Hydrologic Design and Design Storms

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Hydrologic Design and Design Storms
04/18/2005

• Readings Applied Hydrology Sections 13.1-13.2

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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

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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)

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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.

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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)

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TxDOT Recommendations
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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

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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 nN 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-m1
• sequences of length m in n years n-m1

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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

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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 Tyear design
  magnitude
• R P(event occurs at least once in n years)
• Natural inherent risk of failure

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Example 13.2.2

• Expected life of culvert 10 yrs
• Acceptable risk of 10 for the culvert capacity
• Find the design return period

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

The risk associated with failure of culvert when
the flow exceed 95 yr flood in the next 95 years
is
The chance that the capacity will not be exceeded
during the next 50 yrs is 1-0.41 0.59
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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.

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Beargrass Creek Case Study

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

From Risk Analysis and Uncertainty in Flood
Damage Reduction Studies, NRC Report
http//www.nap.edu/catalog.php?record_id9971
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Beargrass Creek Study Area
Ohio River
North Fork
Middle Fork
South Fork
61 mi2 Drainage Area
Buechel Br
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Levee on the Ohio River
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Pump Station at the Levee(Capacity 7800 cfs!)
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Concrete-Lined Channel
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Detention Pond
Inlet Weir
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Beargrass Creek at the Detention Pond
Pond Outlet Pipe
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Damage Reaches
South Fork Beargrass Creek (12 miles)
1
15
14
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Example Reach SF-9
12
11
2
10
Buechel Branch (2.2 miles)
5
9
3
4
7
6
4
8
3
2
5
1
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Beargrass Creek Case Study

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

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Flood Frequency Curve (SF-9)Separate curve for
each reach and each plan
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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
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Water Surface Profiles
South Fork Beargrass Creek (202 cross-sects)
1
15
14
13
12
11
2
Buechel Branch (61 cross-sects)
10
5
9
3
4
7
6
4
8
3
2
5
1
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Water Surface Profiles
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Uncertainty in Stage-Discharge
Constant
Reduces prop. to depth
SD 0.5 ft at 100 yr flow
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Beargrass Creek Case Study

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

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Computation of Expected Annual Damage (EAD)
Discharge (Q)
Discharge (Q)
Exceedance Probability (p)
Stage (H)
Damage (D)
Damage (D)
Stage (H)
Exceedance Probability (p)
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Damage Categories

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

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Structures
p0.002
p0.01
p0.1
p0.999
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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

p0.01
Index for SF-9
p0.1
p0.5
Invert
Rm 10.363
Rm 10.124
Rm 9.960
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Building Damage

• Value of the structure, V
• Value of the contents, C kV
• kV/C, contents to value ratio (40)
• Damage is a function of depth of flooding,
  expressed as ratio,r(h), of value

Depth, h r1(h) r2(h)
3ft 27 35
6ft 40 45
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Uncertainty in Building Damage

• Value of structure,
• SD10 of V for residential
• Commercial distribution described by
• Value of contents (SD of k in CkV)
• Uncertainty in first floor elevation, SD0.2ft
• Uncertainty in damage ratios, r(h)

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Stage-Damage Curve
Multi-family Residential, Reach SF-9
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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(?)

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Beargrass Creek Case Study

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

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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

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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

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Three Plan Development Reaches
1
1
15
14
13
2
12
11
2
10
3
5
9
3
Buechel Branch
4
7
6
4
8
3
2
5
1
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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
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Assessment of Engineering Risk
F(h)

• Conditional probability
• Assumes a particular flood severity
• Annual probability
• Integrates over all flood severities
• Risk measures actually used
• Annual exceedance probability
• Conditional nonexceedance probability

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Exceedance probability
Nonexceedance probability
0
H
Target Stage
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Computation of Engineering Risk Measuresfrom
the Stage-Frequency Curve
Q
H
H
Q
Target Stage
H
f1(Qp)
H
f2(HQ)
f3(Hp)
p
p
Q
pe
p
p
Q

• 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 lt Target stage

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Beargrass Creek Case Study

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

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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?

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Beargrass Creek 100 year Flood Plain Map
Middle Fork
South Fork
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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
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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