Probabilistic Integrated Assessment of "Dangerous" Climate Change

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Science  23 Apr 2004:
Vol. 304, Issue 5670, pp. 571-575
DOI: 10.1126/science.1094147


Climate policy decisions are being made despite layers of uncertainty. Such decisions directly influence the potential for “dangerous anthropogenic interference with the climate system.” We mapped a metric for this concept, based on Intergovernmental Panel on Climate Change assessment of climate impacts, onto probability distributions of future climate change produced from uncertainty in key parameters of the coupled social-natural system—climate sensitivity, climate damages, and discount rate. Analyses with a simple integrated assessment model found that, under midrange assumptions, endogenously calculated, optimal climate policy controls can reduce the probability of dangerous anthropogenic interference from ∼45% under minimal controls to near zero.

Article 2 of the United Nations Framework Convention on Climate Change (UNFCCC) states its ultimate objective as “Stabilization of greenhouse gas concentrations in the atmosphere at a level that would prevent dangerous anthropogenic interference with the climate system” (1). This level should be achieved within a time frame sufficient to allow ecosystems to adapt naturally to climate change, to ensure that food production is not threatened, and to enable economic development to proceed in a sustainable manner. Thus, the criteria for identifying “dangerous anthropogenic interference” (DAI) may be characterized in terms of the consequences (or impacts) of climate change (2). Although these impacts, and a precise definition of DAI, are subject to considerable uncertainty, a plausible uncertainty range can be quantified from current scientific knowledge (3). We argue that climate change policy decisions should be conceptualized in terms of preventing or reducing the probability of DAI, a risk-management framework familiar to policymakers and an outcome to which more than 190 signatories to the UNFCCC have committed.

Research related to global climate change must deal explicitly with uncertainty about future climate impacts. Due to the complexity of the climate change issue and its relevance to international policymaking, careful consideration and presentation of uncertainty is important when communicating scientific results (2, 47). Policy analysis regarding climate change necessarily requires decision-making under uncertainty (810). Without explicit efforts to quantify the likelihood of future events, users of scientific results (including policy-makers) will undoubtedly make their own assumptions about the probability of different outcomes, possibly in ways that the original authors did not intend (11, 12).

Assigning likelihoods to potential future worlds is difficult, as noted by Grübler and Nakicenovic (13), because any such estimates will be highly subjective and based on assessments of future societal behavior and values. Uncertainty, they warn, may alternatively be dismissed or replaced by spurious expert opinion. Although the suitability and effectiveness of techniques for presenting uncertain results is context-dependent, we believe that such probabilistic methods are more valuable for communicating an accurate view of current scientific knowledge to those seeking information for decision-making than assessments that do not attempt to present results in probabilistic frameworks (14).

We present a metric for assessing DAI: a cumulative density function (CDF) of the threshold for dangerous climate change. We demonstrate its utility by applying it to modeled uncertainty in future climate change using an optimizing integrated assessment model (IAM). IAMs are common policy analysis tools that couple submodels of the climate and economic systems, balance costs and benefits of climate change mitigation to determine an “optimal” policy (15), and often exhibit properties not apparent in either submodel alone (16).

We chose Nordhaus' Dynamic Integrated Climate and Economy (DICE) model (17) for our analysis because of its relative simplicity and transparency, despite its limitations (16, 18). The IAM framework allows us to explore the effect of a wide range of mitigation levels on the potential for exceeding a policy-important threshold such as DAI. We do not recommend that our quantitative results be taken literally, but we suggest that our probabilistic framework and methods be taken seriously. They produce general conclusions that are more robust than estimates made with a limited set of scenarios or without probabilistic presentations of outcomes, and our threshold metric for DAI offers a risk-management framework for discussion of future climate change that can be applied to results at all levels of model complexity.

To define our metric for DAI, we estimated a CDF based on the Intergovernmental Panel on Climate Change (IPCC) “Reasons for Concern” (3) (Fig. 1). Each column in the figure represents a reason for concern about climate change in this century, on the basis of dozens of IPCC lead authors' examination of climate impacts literature, thus representing a consensus estimate of DAI. We constructed our CDF by assigning data points at the threshold temperature above which each column becomes red (Fig. 1, solid black line) and assumed that the probability of DAI increases cumulatively at each threshold temperature by a quintile, making the first threshold the 20th percentile (20‰) (19). This CDF is a starting point for our analysis of DAI; it facilitates a concrete sensitivity analysis at various thresholds of dangerous climate change. The median, 50‰ threshold for DAI in Fig. 1, DAI[50‰], is 2.85°C (20).

Fig. 1.

An adaptation of the IPCC Reasons for Concern figure (3), with the thresholds used to generate our CDF for DAI. The IPCC figure conceptualizes five reasons for concern, mapped against climate change through 2100. As temperature increases, colors become redder: White indicates neutral or small negative or positive impacts or risks, yellow indicates negative impacts for some systems, and red means negative impacts or risks that are more widespread and/or greater in magnitude. The risks of adverse impacts from climate change increase with the magnitude of change, involving more of the reasons for concern. For simplicity, we use the transition-to-red thresholds for each reason for concern to construct a CDF for DAI, assuming the probability of DAI increases by a quintile as each threshold is reached (19).

We applied this metric for DAI to a spectrum of results based on uncertainty in three key social and natural model parameters—climate sensitivity, climate damages, and discount rate. We focused on these parameters because they are critical determinants of the policy implications of global climate change. Climate sensitivity—the equilibrium surface temperature increase from a doubling of atmospheric CO2— determines the magnitude of anthropogenic temperature change from a given radiative forcing. The impact of this change is determined by the severity of climate damages from a given global average temperature change, usually reported as a loss of gross economic product. Both factors cannot be determined with high confidence because of the complexity of the system, missing data, and competing frameworks for analysis (21). In an IAM, future costs and benefits are compared by discounting their future value at some discount rate. Modeled policy responses to global climate change, where mitigation costs come long before sizeable benefits from avoided climate damages, are very sensitive to this rate. Sensitivity analysis, where uncertain parameters are varied across a likely range of values, is often used to identify and report ranges of uncertainty. When it is possible to define a probability distribution for the uncertain parameter(s), a second method—Monte Carlo (MC) analysis—can expand on a sensitivity analysis by assigning a probability distribution to model outcomes run as the parameter is varied. We combined both techniques to evaluate the potential for DAI (19).

Using general circulation models, the IPCC has long estimated the climate sensitivity to lie somewhere between 1.5°C and 4.5°C (22), without indicating the relative probability within this range. Other analyses produce both higher and lower values (19). Recent studies produce distributions wider than the IPCC range, with significant probability of climate sensitivity above 4.5°C. We used three such probability distributions: the combined distribution from Andronova and Schlesinger (A&S) (23), and the expert prior (F Expert) and uniform prior (F Uniform) distributions from Forest et al. (24).

In the DICE model, a climate damage function specifying the economic damages from global temperature increase is one of the important linkages between the modeled social and natural systems. We sampled from the probability distributions of Roughgarden and Schneider (18), based on an expert elicitation of a much broader range of climate damage functions than in the original DICE model. We used these probability distributions and those for climate sensitivity to conduct MC analyses with the DICE model (19). Specification of the third uncertain parameter we considered, the discount rate, has a strong normative component, with a variety of defended options (supporting online text). To prevent a high discount rate from masking variation in model results because of variation in other uncertain parameters (supporting online text), we set the pure rate of time preference (PRTP) to 0%—corresponding to a discount rate of roughly 1%—and performed a sensitivity analysis (19). This discount rate falls within the currently debated range, at the lower end (supporting online text).

We examined two types of model output under different assumption sets of the parameters we varied: global average surface temperature change in 2100 (25), which we used to evaluate the potential for DAI (12); and “optimal” carbon taxes (26), which we used to evaluate the magnitude of induced climate policy controls.

We first considered climate sensitivity uncertainty, performing three MC analyses— sampling from each climate sensitivity probability distribution separately (19)—without mitigation policy (to ensure that variation in results are from variation in climate sensitivity). We produced probability distributions for global temperature increase in 2100 (Fig. 2A) and indicate the percentage of outcomes that result in temperature increases above DAI[50‰]. The differences in the probability distributions of Fig. 2A show how the range of uncertainty still present among probability estimates of climate sensitivity cascade to uncertainty in our estimates for temperature change in 2100. In all three, a significant percentage of outcomes falls above DAI[50‰] (dark gray).

Fig. 2.

(A) Probability distributions for each climate sensitivity distribution for the climate sensitivity–only MC analyses with zero damages and 0% PRTP (a ∼1% discount rate). (B) Probability distributions for the joint (climate sensitivity and climate damage) MC analyses. All distributions display a 3-bin running mean and the percentage of outcomes above our median threshold of 2.85°C for dangerous climate change, P{DAI[50‰]}. The joint distributions display carbon taxes calculated in 2050 (T2050) by the DICE model, using the median climate sensitivity from each climate sensitivity distribution and the median climate damage function for the joint Monte Carlo cases (19). When we compare the joint cases with climate policy controls (B) to the climate sensitivity–only cases without climate policy controls (A), sufficient carbon taxes reduce the potential (significantly in two out of three cases) for DAI[50‰].

We introduced climate policy controls by performing a joint MC analysis of temperature increase in 2100, varying both climate sensitivity and the climate damage function (19), again indicating the percentage of DAI[50‰] exceedances (Fig. 2B). With the exception of the A&S distribution, for which the single MC analysis showed relatively lower probability of DAI[50‰], the joint MC runs showed significantly lower percentages of DAI[50‰]. It may seem that the most likely outcome of the joint MC runs is a relatively low temperature increase—an optimistic result. However, low temperature change outcomes result from more stringent model-generated climate policy controls, because of the inclusion of climate damages. Time-varying median carbon taxes are more than $50/ton of C by 2010, and more than $100/ton of C by 2050 in each joint analysis. Low warming and reduced probability of DAI[50‰] are reached if carbon taxes are high, when higher climate sensitivities and higher climate damage functions sampled from their probability distributions combine to force the model “agent” to react. This policyrelevant complexity is captured through a probabilistic framework.

The analysis above only considers the median DAI[50‰] threshold; therefore, these results do not fully describe the relationship between climate policy and the potential for other thresholds for DAI. We characterized the relationship between climate policy controls and the potential for DAI by calculating a series of single MC analyses, varying climate sensitivity (as in Fig. 2A) for a range of fixed damage functions. For each damage function, ranging from the 10th through the 90th percentile of the climate damage probability distribution (18), we performed an MC analysis sampling from each climate sensitivity distribution. We also calculated the carbon tax in 2050 for model runs that use the median climate sensitivity of each probability distribution and the median damage function (19).

Averaging the results from each set of three MC analyses, we determined the probability of outcomes that exceed various DAI thresholds at a given 2050 carbon tax under the assumptions described above (19) (Fig. 3). Each solid line corresponds to a different percentile threshold, DAI[X‰], chosen from our DAI CDF (Fig. 1)—a lower percentile X from the CDF represents a lower temperature threshold for DAI (DAI[10‰] = 1.476°C, DAI[50‰] = 2.85°C, for example). At any DAI threshold, climate policy works: Higher carbon taxes lower the probability of considerable future temperature increase and reduce the probability of DAI. Inspecting the median threshold, DAI[50‰] (Fig. 3, thick black line), indicates that a carbon tax by 2050 of $150 to $200 per ton of C reduces the probability of DAI[50‰] from ∼45% without climate policy controls to nearly zero (27).

Fig. 3.

The modeled relationship between carbon taxes in 2050 (a proxy for general climate policy controls) and the probability of DAI in 2100 (19). Each color band represents a different percentile range from the DAI threshold CDF—a lower percentile from the CDF representing a lower temperature threshold for DAI, as indicated. The solid lines indicate the percentage of outcomes exceeding the stated threshold for DAI[X‰], where X is the percentile from the DAI CDF derivable from Fig. 1, for any given level of climate policy controls. At any DAI[X‰] threshold, climate policy controls significantly reduce the probability of DAI, and at the median DAI[50‰] threshold (thicker black line), a 2050 carbon tax of >$150/ton of C is the model-dependent result necessary to reduce the probability of DAI from ∼45% to near zero. [With a 3% PRTP, this carbon tax is an order of magnitude less and the reduction in DAI is on the order of 10% (27).]

Finally, we demonstrated the effect of varying the discount rate. As before, we ran MC analyses varying climate sensitivity, but at different values for PRTP and with the climate damage function fixed at the median level (19). A higher PRTP increases the discount rate, implying that future climate damages are valued less and calculated policies will be weaker. Averaging over the outcomes for each climate sensitivity distribution, we determined the relationship between the discount rate and the probability of DAI at different temperature threshold levels (Fig. 4). As expected, increasing the discount rate shifts higher the probability distribution of future temperature increase—a lower level of climate policy controls becomes “optimal” and thus increases the probability of DAI. At DAI[50‰] (Fig. 4, thick black line), the probability rises from near zero with a 0% PRTP to 30% with a 3% PRTP, as specified in the original DICE model. It is also clear that at PRTP values higher than 1%, the “optimal” outcome becomes increasingly insensitive to variation in future climate damages driven by variation in climate sensitivity.

Fig. 4.

The modeled relationship between the PRTP—a factor determining the discount rate—and the probability of DAI in 2100 (19). Increasing the PRTP (and therefore the discount rate) reduces the present value of future climate damages and increases the probability of DAI[X‰] as indicated, where X is the percentile from the DAI CDF derivable from Fig. 1. The solid lines indicate the percentage of outcomes above the stated threshold for DAI[X‰] for any given level of PRTP or DAI percentile threshold X. At our median threshold DAI[50‰] (thicker black line), the probability of DAI[50‰] rises from near zero with a 0% PRTP to 30% with a 3% PRTP, as originally specified in the DICE model.

The DICE model is a highly simplified representation of the climate and the economy, and its specific predictions for temperature increase or carbon tax are subject to considerable uncertainty (28). Although it cannot provide high-confidence quantitative answers, it is a transparent model for examining trends and processes, and its qualitative insights should be considered seriously. We present our probability distributions for future climate change to demonstrate three issues: (i) Very different levels are possible for the probability of DAI depending on its definition. (ii) Regardless of its definition, conventional climate policy controls would bring about significant reduction in the probability of DAI. (iii) This probabilistic framework is an effective method for conceptualizing climate change policy decisions.

We chose to create a CDF for DAI based on one plausible interpretation of IPCC work. In certain regions and for certain sectors, different groups might set thresholds for DAI at very different levels. Selection of that threshold can only be made through a decision-making process that combines social and natural assessments, evaluates the effects of climate change and their likelihood, and incorporates value judgments on inherent trade-offs. However, our research shows that regardless of the threshold for DAI, climate policy will reduce the likelihood of exceeding that threshold, and we suggest that this is an effective way to present model results and to demonstrate the value of climate policy, in risk-management terms that policymakers often employ.

Uncertainty in future states of natural and social systems will never be completely removed until future events are directly observed. This unalterable fact requires societies wishing to assess and influence future trends to act on the best current knowledge in the face of uncertainty. We believe that a probabilistic framework—probability distributions and risk diagrams such as Fig. 3—are an effective representation of state-of-the-art results of scientific assessments and should be understood by a wide audience, including policymakers. Policymakers have considerable experience dealing with uncertainty and risk management. For example, “acceptable risk” thresholds for nuclear power, cancer, vehicular safety, etc., are commonplace, even if controversial. The probability of DAI in many of the scenarios we discuss is far higher (by tens of percent) than the “accepted” threshold in some of these fields (though, of course, the dangers are all different). Thus, this research suggests a clear message: It is possible that some thresholds for dangerous anthropogenic interference with the climate system are already exceeded, and it is likely that more such thresholds are approaching. Despite great uncertainty in many aspects of integrated assessment, prudent actions can substantially reduce the likelihood and thus the risks of dangerous anthropogenic interference.

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