Climatic Change (2014) 127:463–474 DOI 10.1007/s10584-014-1283-0

Inaction and climate stabilization uncertainties lead to severe economic risks Martha P. Butler · Patrick M. Reed · Karen Fisher-Vanden · Klaus Keller · Thorsten Wagener

Received: 24 January 2014 / Accepted: 16 October 2014 / Published online: 8 November 2014 © Springer Science+Business Media Dordrecht 2014

Abstract Climate stabilization efforts must integrate the actions of many socio-economic sectors to be successful in meeting climate stabilization goals, such as limiting atmospheric carbon dioxide (CO2 ) concentration to be less than double the pre-industrial levels. Estimates of the costs and benefits of stabilization policies are often informed by

Electronic supplementary material The online version of this article (doi:10.1007/s10584-014-1283-0) contains supplementary material, which is available to authorized users. M. P. Butler () Department of Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, 16802, USA e-mail: [email protected] P. M. Reed Department of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA K. Fisher-Vanden Department of Agricultural Economics, Sociology, and Education, The Pennsylvania State University, University Park, PA 16802, USA K. Keller Department of Geosciences, The Pennsylvania State University, University Park, PA 16802, USA K. Keller Earth and Environment Systems Institute, The Pennsylvania State University, University Park, PA 16802, USA K. Keller Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213, USA T. Wagener Department of Civil Engineering, University of Bristol, University Walk, Bristol, BS8 1TR, UK Present Address: M. P. Butler Department of Meteorology, The Pennsylvania State University, University Park, USA

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Integrated Assessment Models (IAMs) of the climate and the economy. These IAMs are highly non-linear with many parameters that abstract globally integrated characteristics of environmental and socio-economic systems. Diagnostic analyses of IAMs can aid in identifying the interdependencies and parametric controls of modeled stabilization policies. Here we report a comprehensive variance-based sensitivity analysis of a doubled-CO2 stabilization policy scenario generated by the globally-aggregated Dynamic Integrated model of Climate and the Economy (DICE). We find that neglecting uncertainties considerably underestimates damage and mitigation costs associated with a doubled-CO2 stabilization goal. More than ninety percent of the states-of-the-world (SOWs) sampled in our analysis exceed the damages and abatement costs calculated for the reference case neglecting uncertainties (1.2 trillion 2005 USD, with worst case costs exceeding $60 trillion). We attribute the variance in these costs to uncertainties in the model parameters relating to climate sensitivity, global participation in abatement, and the cost of lower emission energy sources.

1 Introduction Managing the risks of global climate change poses significant policy challenges. One way to frame the climate stabilization problem is with a policy scenario that limits atmospheric CO2 concentrations to double preindustrial levels, which corresponds to a 2.5◦ –3 ◦ C increase in global atmospheric temperatures above pre-industrial (NRC 2011). Identifying strategies (UNEP 2010; 2011) to achieve such climate goals, whether by limits to temperature increases or atmospheric concentrations of greenhouse gases, requires a detailed understanding of the physical climate system as well as complex socio-economic scenarios of the future (Edwards 2011). Integrated Assessment Models (IAMs) can be useful to advance this understanding by simulating the linkages between economic activities, greenhouse gas emissions, the carbon cycle, climate and damages (Parson and FisherVanden 1997; Courtois 2004; Keller et al. 2004; Stanton et al. 2009). Here we use an ensemble-based uncertainty analysis combined with a global variance-based sensitivity method (Sobol’ 2001; Saltelli et al. 2008) to analyze a doubled-CO2 climate stabilization policy scenario from the Dynamic Integrated model of Climate and the Economy (DICE) (Nordhaus 2008). As a globally-aggregated IAM, DICE poses a simple, yet comprehensive, representation of the world where economically optimal climate stabilization scenarios can be evaluated. Understanding the controlling assumptions and parameters underlying an IAM policy scenario is important for identifying key uncertainties requiring further research (Pizer 1999; Collins et al. 2012). Previous studies of the DICE model have focused on evaluating single components of the model in isolation: energy and technology (Weyant and Olavson 1999; Popp 2004), the carbon cycle (Schultz and Kasting 1997; Joos et al. 1999), climate thresholds (Keller et al. 2004; McInerney et al. 2012), impacts of incomplete participation in mitigation (Nordhaus 2010), and discounting (Nordhaus 2007b). These studies have broken important new ground, but are silent on key interactions and dependencies across these components. Our main objective is to explore the vulnerabilities of a specific optimized DICE policy scenario to uncertainties in specifying exogenous assumptions. By isolating the policy scenario from the optimization process, we are exploring which combinations of exogenous parameters (e.g., population, technology efficiency, climate sensitivity) control deviations from the policy costs attained under the assumption of perfect information. We accomplish this with a simulation version of the cost benefit form of the DICE model and a

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large sample of candidate states-of-the-world (SOWs) created by sampling selected exogenous parameters simultaneously within feasible ranges. We do not recalibrate the model to find a perfect foresight doubled-CO2 policy scenario for each sampled SOW, and do not claim to assign likelihoods to exogenous parameter combinations. Rather, we measure how exogenous parameters, individually and interactively, affect policy-relevant model outputs if our exogenous assumptions deviate from those of the reference case. Given the policy relevance of the DICE model (EPA 2010, 2013), it is important to understand the vulnerabilities of stabilization policies to uncertainties in specifying these exogenous parameters. Our results could inform subsequent calibration efforts or uncertainty analyses by giving an improved a posteriori understanding of complex, interactive parameter effects.

2 Model We focus our sensitivity analysis on the globally-aggregated DICE IAM (Nordhaus 1994; Nordhaus and Boyer 2000; Nordhaus 2008) to demonstrate the importance of accounting for non-separable, interactive parameter dependencies when characterizing the key factors that control uncertain IAM projections. DICE presents a simple, yet comprehensive, representation of the world where alternative economy-climate scenarios can be tested. A policy outcome from the cost benefit form of DICE is characterized by the emission control rates and investment that maximize the sum of discounted utility of consumption over time subject to the set of constraints imposed in a given scenario. These constraints may be expressed as limits on available fossil fuel resources, atmospheric temperature increases, or in the case of this study, the atmospheric concentration of carbon dioxide. Emission pathways are endogenous to this form of the DICE model. A different, cost effectiveness, form of the model would be used with pre-specified emission control pathways (Meinshausen et al. 2011; Rogelj et al. 2011). For this study, we construct a simulation version of DICE, called CDICE, which reproduces DICE model outcomes for a supplied policy scenario, given the reference values of all exogenous parameters (Butler et al. 2014). With this simulation model, we can explore the vulnerability of the fixed policy scenario to the uncertainty in the DICE model’s exogeous parameters. In this study, we explore the doubled-CO2 climate stabilization policy scenario’s parametric sensitivities for trade-offs between climate damages and abatement costs. Additional policy scenarios are analyzed in Butler et al. (2014). Figure 1 is a schematic overview of the DICE IAM and of the simulation model CDICE. CDICE is a translation of DICE version 2007.delta.8b, which is documented in detail in (Nordhaus 2007a, 2008). The model presents a neoclassical economic growth theory view of the economics of climate change. DICE is a highly aggregated model comprising a single global economy producing a single commodity. This simplified representation of the economy is coupled with a 3-reservoir carbon cycle model and a 2-reservoir climate model. Endogenous industrial emissions are a by-product of production and contribute to atmospheric greenhouse gas concentrations, along with non-CO2 greenhouse gases and emissions from land use change. The total atmospheric burden of greenhouse gases determines the radiative forcing and, ultimately, changes in atmospheric temperature. Global temperature increase has a negative impact on economic output through a simplified damage function. These climate damages can be mitigated by transitioning to a lower emission energy source using a backstop technology. Abatement costs also decrease economic output, yielding a trade-off between the costs of current mitigation activities and the costs of future climate damages (Nordhaus 2008). This cost benefit version of the DICE model is used to

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derive trajectories of industrial emission control rates and investment (the control variables) that maximize the sum of discounted utility of consumption over time (the objective function). Typically, this is modeled using the Generalized Algebraic Modeling System (GAMS, GAMS Development Corporation, USA; GAMS Software GmbH, Germany) employing a non-linear programming reduced-gradient solver (CONOPT3 from AKRI Consulting and Development). Figure 2a shows the trajectories of emission control rates, investment, and the resulting savings rate (investment as a percentage of gross world product) from the GAMS solution of DICE. This solution neglects uncertainties and imposes a constraint on the atmospheric concentration of CO2 not to exceed double the pre-industrial concentration level (without any overshoot). We refer to the outcomes from this DICE GAMS execution as the DICE reference case. The solid black line in Fig. 2b is the resulting emissions pathway from this DICE reference. For our study, we define the doubled-CO2 policy scenario as the emission control and savings rates (Fig. 2a), and use these to control our CDICE simulation version of the DICE model. The DICE and CDICE models are described in detail in the Electronic Supplementary Material. The divergence of the median CDICE emission pathway from

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Fig. 2 a The doubled-CO2 policy scenario from DICE2007, the DICE reference case, is described by its emission control rate (solid line, left axis) and investment (black dashed line, right axis). The gray dashed line is the resulting savings rate (investment as a percent of gross world product). b The distribution of emission pathways from the CDICE ensemble in this study. The solid black line is the deterministic perfect foresight endogenous emissions pathway from the DICE doubled-CO2 policy scenario described in the left panel. The dashed and dotted lines are, respectively, the median and mean emission pathways in the CDICE ensemble. The dark shaded areas represent the 90% of the ensemble centered on the median emission pathway. The light shaded areas include the extremes

the DICE reference is primarily due to the specification of sampling ranges for parameters describing the exogenously-specified total factor productivity trajectory. In the 2007 version of DICE, the default parameters determine a rapidly-rising trajectory, unlike that in earlier or later versions of DICE (Fig. S1 in the ESM). The DICE 2007 rising trajectory permits emissions to continue at higher levels for a longer period of time as the percentage of industrial emissions controlled increases. We have chosen to use sampling ranges that confine the total factor productivity trajectory within more modest bounds (also shown in Fig. S1). The effect of this change is to reduce the industrial emissions earlier and increase abatement costs in later decades of the analysis period relative to the DICE reference. This change is consistent with earlier and later versions of the DICE model (see the ESM for details).

3 Experiment We expose the emission control and savings rate trajectories from the DICE doubled-CO2 stabilization reference policy scenario in CDICE to 8 million alternative SOWs constructed by simultaneously varying 30 of the exogenous parameters that must be specified within the model. The exogenous parameters sampled are shown in bold italics in Fig. 1 and described, along with sampling ranges, in the ESM. Our intent is to test the vulnerability of the doubled-CO2 policy scenario to uncertainties in the reference settings of model parameters. The reference values are sourced variously from historical economic data and calibrations to more comprehensive models (Nordhaus 2007a). First, we analyze an ensemble of SOW outcomes by examining ranges of results using cumulative distributions and comparing these

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to the DICE reference results. We follow this with Sobol’ variance-based global sensitivity analysis (Sobol’ 2001; Saltelli 2002; Saltelli et al. 2008) to determine the exogenous parameters that individually and/or interactively control the variation of climate damages and abatement cost outputs across all sampled SOWs. All parameters are sampled quasirandomly (Sobol’ 2001) from uniform distributions with the exception of climate sensitivity for which we tested three alternative distributions: uniform and two recent estimated distributions based on data-model fusion (Olson et al. 2012; Libardoni and Forest 2011; 2013). The rank order of sensitive parameters for our policy cost metrics did not change across the different distributions. As expected, obvious results are that the range of climate damages is narrower with sharper, more informed climate sensitivity distributions (i.e., extreme values are less likely) and abatement costs are not affected. In this paper, we report results using the updated climate sensitivity distribution from (Libardoni and Forest 2011; 2013), which yields climate damages intermediate between those with the sharper distribution from (Olson et al. 2012) and the uniform distribution. CDICE is run using decadal time-steps for 600 years starting in the year 2000. We analyze an ensemble of more than 8 million SOWs from parameter sets assembled from Sobol’ sequence samples of the 30 exogenous parameters (Sobol’ 2001) to explore parametric sensitivities of climate damage and abatement cost model outputs. Following Nordhaus (2008), we calculate the net present value (NPV) of climate damages and abatement costs using discount factors derived from the real interest rate computed in each SOW. (See the ESM for the relevant model equations.) We use 200 years as the time horizon for the net present value calculations, as discounted values contributing to the net present value sum are very small by 2200. Decomposing the ensemble variance of climate damages and abatement costs yields estimates of the first-order, total-order, and second-order (interaction) indices for each cost measure. The sensitivity index for a parameter can be interpreted as the fraction of the ensemble variance of the metric that can be attributed to uncertainty in the parameter (Saltelli et al. 2008). The first-order sensitivity index is the fraction of the overall metric variance that a single parameter contributes by itself excluding any interactions with other parameters. The total-order sensitivity index captures the fraction of the overall metric variance contributed by a parameter including all higher-order interactions with other parameters. The second-order index is the portion of the total-order sensitivity that can be attributed to specific parameter pairs. Large differences in the sizes of the first- and totalorder indices are indicative of substantial higher-order parameter interactions in the variance decomposition. We show all first-, second- and total-order indices larger than a threshold of 1 % of variance in the figures. Confidence intervals for the sensitivity indices are calculated by bootstrapping the analysis (Efron and Tibshirani 1993; Archer et al. 1997; Tang et al. 2007). Sampling rates are increased until the sensitivity indices converge with acceptable confidence. (See the ESM for details of the method and an illustration of convergence of indices with increased sampling rates.)

4 Sensitivity analysis results In examining the ensemble of SOWs, we find that more than ninety-five percent exceed the sum of the NPV of climate damages and abatement costs of the DICE reference (Fig. S3 in the ESM). The median NPV of total costs across the ensemble is 2.6 trillion 2005 USD, compared to 1.2 trillion 2005 USD for the reference case. The fact that only 44 % of the SOWs exceed the doubled-CO2 concentration target (Fig. S2) suggests significant nonlinearities in the relationship between atmospheric CO2 concentrations and costs. Given the

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significance of the uncertainties in the stabilization costs, it is important to understand the key parameters in the model that control these results. Decomposing the variance of damages and abatement costs (illustrated graphically in Figs. 3 and 4 and quantitatively in Table S1 in the ESM) across the SOWs reveals strong interdependent parametric sensitivities that lead to the nonlinear amplification of the doubled-CO2 stabilization costs. We concentrate here on cost metrics spanning the near-term planning horizon: the NPV of climate damages and abatement costs through 200 years (until the first decade of the 23rd century), and the decadal abatement costs in the mid-21st century (50 years) and the first decade of the 22nd century (100 years). In the resulting figures we illustrate the variance decomposition of these cost metrics attributed to 30 of DICE’s exogenous parameters using radial convergence diagrams (Lima 2011) showing first-, total-, and second-order sensitivity indices. For the NPV of climate damages (Fig. 3a), the second-order parameter interactions between the climate sensitivity parameter (t2xco2) and the exponent in the climate damages function (a3) constitutes 11 % of the variance. Second-order interactions between these two parameters and the total factor productivity parameter (ga0) and the population limit (popasym) are also ≥ 1 % of the total variance. This is a result that would not be apparent in one-at-a-time parameter sensitivity testing (Butler et al. 2014). Earlier studies that focused on technology efficiency (Gillingham et al. 2008) or climate sensitivity (Ackerman et al. 2010) in isolation did not capture the complex interaction effects of these parameters on model-calculated damages. DICE is formulated with a quadratic dependence of climate damages on the increase in atmospheric temperature (Equation S2 in the ESM), although

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Fig. 4 Sensitivities of decadal abatement costs to the sampled parameters at a mid-21st century and b beginning of 22nd century. The legend indicates the extreme values shown. Diagramming conventions are described in the caption for Fig. 3

this choice is somewhat arbitrary (see the discussion in Stanton et al. (2009)). Here we sample both the exponent (a3) and the coefficient (a2) of the non-linear term in the damages formulation and, understandably, find the damages to be more sensitive to the exponent than the coefficient. Notably, the NPV of climate damages is not sensitive to the majority of the climate or carbon cycle parameters in the model and is, instead, overwhelmed by the effects of the climate sensitivity parameter. Contributions to the variance of the NPV of abatement costs (Fig. 3b) are characterized by the interactions between the initial cost of the backstop technology (pback0), the carbon intensity of production (gsigma) and the parameters describing the international participation in the abatement (partf rac2, partf racn). Note that there is very little sensitivity to the total factor productivity parameters (ga0) and the population limit (popasym) for this doubled-CO2 stabilization policy scenario. Sensitivity to the backstop parameters increases as the stabilization criteria become stricter, as seen in the 2◦ C policy scenario in Butler et al. (2014). Policy analysts and stakeholders may be interested in the evolution of climate damages and abatement costs over time, as well as their net present values over the entire planning horizon. We present here the sensitivities of decadal abatement costs (Fig. 4) for the mid-21st century decade and the first decade of the 22nd century. The sensitivities for decadal abatement costs in Fig. 4 show that the specific controlling parameters as well as the parametric interactions change over time. The sensitivity to the international participation parameters shifts over time from the participation fraction in the second decade of the run (partf rac2) to the final level of participation (partf racn) and the rate at which this final level is approached (dpartf rac). Other expected parameter sensitivities (ga0, popasym, and gsigma) and their interactions become more apparent over time (Fig. 4b).

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Assumptions about economic productivity, population projections, and the carbon intensity of production all become more critical over time. The reference DICE doubled-CO2 policy scenario relies on the highly optimistic assumption of complete participation in abatement that is beginning to be challenged in the literature (Clarke et al. 2009; Luderer et al. 2013; Rogelj et al. 2013). Inertia in both the socio-economic and climate systems (Jarvis et al. 2012) coupled with the typically-used 100-year planning horizon (Parson and FisherVanden 1997) mask the urgency for implementing emission control and mitigation strategies (NRC 2011). Given the importance of population, total factor productivity, and carbon intensity of production to these climate damages and abatement cost metrics, it is interesting to note that of the 56 % of the SOWs which meet the doubled-CO2 stabilization limit, the median population function parameters describe a population trajectory that in 2100 of less than 8 billion (Fig. S1). This is lower than the DICE reference value of 8.6 billion and the UN median projection of 9.6 billion (UN 2011). The median trajectory of the carbon intensity of production is also lower than the DICE reference, indicating that a more rapid decrease is required. The median total factor productivity trajectory is near the lower bound sampled. The carbon cycle in this model has little effect on the atmospheric concentration (Table S2). Meeting, or not meeting, the goal of this doubled-CO2 policy scenario depends primarily on the factors affecting industrial emissions. This can be done by lowering the carbon intensity of production or by decreasing gross production with lower energy demands from lower population and lower total factor productivity (Equation S9).

5 Conclusions In our analysis we identified the most sensitive parameters and parameter combinations contributing to the variance of the net present value of climate damages and abatement costs for a fixed doubled-CO2 climate stabilization policy. The climate sensitivity parameter (t2xco2) and the exponent in the damage function (a3) are the leading sensitivities for climate damages. The well-known uncertainty in the climate sensitivity parameter (Knutti and Hegerl 2008; Collins et al. 2012; Annan and Hargreaves 2011) directly translates into a lower confidence that the doubled-CO2 stabilization goal can be achieved. The sensitivity to the exponent of the damage function contributes to the discussion of the underlying model structure of the damage function. The representations of the carbon cycle and the climate system in the DICE model are necessarily simplistic, but perhaps overly so. As is standard practice in the IAM community, the representations for land use change and radiative forcing due to non-CO2 greenhouse gases follow the IPCC’s Extended Concentration Pathways beyond 2100 (Meinshausen et al. 2011). Consequently, our analysis reveals little sensitivity of climate damages to nearly all of the parameters governing the carbon cycle, land use change, and radiative forcing from non-CO2 greenhouse gases. A recent study by Bodman et al. (2013) using observational constraints with the MAGICC model, to which DICE is also calibrated, find the carbon cycle to be a more significant contributor to future temperature projections. The temperature projections are the sole driver of the damage function in DICE. The leading sensitivities for the net present value of abatement costs are the parameters representing the initial cost of the backstop technology (pback0), total factor productivity (ga0), global participation function parameters, and, to a lesser extent, the population limit (popasym) and the carbon intensity of production (gsigma). In this version of DICE, the participation function is perhaps the only means of exploring a delay in undertaking

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mitigation efforts, as discussed in other contemporary analyses (Clarke et al. 2009; Luderer et al. 2013; Rogelj et al. 2013). At this globally aggregated level, a participation function based on delay may prove more useful for policy analysis. The DICE model is an inter-temporal optimization model that is often used to identify an optimal trajectory of mitigation that maximizes the sum of discounted utility over time. In our CDICE analysis, this sum of discounted utility is sensitive only to the functional forms assumed for population dynamics and total factor productivity (Table S2 in the ESM). Our analysis could not identify sensitivity at the 1 % threshold level of variance to any of the backstop technology, carbon intensity of production, or climate-related parameters. In addition to optimizing a single objective function, the reference deterministic formulation used in our analysis assumes perfect knowledge of future SOWs and parameters and neglects future learning (Keller et al. 2007; Keller and McInerney D 2008). Additional uncertainties (e.g., about the pure rate of social time preference (prstp) and the elasticity of marginal utility of consumption (elasmu)) are known to be important, but are not tested here. While the median discounted utility for all SOWs in our ensemble is within 10 % of the DICE reference value for this doubled-CO2 policy scenario, the median net present values of climate damages and abatement costs exceed the DICE reference values by factors of 1.6 and 4.3, respectively. A key concern with DICE and other IAMs is that the structural assumptions and parametric uncertainties used to frame the international policy debate might bias their results to be overly optimistic, underestimating the costs of delayed action (Keller et al. 2007; Nordhaus 2010; Jarvis et al. 2012; Stern 2007; den Elzen et al. 2010). Schwanitz (2013) proposes model evaluation as a standard model-building practice for IAMs with the main goals of increasing confidence in model outcomes and identifying areas for further research and improvement. Our study uses one of several methods proposed by Schwanitz (2013) for IAM model evaluation. In another recent example using the base form of the DICE model, Anderson et al. (2013), using the method of Plischke et al. (2013), identify influential exogenous parameters using a larger suite of parameters and a different set of model outcomes than we studied in our work. In addition to the elasticity of marginal utility of consumption, which we did not sample, they find, as we do, that total factor productivity and population dynamics parameters are important to a range of model outcomes. A number of the findings in our study can easily translate into future research, including improving model structure regarding the damage function and the global participation or delay in mitigation efforts, and exploring optimization of multiple objectives. We do encourage this future research to be done on the more current 2013 version of the DICE model (Nordhaus 2013). Author Contributions All authors jointly designed the study. MPB conducted the experiment and wrote the first draft of the manuscript. All authors edited the manuscript. Acknowledgements This work was supported by the U.S. Department of Energy, Office of Science, Biological and Environmental Research Program, Integrated Assessment Program, Grant No. DE-SC0005171, with additional support from NSF through the Network for Sustainable Climate Risk Management (SCRiM) under NSF cooperative agreement GEO–1240507 and the Penn State Center for Climate Risk Management. The authors thank William Nordhaus for making the DICE model available, and Alex Libardoni, Chris Forest and Roman Olson for providing their empirical climate sensitivity estimates and advice on their use and interpretation. The DICE model and documentation were accessed on 2/5/2011 from http://nordhaus.econ.yale. edu. Current access to the DICE model is at http://www.econ.yale.edu/∼nordhaus/homepage/index.html. The CDICE model code is at https://github.com/mpbutler/CDICE2007. Sobol’ sampling and sensitivity analysis code used in this study are from the MOEA Diagnostic Tool http://www.moeaframework.org. Any opinions, findings, and conclusions expressed in this work are those of the authors, and do not necessarily reflect the views of the National Science Foundation or the Department of Energy.

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