From Emissions to Concentrations

1. From Emissions to Concentrations NCAR ASP Uncertainty Colloquium Mort Webster (Penn State) 28 July 2014

2. Decision-Making Climate Change Uncertainty Uncertainty Quantification Impacts, Adaptation, and Vulnerability Workshop so far…

3. Socio-Economic Drivers of Uncertainty Causal Chain of Uncertainty Emissions Scenarios Monte Carlo Simulation Discussion Outline of this Talk

4. Projecting CO2Emissions:The “Kaya” accounting identity CO2 = Pop  GDP/Pop  E/GDP  CO2/E Population Carbon intensity of energy Per-capita standard of living Energy efficiency of production

5. Carbon: Uncertainties in Sources Land-use change Uncertainties in Sinks Ocean sink for carbon? Land-sink for carbon? Other GHGs: Uncertainties in sinks Atmospheric Chemistry Uncertainties in Emissions to Concentrations?

6. Population Growth Economic Growth Fossil Fuel Availability and Prices Future Energy Technology Costs Economic Sectoral Composition Elasticities of Substitution [Future Policies?] Key Challenge: Technological Change What are the Key Uncertainties in Future Greenhouse Emissions?

7. “Cascade of Uncertainties”

8. Representations for Uncertainty in Emissions • Scenario Approach • One scenario describes a possible combination of assumptions about key drivers/trends over time • Several scenarios jointly describe a range of possible futures • Probabilistic Approach • Characterize each uncertain assumption with a probability distribution, and randomly sample • Generate many samples of possible future outcomes

9. Approach #1: Scenarios Example: IPCC SRES (AR4) Emissions Scenarios

10. Scenarios Example 2 Example: IPCC RCP (AR5) Concentration Scenarios

11. Scenarios Example 3 Example: IPCC SSPs (AR5) Socioeconomic Scenarios

12. Advantages Coherent “storyline” about the future Span a range of futures with a small set Provide common basis for analyses Disadvantages No quantification of likelihood May not cover the relevant range of possible outcomes Most useful set of scenarios will vary by question Value of Scenarios

13. Many successful examples of scenarios used for planning Almost all are a single DM with a single objective Example: Shell Corporation 5-year planning Challenge to this Community Understandable desire to have ONE set of A FEW scenarios used in common across a community Example: IPCC scenarios used by all WGs Problem: MANY different questions and MANY different perspectives Can one set do it all? Scenarios for Global Change Research

14. Our situation (often): We have a model y=g(x) We know that assumption x is uncertain What is the uncertainty in y? How can we find out? Uncertainty and Model Projections Model X Y ???

15. “Flaw of Averages” Sam Savage, Wiley, New York, 2009. It is a pun. It integrates two concepts: A mistake => a “flaw” The concept of the “law of averages”, that that things balance out “on average” Flaw consists of assuming that evaluation based on “average” or “most likely” conditions give correct answers Why Do We Need Uncertainty Propagation?

16. “Jensen’s law” or “Jensen’s Inequality”: E[ f(x) ] ≠ f [ E(x)] if f(x) is convex function Notation: E(x) = arithmetic average, or “expectation” of x In words: E[ f(x)] = average of possible outcomes of f(x) f[ E(x)] = outcome calculated using average x Mathematics of Flaw

17. Given: f(x) = √x + 2 And: x = 1, 4, or 7 with equal probability E(x) = (1 + 4 + 7) / 3 = 4 f[E(x)] = √4 + 2 = 4 f(x) = 3 , 4, or [√7 + 2] ~ 4.65 with equal probability E[f(x)] = (3 + 4 + 4.65) / 3 ~ 3.88 ≤ 4 = f[E(x)] Example

18. E [ f(x) ] = f [ E(x)] ONLY when f(x) linear This is rarely the case! Example: Given: f(x) = x + 2 And: x = 1, 2, or 3 with equal probability E(x) = (1 + 2 + 3) / 3 = 2 f[E(x)] = 2 + 2 = 4 f(x) = 3 , 4, or 5 with equal probability E[f(x)] = (3 + 4 + 5) / 3 = 4 = f[E(x)] When Are They Equal?

19. Average of all the possible outcomes associated with uncertain parameters, Generally does not equal The value obtained from using the average value of the parameters In Words

20. Flaw of Averages: A Picture

21. Probabilistic Uncertainty Propagation Monte Carlo Simulation Construct probability distributions for uncertain model inputs Draw large numbers of samples from the distributions Run the model for each sample set Construct frequency distributions of model outcomes In Geosciences, often called “ensembles” How to Avoid Flaw of Averages?

22. Probability of Rolling a “6” on a 6-sided Die? Probability of Winning Solitaire for a Given Strategy and Well-Shuffled Deck? Average Time to Get to Work? Examples of Monte Carlo Simulation

23. If x is a random variable with density f(x), Then the expectation (mean) of some function g(x) Can be estimated by randomly drawing independent, identically-distributed (iid) samples of x from f(x), and computing the average g(x) of the samples. Monte Carlo Integration The Mathematical Basis

24. Crude (Brute-Force) Monte Carlo Variance Reduction Techniques Control Variates Antithetic Variates Stratified Sampling Latin Hypercube Importance Sampling Reduced-Form Models Monte Carlo Simulation: Variants

25. Stabilization Scenarios(Source: U.S. CCSP Product 2.1a)

26. Global Mean Temperature Change(Deterministic)

27. Results: Temperature ChangeImpacts of Stabilization Paths Level 4 Level 3 Level 2 Level 1 No Policy Global Mean Surface Temperature Increase (oC) (1981-2000) to (2091-2100)

28. What is the Uncertainty in the CCSP Results from One Model (MIT IGSM)? Claim: Choice of Long-Term Stabilization Target Should be Framed as a Risk Management Decision Consider risks of both climate impacts and abatement costs Question for this Study

29. MIT Integrated Global Systems Model

30. 110 Uncertain Parameters, including: Productivity growth rates (historical data) Energy efficiency growth rate (historical data) Ease of substituting inputs (historical data) Costs of new technologies (expert judgment) Main Uncertain Outputs: Emissions (GHGs, urban pollutants) Costs (consumption loss, carbon prices) Uncertainty in Economics

31. GDP Growth Uncertainty

32. Latin Hypercube Monte Carlo 400 random samples of all parameters Impose correlation where justified by empirical data and/or theory Impose each CCSP scenario as an emissions cap over time Not a fixed RF target No banking/borrowing Methodology

33. Uncertainty in CO2 Emissions(No Policy)

34. Carbon Prices in 2020

35. Carbon Price Under Level 1 (450ppm)

36. Global Welfare Loss (%) in 2020

37. Global Welfare Loss (%) in 2020 2020 2100 2060

38. Uncertaintyin TotalPrimary Energy Sources2050

39. Relative Contribution to Variance • Energy Supply • Energy Demand • Scale of Economy • Other Uncertainties • Predict which most affect cum. CO2, carbon prices.

40. Top Ten Drivers of Uncertainty in Abatement Cost

41. Emissions Uncertainty from EPPA Climate Sensitivity Heat Uptake by Deep Ocean (& Carbon Uptake) Radiative Forcing Strength of Aerosols CO2 Fertilization Effect on Ecosystem Trends in Precipitation Frequency Uncertainty in Climate Parameters

42. Communicating the Odds of Temperature Change

43. Communicating the Impact of Policy Stringent Policy (~550 ppm) No Policy

44. USING THE IGSM, WHAT IS THE PROBABILITY OF GLOBAL WARMING for 1980-2100, WITHOUT & WITH A 450,550, 650 or 750 ppm CO2-equivalent STABILIZATION POLICY? (400 random samples for economics & climate assumptions)

45. Reducing the Probability of Exceeding a Temperature Target

46. Cascade of Uncertainties in the Earth System Scenarios Absolutely necessary Nearly impossible to satisfy all “clients” Monte Carlo Simulation Useful for avoiding the Flaw of Averages Useful tool for rigorously constructing a set of scenarios Information from Monte Carlo of Earth System Models Useful for Characterizing Risks Summary

47. “Persons pretending to forecast the future shall be considered disorderly under subdivision 3, section 901 of the criminal code and liable to a fine of $250 and/or six months in prison.” Section 889, New York State Code of Criminal Procedure