# Virtual City Simulator: A Scenario-Based Tool for Multidimensional Urban Flood Long-Term Vulnerability Assessment and Planning in Mediterranean Cities

Ana Noemí Gomez Vaca, Lucía Alexandra Popartan, Guillem Armengol Selvas, Sergi Nuss-Girona, Morgan Abily, Ignasi Rodríguez-Roda

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Ana Noemí Gomez Vaca, Lucía Alexandra Popartan, Guillem Armengol Selvas, Sergi Nuss-Girona, Morgan Abily, et al. Virtual City Simulator: A Scenario-Based Tool for Multidimensional Urban Flood Long-Term Vulnerability Assessment and Planning in Mediterranean Cities. Water, 2025, 17 (24), pp.3538. 10.3390/w17243538. [hal-05420971](https://hal.science/hal-05420971v1)

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Article

# Virtual City Simulator: A Scenario-Based Tool for Multidimensional Urban Flood Long-Term Vulnerability Assessment and Planning in Mediterranean Cities

Ana Noemí Gomez Vaca<fnref n="1" /> ID, Lucía Alexandra Popartan<fnref n="1" /> ID, Guillem Armengol Selvas<fnref n="1" /> ID, Sergi Nuss-Girona<fnref n="1" />,<fnref n="2" /> ID, Morgan Abily<fnref n="3" /> ID and Ignasi Rodríguez-Roda<fnref n="1" />,* ID

## Abstract

Cities are increasingly vulnerable to flooding due to rapid urbanization and climate change, especially in Mediterranean climates. Although hydroinformatics, numerical modeling, and artificial intelligence can simulate and predict floods with high accuracy, critical gaps persist in assessing flood vulnerability, particularly in data-scarce environments. We present the Virtual City Simulator, a decision-making support platform that evaluates long-term multi-dimension vulnerability to flooding. It combines a synthetic Mediterranean urban model with a composite vulnerability to flooding of index based on four dimensions (social, economic, environmental, physical) and three components (exposure, susceptibility and resilience). We have developed the following: (i) a representative virtual Mediterranean city (500,000 inhabitants, 100 km<fnref n="2" />; eight neighborhood typologies), (ii) a database with default values of 36 indicators for the eight typical neighborhoods, and (iii) a user-friendly RStudio/Shiny tool that integrates the virtual city and the database, with editable values for indicators and weights, that calculates the multidimensional vulnerability index to floods, and maps the results by dimension and in an integrated way, allowing comparability among scenarios. To illustrate the potential of the tool, the paper includes three case studies: (i) the business-as-usual scenario, using the default values of the indicators and weights of the database, where the most vulnerable neighborhood and dimensions of the virtual city are identified, (ii) the impact of implementing resilience measures in the previously identified vulnerable neighborhood, and (iii) the application of the tool to a neighborhood in a Mediterranean city (Ruzafa-Valencia), combining the available real data with the virtual city database.

**Keywords:** flood vulnerability; vulnerability index; scenario planning; climate change; data-scarce setting

## 1. Introduction

Urban areas around the world are increasingly vulnerable to flood risks due to two major, converging drivers: rapid urbanization and the intensification of extreme weather events linked to climate change, particularly in the Mediterranean climate [1]. Within urban

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check for
updates

Academic Editor: Enrico Creaco

Received: 3 November 2025

Revised: 25 November 2025

Accepted: 10 December 2025

Published: 13 December 2025

**Citation:** Gomez Vaca, A.N.; Popartan, L.A.; Selvas, G.A.; Nuss-Girona, S.; Abily, M.; Rodríguez-Roda, I. Virtual City Simulator: A Scenario-Based Tool for Multidimensional Urban Flood Long-Term Vulnerability Assessment and Planning in Mediterranean Cities. *Water* **2025**, *17*, 3538. https://doi.org/10.3390/w17243538

**Copyright:** © 2025 by the authors.
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<footnote n="1">¹ LEQUiA, Institute of the Environment, University of Girona, Campus Montilivi, C/Maria Aurèlia Capmany, 69, 17003 Girona, Spain; ananoemi.gomez@udg.edu (A.N.G.V.); luiciaalexandra.popartan@udg.edu (L.A.P.); guillem.armengol@udg.edu (G.A.S.); sergi.nuss@udg.edu (S.N.-G.)</footnote>

<footnote n="2">² APTA, Department of Geography, University of Girona, 17004 Girona, Spain</footnote>

<footnote n="3">³ Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 06003 Nice, France; morgan.abily@univ-cotedazur.fr</footnote>

<footnote>* Correspondence: ignasi.rodriguezroda@udg.edu</footnote>
contexts, it is useful to distinguish the main flood-generating mechanisms. Pluvial floods arise when short, intense rainfall exceeds soil infiltration and the capacity of sewers and surface drainage systems, without requiring any river overflow [2]. By contrast, fluvial floods are linked to longer-duration rainfall and upstream accumulation that cause rivers to overtop their banks and inundate adjacent floodplains [3]. In many settings, flash floods develop within a few hours of extreme rainfall or infrastructure failures (e.g., dam or levee breaches), combining high flow velocities with limited warning time and accounting for a substantial share of flood-related mortality [4].

These dynamics have raised not only the frequency and magnitude of urban floods, but also their complexity, disrupting infrastructure, economic activity and social well-being, especially in dense or socioeconomically marginalized neighborhoods. Substantial advances in hydroinformatics, including 2D hydraulic modeling, high-resolution topography, and efficient numerical schemes, are enabling city-wide applications to tackle and progressively reduce previously under-quantified uncertainties linked to multiple flood drivers, heterogeneous infrastructures, and complex urban hydraulics [5–10]. In practice, this often necessitates simplifying assumption about exposure and, by extension, about vulnerability [11,12].

Flood vulnerability assessment requires a multidimensional approach (social, economic, environmental and physical) that includes components of vulnerability (exposure, susceptibility and resilience) and with a long-term perspective [13], to guide planning and monitoring decisions over time [14–16]. Recent advances show that multi-indicator spatial assessment using a Geographic Information System (GIS) with Multi-Criteria Decision Analysis (MCDA) unifies indicators to map vulnerability and guide priorities. Applications include, among others, social vulnerability in 146 cities [17]; urban environmental quality [18]; living conditions of households [19]; and quality of life in dense cities [20]. Specifically, Afsari [21] presents a GIS-MCDA scenario-based decision support tool to represent risk attitudes, generate alternative vulnerability maps, and test priorities.

However, two gaps constrain the design, comparison, and prioritization of resilience strategies; they are the following: (i) assessment of hazard long-term impact based on multidimensional vulnerability, (ii) data-scarce environments to carry out a multidimensional assessment of vulnerability.

Taking a long-term perspective emphasizes chronic, systemic conditions, e.g., persistent poverty, institutional weakness, that accumulate over time and undermine resilience [22]. Within this framework, scenario-based planning combined with quantitative, multidimensional vulnerability assessment [23], serves both research and policy practice.

The aim of this study is to develop a synthetic Mediterranean urban model with neighborhood typologies and a database of indicators that will allow us to assess the long-term multidimensional vulnerability to floods by developing an interactive decision support tool. We focus on vulnerability and separate hazard from vulnerability to maintain conceptual clarity, which is consistent with classical risk frameworks [22,24,25], and we adopt vulnerability as the propensity of people and systems to experience harm, shaped by exposure, susceptibility (or sensitivity), and adaptive capacity/resilience [26]. Under the EU Floods Directive (2007/60/EC), flood hazard maps are available for most flood-prone areas in Europe, typically providing inundation extent, water depth and flow velocity for 10, 100 and 500 year return periods, but these hazard layers are not integrated into the index proposed here, which is formulated as a stand-alone measure of multidimensional vulnerability that can later be coupled with external hazard scenarios.
## 2. Methodology

This study uses a methodology around three pillars: (1) the design of a city, represented by the most typical Mediterranean neighborhoods, (2) a database with the indicators that define each dimension of each defined neighborhood, and (3) the Virtual City Simulator tool, which includes the calculation of the multidimensional index of long-term vulnerability to floods using the methodology (normalization, aggregation and weighting, and spatialization) [13].

### 2.1. *Design of the City*

The design of the city and the typology selection are aligned with international frameworks of urban characterization, ensuring conceptual coherence and comparability between contexts [27–31]. Taubenböck [32] identifies seven city types using self-organizing maps across 110 cities. While our scheme operates at the intra-urban scale, it remains compatible with this macro-taxonomy and operationalizes it at the neighborhood level, thereby reinforcing coherence across scales [27,29].

In the Mediterranean context, medium-sized cities are characterized and their central role in the regional urban system is underlined [33]. This typology is complemented by (i) functional-zone stratification [28], (ii) the explicit incorporation of infrastructure networks relevant to urban hydrology [34], and (iii) density-profile segmentation [35,36], that supports the construct validity, external comparability, and analytical transferability of the typology device.

We define and select neighborhood morpho-functional typologies as analytical archetypes with three objectives: (i) to identify recurrent patterns in urban form and function; (ii) to ensure comparability across heterogeneous contexts; and (iii) to enable model transferability by substituting synthetic values with observed data [37,38]. These typologies are not intended to reproduce the full diversity of urban realities; rather, they provide standardized, comparable, and transferable units that can be applied across different settings. The model does not replicate a specific location; rather, it develops a city that serves as the basis for all subsequent simulations, starting from the typical conditions of an urban agglomeration of intermediate size (scale associated with rapid growth and complex planning needs).

### 2.2. *Data Estimation*

The data estimation process aligns with international urban characterization frameworks and with guidelines for the construction of composite indicators [28–31]. This configuration supports long-term vulnerability flood analysis and the exploration of resilience strategies via scenarios [22,39].

The process follows three steps: (i) the starting point is the database of the municipality of Girona proposed by Gomez Vaca [40], whose structure and analytical unit are consistent with the neighborhood typology established above. This database encompasses four dimensions (social, economic, environmental and physical) and three components (exposure, susceptibility and resilience), for a total of 36 indicators. (ii) We assign typology-specific default (defined in the design of the city) values to each indicator and mitigate the MAUP (modifiable areal unit problem) by defining homogeneous units and applying consistent aggregation/disaggregation rules [41]; (iii) each indicator range (minimum and maximum) was parameterized by neighborhood typology. These bounds were derived from open-access, Mediterranean-focused datasets and toolkits, including the Copernicus Urban Atlas, Eurostat, Geofabrik and RESCCUE, and were informed by the city's predefined neighborhood typology. To ensure that typology-specific ranges reflect the empirically observed regional distribution, they were compared with the empirical distributions from
the sources [40]. In addition, we took into account the criteria of measurement validity, spatial/temporal commensurability, and replicability, following guidance for composite indices [31,42].

We defined the area and population for each of the typologies established in the design of the city, which were indicated as reference variables, in order to derive and audit the intensive metrics used by the index; provide a scale context and enable transfer to real cases; and verify scale invariance. Any homogeneous rescaling that preserves densities leaves the composite score unchanged, since the index is defined in intensive units and fixed parameters (in line with UN-Habitat, Eurostat/DEGURBA, and JRC/OECD).

## 2.3. *Interactive Tool Development*

We implemented an interactive simulation environment in RStudio (version 2025.05.1+513, Posit Software, PBC) using Shiny's interface [43]. Shiny enables web applications to be authored directly from RStudio, coupling statistical/geo-spatial workflows with a browser-based interface. This "RStudios analytical core with web UI" pattern aligns with contemporary decision-support platforms in planning, e.g., COMPLEX-IT [44] by making model assumptions transparent, outputs reproducible, and results readily interpretable for both experts and stakeholders.

The core logic of this step is also represented in Figure 1, which summarizes the interactive tool's workflow in three steps: (1) Input Data: It starts with the database estimated above. The user can modify the values of the default indicators and weights within the ranges established for each type of neighborhood. (2) Data Processing: The index is computed using the spatial methodology of Gomez Vaca [13] to estimate long-term flood vulnerability via a multidimensional framework in three steps: (i) structuring into four dimensions (social, economic, environmental, and physical) and three components (exposure, susceptibility, resilience), integrating 36 indicators; (ii) double normalization: using the z score method and subsequent with the min-max method, obtaining values of (0–1); and (iii) aggregation with weights (indicators, dimensions, integrated index). (3) Output maps: The spatial distribution of long-term flood vulnerability is visualized with interactive maps at the neighborhood unit for the integrated multidimensional index and each dimension. Scores are classified into ten equal-interval classes on the (0–1) scale (0 = not vulnerable; 1 = highly vulnerable), ensuring comparability across neighborhoods and dimensions.

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Flow inputs–process–outputs interactive simulation tool: from input configuration to output mapping.</figcaption></figure>
# 3. Results

We present results in three parts: (i) the representative virtual Mediterranean city; (ii) the database with default values of 36 indicators for all the neighborhoods; and (iii) the user-friendly tool in RStudio/Shiny. We applied the tool to three case studies to show its potentiality: (i) business as usual, (ii) resilience intervention and (iii) application of the tool to a real Mediterranean neighborhood.

## 3.1. Representative Virtual Mediterranean City

Mediterranean cities are characterized by a center-to-periphery gradient and substantial functional diversity [45]. Building on the UN-Habitat framework of six typologies, we further disaggregated two categories to better reflect the Mediterranean context and its functional diversity. Figure 2 shows the design of the city and its typologies of neighborhoods with the spatial arrangement.

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Spatial distribution of the eight neighborhood typologies in the design of the city.</figcaption></figure>

We consider a reference size of 500,000 inhabitants, as this coincides with the upper limit for medium-sized cities and represents the most common type of urban area in the Mediterranean (focusing on cities rather than metropolitan areas) [33]. We adopt an approximate municipal extent of 100 km² as a prototypical study area, consistent with the
compact Mediterranean urban form [46,47] and suitable for order-of-magnitude estimates in dense urban contexts; this figure serves as a scaling reference rather than an exact cadastral measurement.

We use a reference area and population for each city type for three purposes: (i) to check and review the index metrics (densities, percentages and per capita rates); (ii) to provide size context to facilitate application of the index to real cases; and (iii) to confirm that the index remains unchanged when the scale varies provided the same densities are maintained.

The model features large-scale physical systems such as transport, drainage, and public services, distributed unevenly across the territory, making it possible to study how infrastructure conditions influence vulnerability. Every neighborhood is defined by three main criteria: functional land-use (e.g., residential, commercial, green areas), urban position (from center to periphery), and built density (low, medium, high). Each neighborhood is integrated with core infrastructures (transport, drainage, public services) and demographic estimations. The typologies and their key attributes are summarized as follows in Table 1.

<table><caption>**Table 1.** Comparative summary of typologies (neighborhood typology, functional profile, planning challenges).</caption><thead><tr><td>Typology of Neighborhood</td><td>Functional Profile</td><td>Planning Challenges</td><td>Reference</td></tr></thead><tbody><tr><td>Neighborhood 1: Centralized or historic center<br>Area: 9 km²<br>Population: 85,000 inh.</td><td>Dense mixed-use: residential, commercial, administrative, and cultural in an irregular layout; high economic activity and average income; lack of green space.</td><td>Modernization with heritage preservation; reduction in inequality; improvement of infrastructure without loss of cultural value.</td><td>[27,48,49]</td></tr><tr><td>Neighborhood 2: First Metropolitan Ring: Residential focus and green areas<br>Area: 13 km²<br>Population: 70,000 inh.</td><td>Residential area with good transport links, tree-lined streets, and high livability; moderate economic activity.</td><td>Maintain green residential balance; protect green areas from overdevelopment; strengthen connections with the city center.</td><td>[11,27,50]</td></tr><tr><td>Neighborhood 3: First Metropolitan Ring: Mixed with commercial emphasis<br>Area: 13 km²<br>Population: 100,000 inh.</td><td>Dense, dynamic, and economically active; extensive coverage of services and commerce; exposure by density and soil sealing (imperviousness).</td><td>Growth and soil sealing (imperviousness) control; sustainability measures while maintaining economic dynamism.</td><td>[27,51,52]</td></tr><tr><td>Neighborhood 4: Second Metropolitan Ring: Residential urban with commercial focus<br>Area: 17 km²<br>Population: 150,000 inh.</td><td>High density of multifamily housing; diverse local economy; relatively developed drainage system; limited biodiversity.</td><td>Manage density; promote urban biodiversity; maintain and strengthen drainage system.</td><td>[27,28,53]</td></tr><tr><td>Neighborhood 5: Second Metropolitan Ring: Urban residential<br>Area: 10 km²<br>Population: 40,000 inh.</td><td>Exhibits a dispersed urban morphology, characterized by predominant single-family dwellings and moderate commercial intensity within comparatively green environs.</td><td>Preserve tranquility; improve resilience with infrastructure; contain commercial growth.</td><td>[27,51,54]</td></tr><tr><td>Neighborhood 6: Peri-urban residential<br>Area: 18 km²<br>Population: 30,400 inh.</td><td>Low density and abundant green space/leisure; high income; limited services/infrastructure.</td><td>Prevent degradation of green areas; improve connectivity and infrastructure without compromising environmental quality.</td><td>[27,55,56]</td></tr><tr><td>Neighborhood 7: Industrial and commercial peripheral<br>Area: 12 km²<br>Population: 10,200 inh.</td><td>Industrial economic hub; low residential density; strong road network; shortage of open spaces.</td><td>Economic diversification; mitigation of environmental impacts; improved access to services.</td><td>[27,57]</td></tr><tr><td>Neighborhood 8: Informal or marginal<br>Area: 9 km²<br>Population: 14,400 inh.</td><td>Informal settlements; poor infrastructure; subsistence economies; strong social cohesion.</td><td>Basic infrastructure; social inclusion; and economic formalization to reduce systemic vulnerability.</td><td>[27,58,59]</td></tr></tbody></table>
## 3.2. Database for Eight Types of Neighborhoods

The estimated database provides a description of the four dimensions (social, economic, environmental and physical) with three components (exposure, susceptibility and resilience) for eight neighborhoods of a Mediterranean city, using a total of 36 indicators.

The database contains the following: (i) default values and ranges for 36 indicators (for four dimensions and three components) in eight neighborhood typologies (see Supplementary Materials, Section: Data_Virtual City); (ii) source documentation for the base values and estimated ranges for each indicator (see Supplementary Materials, Section: Source_Data_Virtual City); and (iii) default weights proposed by the authors at two levels: (a) dimension-level weights (Social = 0.30; Economic = 0.25; Physical = 0.30; Environmental = 0.15) and (b) weights of the indicators within the dimension detailed in (Supplementary Materials, Section: Default weights_Virtual City). This structure enables consistent and transparent comparison across typologies while maintaining internal coherence among dimensions and components.

## 3.3. Openly Accessible Virtual City Simulator

We have created an open-access website describing the Virtual City Simulator (VSC), composed of eight neighborhood types and their reference layers. The tool runs on RStudio/Shiny software (version 2025.05.1+513, Posit Software, PBC); this platform integrates Virtual City and a database of 36 indicators for all four dimensions. This tool calculates the multidimensional flood vulnerability index [13] by allowing users to upload and edit the reference values and ranges of the indicators, as well as modify the weights for the 36 indicators and the four dimensions. It displays an interactive map of the eight neighborhoods for each of the four dimensions and an integrated multidimensional map.

Figure 3 visualizes the tool with an interactive map of the eight neighborhoods with all four dimensions and an integrated multidimensional map.

<figure><img src="image_6.png" /><figcaption>Figure 3. Visualization of the tool: https://mapscloud.udg.edu/clepsidra (accessed on 12 August 2025).</figcaption></figure>

The platform includes the calculation method, the model (RStudio/Shiny) and the description of each neighborhood as well as the open access of the tool at https://mapscloud.udg.edu/clepsidra (accessed on 25 October 2025).

The complete RStudio/Shiny source code of the Virtual City Simulator is openly accessible in a public GitHub repository: https://github.com/ananoemi-gomezvaca/
Virtual-City-Simulator (accessed on 25 October 2025). The repository contains the full codebase, including all functions for normalization, weighting, aggregation and mapping, as well as the interface configuration, data files, server logic, package specifications and documentation. Sharing the complete codebase enhances transparency and reproducibility, while also giving other researchers and practitioners the possibility to adjust, expand or reuse the simulator for different urban settings and resilience applications.

The tool is visualized and the steps to follow are Step 1, Assign weights to each dimension; Step 2, Assign weights to the indicators within each dimension; Step 3, Set Indicator Values for Each Neighborhood; and Step 4, Calculate the General Index. The index maps show the eight neighborhoods for the four social, economic, environmental, physical, and multidimensional integrated dimensions. The legend describes the vulnerability index that goes from 0 (least vulnerable) to 1 (most vulnerable). In addition, it includes a legend in each section of the neighborhood, where it includes the name of the neighborhood (Name), the value of the index (Value) and the type of neighborhood according to the eight established typologies (Types).

The Virtual City Simulator functions as a virtual decision-support laboratory to assess long-term flood vulnerability with a multidimensional approach, addressing a key gap in existing tools by providing a participatory environment and in data-scarce contexts, while preserving methodological rigor. The tool is more than just a modeling platform, it functions as a planning interface, a learning environment, and a research infrastructure. Its responsive design and clear map view facilitate dialog between multiple actors, helping stakeholders visualize trade-offs, prioritize interventions, and communicate results with a shared evidence base.

### 3.3.1. Case Study: Business-As-Usual (BAU)

An invariant reference is established to evaluate changes induced by interventions or the replacement of synthetic data [25,60]. Fixing normalization and weightings to BAU preserves comparability between scenarios and avoids user-modification artifacts. The input file contains the original database with default indicator values and the author-proposed default weights.

The city presents moderate and heterogeneous integrated vulnerability, with values between 0.2935 and 0.5217 (see Table 2 and Figure 4). Neighborhood 8 (informal/marginal) has the highest integrated vulnerability (0.5217), with high values in Social (0.7063) and Economic (0.5147), which reveal chronic weaknesses and poor recovery capacity. At the opposite end of the spectrum, Neighborhood 1 (historic/centralized) has the lowest integrated vulnerability (0.2935), consistent with greater institutional and service provision.

<table><caption>**Table 2.** Vulnerability indices by neighborhood Business as Usual (BAU) study.</caption><thead><tr><td>Dimension/ Neighborhood</td><td>Social Index</td><td>Economic Index</td><td>Environmental Index</td><td>Physical Index</td><td>Integrated Index</td></tr></thead><tbody><tr><td>Neighborhood 1</td><td>0.2418</td><td>0.3224</td><td>0.3211</td><td>0.3072</td><td>0.2935</td></tr><tr><td>Neighborhood 2</td><td>0.6118</td><td>0.1541</td><td>0.4148</td><td>0.5087</td><td>0.4369</td></tr><tr><td>Neighborhood 3</td><td>0.4333</td><td>0.6668</td><td>0.2355</td><td>0.3075</td><td>0.4243</td></tr><tr><td>Neighborhood 4</td><td>0.3287</td><td>0.3734</td><td>0.4179</td><td>0.7085</td><td>0.4672</td></tr><tr><td>Neighborhood 5</td><td>0.4814</td><td>0.3283</td><td>0.5932</td><td>0.4578</td><td>0.4528</td></tr><tr><td>Neighborhood 6</td><td>0.4594</td><td>0.2322</td><td>0.4774</td><td>0.5091</td><td>0.4202</td></tr><tr><td>Neighborhood 7</td><td>0.4546</td><td>0.5357</td><td>0.5674</td><td>0.4112</td><td>0.4788</td></tr><tr><td>Neighborhood 8</td><td>0.7063</td><td>0.5147</td><td>0.2610</td><td>0.4733</td><td>0.5217</td></tr></tbody></table>
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Case study: Business-as-usual (default values).</figcaption></figure>

In terms of dimensions, social vulnerability is also particularly critical in Neighborhood 2 (0.6118), associated with higher susceptibility burdens (low educational attainment, dependence on aid) and very low resilience (limited accessibility to community facilities); the lowest values are observed in Neighborhood 1 (0.2418) and Neighborhood 4 (0.3287). Economically, Neighborhood 3 (0.6668) and Neighborhood 7 (0.5357) concentrate exposed assets and activities (industry/services/commerce) with insufficient coverage and financial capacity, while Neighborhood 2 (0.1541) and Neighborhood 6 (0.2322) show the lowest relative vulnerability. The environmental dimension is most unfavorable in Neighborhoods 5 (0.5932) and 7 (0.5674), linked to deficits in permeability and vegetation, and most favorable in Neighborhood 3 (0.2355) and Neighborhood 8 (0.2610). Finally, physical vulnerability is highest in Neighborhood 4 (0.7085), with high exposure of the built environment and urban drainage deficits; the lowest levels correspond to Neighborhood 1 (0.3072) and Neighborhood 3 (0.3075). Overall, the results identify two extreme drivers, social in Neighborhood 8 and physical in Neighborhood 4, that explain the spatial pattern of vulnerability and inform the prioritization of structural and social interventions.

A center-periphery gradient is confirmed: the infrastructural robustness of the urban center mitigates vulnerability, while the functional and informal periphery concentrates
social, economic, and critical network deficits. At the dimension level, the economic dimension (home insurance, municipal financial capacity) emerges as a determinant of the composite index in neighborhoods with acceptable social/environmental values but limited financial resilience (e.g., neighborhood 2). Likewise, physical infrastructure (urban planning and drainage) reduces effective exposure in intermediate neighborhoods (e.g., neighborhood 4), while good environmental performance alone does not compensate for persistent economic or social vulnerabilities.

The combination of persistent socioeconomic deficits and limitations in urban networks/services explains the maximum composite index. In terms of prioritization, it is the natural target for early interventions in the policy scenario. Such results reflect a rigorous gradient of threat from the inner city to the periphery based on variation in infrastructural provision, institutional services and land-use configuration.

### 3.3.2. Case Study: Resilience Intervention in Neighborhood 8

In this intervention, after the BAU identifies the most vulnerable unit Neighborhood 8 and the most critical dimensions (primarily Social, with secondary Economic and Physical), we formulate planning measures to enhance resilience. The intervention is implemented in the tool by editing the indicators of the priority neighborhood/typology. The input file modifies resilience indicators by encoding measures and interventions as adjustments representing municipal planning strategies; the model then recomputes dimension-specific and integrated indices to quantify improvements at neighborhood and city scales.

The selection of intervention measures followed three criteria: (i) they had to be consistent with the conceptual structure of the index, targeting the resilience component rather than altering exposure or susceptibility; (ii) they had to be representative of typical municipal strategies that can be implemented in the short to medium term (for example, strengthening community organization, improving financial protection, and upgrading protective infrastructure); and (iii) they had to be operationalizable within the Virtual City Simulator as changes in specific indicators with a clear planning interpretation.

We therefore focused the intervention on five resilience indicators. First, we increased ID8 (social dimension: community participation) to represent the implementation of neighborhood-level participation programs and community-based organizations. Second, we raised ID17 (economic dimension: housing insurance) to capture policies that expand insurance coverage against flood damages, and ID18 (economic dimension: municipal financial capacity) to reflect an increase in dedicated municipal resources for flood-resilience projects. Third, we modified ID35 (physical dimension: structural protection) to represent additional structural protection measures (e.g., local flood defenses, retrofitting) and ID36 (physical dimension: urbanization plans and projects) to simulate the integration of flood-resilience considerations into ongoing and planned urban development. These changes were implemented in the tool by editing the corresponding indicator values in the input file, while keeping all other indicators and the default dimension weights unchanged, so that the resulting differences in the index can be attributed solely to the resilience intervention.

We focused the intervention on five resilience indicators, adjusting their values to simulate realistic municipal strategies. Specifically, ID8 (social dimension: community participation—increased from 1 to 15), ID17 (economic dimension: housing insurance—increased from 51% to 75%), ID18 (economic dimension: municipal financial capacity—increased from EUR 13,000 to EUR 1.75 M per project), ID35 (physical dimension: structural protection—increased from 3.5 to 11) and ID36 (physical dimension: urbanization plans and projects—increased from 57 to 90), without modifying any other indicator. The weightings of the dimensions remain unchanged per dimension (Social 0.30; Economic 0.25; Physical 0.30; Environmental 0.15) retaining BAU values.
The implementation of these measures resulted in the changes presented in Table 3.

<table><caption>**Table 3.** Contributions of dimensions to the change in the Neighborhood 8 index.</caption><thead><tr><th>Dimension</th><th>BAU</th><th>Resilience Intervention</th><th>Δ Change</th></tr></thead><tbody><tr><td>Social Index</td><td>0.7063</td><td>0.6909</td><td>-0.0154</td></tr><tr><td>Economic Index</td><td>0.5147</td><td>0.3830</td><td>-0.1319</td></tr><tr><td>Environmental Index</td><td>0.2610</td><td>0.2610</td><td>0.0000</td></tr><tr><td>Physical Index</td><td>0.4733</td><td>0.460</td><td>-0.0157</td></tr><tr><td>Integrated Index</td><td>0.5217</td><td>0.4898</td><td>-0.0423</td></tr></tbody></table>

The resilience interventions reduce the multidimensional index from 0.5217 to 0.4898; the largest reduction occurs in the economic dimension (from 0.5147 to 0.3830), while the social (from 0.7063 to 0.6909) and physical (from 0.4733 to 0.4600) dimensions show more modest decreases; the environmental dimension remains unchanged.

### 3.3.3. Case Study: Application to a Real Neighborhood: Ruzafa (Valencia)

To demonstrate the transferability of the methodology in contexts of limited data, the Virtual City Simulator is implemented for the case of Ruzafa (Valencia), a typical Mediterranean city. This application demonstrates the adaptability of the database for the analysis of real Mediterranean neighborhoods, even when the available data is incomplete. The Ruzafa neighborhood is based on its correspondence with the typology "Neighborhood 3: First Ring, Mixed Use with Commercial Emphasis", defined by its compact urban morphology, a pronounced mixed function dominated by commerce and hospitality, and a significant environmental deficit, evidenced by the limitation of green spaces and a high degree of impermeability of the soil [61].

The input file combines values of indicators and original weights, with data from a neighborhood in the real world, maintaining by default the values that do not have empirical data. This hybrid approach preserves analytical consistency, adapts the model to data-limited settings, and enables the generation of indices and map values.

Table 4 shows the data with the partially collected indicators that are adjusted in the tool. The documented database with the sources of the data extracted for the Ruzafa neighborhood is detailed in the Supplementary Materials (Section: Ruzafa_Virtual City).

We assessed flood vulnerability using the tool and visualized the results in the study area for Ruzafa, and obtained an integrated multidimensional index of 0.5357 (Figure 5). This places the neighborhood in the medium-high vulnerability band for the neighborhoods of the first ring with a commercial emphasis, consistent with its compact density, intense economic activity and physical conditions typical of a dense historical expansion.

<table><caption>**Table 4.** Indicators collected from the Ruzafa-Valencia neighborhood.</caption><thead><tr><th>ID</th><th>Dimension</th><th>Indicator</th><th>Value</th></tr></thead><tbody><tr><td>1</td><td>Social</td><td>Population: density (inh./km²)</td><td>≈27,800</td></tr><tr><td>2</td><td>Social</td><td>Immigration: percentage of population (%)</td><td>≈21.8%</td></tr><tr><td>3</td><td>Social</td><td>Gender condition: percentage of femininity (%)</td><td>≈53.6%</td></tr><tr><td>4</td><td>Social</td><td>Age extremes: percentage of population (%)</td><td>≈33.8%</td></tr><tr><td>7</td><td>Social</td><td>Population with low level of education: percentage of population (%)</td><td>≈33%</td></tr></tbody></table>
<table><caption>Table 4. *Cont.*</caption><thead><tr><th>ID</th><th>Dimension</th><th>Indicator</th><th>Value</th></tr></thead><tbody><tr><td>12</td><td>Economic</td><td>Income per person (EUR/person × year)</td><td>14,000</td></tr><tr><td>13</td><td>Economic</td><td>Active workers: percentage of population (%)</td><td>≈48%</td></tr><tr><td>16</td><td>Economic</td><td>Average prices (EUR/useful m²)</td><td>≈4000</td></tr><tr><td>20</td><td>Environmental</td><td>Tree species: (number)</td><td>400</td></tr><tr><td>22</td><td>Environmental</td><td>Spaces with permeability deficit: compact areas (m²/inh.)</td><td>50</td></tr><tr><td>23</td><td>Environmental</td><td>Areas with a deficit of vegetation: areas with little presence of urban trees (m²/inh.)</td><td>7</td></tr><tr><td>26</td><td>Environmental</td><td>Specific plans: (number)</td><td>2</td></tr><tr><td>27</td><td>Physical</td><td>Urban context: density of the built environment (km/km²)</td><td>≈130</td></tr><tr><td>36</td><td>Physical</td><td>Urbanization plans and projects: (number)</td><td>34</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Figure 5. Case study: Ruzafa neighborhood, Valencia, Spain.</figcaption></figure>
The values place economic vulnerability as the highest (0.6052), followed by social vulnerability (0.5407) and physical vulnerability (0.5169). In contrast, environmental vulnerability (0.4471), reflects relatively less pressure in this dimension within the comparative framework (although deficits in green spaces and impermeability persist).

The results guide prioritization towards financial resilience measures (e.g., expanding insurance coverage and strengthening fiscal capacity) and infrastructure actions (drainage and structural protection), while environmental deficits, although present, are not the main determinant of composite vulnerability in this case. The results also demonstrate the practical usefulness of the Virtual City Simulator in transforming partial data into a robust, comparable and operational diagnosis for decision-making.

# 4. Discussion

The present study puts long-term multidimensional flood vulnerability into practice for Mediterranean cities by explicitly separating hazards from vulnerability and structuring vulnerability into three components (exposure, susceptibility, and resilience) and four dimensions (social, economic, environmental, and physical). The approach maintains conceptual clarity in accordance with classical risk frameworks, while allowing for subsequent coupling to external hazard layers when available.

We justify the use of a synthetic Mediterranean Virtual City on three grounds: (i) recurrent morpho-functional patterns in the region can be abstracted into Neighborhood Typologies; (ii) many municipalities must plan under data-scarce conditions; and (iii) the typology acts as a transfer device as defaults can be replaced with observed data as it becomes available. The city scale (~500,000 inhabitants, ~100 km²) provides a size reference for intensities (densities, rates, percentages) and supports scale-invariant comparisons, not a cadastral truth. These choices are aligned with UN-Habitat, Eurostat-DEGURBA, and JRC-OECD frameworks and are intended to standardize, compare, and transfer analyses without claiming to reproduce a specific place.

BAU shows a clear center-periphery gradient in the integrated multidimensional vulnerability index. A clearer understanding of why certain neighborhoods show higher vulnerability in specific dimensions emerges from the interaction between their typology-based characteristics and the indicators that shape each dimension. For example, Neighborhood 8 (informal/marginal) exhibits the highest social and economic vulnerability because it combines structural socioeconomic deficits such as lower income levels, limited insurance coverage, and weak institutional support with low resilience indicators (e.g., limited community participation and constrained municipal capacity). In contrast, Neighborhoods 3 and 7 show elevated economic or physical vulnerability due to high density, soil sealing, and exposure of critical infrastructures, despite stronger social or environmental conditions. Conversely, central or well-served neighborhoods (e.g., Neighborhood 1) present lower integrated vulnerability because higher institutional capacity, service provision, and financial resilience mitigate their physical or environmental weaknesses. These differentiated profiles illustrate how vulnerability does not arise uniformly but depends on the specific combination of exposure, susceptibility, and resilience components within each typology, reinforcing the value of a multidimensional assessment.

In Neighborhood 8, a resilience intervention reduces the integrated index and supports a defensible sequencing. The application to Ruzafa (València), mapped to the “Neighborhood 3: First Ring: Mixed with Commercial Emphasis” typology, confirms transferability under partial data: hybridizing empirical indicators with typology defaults yields operational, comparable diagnoses to prioritize actions and targeted data collection.

Compared with existing GIS-MCDA tools, the Virtual City Simulator provides several comparative advantages in terms of data requirements, scope of application, and
user-friendliness. First, its typology-based synthetic city and pre-parameterized indicator ranges substantially reduce dependency on detailed spatial datasets, which are often unavailable in Mediterranean or data-scarce environments; this allows operational vulnerability assessments even with partial empirical information, as shown in the Ruzafa application. Second, while conventional GIS-MCDA tools focus primarily on static mapping, the Virtual City Simulator supports scenario creation, sensitivity exploration via editable weights and indicators, and the progressive substitution of defaults with observed data, thus bridging the gap between fully data-driven models and conceptual vulnerability frameworks. Third, its interactive RStudio/Shiny interface improves accessibility for non-GIS specialists by enabling transparent editing of indicators, weights, and neighborhood conditions without requiring advanced spatial analysis skills. Additionally, we provide the complete RStudio/Shiny source code, enabling users to adapt indicator structures, replace default typology values with empirical datasets, adjust weighting schemes, or repurpose the platform for other urban-resilience analyses. Open and editable code enhances transparency, reproducibility, and methodological traceability, consistent with best practices in contemporary environmental modeling and open geospatial analytics [62,63]. This aligns with broader scientific calls advocating accessible, verifiable and reusable computational tools [64,65]. Together, these features highlight the tool's innovativeness and practical value as a flexible, accessible decision-support environment for long-term urban flood-vulnerability assessment.

These results sit within an explicit generalization context trade-off. A synthetic, typology-based model improves comparability [27,30,66], but cannot substitute for local specificity (institutions, tenure, behaviors). We therefore treat outputs as decision-guiding, not prescriptive, in line with best practice for composite indicators that stresses transparency and thorough documentation [42]. Translation to a specific city should proceed via (i) progressive substitution of defaults with observed data, (ii) contextual reweighting (e.g., equity-first vs. climate-adaptive priorities), and (iii) edits to preserve reproducibility [67].

We also acknowledge spatial aggregation issues: operating at zone-level typologies enhances interpretability but risks aggregation bias (the Modifiable Areal Unit Problem, MAUP) [68] and can mask marginalized pockets within otherwise resilient areas. Whereas hydraulic flood simulation typically requires higher-resolution (finer-scale) modeling, the four vulnerability dimensions operationalized here are sufficiently homogeneous to be represented at the neighborhood/sector level; moreover, most official statistics are reported at that scale. Our roadmap therefore includes the following: (i) sub-neighborhood grids (≈250–500 m) that inherit typology defaults yet are locally editable, aligning with common open standards (e.g., GHSL 250 m; Urban Atlas updates for the 2021 reference year now in production and release 2025) [69]; (ii) stratified reporting (e.g., deprivation or service-access proxies) so micro-hotspots inform prioritization; (iii) temporal extensions beyond a static scenario; next versions will incorporate infrastructure-decay, demographic drift, and land-use transitions, and optionally couple to dynamic adaptive policy approaches under deep uncertainty, per, e.g., Dynamic Adaptive Policy Pathways (DAPP) [70,71] and Robust Decision-Making (RDM) [72]; and (iv) explicit confidence reporting using uncertainty bounds (5th–95th percentiles from weight sweeps and indicator sampling) and rank-stability tests, enabling decision-makers to see where priorities are robust and where additional data collection would meaningfully reduce uncertainty [73,74]. This situates our approach within the broader GIS–MCDA practice that uses composite, spatially explicit indicators for prioritization, see, for example, the multiscale GIS-based model assessing urban social vulnerability across 146 cities in Eastern India [17], which similarly leverages multi-indicator integration to map vulnerability and guide planning under heterogeneous data conditions.
Finally, the tool is an open, stepwise decision-support laboratory (dimension/indicator weighting, indicator setting, index calculation, map display) that supports co-production with municipal teams, utilities, NGOs, and communities. Its interactive features also make it a powerful platform for planning and training: stakeholders can explore alternative policy pathways, test assumptions, and iteratively refine strategies. This participatory capacity underpins the co-production of resilience strategies and strengthens adaptive planning in the face of increasing climate uncertainty, consistent with emerging frameworks for co-produced resilience assessments [75], particularly where expert knowledge helps bridge data gaps.

## Limitations

When interpreting the results from the Virtual City Simulator, the following bounded conditions should be noted:

- **Scope of the index:** the integrated multidimensional vulnerability index (exposure, susceptibility, resilience across social, economic, environmental, and physical dimensions) does not integrate hazard; therefore, it does not estimate risk or expected damages. Without coupling to external hazard layers, risk-based prioritization is not yet possible. In practical applications, this limitation can be progressively overcome by linking the Simulator's vulnerability outputs to existing flood-hazard products (e.g., EU Floods Directive maps) or to locally modeled inundation depth and velocity layers, thereby moving from a vulnerability-only perspective towards full risk assessment.

- **Spatial aggregation and MAUP:** operating at zone-level Neighborhood Typologies enhances interpretability but introduces potential aggregation bias (MAUP) and can mask micro-pockets of disadvantage within otherwise resilient areas. In the current version, sub-neighborhood grids (≈250–500 m) and stratified reporting are not yet implemented. This can be mitigated in applied studies by complementing typology-level results with local knowledge and finer-scale data where available, and, in future versions of the tool, by incorporating editable sub-neighborhood grids and stratified indicators (e.g., deprivation or service-access proxies) to better capture intra-neighborhood heterogeneity.

- **Data reliability and temporal updating:** in rapidly developing Mediterranean cities, the update frequency of available datasets may affect the accuracy of indicator ranges and, therefore, the resulting vulnerability assessments. Although indicator bounds were parameterized using multiple open-access and regionally relevant sources (e.g., Copernicus Urban Atlas, Eurostat, GHSL, RESCCUE), these datasets differ in their temporal resolution and may not fully capture recent demographic, infrastructural or land-use changes. To mitigate this, the Virtual City Simulator treats these ranges as transparent typology-based priors that can be progressively replaced with more recent municipal, census or remote-sensing data. In practice, we recommend that users update the default database with the latest available statistics and spatial products before each application, so that reliability increases as updated data become available, while maintaining analytical coherence in data-scarce environments.

- **Minimum data requirements:** a practical question concerns the minimum amount of data required for the index to produce meaningful and locally representative results. Technically, the index can always be computed as long as every indicator has a value, whether based on empirical data or on the default typology ranges. However, when applied to real neighborhoods, the reliability of the assessment increases as a larger share of indicators is informed by up-to-date local data rather than by defaults. As a general guideline, we consider that having data for at least one indicator per dimension, and approximately one-third of the 36 indicators overall, provides a
reasonable minimum for producing a vulnerability profile that reflects local conditions rather than mainly the underlying typology. Below this threshold, the index remains operational, but the resulting neighborhood characterization should be interpreted with caution, given the higher dependence on synthetic estimates.

- Temporal staticity: the Virtual City Simulator currently compares static scenarios (e.g., BAU vs. intervention) and does not model dynamic evolution (infrastructure decay, demographic drift, land-use transitions). As a result, relevant feedback and effects are not captured. This limitation can be partially addressed by defining contrasting medium- and long-term scenarios (e.g., densification, infrastructure upgrades, socio-economic change) and, in future developments, by coupling the Simulator with dynamic planning frameworks that explicitly represent temporal trajectories.

- Dependence on normative weights without stability analysis: default weights at the dimension and indicator levels encode a prior planning. Although editable in the tool, the manuscript does not yet present a systematic sensitivity analysis (e.g., weight sweeps) or rank-stability tests, which may affect the robustness of neighborhood comparisons. In applied contexts, we encourage users to explore alternative weighting schemes with stakeholders and to check whether rankings are stable under plausible changes in weights. Future work will include formal global sensitivity analysis and rank-stability diagnostics within the Simulator interface to guide users towards more robust interpretations.

These limitations do not negate the utility of the tool as a decision-support laboratory, but they bound how results should be interpreted and applied, and they indicate concrete directions for subsequent methodological improvements and extensions.

# 5. Conclusions

This study presents the development and application of the Virtual City Simulator, an innovative decision-making tool designed to assess long-term, multidimensional urban flood vulnerability using synthetic modeling and interactive, scenario-based planning. The approach involved the following:

* Integrated, scenario-ready framework. The Virtual City Simulator links the Virtual City (eight Neighborhood Typologies), a 36-indicator database with default values and ranges, and an interactive RStudio/Shiny interface to deliver a transparent, reproducible workflow for long-term, multidimensional flood-vulnerability assessment.

* Actionable diagnostics under data scarcity. By combining the observed neighborhood values with typology-based defaults, the simulator converts partial datasets into operational diagnostics, mapping indices with a multidimensional integrated approach and disaggregated by four dimensions (social, economic, environmental, and physical) on a common scale from 0 to 1.

* Interventions are effective. As shown in the second case study, editing five resilience indicators in the most vulnerable Neighborhood reduces the multidimensional integrated index from 0.5217 to 0.4898, confirming that targeted investments can lead to measurable reductions in vulnerability.

* Transferability to real cases. The application to Ruzafa (Valencia) yields an integrated multidimensional index of 0.5357 and a plausible dimension profile in which the economic dimension is the highest, the social and physical dimensions are similar and lower, and the environmental dimension is the lowest, corroborating the external validity of the Neighborhood Typology mapping and the Simulator's usefulness in real-world planning.

* Estimated database for transfer/validation. We provide an estimated dataset structured in four dimensions and 36 indicators for eight neighborhood typologies, de-
signed to support the application or validation of methodologies in contexts where access to data is limited, maintaining intensive units and traceability for replacement by municipal/census data when they exist.

* Tool with open access. It facilitates prioritizing neighborhoods, evaluating BAU trade-offs vs. intervention, and communicating results transparently for public decision use and call to action.

In sum, the Virtual City Simulator contributes to bridging the gap between technical flood risk modeling and actionable urban planning. Its adaptable, participatory, and data-flexible design makes it a promising asset for cities striving to build more resilient and equitable futures.

**Supplementary Materials:** The following supporting information can be downloaded at: https://doi.org/10.5281/zenodo.17630218 (accessed on 9 December 2025).

**Author Contributions:** Conceptualization, A.N.G.V., L.A.P., G.A.S., S.N.-G. and M.A.; methodology, A.N.G.V., L.A.P., M.A. and I.R.-R.; software, A.N.G.V., M.A. and I.R.-R.; validation, A.N.G.V., L.A.P., M.A. and I.R.-R.; formal analysis, A.N.G.V.; investigation, A.N.G.V., S.N.-G. and M.A.; resources, S.N.-G.; data curation, A.N.G.V.; writing—original draft preparation, A.N.G.V.; writing—review and editing, A.N.G.V., L.A.P., M.A. and I.R.-R.; visualization, A.N.G.V.; supervision, I.R.-R.; project administration, S.N.-G.; funding acquisition, I.R.-R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The original data presented in the study are openly available at https://github.com/ananoemi-gomezvaca/Virtual-City-Simulator (accessed on 25 October 2025). https://mapscloud.udg.edu/clepsidra (accessed on 12 August 2025).

**Acknowledgments:** Ana Noemí Gomez Vaca acknowledges support from the LEQUIA Research Group and support by the IFUdG 2021 (IFUdG21/33) pre-doctoral grant and acknowledges the funding from University de Girona, by D-PATTERN (Ref: PID2023-150071OB-I00) and LEQUIA [2021-SGR-01352] which has been recognized as consolidated research group by the Catalan Government. Lucia Alexandra Popartan acknowledges the support from Juan de la Cierva Formación grant (FJC2021-047857-I) financed by MCIN/AEI/10.13039/501100011033 and European Union "NextGenerationEU"/PRTR. Sergi Nuss-Girona acknowledges the Territorial and Environmental Analysis and Planning (APTA) research group at the University of Girona.

**Conflicts of Interest:** The authors declare no conflicts of interest.

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