1) The document discusses optimizing levee height and setback tradeoffs to minimize costs from flooding over time as conditions change from urban growth and climate change. 2) Modeling results show that considering combined effects of climate change and urbanization may require raising levees and increasing setbacks more than from either factor alone. 3) Adapting levees and widening floodways on the American River could help address increasing Central Valley flooding risks from continued development and trends toward wetter climates with larger floods.

1. 1
Up or Out?
Levee setback vs. levee height
Tingju Zhu
International Food Policy Research Institute
Jay R. Lund
University of California, Davis
http://cee.engr.ucdavis.edu/faculty/lund/CALVIN/

2. 2
Overview
1. Levees
2. Height vs. setback
3. A mathematical formulation
4. Some solution results
5. Implications

3. 3
Levees
1. Levees are common for land protection
2. Imperfect but sometimes optimal
protection
3. Failure by: overtopping, slope failure,
seepage, false sense of security
4. Economic controversies over costs,
benefits, and risks
5. Environmental controversies over
aquatic and terrestrial stream corridors
and interactions

4. 4
Height vs. Setback
1. Every levee design involves a trade-off of
levee height against levee setback
2. Greater height costs more, but allows less
setback to protect more land
3. Less setback (greater height) driven by
difference in land value between protected
and unprotected floodplain land
4. Can be seen as a benefit-cost tradeoff
5. Might be expanded to include
environmental benefits of flood-prone land

5. 5
A Mathematical Formulation
EC(.)= expected annualized total cost
Xs = designed levee setback
Xh = designed levee height
P(.)= failure probability for levee height & setback
D = damageable property value (potential loss in a
flood disaster)
C(.) = annualized cost to build a levee of height
B(.) = annual value of floodplain land (both leveed
and unleveed)
       , , ,s h s h h s hMin EC X X P X X D C X B X X   

6. 6
Optimize Analytically 1
C(.) = annualized cost to build a levee of height
B(.) = annual value of floodplain land (both leveed
and unleveed)
  0
h h h
C BEC P
D
X X X
  
   
  
0
s s s
EC P B
D
X X X
  
   
  

7. 7
Optimize Analytically 2
If levee fails only by overtopping, and
given a levee overtopping flow
Q(Xs, Xh) …
hh X
Q
Q
P
X
P








ss X
Q
Q
P
X
P








By the chain rule and some algebra…

8. 8
Solution
Optimal height vs. set-back trade-off
LHS = marginal economic value of
less setback/marginal channel
capacity with increased setback
RHS = marginal economic value of
greater height/ marginal channel
capacity with increased height
 
s s h h
C BB Q Q
X X X X
   
 
   

9. 9
Implications
Optimal height vs. set-back trade-off is
only a function of land and
construction economics and relative
hydraulic effectiveness.
Not affected directly by flood frequency
or flood damage.
Optimal channel capacity is separate.
 
s s h h
C BB Q Q
X X X X
   
 
   

10. 10
Re-Design of Existing Levee
1. Previous formulation was for a new levee.
2. What if a levee exists – with a setback
and height designed long ago.
3. Three choices:
a) Keep levee as is.
b) Raise levee to an optimal height.
c) Build new levee at optimal location.

11. 11
Solution 1
1. Compare EV cost for each of the
three alternatives.
2. Some decision rules result.
Height
Setback
Xh0 < c
h0X
c
h0X < Xh0 < *
h0X ELSE
Xs0 <
1c
sX Move to ),( **
hs XX
Raise current levee to *
0hX Do nothing if
Xh0 >
*
h0X
1c
sX < Xs0 <
2c
sX Move levee inward and resize to ),( **
hs XX
Do nothing if
Xh0 >
2c
h0X
Xs0 >
2c
sX Move levee inward and resize to ),( **
hs XX

12. 12
Solution 2
Decision rules for an example.
0
10
20
30
40
50
60
70
80
90
0 200 400 600 800 1000 1200 1400 1600
Levee Setback (ft)
LeveeHeight(ft)
Do nothing
Raise to optimal height
at current setback
RebuildRebuild
Optimal
setback
First
Critical
Setback
Second
Critical
Setback

13. 13
Conclusions
1. Levee height vs. setback trade-off
2. Optimal trade-off determined by
construction costs vs. relative land value,
with hydraulic efficiencies.
3. Damage and flood frequency do not affect
optimal substitution of height for setback.
4. Levee re-design also can be analyzed with
some intuitive decision rule results.
5. As conditions change, so sometimes
should levees.

14. 14
Other Big Changes
1. Population growth
2. Land use
3. Social values
4. Economic well-being
5. Crop prices, yields,
etc.
6. Others?
John Landis, UCB, estimates 2002

15. 15
Adaptation Studies for
Climate Change
 Planning studies more than “impact” studies
 Allow and explore substantial adaptation,
preferably with multiple options
 Use future population, land use, and
economic conditions
 For complex systems, some optimization will
be required
 Interpretation and limitations

16. 16
Flooding on the Lower American River
Climate Change
and
Urbanization

17. 17
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
1900 1950 2000 2050 2100 2150
Time (yr)
MeanAnnualFloodPeak(m3
/s)
HCM2 Regression
Historical Trend
Stationary History
=
Three-Day Peak Inflows at Folsom Lake

18. 18
Method
 Optimize levee heights & setbacks over time
 Minimize average total cost of:
• flood damage and frequency
• levee construction
• lost urban and floodplain land value
 Considers changing flood probabilities
 Changing urban land and flood damage
values – 150 year time frame.

19. 19
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Time (yr)
LeveeHeight(m)
0
30
60
90
120
150
180
210
240
270
300
LeveeSetback(m)
HCM2
Historical Trend
Stationary Historical
Climate Change Alone Without Urban Growth

20. 20
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Time (yr)
LeveeHeight(m)
0
30
60
90
120
150
180
210
240
270
300
LeveeSetback(m)
0% 2% 4%
Series6 Series7 Series8
Urbanization rate:
Urban Growth Alone

21. 21
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Time (yr)
LeveeHeight(m)
0
30
60
90
120
150
180
210
240
270
300
LeveeSetback(m)
0% 2% 4%
Urbanization rate:
Combined Effects with Historical Trend in Floods

22. 22
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Time (yr)
LeveeHeight(m)
0
30
60
90
120
150
180
210
240
270
300
LeveeSetback(m)
0% 2% 4%
Urbanization rate:
Combined Effects with HCM2 Scenario

23. 23
Costs: 2% Urbanization & HCM2 Climate
0
200
400
600
800
1,000
1 21 41 61 81 101 121 141
Time (yr)
Cost($Million/yr)
Average Flood Damage
Forgone Land Value
Construction Cost

24. 24
2% Urbanization & HCM2 Hydrology
0
200
400
600
800
1,000
1,200
1,400
1,600
1,800
2,000
0 20 40 60 80 100 120 140
Time (yr)
FloodingFrequency(years)
0
5
10
15
20
25
30
ChannelCapacity(103
m3
/s)
Flood Recurrence Period
Channel Capacity
“100-year” flood
“500-year” flood

25. 25
Observations
1) Climate changes or urbanization alone can
be accommodated by raising levees
2) Combined effects can raise levees and
increase levee setbacks
3) Adding loss of life accelerates levee raising
and floodway widening
4) Adding climate change uncertainty could
slow or speed adaptation
5) Non-levee adaptations are also likely
6) Raising American River levees & perhaps
widening floodway might be desirable

26. 26
Flood Control Conclusions
1) People and societies adapt all the time.
2) Combined effects of climate change and
other factors are important for adaptations
3) Increasing Central Valley flooding problems
– Continued urbanization
– Wet climate warming & apparent flood trends
– Other tributaries have similar problems
– Limits of levees and levee heights alone
4) “100-year” flood planning is a bad wager.

27. 27
Adaptation Studies for
Climate Change
 Planning studies more than “impact” studies
 Allow and explore substantial adaptation,
with multiple options
 Use future population, land use, and
economic conditions
 For complex systems, some optimization will
be required
 Interpretation and limitations