1. Water Resources Planning and Management
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; - 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

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

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

7. Shoal Creek Flood
Precipitation
Streamflow

8. Stream Gauging Q = VA Estimate: Subdivide cross-section
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
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
Exceedence Year
Recurrence Interval
1936
1940 4
1941 1
1942
1958 16
1961 3
1967 6
1972 5
1977
1981
1987
1992
1999 7
2002
2003
2005 2
Number
Years (05-36) 69
Return Period
Exceedance probability

12. Flow Exceedance Distribution
Q is RV: Annual Maximum Flow
qT is 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 Expected annual 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
Measures that reduce damage by reducing discharge
Measures that reduce damage by reducing stage
Measures that reduce damage by reducing existing damage susceptibility
Measures that reduce damage by reducing future damage susceptibility
Reservoir
Channel improvement
Levee or floodwall
Land-use and construction regulation
Diversion
Floodproofing
Acquisition
Watershed management
Relocation
Flood warning and preparedness planning

19. Effect of Flood Management Measures
Impacted Relationship
Stage - Discharge
Stage - Damage
Discharge - Damage
Discharge - Frequency
Damage -Frequency
Reservoir ✓
Levee
Channel mod.
Diversion
Flood Forecasting
Flood Proofing
Relocation
Flood warning
Land use control

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
flow-probability
stage-discharge
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
Probability of failure if water surface reaches stage shown
Probable failure point (PFP)
Probable non-failure point (PNP)
Levee
Without Project
With Project

27. Example Urban basin. Floods have caused significant damage
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
Exceedence Probability
Discharge (m3/s)
0.002
899
0.005
676
0.01
539
0.02
423
0.05
299
0.1
223
0.2
158
0.5 87
0.8 51
0.9 39
0.95 32
0.99
22.9

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
Discharge-Stage
Stage (m)
Discharge (m3/s)
1.97
84.4
2.39
100.4
3.39
168.2
4.07
228.4
4.58
277.5
5.50
383.7
6.70
538.5
7.13
605.8
7.47
651.5
7.75
721.7
8.10
838.2
8.79
1030.8
8.99
1159.1
9.57
1297.1

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
Stage-Damage
Stage (m)
Damage ($1,000)
3.35
0.0
4.27
25.7
4.57
88.6
5.18
339.3
5.49
525.1
6.10
1100.0
6.71
2150.6
8.23
5132.8
8.53
5654.2
9.14
6416.5
9.45
6592.2

32. Flood Damage – Exceedance Frequency
Exceedence Probability
Damage ($1,000)
0.002
5286
0.005
3830
0.01
2133
0.02
817
0.05
168
0.1
18.2
0.2

33. EAD Integration Procedure
Damage (D)
Area between each pair of points is found by Integration.
Area added as last step in integration D0
Area under curve is expected annual damage
First exceedance value should be at zero damage
Last exceedance frequency, p0
Exceedance Probability (p)

34. Expected Annual Flood Damage
Integrating
Exceedence Probability
Discharge (m3/s)
Stage (m)
Damage ($1,000)
Probability Increment
Mean Damage for increment
Weighted Damage
0.002
5286
10,572
898.8
8.32
0.003
4557.9
13,673.8
0.005
676.1
7.57
3830
2981.7
14,908.5
0.01
538.5
6.70
2133
1475.4
14,753.5
0.02
423.0
5.80
817
0.03
492.5
14,773.5
0.05
298.8
4.76
168
92.9
4,645.0
0.1
222.5
4.00
18.2
0.10
9.1
910.0
0.2
158.4
3.24
EAD
74,236
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 , 306 (2003)