**2.1 Threat analysis**

*Forecasting Volcanic Eruptions*

individualize them [5–7].

the areas of affectation [10].

so it is necessary to make a permanent and specific follow-up to each one, because although it is true there are some features common to all, there are others that

It is also important to investigate the history of each volcano through the identification, petrographic analysis, and dating of its multiple pyroclastic deposits, to determine the characteristics that typify them [8, 9]. With this information and other knowledge, it is possible to elaborate, for example, maps of volcanic threats, which although they do not allow to determine when the next eruption will be, if they allow to determine an approximate order of the magnitude of the event and of

In fact, in the world, there are very few experiences of studies oriented to the integral evaluation of risk in the face of natural hazards. So much so that in the case of volcanic risk, most of the scientific-technical and economic efforts have been oriented mainly toward the evaluation of threats, with few methodological considerations for the evaluation of vulnerability and much less of the risk [11]. In other cases, the threat and vulnerability are evaluated independently, which logically presents many difficulties for the integral risk assessment. It is also easy to verify that many of the studies called "vulnerability assessments" are only physical and functional characterizations and diagnoses of vital infrastructure and population [12–14]. These characterizations can hardly be interpreted in terms of georeferenced indexes and/or maps of vulnerability that represent the spatial and temporal exposure of the elements exposed to each threat, much less that they represent the intrinsic and extrinsic response capacities of these elements compared to the threats. What is required, then, is to define to whom and to what this event could affect, its degree of vulnerability to the threat, and the level of risk to which it is subjected,

as basic inputs for decision-making and comprehensive risk management.

the former Colombian Institute of Geology and Mining [17].

natural disasters but political and management disasters."

**2. New conceptual approach**

In this chapter of book, in light of the process of "Systemic Parametrization of the Environmental Dimension" [15], a summary of the conceptual and methodological approach developed by the undersigned is presented through the PIGA Group for Research in Politics, Information, and Management Environmental of the Universidad Nacional de Colombia, to carry out the studies and analysis of vulnerability and risk in a sector of the area of influence of the Cerro Machín volcano [16], taking as a starting point the study of the volcanic threat previously advanced by

Finally, some general conclusions and recommendations are presented with the hope that this new approach constitutes another grain of sand in the difficult task of protecting human beings and their environment from natural threats, particularly from volcanic threats, all through of an integral management of the risk that evaluates and anticipates the threats in a timely manner, that adequately plans and budgets the policies, strategies, instruments, and protocols to be followed in front of them, and that responds with effectiveness against the handling of emergencies and contingencies. In any case, it is expected to understand that "there are no

Traditionally, the definition of risk (R) refers to the probability that something harmful will happen on a given element [18]. The simplest conceptual expression to express the risk has been R = A. V, where A is the threat, understood as a latent condition derived from the probability of occurrence of a physical phenomenon of natural, socio-natural, or anthropic unintentional origin that it can cause damage to the element or group of exposed elements, and V is the vulnerability, understood as

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Consistent with [18, 19], the threat represents the potential for damage of a natural phenomenon and is calculated by quantifying the energy that is applied to a particular site of interest or unit of analysis.

For the purposes of this study, it is assumed that the energy of a threat (as well as that of an environmental impact) can be represented qualitatively according to its intrinsic characteristics of probability of occurrence, intensity, duration, extension, accumulation, synergy, etc. [20], and, therefore, the quantification of this energy is done by means of an index that represents dimensionally and under the same scale the intrinsic characteristics of the different volcanic threats considered.

Consequently, taking as reference, the equation model that calculates the intrinsic importance in environmental impacts [20], the intrinsic threat index (Å) is calculated for each threat j of each analysis scenario based on its main intrinsic characteristics as shows in Eq. (1):

$$\stackrel{\circ}{\mathbf{A}}\_{\rangle} = \mathbf{P}\left(\mathbf{0}, \mathbf{6}, I\_{\rangle} + \mathbf{0}, \mathbf{2}, D\_{\rangle} + \mathbf{0}, \mathbf{1}.E\_{\rangle} + \mathbf{0}, \mathbf{1}.A\_{\rangle}\right) \tag{1}$$

where Å is the intrinsic threat index, P is the probability of occurrence, I is the intensity of the threat, D is the duration of the threat, E is the extension of the threat, and A is the accumulation of the threat.

For the qualitative assessment of each of the characteristics that determine the intrinsic threat index, the environmental impact assessment model is taken as a reference [20], and **Table 1** is generated where the different assessment categories are proposed.


#### **Table 1.**

*Valuation of the intrinsic threat index***.**

#### **2.2 Vulnerability analysis**

For the purposes of this study, vulnerability will be associated with the ability of an element or group of elements not to be totally or partially damaged by the impact of a threat [21]. Conceptually, it will be a function of the degree of spatial and temporal exposure, and of the intrinsic and extrinsic response capacity of the exposed elements.

In order to be able to mathematically integrate the intrinsic threat index (Å) with the vulnerability values, with the help of the Excel tool and after successive tests with field information, Eq. (2) is generated and adjusted for the vulnerability index (V), which is calculated for each exposed element i against each threat j, as described below:

$$V = \text{SE.TE.} \left(\mathbf{1} - IR\mathbf{C}\right)^{\mathbf{1} \cdot \mathbf{x}.\text{ERC}} \tag{2}$$

where V is the vulnerability index, SE is the space exhibition, TE is the temporary exhibition, IRC is the intrinsic response capacity, ERC is the extrinsic response capacity, and α is the form coefficient used in the adjustment of the family of curves corresponding to the vulnerability Eq. (2) (see **Figure 1**).

For the qualitative assessment of each of the characteristics that determine the vulnerability index, **Table 2** is generated, where the different assessment categories are proposed.

#### *2.2.1 The intrinsic response capacity (IRC)*

For the purposes of this study, the intrinsic response capacity (IRC) will be understood as an index that represents dimensionally the capacity of each exposed element (ecosystem, constructed, population) to react and/or physically resist the impact of a threat and/or recover later by itself from the affectation caused.

The IRC is based on the concept of resilience, whose definition of the term comes from the field of physics, referring to "the ability of a material to recover its original form after having been subjected to high pressures," and that in its broadest sense, it is described as "elasticity" [11]. Later, due to multiple similarities and analogies, the concept of resilience extended to the field of natural and social systems but, in any case, always denoting "the degree to which a system recovers or returns to its previous state before the action of an external stimulus" [12].

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factor.

**Table 2.**

*Assessment of the vulnerability index.*

and services [16, 20].

*Toward a New Conceptual and Methodological Approach for the Integral Evaluation…*

Consequently, the IRC will depend on each type of threat in particular and will be calculated independently for each element exposed based on a weighted assess-

> \_\_\_\_\_\_\_\_ ∑*Pn*.*Wn Pnm*á*<sup>x</sup>*

where IRC is the intrinsic response capacity, Pn is the evaluation of attributes according to characteristics of each exposed element, and Wn is the weighting

The intrinsic ecosystem response capacity (ICRe) is defined as the capacity of an ecosystem to react and physically resist the impact of a threat and subsequently recover by itself from the damage caused. It depends on each type of threat in particular and can be calculated independently for each exposed element of the ecosystem (rivers, páramos, forests and stubble, pastures, and crops) based on a weighted assessment of descriptors and attributes related to the environmental state of the ecosystems, in terms of quantity, quality, and ecological availability of environmental goods and services, and the degree of intervention or anthropic pressure, in terms of the use and deterioration caused on said environmental goods

The intrinsic response capacity of constructed elements (IRCc) is defined as the capacity of a constructed element to physically resist the impact of a threat and to maintain its functionality after the affectation received. It depends on each type of threat in particular and can be calculated for each exposed constructed element (buildings, roads, infrastructures) based on the weighted assessment of descriptors and attributes related to their physicochemical characteristics such as construction material (from the structure, elements, base, subbase), the structure (type, mezzanines, anchors), the roof (type of roof), the covering (type of covering), the rolling (rolling layer), the terrain (ground, slope), drains (quantity and condition of drainage works), and general condition (age, conservation, damage) [5, 14, 16].

(3)

ment of attributes, according to the generic Eq. (3):

*IRC* =

*DOI: http://dx.doi.org/10.5772/intechopen.84415*

**Figure 1.** *Family of curves in the vulnerability equation (V).*

*Toward a New Conceptual and Methodological Approach for the Integral Evaluation… DOI: http://dx.doi.org/10.5772/intechopen.84415*


#### **Table 2.** *Assessment of the vulnerability index.*

*Forecasting Volcanic Eruptions*

**2.2 Vulnerability analysis**

described below:

are proposed.

For the purposes of this study, vulnerability will be associated with the ability of an element or group of elements not to be totally or partially damaged by the impact of a threat [21]. Conceptually, it will be a function of the degree of spatial and temporal exposure, and of the intrinsic and extrinsic response capacity of the exposed elements. In order to be able to mathematically integrate the intrinsic threat index (Å) with the vulnerability values, with the help of the Excel tool and after successive tests with field information, Eq. (2) is generated and adjusted for the vulnerability index (V), which is calculated for each exposed element i against each threat j, as

*V* = *SE*.*TE*.(1 − *IRC*)1+∝.*ERC* (2)

where V is the vulnerability index, SE is the space exhibition, TE is the temporary exhibition, IRC is the intrinsic response capacity, ERC is the extrinsic response capacity, and α is the form coefficient used in the adjustment of the family of curves

For the qualitative assessment of each of the characteristics that determine the vulnerability index, **Table 2** is generated, where the different assessment categories

For the purposes of this study, the intrinsic response capacity (IRC) will be understood as an index that represents dimensionally the capacity of each exposed element (ecosystem, constructed, population) to react and/or physically resist the impact of a threat and/or recover later by itself from the affectation caused. The IRC is based on the concept of resilience, whose definition of the term comes from the field of physics, referring to "the ability of a material to recover its original form after having been subjected to high pressures," and that in its broadest sense, it is described as "elasticity" [11]. Later, due to multiple similarities and analogies, the concept of resilience extended to the field of natural and social systems but, in any case, always denoting "the degree to which a system recovers or

returns to its previous state before the action of an external stimulus" [12].

corresponding to the vulnerability Eq. (2) (see **Figure 1**).

*2.2.1 The intrinsic response capacity (IRC)*

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**Figure 1.**

*Family of curves in the vulnerability equation (V).*

Consequently, the IRC will depend on each type of threat in particular and will be calculated independently for each element exposed based on a weighted assessment of attributes, according to the generic Eq. (3):

$$IRC = \frac{\sum Pn.\text{Wn}}{Pn\_{m\text{\'ice}}} \tag{3}$$

where IRC is the intrinsic response capacity, Pn is the evaluation of attributes according to characteristics of each exposed element, and Wn is the weighting factor.

The intrinsic ecosystem response capacity (ICRe) is defined as the capacity of an ecosystem to react and physically resist the impact of a threat and subsequently recover by itself from the damage caused. It depends on each type of threat in particular and can be calculated independently for each exposed element of the ecosystem (rivers, páramos, forests and stubble, pastures, and crops) based on a weighted assessment of descriptors and attributes related to the environmental state of the ecosystems, in terms of quantity, quality, and ecological availability of environmental goods and services, and the degree of intervention or anthropic pressure, in terms of the use and deterioration caused on said environmental goods and services [16, 20].

The intrinsic response capacity of constructed elements (IRCc) is defined as the capacity of a constructed element to physically resist the impact of a threat and to maintain its functionality after the affectation received. It depends on each type of threat in particular and can be calculated for each exposed constructed element (buildings, roads, infrastructures) based on the weighted assessment of descriptors and attributes related to their physicochemical characteristics such as construction material (from the structure, elements, base, subbase), the structure (type, mezzanines, anchors), the roof (type of roof), the covering (type of covering), the rolling (rolling layer), the terrain (ground, slope), drains (quantity and condition of drainage works), and general condition (age, conservation, damage) [5, 14, 16].

The intrinsic response capacity of the population (IRCp) is defined as the capacity of a given population to react and physically resist the impact of a threat and subsequently recover by itself from the affectation caused. It can be calculated for an exposed population group based on a weighted assessment of descriptors and attributes related to planning (perception of risk, level of education, unsatisfied basic needs, participation in drills, participation in emergency committees, knowledge of evacuation routes and shelters), the operation (optimal evacuation distance, type and quality of route, population to be mobilized, active and passive human resources, physical and/or psychological limitations), and logistics (means of transport and communication equipment) [11, 12, 16].

#### *2.2.2 The extrinsic response capacity (ERC)*

For the purposes of this study, the extrinsic response capacity (ERC) will be understood as an index that represents dimensionally the institutional capacity of the entities responsible for the integral management of the risk of responding orderly and efficiently to emergency situations that generate one or more threats determined [16]. It does not depend on the threats, and therefore it is calculated for each exposed population group (country, department, municipality, township, village) according to the generic Eq. (4):

$$ERC = \frac{\sum Pn.\mathcal{M}n}{Pn\_{\text{mix}}} \tag{4}$$

where ERC is the extrinsic response capacity, Pn is the assessment of attributes of institutional capacity, and Wn is the weighting factor.

In accordance with the general functions of an incident command system (ICS) [22], the following descriptors and attributes for the ERC are proposed:

**Planning**: identification and characterization of risks, emergency plans, availability evacuation routes and shelters, simulation programming and coordination, and conformation and coordination of emergency committees.

**Operation**: optimal assistance distance, type and quality of route, population to be assisted, social care, medical assistance, and technical assistance in search and rescue.

**Logistics**: availability and management of supplies, communication system and early warning, transport, and facilities and equipment.

#### **2.3 A new risk equation**

As suggested, for the purposes of this study, comprehensive risk assessment is a process with a holistic, systemic, and environmental approach [16, 20], and, therefore, the definition of risk (R) refers to the probability that something harmful can happen in a certain environment or in a segment or element of it (ecosystem, public sector, economic sector, civil society).

In this context, with the help of the Excel tool and after successive trials with field information and conceptual and methodological approaches that avoided the null values for threats and vulnerabilities, a new expression was adjusted, as an index, for the determination of risk against volcanic threats, as shown in Eq. (5):

$$R = \stackrel{\circ}{\mathbf{A}}^{a}. \mathcal{V}^{b} \tag{5}$$

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**Table 3.**

*Toward a New Conceptual and Methodological Approach for the Integral Evaluation…*

The proposed methodological approach for comprehensive risk assessment involves two fundamental elements, the logical framework matrix and the process

Taking as a reference the logical framework matrix for systemic and integral evaluation of environmental impacts proposed in [20], the logical framework matrices are designed and defined for the integral evaluation of volcanic risk in the scenarios of the onset of crisis and eruption, which is shown in **Tables 3** and **4**.

**Figure 3** schematizes the process diagram proposed for the integral evaluation of volcanic risk, which is consistent with the previously described conceptual framework. To apply and develop this methodology is essential to have GIS tools [23], whose specific process includes a series of activities such as the collection and structuring

*Logical framework matrix for the integral risk assessment—start crisis scenario.*

*DOI: http://dx.doi.org/10.5772/intechopen.84415*

**3. Methodological approach**

*Family of curves in the risk equation (R).*

**Figure 2.**

diagram, as explained below.

**3.2 The process diagram**

**3.1 The logical framework matrix**

where R is the risk index, Å is the intrinsic threat index, V is the vulnerability index, a is [b - c. ln (V)], b and c are the shape coefficients in the fit of the family of curves corresponding to the risk Eq. (5), as shown in **Figure 2**.

*Toward a New Conceptual and Methodological Approach for the Integral Evaluation… DOI: http://dx.doi.org/10.5772/intechopen.84415*

**Figure 2.** *Family of curves in the risk equation (R).*
