Refined Simulation of Old Urban Inundation and Assessment of Stormwater Storage Capacity Based on Surface–Pipe Network–Box Culvert–River Coupled Modeling

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please find the attachment.

Comments for author File: Comments.pdf

Author Response

Comment 1

It is recommended to further clarify the research problem presented in lines 70 to 72. The current description states: “However, existing studies still have limitations, particularly in accurately representing hydraulic processes in complex drainage systems, making it difficult to fully reflect real-world conditions.” This statement regarding the limitations of existing research and the representation of complex drainage systems is rather vague. After all, no matter how accurate a model is, it is difficult to fully and accurately represent hydraulic processes and fully reflect real-world conditions. Therefore, the author could further specify the particular limitations of existing models, such as the trade-off between accuracy and computational efficiency.

Moreover, the GAST-SWMM model’s advantages are not only in its high-precision simulation but also in its GPU acceleration. Traditional simulation methods typically face a time-cost issue when achieving high accuracy, where faster simulations often require sacrificing precision. Therefore, it is suggested to highlight the dual advantages of the GAST-SWMM model in both high-precision simulation and faster simulation speed.

Response 1    

Thank you for the valuable comments from the reviewers. I apologize for the issues with the Introduction of the paper. Based on your feedback, I have rewritten the Introduction accordingly.

The updated version is provided below:

Driven by the dual pressures of global climate change and rapid urbanization, urban flood disasters have shown a concerning trend of increasing frequency and intensity [1-4]. According to data from the World Meteorological Organization (WMO), over the past 50 years, flood-related disasters have occurred almost daily over the past five decades, resulting in an average of 115 fatalities and approximately USD 202 million in economic losses per day [5]. This trend has been strongly evidenced in recent extreme rainfall events in several megacities: during the "7·20" extreme rainstorm in Zhengzhou in 2021, the cumulative precipitation reached 449 mm, with a maximum hourly rainfall of 201.9 mm, setting a new record for hourly rainfall in mainland China. In 2016, a once-in-50-years rainstorm in Xi'an led to waterlogging depths of up to 2.5 meters at Xiaozhai Crossroad, paralyzing the local transportation system [6-8]. These cases not only reveal the vulnerability of cities in the face of extreme rainfall but also highlight the inadequacy of traditional drainage systems under new climatic conditions, underscoring the urgent need for more precise and dynamic simulation and assessment of urban flood processes [9,10].

In response, urban flood modeling has evolved significantly over the past decades. Early studies primarily focused on either surface runoff simulations using two-dimensional (2D) models or sewer network hydraulics using one-dimensional (1D) models such as SWMM. However, these standalone applications were unable to fully capture the interactions between surface and subsurface flows, thereby limiting the accuracy of urban flood process representation [11]. With an improved understanding of the integrated nature of urban flooding, researchers have increasingly recognized the limitations of single models and turned to coupled modeling approaches to achieve more comprehensive and realistic simulations. For example, some studies have achieved coupling between open-source models such as SWMM and self-developed 2D surface flow modules [12], advancing the transition from single-model applications to multi-process and multi-dimensional coupled systems.

Currently, coupled simulations have become the mainstream in urban flood research. Common approaches include: (1) coupling of hydrological models with 1D hydrodynamic models, (2) coupling of hydrological models with 2D surface flow models, (3) coupling of 1D pipe or river network models with 2D surface models, and (4) full-process coupling encompassing hydrology, surface flow, pipe networks, and river networks. Among these, 1D–2D coupled models are the most widely adopted [13], typically realized through the coupling of river networks or drainage systems with surface flow modules. Depending on spatial representation and computational complexity, these couplings can be classified as semi-distributed or fully distributed. The semi-distributed coupling is often driven by a hydrological model and activates 2D inundation calculations only when pipe overflow occurs, providing a balance between computational efficiency and accuracy. In contrast, the fully distributed coupling employs complete hydrodynamic equations to explicitly describe both surface and subsurface processes, thereby achieving higher physical realism at the cost of significantly increased computational demand.

Despite these advances, old urban districts present unique challenges. The complexity of drainage networks and the diversity of underlying surfaces often limit the effectiveness of conventional models under extreme rainfall conditions [14]. Accurate flood simulation in these areas requires consideration of multiple interacting components, including underground drainage pipelines, surface roads, and open channels, which collectively determine the spatiotemporal patterns of runoff generation, convergence, and discharge [15-19]. For example, Min et al. [20] developed a 1D–2D coupled model for downtown Yangon, Myanmar, integrating the open-channel “minor drain system” with the “major runoff system” of streets, sidewalks, and squares. Their results highlighted the difficulty of simulating complex hydraulic interactions in historic urban areas, emphasizing the need for both advanced coupling techniques and computational efficiency [21,22].

Moreover, constrained by spatial limitations and construction conditions, drainage system upgrades in many old urban districts can only be implemented locally, l resulting in multi-level drainage systems composed of pipelines, box culverts, and river networks. The hydraulic processes within these systems are highly complex, with frequent water exchanges among pipelines, box culverts, open channels, and the surface, resulting in dynamic and heterogeneous drainage pathways. Box culverts, in particular, are large drainage structures commonly found in historic city centers. Their hydraulic behavior differs markedly from both conventional pipelines and natural river channels, exhibiting pronounced transient flow characteristics [23,24]. Nevertheless, many existing models simplify them as enlarged pipes, neglecting their unique storage capacity and flow dynamics, which can compromise simulation accuracy.

In summary, flood modeling in old urban areas faces three critical challenges: (1) Model Simplification: Conventional models typically simplify the drainage network into a single layer, neglecting the intricate hydraulic interplay between the multi-level drainage infrastructures specific to old urban areas; (2) Accuracy-Efficiency Balance: high-resolution simulation of complex systems requires capturing multi-scale processes, yet traditional models struggle to balance computational demand with physical fidelity [25,26]; and (3) Unclear System Performance: The operational principles of these unique drainage systems across different rainfall return periods are not well understood, requiring comprehensive modeling to delineate the efficacy of multi-level drainage networks.

This study employs a GPU-accelerated, high-resolution coupled modeling framework that integrates the Accelerated Surface Water Flow and Associated Transport (GAST) model with the Storm Water Management Model (SWMM). This approach enables precise and efficient simulation of water exchange processes among surface flows, sewer networks, box culverts, and open channels in old urban areas. Using detailed drainage pipeline data, high-resolution digital elevation models, land-use information, and hydrological observations, we constructed an urban rainfall–runoff model that captures surface and open-channel flows, conduit flows in underground networks, and their interactions. The framework further allows quantitative assessment of box culvert drainage capacity and urban moat flood attenuation performance, providing both scientific support for urban waterlogging mitigation and a technical foundation for high-performance simulation of complex, multi-level urban drainage systems.

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Comment 2   

For the model validation, the paper mentions using rainfall events from September 11, 2023, and July 29, 2024. While these events provide specific examples of rainfall, the question arises whether these two events adequately represent different types of extreme rainfall scenarios, particularly with regard to seasonal variations and rainfall intensity. Based on Figure 6, both events appear to be typical single-peak rainfall events. If data allows, it is recommended to include validation with double-peak rainfall events, which ensure the model’s robustness and reliability across different scenarios. Also, the paper discusses validating the model based on water depth comparisons, but does not clearly mention the spatial consistency of the results. It would be helpful to address whether the model maintains consistency in spatial distribution across the entire simulation area. Specifically, does the model show significant deviation in certain localized areas, such as low-lying regions or areas with dense drainage networks? The validation region identified by the authors appears to be a specific area, but it is unclear whether the simulated water depth and observed water depth are based on measurements at specific points or if they represent the average water depth across the region. This distinction is important because point-based measurements can vary significantly from area-based averages depending on the topography and drainage conditions. It would be beneficial for the authors to clarify whether the water depths are from specific points or averaged over a larger area. This will help in understanding the scope of the validation and whether the model's performance is being assessed at the necessary level of detail.

Response 2

Thank you for the valuable comments from the reviewers. The issues you raised are highly pertinent, and we fully agree that the initial validation scheme had shortcomings in terms of the representativeness of rainfall events, evaluation of spatial consistency, and clarity of data scales. Based on your suggestions, we have developed the following revision plan to comprehensively strengthen the model validation.

（1）Selection of rainfall events

In the model validation, the rainfall events on September 11, 2023, and July 29, 2024, were selected. These two events caused relatively severe urban flooding among the flooding events that occurred during 2023–2024, making them representative compared with other monitored rainfall events.

Regarding the suggestion to consider bimodal rainfall events, the study area underwent combined drainage separation and flood mitigation works prior to 2023. Consequently, the validation uses post-2023 rainfall data. Among these post-2023 events, occurrences of bimodal rainfall were few, and none resulted in urban flooding. Therefore, bimodal rainfall events were not included in the current validation.

Previous research by our team provides additional support for the reliability of the modeling framework. Hou et al. (2018) applied the GAST model to simulate the centennial flood in Morpeth, UK, evaluating its accuracy, computational efficiency, and stability. The simulated inundation areas differed from observations by only 0.96%~4.36%. Compared to the MIKE21 FM model under the same input conditions, the GAST model achieved a 1.07~19.55-fold improvement in computational accuracy. Furthermore, Liang et al. (2024) applied the GAST-SWMM coupled model to simulate flooding under seven rainfall patterns with different return periods, successfully reproducing urban flood evolution processes across various scenarios with high precision.

Finally, the authors will continue to monitor subsequent rainfall events in the study area and further refine the model to account for bimodal rainfall, long-sequence rainfall patterns, and extreme precipitation events.

References:

• Hou, J., Li, G., Li, G., et al. Application of a high-efficiency, high-accuracy hydrodynamic model in flood evolution. Journal of Hydraulic Engineering, 2018, 37(2): 96–107.
• Liang, X., Hou, J., Chen, G., et al. Analysis of urban flooding response characteristics to design rainfall patterns considering rainfall spatial distribution. Journal of Hydraulic and Water Transport Engineering, 2024, (2): 44–54.

(2) Spatial consistency of simulated water depths

Regarding the reviewer’s concern about spatial consistency, the study area is relatively small and densely built. Although rainfall exhibits some spatial variability, its effect on model performance is limited. High-resolution distributed rainfall data are generally derived from meteorological forecasts, whereas observed grid-scale rainfall data are difficult to obtain. Therefore, we used the average rainfall from the two meteorological stations in the study area. For the selected events, the rainfall intensity at the two stations was almost identical, minimizing spatial inconsistency.

In addition, we have supplemented the spatial information of the validation and simulation points, as shown in Figure 6 and Table 2, demonstrating that the locations of simulated inundation correspond well with the observed waterlogging locations.

Table 2. Comparison of simulated and observed water depths for the rainfall events on July 29, 2024, and September 11, 2023.

Rainfall Event	Location	Name	Observed Water Depth (m)	Simulated Water Depth (m)	Relative Error	Average Relative Error
September 11, 2023	A	Taiyi Road Interchange	0.78	0.76	2.7%	4.7%
	B	Nanshaomen	0.60	0.56	6.7%
July 29, 2024	A	Taiyi Road Interchange	0.70	0.63	10.0%	5.8%
	B	Nanshaomen	0.45	0.43	4.4%
	C	Youyi Road	0.10	0.103	3.0%

Figure 6. Comparison between simulated and observed results for the rainfall events on July 29, 2024, and September 11, 2023.

(3) Data scale for validation

The water depth data used for model validation correspond to maximum water depths rather than point averages. This ensures that the validation captures the most critical flood conditions.

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Comment 3   

It would be beneficial for the authors to clearly specify the design return period of the drainage network in the model and compare it with the simulated rainfall events. This would provide a more accurate context for evaluating the model’s performance and the system's capacity to manage different storm scenarios. Additionally, it would help readers understand how the model simulates drainage system behavior under various return period conditions.

Response 3

We thank the reviewer for the valuable comment. In response, we have added the design return period of the drainage network in Section 3.1 “Study Area Overview” and have revised and refined the related analysis accordingly.

It should be specifically noted that, in order to accurately capture the instantaneous response of the system under peak rainfall, this study uses a 3-hour design rainfall event. This differs from the 24-hour rainfall duration commonly used as the design standard for drainage networks in current Chinese guidelines. The key point is that short-duration design rainfall has a more concentrated peak intensity, resulting in inflow loads per unit time that are significantly higher than those under the long-duration design standard. Therefore, the occurrence of local full-pipe flow or overflows in the simulation does not necessarily indicate that the system fails to meet its design criteria; rather, it reveals that, for the same return period, different rainfall durations—particularly short-duration, high-peak events—impose fundamentally different instantaneous hydraulic loads on the network.

 This finding highlights the critical importance of considering rainfall duration and temporal pattern, in addition to return period, when assessing the resilience of urban drainage systems. It also demonstrates the model’s capability in capturing system responses under extreme short-duration rainfall events.

The specific revisions in the manuscript are as follows (highlighted in red):

3.1. Study Area

Xi'an, one of China's first designated historical and cultural cities, is a key central city in the western region. It is situated in the Guanzhong Basin in the middle reaches of the Weihe River Basin, with an average annual precipitation of 621 mm and an average annual temperature of 13.4℃, between 107.40°–109.49°E and 33.42°–34.45°N [37]. This study focuses on the drainage catchment of the Xi'an Moat, with a total catchment area of 34.27 km². The urban drainage system was designed based on a 3-year return period storm. The location map is shown in Fig. 2.

 

 

The results indicate that both the number and proportion of overloaded pipes and overflow nodes increase continuously with the rainfall return period. Under the 1-year re-turn period rainfall, the proportions of overloaded pipes and overflowing nodes are 8.8% and 4%, respectively, indicating that the system operates in a generally good condition. However, starting from the 2-year return period, the proportions of overloaded pipes and overflowing nodes increase significantly, reaching 27% and 19%, respectively. In this study, a 3-hour design rainfall event was used for the simulations, whereas the drainage network is typically designed based on 24-hour rainfall. Due to the shorter duration, the simulated rainfall has a relatively higher peak intensity, so even 1–2 year return period events may cause full-pipe flow or local overflows in the simulation. Therefore, for the same rainfall return period, different rainfall durations can result in substantially different hydraulic loads on the drainage network.

Under the 50-year return period, more than two-thirds of the pipes are at full capacity, and a similar proportion of nodes experience overflow. The trends of node overflow and pipe overloading under different return periods are illustrated in Fig. 9. A noticeable in-flection point is observed between the 2- and 50-year return periods, which can be considered as the critical resilience threshold of the drainage system. Rainfall events below this threshold can be effectively managed, and the risk of urban flooding remains controllable. Once the rainfall exceeds this threshold, the system quickly approaches saturation, the drainage capacity reaches its limit, and extensive severe flooding is likely to occur.

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Comment 4   

It is recommended that the authors add a section discussing the practical implications of this model for drainage network design or river channel planning. Specifically, the authors could explain how this model can be used to evaluate or optimize the capacity of drainage systems in flood-prone areas, offer design guidelines for urban planners and engineers to improve drainage infrastructure, and provide insights into retrofitting and enhancing flood storage capacity in existing systems such as 2 box culverts and rivers. Additionally, discussing how the model can contribute to sustainable flood management strategies and assist in designing resilient infrastructure in the face of climate change impacts would greatly enhance the paper’s relevance. This would not only make the research a theoretical contribution but also a valuable tool for improving urban flood resilience and infrastructure planning in practice.

Response 4

Thank you for the valuable feedback from the reviewers. Following your insightful suggestion, we have added a new section titled “Discussion and Outlook” after the “Conclusions” section.

The specific additions are as follows:

6. Discussion and Outlook

This study developed and validated a high-performance, high-precision coupled model integrating surface flow, sewer networks, box culverts, and river networks, providing a powerful tool for understanding and simulating the dynamic response of complex drainage systems in old urban areas under extreme rainfall. However, the value of any model lies not only in its simulation capabilities but also in its contribution to scientific understanding and practical guidance for engineering applications. Accordingly, this section discusses the key findings of this study and outlines potential future applications and developments.

6.1 Discussion

(1) Assessment and optimization of drainage system capacity

The model can accurately identify system bottlenecks, such as critical inundation areas and the corresponding rainfall thresholds. Based on these insights, engineers can use the model to test and compare various improvement measures (e.g., pipe diameter enlargement, construction of retention/detention basins, or distributed green infrastructure), enabling a fully quantitative design process from “problem diagnosis” to “solution optimization” and significantly improving investment efficiency.

(2) Flood control scheduling and risk management for river channels

 The model provides crucial technical support for optimizing real-time flood operations. Simulation results allow quantification of the flood mitigation effect of preemptive discharge from urban moats before heavy rainfall, effectively reducing the risk of overflow in critical sections. This analysis provides a quantitative basis for developing science-based, forecast-informed, dynamic river management strategies, shifting from passive emergency response toward proactive, adaptive risk management.

(3) Enhancing overall system resilience

The true value of the model lies in its forward-looking capabilities. By inputting design storms under future climate scenarios, the model can “stress-test” existing infrastructure to assess its long-term reliability. This allows decision-makers to move from reactive responses to proactive planning, prioritizing reinforcement or redundancy for the most vulnerable components, thereby supporting climate-adaptive infrastructure development and long-term resilience strategies.

Reviewer 2 Report

Comments and Suggestions for Authors

After reading this work, the reader gains little insight beyond a case-specific simulation of urban flooding in Xi’an. The paper effectively demonstrates that the GAST–SWMM coupled model can reproduce observed flooding patterns under various rainfall return periods; however, this represents an application rather than a genuine advancement of knowledge. I have several concerns regarding this work and, therefore, cannot recommend it for publication.

1. The state of the art is incomplete, outdated, and lacks a critical perspective. It lists many references on urban flood modelling evolution (from 1D to 2D and coupled models) but lacks critical synthesis and analytical depth. The discussion remains descriptive, offering no clear explanation of how previous approaches fall short or why the proposed GAST–SWMM coupling represents a genuine advancement. The authors mostly cite older or regional Chinese studies, with limited engagement with recent international developments. Some citations are outdated,  while the most recent high-impact studies (2020–2025) on urban flood modelling are largely absent. To help the authors in this task, I have prepared a list of references that the authors should discuss and include in their work. 

2. The research gap is vaguely stated as “existing studies still have limitations in accurately representing hydraulic processes in complex drainage systems.”
   This statement is too generic and could apply to almost any urban flood model. The authors do not specify which hydraulic processes are poorly represented. Without a clearly defined gap, the reader cannot appreciate the paper’s novelty or scientific motivation.

3. The proposed coupling of surface, pipe, culvert, and river systems is not convincingly novel. Similar 1D–2D coupled models have been widely published. The paper does not clarify what methodological advances or unique modelling strategies distinguish it from existing research. The coupling framework appears largely standard, and the description suggests more of an application study than a methodological innovation.

4. Another critical issue concerns the intrinsic limitations of the proposed framework. Its application depends on the availability of detailed and accurate sewer system data, particularly regarding underground pipes. In practice, such data are often incomplete or entirely unavailable, which significantly restricts the transferability of the approach. Without addressing these constraints, the framework risks being impractical in many real-world contexts. Simplified approaches or sub-grid parameterisations should therefore be considered to make the methodology more broadly applicable. I encourage authors to discuss this limitation with reference to the papers 1-4 I mentioned at the end of my report.

5. Model parameterisation (e.g., infiltration rates, Manning’s coefficients) is said to be based on “similar studies,” but no justification or sensitivity testing is provided.
6. The conclusions largely restate results without critical reflection. No theoretical or methodological innovation is highlighted.

Cited works:

1. DOI: https://doi.org/10.1080/15732479.2017.1356858
2. DOI: https://doi.org/10.3390/w15112043
3. DOI: https://doi.org/10.1016/j.jhydrol.2024.131043
4. DOI: https://doi.org/10.1016/j.jhydrol.2025.133617

Author Response

Comment 1

The state of the art is incomplete, outdated, and lacks a critical perspective. It lists many references on urban flood modelling evolution (from 1D to 2D and coupled models) but lacks critical synthesis and analytical depth. The discussion remains descriptive, offering no clear explanation of how previous approaches fall short or why the proposed GAST–SWMM coupling represents a genuine advancement. The authors mostly cite older or regional Chinese studies, with limited engagement with recent international developments. Some citations are outdated,  while the most recent high-impact studies (2020–2025) on urban flood modelling are largely absent. To help the authors in this task, I have prepared a list of references that the authors should discuss and include in their work.

1. DOI: https://doi.org/10.1080/15732479.2017.1356858
2. DOI: https://doi.org/10.3390/w15112043
3. DOI: https://doi.org/10.1016/j.jhydrol.2024.131043
4. DOI: https://doi.org/10.1016/j.jhydrol.2025.133617

Response 1

Thank you for your valuable suggestions. We fully acknowledge and accept all the issues you have raised, including the lack of a critical synthesis in the literature review, insufficient attention to recent international advances, and the unclear demonstration of how this study advances beyond existing work. These critiques are highly pertinent, and we apologize for the shortcomings present in the initial manuscript.

We are especially grateful for the time and effort you took to provide a list of references for discussion and citation. This invaluable resource has offered essential guidance for revising the manuscript and accurately situating our work within the international research frontier. In response to your comments, we have thoroughly rewritten and deepened the Introduction section of the paper.

The specific revisions are as follows:

Driven by the dual pressures of global climate change and rapid urbanization, urban flood disasters have shown a concerning trend of increasing frequency and intensity [1-4]. According to data from the World Meteorological Organization (WMO), over the past 50 years, flood-related disasters have occurred almost daily over the past five decades, resulting in an average of 115 fatalities and approximately USD 202 million in economic losses per day [5]. This trend has been strongly evidenced in recent extreme rainfall events in several megacities: during the "7·20" extreme rainstorm in Zhengzhou in 2021, the cumulative precipitation reached 449 mm, with a maximum hourly rainfall of 201.9 mm, setting a new record for hourly rainfall in mainland China. In 2016, a once-in-50-years rainstorm in Xi'an led to waterlogging depths of up to 2.5 meters at Xiaozhai Crossroad, paralyzing the local transportation system [6-8]. These cases not only reveal the vulnerability of cities in the face of extreme rainfall but also highlight the inadequacy of traditional drainage systems under new climatic conditions, underscoring the urgent need for more precise and dynamic simulation and assessment of urban flood processes [9,10].

In response, urban flood modeling has evolved significantly over the past decades. Early studies primarily focused on either surface runoff simulations using two-dimensional (2D) models or sewer network hydraulics using one-dimensional (1D) models such as SWMM. However, these standalone applications were unable to fully capture the interactions between surface and subsurface flows, thereby limiting the accuracy of urban flood process representation [11]. With an improved understanding of the integrated nature of urban flooding, researchers have increasingly recognized the limitations of single models and turned to coupled modeling approaches to achieve more comprehensive and realistic simulations. For example, some studies have achieved coupling between open-source models such as SWMM and self-developed 2D surface flow modules [12], advancing the transition from single-model applications to multi-process and multi-dimensional coupled systems.

Currently, coupled simulations have become the mainstream in urban flood research. Common approaches include: (1) coupling of hydrological models with 1D hydrodynamic models, (2) coupling of hydrological models with 2D surface flow models, (3) coupling of 1D pipe or river network models with 2D surface models, and (4) full-process coupling encompassing hydrology, surface flow, pipe networks, and river networks. Among these, 1D–2D coupled models are the most widely adopted [13], typically realized through the coupling of river networks or drainage systems with surface flow modules. Depending on spatial representation and computational complexity, these couplings can be classified as semi-distributed or fully distributed. The semi-distributed coupling is often driven by a hydrological model and activates 2D inundation calculations only when pipe overflow occurs, providing a balance between computational efficiency and accuracy. In contrast, the fully distributed coupling employs complete hydrodynamic equations to explicitly describe both surface and subsurface processes, thereby achieving higher physical realism at the cost of significantly increased computational demand.

Despite these advances, old urban districts present unique challenges. The complexity of drainage networks and the diversity of underlying surfaces often limit the effectiveness of conventional models under extreme rainfall conditions [14]. Accurate flood simulation in these areas requires consideration of multiple interacting components, including underground drainage pipelines, surface roads, and open channels, which collectively determine the spatiotemporal patterns of runoff generation, convergence, and discharge [15-19]. For example, Min et al. [20] developed a 1D–2D coupled model for downtown Yangon, Myanmar, integrating the open-channel “minor drain system” with the “major runoff system” of streets, sidewalks, and squares. Their results highlighted the difficulty of simulating complex hydraulic interactions in historic urban areas, emphasizing the need for both advanced coupling techniques and computational efficiency [21,22].

Moreover, constrained by spatial limitations and construction conditions, drainage system upgrades in many old urban districts can only be implemented locally, l resulting in multi-level drainage systems composed of pipelines, box culverts, and river networks. The hydraulic processes within these systems are highly complex, with frequent water exchanges among pipelines, box culverts, open channels, and the surface, resulting in dynamic and heterogeneous drainage pathways. Box culverts, in particular, are large drainage structures commonly found in historic city centers. Their hydraulic behavior differs markedly from both conventional pipelines and natural river channels, exhibiting pronounced transient flow characteristics [23,24]. Nevertheless, many existing models simplify them as enlarged pipes, neglecting their unique storage capacity and flow dynamics, which can compromise simulation accuracy.

In summary, flood modeling in old urban areas faces three critical challenges: (1) Model Simplification: Conventional models typically simplify the drainage network into a single layer, neglecting the intricate hydraulic interplay between the multi-level drainage infrastructures specific to old urban areas; (2) Accuracy-Efficiency Balance: high-resolution simulation of complex systems requires capturing multi-scale processes, yet traditional models struggle to balance computational demand with physical fidelity [25,26]; and (3) Unclear System Performance: The operational principles of these unique drainage systems across different rainfall return periods are not well understood, requiring comprehensive modeling to delineate the efficacy of multi-level drainage networks.

This study employs a GPU-accelerated, high-resolution coupled modeling framework that integrates the Accelerated Surface Water Flow and Associated Transport (GAST) model with the Storm Water Management Model (SWMM). This approach enables precise and efficient simulation of water exchange processes among surface flows, sewer networks, box culverts, and open channels in old urban areas. Using detailed drainage pipeline data, high-resolution digital elevation models, land-use information, and hydrological observations, we constructed an urban rainfall–runoff model that captures surface and open-channel flows, conduit flows in underground networks, and their interactions. The framework further allows quantitative assessment of box culvert drainage capacity and urban moat flood attenuation performance, providing both scientific support for urban waterlogging mitigation and a technical foundation for high-performance simulation of complex, multi-level urban drainage systems.

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22. Francipane, A.; D. Pumo; M. Sinagra; G. La Loggia; L.V. Noto. A paradigm of extreme rainfall pluvial floods in complex urban areas: the flood event of 15 July 2020 in Palermo (Italy). Nat. Hazards Earth Syst. Sci. 2021, 21, 2563-2580.
23. Mutua, B.M.; Y. Miyazaki. Two-dimensional longitudinal dynamic response of two-units box culvert on a liquefiable ground. Nat. Hazards Earth Syst. Sci. 2024, 10, 1295-1300.
24. Willis, T.D.M. Systematic analysis of uncertainty in flood inundation modelling. 2014.
25. Hou, J.; G. Li; G. Li; Q. Liang; Z. Zhi. Application of efficient high-resolution hydrodynamic model to simulations of flood propagation. J. Hydroelectr Eng. 2018, 37, 96-107.
26. Hou, J.; R. Wang; G. Li; G. Li. High-performance numerical model for high-resolution urban rainfall-runoff process based on dynamic wave method. J. Hydroelectr Eng. 2018, 37, 40-49.

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Comment 2

The research gap is vaguely stated as “existing studies still have limitations in accurately representing hydraulic processes in complex drainage systems.”

This statement is too generic and could apply to almost any urban flood model. The authors do not specify which hydraulic processes are poorly represented. Without a clearly defined gap, the reader cannot appreciate the paper’s novelty or scientific motivation.

Response 2

Thank you for your valuable suggestions. Your point regarding the overly broad articulation of the research gap is highly pertinent, as it indeed affected the clarity with which the paper’s innovative contributions were presented. We fully accept your critique. In the revised manuscript, we have substantially refined the Introduction section to more clearly and precisely define the research gap addressed by this study.

The specific revisions are as follows:

Despite these advances, old urban districts present unique challenges. The complexity of drainage networks and the diversity of underlying surfaces often limit the effectiveness of conventional models under extreme rainfall conditions [14]. Accurate flood simulation in these areas requires consideration of multiple interacting components, including underground drainage pipelines, surface roads, and open channels, which collectively determine the spatiotemporal patterns of runoff generation, convergence, and discharge [15-19]. For example, Min et al. [20] developed a 1D–2D coupled model for downtown Yangon, Myanmar, integrating the open-channel “minor drain system” with the “major runoff system” of streets, sidewalks, and squares. Their results highlighted the difficulty of simulating complex hydraulic interactions in historic urban areas, emphasizing the need for both advanced coupling techniques and computational efficiency [21,22].

Moreover, constrained by spatial limitations and construction conditions, drainage system upgrades in many old urban districts can only be implemented locally, l resulting in multi-level drainage systems composed of pipelines, box culverts, and river networks. The hydraulic processes within these systems are highly complex, with frequent water exchanges among pipelines, box culverts, open channels, and the surface, resulting in dynamic and heterogeneous drainage pathways. Box culverts, in particular, are large drainage structures commonly found in historic city centers. Their hydraulic behavior differs markedly from both conventional pipelines and natural river channels, exhibiting pronounced transient flow characteristics [23,24]. Nevertheless, many existing models simplify them as enlarged pipes, neglecting their unique storage capacity and flow dynamics, which can compromise simulation accuracy.

In summary, flood modeling in old urban areas faces three critical challenges: (1) Model Simplification: Conventional models typically simplify the drainage network into a single layer, neglecting the intricate hydraulic interplay between the multi-level drainage infrastructures specific to old urban areas; (2) Accuracy-Efficiency Balance: high-resolution simulation of complex systems requires capturing multi-scale processes, yet traditional models struggle to balance computational demand with physical fidelity [25,26]; and (3) Unclear System Performance: The operational principles of these unique drainage systems across different rainfall return periods are not well understood, requiring comprehensive modeling to delineate the efficacy of multi-level drainage networks.

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Comment 3

The proposed coupling of surface, pipe, culvert, and river systems is not convincingly novel. Similar 1D–2D coupled models have been widely published. The paper does not clarify what methodological advances or unique modelling strategies distinguish it from existing research. The coupling framework appears largely standard, and the description suggests more of an application study than a methodological innovation.

Response 3

Thank you for your valuable suggestions. We completely agree with your observation that the coupled framework used in this study is not innovative in itself. We acknowledge that 1D-2D coupled models have become a mainstream technique for urban flood simulation and have been applied in numerous outstanding studies.

The core innovation of our research lies in conducting an in-depth investigation into the coupling mechanisms, computational efficiency, simulation accuracy, and the clarification of drainage patterns under different return periods for mature methods applied to the specific and complex environment of "old urban areas with intricate drainage systems."

Following your advice, we have more clearly and prominently elaborated on these aspects in the revised introduction of the paper. We believe the significance of this study is its provision of a solution with superior accuracy, efficiency, and practicality for addressing specific types of urban flood issues (such as data-intensive and system-complex old urban areas). It offers urban planners and engineers design guidelines for improving drainage infrastructure and provides insights for renovating existing systems (such as box culverts and rivers) and enhancing storage capacity. This will not only position our findings as a theoretical contribution but also as a practical tool for improving urban flood resilience and infrastructure planning.

Additionally, based on your suggestions, we have further refined the introduction to provide a more in-depth explanation of the research content and background.

The specific revised sections are as follows:

In response, urban flood modeling has evolved significantly over the past decades. Early studies primarily focused on either surface runoff simulations using two-dimensional (2D) models or sewer network hydraulics using one-dimensional (1D) models such as SWMM. However, these standalone applications were unable to fully capture the interactions between surface and subsurface flows, thereby limiting the accuracy of urban flood process representation [11]. With an improved understanding of the integrated nature of urban flooding, researchers have increasingly recognized the limitations of single models and turned to coupled modeling approaches to achieve more comprehensive and realistic simulations. For example, some studies have achieved coupling between open-source models such as SWMM and self-developed 2D surface flow modules [12], advancing the transition from single-model applications to multi-process and multi-dimensional coupled systems.

Currently, coupled simulations have become the mainstream in urban flood research. Common approaches include: (1) coupling of hydrological models with 1D hydrodynamic models, (2) coupling of hydrological models with 2D surface flow models, (3) coupling of 1D pipe or river network models with 2D surface models, and (4) full-process coupling encompassing hydrology, surface flow, pipe networks, and river networks. Among these, 1D–2D coupled models are the most widely adopted [13], typically realized through the coupling of river networks or drainage systems with surface flow modules. Depending on spatial representation and computational complexity, these couplings can be classified as semi-distributed or fully distributed. The semi-distributed coupling is often driven by a hydrological model and activates 2D inundation calculations only when pipe overflow occurs, providing a balance between computational efficiency and accuracy. In contrast, the fully distributed coupling employs complete hydrodynamic equations to explicitly describe both surface and subsurface processes, thereby achieving higher physical realism at the cost of significantly increased computational demand.

Despite these advances, old urban districts present unique challenges. The complexity of drainage networks and the diversity of underlying surfaces often limit the effectiveness of conventional models under extreme rainfall conditions [14]. Accurate flood simulation in these areas requires consideration of multiple interacting components, including underground drainage pipelines, surface roads, and open channels, which collectively determine the spatiotemporal patterns of runoff generation, convergence, and discharge [15-19]. For example, Min et al. [20] developed a 1D–2D coupled model for downtown Yangon, Myanmar, integrating the open-channel “minor drain system” with the “major runoff system” of streets, sidewalks, and squares. Their results highlighted the difficulty of simulating complex hydraulic interactions in historic urban areas, emphasizing the need for both advanced coupling techniques and computational efficiency [21,22].

Moreover, constrained by spatial limitations and construction conditions, drainage system upgrades in many old urban districts can only be implemented locally, l resulting in multi-level drainage systems composed of pipelines, box culverts, and river networks. The hydraulic processes within these systems are highly complex, with frequent water exchanges among pipelines, box culverts, open channels, and the surface, resulting in dynamic and heterogeneous drainage pathways. Box culverts, in particular, are large drainage structures commonly found in historic city centers. Their hydraulic behavior differs markedly from both conventional pipelines and natural river channels, exhibiting pronounced transient flow characteristics [23,24]. Nevertheless, many existing models simplify them as enlarged pipes, neglecting their unique storage capacity and flow dynamics, which can compromise simulation accuracy.

In summary, flood modeling in old urban areas faces three critical challenges: (1) Model Simplification: Conventional models typically simplify the drainage network into a single layer, neglecting the intricate hydraulic interplay between the multi-level drainage infrastructures specific to old urban areas; (2) Accuracy-Efficiency Balance: high-resolution simulation of complex systems requires capturing multi-scale processes, yet traditional models struggle to balance computational demand with physical fidelity [25,26]; and (3) Unclear System Performance: The operational principles of these unique drainage systems across different rainfall return periods are not well understood, requiring comprehensive modeling to delineate the efficacy of multi-level drainage networks.

This study employs a GPU-accelerated, high-resolution coupled modeling framework that integrates the Accelerated Surface Water Flow and Associated Transport (GAST) model with the Storm Water Management Model (SWMM). This approach enables precise and efficient simulation of water exchange processes among surface flows, sewer networks, box culverts, and open channels in old urban areas. Using detailed drainage pipeline data, high-resolution digital elevation models, land-use information, and hydrological observations, we constructed an urban rainfall–runoff model that captures surface and open-channel flows, conduit flows in underground networks, and their interactions. The framework further allows quantitative assessment of box culvert drainage capacity and urban moat flood attenuation performance, providing both scientific support for urban waterlogging mitigation and a technical foundation for high-performance simulation of complex, multi-level urban drainage systems.

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Comment 4

Another critical issue concerns the intrinsic limitations of the proposed framework. Its application depends on the availability of detailed and accurate sewer system data, particularly regarding underground pipes. In practice, such data are often incomplete or entirely unavailable, which significantly restricts the transferability of the approach. Without addressing these constraints, the framework risks being impractical in many real-world contexts. Simplified approaches or sub-grid parameterizations should therefore be considered to make the methodology more broadly applicable. I encourage authors to discuss this limitation with reference to the papers 1-4 I mentioned at the end of my report.

Response 4

Thank you for raising this insightful point, which touches upon the core challenge of transitioning urban hydrological models from research to widespread application. We fully agree that the accessibility of underground pipeline data is indeed a common practical bottleneck, which can limit the direct transferability of any method reliant on detailed data.

We would like to take this opportunity to further clarify the core positioning of our study. This paper aims to explore refined and efficient coupled simulations of the hydrological-hydrodynamic processes in old urban districts, which are characterized by highly complex and unique drainage systems, under data-complete conditions. The sewer network data used in this study were provided by the Xi’an Municipal Design Institute, offering comprehensive coverage that adequately represents the drainage system of the study area. The topographic data were provided by the Xi’an Surveying and Mapping Institute, consisting of a high-resolution 1:5000 DEM. The land-use data were also supplied by the same institute and categorized into eight classes: roads, forests, croplands, buildings, bare land, mixed-use areas, water bodies, and rooftops.

We believe that establishing such a high-resolution benchmark model is crucial. It not only enhances our understanding of the hydraulic processes within complex urban drainage systems but also provides a reliable reference for evaluating and calibrating simplified models, such as the Simplified approaches or sub-grid parameterizations you mentioned.

At the same time, we greatly appreciate your valuable suggestion regarding the improvement of methodological practicality. In the revised manuscript, we will add a dedicated section entitled “Discussion and Outlook”, which will emphasize how benchmark studies like ours can guide the improvement of physical representations and parameterization in simplified models, thereby achieving a balance between accuracy and applicability.

Through this additional discussion, we aim to make it clearer to readers that our study not only presents a high-precision modeling case but, more importantly, serves as a bridge connecting high-fidelity research and real-world applications.

We sincerely thank you for your insightful comments, which have helped us to further enhance the depth and breadth of our manuscript.

The specific revisions are as follows:

6.2 Outlook

The strengths of this study largely stem from the availability of refined datasets. However, its reliance on detailed underground drainage data—such as geometric configurations and topological connectivity—poses a major obstacle to its wider application in data-scarce areas. In addition, the model’s complexity and relatively high computational cost impose certain requirements on users ’expertise and computational resources. These are common challenges faced by physically based models in the pursuit of high fidelity. Recognizing such limitations is not an endpoint, but rather a new starting point toward broader applicability. The outcomes of this study have laid a crucial foundation for developing the next generation of versatile flood modeling toolkits. Future research can be deepened along the following directions:

(1) Serving as a benchmark for simplified models

The validated high-precision model in this study can serve as a reliable “virtual reality.” The high-fidelity datasets it generates under various scenarios-such as surface water depth and sewer flow-can be used to calibrate, validate, and optimize key parameters of simplified or conceptual models designed for data-scarce regions, thereby substantially improving their physical soundness and predictive accuracy.

(2) Developing a hierarchical and hybrid modeling strategy

For large cities or metropolitan regions, a flexible modeling paradigm can be established. In data-rich core or high-risk areas, the refined framework presented here can be used for detailed simulation and design evaluation, while in data-scarce peripheral or preliminary screening zones, the calibrated simplified models can be employed. The two components can be dynamically coupled along their boundaries, achieving an optimal balance between precision and efficiency.

In summary, this study not only provides specific technical solutions for flood mitigation in the case region but, more importantly, establishes a highly reliable benchmark that bridges the gap between “high-fidelity research” and “broad-scale application.”

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Comment 5

Model parameterization (e.g., infiltration rates, Manning’s coefficients) is said to be based on “similar studies,” but no justification or sensitivity testing is provided.

Response 5

Thank you for the valuable feedback from the reviewers. Your comment regarding the lack of justification for parameter values and the absence of sensitivity analysis is highly pertinent, and we fully agree that this is crucial for ensuring the reliability and credibility of the model results.

In the revised manuscript, we have made the following improvements:

(1) Preliminary selection and calibration of model parameters

In Section 3.2.1, we specify that the infiltration parameters were initially selected based on studies conducted in regions with similar characteristics [38], and the Manning’s coefficients were determined with reference to urban drainage design standards and relevant literature [39,40]. In Section 3.2.2, we indicate that the pipe roughness coefficients were initially chosen based on relevant references [41]. According to previous studies and relevant design standards, the ranges of Manning’s coefficients and stable infiltration rates for different land use types are as follows:

Appendix Table. Ranges of Manning’s coefficients and stable infiltration rates for different land use types.

Land Use Type	Manning’s Coefficient Range	Stable Infiltration Rate (mm/h) Range
Water Bodies	0.013–0.016	0–1
Roads	0.15–0.40	30–60
Woodland	0.03–0.05	10–30
Cropland	0.012–0.016	0–1
Buildings	0.02–0.04	10–25
Bare Land	0.020–0.030	3–10
Mixed-Use Land	0.012–0.016	0–1
Roofs	0.008–0.035	0–1

The roughness coefficient for sewer pipes was within the range of 0.012–0.013.

Based on these ranges, we performed trial-and-error calibration and conducted multiple parameter adjustments to determine the final values. The final infiltration and Manning’s parameters are listed in Table 1, and the final calibrated pipe roughness coefficient was determined to be 0.012.

Table 1. Manning’s Roughness Coefficients and Steady Infiltration Rates for Different Land Use Types.

Land use type	Manning’s n	Steady infiltration rate (mm/h)
Water Bodies	0.010	0
Roads	0.014	0
Woodland	0.200	37.55
Cropland	0.045	20
Buildings	0.014	0
Bare Land	0.030	19.43
Mixed-Use Land	0.025	5
Roofs	0.014	0

(2) Validation of model parameters

In Section 3.3, two observed rainfall events were used for validation. The results show that the maximum relative error between simulated and observed water depths did not exceed 10.0%, and the average relative error ranged between 4.7% and 5.8%, as shown in Table 2 and Figure 6.

Table 2. Comparison of simulated and observed water depths for the rainfall events on July 29, 2024, and September 11, 2023.

Rainfall Event	Location	Name	Observed Water Depth (m)	Simulated Water Depth (m)	Relative Error	Average Relative Error
September 11, 2023	A	Taiyi Road Interchange	0.78	0.76	2.7%	4.7%
	B	Nanshaomen	0.60	0.56	6.7%
July 29, 2024	A	Taiyi Road Interchange	0.70	0.63	10.0%	5.8%
	B	Nanshaomen	0.45	0.43	4.4%
	C	Youyi Road	0.10	0.103	3.0%

Figure 6. Comparison between simulated and observed results for the rainfall events on July 29, 2024, and September 11, 2023.

(3) The specific revisions in the manuscript are as follows (highlighted in red)

3.2. Model Construction

3.2.1. Surface Runoff Model Construction

A surface runoff and river network routing model for the drainage sub-catchments of the Xi’an Moat was developed based on the GAST model. The underlying surface data, including land use and high-resolution digital elevation model (DEM) data, were provided by the Xi’an Municipal Institute of Surveying and Mapping. The DEM has a spatial resolution of 5 m (Fig. 3(a)), and land use is classified into eight categories (Fig. 3(b)): water bodies, roads, woodland, cropland, buildings, bare land, mixed-use land, and roofs. The study area covers 34.27 km², and the model is discretized into 2.444 million grids with a resolution of 5 m.

Regarding model parameterization, we first conducted preliminary parameter selection. Infiltration rates were primarily referenced from studies in regions with similar conditions [38], while Manning’s coefficients were determined mainly based on urban drainage design standards and relevant literature [39, 40]. Subsequently, a trial-and-error calibration approach was employed, adjusting key parameters according to the simulation outcomes and observed data to ensure that the model could reasonably reproduce surface runoff and sewer network hydraulic behavior. The final calibrated parameters are listed in Table 1.

3.2.1. Drainage Network Routing Model Construction

An urban underground drainage network model was constructed based on SWMM, with pipe network data provided by the Xi’an Municipal Institute of Surveying and Map-ping. The model consists of 5,569 nodes, one outlet, and 5,570 conduits, including 5,452 circular pipes and 118 rectangular box culverts. Stormwater outside the moat is conveyed through the drainage system into the outer box culverts at 27 junctions, while stormwater inside the moat is discharged into the inner box culverts at 18 junctions. The layout of the drainage network is shown in Fig.4. Both circular pipes and box culverts are made of reinforced concrete.

For the parameterization of the sewer pipes’ Manning’s coefficient, an initial value was first selected based on relevant literature [41]. Subsequently, a trial-and-error calibration was conducted, adjusting key parameters according to the simulation results and observed data to ensure that the model could reasonably reproduce the hydraulic behavior of the sewer network. The final calibrated Manning’s coefficient was set to 0.012, which not only falls within the recommended range in the literature but also achieves a good balance between physical realism and modeling accuracy.

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Comment 6

The conclusions largely restate results without critical reflection. No theoretical or methodological innovation is highlighted.

Response 6

Thank you for your valuable suggestions. We agree that the original conclusions lacked critical reflection. To address this, we have added a dedicated “Discussion and Future Outlook” section. This new section explicitly synthesizes our findings, highlights the theoretical and methodological implications of our work, and outlines future research directions, thereby strengthening the paper's contribution.

The specific additions are as follows:

6. Discussion and Outlook

This study developed and validated a high-performance, high-precision coupled model integrating surface flow, sewer networks, box culverts, and river networks, providing a powerful tool for understanding and simulating the dynamic response of complex drainage systems in old urban areas under extreme rainfall. However, the value of any model lies not only in its simulation capabilities but also in its contribution to scientific understanding and practical guidance for engineering applications. Accordingly, this section discusses the key findings of this study and outlines potential future applications and developments.

6.1 Discussion

(1) Assessment and optimization of drainage system capacity

The model can accurately identify system bottlenecks, such as critical inundation areas and the corresponding rainfall thresholds. Based on these insights, engineers can use the model to test and compare various improvement measures (e.g., pipe diameter enlargement, construction of retention/detention basins, or distributed green infrastructure), enabling a fully quantitative design process from “problem diagnosis” to “solution optimization” and significantly improving investment efficiency.

(2) Flood control scheduling and risk management for river channels

 The model provides crucial technical support for optimizing real-time flood operations. Simulation results allow quantification of the flood mitigation effect of preemptive discharge from urban moats before heavy rainfall, effectively reducing the risk of overflow in critical sections. This analysis provides a quantitative basis for developing science-based, forecast-informed, dynamic river management strategies, shifting from passive emergency response toward proactive, adaptive risk management.

(3) Enhancing overall system resilience

The true value of the model lies in its forward-looking capabilities. By inputting design storms under future climate scenarios, the model can “stress-test” existing infrastructure to assess its long-term reliability. This allows decision-makers to move from reactive responses to proactive planning, prioritizing reinforcement or redundancy for the most vulnerable components, thereby supporting climate-adaptive infrastructure development and long-term resilience strategies.

6.2 Outlook

The strengths of this study largely stem from the availability of refined datasets. However, its reliance on detailed underground drainage data-such as geometric configurations and topological connectivity-poses a major obstacle to its wider application in data-scarce areas. In addition, the model’s complexity and relatively high computational cost impose certain requirements on users ’expertise and computational resources. These are common challenges faced by physically based models in the pursuit of high fidelity. Recognizing such limitations is not an endpoint, but rather a new starting point toward broader applicability. The outcomes of this study have laid a crucial foundation for developing the next generation of versatile flood modeling toolkits. Future research can be deepened along the following directions:

(1)  Serving as a benchmark for simplified models

The validated high-precision model in this study can serve as a reliable “virtual reality.” The high-fidelity datasets it generates under various scenarios-such as surface water depth and sewer flow-can be used to calibrate, validate, and optimize key parameters of simplified or conceptual models designed for data-scarce regions, thereby substantially improving their physical soundness and predictive accuracy.

(2) Developing a hierarchical and hybrid modeling strategy

For large cities or metropolitan regions, a flexible modeling paradigm can be established. In data-rich core or high-risk areas, the refined framework presented here can be used for detailed simulation and design evaluation, while in data-scarce peripheral or preliminary screening zones, the calibrated simplified models can be employed. The two components can be dynamically coupled along their boundaries, achieving an optimal balance between precision and efficiency.

In summary, this study not only provides specific technical solutions for flood mitigation in the case region but, more importantly, establishes a highly reliable benchmark that bridges the gap between “high-fidelity research” and “broad-scale application.”

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have done an excellent job addressing my comments and suggestions. The paper has improved significantly and can be accepted in its current form.