Flood Management

1. Flood Management Water Resources Planning and Management Daene C. McKinney

2. Floods • Floods affect the lives of more than 65 million people per year • More than any other type of disaster, including war, drought and famine • In East and Southeast Asia, during the monsoon season, rivers swell to over 10 times the dry season flow • About 13% (of 45,000) of all large dams in the world – in more than 75 countries – have a flood management function USGS - top; www.ci.austin.tx.us - bottom

3. Hydrologic Cycle Precipitation, P(t) Runoff, streamflow, Q(t)

4. Flood Damage • Injuries and loss of life • Social disruption • Income loss • Emergency costs • Physical damage • Structures, utilities, autos, crops, etc. • Lost value of public agency services • Police & fire protection, hospitals, etc. • Tax loss • Property and sales www.ci.austin.tx.us

5. Streamflow Hydrograph Basin Lag Centroid of Precipitation Peak Time of Rise Recession Limb Discharge, Q Rising Limb Baseflow Recession Inflection Point Baseflow Recession Baseflow Time Beginning of Direct Runoff End of Direct Runoff

6. Storm Runoff • Rainfall – Divided • Direct runoff (Pe) • Initial loss (before DRO, Ia) • Continuing loss (after DRO, Fa) Precipitation Time

7. Shoal Creek Flood - 1981 Precipitation Streamflow www.ci.austin.tx.us

8. Stream Gauging • Q = VA • Estimate: • Cross-sectional area • ”Average” velocity • Subdivide cross-section • Determine "average" flow for each subdivision • Sum for total flow

9. Stage - Discharge Curve • Stage (height) and discharge (flow rate)

10. Extreme Events & Return Period • Extreme events: • Random variable (Q); Realization (q); Threshold qT • Extreme event • if Q ≥ qT • Recurrence interval t= Time between occurrences of Q ≥ qT • Return Period T = E[t] = Average recurrence interval

11. Guadalupe River near Victoria Exceeded 16 times, 16 recurrence intervals in 69 years Return Period Exceedance probability

12. Flow Exceedance Distribution • Q is RV: Annual Maximum Flow • qTis flow with return period of T years • Flow exceedance probability • Exceedance Distribution Flow exceedance distribution

13. Events Considered in Design • Return periods (T) • 1 – 100 years (Minor structures) • Highway culverts & bridges, Farm structures, urban drainage, air fields, small dams (w/o LOL) • 100 – 1000 years (Intermediate structures) • Major levees, intermediate dams • 500 – 100,000 years (Major structures) • Large dams, intermediate & small dams (w LOL) • Probable Maximum Precipitation (PMP) • Probable Maximum Flood (PMF)

14. Flood Damage • Event damage • Damage from flood events (e.g., 10-, 50-, 100-year events) • Used for emergency planning • Expected annual damage • Average annual damage for events that could occur in any year • Used for project B/C analyses

15. US Federal Flood Programs • Two agencies • US Army Corps of Engineers (USACE) • Focused on reducing flood damage through implementation of various protection works • Federal Emergency Management Agency (FEMA) • Focused on flood insurance as a means for partial recovery of losses for property owners • Floodplains flooded by the 100-year flood are subject to • land-use management provisions (no development in the floodway, properties must be elevated, etc.) and • flood insurance is mandatory for properties located within this zone if communities are to remain eligible for certain disaster relief programs.

16. Flood Damage Reduction(a US Corps of Engineers Perspective) • Identify a plan that will reduce flood-damage and contribute to national economic development (NED) and is consistent with environmental protection • Benefits • Locational (BL): Increase in income from additional floodplain development • Intensification (BI): Increase in income from existing floodplain activities • Inundation reduction (BIR): Plan-related reduction in physical economic damage, income loss and emergency costs • Costs: Total implementation costs + OM&R costs (C)

17. Inundation Reduction • Economic damages With and Without plan • Expected Annual Flood Damage • Risk of various magnitudes of flood damage each year • Weight damage by probability of event occurring

18. Flood-Damage Reduction Measures

19. Effect of Flood Management Measures

20. Planning Study • Which measures, Where to locate, What size, How to operate • Formulate  Evaluate  Compare various alternative plans • Reconnaissance phase: • Find at least one plan that • Has positive Net Benefits • Satisfies environmental constraints • Is acceptable to local stakeholders • Estimate flood damages Without plan • Feasibility phase: • Refine and search the set of feasible plans • Detailed studies of channel capacity, structural configurations, etc. • Evaluate economic objective, environmental compliance, etc. • Design phase

21. Computing Expected Annual Damage stage-discharge flow-probability stage-damage • Compute • Damage exceedance distribution • Probability that Flood Damage (FD) is ≥ specified level (fdT) • Expected Annual Flood Damage damage-probability Expected Annual Damage

22. Computation of Expected Annual Damage • Construct basic relationships for without-plan situation • Flow exceedance distribution • Stage-discharge curve • Stage-damage curve • Damage exceedance distribution • Compute the area beneath the damage-exceedance distribution (expected annual flood damage) for each location and sum to obtain the total expected annual flood damage • Repeat step (1) for each alternative flood plain management plan under investigation • Repeat step (2) • Subtract results of step (4) (with plan) for each plan from without-plan results. The differences will be expected annual flood damage reduction for each plan

23. Expected Annual Flood Damage Stage-discharge curve Stage-damage curve Flow exceedance distribution Damage exceedance distribution Calculating Expected Annual Flood Damage

24. Benefits of E[FD] Reduction • Expected Annual Flood Damage reduction • Difference between E[FD] with and without protection Calculating Expected Flood Damage Reduction Benefits

25. Floodplain Protected by a Levee • Probability of overtopping or geo-structural failure • Need stage-discharge relationships in the channel and on the floodplain • Flood stage in the floodplain protected by a levee is a function of • Flow in the stream or river channel, • Crosssectional area of the channel between the levees on either side, • Channel slope and roughness, • Levee height. • If floodwaters enter the floodplain • Water level in the floodplain depends on the topological characteristics of the floodplain

26. Levees • Probability of levee failure function of • Levee height • Distribution of flows • Probability of geostructural failure • Probability of levee failure • 15% = probable non-failure point, PNP • 85% = probable failure point, PFP Without Project Probable failure point (PFP) Probable non-failure point (PNP) With Project Levee Probability of failure if water surface reaches stage shown

27. Example Inundated 130 businesses and 732 residences, second-story flooding, eight lives lost. • Urban basin. • Floods have caused significant damage • Flow is measured at a USGS gauge nearby • communities in the basin have been flooded periodically • Increased development in the upper portion of the basin promises to worsen the flood problem, as urbanization increases the volume and peak discharge

28. Example • Flood problem analyzed to identify opportunities for damage reduction • Set of damage reduction alternatives formulated • Evaluate each alternative in terms of economic performance • Display the results so that alternatives can be compared • Identify and recommend a superior plan from amongst the alternatives • The standard for damage-reduction benefit computation is the without-project condition. Expected annual damage should be computed • For the computation, discharge-frequency, stage-discharge, and stage-damage relationships were developed following standard procedures

29. Discharge - Probability Function • The existing, without-project discharge-frequency relationship was developed from the sample of historical annual maximum discharge observed at the USGS gauge

30. Stage - Discharge Function • The present, without project stage-damage relationship at the USGS gauge index point was developed from water-surface profiles computed with a computer program

31. Stage - Damage Function • Developed with the following procedure: • Categorize structures in the basin • Define an average-case stage-damage relationships for categories • Add emergency costs

32. Flood Damage – Exceedance Frequency

33. EAD Integration Procedure Damage ($) • Area between each pair of points is found by Integration. Area added as last step in integration Area under curve is expected annual damage First exceedance value should be at zero damage Last exceedance frequency Exceedance Probability

34. Expected Annual Flood Damage Trapezoid Rule:

35. Uncertainty • In flood damage-reduction planning, uncertainties include • Future hydrologic events: streamflow and rainfall • choice of distribution and values of parameters • Simplified models of complex hydraulic phenomena • geometric data, misalignment of structure, material variability, and slope and roughness factors • Relationship between depth and inundation damage • structure values and locations, how the public will respond to a flood • Structural and geotechnical performance when subjected to floods

36. Introducing Uncertainty • Assign probability density functions to evaluation functions • At any location an orthogonal slice would yield the PDF of uncertainty • EAD and benefits determined in the same way as before, however, a Monte Carlo sampling is used to sample from the functions to produce independent probability – damage functions that are integrated to compute EAD • Monte Carlo sampling is repeated (replicates) until stable expected values are computed. Darryl W. Davis, Risk Analysis in Flood Damage Reduction Studies — The Corps Experience, World Water Congress 2003 118, 306 (2003)