RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 10, ES1004, doi:10.2205/2007ES000267, 2008
Damage from natural disasters: Fast growth of losses or stable ratio?M. V. RodkinGeophysical Center, Russian Academy of Sciences, Moscow, Russia V. F. Pisarenko International institute for earthquake prediction theory and mathematical geophysics, Russian Academy of Sciences, Moscow, Russia Contents
Abstract[1] The analysis of an average amount of damage from natural disasters as in the death toll and in money equivalent allows to conclude a fast nonlinear growth of damage amount with time. The result was used to be ascribed to growth of population, development of potentially hazardous industries, and general deterioration of environment. Extrapolation of the tendency for an increase of average damage amount suggests that all the economic gain will be taken up by greater losses from natural disasters by the mid-XXI century. Empirically, the distribution of damage amount from disasters, as a rule, is governed by laws of the heavy tail of the distribution. However, an ordinary approach based on average values will be incorrect for such distributions, because in this case formally evaluated average values prove to be infinite. The application of statistically more correct approaches for description of disaster pattern results in qualitative change in prediction character. It becomes possible to establish limits of nonlinear growth of damage amount; while the comparison of the latter with data on social-economic development makes it possible to interpret damage pattern as an example of realization of principles in terms of the sustainable development concept. It turns out, that by increase of damage in cost, normalized values of losses tend to decrease with the social-economic development. The above analysis was based mainly on statistical data for seismic disasters, however, the authors believe that the results obtained, can be applied to other types of natural disasters as well. Introduction[2] Mass media is abound in information about natural disasters: hurricanes, earthquakes, floods, droughts occur in one or another place of the globe. Consequences of such disasters sometimes are horrific. So, the death toll of the 2004 Sumatra earthquake amounted to 320 thousand people, in the Tien Shan 1976 earthquake in China according to different sources there were as many as 240 to 650 thousand. During floods in China and Bangladesh in 1931 and 1970, casualties numbered 1300 and 500 thousand, respectively. For the development of the mankind it is important to understand a recurrence pattern of natural disasters and to predict a possible damage.
[4] However, the statistical approach used in the analysis of disaster pattern and hence the prediction results are not quite correct. The problem is the presence of occasional anomalously great damage amount comparable with net damage estimates. So, the death toll from the two above mentioned - Tien Shan and Sumatra earthquakes - amounts to about one-third of casualties from earthquakes for the entire XX century. Such a comparison makes one think that the conventional approach based on calculation of average values cannot give reliable estimates, hence other statistical approaches are required to study the damage pattern from disasters. The correct analysis of the damage pattern is given below, so the character of the resultant prediction will undergo a qualitative change. Thus, the prediction of not disastrous growth, but a model of quasi-stationary relative damage values tending to decrease with fast social-economic development seems a more justified. Stationary Model of Nonlinear Growth of Damage From Seismic Disasters[5] The study of natural disaster pattern was based on the authors' compiled database of damage from earthquakes [Rodkin and Pisarenko, 2000]. Such a choice was caused by the fact, that data allowing to reliably track the character in change of the death toll from natural disasters over the last century are available only for earthquakes, moreover starting from the 1950-1960s the data on the economic damage are fairly comprehensive. As to the other natural disasters, the information is not abundant. However, the data available convincingly imply a qualitative uniformity of damage patterns from different types of natural and natural-technogenic disasters and make one assume, that the obtained conclusions may be used not only in case of earthquakes but may be applied to other types of natural disasters. The presented results of the damage pattern from earthquakes were obtained by Pisarenko and Rodkin [2003a, 2003b], Rodkin and Pisarenko [2000, 2004, 2006], etc. [6] The above mentioned general tendency of nonlinear growth of cumulative damage is well exemplified by earthquakes. A number of the 1900-1999 earthquakes resulted in casualties growth with time as t1.4 and the total death toll as t1.6. This might result in the conclusion about non-stationary growth of damage from earthquakes. However, such a conclusion is not correct.
[9] Figure 3a shows that sequence of values for the death toll in events of scale-range III does not change systematically. The curve of cumulative sum of logarithms in fact does not differ from straight line suggesting stability of the death toll logarithm mean. Hence a conclusion about stationary of a number of strongest seismic events and distribution of the death toll from such earthquakes. A sequence of values of cumulative death toll in events of scale-range II (Figure 3b) also does not show important changes, whereas growth of cumulative sum shifts slightly from a straight line. Only the event pattern of scale-range I reveals a strong non-stationarity. A number of such events grows fast (Figure 2), while an average death toll in case of unit event tends to decrease (Figure 3c). However, such changes is naturally to attribute to a better record system and not to a change in recurrence pattern of seismic events. [10] Thus, a strong non-stationarity of seismic event pattern is reported only for weak events totaling less then 1% of the total death toll. Such a non-stationarity cannot explain an observed tendency of a strong growth of the death toll with time.
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[12] Another condition (typical of damage cases) that the power distribution starts to be fulfilled with some minimal damage quantity a is entered into equation (1). The condition is caused by a fairly incomplete statistic on minor disasters. Noteworthy, that an actual law of distribution for a number of weak disasters is not of real interest, because they contribute slightly to the total damage amount.
[14] Atypical (imitating the presence of non-stationarity) behavior of cumulative damage values is due to the
fact, that mean value and dispersion are infinite for power distribution of eq, (1) type with an exponent of
power of distribution
b
[15] In case of heavy tail power-law distributions, medians, i.e. values accounting for not more than 50% of
elements of a sample and no less than other 50% of elements, are used instead of mean values that are formally
infinite. In our case of special interest is an estimate of
median of expected total damage in time
t,
[16] Equations (2) and (3) show that the quantities
mn and
[17] Let us sum up. The analysis of the power pattern of the damage value distribution (1) implies, that nonlinear growth of cumulative damage can occur within the framework of the stationary model, i.e. empirically observed nonlinear growth of damage is not necessarily assumes the non-stationary disaster pattern. In case of earthquakes, it turns out that the observed tendency of damage growth with time might be easily attributed to the presence of the heavy tail of the damage distribution (a number of casualties and economic losses) caused by occasional earthquakes. Actually, according to relations (2) and (3) an expected nonlinear growth of the death toll is given by exponent 1/b = 1/0.7 =1.4; whereas an empirically revealed law of average growth amounted to 1.6. It is obvious that an observed growth of casualties caused by earthquakes accounted for an important scatter in behavior of different statistical achievements is not in conflict with the stationary model (1). Actual non-stationarity (discussed below) is of secondary importance. [18] Naturally, in case of other types of natural disasters, for example, hurricanes, whose recurrence pattern depends on climate changes, a real non-stationarity may be of great importance. However, at least partly the observed effect of nonlinear growth of damage amounts with time, will be due to the power distribution law of damage, caused by individual hurricanes. Noteworthy, for the case of the number of people, who became homeless during floods the readers are referred to the paper by Pisarenko [1998] showing a key role of this factor. [19] The presented schematic diagram shows the growth of damage with time for the case of the heavy tale distribution. However, two important questions remain unsolved. First, within which range simulation of damage distribution can be described by the power law, and hence when is nonlinear growth of total damage with time to be expected. Second, what is the relation between damage amount and such important social-economic processes as the growth the population and the development of technosphere. Let us discuss these issues. The Relation Between Damage Pattern Caused by Earthquakes and Social-Economic Development of the Society
[20] It is obvious, that the death toll from any disaster cannot exceed population of the Earth, while
material damage cannot be higher than the total cost of technosphere. It means, that the power law of damage
distribution cannot be realized in case of very great damage. A real pattern of damage distribution will not
satisfy the power-law distribution at
b<1 for events
x>A, where
A is necessarily not above an event of
the "doomsday'' type. An event with an extent of
x [21] A number of approaches to characterization of maximal possible event A and the recurrence period of such event Ta have proposed and verified, using the data of the Harvard Catalogue of Seismic moments, in the works [Pisarenko and Rodkin, 2003b; Rodkin, 2003b; Rodkin and Pisarenko, 2007]. To more correctly determine these parameters it is better to divide the available data aggregate into the uniform groups. Further we will discuss a relation between statistical characteristics of natural disaster pattern and social-economic parameters, therefore we will deal with damage amounts, so breaking is to be accounted for social-economic development. Namely, let us compare a pattern of losses from seismic disasters in different regions: in North America, Europe, Japan, Latin America, Asia, Indochina (Table 1). To determine a value of a characteristic maximally possible disaster A and time of its recurrence Ta will combine the selected regions into two groups with respect to higher (North America, Europe, Japan) and lower (Latin America, Asia, Indochina) level of economic development. Such a distribution complies with the commonly accepted subdivision into developed and developing countries.
[22] To find changes in the disaster pattern due to rapid growth of the social-economic development in the
XX century, we will discuss separately data for 1900-1959 and 1960-1999; because of differences in catalogue
accumulation, a number of events within these two time intervals are almost the same. Assuming the distribution
stationarity of the death toll during these periods of time, we estimate specific quantities of cumulative death
toll
![]() ![]() [24] A similar estimate was based on a less representative data on flood losses from the database EM-DAT: The International Disaster Database http://www.em-dat.net. Table 2 presents also the estimate suggesting the decrease in the death toll in the developed countries from the floods. [25] The described approach gives an answer to the first of the above stated question, i.e. to evaluate the limits of application of the power-law distribution with exponent of power b<1. As a result, the length of time when such an approach was used is given by time interval Ta, and maximal disaster described by this relation is defined by characteristic maximal disaster A. At the same time it implies a probable characteristic relation between a disaster pattern and social-economic development. [26] Now let us consider the relation between damage from seismic disasters and social-economic parameters. The population of the world is known to have increased four-fold during the XX century. However, the growth of disasters with casualties numbered more than a 100 persons has not been reported (Figure 2). This makes it possible to assume the presence of a factor compensating for potential growth of vulnerability of society with increase of population. It would appear natural to attribute such a compensation to the advancement of technosphere. If it is really associated with the above factor, then with due account for difference in the technical development in the developed and developing countries, one should assume overcompensation and undercompensation in the first and second case, respectively.
[28] Now let us compare data from different regions (Table 1). The relation between the damage
characteristics and social-economic parameters follows from the comparison of data on damages and those
of per capita national product (information from database http://unescostat.unesco.org/database). There
is correlation between an average ratio of material damage per dead ("damage/casualties'') and a national
product per head ("per capita product''). This ratio shows a relatively constant value of 5.2
[29] Now material damage from earthquake is to be discussed. Material earthquake losses are known to
increase with time. However, to understand the impact of natural disasters on the development of the society
one should envisage not this particular effect (fairly expected), but changes of relative losses normalized to
current level of national wealth. An annual per capita product - comparison of man-years required to
compensate for damage - is taken as the unit of measurement. Damage from major earthquakes in different
regions measured in this units turned to be almost the same, namely (200
[31] Considering the relation between natural disaster pattern and social-economic development it is pertinent to ask how short a time interval should be for such a relation to be realized. The fastest and more important changes in social-economic situation take place during the periods of social-economic cataclysms. Hence, the question, whether such cataclysms can give rise to changes in vulnerability of the society resulted from natural disasters. To preliminary discuss this issue we made an attempt to compare changes in disaster pattern in such large countries as Russia and China who have undergone staggering social-economic shock.
[33] There is just a few earthquakes in Russia, therefore the database created in the Laboratory of the geological risk analyzes of IGE RAS was used to analyze the disaster pattern; this database includes data on natural and natural-technogenic disasters that have taken place in the present territory of Russia since the X century till resent [Ragozin et al., 2003]. The database contains more than 1300 extreme events differing in genesis, negative consequences and in other characteristics. 193 cases of most hazardous events: earthquakes, landslides, mudflows, floods, avalanches, hurricanes, tsunami, and other abiotic disasters have been chosen. All the above cases according to the rules of the EMRCOM (Provisions on classification of emergency situations of natural and technogenic character. Adopted by the Decree of the Government of RF no. 1094 of 13.09.1996) meet the provisions on emergency situations of the federal level. According to the database compilers such a selection provides acceptable completeness and uniformity of data on a number of disasters [Ragozin et al., 2004].
[35] Figure 10 also shows (may be accidental) decrease in average number of disasters in the mid-1990s and a new much weaker peak during 1998-1999. Hypothetically, it is possible to associate these peculiar features with economic revival in the mid-1990s and with the crisis of the 1998, that also resulted in delay of wages and salaries, and freezing of many projects. [36] A hypothesis about the relation between changes in number of disasters and short-term changes in a social-economic situation seems quite realistic, and the data of analysis for Russia and China strongly support the hypothesis. If we assume, that even extensive preventive engineering measures cannot be accomplished during a short time interval, still infrastructure, management, and communication systems might be markedly improved; as a result all the above can lessen the burden from disasters. One has to remember, that the Emergency Committee (EMRCOM), powerful in resources available, was set up in Russia during the time interval in question. [37] The above presented conclusions about the relation between seismic losses and social-economic conditions are in good agreement with results obtained by other authors. A statement that regions with a fairly low level of economic development are less resistant to earthquake impact was published in [Sobolev, 1997]. Similar conclusions about the relation between characteristics damage amount from natural disasters and a level of social-economic development are presented in the work by Kahn [2003]. The study provides an analysis of data on 225 strong (major) natural disasters over a period of 1990-2001. The author presents relation between a characteristic death toll from natural disasters and social-economic situation in different countries. As a result, the analysis revealed a number of empirical relations. For example, the growth of gross national product (GNP) since the year 2000 will amount to 15000 dollars per capita per year will correspond meanly to decrease in a number of casualties by 500 people in year for a 100 million of population. Another important factor affecting an average death toll from disasters is a management structure; countries with less developed democratic institutions turned to be relatively less vulnerable (in terms of normalized casualties from natural disasters). Damage Pattern From Natural Disasters as an Example of Realization of the Sustainable Development Concept in Practice[38] The above mentioned empirical relationship (and some other references omitted for reasons of space) makes us doubt the validity of a pessimistic prediction of a catastrophic growth of damage caused by natural disasters, that was mentioned in the beginning of the paper. In fact, the growth in number of disasters is mainly caused by the better record system of weak disasters. As to nonlinear growth of total damage with time, this effect (at least partly) arises from the power-series distribution of damage amount and not by its non-stationary growth. [39] Proceeded from the relation between the seismic disaster pattern and social-economic parameters there are all grounds to assume a decrease in intensity of the disaster flow with a large number of casualties in the developed countries, and then a further extension of this tendency to the developing countries (as their economic and social situation develops and as the rate of population growth slows down). If the tendency to growth of absolute values of material losses is preserved, than a relative stability, and possibly, a decrease of normalized values (in units of private income) seems to be quite feasible. [40] An attention is called to a marked uniformity of normalized values of damage from earthquakes in different countries. There is an impression, that some social communities and mankind as a whole has adapted in the course of its historical development a certain permissible (depending on concrete social-economic conditions) to a level of damages from natural disasters. It is possible to assume that if such a relation remains persistent, it will result in an optimal link between the profit from the use of some or other natural resources and losses caused by their use in the course of natural disasters (for example, the use of fertile soils in the river valleys presupposes flood damage). Thus, in case of damages from natural disasters, the principles of the sustainable development turn to be implemented. An example of the realization of the sustainable development concept in practice promises that this optimistic concept can be realized also under more complicated conditions, when people and environment will be more closely interrelated. An example of a possible practical realization of the sustainable development concept becomes even more important, because the discussion on this issue is dominated by a pessimistic viewpoint, namely, that "despite unprecedented large scale discussion of sustainable development, the world keeps developing along the trajectory of non-sustainable development'' [Kondratiev and Losev, 2002, p. 598]. Inferences and Conclusion[41] It is common to consider that the noted growth of damage from natural disasters depends on the increase in number of population, the development of potentially hazardous industries, and general deterioration of geological environment. A standard extrapolation of growth of an average amount of damage makes it possible to predict, that the entire economic gain can be taken up by still increasing losses from natural disasters by the mid-XXI century. However, the statistical approach based on mean values used in calculation is not quite correct in this particular case. The empirical distribution of amounts of damage from natural disasters, as a rule, corresponds to the power-law heavy tail distribution, and and formally estimated means turn to be infinite for such distributions. [42] The application of more correct statistical approaches to describe a disaster pattern results in a qualitative change of the prediction pattern, when nonlinear growth (at least partly) does not depend on an actual nonlinear growth of damage amount, but is governed by the power distribution law of damage amount. The obtained comparison gives grounds to interpret damage caused by disasters as an example of the implementation of the sustainable development concept. The rise of cost due to damage will show a tendency to decrease of normalized values of losses as the social-economic situation develops. The presented analysis was based mainly on statistical data on seismic disasters, however, the authors believe that the obtained results can be, to a greater extent, used by the study of other types of natural disasters. Acknowledgments[43] The performed work was supported by the RFBR (grant no. 05-05-65276) and with due account for the program of the Presidium of the RAS: "Environmental and climate changes: natural disasters''. ReferencesKahn, E. M. (2003), The Death Toll From Natural Disasters: The Role of Income, Geography and Institutions, http://ssrn.com/abstract=391741 or doi: 10.2139/ssm.391741, University of California, Los Angeles. Kondratiev, K. Ya., and K. S. Losev (2002), Illusions and reality of the sustainable development strategy, Vestnik RAN (in Russian), 72, (7), 592. Kronrod, T. L., and A. K. Nekrasova (1996), Seismic risk in largest cities of the world: Assessment verification, Computational Seismology (in Russian), 28, 225. Osipov, V. I. (2001), Natural disasters at the turn of the XXI century, Vestnik RAN (in Russian), 71, (4), 291. Osipov, V. I. (2002), Natural risk management, Vestnik RAN (in Russian), 72, (8), 678. Pisarenko, V. F. (1998), Nonlinear growth of cumulative flood losses with time, Hydrological Processes, 12, (3), 461, doi:10.1002/(SICI)1099-1085(19980315)12:3<461::AID-HYP584>3.0.CO;2-L. [CrossRef] Pisarenko, V. F., and M. V. Rodkin (2003a), Damage from earthquakes, Computational Seismology (in Russian), 34, 205. Pisarenko, V. F., and M. V. Rodkin (2003b), Problems in assessment of the long-term seismic hazard, Nauka i Technologia v Rossii (in Russian), No. 4-5, 8. Ragozin, A. L., A. V. Uvarova, and S. A. Chumachenko (2003), Supplement catalogue of major nonantropogenic disasters in the territory of Russia over 1000 years, in: Prirodnye Opasnosti Rossii, vol. 6, Otsenka i Upravlenie Prirodnymi Riskami (in Russian), p. 12, KRUK, Moscow. Ragozin, A. L., A. V. Uvarova, and S. A. Chumachenko (2004), First results of the dynamics analysis of major disasters in the territory of Russia, in: Sergeevskie Chtenia, Issue 6, Inzhenernaya Geologia i Okhrana Geologicheskoi Sredy (in Russian), p. 185, GEOS, Moscow. Rodkin, M. V., and V. F. Pisarenko (2000), Economic damage and casualties from earthquakes: Statistical analysis, Computational Seismology (in Russian), 31, 42. Rodkin, M. V., and V. F. Pisarenko (2004), Earthquakes losses and casualties, A statistical analysis, in: Computational Seismology and Geodynamics, edited by D. K. Chowdhury, vol. 6, p. 85, Am. Geophys. Un., Washington D.C.. Rodkin, M. V., and V. F. Pisarenko (2006), Extreme earthquake disasters - verification of the method of parametrization of the character of distribution of the rare major events, Advanced in Geosciences, 1, 75. Rodkin, M. V. (2007), Heavy-tailed distributions: application to disaster analysis, Computational seismology, No. 38, 240. Sobolev, G. A., Ed. (1997), Assessment of Seismic Hazard and Seismic Risk (in Russian), 52 pp., FTzNTP RP "Bezopasnost'', Moscow. Vorobiev, Yu. L., G. G. Malinetsky, and V. I. Osipov (2000), Disasters and Society (in Russian), 332 pp., Kontakt-Kultura, Moscow. Received 8 December 2007; accepted 18 January 2008; published 14 February 2008. Keywords: natural disasters, hazards, risk, assessment. Index Terms: 1240 Geodesy and Gravity: Satellite geodesy: results; 1242 Geodesy and Gravity: Seismic cycle related deformations; 8488 Volcanology: Volcanic hazards and risks. ![]() Citation: 2008), Damage from natural disasters: Fast growth of losses or stable ratio?, Russ. J. Earth Sci., 10, ES1004, doi:10.2205/2007ES000267. (Copyright 2008 by the Russian Journal of Earth SciencesPowered by TeXWeb (Win32, v.2.0). |