**4. Risk models**

#### **4.1. Risk modeling of natural hazards in the cities of Iquique, Puerto Montt, and Puerto Varas**

To comply with the stated objective, four assessment models were run to deliver a synthetic index (DRI) of disaster risk level of each single city block under study.

#### **4.2. Construction of thresholds**

With the configuration of a proportional metric with AM, it was feasible to mathematically construct theoretical thresholds representing the measurement scales of each model. The thresholds were built using the scales of the terminal criteria as information basis, also known as transformation functions, and their corresponding weights. It should be clarified that the assigning of weights to the strategic criteria, as well as to the measurement scales, reflect the national and local realities regarding this subject.

The thresholds help to establish points of reference or classification of each model according to their level of vulnerability to natural hazards. Thus, it can be seen that they do not corre‐ spond to ranges of uniform size; on the contrary, they are measures that seek to represent reality in the best possible way.

Next, the four multi‐criteria models on the AHP platform (Hazard, Exposure, Social Vulner‐ ability and SR), all in AM mode are presented below. The weighting of the criteria of each model can be seen in brackets to the right of each criterion.

#### **4.3. Hazard models (H)**

The exposure variable (E) is weighted by the hazard, as it does not exist if there is no population or its belongings exposed. Thus, its magnitude depends on the relevance of the phenomena as well as the possible social impact it may have, two components of risk that are closely related.

176 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

**•** Laura Acquaviva, architect, specialist in disaster recovery processes, PNUD consultancy. **•** Fabiola Barrenechea, geographer, Risk Management Department, National Emergency.

**•** Miguel Contreras, specialist in social geography, Assistant Professor of the Geography

**•** Consuelo Cornejo, psychologist, Civil Protection Office Head of the National Emergency

**•** Edilia Jaque, specialist in disasters risk reduction issues, Deputy Dean of the Faculty of

**•** Jorge Ortiz Véliz, Associate Professor for the Geography Department at Universidad de

**•** Silvia Quiroga, geographer, consultant in risk management issues at OFDA/USAID,

**•** Jessica Romero, geographer, evacuation programs area, National Emergency Office

**4.1. Risk modeling of natural hazards in the cities of Iquique, Puerto Montt, and Puerto**

To comply with the stated objective, four assessment models were run to deliver a synthetic

With the configuration of a proportional metric with AM, it was feasible to mathematically construct theoretical thresholds representing the measurement scales of each model. The thresholds were built using the scales of the terminal criteria as information basis, also known as transformation functions, and their corresponding weights. It should be clarified that the assigning of weights to the strategic criteria, as well as to the measurement scales, reflect the

Architecture, Urbanism and Geography at the Universidad de Concepción.

The four models were adapted from the Castro‐Correa doctoral study (2014).

index (DRI) of disaster risk level of each single city block under study.

**3.4. Specialists consulted**

Office (ONEMI).

Office (ONEMI).

(ONEMI).

**4. Risk models**

**4.2. Construction of thresholds**

national and local realities regarding this subject.

**Varas**

The specialists consulted for the evaluation were:

Department of Universidad de Chile.

Chile, specialist in urban geography.

professor at Universidad Nacional de Cuyo.

Two different models were run for the cities located in different geographical locations, as geological positions and morpho‐climates influence the existence of certain types of hazards. A model of hazards for Iquique (HI), a city located at a zone corresponding to a coastal desert area, and one for Puerto Montt and Puerto Varas (HP), cities located in the southern rainy and cold region, were defined. Next, the adjustments carried out in each (HI) and (HP) are explained (**Table 1** and **Table 2**).


**Table 1.** Criteria definition table for the model of hazards in the city of Iquique (HI).


**Table 2.** Criteria definition table for the model of hazards in the cities of Puerto Montt and Puerto Varas (HP).

#### **4.4. Hazard model for the city of Iquique (HI)**

In the model Hazards Iquique (HI), the geological hazards with a weight of 77.8% outweigh the weather hazards (22%) due to the low rainfall experienced in the city. The seriousness of the geological hazards, earthquakes and tsunamis, is the reason for their importance (46.7%) in comparison to all other hazards considered for the city. The model rates the importance of geological hazards at 46.7% in comparison with other hazards, mainly because of the serious‐ ness of earthquakes and tsunamis in Iquique.

#### **4.5. Hazard model for the cities of Puerto Montt and Puerto Varas (HP)**

In this case of HP, the geological hazards (67.1%) exceeded the climatic ones (32.9%), but the difference between the two is not as great as in the case of Iquique. The city of Puerto Varas is not located in the coastal zone and Puerto Montt is protected from large tsunamis, so the main geological hazard is the seismic one (44.2%). Another hazard of geological origin, volcanoes, is weighted low (17.6%), as it is only present in the form of ash fall and not lava or lahars (**Table 2**).

#### **4.6. Exposure model for the three cities (E)**

Climatology Hazards due to precipitation

Geology Geological hazards Tsunami Hazards due to Tsunami

Seismic acceleration Acceleration of soil

Volcanism Volcanism hazards due to ash fall

**4.4. Hazard model for the city of Iquique (HI)**

ness of earthquakes and tsunamis in Iquique.

Floods1 Flooding hazards due to raining waters Floods2 Flooding hazards due to river overflow

Seismicity Sesimic hazards due to earthquakes over six in magnitude scale

178 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

**4.5. Hazard model for the cities of Puerto Montt and Puerto Varas (HP)**

**Table 2.** Criteria definition table for the model of hazards in the cities of Puerto Montt and Puerto Varas (HP).

In the model Hazards Iquique (HI), the geological hazards with a weight of 77.8% outweigh the weather hazards (22%) due to the low rainfall experienced in the city. The seriousness of the geological hazards, earthquakes and tsunamis, is the reason for their importance (46.7%) in comparison to all other hazards considered for the city. The model rates the importance of geological hazards at 46.7% in comparison with other hazards, mainly because of the serious‐

In this case of HP, the geological hazards (67.1%) exceeded the climatic ones (32.9%), but the difference between the two is not as great as in the case of Iquique. The city of Puerto Varas is The model for E is a fairly simple one and consists of four criteria or variables that allow measuring exposure of people and their livelihoods to the hazards defined in the previous model. The criteria are: Population, Housing, Critical Facilities, and Productive Activities (**Table 3**).


**Table 3.** Criteria definition table for the model of exposure (E).

#### **4.7. SR model for the three cities (SR)**

The next model measures the population's SR. This corresponds to measuring the perception of the population's possibility of facing adverse events, specifically to evaluate their resilience capabilities. As resilience mitigates risk, the model operates in the opposite direction of risk, which explains the use of SR as (1‐SR), a risk modulator, in Eq. (1) (**Table 4**).

Self‐management perception People's perception about their own preparation, formal knowledge, and confidence in local government to face adverse events


**Table 4.** Criteria definition table for the model of subjective resilience (SR).

When reviewing the model, it is possible to verify that the two variables or criteria most important to measure the subjective perception of the population are: the level of preparation of the population to face these events (30.2%) and the level of acceptance of the situation (18.1%). Slightly less importance was given to the level of formal knowledge (formal education) (15.1%), which was valued equivalent to the level of confidence that exists for local institutions (15.1%) to face extreme situations.

#### **4.8. Prevalent social vulnerability model for the three cities (PSV)**

Self‐management perception People's perception about their own preparation, formal knowledge, and confidence in

Degree of confidence of people in the local authorities

When reviewing the model, it is possible to verify that the two variables or criteria most important to measure the subjective perception of the population are: the level of preparation of the population to face these events (30.2%) and the level of acceptance of the situation (18.1%). Slightly less importance was given to the level of formal knowledge (formal education) (15.1%), which was valued equivalent to the level of confidence that exists for local institutions

Level of attachment to material goods (perception) when facing adverse events

Self‐protection perception People's perception about their own responsibility, concerns, acceptance, and attachment to material goods to face adverse events

local government to face adverse events Preparation Level of preparation of people to face adverse events (perception)

Formal knowledge Formal knowledge about how to face adverse events

180 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

Responsibility Level of responsibility (perception) to face adverse events

**Table 4.** Criteria definition table for the model of subjective resilience (SR).

(perception) to face adverse events

Confidence in local government

Attachment to material

goods

Acceptance Level of acceptance

(15.1%) to face extreme situations.

The model of PSV is the most complex one and is linked to the non‐subjective prevailing vulnerability, that is, the vulnerability of the population before the occurrence of an extreme event that responds to the factors identified in the model (**Table 5**).


**Table 5.** Criteria definition table for the model of social vulnerability.

The two most important criteria are residential vulnerability (42.3%) and socio‐demographic vulnerability (35.9%). On the other hand, the most relevant criteria or measuring indicators within socioeconomic vulnerability is unemployment (12.4%). Within residential vulnerabil‐ ity, it is the substandard housing (12%), the number of families per dwelling (10.3%), and overcrowding (8.2%), whereas in socio‐demographic vulnerability, the most relevant criteria include physical‐motor disability (9.5%) and intellectual disability (6.2%). These six indicators account for almost 60% of the total weight of the 20 indicators that make this model, demon‐ strating its importance as factors that explain the PSV.
