Download February 3

Project Storm Fury
Review
A stochastic variable has the following
probability distribution:
Values of X
Probability distribution
of X
x
P(X=x)
$1
P(X=1) = 1/3
$2
P(X=2) = 1/3
$3
P(X=3) = 1/3
Review
• What is X’s cumulative probability
distribution?
• What is its expected value (X=?)
• What is the Variance of X?
• What is its standard deviation?
Review
What is the Variance of X?
VarX =  xi2 P(X=xi) - 2
= [1(1/3) + 22(1/3) + 32(1/3)] - 22
= (1/3 + 4/3 + 3) - 4
= 2/3
What is its standard deviation ()?
X = SqrRoot(VarX) = (2/3)1/2
= .8165
Total Property Damage
($ of 1969)
Maximum sustained winds
over time
Alternative Hypotheses
• H1, the “beneficial” hypothesis. The
average effect of seeding is to reduce
maximum sustained wind speed.
• H2, the “null” hypothesis. Seeding has no
effect on hurricanes. No change is induced
in maximum sustained wind speed.
• H3, the “detrimental” hypothesis. The
average effect of seeding is to increase the
maximum sustained wind speed.
Mathematical expressions
• P(w' | H2) = P(w) = fN(100%, 15.6%)
• P(w' | H1) = ƒN(85%, 18.6%)
• P(w' | H3 ) = ƒN(110%, 18.6%)
Probability density function
for Debbie results
• P(69%, 85% | H1) = 1.50 x 2.14 =3.21
• P(69%, 85% | H2) = 0.372 x 1.64 = 0.61
• P(69%, 85% | H3) = 0.195 X 0.886 = 0.173
P(H1 | 69%, 85%) = (3.21 x 1/3)/(3.21 x
1/3 + 0.61 x 1/3 + 0.173 x 1/3) = .81
P(H2 | 69%, 85%) = .15
P(H3 | 69%, 85%) = .04
Prior probabilities - pre and
post Debbie
• P(H1) = .15
• P(H2) = .75
• P(H3) = .10
• P(H1) = .49
• P(H2) = .49
• P(H3) = .02
.81(.15)/ [.81(.15) +.15(.75) + .04(.1)] = .51
.15(.75)/ [.81(.15) +.15(.75) + .04(.1)] = .47
.04(.1)/ [.81(.15) +.15(.75) + .04(.1)] = .02
The Seeding Decision
Probabilities assigned to wind changes occurring
in the 12 hours before hurricane landfall
Cumulative probability functions
Probabilities assigned to wind changes occurring
in the 12 hours before hurricane landfall.
Discrete approximation for five outcomes.
Interval of changes in
maximum sustained wind
Representative value in
discrete approximation
Probability that wind
change will be
within interval
(%)
If seeded
If not seeded
Increase of 25% or more
32
0.038
0.054
Increase of 10 to 25%
16
0.143
0.206
0
0.392
0.480
Reduction of 10 to 25%
-16
0.255
0.206
Reduction of 25% or more
-34
0.172
0.054
Little change, +10 to -10%
The seeding decision for the
nominal hurricane
$21.7M
The expected value of perfect
information
The value of further tests
Review
1.
2.
3.
4.
5.
6.
7.
Decide whose benefits and costs count, and how much. This
is typically referred to as determining standing.
Select the portfolio of alternative initiatives.
Catalog potential consequences and select measurement
indicators.
Predict quantitative consequences over the life of the project
for those who have standing.
Monetize (attach cash values to) all the predicted
consequences.
Discount for time to find present values.
Sum up benefits and Costs for each initiative and Perform
sensitivity analysis underlying key assumptions
Adapting to Climate Change 1
Adapting to Climate Change 2
Adapting to Climate Change 3
Adapting to Climate Change 4
Adapting to Climate Change 5
Source: Oregon Environmental Quality Commission, Oregon Climate
Change Adaptation Framework. December 10, 2010, Salem OR