Possible global warming futures Minh Ha-Duong
[email protected]
CNRS, France HDGC, Carnegie Mellon
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SRES: Forecasts or scenarios? +5.5◦ C in 2100: are IPCC scenarios forecasts? No, we can’t have probabilities Yes, they are not all equally likely
Resolve the controversy using imprecise probabilities, a more general information theory. . .
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Outline Possibility as imprecise probabilities Assessing the possibility of global warming Communicating information about distant futures
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Global warming in 2100 Possibility 1
0.5
1
2
3
4
5
6
7
DT 2100
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1. Imprecise probabilities
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Using a set of probabilities C Example with 3 alternative states of the world. Red
z
1
1
y
0 1 x
Black
Yellow
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Rationality with imprecise probabilities C is called the credal set, it represent beliefs.
How to act? Rationally and precaution:
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Rationality with imprecise probabilities C is called the credal set, it represent beliefs.
Accept the gamble A if and only if the expected value of A is positive for all probabilities p ∈ C
This criteria avoids sure loss (no arbitrage), but...
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The precautionary order is incomplete Policy A is preferred to B iff A’s expected net benefit is greater than B ’s for all p ∈ C
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The precautionary order is incomplete Policy A is preferred to B iff A’s expected net benefit is greater than B ’s for all p ∈ C
Application to possible futures: A is more probable than B if and only if for all p ∈ C, p(A) > p(B)
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More information, smaller credal set
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Possibility as imprecise probabilities A nonnegative function π(x) defined for x ∈ Ω is called a possibility distribution if its maximum is 1. Π(E) = max π(x) for any E ⊂ Ω x∈E
The credal set consists of all probabilities p such that: p(E) ≤ Π(E)
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Interpretation cf. Zadeh (1978) and Shackle (1954) degree of surprise Possibility 1 corresponds to the least surprising outcome. π(A or B) = max(π(A), π(B)) π(A and B) = min(π(A), π(B))
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3 probabilities in a credal set Possibility 1
0.5
1
2
3
4
5
6
7
DT 2100
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2. The possibility of global warming
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Assessing global warming futures
Rationally subjective, based on published literature. Warming 2100 = CO2 concentration × 13 climate sensitivity
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Summarizing model results on [CO2] M : Atmospheric carbon dioxide concentration in 2100
Source: All 56 ‘no-intervention’ records in Morita’s SRES database The possibility of M is proportional to the number of models predicting concentration 5% close to M
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Histogram of available results Number of model runs 17 15
10 7 3 600
800
1000
[CO2] 1200(2100) Possible global warming futures – p.16/36
Possibility of CO2 concentration in 2100 Possibility 1 0.8 0.6 0.4 0.2
709 600
800
1000
[CO2] 1200(2100) Possible global warming futures – p.17/36
Experts judgment on climate sensitivity ∆T(2×CO2 ): Equilibrium global warming for a doubling of pre-industrial CO2 concentration
16 experts elicitation survey by Keith-Morgan
1. Transform elicited probabilities into possibility 2. Discount experts pretending to know better (standard deviation lower than peer average/2). 3. Fusion without the independence assumption (hyper-cautious conjunction)
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Subjective assessment of ∆T(2×CO2) Possibility 1 0.8 0.6 0.4 0.2
2.85 -5
-2.5
2.5
5
7.5
DT at 10 2xCO2
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C is the joint possibility distribution.
Assuming no interaction, the possibility of a future is the minimum of the possibility of each of its components.
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The joint possibility distribution 6 Climate sensitivity °C for 2xCO2
Possibility 1 Least surprise
5
4
3
2
1
0 500
year 2100 CO2 concentration, ppmv 600
700
800
900
0 Most surprise
1000 Possible global warming futures – p.21/36
◦
The possibility of 2.4 C warming 6 Climate sensitivity °C for 2xCO2 5
4
3
2
1
0 500
year 2100 CO2 concentration, ppmv 600
700
800
900
Possible global warming futures – p.22/36 1000
Global warming 2100 possibility Possibility 1
0.5
2.4 1
2
3
4
5
6
7
DT 2100
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3. Communicating information about distant futures
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The problematic gap
A recurring dilemma of Futures research: Forecasts with probabilities Scenarios without any quantitative likelihood Proposition: Possible futures with possibilities.
Example: Intergovernmental Panel on Climate Change emissions scenarios.
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Sampling futures not arbitrarily We know a joint possibility distribution on CO2 concentration and climate sensitivity.
We want to describe 3 possible futures (with their π ) that represent well our information
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P1. Maximize possibility of the futures-set Select the business-as-usual, least surprising future. Possibility 1
0.5
2.4 1
2
3
4
5
6
7
DT 2100
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P2: Reveal only desirable gambles
The announced possibility π should be no less than the known possibility.
−→ Possible global warming futures – p.28/36
P3: No future more probable For any two possible futures A and B , there is at least one probability p in C such that p(A) > p(B)
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P4: Minimize the possibility of missing Give bounds as wide as possible, but P3 implies: the possibility of these should be > 1/3. Possibility 1
1.1
4.5
0.5 0.34
2.4 1
2
3
4
5
6
7
DT 2100 Possible global warming futures – p.30/36
P4: Minimize the possibility of missing Give bounds as wide as possible, but P3 implies: the possibility of these should be > 1/3. Possibility 1
0.5
1
2
3
4
5
6
7
DT 2100 Possible global warming futures – p.31/36
Possible global warming futures Sensitivity ◦ C/ 2×CO2 2.85 1.43 3.95
[CO2 ] ppmv 709 618 944
π
Baseline 1 Low 0.34 High 0.34
Warming ◦C 2.4 1.1 4.5
6 Climate sensitivity °C for 2xCO2 5
.34
4
3
.95 2
1
0 500
.34 year 2100 CO2 concentration, ppmv 600
700
800
900
1000 Possible global warming futures – p.32/36
Relation with IPCC scenarios 6 Climate sensitivity °C for 2xCO2 5
4
3
2
1
b1 b2 0 500
a1b
a2
a1f
year 2100 CO2 concentration, ppmv 600
700
800
900
1000 Possible global warming futures – p.33/36
Summary and conclusion
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Hierarchy of knowledge Information about futures can be given as: Credal set Possibility distribution Set of possible futures Least surprising future
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Concluding remarks +2.85◦ C the least surprising global warming in 2100 In the range +1.43◦ C to +3.95◦ C, the bounds are no less probable than the central value. Next step: Precautionary policy analysis in Integrated Assessment Models with uncertainty. And time. Thanks.
HDGC lunch seminar at Carnegie Mellon University, April 30th 2003
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