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Данные по катастрофам. Тенденции изменения в современном мире Data on natural disasters. Tendencies of change in the recent world M.V.R ODKIN , V.F.Pisarenko Geophysical Centre RAS,, Moscow, firstname.lastname@example.org ; MITPRAN RAS , Moscow , vlad @ sirius . mitp . ru
Данные по катастрофам. Тенденции изменения в современном мире
Data on natural disasters. Tendencies of change in the recent world
Geophysical Centre RAS,, Moscow, email@example.com;
MITPRAN RAS, Moscow, firstname.lastname@example.org
The numbers of victims from natural disasters (earthquakes, floods, hurricanes, etc.) as well as losses from these disasters have a tendency to a non-linear increase with time. This effect is commonly treated as a consequence of the growth of the Earth’s population, the spreading of potentially dangerous technologies and of the environment degradation. The process of increase of the loss values is assumed to be non-stationary that evidently interferes with the idea of the sustainable development of society.
But the similar effect of the apparent instability can occur in the fairly stable model if the character of distribution of the losses can be described by the power law with the power index value <1. This type of the distribution is very typical of the loss values from the different types of disasters and, thus, the apparent effect of the non-linear growth in the loss values could be typical also.
This effect is discussed below in connection with the change taking place in the social and economic situation in different regions.
Examples of increase of yearly numbers of events (left) and loss values (right) from natural catastrophes world-wide (from www.em-dat.net/documents )
Number of disasters (N) and number of suffering people (S)
in Russia from all disasters and from natural disasters only (N’, S’).
Below the case of losses from earthquakes in the world is examined (because of the better statistics for this kind of disasters).
But maybe the character of distribution of events in the chosen intervals could change.
The sequences of number of victims Vi and cumulative numbers Vi for the different used ranges of disasters are given.
The numbers of victims and economic losses from earthquakes (as well as from most of the others natural and man-made disasters) have a clear tendency to a non-linear increase with time.
But the flow rate of the strong seismic disasters that cause more than 99% of the total damage is shown to be stable.
This disagreement can be explained if the specific character of distribution of loss values from the strong seismic disasters is taken into account.
The effect of non-linear increase in loss values with time could be connected with the specific character of distribution of loss values in the case if the distribution of losses obeys the power distribution law with power index <1. In this case this effect could be an “apparent” effect.
The power distribution law with <1 is rather typical of losses from different types of disasters.
The specific feature of this distribution law is a highly increased probability of occurrence of huge events.This causes a statistical tendency of increase of loss value with time.
Examples: Power-law distributions of loss values in USA from earthquakes(E), hurricanes (H), and floods (F), (from coastal.er.usgs.gov/hurricane_forecast/barton4.htm)=-0.74 (F), =-0.98 (H), and =-0.41 (E).Note, all values <1.
Distributions of yearly numbers of victims V (a) and economic losses L (c) and of the numbers of victims V from the individual strong earthquakes (b).
The Pareto law with distribution function F(x) is used :
F(x) = 1 (A/x); xA, (1)
When 1 the Pareto law (1) has a “heavy tail” with infinite mean value and dispersion. Using of the routine statistic procedures is incorrect in this case, and the order statistics has been used.
Medians of the cumulative effect n and the maximum event Vnvalue increase with the number of events in a non-linear manner:
n ~n1/and Vn ~n1/,<1 (2)
similarly, in the case of the stable time flow of events we have:
t ~t1/andVt~t1/ (2а)
Effect (2) taking place in the fairly stable model can be incorrectly treated as the evidence of tendency of the unstable growth of loss values from disasters with time.
The power distribution law (1) with power index <1 has an infinite mean value that is nonsense in practical sense. It means that the real distribution law of rarest huge events should differ from this law.
The model case of seismic disasters distribution:The
Results of modeling of the regime of increase of the cumulative number of victims from earthquakes V(t)
Связь с социально-экономическими условиями
Connection with social and economic situation
The regime of loss growth depends on the social/economic situation
(numbers of fatalities)
In all cases the recurrence time Tc is a few dozens years only, it means the loss increase in this model is restricted to the similar time intervals.
A number of correlation exist between economical and loss characteristics,
loss/victims number ratio value and year per capita income correlationThe Th
The distribution of values of (economic loss)/(number of victims) ratio differs essentially in the developing (1) and in the developed countries (2)
The flow rate of the strong (>100 casualties) seismic disasters increases in the developing countries (1) and decreases in the developed countries (2)
(it can be seen clearly in comparison with the linear prognosis performed using the data for 1900-1940 years)
Thus, being norm the loss values appear to be rather stable, and even have a tendency to decrease.
Results of the use and of the absence of anti-seismic construction approach:
Niigata (Japan) 1964; Mexico City, 1985; and Neftegorsk (Sakhalin), 1995
3. Relations of the numbers of casualties and loss values from earthquake with social and economic parameters were examined, and a number of correlations were revealed. This results give ground to expect a decrease in a number of disasters with large numbers of fatalities with economic and social development despite the increase in population and urbanization. This prognosis is much more optimistic than those presented before in result of a formal extrapolation of observed numbers of fatalities and loss values.