04/18/2005
Hydrologic Design and Design
Storms
Readings: Applied Hydrology Sections 13.1-13.2
Hydrologic extremes
• Extreme events
– Floods
– Droughts
• Magnitude of extreme events is related to their
frequency of occurrence
Magnitude 
1
Frequency of occurence
• 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
2
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)
3
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.
4
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)
5
6
TxDOT Recommendations
Recommended Design Frequencies (years)
Design
-
Functional Classification and Structure Type
Check
Flood
100
2 5 10 25 50
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)
Minor arterials and collectors (including frontage roads):
- -
-
-
-
 culverts
-
 small bridges
- -
 major river crossings
- -
-
Local roads and streets (off-system projects):
- -
-
 culverts
-
-
-
-
-
X
-
X (X) X -
X
X (X) X
X
X (X)
X
-
-
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 -
-
 inlets for depressed roadways*
- -
-
-
Storm drain systems on other highways and frontage:
- -
-
-
-
 inlets and drain pipe
X (X) -
-
-
 inlets for depressed roadways*
- -
(X) X
-
-
-
X
X
X
-
Notes.
* A depressed roadway provides nowhere for water to drain even when the curb height is
exceeded.
( ) Parentheses indicate desirable frequency.
7
X
X
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
8
Empirical/Probabilitic
• P(most extreme event of last N years will be
exceeded once in next n years) P( N , n)  n
N n
• 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
P ( N , n, m ) 
n  m 1
( N  m  1)  (n  m  1)
9
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
20  5  1
P(40,5,20) 
 0.308
40  20  2  5  2
10
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
 1
R  1  1  
 T
n
– R = P(event occurs at least once in n years)
• Natural inherent risk of failure
11
Example 13.2.2
• Expected life of culvert = 10 yrs
• Acceptable risk of 10 % for the culvert
capacity
• Find the design return period

 1
R  1  1  
 T
n
10
 1
0.10  1  1  
 T
T  95 yrs
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
50
in the next 95 years is:
1

R  1  1  
 95 
R  0.41
The chance that the capacity will not be exceeded during the next 50 yrs is 10.41 = 0.59
12
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.
13
14
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_id=9971
Beargrass Creek Study Area
North Fork
Middle Fork
South Fork
Buechel Br
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
Damage Reaches
1
15
14
13
11
2
12
10
5
9
3
6
4
5
7
4
8
3
2
1
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 Curve
Reach SF-9, Without Plan Conditions
Prob
Mean Mean Mean
(cfs) +2 SD -2 SD
Log10
(SD)
0.01
4310
3008
6176
0.0781
0.5
1220
1098
1356
0.0229
log 10 Q   log 10 Q  K *  log10 Q
Water Surface Profiles
1
15
14
13
11
2
12
10
5
9
3
6
4
5
7
4
8
3
2
1
Water Surface Profiles
Uncertainty in Stage-Discharge
Reduces prop.
to depth
Constant
SD= 0.5 ft at 100 yr flow
Beargrass Creek Case Study
•
•
•
•
•
Description of the Study Area
Hydrology & Hydraulics
Economic Analysis
Project Planning
Assessment of the Risk Based Analysis
Methodology
Discharge (Q)
Discharge (Q)
Computation of Expected Annual Damage (EAD)
Exceedance Probability (p)
Damage (D)
Damage (D)
Stage (H)
Stage (H)
Exceedance Probability (p)
1
EAD 
 D( p )dp
0
Damage Categories
•
•
•
•
•
•
•
•
Single-family residential
Multi-family residential
Commercial buildings
Public buildings
Automobiles
Cemeteries
Traffic disruption
Utilities
Structures
p=0.002
p=0.01
p=0.1
p=0.999
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
Index for SF-9
p=0.01
p=0.1
p=0.5
Invert
Rm 10.363
Rm 10.124
Rm 9.960
Building Damage
D  r1 hV  r2 (h)C
• 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
h
First Floor Elevation
Depth, h
r1(h)
r2(h)
3ft
6ft
27%
40%
35%
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)
h
First Floor Elevation
D  r1 hV  r2 (h)C
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 stagedamage 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
Three Plan Development Reaches
1
1
15
14
13
11
2
12
2
10
3
3
5
9
6
4
5
7
4
8
3
2
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
F(h)
• Conditional probability
– Assumes a particular flood
severity
1
Exceedance probability
• Annual probability
– Integrates over all flood
severities
Nonexceedance
probability
• Risk measures actually used
– Annual exceedance probability
– Conditional nonexceedance
probability
0
Target Stage
H
Computation of Engineering Risk Measures
from the Stage-Frequency Curve
Q
H
H
Q*
Target Stage
H*
f1(Q|p)
H*
f2(H|Q)
p
p*
f3(H|p)
p
Q
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
p*
pe
Conditional nonexceedance probability
– Find H* for given p* at each
replicate
– Find % of replicates for which
H* < Target stage
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 Crosssections
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