1

Risk and Reward

Casey Brown

Associate Professor of Civil and Environmental Engineering

University of Massachusetts

UMass Hydrosystems Research Group

2

Uncertainty = Risk + Opportunity?Risk = an expected value

Risk = product of the consequences of a hazard and the probability that the hazard will occur

- Risk = expected loss

For example, Risk = flood damage X probability of flood

Risk = $100,000,000 X 0.01 = $1M

In some fields, risk = probability of negative event

Risk of being hit by asteroid = 10-9

3

Uncertainty = Risk + Opportunity?• Opportunity = product of the consequences of an event

and the probability that the event will occur

• Opportunity = expected loss or gain

4

Risks and Opportunities

Op

po

rtu

nit

y

5

Uncertainty: Pigs, Ducks, Skunks

Unkunk

= an unknown unknown

related: surprises; black swans

Kunk

= a known unknown

Skunk

= a known that stinks(Klemes, 2002)

(Taleb, 2007)

6

Geography Department, U. OregonEmission Scenarios General Circulation Models (GCMs)

Downscaling

Hydrologic Model

Water Resources System Model

Water System Performance Under Future

Climate Scenarios

Greene County, PA Department of Econ. Development

Wisconsin Valley Improvement Company

7

Decision Frameworks for Climate Change

• How will the science improve decisions?

• Usual mode of engagement: Prediction - centric• Science reduces the uncertainty affecting the decision• E.g., Science: the most likely future condition is A

• Decision – under Future A, Option 1 is my best choice

• Mode of engagement under climate change• Science characterizes uncertainty (may increase)• E.g., Science: here is a wide range of possible futures, and we’re not

sure they delimit the true range• Decision – um …

UMass Hydrosystems Research Group

8

9

“Decision Scaling”, Brown and Wilby, 2012 (EOS)

Decision-centric Climate Science

Figure 1 Steps in decision scaling vs. traditional approach

• Focus on identifying the vulnerabilities of the system

• Identify climate changes that are problematic

• Evaluate options to improve robustness to such climate changes

10

The Summary

• Inherent, irreducible uncertainties of climate system • Requires a shift of emphasis from “reduce uncertainty” to risk reduction

• Decision-based approaches allow specification of the information that is actually needed (maybe less than you think!)

• GCMs provide information that can be useful for managing risks when treated appropriately

• When using uncertain information (climate change, seasonal forecast), must manage the residual risk

11

RISK AND DEVELOPMENTUpside and downside

12

Per Capita GDP vs Latitude

(Sachs, 2001)

13

Rainfall Variability and GDP

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 50 100 150 200 250 300

GDP and Rainfall Variability

Mean Annual Rainfall

Monthly Rainfall Variability

Bubble Size = GDP per capita

(Blue = low interannual variability of rainfall)

14

Rainfall Variability and GDP

GDP and Rainfall Variability

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 50 100 150 200 250 300

Mean Annual Rainfall

Monthly Rainfall Variability

Bubble Size = GDP per capita

(Blue = low interannual variability of rainfall)

Wealthy nations share a small window of favorable climate (low variability;

moderate rainfall)

15

Hydroclimate risk to economic growthin sub-Saharan Africa

Casey Brown · Robyn Meeks · Kenneth Hunu · Winston Yu Climactic Change 2011

• Hydroclimate variability is the dominant and negative climate effect on economic growth

• 10% increase in drought area causes a 40% reduction in annual growth in SSA

• Globally, 10% increase in drought area causes a 30% reduction in annual growth

16

Risks and Opportunities

Op

po

rtu

nit

y

17

1987

1989

1991

1993

1995

1997

1999

2001

0

100

200

300

400

500

600

GDP per Capita ($)

GDP per cap

Linear (GDP per cap)

Adjust GDP per cap

Linear (Adjust GDP per cap)

1987

1989

1991

1993

1995

1997

1999

2001

0

100

200

300

400

500

600

GDP per Capita ($)

GDP per cap

Linear (GDP per cap)

Status Quo GrowthGrowth with 10% reduction in drought effect

18

FLOOD RISK MANAGEMENTAn example of risk estimation and management

19

Flood Control Storage

20

Overflowing Dam: limits of control

21

Flood Risk Estimation and “Nonstationarity”

• Traditional approaches based on stationarity – the past represents the future• Synthetic streamflows and critical period analysis• Flood risk estimated from historical record = “100 year flood”• Fixed water allocation

• Recognition of Temporal Structure in the hydrologic record• ENSO, PDO and extended departures from long term mean• Flood risk and rainfall totals vary between years and decades• Monitoring, forecasting, early warning systems

• Recognition of climate change and Nonstationarity• Klemes (1974): “… by assuming nonstationarity we acknowledge nonexistence of

preset limits and directions … unpredictability… and subscribe to philosophical indeterminism”

• Emphasis on diagnosing change and its implications• Growing recognition of limited ability to predict the future• Are our risk management strategies resilient to an uncertain future?

22

24

Example application: Iowa River

June 2008 floods

Spillway use:

-1993-2008-2013

Are floods increasing?

Proposed adaptations:

Reservoir re-operation

Raise Levees

25

R. Vogel

26

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

0

1

2

3

4

5

6x 10

4

y = 0.09*x + 1.5e+004

Trend in historic record

Stream gage

27

Steinschneider et al.: The integrated effects of climate and hydrologic uncertainty on

future flood risk assessments, in preparation.

Integrated Uncertainties

28

0.01

Exceedance Probability

29

0.01

Exceedance Probability

30

Is the physical uncertainty the easy part?Peak Flow

Exceedance Probability

Damage Function

“Optimal” Flood Risk Reduction Plan

Actual Flood Risk Reduction Decision

“the wicked”

Rittel and Webber (1973)

“Nonstationarity”

GB Shaw: “Every profession is a conspiracy against the laity”

34

RISK MANAGEMENT Evaluating alternatives

35

Benefits – reduction in risk (avoided expected losses)

- change of probability or consequence- Notice, this is an expected value

Costs – the costs of reducing risks (can be nonfinancial)

Decision: Find the alternative that yields maximum benefit/cost ratio

Benefit Cost Analysis of Risk Management

36

Optimal Flood Risk Management

dsZ damages) costsmeasuresoption (cost measurespermanent min

dssXXDssXcspXcm

i

j

iOPOjOjPiPi

1 0 1

))(,()),(()()(

wheres = flood stage p(s) = probability of given flood stageXP = Permanent flood control measure XO = option flood control measurecP, cO = costs of measuresD = damage function based on flood stage, flood control measures

Lund (2002):

37

Fort Hood: Water Supply and Flood Risk

Lake Belton FactsCapacity: 1,357 MCM~60% Flood Storage~40% Water SupplyDrainage: 9,220 km2

38

Typical Reservoir Storage Allocation

39

40

Existing Conservation Pool – Robust Performance

41

Alternative 1

42

Alternative 4

43

Best Performing Alternatives for given climate change

44

INTERNATIONAL UPPER GREAT LAKES STUDY

45

45

International Upper Great Lakes Study

• 20% of world’s freshwater• 40 million people affected• Multiple Objectives:

• Ecosystem• Navigation• Recreation• Hydroelectricity

Production• Coastal real estate

46

47

Great Lakes in the news:Deep trouble: Great Lakes water levels fall to economically perilous lows

Great Lakes levels up slightly, but 'boaters are going to be shocked'•By Jim Lynch•The Detroit News

                                                                                            

Climate change lowering Great Lakes levels, retired Army Corps expert tells Bay City crowd

Great Lakes water levels still remain far below average, official saysMar 4, 2013   •

48

Great Lakes “System”

49

1900 1920 1940 1960 1980 2000500

1000

1500

2000

2500

3000

3500

4000

4500

5000

f(x) = − 1.39236720486723 x + 4728.09890653646R² = 0.00820228179991578

Lake Superior Annual Average NBS with Linear Re-gression Analysis for Historical Data Set

Year

Ave

rag

e A

nn

ual

NB

S

1960-2010y = -11.497x + 24803R2 = 0.099 F = -2.33

1900 1920 1940 1960 1980 2000 2020500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

f(x) = 0.972855972855983 x + 1289.49299949299R² = 0.00175756803951155

Lake Michigan-Huron Annual Average NBS with Linear Regression Analysis for Historical Data Set

Year

Ave

rag

e A

nn

ual

NB

S

1960-2010y = -0.957x + 5180R2 = 0.0003F = -0.13

1900 1920 1940 1960 1980 2000 2020-200

200

600

1000

1400

1800

2200

2600

f(x) = 4.13143500643501 x − 7456.19717932219R² = 0.215310770453961

Lake Erie Annual Average NBS with Linear Re-gression Analysis for Historical Data Set

Year

Ave

rag

e A

nn

ual

NB

S 1960-2010y = 1.882x - 2976R2 = 0.011F = 0.74

50

51

Lake Superior historic monthly water levels

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010182.5

183

183.5

184

Lake

Lev

el (

m)

Years

Lake Superior Average Monthly Level (1918-2010)

Historic Range = 1.2 m

52

52

-30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 220

2

4

6

8

10

12

14

16

18

NBS %Change Superior Histogram BaseCase

NBS %Change

Nu

mb

er o

f M

od

els

Climate Change Projections of Net Basin Supply -

Lake Superior, 2050

53

Problem

Select a lake regulation plan that satisfies multiple stakeholder objectives for the next 30 years

54

Challenges• System not well understood• Multi-million investment in climate science yielded greater

uncertainty• Future highly uncertain (deep or severe)• Multiple competing objectives with non-additive costs and

benefits• Stakeholders would not agree on scenarios

• “True Believers” vs “Skeptics”

• Decision to last 20-30 years

55

ResponseUNKUNKS• What will people care about in 20 years?

KUNKS• Define performance in commensurate, stakeholder defined

terms• Decompose risk into system responses and climate

assumptions• Accommodate all plausible scenarios• Speak in terms of plausibility

SKUNKs• We only partially understand the lake system • The correct answer will be known only in retrospect (prepare

for failure)

56

Stakeholder Defined Consequences

182.8

183

183.2

183.4

183.6

183.8

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonth

Lake

Lev

el

Box Plot of Lake Superior Levels (1918-2010)

182.8

183

183.2

183.4

183.6

183.8

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Upper C

Upper B

Zone A

Lower C

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Lower B

Coastal Coping Zones

57

Acceptable Lake Levels

58

58

1

1

1

1

1 2

2

2

2

23

3

3

4

4

4

5

5

5

10

10

3

34

515

Contours of Equal Expected Value of Zone C Occurrences on Lake Superior with Plan P77A

% Change Mean NBS

% C

hang

e N

BS

Std

Dev

1

1

1

1

1 2

2

2

2

23

3

3

4

4

4

5

5

5

10

10

3

34

515

-20 -15 -10 -5 0 5 10 15 20-40

-30

-20

-10

0

10

20

30

40

Contours of “Robustness” to a Given Level of Hazard(Historical = 1)

Moody and Brown, WRR, 2012

59

P77A

% Change Mean NBS

% C

hange N

BS

Std

Dev

-20 -10 0 10 20-40

-20

0

20

40P77B

% Change Mean NBS

% C

hange N

BS

Std

Dev

-20 -10 0 10 20-40

-20

0

20

40

PPreg

% Change Mean NBS

% C

hange N

BS

Std

Dev

-20 -10 0 10 20-40

-20

0

20

40PProj

% Change Mean NBS

% C

hange N

BS

Std

Dev

-20 -10 0 10 20-40

-20

0

20

40

Nat64

% Change Mean NBS

% C

hange N

BS

Std

Dev

-20 -10 0 10 20-40

-20

0

20

40P129

% Change Mean NBS

% C

hange N

BS

Std

Dev

-20 -10 0 10 20-40

-20

0

20

40

55MR49

% Change Mean NBS

% C

hange N

BS

Std

Dev

-20 -10 0 10 20-40

-20

0

20

40Bal26

% Change Mean NBS

% C

hange N

BS

Std

Dev

-20 -10 0 10 20-40

-20

0

20

40

Bal26S

% Change Mean NBS

% C

hange N

BS

Std

Dev

-20 -10 0 10 20-40

-20

0

20

40Nat64D

% Change Mean NBS

% C

hange N

BS

Std

Dev

-20 -10 0 10 20-40

-20

0

20

40

Contours of “Robustness” for Candidate Regulation Plans

60

Climate Robustness Index

F(X) = Binary function based on threshold of acceptable performancePr(X) = uniform distribution over range of plausible climate changeClimate Informed: Pr(X) based on GCM projections

(Moody and Brown, WRR 2013)

61

61

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P77A

P77B

PPreg

PProj

Nat64

P129

55MR49

Bal26Bal26S

Nat64D

Exp

ecte

d V

alue

of

Less

the

n or

equ

al H

isto

ric Z

one

C U

sing

GC

M C

limat

e

Expected Value of Less then or equal Historic Zone C Using Stochastic Climate

Comparison of Plan Expected Value on Lake Superior Using Stochastic versus GCM ClimateRegulation Plan Performance: Stationarity vs Climate Change

Robustness under Climate Change Projections

Ro

bu

stn

es

s u

nd

er

Sta

tio

na

rity

62

% Mean NBS

%

NB

S S

td D

ev

-20 -15 -10 -5 0 5 10 15 20-40

-30

-20

-10

0

10

20

30

40

50

-20 -15 -10 -5 0 5 10 15 200

0.05

0.1

% Mean NBS

Em

piric

al P

roba

bilit

y D

ensi

ty

Historic

Stochastic

PaleoStatistical GCM

RCM

Residual Risk for a given plan

63

Low MH High MH Low SP High SP0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

Ran

ge

Historic

Stochastic

PaleoGCM

RCM

Residual Risk for Plan 2013

64

64

• Inherent, irreducible uncertainties of climate system • Requires a shift of emphasis from “reduce uncertainty” to risk management

• “Nonstationarity” requires a shift from the Static Design Paradigm to a Dynamic Design and Operations Paradigm

• Couple Infrastructure Design with Dynamic Management:

• Adaptively Manage the plan – • Requires new institutional structure• Monitoring and Forecasts – the current state of the system and its near term

evolution

• Option Approach – Small steps now to enable larger steps if needed

Embracing Uncertainty!

Brown, 2010 (JWRPM)

65

65

Current Management of Lake Superior Regulation

Lake SystemManagement Plan

Public Complaints

“forcing”

“output”

IF Complaints > Tolerance then Study for new Management Plan

e.g., gate setting

e.g. Lake Level

Cycle Period = 30 years

66

66

Adaptively Manage Regulation Plan

Lake System Model

Operational Rule

Measurement

“forcing”

“output”

Brown et al., 2010 (JAWRA)

Management Plan

forecasting

monitoring

Bayes Decision: selectionthresholds

Seasonal inflowsTemperatureLevels

Seasonal inflowsTemperatureLevels

e.g. Performance Indicators

GCM;Stochastic Forecast

MONITORING

DECISION-SUPPORT

OPTIONS

67

Conclusion• Successfully managing water resources amid climate

variability and change will be a great challenge of this century

• Inherent, irreducible uncertainties of climate system• Reducing epistemic uncertainty may increase aleatory uncertainty• (Better understanding results in greater uncertainty)

• Requires a shift of emphasis from “reduce uncertainty” to framing and managing uncertainty

• Eliciting stakeholder definitions of risk is challenging• Decision-centric approaches are nascent but promising

• Don’t be a sacred scholar! Remember GB Shaw.

68

Thanks! Questions: casey@umass.edu

69

Further Reading• Brown, C. and R. L. Wilby (2012), An alternate approach to assessing climate risks, Eos Trans.

AGU, 93(41), 401, doi:10.1029/2012EO410001.• Moody, P. and C. Brown (2012), Modeling stakeholder-defined climate risk on the Upper Great

Lakes, Water Resources Research, 48, W10524, doi:10.1029/2012WR012497.• Brown, C., Y. Ghile, M. A. Laverty, and K. Li (2012),

Decision scaling: Linking bottom-up vulnerability analysis with climate projections in the water sector, Water Resour. Res., doi:10.1029/2011WR011212.

• Brown, C., Werick, W., Fay, D., and Leger, W. (2011) “A Decision Analytic Approach to Managing Climate Risks - Application to the Upper Great Lakes” Journal of the American Water Resources Association, 47, 3, doi/10.1111/j.1752-1688.2011.00552.x.

• Hallegatte, S., Shah, A., Lempert, R., Brown, C., and S. Gill (2012) "Investment Decision Making under Deep Uncertainty:  Application to Climate Change. World Bank Policy Research Working Paper #6193.

• Brown, C. (2011) “Decision-scaling for robust planning and policy under climate uncertainty.” World Resources Report, Washington DC. Available online at http://www.worldresourcesreport.org