Global Warming and a Potential Tipping Point in the Atlantic Thermohaline Circulation: The Role of Risk Aversion

Abstract

The risk of catastrophes is one of the greatest threats of climate change. Yet, conventional assumptions shared by many integrated assessment models such as DICE lead to the counterintuitive result that higher concern about climate change risks does not lead to stronger near-term abatement efforts. This paper examines whether this result still holds in a refined DICE model that employs the Epstein–Zin utility specification and that is fully coupled with a dynamic tipping point model describing the evolution of the Atlantic thermohaline circulation (THC). Risk is captured by the possibility of a future collapse of the circulation and it is nourished by fat-tailed uncertainty about climate sensitivity. This uncertainty is assumed to resolve in the middle of the second half of this century and the near-term abatement efforts, which are undertaken before that point of time, can be adjusted afterwards. These modelling choices allow posing the question of whether aversion to this specific tipping point risk has a significant effect on near-term policy efforts. The simulations, however, provide evidence that it has little effect. For the more likely climate sensitivity values, a collapse of the circulation would occur in the more distant future. In this case, acting after learning can prevent the catastrophe, implying the remarkable insensitivity of the near-term policy to risk aversion. For the rather unlikely and high climate sensitivity values, the expected damage costs are not great enough to justify taking very costly measures to safeguard the THC. Our simulations also provide some indication that risk aversion might have some effect on near-term policy, if inertia limiting the speed of decarbonisation is accounted for. As it is highly uncertain how restrictive this kind of inertia will be, future research might investigate the effects of risk aversion if additional uncertainty about inertia is considered.

Appendices

Appendix 1: Robustness Check

As this research clearly relates to the study by Ackerman et al. (2013), here we clarify whether our model could reproduce their results. We may demonstrate this for their $E_1$ model run. We keep the default damage function of the original DICE model, i.e. we set $a_2 = 0.0028388$ and ignore the feedback from the THC module to DICE. Note that there are different assumptions in the two models. Firstly, we apply the updated transient temperature change equation from Cai et al. (2012a), where, in contrast to Nordhaus (2008) and Ackerman et al. (2013), the radiative forcing depends only on current carbon concentration in the atmosphere. Secondly, while the EZ-DICE model by Ackerman et al. (2013) is designed for decadal time steps, our model incorporates annual time steps as the DICE-CJL model by Cai et al. (2012a).

Comparing the results of the two models, we recognise that the assumptions in our model offer a more differentiated view of the optimal policy (Fig. 15). While in Ackerman et al. (2013) only one policy path is given for three very different climate sensitivity values, $S_3$–$S_5$, our model produces two distinct control trajectories. The discrepancy mainly comes from the model recalibration by Cai et al. (2012a) associated with the refined time scale. This is explained and discussed in more detail by Marten and Newbold (2013).

Fig. 15

Comparison of the optimal emission redution policies generated by the two models, the EZ-DICE model by Ackerman et al. (2013) (left) and the IAM in our paper, in which the feedback from the THC to DICE model is ignored (right)

Appendix 2: Numerical Solution

Here, we draw attention to the non-convex nature of the optimisation problem. This non-convexity occurs, for instance, when considering tipping elements that switch to another state at some point in time. As finding the computational solution to such a problem is non-trivial, we explain our numerical approach in more detail in the following.

Fig. 16

Frequency of solutions found by a multi-start approach for different initial values

The more refined time step compared to DICE gives rise to a higher dimension of the decision variables space, which amounts to 1200 variables (consumption and abatement paths over 600 years). Furthermore, the existence of the THC stability threshold induces local optima, which creates numerical problems that are commonly tackled by global optimisation methods. Yet, the global solvers available in GAMS are rather restricted with respect to the allowable size of the model. Instead we implement a multi-start heuristic approach to the CONOPT3 solver in the GAMS environment using different initial values.¹² The algorithm in CONOPT3 is based on a generalised reduced gradient (GRG) technique, which relies on the gradient information and has a comparative advantage in handling large models such as ours.¹³ The three pillars of successfully applying the solver to a non-linear problem are the initial values, scaling, and bounds. Furthermore, the solver is designed to operate with smooth functions only, which is why throughout the model design process, e.g. developing the damage cost function $f_{THC}$, we verify this property to ensure convergence.

The approach we implement calls the NLP solver CONOPT3 from 100 random initial vectors within the bounds of the variables. The highest value from the multi-starts corresponds to the approximation of the global solution, which is used in the analyses. The histogram in Fig. 16 depicts the solutions of the multi-start approach for the default simulation (Fig. 5). Out of 100 model runs, 50 converge to a feasible solution with 18 converging to the optimum. As mentioned above, many of the solutions recovered by our algorithm are local. In this respect, a good alternative could be to refer to the differential evolution algorithm, which converges to the same solution for many initial conditions (see Keller et al. 2004; Moles et al. 2004).

To illustrate the non-convexity of the problem, we perturb the near-term optimal emissions-control rate and inspect the associated change in the objective function (first-period Epstein–Zin utility). As the reference we choose the value of the first-period Epstein–Zin utility that corresponds to the optimal emissions-control rate for the scenario in which the THC-related damage costs are neglected. Figure 17 depicts the relative change of the first-period Epstein–Zin utility value for different abatement rates in the year 2075. The point G is associated with global optimum. An increase in the abatement rate leads to a decrease in utility. The reason is that the benefits associated with delaying the THC collapse do not exceed the near-term costs. Utility is continuously decreasing with the emissions-control rate in the near-term until the abatement efforts are sufficient to prevent the THC collapse in state $S_5$. As soon as the circulation is safeguarded, the THC-induced damage costs over the long period of time sum up to nearly zero. This is reflected in the sudden increase in the first-period Epstein–Zin utility at about 68.6 % of abatement in the year 2075. Nevertheless, the costs of preventing the THC collapse in $S_5$ exceeds the benefits. Thus, preserving the THC describes only a local optimum, which is depicted by L.

Fig. 17

Relative percentage change in the first-period Epstein–Zin utility for different values of abatement rates in the year 2075. The percentage change is considered relative to the first-period Epstein–Zin utility for the emissions-control rate that neglects potential THC-related damages. The points G and L indicate the location of the global and local optimum, respectively

Appendix 3: Calibration

Please refer to Table 2 for parameters crucial to the present study and to Table 3 for the THC model parameters. For the DICE-CJL model parameters, refer to Cai et al. (2012a) as well as Cai et al. (2012b) and the accompanying website.

Table 2 Parameters crucial to the present study

Table 3 The THC model parameters (Zickfeld et al. 2004)

Appendix 4: Sensitivity Analysis with Respect to $m_{crit}$

Here, we discuss briefly an alternative calibration for $m_{crit}$. For the simulation illustrated in Fig. 18, we adopt the assumption that $m_{crit}$ is zero. In Sect. 3 we conjecture that this assumption might render the threat of a THC collapse and the aversion to the risk involved as less important. Figure 18 confirms this conjecture. Risk aversion has little effect on near-term policy. In both cases of alternative attitudes to risk, the near-term policy efforts are lower than in the baseline case (by 6.58 percentage points), as the THC damage costs are incurred only when circulation stops altogether. These reduced efforts lead to a slowdown in more states of nature than in the baseline case.

Changing the value of $m_{crit}$ by $\pm 3$ Sv, as in Figs. 19 and 20, shows that the results on the effects of risk aversion are rather robust with respect to $m_{crit}$.

Fig. 18

Sensitivity of the results with respect to $m_{crit}=0$ Sv i.e. THC-related damages are associated with the circulation breakdown. a, c Optimal emission reduction policy. b, d Possible trajectories of the overturning strength

Fig. 19

Sensitivity of the results with respect to lower value of critical weakening, $m_{crit}=7$ Sv. a, c Optimal emission reduction policy. b, d Possible trajectories of the overturning strength

Fig. 20

Sensitivity of the results with respect to higher value of critical weakening, $m_{crit}=13$ Sv. a, c Optimal emission reduction policy. b, d Possible trajectories of the overturning strength