Flood Management

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					CE 385 D – Water Resources
Planning and Management

  Flood Management - 1

     Daene C. McKinney
                                      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
Precipitation, P(t)
                      Hydrologic Cycle




                                         Runoff,
                                         streamflow, Q(t)
                  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
    Streamflow Hydrograph
Centroid of                               Basin Lag
Precipitation
                                          Peak

                           Time
                           of Rise
           Discharge, Q




                                           Inflection                  Baseflow
                                           Point                       Recession
   Baseflow
   Recession                              Baseflow

                          Beginning of                  End of        Time
                          Direct Runoff                 Direct Runoff
                Storm Runoff




                              Precipitation
                                                    P
                                                    a
                                                   a
                                                   P IF
                                                    e

                                                    Pe


• Rainfall – Divided                          Ia   Fa
  1. Direct runoff (Pe)                                  Time
                                   tp
  2. Initial loss (before DRO, Ia)
  3. Continuing loss (after DRO, Fa)
                      Shoal Creek Flood - 1981
                                     20000                                                                   0




                                                                                                                 Precip (in)
                                     18000                                                                   1

                                     16000                                                                   2

                                     14000                                                                   3
                                                                                       Precipitation
                      Runoff (cfs)

                                     12000

                                     10000

                                     8000

                                     6000                                                      Streamflow
                                     4000

                                     2000

                                        0
                                             0.0   1.0   2.0   3.0      4.0      5.0     6.0    7.0    8.0
                                                                     Time (hr)




www.ci.austin.tx.us
               Stream Gauging
• Q = VA
• Estimate:
   – Cross-sectional area
   – ”Average” velocity
• Subdivide cross-section
• Determine "average" flow
  for each subdivision
• Sum for total flow
        Stage - Discharge Curve
• Stage (height) and discharge (flow rate)
                                 20

                                 18

                                 16

                                 14
                    Stage (ft)   12

                                 10

                                 8

                                 6

                                 4

                                 2

                                 0
                                      0   5000   10000       15000         20000   25000   30000
                                                         Discharge (cfs)
  Extreme Events & Return Period
                                               1
• Extreme events:      Magnitude 
                                     Frequency of occurence

• 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
 Guadalupe River near Victoria
  000
   ,
q 50 Exceeded 16 times, 16 recurrence intervals in 69 years
T
                                                              Exceedence     Recurrence
                                                                 Year         Interval
                                                                 1936
                                                                 1940            4
                                                                 1941           1
                                                                 1942           1
                                                                 1958           16
                                                                 1961           3
                                                                 1967           6
                                                                 1972           5
                                                                 1977           5
                                                                 1981           4
                                                                 1987           6
                                                                 1992           5
                                                                 1999           7
                                                                 2002           3
                                                                 2003           1
                                                                 2005           2
                                                               Number           16
                                                             Years (05-36)      69

                                                                       69
                                                        E(t )  t        4.3years
                                                                       16
                                           1                                    1
    T  E(t )              Pr(Q  qT )                Pr(Q  50,000)              0.23
                                           T                                   4.3
   Return Period         Exceedance probability   
           Flow Exceedance Distribution
     • Q is RV: Annual Maximum Flow
     • qT is flow with return period of T years
                                                   
                                                   Qq
                                                    ]
                                                  Pr[
     • Flow exceedance probability
                           1
             Pr[Q  qT ] 
                           T
                                                  1
     • Exceedance Distribution                        T

        Pr[Q  qT ]  1 Pr[Q  qT ]
                                                                 qT                    q
                       1 FQ (qT )
                                                          Flow exceedance distribution



    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)
               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
     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.
           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)


                           NB  BL  BI  BIR  C



               
          Inundation Reduction
• Economic damages With and Without plan

         NB  BL  BI  BIR  C
         BIR  DamageWithout Plan  DamageWith Plan


• 
  Expected Annual Flood Damage
  – Risk of various magnitudes of flood damage each year
  – Weight damage by probability of event occurring

          NB  BL  BI  EDW /O   EDW   C



   
  Flood-Damage Reduction Measures
Measures that        Measures that      Measures that        Measures that
reduce damage by     reduce damage by   reduce damage by     reduce damage by
reducing discharge   reducing stage     reducing existing    reducing future
                                        damage               damage
                                        susceptibility       susceptibility
Reservoir            Channel            Levee or floodwall   Land-use and
                     improvement                             construction
                                                             regulation
Diversion                               Floodproofing        Acquisition
Watershed                               Relocation
management
                                        Flood warning and
                                        preparedness
                                        planning
   Effect of Flood Management Measures
                                          Impacted Relationship
                    Stage -     Stage -     Discharge -   Discharge -   Damage -
                    Discharge   Damage      Damage        Frequency     Frequency
Reservoir                                                      ✓            ✓
Levee                  ✓           ✓             ✓             ✓            ✓
Channel mod.           ✓                         ✓             ✓            ✓
Diversion                                                      ✓            ✓
Flood Forecasting                                              ✓            ✓
Flood Proofing                     ✓             ✓                          ✓
Relocation                         ✓             ✓                          ✓
Flood warning                      ✓             ✓                          ✓
Land use control                   ✓             ✓             ✓            ✓
                        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
             Computing Expected Annual Damage
               flow-probability                     stage-discharge                stage-damage
         p
                                                H                              H


                                                                    
                                       q                                   q                 Damage


• Compute
     – Damage exceedance distribution
                                                                                 
     – Probability that Flood Damage                     damage-probability
       (FD) is ≥ specified level (fdT)
                                                    Damage
                             1
         p  Pr[FD  fdT ] 
                             T
• Expected Annual Flood                                                                 Expected
                                                                                      Annual
  Damage 
       E[FD]   p(FD)dFD                                                             Damage
                  0                                                            p
Computation of Expected Annual Damage
1.   Construct basic relationships for without-plan situation
     –   Flow exceedance distribution
     –   Stage-discharge curve
     –   Stage-damage curve
     –   Damage exceedance distribution
2.   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
3.   Repeat step (1) for each alternative flood plain management plan under
     investigation
4.   Repeat step (2)
5.   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
Expected Annual Flood Damage
         Stage-discharge curve                Stage-damage curve




                                                                    [FD
                                                                    E ]



    Flow exceedance distribution         Damage exceedance distribution

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




                      Calculating Expected Flood Damage Reduction Benefits
   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
                                       Levees
• Probability of levee failure                           • Probability of levee failure
  function of                                                   – 15% = probable non-failure
   – Levee height                                                 point, PNP
   – Distribution of flows                                      – 85% = probable failure point,
   – Probability of geostructural                                 PFP
     failure
                                                      Stage                       Damage
                 Probable failure point (PFP)
                                                                                    Without
                       Probable non-failure                                         Project
                                                                          
                                  
                       point (PNP)
         Levee
                                                                                                    With
                                                                                                    Project
                                                  0.0 0.15         0.85 1.0
                                                Probability of failure if water
                                                surface reaches stage shown                        Stage

                                                    

                                                                                              
                           Example
                                                                     Inundated 130 businesses and
• Urban basin.                                                       732 residences, second-story
                                                                     flooding, eight lives lost.
• Floods have caused significant
  damage
• Flow is measured at a USGS                                18
  gauge nearby                                              16




                                   Damage ($million 1978)
                                                            14
• communities in the basin have                             12
  been flooded periodically                                 10
• Increased development in the                               8
  upper portion of the basin                                 6
                                                             4
  promises to worsen the flood
                                                             2
  problem, as urbanization                                   0
  increases the volume and peak
                                                                 0            200           400     600
  discharge
                                                                              Discharge (m3/sec)
                            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
  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
                                               1000
   Exceedence Discharge                         900
   Probability  (m3/s)
                                                800
         0.002        899
         0.005        676                       700
                            Discharge (m3/s)




          0.01        539                       600
          0.02        423
                                                500
          0.05        299
            0.1       223                       400
            0.2       158                       300
            0.5        87
                                                200
            0.8        51
            0.9        39                       100
          0.95         32                        0
          0.99       22.9                             0   0.1   0.2   0.3    0.4     0.5     0.6     0.7   0.8   0.9   1
                                                                            Exceedence Probability
           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                          1400.0
             Discharge
  Stage (m) (m3/s)                           1200.0
        1.97       84.4
        2.39      100.4                      1000.0
        3.39      168.2
                          Discharge (m3/s)




        4.07      228.4                       800.0
        4.58      277.5
        5.50      383.7                       600.0
        6.70      538.5
        7.13      605.8                       400.0
        7.47      651.5
        7.75      721.7                       200.0
        8.10      838.2
        8.79     1030.8                         0.0
        8.99     1159.1                               0.00   2.00   4.00               6.00   8.00   10.00
        9.57     1297.1                                                    Stage (m)
           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

                                          7000.0
     Stage-Damage
             Damage                       6000.0
   Stage (m) ($1,000)
                                          5000.0
        3.35      0.0
                        Damage ($1,000)




        4.27     25.7                     4000.0
        4.57     88.6
        5.18 339.3                        3000.0
        5.49 525.1
        6.10 1100.0                       2000.0
        6.71 2150.6
                                          1000.0
        8.23 5132.8
        8.53 5654.2                          0.0
        9.14 6416.5                                0.00   2.00   4.00               6.00   8.00   10.00
        9.45 6592.2                                                     Stage (m)
Flood Damage – Exceedance Frequency
                                        6000

Exceedence Damage
Probability ($1,000)                    5000
   0.002      5286
   0.005      3830
    0.01      2133                      4000
    0.02      817      Damage ($1000)
    0.05      168
                                        3000
     0.1      18.2
     0.2       0
                                        2000



                                        1000



                                          0
                                               0   0.02   0.04   0.06   0.08    0.1     0.12   0.14   0.16   0.18   0.2
                                                                        Exceedence Frequency
         EAD Integration Procedure
                    Damage ($)
• Area between                     Area added as
                                   last step in
                                   integration
  each pair of
  points is found
  by Integration.
                                                   Area under
                                                   curve is
                                                   expected
                                                   annual damage
                                                                   First
                                                                   exceedance
                                                                   value should be
                                                                   at zero damage




                      Last
                      exceedance         Exceedance Probability
                      frequency
Expected Annual Flood Damage
                                                          Integrating
                                                      Mean
                                                     Damage
    Exceedence Discharge         Damage Probability      for    Weighted
    Probability (m3/s) Stage (m) ($1,000) Increment increment Damage
                                             0.002     5286      10,572
       0.002        898.8 8.32     5286
                                             0.003    4557.9 13,673.8
       0.005        676.1 7.57     3830
                                             0.005    2981.7 14,908.5
        0.01        538.5 6.70     2133
                                              0.01    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
                                              0.05     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       0
                                                        EAD      74,236

                                        n
                    E(D)  p0 D0   p j  p j1 
                                                   D j  D j1 
Trapezoid Rule:                                          2
                                        j1
                          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
               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)