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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

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  • 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