Urban-scale building assessment and energy vulnerability mapping through an interactive geo-referenced web tool: demonstration applicability to southern Spain

Received: 14 January 2025 / Accepted: 11 June 2025 © The Author(s) 2025 Extended author information available on the last page of the article Urban-scale building assessment and energy vulnerability mapping through an interactive geo-referenced web tool: demonstration applicability to southern Spain C. M.Calama-González1· R.Escandón2· R.Suárez2· E.Abajo-Casado3· A. R.DiánezMartínez3 Environment, Development and Sustainability https://doi.org/10.1007/s10668-025-06490-z Abstract Building decarbonization through energy renovation is a key challenge across the European Union, particularly in social housing sectors marked by high vulnerability. To support this goal, this study introduces a GIS-based open-access web tool for evaluating the energy performance and social vulnerability of the existing residential stock at the urban scale. The tool integrates data from public and open-source databases into a georeferenced environment, enabling systematic characterization of geometric, constructional, energy and social parameters at the urban-level, and supporting bottom-up and top-down approaches. This allows for performance evaluations, simulation model construction and the identification of high-priority buildings through energy and socioeconomic vulnerability indicators. Results from the city of Seville, used as a case study involving 2,888 dwellings) reveal that over 90% of buildings present severe winter energy vulnerability, while summer vulnerability is generally low. Socioeconomic analysis shows that more than a third of buildings house users living in severe poverty conditions. The combined vulnerability index highlights specific neighbourhoods, such as Polígono Sur, with particularly acute vulnerability levels. The tool’s scalability was demonstrated by extending it to 41 municipalities in southern Spain. This study concludes that this approach enables detailed diagnosis of structural and energy-related inequalities, integrating and analysing existing open data to perform thorough building performance assessment at urban level, and offers a rapid and reliable method for acquiring key building data and ensuring long-term adaptability through continuous updates. Highlights ● An open-access georeferenced tool is created to assess housing in southern Spain ● Data for energy characterisation and socioeconomic aspects are provided ● Building energy and socioeconomic vulnerability levels may be evaluated ● The most vulnerable buildings may be detected for future retrofit processes ● A useful data tool is generated to support bottom-up and top-down building analysis Keywords Extensive building database · GIS-based analysis · Urban mapping · Social vulnerability assessment · Energy efficiency 1 3 C. M. Calama-González et al. 1 Introduction The building sector represents one of the most significant energy consumers within the European Union (EU), accounting for approximately 40 % of energy consumption and around 36 % of carbon dioxide emissions (Li et al., 2017). At present, around 75 % of the EU's 210 million residential buildings, up to 80 % of which are expected to still be in use in 2050 according to projections, are energetically inefficient (Fabri et al., 2016). Given the slow pace of annual building replacement (Hartless, 2003), the highest potential for energy savings can be found in the existing building stock (European Commission, 2011). Therefore, a pivotal strategy in the sector's decarbonization efforts is to diminish energy demand and enhance energy efficiency in existing buildings, while also ensuring both health and comfort (Pasichnyi et al., 2019). In this regard, building energy performance and climate policy remain top priorities for the EU, predominantly since the Energy Performance of Buildings Directive (European Commission, 2010a) and its subsequent revisions up until the latest iteration for 2030 (European Commission, 2024). In order to address the climate emergency and the associated energy challenges through building retrofit, it is imperative to fully understand energy performance (Jiang et al., 2013) and energy vulnerability (SánchezGuevarra et al., 2019; Calama-González et al., 2024;) in the current sector. This in turn will enable the development of well-tailored retrofit actions, which can mainly be approached from two fundamental perspectives: global or local (Caputo & Pasetti, 2017). In the urban context, building energy characterization poses a challenge due to the large number of buildings and the extensive information to be systematically collected, classified, and analysed. One of the most commonly employed approaches for building characterization and performance assessment is the analysis of information contained in Energy Performance Certificates (Johansson et al., 2016). Hjortling et al. (2017) analysed 186,021 buildings in Sweden, using a combination of CSV format text files and the MySQL database management system. They determined how variables such as climatic zone, year of construction, and building typology influence the energy consumption of buildings. Similarly, Streicher et al. (2018) examined information from approximately 10,400 residential buildings in Switzerland, conducting statistical analysis to estimate the thermal performance level in terms of U-values of different building archetypes. This involved identifying building groups classified by year of construction and building and urban typology. Gangolells et al. (2016) created a Microsoft Excel file to extract information relating to emissions, primary energy consumption, building type, year of construction, climatic zone, and energy consumption of building systems (heating, cooling, hot water, and lighting) from 129,635 certificates, statistically analysing them. Another approach to mapping the existing building stock and assessing energy performance is based on urban morphology, providing a greater insight into envelope construction (exterior walls, roof, windows and doors, and foundation or floor in contact with the ground) and building typology. Tsirigoti and Bikas (2017) compiled information on urban blocks in Thessaloniki and studied 10 of them in order to ascertain the influence of geometry and compactness on energy efficiency. As part of the SHERIFF Research Project, Cuerda et al. (2014) carried out a classification and characterization of building facades in 13 neighbourhoods in Madrid for energy evaluation, collecting information from various sources (cadastre, building plans, local public administrations, municipal archives...). Dascalaki et al. (2010) also focused their studies on the urban context through the DATAMINE Project, 1 3 Urban-scale building assessment and energy vulnerability mapping… which includes 12 pilot studies across various European countries. These authors developed an extensive Excel database containing information on 250 existing buildings in different regions of Greece. They evaluate 255 parameters, covering general building information (usage, location, orientation, climatic zone, year of construction...); construction characterization of the thermal envelope (U-values of opaque and transparent areas, shading systems, thermal bridges...); and energy performance (energy demand, Heating Ventilation and Air-Conditioning (HVAC) systems, energy and electricity consumption, CO2 emissions...), among other aspects. The primary sources of information used are audit reports, visual inspections, and Energy Performance Certificates of the buildings. Similarly, other studies involve the use of cadastral data and vectorial cartography (2018b; Oregi et al., 2018a) on an urban scale. Martín-Consuegra et al. (2018) proposed a methodology analysing the thermal behaviour of building envelopes through the threedimensional generation of building models (using SHP vectors). They presented urban energy efficiency indicators for 1,424 dwellings based on envelope characterization, heat transmission coefficients, and envelope energy losses, all correlated using Python software. Yang et al. (2020) obtained energy heating demand of four building archetypes in the city of Leiden (Netherlands), defined from the TABULA database, obtaining missing information from steady assumptions and calculations. These authors converted energy demand into energy consumption using the TABULA supply system simulation method (TABULA Project, 2013), and mapped the results in terms of natural gas consumption. Fernández et al. (2020) also characterize heating energy demand at the building stock level using the city of Bilbao as case study and constructing 17 representative building archetypes, which are assessed in the Design Builder dynamic simulation software. In the use of cadastral data, Geographic Information System (GIS) also becomes a key open access source platform frequently used to efficiently and rapidly collect, manage, evaluate and visualize extensive data (Atesoglu et al., 2025). For instance, Jakob et al. (2013) utilized geo-referenced data and information from a GIS environment as input variables for building stock modelling and subsequent energy performance analysis. Oezdemir et al. (2017) combined geospatial analysis via GIS and on-site study in order to analyse 179 residential buildings in Germany. Kleemann et al. (2017) also employed a GIS platform to provide information on gross volume, construction period, use, and material composition of approximately 580,000 data points, corresponding to buildings or building components in Vienna. However, the two latter studies primarily focus on anthropogenic stock assessment, from the specific perspective of the consumption of resources in buildings. The DATAMINE project mentioned above is expanded by Droutsa et al. (2016) through the European TABULA and EPISCOPE Projects (2024). The objective is to create a harmonized structure of national typologies to aid cross-country comparisons of the residential building stock. This collaborative effort from 16 countries has facilitated the classification of buildings, their constructive and thermal definition, and their active systems (space heating, domestic hot water...). This information was obtained from Energy Performance Certificates, cartographic documentation, geometric data, and national statistical survey data through a GIS platform, with the ultimate aim of evaluating energy performance of buildings. Similarly, Sánchez-Aparicio et al. (2020) presented the HeritageCare platform, a webGIS tool to generate a digital database for preventive building conservation of historical and cultural heritage buildings, and compiling information from various resources (on-site monitoring, 360º virtual tours, geospatial data, etc.). Although this approach is interesting, 1 3 C. M. Calama-González et al. only data on a historic library in Salamanca is included and extensive prior manual analysis is also needed. Furthermore, Fabbri et al. (2012) considered heritage buildings (966 urban units) in a case study in the city of Ferrata (Italy) to propose a tool to include information on morphological and historical characteristics of buildings, as well as cadastre data and energy performance indexes, generating a useful data platform in a GIS environment. Deng et al. (2021) proposed a method to determine building primary use (hotel, shopping mall, office, residential…) in the city of Changsha through a GIS-based dataset, considering the building’s footprint and community boundaries, simply offering quantitative information on the use classification of the stock. Kucukpehlivan et al. (2023) used a GIS platform to define the impacts of urban planning, taking the city of Eskisehir (Turkey) as a case study. They presented various indicators of points of interest (dwellings, cultural and commercial buildings, public service buildings, etc.), displaying the results through self-produced maps. Similarly, Zeren Cetin et al. (2023) used a GIS environment to evaluate the impact of surface temperature increases caused by climate change in the urban area of Bartin (Turkey), assessing sleep deprivation and thermal stress experienced by users. Prades-Gil et al. (2023) constructed building models from cadastral and altimetric databases using a GIS-based environment in order to evaluate heating and cooling energy demand though a bottom-up approach where a total of 1026 buildings in the city of Valencia are analysed, extrapolating the results to the whole region. Mutani et al. (2024) analysed 8 representative building archetypes in the city of Santiago de Chile, assessing their energy demand and potential energy saving taking into account four retrofitting interventions. Then, these authors extrapolate the results obtained to the commune of Renca, a suburb of the city, mapping the results and offering a visual static classification of the energy performance based on the analysed archetypes. Beltrán-Velamazán et al. (2024) created a national-scale urban tool of Spain based on information from Energy Performance Certificates and open big data databases, such as Cadastral Cartography Services or National Statistics Institute. These authors integrated data on geographical, physical, and useand energy-related variables through a bottom-up process in a GIS tool. Using the city of Bilbao (Spain) as a case study Villanueva-Díaz et al. (2024) provided an automated method for recording geometric and thermal properties in residential buildings on an urban scale via a GIS tool. These authors compile existing information from public databases related to one city, only presenting an automated methodology and the dataset used, but without creating and sharing to the community a public and open visualization tool for the results obtained. Aruta et al. (2025) created a tool to determine energy performance of a district, obtained through simplified steady state calculations and references buildings (minimum thermal and energy requirements). These authors showed an application example to the city of Naples, validating the tool through punctual dynamic building simulation results only for the climate conditions of the aforementioned city. Although future works will be focused on the integration of this tool with GIS software for mapping purposes, the authors do not make the designed tool available. Another relevant work is the study conducted by Modrego-Monforte et al. (2023), who presented a multicriteria methodology to assess the vulnerability of the residential stock in the Donostia-San Sebastian city based on the use of a GIS tool. These authors elaborate static plans derived from the conducted vulnerability analysis taking into account spatial parameters (dwelling area, percentage of façade openings, building structure…), environmental characteristics (natural ventilation, building compactness, thermal transmittance…), energy criteria (heat1 3 Urban-scale building assessment and energy vulnerability mapping… ing energy demand, electricity demand…) and social aspects (population ageing, migrant population, population with basic education…). The majority of these studies propose automated data collection methodologies (primarily related to geometric, constructional, thermal, and energy parameters) as a preliminary step in the assessment of building thermal and energy performance at the urban scale. Geometric information is typically sourced from the Cadastre platform of the municipality under analysis, with data update frequency varying depending on the region, while energyrelated data is generally derived from publicly available Energy Performance Certificates. Although numerous studies depict the current performance of buildings, mainly through static urban mapping or graphical representations, there is a notable absence of integrated assessments that simultaneously address both energy efficiency and socioeconomic vulnerability of the existing building stock. Furthermore, most studies present their findings through numerical datasets or static figures included within the publications, often focusing on a single municipality or specific urban development as a case study. In other words, there is a lack of open-access, interactive tools that enable easy visualization of current building performance and vulnerability outcomes, crucial aspects for retrofitting purposes.In contrast to similar works conducted in the field, the aim of this article is to provide an openaccess web tool to assess the energy characterization and vulnerability of existing public social housing buildings in southern Spain (Mediterranean climate) from a dual analysis: the energy and socioeconomic perspectives. This considers the building stock level (not only single-building level) and a methodological approach based on a GIS. This tool proposes a systematic method for compiling useful information, gathered from open-source databases, to determine the most representative geometric, constructive, energy and socioeconomic aspects of residential buildings in southern Spain. This GIS tool may be used to obtain input data for generating energy simulation models at both building and stock levels or similar thermal calculations for the assessment of building energy performance, which could support bottom-up or top-down analysis. It could also be of use to householders, stakeholders or public administrations in the retrofit processes since it enables the visualization of the most vulnerable existing buildings which should undergo high-priority retrofit actions, taking into consideration vulnerability relating to building energy performance and users’ socioeconomic limitations. Unlike similar works, the novelty of this research is that this tool implements open-access data to provide a vulnerability classification of the public social housing buildings in southern Spain (region of Andalusia). Furthermore, general and vulnerability data on these buildings are also made available as a free, open-access and interactive web tool for any user or Administration, with basic technical knowledge. The manuscript has been structured as follows: section 2 provides information on the methodological approach, describing the building characterization database used in this work, as well as the definition of the vulnerability indicators (energy vulnerability indicator, socioeconomic vulnerability indicator and global vulnerability indicator) and the creation of the data web-tool; a real applicability example is described in section 3, offering main quantitative results; while in section 4, a comparison with similar works is presented; lastly, main conclusions reported in this research are included in section 5. 1 3 C. M. Calama-González et al. 2 Materials and methods Figure 1 shows the schematic diagram of the methodological workflow followed in this research, with the stages described in greater detail in the subsequent subsections. 2.1 Creation of an extensive building characterization database For this study, information was first gathered from the public and open-access database on public social housing buildings in southern Spain, compiled and managed by the Andalusian Housing and Retrofit Agency (AVRA, 2023). After initial processing and preliminary filtering treatment the content of this database was expanded and improved by incorporating new study variables. This was to focus the analysis on the predominant existing building stock, rented H-block and linear block multifamily housing typologies, built between 1950 and 2010 in southern Spain. This predominant stock, comprising approximately 30,600 public dwellings, represents around 77.5 % of the total public housing stock in Andalusia (CalamaGonzález, 2020). The final updated database includes the variables described in Table 1, all obtained from public resources and tools. 2.2 Assessment of vulnerability indicators Two main indicators have been considered in the vulnerability assessment of the existing housing stock in southern Spain. The first relates to energy vulnerability associated with the analysis of the energy performance of the existing building itself. The second vulnerability indicator relates to the economic capacity of the social user of the dwelling. By combining both, a global vulnerability index is defined, allowing for the analysis of the current energy performance of the building, while also taking into account the social dimension of the users. These aspects are crucial when addressing the energy retrofit process of the building sector, where the main target addresses the reduction of building decarbonization to achieve energy objectives within the frameworks for 2030 and 2050, by prioritizing strategies applied to the most vulnerable part of the building stock from both energy and social perspectives. Fig. 1 Methodology workflow and stages followed 1 3 Urban-scale building assessment and energy vulnerability mapping… 2.2.1 Definition of the energy vulnerability indicator (EVI) For the assessment of the EVI of the social housing stock in southern Spain, an analysis of the energy demand of the buildings is proposed, initially to focus the vulnerability indicator on the performance of the building itself, and secondly, to overcome the limitations stemming from the influence of users during the operation of HVAC systems and their lack of knowledge relating to the exact efficiency value of these systems. The work stages were developed as follows: 1. Firstly, the energy demand variables included in the original public AVRA database were identified. The specific values are available for heating and cooling energy demand (in kWh/m2 per year) for each building included in the database. This information is previously obtained from the Building Evaluation Report, a Spanish standardised document detailing the state of conservation of the building, its level of adaptation and accessibility, and its energy efficiency aspects. In this case, these reports may be freely accessed from the official website of the Regional Ministry of Development, Territorial Structuring and Housing of the Junta de Andalucía Government. It is important to highlight that Type Variable Unit Description General data AVRA building complex code - In original AVRA database AVRA building code - Cadastral Reference - Province - Town - Spanish climatic area - Obtained from the Spanish Building Technical Code (CTE, 2019) Geometric Data Construction year - In original AVRA database Typology - Obtained from Google Maps tool Orientation º Number of dwellings (per building complex) - In original AVRA database Number of dwellings (per building) - Number of floors above ground -Obtained from the Electronic Platform of the Spanish Cadastre (Online Cadastral Office, 2024) Number of floors below ground - Average dwelling area m2 Retail space area m2 Total built area m2 Total occupied area m2 Window-to-wall ratio % In original AVRA database Energy Data Global emissions per year kWh/ m2 per year Heating demand Cooling demand Table 1 Variables included in the updated version of AVRA building database 1 3 C. M. Calama-González et al. these data is periodically updated, enhancing the expandability and scalability of the study. 2. Energy demand thresholds were then defined, so that buildings exceeding these limit values were considered vulnerable in terms of energy. These thresholds were determined based on the 2013 version of the Basic Document for Energy Saving of the Spanish Technical Building Code (CTE, 2013), taking into account the limitation of heating and cooling energy demand in privately owned residential buildings included in the regulations. It should be noted that the regulations specify different limit values for energy demand depending on the Spanish climatic zone (Calama-González, 2020) as well as the seasonal period (winter or summer). 3. At a later stage, based on the energy thresholds specified in the Spanish regulations, different degrees or levels of energy vulnerability of the dwellings (from 0 to 3) were defined, again depending on the climatic zone and seasonal period within Spain. These levels were obtained from the establishment of energy ranges in which the upper and lower limit demand values accumulate based on the previous level. Thus, according to the intensity of their energy vulnerability, the dwellings were classified into 4 categories: no risk, low, medium and severe. In other words, category 0 corresponds to dwellings that meet the regulatory threshold values; category 1 includes dwellings with demand values up to twice the regulatory limit; category 2 comprises those with demand values up to three times the regulatory limit, and, finally, category 3 includes dwellings with demand values exceeding three times the regulatory limit. Table 2 provides a summary of the energy thresholds defined for the EVI analysis. 4. Bearing all this in mind, the EVI for the winter season and the EVI for the summer season were obtained. Additionally, annual information was provided by calculating the annual EVI. This annual indicator results from the weighted average of the summer and winter indicators, where each indicator is assigned the same weight, that is, 50 % (Equation 1). EVIannual =(EVIwinter +EVIsummer)/2 (1) Table 2 Value ranges considered in the energy vulnerability indicator (EVI) derived from applicable Spanish regulations (CTE, 2013) EVI Spanish climatic zone A3 A4 B3 B4 C3 Heating energy demand (kWh/ m2) No vulnerability = 0 ≤15 ≤15 ≤15 ≤15 ≤20+s Low = 1 15 to 30 15 to 30 15 to 30 15 to 30 20+s to 2·(20+s) Medium = 2 30 to 45 30 to 45 30 to 45 30 to 45 2·(20+s) to 3·(20+s) Severe = 3 >45 >45 >45 >45 >3·(20+s) Cooling energy demand (kWh/m2) No vulnerability = 0 ≤15 ≤20 ≤15 ≤20 ≤15 Low = 1 15 to 30 20 to 40 15 to 30 20 to 40 15 to 30 Medium = 2 30 to 45 40 to 60 30 to 45 40 to 60 30 to 45 Severe = 3 >45 >60 >45 >60 >45 s refers to the ratio 1000/built area of the building. A further description of the Spanish climatic zones may be found in (Calama-González, 2020) 1 3 Urban-scale building assessment and energy vulnerability mapping… This entails the creation of 7 levels to assess the intensity of annual energy vulnerability (level 0 to 3 every 0.5), defined in ascending order of intensity: no vulnerability, low, medium-low, medium, medium-high, high and severe. 2.2.2 Definition of the socioeconomic vulnerability indicator (SVI) The SVI of the Andalusian social housing stock was evaluated through the analysis of the social profile and economic capacity of the users living in these homes. An indirect analysis method based on the census section was used to define this SVI. The process followed is explained below: 1. Firstly, the economic capacity of the users was determined. This variable is defined based on the study of the median income per consumption unit, considering the total income received after deducting taxes and other social transfers. To standardize the median value and allow for income comparison between households with different numbers of ocupants, the “household equivalent income” was used. This median value of the equivalent income per consumption unit (N) of the users was obtained from public data contained in the Survey on Living Conditions (INE, 2021), document prepared by the Spanish National Institute of Statistics in 2021, with data referring to the year 2020. This open-access information was freely obtained from the official website of the Spanish National Institute of Statistics. A.csv file with a homogeneous structure and section organization is downloaded, containing all the selected study variables. The aforementioned Institute regularly updates this data, maintaining the structure of the files over time, which allows the tool to be updated and expanded over time. 2. Subsequently, thresholds for poverty and severe poverty were defined. To do this, the"At risk of poverty and exclusion"indicator was evaluated following the guidelines of the Europe 2020 Strategy (European Commission, 2010b) and the AROPE report (AROPE, 2021) on the state of poverty in Spain. This indicator defines a poverty threshold and a severe poverty threshold corresponding to incomes below 60 % and 40 % of the median equivalent income per consumption unit, respectively. Taking both this and the survey mentioned above into account, the national value of the median equivalent income per consumption unit in Spain for 2020 was 16,043 €. Thus, the poverty threshold was established for incomes equal to or less than 9,625.80 €, while the severe poverty threshold referred to incomes equal to or less than 6,417.20 €. 3. Finally, 4 levels of the SVI were defined to assess socioeconomic ranges (from 0 to 3 corresponding to: no risk, low, medium and severe), classifying householders according by poverty intensity. To do this, the methodology established in the Household Income Distribution Atlas (INE, 2022), was applied, resulting in the ranges indicated in Table 3. 4. Furthermore, other social parameters that may significantly influence users’ degree of vulnerability are also included as socioeconomic data to complement the economic analysis of users. Three specific demographic indicators, again obtained from the INE survey (INE, 2021), were analysed: 1) percentage of elderly people (%), referring to the number of individuals aged 65 or older per hundred people in the total population; 2) old-age ratio (%), relating to the number of individuals aged 85 or over per hundred people aged 65 or over; 3) registered unemployment rate (%), representing the 1 3 C. M. Calama-González et al. Seville normally refers to the medium-low level (35.7 % of buildings) and both the extra high and severe levels (17.4 % and 17.1 % of the buildings, respectively). However, 13 % of the houses in the city present medium-high GVI and 10.2 % are classified as medium GVI vulnerability. It is remarkable that no cases are found with the lowest and highest vulnerability levels (no vulnerability, extra low, very severe and extra severe) in Seville. The area of Polígono Sur is a clear example of a neighbourhood with significant vulnerability issues given that: 34.9 % of the buildings present extra high GVI, 34.4 % present severe GVI, and 22.9 % are within the medium-high GVI level (Fig. 7). 4 Discussion: comparison with other studies A significant portion of similar studies conducted in the field whose objective is the assessment of the current performance of existing buildings (as a fundamental preliminary step prior to implementing energy retrofitting strategies) are mainly based on the analysis of representative or archetype buildings. These archetypes are generally defined through data collection primarily derived from Energy Performance Certificates, as well as cartographic documents and statistical surveys, defining building databases, as was developed in the TABULA and EPISCOPE Projects (2024). Once these archetypes are defined, these representative buildings are assessed using energy simulation tools or simplified static energy calculations. Through bottom-up approaches, the results obtained from the simulated representative buildings are later extrapolated to entire building stocks at the neighbourhood or city level, typically using GIS environments as visualization tools. This methodology is generally adopted by Yang et al. (2020), Fernández et al. (2020), or Prades-Gil et al. (2023) to analyse building archetypes in the cities of Leiden (Netherlands), Bilbao (Spain), and Fig. 6 Capture of the web map generated. Example for data visualization in Polígono Sur neighbourhood (Seville): SVI 1 3 Urban-scale building assessment and energy vulnerability mapping… Valencia (Spain), respectively. However, these authors report results only in terms of energy demand and consumption, without evaluating other parameters or providing additional information for the development of future building-level energy models. Another relevant example is the study by Mutani et al. (2024), who, following the same archetype definition criteria, analyse energy-related parameters in the Renca district of Santiago de Chile (Chile). In contrast to these studies, where extrapolation errors may arise from assigning representative morphological and typological values to buildings that, due to their irregularities or specific characteristics, may not fit these standardized schemes, the present work is based on actual energy data specific to each building. This information was directly obtained from the Energy Performance Certificates of each construction, which are publicly available and freely accessible through official databases. Therefore, no intermediate archetypal simplification process is applied; instead, the specific energy data of each building is directly linked to itself in the GIS environment, avoiding extrapolation altogether. Furthermore, unlike the work of Sánchez-Aparicio et al. (2020), who applied the HeritageCare GIS platform for the city of Salamanca (Spain), or Fabbri et al. (2012), who conducted a study within a GIS environment in the city of Ferrara (Italy), both of which focused exclusively on historically significant and monumentally valuable buildings, the present study targets the broader and more representative building stock of cities, specifically, the existing residential stock and, more precisely, the housing stock managed by public administrations. This ultimate aspect adds further value to the work, as it provides public stakeholders involved in the retrofitting process with a tool that contains crucial information for planning energy retrofit strategies, offering value data to allow prioritizing retrofit measures applied to the most vulnerable areas. Other authors, such as Deng et al. (2021), employed GIS-based tools solely to classify buildings by use across a city map in their study of Changsha (China). Some studies Fig. 7 Capture of the web map generated. Example for data visualization in Polígono Sur neighbourhood (Seville): GVI 1 3 C. M. Calama-González et al. present automated methodologies where GIS tools are used to gather relevant information across various cities. For instance, Villanueva-Díaz et al. (2024) provide geometric and thermal property data of several buildings in the city of Bilbao (Spain), while Aruta et al. (2025) propose a novel method for performing simplified thermal and energy calculations for multiple buildings in Naples (Italy). Nevertheless, none of these authors make such tools publicly available, offering only a methodological description. This limitation means that, in some cases, their methods cannot be replicated by other researchers or applied to different regions, as they have only been validated for specific case studies. Among the reviewed literature, the work of Beltrán-Velamazán et al. (2024) stands out as particularly aligned with the present article. These authors integrate into a GIS tool critical geographic, physical, and energy information for various buildings at a national level, using data from multiple open and publicly available sources, specifically Energy Performance Certificates, Cadastral Platforms, and the National Statistics Institute of Spain. However, in contrast to this work, the present study introduces an innovative contribution by offering valuable insights into both the energy vulnerability of buildings and the socioeconomic vulnerability of their users, directly linking two key indicators that are highly relevant and must be considered in the retrofit processes. In addition, and unlike the study by Modrego-Monforte et al. (2023), who propose a GIS-based methodology to assess the vulnerability of the building stock in the city of Donostia-San Sebastián (Spain) using static result images, the current article explicitly creates and shares an open-access, interactive tool that allows for the visualization of vulnerability analysis results and the characterization of the building stock (as Suplemmentary Data). This tool proves highly useful for both stakeholders involved in the retrofit process and the general public. Moreover, the tool developed in this study includes information from various municipalities in southern Spain, specifically the Andalusian region, and unlike the previously mentioned work, it is not limited to a single city (even though only one city is visually presented as an example). Beyond vulnerability assessment, the designed tool created in this study also includes additional geometric, physical, energy, and social data of great relevance for the development of dynamic single-level building energy simulation models. In summary, this work presents and shares an open-access, free-to-use tool that can be executed in any web browser, as described in Section 2.3. 5 Conclusions This study presents an interactive geo-referenced data web-tool for general building characterization and energy vulnerability assessment to be used by householders, stakeholders and public administrations in the retrofit process. It also describes the methodology followed. This tool contains information on building characterization and the degree of energy and socioeconomic vulnerability of the public social housing stock in southern Spain, considering the predominant multi-family H-block and linear block buildings. In this article, an applicability example was shown for the city of Seville, but data of 41 southern Spain municipalities were considered. Overall, this research has proved that, once the existing open data available is correlated and simultaneously analysed, it can provide an initial approximation and global assess1 3 Urban-scale building assessment and energy vulnerability mapping… ment of the current state of the existing buildings at stock or regional level. This approach allows the scope, disparities and causes of vulnerability to be identified, which enables a detailed and accurate diagnosis at the regional scale, as well as the design of more appropriate and effective policies. Thus, the usability of the methodology defined has also been demonstrated through its application at a local scale, proving to be an effective method to rapidly obtain general and energy data on an extensive sample, fostering concrete local actions allowing the problem to be addressed. This dual approach at regional or local level facilitates the development of differentiated and coordinated energy and social long-term policy actions, ultimately aiming to mitigate structural problems. These aspects will help target public aid and funding toward the most vulnerable areas, strategic allocating public resources. Furthermore, the creation of a free open-access tool allows the incorporation of new information at any time, making the interface a dynamic resource which can be improved over time using updated information obtained from public datasets. This aspect democratizes information and empowers citizens, social stakeholders and public administrations in the decision-making process. The developed tool integrates GIS technologies to make it interactive and capable of accurate and generally rapid data analysis. Moreover, it is based on an open-source nature, ensuring accessibility for end users and policymakers, among other public. The tool offers comprehensive coverage since it addresses engineering, social and environmental factors that characterised public social housing in southern Spain, providing a holistic view of this stock. And, furthermore, the scalability of the tool must be highlighted, given that it may be updated and even expanded with new data obtained from public databases, ensuring its ongoing relevance. The files included in the tool contain information on the current state and energy performance of the social housing stock of each municipality, which is useful for subsequent energy analysis or dynamic simulation in these buildings, as it provides fundamental parameters for the definition of energy simulation models for both bottom-up and top-down approaches. Additionally, relevant data is provided for decision-making in the renovation process, focusing on the residential building sector most affected by energy and social vulnerability. On the other hand, some limitations ought to be also mentioned. For instance, the dependence on public open data, which may result in limited-quality datasets, and the regional focus, since the tool is specifically designed for southern Spain. This aspect may limit the applicability of the tool to other regions, depending on the format of open-source data obtained from public datasets created and managed by public administrations, which may require a previous data adaptation process of input variables to be used in the GIS tool. Despite the possible dynamic outcomes, which may vary considering input data and assessment criteria, the incorporation of new evaluation objectives may be easily implemented, enhancing its future applications. Acknowledgments Escandón acknowledges the financing of the VI PPIT-US, through the 2020 Call for Contracts for Access to the Spanish Science, Technology and Innovation System for the Development of the US's Own R&D&I Program. Author contributions C.M. Calama-González: Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Software, Writing – original draft, Writing – review & editing. R. Escandón: Resources, Writing – review & editing, Funding acquisition, Project administration. R. Suárez: Conceptualization, Methodology, Supervision, Writing – review & editing. E. Abajo-Casado: Methodology, Software, Writing – review & editing. A.R. Diánez-Martínez: Methodology, Software, Writing – review & editing. 1 3 C. M. Calama-González et al. Funding Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This research was funded by the European Regional Development Fund (FEDER) and the Regional Government of Junta de Andalucía, through the research project “Energy Retrofitting of the Andalusian social housing. Optimization of passive solutions in residential stocks with a high vulnerability index” (US.22-06). Data availability Data will be made available on request. Declarations Competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. References Aruta, G., Ascione, F., Bianco, N., Bindi, L., & Iovane, T. (2025). Energy classification of urban districts to map buildings and prioritize energy retrofit interventions: A novel fast tool. Applied Energy,377, 124664. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . a p e n e r g y . 2 0 2 4 . 1 2 4 6 6 4 Atesoglu, A., Ozel, H. B., Varol, T., Cetin, M., Baysal, B. U., & Bulut, F. S. (2025). Monitoring land cover/ use conversions in Türkiye wetlands using collect earth. Journal of the Indian Society of Remote Sensing, 1-16. https://doi.org/10.1007/s12524-024-02111-w AVRA. (2023). Agencia de Vivienda y Rehabilitaci´on de Andalucía. Available online: h t t p : / / w w w . j u n t a d e a n d a l u c i a . e s / a v r a . Accessed 10 June 2004. Beltrán-Velamazán, C., Monzón-Chavarrías, M., & López-Mesa, B. (2024). A new approach for nationalscale building energy models based on energy performance certificates in European countries: The case of Spain. Heliyon, 10(3). h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . h e l i y o n . 2 0 2 4 . e 2 5 4 7 3 Calama-González, C. M., Suárez, R., & León-Rodríguez, A. L. (2020). Building characterisation and assessment methodology of social housing stock in the warmer mediterranean climate: The case of southern Spain. IOP Conference Series: Earth and Environmental Science,410(1), 012049. h t t p s : / / d o i . o r g / 1 0 . 1 0 8 8 / 1 7 5 5 - 1 3 1 5 / 4 1 0 / 1 / 0 1 2 0 4 9 Calama-González, C. M., Escandón, R., Suárez, R., Alonso, A., & León-Rodríguez, Á. L. (2024). Household energy vulnerability evaluation in southern Spain through parametric energy simulation models and socio-economic data. Sustainable Cities and Society,105276, 1–17. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . s c s . 2 0 2 4 . 1 0 5 2 7 6 Caputo, P., & Pasetti, G. (2017). Boosting the energy renovation rate of the private building stock in Italy: Policies and innovative GIS-based tools. Sustainable Cities and Society,34, 394–404. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . s c s . 2 0 1 7 . 0 7 . 0 0 2 CTE. (2013). Spanish technical building code. Basic document: energy saving. Spanish Government. Available online: https://www.codigotecnico.org. Accessed 10 June 2004. CTE. (2019). Spanish technical building code. Basic document: energy saving. Spanish Government. Available online: https://www.codigotecnico.org. Accessed 10 June 2004. Cuerda, E., Pérez, M., & Neila, J. (2014). Facade typologies as a tool for selecting refurbishment measures for the Spanish residential building stock. Energy and Buildings,76, 119–129. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . e n b u i l d . 2 0 1 4 . 0 2 . 0 5 4 Dascalaki, E. G., Droutsa, K., Gaglia, A. G., Kontoyiannidis, S., & Balaras, C. A. (2010). Data collection and analysis of the building stock and its energy performance—An example for Hellenic buildings. Energy and Buildings,42(8), 1231–1237. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . e n b u i l d . 2 0 1 0 . 0 2 . 0 1 4 1 3 Urban-scale building assessment and energy vulnerability mapping… Deng, Z., Chen, Y., Pan, X., Peng, Z., & Yang, J. (2021). Integrating GIS-based point of interest and community boundary datasets for urban building energy modeling. Energies,14(4), 1049. h t t p s : / / d o i . o r g / 1 0 . 3 3 9 0 / e n 1 4 0 4 1 0 4 9 Droutsa, K. G., Kontoyiannidis, S., Dascalaki, E. G., & Balaras, C. A. (2016). Mapping the energy performance of hellenic residential buildings from EPC (energy performance certificate) data. Energy,98, 284–295. https://doi.org/10.1016/j.energy.2015.12.137 EPISCOPE and TABULA European Projects. (2024). Intelligent energy Europe. Programme of the European Union. Available online: https://episcope.eu/welcome/. Accessed 10 June 2004. European Commission. (2010a). Directive (EU) 2010/31 of the European parliament and of the council of 19 May 2010 on the energy performance of buildings. Available online: h t t p s : / / e u r - l e x . e u r o p a . e u / e l i / d i r / 2 0 1 0 / 3 1 / o j / e n g. Accessed 10 June 2004. European Commission. (2010b). Europe 2020: A strategy for Smart, sustainable and inclusive growth. Available online: h t t p s : / / e u r - l e x . e u r o p a . e u / l e g a l - c o n t e n t / E N / T X T / P D F / ? u r i = C E L E X : 5 2 0 1 0 D C 2 0 2 0 . Accessed 10 June 2004. European Commission. (2011). Communication from the commission to the European parliament, the council, the European economic and social committee and the committee of the regions. Energy efficiency plan 2011. Available at: h t t p s : / / e u r - l e x . e u r o p a . e u / L e x U r i S e r v / L e x U r i S e r v . d o ? u r i = C O M : 2 0 1 1 : 0 1 0 9 : F I N : E N : P D F . Accessed 10 June 2004. European Commission. (2024).Directive (EU) 2024/1275 of the European parliament and of the council of 24 April 2024 on the energy performance of buildings (recast). Available online: h t t p s : / / e u r - l e x . e u r o p a . e u / e l i / d i r / 2 0 2 4 / 1 2 7 5 / o j / e n g. Accessed 10 June 2004. Fabbri, K., Zuppiroli, M., & Ambrogio, K. (2012). Heritage buildings and energy performance: Mapping with GIS tools. Energy and Buildings,48, 137–145. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . e n b u i l d . 2 0 1 2 . 0 1 . 0 1 8 Fabbri, M., De Groote, M., & Rapf, O. (2016). Building renovation passports. Customised roadmaps towards deep renovation and better homes. BPIE, Report, October: h t t p s : / / w w w . b p i e . e u / p u b l i c a t i o n / r e n o v a t i o n - p a s s p o r t s /. Accessed 02 May 2004. Fernandez, J., del Portillo, L., & Flores, I. (2020). A novel residential heating consumption characterisation approach at city level from available public data: Description and case study. Energy and Buildings,221, 110082. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . e n b u i l d . 2 0 2 0 . 1 1 0 0 8 2 Gangolells, M., Casals, M., Forcada, N., Macarulla, M., & Cuerva, E. (2016). Energy mapping of existing building stock in Spain. Journal of Cleaner Production,112, 3895–3904. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . j c l e p r o . 2 0 1 5 . 0 5 . 1 0 5 Hartless R (2003) Application of energy performance regulations to existing buildings. Final report of the Task B4, ENPER TEBUC Project, SAVE 4.1031/C/00-018. Watford, UK: Building Research Establishment. Hjortling, C., Björk, F., Berg, M., & af Klintberg, T. (2017). Energy mapping of existing building stock in Sweden-analysis of data from energy performance certificates. Energy and Buildings,153, 341–355. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . e n b u i l d . 2 0 1 7 . 0 6 . 0 7 3 INE. (2021). Encuesta de Condiciones de Vida. Año. Available online: h t t p s : / / i n e . e s / d y n g s / I N E b a s e / e s / o p e r a c i o n . h t m ? c = E s t a d i s t i c a _ C & c i d = 1 2 5 4 7 3 6 1 7 6 8 0 7 & m e n u = u l t i D a t o s & i d p = 1 2 5 4 7 3 5 9 7 6 6 0 8 . Accessed 10 June 2004. INE. (2022). Instituto Nacional de Estadística. Atlas de distribución de renta de los hogares. Año 2020. Available online: h t t p s : / / i n e . e s / e x p e r i m e n t a l / a t l a s / e x p e r i m e n t a l _ a t l a s . h t m . Accessed 10 June 2004. Informe AROPE. (2021). El Estado de la Pobreza en las Comunidades Autónomas. Available online: h t t p s : / / w w w . e a p n . e s / e s t a d o d e p o b r e z a / . Accessed 10 June 2004. Instituto de Estadística y Cartografía. (2024). Estadísticas Censales de Andalucía. Available at: h t t p : / / w w w . j u n t a d e a n d a l u c i a . e s / i n s t i t u t o d e e s t a d i s t i c a y c a r t o g r a fi a / g e o s e r v e r - i e c a / i e p a b r a / w f s . Accessed 10 June 2004. Jakob, M., Wallbaum, H., Catenazzi, G., Martius, G., Ngeli, C., Sunarjo, B., (2013). Spatial building stock modelling to assess energy-efficiency and renewable energy in an urban context. In: Proceedings of CISBAT 2013, September 4-6, Lausanne (Switzerland), 10471052. Jiang, P., Dong, W., Kung, Y., & Geng, Y. (2013). Analysing co-benefits of the energy conservation and carbon reduction in China’s large commercial buildings. Journal of Cleaner Production,58, 112–120. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . j c l e p r o . 2 0 1 3 . 0 4 . 0 3 9 Johansson, T., Vesterlund, M., Olofsson, T., & Dahl, J. (2016). Energy performance certificates and 3-dimensional city models as a means to reach national targets–A case study of the city of Kiruna. Energy Conversion and Management,116, 42–57. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . e n c o n m a n . 2 0 1 6 . 0 2 . 0 5 7 Kleemann, F., Lederer, J., Rechberger, H., & Fellner, J. (2017). GIS-based analysis of Vienna’s material stock in buildings. Journal of Industrial Ecology,21(2), 368–380. https://doi.org/10.1111/jiec.12446 Kucukpehlivan, T., Cetin, M., Aksoy, T., Kurkcuoglu, M. A. S., Cabuk, S. N., Pekkan, O. I.,... & Cabuk, A. (2023). Determination of the impacts of urban-planning of the urban land area using GIS hotspot analysis. Computers and Electronics in Agriculture, 210, 107935. https://doi.org/10.1016/j.compag.2023.107935 1 3 C. M. Calama-González et al. Li, Y., Rezgui, Y., & Zhu, H. (2017). District heating and cooling optimization and enhancement–Towards integration of renewables, storage and smart grid. Renewable and Sustainable Energy Reviews,72, 281– 294. https://doi.org/10.1016/j.rser.2017.01.061 Martín-Consuegra, F., de Frutos, F., Oteiza, I., & Agustín, H. A. (2018). Use of cadastral data to assess urban scale building energy loss. Application to a deprived quarter in Madrid. Energy and Buildings,171, 50–63. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . e n b u i l d . 2 0 1 8 . 0 4 . 0 0 7 Modrego-Monforte, I., Barrena-Herrán, M., & Grijalba, O. (2023). A multi-criteria analysis GIS tool for measuring the vulnerability of the residential stock based on multidimensional indices. Land,12(8), 1551. https://doi.org/10.3390/land12081551 Mutani, G., Alehasin, M., Yang, H., Zhang, X., & Felmer, G. (2024). Urban building energy modeling to support climate-sensitive planning in the suburban areas of Santiago de Chile. Buildings,14(1), 185. h t t p s : / / d o i . o r g / 1 0 . 3 3 9 0 / b u i l d i n g s 1 4 0 1 0 1 8 5 Oezdemir, O., Krause, K., & Hafner, A. (2017). Creating a Resource cadaster—a case study of a district in the Rhine-Ruhr metropolitan area. Buildings,7(2), 45. https://doi.org/10.3390/buildings7020045 Online Cadastral Office. (2024). (Sede Electrónica del Catastro, in Spanish). Available at: h t t p s : / / w w w . s e d e c a t a s t r o . g o b . e s . Accessed 10 June 2004. Oregi, X., Hermoso, N., Arrizabalaga, E., Mabe, L., & Munoz, I. (2018a). Sensitivity assessment of a district energy assessment characterisation model based on cadastral data. Energy Procedia,147, 181–188. https://doi.org/10.1016/j.egypro.2018.07.053 Oregi, X., Hermoso, N., Prieto, I., Izkara, J. L., Mabe, L., & Sismanidis, P. (2018b). Automatised and georeferenced energy assessment of an Antwerp district based on cadastral data. Energy and Buildings,173, 176–194. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . e n b u i l d . 2 0 1 8 . 0 5 . 0 1 8 Pasichnyi, O., Wallin, J., Levihn, F., Shahrokni, H., & Kordas, O. (2019). Energy performance certificates— New opportunities for data-enabled urban energy policy instruments? Energy Policy,127, 486–499. https://doi.org/10.1016/j.enpol.2018.11.051 Prades-Gil, C., Viana-Fons, J. D., Masip, X., Cazorla-Marín, A., & Gómez-Navarro, T. (2023). An agile heating and cooling energy demand model for residential buildings. Case study in a mediterranean city residential sector. Renewable and Sustainable Energy Reviews,175, 113166. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . r s e r . 2 0 2 3 . 1 1 3 1 6 6 QGIS. (2019). Cross-Platform Desktop Geographic Information System QGIS v.3.18 GNU GPLv2 QGIS Developmnet Team. Available at: https://www.qgis.org/es/site. Accessed 10 June 2004. Sánchez-Aparicio, L. J., Masciotta, M. G., García-Alvarez, J., Ramos, L. F., Oliveira, D. V., Martín-Jiménez, J. A.,... & Monteiro, P. (2020). Web-GIS approach to preventive conservation of heritage buildings. Automation in Construction, 118, 103304. https://doi.org/10.1016/j.autcon.2020.103304 Sanchez-Guevara, C., Peiró, M. N., Taylor, J., Mavrogianni, A., & González, J. N. (2019). Assessing population vulnerability towards summer energy poverty: Case studies of Madrid and London. Energy and Buildings,190, 132–143. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . e n b u i l d . 2 0 1 9 . 0 2 . 0 2 4 Streicher, K. N., Padey, P., Parra, D., Bürer, M. C., & Patel, M. K. (2018). Assessment of the current thermal performance level of the Swiss residential building stock: Statistical analysis of energy performance. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . e n b u i l d . 2 0 1 8 . 0 8 . 0 3 2 TABULA Project Team. (2013). TABULA calculation method– energy use for heating and domestic hot water. Institut Wohnen und Umwelt GmbH: https://episcope.eu/iee-project/tabula/. Accessed 10 June 2004. Tsirigoti, D., & Bikas, D. (2017). A cross scale analysis of the relationship between energy efficiency and urban morphology in the Greek City context. Procedia Environmental Sciences,38, 682–687. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . p r o e n v . 2 0 1 7 . 0 3 . 1 4 9 Villanueva-Díaz, C., Álvarez-Sanz, M., Campos-Celador, Á., & Terés-Zubiaga, J. (2024). The open data potential for the geospatial characterisation of building stock on an urban scale: Methodology and implementation in a case study. Sustainability,16(2), 652. https://doi.org/10.3390/su16020652 Yang, X., Hu, M., Heeren, N., Zhang, C., Verhagen, T., Tukker, A., & Steubing, B. (2020). A combined GISarchetype approach to model residential space heating energy: A case study for the Netherlands including validation. Applied Energy,280, 115953. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . a p e n e r g y . 2 0 2 0 . 1 1 5 9 5 3 Zeren Cetin, I., Varol, T., & Ozel, H. B. (2023). A geographic information systems and remote sensing–based approach to assess urban micro-climate change and its impact on human health in Bartin, Turkey. Environmental Monitoring and Assessment,195(5), 540. https://doi.org/10.1007/s10661-023-11105-z Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 1 3 Urban-scale building assessment and energy vulnerability mapping… Authors and Affiliations C. M.Calama-González1· R.Escandón2· R.Suárez2· E.Abajo-Casado3· A. R.DiánezMartínez3 C. M. Calama-González [email protected] 1 Departamento de Construcciones Arquitectónicas y su Control. Escuela Técnica Superior de Edificación, Universidad Politécnica de Madrid. Avda, Juan de Herrera 4, 28040 Madrid, Spain 2 Instituto Universitario de Arquitectura y Ciencias de la Construcción, Escuela Técnica Superior de Arquitectura, Universidad de Sevilla, Av. de Reina Mercedes 2, 41012 Seville, Spain 3 Departamento de Matemática Aplicada I, Escuela Técnica Superior de Arquitectura, Universidad de Sevilla, Av. de Reina Mercedes 2, 41012 Seville, Spain 1 3