Pluvial flood risk assessment and nature-based mitigation in urban environments: a pragmatic Curve Number and Initial Abstraction approach

1 Introduction

Urban pluvial flooding constitutes a pressing hydrological hazard facing both developed and developing nations (Yu et al., 2016) and arises from the convergence of unfavorable hydrological, meteorological, and land use conditions, frequently compounded by failures in existing drainage infrastructure (Chen et al., 2021, Rözer et al., 2021). This phenomenon typically occurs when heavy and/or prolonged precipitation events generate surface ponding and overland flow, either before rainfall can enter the underground drainage network or when the drainage system attains full hydraulic capacity and fails due to overflow (Falconer et al., 2009; Palla et al., 2018; Samela et al., 2020). The severity and frequency of urban pluvial flooding are further exacerbated by ongoing climate change, which intensifies extreme precipitation events (Green et al., 2026), and by rapid urbanization and land alteration, which progressively reduce the pervious surface area available for natural infiltration (Ercolani et al., 2018).

In response to the increasing pluvial flood risk in urban areas due to climate change and growing anthropogenic pressure on cities, engineers and urban planners have recently integrated traditional engineering stormwater management with a range of decentralized, source-control practices, variously termed nature-based solutions (NBS), low-impact development (LID) infrastructure, best management practices (BMPs), and sustainable urban drainage systems (SUDS). Although these terms are not fully interchangeable and their technical scope and usage vary across countries, they share a common underlying principle: restoring, or at least approximating, the pre-urbanization hydrological response of the urban catchment, favoring infiltration, evapotranspiration, and temporary storage over the rapid conveyance of runoff typical of conventional piped drainage systems (Fletcher et al., 2015; Eckart et al., 2017). Interventions such as green and green–blue roofs, porous pavements, green walls, grass swales, and infiltration and bioinfiltration trenches (Lucas, 2010; Wilson et al., 2013) are intended to beneficially impact runoff water quality in urban areas by removing pollutants and to decrease the runoff load on the urban drainage system by reducing runoff volume and peak discharge (Sharmin et al., 2022). Some of these practices, such as green and green–blue roofs, green walls, and bioretention systems, additionally provide indirect beneficial effects such as mitigation of the urban heat island effect, which is related to the intensification of storms in cities with respect to surrounding areas (Berardi et al., 2014; Liu and Niyogi, 2019).

Green roofs consist of a vegetated growing medium and a drainage layer (Goussous et al., 2015), whereas green–blue roofs incorporate an additional empty storage layer beneath the traditional living layer to enhance detention capacity (Sharmin et al., 2022). The flood mitigation potential of these interventions has been evaluated in numerous studies. Palla and Gnecco (2015) numerically demonstrated, using the Colle Ometti urban catchment in Genoa (Italy) as a case study that reductions in peak flow and runoff volume were linear functions of the effective impervious area reduction for a rainstorm with a return period (T) of 2 years and that these efficiency metrics reduced significantly with increasing T. Pampaloni et al. (2022) similarly showed that the peak flow reduction exerted by green roofs decreased with the rainfall return period for an urban catchment in Florence, Italy. Ferreira and da Rocha (2023) showed, by using the U.S. Army Engineer Hydrologic Engineering Center (HEC)-Hydrologic Modeling System (HMS) and HEC-River Analysis System (RAS) models that green roof technology was able to reduce peak flows and flooding of the Aricanduva River in the highly urbanized area of São Paulo, Brazil. Neumann et al. (2024) employed a coupled one-dimensional (1D)–two-dimensional (2D) model to demonstrate that the flood mitigation effectiveness of green roofs is most pronounced when installations are located close to floodable areas. Öztürk et al. (2024) used 2D HEC-RAS to evaluate, for a small area in Erkilet District, Turkey, the effectiveness of green roofs and pervious pavement in mitigating the impacts of a historical flood event that occurred in September 2022, showing that the influence of NBS depends on location and configuration. Finally, Sciuto et al. (2025) combined the use of 2D HEC-RAS and SWMM (Rossman, 2010) to evaluate the impacts of NBS interventions, including green roofs, on flooded areas for a small watershed near Catania, Italy, and showed that NBS implementation leads to a reduction in flooding volumes, with efficiency that decreases with the increase of the storm return period. In conclusion, the literature shows that green and green–blue roofs have the potential to mitigate pluvial flooding in urban areas, albeit their efficiency depends on the position and dimensions of the intervention, and it reduces for higher return periods.

Numerical modeling plays a crucial role in supporting pluvial flood hazard assessment and the development of effective risk management strategies (Pirone et al., 2026). Accurate simulation of pluvial flooding in urban areas requires the capability to represent not only surface flow propagation but also the complex interactions among the various components of the underground and surface urban drainage system (Ming et al., 2025), while ignoring the presence of the urban drainage system can lead to an overestimation of the inundated areas (Cea et al., 2025). The integrated modeling of surface and underground channel flow is usually accomplished by coupling a 1D model for the flow propagation within sewer channels and a 2D model for the surface flood simulation (Chang et al., 2015; Leandro and Martins, 2016; Fernández-Pato and García-Navarro, 2021). Although such coupled 1D–2D models offer considerable accuracy, their application is contingent upon detailed, locally resolved data characterizing the underground drainage system (pipe geometries and network layouts), which are rarely available in practice (Wang et al., 2018; Cao et al., 2020). Consequently, detailed coupled models remain rarely applicable at the city-scale owing to their intensive data requirements and high computational costs (Ming et al., 2025).

In the case of large-scale applications or a scarcity of urban drainage network data, surrogate representations of the drainage system may be incorporated directly into 2D hydrodynamic models (Cea et al., 2025; Ming et al., 2025; Costabile et al., 2026). Among these, two broad families of approaches that require neither substantial modifications to existing hydrodynamic models nor prior knowledge of drainage system inlet locations are documented in the literature. In the first family of approaches, hydrologic losses are artificially amplified, or the storm hyetograph is equivalently cut, to represent conditions in which the urban drainage system can absorb and convey all rainfall intensities below a design threshold (Wang et al., 2018; Cao et al., 2020; Padulano et al., 2021). In the second family of approaches, the net rainfall is reduced to represent conditions in which the drainage system can manage the rainfall volume corresponding to a given design storm (Oberauer and Lehmann, 2023; 2024; Cea et al., 2025). Oberauer and Lehmann (2023), (2024) discuss the two families of approaches, finding that the second should be more theoretically grounded, albeit while to more realistic results in application.

A reasonable compromise between the two surrogate modeling methodologies can be grounded in the principle that a drainage system should be designed to accommodate all storm events corresponding to a given level of service represented by the return period T. In engineering practice, this requirement is typically relaxed by ensuring that the drainage system can cope with all the rectangular hyetographs with total rainfall depth h _*d,T* that are extracted from the intensity–duration–frequency (IDF) curve for a design return period T and different storm durations d (Chow, 1962; Meynink and Cordery, 1976). This design rationale suggests that, when simulating a storm of duration d, the urban surfaces served by the drainage system absorb the rainfall depth h _*d,T* before flooding initiation. The strategy is implemented in the present work through a slight modification of the Soil Conservation Service (SCS) Curve Number (CN) method (Soil Conservation Service, 1985), whose application requires the definition of two parameters, namely, the Initial Abstraction (I _*a*), accounting for losses before runoff onset (Bonta et al., 2025), and the Curve Number (CN), which is representative of the maximum potential loss (Hawkins et al., 2009). Typical CN values for urbanized areas are discussed extensively in the literature (Simpson et al., 2023; Alivio et al., 2024; Sciuto et al., 2025), whereas I _*a* is conventionally expressed as a function of CN. In the present paper, we decouple I _*a* from CN and choose the value I _*a* = h _*d,T* to mimic the desired behavior in the areas served by the drainage system (see Supplementary Appendix A).

Values of I _*a* and CN have also been reported for representative sustainable urban drainage interventions (Bean et al., 2007; Schwartz, 2010; Martin and Kaye, 2014; 2016; Fassman-Beck et al., 2016; Hill et al., 2017; Soulis et al., 2017; Liu et al., 2020; Madrazo-Uribeextebarria et al., 2023; Squier-Babcock and Davidson, 2025; Osawa et al., 2025), mainly obtained by direct analysis of runoff produced by experimental reduced-scale installations. The experiments show that, despite the presence of vegetated components, the CN values of pervious pavements and green roofs are generally high and close to those of impervious surfaces, whereas the suggested values of I _*a* are equal to the maximum water storage in the growing media (Fassman-Beck et al., 2016). This indicates that the beneficial effect of green roofs and porous pavements is attributable primarily to initial retention and detention effects, rather than to an increase in infiltration capacity. Nonetheless, the CN and I _*a* values evaluated for small-scale installations do not account for the interaction of these interventions with the drainage system that receives the unabsorbed fraction of rainfall. In the literature on 2D urban flooding simulation, different approaches are used for the choice of CN and I _*a* assigned to areas covered by NBS interventions. For example, Öztürk et al. (2024) used the green roof CN values suggested in the previous literature for the setup of their 2D HEC-RAS numerical simulations, whereas Sciuto et al. (2025) adopted an approach where roughness coefficients and CN and I _*a* values are chosen to align the results in terms of peak flows and runoff volume with those obtained with SWMM.

The city of Naples, Italy, provides a case study that is particularly relevant to the present discussion. Naples is rich in architectural and historic heritage and is characterized by a compact urban fabric, high terrain elevation difference between the coastal and internal areas, high population density, and frequent disruptions due to pluvial flooding (Amato, 2009), including recent fatalities (Braca et al., 2002). Existing studies addressing pluvial flood hazard in this city have been limited in areal extent, focusing on individual districts such as Ponticelli (Salzano, 2015; Apreda, 2017), Fuorigrotta (Padulano et al., 2021), and parts of the eastern municipality, employing a range of modeling approaches including hydrodynamic modeling (with both explicit and surrogate representations of the drainage network) and indicator-based analysis (Apreda et al., 2019). These investigations have variously assessed inundation extent, climate projection uncertainty (Padulano et al., 2021), and flood impact through vulnerability and exposure frameworks (Apreda et al., 2019; Zuccaro and Leone, 2021). Nevertheless, while such integrated frameworks have been applied to smaller districts or catchments in other cities (e.g., Öztürk et al., 2024; Sciuto et al., 2025), no city-scale pluvial flood hazard assessment integrating NBS mitigation measures has previously been undertaken for the entire municipality of Naples.

The foregoing review identifies different gaps in the existing literature that the present study aims to address. The first concerns the adaptation of the widely used SCS-CN approach, which allows spatially variable hydrologic losses, to incorporate a surrogate representation of the rainfall volume that the urban drainage system can manage before surface flooding occurs. The second concerns the representation of sustainable urban drainage interventions, such as green roofs, through modified values of CN and I _*a* that account not only for the intrinsic hydraulic characteristics of the interventions but also for their cascade interaction with the downstream drainage system (i.e., the contribution of a green roof to surface flooding is activated only when the residual runoff generated by the installation exceeds the available capacity of the receiving drainage system). Although Öztürk et al. (2024) and Sciuto et al. (2025) have modified CN and I _*a* values to simulate the effect of green roofs in pluvial flood simulations, these studies did not explicitly account for the cascade interaction between green roofs and the downstream drainage system.

Given these gaps, the main objective of this study is to develop a pragmatic modeling strategy to simulate rainfall-induced surface flooding over a large urban area with limited availability of detailed drainage infrastructure data and to evaluate the potential of small-scale NBS (specifically, green roofs) in reducing flood extents and peak water depths at the city-scale. The approach is based on modeling scenarios without (baseline scenario) and with (what-if scenario) the application of risk mitigation measures. The strategy employs modified Initial Abstraction values I _*a* (Supplementary Appendix A) to represent, in surrogate form, (i) the ability of the drainage system to manage rainfall volumes and (ii) the cascade interaction between green roofs and the drainage system. The approach is implemented within the 2D hydrodynamic model HEC-RAS (version 6.7), wherein the rain-on-grid (RoG) framework is used to simulate surface runoff generation and propagation. This configuration facilitates scalable applications over large urban areas, although it necessarily entails some simplification of drainage processes, which may affect local accuracy in areas with highly heterogeneous drainage infrastructure and bidirectional exchange between the surface and the underground drainage network. The city of Naples serves as an applicative case study.

The remainder of this paper is structured as follows. Section 2 presents the proposed methodology in detail and describes the data collection and processing for the case study. Sections 3 and 4 report and discuss the results, respectively. Section 5 draws the main conclusions of the study.

2 Methodology

The methodological framework developed in this study (Figure 1) integrates several components:

• the characterization of the study area and the collection of the input data required for hydrodynamic modeling;
• the surrogate representation of the urban drainage system and the cascade interaction with green roofs through modified SCS-CN parameters (Supplementary Appendix A);
• the setup and execution of 2D rain-on-grid hydrodynamic simulations to produce pluvial flood hazard maps for the city of Naples under synthetic and real rainfall scenarios with short return periods;
• the assessment of the green roof potential to reduce flood extents and peak water depths in a realistic setting (deployment on a subset of residential buildings identified as suitable candidates for their installation), implementing a what-if design scenario; and
• the assessment of the pluvial flood risk at the census unit level as a function of maximum water depths and resident population exposure.

Flood risk is conventionally defined as the interaction of three components: hazard, exposure, and vulnerability (IPCC, 2014; 2023; Rosenzweig et al., 2024). In the present study, pluvial flood hazard is derived from hydrodynamic modeling, whereas exposure is quantified through population spatial distribution data. Consistent with a social risk perspective rather than an economic damage assessment (Meyer et al., 2009), the analysis focuses on the potential impact of pluvial flood events on urban populations. Vulnerability, understood as the set of socioeconomic and physical conditions that modulate the susceptibility of a population to adverse flood impacts, is not explicitly incorporated in this analysis. This choice implies the assumption of uniform vulnerability across all population subgroups, which represents a deliberate simplification acknowledged as such. The resulting metric should be interpreted as a simplified pluvial flood risk indicator in which vulnerability is held uniform.

2.1 2D hydrodynamic model

The 2D Hydrologic Engineering Center-River Analysis System (HEC-RAS, version 6.7), developed by the U.S. Army Corps of Engineers, was employed to generate pluvial flood inundation maps using the rain-on-grid approach (Varra et al., 2025). The software solves either the full shallow water equations (SWEs) or their approximation, the diffusion wave equations (DWEs), within a finite volume discretization framework (Brunner, 2020; 2024). The governing continuity and momentum equations of the 2D SWE can be written as follows:

∂ ζ ∂ t + ∂ h u ∂ x + ∂ h v ∂ y = q , (1)

∂ h u ∂ t + ∂ h u 2 ∂ x + ∂ h u v ∂ y = f c h v − g h ∂ ζ ∂ x − g h S f , x + ∂ ∂ x h ρ T x x + ∂ ∂ y h ρ T x y , (2)

∂ h v ∂ t + ∂ h u v ∂ x + ∂ h v 2 ∂ y = f c h u − g h ∂ ζ ∂ y + − g h S f , y + ∂ ∂ x h ρ T y x + ∂ ∂ y h ρ T y y . (3)

In Equations 1–3, t denotes the time; x and y are the horizontal coordinates; ζ (x, y, t) = z(x,y) + h(x, y, t) is the water surface elevation (m); h(x, y, t) is the flow depth (m); z(x, y) is the bed elevation (m); g is the gravitational acceleration (m s⁻²); u(x, y, t) and v(x, y, t) are the depth-averaged velocity components along x and y, respectively (m s⁻¹); f _*c* is the Coriolis coefficient (s⁻¹); ρ is the water density (kg m⁻³); S f , x = n M 2 u u 2 + v 2 / h 4 / 3 and S f , y = n M 2 v u 2 + v 2 / h 4 / 3 are the components of the friction slope along x and y, respectively; n M is the Manning roughness coefficient (s m^−1/3); and q is the source term accounting for precipitation, infiltration, and evaporation. Finally, the components of the turbulent and dispersive stress tensor T x x, T x y = T y x, T y y are also included. The reader is addressed to HEC-RAS technical manuals (Brunner, 2020; 2024) for a complete formulation of the mathematical model. Due to a trade-off between result accuracy and computational efficiency, the model was run with the DWE setting, which neglects the inertial, turbulence, and Coriolis terms in the momentum conservation equations. Although it is recognized that the efficiency and accuracy of the DWE model may be affected on high-slope terrain, its implicit march-in-time implementations allow high speedups (Fernández-Pato and García-Navarro, 2016), and their numerical results are less sensitive than those of the SWE model on grid refining (Caviedes-Vouillème et al., 2020).

The software can explicitly incorporate urban drainage networks. However, to consider the presence of an urban drainage system in the absence of detailed spatial and geometric data, a modified version of the SCS-CN was applied here to estimate Initial Abstraction and infiltration losses (Supplementary Appendix A).

2.2 Description of the study area

The proposed methodology is applied to assess pluvial flood risk in the city of Naples, the regional capital of Campania, Italy (Figure 2). Naples extends along the Bay of Naples (Figure 2), on the southern Tyrrhenian coast, and encompasses a total area of approximately 119 km². According to provisional census data released in November 2025 by the Italian National Institute of Statistics (ISTAT), the city has a resident population of 905,259 inhabitants, making it one of the most densely populated metropolitan areas in Europe.

Naples features numerous areas characterized by high susceptibility to pluvial inundation (Amato, 2009); however, a limited portion of the eastern city, traversed by a network of drainage canals (Figure 2), is additionally exposed to flooding resulting from the overflow of these hydraulic structures. Coastal flood susceptibility is comparatively minor, although the marine storm of 28 December 2020 produced destructive impacts across an extensive coastal stretch unprotected by outer breakwaters (Mattei et al., 2021).

For this study, the urban territory of Naples was partitioned into two distinct hydrographic catchments, hereafter referred to as the Eastern Basin and the Western Basin (Figure 2). The Eastern Basin extends beyond the municipal boundaries to encompass the slopes of Mount Vesuvius, whereas the Western Basin extends marginally beyond the administrative limits of the city of Naples (Figure 2). The Western Basin covers a total area of 99.84 km², with a mean catchment slope of 21.73%, whereas the Eastern Basin covers 100.71 km², with a mean slope of 12.88%. With reference to the NBS deployment, the study focuses on the eastern area of Naples, which is characterized by morphological and functional heterogeneity, and is a key zone for urban regeneration.

The rainfall climate of Naples exhibits pronounced seasonal variability, with peak monthly precipitation occurring during the autumn season (September to November) and a progressive decline toward minimum values in August. Consistent with this seasonal pattern, approximately 80% of major historical flood events documented in written records dating back to the 11th century have been recorded during the autumn months (Amato, 2009). In recent history, a severe rainstorm event on 15 September 2001 inflicted damage that prompted the emergency transfer of 25 million euros from the State to the Municipality (Atti Parlamentari Camera dei Deputati, 2002) and resulted in two fatalities (Braca et al., 2002). According to Spano et al. (2021), whose analysis draws on the methodology proposed by Padulano et al. (2019), updated IDF curves for Naples based on an ensemble of 19 EURO-CORDEX regional climate models indicate an increase in the frequency of extreme rainfall events over the 2071–2100 period, particularly under RCP8.5: an hourly rainfall intensity currently associated with a 10-year return period could occur, on average, once every four years by the end of the century.

2.3 Data selection and processing

The data collection and processing steps are discussed in the following sections. Data were collected from different sources, all free and public (Table 1).

TABLE 1. Details of input data used in the study.

2.3.1 Rainfall data

This study adopts a rain-on-grid modeling approach in which design precipitations extracted from the depth–duration–frequency (DDF) curve are applied across each catchment. For the construction of the DDF curves, the annual maximum rainfall intensities for multiple storm durations were evaluated from the records of six rain gauge stations managed by the Civil Protection Department of the Campania Region (Table 1), located both within and in the vicinity of the municipal boundaries of Naples (Figure 2). The analysis is based on subhourly (10-min) historical rainfall records spanning the period 2000–2024 for the estimation of the average annual maximum intensity related to different durations, and it is integrated with a regionalization approach for the evaluation of the rainfall growth factor (Rossi and Villani, 1992) based on the adoption of the two-component extreme value (TCEV) distribution for rainfall maxima (Rossi et al., 1984). To derive a spatially representative rainfall intensity value for Eastern and Western Basin centroids, an inverse distance weighting (IDW) interpolation was applied to the annual maximum series. The resulting intensity values were subsequently corrected by an areal reduction factor (Rossi and Villani, 1995), depending on rainfall duration and catchment area, to account for the spatial variability of precipitation over the basin extent.

The design rainfall events used as input for the hydrodynamic simulations were derived through the alternating block method (Chow et al., 1988). This technique generates synthetic hyetographs statistically consistent with the local DDF curve, distributing precipitation over discrete time steps of 5 minutes with the most intense block placed at the midpoint of the storm. Hyetographs were constructed for total storm durations of 30 minutes, 1, and 3 hours, considering a return period of T = 10 years. The three storm durations selected, whose total rainfall depths and maximum 5-min intensities are reported in Table 2, were chosen to encompass the range of hydrometeorological conditions most relevant to pluvial flood generation in the study area. A 10-year return period is consistent with the design standards recommended for urban stormwater drainage systems (UNI, 2008) and is widely used for assessing pluvial flood hazards (Guerreiro et al., 2017) and the performance of flood mitigation measures in urban areas (Palla and Gnecco, 2015; Orsi et al., 2025). It is well established in the literature that the flood mitigation effectiveness of NBS, in terms of reductions in peak flow and water depth, diminishes progressively as rainfall intensity increases (Pampaloni et al., 2022; Webber et al., 2020). Consequently, a 10-year return period represents a scenario in which NBS are expected to deliver meaningful mitigation performance. The evaluation of more extreme events, while relevant for residual risk quantification, falls outside the primary scope of this investigation.

TABLE 2. Characteristics of the synthetic and real storms.

In addition to the synthetic design storms, we also consider here a recorded affected for the analysis, namely, the storm of 23 September 2023, which lasted approximately 3 hours. The event was heterogeneous in time and space and mostly affected the Eastern Basin. The return period attributable to the rainfall collected by the Torre del Greco and Ercolano rain gauges was about T = 2 years, with a maximum 1-hour intensity corresponding to a return period of T = 5 years, whereas the Capodimonte and Camaldoli rain gauges collected rainfall with a return period of less than T = 2 years. This event not only triggered widespread pluvial flooding phenomena, particularly across the eastern district of Naples, underscoring the vulnerability of the city to relatively frequent precipitation events, but also prompted the production of volunteered geographic information (VGI) useful for the qualitative consistency check of the proposed model.

2.3.2 Topographic data

High-resolution topographic data were employed as the geometric basis for the hydrodynamic model. Specifically, both a digital terrain model (DTM), representing bare-ground elevations (Figure 2), and a digital surface model (DSM), incorporating aboveground features such as buildings and vegetation, were obtained at a spatial resolution of 1 m from the Geoportal of the Metropolitan City of Naples (Table 1).

A well-recognized challenge in large-scale urban flood modeling is the presence of complex infrastructural elements, including bridges, culverts, and underpasses, whose geometric and hydraulic characteristics are frequently unavailable or difficult to accurately represent within large-scale models, often necessitating extensive manual intervention (Van Dau et al., 2024).

Because we are interested in the ground runoff of rainfall, it is essential that the terrain representation accurately reproduces natural and anthropogenic flow pathways. Accordingly, a systematic identification and correction of elevation artifacts within the DSM was carried out before model setup, targeting those features that obstruct surface drainage or alter the expected flow directions. Two categories of artifacts were identified and corrected. The first concerns bridges spanning roadways or other transport corridors: in the raw DSM, such structures effectively occlude the underlying road surface, blocking the corresponding passage. This is exemplified in Figure 3a, which shows the railway line at the Gianturco junction intersecting Via Emanuele Gianturco. In such cases, the correction was applied by locally replacing the DSM elevations beneath the bridge deck with values interpolated from the road surface immediately adjacent to the tunnel portals, thus reinstating the continuity of the underlying flow path (Figure 3b). The second category involves elevated highway structures that extend over lower-lying roads for considerable distances, causing the terrain below to be masked across large areas of the DSM. A representative example is shown in Figure 3c, where Highway A3 overlies Via Argine in the vicinity of its intersection with Via Ferrante Imparato. In these instances, the highway deck elevations were replaced with ground values derived from adjacent surfaces, restoring the correct terrain representation beneath the overpass (Figure 3d).

To improve the accuracy of the bare-ground terrain representation, vegetated areas were identified and delineated using the normalized difference vegetation index (NDVI). The NDVI was derived from a SENTINEL-2 multispectral image downloaded from the Copernicus Data Space Ecosystem Portal (Table 1). The image acquisition falls in the period between 1 and 30 April 2025 and had a cloud cover of 0.19% over the entire scene. The NDVI was calculated using Equation 4:where B ₈ and B ₄ represent the near-infrared and red bands, respectively. To isolate the vegetative component, a threshold of NDVI ≥ 0.2 was applied, in accordance with established practice in the remote sensing literature for discriminating vegetated from non-vegetated surfaces in urban environments (Zaitunah and Samsuri, 2021; Martins et al., 2025). This filter was further refined by integrating the land use and land cover (LULC) classification layer (Section 2.3.3), which was used as a mask to exclude erroneously classified non-vegetated surfaces, water bodies, and shadowed areas within certain urban zones. The resulting vegetation mask was subsequently used to replace the DSM elevation values with the corresponding DTM bare-ground values within all identified vegetated areas, thereby ensuring that surface canopy heights do not artificially block flow pathways.

N D V I = B 8 − B 4 B 8 + B 4 , (4)

2.3.3 Land use and land cover and roughness values

The land use and land cover (LULC) map of the city of Naples was derived through a detailed classification of the Copernicus Land Monitoring Service Urban Atlas 2018 database (Table 1). The original Urban Atlas legend was subsequently subjected to a targeted refinement process to improve its representativeness for urban flood modeling. This refinement encompassed two main modifications: the introduction of a dedicated thematic category to account for the presence of green roofs and the selective reclassification of specific urban areas where the original dataset was found to overestimate surface permeability in high-density built-up zones (Figure 4a).

The hydrodynamic simulations incorporate spatially distributed Manning’s roughness coefficients, assigned on the basis of land cover type and derived from technical guidelines and values reported in the literature (Papaioannou et al., 2018). The Manning’s roughness coefficient assigned to each LULC class is reported in Table 3. It is acknowledged that surface roughness parameters represent a potentially significant source of uncertainty in hydrologic–hydrodynamic modeling. For this reason, a screening sensitivity analysis was performed to evaluate the sensitivity of the main hydraulic outputs to plausible variations in the parameters controlling runoff generation and surface flow resistance (as explained in Section 2.4).

TABLE 3. Manning’s roughness values for various land use and land cover (LULC) types. Curve Number (CN) values determined by integrating the LULC and hydrological soil group (HSG) information.

2.3.4 Soil permeability, infiltration, and Curve Number values

The transformation of rainfall to flood runoff in the city area was evaluated by using the SCS-CN empirical method (Soil Conservation Service, 1985), which makes use of two parameters, namely, the Curve Number (CN) and the Initial Abstraction (I _*a*). The CN parameter is assigned to the different areas of the computational domain based on the hydrological soil groups, land use, and vegetation cover. Soil texture and type significantly influence infiltration capacity and surface runoff, affecting the flooding susceptibility of areas. The SCS method classifies soils into four hydrological soil groups (HSGs)—A, B, C, and D—based on infiltration rates and runoff potential, with group A having the highest infiltration and lowest runoff and group D having the opposite characteristics. The study area includes two HSGs, B and C, corresponding to distinct geological formations (Figure 4b), volcanic complexes with coarse texture and fine-grained alluvial deposits, respectively, determined by analyzing a map of regional soil features (Table 1). For the present study, CN values were determined, based on existing literature, for average antecedent soil moisture conditions by integrating LULC and HSG information (Table 3). In areas not directly served by a drainage network, the Initial Abstraction (I _*a*) is calculated as a fixed fraction of the storage S (e.g., I _*a* = 0.2 S), where S depends on the CN value only (see Supplementary Appendix A.1).

A modified approach (see Supplementary Appendix A.2.1) was adopted to consider, in a surrogate form, the presence of a drainage network for a subset of land use and land cover descriptions, namely, “continuous urban fabric,” “fast transit roads and associated land,” “other roads and associated land,” and isolated buildings. This approach is based on the observation that a commonly adopted engineering practice is designing urban drainage systems able to cope with all the rectangular hyetographs of duration d and rainfall depth h _*d,T* extracted from the DDF curve for a given return period T (Chow, 1962; Meynink and Cordery, 1976). To represent this condition, I _*a* was decoupled from S, and, for impermeable surfaces connected to the drainage system (streets, roofs, and sidewalks), it was assumed equal to the rainfall depth h _*d,T* associated with T = 2 years for the considered storm duration d. Consequently, I _*a* of impervious surfaces connected to the drainage network is not a fixed parameter, but rather a variable quantity dependent on both the storm event duration and the shape of the DDF curve. In this study, the selected return period is T = 2 years, in agreement with the observation that several components of the urban drainage system in the city of Naples may undergo critical conditions under rainfall events with this probability level (Gisonni, 2000), not only due to insufficient design but also due to sediment deposition, debris accumulation, and channel collapse (Schiavone, 2000). For this reason, the selected return period of T = 2 years for the calculation of I _*a* must be understood as a nominal level of service used to define the rainfall volume that the drainage system can manage and not necessarily a design parameter. In this respect, I _*a* could be taken as a variable across the two-dimensional domain to consider non-uniformity of maintenance conditions and drainage network performance. The surrogate I _*a* values calculated for the Eastern and Western Basins are reported in Table 4.

TABLE 4. Initial abstraction values (I _*a*) for impervious surfaces and green roofs connected to the drainage system considering different storm durations.

Synthetic storm.

23 September 2023 storm.

2.3.5 Census units and population data

Detailed knowledge of population distribution is fundamental for flood risk assessment and management, and these data are generally made available through national censuses and aggregated into predefined administrative or statistical units (Calka et al., 2017). The 5,726 census units in the city of Naples represent the basic spatial subdivisions used for demographic and socioeconomic analyses, constituting the smallest administrative units for which official statistical information is available. In the present study, the population recorded in 2021 for each census unit is used as a proxy for exposure, which is defined here as the spatial overlap between hazard information derived from the flood model results and population data (Smith et al., 2019). In contrast, population vulnerability is not explicitly addressed in this analysis.

2.3.6 What-if scenario: criteria for green roof installation and hydrologic representation

Due to the cultural and architectural heritage of Naples, the implementation of NBS interventions must comply with strict technical constraints. Within this context, the study identifies a subset of buildings in the eastern area of the city on which green roofs can be feasibly installed by considering a set of selection criteria that cover the following dimensions: building use, typological classification, construction period, construction technique, roof geometry, and available surface area.

Only residential buildings were considered eligible. In terms of typology, linear, block, and tower buildings were identified as suitable (D’Ambrosio et al., 2023), whereas single-family housing was excluded according to a cost–benefit analysis. The building sample was selected from the spatial dataset of buildings included in the 1:5,000 scale topographic database of the city of Naples and restricted to only those constructed between 1981 and 2004. This period corresponds to a transitional phase in building energy regulation characterized by standards below current requirements (Ascione et al., 2013), making such buildings amenable to retrofit. Regarding construction technique, four structural configurations were considered based on scientific literature and regulatory frameworks: steel structures with reinforced concrete envelopes, reinforced concrete structures with brick infill, reinforced concrete structures with tuff block infill, and reinforced concrete structures with prefabricated concrete panels. These construction types are compatible with retrofit interventions that do not require alterations to historically or architecturally valuable elements and are well suited to the integration of modular and prefabricated components (Ackerman, 2012; D’Ostuni et al., 2022). Roof geometry and surface area were also considered. Buildings with moderately sloping flat roofs (inclination between 0° and 15°) were retained, as such surfaces facilitate the integration of drainage and irrigation systems and generally offer greater accessibility and multifunctional potential (FLL, 2018). Roof areas between 300 and 1,500 m² were considered suitable (Fraunhofer, 2020; GBC Italia, 2021), ensuring adequate space for drainage systems, vegetation substrates, and associated technical components while maximizing ecosystem benefits relative to implementation costs. Additional factors considered include maintenance requirements, roof safety, usability, and potential shading from adjacent buildings or rooftop equipment. Buildings meeting all the above criteria are shown in Figure 5. The total area identified for green roof implementation corresponds to approximately 1.15% of the total area of the eastern sector of Naples, highlighting the relatively limited spatial extent of a credible intervention in a realistic context with technical feasibility constraints.

In the context of the SCS-CN method, a modified approach is adopted to consider the physical cascade between the green roof and the drainage network, based on the observation that only a fraction of the total rainfall that exceeds the retention/detention capabilities of the green roof is conveyed to the drainage system and contributes to flooding. In Supplementary Appendix A.2.2, it is shown that the I _*a* parameter to be assigned to the cascade of the green roof/drainage system is greater than the I′ _*a* associated with the green roof alone. Drawing on available literature (Fassman-Beck et al., 2016; Squier-Babcock and Davidson, 2025), we assigned values of CN = 84 and I′ _*a* = 20 mm to the green roofs in the present work, whereas the equivalent-cascade I _*a* values are calculated as shown in Supplementary Appendix A.2.2. The I _*a* values for the equivalent-cascade corresponding to different durations are reported in Table 4.

2.4 Numerical setup and scenarios

Flood dynamics were simulated using the 2D hydrodynamic model HEC-RAS 6.7. The computational domain was discretized for both the Eastern and Western Basins using a uniform mesh consisting of triangular cells with an average side length of 10 m. Although the numerical grid is relatively coarse, numerical accuracy is improved by exploiting the subgrid capabilities of HEC-RAS (Brunner, 2020; 2024) which allow the flow volume associated with each computational cell to be redistributed among the underlying raster cells contained within it. The triangular meshes, counting 2,426,658 and 2,407,519 cells for the Eastern and Western Basins, respectively, were generated using HEC-RAS 2025 (alpha version) and subsequently imported into HEC-RAS 6.7. Buildings were accounted for through their elevation values derived from the DEM, such that the computational grid was defined over the entire domain, including built structures. The numerical stability of the simulations was ensured by adopting an adaptive time step. A sea-level boundary condition was imposed along the mesh perimeter in contact with the sea.

The combination of a high cell count and complex urban morphology results in high computational demand. Considering the spatial extent of the study area, the number of simulations required, and the objective of conducting a city-scale flood hazard assessment, a trade-off between model complexity and computational efficiency was made. Accordingly, the DWE formulation was adopted, which, although less computationally intensive than the full SWE, yielded consistent results in delineating flood-prone areas and reproducing runoff propagation across the urban environment. Nonetheless, it is acknowledged that, for site-specific applications or in areas where local flow accelerations are relevant, adopting the full SWE formulation may be more appropriate.

Two scenarios were defined to evaluate the extent of pluvial flooding and the potential mitigation capacity of green roofs (what-if scenario):

• - The baseline scenario characterizes surface ponding and runoff propagation across the full study area by enveloping the results of the flooding simulations corresponding to the family of design hyetographs with a return period of T = 10 years (Section 2.3.1) with a surrogate representation of the urban drainage system (Supplementary Appendix A.2.1).
• - The what-if scenario uses the same input data as the baseline but incorporates green roofs on the selected subset of residential buildings in the eastern sector of Naples as the risk mitigation strategy (Section 2.3.5; Figure 5). Within HEC-RAS, green roofs were modeled using CN values drawn from the literature (see Section 2.3.6), complemented by the novel application of I _*a* coefficients to account for the water retention capacity of the green roofs (Supplementary Appendix A.2.2). Simulations under this scenario were restricted to the eastern catchment, where the green roof installations are located.

To accommodate the two scenarios, the three rainfall inputs, and the subdivision of the urban territory of Naples into two distinct hydrographic catchments, a total of nine simulations (three in the Western Basin and six in the Eastern Basin) were performed.

2.4.1 Supplementary sensitivity analyses and model consistency

To assess the robustness of the proposed modeling framework, a set of supplementary analyses was conducted under selected rainfall scenarios.

A screening sensitivity analysis was performed for the Eastern Basin using the 1-h synthetic storm associated with a 10-year return period. This analysis was intended to evaluate the sensitivity of the main hydraulic outputs to plausible variations in the parameters controlling runoff generation and surface flow resistance, rather than to provide a comprehensive probabilistic uncertainty quantification. Manning’s roughness coefficients were uniformly varied by ±10%, whereas CN values were perturbed additively by ±5 units. An additive perturbation was selected because CN is a bounded empirical index, and a percentage variation would be inappropriate for values approaching the upper limit. Impervious land cover classes already assigned CN = 98 were not increased further. Overall, four additional simulations were conducted to assess the effects of these parameter perturbations.

The sensitivity to the Initial Abstraction (I _*a*) was separately assessed during the rainfall event of 23 September 2023. Within the proposed modeling framework, variations in I _*a* are equivalent to changes in the nominal service level of the drainage network, commonly expressed in terms of the return period. Accordingly, return periods of T = 1 year and T = 2 years were considered for both the baseline and what-if scenarios.

Finally, an additional simulation was conducted to assess the consistency of the model, as described in the following section.

2.5 Qualitative consistency check

A qualitative consistency check was conducted to assess the model’s ability to reproduce the main areas affected by pluvial flooding by comparing simulated inundation extents with conditions documented during the storm event of 23 September 2023 (Section 2.3.1). The comparison was performed using photographs and videos available on online social media platforms. Although these observations are informal and spatially sparse, they may provide useful qualitative evidence for evaluating whether the model identifies flood-prone areas that are consistent with real-world observations (Sciuto et al., 2025).

In Figure 6, the qualitative comparison between the simulated inundation and the available observational evidence is presented. Figure 6a shows the spatial distribution of maximum simulated water depths across the eastern sector of Naples with the points where evidence of flooding is available from social media. The remaining panels (Figures 6b–e) show the locations selected as representative of distinct pluvial flooding conditions documented during the event.

At the location shown in Figure 6b, the model correctly identifies water accumulation at a road underpass, where photographic evidence documents partially submerged vehicles and marked surface ponding, a condition consistent with the simulated relatively high flow depths. In Figure 6c, the simulation reproduces a broad inundated area along a main road with simulated water depths ranging from low to moderate, consistent with the available imagery. In Figure 6d, the model captures, albeit incompletely, the flooding that developed along the tram tracks near a railway underpass. Collectively, these results suggest that the surrogate drainage system representation and the corrections applied to the DSM are effective in reconstructing the main surface runoff pathways and identifying areas susceptible to rainwater accumulation. Nonetheless, discrepancies between simulations and observations remain. In Figure 6e, flooding documented in the available imagery is not reproduced by the model. Such differences may be attributable to local factors not explicitly represented in the numerical simulations, including temporary obstructions or localized malfunctions of drainage inlets and small-scale topographic irregularities. Such limitations are expected in large-scale urban hydrodynamic modeling applications conducted in the absence of detailed drainage data. Notwithstanding these uncertainties, the qualitative consistency check exhibits a sufficient correspondence between the simulated flood patterns and the observed inundation areas, with two satisfactorily captured points, one partially captured point, and one missed location (Table 5). Overall, the qualitative consistency check suggests that the modeling framework identifies several of the main urban flood hotspots generated during frequent precipitation events, providing supporting evidence for its use in the comparative assessment of nature-based solution mitigation scenarios.

TABLE 5. Qualitative consistency check between documented flooding conditions by citizens on social media (Figure 6) and simulated inundation at selected locations during the 23 September 2023 event.

3 Results

This section presents the results of the 2D hydrodynamic simulations carried out to evaluate the impacts of pluvial flooding in the study area and to assess the potential mitigation effects associated with the implementation of green roofs. The analysis focuses on three main aspects: (i) the spatial distribution of flood extents, maximum water depths, and flow velocities obtained from the numerical simulations; (ii) the classification of flood hazard levels based on water depth thresholds; and (iii) the estimation of the affected population at the census unit scale. The comparison between the baseline scenario and the scenario including green roof implementation allows the potential benefits of this nature-based solution to be quantified in terms of reductions in inundated areas, flood depths, and population exposure to pluvial flood hazards.

3.1 Flood extents and maximum water depths

Flooded areas were identified by applying a minimum threshold of 1 cm to exclude cells with negligible water depth. The performance of the proposed intervention strategy was assessed using the maximum simulated water depth in each raster cell within the area of interest (Webber et al., 2020).

3.1.1 Baseline scenario

The baseline scenario represents the business-as-usual configuration, in which no mitigation measures were implemented. This scenario was used as the reference case against which the mitigation effect of the green roof intervention was evaluated.

Figure 7a shows the envelope of maximum simulated water depths across the city of Naples under the baseline scenario. The map highlights the spatial extent of pluvial flooding and the spatial variability of maximum water depths across the urban area. Although most inundated cells are characterized by relatively shallow depths, generally below 0.2 m, localized areas exhibit higher values. This pattern is also reflected in the overall distribution of inundation depths. The inundated area covers approximately 12.1 km², corresponding to 12.4% of the non-built urban surface of Naples. The 0.01–0.05 m, 0.05–0.10 m and 0.10–0.20 m classes account for 46.37%, 22.07%, and 16.11% of the flooded area, respectively, whereas the 0.20–0.50 m, 0.50–1.00 m and >1.00 m classes represent 10.94%, 3.23%, and 1.28%, respectively. The two detailed panels in Figure 7 provide further insight into the spatial patterns of pluvial flooding at the local scale. In the peripheral area shown in Figure 7b, floodwater is mainly concentrated along roads, open paved surfaces, and linear incisions that facilitate the conveyance of rainwater. In contrast, the historical city center shown in Figure 7c displays a more fragmented and spatially complex inundation pattern. This is consistent with the dense urban fabric, narrow streets, irregular building layouts, and limited availability of open permeable surfaces, which together influence the direction and concentration of surface runoff along the southward topographic gradient. These patterns confirm that the urban system response to rainfall is controlled not only by topographic gradients and local depressions but also by the street network layout (Zhou et al., 2022; Mei et al., 2023).

Despite the relatively coarse computational mesh adopted in the simulations and the simplified representation of drainage processes, the model reproduces the main hydrodynamic features of stormwater propagation in a densely urbanized environment. In particular, the results in Figure 7 capture the flow pathways along major streets, alleys, and interbuilding spaces and identify localized accumulation areas where flow depth increases. This confirms the suitability of the modeling framework for analyzing city-scale pluvial flood patterns. In Supplementary Figure S1, the spatial distribution of maximum water depths across the eastern sector of Naples under the baseline scenario is illustrated.

3.1.2 What-if scenario

Figure 8a presents the spatial distribution of the differences in maximum water depth between the baseline and what-if scenarios, based on the implementation of green roof solutions in the eastern sector of Naples. Positive values indicate reductions in maximum water depth attributable to the implementation of green roofs, whereas very small negative values (up to 2 mm) in limited areas are suggestive of a time misalignment between true and numerical peak flow instants in the two scenarios. Figure 8b,c provides zoomed views of the areas in which the observation points identified in Figure 6 are located.

The green roof design scenario produces spatially widespread but mostly small reductions in maximum water depth across the analyzed portion of the catchment. These reductions are predominantly concentrated along streets, alleys, and open spaces between buildings, exhibiting a local-to-downstream propagation mechanism. The most substantial attenuation occurs in the immediate vicinity of buildings with green roofs, with mitigation effects diminishing progressively with distance from the treated buildings. In most affected cells, depth reductions amount to less than 5 cm. Although modest in magnitude, the spatial continuity of these reductions suggests that green roofs contribute to a local attenuation of surface runoff across the catchment. In a few locations, depth reductions reach values between 5 and 60 cm, indicating that localized topographic conditions can beneficially amplify the mitigation effect. Quantitatively, the adoption of green roofs reduced the total flooded area from 4.09 to 4.04 km², corresponding to a decrease of approximately 49,288 m² (4.93 ha), or 1.20% relative to the baseline scenario. Concurrently, the total flood volume decreased by 7,721 m³, representing a 2.04% reduction. The larger reduction in flood volume compared with the flooded area suggests that green roofs not only reduce the extent of flooding but also lower water depths in areas that remain flooded.

Overall, the results confirm that green roof implementation produces measurable, yet modest, reductions in maximum water depths, which are most pronounced in the immediate surroundings of treated buildings. The modest propagation of these reductions along surface runoff pathways further demonstrates that the positive effects of green roofs extend beyond the directly treated locations, contributing to flood attenuation across a broader portion of the urban catchment.

3.1.3 Screening sensitivity analysis

Four simulations with parameter perturbations were performed (Table 6): a positive perturbation (n _*M* + 10% and CN + 5) for the baseline and green roof scenarios, respectively; negative perturbation (n _*M* − 10% and CN − 5) for the baseline and green roof scenarios, respectively. The sensitivity results were evaluated in terms of flooded area, flood volume, and the corresponding absolute and relative differences between the baseline and green roof scenarios (Table 6).

TABLE 6. Screening sensitivity analysis of the flood mitigation effect of green roofs to perturbations in Curve Number (CN) and Manning’s roughness coefficient (n_M), under a 1-h synthetic storm with a 10-year return period for the eastern sector of Naples.

As expected, perturbing Manning’s roughness coefficient and CN in the positive direction (n _*M* + 10%, CN + 5) increases surface flow resistance and reduces infiltration capacity, resulting in larger flooded areas and flood volumes relative to the standard configuration for both the baseline and green roof scenarios (e.g., the baseline flooded area increases from 3.41 to 4.02 km², and the baseline flood volume increases from 248,996.16 to 305,336.19 m³). Conversely, the negative perturbation (n _*M* − 10% and CN − 5) reduces both metrics relative to the standard configuration (the baseline flooded area reduces from 3.41 to 3.04 km², and the baseline flood volume reduces from 248,996.16 to 216,863.88 m³), consistent with the expected increase in infiltration and decrease in flow resistance. This consistent response confirms that the model behaves as physically expected under variations of these influential parameters.

More importantly, the absolute reduction in flooded area and flood volume attributable to green roof implementation (the difference between the baseline and green roof scenarios in Table 6) remains stable across all three parameter configurations: the reduction in flood volume ranges from 5,704.10 m³ (negative perturbation) to 5,708.53 m³ (positive perturbation), a minimal variation around the standard configuration value of 5,708.44 m³; the reduction in flooded area remains at 0.05–0.06 km² throughout. While perturbing CN (±5 units) and Manning’s n _*M* (±10%) substantially alters the absolute magnitude of simulated flooding, by approximately 11%–18% for flooded area and 13%–23% for flood volume, relative to the standard configuration, it leaves the mitigation effect attributable to green roofs nearly unchanged. This indicates that the reported reduction in maximum flood depths due to green roof implementation is not an artifact of the specific CN and Manning’s values adopted but rather a robust feature of the NBS representation in the numerical model.

The sensitivity to Initial Abstraction (I _*a*) was assessed separately for the rainfall event of 23 September 2023. Within the proposed modeling framework, variations in I _*a* are equivalent to changes in the nominal service level of the drainage network, commonly expressed in terms of the return period. Accordingly, return periods of T = 1 year and T = 2 years were considered for both the baseline and what-if scenarios (Table 7). For both return periods, the green roof implementation in the what-if scenario results in reductions in flooded area and flooding volume. However, these reductions are appreciable in the simulations with T = 1 year, whereas they become marginal in the simulations with T = 2 years (Table 7). This behavior can be attributed to the higher drainage efficiency represented in the surrogate model when the assumed level of service is increased from T = 1 to T = 2 years. The enhanced drainage capacity reduces the rainfall volume available for flooding and, consequently, limits the beneficial mitigation effect provided by the NBS intervention.

TABLE 7. Screening sensitivity analysis of the flood mitigation effect of green roofs to changes in the nominal service level of the drainage network under the 23 September 2023 rainfall for the eastern sector of Naples.

3.2 Discharge and maximum flow velocities

Figure 9 shows the envelope of maximum simulated flow velocities across the city of Naples under the baseline scenario. At the city-scale (Figure 9a), the velocity field exhibits a highly structured spatial pattern, closely aligned with the road network and the main topographic flow corridors. This confirms that, even under moderate rainfall conditions, streets and open paved areas act as preferential pathways for overland flow propagation. Most of the flooded cells are characterized by relatively low to moderate velocities, generally below 0.5 m/s. However, localized corridors display higher values, with velocities exceeding 1 m/s and, in some cases, reaching values greater than 1.5 m/s. These higher-velocity areas are mainly concentrated along continuous and sloping road segments, where runoff is conveyed downslope and flow acceleration may occur. In the peripheral area shown in Figure 9b, discontinuous open spaces generally show lower velocities, indicating more dispersed or locally ponded flow conditions. The historical city center (Figure 9c) displays a markedly different velocity pattern. Here, the dense and irregular urban fabric, characterized by narrow streets, closely spaced buildings, and complex intersections, produces a fragmented but locally intense network of flow pathways. Several narrow streets and junctions exhibit high simulated velocities, reflecting the combined effect of channelization by building footprints and local topographic gradients. Figure 9 complements the maximum water depth map in Figure 7 by showing that pluvial flood hazards in Naples are not only associated with localized ponding or inundation depth but also with the dynamic propagation of stormwater along the urban street network. In Supplementary Figure S2, the spatial distribution of maximum flow velocities across the eastern sector of Naples under the baseline scenario is illustrated.

Figure 10 illustrates the spatial distribution of differences in the maximum flow velocity envelopes between the baseline and what-if scenarios across the eastern catchment. Overall, the velocity differences are generally modest, with most of the domain exhibiting negligible variations approaching 0 m/s. Localized increases and decreases in velocity are observed predominantly along the main runoff pathways and road axes; however, these variations remain limited in magnitude. The results, therefore, suggest that, under the scenario examined, the implementation of green roofs exerts a limited influence on surface flow velocities, whereas more pronounced effects are evident in the reduction of maximum water depths.

Discharge time series were extracted at two control cross-sections located in the downstream part of the eastern sector of the study area. Figure 11 presents the resulting hydrographs for the 1 h synthetic storm associated with a 10-year return period under both the baseline and what-if scenarios. Section 1 is located closer proximity to the area where green roofs are implemented in the what-if scenario, whereas Section 2 is situated 627 m farther downstream. A comparison of the two scenarios indicates that, in Section 1, green roof implementation results in a discernible reduction in peak discharge, accompanied by only a marginal delay in peak timing. By contrast, in Section 2, no appreciable delay in peak timing nor substantial reduction in peak discharge is observed. This finding is consistent with the established understanding that the effectiveness of detention measures tends to decrease rapidly with increasing distance downstream from the intervention area (Ayalew et al., 2015; Cimorelli et al., 2016).

3.3 Flood hazard classification

Different hazard models can be adopted that typically exploit water depth and/or flow velocity as main variables (Padulano et al., 2021). Here, three hazard classes were identified according to the water depth thresholds proposed by Kaspersen and Halsnæs (2017): H1 (<5 cm), considered generally safe; H2 (≥5 and <20 cm), unsafe for health, basements, roads and railways; and H3 (≥20 cm), unsafe for health, basements, roads, railways, buildings and historical/cultural assets. It is assumed that a 5 cm flow depth at the ground is sufficient to inhibit the movement of pedestrians and slow down vehicular circulation, generating traffic disruption and potentially interfering with emergency rescue vehicles. The hazard classification was applied to the baseline and what-if scenarios, using the corresponding envelope of maximum water depths. The resulting hazard classification maps for both scenarios are shown in Supplementary Figure S3.

A building scale GIS analysis was performed to assess how the hazard classification of individual buildings changes following green roof implementation. A 2-m buffer was generated around each building footprint to mitigate potential misalignment between the 1-m resolution flood depth raster files (envelope of maximum water depths for the baseline and what-if scenarios) and the building boundaries. For each buffer, the maximum water depth was extracted from both the baseline and the what-if scenarios, and each building was assigned to one of the three hazard classes (H1, H2, or H3) under both scenarios. The analysis, conducted on the 11,852 buildings located in the eastern sector, shows that 99 buildings (0.84% of the total) were reclassified into a lower hazard class following green roof implementation: 53 buildings (0.45%) shifted from H3 to H2, 42 (0.35%) from H2 to H1, and 4 (0.03%) from H3 to H1. Of these, 46 buildings (0.39% of the total) were reclassified into hazard class H1. A shift to a higher hazard class was observed for only five buildings (0.04%; four from H1 to H2 and one from H1 to H3), an outcome that may be attributed to (i) time discretization, which causes a slight temporal misalignment between true and numerical peak flow instants and consequent underestimation of the peak flow depth in the baseline scenario and (ii) different flow delays introduced by NBS that can cause effect superposition in the green roof scenario, with a mechanism similar to that described by McCuen (1974). The remaining 11,748 buildings retained their original hazard classification.

Interestingly, among the 99 buildings that were reclassified into a lower hazard class, only 43 actually feature a green roof (21 shifting from H3 to H2, 19 from H2 to H1, and 3 from H3 to H1), out of the 350 buildings on which the intervention was implemented 2.95% is obtained by dividing 350 by 11,852, which are all the buildings located in the eastern sector. So, the 350 buildings where the intervention was implemented represent 2.95% of all buildings in the eastern sector). Therefore, relative to the total intervention buildings, 6% of the buildings shifted from H3 to H2, 5.43% from H2 to H1, and 0.86% from H3 to H1. The remaining 56 reclassified buildings do not feature a green roof themselves, and their improved hazard classification is therefore attributable to the propagation of the mitigation benefit to neighboring and downstream buildings.

3.4 Pluvial flood risk indicator

Our study focuses on the impact of pluvial floods on urban populations. The affected population per census unit in the city of Naples for the baseline scenario was estimated by overlaying the hazard classification map described in Section 3.3 with the census unit boundaries and resident population data (Section 2.3.5). For each census unit, the number of raster cells falling within each hazard class (H1, H2, and H3) was computed and used to derive the corresponding area fractions. The resident population was then disaggregated across the three hazard classes proportionally to these fractions. Each census unit was assigned the maximum hazard class recorded within its boundaries.

The affected population was defined as the sum of the population falling within hazard classes H2 and H3. The corresponding map for the baseline scenario is shown in Figure 12a. The affected population per census unit was also estimated for the green roof scenario.

For each census unit, the difference in affected population between the baseline and what-if scenario estimates was computed and represented in Figure 12b. This figure shows a small but perceivable reduction in the affected population, expressed as a percentage difference, indicating that the implementation of green roofs contributes to reducing population exposure to pluvial flood hazards across several census units. Figure 12b also shows that there is a slight decrease in the affected population even in census units that do not contain green roof interventions.

4 Discussion

The qualitative consistency check performed against the storm event of 23 September 2023 provides useful insights into both model performance and the characteristics of pluvial flood hazards in Naples. The sufficient correspondence between simulated flood patterns and the locations documented through citizen video content suggests that the modeling approach is suitable for comparative, city-scale screening. It also corroborates the potential of VGI as a source of supporting observational evidence in urban flood modeling, a role increasingly recognized in the recent literature (Webber et al., 2020; Drews et al., 2023; Sciuto et al., 2025).

Following the consistency check phase, the model was applied to simulate surface ponding and runoff propagation across the entire municipality of Naples in a 10-year return period baseline scenario obtained by enveloping the results of three design rainfall events (with storm durations of 30 minutes, 1 hour, and 3 hours, Sec. 2.3.1). The baseline scenario is characterized by spatially extensive but mostly shallow pluvial flooding, with localized hotspots of greater water depth (Figure 7). The inundation pattern exhibits pronounced spatial variability, with the hydraulic response strongly governed by the street network layout and local topographic gradients. Peripheral flat areas tend to exhibit lower and more spatially distributed flow velocities, with runoff either dispersing across open surfaces or accumulating in local depressions (Figure 9). By contrast, the historic city centre promotes a denser network of narrow flow pathways, in which building footprints and irregular street geometry concentrate and accelerate surface runoff along the topographic gradient (Figure 9). Despite the surrogate representation of the urban drainage system and the relatively coarse computational mesh adopted, the subgrid treatment allows reproducing the main hydrodynamic characteristics of stormwater propagation in a densely urbanized environment with complex topography, supporting the application of the proposed modeling approach for city-scale pluvial flood assessment.

The flooding analysis was subsequently repeated, incorporating green roofs on a selected subset of residential buildings in the eastern sector of Naples (Section 2.3.6). Within HEC-RAS, green roofs were modeled using CN values drawn from the literature, complemented by the novel application of Initial Abstraction coefficients to account for the water retention capacity of green roofs (Supplementary Appendix A).

The choice of a 10-year return period for the mitigation assessment is consistent with the established understanding that NBS flood mitigation effectiveness, in terms of reductions in peak flow and inundation depth, diminishes progressively as rainfall intensity increases (Webber et al., 2020; Pampaloni et al., 2022), making moderate return periods the most meaningful context in which to evaluate NBS performance. Furthermore, although many studies in the literature implement NBS over unrealistically large portions of the computational domain without accounting for the technical constraints that limit the feasibility of specific interventions, the present study deliberately adopted a more realistic and conservative approach in which green roofs were installed exclusively on a subset of residential buildings identified as technically suitable, yielding a plausible near-to-medium-term deployment scenario. The analysis is intentionally focused on a single NBS typology, as the exploration of combined NBS strategies and their synergistic effects is deferred to future research.

In the what-if scenario, the implementation of green roofs reduces maximum water depths across parts of the eastern sector (Figure 8), particularly along selected runoff pathways and in accumulation areas near treated buildings. For most of the affected cells, depth reductions remain below 5 cm; however, localized depth reductions between 5 and 60 cm are observed at specific locations, indicating that favorable topographic conditions, such as depressions or convergent flow paths close to treated buildings, can amplify the local mitigation effect. These outcomes are consistent with the broader literature on the flood mitigation performance of green roofs under low- to moderate-return-period storm events. Sciuto et al. (2025), simulating a 10-year return period event with green roofs, rain barrels, and permeable pavements implemented across 23.2% of the total domain, report water depth reductions of approximately 1 cm in 71.65% of cases, reaching 3 cm in 20.60% of cases, and a maximum of 11 cm in 7.75% of cases. Webber et al. (2020) report depth reductions of comparable magnitude for green roofs covering 39% of the total catchment area under a 10-year storm. Öztürk et al. (2024), replacing all rooftops within the computational domain with green roofs, report maximum water depth reductions of up to 4% under a real flood event simulation. The convergence of these findings across different urban contexts and modeling frameworks reinforces the conclusion that the absolute magnitude of flood depth reductions achievable through green roofs is inherently limited. The present study also confirms this understanding under realistic scenarios with partial deployment of these systems. The robustness of this modest but consistent mitigation effect was further verified through a dedicated screening sensitivity analysis (Table 6). Although perturbing Manning’s roughness coefficient (±10%) and Curve Number (±5 units) substantially altered the absolute magnitude of simulated flooding, the corresponding reduction attributable to green roof implementation remained virtually unchanged across all configurations tested, indicating that the reported mitigation effect is not an artifact of the specific parameter values adopted but a robust feature of the NBS representation in the numerical model.

With respect to flow velocities, the green roof scenario produces only marginal changes relative to the baseline scenario (Figure 10), suggesting that, under the conditions examined, these interventions are more effective in attenuating peak water depths than in modifying the overall dynamics of surface flow propagation.

The flood mitigation effectiveness of green roofs is most pronounced in the immediate vicinity of the installations and diminishes progressively along the downstream runoff pathway, as directly illustrated by the discharge time series extracted at the two control cross-sections (Figure 11). This is consistent with the common hydrologic wisdom that the beneficial effects introduced by detention/retention devices rapidly reduce with increasing distance downstream from the intervention area (Ayalew et al., 2015; Cimorelli et al., 2016). Nonetheless, Figure 12b demonstrates that reductions in the affected population are not confined to census units containing green roof installations but extend to adjacent and downstream units. This result is consistent with the recent findings of Roggero et al. (2025), who showed that decentralized blue–green flood adaptation measures tend to protect surrounding areas rather than the locations where they are installed, even in flat urban terrain. This pattern is corroborated at the building scale (Section 3.3): of the 99 buildings that were reclassified into a lower hazard class following green roof implementation, only 43 actually feature a green roof, whereas the remaining 56 benefit from the propagation of the mitigation effect from neighboring treated buildings.

This spatial asymmetry between the location of the intervention and the distribution of its benefits has direct implications for governance and policy design. When the advantages of green roof implementation accrue primarily to neighboring or downstream areas rather than to the building owner bearing the installation cost, individual incentives for voluntary uptake are weakened. In the absence of corrective mechanisms, this dynamic, commonly described in economics as a positive externality, may result in systematically lower levels of NBS deployment than would be socially optimal. Targeted incentive schemes, such as subsidies or tax relief for green roof installation, combined with regulatory requirements embedded in urban planning instruments, could help align private decisions with collective flood risk mitigation objectives and maximize the catchment scale benefits of NBS deployment. In particular, Neumann et al. (2024) demonstrated that the flood mitigation effectiveness of NBS is most pronounced when interventions are positioned in proximity to flood-prone areas, and this is confirmed by the present study. This implies that spatially targeted deployment strategies, prioritizing buildings located upstream of or adjacent to known inundation hotspots, would yield greater flood risk mitigation per unit of installed green roof area than uniform or randomly distributed deployment and should therefore inform the spatial planning of NBS implementation programs.

In the present study, the explicit representation of the cascade interaction between green roofs and the urban drainage system is accounted through the modified Initial Abstraction formulation derived in Supplementary Appendix A. Unlike previous studies that have modified CN and I _*a* values to simulate the effect of green roofs in 2D hydrodynamic models (Öztürk et al., 2024; Sciuto et al., 2025), the present approach accounts for the fact that green roofs operate in cascade with the downstream drainage network: the contribution of a green roof to surface flooding is activated only when the residual runoff generated by the installation exceeds the available capacity of the receiving drainage system. This formulation ensures that the beneficial effect of green roofs is not underestimated in scenarios where the drainage system retains sufficient capacity to receive the runoff fraction produced by the vegetated substrate. More broadly, the modified SCS-CN framework developed in this study represents a pragmatic and transferable strategy for incorporating surrogate drainage representations into rain-on-grid simulations, particularly in contexts where detailed sewer network data are unavailable. Clearly, the magnitude of the green roof mitigation benefit is sensitive to the assumed nominal service level of the drainage network: the sensitivity analysis conducted against the real rainfall event of 23 September 2023 (Table 7) shows that the beneficial effect of green roofs is far more pronounced when the drainage network is assumed to operate at a lower service level (T = 1 year) than under the more optimistic T = 2 years configuration adopted as the standard assumption in this study.

Although the proportion of buildings where green roofs have been implemented may appear modest with respect to the total area, it should be interpreted considering the inherent constraints governing the deployment of nature-based solutions in dense urban environments. However, as noted by Webber et al. (2020), even targeted interventions with spatially restricted coverage can play a meaningful role in advancing urban resilience at a larger scale. Therefore, although green roofs can provide measurable flood mitigation benefits, their performance should be interpreted as part of an integrated urban flood risk management strategy rather than as a standalone solution.

The flood risk maps produced in this study provide a spatially explicit decision-support tool that can directly inform the prioritization of NBS interventions by urban planners and stormwater management authorities. By combining hydrodynamic modeling outputs with census-level population exposure data, the maps translate complex simulation results into an accessible and actionable representation of spatial risk, suitable for integration into urban resilience strategies and adaptation planning frameworks. The chosen format facilitates effective visual communication to a wide range of stakeholders, including municipal administrators, civil protection agencies, community organizations, and the general public, enabling the identification of priority intervention areas and supporting evidence-based deliberation on the allocation of resources for pluvial flood risk reduction at the city-scale.

5 Limitations and future research

The present study is subject to several limitations concerning the methodology and the case study that should be acknowledged when interpreting the results.

With reference to the methodology, we observe that the surrogate representation of the urban drainage system and the cascade interaction between green roofs and the drainage network, implemented through modified SCS-CN parameters, require further testing and calibration against detailed hydraulic data to strengthen the transferability and robustness of the proposed approach. Although spatial heterogeneity in drainage response may be partially accounted for through spatially variable CN and I _*a* coefficients, the surrogate representation of the urban drainage system may not fully capture spatial variations in drainage dynamics. The adopted approach necessarily simplifies the complex bidirectional exchange interactions between surface flow and subsurface infrastructure by neglecting the potential discharge of subsurface drainage to the surface under channel pressurization conditions. From a dynamic point of view, the surrogate modeling approach adopted in this study represents both green roofs and the underground drainage system without an explicit routing scheme. Consequently, the temporal distribution of the residual net rainfall entering the 2D domain largely follows that of the design hyetograph, although with a reduced magnitude. Within this framework, any delay in peak discharge arises primarily from the lower flood wave celerity across the 2D computational domain. Therefore, the proposed approach may capture the volumetric mitigation provided by green roofs but does not reproduce the additional peak-delaying effect associated with their internal storage-and-release dynamics, which would require an explicit, physically based representation of both the green roofs and the underground drainage system. The use of amplified Initial Abstraction values mostly exerts its effect on the initial part of the rainfall, which could not dynamically reflect how the drainage network manages rainfall.

With reference to the case study, the absence of hydrometric monitoring stations within the urban area precluded rigorous quantitative model calibration and validation. The consistency check presented in this study relies on a limited set of observed flood locations associated with a single storm event, documented through citizen videos published on social media. Although this qualitative evidence supports the plausibility of the simulated flood patterns, it does not substitute for systematic quantitative validation against measured water depths. The assessment of green roof suitability and the consequent flood mitigation analysis were restricted to residential buildings. Future investigations should extend this evaluation to other building typologies, including commercial, industrial, and public infrastructure, and consider a broader portfolio of nature-based solutions, such as permeable pavements and rain gardens.

6 Conclusion

Rainwater management constitutes one of the foremost challenges confronting urban areas within a global context of accelerating urbanization, anthropogenic land use changes, and intensifying climate change impacts. The increasing impacts of pluvial flooding events resulting from extreme precipitation underscore the need for integrated approaches that combine physically based modeling with nature-based solutions (NBS) to complement and enhance existing stormwater infrastructure. The present study addresses this challenge through a city-scale pluvial flood hazard and risk assessment for the municipality of Naples, Italy, a historically significant urban environment characterized by complex topography and limited drainage infrastructure data, and evaluates the flood mitigation potential of green roofs as a representative small-scale NBS.

The main methodological contribution of this study lies in the adaptation of the SCS-CN method to incorporate, through modified Initial Abstraction coefficients, a surrogate representation of both the urban drainage system capacity and the cascade interaction between green roofs and the downstream drainage network. This approach enables spatially distributed hydrologic loss modeling within a two-dimensional hydrodynamic framework, implemented in HEC-RAS 6.7 via the rain-on-grid approach, without requiring detailed knowledge of the subsurface drainage infrastructure.

The qualitative consistency check against the storm event of 23 September 2023, conducted using citizen-generated video content as volunteered geographic information, supports the ability of the modeling framework to reproduce the main urban flood hotspots under real rainfall conditions. The baseline scenario (design rainfall events with a return period of 10 years and durations of 30 minutes, 1, and 3 hours) reveals that pluvial flooding in Naples is spatially extensive but predominantly characterized by shallow water depths, with localized hotspots of greater inundation occurring at road intersections and topographic depressions and along preferential runoff pathways defined by the street network. The hydraulic response is strongly governed by local morphology and urban geometry, with the historic city centre exhibiting a denser network of accelerated flow pathways compared with peripheral areas. The flood risk assessment, conducted at the census unit level by combining simulated maximum water depths with resident population exposure data, identifies the spatial distribution of the most susceptible urban subunits.

The what-if scenario demonstrates that targeted NBS deployment on technically suitable residential buildings in the eastern sector produces measurable, spatially distributed reductions in maximum water depth and affected population, particularly in the immediate vicinity of treated buildings and along downstream runoff pathways. Although the absolute magnitude of depth reductions remains modest for most affected cells, consistent with findings reported in the broader literature for comparable return periods and higher NBS coverage ratios, localized reductions of greater magnitude are observed in low-lying accumulation areas close to treated buildings. Critically, the benefits of green roof implementation are shown to extend beyond the directly treated locations, propagating to adjacent and downstream census units. This spatial asymmetry between intervention location and benefit distribution has direct implications for policy design: because a substantial share of the mitigation benefits accrues to areas other than those bearing the installation cost, a market-based deployment alone is unlikely to achieve socially optimal levels of NBS uptake. Targeted incentive schemes and regulatory frameworks are therefore essential to maximize the collective flood risk reduction potential of NBS at the urban scale.

The proposed framework is potentially transferable across diverse urban contexts and offers a decision-support tool for the integration of NBS into urban flood risk management strategies, particularly in complex and large cities. It is important to acknowledge that, although the expansion of permeable surfaces through NBS in urbanized areas can contribute to attenuating the adverse effects of flood events, their efficacy remains inherently limited and diminishes as rainfall intensity increases. Consequently, structural engineering measures retain their fundamental importance, and NBS should be regarded as complementary interventions only.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fenvs.2026.1907724/full#supplementary-material

Supplementary material Supplementary material at the source

Supplementary material Supplementary material at the source

Footnotes

Edited by: Michele Turco, University of Calabria, Italy

Reviewed by: Ahmad Rashiq, Integral University, India

Sakine Koohi, Imam Khomeini International University, Iran