Applied Hydrology
Flood Risk Analysis – the USACE
Approach
Professor Ke-Sheng Cheng
Dept. of Bioenvironmental Systems Engineering
National Taiwan University
RSLAB-NTU
Lab for Remote Sensing Hydrology
and Spatial Modeling
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The Levee Certification Program
Many flood damage reduction projects
involve the construction of levees. The
USACE’s (US Army Corps of Engineers)
historical approach to coping with
hydrological and hydraulic uncertainties of
large floods was based on a best estimate of
the levee height required to withstand a
given flood, which was then augmented by a
standard increment of levee height called
“freeboard”.
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The best estimate has traditionally been
based on the expected height of a design
flood (for example, the100-year flood).
A standard freeboard of 3 feet was then
added above the expected height.
With the Corps adoption of risk analysis
techniques in early 1990s, the freeboard
standard for levee certification was
abandoned in favor of the new risk analysis
standard.
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The new USACE approach was reviewed by
the Committee on Risk-Based Analysis for
Flood Damage Reduction of the National
Research Council which is organized by the
National Academy of Sciences and the
National Academy of Engineers.
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Lab for Remote Sensing Hydrology
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The committee recommends that the federal
levee certification program focus not upon
some level of assurance of passing the 100year flood, but rather upon “annual
exceedance probability” – the probability
that an area protected by a levee system will
be flooded by any potential flood.
How sure can we be that if we protect ourselves from a flow of 100year return period, we will actually be protecting ourselves from all
flows that occur less frequently, on average, than once in 100 years?
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Lab for Remote Sensing Hydrology
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USACE Risk Analysis Techniques
The Corps’s objective in flood damage
reduction studies is to determine the
expected annual damage (EAD) along a
section of river caused by possible floods,
and to compare changes in those damages as
a function of project alternatives.
For a flood of annual probability p (p=1/T, T:
return period), a corresponding value of
flood damage D(p) can be estimated.
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The EAD is the average value of such
damages taken over floods of all different
annual exceedance probabilities and over a
long period of years.
1
EAD   D( p)dp
0
The current Corps method divides the
calculation of EAD into three steps:
Determining flood frequencies, which describe
the probability of floods equal or greater than
some discharge Q occurring within a given
period of time (usually 1-year).
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Determining stage-discharge relations, which
describe how high the flow of water in a reach of
river (the stage) might be for a given discharge.
Determining damage-stage relations, which
describe the amount of damage that might occur,
given a certain height of flow.
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Basis of the Corps’s EAD Computation
Annual exceedance
probabilities of p = 0.5,
0.2, 0.1, 0.04, 0.02, 0.01,
0.004, and 0.002 are
used for EAD
calculation.
1
EAD   D( p)dp
0
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There are uncertainties in
the probability of exceedance distribution of
annual peak flows
the discharge-stage function
the stage-damage function
Stochastic simulation techniques are used to
generate a single realization of each of the
three relationships.
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Uncertainty in annual peak flow
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Peak flow records are commonly used to
estimate the chance of a flood of a given or
greater magnitude. But such estimates are
uncertain due to
Limited number of observations of past peak
flows
The changing and varying character of the
drainage basin that influences the peak flow
resulting from a specific rainfall.
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Monte Carlo simulation is used to generate new
realizations of each of the three curves using
various exceedance probabilities.
The Monte Carlo simulation is repeated for a few
thousand cycles of generating realizations and
computing EAD.
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Assessment of Engineering
Performance
The target stage is defined as the water
surface elevation in a reach at which
significant economic damage occurs.
The 1% chance of flooding damage is found
from the flood-frequency curve. A fraction
of this damage (usually 10%) is taken and
used to determine the corresponding stage
from the damage-stage curve, which then
becomes the target stage for the reach.
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Engineering performance can be measured
by conditional probabilities dependent on
the occurrence of a flood of a given severity
(e.g., the 100-year flood) or dependent on the
annual probabilities integrated over all the
floods that could occur within a given year.
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Corps’s method for measuring
engineering performance
Annual exceedance probability – the probability
that the target stage will be exceeded in any year
considering all potential floods.
Conditional nonexceedance probability – the
probability that the target stage will not be
exceeded given a specific flood severity.
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In each cycle of the above Monte Carlo
procedure, a new realization of the floodfrequency curve and the stage-discharge
curve is generated. The flood-frequency is
defined at discrete intervals of annual flood
probability (p = 0.5, 0.2, 0.1, 0.04, 0.02, 0.01,
0.004, and 0.002).
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Distribution of the target stage
nonexceedance probability
 Each cycle of the Monte Carlo procedure yields an
estimate of the annual exceedance probability for
the target stage.
 N cycles of the Monte Carlo procedure are
conducted to yield a distribution of the annual
exceedance probability for the target stage.
 The chance that the target stage will be exceeded at
least one in n years is computed as 1  (1  pe )n,
where pe is the expected annual exceedance
probability.
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Conditional nonexceedance
probabilities at the target stage
For each value of p*, there corresponds an
H*, determined in a similar manner.
After N Monte Carlo cycles are completed, a
set of N values of H* exists, of which a subset,
n, have stages not exceeding the target stage.
The conditional nonexceedance probability
of the target stage is given by n/N.
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