**3. Methodology**

The methodology for this study is a multi‐model approach with four models, each one based in the AHP (Saaty, 1980, 1996), with the goal of assessing disaster risk in a holistic view. This method uses hard data and expert opinion, and provides its own evaluations (based on their knowledge and experience) to obtain the relative weights of the criteria. Through a mathe‐ matical process known as hierarchy superposition, the model obtains the value for each alternative using a rating scale (absolute measurement (AM)). The alternatives correspond to the city blocks,2 and the values correspond to the level of hazard, exposure, and vulnerability.

The process described above allowed us to build a comprehensive index for disaster risk (Disaster Risk Index (DRI)) at block level with four different AHP models (hazards, exposure, prevailing social vulnerability (PSV), and subjective resilience (SR)).

The four models were applied to the three Chilean cities: Iquique (located in the north of Chile), Puerto Montt, and Puerto Varas (both located in the South of Chile). The analysis of the cities was performed at block level, ranking them according to the level of risk, considering the hazards (hazards and exposure), and the social dimension (vulnerability and resilience). This method allowed the study of the functional interactions between the disaster risk components (hazard and social dimension) and its overall impact on the system. The recurring spatial patterns of risk in the study area were evaluated through this multi‐model scheme in order to determine the factors that explain the increase of fragility.

The assessment based on the DRI is the result of four evaluation models, namely:

H: Hazard (in negative terms)

E: Exposure (in negative terms)

PSV: Prevailing social vulnerability (in negative terms)

SR: Subjective resilience (in positive terms and acting as a general modulator as an indicator of resilience).

When these four elements are present in a specific order of magnitude, we face a possible disaster.

The outcomes of the four models are synthesized into one to reveal the final value of disaster risk. The values obtained from the four models (which belong to absolute ratio scale) are combined in a way that is mathematically correct. Accordingly, the values of each model have to be commensurate with the values of each of the other models considered.

To accomplish that, the system is divided into two parts or associated functions intrinsically related: H (for hazard) and E (for exposure) on the one hand, and PSV (for PSV) on the other. First, we need to commensurate H with E, by weighting the importance of H and E with the parameters of weight "h" and"e", using "hH+eE". Then, weighted sum of both parts (hazard and exposure from one side with vulnerability from the other) is calculated as: α<sup>1</sup> (hH + eE + HE) + α2 (PSV). With: α1: the importance of hazard and exposure, and α2: the importance of the PSV. Of course, h + e = 1.0 and α1 + α<sup>2</sup> = 1.0. Then, a modulation by (1‐SR) over the result of both parts is performed.

It is important to note that SR operates in positive terms, it signifies a value for "capacity of self‐protection" or "existing resilience" in the population considered in the study.

Thus, the final expression for DRI is presented as:

<sup>2</sup> A block is an urban space built or intended for building, bounded by streets on all sides.

Disaster Risk Assessment Developing a Perceived Comprehensive Disaster Risk Index: The Cases of Three Chilean Cities http://dx.doi.org/10.5772/62994 173

$$\text{DRI} = \left\{ a\_1 \left( hH + eE + H^\*E \right) + a\_2 \left( PSV \right) \right\} \, ^\ast \left\{ 1 - SR \right\} \tag{1}$$

It should be noted that the values of the weights: h, e, α1, α<sup>2</sup> depend on each situation (of the case study).

The weights (h, e) and (α1, α2) were obtained using expert opinion, comparing first the importance of H with E, then the importance of pair (H, E) with PSV. This comparison has to be performed for each location. Also, h, e, α1, and α<sup>2</sup> represent the values that allow us to add the different absolute scales of measurement involved in EQ1 (hazard and exposure repre‐ sented by H and E, and social vulnerability represented by PSV).

*Note: The theoretical case of "SR" = 1 (100% capacity for self‐protection or resilience), then DRI = 0, (no risk of disaster), irrespective of the values of hazard or exposure.*

In parallel, theoretical thresholds were calculated for each model and then combined using EQ1, giving an evaluative threshold for a general qualification. The levels to compare the different output values obtained for DRI are: high risk of disaster, medium‐high risk, medium‐ low risk, and low risk of disaster. Each level with a threshold number is built from the local scales of measurement of each model (H, E, PSV, SR) and synthesized using EQ1.

The weighting values of H and E (pair‐comparing hazard with exposure) is: h= e= 0.5. This means that hazard and exposure are equally important in the three cities or cases of study.

The weighting values of hazard and exposure with respect to PSV for the three cities are:

*City of Iquique*: The weighting value for hazard and exposure is 67% and PSV is 33%. This implies that one unit of H and E is twice more important than one unit of PSV.

*City of Puerto Montt and city of Puerto Varas*: The weighting value for hazard and exposure is 58% and PSV is 42%. This implies that one unit of H and E is 1.38 times more important than one unit of PSV.

A complete explanation of these values (the weights of the models for each city) is given later in "Degree of consistency of decision‐makers in comparisons."

#### **3.1. Model criteria**

alternative using a rating scale (absolute measurement (AM)). The alternatives correspond to

The process described above allowed us to build a comprehensive index for disaster risk (Disaster Risk Index (DRI)) at block level with four different AHP models (hazards, exposure,

The four models were applied to the three Chilean cities: Iquique (located in the north of Chile), Puerto Montt, and Puerto Varas (both located in the South of Chile). The analysis of the cities was performed at block level, ranking them according to the level of risk, considering the hazards (hazards and exposure), and the social dimension (vulnerability and resilience). This method allowed the study of the functional interactions between the disaster risk components (hazard and social dimension) and its overall impact on the system. The recurring spatial patterns of risk in the study area were evaluated through this multi‐model scheme in order to

SR: Subjective resilience (in positive terms and acting as a general modulator as an indicator

When these four elements are present in a specific order of magnitude, we face a possible

The outcomes of the four models are synthesized into one to reveal the final value of disaster risk. The values obtained from the four models (which belong to absolute ratio scale) are combined in a way that is mathematically correct. Accordingly, the values of each model have

To accomplish that, the system is divided into two parts or associated functions intrinsically related: H (for hazard) and E (for exposure) on the one hand, and PSV (for PSV) on the other. First, we need to commensurate H with E, by weighting the importance of H and E with the parameters of weight "h" and"e", using "hH+eE". Then, weighted sum of both parts (hazard and exposure from one side with vulnerability from the other) is calculated as: α<sup>1</sup> (hH + eE + HE) + α2 (PSV). With: α1: the importance of hazard and exposure, and α2: the importance of the PSV. Of course, h + e = 1.0 and α1 + α<sup>2</sup> = 1.0. Then, a modulation by (1‐SR) over the result

It is important to note that SR operates in positive terms, it signifies a value for "capacity of

self‐protection" or "existing resilience" in the population considered in the study.

A block is an urban space built or intended for building, bounded by streets on all sides.

to be commensurate with the values of each of the other models considered.

The assessment based on the DRI is the result of four evaluation models, namely:

prevailing social vulnerability (PSV), and subjective resilience (SR)).

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

determine the factors that explain the increase of fragility.

PSV: Prevailing social vulnerability (in negative terms)

H: Hazard (in negative terms) E: Exposure (in negative terms)

of both parts is performed.

Thus, the final expression for DRI is presented as:

of resilience).

disaster.

2

and the values correspond to the level of hazard, exposure, and vulnerability.

the city blocks,2

To build the comprehensive DRI, there was a need for adjustments to address the specificities of the hazards present in each city. These adjustments were made in the hazard model, as Iquique (city in the north of Chile) faces substantially different hazards from those found in the cities of Puerto Montt and Puerto Varas (cities located in the south of Chile), as will be explained later in this chapter.

#### **3.2. Criteria and subcriteria weights**

To determine the weights of each variable used, an expert enquiry was made with specialists in the area (listed below). This was performed through a pair‐comparison matrix taking its principal eigenvector as the representative of their priorities (which correspond to their metric of preferences), accompanied with the consistency index of their comparisons (which corre‐ spond to the consistency of that metric).

The four models obtained represent the consensus of these opinions, which were statistically acceptable with a high level of consistency for the four constructed models (exposure, hazard, prevalent social vulnerability, and SR). The consistency, according to this method, indicates that it is a possible measure to be used numerically and its compliance can work numerically with these figures (this rule constitutes a stable measure). The index measures the degree of coherence among the answers of each actor and experts involved in the pair‐comparison process.

#### **3.3. Degree of consistency of decision makers' comparisons**

Once sorted and entered, the answers in the different models, the level of consistency of answers was checked, grouped by pair‐wise comparison matrix, using the formula by Saaty (1980) for consistency:

$$\begin{aligned} \text{CI} &= \left[ \left( \lambda\_{\text{max}} - n \right) / \left( n - 1 \right) \right] \\ \text{RC} &= \text{CI} / \text{RI} < 0.1 \text{(10\%)} \end{aligned} \tag{2}$$

Where:

CI = consistency index

λmax = highest eigenvalue in comparison matrix (associated with the principal eigenvector)

n = dimension of the comparison matrix

RI = random index of consistency (Saaty, 1980)

RC = ratio of consistency

In cases where the consistency ratio exceeds numeral 0.1 (10%), the response is discarded.

Note: In general, 10% is the value corresponding to the threshold of acceptability of inconsis‐ tency. But, if the pair‐comparison matrix is a 3 × 3 matrix, the numeral should not exceed 5%.

Overall results for consistency:

Hazard model (H): 0% = 100% consistency

Exposure model (E): 2% = 98% consistency

Subjective resilience model (SR): 3% = 97% consistency

Non‐subjective prevalent vulnerability model (PSV): 3% = 97% consistency

Expert judgments provide a high level of confidence to the construction of models and their interpretation (completeness and accuracy in assessing the importance(s)). Using the judg‐ ments, arranged in pair‐wise comparison matrix for each level of the hierarchy, and the mathematical operator eigenvector, the AHP methodology delivery priorities are outlined in the four models: SR, prevalent social vulnerability, hazard, and exposure.

principal eigenvector as the representative of their priorities (which correspond to their metric of preferences), accompanied with the consistency index of their comparisons (which corre‐

The four models obtained represent the consensus of these opinions, which were statistically acceptable with a high level of consistency for the four constructed models (exposure, hazard, prevalent social vulnerability, and SR). The consistency, according to this method, indicates that it is a possible measure to be used numerically and its compliance can work numerically with these figures (this rule constitutes a stable measure). The index measures the degree of coherence among the answers of each actor and experts involved in the pair‐comparison

Once sorted and entered, the answers in the different models, the level of consistency of answers was checked, grouped by pair‐wise comparison matrix, using the formula by Saaty

( )( )

λmax = highest eigenvalue in comparison matrix (associated with the principal eigenvector)

In cases where the consistency ratio exceeds numeral 0.1 (10%), the response is discarded.

Note: In general, 10% is the value corresponding to the threshold of acceptability of inconsis‐ tency. But, if the pair‐comparison matrix is a 3 × 3 matrix, the numeral should not exceed 5%.

Expert judgments provide a high level of confidence to the construction of models and their interpretation (completeness and accuracy in assessing the importance(s)). Using the judg‐

/ 0.1 10%

=−−

λ

= <

*CI n n max*

( )

*RC CI RI* (2)

/ 1

spond to the consistency of that metric).

**3.3. Degree of consistency of decision makers' comparisons**

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

process.

Where:

(1980) for consistency:

CI = consistency index

RC = ratio of consistency

Overall results for consistency:

Hazard model (H): 0% = 100% consistency Exposure model (E): 2% = 98% consistency

Subjective resilience model (SR): 3% = 97% consistency

Non‐subjective prevalent vulnerability model (PSV): 3% = 97% consistency

n = dimension of the comparison matrix

RI = random index of consistency (Saaty, 1980)

The variable for SR was obtained through surveys on social perception of a representative sample of the resident population in each of the cities. However, as the surveys do not allow generalization of the results to the entire block, they cannot be represented spatially as the other variables of vulnerability. Thus, our study does not produce SR mapping. The value of SR in our study represents the city as a whole.<sup>3</sup>

SR is of great importance for the development of prevention plans that promote the strength‐ ening of a self‐care culture and social participation in risk management in the community, where citizens feel responsible for reducing susceptibility conditions and taking action together with the responsible institutions.

The National Risk Reduction Platform created in Chile by the National Emergency Office of the Ministry of Inner Affairs in May 2013 also targets this objective, recognizing the role of the population in disaster risk management. The Platform is aware that the downward trend observed in the loss of human life in recent extreme events experienced in Chile is mainly due to people's actions that have incorporated the experience of past generations for their protec‐ tion.

SR measured through perception is a continually changing variable, influenced by factors such as age, knowledge, experience, gender, education level, and cultural factors.

For this reason, SR has been incorporated into the model as a modulator element of the existing level of risk. The values for hazard, exposure and PSV have been weighted by the value calculated for SR.

The H and E modules are considered the most important dimensions in the shaping of the overall risk indicator. In the case of Iquique, 67% of relevance is assigned for H and E due to the geographical location of the city in an area subject to particularly dangerous phenomena such as earthquakes and tsunamis. However, the scale or measurement model of the PSV was assigned 33% importance. This result could be explained by the fact that most of the vulnerable populations are mainly located outside the area of higher risk.

In the case of Puerto Montt and Puerto Varas, even though H and E continue to be the most relevant dimensions, the weighting assigned to them is lower (58%) as tsunami is not a significant hazard in this geographical zone. Vulnerability is assigned 42% weight, an impor‐ tant problem in the cities with many socially fragile zones, usually associated with old informal settlements consolidated within urban areas.

<sup>3</sup> The subjective resilience that measures the social risk perception is a dynamic condition which depends upon many factors. For this reason, and due to the fact that in this case it is a result of a survey applied to a percentage of the population, it was measured through an index that represents the city's population generalized perception in a specific determined time, and which allows to establish relationships based upon the other criteria considered to assess risk. Thus, a sensibility analysis has been generated to assess the prevalence of this dimension over the final result of the DRI.

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.

#### **3.4. Specialists consulted**

The specialists consulted for the evaluation were:


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