ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Flood Standard

Carel Eijgenraam

CPB Netherlands Bureaufor Economic Policy Analysis

An optimal Safety Standard for Dike-ring areas

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Map of Dike-Ring Areas

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Main topics

1. What is the most efficient level of safety? or:What is the optimal height of a dike?

2. How can the theoretical results be translated into legal safety standards?

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing • Absolute safety against flooding is impossible.

There will always be damage by flooding.

• More safety and less risk on damage are ALWAYS possible,but at rising costs.

• Making choices is possible and necessary, e.g. on the height of dikes.

• Economic question with a rational solution, but in the end a political decision has to be taken (imponderables, risk aversion)

Starting points forsafety standards

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing Central question:

• At which size of investment in prevention,e.g. in heightening dikes,are the social costs of an additional investment bigger than the social benefits of the extra decrease of the expected loss?

• At this point: stop investing.

Choosing on safety

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Cost Minimisationfor one-time investment

A

R = future expected loss = chance × loss

C = I + R

I = investment costs

X̂

Cost (euro)

Heightening dike (m)

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Cost Minimisation dynamic

Changes in the future:• deterioration water system e.g. climate change, subsidence of land => probability of flooding rises• growth of population and wealth

=> loss by flooding increases

In combination: expected loss increases(= probability x loss by flooding)

=> Changes lead to more than one decision on investment

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Driving Forces of the Investment Strategy

Two influences on decision:• discount rate (δ > 0):

– postpone investment expenses

• fixed investment costs:– do as much as possible at one time

Consequence: Heightening in jumps=> safety level is not constant, but fluctuating

Two questions to answer:• when?• how much?

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Optimal Strategy Dike Ring:Interval for expected loss

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Rising costs ==>Rising optimal loss interval

time

S–

S+

Expected damage per year (euros)

when ?

how much? =how long?

high

low

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Probabilities of Flooding for dike ring 43 Betuwe

0.00000

0.00050

0.00100

0.00150

0.00200

0.00250

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

PMIDDEN PPLUS PMIN P PWET

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Legal Safety Standards

Discussion about new legal safety standards for dike-ring areas

My personal policy advise:Use the middle of the interval as test

when action becomes desirable• understandable standard• only depending on average costs• enough time left for preparation and

construction of big actions

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Middle Probability of Flooding

S = δ × standard size × average optimal costs p.u.

mean

(t)

P =

mid

tS / V

mean

(t) t

P = Probability of flooding p.y.V = Wealth (damage by flooding)S = Expected loss p.y. (P x V)

Standard size = action that diminishes P with factor e (= 2,72...)

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Probability of Flooding when Investing continuously

probability

time

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Middle Probability of Floodingas standard test for action

P =mid

t

yearly cost of ‘standard’ action

Wealth

P ≈ “constant” x mid

t

lenght of dike

number of inhabitantst

t

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Middle optimal safety (2,5%) andinhabitants per km dike (log)

100

1000

10000

100000

100 1000 10000 100000

safetymiddle probability

inhabitants / leghth of dike

44

45

50

41

42

1151

49

432000

1250

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Two common ideas in the discussion about standards

• More differentiation seems efficient:more people/value => more safety(both between areas and in time)– compare 50 with 51 and 49

• Base new standards on CBA

• Both ideas on efficiency do raise questions on equality

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Two consequences of using Cost Benefit-Analysis

• Costs matter as much as benefits.– compare dike-ring areas 45 and 43

• Outcome is roughly in line with distributing the same amount of money to every inhabitant of a dike ring, irrespective the situation of that dike ring.

==> CBA leads to equality in input, not to equality in output.

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Other Policy Considerations

• Guarantee minimum level for personal safety

• Standard for societal risk,

if more than proportional (CBA)?

Takes the highest safety standard of the three (CBA, PS, SR)

ISDF42008-05-08

130

Saf

ety

Sta

ndar

d fo

r F

lood

ing

Important Messages onSafety of Dike-ring Areas

1. Not the probability of flooding, butthe expected loss is the pivotal variable in making decisions about the safety of dike-ring areas.

2. Derive the legal safety standard for the probability of flooding from the expected loss.

3. My policy advice:Use the Middle Probability of Flooding as basis for the standard for testing the safety of the whole dike ring.

4. Add a text in the law that makes robust designs and actions possible.