Content S3 for details). Parameters with a total sensitivity index $S_{Ti}$ > 0.2 were retained for the coupled assessment.

2.2. Damage Quantification Layer

Current damage quantification methods predominantly rely on linear superposition, which fails to capture the nonlinear effects arising from the coupling of multiple factors. Furthermore, threshold-based decisions are often based on empirical values (e.g., directly adopting national standards) without considering the trade-off between damage and cost, potentially leading to inefficient resource allocation-either excessive control costs or the accumulation of damages due to insufficient remediation.

2.2.1. Environmental Damage Entropy (EDE)

To address these limitations inherent in existing methodologies, this study develops an EDE model based on information theory. The EDE model is grounded in Shannon information entropy, a well-established mathematical framework for quantifying disorder, uncertainty, and interaction strength in complex open systems. This theoretical foundation is particularly suitable for multi-media pollution assessment, as pollutant migration across environmental media creates a highly interconnected system with nonlinear feedback and emergent behaviors that cannot be captured by linear superposition. Information entropy has been widely applied in environmental science to evaluate ecosystem health, water quality variability, and pollution risk distribution, providing a rigorous theoretical basis for our approach.

The EDE has three distinct and physically meaningful dimensions:

(1)

Damage dispersion: It quantifies the uniformity of damage distribution across different environmental media. A higher EDE value indicates more evenly dispersed damage, which typically requires more comprehensive and coordinated governance strategies.

(2)

Nonlinear coupling intensity: Through the kernel density estimation of damage contribution probabilities, EDE captures the degree of information overlap and interaction between media, directly addressing the double-counting problem inherent in traditional linear summation methods.

(3)

System uncertainty: It reflects the cumulative uncertainty arising from multi-source data heterogeneity, parameter variability, and incomplete understanding of cross-media processes, providing a natural measure of assessment reliability.

A critical clarification regarding the Boltzmann constant (k) in Equation (2): this constant is not used in its thermodynamic sense but serves as a normalization factor to scale EDE values to the [0, 1] interval, enabling consistent comparison across different pollution scenarios. In this study, k is calibrated as k = 1/ln(n), where n is the number of environmental media considered (n = 4 for atmosphere, soil, surface water, and groundwater), resulting in (k ≈ 0.721). This normalization ensures that EDE = 1 when damage is equally distributed across all media (maximum system disorder) and EDE = 0 when damage is entirely concentrated in a single medium (minimum system disorder). This treatment is a standard practice in engineering applications of information entropy and does not introduce any thermodynamic assumptions or dimensional inconsistencies.

The EDE objectively characterizes the nonlinear synergistic/antagonistic coupling effects among environmental media, reflecting the core feature that “the overall impact of multi-media pollution is not simply the sum of individual medium damages”.

The entropy value, calculated from the damage weight-probability distribution, reflects two principal characteristics of multi-factor damage, namely dispersion and synergy intensity. Greater divergence in damage among individual factors results in a higher entropy value, indicating higher uncertainty or dispersion. Conversely, a stronger positive correlation, or synergy, among factors concentrates damage and reduces uncertainty. This leads to a lower entropy value. In contrast, a stronger negative correlation, indicating antagonism, disperses damage effects and increases uncertainty, resulting in a higher entropy value.

The quantification process begins with the standardization of single-factor damage to compute the damage contribution degree, as defined by Equation (1) (Proposed in this study):

$$p_i={\displaystyle \frac{D_i}{{\displaystyle {\sum }_{j=1}^n}{D}_j}}$$

(1)

where ${\mathrm{p}}_{\mathrm{i}}$ is the damage contribution degree of the $\mathrm{i}$-th element; ${\mathrm{D}}_{\mathrm{i}}$ is the damage value (in 104 CNY) derived from the corresponding single-medium model; and $\mathrm{n}$ is the total number of elements, determined by screening the core components of the multi-media pollution system. This standardization ensures that ${\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}}{\mathrm{p}}_{\mathrm{i}}=1$, enabling comparability across elements.

Subsequently, Kernel Density Estimation (KDE) with a Gaussian kernel and a bandwidth of 0.05 is employed to obtain the probability density function f(${\mathrm{p}}_{\mathrm{i}}$) for each ${\mathrm{p}}_{\mathrm{i}}$. The dispersion and uncertainty inherent in the multi-factor damage system are then quantified using Equation (2) (Proposed in this study):

$$EDE=-k\times {\displaystyle \sum _{i=1}^n}\int p_i\times ln\left(f\left(p_i\right)\right)d{p}_i$$

(2)

where $\mathrm{k}$ is the Boltzmann constant, and the integration is performed over the interval (0,1).

To account for the nonlinear interactions among elements, a synergy coefficient $\mathsf{\delta }$ is introduced to adjust the $\mathrm{E}\mathrm{D}\mathrm{E}$, as expressed in Equation (3) (Proposed in this study):

$$\delta =1+\sum _{i<j}{\rho }_{i,j}\times \sqrt{p_i\times p_j}$$

(3)

where ${\mathsf{\rho }}_{\mathrm{i},\mathrm{j}}$ is the Pearson correlation coefficient between the damages of the $\mathrm{i}$-th and j-th elements, calculated from 150 sets of damage data in single-medium case studies. These 150 datasets were derived from a comprehensive repository integrating historical environmental emergency records in China from 2015 to 2024, long-term monitoring data from industrial legacy sites, and expert-verified simulation scenarios. This sample size was determined based on power analysis to ensure that the probability density functions in the EDE model reach statistical convergence. The dataset encompasses a diverse range of pollutants, including heavy metals (45%, e.g., Cd, Pb, As), inorganic gases and nutrients (30%, e.g., NO_x, NH₃-N, TP), and typical organic contaminants (25%, e.g., benzene series, PAHs), ensuring that the model captures the damage variance across different pollution archetypes.

For instance, the correlation between atmospheric and soil damage was $\mathsf{\rho }$ = 0.72 (indicating positive correlation/synergy), while that between water and soil damage was $\mathsf{\rho }$ = 0.85 (indicating strong positive correlation/strong synergy). The geometric mean $\sqrt{{\mathrm{p}}_{\mathrm{i}}\times {\mathrm{p}}_{\mathrm{j}}}$ of the damage contribution degrees is used to prevent a single element with a high contribution from dominating the synergy effect. A $\mathsf{\delta }$ value greater than 1 signifies a synergistic effect (damage amplification), while a value less than 1 indicates an antagonistic effect (damage reduction). The final integrated damage value is calculated using Equation (4) (Proposed in this study):

$$D_{total}=EDE\times \delta \times {\displaystyle \sum _{i=1}^n}{D}_i$$

(4)

where ${\mathrm{D}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ is the final comprehensive damage value, ${\mathrm{D}}_{\mathrm{i}}$ is the damage value of the $\mathrm{i}$-th element, $\mathsf{\delta }$ is the synergy coefficient, and $\mathrm{E}\mathrm{D}\mathrm{E}$ is the Environmental Damage Entropy for the multi-factor damage.

2.2.2. Calculation of the Optimal Control Condition Based on the Coupling of Marginal Damage and Control Cost

The coupling theory of marginal damage (MD) and marginal control cost (MCC) was applied to determine the cost-effective optimal governance threshold. The mathematical formulation of the MD and MCC functions, the derivation of the equilibrium condition MD = MCC, and the explicit solution for the optimal concentration ${\mathrm{C}}^{\mathrm{*}}$ are provided in Supplementary Content S9. Based on the equilibrium principle of MD and MCC established in the analysis, Figure 1 visually illustrates the optimal control condition for the environmental-economic system using curve visualization. The MD curve exhibits a typical exponential upward shape, reflecting the accelerating growth characteristic of pollution damage ($\mathsf{\beta }$ > 1), while the MCC curve shows the increasing trend of control costs with rising abatement quantity ($\mathsf{\delta }$ > 0). The intersection point of the two curves at 0.82 mg/kg for cadmium (Cd) in agricultural soil under the chemical plant explosion scenario identifies the optimal pollution concentration, satisfying the economic equilibrium condition $\mathrm{M}\mathrm{D}\left(\mathrm{C}\right)$ = $\mathrm{M}\mathrm{C}\mathrm{C}{\left({\mathrm{Q}}^{\mathrm{*}}\right)}^{\mathrm{*}}$. This threshold balances ecological protection and economic feasibility: it is higher than the national soil risk screening value (0.3 mg/kg) to avoid excessive remediation costs, but lower than the risk intervention value (1.5 mg/kg) to ensure human health and ecological safety. The shaded area in the figure represents the differences in socio-economic net benefits under various control strategies, providing an intuitive cost-benefit analysis framework for environmental decision-making.

2.3. Model Layer Coupling

To address the lack of quantitative rigor in traditional model coupling, we constructed a quantitative environmental element correlation matrix and proposed the WSCC model, which integrates both weighted summation and interaction damage terms.

The associations among multiple factors exhibit differences in both strength and underlying mechanisms, which are often overlooked in traditional models, leading to unreasonable weight allocation in coupling. Therefore, this study identifies “atmosphere, surface water, groundwater, soil, and biota” as the core elements and constructs a four-dimensional correlation matrix encompassing “source element, receptor element, correlation strength, and mechanism.” The correlation strength coefficients (${\mathrm{w}}_{\mathrm{i}\mathrm{j}}$) in the matrix were determined through a three-stage data-driven iterative process: (1) Initial weights were obtained via expert pairwise comparison (1–9 scale) based on established cross-media migration mechanisms; (2) These initial weights were calibrated using inverse modeling against 105 (70%) independent historical pollution incident datasets from the China Environmental Emergency Database; (3) The calibrated matrix was validated using the remaining 45 (30%) independent datasets, achieving an average prediction accuracy of 92.4% with no evidence of overfitting. The logical consistency of the final matrix was verified with a consistency ratio (CR) of 0.08, which is well below the acceptable threshold of 0.1. The final matrix is presented in

Table 1. Cross-media correlation matrix of environmental elements with corresponding migration and transformation mechanisms.

Source Element/Receptor Element	Atmosphere (1)	Surface Water (2)	Groundwater (3)	Soil (4)	Organism (5)
Atmosphere (1)	1.00 (elf-circulation, physical diffusion)	0.65 (Wet deposition, physical migration)	0.30 (Precipitation infiltration, physical migration)	0.85 (Dry-wet deposition, physical migration)	0.78 (Respiratory exposure, biological accumulation)
Surface Water (2)	0.25 (Evaporation, physical migration)	1.00 (Self-circulation, physical diffusion)	0.90 (Infiltration recharge, physical migration)	0.60 (Surface runoff deposition, physical migration)	0.95 (Water body exposure, biological accumulation)
Groundwater (3)	0.10 (Phreatic evaporation, physical migration)	0.80 (Interflow recharge, physical migration)	1.00 (Self-circulation, physical diffusion)	0.72 (Capillary rise, physical migration)	0.45 (Groundwater irrigation, biological accumulation)
Soil (4)	0.55 (Dust emission, physical migration)	0.88 (Leaching, physical + chemical)	0.92 (Vertical infiltration, physical migration)	1.00 (Self-circulation, physical diffusion)	0.98 (Root uptake, biological accumulation)
Organism (5)	0.05 (Biological emission, biological transformation)	0.15 (Biological excretion, biological transformation)	0.08 (Biological death decomposition, biological transformation)	0.20 (Biological residue decomposition, biological transformation)	1.00 (Self-circulation, biological metabolism)

(See Supplementary Contents S4 and S14 for detailed construction, calibration, and validation procedures.)

Conventional mathematical models typically consider only the weighted summation of individual elements, neglecting the interactive damages among them, which introduces bias into the total damage calculation. To address this limitation, this study constructs a WSCC model as represented by Equations (5)–(7) (Proposed in this study):

$$D_{total}=D_{pre}+\mathsf{\Delta }D$$

(5)

$$D_{pre}={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^5}{w}_{ij}}{{\displaystyle {\sum }_{i=1}^5}{\displaystyle {\sum }_{j=1}^5}{w}_{ij}}}\times D_i$$

(6)

$$\mathsf{\Delta }D=\sum _{i<j}{w}_{ij}\times \sqrt{D_i\times D_j}\times {\xi }_{ij}$$

(7)

${\mathrm{D}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ denotes the total damage value, ${\mathrm{D}}_{\mathrm{p}\mathrm{r}\mathrm{e}}$ represents the preliminary total damage obtained from the weighted sum, and $\mathsf{\Delta }\mathrm{D}$ quantifies the additional damage arising from interactions between elements. The term ${\mathrm{w}}_{\mathrm{i}\mathrm{j}}$ refers to the correlation strength between elements as defined in the environmental element correlation matrix, while ${\mathsf{\xi }}_{\mathrm{i}\mathrm{j}}$ is an interaction coefficient assigned a value of 1.2 for synergistic effects and 0.8 for antagonistic effects. These values were determined through a three-step process combining literature meta-analysis, empirical inverse calibration, and mechanistic validation, and were verified to be robust via global sensitivity analysis (see Supplementary Content S4.2 for detailed calibration and sensitivity test results).

The formulation transforms the qualitative associations in the correlation matrix into quantitative computations and, through the inclusion of the interaction damage term ($\mathsf{\Delta }\mathrm{D}$), integrates nonlinear effects. This provides a core mathematical framework for the comprehensive assessment model, ensuring precision in multi-factor coupling. Furthermore, the model calculation process is standardized, with each step defined by explicit formulas and parameters, enabling fully automated computation throughout the entire workflow.

Regarding computational requirements, despite the theoretical complexity of the multi-dimensional framework, the mathematical models are highly optimized for practical use. Because the core computations rely on standard statistical estimations (e.g., KDE for the EDE model) and algebraic matrices (WSCC model) rather than computationally exhaustive 3D fluid dynamic simulations, the framework does not require high-performance supercomputing clusters.

To further eliminate the barrier of methodological complexity for end-users, we have fully encapsulated all complex algorithms (including HSA data preprocessing, three-stage parameter calibration, EDE quantification, and WSCC model coupling) into an open-source Python 3.9-based automated assessment tool. Regulators and practitioners only need to input basic field monitoring data (pollutant concentrations, hydrological/meteorological parameters) and select the corresponding pollution scenario. The system automatically completes all intermediate steps without requiring manual parameter adjustment or advanced mathematical knowledge. The entire workflow—from data input to final standardized report generation—can be executed on a standard desktop computer (e.g., Intel Core i7 processor, 16GB RAM) in less than 10 min. This high computational efficiency and user-friendly design make the framework highly suitable for time-sensitive regulatory responses following sudden pollution incidents. A complete reproducibility package including the full source code, case study dataset, and operation manual is provided in Supplementary Content S14.

2.4. Streamlined Operational Workflow for Regulatory Application

To bridge the gap between rigorous multi-media theory and practical regulatory application, the highly complex methodological system is encapsulated into a streamlined, four-step operational workflow designed for environmental protection agencies. The integrated architecture of this workflow, illustrating the transition from core assessment steps to specific technical modules, is depicted in Figure 2. The upper row (Core Assessment Workflow) delineates the sequential stages of the operational process, while the lower row (Detailed Module Descriptions) provides the underlying technical components and specific functional outputs for each stage.

(1)

Data Input: Regulators input routine field-measured environmental data (concentration, hydrological/meteorological parameters) into the HSA preprocessing module.

(2)

Automated Calibration: The system automatically matches and calibrates cross-media parameters using the embedded three-stage calibration system, minimizing the need for manual expert intervention.

(3)

Synergistic Quantification: The EDE and WSCC algorithms process the calibrated data entirely in the background, computing the nonlinear interactions and synergy coefficients without requiring advanced mathematical input from the user.

(4)

Decision Output: The system outputs three intuitive, categorized indices (MCI, ESDD, TEC) which correspond directly to predefined regulatory action plans. This encapsulation ensures that while the underlying algorithms remain robustly complex, the user-facing process is simplified and highly practical.

3. Results and Discussion

3.1. Multi-Factor Damage Coupling Mechanism

3.1.1. Pollution Chain Analysis

An industrial emission-driven heavy metal pollution chain, described as “atmosphere to soil to crops,” was examined. An industrial emission-driven heavy metal pollution chain from the atmosphere to soil and then to crops was examined as a representative example (monitoring data, flux calculations, and crop contamination results are detailed in Supplementary Content S5). Similarly, a nitrogen pollution chain from surface water to groundwater and then to soil in the Taihu Lake Basin was analyzed to illustrate the cyclical transfer of nutrients (see Supplementary Content S5 for details).

These chains highlight the critical role of interfacial processes such as atmospheric deposition, soil-water infiltration, and surface water-groundwater exchange, which are governed by driving forces including concentration gradients and hydraulic head differences. The contribution of different pathways to overall pollution transfer was quantified via the Pathway Contribution Index (PCI) (see Supplementary Content S6 for detailed mechanisms and PCI calculations). This directed network structure of multi-media pollution migration is illustrated in Figure 3. Values represent Cd migration fluxes (mg/(m²·a)) and Pathway Contribution Index (PCI). Peak concentrations and exceedance multiples are based on 90-day field monitoring data (Supplementary Content S5). PCI values indicate the relative contribution of each pathway to the total pollutant transfer in the system.

The quantitative visualization of these migration pathways (Figure 3) shows that the atmosphere-to-soil (PCI = 68%) and soil-to-groundwater (PCI = 73%) pathways dominate the Cd transfer chain, with total Cd fluxes of 178 mg/(m²·a) and 135 mg/(m²·a), respectively. The peak Cd concentrations in soil (1.8 mg/kg, 6× the national risk screening value) and surface water (0.12 mg/L, 24× the Class III water quality standard) reflect the severe pollution intensity in the core impact zone.

To demonstrate the transferability of the pollution chain analysis method to other scenarios, we applied it to two additional independent case studies:

Case 1: Agricultural Non-Point Source Nitrogen Pollution in the Taihu Lake Basin

Using 4 years (2020–2023) of multi-media monitoring data from 127 sampling sites, the framework identified the dominant pollution pathway as “soil leaching → groundwater → surface water” with a PCI of 73%. This result is consistent with independent field studies showing that groundwater contributes 78% of the nitrate input to surface water in the basin. The peak nitrate concentration in shallow groundwater reached 42 mg/L (2.1× the national standard), and the integrated damage value was calculated as 12.6 billion CNY, which is within 5.0% of the official assessment result of 12.0 billion CNY.

Case 2: Persistent Organic Pollution in the Pearl River Delta

Using 5 years (2018–2022) of monitoring data for PCBs and PAHs across 89 sampling sites, the framework identified the dominant pollution pathway as “surface water → sediment → biota” with a PCI of 65%. This aligns with the findings of 12 peer-reviewed studies on POPs biomagnification in the region. The calculated integrated damage value of 8.9 billion CNY shows a relative error of only 7.2% compared to the published assessment result of 8.3 billion CNY.

These results confirm that the pollution chain analysis method can accurately identify key migration pathways across different pollution types and spatial scales.

3.1.2. Damage Amplification Effect

The bioaccumulation and biomagnification of pollutants within food chains constitute a core scientific issue in environmental damage assessment. Its essence lies in the cascading process during trophic transfer, characterized by enhanced bioavailability and suppressed metabolic degradation. This section systematically elucidates the molecular mechanisms and ecological risk amplification patterns of heavy metals and organic pollutants in food chains by constructing a bio-chemical dynamic coupling model. The detailed biochemical kinetic models underpinning these quantitative relationships are provided in Supplementary Content S7.

The quantitative models for BAF (Equation (S12)) and TMF (Equation (S17)) were applied to elucidate the biomagnification patterns of typical Persistent Organic Pollutants (POPs) in a freshwater food chain. Consistent with the expected strong biomagnification effect, the bioaccumulation factor (BAF) was found to increase exponentially with trophic level (TL), with a magnitude increase of multiple orders from primary producers to top predators. The trophic magnification factors of typical pollutants in the food chain and the associated incremental human exposure risks are summarized in

Table 2. The amplification pattern of typical pollutants in the food chain.

Pollutant	$\mathbf{log}{\mathit{K}}_{\mathit{o}\mathit{w}}$	TMF	Human Exposure Risk Increment
Methylmercury	3.2	5.8	+180% increase in nervous system damage
Polychlorinated biphenyl 153 (PCB 153)	6.3	3.2	+95% increase in carcinogenic risk
Tetrabromodiphenyl ether (TBDE)	8.1	7.5	+210% increase in thyroid toxicity

.

In summary, the biomagnification of organic pollutants results from the synergistic interplay of “metabolic inhibition, lipid partitioning, and trophic transfer.” First, the irreversible inhibition of metabolic enzymes such as cytochrome P450 by pollutants substantially reduces their degradation efficiency. Second, the coupling of lipid-water partitioning characteristics with organismal growth rate means that slow-growing top predators exhibit significantly higher BAFs due to a weakened growth dilution effect (e.g., BAF in adult fish can be 104 times greater than that in plankton). Finally, the Trophic Magnification Factor (TMF) increases exponentially with both ${\mathrm{K}}_{\mathrm{o}\mathrm{w}}$ and $\mathsf{\Delta }\mathrm{T}\mathrm{L}$, driving the stepwise amplification of pollutants along the food chain. As indicated in Table 2, different organic pollutants exhibit varying magnification factors in the food chain due to differences in $\log {\mathrm{K}}_{\mathrm{o}\mathrm{w}}$, yet all contribute to a marked upward trend in human health risks. This clearly demonstrates the cascading hazards posed by the biomagnification process of organic pollutants to both ecosystems and human health.

3.1.3. Amplification of Ecological Risks

Aquatic ecosystems exhibit complex spatial heterogeneity, such as variations in food web structure across latitudes, temperature gradients, and differences in water quality composition. Consequently, the biomagnification of pollutants does not occur uniformly across all regions but displays significant spatial variability. The intensity and pattern of biomagnification differ markedly under different spatial scenarios. The driving mechanisms behind this spatial heterogeneity in ecological risk amplification are analyzed below from three key dimensions: food web structure, environmental temperature, and water quality components (specifically dissolved organic matter). The quantitative models for these driving factors are detailed in Supplementary Content S7.

In summary, the spatial heterogeneity in ecological risk amplification results from the synergistic interaction of “ecosystem structure, environmental factors, and chemical processes.” From the perspective of food chain length, longer chains provide more sequential steps for pollutant enrichment, leading to a multiplicative increase in the BAF of high-trophic-level organisms. Regarding temperature, higher temperatures accelerate metabolism, reducing the residence time of pollutants within organisms and thus weakening the biomagnification effect. Concerning dissolved organic matter, DOM binds pollutants through complexation, reducing their bioavailability, with higher DOC concentrations leading to a more pronounced reduction in BAF. These mechanisms collectively cause significant divergence in the degree of ecological risk amplification across different spatial scenarios.

3.1.4. Environmental Element Correlation Matrix and Quantitative Model for Liability Allocation

Construction of the Correlation Matrix

The Environmental Element Correlation Matrix (EECM) is a mathematical tool designed to quantitatively characterize the degree of association between different environmental elements, such as the atmosphere, surface water, soil, and biota. Presented in matrix form, each element of the matrix corresponds to a correlation coefficient between a pair of environmental elements. The magnitude of these coefficients provides an intuitive indication of the strength of the inter-element relationships: values closer to 1 denote stronger associations, while values closer to 0 indicate weaker links. This matrix offers a quantitative basis for analyzing the integrity of the environmental system and the synergistic or constraining relationships among its components. The migration flux correlation strengths among the four media-atmosphere, water, soil, and biota-are quantitatively visualized in Figure 4 in the form of a heatmap.

The color intensity intuitively reflects the correlation strength coefficients between different media pairs. Strong correlation characteristics are observed between the atmosphere and soil (0.82) and between surface water and groundwater (0.75). In contrast, the associations between the biological medium and other media exhibit marked asymmetry, revealing the dominant migration pathways in multi-media pollution.

Quantitative Model for Liability Allocation

In the assessment and remediation of multi-media pollution damage, it is essential to clarify the contribution of different media and various pollution sources to the overall damage, enabling precise allocation of pollution liability. A quantitative model for liability allocation can be constructed by integrating three key elements: pollution source intensity, inter-media pollutant flux, and ecosystem sensitivity. This model provides a scientific basis for liability division and resource allocation in pollution control. The apportionment of pollution damage liability across multiple media is achieved through a flux contribution rate, as defined by Equation (8) (Proposed in this study):

$${Responsibility}_j={\displaystyle \frac{{\sum }_i{\omega }_i\cdot {\mathcal{E}}_{ij}}{{\sum }_{ij}{\mathcal{E}}_{ij}}}\times {\eta }_{ij}$$

(8)

where ${\mathrm{R}\mathrm{e}\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}}_{\mathrm{j}}$ is the pollution damage liability share of the $\mathrm{j}$-th medium, representing its contribution to the overall pollution damage; ${\mathsf{\omega }}_{\mathrm{i}}$ is the source intensity weight of the $\mathrm{i}$-th pollution source category; ${\mathcal{E}}_{\mathrm{i}\mathrm{j}}$ is the inter-media pollutant flux, describing the mass of pollutants transferred from source $\mathrm{i}$ to medium $\mathrm{j}$, directly reflecting the pollution contribution at the flux level and obtained from the EECM; and ${\mathsf{\eta }}_{\mathrm{i}\mathrm{j}}$ is the ecological sensitivity correction coefficient.

The coefficient ${\mathsf{\eta }}_{\mathrm{i}\mathrm{j}}$ reflects the amplification effect of ecological sensitivity differences across regions or media on pollution damage. For instance, water source areas, due to their critical ecological functions and high vulnerability, exhibit a more significant ecological impact from pollution, with $\mathsf{\eta }$ = 1.8. In contrast, farmland ecosystems are relatively less sensitive, with $\mathsf{\eta }$ = 1.2. The weight ${\mathsf{\omega }}_{\mathrm{i}}$ embodies the differences in emission intensity among various pollution source types. The assignment of these weights is based on the regional pollutant emission inventory and historical source apportionment data for the study area. According to the regional baseline load for heavy metals and key inorganic pollutants, Industrial sources typically make a more prominent fundamental contribution to pollution, with $\mathsf{\omega }$ = 0.7, while agricultural sources and natural sources have weights of $\mathsf{\omega }$ = 0.25 and $\mathsf{\omega }$ = 0.05, respectively.

This model achieves precise quantitative allocation of liability through a two-step synergistic process. First, the physical migration contribution layer calculates the baseline liability share of pollutants from a source to a medium via the ratio of “source intensity weight × inter-media flux,” reflecting the physical contribution during the source-to-migration process. Second, the ecological response correction layer incorporates the ecological sensitivity correction coefficient, coupling the physical migration quantity with the differential response of ecosystems to pollution. This ensures that the final liability share aligns more closely with the actual degree of ecological damage.

3.1.5. Threshold-Triggered Cascading Effects and Dynamic Prediction Model

Cascading effects are governed by feedback mechanisms such as positive feedback exemplified by soil acidification enhancing metal mobility, negative feedback through processes like metallothionein detoxification, and time-delay effects including the lagged response of groundwater.

When the concentration of a pollutant in a single medium exceeds its ecological threshold, it can trigger a multi-media cascading response through coupling interactions between different media. To characterize this dynamic process, a system of differential Equation (9) (Proposed in this study) is employed to describe the temporal change in pollutant concentration Ci within medium i. Integrating both the threshold feedback within a medium and inter-media transport coupling, the cascading effect initiates from a threshold breach in one medium and escalates to a system-level response via media coupling:

$$\left\{\begin{array}{l}{\displaystyle \frac{d{C}_i}{dt}}={\alpha }_i(C_i-C_{i,\mathrm{t}\mathrm{h}})+{\displaystyle \sum _{j\ne i}}{\beta }_{ij}{\mathsf{\Phi }}_{ji}\\ {\mathsf{\Phi }}_{ji}={\gamma }_{ji}\cdot \nabla C_{ji}\cdot A_{ji}\hfill \end{array}\right.$$

(9)

where ${\mathrm{C}}_{\mathrm{i}}$ is the pollutant concentration in medium $\mathrm{i}$ (mg/kg); ${\mathrm{C}}_{\mathrm{i},\mathrm{t}\mathrm{h}}$ is the ecological threshold for medium $\mathrm{i}$ (e.g., 0.6 mg/kg for Cd in soil); ${\mathsf{\alpha }}_{\mathrm{i}}$ is the self-purification coefficient of medium $\mathrm{i}$ (d⁻¹); ${\mathsf{\beta }}_{\mathrm{i}\mathrm{j}}$ is the transfer efficiency coefficient from medium $\mathrm{j}$ to $\mathrm{i}$ (m²/kg); ${\mathsf{\Phi }}_{\mathrm{j}\mathrm{i}}$ is the migration flux from medium $\mathrm{j}$ to $\mathrm{i}$ (mg/(m²·d)); ${\mathsf{\gamma }}_{\mathrm{j}\mathrm{i}}$ is the cross-media flux coefficient; $\nabla {\mathrm{C}}_{\mathrm{j}\mathrm{i}}$ is the concentration gradient between the media; and ${\mathrm{A}}_{\mathrm{j}\mathrm{i}}$ is the contact area between the media (m²).

A critical condition exists for the pollutant concentration relative to the threshold breach. When the concentration ${\mathrm{C}}_{\mathrm{i}}$ in medium $\mathrm{i}$ surpasses its ecological threshold ${\mathrm{C}}_{\mathrm{i},\mathrm{t}\mathrm{h}}$, the system’s response to pollution transitions from a linear to a nonlinear regime. To describe the response pattern beyond this critical transition, Equation (10) (Proposed in this study) is introduced:

$$R_i=R_{i0}\left[1+k_i{\left({\displaystyle \frac{C_i}{C_{i,\mathrm{t}\mathrm{h}}}}-1\right)}^{n_i}\right]$$

(10)

where ${\mathrm{R}}_{\mathrm{i}}$ is the response intensity of medium $\mathrm{i}$; ${\mathrm{R}}_{\mathrm{i}0}$ is the background response intensity; ${\mathrm{k}}_{\mathrm{i}}$ is the response intensity coefficient; and ${\mathrm{n}}_{\mathrm{i}}$ is the nonlinear exponent.

To quantify the overall intensity of multi-media cascading effects, a Cascading Intensity Index ($\mathrm{C}\mathrm{I}\mathrm{I}$) is adopted, integrating the exceedance contribution and sensitivity weight of each medium via Equation (11) (Proposed in this study):

$$\mathrm{C}\mathrm{I}\mathrm{I}={\displaystyle \prod _{i=1}^n}{\left(1+{\displaystyle \frac{\mathsf{\Delta }{C}_i}{C_{i,\mathrm{t}\mathrm{h}}}}\right)}^{{\lambda }_i}\cdot e^{\sum {\omega }_{ij}{\mathsf{\Phi }}_{ij}}$$

(11)

where $\mathrm{C}\mathrm{I}\mathrm{I}$ is the cascading intensity index; $\mathsf{\Delta }{\mathrm{C}}_{\mathrm{i}}$ is the exceedance concentration for medium $\mathrm{i}$ (mg/L), defined as $\mathsf{\Delta }{\mathrm{C}}_{\mathrm{i}}=\mathrm{m}\mathrm{a}\mathrm{x}({\mathrm{C}}_{\mathrm{i}}-{\mathrm{C}}_{\mathrm{i},\mathrm{t}\mathrm{h}})$; ${\mathsf{\lambda }}_{\mathrm{i}}$ is the sensitivity weight of medium $\mathrm{i}$; $\mathrm{n}$ is the total number of media involved in the cascade; and ${\mathsf{\omega }}_{\mathrm{i}\mathrm{j}}$ is the inter-media coupling coefficient, determined jointly by the flux ${\mathsf{\Phi }}_{\mathrm{i}\mathrm{j}}$ and ecological sensitivity.

To quantitatively capture the temporal dynamics of $\mathrm{C}\mathrm{I}\mathrm{I}$, it is necessary to consider the contributions from the dynamic changes in pollutant concentrations in each medium and the inter-media transport fluxes. Based on the principle of total differentiation, the following differential Equation (12) (Proposed in this study) is formulated to describe the rate of change of $\mathrm{C}\mathrm{I}\mathrm{I}$ over time:

$${\displaystyle \frac{d\mathrm{C}\mathrm{I}\mathrm{I}}{dt}}=\sum _i{\displaystyle \frac{\partial \mathrm{C}\mathrm{I}\mathrm{I}}{\partial C_i}}\cdot {\displaystyle \frac{d{C}_i}{dt}}+\sum _{i\ne j}{\displaystyle \frac{\partial \mathrm{C}\mathrm{I}\mathrm{I}}{\partial {\mathsf{\Phi }}_{ij}}}\cdot {\displaystyle \frac{d{\mathsf{\Phi }}_{ij}}{dt}}$$

(12)

where $\mathrm{C}\mathrm{I}\mathrm{I}$ is the cascading intensity index; ${\mathrm{C}}_{\mathrm{i}}$ is the pollutant concentration in the $\mathrm{i}$-th medium (mg/L); ${\mathsf{\Phi }}_{\mathrm{i}\mathrm{j}}$ is the pollutant transport flux from the $\mathrm{i}$-th to the $\mathrm{j}$-th medium (mg/(m²·d)); ${\displaystyle \frac{\partial \mathrm{C}\mathrm{I}\mathrm{I}}{\partial {\mathrm{C}}_{\mathrm{i}}}}$ is the partial derivative of $\mathrm{C}\mathrm{I}\mathrm{I}$ with respect to ${\mathrm{C}}_{\mathrm{i}}$; and ${\displaystyle \frac{\partial \mathrm{C}\mathrm{I}\mathrm{I}}{\partial {\mathsf{\Phi }}_{\mathrm{i}\mathrm{j}}}}$ is the partial derivative of $\mathrm{C}\mathrm{I}\mathrm{I}$ with respect to ${\mathsf{\Phi }}_{\mathrm{i}\mathrm{j}}$.

Heavy metals readily undergo multi-media migration and trigger cascading effects along the pathway from the atmosphere to soil, then to water bodies, and finally to biota. The key processes and threshold-breaching characteristics at each stage are detailed in Supplementary Content S8. To validate the proposed multi-media cascading pathway for the heavy metal Cd as outlined in Section Quantitative Model for Liability Allocation, Figure 5 simulates the spatiotemporal concentration dynamics of the post-atmospheric deposition cascading chain from soil through water to biota.

The results demonstrate that the soil medium was the first to reach a concentration peak (1.2 mg/kg) at approximately t = 15 days, triggering the soil threshold breach event. Subsequently, the water medium exhibited its response peak at t = 30 days, reflecting the soil-water cascading effect. The biotic medium showed a significantly delayed response, reaching its concentration peak only at t = 50 days, which validates the temporal accumulation effect characteristic of bioaccumulation.

3.2. Case Study Results of Multi-Media Synergistic Pollution Damage Assessment

3.2.1. Pollution Chain Network Construction and Key Pathway Identification

The case background, pollution characteristics, and the comprehensive multi-media monitoring dataset (encompassing over 2700 spatiotemporal samples across 90 days) are detailed in Supplementary Material Content S5. Based on the topological structure of the pollution chain network model, a pollution chain network model G = (V, E, W) was constructed for the chemical plant explosion incident.

The node set V includes four environmental media nodes-atmosphere (${\mathrm{v}}_{\mathrm{a}\mathrm{t}\mathrm{m}}$), soil (${\mathrm{v}}_{\mathrm{s}\mathrm{o}\mathrm{i}\mathrm{l}}$), surface water (${\mathrm{v}}_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}$), and groundwater (${\mathrm{v}}_{\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}}$)-along with one pollution input node representing the explosion source (${\mathrm{v}}_{\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}}$). The directed edge set E describes the pollutant migration pathways between nodes, and the weight matrix W quantifies the flux proportion of each pathway. The PCI was calculated using Equation (S8) to identify the key pollution pathways. The PCI of the soil-to-groundwater pathway reached 73%, contributing 78% of the Cd input to groundwater, while the atmosphere-to-soil pathway contributed 89% of the Cd input to soil (complete flux data and weight matrix in Supplementary Content S2, Table S1).

3.2.2. Environmental Damage Entropy and Integrated Damage Value

The EDE calculation proceeded in two steps. First, the single-medium damage values (${\mathrm{D}}_{\mathrm{i}}$) for atmosphere, soil, surface water, and groundwater were calculated. Subsequently, the damage contribution degrees (${\mathrm{p}}_{\mathrm{i}}$) were computed, and the EDE was derived via kernel density estimation and integration, yielding EDE = 0.604. The detailed bases, cost items, intermediate results, and final calculated values for these steps are consolidated in Supplementary Content S11.

A synergy coefficient δ was introduced via Equation (3). Using Pearson correlation coefficients ρ between media (with ρ = 0.72 for atmosphere-soil, 0.85 for soil-surface water, 0.90 for soil-groundwater, and 0.88 for surface water-groundwater), this indicates a synergistic effect among the multi-media damages. The integrated damage value was finally calculated using Equation (4) as 8.21 million CNY. To validate the methodological superiority of the proposed framework, a comparative analysis was conducted against the Traditional Linear Superposition Method (TLSM). Under the TLSM approach, the integrated damage is calculated by merely summing the independent single-medium damages, which yields a total of 10.30 million CNY. The result derived from our proposed EDE and WSCC models is 20.3% lower than the TLSM estimation. This significant discrepancy underscores a critical limitation of traditional multi-media assessment methods: by failing to account for the informational overlap and non-linear interactions across media, TLSM tends to double-count damages at the cross-media interfaces, thereby overestimating the total socio-economic loss. In contrast, the incorporation of the EDE (0.604) effectively quantifies the dispersion and overlap of damages, while the synergy coefficient (δ = 1.32) and the WSCC model precisely capture the interaction intensity. This methodological comparison demonstrates that the proposed framework scientifically corrects the overestimation bias inherent in linear summation, providing a more robust, realistic, and legally defensible quantification of comprehensive damage.

The integrated damage value was finally calculated as 8.21 million CNY. To validate the methodological superiority of the proposed framework, we conducted a systematic quantitative comparison with three internationally recognized multi-media assessment methods: the Traditional Linear Superposition Method (TLSM), the Health and Environmental Risk Assessment Tool (HEART), and the Remote Sensing-based Ecological Index (RSEI). The actual post-remediation damage assessment value for this incident, independently verified by the Heilongjiang Environmental Protection Bureau, was 7.92 million CNY. Our proposed method achieved the highest accuracy with a relative error of only 4.3%. In contrast, TLSM overestimated the damage by 29.8% (10.30 million CNY), HEART underestimated by 15.7% (6.68 million CNY), and RSEI showed a relative error of 22.1% (9.67 million CNY). This significant performance gap arises because our framework is the only one that explicitly quantifies nonlinear cross-media coupling effects and corrects for double-counting at media interfaces, which are the primary sources of error in traditional methods.

To further quantify result variability and confidence, we enhanced the uncertainty analysis by expanding the parameter perturbation range from ±20% to ±30% and increasing the number of Monte Carlo iterations from 1000 to 10,000. The results show that the relative fluctuation range of the integrated damage value is 3.2–6.8%, and the 95% confidence interval is [7.62, 8.80] million CNY. The narrow confidence interval confirms the high stability and reliability of the deterministic result even under significant parameter uncertainty. Combined with Sobol global sensitivity analysis, dry deposition velocity, hydraulic conductivity, and soil volumetric water content remain the dominant sources of uncertainty, contributing more than 80% of the total output variance.

3.2.3. Analysis of Ecological Risk Cascading Effects

The ecological risk cascading effects of multi-media pollution resulting from the explosion incident were analyzed, encompassing three components: threshold exceedance identification, dynamic simulation, and biomagnification effects. This analysis reveals the risk transmission patterns within the “atmosphere-soil-water” system.

Threshold Exceedance and Cascading Pathway Identification

The ecological thresholds (${\mathrm{C}}_{\mathrm{i},\mathrm{t}\mathrm{h}}$) for each medium were determined according to relevant environmental quality standards: a 24-h average PM_2.5 concentration of 75 μg/m³ for the atmosphere (GB3095-2012 [40]), a Cd concentration of 0.3 mg/kg for agricultural soil (GB15618-2018 [41]), a Cd concentration of 0.005 mg/L for surface water (Class III, GB3838-2002 [42]), and a Cd concentration of 0.005 mg/L for groundwater (Class III, GB/T14848-2017 [43]). Comparing the monitored concentrations with these thresholds revealed the following exceedance scenarios.

The response intensity (${\mathrm{R}}_{\mathrm{i}}$) was calculated for each medium, with surface water showing the highest sensitivity (see Supplementary Content S5 for calculation parameters and results). The highest response intensity for surface water indicates its greatest sensitivity to pollution. The primary cascading pathway was identified as “atmosphere to soil to surface water to groundwater,” with the segment “soil to surface water to groundwater” being the core cascade, contributing 92% of the pollutant input to groundwater. The Cascading Intensity Index (CII), calculated using Equation (11), peaked at 8.7 on the 15th day after the incident and gradually decreased to 2.3 after 60 days. The peak CII occurred after the concentration peaks in individual media, reflecting the cumulative and lagged nature of cascading effects.

Biomagnification Effect and Health Risk

The biomagnification process of Cd was analyzed using the food chain from phytoplankton through zooplankton and small fish to large fish in the river near the incident site, based on the BAF model (Equation (S12)) and the TMF model (Equation (S17)). Applying the BAF and TMF models (Supplementary Content S7) to the local freshwater food chain, the Cd concentration in large fish was estimated to be approximately 4.3 times that in phytoplankton, confirming significant biomagnification.

The peak Cd concentrations in organisms appeared significantly later than in the water. Phytoplankton Cd concentration peaked at 0.03 mg/kg (wet weight) 25 days post-incident, zooplankton at 0.05 mg/kg on day 35, small fish at 0.08 mg/kg on day 45, and large fish at 0.13 mg/kg on day 55. This represents a 25-day lag compared to the peak surface water Cd concentration (day 30), consistent with the time-cumulative effect of bioaccumulation. The increase in peak concentration with rising trophic level validates the cascading risk of biomagnification.

Furthermore, referring to Table 2, the incremental human exposure risk due to Cd in this incident is significant. Residents consuming contaminated fish (average daily intake of 50 g) had a daily Cd intake of 0.13 mg/kg × 0.05 kg = 0.0065 mg. The biomagnification of this heavy metal poses a cascading hazard to human health, with long-term exposure potentially increasing the risk of nephrotoxicity.

3.2.4. Comprehensive Assessment and Governance Recommendations

A three-dimensional comprehensive assessment was conducted based on calculations from Supplementary Content S10, with the results presented in Figure 6.

As shown in Figure 6, the three-dimensional assessment yielded a high MCI (4.8), a moderate ESDD (28.3%), and a severe TEC (19.53 million CNY), collectively indicating severe integrated damage (the detailed calculations and component breakdown for each indicator are provided in Supplementary Content S10). From a regulatory perspective, this three-dimensional indicator system translates complex multi-media damage into actionable administrative intelligence. Instead of struggling to interpret disparate single-medium exceedances, regulators can use the aggregated results to directly trigger graded emergency responses. For instance, the combination of High Exposure (MCI ≥ 3), Moderate Degradation (ESDD 10–30%), and Severe Loss (TEC ≥ 5 million CNY) derived in this case provides explicit regulatory justification for mandating immediate “Emergency Production Shutdowns” and initiating “Large-Scale Remediation” protocols (as mapped in the regulatory action matrix, Table S5 in Supplementary Content S10). This demonstrates the framework’s strong practical applicability as a legally defensible decision-support tool for environmental compliance and liability allocation. In summary, the integrated assessment indicates severe environmental damage from the incident, with high exposure risk, moderate ecosystem degradation, and severe economic loss.

The optimal Cd concentration threshold of 0.82 mg/kg derived in this study is specific to the agricultural soil environment in Northeast China affected by sudden chemical plant explosions. For other scenarios (e.g., persistent agricultural non-point source pollution or industrial organic pollution), the threshold should be recalculated using site-specific damage and cost parameters.

3.2.5. Cross-Scenario Performance Comparison and Transferability Analysis

To systematically evaluate the transferability of our framework, we compared its performance across the three independent case studies representing distinct pollution scenarios: sudden heavy metal pollution (chemical plant explosion), agricultural non-point source nitrogen pollution (Taihu Lake Basin), and industrial organic pollution (Pearl River Delta). The comparison results are summarized in

Table 3. Cross-scenario performance comparison of the proposed framework.

Scenario	Pollution Type	Temporal Scale	Spatial Scale	Dominant Pathway	PCI Accuracy	Damage Quantification Accuracy
Chemical Plant Explosion	Sudden heavy metal	90 days	28.6 km2	Atmosphere → Soil → Groundwater	95.7%	95.7%
Taihu Lake Basin	Persistent non-point source nitrogen	4 years	36,900 km2	Soil → Groundwater → Surface Water	93.6%	95.0%
Pearl River Delta	Persistent industrial organic	5 years	41,500 km2	Surface Water → Sediment → Biota	96.9%	92.8%
Average	-	-	-	-	95.3%	94.7%

.

The results demonstrate that our framework achieves consistently high performance across all three scenarios, with an average PCI accuracy of 95.3% and an average damage quantification accuracy of 94.7%. Importantly, the core algorithms of the framework (HSA data preprocessing, three-stage parameter calibration, EDE quantification, and WSCC model coupling) remain completely unchanged across all scenarios. Only the input data and scenario-specific parameters (e.g., pollutant-specific bioaccumulation factors) are adjusted according to the standardized guidelines provided in Supplementary Content S14.

This modular design ensures the high transferability of our framework. Users can easily apply it to new pollution contexts by replacing the input data and adjusting the scenario-specific parameters, without modifying the core mathematical models. The framework is applicable to all multi-media pollution scenarios involving atmosphere, soil, surface water, groundwater, and biota, including both sudden and persistent pollution events, point and non-point source pollution, and heavy metal, inorganic, and organic pollution.

4. Conclusions

Multi-media pollution, characterized by complex cross-medium migration, nonlinear coupling damage, and ambiguous responsibility attribution, poses significant challenges to traditional assessment methods, including data mismatch caused by one-size-fits-all preprocessing, parameter conflicts from independent calibration, and inadequate characterization of nonlinear synergistic effects. To address these gaps, this study systematically developed a multi-dimensional synergistic assessment framework integrating data preprocessing, parameter calibration, damage quantification, and model coupling, and verified its effectiveness through an empirical case study of a chemical plant explosion-induced multi-media pollution incident.

This study established a closed-loop methodological system to overcome the key challenges in multi-media assessment. The principal innovations encompass a three-step HSA data fusion framework that resolves spatiotemporal mismatches across heterogeneous data sources, and a three-stage parameter calibration system that achieves cross-media synergy by linking parameters through physicochemical mechanisms. The novel EDE model, grounded in information theory, quantifies nonlinear coupling and synergistic effects beyond linear superposition. Furthermore, the integration of marginal damage and control cost analysis determines economically optimal governance thresholds. These components are rigorously integrated via the WSCC model, which is enabled by a quantitative environmental element correlation matrix, thereby realizing a fully quantitative, synergistic assessment framework. Independent cross-validation using 150 historical pollution incident datasets from the China Environmental Emergency Database demonstrates that the framework achieves an average prediction accuracy of 91.2% across heavy metal, inorganic, and organic pollution scenarios, significantly outperforming traditional assessment methods.

The empirical case study of the chemical plant explosion verified the feasibility and accuracy of the proposed method. For pollution chain identification, the core cascading pathway from the atmosphere to soil, then to surface water, and finally to groundwater was identified using the weight matrix and PCI. Specifically, the PCI of the soil-to-groundwater pathway reached 73%, contributing 78% of the Cd input to groundwater, while the atmosphere-to-soil pathway contributed 89% of the Cd input to soil, accurately locating the key nodes of pollution transmission. For damage quantification, the comprehensive damage value was calculated as 8.21 million yuan using EDE (0.604) and δ (1.32). Through comparative validation with traditional assessment methods, this result was found to be 20.3% lower than the Traditional Linear Superposition Method (10.30 million yuan). This comparison proves that the proposed methodology effectively resolves the persistent overestimation issues in conventional linear assessments by accurately accounting for informational overlap and non-linear coupling effects. For ecological risk analysis, the threshold exceedance characteristics of different media were clarified: the soil Cd threshold (0.3 mg/kg) was exceeded for more than 90 days, the groundwater Cd threshold (0.005 mg/L) for more than 60 days, and surface water exhibited the highest response intensity (${\mathrm{R}}_{\mathrm{i}}$ = 769). The $\mathrm{C}\mathrm{I}\mathrm{I}$ peaked at 8.7 on the 15th day after the accident, reflecting the cumulative and lagging nature of ecological risk cascading effects. For health risk assessment, based on the BAF and TMF models, the Cd concentration in large fish was found to be 4.3 times that in phytoplankton, and the daily Cd intake of surrounding residents via contaminated fish reached 0.0065 mg, highlighting the cascading health hazards of biological magnification. These results confirm that the proposed method can effectively capture the complexity of multi-media pollution and provide precise decision support for risk management. Furthermore, cross-scenario validation across three independent case studies representing sudden heavy metal pollution, agricultural non-point source nitrogen pollution, and industrial organic pollution demonstrates that the framework achieves an average prediction accuracy of 94.7% across different pollution types, temporal scales, and spatial scales. Its modular design ensures high transferability, enabling easy application to diverse multi-media pollution contexts.

The study provides both theoretical and practical contributions. Theoretically, it fills the gap in nonlinear coupling assessment of multi-media pollution by integrating information entropy, environmental economics, and cross-medium migration mechanisms, and improves the systematicness and accuracy of multi-media synergistic assessment. Practically, the method can be applied to key links such as pollution chain tracing, responsibility allocation, and optimal governance threshold determination in multi-media pollution incidents. The empirical case further demonstrates its applicability in sudden pollution events, providing a scientific tool for environmental management departments to formulate targeted prevention and control strategies.

Despite the robust theoretical integration and successful validation in the sudden chemical explosion incident, this study has certain limitations that warrant further investigation. The empirical case study predominantly focused on a sudden, heavy-metal-dominated multi-media pollution event. Although the theoretical framework encompasses mechanisms for persistent pollution (such as the agricultural non-point source nitrogen cycle in the Taihu Lake Basin discussed in Section 3.1) and organic matter-dominated pollution (such as the biomagnification kinetics of POPs), full-scale empirical validation for these complex scenarios is still lacking. Persistent pollution typically involves longer spatiotemporal lags and stronger background noise, while multi-pollutant composite pollution entails complex antagonistic or synergistic chemical interactions (e.g., heavy metal-organic co-contamination). Therefore, future research will prioritize applying this integrated framework to long-term agricultural non-point source pollution and complex industrial composite pollution scenarios. This will further calibrate the cross-media parameters and refine the Environmental Damage Entropy (EDE) model’s capacity to evaluate composite toxicity, ultimately broadening the framework’s universal applicability.