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M.V.RODKIN, V.F.Pisarenko
Geophysical Centre RAS,, Moscow, [email protected];
MITPRAN RAS, Moscow, [email protected]
.
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.
The problems: The problems: 1. Does the tendency of the loss values increase exist really?1. Does the tendency of the loss values increase exist really? 2. How long this tendency can be extrapolated?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
Examples of increase of yearly numbers of events (left) and loss values (right)
from natural catastrophes world-wide (from www.em-dat.net/documents )
. Mean increase rates of looses from disasters in Russia are following:Mean increase rates of looses from disasters in Russia are following:
Number of victims – 4.3%;Number of victims – 4.3%;Number of suffering - 8.6%;Number of suffering - 8.6%;
Economic losses - 10.4%Economic losses - 10.4%
Data of loss value increase with time in Russia:Data of loss value increase with time in Russia: Number of disasters (N) and number of suffering people (S) Number of disasters (N) and number of suffering people (S)
in Russia from all disasters and from natural disasters only (N’, S’)in Russia from all disasters and from natural disasters only (N’, S’)
1993 1994 1995 1996 1997
0
500
1000
1500
N S , thoupeople
50
100
N
S
N '
S '
.
Increase in cumulative numbers N of earthquake disasters with different Increase in cumulative numbers N of earthquake disasters with different number of victims V.number of victims V.
(III) - V>100 (III) - V>100 (more 99% of total number of victims);(more 99% of total number of victims);(II) - 100(II) - 100V>10 (about 1% of total loses);V>10 (about 1% of total loses);
(I) - V(I) - V10 ( < 0.1% of total losses)10 ( < 0.1% of total losses)
Thus, only the strongest events are important, but the flow rate Thus, only the strongest events are important, but the flow rate of these events appears to be stable with timeof these events appears to be stable with time
Below the case of losses from earthquakes in the world is Below the case of losses from earthquakes in the world is examined examined (because of the better statistics for this kind of disasters)(because of the better statistics for this kind of disasters)
1900 1940 1980
t, years
0
100
200
300
N
III -
II-
- I
Thus, we have, that the regime of strongest disasters (III type, more 100 Thus, we have, that the regime of strongest disasters (III type, more 100 victims, causing more than 99% of total number of victims) is stablevictims, causing more than 99% of total number of victims) is stable
1900 1920 1940 1960 1980 years
0
10
Vi
0
400
800
1200
V i
1900 1920 1940 1960 1980 2000
0
4000
8000
12000
V i
0
100
Vi
1900 1920 1940 1960 1980 2000
0
200
400
600
800
1000
ln (V i) V i
102
104
а b
с
V>100 100V>10
V<1 0
But maybe the character of distribution of events in the chosen intervals could change.But maybe the character of distribution of events in the chosen intervals could change.
The sequences of number of victims Vi and cumulative numbers The sequences of number of victims Vi and cumulative numbers Vi for the Vi for the different used ranges of disasters are given.different used ranges of disasters are given.
.
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.
Examples: Examples: Power-law distributions of loss Power-law distributions of loss values in USA from values in USA from earthquakesearthquakes (E)(E), , hurricaneshurricanes (H), and floods (F), ((H), and floods (F), (from from coastal.er.usgs.gov/hurricane_forecast/coastal.er.usgs.gov/hurricane_forecast/barton4.htmbarton4.htm))
=-0.74 (F), =-0.98 (H), and =-0.41 (E) . Note, all values values <1. <1.
.
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.
.
It can be seen that all of the presented distributions obey the power It can be seen that all of the presented distributions obey the power law with power index law with power index <1 <1 ((=0.77=0.770.11; 0.11; =0.73=0.730.11; 0.11; =0.65=0.650.16)0.16)
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)
1 100 10,000
V , victim s
1
10
100
N а
1 100 10,000
L , thou .$
1
10
100
N c
1 100 10,000
V , victim s
1
10
100
1000
N b
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); 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 Vn value 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/ and Vt~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 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 eventsThe 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)
1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0n u m b e r o f v ic t im s , N
0.001
0.01
0.1
1
10
n/ye
ar
Zone of the power-law d istribution w ith "heavy ta il",non-linear increase in loss va lue w ith tim e
Zone of d istribution w ithout "heavy ta il",linear increase w ith tim e (right fromthe boundary)
boundaryzone
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:
1 10 100
T, "years"
100
1000
10000
100000
C um ulative Loss Value
Tc, recurrence tim e
C , critica l event m agnitude
Blue lineBlue line - analytical solution;- analytical solution; + + - numerical boot-strap modelling- numerical boot-strap modelling
It can be seen the change in the regime of growth of the It can be seen the change in the regime of growth of the medians of the cumulative numbers of victims from the non-medians of the cumulative numbers of victims from the non-linear regime to the linear one: V~tlinear regime to the linear one: V~t
Results of modeling of the regime of increase of the cumulative Results of modeling of the regime of increase of the cumulative number of victims from earthquakesnumber of victims from earthquakes V(t) V(t)
1 10 100
t , y ear s
1
10
100
1000
V ( t ) , thou .
peop le
V~t
V~t
.
Связь с социально-экономическими условиями
Connection with social and 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.
The regime of loss growth depends on the social/economic situationThe regime of loss growth depends on the social/economic situation
1 10 100
t, years
1 0
1 0 0
1 0 0 0
1 0 0 0 0
1 0 0 0 0 0
V(t)
1 10 100
t, years
1000
10000
100000
1000000V(t)
Vc
Vc
Vc Vc
Vc
Vc
Vc <Vc
Examples of C and Tc values for different types of disasters (numbers of fatalities)
Disaster type Regions,countries
Recurrence time
Tc, years
Characteristic boundary event
magnitude,Vc, victims
number
Really observed
maximum disaster, fatalities number
Data source
earthquakes Developed countries1900 - 19591960 - 1999
3330
9500024000
11000017000
Significant earthquakes
earthquakes Developing countries,1900 - 1959,1960 - 1999
4065
270000260000
200000240000
Significant earthquakes
floods North America and European Union
1950-19801980-2005
1510
1500500
650200
Em-dat
hurricanes Atlantic Ocean1850-1950
30 20000 11000 Disaster center
floods SE and S Asia1984-2006
20 10000 6000 Em-dat
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
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.
A number of correlation exist between economical and loss characteristics,an example:
loss/victims number ratio value and year per capita income correlation
0.1 1 10 100
Р , thou . $ /m an
0.1
1
10
100
L,10 6
$ / v ic t im
The distribution of values of (economic loss)/(number of victims) ratio differs essentially in the developing (1) and in the developed countries (2)
0.001 0.1 10
L , 106 $/victim
1
10
100
N
2
1
The flow rate of the strong (>100 casualties) seismic disasters The flow rate of the strong (>100 casualties) seismic disasters increases in the increases in the developing countries (1) and decreases in the developed countries (2) developing countries (1) and decreases in the developed countries (2)
(it can be seen clearly in comparison with the linear prognosis performed using (it can be seen clearly in comparison with the linear prognosis performed using the data for 1900-1940 years)the data for 1900-1940 years)
1900 1920 1940 1960 1980 t, years
0
100
200
N
1
2
V>100 people
Social and Economic Characteristics of Damaging Earthquakes for 1900-1999 in Different Regions
Region
(1)
Mean Number of casualties
(2)
Mean loss in
$
million
(3)
Mean ratio loss/casu-alties in $ million per
victim
(4)
Annual per capita product,
$ 1000 (as of 1970)
(5)
Ratio of values in columns
(4)/(5) 1000
(6)
Ratio of values in columns
(3)/(5) 1000
man-years (7)
North America
45
800
32 4.5 7.1
180
South Europe
800
340
8 1.5
5.3
230
Japan 2500 430 5.5 1.6 3.4 270 Latin America
560
130
1.3 0.5 2.6 260
Asia 2800 50 1. 0.2 5. 250 Indo-China
480
18
1.2 0.15 8. 120
Max/min ratio in columns
70
45
32 30 3 2.
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
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.
Shirt-term change in regime of loss values, social aspectShirt-term change in regime of loss values, social aspect
1900 1920 1940 1960 1980 2000
T , y ea rs
0
0.01
0.02
0.03
0.04
N
.
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
Coclusins: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.
4. 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.
5. 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 attentionThank you for attention.
