Possible global warming futures

Transcription

1 Possible global warming futures Minh Ha-Duong Centre International de Recherches sur l Environnement et le Développement, CNRS, France Possible global warming futures p.1/45

2 About precaution and global warming Taking stock: Precaution and the climate change risk When probabilities are imprecise Recent results: Assessing the possibility of global warming Communicating the uncertainty Possible global warming futures p.2/45

3 1. Precaution and climate risk... Possible global warming futures p.3/45

4 Economic analysis of climate policies Optimal timing of action with sequential decision Irreversibility, inertia and rapid climate change Stylized stochastic integrated assessment models (DIAM): Which CO 2 emissions time profile maximizes the discounted sum of intertemporal utility? Possible global warming futures p.4/45

5 Economic analysis of climate policies Optimal timing of action with sequential decision Irreversibility, inertia and rapid climate change Stylized stochastic integrated assessment models (DIAM): Which CO 2 emissions strategy minimizes the discounted sum of intertemporal utility? From cost-efficiency to cost-benefit. Possible global warming futures p.4/45

6 Optimal emission strategies GtC Ha-Duong et al. (1997) Nature IS92a reference W U Kyoto S550 years Possible global warming futures p.5/45

7 Stochastic rapid climate change Ha-Duong et al. (1998) Int. J. of Environment and Pollution Productivity loss High impact p=0.2 Average Low impact p= Atmospheric CO2 concentration (ppmv) Possible global warming futures p.6/45

8 Reducing CO 2 emissions cost function Ha-Duong and Keith, submitted to Climatic Change 350 $ / tc Quadratic abatement cost Abatement cost with carbon sequestration Fraction of emissions abated Possible global warming futures p.7/45

9 Optimal trajectories with sequestration ppmv CO Low impact High impact 400 Reference No sequestration 350 Leak rate 0.5% Year Possible global warming futures p.8/45

10 Related works on precaution Transparency and control (in Integrated Assessment) A pro-active stratospheric ozone protection scenario (in Global Environmental Change) Real options (in Energy economics) Risk aversion and intergenerational equity... But do we really know the probabilities? Possible global warming futures p.9/45

11 2. Imprecise probabilities Possible global warming futures p.10/45

12 Problems with precise probabilities +5.5 C in 2100: are IPCC scenarios forecasts? No, we can t have probabilities Yes, they are not all equally likely Imprecise probabilities offer a more general information theory... Possible global warming futures p.11/45

13 Using a set of probabilities C Example with 3 alternative states of the world. Red z 1 1 y 0 1 x Black Yellow Possible global warming futures p.12/45

14 Rationality with imprecise probabilities C is called the credal set, it represent beliefs. How to act rationally? Possible global warming futures p.13/45

15 Rationality with imprecise probabilities C is called the credal set, it represent beliefs. Accept the gamble Π paying off Π(ω) if and only if: for all p C, E p (Π) > 0 This criteria is rational, it avoids sure loss (no arbitrage), but... Possible global warming futures p.13/45

16 The precautionary order is incomplete Incomplete risk ranking: outcome Red is more probable than outcome Black if and only if: for all p C, p(red) > p(black) Possible global warming futures p.14/45

17 The precautionary order is incomplete Incomplete risk ranking: outcome Red is more probable than outcome Black if and only if: for all p C, p(red) > p(black) Incomplete preferences: Policy A leading to payoff Π A is preferred over policy B leading to payoff Π B if and only if: Π A Π B is an acceptable gamble. Possible global warming futures p.14/45

18 redal sets from possibility to probability Possible global warming futures p.15/45

19 Possibility as imprecise probabilities The credal set consists of all probabilities p such that: p(e) max x E π(x) for any E Ω A nonnegative function π(x) defined for x Ω is called a possibility distribution if its maximum is 1. Possible global warming futures p.16/45

20 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)) Possible global warming futures p.17/45

21 Second half: C for global warming in 2100 Possible global warming futures p.18/45

22 3 probabilities in a credal set Possibility DT 2100 Possible global warming futures p.19/45

23 3. The possibility of global warming Possible global warming futures p.20/45

24 Assessing global warming futures Rationally subjective, based on published literature. Warming 2100 = CO 2 concentration 1 3climate sensitivity Possible global warming futures p.21/45

25 Summarizing model results on [CO 2 ] 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 Possible global warming futures p.22/45

26 Histogram of available results Number of model runs [CO2] (2100) Possible global warming futures p.23/45

27 Possibility of CO 2 concentration in 2100 Possibility [CO2] (2100) Possible global warming futures p.24/45

28 Experts judgment on climate sensitivity T(2 CO 2 ): Equilibrium global warming for a doubling of pre-industrial CO 2 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) Possible global warming futures p.25/45

29 Subjective assessment of T(2 CO 2 ) Possibility DT at 2xCO 2 Possible global warming futures p.26/45

30 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. Possible global warming futures p.27/45

31 The joint possibility distribution 6 5 Climate sensitivity C for 2xCO2 Possibility 1 Least surprise year 2100 CO2 concentration, ppmv Most surprise Possible global warming futures p.28/45

32 The possibility of 2.4 C warming 6 Climate sensitivity C for 2xCO year 2100 CO2 concentration, ppmv Possible global warming futures p.29/45

33 Global warming 2100 possibility Possibility DT 2100 Possible global warming futures p.30/45

34 4. Communicating the uncertainty Possible global warming futures p.31/45

35 The problematic gap A recurring dilemma of Futures research: Forecasts have probabilities Scenarios do not have a quantitative likelihood Example: Intergovernmental Panel on Climate Change emissions scenarios. Proposition: Threads with possibilities. Possible global warming futures p.32/45

36 Principles for sampling futures We have: Big frame of reference. Ω = R 2 (CO 2 concentration and climate sensitivity) Complicated beliefs represented by a credal set C on Ω. We want: Small frame of reference Θ = 3 or 4 futures from Ω. Possibility distribution π on Θ. How to find Θ and π based on Ω and C? Possible global warming futures p.33/45

37 P1: Reveal only desirable gambles Possibility π should be no less than the maximum probability according to C. Possible global warming futures p.34/45

38 P2. Maximize thread-set plausibility Θ should be the most plausible subset of Ω considering our information C: Select the business-as-usual, least surprising future. Possibility DT 2100 Possible global warming futures p.35/45

39 P3: No thread more probable For any two threads A and B, there is at least one probability p in C such that p(a) > p(b) Possible global warming futures p.36/45

40 P4: Minimize the possibility of missing We need two threads to bracket the future. P3 implies: the possibility of these should be > 1/3. Possibility DT 2100 Possible global warming futures p.37/45

41 P4: Minimize the possibility of missing We need two threads to bracket the future. P3 implies: the possibility of these should be > 1/3. Possibility DT 2100 Possible global warming futures p.38/45

42 Results: Global warming threads Sensitivity C/ 2 CO2 π [CO 2 ] ppmv Baseline Low High Warming C 6 5 Climate sensitivity C for 2xCO year 2100 CO2 concentration, ppmv Possible global warming futures p.39/45

43 Relation with IPCC scenarios 6 Climate sensitivity C for 2xCO b1 b2 a1b a2 a1f year 2100 CO2 concentration, ppmv Possible global warming futures p.40/45

44 Part two summary Possible global warming futures p.41/45

45 Hierarchy of knowledge Rational (incomplete) preferences about a very long term issue can be based on: All available evidence Credal sets for various parameters Beliefs on the joint distribution Possibility of global warming Set of 3 threads Least surprising future Possible global warming futures p.42/45

46 Conclusion Possible global warming futures p.43/45

47 Concluding remarks +2.4 C the least surprising global warming in 2100 In the range +1.1 C to +4.5 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. Possible global warming futures p.44/45

48 Questions? You like it? Possible global warming futures p.45/45