## Abstract

This paper is dedicated to the study of risk perception issues. A formal algorithm for the quantitative analysis of social factors of disaster risk is proposed. A modified form of the damage function based on the prospect theory and decision making under uncertainty due to cognitive bias and the handling of risk is proposed. Relationships for analysis of the most probable damage according to age, education and income of the population are proposed. Using multi-source statistics, the interconnected influence of education and long-term experience (education function) on the one hand, and short-term information (risk perception function) on the other hand to develop the damage function as a measure of vulnerability toward disasters has been demonstrated. As the result of the data analysis demonstrates, up to half of the damage function might be caused by social factors: education, long-term experience and responsible behaviour of information agents. It was concluded that public efforts based on ethical principles and directed toward empowering people and developing the human capacity through education can have a positive response in reducing vulnerability and enhancing the adaptive capacity toward the disasters including climate-related threats.

Geoethics is the multidisciplinary branch of geoscience, which provides a reference and guidelines for behaviour in addressing concrete problems of human life by trying to find socio-economic solutions compatible with a respect for the environment and the protection of nature and land in view of global change, anthropogenic activity and disasters. Among other important themes, geoethics deals with problems related to the risk management and the mitigation of varied hazards. These problems require a solid scientific basis to develop applicable policy (Peppoloni & Di Capua 2012). At the same time, scientific basis requires correct mathematics, firstly statistics based on inferential (non-descriptive) approaches, which allow the summary of statistical population properties. The solution of this task determines the necessity of the development of new statistical procedures for the analysis of social factors of disaster risk in the context of geoethics studies.

The intensity of the impacts of natural disasters is increasing with the spread of climatic and ecological changes. The frequency of disasters and the recurrence of catastrophes characterized by essential spatial heterogeneity are increasing. The distribution of losses is fundamentally nonlinear and reflects the complex interrelation of natural, social and environmental factors in the changing world on a multi-scale range. We are faced with new types of risks, which require a comprehensive security concept (Ermoliev & Hordijk 2006).

The main components of the modern security concept are human issues (Lutz & Samir 2011). Modern understanding of complex security and complex risk management requires analysis of all natural and social phenomena, the involvement of all available data, the construction of advanced analytical tools and the transformation of our perception of risk and the related security issues (National Research Council 2006).

Traditional deterministic models used for risk analysis are difficult to apply to the analysis of social issues, as well as to the analysis of multi-scale, multi-physics phenomena quantification (Ermoliev & Winterfeldt 2012). In addition, parametric methods are not absolutely effective because the system analysed is essentially non-ergodic. It means we are substantially limited in our ability to forecast a future state of the system based on the observed state. The stochastic models of risk analysis are applicable for quantitative analysis of social issues such as human behaviour and risk perception. Integrated security analysis requires a quantitative estimation of the influence of social factors on disaster damage (Butz *et al.* 2014).

Therefore, the issues of risk and threat perception should be described in the framework of risk analysis models, using appropriate tools and approaches (Linnerooth–Bayer *et al.* 2005).

## Disaster statistics: risk and vulnerability

The problem with correct statistics is the usual problem of risk and vulnerability analysis. In the framework of the most common and the most comprehensive case, the risk can be presented as the superposition of the distribution function (*f*(*x, y*)) and the damage function (*p*(*x, y*)) (Ermoliev & Winterfeldt 2012):
(1)

The distribution function is more ‘physical’ and describes an impact of expanded disaster; the damage function describes the distribution of the damaged assets: infrastructure, people, natural features, etc. To analyse the role of social factors in risk measurement variation, a large number of disasters were studied.

Natural disasters (894) in Ukraine from 1960–2012 were selected and analysed. General trends have been detected; the period 1991–2010 was selected for detailed analysis, as it is the time interval with the most reliable statistics (National Report 2004, 2006, 2010) validated by satellite observations (Kostyuchenko *et al.* 2013). Socio-economic data has been analysed on a sample of 42 disasters, including the 11 most severe events. The list of major disasters includes six floods, three storms, one cold wave and one epidemic. Total losses from the most serious events were approximately 1.64 billion Euro; 2 698 797 people were affected, and 368 people were killed. Analysis was aimed at evaluating the influence of risk perception on the damage function.

The smoothed distributions of frequency (in terms of mean probability of disaster during the selected time interval per square unit) of various types of disasters per year calculated per 1000 km^{2} for the studied period are presented in Figure 1. The proposed algorithm for the regularization allows for the gaps in the data to be filled, for the normalization of the distributions, spatially and temporally, and for the control of the data uncertainty (Kostyuchenko *et al.* 2013).

The distribution presented demonstrates an increasing frequency of disasters. In addition, the data analysed shows the growth of direct losses. The registered increase in losses is connected with the observed increasing frequency and intensity of the disasters. It could also be explained by the increasing cost of the damaged infrastructure. To analyse the damage distribution in the context of the economic development, the index of damage (IoD) was calculated (Fig. 2).

This index was calculated using the algorithm: , where *i* is the time step (in our case, calculated year), is the estimated direct losses from disaster *d* of separate type *n* and *pCGDP* is the per capita gross domestic product (GDP) (World Bank 2013). The distribution presented demonstrates that the relative natural disaster damage (calculated per 1000 km^{2}) during 1990 is slightly increasing, which is probably connected to the impact of climate change. Common trends in the world and in Europe demonstrate decreasing IoD, which is connected with economic growth (increasing economic sustainability toward catastrophic events) and the successful implementation of risk management strategies. At the same time, in the territory of Ukraine since the 1980s and especially since the 1990s, IoD is increasing dramatically. It is connected with the economic degradation and the absence of adequate systemic strategies for risk management.

Therefore, the territory investigated is highly vulnerable toward disasters, and the role of social factors should be quantitatively assessed.

## Method of analysis of socio-economic factors of disaster risks

Basing on the prospect theory and decision making under uncertainty on a cognitive bias and handling of risk (Kahneman & Tversky 2000), we propose to modify the damage function to the following: *p*(*x*, *y*|α(*t*)). The modified damage function includes an awareness function α(*t*), which is the superposition of the risk perception function (*r*_{p}) and the function of education and long-term experience (*c*) so that α(*t*)→(*c*+*r*_{p}), as shown in Tversky & Kahneman (1974).

The education function *c*(*t*) describes the trend of education and experience. The risk perception function *r*_{p} reflects the security concept of human behaviour and is the basis for the prediction of socio-economic and socio-ecological processes. In addition, there is an important positive feedback of the risk perception function to the distribution function. Risk perception depends essentially on recent events.

The awareness function might be presented in a generalized view as follows: (2)

Using this form, we can try to represent a separate parameter distribution.

For the assessment of losses connected with the basic education level of the affected people, the regression proposed is from Frankenberg *et al.* (2013):
(3)
where *a _{0}* is the constant coefficient,

*p*is the basic level of physical losses at site (

_{0}*x, y*),

*E*is the education level of the group of people

_{i,t}*i*in time

*t*at site (

*x, y*) and

*A*is the age of the group of people

_{i,t}*i*in time

*t*at site (

*x, y*).

Using the available statistics, we have no instruments to measure the risk perception function directly. Therefore, we need to apply indirect algorithms to estimate it.

In this form, the component might be interpreted as an uncertainty coefficient (Huber 1981). Therefore, if a few quite reliable intervals τ within the long period *t* are available for observations of *M* sites (*x, y*) from two sources/records, we may propose the following uncertainty estimation:
(4)

This equation might be used as the simple form for the estimation of the risk perception function of a group of people *i* with an education level *E* and an age range *A* at site (*x, y*) during time interval τ within the geographic region *M* and an observation period *t*.

## Results and discussion

Disaster data were analysed using the modified kernel-based nonlinear principal component analysis algorithm (Scheolkopf *et al.* 1998; Kostyuchenko *et al.* 2013). As a result, the spatially and temporally regularized distributions with normalized reliability were obtained.

Figures 3 and 4 present the averaged distributions of probability of the effect on the individual and the property damage depending on the education for the most severe natural disasters in Ukraine 1991–2012 (FAO/ADPC 2006; National Report 2010).

The distribution in Figure 3 demonstrates that educated and informed people are better protected toward threats. This corresponds to the average world trends (FAO/ADPC 2006).

Moreover, the distribution reflects the disparity in the property distribution in Ukraine and an important connection with social fairness patterns.

Unfortunately, as is usual in the study of disasters, the sample is essentially limited; these data are not highly reliable. Average uncertainty is approximately 14% for disaster statistics, and approximately 20% for demographic data.

The risk component caused by the education (and indirectly by the age) is closely connected with economic parameters, such as income per capita. Surveys show that these interrelations are varied and that they are significantly heterogeneous spatially and temporally.

In Figure 5, the smoothed distribution of the probability of the effect on the individual depending on personal income is presented. The distribution of probability of property damage depending on education is presented in Figure 6.

These distributions look predictable and correspond to average world trends (FAO/ADPC 2006); increasing income leads to increased protection.

This distribution demonstrates interesting characteristics about Ukrainian society: the poorest and the richest people are the most vulnerable toward catastrophes. The poor are vulnerable because of the lack of infrastructure and resource accessibility; the rich are vulnerable because they neglect security regulations. These are the different aspects of the decision-making problem under uncertainty (Yudkowsky 2006).

In general, the case of the linearized form might be proposed as follows (Kellenberg & Mobarak 2008):
(5)
where *a _{n}* is the regression empirical coefficient,

*F*is the frequency of disasters at site (

^{d}_{i,t}*x*,

*y*),

*I*is the per capita income of the group of people

_{i,t}*i*in time

*t*at site (

*x*,

*y*),

*P*is the population in time

_{i,t}*t*at site (

*x*,

*y*),

*P*is the urban population in time

^{U}_{i,t}*t*at site (

*x*,

*y*) and ξ is the uncertainty coefficient.

Equation (5), which describes fatalities from natural disasters, corresponds to the observed distributions. This regression is a good correlation with results of other studies (Kahn 2005).

Available disaster statistics were analysed using the proposed approach in equations (3) and (4). The result demonstrates the dynamic interconnected influence of the education function and the risk perception function to the damage function as the measure of vulnerability toward disasters (Fig. 7). As a result, we can separately analyse the impact of education, long-term experience and short-term information to the loss dynamics.

As it follows from the figures presented, the risk perception function is approximately 9–18% of the awareness function and it depends on education, age, income and the social status of the people. It was estimated also that the amount of awareness function in the damage function, and consequently in the risk function, is approximately 21–49%.

It means that no less than 7–11% of the direct losses depend of the short-term responsible behaviour of the ‘information agents’, i.e. the social activity of experts and scientists, the correct discussions of ethical issues in geosciences and the media. The other 8–10% of the losses are connected with the level of public and professional education. This area should also be a field of responsibility for geoscientists.

Therefore, the cost of systemic education and long-term preparedness work is no less than 10–15% of the total catastrophic losses, and the cost of responsible information and policy making is from 8–20% (in case of major disasters).

## Conclusions

A method of quantitative assessment of socio-economic parameters of vulnerability toward disasters is proposed. This method is based on the analysis of limited samples but can be extended to the entire population, unlike the usual descriptive procedures. A formal algorithm for quantitative analysis of social factors of disaster risk is also proposed. Equations (3) and (4) determine a relation between education, age, experience and the damage function of risk. Equation (5) allows for the estimation of the vulnerability (in terms of probable damage) considering the financial status of the population.

The result of the data analysis demonstrates that up to half of the damage function might be caused by social factors: education, long-term experience and the responsible, ethical behaviour of information agents.

The cost of systemic education and long-term preparedness work is no less than 10–15% of the total catastrophic losses, and the cost of responsible information and short-term policy making is 8–20% (in case of major disasters). It was statistically demonstrated using quantitative indicators how education and income inequality influence vulnerability. For adequate disaster preparedness, the issues of social fairness should be analysed on the correct quantitative basis.

In the view of slow long-term global changes and the escalation of the corresponding threats, the role of systematic awareness and education is essentially increasing. In the case of catastrophic events, the value of responsible behaviour by information agents is a key factor for vulnerability.

The cost of correct information, scientific forecasts, policy making and responsible behaviour in a changing world facing disasters is very high. Our study, based on a formal objective approach, shows that highly educated individuals and communities are better prepared for disasters and suffer lower negative impact (Butz *et al.* 2014). It also allows for the conclusion that public investment in empowering people and developing the human capacity through education can have a positive response in reducing vulnerability and enhancing adaptive capacity toward disasters.

## Acknowledgments

The authors are grateful to anonymous referees for the constructive suggestions that resulted in important improvements to the paper, to colleagues from the International Institute for Applied Systems Analysis and from the International Association for Promoting Geoethics for their critical and constructive comments and suggestions.

- © 2015 The Geological Society of London