risk and reward
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Risk and Reward. Casey Brown Associate Professor of Civil and Environmental Engineering University of Massachusetts. UMass Hydrosystems Research Group. Uncertainty = Risk + Opportunity?. Risk = an expected value - PowerPoint PPT PresentationTRANSCRIPT
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Risk and Reward
Casey Brown
Associate Professor of Civil and Environmental Engineering
University of Massachusetts
UMass Hydrosystems Research Group
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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
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Uncertainty = Risk + Opportunity?• Opportunity = product of the consequences of an event
and the probability that the event will occur
• Opportunity = expected loss or gain
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Risks and Opportunities
Op
po
rtu
nit
y
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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)
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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
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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
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“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
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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
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RISK AND DEVELOPMENTUpside and downside
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Per Capita GDP vs Latitude
(Sachs, 2001)
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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)
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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)
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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
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Risks and Opportunities
Op
po
rtu
nit
y
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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
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FLOOD RISK MANAGEMENTAn example of risk estimation and management
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Flood Control Storage
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Overflowing Dam: limits of control
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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?
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Example application: Iowa River
June 2008 floods
Spillway use:
-1993-2008-2013
Are floods increasing?
Proposed adaptations:
Reservoir re-operation
Raise Levees
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R. Vogel
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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
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Steinschneider et al.: The integrated effects of climate and hydrologic uncertainty on
future flood risk assessments, in preparation.
Integrated Uncertainties
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0.01
Exceedance Probability
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0.01
Exceedance Probability
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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”
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RISK MANAGEMENT Evaluating alternatives
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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
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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):
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Fort Hood: Water Supply and Flood Risk
Lake Belton FactsCapacity: 1,357 MCM~60% Flood Storage~40% Water SupplyDrainage: 9,220 km2
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Typical Reservoir Storage Allocation
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Existing Conservation Pool – Robust Performance
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Alternative 1
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Alternative 4
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Best Performing Alternatives for given climate change
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INTERNATIONAL UPPER GREAT LAKES STUDY
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International Upper Great Lakes Study
• 20% of world’s freshwater• 40 million people affected• Multiple Objectives:
• Ecosystem• Navigation• Recreation• Hydroelectricity
Production• Coastal real estate
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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 •
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Great Lakes “System”
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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
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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
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-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
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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
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Problem
Select a lake regulation plan that satisfies multiple stakeholder objectives for the next 30 years
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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
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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)
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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
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Acceptable Lake Levels
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1
1
1
1
1 2
2
2
2
23
3
3
4
4
4
5
5
5
10
10
3
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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
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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
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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
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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)
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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
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% 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
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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
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• 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)
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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
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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
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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.
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Thanks! Questions: [email protected]
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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