The proposed methodology is explained in detail in this section, together with the assumptions that are made at each of the stages. This methodology can be applied to triggering events of different types, such as earthquakes, tsunamis, landslides, floods, and hurricanes, if data that characterize the geographical extent and distribution of hazard intensities are available. Also, the methodology is fully scalable, meaning that when data are available, it can be used at urban, subnational, and national levels.
Selection of the Event of Interest
The first stage of the proposed methodology corresponds to the selection of the triggering event. The trigger can have different origins (for example, earthquake, tsunami, flood) and can be either a historical or a future event, which, although not having yet occurred, is known to be possible in the domain under study (that is, the maximum credible event).
Data requirements for the hazard component are the footprints that describe the geographical distribution of hazard intensities and are available in terms of intensity measures that correlate well with the structural damage (for example, spectral acceleration for earthquakes; water depth for floods). With this approach, cascading events can also be considered, meaning that, for instance, if excess rainfall triggers a flood or a landslide, the damage inflicted on residential units by the different hazards can be determined. Care must be taken when considering a multihazard approach to ensure that the loss estimation considers the simultaneous participation of different hazard intensities to avoid either under or overestimations of the risk (Ordaz 2015).
Estimation of Structural Damage in the Domain Under Study
Besides the hazard data, exposure and vulnerability inputs are needed for the damage and loss estimation. Exposure databases must include attributes that characterize the structural components of each asset that is susceptible to damage due to the action of the considered hazard and that is located within the domain under study. For each of the assets, a set of attributes are described such as construction material, age, number of stories and main use, among others. These characteristics allow the definition of building classes or typologies, which group elements with characteristics in common. For the estimation of IDPs, an entry in the exposure database must reflect also their human occupancy. Even if population is a dynamic exposure parameter, since only the residential sector is considered in this methodology, the distribution of the total population among the identified buildings is required. These exposure databases can be developed at different resolution levels depending not only on the scope of the assessment and the available resources, but also on the available data.
For each of the identified building classes, a unique physical vulnerability relationship needs to be assigned for each of the hazards of interest. This determination provides a connection between different hazard intensity values and the expected damages and losses in each case.
The damage and loss assessment stage follows an event-based approach that uses the methodology proposed by Ordaz (2000). In our case, a deterministic approach is used from the temporal perspective, which considers that the event has already occurred and assigns an occurrence frequency equal to 1.0. From the damage and loss perspective, its assessment can be considered as fully probabilistic since the uncertainties related to hazard and structural vulnerability components can be quantified and propagated. The full details of the methodology are available in Salgado-Gálvez, Zuloaga-Romero, Bernal et al. (2014). The scenario-based approach has been used in other studies to validate and calibrate different components of catastrophe risk models (Salgado-Gálvez, Barbat et al. 2016; Lamego et al. 2017). Losses are calculated using the following expression:
$$\nu (l) = \sum\limits_{i = 1}^{N} { \, \Pr (L > l\left| {{\text{Event}}_{\text{i}} )} \right.} \cdot F_{A} ({\text{Event}}_{\text{i}} )$$
(2)
where v(l) is the exceedance rate for loss of loss l, N is the total number of hazard events, FA (Eventi) is the annual frequency of occurrence of the ith hazard event, and Pr(L > l|Eventi) is the probability of exceeding l, given that the ith event has occurred. When a single event approach is selected, N is equal to 1, as its occurrence frequency, FA. For the selected event, with the hazard intensities in the domain under study and for each entry included in the exposure database, the losses are calculated using the vulnerability functions assigned to each building class. This process is subsequently repeated for each entry. Once the assessment is finished, each entry in the exposure database will have associated a mean damage ratio (MDR) that will be used in the following stage.
Estimation of the Number of IDPs Because of Damage in Residential Units
The definition of IDP used in this methodology is the same provided in the introduction of the article. A person is considered as internally displaced if he or she must leave home either because of a preventive evacuation before the occurrence of the event or because the residential unit has suffered a degree of damage that makes it unsafe for immediate use. Also, it is assumed that all displacement occurs within the borders of the affected country. For the estimation of IDPs, different hazard intensity thresholds are assigned to the building classes. When these values are exceeded, it is assumed that their immediate occupation is not safe. Even if only for a matter of hours, the inhabitants cannot return to their homes and are classified as IDPs. Figure 1 shows an example of these binary relationships for the case of earthquakes and masonry units, where once peak ground acceleration (PGA) has exceeded approximately 0.2 g, all the occupants of that residential unit are considered as IDPs.
Estimation of Cleaning, Repair, and Recovery Times
FEMA (2017a, b), the Federal Emergency Management Agency, provides reference recovery times for residential units, classified into single family and multifamily structures, as a function of either hazard intensities or structural damage states. For the case of floods, these relationships are directly related to water depth, whereas for earthquakes and hurricanes they are available in terms of structural damage states. For the second case, using the MDR obtained in stage 2 (Sect. 2.2), an indicative cleaning, repair, and recovery time can be assigned to each affected building.
In the structural engineering field (on which most of the assumptions of this stage are based), qualitative damage states are widely used for the development of vulnerability models (for example, by FEMA in the United States or the RISK-UE project in Europe (Mouroux and Le Brun 2006), among others). These damage states are classified into different descriptions (usually with 4 or 5 categories) and there is no standard for their definition or classification.
In our methodology, the five structural damage states used by HAZUS (FEMA 2017b) are used, since the repair times have been chosen from that reference. Each of these damage states has a description (FEMA 2017b) and based on them, a linkage between the damage and MDRs obtained in stage 2 is made. For this linkage, values found in the disaster recovery literature can be used, which consider not only the direct physical damage but other socioeconomic and resilience factors that are known to have a relevant role in this aspect (Cardona 2001; Aijazi 2014; Pribadi et al. 2014; Mamula-Seadon 2015; Salgado-Gálvez, Zuloaga Romero, Velás1uez et al. 2016). The values used are shown in Table 1.
Table 1 Relationships between mean damage ratio (MDR) ranges and structural damage states
According to each damage state, the number of years needed for a complete recovery of each residential unit (classified into single or multifamily) is shown in Table 2. These values correspond to the proposal of FEMA (2017b) that is to date the most reliable and open data source for these purposes. These values have been calibrated with data from the United States (mainly from California after the Loma Prieta and Northridge earthquakes), and their use can be extended to other regions when no information is available. On the other hand, Fig. 2 shows an example of the recovery function based on MDR for multifamily dwellings.
Table 2 Recovery time (in years) for single and multifamily dwellings by structural damage states
Estimation of the Length Aggravating Factor Based on the Overall Damage
In addition to the estimation of the MDR for each asset included in the exposure database, as performed in stage 2 (Sect. 2.2), and used in stage 4 (Sect. 2.4) for the estimation of cleaning, repair, and recovery times, a delay factor based on the overall MDR for the whole domain under study (for example, city or country) is also introduced.
This is founded on the logic that the largest overall damage within the domain under study results in the most complicated recovery and repair process because of scarcity of construction materials and a possible demand surge for materials and labor that can exist. The delay factor values proposed in the model are shown in Table 3. The definition of these factors is subjective and aims to highlight the relevance that the demand surge may have on the length of the recovery processes. Specific values could be obtained at local or regional scale to better capture this issue after a particular event.
Table 3 Delay factors per overall MDR levels
Once the recovery time for all residential units is known, this time represents the displacement length since it is assumed that once the affected structures are safe to be used again, IDPs will return home. This is an assumption that omits cultural, social, and economic factors and incentives that cannot be modeled.
Estimation of the Number of Life-Lost Years Because of Internal Displacement
This stage performs the combination of the outcomes of stages 3, 4, and 5 (Sects. 2.3, 2.4, and 2.5). With them, the total number of life-lost years because of internal displacement (YLD), in the domain under study, is obtained. YLD is estimated in the following way:
$${\text{YLD}} = \sum\limits_{i = 1}^{N} {({\text{Recovery time}}_{i} *{\text{IDP}}_{i} ) + } \sum\limits_{j = 1}^{M} {({\text{Recovery time}}_{j} *{\text{IDP}}_{j} )}$$
(3)
where N is the number of individual units, M the number of multifamily units, IDPi the internal displaced people who inhabited individual units, and IDPj the internal displaced people who inhabited multifamily units.
Estimation of the Total Number of Employed IDPs
Using the population distribution (in ranges of at least 5–10 years), the share of those who are within the working-age range is obtained. Since working-age legal conditions can vary from place to place, the one that is applicable for the domain under study should be used. If that information is not clear, either because legislation on the topic does not exist or because its enforcement is poor, reference values such as the ones used by the OECD—those between 15 and 64 years (OECD 2018)—can be used.
This share of people is also affected by the labor force participation rate to reflect the number of people, within the working age, who are either employed or actively seeking a job. Finally, to consider only those within the labor force who are employed, the unemployment rate of the domain under study is also considered. In this case, it is assumed that the share of working-age people within the individual or multifamily dwellings is the same, so no differentiation at all is made at this point.
The estimation of this value can be performed in the same way as shown in Eq. 3, with the difference that only the share of employed IDPs is considered.
$${\text{YLD}}_{\text{employed}} = \sum\limits_{i = 1}^{N} {({\text{Recovery time}}_{i} *{\text{IDP}}_{{i({\text{employed}})}} ) + } \sum\limits_{j = 1}^{M} {({\text{Recovery time}}_{j} *{\text{IDP}}_{{j({\text{employed}})}} )}$$
(4)
Estimation of the Lost Economic Production Because of Internal Displacement
In this final stage, based on the overall YLD for the chosen event, and considering only those associated to the working-age group, the lost economic production (LEP) is estimated in the following way:
$${\text{LEP}} = {\text{YLD}}_{\text{employed}} *{\text{GDP}}_{\text{per capita}}$$
(5)
where LEP is the lost economic production based on an egalitarian principle that assumes all individuals (IDPs) contribute in the same manner to economic output. Because GDP per capita has been used as an indicator of how much each person contributes to output (GDP), it is likely an underestimation of the lost economic production occurs, since it is assumed that even those who are not within the labor force contribute something to it. For this reason, the need to explore other metrics directly related to production (for example, GDP per employed person), with emphasis on the most vulnerable population (from a socioeconomic perspective), remains.