Beargrass Creek Case Study Description of the Study Area Hydrology & Hydraulics Economic Analysis Project Planning Assessment of the Risk Based Analysis

Beargrass Creek Case Study

• Description of the Study Area

• Hydrology & Hydraulics

• Economic Analysis

• Project Planning

• Assessment of the Risk Based Analysis Methodology

Beargrass Creek Study Area

North Fork

Middle Fork

South Fork

Buechel Br

Ohio River

61 mi2

Drainage Area

Levee on the Ohio River

Pump Station at the Levee(Capacity 7800 cfs!)

Concrete-Lined Channel

Detention Pond

Inlet Weir

Beargrass Creek at the Detention Pond

Pond Outlet Pipe

1

2

3

4

5

6 7 8

10

1112

13

1415

12

34

5

Buechel

Branch

(2.2 m

iles)

South Fork Beargrass C

reek (12 miles)

Damage Reaches

9 Example Reach SF-9







Flood Frequency Curve (SF-9)Separate curve for each reach and each plan

Uncertainty in Frequency CurveReach SF-9, Without Plan Conditions

Prob Mean

(cfs)

Mean +2 SD

Mean -2 SD

Log10 (SD)

0.01 4310 3008 6176 0.0781

0.5 1220 1098 1356 0.0229

QKQQ10log1010 *loglog

1

2

3

4

5

6 7 8

10

1112

13

1415

12

34

5

Buechel

Branch

(61 cr

oss-sec

ts)

South Fork Beargrass C

reek (202 cross-

sects)Water Surface Profiles

9

Water Surface Profiles

Uncertainty in Stage-Discharge

SD= 0.5 ft at 100 yr flow

ConstantReduces prop.to depth







Computation of Expected Annual Damage (EAD)

Stage (H)

Dis

char

ge (

Q)

Exceedance Probability (p)

Dis

char

ge (

Q)

Stage (H)

Dam

age

(D)

Exceedance Probability (p)D

amag

e (D

)

1

0

)( dppDEAD

Damage Categories

• Single-family residential• Multi-family residential• Commercial buildings• Public buildings• Automobiles• Cemeteries• Traffic disruption• Utilities

p=0.999

p=0.1p=0.01p=0.002

Structures

Index Location

• Each damage reach has an index location

• All structures are assumed to exist there

• First floor elevation adjusted to reflect the change in location within the reach Rm 9.960

Rm 10.363

Rm 10.124

Index for SF-9

Invert

p=0.01

p=0.1p=0.5

Building Damage

• Value of the structure, V• Value of the contents,

C = kV • k=V/C, contents to value

ratio (~40%)• Damage is a function of

depth of flooding, expressed as ratio,r(h), of value

First Floor Elevation

h

ChrVhrD )(21

Depth, h r1(h) r2(h)

3ft 27% 35%

6ft 40% 45%

Uncertainty in Building Damage• Value of structure,

– SD=10% of V for residential

– Commercial distribution described by

• Value of contents (SD of k in C=kV)

• Uncertainty in first floor elevation, SD=0.2ft

• Uncertainty in damage ratios, r(h)

First Floor Elevation

h

ChrVhrD )(21

Stage-Damage Curve

Multi-family Residential, Reach SF-9

Stage-Damage Curves

• Each structure is treated individually

• Stage-damage curve with uncertainty is produced for each damage category for each reach

• Added together to give the total stage-damage curve for the reach(?)







Planning Team

• Three key people:– Planner: formulates project alternatives, works

with local sponsor– Hydraulic Engineer: determines discharge and

stage data– Economist: estimates damage, costs, benefits

and does the risk analysis

Planning Methodology

• Identify potential project components (detention ponds, levees, …)– 22 initially proposed, 11 on Beargrass Creek, and 11 on

Buechel Branch

• Evaluate them all individually to see if net benefits are positive– 8 components on Buechel Branch eliminated

• Combine components into plans, incrementally – 10 components in NED plan: 8 detention ponds,

1 floodwall, 1 channel improvement

1

2

3

4

5

6 7 8

10

1112

13

1415

12

34

5

Buechel

Branch

Three Plan Development Reaches

932

1

Risk of Flooding

• Establish a target stage at each damage reach index point

• Find annual probability of exceeding that stage

• Find reliability of passing design floods

Target Stage

Assessment of Engineering Risk

• Conditional probability– Assumes a particular flood

severity

• Annual probability– Integrates over all flood

severities

• Risk measures actually used– Annual exceedance probability

– Conditional nonexceedance probability

Target Stage H

F(h)

0

1

Nonexceedance probability

Exceedance probability

Computation of Engineering Risk Measuresfrom the Stage-Frequency Curve

Annual exceedance probability– Find pe for target stage at each Monte

Carlo replicate– Get expected value and median of pe

values over all simulations– Get long term risk as 1-(1-pe)n

Conditional nonexceedance probability– Find H* for given p* at each

replicate– Find % of replicates for which

H* < Target stage

Q

Q*

f2(H|Q)

H*

p

f1(Q|p)

p*

Q*H

p

f3(H|p)

p*

H*

H

pe

Target Stage

Q







Overall Assessment

• The core methodology is solid and is an advance in engineering practice of flood risk assessment

• Focus is completely on damage reaches considered as statistically independent entities

• Whole project risk and 25%,50%,75% damage values cannot be built up this way

• Can specification of standard deviations of analysis variables be improved?

Beargrass Creek 100 year Flood Plain Map

Middle Fork

South Fork

Spatial Subdivision of the Region

Spatial Unit Used for

Whole River Expected Annual Damage (EAD), Benefit-Cost analysis

3 Main River Reaches Incremental analysis to get NED plan

22 Damage Reaches Basic unit for analysis using HEC-FDA

263 Hydraulic Cross-sections

Water surface elevation profile computation

2150 Structures Structure inventory

Whole Project Risk Assessment

• Take a flood of severity, p, and integrate the damage along the reach– Without any plan (o)– With a plan (w)– Benefit of plan is B = Do - Dw

• Randomize the flood discharge and stage for the whole project rather than for each reach

• Compute project-based damage values for each randomization and use them to get B25, B75 values

Documents

Beargrass Creek Case Study Description of the Study Area Hydrology & Hydraulics Economic Analysis Project Planning Assessment of the Risk Based Analysis