A Five-Dimensional Comprehensive Evaluation of the Yellow River Basin’s Water Environment Using Entropy–Catastrophe Progression Method: Implications for Differentiated Governance Strategies

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study presents a novel approach that transcends the limitations of single-dimensional research focused solely on water quality or water quantity, by proposing a five-dimensional water environment evaluation framework. This manuscript addresses a topic of significant academic interest and holds substantial potential to attract attention in the field. With a few minor revisions to strengthen the justification of both its analytical and classification methodologies, the paper could be well-suited for publication in the journal Water.

(1) The authors emphasize that a comprehensive assessment is essential in the Yellow River Basin, due to its complex and closely interlinked system. It would be beneficial, however, to highlight more clearly the differences between this research and existing comprehensive evaluation studies. For instance, Zhao et al. and Wang et al. employ a system dynamics model (DPSIR) to evaluate integrated development by incorporating both natural and socioeconomic factors. How does the framework in the present paper differ from their approach, and what factors led to these differences? An expanded explanation would be helpful.

(2) A more detailed explanation of why the Entropy-Catastrophe Progression method was chosen would be appreciated. There exist various multi-criteria decision-making (MCDM) methods, such as the Analytic Hierarchy Process (AHP), Fuzzy Comprehensive Evaluation, Grey System Theory, and Data Envelopment Analysis (DEA). It would be valuable to discuss the rationale for selecting this particular method in the context of this study.

(3) The data used in this paper appear to be primarily sourced from the 2022 China Statistical Yearbook, the 2022 China Environmental Statistical Yearbook, and the 2022 Water Resources Bulletin, with some additional data references. Have the authors attempted any cross-verification of these data with other sources from previous studies? Doing so could increase confidence in both the data set and the reliability of the comprehensive evaluation.

(4) After calculating the comprehensive water environment evaluation index for each province in the Yellow River Basin using the Entropy-Catastrophe Progression method, the authors employ the Natural Breaks classification. It would be helpful to explain why Natural Breaks was chosen over other commonly used classification methods, such as Equal Interval, Quantile, Standard Deviation, or Geometric Interval.

(5) In Figures 2 and 3, it would be interesting to see whether the region near the Yellow River can be analyzed in greater detail. A more refined level of analysis might offer deeper engineering insights for experts in this area.

(6) It would also be helpful to compare the final comprehensive evaluation results with indices (or numerical findings) reported by earlier studies, and discuss any similarities or differences. If the outcomes closely mirror existing research, the novelty of this paper might be called into question, so it would be advisable to address this point transparently.

(7) This paper’s strongest feature appears to be the multidimensional framework of “quality-quantity-space-flow-biota,” comprising a total of 19 indicators. To clearly demonstrate how this approach differs from previous comprehensive evaluations (e.g., single-dimensional or integrated), it may be beneficial to include a section with a tabular comparison, thereby highlighting how this paper represents an advanced or refined version of past methods.

(8) Lastly, if possible, the authors might consider incorporating data from other research in the literature, and apply those data to this comprehensive evaluation framework. Doing so could enhance the reliability of the results and further validate the significance of the study by contrasting directly with various external data sets.

Author Response

Comments: This study presents a novel approach that transcends the limitations of single-dimensional research focused solely on water quality or water quantity, by proposing a five-dimensional water environment evaluation framework. This manuscript addresses a topic of significant academic interest and holds substantial potential to attract attention in the field. With a few minor revisions to strengthen the justification of both its analytical and classification methodologies, the paper could be well-suited for publication in the journal Water.

Reply: We sincerely thank the reviewers for recognizing the innovation and academic value of our study. In response to your suggestions regarding methodological and classification improvements, we have implemented the following revisions:

Detailed Methodology Description:

Added comparisons between our five-dimensional framework and existing methods (e.g., DPSIR, WQI), emphasizing its advantages in ecological integrity, dynamic weighting, and nonlinear analysis.

Provided a clear rationale for selecting the entropy-catastrophe progression method, highlighting its ability to capture indicator competition and threshold effects.

Natural Breaks Method:

Added an analysis of the applicability of the Natural Breaks method in the Methods section, validating its alignment with the geographic and anthropogenic patterns of the Yellow River Basin.

Enhanced Result Validation:

Compared our findings with existing studies on the Yellow River Basin to demonstrate the novelty of our framework, showing that the multidimensional approach captures systemic contradictions overlooked by traditional methods.

The revised study systematically improves methodological rigor and result interpretation, providing a more precise decision-making tool for differentiated governance in the Yellow River Basin. We are grateful for the reviewers' valuable suggestions.

Detailed comments: (1) The authors emphasize that a comprehensive assessment is essential in the Yellow River Basin, due to its complex and closely interlinked system. It would be beneficial, however, to highlight more clearly the differences between this research and existing comprehensive evaluation studies. For instance, Zhao et al. and Wang et al. employ a system dynamics model (DPSIR) to evaluate integrated development by incorporating both natural and socioeconomic factors. How does the framework in the present paper differ from their approach, and what factors led to these differences? An expanded explanation would be helpful.

(2) A more detailed explanation of why the Entropy-Catastrophe Progression method was chosen would be appreciated. There exist various multi-criteria decision-making (MCDM) methods, such as the Analytic Hierarchy Process (AHP), Fuzzy Comprehensive Evaluation, Grey System Theory, and Data Envelopment Analysis (DEA). It would be valuable to discuss the rationale for selecting this particular method in the context of this study.

Reply: We thank the reviewers for their important comments on the study's innovation and methodology. In the revised manuscript, we have added targeted discussions in the second paragraph of the Introduction and the Conclusion to systematically explain the limitations of existing research and the unique contributions of our study.

Addressing the Limitations of Existing Research:

1.Incomplete Ecological Indicator Systems:

While the DPSIR model integrates socioeconomic and natural factors, it lacks sufficient ecological attributes and does not cover key indicators such as aquatic spatial structure and biodiversity.

Studies on the water-energy-food nexus also fail to quantify aquatic spatial parameters, resulting in overlooked effects of landscape fragmentation on ecological functions.

Our five-dimensional framework ("quality-quantity-space-flow-biota") systematically incorporates comprehensive ecological indicators, addressing the gaps in existing research.

2.Deficiencies in Dynamic Weighting and Nonlinear Analysis:

Methods such as system dynamics and SBM models rely on fixed weights and linear assumptions, making them unable to represent dynamic competition between indicators or threshold effects.

Our use of the entropy-catastrophe progression method dynamically weights indicators and identifies critical thresholds through bifurcation equations, overcoming the limitations of traditional linear approaches.

The specific revisions are as follows:

Although these studies have analyzed the environment from multiple dimensions, several limitations remain: (1) The ecological indicator system lacks integrity. For example, Zhao et al. [24] mainly focused on socio-economic driving mechanisms, with only 3 of the 12 indicators involving ecological attributes. Similarly, Gu et al. [27] fail to quantify parameters related to aquatic spatial structure. (2) Dynamic weighting and nonlinear analysis among indicators remain unaddressed, hindering the characterization of dynamic competitive relationships between indicators. Moreover, existing approaches assume gradual system evolution, neglecting potential abrupt changes triggered by specific indicators and threshold effects on system stability. For instance, system dynamics models [25] and SBM models [26] rely on fixed weight assignments and linear equilibrium assumptions.  Given the complex system composition of the Yellow River Basin, it is urgent to explore an appropriate evaluation method to evaluate the water environment comprehensively.

In view of the previous research results mentioned above, this study constructed a five-dimensional comprehensive evaluation framework of the water environment, "quali-ty-quantity-space-flow-biota," based on the system attributes of the water environment. By analyzing the multifaceted impacts of human activities on the water environment, we used the entropy method to dynamically assign weights, capture the competitive relation-ships between indicators, and combine the catastrophe progression method to identify critical thresholds. This approach achieved a methodological transition from linear equilibrium analysis to nonlinear mutation warning, and provided a dynamical and adaptive evaluation tool for the management of complex human-water systems. Compared with existing basin-scale water environment evaluation studies, this framework showed obvious advantages in ecological integrity, dynamic weighting, and nonlinear analysis. Comprehensive evaluation of the impact of human activities on the water environment of the Yellow River Basin is of great significance to promoting ecological protection and high-quality development of the Yellow River Basin.

Detailed comments: (4) After calculating the comprehensive water environment evaluation index for each province in the Yellow River Basin using the Entropy-Catastrophe Progression method, the authors employ the Natural Breaks classification. It would be helpful to explain why Natural Breaks was chosen over other commonly used classification methods, such as Equal Interval, Quantile, Standard Deviation, or Geometric Interval.

Reply: We thank the reviewers for their suggestions on classification methods. In the revised Methods section, we have added a detailed explanation of the Natural Breaks method and further elaborated on its applicability and advantages.

The specific revisions are as follows:

Natural Breaks Classification Method

This study used the natural breaks method to classify the comprehensive evaluation results of the water environment. The method is based on the Jenks optimization algorithm, which identifies the natural grouping structure inherent in data by minimizing in-tra-class variance and maximizing inter-class variance. It has the characteristics of adaptive data distribution and objective classification and is highly applicable to evaluating ecological indicators.

Detailed comments: (5) In Figures 2 and 3, it would be interesting to see whether the region near the Yellow River can be analyzed in greater detail. A more refined level of analysis might offer deeper engineering insights for experts in this area.

Reply: We thank the reviewers for their detailed suggestions on presenting the results. In the revised Results section, we have enhanced the interpretation of data, spatial heterogeneity analysis, and connections to the literature.

1.Water Quality Dimension:

Added analysis of pollutant emissions in midstream coal industrial zones (e.g., Ordos, Yulin) to clarify the causes of spatial heterogeneity (upstream ecological barriers vs. midstream industrial clusters).

2.Water Quantity Dimension:

Linked the "arid west-humid east" climate pattern to inter-basin water transfer needs, highlighting the coupling of natural and anthropogenic factors.

3.Aquatic Space Dimension:

Quantified the impacts of urbanization-induced habitat fragmentation and arid evaporation on aquatic spaces to strengthen mechanistic explanations.

4.Water Flow Dimension:

Cited relevant literature to validate the ecological blocking effects of dams.

5.Aquatic Biota Dimension:

Used native species (e.g., northern copperfish, Qinghai Lake naked carp) population changes to align with existing research on biodiversity decline.

The specific revisions are as follows:

Research Results

1. Comprehensive Evaluation Index Calculation Based on the Entropy-Catastrophe Progression Method

In this study, the entropy-catastrophe progression method was used to construct a comprehensive t evaluation index of water environmen in the Yellow River Basin. The calculation process consisted of three stages: (1) Data Standardization and Intra-Dimensional Weighting: Dimensional differences were eliminated through range standardization, and dynamic weights for indicators within each dimension were computed using the entropy method (Fig. 2); (2) Nonlinear Inter-Dimensional Weight Allocation: The bifurcation set equations of catastrophe models were utilized to transform standardized dimension scores into normalized weights (Water Quality: 0.19; Water Quantity: 0.27; Aquatic Space: 0.23; Water Flow: 0.12; Aquatic Biota: 0.19), capturing critical threshold effects; (3) Composite Index Synthesis: The three-level coupling of "indicator-dimension-system" was realized through weighted superposition, and then a comprehensive evaluation result with significant spatial heterogeneity was generated.

As shown in Fig. 2, the water quality dimension (Q) hadthe highest weight for water quality of Class I-III (Q3 = 0.4919) , indicating that it was  the core driving factor of water quality evaluation. In the aquatic space dimension (W), the aggregation degree of aquatic space (W4 = 0.3732) exhibited significant weighting, highlighting the critical importance of spatial integrity to ecological functionality. The water quality score was dominated by Q3, while aquatic space fragmentation (W4 = 0.009) was significantly elevated in the aquatic space dimension.  This method combined dynamic weighting with nonlinear mapping, effectively solving the limitations of traditional models in threshold recognition and spatial adaptability, and providing high-precision decision-making support for differentiated management of the Yellow River Basin.

Evaluation Results of Each Water Environment Dimension

In terms of quality, Qinghai Province had the best quality, while Shanxi Province had the worst quality, with Class I-III concentrations at 90% and 72% respectively. The provinces with the largest number of industrial wastewater treatment facilities were: Shandong, Si-chuan, and Henan.  As shown in Figure 2, the province with the best water quality was Qinghai Province (Q=0.21). The overall water quality was ranked from good to bad as fol-lows: upstream > downstream > midstream. The water quality score of the midstream provinces (Shaanxi and Inner Mongolia) (Q=0.07) was significantly lower than that of the downstream, which might be directly related to the pollutant emissions in the coal indus-try-intensive areas in the midstream (such as Ordos and Yulin).

Water Quantity Dimension. Qinghai Province had the highest per capita water volume, 12,206.9 m³, while Ningxia (122.5 m³) and Henan Province (252.5 m³) were experiencing severe water shortages. The provinces with the largest proportion of water-saving irriga-tion area were: Shandong (21.9%) and Henan (13.2%). As shown in Figure 2, the provinces with good water quantity were Qinghai Province (V=0.14) and Sichuan Province (V=0.14), while the provinces with poor water quantity were Gansu Province (V=0.058) and Inner Mongolia Autonomous Region (V=0.063). These results were consistent with the precipita-tion in the Yellow River Basin. The average annual precipitation in the upper and lower reaches was 500 mm and 200 mm respectively, showing a pattern of dryness in the west and wetness in the east.

Aquatic Space Dimension. Shandong Province had the highest aquatic spatial aggrega-tion (0.064), while Shaanxi Province (0.009) and Gansu Province (0.008) had the lowest. The aquatic space protection rate in Qinghai and Gansu provinces was relatively high, both reaching more than 30%. The provinces with the largest proportion of water-saving irrigation area were: Shandong (21.9%) and Henan (13.2%). As shown in Figure 2, the provinces with good water area dimensions were Qinghai Province (W=0.21) and Shan-dong Province (W=0.20), while the provinces with poor water area dimensions were Shanxi Province (W=0.02) and Ningxia Province (W=0.04). The water area in the middle reaches was significantly worse than that in the upper and lower reaches. In recent years, urbanization had squeezed the water area in the middle reaches, causing serious aquatic area fragmentation, resulting in the rupture of ecological corridors and weakening soil and water conservation capacity.

Water Flow Dimension. Inner Mongolia Autonomous Region had the highest coefficients of three flow indices, while Sichuan Province had the lowest. As shown in Figure 2, the provinces with better water flow dimension indices were Inner Mongolia Autonomous Region (L=0.36) and Qinghai Province (L=0.23), while Sichuan Province (L=0.01) and He-nan Province (L=0.02) were relatively poor. In Henan Province, cascade hydropower sta-tions (such as Xiaolangdi) and irrigation water diversion had led to a near-break in con-nections between rivers, hindering fish migration and reducing the connectivity of aquatic habitats.  These observations confirmed previous research[20] that dams hindered fish migration and that Sichuan Province was generally less affected due to the shorter Yellow River in its territory.

Aquatic Biota Dimension. Henan Province had the most freshwater fish fishing, Sichuan Province had the most freshwater fish farming, and Gansu Province had the lowest num-bers for both. As shown in Figure 2, Shandong Province (O = 0.330), Henan Province (O = 0.329), and Sichuan Province (O = 0.254) had higher aquatic biota scores compared with other provinces.  The shrinkage and pollution of aquatic habitats in Gansu Province (O=0.000) had led to a sharp decline in the number of native fish populations (such as Coreius septentrionalis). Despite being located in the Sanjiangyuan Nature Reserve, the degradation of alpine wetlands had slowed the recovery of cold-water fish populations (such as Gymnocypris przewalskii) in Qinghai Province(O=0.008).

Detailed comments: (3) The data used in this paper appear to be primarily sourced from the 2022 China Statistical Yearbook, the 2022 China Environmental Statistical Yearbook, and the 2022 Water Resources Bulletin, with some additional data references. Have the authors attempted any cross-verification of these data with other sources from previous studies? Doing so could increase confidence in both the data set and the reliability of the comprehensive evaluation.

 (6) It would also be helpful to compare the final comprehensive evaluation results with indices (or numerical findings) reported by earlier studies, and discuss any similarities or differences. If the outcomes closely mirror existing research, the novelty of this paper might be called into question, so it would be advisable to address this point transparently.

 (7) This paper’s strongest feature appears to be the multidimensional framework of “quality-quantity-space-flow-biota,” comprising a total of 19 indicators. To clearly demonstrate how this approach differs from previous comprehensive evaluations (e.g., single-dimensional or integrated), it may be beneficial to include a section with a tabular comparison, thereby highlighting how this paper represents an advanced or refined version of past methods.

 (8) Lastly, if possible, the authors might consider incorporating data from other research in the literature, and apply those data to this comprehensive evaluation framework. Doing so could enhance the reliability of the results and further validate the significance of the study by contrasting directly with various external data sets.

Reply: We thank the reviewers for their valuable comments on the methodological rigor and novelty of our study. In response, we have systematically improved the revised manuscript and provide a consolidated reply below:

1. The advantages and necessity of the study were obtained by comparing the existing environmental assessment studies of the Yellow River basin

In the Discussion section, we added comparisons with traditional water quality studies, connectivity research, and ecological assessments to highlight the innovation of our framework in considering the comprehensive ecological system of the basin.

2.Through the comparison between this study and the existing comprehensive evaluation methods, the advanced nature of the method is highlighted:

Incomplete ecological indicator systems: They lack key ecological indicators such as aquatic spatial structure and biodiversity. Our five-dimensional framework addresses this gap. Deficiencies in dynamic weighting and nonlinear analysis: Methods like system dynamics and SBM models rely on fixed weights and linear assumptions, failing to capture dynamic competition or threshold effects. Our entropy-catastrophe progression method overcomes these limitations by dynamically weighting indicators and identifying critical thresholds.

To address the shortcomings in the original manuscript, we have added a Discussion section that includes comparisons with existing research.

The specific revisions are as follows:

Discussion

The water environment issues in the Yellow River Basin are characterized by complexity, systematicity, and dynamic evolution. The traditional single-dimensional or simplified indicator system is difficult to fully reflect the multidimensional contradiction be-tween ecological security and sustainable development. This study is based on19 indicators in the five-dimensional framework of "quality-quantity-space-flow-biota" and combined with the entropy-catastrophe progression method to reveal the comprehensive state and regional heterogeneity of the water environment system in the Yellow River Basin. Compared with existing research, the advantages and necessity of this study are reflected in the following aspects:

1. Systemic Advantages of the Multidimensional Framework in Aquatic Ecological Evaluation

Conventional studies on the water environment in the Yellow River Basin tend to focus on single dimensions or simplified indicators (e.g., water quality, runoff, and sediment), which have in-depth insights into specific areas but fail to uncover the synergistic effects of the system. For example, Fu et al. [9] used the grey clustering method to evaluate the water quality of 12 monitoring sections in the basin and concluded that water quality of the basin was "generally good", but this conclusion only reflected the compliance with chemical standards. Our study found that the proportion of Class I-III water quality in Shanxi Province (72%) had improved significantly compared to historical levels, but the scores of aquatic biota (O=0.004) and aquatic space (W=0.022) dimensions ranked lowest in the basin, indicating that there is a significant deviation between traditional water quality evaluation and ecological health. Similarly, Qin et al. [8] used the FVCOM model to analyze the impact of runoff on estuarine salinity dispersion, but overlooked the interference of human factors on water-sediment balance. Although Ma et al. [13] established a runoff-sediment-precipitation response model, their analysis of human intervention measures (such as soil and water conservation projects) was still limited to correlation studies.

The water evaluation system of this study not only incorporates natural factors (such as precipitation and vegetation coverage), but also innovatively incorporates human activity indicators (such as water-saving irrigation area ratio and per capita water resources). This approach reveals the dual dilemma of "insufficient water conservation through engineering and severe water shortage in resources" that is common in the mid-upper provinces, such as Gansu (V=0.058) and Ningxia (V=0.071), except Qinghai. Although existing studies (e.g., Yujun et al. [20]) emphasize that dam construction leads to reduced connectivity across the entire basin, they lack regional specificity. Our streamflow evaluation sys-tem quantifies the structural integrity of the river network through the α, β, and γ indices, identifying significant spatial heterogeneity in the midstream provinces. For instance, He-nan Province (L=0.06) scored significantly lower than upstream regions such as Inner Mongolia (L=0.36). Existing studies [15, 16] utilized vegetation coverage indicators (such as NDVI) to reveal the spatial disparities between upstream arid areas (such as Inner Mongolia, Ningxia, and northern Gansu, with average annual FVC <0.3) and downstream humid provinces (such as Henan and Shandong, with an average annual FVC >0.6), how-ever, their research framework ignored aquatic spatial structure metrics. This study shows that despite the midstream provinces have restored vegetation through initiatives such as returning farmland to forest, their aquatic space scores (W=0.06–0.09) remain significantly lower than those of the upstream Qinghai Province (W=0.21) and downstream Shandong Province(W=0.20). Key issues include low aquatic space aggregation, reduced maximum patchiness indices, and aquatic landscapes fragmentation, which weaken ecological corridor functions and offset the benefits of vegetation restoration. These findings expose the compound challenges facing the mid-stream region: " water quality improvement, severs water shortage, and fragmented aquatic spaces."

2. Enhanced Dynamicity and Objectivity via the Entropy-Catastrophe Progression Method

Traditional water environment evaluation methods (e.g., WQI, DPSIR models, principal component analysis) usually rely on static weights or subjective assignments, failing to capture nonlinear dynamic features. The entropy-catastrophe progression method ad-dresses these limitations.

Compared to existing studies based on ecological assessments of vegetation coverage and land-use change [14–16], analyses of the impact of dams on river connectivity [20], or water quality evaluation based on WQI [10], this study integrated multi-source data (e.g., remote sensing data on aquatic space aggregation W4, per capita water resources statistics V2, and water quality monitoring data Q4). This approach systematically reveals multidimensional spatial heterogeneity: the upstream Qinghai Province has excellent water quality (Q=0.21), but neighboring provinces face severe water shortage (Gansu: V=0.06; Inner Mongolia: V=0.06; Ningxia: V=0.07). Midstream reaches of Shaanxi (W=0.06) and Shanxi (W=0.02) suffered from severs aquatic space fragmentation. The river network structural was quantified using the α, β, and γ indices, and it was found that Inner Mongolia (L=0.36) had the highest water flow. The lower reaches of Shandong (O=0.330) and Henan (O=0.329) provinces exhibited superior aquatic biodiversity compared to the mid-upper regions.

Conventional linear models have serious flaws. For example, the DPSIR model [24] employs fixed weights and ignores dynamic interactions (e.g., nonlinear coupling be-tween industrial wastewater treatment infrastructure and water quality compliance). The system dynamics models [25] assume that the system evolves gradually and ignore the sudden ecological changes caused by the fragmentation aquatic organisms. Fuzzy set evaluations [27] can handle uncertainty, but fail to quantify the impact of thresholds on system stability. In contrast, the catastrophe progression method can determine critical thresholds. For example, Gansu Province had a low score for water flow (L=0.01), but its composite index dropped sharply (0.028) despite having moderate water quality (Q=0.107) and a high number of aquatic biota (O=0.126). This nonlinear response cannot be achieved in linear models such as the SBM model [26]. In contrast, the water sflow score in Inner Mongolia (L=0.36) is close to the upper critical value of the swallowtail catastrophe model(0.4), indicating the improved connectivity may bring exponential ecological bene-fits. This mechanism allows the region to maintain a "good" overall rating (0.030) despite weak water volume (V=0.063) and aquatic biota (O=0.097).

2. Enhanced Dynamicity and Objectivity via the Entropy-Catastrophe Progression Method

Traditional water environment evaluation methods (e.g., WQI, DPSIR models, principal component analysis) usually rely on static weights or subjective assignments, failing to capture nonlinear dynamic features. The entropy-catastrophe progression method ad-dresses these limitations.

Compared to existing studies based on ecological assessments of vegetation coverage and land-use change [14–16], analyses of the impact of dams on river connectivity [20], or water quality evaluation based on WQI [10], this study integrated multi-source data (e.g., remote sensing data on aquatic space aggregation W4, per capita water resources statistics V2, and water quality monitoring data Q4). This approach systematically reveals multidimensional spatial heterogeneity: the upstream Qinghai Province has excellent water quality (Q=0.21), but neighboring provinces face severe water shortage (Gansu: V=0.06; Inner Mongolia: V=0.06; Ningxia: V=0.07). Midstream reaches of Shaanxi (W=0.06) and Shanxi (W=0.02) suffered from severs aquatic space fragmentation. The river network structural was quantified using the α, β, and γ indices, and it was found that Inner Mongolia (L=0.36) had the highest water flow. The lower reaches of Shandong (O=0.330) and Henan (O=0.329) provinces exhibited superior aquatic biodiversity compared to the mid-upper regions.

Conventional linear models have serious flaws. For example, the DPSIR model [24] employs fixed weights and ignores dynamic interactions (e.g., nonlinear coupling be-tween industrial wastewater treatment infrastructure and water quality compliance). The system dynamics models [25] assume that the system evolves gradually and ignore the sudden ecological changes caused by the fragmentation aquatic organisms. Fuzzy set evaluations [27] can handle uncertainty, but fail to quantify the impact of thresholds on system stability. In contrast, the catastrophe progression method can determine critical thresholds. For example, Gansu Province had a low score for water flow (L=0.01), but its composite index dropped sharply (0.028) despite having moderate water quality (Q=0.107) and a high number of aquatic biota (O=0.126). This nonlinear response cannot be achieved in linear models such as the SBM model [26]. In contrast, the water sflow score in Inner Mongolia (L=0.36) is close to the upper critical value of the swallowtail catastrophe model(0.4), indicating the improved connectivity may bring exponential ecological bene-fits. This mechanism allows the region to maintain a "good" overall rating (0.030) despite weak water volume (V=0.063) and aquatic biota (O=0.097).

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper introduced a comprehensive evaluation framework from five-dimensions ("quality-quantity-space-flow-biota") with 19 indicators to evaluate the Yellow River Basin's water environment. Entropy method coupled with the catastrophe progression method are used to characterize the nonlinear relationships within water environment systems. The study found that the comprehensive water environment status of the Yellow River Basin exhibits spatial heterogeneity, with better conditions in the upstream and downstream compared to the midstream.

Major comments:

1. This paper employs an entropy method to assign weights to 19 indicators across 5 dimensions. Is this weighting process conducted separately for individual indicators within each dimension or uniformly across dimensions? The text appears unclear on this point. If weights are assigned within individual dimensions, do different dimensions themselves have respective weights?
2. Equations (2) and (3) present two distinct calculation formulas for r_qp. Which one is correct?
3. In Figure 2, there are inconsistencies between the scores displayed in the bar chart and those shown in the distribution map on the left. For example, the Water Quantity score for Shan-dong province conflicts between the bar chart and distribution map. Please verify whether there are errors in the legend.
4. The calculation results of the Catastrophe Progression Method are inadequately presented in the Results section. Additional clarification and explanation are required.
5. Avoid Chinglish for the whole paper.
6. Highlights format need to be improved.
7. The paper needs significantly improve the statement of academic values. What’s the major contribution on the physical insights in the water quality of yellow river and the advances of the evaluation method. More discussion and comparison are expected.

Minor comments:

1. Please double check the typos in the text and equations, e.g., “X_{p mix}” in Equation (2), line 188 should be “X_{p min}”, and “Qing-hia” in Figure 2., line 295 should be “Qing-hai”

Author Response

Comments: This paper introduced a comprehensive evaluation framework from five-dimensions ("quality-quantity-space-flow-biota") with 19 indicators to evaluate the Yellow River Basin's water environment. Entropy method coupled with the catastrophe progression method are used to characterize the nonlinear relationships within water environment systems. The study found that the comprehensive water environment status of the Yellow River Basin exhibits spatial heterogeneity, with better conditions in the upstream and downstream compared to the midstream.

Reply: We sincerely appreciate the reviewers' meticulous evaluation and valuable comments. In response to your concerns, we have systematically revised the manuscript with a focus on enhancing methodological rigor, deepening result interpretation, and improving data transparency.

A new Discussion section has been added to compare our study with existing research, highlighting the innovation of our multidimensional framework in capturing systemic contradictions overlooked by traditional methods.

1.Regarding the incompleteness of ecological indicator systems in existing studies: While the DPSIR model integrates socioeconomic and natural factors, it lacks sufficient ecological attributes and does not cover key indicators such as aquatic spatial structure and biodiversity. Studies on the water-energy-food nexus also fail to quantify aquatic spatial parameters, resulting in unaddressed effects of landscape fragmentation on ecological functions.

Our five-dimensional framework ("quality-quantity-space-flow-biota") systematically incorporates comprehensive ecological indicators, filling the gap in ecological dimensions left by previous research.

2.Regarding the deficiencies in dynamic weighting and nonlinear analysis in existing studies: Methods such as system dynamics and SBM models rely on fixed weights and linear assumptions, making them unable to represent dynamic competition between indicators or threshold effects.

Our entropy-catastrophe progression method dynamically weights indicators and identifies critical thresholds through bifurcation equations, overcoming the limitations of traditional linear approaches.

The revised manuscript significantly improves methodological clarity, result reliability, and policy relevance. We sincerely welcome further guidance from the reviewers.

Detailed comments: (1) This paper employs an entropy method to assign weights to 19 indicators across 5 dimensions. Is this weighting process conducted separately for individual indicators within each dimension or uniformly across dimensions? The text appears unclear on this point. If weights are assigned within individual dimensions, do different dimensions themselves have respective weights?

Reply: Thank you for your question. Below, I explain the specific calculation process of the entropy-catastrophe progression method used in this study, this study adopts a two-stage weight allocation strategy to ensure the independence of indicator weights within each dimension and the systematicity of weights across dimensions:

Stage 1: Intra-Dimensional Indicator Weight Allocation

Method: The entropy method is applied separately to indicators within each dimension (quality, quantity, space, flow, biota) to calculate their weights within their respective dimensions.

Stage 2: Inter-Dimensional Weight Allocation

Method: The catastrophe progression method determines the weights of each dimension in the comprehensive index. Based on the bifurcation set equations of catastrophe models (e.g., butterfly catastrophe), the standardized scores of each dimension are converted into normalized weights.

For this issue, we have added the following explanation to the Methods section of the manuscript.

The specific revisions are as follows:

This study used the entropy-catastrophe progression method to calculate the comprehensive evaluation index of water environment of the Yellow River Basin. A two-stage weight allocation strategy is adopted to ensure the independence of indicator weights within each dimension and the systematic coordination of weights between dimensions.

Detailed comments: (2) Equations (2) and (3) present two distinct calculation formulas for r_qp. Which one is correct?

Reply: We sincerely apologize for such an elementary error. The presence of two similar formulas is because Formula (2) is selected for standardization when the evaluation indicator is positive, while Formula (3) is used for negative indicators.

The specific revisions are as follows:

Where X_qp represents the actual value of evaluation object p for indicator q, X_{p min} is the minimum value of evaluation object p, X_{p max} is the maximum value of evaluation object p, and r_qp represents the standardized value of X_qp. For positively oriented indicators, Equation (2) is selected for standardization, while Equation (3) is applied to negatively oriented indicators. This process ultimately yields the standardized matrix R.

Detailed comments: (3) In Figure 2, there are inconsistencies between the scores displayed in the bar chart and those shown in the distribution map on the left. For example, the Water Quantity score for Shan-dong province conflicts between the bar chart and distribution map. Please verify whether there are errors in the legend.

Reply: We sincerely apologize for such an elementary error. The correction has been made in Figure 2.

The specific revisions are as follows:

Figure 2. Evaluation Results of Each Water Environment Dimension (The spatial distribution map illustrates the spatial differences in scores for a particular water environment dimension among provinces. The bar chart represented the scores of each province for a particular water dimension, and the pie chart showed the weight distribution of indicators within that water Environment dimension.)

Detailed comments: (4) The calculation results of the Catastrophe Progression Method are inadequately presented in the Results section. Additional clarification and explanation are required.

Reply: We sincerely appreciate the reviewer's important suggestion regarding the presentation of the catastrophe progression method results. In response, we have added a detailed description of the calculation process and threshold effect analysis in Section 4.1 ("Comprehensive Evaluation Index Calculation Based on the Entropy-Catastrophe Progression Method") of the Results section.

The specific revisions are as follows:

Research Results

1. Comprehensive Evaluation Index Calculation Based on the Entropy-Catastrophe Progression Method

In this study, the entropy-catastrophe progression method was used to construct a comprehensive t evaluation index of water environmen in the Yellow River Basin. The calculation process consisted of three stages: (1) Data Standardization and Intra-Dimensional Weighting: Dimensional differences were eliminated through range standardization, and dynamic weights for indicators within each dimension were computed using the entropy method (Fig. 2); (2) Nonlinear Inter-Dimensional Weight Allocation: The bifurcation set equations of catastrophe models were utilized to transform standardized dimension scores into normalized weights (Water Quality: 0.19; Water Quantity: 0.27; Aquatic Space: 0.23; Water Flow: 0.12; Aquatic Biota: 0.19), capturing critical threshold effects; (3) Composite Index Synthesis: The three-level coupling of "indicator-dimension-system" was realized through weighted superposition, and then a comprehensive evaluation result with significant spatial heterogeneity was generated.

Detailed comments: (5) Avoid Chinglish for the whole paper.

Reply: Thank you for your suggestion. During the revision stage, we invited relevant experts to polish the language of the manuscript.

Detailed comments: (6) Highlights format need to be improved.

Reply: Thank you for your suggestion. We have addressed the formatting issues in the manuscript.

Detailed comments: (7) The paper needs significantly improve the statement of academic values. What’s the major contribution on the physical insights in the water quality of yellow river and the advances of the evaluation method. More discussion and comparison are expected.

Reply: We sincerely appreciate the reviewer's important comments on the academic value and methodological innovation of our study. In the revised Discussion section, we have added systematic comparisons and mechanistic analyses to clarify the core contributions of our research:

1.Comprehensive Evaluation of the Yellow River Basin's Water Environment:

Existing studies failed to fully incorporate key ecological indicators such as aquatic spatial structure and biodiversity, resulting in insufficient ecological attributes. Our five-dimensional framework ("quality-quantity-space-flow-biota") systematically integrates comprehensive ecological indicators, filling the gap left by previous research.

2.Advancements in the Entropy-Catastrophe Progression Method:

Existing comprehensive evaluation methods suffer from incomplete ecological indicator systems and deficiencies in dynamic weighting and nonlinear analysis, making them unable to represent dynamic competition between indicators or threshold effects. Our entropy-catastrophe progression method dynamically weights indicators and identifies critical thresholds through bifurcation equations, overcoming the limitations of traditional linear approaches.

The specific revisions are as follows:

Discussion

The water environment issues in the Yellow River Basin are characterized by complexity, systematicity, and dynamic evolution. The traditional single-dimensional or simplified indicator system is difficult to fully reflect the multidimensional contradiction be-tween ecological security and sustainable development. This study is based on19 indicators in the five-dimensional framework of "quality-quantity-space-flow-biota" and combined with the entropy-catastrophe progression method to reveal the comprehensive state and regional heterogeneity of the water environment system in the Yellow River Basin. Compared with existing research, the advantages and necessity of this study are reflected in the following aspects:

1. Systemic Advantages of the Multidimensional Framework in Aquatic Ecological Evaluation

Conventional studies on the water environment in the Yellow River Basin tend to focus on single dimensions or simplified indicators (e.g., water quality, runoff, and sediment), which have in-depth insights into specific areas but fail to uncover the synergistic effects of the system. For example, Fu et al. [9] used the grey clustering method to evaluate the water quality of 12 monitoring sections in the basin and concluded that water quality of the basin was "generally good", but this conclusion only reflected the compliance with chemical standards. Our study found that the proportion of Class I-III water quality in Shanxi Province (72%) had improved significantly compared to historical levels, but the scores of aquatic biota (O=0.004) and aquatic space (W=0.022) dimensions ranked lowest in the basin, indicating that there is a significant deviation between traditional water quality evaluation and ecological health. Similarly, Qin et al. [8] used the FVCOM model to analyze the impact of runoff on estuarine salinity dispersion, but overlooked the interference of human factors on water-sediment balance. Although Ma et al. [13] established a runoff-sediment-precipitation response model, their analysis of human intervention measures (such as soil and water conservation projects) was still limited to correlation studies.

The water evaluation system of this study not only incorporates natural factors (such as precipitation and vegetation coverage), but also innovatively incorporates human activity indicators (such as water-saving irrigation area ratio and per capita water resources). This approach reveals the dual dilemma of "insufficient water conservation through engineering and severe water shortage in resources" that is common in the mid-upper provinces, such as Gansu (V=0.058) and Ningxia (V=0.071), except Qinghai. Although existing studies (e.g., Yujun et al. [20]) emphasize that dam construction leads to reduced connectivity across the entire basin, they lack regional specificity. Our streamflow evaluation sys-tem quantifies the structural integrity of the river network through the α, β, and γ indices, identifying significant spatial heterogeneity in the midstream provinces. For instance, He-nan Province (L=0.06) scored significantly lower than upstream regions such as Inner Mongolia (L=0.36). Existing studies [15, 16] utilized vegetation coverage indicators (such as NDVI) to reveal the spatial disparities between upstream arid areas (such as Inner Mongolia, Ningxia, and northern Gansu, with average annual FVC <0.3) and downstream humid provinces (such as Henan and Shandong, with an average annual FVC >0.6), how-ever, their research framework ignored aquatic spatial structure metrics. This study shows that despite the midstream provinces have restored vegetation through initiatives such as returning farmland to forest, their aquatic space scores (W=0.06–0.09) remain significantly lower than those of the upstream Qinghai Province (W=0.21) and downstream Shandong Province(W=0.20). Key issues include low aquatic space aggregation, reduced maximum patchiness indices, and aquatic landscapes fragmentation, which weaken ecological corridor functions and offset the benefits of vegetation restoration. These findings expose the compound challenges facing the mid-stream region: " water quality improvement, severs water shortage, and fragmented aquatic spaces."

2. Enhanced Dynamicity and Objectivity via the Entropy-Catastrophe Progression Method

Traditional water environment evaluation methods (e.g., WQI, DPSIR models, principal component analysis) usually rely on static weights or subjective assignments, failing to capture nonlinear dynamic features. The entropy-catastrophe progression method ad-dresses these limitations.

Compared to existing studies based on ecological assessments of vegetation coverage and land-use change [14–16], analyses of the impact of dams on river connectivity [20], or water quality evaluation based on WQI [10], this study integrated multi-source data (e.g., remote sensing data on aquatic space aggregation W4, per capita water resources statistics V2, and water quality monitoring data Q4). This approach systematically reveals multidimensional spatial heterogeneity: the upstream Qinghai Province has excellent water quality (Q=0.21), but neighboring provinces face severe water shortage (Gansu: V=0.06; Inner Mongolia: V=0.06; Ningxia: V=0.07). Midstream reaches of Shaanxi (W=0.06) and Shanxi (W=0.02) suffered from severs aquatic space fragmentation. The river network structural was quantified using the α, β, and γ indices, and it was found that Inner Mongolia (L=0.36) had the highest water flow. The lower reaches of Shandong (O=0.330) and Henan (O=0.329) provinces exhibited superior aquatic biodiversity compared to the mid-upper regions.

Conventional linear models have serious flaws. For example, the DPSIR model [24] employs fixed weights and ignores dynamic interactions (e.g., nonlinear coupling be-tween industrial wastewater treatment infrastructure and water quality compliance). The system dynamics models [25] assume that the system evolves gradually and ignore the sudden ecological changes caused by the fragmentation aquatic organisms. Fuzzy set evaluations [27] can handle uncertainty, but fail to quantify the impact of thresholds on system stability. In contrast, the catastrophe progression method can determine critical thresholds. For example, Gansu Province had a low score for water flow (L=0.01), but its composite index dropped sharply (0.028) despite having moderate water quality (Q=0.107) and a high number of aquatic biota (O=0.126). This nonlinear response cannot be achieved in linear models such as the SBM model [26]. In contrast, the water sflow score in Inner Mongolia (L=0.36) is close to the upper critical value of the swallowtail catastrophe model(0.4), indicating the improved connectivity may bring exponential ecological bene-fits. This mechanism allows the region to maintain a "good" overall rating (0.030) despite weak water volume (V=0.063) and aquatic biota (O=0.097).

Detailed comments: Please double check the typos in the text and equations, e.g., "Xp mix" in Equation (2), line 188 should be "Xp min", and "Qing-hia" in Figure 2, line 295 should be "Qing-hai".

Reply: We sincerely appreciate the reviewer's meticulous attention to detail. We have conducted an additional full-text proofreading to ensure typographical accuracy.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

In the revised manuscript, the authors have improved the description of the research methodology, clarifying the use of "Entropy Weighting to assign weights to indicators within each dimension" and the "Catastrophe Progression Method to assign weights across different dimensions." They also updated the results analysis and discussion sections, corrected errors in the figures, and enhanced the clarity of the conclusions, thereby meeting the overall requirements for publication.

One minor correction remains: In Figure 2a, the data labels for the four indicators in the pie chart of "indicator weights" are incorrect and need revision.

Author Response

Comments: In the revised manuscript, the authors have improved the description of the research methodology, clarifying the use of "Entropy Weighting to assign weights to indicators within each dimension" and the "Catastrophe Progression Method to assign weights across different dimensions." They also updated the results analysis and discussion sections, corrected errors in the figures, and enhanced the clarity of the conclusions, thereby meeting the overall requirements for publication.

One minor correction remains: In Figure 2a, the data labels for the four indicators in the pie chart of "indicator weights" are incorrect and need revision.

Reply:

We sincerely appreciate the reviewer’s meticulous review! In response to the incorrect labeling of indicator weights in Figure 2(a), we have implemented the following corrections:

Due to an oversight, the numerical labels for the four indicator weights (Q1-Q4) in the original pie chart did not match the calculated results in the main text.

Rechecked the weight values for the water quality dimension (Q1=0.08, Q2=0.28, Q3=0.49, Q4=0.15) and updated the pie chart labels accordingly;

In the revised Figure 2(a), the proportions of the pie sectors now strictly align with the weight values, ensuring consistency between the graphic data and textual analysis.

The corrected Figure 2(a) has been updated on page X of the manuscript.

Thank you again for your rigorous feedback! This revision further enhances data accuracy and result reliability.

Author Response File: Author Response.pdf