hydrologic design and design storms readings: applied hydrology sections 13.1-13.2 04/18/2005

Hydrologic Design and Design Storms

Readings: Applied Hydrology Sections 13.1-13.2

04/18/2005

2

Hydrologic extremes

• Extreme events– Floods – Droughts

• Magnitude of extreme events is related to their frequency of occurrence

• The objective of frequency analysis is to relate the magnitude of events to their frequency of occurrence through probability distribution

• It is assumed the events (data) are independent and come from identical distribution

occurence ofFrequency

1Magnitude

3

Hydrologic design

• Water control– Peak flows, erosion, pollution, etc.

• Water management– Domestic and industrial use, irrigation, instream flows, etc

• Tasks– Determine design inflow– Route the design inflow– Find the output

• check if it is sufficient to meet the demands (for management)• Check if the outflow is at safe level (for control)

4

Hydrologic design scale• Hydrologic design scale – range in magnitude of the

design variable within which a value must be selected

• Design considerations– Safety – Cost

• Do not design small structures for large peak values (not cost effective)

• Do not design large structures for small peak values (unsafe)

• Balance between safety and cost.

5

Estimated Limiting Value (ELV)

• Lower limit on design value – 0• Upper limit on design value – ELV• ELV – largest magnitude possible for a hydrologic

event at a given location, based on the best available hydrologic information. – Length of record– Reliability of information– Accuracy of analysis

• Probable Maximum Precipitation (PMP) / Probable Maximum Flood (PMF)

7

TxDOT RecommendationsRecommended Design Frequencies (years)

- Design Check Flood

Functional Classification and Structure Type 2 5 10 25 50 100 Freeways (main lanes): - - - - - -

culverts - - - - X X

bridges - - - - X X

Principal arterials: - - - - - -

culverts - - X (X) X X

small bridges - - X (X) X X

major river crossings - - - - (X) X

Minor arterials and collectors (including frontage roads): - - - - - -

culverts - X (X) X - X

small bridges - - X (X) X X

major river crossings - - - X (X) X

Local roads and streets (off-system projects): - - - - - -

culverts X X X - - X

small bridges X X X - - X

Storm drain systems on interstate and controlled access highways (main lanes):

- - - - - -

inlets and drain pipe - - X - - X

inlets for depressed roadways* - - - - X X

Storm drain systems on other highways and frontage: - - - - - -

inlets and drain pipe X (X) - - - X

inlets for depressed roadways* - - - (X) X X

Notes. * A depressed roadway provides nowhere for water to drain even when the curb height is exceeded. ( ) Parentheses indicate desirable frequency.

8

Hydrologic design level

• Hydrologic design level – magnitude of the hydrologic event to be considered for the design or a structure or project.

• Three approaches for determining design level– Empirical/probabilistic– Risk analysis– Hydroeconomic analysis

9

Empirical/Probabilitic

• P(most extreme event of last N years will be exceeded once in next n years)

• P(largest flood of last N years will be exceeded in n=N years) = 0.5

• Drought lasting m years is worst in N year record. What is the probability that a worse drought will occur in next n years?– # sequences of length m in N years = N-m+1– # sequences of length m in n years = n-m+1

)1()1(

1),,(

mnmN

mnmnNP

nN

nnNP

),(

10

Example 13.2.1

• If the critical drought of the record, as determined from 40 yrs of data, lasted 5 yrs, what is the chance that a more severe drought will occur during the next 20 yrs?

• Solution: N = 40, m = 5 and n = 20

308.02522040

1520)20,5,40(

P

11

Risk Analysis

• Uncertainty in hydrology – Inherent - stochastic nature of hydrologic phenomena– Model – approximations in equations– Parameter – estimation of coefficients in equations

• Consideration of Risk– Structure may fail if event exceeds T–year design

magnitude

– R = P(event occurs at least once in n years)• Natural inherent risk of failure

n

TR

111

12

Example 13.2.2• Expected life of culvert = 10 yrs• Acceptable risk of 10 % for the culvert

capacity• Find the design return period

yrsT

T

TR

n

95

11110.0

111

10

What is the chance that the culvert designed for an event of What is the chance that the culvert designed for an event of 95 yr return period will not have its capacity exceeded for 50 95 yr return period will not have its capacity exceeded for 50 yrs?yrs?

41.0

95

111

50

R

R

The risk associated with failure of culvert when the flow exceed 95 yr flood The risk associated with failure of culvert when the flow exceed 95 yr flood in the next 95 years is:in the next 95 years is:

The chance that the capacity will not be exceeded during the next 50 yrs is 1-The chance that the capacity will not be exceeded during the next 50 yrs is 1-0.41 = 0.590.41 = 0.59

13

Hydroeconomic Analysis

• Probability distribution of hydrologic event and damage associated with its occurrence are known

• As the design period increases, capital cost increases, but the cost associated with expected damages decreases.

• In hydroeconomic analysis, find return period that has minimum total (capital + damage) cost.

Beargrass Creek Case Study

• Description of the Study Area• Hydrology & Hydraulics• Economic Analysis• Project Planning• Assessment of the Risk Based Analysis

Methodology

http://www.nap.edu/catalog.php?record_id=9971

From “Risk Analysis and Uncertainty in Flood Damage Reduction Studies”, NRC Report:

http://www.nap.edu/catalog.php?record_id=9971

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

1314

15

12

34

5

Buechel Branch (2.2 miles)

South Fork Beargrass Creek (12 miles)

Damage Reaches

9 Example Reach SF-9



Methodology

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

1314

15

12

34

5

Buechel Branch (61 cro

ss-sects

)

South Fork Beargrass Creek (202 cross-s

ects)Water Surface Profiles

9

Water Surface Profiles

Uncertainty in Stage-Discharge

SD= 0.5 ft at 100 yr flow

ConstantReduces prop.to depth



Methodology

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=0.1

p=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(?)



Methodology

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

1314

15

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



Methodology

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

hydrologic design and design storms readings: applied hydrology sections 13.1-13.2 04/18/2005

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