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Probability can also be
expressed as a probability of a
magnitude being equaled or
exceeded in a particular time
period, here 30 years. In this
case the probability axis
(return period) is plotted on a
linear scale (a year is the same
anywhere on the scale) so the
distribution of events takes on
the curve common to many
natural phenomena—that is,
you’re essentially looking at a
tail of a normal distribution.
This brings us to;
magnitudefrequency
relationships (pp.
56-59)
Events can be expressed
in Return period, or some
form of “probability of
exceedance” (or in this
case, p of “nonexceedance”, where event
magnitudes (in this case
maximum wind gusts) are
ranked, and plotted against
logarithm of their
frequency. This describes
a more or less straight line,
from which interpolations
can be made.
We’ll see many maps of 30
year ground motions for
California earthquakes. Why
might 30 years be a common
time period for such analysis?
As hazards scholars we’re interested in the rare events, the tails
of the distribution. So when you see a plot of probability vs.
magnitude (against a linear axis), it often curves like Fig. 4.4 in the
text.
Look familiar?
How to Choose “return interval” for
risk management
What probability or return interval matters, where
to set the target or threshold?
Several approaches:
• Arbitrary but socially useful:
– 30 year return or P in 30 years
– 100 year r: frequent enough that development
should be prepared for it, but safety
regulations not onerous as for, say, a really
rare 500 yr or 1,000 year r.
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Here’s example ground motion risk map---we go over steps in EQ risk
assessment in future lectures.
10% chance in 50 years
As hazards scholars we’re interested in the rare events, the tails
of the distribution. So when you see a plot of probability vs.
magnitude (against a linear axis), it often curves like Fig. 4.4 in the
text.
OK, so how does
this become
this?
Look familiar?
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Log graph paper can be used to
plot raw data that reflects
exponential growth (the larger
the quantity gets, the faster it
grows---it may for example be
squared or cubed for each unit
of growth), so that it creates a
straight line (visually linear
relationship). This allows easier
extrapolation and it also saves
space!
Simple Calculation of TR and p:
• Recurrence interval (years of observation / #
of events; expressed in the unit time period):
Tr = years of observation / # of events
• Probability in any time period (# events /
years, expressed in decimal or percent): p = #
events/years
– Percent can also be calculated as: p% = 100/r
Here’s an example of a distribution of maximum annual
streamflows, in cubic feet per second, for a small river. Note
not all of the observations fall right on the line, so the
distribution is not perfectly “normal” in shape.
Exercise 1: frequency distribution, probability, and
return period of Boulder daily snowfalls from 55
years (winters) of data.
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Temporal trends also change the distribution: Temporal trends
mean that the descriptive statistics and probabilities change over time.
Mean, variance, and auto-correlation could all change. WHY?
The Swiss rainfall record above looks random over time, but the Sahelian record
below looks like it became more cyclical after about 1950.
In this set of theoretical time series from the text, the event time series
shows a temporal trends in a and b (decrease over time in A; greater
variability over time in B). The time series can also be compared to
vulnerability, or society’s threshold of impacts, which can change
independently of physical trend (narrowing in C).
• Ouch! Any temporal trend in average
or variance means more data may not
yield a better measure of central
tendency or probability, since they are
always changing!
Trend: decrease
Trend: increase
variance
Trend: stable,
but tolerance
or vulnerability
narrows.
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• Risk = probability times consequence
• We have covered probability
• Consequence can be measured in many ways: dollars of
damage, fatalities, population exposed, etc..
• Compare consequences and risk:
Return to the Burton, Kates and White reading, starting on p. 34
“Response to Hazards”
– .1 X 1,000 lives = 100 (ten year event)
– .01 X 1,000 lives = 10 (one hundred year event)
– .01 X 10,000 lives = 100 (one hundred year event)
• Consequence (or impact) can often be reduced and risk
assessment is almost always associated with risk management
or mitigation:
Risk = probability X loss
mitigation
In theory, risk assessment can be used to help
make decisions about Reponses to hazards.
Human response is affected by:
•Perception: risk assessment, “sense”
of the hazard.
•Awareness of mitigation options
•Evaluation of mitigation options
The Range of Response
• Adjustment (or Adaptation, we’ll use the terms
interchangeably though some authors want
them more defined, usually as short vs long-term
• Cultural adaptations have long been a part of
human development---e.g., the way traditional
farmers grew crops or built their homes.
• Adjustment: can be purposeful or inadvertent:
Together define: “absorptive capacity”
Here Burton Kates and White lay out a decision-tree of possible adjustments.
Change in location may make obvious sense, but is likely to be the most difficult
and costly adjustment—who wants to leave their home? Still, in very hard hit
areas, like New Orleans after Katrina, permanent re-location may be more
common.
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Hurricane
Flood
Earthquake
Tsunami
Protection (Prevention): modify the event:
(Dams, levees, cloud seeding, etc.)
wildfire
Magnitude, frequency,
duration, extent
Natural Events
System
Environmental Hazard
Human use
System
Impacts
Burton, Kates and
White often surveyed
people about their
adjustments, in this
case traditional
farmers in Tanzania
and Nigeria.
Response
economic loss
Exposure /
Vulnerability
Agriculture
Settlement
Transportation
Housing
Adaptation: modify human
vulnerability (land use
regulations, preparedness,
etc.)
Mitigation: Modify the Loss
Burden (Disaster aid,
insurance)
So, how do people choose adjustments?
Theory:
People collect information and weigh options (costs
vs. benefits), then make a choice of adjustment.
Prescriptive or Normative Formulation:
• Rational choice theory: people collect all
available information, weigh options, and
choose adjustments that maximize expected
benefits (or utility).
• aka Maximized Expected Utility: risks vs.
benefits and costs: objective costs and
benefits.
Descriptive theory:
• Subjective Expected Utility: perceived
probability and perceived costs and benefits.
• Bounded Rationality: personal, social, cultural
factors impinge---non-hazard-related goals,
limited knowledge of adjustment, etc.
The latter explains much of the “illogical”
exposure and adaptation to hazards we can
observe.
Read: The Fisherman’s Choice.
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Let’s focus mostly on rational choices based on given
probabilities and assessed consequences.
20% chance
Hurricane
No Hurricane
Evacuate
-1
-1
-1
Remain
-3
0
-0.6
30% chance
Hurricane
No Hurricane
Evacuate
-1
-1
-1
Remain
-3
0
-0.9
Make sure you understand the ideas in this table, and that you could
calculate a simple pay-off matrix like in B and C, and explain how a
decision-maker might try to “minimize regrets.”
50% Chance
40%
Evacuate
-1
-1
-1
Remain
-3
0
-1.2
Hurricane
No Hurricane
Evacuate
-1
-1
-1
Remain
-3
0
-1.5
No Hurricane
Evacuate
1
1
1
Remain
0
2
1
60% Chance
50%
Hurricane
Hurricane
No Hurricane
Evacuate
1
1
1
Remain
0
2
0.8
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