Evaluating wildfire vulnerability of Mediterranean dwellings using fuzzy logic applied to expert judgement

VAT methodology

In order to reduce the risk of home loss at the WUI, a coupled approach that reduces the vulnerability of a home to fire along with the probability of its exposure conditions is necessary (Calkin et al. 2014; Caton et al. 2017). The causes of fire entering a dwelling located at the WUI can be summarised, therefore, into two intermediate events of a fault tree, as shown in Fig. 1: one involving the exposure conditions and the other involving structural vulnerabilities typical of Mediterranean constructions. For the fire to enter a dwelling, both of these events must occur. The different paths that lead to these two intermediate events in a Mediterranean environment, identified through a literature review of past events (Vacca et al. 2020b), are further explored to develop the sketch model in Fig. 2. Quantification of the probability of failure of each of the events has proved to be difficult, as information on paths that lead to ignition during past fires is not always available or reliable, as it is mostly collected without the possibility of thorough investigation owing to lack of information or resources. To deal with this difficulty, a model that combines fuzzy logic with classical logic has been developed. It is based on the use of fuzzy sets that provide means to model the uncertainties associated with lack of information (Sivanandam et al. 2007).

Fig. 1. 

Events that lead to fire entering a building at the WUI.

Fig. 2. 

Scheme for vulnerability assessment to wildland fires for dwellings at the WUI. FIS, fuzzy inference system; POF, probability of failure; ORN, ornamental vegetation; ART, artificial fuels; WLD, wildland vegetation; _1, refers to zone 1 (area within a radius of 10 m from the dwelling); _2, refers to zone 2 (a 10–30 m ring around the dwelling).

Fire exposure of the dwelling

When it comes to the ways a fire can reach a dwelling, two areas around the structure have been identified following the previously mentioned guidelines: Zone 1 includes the area in a radius of 10 m from the dwelling, while Zone 2 consists of a 10–30 m ring around the dwelling (Government of Alberta 2013; NFPA 2022). For Zone 2, a ring from 10 to 50 m was initially considered by the authors, therefore taking into account some of the European guidelines, but during the analysis of the case studies presented further in this work, it was noted that parcels do not often reach this size, and the selected zone would frequently include not only adjacent neighbours, but also those located further, adding too many variables that cannot directly be controlled by the homeowner.

In both of the selected zones, three types of fuels are considered: ornamental vegetation, artificial fuels (e.g. liquefied petroleum gas (LPG) tanks, garden furniture, sheds) and wildland vegetation. For each zone, a set of fuel management rules that can reduce the probability of the fire reaching the dwelling is established (Table 2); rules are stricter for Zone 1 owing to the close proximity to the dwelling. When it comes to vegetation, these rules are selected based on a review of existing guidelines for the management of vegetation specific to Mediterranean-type landscapes. Therefore, the analysis is limited to guidelines of the following countries or regions: France (Préfet de Vaucluse 2013; Préfet des Alpes-de-Haute-Provence 2013; Préfet de Bouches-du-Rhône 2014; Préfet des Alpes-Maritimes 2014; Préfet du Var 2015; Préfet de la Haute-Corse 2022), Portugal (Autoridade Florestal National 2008), Spain (Generalitat de Catalunya 2005; Manca and López 2014; Generalitat de Catalunya 2019), California (Cal Fire 2022), South Australia (South Australia Country Fire Service 2022) and Victoria (Victoria Country Fire Authority 2022). The Italian guidelines were also analysed; however, they do not include specific rules for the spacing of vegetation or artificial fuels within the defensible space. Overall, the strictest rules for distancing of wildland fuels are considered. When available, rules are derived from scientific findings, as is the case for the distancing of fuels from glazing systems or that between vegetation and artificial fuels. Information on spacing between artificial fuels or fuel packs (such as sheds, garden furniture, vehicles) to avoid fire spread through these types of fuels was not found in the analysed guidelines or in any scientific study. Therefore, the distance selected for these rules comes from an extrapolation of the case study of the Camp Fire in California, in which fire spread from artificial fuel to artificial fuel (or a dwelling with a façade made of combustible materials) was recorded (Maranghides et al. 2021).

The impact of firebrands on the different types of fuels is indirectly included within the rules in Table 2. We assume that firebrand attack is likely to be an ignition source for fuels present in Zones 1 and 2. Now, if any fuel is ignited by firebrands and it is well managed, it will not cause fire spread to other fuels or impact the dwelling’s vulnerable elements. Failure occurs when compliance with the rules in Table 2 is not met.

Structural vulnerabilities

Structural vulnerabilities of the dwelling are also identified based on the different paths through which fire could enter. According to Vacca et al. (2020b), there are four main paths, which are associated with either gaps that already existed in the dwelling owing to bad maintenance, or that can be caused by the fire itself. These pathways involve glazing systems, roof, vents and structural damage to the dwelling’s envelope due to heat accumulation in semi-confined spaces. The failure sequence for each one of these elements is identified as shown in Fig. 2: the failure of a glazing system depends on the thickness of the glass pane (the type considered is annealed glass, given it is the most common in residential windows) and the type of shutters, with different degrees of protection depending on the material; the failure of the roof depends on the roof covering material, as well as the level of maintenance of the roof itself; the probability of fire entrance through vents is determined by the material and condition of their protection; the failure of the envelope of a semi-confined space is determined by the percentage of glazing systems present in the envelope, the amount of combustible materials stored in the space, and the material and thickness of the envelope that allows it to maintain the load bearing capacity of the structural element exposed to fire (Vacca et al. 2022). The impact of firebrands on the dwelling is implicitly considered in the failure of the four different building vulnerabilities. Given that firebrands can enter the building through gaps existing because of the building’s characteristics or gaps created owing to poor maintenance of the building itself, the presence of firebrands is strongly taken into account.

Model description

The structure of the developed model is given in Fig. 2. Note that, according to Figs 1 and 2, two system variables lead to the final output of the model (i.e. fire inside the dwelling) through a classical logical AND gate; these are: (i) probability of fire reaching the dwelling (POF_1) and (ii) probability of failure of the dwelling due to its vulnerabilities to fire (POF of the dwelling). In the same way, this last variable (ii) is obtained through a classical logical OR gate according to the values obtained for the probabilities of failure of the four elements that constitute pathways for the fire into the house, i.e. glazing systems, roof, vents and semi-confined spaces that can suffer structural damage due to heat accumulation. The probability (i) (POF_1) depends on compliance with the different rules set for fuels located in the two considered zones previously described (Table 2). All the probabilities of failure defined before the two classical logical gates are obtained through the use of fuzzy logic. This is a soft computing analytical technique that has already been used extensively in environmental risk assessments (e.g. Seguí et al. 2013) and has also been recently applied in resilience evaluation of flood-prone communities (Oladokun and Montz 2019), among other applications.

Seven fuzzy inference systems (FISs) are defined, as shown in Fig. 2. When a FIS is defined, the generic process shown in Fig. 3 must be followed. Initially, the variables that are relevant in the system must be identified (output and inputs). For example, to establish the probability of fire reaching Zone 1, i.e. ‘probability of failure of Zone 2’ because fire can spread through this zone (POF_2 in Figs 2 and 3), we identified three input variables associated with the quality of the ‘management of ornamental, artificial and wildland fuels in Zone 2’ (MANAGEMENT ORN_2, MANAGEMENT ART_2, MANAGEMENT WLD_2 in Figs 2 and 3, respectively). These variables must then be fuzzified, meaning that they need to be defined as fuzzy sets by identifying their universe of discourse (e.g. ‘complying rules percentage’, from 0 to 100%) and by selecting a set of linguistic terms (i.e. fuzzy subsets) that accurately describe them (e.g. ‘good’ and ‘bad’ are fuzzy subsets of the fuzzy sets denoted as ‘management of ornamental, artificial and wildland fuels in Zone 2’). Subsequently, a membership function for each fuzzy subset must be defined to quantify the degree of belonging of any value in the universe of discourse to each fuzzy subset (FUZZIFICATION block in Fig. 3) (Sivanandam et al. 2007). Then the inferring process is performed by using a set of rules that connect antecedents (input variables) with the consequent (output variable). These rules usually have a structure such as: ‘IF …, THEN …’. An aggregation process is required to take into account the different rules that activate according to the inputs. Then, because the output is also defined as a fuzzy set, a defuzzification process (centroid calculation) is necessary in order to transform the fuzzy results into a precise output.

Fig. 3. 

Generic fuzzy inference process associated with the probability of fire reaching Zone 1, i.e. ‘probability of failure of Zone 2’ (POF_2 in Fig. 2). MANAGEMENT ORN_2, MANAGEMENT ART_2, MANAGEMENT WLD_2 refer to the management of ornamental, artificial and wildland fuels in Zone 2, respectively (based on Darbra et al. 2008).

A very simple but complete example on how fuzzy inference works is given as Supplementary material. This case is about how to infer the probability of failure associated with the roof for one of the dwellings included in the first case study presented in this paper. A Python library for fuzzy logic (simpful) (Spolaor et al. 2020) was used to handle all the inference systems defined in the present work.

Parameterisation of the FISs

A poll for WUI fire experts was prepared to parametrise the FISs present in the model. A pre-selection of possible pollees was done according to their WUI expertise either because of their professional experience as WUI fire risk managers or because of their research activity evidenced by scholarly output. Then, the poll was delivered by email using an Excel file specifically designed for this purpose (available as Supplementary material). Other expert knowledge elicitation techniques incorporate group activities, such as the Delphi-like approach (Drescher and Edwards 2018). In our case, to minimise the volunteering time required from the experts, this type of approach was not considered. All the replies were evaluated using simple statistical approaches and results were validated taking into account whether the elicited outcomes were plausible and conformed to authors’ expectations (Drescher et al. 2013).

More specifically, the experts’ input helped to determine membership functions, as they were asked to provide a lower and upper bound, or a best estimate for the fuzzy subsets that defined each fuzzy set present in the model. The percentage of experts that considered the different values for each fuzzy subset was computed and then weighted average values were calculated to set membership functions. For a given fuzzy set (e.g. thickness of the glazing systems), triangular membership functions were defined for those fuzzy subsets that were not at the limits of the universe of discourse of the fuzzy set (e.g. medium thickness of the glazing systems), and trapezoidal functions for those at the limits (e.g. thin and thick glazing systems).

Additionally, the poll included the fuzzy rules, for which the experts could choose the linguistic value of the output variable (i.e. consequent). When more than one input variable was combined in a rule, the logical operator AND was used. An example of the selection for the rules’ consequent is shown in Fig. 4. To elicit each rule consequent (e.g. ‘If windows thickness is thin and shutters protection is PVC, then probability of failure is …’), a weighted average was calculated by assigning a number to each subset (probability of failure: Extreme,  4; High,  3; Medium,  2; Low,  1). Then, data were linearly transformed so that the result was in the range 0–1 and categorical values were set back according to the following ranges: [0, 0.25], Low; [0.25, 0.50], Medium; [0.50, 0.75], High; [0.75, 1], Extreme.

Fig. 4. 

Example of rules present in the questionnaire prepared to collect experts’ knowledge.

Homeowners questionnaire

The model presented previously has to be used together with a questionnaire that homeowners must fill in. There are different types of questions in the questionnaire: some are yes/no, others are percentages, others are multiple choice, etc. They include all the information needed to run the vulnerability assessment model for a specific property. The complete questionnaire is available as Supplementary material.

Once the questionnaire is completed, the replies are introduced into the model to calculate the probabilities of failure of the different elements considered, which are then used to calculate the probability of a fire entering a dwelling.

FIS parameterisation outcomes

The poll for WUI fire experts that was prepared to parametrise the fuzzy inference systems present in the model was completed by 13 experts who, according to personal data gathered through the questionnaire, came from six different countries: Spain (6), Australia (3), Chile (1), France (1), Portugal (1) and UK (1), and were working in civil defence (1), private companies (2) or research institutions (10).

In Fig. 5, an example of the procedure followed to define the membership functions of the fuzzy subsets that define two fuzzy sets of the model (‘window coverage’ and ‘probability of failure’) is shown. Poll replies (Fig. 5 top subplots) were used to specifically set these functions by taking into account the percentage of experts that considered the different values for each fuzzy subset (Fig. 5 middle subplots). Weighted average values were calculated (i.e. dashed vertical lines in Fig. 5 middle subplots) and vertices could be set accordingly to define membership functions (e.g. Fig. 5 bottom subplots).

Fig. 5. 

Fuzzy subsets definition for ‘window coverage in the semi-confined space’ and ‘probability of failure’ fuzzy sets according to poll results. Top plots: answers given by the 13 experts. Middle plots: poll results (dashed lines indicate weighted averaged values). Bottom plots: fuzzy membership functions elicited according to middle plot results for the corresponding fuzzy subsets. SCS, semi-confined space.

In Table 3, for each fuzzy set (i.e. first column in Table 3), specific weighted average values obtained from poll replies are shown. One specific result worth mentioning is related to the probability of failure associated with the vents. Experts considered that having non-combustible vents in bad condition gives a slightly higher probability of failure than having vents made out of combustible material (e.g. plastic).

Descriptions and/or questions posed to discriminate between the different subsets are presented in the questionnaire (available as Supplementary material). For example, the roof is assumed to be badly maintained if there are missing, displaced or broken tiles, if the underlying roof sheeting is exposed, or if there are unsealed spaces between the roof and the external walls or between the roof covering and the roof decking. Also, if a regular cleaning of debris piling up on the roof or gutters is not done, the roof is assumed to be badly maintained.

Another result of the poll was the consequent of the fuzzy rules associated with each fuzzy inference system. An example of the results obtained for several rules’ consequents of FIS1 (defined in Fig. 2) is shown in Fig. 6. The plot shows the distribution of replies given by the experts to the five rules of FIS1 associated with the presence of thin glazing systems, and on the right side of this figure, the final consequent assigned to each rule is shown.

Fig. 6. 

Number of replies given by experts to several rules’ consequents of the fuzzy inference system associated with the ‘probability of failure of the glazing systems’ (i.e. FIS1 in Fig. 2). The subset finally assigned is shown on the right side of the plot.

The model was constructed without considering different weights for the variables involved in each fuzzy inference system explicitly. An analytical hierarchy process could have been applied to acknowledge the different importances; however, according to the results obtained, we believe that experts are considering different weights implicitly when establishing rules consequents. For example, consequents defined according to experts’ responses for the three rules shown in Table 4 indicate that the probability of fire reaching Zone 1 is larger when wildland fuels are badly managed in comparison with badly managed ornamental vegetation or artificial fuels in Zone 2.

Case study 1: Lloret de Mar, Spain (2021)

The owners of five dwellings (Fig. 7) affected by a WUI fire that took place in July 2021 in Lloret de Mar, Spain (Fig. 8) were interviewed during a working session that was organised several months after the fire in collaboration with the city council. During that session, clear instructions were given for the evaluation of properties as they were before the fire. The homeowners were very collaborative and were able to fill in the questionnaire with our help. Their answers (shown in Table 5) were used to quantify the probability of fire entering their dwellings using our VAT model (Table 6). They got our feedback on the different issues (fuel management, structural constraints, etc.) that needed to be addressed in order to reduce this probability. For comparison purposes, Tables 5 and 6 also include a hypothetical worst-case scenario, for which the worst characteristics of a dwelling and of fuel management are considered and the highest probabilities of failure are estimated.

Fig. 7. 

Monitored properties (H11 to H15) affected by the WUI fire in Lloret de Mar, Spain (July 2021) (Google Earth, earth.google.com). Red line: 10 m around dwellings; yellow line: 30 m around dwellings. Green lines indicate elevation contours (Institut Cartogràfic i Geològic de Catalunya, https://www.icgc.cat/). The location of the burning van that initiated the upslope fire is shown.

Fig. 8. 

Photographs of the WUI fire in Lloret de Mar, Spain (July 2021): (a) burning van that initiated the upslope fire (O. Torres); (b) general view of the passage of the fire (Bombers de la Generalitat); photos of the dwellings after the fire: (c) H11; (d) H12; (e) H13; (f) H14; (g) H15.

The WUI fire under study started when a damaged van that had stopped on the hard shoulder of a road (Figs 7 and 8a) caught fire at ~11 a.m. with a sea breeze blowing. The flames from the van ignited the vegetation next to it, which was mainly composed of pine trees and a dense understorey. Topography and fuel continuity played an important role in the propagation and intensity of the fire. It spread rapidly upwards through a steep slope until fuel discontinuity due to the presence of houses triggered the main fire front to propagate following the left drainage area in between H11, and H12 and H14 (see in Fig. 7 the ‘V’-shaped contour lines pointing uphill).

This fire prompted evacuation orders and several homes were threatened, various elements present outdoors were burned (e.g. vehicles, fences and garden furniture), and one house was severely damaged (H12 in Figs 7 and 8d) owing to the fire entering the dwelling as a result of the breakage of a window pane.

All monitored houses were built with non-combustible materials such as concrete, stone or bricks. H11, H14 and H15 were built between 10 and 30 years ago, whereas H12 and H13 were over 30 years old. All homeowners stated that their house was well maintained when the fire occurred.

As can be seen in Table 5, all houses had shutters of different materials, but none had fire-rated ones. Moreover, H12 had PVC shutters but during the fire they were left open and as such did not provide any protection; therefore, both situations (i.e. no shutters and PVC shutters) were considered for the vulnerability assessment. All but H13 also had double glazing systems (a thickness value of 14 mm was assumed for this type of systems). As for the roof, all had a construction typical of Mediterranean houses, with a roof covering made out of clay tiles. All roofs, with the exception of the one of H13, were stated to be in good condition. H13 was also the only dwelling to have vents, which at the time of the fire were not protected. All houses had porches with different types of outdoor furniture. H12 also had a car shed made out of wood and clay tiles that was completely destroyed by the fire. When it comes to the two zones analysed surrounding the dwellings, it can be seen that there was no compliance at all with the rules for the management of wildland fuels in Zone 2, while only two houses complied with these rules completely in Zone 1. With regard to ornamental vegetation, all properties complied with at least some of the rules, with a minimum of 11% compliance for Zone 1 of H13. None of the dwellings reached 100% compliance in Zone 1, and it can be seen that, overall, compliance was higher in Zone 2. For the presence of artificial fuels, the lowest compliance was 25% in both zones, and H14 was the only property that fully complied in both zones with the rules set for artificial fuels.

According to information provided in Tables 5 and 6, the dwellings with the highest probability of fire entrance were H13 (87%) and H12 (63% considering no shutters). The probability value associated with H13 is quite large if we consider the values obtained for the other dwellings and that the worst value attainable using this method is 88% (see Table 6). H13 presented the highest probability of failure of the dwelling itself (99%). Vulnerable elements in the structure of H13 were the shutter material, glazing thickness and vent design. Moreover, regarding the probability of fire reaching the dwelling (POF_1), H13 had a value of 88%. This value was high because there was no compliance with the rules for management of wildland fuels in both zones and compliance was low for ornamental vegetation.

H12 had also a high probability of fire reaching the dwelling (75%) because compliance with fuel management rules was low in both zones (as can be seen in Table 5, no fuel type management section reached a compliance value of 100%). H12 presented a probability of failure of the dwelling itself of 74 or 85% (depending on consideration of shutters or not). Vulnerable elements in the H12 structure were shutter material and the presence of an SCS with a high amount of combustible fuel (the car was parked in the car shed when the fire occurred).

Of these two houses (H12 and H13) with the highest probability of fire entering, H13 suffered minor damages outside the house, while the fire entered H12. This is probably because fire behaviour was more intense and rapidly spreading in the drainage area between H11, and H12 and H14 (see elevation contours in Fig. 7). In contrast, fire was propagating more slowly in the area around H13 because it was not channelled there. Also, when the wildfire was threatening the area, people living in H12, who were at that moment inside the house, evacuated and did not close windows or PVC shutters nor placed their vehicle inside the garage. The car was located close to the porch as well as close to a window. These actions left artificial fuel (the car) available for burning and made windows more vulnerable. If evacuation had been well prepared, the probability of fire entering this house would have been lower (55% probability had the shutters been pulled down). In contrast, H13 was locked (shutters closed) because the residents were not at home that day.

This indicates that, although the house that was severely damaged was not the most vulnerable in the area, it was affected by fire owing to a badly prepared evacuation. Thus, it is important to keep in mind that houses will have a better chance of surviving a wildfire if people living in the WUI are well prepared and informed about the actions that need to be undertaken before evacuating.

Case study 2: El Pont de Vilomara, Spain (2022)

Six houses from the River Park residential development in El Pont de Vilomara, Spain, (Fig. 9) were also used to test the VAT tool. They were affected by a WUI fire that took place in July 2022 (Fig. 10), prompting evacuation orders and affecting many dwellings. Five of these houses were located on the same street, on the hilltop of Turó de Solanes (H21, H22, H23, H25, H26). Another was located further down on the same slope (H24). The main characteristics of the dwellings considered for this study are given in Table 7. These data were obtained through interviews with the homeowners performed informally after the fire, and also by inspection of photographs that were made available by the firefighters.

Fig. 9. 

Monitored properties (H21 to H26) affected by the WUI fire in El Pont de Vilomara, Spain (July 2022) (Google Earth, earth.google.com). Red line: 10 m around dwellings; yellow line: 30 m around dwellings. Green lines indicate elevation contours (Institut Cartogràfic i Geològic de Catalunya, https://www.icgc.cat/).

Fig. 10. 

Photographs of the WUI fire in El Pont de Vilomara, Spain (July 2022): (a) overview of the area after the fire; (b) H21; (c) H22; (d) H23; (e) H24; (f) H25; (g) H26. Source: S. Boixader and Bombers de la Generalitat.

The fire propagated following seawinds channelled through the Llobregat river valley. The River Park residential development was positioned over the main propagating axis of the fire that impacted on this development only 2 h after its start. Owing to the location of the residential development (i.e. on top of the hill), several dwellings received the impact of the fire simultaneously. Moreover, although there were treated fringes mid-slope (see Fig. 9), they were not effective and the fire was propagating through the pine tree crowns.

According to Table 7, all houses had double-pane glazing systems and vents. However, most of the houses did not have shutters for protecting all the windows (except H21), and combustible or non-protected vents were observed in two of the houses (H26 and H25, respectively). Roofs were in general well maintained and all, except H25, had a semi-confined space with thick and non-combustible walls connecting the house. The percentage by volume occupied by combustible material in the SCSs was lower than 50% and the largest value was observed in H26 (50%). Two houses had a very high percentage of window coverage in the SCS (80% H21 and 70% H24). Regarding fuel management in the two zones surrounding the house, it can be seen that, as for the houses presented in Table 5, there was no compliance at all with the rules for the management of wildland fuels in Zone 2. However, in Zone 1, two houses (H21 and H22) complied with these rules completely. Regarding ornamental vegetation, all properties complied with at least 44% of the rules in Zone 1. For artificial fuels, the compliance level in Zone 1 was larger than 25%.

The results obtained using the VAT model are shown in Table 8. The dwellings with the highest probability of fire entrance were H26 (81%) and H23 (67%). For the other dwellings, the estimated probability was lower than 60%.

Vulnerable elements in H26 were the unprotected glazing systems, the bad condition of the roof and the combustible vents. With regard to the probability of fire reaching the dwelling (POF_1), H26 had a value of 83%. This value was high because there was no compliance with the rules for the management of fuels in Zone 2, and the compliance was low (less than 60%) in Zone 1.

H23 presented a probability of fire reaching the dwelling (POF_1) similar to that obtained for H26, but the probability of failure of the dwelling itself was lower (81% vs 98%, respectively), resulting in a lower overall probability of fire entrance (67% vs 81%, respectively). The vulnerable elements identified for this dwelling were different, the most important being the presence of unprotected glazing systems and a moderate window coverage of the SCS (25% according to Table 7).

The fire affected H24 and H26 severely (see Fig. 10), both aligned with the slope of the terrain and next to absentee-owned parcels on two sides of the house aligned with fire propagation. According to the observed damage, the fire probably entered through breakage of the glazing systems. The results obtained with VAT showed that the probability of fire entering H24 was lower compared with H26 but still almost 60%, so we were able to determine that the degree of vulnerability of H24 was high.