building strong ® hydrologic engineering center use of information on hydrologic extremes: us army...
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BUILDING STRONG®Hydrologic Engineering Center
Use of Information on Hydrologic Extremes: US Army Corps of Engineers Perspective
Beth Faber, PhD, PEUSACE, IWR, Hydrologic Engineering Center
Statistical Assessment of Extreme Weather Phenomena under Climate Change
Boulder, CO June 13-17, 2011
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USACE Mission Areas
The US Army Corps of Engineers has a “mission” in several areas of water management
Most deal with streamflow, some with average annual volumes, some with extremes (high or low)o Flood Risk Managemento Ecosystem Restorationo Navigation (inland, coastal)o Water Supplyo Hydropowero Recreation
concerned with extreme HIGH flows
concerned with extreme LOW flows
concerned with annual flow volumes
concerned with sea level
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USACE “Response” to Climate Change
Our understanding of our hydrologic environments and how we describe them must account for change over time, that is difficult to predicto formerly, used the past variability to describe future variabilityo and, we’re accustomed to predictable change in that variability…
Corps’ response to climate change is mainly in two areaso Decision-making
• how we incorporate a new kind of uncertaintyo Data (to inform decision-making)
• how we describe the environments the public exists within (inland hydrology, storms, sea-level)
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Data, and use of data
I’m going to show what data we use, how we summarize it, and how it enters our decision-makingo local-scale daily hydrology, or daily temp/precip
What we need to know from climate scientists:o How can we evaluate climate change impact on extremes?o What are the climate models good at? What aren’t they good at?o What outputs have value, that we can base decisions on?o How should we down-scale spatially and temporally?o What’s the meaning of the model “ensemble”? Does it span the
uncertainty? Does it capture the distribution of uncertainty?
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Natural Variability
We’re used to dealing with natural variabilityo Our projects are designed to perform for the range of hydrologyo Describe hydrology by both annual statistics and by probability
distributions of extreme events (frequency curves) Questions for climate scientists and statisticians:
1. Have the observed climate trends exceeded the range of natural variability?
2. At what point would the plausible climate futures exceed the natural variability (or change it)?
3. How can we estimate the variability of the future?
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Decision-making
We’re accustomed to making decisions with uncertain infoo All of our hydrologic statistics and modeling are uncertaino Decisions span a reasonable range of the uncertaintyo But, decisions that span very large uncertainty and array of
possible outcomes become less effective
Now focused on adaptive decision-making (hedge and adjust)o Robust actions that are acceptable for a range of outcomeso Staged decisions that are revisited and adjusted over timeo Decisions that don’t exclude other future actions or avenueso The life-span of a decision affects the uncertainty includedo Uncertain info, want to reduce the impact of being wrong
BUILDING STRONG®Hydrologic Engineering Center
USACE Mission Areas
The US Army Corps of Engineers has a “mission” in several areas of water management
Most deal with streamflow, some with average annual volumes, some with extremes (high or low)o Flood Risk Managemento Ecosystem Restorationo Navigation (inland, coastal)o Water Supplyo Hydropowero Recreation
concerned with extreme HIGH flows
concerned with extreme LOW flows
concerned with annual flow volumes
concerned with sea level
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Biggest Issue – Extreme Highs
The Corps’ most prominent mission area is flood risk managemento Formerly referred to as “flood control” or “flood damage
reduction”o The new term reflects a new way of thinking and making
decisions about flood risko More about getting out of the way than changing or blocking
the flow, and consciously addressing the risk For flood risk management, the most important input to
characterize hydrology is the probability distribution of annual peak flows (flood-frequency curve)
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Flood Risk Management
Risk analysis and risk management require estimates of the probability of extreme events with negative consequenceso Risk = Probability × Consequence
Need a relationship between flood magnitude and annual exceedance probabilityo might differ for the present and the planning horizon
This relationship allows us to perform probabilistic analyses involving high streamflows and their consequences (damage, lives lost)
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0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .0021000
10000
100000
1000000
An
nu
al
Pe
ak
Str
ea
mfl
ow
(c
fs)
Annual Exceedance Probability
fitted curve
lower 90% conf
upper 90% conf
Typical Flood Frequency CurveLo
g S
cale
Normal Probability Scale
Return Period 2 5 10 25 50 100 200 500
90% confidence interval
EXTREME
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Flood Frequency Analysis
When possible, we infer probability from a record of annual maximum observations (Bulletin 17B)o using the past variability as a representation of the futureo use LogPearson type III distribution (least wrong for 100yr event)
Treat annual peak flows as a random, representative sample of realizations from the flood population of interest
Generally, we assume the sample is IIDo annual peak flows are random and independento peak flows are identically distributed – homogeneous data seto sample is adequately representative of the population
These assumptions are becoming more difficult…
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0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .0021000
10000
100000
1000000
An
nu
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Pe
ak
Str
ea
mfl
ow
(c
fs)
Annual Exceedance Probability
sample data
fitted curve
lower 90% conf
upper 90% conf
Generation of the Flood Frequency Curve
1903 – 2009109 years
Log
Sca
le
Normal Probability Scale
Return Period 2 5 10 25 50 100 200 500
LogPearson III
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0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .0021000
10000
100000
1000000
An
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Pe
ak
Str
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mfl
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(c
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Annual Exceedance Probability
sample data
fitted curve
lower 90% conf
upper 90% conf
Uncertainty in the Flood Frequency Curve
1965 – 200945 years
Log
Sca
le
Normal Probability Scale
Return Period 2 5 10 25 50 100 200 500
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Corps Activities that require Flood-Frequency
Corps of Engineers responsibilities involve both water management and development of infrastructure
Make decisions based on probabilistic analysis, and where possible, explicit incorporation of uncertaintyo … uncertainty in probabilistic estimates of flow, and uncertainty
in other modeling (hydrologic, hydraulic and economic) We use the probabilistic description of flooding in:
o Safety of projectso Scale of projects (and updated “performance”)o Operation of projects
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Safety of Projects
In the past, required that projects can withstand the occurrence of the Probable Maximum Flood (PMF) without failure (e.g., sizing of spillway)o note: capacity exceedance ≠ failure
Now, we evaluate overall risk (exceedance OR failure), and target a tolerable risk to remain belowo Risk = probability of occurrence × consequenceo Evaluate all possible failure modes and their likelihoods, as
well as the likelihoods of loading thresholds (from the flood-frequency curve)
levees, dams, locks, ports, hydropower
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16
Lik
eli
ho
od
Consequences
1
2
3
56
4
Tolerable Risk Limit
Dynamics of Likelihood vs. Consequences:
1. original estimate of risk2. risk management implemented
probability: strengthen, raise capacity
consequence: remove structures
3. due to aging and wear&teardue to climate change?
4. due to maintenance, repairs, and improved operations
5. resulting from development pressure
6. on-going risk management activitiesa) Land use managementb) Flood proofingc) Warnings and preparedness
plans
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Scale of Projects
This is the “Planning” function Federal dollars are spent to provide an equal or greater
benefit to the Nationo formerly, the explicit benefit of a project was a reduction in
annualized flood damage (levees, dams, “non-structural” actions)o now, also incorporate reduction in loss of life
Projects are scaled (sized) such that either net benefits (benefit – cost) or benefit/cost ratio are maximizedo no defined target, but now must be below tolerable risk limit
Annualized benefit is the reduction in mean annual damage (or, EAD), based on the probability distribution of peak annual flow
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EAD = Expected Annual Damage The probability distribution of annual flood damage for a
river reach is computed by combining summary curves developed from hydrologic frequency, hydraulic and economic analyses:
flow-frequency curve to obtain a: flow-stage curve damage-frequency
curvestage-damage curve
The mean of the damage-frequency curve is the expected value of annual damage, or EAD.
Computing EAD with summary curves
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Pea
k F
low
(cf
s)
Exceedance Probability1 0Stage (ft)
Flo
w (
cfs)
Stage (ft)
Dam
age
($)
p
Exceedance Probability1 0
Dam
age
($)
p
Computing EAD with summary curves
AREA = mean = Expected Annual
Damage
0
DdF(D)EADF(D)
F(Q)
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Pea
k F
low
(cf
s)
Exceedance Probability1 0Stage (ft)
Flo
w (
cfs)
Stage (ft)
Dam
age
($)
p
Exceedance Probability1 0
Dam
age
($)
p
Use Monte Carlo simulation to sample many realizations of each curve to compute many realizations of EAD
Uncertainty in EAD
AREA = mean = Expected Annual Damage
0
DdF(D)EADF(D)
F(Q)
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Project Performance
Another measure for project scale is the performance of the project, and how it might change over timeo Project performance is a combination of the likelihood of
capacity exceedance and the likelihood of failure A flood protection project is designed having a certain
probability of capacity exceedance a change in the flood-frequency curve causes
a change in the probability of capacity exceedance This change might cause a difference with regard to the
National Flood Insurance Program
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100-year Levee Certification
0.50.99 .95 .9 0.75 0.25 0.1 .05 .0110.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
Probability of Exceedance
Sta
ge
(ft)
90%
90% conditional non-exceedance probability for the 1%-chance event…
estimated stage-frequency curve
60
55
50
45
40
35
30
25
20
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Operation of Projects
This is the Corps’ Water Management function Reservoirs have Guide Curves (GC) that specify the
upper bound of storage Below GC is Conservation space for storing water for
later useo navigation, hydropower, water supply, flow maintenance,
flow temperature control, (and recreation – don’t use!) Above GC is Flood space for storing flood flows
o Store flood volume until can release safely downstreamo Either maintain a flood pool, or draft enough space to store
forecasted snowmelt flood
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Flood Pool
Conservation Pool
flood benefits are proportional to flood volume
supply benefits are proportional to supply volume
Guide Curve
Reservoir Storage Pools
An increase in the flood-frequency curve would let existing flood pool offer less protection (larger chance exceedance), or require a larger flood pool
More variability in flow, or a decrease in average annual volume would decrease the yield of the Conservation pool
A decrease the low-flow frequency curve would require more yield for streamflow maintenance
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Seasonal Reservoir Pools
Get more benefit to each use when have more volume serving it – so multi-use space is efficient
When there’s a limited flood season, or only snowmelt runoff flooding, use seasonal pools
A seasonal Guide Curve calls for a flood pool during part of the year, and allows it to fill when there is little or no probability of floodingo a change in the flood season would require changing GC
When only snowmelt runoff flooding (Pacific Northwest), draft a flood pool volume based on runoff forecasts
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Seasonal Flood Pool – Rain Flooding
rain flood season
flood pool
conservation pool
supply volume
flood volume
Oct Jan Apr Jul Oct
Guide Curve
Guide Curve
snowmelt runoff
Re
se
rvo
ir V
olu
me
What if earlier snowmelt runoff before rain-flood season is over?
Convenient timing: snowmelt starts when rainy season ends, catch volume.
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Seasonal Flood Pool – Rain Flooding
rain flood season
flood pool
conservation pool
supply volume
flood volume
Oct Jan Apr Jul Oct
Guide Curve
Guide Curve
snowmelt runoff
Re
se
rvo
ir V
olu
me
What if earlier snowmelt runoff before rain-flood season is over?
Convenient timing: snowmelt starts when rainy season ends, catch volume.
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Seasonal Flood Pool – Snowmelt Flooding
snowmelt flood
season
flood pool
conservation pool
Re
se
rvo
ir V
olu
me
supply volume
flood volume
Oct Jan Apr Jul Oct
Variable Guide Curves
Guide Curve
With snowmelt forecast, draft enough to catch flood peak. But some forecasts are based on historical record…
snowmelt runoff
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Frequency Analysis, non-stationarity
Standard (B17B) frequency analysis assumes data is IID (independent and identically distributed)o use the past to estimate likelihood for the future
Some change can be dealt with, if the change is recognizable and predictableo example: urbanizationo adjust earlier flood peak data to current basin conditiono KEY: the trend must be observable to be removed, and
predictable to have an estimate of a future condition Climate change/trend is more difficult to recognize,
more difficult to predict
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Adjustment for Urbanization
10
100
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1919
1924
1929
1934
1939
1944
1949
1954
1959
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1969
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1984
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1999
2004
an
nu
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ea
k f
low
0
1
2
3
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8
9
10
% im
pe
rvio
us
are
a
actual data
adjusted data
% imperv area
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0.99 0.90.95 0.8 0.2 0.1 0.05 0.010.02 0.0020.0050.510
100
1000
10000
100000
Exceedance Probability
Str
ea
mfl
ow
(c
fs)
actual data
fitted actual curve
adjusted data
fitted adjusted curve
Adjustment for Urbanization
Return Period 2 5 10 25 50 100 200 500
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Decisions under uncertainty
How can we address this increased uncertainty about future hydrology?
There are two opposite approaches:1. Find a way to make better estimates of the future2. Work with the uncertainty. Make decisions (project
scaling, operation plans) more robust (able to perform well in a wider array of conditions) and able to adapt as change is recognized (realized)
o NOTE: adaptation is quite feasible for project operations, but less so for infrastructure development. Plan for staged development of infrastructure, but more costly in the end
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How can we do better frequency analysis?
If our gaged flood records are not IID, how should we do frequency analysis?o Fit parameters that vary as a function of time?o Other covariates?o Attempt to adjust all historical floods to an estimated
present or future condition?o Run climate models longer to capture a stationary
(current or future) condition?o Attempt frequency analysis on shorter periods?
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0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .002100
1000
10000
100000
An
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(c
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Annual Exceedance Probability
sample data
fitted curve
lower 90% conf
upper 90% conf
1909 – 2011 103 years
Return Period 2 5 10 25 50 100 200 500
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0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .002100
1000
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An
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Annual Exceedance Probability
1st 30 yrs
0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .002100
1000
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100000
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Annual Exceedance Probability
1st 30 yrs
2nd 30 yrs
0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .002100
1000
10000
100000
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Annual Exceedance Probability
1st 30 yrs
2nd 30 yrs
3rd 30 yrs
Return Period 2 5 10 25 50 100 200 500
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0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .002100
1000
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100000
An
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Annual Exceedance Probability
1st 30 yrs
0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .002100
1000
10000
100000
An
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(c
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Annual Exceedance Probability
1st 30 yrs
2nd 30 yrs
0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .002100
1000
10000
100000
An
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Annual Exceedance Probability
1st 30 yrs
2nd 30 yrs
3rd 30 yrs
Return Period 2 5 10 25 50 100 200 500
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0.99 0.95 0.9 0.8 0.5 0.2 0.1 0.05 0.02 .01 .005 .002100
1000
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Annual Exceedance Probability
Random 30-year Samples from full-period Frequency Curve
Return Period 2 5 10 25 50 100 200 500
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Short-record Frequency Curves
It’s difficult to make assumptions based on frequency curves from short records
The uncertainty in those short-record frequency curves overwhelms any change we might see in the short-term
Need more data to infer probability distributions, to reduce uncertainty so that it’s less than the change due to climate.