1
Up or Out?
Levee setback vs. levee height
Tingju Zhu
International Food Policy Research Institute
Jay R. Lund
University...
2
Overview
1. Levees
2. Height vs. setback
3. A mathematical formulation
4. Some solution results
5. Implications
3
Levees
1. Levees are common for land protection
2. Imperfect but sometimes optimal
protection
3. Failure by: overtopping...
4
Height vs. Setback
1. Every levee design involves a trade-off of
levee height against levee setback
2. Greater height co...
5
A Mathematical Formulation
EC(.)= expected annualized total cost
Xs = designed levee setback
Xh = designed levee height
...
6
Optimize Analytically 1
C(.) = annualized cost to build a levee of height
B(.) = annual value of floodplain land (both l...
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
...
8
Solution
Optimal height vs. set-back trade-off
LHS = marginal economic value of
less setback/marginal channel
capacity w...
9
Implications
Optimal height vs. set-back trade-off is
only a function of land and
construction economics and relative
hy...
10
Re-Design of Existing Levee
1. Previous formulation was for a new levee.
2. What if a levee exists – with a setback
and...
11
Solution 1
1. Compare EV cost for each of the
three alternatives.
2. Some decision rules result.
Height
Setback
Xh0 < c...
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 Setb...
13
Conclusions
1. Levee height vs. setback trade-off
2. Optimal trade-off determined by
construction costs vs. relative la...
14
Other Big Changes
1. Population growth
2. Land use
3. Social values
4. Economic well-being
5. Crop prices, yields,
etc....
15
Adaptation Studies for
Climate Change
 Planning studies more than “impact” studies
 Allow and explore substantial ada...
16
Flooding on the Lower American River
Climate Change
and
Urbanization
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...
18
Method
 Optimize levee heights & setbacks over time
 Minimize average total cost of:
• flood damage and frequency
• l...
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
1...
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
1...
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
1...
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
1...
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)
Ave...
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 (...
25
Observations
1) Climate changes or urbanization alone can
be accommodated by raising levees
2) Combined effects can rai...
26
Flood Control Conclusions
1) People and societies adapt all the time.
2) Combined effects of climate change and
other f...
27
Adaptation Studies for
Climate Change
 Planning studies more than “impact” studies
 Allow and explore substantial ada...
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Up or Out?—Economic-Engineering Theory of Flood Levee Height and Setback

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Up or Out?—Economic-Engineering Theory of Flood Levee Height and Setback

  1. 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. 2 Overview 1. Levees 2. Height vs. setback 3. A mathematical formulation 4. Some solution results 5. Implications
  3. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 16 Flooding on the Lower American River Climate Change and Urbanization
  17. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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