The variety of methodologies and concepts regarding vulnerability in general has been highlighted and demonstrated in several publications (e.g. Fuchs et al., 2012; Papathoma-Köhle et al., 2011). The most common approaches for assessing vulnerability in general are vulnerability matrices, vulnerability curves and indicator-based approaches (Kappes et al., 2012). Vulnerability matrices provide only qualitative information on vulnerability based on descriptions of damage patterns. Regarding physical vulnerability, vulnerability curves are the most common method for assessing physical vulnerability as far as mountain hazards are concerned (Papathoma-Köhle et al., 2011). The vulnerability of buildings to natural hazards is determined by a number of attributes such as building material, size and condition (Fuchs et al., 2007; Tarbotton et al., 2015) as well as the availability of local structural protection (Holub et al., 2012). However, these attributes and their combination vary from building to building. This makes data collection a time-consuming process which requires a detailed building-to-building investigation. Consequently, decision makers and practitioners prefer to use data from past events to develop empirical vulnerability models such as vulnerability curves (Tarbotton et al., 2015). Another reason that makes vulnerability curves so popular among practitioners is that they connect directly the intensity of a process with the corresponding degree of loss, providing concrete quantitative results and translating potential events into monetary damage (Mazzorana et al., 2009). Tarbotton et al. (2015) suggest that the accuracy and reliability of the results of empirical vulnerability curves depend on a series of factors including: the survey method for the data collection, the accuracy of the data regarding the building damage as well as the building characteristics and the statistical method used for the analysis of the data. In more detail, according to the same authors, the survey method may be remote (e.g. the building damage and type may be identified by the use of ortho-photos) or on site (field survey). The remote survey methods are faster and cheaper but also inaccurate, whereas the field survey is accurate but time-consuming and expensive. Moreover, for the development of the vulnerability curves the intensity has to be expressed in a measurable way (e.g. height of deposit or impact pressure). The choice of the parameter of the intensity that will be used for its expression influences the result (Tarbotton et al., 2015). Additionally, Tarbotton et al. (2015) point out that the uncertainty of the results is increasing with the use of interpolation in order to identify the intensity of a process on individual buildings. Last but not least, the number of buildings used for the development of a vulnerability curve also influences the accuracy and validity of the results. In case of earthquakes or floods the assessment of the intensity per building is easier and the number of affected buildings is large. Intensity per building is often the product of interpolation and the structural characteristics of the buildings are ignored. In these cases, however, it is relatively uncomplicated to develop reliable vulnerability curves due to sufficient data availability. For other hazard types, such as rock falls, this is not the case since a single event affects only a limited amount of elements at risk and the assessment of the process intensity on each of them is a challenging process. Moreover, vulnerability curves do not consider the individual features of the buildings or characteristics related to their location and surroundings (Fuchs, 2009). Although they provide concrete information regarding the loss, they do not provide information concerning the drivers of vulnerability or potential ways of reducing it.

As far as debris flow is concerned, the first approaches for physical vulnerability assessment were qualitative (Fell and Hartford, 1997; Liu and Lei, 2003; Romang, 2004), including in some cases vulnerability matrices (Leone et al., 1995, 1996; Sterlacchini et al., 2007; Zanchetta et al., 2004) showing a descriptive relationship between the damage and intensity of the flow. However, recently the number of vulnerability curves for debris flows has considerably increased and several studies may be found in the literature (Fuchs et al., 2007; Papathoma-Köhle et al., 2012; Quan Luna et al., 2011; Totschnig and Fuchs, 2013; Totschnig et al., 2011). Each vulnerability curve has been developed for a specific area, is based on a particular catastrophic event and expresses the intensity of the process in various ways. For example, there are curves based on data for a small (e.g. 13 buildings in Fuchs et al., 2007) or a larger number of buildings (1560 buildings in Lo et al., 2012). In some cases, due to lack of empirical data, information on the process had to be derived through modelling (Quan Luna et al., 2011; Rheinberger et al., 2013) that expressed the flow not only as debris height but also as velocity, viscosity or impact pressure. As far as the degree of loss is concerned, relevant information could be provided in some cases by the authorities. Nevertheless, where damage data were not available, damage costs were assessed based on photographic documentation (e.g. Papathoma-Köhle et al., 2012). Last but not least, it is worth mentioning that a number of studies focus on laboratory experiments in order to determine the interaction between the flow and the structural components of the buildings (Gems et al., 2016; Zhang et al., 2016).

In contrast, shortage of empirical data often leads to the development of vulnerability indices based on the selection, weighting and aggregation of vulnerability indicators. IBMs have been used mainly for other vulnerability dimensions, such as social or economic vulnerability. However, recently a considerable number of studies are available that make use of vulnerability indicators for the assessment of other vulnerability dimensions (e.g. physical). Vulnerability indicators, according to Birkmann (2006), are “variables which are operation representations of a characteristic quality of the system able to provide information regarding the susceptibility, coping capacity and resilience of a system to an impact of an albeit ill-defined event linked to a hazard of a natural origin”. The importance of developing and using indicators has been also stressed in Hyogo Framework, by identifying, as a key activity, the development of “systems of indicators of disaster risk and vulnerability at national and sub-national scales that will enable decision makers to assess the impact of disasters on social, economic and environmental conditions and disseminate the results to decision makers, the public and populations at risk” (UN, 2007). However, using indicators to assess vulnerability (any dimension of it) may be problematic due to a number of reasons (Barnett et al., 2008). In more detail, Barnett et al. (2008) suggest that the use of vulnerability indicators and indices for national scale is less meaningful, whereas for larger scale it might lead to policy relevant results; however, it still bears many uncertainties. The same authors also stress that challenges are mainly related to the selection of indicators, their standardisation, the availability of required data, their weighting and the method of aggregation for the development of a vulnerability index, concluding that empirical investigation (e.g. vulnerability curves) may lead to better results. Nevertheless, vulnerability indicators are very often used for the assessment of social vulnerability as, for example, in the Social Vulnerability Index of Cutter et al. (2003). Regarding physical vulnerability, although vulnerability curves are more popular than vulnerability indicators, studies using indicators for assessing physical vulnerability are on the rise. Some of these studies focus only on the development of inventories of elements at risk and their characteristics (Papathoma-Köhle et al., 2007) or they make an additional step towards exposure assessment (Fuchs et al., 2015). Barroca et al. (2006) developed a vulnerability analysis tool for floods based on a system of indicators describing the elements at risks, their spatial relation, the prevention, emergency and reconstruction systems. Barroca et al. (2006) suggest that the vulnerability assessment tool is simple and flexible and can be used by different users without requiring expert knowledge for its use. Moreover, Müller et al. (2011) assessed urban vulnerability towards flood using indicators for physical and social vulnerability. Concerning physical vulnerability, four indicators were selected (construction material, building position, proportion of green spaces and local structural protection) and ranked based on expert judgement. Most of the IBMs found in the literature are applied at local scale. The study of Balica et al. (2009) is noteworthy because the selected indicators used to develop indices for flood vulnerability are available for three scales (river basin, sub-catchment and urban area). Balica et al. (2009) suggest that the IBM is powerful because it supports decision makers in prioritisation underpinning transparency. Apart from floods, physical vulnerability has been investigated with means of indicators also for other hazard types such as landslides. Silva and Pereira (2014) assess physical vulnerability of buildings to landslides based on the building resistance and the landslide magnitude. The building's resistance is determined by a number of indicators including construction technique and material, number of floors, floor and roof structure and conservation status. Last but not least, Kappes et al. (2012) developed an IBM for multi-hazard in mountain areas which is presented in detail and applied in the present study. In general, in most of the studies, indicators are weighted empirically and no validation of their selection and weighting has been implemented using the damage pattern and loss from a real event.

One of the first attempts to use indicators for the assessment of physical vulnerability was made by Papathoma and Dominey-Howes (2003) and Papathoma et al. (2003). Specifically, they developed a methodology for assessing the physical vulnerability of buildings to tsunami at coastal areas in Greece using indicators. The main concept of the Papathoma Tsunami Vulnerability Assessment Model (PTVA) was the combination of an inundation scenario with “attributes relating to the design, condition and surroundings of the building” (Tarbotton et al., 2012). The methodology was based on the fact that two buildings located exactly at the same place despite experiencing the same process intensity do not always suffer the same loss. The reason for this is the variety of building characteristics concerning the building itself and its surroundings. A number of buildings characteristics related to the damage pattern following a tsunami event were selected (indicators) and a GIS database with the buildings and their attributes was created. The indicators were weighted using expert judgement and a vulnerability index was given to each building. The result was a series of maps for a number of coastal segments in Greece showing the spatial pattern of the relative physical vulnerability of the buildings. In this way, authorities and emergency services could focus their limited resources on specific buildings rather the whole potentially inundated area. The method was later validated (Dominey-Howes and Papathoma, 2007) using data from Maldives following the 2004 Indian Ocean tsunami. The validation showed that the selected vulnerability indicators correlate well with the severity of the damage; however, recommendations for improvement led to an improved version of the method: PTVA-2. PTVA-2 was used in the USA (Dominey-Howes et al., 2010) for the estimation of the probable maximum loss from a Cascadia tsunami in Oregon (USA). The main difference to PTVA-1 was the inclusion of the water depth above ground as an attribute in the calculation of the overall vulnerability. In this way, the method became more intensity dependant than before. PTVA-3 was developed by Dall'Osso et al. (2009a) and was tested in Australia (Dall'Osso et al., 2009b) and in Italy (Dall'Osso et al., 2010). PTVA-3 made a step towards and more reliable weighting of the vulnerability indicators by using analytical hierarchy process (AHP) rather than expert judgement to weight the attributes.

The first attempt to use vulnerability indicators for mountain hazards was made by Papathoma-Köhle et al. (2007) with the development of an elements at risk database containing indicators regarding the physical vulnerability of buildings to landslides. However, due to the lack of data regarding the hazardous process itself and the limited availability of data regarding the building characteristics the study constitutes only a good basis for further research. The next attempt was made by Kappes et al. (2012), who introduced a methodology for vulnerability assessment using vulnerability indicators, e.g. characteristics of the building that are responsible for its susceptibility to damage and loss due to mountain hazards, based on the PTVA model. The methodology is presented in the following chapter. It is clear that as far as mountain hazards are concerned, there is definitely a need to improve and modify indicator-based approaches in order to be used for vulnerability assessment and as basis for risk reduction strategies.

The two methodological concepts have been always used separately rather than in combination from scientists and practitioners. A first effort to combine them has been made by Papathoma-Köhle et al. (2015). Papathoma-Köhle et al. (2015) developed a tool which uses the vulnerability curve presented in the following chapters as a core to implement three functions: updating and improvement of the curve with data from new events, damage and loss assessment for future events and damage documentation of new events. However, the tool has the possibility to include information regarding building characteristics. This provides the opportunity to investigate the correlation of damage patterns and the building characteristics in the future.

The spatial distribution of damage and intensity data used for the development of vulnerability curves is not often displayed on a map, although this would be simple with the use of GIS. The curves are mainly used as a tool that displays geographically distributed information on a xy axis system and may predict the degree of loss of a building should it experience a specific intensity. However, in the present article the spatial pattern of the intensity and the degree of loss are displayed in two maps in Fig. 6. The comparison of the results of the IBM (Fig. 8) with the intensity of the process per building of the 1987 event and the spatial distribution of the degree of loss (Fig. 6) (Papathoma-Köhle et al., 2012) shows that the results of both methods are generally compatible. The buildings that experienced a high degree of loss (Fig. 6) are often the ones with a high RVI, especially in the case of RVIVR. However, the visual comparison of the maps highlights some exceptions. Some buildings that experienced a very high degree of loss have been assigned with a low vulnerability index and vice versa. For example, the buildings in Ennewasser, which were confronted with low intensities and, for this reason, also suffered a relative lower degree of loss, were classified as highly vulnerable by the IBM. This observation highlights an important aspect of the method: the fact that the IBM is not hazard intensity specific, in contrast to the vulnerability curve method that includes information regarding the intensity. It is clear that the two approaches define vulnerability in a different way, namely as a result of intrinsic characteristics in one case (IBM) or as a consequence of a specific hazard intensity in the other (vulnerability curves). In contrast, there are buildings in Gand that, although they have experienced a high degree of loss, are assigned with a low RVI. The high degree of loss is expected since, according to Fig. 6, the same building also experienced high intensity. It is, therefore, clear that the results show inconsistencies because the intensity is not considered by the IBM. Nevertheless, some vulnerability indicators are directly connected to the intensity that a building experiences, e.g. surrounding vegetation or protection from other buildings or proximity to the road network.

By visualising the spatial pattern of the degree of loss and the observed intensity, as well as their relationship through vulnerability curves, additional valuable information regarding the importance of vulnerability indicators may become available and, in this way, the IBM may be modified, extended and substantially improved. For example, the low intensities recorded on buildings in Ennewasser may be related to the presence of surrounding vegetation, which highlights the importance of the relevant vulnerability indicator. This leads to the conclusion that both methods, although based on a different concept, shed light on two different aspects of the physical vulnerability: specifically, the intrinsic characteristics of the buildings and the expected degree of loss under a given intensity respectively; therefore, they should be used in combination rather than in conflict. Apart from the visual comparison of the results, a closer look to the results for each building in Table 2 reveals even more about the advantages and disadvantage of both methods.

In Table 2 the results of both methods are displayed for each of the 51 buildings of the case study. The comparison of the results leads to a number of interesting observations.

The RVI values vary from 0.43 to 0.88. No extreme values are observed. There are no buildings with RVI = 1. This is to be expected since there are no buildings in the area with extreme scores (e.g. material = wood or condition = ruin).

Table 3 shows that although the set of indicators fulfils many criteria, there is still room for improvement of the indicator set itself, the description and assignment of the scores for each indicator and the collection of the required data.

In contrast to the vulnerability curves, IBMs are not established and applied by practitioners in the same dimension. For this reason, the comparison between the two concepts is not only essential but also very challenging due to the different way that they approach vulnerability. However, this comparison may highlight the benefits of the IBMs, point out its weaknesses and lead to a list of recommendations not only for the improvement of the indicator-based concept but also for the improvement of the assessment of physical vulnerability in the future.

The comparison of the two methods highlighted the following benefits of using indicators for assessing physical vulnerability of buildings to torrential hazards.

Contrary to vulnerability curves, the IBM prompts the user to develop an inventory of the elements at risk and a database of building characteristics. This may enable the development of strategies for the reduction of vulnerability at a very local level, as well as the development of local structural protection measures. In this way, the focus and the resources will be concentrated on limited amount of buildings.

Based on the comparison of the two methods and the outline of the advantages and disadvantages of it as far as the assessment of physical vulnerability is concerned a number of recommendations for improvement may be made.

Reduction of data collection effort and time through the use of modern technologies (GIS and remote sensing): information regarding the surroundings or the building row is easily collected by using GIS maps and/or remote sensing where needed. For other types of information such as openings, existence of basement and building material and condition an additional field survey may be necessary. Alternative data collection methods (e.g. distribution of standardised questionnaires to the building owners) may also be introduced.

The above comparison of the two methodological concepts clearly shows that decision makers and other potential end users are actually in need of both methods during the four phases of the disaster management cycle for various reasons. An effort to place the available methodological concepts (including in this case also vulnerability matrices) within the phases of the disaster cycle has been made by Papathoma-Köhle and Ciurean (2014). Figure 9 additionally shows the importance of vulnerability assessment in every phase of the disaster cycle, highlighting the relevant methods for each phase. For example, during the mitigation phase vulnerability curves may be used for the loss estimation of future events and the design of mitigation measures. The results in this case may be used for public awareness and education as well as for recommendations for reinforcement. However, vulnerability maps based on the vulnerability indicators may guide the emergency and evacuation planning process during the preparedness phase. Additionally, during the response phase, vulnerability maps are essential to indicate the buildings that are more likely to have been damaged, whereas the recovery phase is the ideal phase for validating the weighting of indicators. Moreover, during the recovery phase the results of the vulnerability assessment may be used as guidance for relocation of buildings. The centre of the disaster management cycle consists of an information pool including two types of data: empirical data from past events and an inventory of the elements at risk and their characteristics. The exchange of information between the pool and the different phases of the disaster cycle is also demonstrated in Fig. 9 through the black arrows.

In short, decision makers, authorities and disaster managers need a quantitative representation of physical vulnerability based on empirical data (curves) as well as relative vulnerability values for individual elements that are directly connected to their characteristics (indicators) and may support prioritisation of resources and small local interventions for vulnerability reduction. The fact that both approaches are significant stresses the need for a “holistic physical vulnerability framework for practitioners” that will enable practitioners not only to choose the relevant method according to their aim and the available resources but also to make full use of the fact that they both complement each other.

The interactions and possibilities for combination of the approaches should be included in a “holistic physical vulnerability framework for practitioners” (Fig. 10).

The framework consists of two major parts. The left one represents the empirical, ex post part, following the occurrence of a debris flow, and the right one is the ex ante part referring to the time period before a hazard occurs. The left part is connected to the use and development of vulnerability curves and the right one relates to the use of IBMs. Between them there are two main exchange possibilities, namely the updating of indicators and the refinement of their weighting through information derived from empirical data. In other words, based on empirical data of real events new indicators may be identified and the weighting of existing ones may be improved since damage data provide information on the interaction of buildings and natural processes and the role that structural characteristics may play as far as the consequences are concerned. On the right side, the framework lists the vulnerability indicators in several categories, recognising that some of them are closely connected to the intensity, such as the surroundings and the building row towards the river or towards the slope. A group of indicators related to resilience is also added. The challenge of involving the intensity of the process in the IBM is also tackled by introducing a “scenario” based on data provided from the empirical side of the framework. The scenario may be based on a specific past event and it should include information regarding not only the debris height per building but also the direction of the flow and, ideally, the impact pressure or the velocity of the flow. This is the first “interaction” between the two sides (1). Information on the intensity of the event is also used to inform the group of indicators related to the intensity (2). The scores of the variables for each indicator will be formed according to the scenario as it is indicatively demonstrated in Table 4. In the same way, exchange of information is necessary in the other direction. Information regarding the buildings is also needed for the development of a vulnerability curve since data concerning the size and the value of the building are necessary for the calculation of the degree of loss (3). By using a specific scenario, the calculation of the IBM is not anymore intensity independent and the prediction capability of the method increases. Moreover, in contrast to the curves, additional information on the process, such as the flow direction, may be used.

The framework of Fig. 10 could be further improved by including more detailed information about their weighting and their aggregation to an index, possibilities for the identification of uncertainties and their quantification, as well as the consequences of change (climate and socioeconomic to both sides of the framework).