Table 1 Description, examples, advantages and disadvantages of different types of vulnerability assessments for volcanic hazards. Note that the advantages and disadvantages refer to the example implementation of the vulnerability assessments, not the approaches themselves

Qualitative descriptions

Qualitative description of probable impacts to infrastructure based upon the presence of a volcanic hazard.

Review and documentation of critical infrastructure impacts from historic eruptions (Wilson et al. 2012a; Wilson et al. 2014).

Detailed explanation of likely impacts and vulnerabilities for each infrastructure sector, highlighting potential mitigation strategies.

No indication of the differing levels of vulnerability at a particular site.

Difficult to compare multiple locations.

No spatial extent of vulnerability.

Vulnerability indicators

Vulnerability indicators are an attribute or property of a system which influences vulnerability or resilience to volcanic hazards. The degree to which this attribute influences vulnerability can be expressed qualitatively (e.g., high, medium, low) or with numerical values that can be summed to provide an overall vulnerability value/score.

Infrastructure vulnerability indicators to assess vulnerability to volcanic hazards on Vulcano Island, Italy (Galderisi et al. 2012).

Identifies which attributes influence vulnerability and/or resilience, providing a basis for further research.

Provides relative spatial distribution of areas of different vulnerability.

Assigning qualitative descriptions or numerical values to indicators is subjective.

Difficult to have common indicators and rankings for different spatial scales and different infrastructure designs.

Impact states (IS)

Impact state scales categorise infrastructure damage or disruption into a set number of defined states, typically ranging from no damage to complete destruction. Each state is typically assigned a numerical vulnerability value such as repair cost, damage ratio (repair cost relative to replacement cost) or percentage of damage.

Damage scale for classification of tephra induced building damage following 1991 Mt. Pinatubo eruption (Spence et al. 1996).

Allows simple classification of impact into a number of states.

Highlights areas of relatively high/low vulnerability.

Provides distribution of impact states and comparison between impacted areas.

Easy to process post-eruption.

Qualitative impact descriptions do not cover all aspects of impact or infrastructure design.

Threshold levels

Similar to damage states in that impacts are categorised into a set number of states; however, in addition to the vulnerability values, each impact state is also assigned hazard intensity threshold values (e.g., tephra thickness, dynamic pressure).

Threshold level scales developed to indicate hazard intensity for each damage state for buildings and critical infrastructure (Spence et al. 2004; Jenkins et al. 2014b, Wilson et al. 2014).

Provides a relationship between impact state (i.e., damage and disruption) and hazard intensity.

Accounts for some uncertainty within vulnerability estimates through the range of hazard intensity threshold values provided.

Selected hazard intensity metrics may not be appropriate to estimate impacts for all infrastructure components.

The wide range of infrastructure design and operation characteristics influences vulnerability.

Fragility and vulnerability functions

Quantitative functions (i.e., mathematical equations).

Vulnerability functions express relative loss or economic cost to hazard intensity.

Fragility functions express the probability of a level of impact being equalled or exceeded for a given hazard intensity.

Fragility functions developed for tephra fall impacts on buildings and electrical transmission systems (Spence et al. 2005; Zuccaro et al. 2008; Wardman et al. 2012b).

Impact intensity relationship is provided as a changing probability estimate over a range of hazard intensities.

Mathematical approach accounts for some of the uncertainty associated with these assessments.

The functions can directly inform quantitative risk assessments for impact and loss estimation.

Requires large statistically valid datasets for robust correlations.

Selected hazard intensity metric may not be the most appropriate to estimate impact for all infrastructure components.

Functions are only applicable to the infrastructure typology they were derived for and may not be applicable elsewhere without modification.