-Natural Disasters –
“ A naturally occurring or
man-made geologic condition or
phenomenon that presents a
risk or is a potential danger to
life or property”
(American Geologic Institute, 1984)
Major Earthquakes
Magnitude 6.6 Bam IRAN
2003 December 26 01:56:52 UTC
Hazard
Naturally occurring, or human-induced
process or event, with the potential to
create loss…future danger
Risk
The actual exposure to something of
human value to a hazard – regarded as
the probability of a hazard occurring
Disaster
When large numbers of people are
killed, injured or affected in some
way..actually happens
Effect of Hazards on
Global Economy
$50 bill/year
•1/3 represents
cost of prediction
prevention & mitigation
(Alexander, 1999)
Global average
250,000 deaths/year
~95% in 3rd world countries
(Alexander, 1999)
For U.S.
Why Is Disaster Impact Growing?
•Population Growth
•Land Pressure
•Urbanization
•Inequality
•Political Change
•Economic Growth
•Technological Innovations
•Global Interdependence
(Alexander, 1999)
Predicting
Hazard
Preventing
Risk
Mitigation
Disaster
Risk Assessment
1.Identification of hazards likely to
result in disasters.
2.Estimation of the risk of such events
– i.e. probability
3.Evaluation of the social consequence
of the derived risk – i.e. the likely
loss associated with the risk
4.Checks and Balance
Risk Assessment
1.Identification of hazards likely to
result in disasters.
2.Estimation of the risk of such events
– i.e. probability
3.Evaluation of the social consequence
of the derived risk – i.e. the likely
loss associated with the risk
4.Checks and Balance
Example of Probability estimation
Hemoccult Blood Test
• 300 in every 100,000 have cancer
• Hemoccult test will be positive in
half the occurrences of cancer
• 3% chance that person without
cancer will test positive
A patient receives news of a positive
test. What is the probability that the
patient has cancer?
Hemoccult Blood Test
•Of 300 who have cancer 150 will test positive
•Of the 99,700 who do not have cancer 3,000
will also test positive (0.3 x 99,700)
•Total of 3,150 positive tests
•Thus, 150/3150 have cancer
1 in 20 chances that the patient
actually has cancer
Risk Assessment
1.Identification of hazards likely to
result in disasters.
2.Estimation of the risk of such events
– i.e. probability
3.Evaluation of the social consequence
of the derived risk – i.e. the likely
loss associated with the risk
4.Checks and Balance
Risk Assessment
1.Identification of hazards likely to
result in disasters.
2.Estimation of the risk of such events
– i.e. probability
3.Evaluation of the social consequence
of the derived risk – i.e. the likely
loss associated with the risk
4.Checks and Balance
Risk Assessment
Statistical analysis of risk is based on
probability.
R = p x L
Risk
probability
Loss
Risk =
Hazard (probability) x Loss (expected)
Preparedness (loss mitigation)
Cost – benefit analysis
total
risk
risk
risk
vulnerability = amplification – mitigation ± perception
measures
measures
factors
net impact
total benefits total costs costs of
of disasters = of inhabiting – of disaster ± adaptation
hazard zone
impact
to hazard
Risk Probabilities
•Food Poisoning by botulism
•Tornado
•Car Crash
•Fire
•Murder
•Airplane Crash
•Firearms Accident
•Asteroid or Comet Impact
•Flood
•Venomous bite or sting
•Electrocution
Risk Perception
Risk Probabilities
Risk Probabilities
Time and Space
Very important for understanding how
disasters occur and are managed
Geologic Time
Timescales of geophysical phenomena
•The Magnitude-frequency principle – the amount
of energy released by an event of a given size is a
product of their magnitude x frequency
Large infrequent vs. small and frequent
Estimation of recurrence interval
Randomness in Natural Events
Cyclicity of events
Geologic Space
Geologic Space
Risk Assessment
Risk Perception
Subjective
Hazard Perception
•Past Experience
•Present attitudes
•Personality and values
•Future expectations
•Media
•Government
•Geography
Misconceptions about Disasters
•No respect for Nature (Technocentric)
•Disasters are unique and exceptional
events
•Politicians and Policy
•Misinformation and misconceptions
concerning specific aspects of ND
Hazard Perception
•Determinate – Not excepting of the
random element of hazards. Desire to
view hazard occurrence in ordered fashion
•Dissonant – threat denial. Hazards are
viewed as freak occurrences, or dismissed
all together
•Probabilistic – the most sophisticated.
Accepts that hazards will occur and also
perceives that many events are random
Risk
~1000 x greater acceptance
Perceived social benefit of risk
Some Science
and
Math Background
Accuracy
Vs.
Precision
Accuracy
We define accuracy in science as
…an estimate of the probable error of a measurement compared with
the 'true' value of the property being measured.
•We do not actually know the 'true' value of any
phenomenon (including 'constants', such as the mass of
the electron).
•Therefore, we are always forced to estimate the
accuracy of a measurement.
•In general, more measurements (estimates) of a value
should reveal a more accurate estimate: 1000
measurements should be more accurate than 10.
•This process is not linear; as the number of
measurements increases the 'improvement' in accuracy
diminishes to a point where it is not worthwhile making
more estimates.
Precision
The term precision is used in science in two ways:
•as an indication of the 'spread' of values
generated by repeated measurements.
•as the number of significant figures with which a
measurement is given.
•If the distribution (spread) of measurements is wide
then we have low precision; if the measurements have a
narrow spread (all similar) then we have high precision.
•Precision is a property of the experiment and/or
apparatus that is being used to generate the
measurements.
•What does it mean if a machine is producing a high
precision result with low accuracy?
What is a meter?
•1793 – to test Newtonian mechanics, a geodetic survey
was undertaken to measure the curvature of the earth
•Used this to establish a standard of measurement
•Determined the distance from the equator to pole along
a line of meridian and divided it into 1.0x107 equal
parts.
•Length was translated onto a bar of platinum-iridium
alloy
•1960 – redefined as a specific number of wavelengths
(1,650,763.73) of a particular spectral line in the
electromagnetic radiation emanating from an excited
krypton-86 atom.
•1983 – redefined as a distance traveled by light in a
vacuum during the time interval of 1/299,792,458 of a
second
Fractals
(Mandelbrot, 1964).
Fractals
Scale invariance - a consistent relationship between the size of
something and the frequency with which it occurs or the size of the
measuring stick that you use to measure it with. The exponent of
this relationship is called the fractal (Mandelbrot, 1964).
Question - "How long is the coast of Britain?"
•Answer - undefinable because the length
is dependent on the scale at which you
measure it.
•The longer the measuring stick the shorter the length.
Error
Vs.
Uncertainty
Error
Error refers to the disagreement
between a measurement and the
true or accepted value.
Uncertainty
Is an interval around a measured
value such that any repetition of
the measurement will produce a new
result that lies within this interval
Sometimes stated as a probability
in the format “value ± 1 SD” (68%)
Uncertainty
There are always uncertainties when taking
measurements
1. from the estimating process itself
2. precision of the measuring device.
Estimating
There are always uncertainties when taking
measurements
1. from the estimating process itself
2. precision of the measuring device.
Estimating
Estimating
3.1 +/- 0.1 units
Estimating
3.1 +/- 0.1 units
3.07 +/- .05 units
Estimating
Instruments precision +/- 0.1 units
So our estimated measurement is probably better
than w = 3.1 +/- 0.1 units, but not as good as w
= 3.07 +/- 0.05 units
Estimating
Multiple
Measurements
average or mean value
x1 + x2 + x3 + ... + x N 1
x=
=
N
N
N
∑x
i =1
i
Estimating
Multiple
Measurements
Length
(cm)
Deviation
from mean
58.0
58.2
59.1
57.3
57.5
54.6
53.6
59.5
58.0
59.0
57.1
0.6
0.8
1.7
0.1
0.1
2.8
3.8
2.1
0.6
1.6
0.3
average or mean value
x1 + x2 + x3 + ... + x N
1
x=
=
N
N
N
∑x
i =1
i
Estimating
Multiple
Measurements
Length
(cm)
Deviation
from mean
58.0
58.2
59.1
57.3
57.5
54.6
53.6
59.5
58.0
59.0
57.1
631.9
0.6
0.8
1.7
0.1
0.1
2.8
3.8
2.1
0.6
1.6
0.3
14.5
631.9 / 11 = 57.44545455
= 57.45 (mean)
What is the
% uncertainty?
14.5 / 11 = 1.318181
(average deviation)
57.45 ± 1.32
57.45 ± 2.30%
Significant Figures:
1. Non-zero digits are always significant.
3. A final zero or trailing zeros in the decimal portion ONLY
are significant. For example, in 0.02340 the first two
zeros from the left are not significant but the zero
after the 4 is significant.
4. If there is no decimal point explicitly shown, the rightmost
non-zero digit is the least significant figure. For
example, in 3400 the 4 is the least significant figure
since neither zero is significant in this case.
5. Any zeros between two significant digits are
significant. For example, 6.07 has three significant
figures.
Significant Figures:
MULTIPLICATION or DIVISION
Keep the same number of sig figs as the number with the
least number of sig figs.
Example: 1.2 x 4.56 = 5.472 on the calculator.
Answer = 5.5
ADDITION or SUBTRACTION
Keep the same number of decimal places as the nummer
with the least amount.
Example: 1.234 + 5.67 = 6.904 on the calculator.
Answer =6.90
Arithmetic mean is commonly called the
average. The mean is the sum of all values
divided by the number of values.
Mode is the most frequently occurring value in
a distribution and is used as a measure of
central tendency (can have multiple modes).
Median is the middle of a distribution: half the
scores are above the median and half are
below the median (less sensitive to extremes –
good for skewed distributions).
mode < median < mean
Standard Deviation
68.2%
95.5%
99.7%
Variance
The variance is a measure of how spread out a distribution is.
σ =
2
(
−
μ
)
X
∑
μ
= mean of population
X
= individual population value
N
= total # in population
N
2
Standard Deviation =
=
X
(
−
μ
)
∑
σ
2
N
d1 + d 2 + ... + d N
=
N
μ = mean of population
2
X
N
2
= individual population value
= total # in population
2
Length
(cm)
Deviation
from mean
Deviation from
mean squared
58.0
58.2
59.1
57.3
57.5
54.6
53.6
59.5
58.0
59.0
57.1
631.9
0.6
0.8
1.7
0.1
0.1
2.8
3.8
2.1
0.6
1.6
0.3
14.5
0.4
0.6
2.9
0.0
0.0
7.8
14.4
4.4
0.4
2.6
0.1
33.6
631.9 / 11 = 57.44545455
= 57.4 (mean)
57.4 ± 1.3
57.4 ± 1.7
14.5 / 11 = 1.3
(average deviation)
∑( X − μ)
N
2
=
33.6
11
= 1.7
(standard deviation)
Data
•Graph should have a title
•Axes should be labeled
Dow Jones Industrial
Average over the last
13 weeks
•Vertical axis (ordinate) is always a
function of (dependent variable) the
horizontal axis (independent variable
(abscissa)
•Choose appropriate scale
•Connecting points is justified only if
there is a functional dependence
CRED –
Center for Research on
the Epidemiology of Disaster
OFDA –
Office of Foreign
Disaster Assistance
Deceptive use of area/volume to depict data
Deceptive use of area/volume to depict data
Linear Relationship
Stream Discharge (m3 s-1) vs. Stream Velocity for a
constant Cross-sectional Stream Area
12
10
8
6
4
2
0
0
100
200
300
400
500
600
Linear Relationship
120
y = 2x + 5
100
80
y
Slope = 2
60
40
20
5
0
0
5
10
15
20
25
x
30
35
40
45
50
m=
n∑ ( xy ) − ∑ x ∑ y
n∑ ( x ) − (∑ x )
2
2
y − m∑ x
∑
b=
n
2
r
= statistical significance of line fit
r=
n∑ ( xy ) − ∑ x ∑ y
[n∑ ( x ) − (∑ x) ][n∑ ( y ) − (∑ y ) ]
2
2
2
2
y = mx + b
y = 0.58x + 1.7
slope = 0.58
b (y-intercept) = 1.7
2
r
= 0.97
Exponential Relationship
y=
bx
ma
Relationship where the amount of increase or decrease, is
a function of where you are in the number sequence –
simply put, the amount of change in x is a function of x.
Population Growth Rate
6,261,118,623
6,361,827,322
6,490,953,148
Growth today ~ 1.3%
Doubling time 53 years
Exponential Relationship
Earthquake magnitude scale
Power-Law Relationship
y=
b
mx
Distributions for which there are a large number of
common events and a small number of rarer events.
Power-Law Relationship
Trigonometric Functions
Cosine, Sine, Tangent
Linear space data plots
Stream Discharge (m3 s-1) vs. Stream Velocity for a
constant Cross-sectional Stream Area
12
10
8
6
4
2
0
0
100
200
300
400
500
600
Linear Data Plots
•Very common plots
•Distance along axis is directly proportional to parameter
value
Linear-linear plots have two shortcomings:
(1)If the data span a large range, the data at smaller
range will be all located on top of each other.
(2) It is not easy to find the functional trend of data if it
is not nearly linear, e.g., it is hard to differentiate
between y = x3 and y = exp(x).
7E+14
Power
y =Law
2x +Distribution
5
[y = x5]
6E+14
5E+14
4E+14
3E+14
Power Law Distribution [y = x5]
2E+14
Exponential [y = ex]
1E+14
0
3500000
0
5
10
15
20
25
30
3000000
25000
2500000
20000
Y
Exponential [y =
2000000
ex]
1500000
15000
1000000
10000
500000
5000
0
0
5
10
X
0
0
2
4
6
8
10
15
20
Semi-Log Data Plots
•One axis is linear, other axis is logarithmic
•Equal distance between two major tick marks is equally
to a factor of 10 change in the value.
•Shape of curve in a semi-log plot is not the same as the
function, e.g., a line on log-linear plot does not correspond
to y=ax+b, rather to log(y)=ax or y=exp(ax), an exponential
function. (a line in linear-log plot corresponds to an
logarithmic function).
•Ideal for plotting exponential functions.
•Zero or negative values are not allowed for the log axis as
log of negative numbers do not exist.
100000
25000
Linear - Log
Log - Linear
10000
20000
1000
15000
Exponential [y = ex]
100
10000
10
5000
1
0
0
2
4
6
8
10
1
10
3000
10000
Linear - Log
Log - Linear
2500
1000
2000
1500
100
Power Law Distribution [y = x2]
1000
10
500
0
1
0
5
10
15
20
25
30
35
40
45
50
1
10
100
Log-Log Data Plots
•Both axis are logarithmic
•A log-log plot is the same as plotting log(y) versus log(x)
in linear fashion.
100000
Exponential [y =
10000
ex]
Power Law Distribution [y = x2]
10000
1000
1000
100
100
10
10
1
1
1
10
1
10
100