Technical System for Urban Stormwater Carrying Capacity Assessment and Optimization

Abstract

The combined effects of rapid urbanization and climate change are increasingly exacerbating the risk of urban flooding. This study develops a data-efficient framework for estimating a city’s Urban Stormwater Carrying Capacity (USCC)—the maximum stormwater volume that can be safely infiltrated, stored, and conveyed. The framework couples three rainfall scenarios—frequent, heavy, and extreme—with nine widely adopted drainage and storage measures, ranging from green spaces and permeable pavements to pipes and underground emergency reservoirs, and expresses USCC through a streamlined water-balance equation. Applied to the 24 km² Zhangmian River district in Weifang, China, the framework yields capacities of 4.84, 5.86, and 9.80 × 10⁶ m³ for the three scenarios, respectively; underground reservoirs supply ≈ 40% of the extreme-event capacity. Sensitivity analysis shows that increasing the imperviousness coefficient from 0.65 to 0.85 raises peak drainage demand by 30.8%, whereas halving reservoir depth lowers total capacity by 27.8%. Because the method requires only rainfall depth, land-cover data, and basic facility dimensions, it enables rapid, transparent scenario testing and helps planners prioritize cost-effective upgrades. The approach is transferable to other cities and can be extended to incorporate water quality or digital-twin modules in future research.

1. Introduction

The growing frequency and severity of urban flooding have become critical challenges in the global urbanization process, restricting sustainable urban development [1]. By 2025, over 60% of the global urban population will reside in flood-prone areas, a trend exacerbated by rapid urbanization and climate change [2]. The expansion of impervious surfaces has disrupted the natural hydrological cycle, intensifying surface runoff under extreme rainfall conditions [3]. Concurrently, the frequency and intensity of extreme precipitation events are rising. The IPCC Sixth Assessment Report indicates that such events have increased by approximately 7% over the past 50 years and are expected to escalate further [4]. Aging and under-capacity drainage systems—due to outdated standards and insufficient maintenance—struggle to cope with excessive stormwater volumes, resulting in recurring urban floods [5]. For example, during the 2021 storm in Zhengzhou, China, a 24-h rainfall of 617 mm far exceeded system capacity, causing 302 fatalities and massive economic damage [6]. These incidents expose the vulnerability of traditional drainage models and underscore the urgent need to enhance urban stormwater resilience.

In response to these escalating risks, various strategies have been proposed globally, including Low Impact Development (LID), Sustainable Urban Drainage Systems (SUDS), Water Sensitive Urban Design (WSUD), and Green Infrastructure (GI) [7]. These methods aim to reduce stormwater volume through source control, infiltration, and distributed storage. For instance, LID facilities such as rain gardens have demonstrated 30–50% peak flow reduction under moderate rainfall, with a delay in runoff concentration of up to one hour [8]. In China, the Sponge City program—launched in 2013—combines such concepts using permeable pavements and sunken green spaces [9]. Pilot projects (e.g., Wuhan) show 20–40% total runoff reduction during heavy rainstorms, improving system resilience [10]. Recent efforts have also explored integrating Geographic Information Systems (GIS) and hydrological models to assess urban stormwater carrying capacity. Jato-Espino et al. (2016), for example, utilized GIS and stormwater modeling to prioritize the placement of permeable pavements, demonstrating their potential to reduce runoff and support pipe network performance in urban catchments [11]. Globally, studies have further advanced integrated approaches. In Australia, Burns et al. (2015) proposed a hybrid framework combining green and gray infrastructure, achieving up to 45% runoff reduction in urban catchments [12]. In the Netherlands, Molenveld and van Buuren (2019) discussed flood risk and resilience, emphasizing adaptive governance approaches for managing flood risks in a changing climate [13]. In South Africa, Armitage et al. (2014) explored the adaptation of SUDS for African urban contexts, highlighting the need for context-specific solutions in water-scarce regions [14]. These advancements underscore the importance of multi-faceted strategies in urban flood management. Numerous studies have addressed the design of technical systems, quantitative assessment of stormwater capacity, and management optimization. Palla and Gnecco (2015) developed a hydrology-based framework in Genoa, Italy, achieving a 40% peak runoff reduction under a 20-year storm [15]. Eckart et al. (2017) combined green and gray infrastructure in Windsor, Canada, reducing runoff by 30% during moderate events [16]. Zhang and Chui (2018) reviewed LID spatial optimization strategies, showing a 25–35% improvement in watershed-scale capacity [17]. Chen et al. (2024) applied a hybrid model in Beijing, enhancing water quality resilience by 1.0–4.0% under extreme rainfall [18]. Recent research has also explored systemic approaches to urban stormwater management. For example, Reinstaller et al. (2024) presented a multi-objective assessment of mitigation strategies for resilient urban flood management, considering various scenarios and indicators to evaluate efficiency [19]. Similarly, Sharifi et al. (2024) investigated the application of artificial intelligence in digital twin models for stormwater infrastructure systems in smart cities, highlighting the potential of real-time data and advanced modeling for enhanced management [20]. In Brazil, Miguez et al. (2015) proposed a flood resilience framework integrating green infrastructure and urban planning, demonstrating significant flood reduction in Rio de Janeiro [21]. These studies highlight the need for comprehensive frameworks that address both routine and extreme conditions.

Despite these advances, limitations remain. Many studies focus on individual measures or small-scale simulations, lacking an integrated framework that combines engineering, non-engineering, and management strategies [22]. For example, LID and SUDS excel in source reduction but often lack coordination with terminal drainage under extreme conditions [23]. Furthermore, existing models do not adequately address the complexity of urban hydrology, including high imperviousness, dense infrastructure, and socio-functional diversity [24]. To bridge these shortcomings, the concept of Urban Stormwater Carrying Capacity (USCC) is introduced, defined as the maximum runoff volume a city can manage through infiltration, storage, and drainage under specific rainfall scenarios. USCC is categorized into narrow-sense (routine rainfall management) and broad-sense (extreme event resilience), providing a dual-layered approach to urban flood management. The application of the carrying capacity concept in urban contexts is still underdeveloped. Early research focused on river systems; for instance, Knight and Shiono (1996) estimated river channel capacities using hydraulic models [25], and Pender and Faulkner (2011) examined flood coordination at the catchment scale [26]. However, these studies largely overlook urban-specific conditions such as surface hardening and human-induced alterations [27].

The evolution of carrying capacity in stormwater research has progressed from natural systems to urban contexts. Initial studies emphasized the hydrological limits of rivers and floodplains [28,29]. More recent research, such as by Yan et al. (2011), applied the concept to large basins using hydrological simulation [30]. Yet, most remain rooted in natural settings, lacking consideration of urban complexity and infrastructure interactions [30,31]. As extreme events become more frequent, the limitations of traditional approaches become increasingly apparent, underscoring the need for frameworks tailored to urban environments [32].

To address these gaps, this study introduces the concept of Urban Stormwater Carrying Capacity (USCC) and proposes the “2-3-9” technical framework, designed to improve urban flood resilience through a combination of system-level analysis and facility synergy. USCC is defined as the maximum runoff volume a city can manage through infiltration, storage, and drainage under specific rainfall scenarios, highlighting the interplay between hydrology and infrastructure performance. The framework integrates dual management dimensions (narrow-sense and broad-sense USCC), three rainfall scenarios (R₁: light to moderate; R₂: heavy to very heavy; R₃: extreme), and nine facility types (I₁–E₉), forming a full-cycle stormwater management system from source reduction to emergency response.

Compared to existing models, this framework offers three key innovations: it (1) enables multi-level, multi-facility integration; (2) extends the carrying capacity concept to complex urban systems; and (3) enhances adaptability under both normal and extreme rainfall through scenario-specific strategies. Theoretically, the framework broadens the application of carrying capacity in stormwater science. Practically, it supports sponge city planning, infrastructure optimization, and risk-based resource allocation. The following sections detail the definition of USCC, the structure of the “2-3-9” framework, a validation case study in Weifang, and the operational workflow, aiming to provide robust support for sustainable urban flood management.

2. Methodology

2.1. Definition and Connotation of Urban Stormwater Carrying Capacity

2.1.1. Definition of Urban Stormwater Carrying Capacity

(1) Basic Concept

This study introduces the concept of Urban Stormwater Carrying Capacity (USCC) as the maximum capacity of an urban area to store, infiltrate, regulate, and discharge rainfall-generated runoff through the coordinated use of natural and engineered facilities. USCC reflects a city’s ability to manage rainfall impacts of varying intensities via integrated operation of drainage networks, green infrastructure, water bodies, storage systems, and emergency spaces. This capacity is influenced by both natural factors (e.g., rainfall intensity, soil permeability, slope) and human factors (e.g., drainage design, urbanization, management efficiency).

Unlike traditional flood management approaches that assess single-facility capacity, USCC emphasizes systemic and dynamic urban responses. It integrates hydrological processes, infrastructure performance, and socio-functional dynamics into a unified framework. Scientifically, USCC draws on water balance and runoff partitioning theories; strategically, it supports climate adaptation; and practically, it informs planning and resource allocation. As a core metric of resilience to extreme rainfall, USCC helps identify system bottlenecks and enables scenario-based optimization, especially in high-density areas.

(2) Quantitative Representation

To operationalize the USCC concept, this study defines the following four quantitative indicators (

Table 1. Key quantitative indicators for evaluating urban stormwater carrying capacity.

Indicator	Unit	Definition and Application
Total stormwater carrying volume	104 m3	Overall capacity; planning and resilience assessment
Rainfall depth capacity	mm	Cross-region flood resilience comparison
Unit-area capacity	104 m3/km2	Spatial optimization; land use planning
Stormwater carrying coefficient	Dimensionless	Efficiency indicator for infrastructure performance and synergy

) to represent its multidimensional characteristics:

Total stormwater carrying volume (10⁴ m³): the cumulative volume of runoff that can be managed by the urban drainage-storage system, integrating infiltration, detention, and discharge capacity.

Rainfall depth carrying capacity (mm): the depth of rainfall that can be absorbed per unit area, enabling cross-city comparison and policy benchmarking.

Unit-area stormwater carrying volume (10⁴ m³/km²): a spatial indicator reflecting the balance between land use intensity and stormwater management capacity.

Stormwater carrying coefficient (%): the ratio of runoff effectively handled to total rainfall, capturing system efficiency and infrastructure synergy.

This indicator system translates the USCC concept into a functional analytical tool. Compared to conventional single-parameter approaches (e.g., pipe flow rate), it captures the full complexity of urban hydrology. The carrying coefficient can be dynamically updated using real-time monitoring to reflect infrastructure aging or operational conditions, enhancing its value for adaptive planning.

(3) Classification

Urban Stormwater Carrying Capacity (USCC), using nine facility types (I₁–E₉) from green spaces to dual-purpose underground spaces (

Table 2. Coding system for the nine stormwater storage and drainage facility types.

Code	Facility Type	Primary Function	Description
I1	Green spaces	Infiltration	Vegetation interception and soil infiltration
I2	Permeable pavements	Infiltration	High-permeability materials facilitating infiltration
S3	Source detention facilities	Storage	Initial runoff interception and purification
D4	Drainage systems	Drainage	Efficient conveyance to prevent waterlogging
S5	Water bodies	Storage	Natural detention and peak flow mitigation
S6	Dual-purpose surface spaces	Storage	Temporary surface accumulation and infiltration
D7	Overland flow corridors	Drainage	Directed discharge of excess runoff
S8	Temporary floodable roads	Storage	Short-term detention to alleviate drainage load
E9	Dual-purpose underground spaces	Emergency storage	Non-conventional storage under extreme rainfall

Note: I = Infiltration facilities; S = Storage facilities; D = Drainage facilities; E = Emergency facilities. The numeric codes (1–9) reflect the typical sequence of facility activation during stormwater events.

), is divided into two levels based on rainfall intensity and management objectives.Narrow-sense USCC (USCC_N): focuses on managing routine rainfall (e.g., 30-year return period) through standard infrastructure (I₁–S₅) to prevent ponding and maintain daily functionality.

Broad-sense USCC (USCC_B): addresses extreme rainfall (e.g., ≥100-year return period) by incorporating emergency facilities (S₈–E₉) and cross-system coordination to ensure urban resilience and prevent systemic failure.

This risk-tiered classification underpins the scenario-specific design in the “2-3-9” framework. USCC_N reflects baseline capacity under normal conditions, while USCC_B captures resilience under extreme events. The activation of emergency components in USCC_B is essential for raising the system’s upper-performance limit, particularly under changing climate regimes.

(4) Scope of the Study

This study focuses on flood risk management in urban built-up areas. It evaluates both surface and subsurface stormwater systems to construct a dynamic, quantitative USCC assessment framework. The analysis covers nine facility types (I₁–E₉), encompassing source control, conveyance, storage, and emergency detention. While water quality is not included in this phase, this study provides a foundation for resilient, evidence-based infrastructure planning and optimization under varying rainfall scenarios.

2.1.2. Connotations of Urban Stormwater Carrying Capacity

Urban Stormwater Carrying Capacity (USCC) is not merely a technical metric, but a multidimensional concept that integrates natural processes, engineered systems, and human activities. It extends beyond conventional hydrological assessments by capturing the capacity of complex urban systems to absorb, regulate, and respond to rainfall. This study conceptualizes USCC through three dimensions—physical, ecological, and socio-economic—to support the theoretical foundation of the “2-3-9” framework.

(1) Physical Dimension: Coupling of Hydrological Processes and System Performance

The physical dimension reflects the interaction between rainfall–runoff generation and the performance of urban infrastructure. Runoff is governed by rainfall intensity, duration, and spatial distribution, while infiltration and conversion are influenced by soil permeability, slope, and surface hardening [17]. Stormwater carrying capacity is thus determined by the combined effects of the following:

Infiltration capacity, enhanced by facilities like green spaces and permeable pavements, which reduce runoff. Studies show permeable surfaces can lower runoff coefficients from 0.9 to 0.6–0.7 [8]. Storage capacity, offered by detention basins, wetlands, and water bodies that buffer peak flows. Conveyance efficiency, dictated by drainage design and pump capacity, allowing rapid runoff discharge.

Insufficient performance in any one element, such as limited conveyance, may result in flooding. This framework provides the physical rationale behind facility classification and modeling in the “2-3-9” system.

(2) Ecological Dimension: Restoration of the Hydrological Cycle and Enhancement of Environmental Benefits

The ecological dimension captures the feedback between stormwater systems and urban ecosystems. Infiltration and retention help restore disrupted hydrological cycles and recharge groundwater [33]. Green spaces and wetlands play a key role in non-point source pollution control, using vegetation and soil microbes to remove nutrients and suspended solids [10], while also providing habitats that support biodiversity.

Green infrastructure also improves microclimates via evapotranspiration, mitigating urban heat island effects. Vegetative cover and permeable pavements have been shown to lower surface temperatures and reduce local heat accumulation. This dimension links USCC to ecosystem services and aligns with proactive design strategies embedded in the “2-3-9” framework.

(3) Socio-Economic Dimension: Disaster Risk Reduction and Resource Optimization

The socio-economic dimension addresses the relationship between USCC and urban resilience. Increased capacity reduces both direct losses (e.g., property damage, transport disruption) and indirect impacts (e.g., business downtime). Research shows that flood damage correlates positively with water depth, with every 10 cm increase resulting in significant economic escalation [3].

USCC also supports rainwater harvesting and reuse, lowering dependence on external freshwater supplies. Reclaimed stormwater can be used for irrigation, industrial cooling, and other non-potable needs. Moreover, USCC assessments can identify mismatches between urban density and infrastructure capacity. In high-density areas, higher imperviousness leads to more runoff, underscoring the importance of balancing development with infrastructure investment. This dimension directly informs lifecycle planning and emergency system design, particularly for passive facilities (S₈–E₉) in the “2-3-9” framework.

2.2. Classification of Urban Stormwater Storage and Drainage Facilities

To support the technical framework of Urban Stormwater Carrying Capacity (USCC), this study classifies stormwater facilities based on activation sequence, functional characteristics, and operational status during rainfall events. Facilities are grouped into two categories—active and passive—encompassing nine types (Figure 1). This classification defines each facility’s hydrological role and interaction, supporting planning, design, and operation within the “2-3-9” system. It also accounts for surface permeability, retention capacity, and spatial distribution from source to terminal discharge, reflecting the layered structure of urban stormwater systems.

2.2.1. Active Stormwater-Bearing Facilities

Active facilities operate continuously across rainfall events and form the foundation of stormwater management. They are distributed along the runoff pathway—from source to outfall—and provide multi-level regulation through source reduction, process control, and terminal discharge (

Table 3. Comparison of functional characteristics between active and passive stormwater-bearing facilities.

Category	Activation Condition	Core Function	Representative Facilities
Active facilities	Regular operation	Capture–Infiltration–Conveyance–Storage	Green spaces, permeable pavements, source detention facilities, drainage systems, water bodies, dual-purpose surface spaces, overland flow corridors
Passive facilities	Extreme rainfall events	Emergency detention and risk buffering	Temporary floodable roads, dual-purpose underground spaces

). Seven facility types are included, as follows:

Green spaces (e.g., parks, roadside vegetation) reduce runoff through vegetation interception and soil infiltration, also offering ecological benefits such as microclimate regulation and biodiversity enhancement.

Permeable pavements (e.g., porous concrete, asphalt) facilitate infiltration and groundwater recharge. Common in sidewalks and parking areas, they also filter pollutants and support runoff reuse.

Source detention facilities (e.g., rain gardens, bioretention cells) intercept and treat initial runoff through vegetation–soil systems. They integrate well into urban landscapes and align with sponge city concepts.

Drainage systems, including pipes and open channels, provide efficient runoff conveyance. Modern systems often incorporate temporary storage and smart control technologies for adaptive scheduling.

Water bodies (e.g., rivers, lakes, detention ponds) act as natural buffers for peak flow and provide ecological and recreational functions, requiring clear capacity thresholds and water quality controls.

Dual-purpose surface spaces (e.g., plazas, green corridors) temporarily detain or infiltrate runoff during heavy rains while supporting everyday public use.

Overland flow corridors guide excess runoff through designated channels, reducing localized flood risks. Their design integrates ecological buffers to control erosion and pollutant transport.

2.2.2. Passive Stormwater-Bearing Facilities

Passive facilities are activated during extreme rainfall and serve as emergency buffers. Under normal conditions, they perform non-hydrological functions (e.g., transport, commercial use, civil defense) but are temporarily converted to storage under high-intensity events. Two facility types are identified:

Temporary floodable roads, including underpasses and surface segments, detain runoff through natural depressions. Underpasses require pumps and basins, while surface flooding is governed by curbs and terrain. Real-time monitoring and emergency plans are essential to ensure safety.

Dual-purpose underground spaces (e.g., parking garages, basements) offer unconventional storage through protected inlets (e.g., flood barriers). Design must balance flood capacity with waterproofing and structural safety.

Passive facilities, while effective, have drawbacks. Temporary floodable roads (S8) may hinder emergency access during floods, and dual-purpose underground spaces (E9) risk structural issues or unauthorized entry. Elevated access points, robust structural designs, and secure systems can mitigate these challenges.

The coordination of active (I₁–D₇) and passive (S₈–E₉) facilities establishes a dual-layered management system: routine regulation under normal conditions, and emergency buffering under extremes. This reflects the nested structure of narrow- and broad-sense USCC and forms the operational basis for the capacity calculations and scenario applications in the framework.

2.3. Method for Calculating Urban Stormwater Carrying Capacity

The quantitative assessment of Urban Stormwater Carrying Capacity (USCC) is central to the “2-3-9” framework. This section develops a multi-level theoretical model grounded in water balance and runoff partitioning theories. The model comprises three components: (1) a simplified water balance framework, (2) a multi-path runoff partitioning logic, and (3) a unified expression of stormwater capacity. This structure ensures scientific rigor and practical applicability.

2.3.1. Theoretical Model Development

To assess USCC dynamically across rainfall scenarios, this section introduces a hierarchical model and consistent notation (

Table 4. Notation for hydrological quantities and facility-based absorption.

Symbol	Description	Unit
Qs	Surface runoff depth	mm
Qtotal	Total runoff volume	m3
Qinfiltration	Infiltrated volume (VI1 + VI2)	m3
Qstorage	Stored volume (S3, S5, S6, S8, E9)	m3
Qdrainage	Drained volume (D4 + D7)	m3
Qoverflow	Excess runoff	m3
QD4, QD7	Instantaneous discharge (D4, D7)	m3/s

), linking runoff depth (Qs), infiltration (Q_infiltration), storage (Q_storage), and drainage (Q_drainage) with facility-level capacities (V_I1–V_E9, in m³). Instantaneous flows (Q_D4, Q_D7) are converted into cumulative volumes.

(1) Water Balance Framework

The base model follows the following principle:

P = E + I + Q_s + ΔS

(1)

where P is total precipitation, E is evaporation, I is infiltration, Q_s is surface runoff, and ΔS is the change in surface storage. For typical short-duration urban rainfall events (<24 h), both E and ΔS are negligible [34], allowing the equation to be simplified as follows:

P ≈ I + Q_s

(2)

This shows that USCC is governed by infiltration and runoff management capacity, particularly critical in impervious urban settings under intense rainfall.

(2) Runoff Partitioning Logic

To account for diverse facility types, total runoff is decomposed as follows:

Q_total = Q_infiltration + Q_storage + Q_drainage + Q_overflow

(3)

where Q_infiltration captures source control, Q_storage accounts for temporary detention, and Q_drainage reflects conveyance performance. Q_overflow represents unmet runoff, typically managed by emergency infrastructure. This equation illustrates how coordinated facilities dissipate runoff volume and define operational thresholds.

(3) Comprehensive Model Formulation

Assuming Q_overflow ≈ 0 under effective system design, the practical expression of USCC becomes the following:

USCC = Q_infiltration + Q_storage + Q_drainage

(4)

Each term is derived by summing relevant facility capacities (see Section 2.3.2). For example, Q_drainage = V_D4 + V_D7.

Equation (4) assumes that under an effective system design, the total stormwater volume is fully managed by infiltration, storage, and drainage facilities, with Q_overflow ≈ 0. Here, ‘effective system design’ refers to a stormwater management system where the combined capacity of all facilities (I₁–E₉) is sufficient to handle the total runoff volume (Q_total) for the given rainfall scenario, ensuring no significant overflow. This assumption is validated by the case study in Section 4, where the carrying coefficients(η) for all rainfall scenarios (R₁, R₂, R₃) are greater than 1 (e.g., R₁: η = 3.96, R₂: η = 1.03, R₃: η = 1.36). Since η > 1 indicates that the current USCC exceeds the target volume, it confirms that the system design effectively eliminates overflow under both routine and extreme conditions.

While the assumption of Q_overflow ≈ 0 is made under the condition of effective system design, it is acknowledged that in real-world scenarios, particularly under rainfall events exceeding design thresholds, overflow may still occur. The “2-3-9” framework addresses this by incorporating passive facilities (S₈–E₉) in the broad-sense USCC (USCC_B) to handle extreme events (e.g., R₃). Future iterations of the framework could integrate probabilistic modeling or real-time monitoring to further enhance its adaptability to unforeseen extreme conditions.

The effectiveness of the “2-3-9” framework lies in the Q-component synergy, which refers to the enhanced overall stormwater carrying capacity achieved through the coordinated interaction of infiltration (Q_infiltration), storage (Q_storage), and drainage (Q_drainage) components via the nine facility types (I₁–E₉). This synergy ensures that the system can adaptively manage stormwater across various rainfall scenarios (Figure 2).

This formulation quantifies the total runoff volume a city can absorb, store, and discharge under defined scenarios. Within the “2-3-9” framework, active facilities (e.g., green spaces, pipes) manage routine flows, while passive ones (e.g., E₉) support capacity during peak events. This model serves as the analytical core of scenario-based USCC evaluation and system optimization.

(4) Theoretical Implications

This model bridges classical hydrological theory with facility-level classification, translating complex stormwater processes into a structured, quantitative tool. By structuring USCC into infiltration, storage, and drainage paths, Equation (4) clearly defines each facility’s role and lays a foundation for facility configuration, real-time monitoring, and scenario planning. It also supports flexible adaptation to varying rainfall intensities and evolving urban development pressures.

2.3.2. Estimation Method for Facility-Based Stormwater Absorption Capacity

This section outlines methods to calculate the stormwater absorption capacities of nine facility types within the “2-3-9” framework, categorized into infiltration, storage, drainage, and emergency functions (

Table 5. Key parameters for stormwater absorption capacity estimation.

ID	Facility Name	Parameter Type	Symbol	Unit	Typical Value (Weifang)	Value Range	Measurement/Estimation Method	Source	Sensitivity Ranking
I1	Green space	Infiltration coefficient	KI1	m/s	3.5 × 10−6	10−7–10−5	Field test	Field test (double-ring infiltrometer, ASTM D3385-09)	Medium
I1	Green space	Effective area	AI1	km2	4.11	—	GIS	Weifang City Land Use GIS Dataset (2023)	Low
I2	Permeable pavement	Infiltration coefficient	KI2	m/s	1.0 × 10−4	10−5–10−3	Code	Design code GB/T 25993-2023 (B-grade permeable paving)	Medium
I2	Permeable pavement	Effective area	AI2	km2	0.138649	—	GIS	Weifang City Land Use GIS Dataset (2023)	Low
S3	Source detention facility	Storage volume	VS3	104 m3	1.8	—	Survey	Field survey (Weifang City stormwater facility inventory, 2023)	Medium
D4	Drainage system	Manning roughness	nD4	—	0.013	0.011–0.015	Code	Design code GB 50014-2016	Medium
D4	Drainage system	Catchment area	AD4	km2	24	—	GIS	Weifang City Drainage Network GIS Dataset (2023)	Low
S5	Water body	Storage depth	HS5	m	1.94	—	Design	Design specification	Medium
S6	Dual-purpose surface space	Storage volume	VS6	104 m3	3	—	Survey	Field survey (Weifang City public space inventory, 2023)	Medium
D7	Overland flow corridor	Cross-sectional area	CSD7	m2	163.7	—	Survey	Field survey	Low
S8	Temporary floodable road	Ponding depth	HS8	m	0.15	—	Code	Design code	Low
E9	Dual-purpose underground space	Storage depth	HE9	m	1	—	Survey	Field survey	High

). These methods, grounded in hydrological principles (e.g., Darcy’s Law, Manning’s Equation), enable quantitative Urban Stormwater Carrying Capacity (USCC) assessment.

(1) Infiltration Facilities

Infiltration facilities dissipate stormwater through soil or porous materials and are primarily used for source control. Their absorption capacity is expressed as the total infiltrated volume.

Green space absorption capacity is based on soil infiltration properties and is calculated as follows:

V_I1 = K_I1 × J × A_I1 × t_I1

(5)

where V_I1 is the volume of rainwater absorbed by green spaces (m³), K_I1 is the saturated hydraulic conductivity of the soil (m/s), J is the hydraulic gradient (dimensionless, typically approximated by surface slope), A_I1 is the effective infiltration area (m²), and t_I1 is the infiltration duration during rainfall (s). This formula is based on Darcy’s Law under the assumption of steady-state saturated flow, and K_I1 should be obtained via field tests, such as the double-ring infiltrometer.

Permeable pavement absorption capacity depends on the infiltration performance of its materials and is calculated as follows:

V_I2 = K_I2 × J × A_I2 × t_I2

(6)

where V_I2 is the infiltrated volume (m³), K_I2 is the infiltration coefficient of the pavement (m/s), J is the hydraulic gradient, A_I2 is the effective permeable area (m²), and t_I2 is the infiltration duration. The value of K_I2 is determined by the porosity and structure of the pavement material and may be obtained from lab testing or design codes.

The sum Q_infiltration = V_I1 + V_I2 represents the total stormwater managed by infiltration facilities.

(2) Storage Facilities

Storage facilities manage stormwater through physical detention space, typically for intermediate (process-based) control. Their absorption capacity is expressed as stored volume.

Source detention facilities, such as rain gardens, are sized based on their designed storage volume and calculated by the following equation:

V_S3 = A_S3 × H_S3

(7)

where V_S3 is the storage capacity (m³), A_S3 is the plan area (m²), and H_S3 is the effective storage depth (m).

Water bodies provide volume buffering and their storage capacity is expressed as follows:

V_S5 = A_S5 × H_S5

(8)

where A_S5 is the surface area (m²) and H_S5 is the detention depth above the normal water level (m).

Dual-purpose surface spaces, such as public squares or parks, are modeled similarly as follows:

V_S6 = A_S6 × H_S6

(9)

where A_S6 is the area available for stormwater detention (m²), and H_S6 is the maximum allowable water depth (m).

(3) Drainage Facilities

Drainage facilities discharge stormwater through designed flow conveyance systems. Their capacity is determined using flow rate and volume estimates.

Drainage network capacity is calculated using the Manning formula, as follows:

$$Q_{D4}={\displaystyle \frac{{CS}_{D4}\times {R_{D4}}^{\frac{2}{3}}\times {S_{D4}}^{\frac{1}{2}}}{n_{D4}}}$$

(10)

where Q_D4 is the flow rate (m³/s), n_D4 is Manning’s roughness coefficient, CS_D4 is the cross-sectional area (m²), R_D4 is the hydraulic radius (m), and S_D4 is the slope (dimensionless).

Alternatively, drainage network capacity can be calculated using runoff principles, as follows:

Q_D4 = C_D4 × I_D4 × A_D4

(11)

where C_D4 is the runoff coefficient (dimensionless), I_D4 is rainfall intensity (m/s), and A_D4 is the contributing area (m²). By combining Equations (10) and (11), I_D4 can be solved and then integrated over time using intensity–duration curves to obtain H_D4.

The cumulative discharge volume is as follows:

V_D4 = H_D4 × A_D4 × C_D4

(12)

Overland flow corridors (typically open channels) are modeled similarly as follows:

$$Q_{D7}={\displaystyle \frac{{CS}_{D7}\times {R_{D7}}^{\frac{2}{3}}\times {S_{D7}}^{\frac{1}{2}}}{n_{D7}}}$$

(13)

Q_D7 = C_D7 × I_D7 × A_D7

(14)

V_D7 = H_D7 × A_D7 × C_D7

(15)

The total drainage capacity is the sum of V_D4 and V_D7, which forms the Q_drainage component in the USCC model.

(4) Emergency Facilities

Emergency facilities provide temporary detention during rainfall events that exceed standard design thresholds. Their capacity is expressed in terms of volume.

For underpass-type temporary floodable roads:

V_S8,up = A_S8,up × H_S8,up

(16)

where A_S8,up is the ponding area (m²) and H_S8,up is the maximum allowable depth (m), typically set by design codes.

For overflow-type floodable roads (e.g., where curb height is exceeded):

V_S8,FR = A_S8,FR × H_S8,FR

(17)

where H_S8,FR is determined by surrounding terrain or building elevations.

For dual-purpose underground spaces, such as civil defense structures, garages, or commercial basements:

V_E9 = A_E9 × H_E9 × α

(18)

where A_E9 is the total usable area (m²), H_E9 is the allowable storage depth (m) based on structural safety limits, and α is a safety utilization factor (typically 0.8–1.0) to account for operational uncertainty.

This methodology decomposes the total USCC into functional components and facility types. It ensures repeatability and adaptability under varying rainfall scenarios using standardized inputs (e.g., K, n, H), thereby enabling robust capacity evaluation and system design.

2.4. Classification of Urban Rainfall Scenarios and Management Strategies

To evaluate USCC performance across different rainfall conditions, this study classifies 24-h cumulative rainfall into three scenarios—R₁, R₂, and R₃—based on GB/T 28592-2012. Each scenario is aligned with the narrow- and broad-sense USCC definitions (Section 2.1.1) and supports the theoretical modeling and capacity estimation procedures introduced in Section 2.3. The goal is to guide facility configuration and operational planning through tiered management strategies.

Table 6. Classification of rainfall scenarios and corresponding management strategies.

Rainfall Scenario	24-h Rainfall (mm)	Management Objective	Management Strategy
R1 (Light to moderate rain)	Light rain < 10 mm; moderate rain 10–24.9 mm; heavy rain 25–49.9 mm	Ensure normal drainage with no significant surface ponding	Prioritize source control via I1–S3; supplement with D4 for runoff conveyance.
R2 (Heavy to very heavy rain)	Heavy rain 50–99.9 mm; very heavy rain 100–249.9 mm	Control flooding, protect key zones	On top of R1, activate D7 and S6 to direct excess runoff; temporarily use S8 for detention.
R3 (Extreme rainstorm)	≥250 mm	Ensure safety, minimize losses, enable recovery	Deploy all facilities (I1–E9); maximize drainage and storage; activate E9 post-evacuation; initiate emergency protocols.

summarizes the rainfall thresholds, management objectives, and response strategies for each scenario.

This rainfall scenario classification follows GB/T 28592-2012 and is refined according to best practices in stormwater management. It establishes a tiered response framework under the principle of no ponding under light rain, no disaster under heavy rain, and effective response under extreme events.

In R₁, management focuses on maximizing Q_infiltration via I₁–S₃ and ensuring Q_drainage through coordinated operation of I₁–S₅ to meet routine needs. R₂ introduces S₆–S₈ to build overflow pathways, enabling joint operation of Q_storage and Q_drainage to maintain critical functions. Under R₃, E₉ is activated, and the full infrastructure set (I₁–E₉) is mobilized, with E₉ forming the core of expanded Q_storage to protect life and support recovery.

These strategies align with the facility classification (Section 2.2) and theoretical model (Section 2.3.1), forming the methodological basis for capacity estimation (Section 2.3.2) and case validation (Section 2.6).

As illustrated in Figure 3, R₁ management relies on I₁–S₃ with support from D₄ and S₅. In R₂, D₇, S₆, and S₈ are added to handle overflow. Under R₃, full activation of E₉ shifts the system from narrow- to broad-sense USCC, enhancing resilience and ensuring functional stability during extreme rainfall.

2.5. Quantitative Evaluation Framework for Urban Stormwater Carrying Capacity

Figure 4 presents a comprehensive flowchart illustrating the overall workflow of the proposed methodology for assessing and optimizing USCC. It details the sequential steps, data inputs, and materials used, providing a clear overview of the ‘2-3-9’ framework.

To operationalize the “2-3-9” framework for USCC assessment, this study develops a quantitative evaluation system grounded in water balance and runoff partitioning theories. The framework follows a five-step process: target setting, status assessment, gap analysis, optimized configuration, and feedback. It integrates the definitions (Section 2.1), facility classification (Section 2.2), computational models (Section 2.3), and rainfall scenarios (Section 2.4), providing a structured and scalable method for flood resilience planning (Figure 5).

The framework was applied in the Weifang pilot area, resolving planning ambiguities and offering a flexible tool for decision-makers.

(1) Setting USCC Target Levels

USCC targets establish benchmarks for scenario-based evaluation and align with rainfall scenarios R₁–R₃ and the corresponding dimensions of USCC (Section 2.1.1), as follows:

Tier I (R₁): ensure normal drainage with no surface ponding via I₁–S₅.

Tier II (R₂): prevent flooding and protect key functions using I₁–S₈.

Tier III (R₃): maintain safety and operational continuity through full system activation (I₁–E₉).

Each tier is associated with a design return period (T), as shown in

Table 7. Target classification for USCC.

Target Level	Rainfall Scenario	Stormwater Management Objective	Return Period T (Years)	Design Rainfall Htarget (mm)
I	R1	No surface ponding	2–5 years	H1
II	R2	No urban flooding	20–50 years	H2
III	R3	No functional failure	≥100 years	H3

, with rainfall values (H_target) derived from regional hydrological data.

(2) Calculating the Target USCC Volume

Using the rainfall depth and urban area, the required stormwater absorption volume is calculated as follows:

V_target = H_target × A_city

(19)

where V_target is in m³, H_target (m) is the design rainfall, and A_city (m²) is the urban area. This serves as the baseline for system comparison.

(3) Assessing Existing Capacity

The actual capacity is calculated as follows:

$$V_{current}={\sum }_{i=1}^9{V}_i$$

(20)

where each V_i corresponds to facility types I₁–E₉, with formulas from Section 2.3.2. Required input parameters (e.g., K_I1, R_D4, t) are obtained from field data or hydrological models.

(4) Gap Analysis and Optimization

The capacity gap is defined as follows:

ΔV = V_current − V_target

(21)

If capacity is insufficient (ΔV < 0), targeted measures are applied to the corresponding component—source control (I₁–I₂), storage (S₃–S₆), or drainage (D₄–D₇).

Optimization may apply linear programming or multi-objective methods to adjust facility contributions while satisfying V_current ≥ V_target.

(5) Monitoring and Feedback Mechanism

A real-time monitoring system collects key hydrological data, including rainfall (H), flow rates (Q_D4), and storage levels (S₅), through sensors and remote sensing. These inputs enable continuous updates of facility-level capacities (V_i), which are aggregated to recalculate the total USCC (V_current) via Section 2.3.2.

If ΔV falls below zero and exceeds 10% of the target volume (V_target), adaptive adjustments are triggered—such as extending overland flow corridors (D₇) or increasing underground storage (E₉). This feedback loop allows the system to respond dynamically to changing hydrological conditions and maintain performance under variable scenarios.

2.6. Validation of Urban Stormwater Carrying Capacity Assessment: A Case Study in Weifang

This section applies the “2-3-9” framework to the Zhangmian River area in Weifang City to validate the proposed USCC assessment method. The analysis integrates USCC definitions (Section 2.1), facility classification (Section 2.2), capacity models (Section 2.3), rainfall scenarios (Section 2.4), and the evaluation framework (Section 2.5), enabling a comprehensive assessment of system performance and optimization potential.

2.6.1. Overview of the Study Area

The study area spans 24 km² along both sides of the Zhangmian River, forming a distinct hydrological unit. Land use is predominantly residential, with notable spatial variation: north of Baotong Street is largely undeveloped (≈10% impervious), the central section consists of new residential blocks (≈60%), and the southern zone includes older, high-density neighborhoods (≈75%). The composite runoff coefficient (C) is estimated at 0.65 based on weighted land use. The topography is flat, and drainage relies on both river channels and piped networks, making it a representative case for USCC evaluation in urban built environments.

2.6.2. Calculation of Stormwater Carrying Capacity

Based on the facility classification (Section 2.2) and capacity estimation methods (Section 2.3.2), the absorption capacities of active (I₁–D₇) and passive (S₈–E₉) facilities in the Zhangmian River area were calculated (unit: 10⁴ m³). Data were sourced from 2023 statistics, field surveys, and calibrated parameters. Following the modeling approach in Section 2.3.1 and the evaluation framework in Section 2.5, assessments were conducted under three rainfall scenarios defined in Section 2.4: R₁: light to moderate rain (3-year return, H_target = 51 mm); R₂: heavy to very heavy rain (30-year return, H_target = 236 mm); and R₃: extreme rainstorm (100-year return, H_target = 300 mm). Rainfall parameters were derived from regional hydrological statistics.

(1) Capacity of Active Facilities

Seven active facility types were evaluated: green spaces (I₁), permeable pavements (I₂), source detention (S₃), drainage networks (D₄), water bodies (S₅), dual-purpose surfaces (S₆), and overland flow corridors (D₇). Input data were obtained from land use mapping, field tests, and standard design values.

Infiltration capacity was primarily provided by I₁ and I₂, with a combined volume exceeding 100 × 10⁴ m³, reflecting strong source control potential.

Storage capacity was distributed across rain gardens, open spaces, and water bodies, with S₅ alone contributing over 310 × 10⁴ m³, forming the system’s core under R₁–R₂.

Drainage capacity, calculated from catchment hydraulics, showed that D₄ and D₇ jointly discharged over 160 × 10⁴ m³, supporting efficient conveyance under higher-intensity events.

Together, these active components demonstrated robust performance across infiltration, retention, and drainage, ensuring adaptability under R₁ and R₂ scenarios.

(2) Capacity of Passive Facilities

Under R₃, passive facilities—temporary floodable roads (S₈) and underground spaces (E₉)—were assessed for their emergency detention roles.

While S₈ offered limited capacity, its strategic placement helped buffer localized overflow. The primary contribution came from E₉, with a usable volume of 394 × 10⁴ m³—approximately 40% of the total capacity under R₃. These spaces were assumed fully deployable post-evacuation.

Passive components thus provided critical redundancy, significantly enhancing system resilience under 100-year events. Their integration within the “2-3-9” framework underscores the value of combining standard infrastructure with adaptive spatial reserves for peak-event management.

(3) USCC Evaluation

Based on the indicators in Section 2.1.1 (Table 1) and the model in Section 2.3.1, the USCC performance under R₁–R₃ is summarized in

Table 8. USCC performance under R₁–R₃ scenarios.

Scenario	Htarget (mm)	Vtarget (104 m3)	Activated Facilities	Vcurrent (104 m3)	Hcurrent (mm)	η	Q Distribution (%)	Target Achievement
R1	51	122.4	I1–S5	484.1	202	3.96	Qinfiltration: 21%, Qstorage: 64%, Qdrainage: 15%	No ponding under light rain; significant surplus
R2	236	566.4	I1–S8	585.5	244	1.03	Qinfiltration: 17%, Qstorage: 54%, Qdrainage: 29%	No flooding under heavy rain; functions maintained
R3	300	720.0	I1–E9	979.5	408	1.36	Qinfiltration: 10%, Qstorage: 72%, Qdrainage: 18%	Withstands extreme rain; core functions protected

:

In R₁ (3-year return), the USCC_N reaches 484.1 × 10⁴ m³ (H = 202 mm, η = 3.96), indicating substantial overcapacity. Storage accounts for 64%, primarily from S₅. While robust, η suggests potential redundancy.

Under R₂ (30-year return), the system manages 585.5 × 10⁴ m³ (H = 244 mm, η = 1.03), meeting design expectations. Q_drainage increases by 98.2 × 10⁴ m³ via S₆–D₇, boosting capacity by 17%.

In R₃ (100-year return), USCC_B reaches 979.5 × 10⁴ m³ (H = 408 mm, η = 1.36), exceeding the target. E₉ contributes 40% of Q_storage, confirming the critical role of emergency detention.

(4) Optimization Recommendations

From the gap analysis (Section 2.5), the following targeted strategies were proposed for each scenario:

R₁: Despite high η (3.96), no adjustment is recommended. Facilities I₁–S₅ are foundational and essential for higher-intensity events; downsizing may compromise system resilience.

R₂: Minor surplus observed, particularly in drainage. Extending or reconfiguring D₇ could further optimize flow distribution during peak conditions.

R₃: Excess capacity stems from E₉ (394 × 10⁴ m³). Increasing its volume to 500 × 10⁴ m³—e.g., by deepening the space—would improve adaptability and rebalance Q components, reducing Q_storage share from 72% to ~65%.

These refinements reflect the scalability and flexibility of the “2-3-9” framework, enabling adaptive, performance-driven infrastructure planning under varied hydrological stressors.

2.6.3. Scenario-Based Evaluation Summary

In all three rainfall scenarios (R₁–R₃), the USCC of the Zhangmian River area exceeds the respective target rainfall thresholds, confirming the validity of the capacity model in Section 2.3 and the framework in Section 2.5. The system meets the goals of “no ponding” under R₁, “no flooding” under R₂, and “no functional failure” under R₃, consistent with the objectives defined in Section 2.4. As shown in Figure 6 and Table 8, active facilities (I₁–D₇) perform effectively under routine scenarios, while passive facilities (S₈–E₉) significantly enhance Q_storage under extreme events (e.g., up to 72% in R₃), addressing the increasing challenges of extreme rainfall as noted in the introduction [4]. The optimization proposals based on ΔV further illustrate the systemic and adaptive nature of the “2-3-9” framework.

3. Results

The proposed “2-3-9” USCC framework was applied to the 24 km² Zhangmian River district case study. This section presents the key findings, including the framework’s performance across the three design rainfall scenarios, the outcomes of the application workflow and optimization steps, and the results of sensitivity analyses on critical parameters.

3.1. Framework Implementation and Evaluation of the “2-3-9” Technical System

3.1.1. Realization and Optimization of the Dual Management Dimensions

As defined in Section 2.1.1, the “2-3-9” framework applies dual management dimensions by activating different facilities based on rainfall intensity. Narrow-sense USCC is engaged for R₁ (3-year return period, H_target = 51 mm) and R₂ (30-year, H_target = 236 mm) using primarily source and intermediate facilities (I₁–S₈), while broad-sense USCC addresses extreme events (R₃, 100-year, H_target = 300 mm) by deploying emergency storage and drainage measures (S₈–E₉) to enhance resilience. The quantitative results from the Zhangmian River area are as follows:

R₁: USCC_N = 484.1 × 10⁴ m³ (H_actual = 202 mm, η = 3.96); Q_infiltration = 101.7 × 10⁴ m³ (21.0%), Q_storage = 312.2 × 10⁴ m³ (64.5%), Q_drainage = 70.2 × 10⁴ m³ (14.5%)

R₂: USCC_N = 585.5 × 10⁴ m³ (H_actual = 244 mm, η = 1.03); Q_infiltration = 101.7 × 10⁴ m³ (17.4%), Q_storage = 315.4 × 10⁴ m³ (53.9%), Q_drainage = 168.4 × 10⁴ m³ (28.7%)

R₃: USCC_B = 979.5 × 10⁴ m³ (H_actual = 408 mm, η = 1.36); Q_infiltration = 101.7 × 10⁴ m³ (10.4%), Q_storage = 709.4 × 10⁴ m³ (72.4%), Q_drainage = 168.4 × 10⁴ m³ (17.2%)

In R₁–R₂, narrow-sense USCC utilizes I₁, I₂, S₃, and S₅ for effective infiltration and storage, while D₄ and D₇ enhance drainage, shifting Q_storage from 64.5% to 53.9% and Q_drainage from 14.5% to 28.7%. In R₃, broad-sense USCC leverages S₈–E₉, with E₉ alone contributing 394 × 10⁴ m³ (40.2% of total), elevating Q_storage to 72.4%.

Further optimization analysis shows that increasing E₉’s storage depth (H_E9) from 1.0 m to 1.5 m (thereby expanding its capacity to 500 × 10⁴ m³) would raise USCC_B to 1085.5 × 10⁴ m³ (with H_actual increasing to 452 mm and η to 1.51). This enhancement boosts Q_storage to 75.1% and correspondingly reduces Q_drainage to 15.5%, indicating improved system resilience under extreme rainfall. The scenario analyses also revealed that no adjustment is necessary for R₁ despite the high carrying coefficient (η = 3.96), because the facilities I₁–S₅ active in R₁ also contribute to higher-intensity scenarios (ensuring built-in capacity for R₂–R₃). Future studies could explore optimizing facility configurations to balance cost efficiency with resilience. In contrast, for the R₃ scenario, the above-mentioned expansion of E₉’s capacity demonstrates the scalability of emergency infrastructure: η increases from 1.36 to 1.51 and the Q_storage/Q_drainage ratio rises from 4.21 to 4.85 with the deeper reservoir, reflecting a significant improvement in extreme-event performance.

3.1.2. Effectiveness of Refined Management Across Three Rainfall Scenarios

Following the guidelines of GB/T 28592–2012, three representative rainfall scenarios were implemented in the “2-3-9” framework—R₁ (light to moderate rain), R₂ (heavy rain), and R₃ (extreme rain)—to enable tiered, scenario-specific stormwater management. Evaluation results for the Zhangmian River area are summarized in Table 8, and Figure 7 illustrates the variation of the carrying coefficient (η) across these scenarios.

In R₁, the system absorbed 202 mm of rainfall (η = 3.96), far exceeding the 51 mm design target. Storage dominated (64%), with S₅ alone contributing the majority. While effective for routine protection, the result suggests potential overdesign and room for resource optimization.

In R₂, the system handled 244 mm (η = 1.03), meeting design expectations. Additional facilities—S₆ (3 × 10⁴ m³), D₇ (98.2 × 10⁴ m³), and S₈ (0.21 × 10⁴ m³)—were activated to improve overflow management. Q_drainage rose from 15% (R₁) to 29% (168.4 × 10⁴ m³), validating the enhanced flow path strategy outlined in Section 2.4.

In R₃, total capacity reached 979.5 × 10⁴ m³ (H = 408 mm, η = 1.36). Passive facilities, especially E₉, contributed 394 × 10⁴ m³—over 55% of Q_storage and 40% of total capacity—raising Q_storage to 72.4%. The combined effect of S₈ and E₉ ensured system stability and core functional continuity under extreme conditions.

3.1.3. Synergistic Performance of the Nine Stormwater Facilities

The “2-3-9” framework establishes an integrated management chain from source to outlet by coordinating nine types of stormwater infrastructure (I₁–E₉). Their activation patterns and functional contributions under different rainfall scenarios are illustrated in Figure 8.

In R₁ (H_target = 51 mm), I₁–S₅ were activated. Under rainfall <24.9 mm, I₁ (51.8 × 10⁴ m³) and S₃ (1.8 × 10⁴ m³) dominated infiltration (21%, 101.7 × 10⁴ m³). For 25–49.9 mm events, D₄ (70.2 × 10⁴ m³) and S₅ (310.4 × 10⁴ m³) were added, with S₅ contributing most to Q_storage (64.5%).

In R₂ (H_target = 236 mm), S₆ (3 × 10⁴ m³), S₈ (0.21 × 10⁴ m³), and D₇ (98.2 × 10⁴ m³) were added. Q_drainage increased to 168.4 × 10⁴ m³ (29%), while Q_storage reached 315.41 × 10⁴ m³ (53.9%). The Q_storage/Q_drainage ratio dropped from 4.45 (R₁) to 1.87, indicating improved drainage coordination.

In R₃ (H_target = 300 mm), passive facilities dominated. E₉ (394 × 10⁴ m³) and S₈ jointly contributed 40.2% of USCC_B. Q_storage rose to 72.4% (709.41 × 10⁴ m³), with a Q_storage/Q_drainage ratio of 4.21. After optimizing E₉ to 500 × 10⁴ m³, the ratio increased to 4.85, demonstrating enhanced synergy and improved resilience under extreme conditions.

3.2. Application and Optimization of the Technical Framework

This section evaluates the implementation and optimization potential of the “2-3-9” framework using the Zhangmian River area (Weifang) as a case study. Based on the quantitative process in Section 2.5, the R₂ scenario (H_target = 236 mm) is used to examine performance across five steps: target setting, current capacity assessment, capacity gap analysis, optimization recommendations, and monitoring and feedback. The outcomes of each step in the Zhangmian River area application are detailed below.

(1) Target Setting

According to local flood control standards, the design rainfall for the R₂ scenario was set at H_target = 236 mm, with the total built-up area of A_city = 24 km². Using Equation (19), the corresponding target stormwater absorption volume was calculated as follows: V_target = H_target × A_city = 566.4 × 10⁴ m³.

This value served as the quantitative benchmark for evaluating the system’s performance under R₂ conditions.

(2) Current Capacity Assessment

As calculated in Section 2.6.2, the current absorption capacity under R₂ conditions was V_current = 585.51 × 10⁴ m³, corresponding to an actual rainfall depth of H_current = 244 mm. This reflects the combined performance of activated facilities I₁–S₈ in the study area.

(3) Gap Analysis

Using Equation (21), the capacity gap was determined as follows: ΔV = V_current − V_target = 19.11 × 10⁴ m³, with a carrying coefficient of η = H_current/H_target = 1.03 (i.e., a 3.3% surplus). This indicates that the system fully meets flood control targets with slight overcapacity.

(4) Optimization Recommendations

Given the marginal surplus (η = 1.03), no immediate structural adjustments are necessary. The slight redundancy may enhance the system’s ability to absorb fluctuations in future rainfall events. It is recommended that regular maintenance (e.g., soil loosening in green spaces, pipeline cleaning, sediment removal in water bodies) be conducted to preserve facility performance and maintain the current USCC level.

(5) Monitoring and Feedback

To support adaptive management, a monitoring system is proposed to track real-time rainfall and facility operation data (e.g., D₄ pipe flow in m³/s, S₅ water level in meters). The system integrates hydrological sensors (e.g., rain gauges, flow meters, water level sensors) and remote sensing technology.

Actual rainfall (H_actual) is compared with the R₂ design threshold (236 mm) to determine scenario exceedance. Facility performance is dynamically updated using flow integration (D₄) and volume–depth calibration (S₅) to estimate real-time Vi, which is aggregated to compute the updated V_current.

If H_actual > H_target and ΔV < 0 (e.g., dropping to −5 × 10⁴ m³), minor structural optimizations may be triggered—such as increasing the cross-sectional area of D₇ by 6%, which would raise V_D7 by approximately 6 × 10⁴ m³.

These monitoring insights provide a feedback loop for dynamic calibration of facility performance, ensuring long-term stability and adaptability of the stormwater system.

3.3. Sensitivity and Optimization Analysis of Key Parameters Affecting USCC

To evaluate how key design parameters influence USCC outcomes, sensitivity analysis was performed on two variables: the composite runoff coefficient (C) and underground storage depth (H_E9), under R₂ (H_target = 236 mm) and R₃ (H_target = 300 mm). Impacts on V_current, η, and Q components were assessed using the models in Section 2.3.2 (Equations (10)–(15)).

3.3.1. Sensitivity to the Composite Runoff Coefficient (C)

The runoff coefficient (C) reflects changes in impervious surface coverage. Increases in C directly raise the drainage demand (Q_drainage) as indicated by Equations (11) and (14), without altering the capacities of infiltration and storage facilities. Consequently, drainage infrastructure such as pipes and flow corridors must be upgraded or expanded to match the higher runoff.

Under the R₂ baseline, the USCC performance was as follows: V_current = 585.51 × 10⁴ m³, H_current = 244 mm, η = 1.03, Q_infiltration = 101.7 × 10⁴ m³ (17.4%), Q_storage = 315.41 × 10⁴ m³ (53.9%), Q_drainage = 168.4 × 10⁴ m³ (28.7%), C = 0.65 (baseline).

When C increases to 0.75, the required Q_drainage increases by 15.4% to 194.31 × 10⁴ m³. To meet this demand, D₇ must increase its discharge from 98.2 to 124.11 × 10⁴ m³ (a 26.3% increase).

At C = 0.85, the required Q_drainage rises by 30.8% to 220.22 × 10⁴ m³, requiring D₇ to expand to 150.02 × 10⁴ m³ (53.3% increase), or alternative channels must be added.

The updated total stormwater capacity becomes the following: C = 0.75, V_current = 611.42 × 10⁴ m³, H_current = 255 mm, η = 1.08; C = 0.85, V_current = 637.33 × 10⁴ m³, H_current = 266 mm, η = 1.13.

This confirms that Q_drainage is highly sensitive to increases in C, while Q_infiltration and Q_storage remain unchanged. In high-density areas, increasing D₇’s cross-sectional area to 250 m² or adding overflow corridors may be necessary. The results highlight the need for enhanced source control strategies in future urban development and renewal plans.

3.3.2. Sensitivity to Underground Storage Depth (H_E9)

The depth of underground storage (H_E9) critically influences emergency detention capacity under extreme rainfall (R₃). If H_E9 is reduced from 1.0 m to 0.5 m:

Initial conditions: USCC_B = 979.51 × 10⁴ m³ (H_current = 408 mm, η = 1.36), Q_infiltration = 101.7 × 10⁴ m³ (10.4%), Q_storage = 709.41 × 10⁴ m³ (72.4%), Q_drainage = 168.4 × 10⁴ m³ (17.2%),V_E9 = 394 × 10⁴ m³.

After reduction: V_E9 = 197 × 10⁴ m³ (50% decrease), Q_storage drops to 512.41 × 10⁴ m³, USCC_B = 782.51 × 10⁴ m³, H_current = 326 mm, η = 1.09 (down from 1.36), ΔH = 82 mm.

Q component proportions adjust as follows: Q_infiltration = 13.0% (+2.6%), Q_storage = 65.5% (–6.9%), Q_drainage = 21.5% (+4.3%).

To restore η to 1.36, a supplemental 197 × 10⁴ m³ is needed. Options include the following: increasing the D₇ cross-section by 90% (from 163.7 m² to 311 m²), boosting V_D7 to 186 × 10⁴ m³ (USCC_B ≈ 968.51 × 10⁴ m³); adding new flow corridors (~49 × 10⁴ m³) and expanding S₅ (e.g., increasing H_S5 by 0.6 m to gain 148 × 10⁴ m³). The second option restores USCC_B to 979.51 × 10⁴ m³, close to the original performance.

These findings demonstrate that reducing H_E9 by 50% causes a 27.8% decline in Q_storage, η drops from 1.36 to 1.09, and the surplus capacity (ΔH) narrows from 108 mm to just 26 mm—significantly weakening emergency resilience. This underscores the pivotal role of E₉ in extreme scenarios and the need to preserve its depth in design.

3.3.3. Sensitivity Trends

Figure 9 illustrates how changes in these key parameters (C and H_E9) reshape the distribution of runoff among infiltration, storage, and drainage components. For increases in imperviousness, as C rises from 0.65 to 0.75 and 0.85, Q_drainage in the R₂ scenario climbs from 28.7% of total runoff to about 31.8% and 34.6%, respectively, while Q_storage correspondingly declines (from 53.9% down to ~49.5%). In contrast, when the emergency storage depth H_E9 is halved, the R₃ scenario sees Q_storage drop from 72.4% to 65.5% of total volume and Q_draiage increase from 17.2% to 21.5%, with the carrying coefficient η decreasing by roughly 27%. These trends confirm that highly urbanized areas (high C) will put disproportionate pressure on drainage infrastructure and that adequate depth in emergency reservoirs (H_E9 ≥ 1 m) is essential to preserve capacity during extreme events. Without such design considerations, cities would face a sharp decrease in stormwater carrying capacity and an elevated risk of flooding when conditions push beyond baseline parameters.

4. Discussion

The results above are interpreted here in the context of the existing literature and the broader implications for urban stormwater management. Key aspects of the “2-3-9” framework—its dual-level management strategy, integrated use of diverse facilities, comparative advantages over conventional approaches, parameter sensitivity, and scalability—are discussed, along with potential applications in different global settings.

4.1. Multi-Scenario Management and Adaptive Capacity

One of the prominent strengths of the “2-3-9” framework is its ability to manage stormwater across a spectrum of rainfall events by utilizing a dual (narrow- vs. broad-sense) management structure. This design enables a high carrying coefficient under frequent and moderate storms (η = 1.03–3.96 for R₁–R₂) while still providing substantial capacity for extreme events (η = 1.36–1.51 for R₃, when optimized). Such dynamic allocation of runoff (with Q_storage dominating under routine conditions and emergency storage activating under extreme conditions) represents a significant improvement over traditional static design standards that are typically based on a single return period [5]. It directly addresses the escalating challenges of extreme rainfall under climate change, which static systems struggle to accommodate [4].

Compared to prior studies, our multi-tiered approach fills a notable gap. For instance, Fletcher et al. (2015) achieved ~35% runoff reduction in Australian catchments using integrated LID/SUDS techniques for typical storms [7], but their approach did not incorporate provisions for handling rarer, high-magnitude events. Similarly, Palla and Gnecco (2015) reported about a 40% peak runoff reduction using LID measures in a 20-year storm [15], yet their strategy did not differentiate between rainfall intensities and lacked a hierarchical response mechanism. Jia et al. (2013) applied a SWMM-based design in a Chinese pilot city and attained roughly 25% total runoff reduction during heavy storms [35], but they did not include explicit strategies for extreme rainfall scenarios. Chen et al. (2024) focused on water quality improvements (achieving a 1–4% enhancement in resilience) through a green–gray optimization in Beijing [18], but observed only marginal runoff volume control (0.04–0.3%) and did not implement a tiered management approach.

In contrast, the “2-3-9” framework’s dual-layer structure explicitly combines routine (R₁–R₂) and emergency (R₃) management. Our case study demonstrated that as conditions intensified from R₁ to R₃, the system seamlessly shifted emphasis from conventional infiltration/storage methods to extraordinary emergency measures. The Q_storage fraction increased from ~54% under moderate events to over 72% under extreme conditions, while Q_drainage adjusted from ~15% to ~29%. This flexibility in balancing storage and drainage according to event severity illustrates a more systematic and resilient solution for urban stormwater management across all magnitudes of rainfall. The framework ensures that even unprecedented downpours can be accommodated by tapping into additional passive capacity, markedly enhancing urban flood protection beyond what earlier single-tier or single-scenario methods could offer.

4.2. Synergistic Use of Multi-Scale Facilities

Another key advantage of the framework is the integrated utilization of the full range of stormwater facilities (I₁ through E₉) and the resulting synergistic performance gains. By orchestrating source controls, intermediate storage and conveyance, and large-scale emergency measures within one framework, the approach leverages the strengths of each component level. This full-chain design compares favorably to prior approaches that often emphasized only a subset of the water management continuum. For example, Eckart et al. (2017) combined green and gray infrastructure in a Canadian city and achieved ~30% runoff reduction [16], but their focus was mainly on source infiltration and end-of-pipe solutions, leaving mid-process storage potential underdeveloped. Ahiablame and Shakya (2016) reported a 33% runoff reduction in U.S. watersheds using various LID combinations [36], yet their framework lacked dedicated passive emergency storage for extreme events, limiting its adaptability.

In contrast, the “2-3-9” system coordinates measures spanning from infiltration (I₁–I₃) and on-site detention (S₃, S₅, S₆) to conveyance (D₄, D₇) and emergency retention (S₈, E₉). This comprehensive integration yielded a well-distributed absorption profile in our results: roughly 10–21% of runoff was managed via infiltration, 64–72% via storage, and 15–29% via controlled drainage across the scenarios. Notably, under the extreme scenario (R₃), a single facility (E₉) contributed about 40% of the total capacity, dramatically bolstering the system’s resilience. Such multifaceted synergy means that no single failure point can overwhelm the system; instead, source measures reduce the base load, mid-stage storages regulate the flow, and emergency units contain the excess, all working in concert. This level of integration and functional overlap offers a more adaptive and robust stormwater solution than siloed, single-scale interventions seen in many conventional designs.

4.3. Comparison with Conventional Stormwater Management Approaches

The benefits of the “2-3-9” technical framework can be further appreciated by comparing its performance and design philosophy with several conventional stormwater management paradigms, as follows:

Low Impact Development (LID): LID practices (e.g., bioretention gardens and permeable pavements) are effective for managing runoff from frequent, smaller storms through localized infiltration and detention. However, their decentralized nature often struggles with larger storm events due to limited storage at each site. In our case, the “2-3-9” framework achieved a narrow-sense capacity of 585.51 × 10⁴ m³ for R₂ (η = 1.03) with 17.4% of runoff infiltrated (101.7 × 10⁴ m³). Under an extreme scenario (R₃), the total capacity reached 979.51 × 10⁴ m³ (η = 1.36) with 72.4% of the volume stored (709.41 × 10⁴ m³), supported by both source control measures and centralized emergency facilities (including 394 × 10⁴ m³ from E₉). This demonstrates that while LID contributes to the foundation of stormwater management, the “2-3-9” system extends capacity by incorporating large-scale storage and conveyance to handle heavy rainfall that would overwhelm purely decentralized setups.

Sustainable Drainage Systems (SUDS): SUDS and related green infrastructure approaches (e.g., vegetated swales, wetlands, retention ponds) improve runoff water quality and reduce volumes for moderate storms, but they often revert to conventional pipe drainage once their capacity is exceeded. These methods may not explicitly plan for extraordinary events beyond a certain design storm. In contrast, the “2-3-9” framework ensures continuity between everyday and extreme conditions by linking each LID/SUDS element with emergency measures. For example, in our study the overland emergency corridor D₇ (98.2 × 10⁴ m³ capacity) and the underground reservoir E₉ together handled a substantial drainage load under R₃, achieving Q_drainage = 168.4 × 10⁴ m³ (17.2% of total). This continuous routing from source controls to emergency outlets means that even when green infrastructure capacity is exceeded, there is a planned pathway for excess water. The result is that the system maintains functionality during extreme events, rather than suffering uncontrolled overflows as often happens when SUDS designs are overwhelmed.

“Sponge City” Implementations: The Sponge City concept (prominent in China) emphasizes infiltration and surface storage via green infrastructure to achieve roughly 20–40% runoff reduction in urban areas. While effective, its performance is constrained by the finite storage in surface facilities and soils. Our framework builds upon the Sponge City ethos by adding scalable storage and drainage elements. In the Zhangmian case, the standard Sponge City interventions alone (e.g., permeable surfaces, rain gardens) would not have fully met the R₂ target volume of 566.4 × 10⁴ m³. In fact, our results show that by augmenting green infrastructure with engineered measures, the study area’s capacity slightly exceeded the R₂ requirement (585.51 vs. 566.4 × 10⁴ m³), providing a small surplus. Moreover, under R₃ conditions, the inclusion of a large underground reservoir (E₉) contributed 55.5% of the stored runoff, raising η to 1.36. This indicates stronger adaptability under extreme conditions compared to a typical Sponge City approach, as the “2-3-9” system’s emergency storage can accommodate volumes well beyond what surface green infrastructure can hold.

GIS–Hydrological Modeling Approaches: Modern urban flood planning often employs GIS-based hydrological modeling to map flood risks and test interventions. While powerful for scenario analysis, such models sometimes focus on terrain-driven runoff and may not incorporate the dynamic operation of passive emergency facilities. For example, a model might simulate how topography and land use affect flooding but overlook how an emergency reservoir or designated floodable area could be utilized in real time. In our framework, by explicitly integrating passive elements like S₈ (temporary surface flood zones) and E₉ (underground basin), we found that these facilities contributed about 40.2% of total capacity in the worst-case scenario. This built-in flexibility and redundancy is often not captured in purely model-driven plans. The “2-3-9” approach thus complements GIS–hydrological analyses by providing a structural strategy to include passive, on-demand capacities in urban layouts, ensuring that model recommendations are supported by an infrastructure that can respond dynamically to extreme events.

In summary, the “2-3-9” framework outperforms conventional LID, SUDS, Sponge City, and model-centric approaches in several dimensions: total stormwater capacity (e.g., safely handling ~5.86 × 10⁶ m³ for a 30-year event and ~9.80 × 10⁶ m³ for a 100-year event in our case study), system integration (with up to 72.4% of runoff managed via storage, indicating a high level of internal regulation), and adaptability (roughly 40% of capacity coming from passive emergency features that only activate when needed). Its scenario-based design (R₁–R₃) and dual-dimension management enable the urban drainage system to evolve from source reduction to full-scale emergency response in a coordinated manner. This ensures that resilience is ingrained across the entire spectrum of storm events, providing city planners with a robust, adaptive template for future stormwater infrastructure.

4.4. Implications of Sensitivity Analysis for Urban Planning

The sensitivity analyses shed light on how changes in urban development parameters or design choices can impact stormwater system performance, offering practical guidance for planners. Previous research into system sensitivity provides a useful point of comparison. Pahl-Wostl et al. (2013) observed that increasing imperviousness (higher runoff coefficients) could raise drainage demands by around 20% [37], but their work did not translate these increases into specific infrastructure augmentation requirements. Chen et al. (2024) noted that reducing storage depth affected water quality resilience by 10–15% [18], yet their analysis of runoff-volume sensitivity was limited and did not quantify the effect on overall flood-carrying capacity.

The framework moves beyond these general findings by quantifying the sensitivity of both system-wide output and individual infrastructure components to parameter changes. For the Zhangmian case, we found that raising the runoff coefficient C from 0.65 to 0.85 could increase the needed drainage volume by roughly 30% (from 28.7% to ~34.6% of total runoff) and would likely require enlarging key conduits (like D₇) by over 50% to accommodate the extra flow. Likewise, halving the depth of the emergency reservoir (H_E9 from 1.0 m to 0.5 m) was shown to cause about a 27.8% drop in storage capacity and a corresponding fall in η from 1.36 to ~1.09, essentially erasing the safety margin for extreme storms. Crucially, our analysis also provides actionable design insights. For instance, to counteract a higher C, the model suggests the specific expansion of drainage cross-sections (e.g., increasing D₇ to ~250 m²) or adding new outfalls, and to mitigate a loss in H_E9, ensuring a minimum detention depth of around 1 m (or providing equivalent alternate storage) is recommended. By numerically capturing these relationships, the “2-3-9” framework offers a more precise sensitivity evaluation than earlier qualitative assessments. These results underscore the importance of incorporating adaptable design thresholds in urban planning—such as limiting imperviousness or providing extra contingency storage—to ensure that cities remain resilient even as land-use or climate variables shift. In practice, urban planners can use these sensitivity insights to prioritize interventions (for example, deciding whether reducing runoff via green roofs or expanding pipe capacity yields greater benefit) and to future-proof critical infrastructure against foreseeable increases in runoff due to urban growth or climate change.

4.5. Framework Scalability and Future Work

The successful implementation of the “2-3-9” system in a medium-sized district demonstrates its adaptability to larger or denser urban contexts. If applied to a bigger catchment (e.g., a 50 km² city area with higher imperviousness, C ≈ 0.85), the framework’s principles would remain the same but the absolute capacities of certain facilities would need to scale up accordingly. Our analysis indicates that passive emergency storage (E₉) and major drainage conduits (D₇) are the components most in need of augmentation in such cases to meet the excess stormwater demand. Fortunately, the modular nature of the framework means a city could add multiple distributed E₉-type reservoirs or widen overland corridors as needed to maintain protection levels.

Furthermore, integrating smart technologies—for example, IoT-based sensors and real-time control systems (often termed “digital twin” models for urban drainage)—could greatly enhance the framework’s responsiveness. By monitoring rainfall and system performance in real time (as described in Section 3.2, Step 5: Monitoring and Feedback) and perhaps automating the operation of valves, pumps, or movable weirs, cities can dynamically optimize the usage of storage and drainage elements during an event. This would be especially beneficial as the framework is scaled up, ensuring that even complex, large networks of facilities act in a coordinated and efficient way under stress.

Building on the current study, there are several directions for future work to broaden the framework’s applicability and effectiveness. One important avenue is the integration of water quality considerations (“quantity–quality coupling”) into the USCC framework. While our focus was on volume, urban runoff quality (e.g., pollutant loads) is also critical; future versions of the model could include treatment-oriented facilities or water-quality modeling to ensure that flood mitigation efforts do not inadvertently cause water contamination downstream. Additionally, refining facility-level operation and maintenance strategies will be crucial for long-term success; for example, determining optimal maintenance schedules for pervious pavements or green roofs in the I₁–I₃ category to keep infiltration rates high, or developing sediment management protocols for S₅/S₆ to preserve storage volume. Economic and social factors should also be woven into the decision-making process—evaluating the cost-effectiveness of different infrastructure enhancements, or assessing the community impacts of dedicating land for floodable spaces (S₈), for instance. Collecting long-term monitoring data from implementations of this framework (in terms of performance metrics, maintenance costs, and flood incidence outcomes) would support a more comprehensive analysis of benefits across multiple dimensions of resilience; not just hydrological effectiveness, but also ecological health, lifecycle cost efficiency, and social acceptance. By expanding its scope in these ways, the “2-3-9” framework can evolve into a holistic urban water management tool that aligns with broader goals of sustainability and climate adaptation.

4.6. Global Applicability of the “2-3-9” Framework: International Case Studies

While the “2-3-9” framework was developed and tested in a Chinese context, its core principles are designed to be adaptable to diverse urban environments worldwide. To illustrate its international applicability, we consider three example cities with distinct stormwater management challenges—Tokyo, Japan; New Orleans, USA; and Cape Town, South Africa—and discuss how the framework could improve their resilience.

4.6.1. Tokyo, Japan

Tokyo, one of the world’s most densely populated cities, regularly faces typhoon-induced deluges and has implemented massive engineered solutions, including the Metropolitan Area Outer Underground Discharge Channel (MAOUDC), the world’s largest underground floodwater diversion facility [38]. This system comprises five colossal silos and 6.4 km of tunnels to store and redirect floodwater, protecting Tokyo from river overflow during heavy rainfall. The “2-3-9” framework could complement Tokyo’s existing infrastructure by integrating more green infrastructure elements (I₁–I₃, such as parks and permeable pavements) into the urban landscape. These measures would help reduce the runoff volume entering the drainage system, thereby alleviating pressure on the MAOUDC during extreme events. Additionally, the framework’s emphasis on emergency facilities (E₉) aligns well with Tokyo’s approach to managing severe storms, suggesting that the “2-3-9” system could be scaled up for mega-cities like Tokyo to provide extra decentralized storage. In practice, Tokyo could use the framework to distribute stormwater management across multiple layers: enhanced infiltration and detention at the surface for routine storms, and coordinated use of its underground tunnels and potential new emergency basins for rare, extreme events. This layered defense would improve overall system efficiency and sustainability by relying less on energy-intensive pumps and more on passive, nature-based processes whenever possible.

4.6.2. New Orleans, USA

New Orleans presents a unique challenge due to its low-lying geography and history of severe flooding (e.g., Hurricane Katrina in 2005). The city’s stormwater management relies heavily on levees and large pump stations to evacuate water, but recent efforts have promoted green infrastructure to enhance urban resilience [39]. The “2-3-9” framework’s multi-facility approach could be particularly beneficial in New Orleans. By implementing a range of facilities from infiltration to emergency storage, the city could distribute stormwater management more effectively, reducing dependence on pumps. For example, during routine rainfall (R₁), active facilities like rain gardens, permeable pavements, and local detention basins (I₁–I₃, S₃, S₅) could handle daily stormwater, thus easing the load on the pumping system. In heavier storms (R₂), enhanced conveyance (D₇, e.g., improved overland flow routes or canals) and additional storage (S₆ ponds, S₈ floodable parks) would manage overflow, channeling water to safe holding areas. Under extreme events (R₃), passive emergency measures (E₉) such as dedicated underground storage tanks or sacrificial floodable zones (e.g., designated streets or parking lots that temporarily hold water) could provide critical extra capacity. This tiered strategy means New Orleans could tailor its tactics to rainfall intensity, improving overall flood resilience. For instance, in a moderate storm, the city might never need to activate emergency pumps because green and gray infrastructure absorb the runoff, whereas, in a 100-year deluge, the framework ensures that even if pumping capacity is exceeded, water is directed into planned storage areas instead of causing unmitigated flooding. Such an approach would drastically lower flood risk and reduce strain on New Orleans’ aging pump infrastructure, creating a more robust defense against both ordinary rainstorms and catastrophic events.

4.6.3. Cape Town, South Africa

Cape Town faces the dual challenges of urban flooding and water scarcity. The Greater Cape Town Water Fund initiative, for example, focuses on restoring natural catchments by removing invasive species, which increases water availability and reduces runoff peaks [14]. The “2-3-9” framework’s emphasis on integrating natural and engineered systems aligns with Cape Town’s efforts. Facilities like wetlands, bioswales, and green spaces (I₁–I₃) could help manage stormwater while contributing to groundwater recharge—a valuable co-benefit in a water-scarce region. Additionally, the framework’s systematic approach to different rainfall intensities could help Cape Town balance water management during both drought and flood conditions. By categorizing rainfall into tiers (R₁, R₂, R₃), Cape Town could prioritize water conservation during smaller storms or dry periods (e.g., by maximizing infiltration and minimizing drainage losses) and focus on flood mitigation during heavy rains (by utilizing full drainage and emergency storage capacity). For instance, under R₁ conditions, the city might retain as much water as possible in soil and aquifers (benefiting supply), whereas, under R3 conditions, it would swiftly convey excess water to reservoirs or the ocean to prevent flood damage. The “2-3-9” framework thus offers a strategy for dynamic water management that addresses both extremes of Cape Town’s climate. Implementing such a plan might involve expanding retention ponds (S₆) that double as recreational areas, installing permeable pavement city-wide, and creating emergency floodplains on municipal land that can be deliberately inundated during exceptional storms. Over time, this integrated approach would enhance Cape Town’s resilience by ensuring that each drop of rain is either a resource to capture or a hazard to safely divert, depending on the context.

In all three examples above, the “2-3-9” framework demonstrates a versatile blueprint that can be adapted to local conditions. Tokyo could benefit from infusing green infrastructure into its highly engineered system; New Orleans could strengthen its defenses by diversifying beyond pumps and levees; and Cape Town could use a dual-purpose strategy to tackle both flooding and drought. To fully realize these benefits, further detailed case studies and pilot implementations in such cities would be valuable. These would allow calibration of the framework’s parameters to local rainfall patterns, geographies, and infrastructure, and potentially uncover city-specific adjustments needed to maximize effectiveness. Overall, the evidence from our work—together with these global considerations—suggests that the “2-3-9” framework can serve as a broadly applicable tool for urban stormwater management, enhancing resilience and sustainability in the face of a changing climate.

4.7. Model Validation Methods

The current validation relies on standard design rainfall scenarios due to the unavailability of historical flood records for the Zhangmian River area. While this approach aligns with engineering practices, future research could strengthen validation by incorporating observed flood data or real-time event monitoring to assess the framework’s performance under actual flood conditions.

To enhance the robustness and credibility of the “2-3-9” framework, several validation methods are proposed for future research and practical implementation. These methods aim to confirm the framework’s predictive accuracy and applicability across diverse urban contexts: Comparison with Historical Data: The framework’s USCC predictions can be validated by comparing modeled outputs with historical stormwater management data from the Zhangmian River area. For instance, records of past rainfall events, runoff volumes, and flood occurrences could be analyzed to assess whether the calculated USCC values align with actual system performance. This approach would provide empirical evidence of the model’s ability to replicate real-world conditions.

Field Measurements: Real-time field measurements during rainfall events offer a direct means to validate the framework. Data on rainfall intensity, runoff volumes, infiltration rates, storage capacities, and drainage flows can be collected using hydrological sensors (e.g., rain gauges, flow meters, and water level sensors). These measurements would be compared with the model’s predictions to evaluate its accuracy and identify potential discrepancies, particularly under varying rainfall scenarios (R₁–R₃).

Comparison with Alternative Modeling Approaches: Benchmarking the “2-3-9” framework against established urban hydrological models, such as the Storm Water Management Model (SWMM) or the Hydrologic Engineering Center’s Hydrologic Modeling System (HEC-HMS), can provide insights into its relative performance. By simulating identical rainfall scenarios and urban conditions, differences in predicted runoff, storage, and drainage can be analyzed to highlight the framework’s strengths and areas for refinement.

Extended Sensitivity Analysis: While sensitivity analyses for the composite runoff coefficient (C) and underground storage depth (H_E9) have been conducted, further analyses could explore additional parameters, such as land use variations, soil permeability, or climate-driven changes in rainfall patterns. These studies would test the model’s robustness and adaptability, ensuring its reliability under diverse environmental conditions.

Expert Validation: Engaging experts in urban hydrology and stormwater management to review the framework can provide qualitative validation. Expert feedback on the model’s assumptions, structure, and applicability would enhance its scientific rigor and practical relevance, particularly for implementation in varied urban settings.

Implementing these validation methods will strengthen the scientific foundation of the “2-3-9” framework, ensuring its reliability and fostering broader acceptance in urban stormwater management practices. Future studies should prioritize these approaches to refine the model and expand its applicability.

4.8. Limitations of the Study

Despite the robust design of the “2-3-9” framework, this study has certain constraints that should be considered when interpreting its findings. The economic costs associated with the construction, operation, and maintenance of the proposed stormwater facilities are not addressed, limiting the framework’s immediate applicability for urban planners balancing cost-effectiveness with flood resilience. Additionally, the framework focuses exclusively on water quantity management, omitting critical water quality considerations, such as pollutant control in runoff, which are essential for holistic stormwater management. Furthermore, social factors, including community engagement, land use constraints, and public acceptance of the facilities, are not incorporated, despite their importance for the successful implementation of urban stormwater strategies.

5. Conclusions

This study developed and evaluated the “2-3-9” technical framework to systematically quantify and optimize Urban Stormwater Carrying Capacity (USCC). By integrating dual-layered management dimensions (narrow- and broad-sense USCC), three rainfall scenarios (R₁–R₃), and nine categories of detention and drainage facilities (I₁–E₉), the framework demonstrated both scientific validity and practical applicability in the Zhangmian River area of Weifang. Under regular rainfall conditions (R₁: η = 3.96; R₂: η = 1.03), narrow-sense USCC relied on active facilities for efficient runoff mitigation, while under extreme events (R₃: η = 1.36), broad-sense USCC enhanced emergency capacity through passive infrastructure. The Q_storage proportion increased from 53.9% to 72.4%, validating the adaptability of the hierarchical management approach. Compared to the conventional single-scenario or single-facility method, the “2-3-9” framework significantly improves urban stormwater resilience through integrated multi-scenario and multi-facility coordination, offering a new systemic perspective for theoretical research.

In terms of practical application and optimization, the framework was validated through a full-cycle process—goal setting, current condition assessment, gap analysis, optimization recommendations, and dynamic monitoring—demonstrating value in enhancing flood control and resource efficiency. For example, in the R₂ scenario (target H = 236 mm), the current volume (V = 5.8551 million m³) slightly exceeded the target (V = 5.664 million m³), yielding η = 1.03 and indicating sufficient flood control capacity with minor redundancy (ΔV = 0.1911 million m³). Dynamic monitoring can further calibrate facility performance. Compared to existing approaches, the framework achieved higher carrying capacity in R₃ through facility E₉ (3.94 million m³, 55.5% of Q_storage), resulting in a total USCC_B of 9.7951 million m³. This highlights superior adaptability in high-density urban environments and provides a practical optimization pathway for urban planning.

Sensitivity analysis further revealed how the framework responds to variations in key parameters, offering a scientific basis for system optimization. In the R₂ scenario, increasing the composite runoff coefficient (C) from 0.65 to 0.85 raised Q_drainage demand by 30.8%, requiring adjustments such as increasing the D₇ cross-sectional area to 250 m². In the R₃ scenario, halving underground facility depth (H_E9) reduced Q_storage by 27.8% and lowered η from 1.36 to 1.09, indicating that H_E9 should be maintained at ≥1 m to ensure emergency capacity. In contrast to previous studies, this work provides a more rigorous assessment of Q component dynamics and introduces targeted, practically applicable design strategies, reflecting enhanced precision and relevance for engineering applications. Such analysis provides targeted guidance for facility configuration under high-density and extreme rainfall conditions, enhancing the framework’s practical relevance.

While the “2-3-9” framework represents a significant advancement in urban stormwater management, it is important to acknowledge its limitations. Firstly, the current study focuses solely on flood risk management and does not incorporate water quality considerations, which are crucial for comprehensive urban water management. Secondly, although the framework was successfully applied in the Weifang case study, its applicability to other geographical and climatic contexts may require further validation and adaptation. Additionally, while sensitivity analysis was conducted on key parameters (e.g., runoff coefficient C and underground storage depth H_E9), there may be other factors that influence the model’s performance, which were not explored in this study. Lastly, the reliance on standard values and estimates for certain parameters introduces potential uncertainties that should be addressed in future research.

For urban planners, engineers, and policymakers, the “2-3-9” framework offers a robust tool for assessing and optimizing urban stormwater carrying capacity. By providing a systematic approach to integrate multiple facility types and management strategies, it can guide the design and implementation of resilient stormwater systems. Practitioners are encouraged to adopt the USCC metric as a key performance indicator and to consider the framework’s hierarchical management approach when planning for both routine and extreme rainfall events. Implementing real-time monitoring systems and adaptive management strategies will be essential for maintaining system performance over time. Furthermore, as urban areas continue to grow and face increasing climate challenges, the framework’s scalability and potential for integration with water quality management and digital technologies make it a forward-looking solution for sustainable urban development.

Municipalities and infrastructure planners can enhance urban flood resilience by adopting the USCC metric to inform stormwater planning, integrating green and gray infrastructure for cost-effective flood management, investing in real-time monitoring systems to enable adaptive responses, and launching pilot projects to validate scalability and foster stakeholder support, as demonstrated in the framework’s application and case studies (Section 2.2, Section 2.5 and Section 2.6).

In conclusion, the “2-3-9” framework—through its dual management dimensions, three rainfall scenarios, and nine facility types—offers an integrated approach for assessing and optimizing urban stormwater carrying capacity. The Weifang case study confirms its capacity to manage regular rainfall (R₂: H_actual = 244 mm) while maintaining system stability under extreme events (R₃: H_actual = 408 mm), surpassing the limitations of traditional single-method strategies. Sensitivity analysis further refined parameter configurations, supporting flexible and science-based urban planning. Future research could expand this framework by integrating water quality management and digital technologies, enabling multi-objective optimization and smart applications to support global urban flood resilience and sustainable development.