Flood Risk Management:

Adapting to nonstationarity

Casey Brown, PhD, PEAssociate Research Scientist

IRI for Climate and Society, Columbia University

International Training Workshop on Typhoon and Flood Disaster Reduction

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Summary

1.1. Infrastructure designed to mitigate variabilityInfrastructure designed to mitigate variability–– based on stationary view of climatebased on stationary view of climate

2.2. HydroclimatologyHydroclimatology reveals stationary climate is not reveals stationary climate is not supported supported

3.3. Climate Risk Management for WR Climate Risk Management for WR –– adapting to adapting to nonstationaritynonstationarity

–– Enhancing the performance of a shared water system via Enhancing the performance of a shared water system via Economic Mechanisms and seasonal climate forecastsEconomic Mechanisms and seasonal climate forecasts

–– Prediction of flood risk and possible responsesPrediction of flood risk and possible responses

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Part 1:Engineering to Manage Variability

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Stakhiv, CoE, 2007FOR IT

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Part 2:Nonstationarity of hydroclimatology

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Part 3:Adaptation to Nonstationarity

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Barlow et al., 2001FOR IT

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Barlow et al., 2001FOR IT

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Seasonal Climate forecast

(Hamlet and Lettenmaier, 1999)FOR IT

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Cluster 3

0%

20%

40%

60%

80%

1 2 3 4 5 6 7 8 9 10 11 12Month

Cluster 2

0%5%

10%15%20%25%

1 2 3 4 5 6 7 8 9 10 11 12Month

Cluster 4

0%

10%

20%

30%

40%

1 2 3 4 5 6 7 8 9 10 11 12Month

Ann. Max. Flood Seasonality in the West

3133

1

3

333 33

3

33

3

43

44

444

111114

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1

11111 14

1344444

44444444

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11131

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11111

1

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31 11

22

2211

2 3222 22 122 2

2222 122 2

222 22 12 22 12222222 12 12222 12 24 11

Cluster 1

0%10%20%30%40%50%60%

1 2 3 4 5 6 7 8 9 10 11 12Month

Pizarro & Lall, 2002

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Partial CorrelationsPizarro & Lall, 2002

Flood with NINO3 | PDO Flood with PDO | NINO3

++

-

-

+-+ +

++

-

+

+

++

+++

+

+

+++

-++

+

-

++

--

+

++

+--

+-

+---

- -

- -- ++ +-+ +

+ --

+ + -

+- ---- -

Correlation > 0.37 Correlation >0.23

--

-

--- - -

+

-

+

-+

+-

++

-

++

+

-

--++--

-++++

++---+

-

+-

++-

--

-

+

---

++

-+ --

++

----

- -

-- +-

--++

++ + ----

-+

Correlation > 0.37 Correlation >0.23FOR IT

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Season/Year Ahead Forecasting

• Projection Pursuit regression (PPR) used to build and test models in a cross-validated mode.

• Use 1st 30 years to choose predictors and number of basis functions

• Predict flood for year 30+k+1 using climate data for previous season or year (2 separate models) and model refit to 30+k years of data.

Each time 100 models are fit using 90% of the available data sampled randomly and forecasts from these 100 models are – (a) averaged to determine the forecast for the next year– Used to derive uncertainty bands for the forecast

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Predictors Considered One Season Ahead

• Cluster 1: December through February (DJF) composites of NINO3, and PDO; February minus December differences of the NINO 3 and PDO.

• Cluster 2: September through November (SON) composites of NINO3 and PDO; November minus September differences of the NINO 3 and PDO.

• Cluster 3: Same as Cluster 1.

• Cluster 4: the January through April (JFMA) composites of NINO3 and PDO, and April minus January differences of the NINO3 and PDO.

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Forecast- Season Ahead Examples

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Unexplained Variance under cross validation- season ahead

Stations with forecasts

Cluster #

1: 21/31

2: 10/24

3: 8/9

4: 6/16FOR ITW

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Unexplained Variance under cross validation- year ahead

Stations with forecasts

Cluster #

1: 20/31

2: 11/24

3: 5/9

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Dynamic Risk Management: Prospects for Multi-purpose reservoir management

• Noting the usual risk averse strategy used by Water Managers, can the forecasts be used to increase the water supply yield in a given year, while maintaining the long term yield and its reliabilityand the target long term flood control goals as lower bounds?

• Flood Control and Water Supply Goals

• Consider Flood Volume Forecast

• Consider Monthly Inflow Forecasts

• Consider Both

• Acceptable Flood Risk in any year =0.01

• Minimum Water Supply Yield Reliability = 0.99FOR IT

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Typical Reservoir Operation

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ApproachMonte Carlo Experiment (1000 simulations):1. Size Active and Flood Control Storage using 1st 30 years of record

corresponding to Water Supply = 60% of mean annual flow, and flood control and water supply reliabilities =0.99

2. Each year forecast (a) 99th peak flood quantile and (b) ensemble of monthly inflow sequences

3. If flood forecast is used – resize flood pool to the forecast volume active storage pool changes

4. Using beginning of year storage, and updated active pool capacity, solve for maximum yield at 0.99 reliability subject to long term yield as a lower bound, and achieving target long term end of period storage withprobability 0.99

5. Compute Performance statisticsData from Clarks Fork at St. Regis, MT – here results for synthetic case – SNR 10, 5, 1 presented

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Multipurpose Reservoir Operation Using Seasonal Forecasts- Results

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Dynamic Risk Management: Prospects for Financial management

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Insurance Applications

• Negative spatial correlation across insured assets can help reduce premiums, by reducing variance in payments, thus reducing exposure for insurer at the same profit level.

• Skilled forecasting can:– Help better price a cat bond by estimating the

variation in the risk level over the life of the bond– Help manage portfolios of flood triggered and other

seasonal dependent cat bonds (e.g., hurricanes, windstorms) according to the risk averseness of investor.

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Climate Information for Design

1. does 1. does gcmgcm output improve upon assumption of climate output improve upon assumption of climate stationaritystationarityfor estimating future flood risk given anthropogenic climate for estimating future flood risk given anthropogenic climate change?change?

2. can 2. can gcmgcm output outperform statistical models of output outperform statistical models of nonstationaritynonstationarity(nino34, (nino34, pdopdo, time index, [co2])?, time index, [co2])?

3. what is the 100 year flood for the next 100 years?3. what is the 100 year flood for the next 100 years?(how should various forms of information be used/combined?)(how should various forms of information be used/combined?)

Research Questions

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Typical Reservoir Storage Allocation

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Snow

1940 1950 1960 1970 1980 1990 20000

2

4

6

8

10

12 x 104

Time(year)

Disc

harg

e(cf

s)

Uncertainty boundsObserved Annual Flood100 Year Flood

R:0.78

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Temperature

1930 1940 1950 1960 1970 1980 1990 20000

2

4

6

8

10

12 x 104

Time(year)

Disc

harg

e(cf

s)

Uncertainty boundsObserved Annual Flood100 Year Flood

R:0.37

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Temperature+Snow

1940 1950 1960 1970 1980 1990 20000

2

4

6

8

10

12 x 104

Time(year)

Disc

harg

e(cf

s)

Uncertainty boundsObserved Annual Flood100 Year Flood

R:0.80

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PDO

1930 1940 1950 1960 1970 1980 1990 20000

2

4

6

8

10

12 x 104

Time(year)

Disc

harg

e(cf

s)

Uncertainty boundsObserved Annual Flood100 Year Flood

R:0.44

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PDO+NINO3

1930 1940 1950 1960 1970 1980 1990 20000

2

4

6

8

10

12 x 104

Time(year)

Disc

harg

e(cf

s)

Uncertainty boundsObserved Annual Flood100 Year Flood

R:0.48

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Correlation Map Between Montana Flood and SSTs

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SST

1930 1940 1950 1960 1970 1980 1990 20000

2

4

6

8

10

12 x 104

Time(year)

Disc

harg

e(cf

s)

Uncertainty boundsObserved Annual Flood100 Year Flood

R:0.53

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GCM

1960 1965 1970 1975 1980 1985 1990 1995 20000

2

4

6

8

10

12 x 104

Time(year)

Disc

harg

e(cf

s)

Uncertainty boundsObserved Annual Flood100 Year Flood

R:0.25

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Unconditioned estimate of design flood

Stationary PDO PDO&Nino3 SST Snow Pack GCM SST PC6

7

8

9

10

11

12x 10

4

100

Ret

urn

Perio

d Fl

ood(

cfs)

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Std Dev of Estimate

02000400060008000

100001200014000

Temp,S

now

SnowSST PC1PDO,N

ino

SST

PDO

GCM

Temp

Histori

calSt

d D

ev (c

fs)

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Inflow to Angat Reservoir

0

50

100

150

200

250

300

350

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

Month

Stre

amflo

w (i

n hm

3)

0

50

100

150

200

250

300

350

400

450

500

Rai

nfal

l (m

m)

StreamflowRainfall

3-months lag correlation

ρ(Nino3.4,QJJAS) = -0.20

ρ(Nino3.4,QOND) = -0.51

JJAS – 30%

OND – 46%

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Northeast Monsoon (Oct – Dec)FOR IT

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1997 El Nino

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1998 La Nina

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Seasonal Climate Forecast

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Angat Reservoir – Manila Water Supply

A aerial view of the Angat Hydroelectric Plant

Courtesy of Mr. Rodolfo German (Angat dam)FOR IT

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Reservoir ManagementHydropower

Water Delivery

Storage

SpillInflows 0

1020

3040

50

6070

8090

100

1 2 3 4 5 6 7 8 9 10 11 12

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Angat Decision RuleANGAT H.E. PLANT

150

160

170

180

190

200

210

220

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

ELEV

ATI

ON

(m)

1996 1997 1998 1999 2000 2001 UPPER LOWER

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0

1020

3040

50

6070

8090

100

1 2 3 4 5 6 7 8 9 10 11 12

Dynamic Rule Curve

Inflow

Flood

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0102030405060708090

100

1 2 3 4 5 6

More Inflow

Greater Flood Risk

More Release Possible

Wet Forecast

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Forecasted InflowsANGAT OPERATION CURVES November 8 - July 31, 2007

155

165

175

185

195

205

215

7-No

v

NOV

8-16

NOV

17-3

0

DEC

Jan

Feb

MAR

1-3

MAR

4-31

APR

MAY

JUNE

JULY

ELE

VATI

ON

(met

ers)

Series2 Series3 Series4 Series1 Series5 Series6 Series7 Series8 Series9 Series10Series11 Series12 Series13 Series14 Series15 Series16 Series17 Series18 Series19 Series20

Years below 180 at March 30 349 of 1000 = 35%

Years below 180 at June 30 444 of 1000 = 44%FOR IT

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Increased Hydropower

0

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600

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1000

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1400

1987 1989 1991 1993 1995 1997 1999 2001

Year

Hyd

ropo

wer

Gen

erat

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in G

WH

)

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50

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150

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250

300

350

400

Observed In

flow

ActualUpdated ForecastOctober ForecastObserved

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Irrigation Improvement

0

50

100

150

200

250

1987 1989 1991 1993 1994 1997Year

Allo

cati

on f

or I

rrig

atio

n (

in h

m3

) DecemberNovemberOctober

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Dry Forecast

0

10

2030

40

50

60

7080

90

100

1 2 3 4 5 6

Less Inflow

Less Flood Risk

More Storage Possible - but not sufficient

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0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

1996 1997 1998 1999 2000 2001 2002 2003 2004

Prod

uctio

n/H

arve

sted

Are

a

Production (M T) Area Harvested (ha)

Irrigated Palay Production in AMRIS

1 – First Semester Harvest (Nov – Mar cropping season/dry) 2 – Second Semester Harvest (Jun – Oct cropping season/wet)

1998 (1) - 86.60 %

1998 (2) - 43.94 %

Impacts on Irrigation

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Economic Instruments for Adaptation

Premises:In most years thereIn most years there’’s sufficient waters sufficient waterPermanent sale of water rights not desirablePermanent sale of water rights not desirable

––In most years available water would be unusedIn most years available water would be unused––Reduce incentive for efficiency improvementsReduce incentive for efficiency improvements

Value of municipal/industrial water exceeds agricultural valueValue of municipal/industrial water exceeds agricultural valueMunicipal water agency budgets are constrainedMunicipal water agency budgets are constrained

Instrument Design for Instrument Design for AngatAngat::–– No market and price for option of No market and price for option of agag. water = 0. water = 0–– Water price based on estimate of value in Water price based on estimate of value in agag. use (residual method). use (residual method)–– Preseason and inPreseason and in--season flows correlated season flows correlated –– Joint distribution (normal Joint distribution (normal –– lognormal) of inflows modeled with (lognormal) of inflows modeled with (ImanImanand Conover, 1982)and Conover, 1982)–– Reservoir Index InsuranceReservoir Index Insurance

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Instrument Design for Instrument Design for AngatAngat

Demand (NDJF)Urban = 462 MCM Ag = 363 – 425 MCM

Inflows (NDJF) = 1030 MCM

Assumptions–– Planting decision made in November (Oct observed) Planting decision made in November (Oct observed) –– No market and price for option of No market and price for option of agag. water = 0. water = 0–– Water price based on estimate of value in Water price based on estimate of value in agag. use (residual . use (residual

method)method)–– Preseason and inPreseason and in--season flows correlated (r = 0.3)season flows correlated (r = 0.3)–– Joint distribution (normal Joint distribution (normal –– lognormal) of inflows modeled with lognormal) of inflows modeled with

((ImanIman and Conover, 1982)and Conover, 1982)–– Reservoir Index InsuranceReservoir Index Insurance

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Reservoir Index Insurance

••Smooth supply costs/predictabilitySmooth supply costs/predictability••Avoids impediments to crop insurance (moral Avoids impediments to crop insurance (moral hazard; selection bias) hazard; selection bias) ••Not limited to landownersNot limited to landowners••Less basis risk vs. rainfall index insuranceLess basis risk vs. rainfall index insurance

Previous Work Previous Work –– Global Agricultural RiskGlobal Agricultural Risk(J. (J. SkeesSkees, U. Kentucky), U. Kentucky)FOR IT

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Insurance + Contracts

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Option Exercise Decision

np ?

nppp + nipi

Observe preseason flows

Decide preseason options to exercise

TotalCost

Observe In-season flows

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Water Manager’s Cost

( ) ( )( ) ( )( ) ( )

4

33

202

1

min ( ) min( , )U

P P

l TP P I I P Il

lI

P P T T P I P Iln nl

P I P I P Il

W Q n q Q g Q Q dQPE C n P A U n q g Q Q dQq

Q Q n q g Q Q dQ≤ ≤

⎛ ⎞− − −⎜ ⎟⎜ ⎟

= + + −⎜ ⎟⎜ ⎟⎜ ⎟+ + −⎝ ⎠

∫∫∫

( ) 3

*3 2

2 1

max ,0

min( , )

TP P I I

IP P T T P I

P I P I

W Q n q Q if Q lPC n P A U n q if l Q lq

Q Q n q if l Q l

⎧ − − − ≥⎪⎪= + − ≥ ≥⎨⎪ + − ≥ ≥⎪⎩

Ex Post Cost

Water Manager’s Decision Problem

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Costs vs Seasonal Inflows

0

500

1000

1500

2000

0 500 1000 1500 2000 2500 3000 3500 4000

October-February Inflows (mcm)

Cos

ts (M

illio

n Pe

sos) Options No OptionsPerfect

Option Cost Function

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Inseason/Preseason ~ 2 (PP=2.35, PI=5)

0

500

1000

1500

2000

2500

3000

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

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1994

1996

1998

2000

2002

2004

Cos

ts in

Mill

ion

Pes

os

Ag. CostsContracts

Timeseries of Costs

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Water Supply Costs (low in-season cost)

PP=2.35, PI=2.93

0

200

400

600

800

1000

120019

68

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Cos

ts in

Mill

ion

Peso

s

ContractsInsured

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PP=2.35, PI=5

-500

0

500

1000

1500

200019

68

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Cos

ts in

Mill

ion

Peso

s

Current Ag LossContractsInsured

Water Supply Costs (High in-season cost)

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Summary

Proposed:Dry Year Options + Insurance to manage climate riskDry Year Options + Insurance to manage climate risk

–– Benefits: • Increase the productivity of water in most years• Reduce the financial impact of climate shocks

– Risks• Insurance premium = $4 – 5 Million/year• Agricultural sector refuses to sell• No takers in insurance industry

•• Future WorkFuture Work– Forecast use to reduce contract cost

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Economic Instruments for Adaptation

• Climate risk management as strategy for Climate risk management as strategy for climate change adaptationclimate change adaptation

–– Early Warning of Drought and Flood – Dynamic Reservoir Management– Conjunctive Use of Surface and Groundwater→ Mechanisms for equitable and efficient water allocation

•• Previous work on Economic InstrumentsPrevious work on Economic Instruments–Michelsen and Young (1993) – optioning ag. water rights–Wilchfort and Lund (1997) – assessing options and spot market–Characklis et al (2006) – options, permanent rights, market

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Conclusion

1.1. Infrastructure designed to mitigate variabilityInfrastructure designed to mitigate variability–– based on stationary view of climatebased on stationary view of climate

2.2. HydroclimatologyHydroclimatology reveals stationary climate is not reveals stationary climate is not supported supported

3.3. Climate Risk Management for WR Climate Risk Management for WR –– adapting to adapting to nonstationaritynonstationarity

–– CRM system to manage variability financiallyCRM system to manage variability financially

–– Estimating changing flood risk and designing dynamic Estimating changing flood risk and designing dynamic responsesresponses

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Summary

• Flood Probabilities vary in response to variations in climatic factors• Climate is bound to change – natural and anthropogenic factors• Long run statistics of climate and its effects on floods are not

predictable• If we assume that the structural teleconnections, i.e., the physics of

climate remain stable, then there is a basis for predicting season to year ahead climate/flood statistics

• Prospects for using these forecasts to adapt to changing climate by modifying reservoir operation and by using a hierarchy of financial instruments are demonstrated. Risk aversion is maintained at thesame level as in the static risk management paradigm.FOR IT

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P, T, SWE foryear t

Peak annual flow for year t

parameters ofextreme value distribution

Design floodestimate andvariance

for n years, say ½ the fullrecord ditto pzTx σμ +=)(O

bservations

P, T, SWE foryear t

Peak annual flow for year t

parameters ofextreme value distribution

Design floodestimate andvariance

for n years, say ½ full record

now use 2nd half of record

pzTx σμ +=)(GC

M output

Experimental Design

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Preliminary Conclusions

1. The design flood is 1. The design flood is nonstationarynonstationary (dependent on the sample) and (dependent on the sample) and exhibits temporal structureexhibits temporal structure

2. The design flood exhibits links to ocean circulation; possib2. The design flood exhibits links to ocean circulation; possible le avenue for GCM provided informationavenue for GCM provided information

3. Preliminary indication of variance reduction through incorpo3. Preliminary indication of variance reduction through incorporation ration of of nonflownonflow datadata

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Climate Information for Design

:as drepresente isn underdesigor over ofcost The chosen. flooddesign theis )]([)(ˆ)(

n.informatioperfect given valueflooddesign optimal theis )(ˆ

TxTxTx

Tx

Δ+=

design.over than morecost can designunder eg, ,)(ˆ around asymetric becan and

)])([f(

Tx

TxΔ

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the Burden of Proof

The High BarThe High Bar

Adaptation:Adaptation: Investments to reduce the impact of climate changeInvestments to reduce the impact of climate changeExpected Net Benefits of Action > Expected Net Benefits of InactExpected Net Benefits of Action > Expected Net Benefits of Inactionion

CostLp t <+Δ )

)1((

ρThe Low BarThe Low Bar

Hydrologic Engineering DesignHydrologic Engineering DesignReservoir design based on estimates of demand and hydrologic recReservoir design based on estimates of demand and hydrologic record ord

(drought of record; 100 year flood)(drought of record; 100 year flood)FOR IT

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Typical Reservoir Storage Allocation

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Climate Information for Design

:as drepresente isn underdesigor over ofcost The chosen. flooddesign theis )]([)(ˆ)(

n.informatioperfect given valueflooddesign optimal theis )(ˆ

TxTxTx

Tx

Δ+=

design.over than morecost can designunder eg, ,)(ˆ around asymetric becan and

)])([f(

Tx

TxΔ

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Climate Information for Design

then

ˆˆ)(ˆ n,informatio fullWith quantile.pth theis p and dist. thefrom valueflooddesign theis z where

)( as estimated is floodDesign

p

p

zTx

zTx

σμ

σμ

+=

+=

. of magnitude theand oflocation on the based sestimation evalcan weand

)ˆ(ˆ)]([

σμ

σσμμ pzTx −+−=Δ

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Casey Brown, Hyun Han Kwon, Upmanu LallInternational Research Institute for Climate and Society

IRIhttp://iri.columbia.edu61 Route 9WPalisades, NY 10964-8000

The Burden of Proof for Climate Change Assessments:

Questions Important for the Water Sector

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