building strong ® hydrologic engineering center use of information on hydrologic extremes: us army...

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


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


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)


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?


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?


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


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


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)


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)


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


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…


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)


sample data

fitted curve

lower 90% conf

upper 90% conf

Generation of the Flood Frequency Curve

1903 – 2009109 years

Log

Sca

le


Return Period 2 5 10 25 50 100 200 500

LogPearson III


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)


sample data

fitted curve

lower 90% conf

upper 90% conf

Uncertainty in the Flood Frequency Curve

1965 – 200945 years

Log

Sca

le


Return Period 2 5 10 25 50 100 200 500


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


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


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


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


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


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)


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)


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


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


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


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


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


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.


Timing of Flow Volume in California


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


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


Adjustment for Urbanization

10

100

1000

10000

1919

1924

1929

1934

1939

1944

1949

1954

1959

1964

1969

1974

1979

1984

1989

1994

1999

2004

an

nu

al p

ea

k f

low

0

1

2

3

4

5

6

7

8

9

10

% im

pe

rvio

us

are

a

actual data

adjusted data

% imperv area


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


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


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?


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

nu

al

Pe

ak

Str

ea

mfl

ow

(c

fs)


sample data

fitted curve

lower 90% conf

upper 90% conf

1909 – 2011 103 years

Return Period 2 5 10 25 50 100 200 500


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

nu

al

Pe

ak

Str

ea

mfl

ow

(c

fs)


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

nu

al

Pe

ak

Str

ea

mfl

ow

(c

fs)


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

nu

al

Pe

ak

Str

ea

mfl

ow

(c

fs)


1st 30 yrs

2nd 30 yrs

3rd 30 yrs

Return Period 2 5 10 25 50 100 200 500


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

nu

al

Pe

ak

Str

ea

mfl

ow

(c

fs)


Random 30-year Samples from full-period Frequency Curve

Return Period 2 5 10 25 50 100 200 500


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.

building strong ® hydrologic engineering center use of information on hydrologic extremes: us army...

Documents

avenues o

o whats

natural variability

future variability o

areas o decisionmaking

range of hydrology o

uncertain o decisions

time o decisions