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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, ; MITPRAN RAS , Moscow , vlad @ sirius . mitp . ru

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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.RODKIN, V.F.Pisarenko

Geophysical Centre RAS,, Moscow,;



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 )

  • The problems:
  • 1. Does the tendency of the loss values increase exist really?
  • 2. How long this tendency can be extrapolated?
  • If this tendency is valid for a long time interval it would contradict with the very idea of the sustainable development

Data of loss value increase with time in Russia:

Number of disasters (N) and number of suffering people (S)

in Russia from all disasters and from natural disasters only (N’, S’)

  • Mean increase rates of looses from disasters in Russia are following:
  • Number of victims – 4.3%;
  • Number of suffering - 8.6%;
  • Economic losses - 10.4%

Below the case of losses from earthquakes in the world is examined (because of the better statistics for this kind of disasters)

  • Increase in cumulative numbers N of earthquake disasters with different number of victims V.
  • (III) - V>100 (more 99% of total number of victims);
  • (II) - 100V>10 (about 1% of total loses);
  • (I) - V10 ( < 0.1% of total losses)
  • Thus, only the strongest events are important, but the flow rate of these events appears to be stable with time

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.

  • Thus, we have, that the regime of strongest disasters (III type, more 100 victims, causing more than 99% of total number of victims) is stable

Thus, we have:

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.


An alternative approach:

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=-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)

  • It can be seen that all of the presented distributions obey the power law with power index <1 (=0.770.11; =0.730.11; =0.650.16)
specific properties of the power law distribution with power index value 1
Specific properties of the power law distribution with power index value 1

The Pareto law with distribution function F(x) is used :

F(x) = 1 (A/x); xA, (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 clue parameter is the magnitude C and the recurrence time Tc of the critical event corresponding to the boundary between the power distribution law with <1 and the unknown distribution law of rarest huge events
  • The model distribution law (left) and the corresponding law of increase of typical cumulative loss values (right). Change in the distribution law (left) causes the change in regime of the increase of cumulative loss value with time (right)

Results of modeling of the regime of increase of the cumulative number of victims from earthquakes V(t)

  • Blue line- analytical solution; + - numerical boot-strap modelling
  • It can be seen the change in the regime of growth of the medians of the cumulative numbers of victims from the non-linear regime to the linear one: V~t

Связь с социально-экономическими условиями

Connection with social and economic situation


The regime of loss growth depends on the social/economic situation

  • The analysis was performed for the first (red) and the second
  • (blue) half of the XX-century and for the developed (a) and
  • for the developing (b) countries. Linear regime is shown by lines.
  • The characteristic disaster size Vc corresponding to the beginning of the linear regime of V(t) growth had decreased essentially in the developed countries.
Examples of C and Tc values for different types of disasters

(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.

the th

A number of correlation exist between economical and loss characteristics,

an example:

loss/victims number ratio value and year per capita income correlation

The Th
  • The loss value/victim number ratio L increases with the increase of the year per capita income value P as
  • (approximately) L~ P2.
  • Data for the strong earthquakes occurring at the territory
  • of major cities were used.

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)

Social and Economic Characteristics of Damaging Earthquakes for 1900-1999 in Different Regions

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


Shirt-term change in regime of loss values, social aspect

  • Number of strong catastrophes in the Russian Federation. Points - number of events per million habitants, line - mean 5-year number of catastrophes. It can be seen an increase in a number of disasters during economical and social crisis in 1990-s years.
  • Change in night lights in the Russian North Central part of the Cola peninsular (left) and in the Moscow region (right) in the interval from 1993 until 2000 year.
  • Red color corresponds to origin of new lights, and blue color means that lights die out.
  • Die out in night lights (given in blue color) predominates in the suffered region
  • 1. The alternative explanation to the opinion on the non-stationary increase in loss values from natural disasters with time is presented. The non-linear growth in cumulative numbers of casualties and losses from disasters can be explained in terms of the stable model in the case when the loss values distribution has a “heavy tail”.
  • 2. Nonlinearity in the growth of earthquake-caused casualties and losses occurs (at the planetary scale) over time interval about 20-30 years. When longer time intervals are considered, the size of the maximum disaster stops increasing owing to the natural restrictions on the amount of maximum loss. The total loss from earthquakes increases approximately linearly with time at intervals 50 years and longer.

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.

  • Being norm to the year per capita income the typical loss characteristics from earthquakes appear to be rather stable in the countries with very different level of economic development.
  • The result can be applied to other types of disasters even in more complex cases when disaster’s distribution is connected with the climate change
  • Thank you for attention.