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)
6
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
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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.
14
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:
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
Beargrass Creek Case Study
• Description of the Study Area• Hydrology & Hydraulics• Economic Analysis• Project Planning• Assessment of the Risk Based Analysis
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
Beargrass Creek Case Study
• Description of the Study Area• Hydrology & Hydraulics• Economic Analysis• Project Planning• Assessment of the Risk Based Analysis
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(?)
Beargrass Creek Case Study
• Description of the Study Area• Hydrology & Hydraulics• Economic Analysis• Project Planning• Assessment of the Risk Based Analysis
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
Beargrass Creek Case Study
• Description of the Study Area• Hydrology & Hydraulics• Economic Analysis• Project Planning• Assessment of the Risk Based Analysis
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