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For RCP2. It is an answer to the question of what the canonical social planner would be willing to pay today to follow the deterministic temperature trajectory rather than to face an uncertain future.

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Another way to think about it is the value of insurance against aleatory uncertainty about future temperatures, if such an insurance product could be bought. If the social planner knew to expect RCP2. A social planner that knew to expect RCP8. So far, we have only considered the cost of aleatory uncertainty while assuming fixed values of the model parameters. Integrated assessment modellers typically capture this by rerunning the deterministic model for a sample of ECS values and producing a distribution of climate damages 7.

We can do the same thing with the stochastic model, which tells us how the cost of aleatory uncertainty changes when there is also epistemic uncertainty. The risk premia reported in Fig. When faced with RCP2. Faced with RCP8. This plot shows what the canonical social planner would be willing to pay to avoid aleatory uncertainty when there is also underlying epistemic uncertainty. To compute these risk premia, we first obtain an ensemble of temperature trajectories by solving the deterministic EBM for a distribution of values of the equilibrium climate sensitivity ECS.

Next, we obtain a second ensemble by solving the stochastic energy balance model for the same distribution of ECS values. Both ensembles reflect the same epistemic uncertainty, but only the second incorporates aleatory uncertainty as well. These risk premia can be decomposed into two parts: the darker portion of each bar shows the risk premium when all uncertainty is aleatory same as in Fig.

This risk interaction effect arises because a high draw from the ECS distribution produces both greater mean warming and greater variability, which makes the high draws disproportionately more costly. This results in damage distributions with a fatter right tail.

These risk premia are substantially higher than before as a result of how these two sources of uncertainty interact.

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The effect of a higher ECS on the variance of temperature would be weaker if a fluctuation—dissipation theorem applied 9 , 10 , 11 , but it would not alter the fact that high draws become disproportionately more costly. This implies that the addition of stochasticity will produce damage distributions with an even fatter right tail than in the deterministic case. This is a distinct effect arising from the interaction of epistemic and aleatory uncertainties.

Since we cannot remove aleatory uncertainty, this risk premium is best thought of as a previously unaccounted for cost of climate change. It is worth making special note of the distinction between the risk premia that we have estimated here and the marginal damage caused by releasing an additional tonne of CO 2 , the so-called social cost of carbon SCC.

The risk premium measures the additional cost of living with aleatory uncertainty as compared to living in a deterministic world. The SCC, by contrast, measures the cost of releasing just one more tonne of CO 2 within a stochastic or deterministic framework. Even though the risk premium is substantial, we may well face the same temperature variability whether or not we release an additional tonne of CO 2. The crucial point to note is that the SCC and the risk premium provide answers to two different questions.

The risk premium primarily tells us about costs that we need to prepare for because they cannot be avoided in this way. The way to avoid them, rather, is through adaptation. The cost of adaptation is beyond the scope of the present investigation, but our findings suggest that the benefits are much greater than previously believed. Adding temperature variability to a simple integrated assessment model results in greater economic damages from climate change. What is new here is neither the physics nor the economics—both of which closely follow canonical models in their respective fields—but we find that the careful combination of insights from these two disciplines reveals trillions of dollars of previously uncounted damages.

These damage estimates are substantial, but it is worth noting that they are likely to be on the conservative side. One reason for this is the typically high discount rate that is assumed for this type of analysis, which we have followed here 4.

Another reason our estimates are conservative is the handling of temperature autocorrelation. The climate system represented by Eq. The autocorrelation in our model increases the probability of persistent events of this nature compared to a simple white noise time series, but if the climate system exhibits true long-range dependence 13 , long runs of extreme temperatures are even more likely than this simple model predicts.

In this case, temperatures would be more likely to persistently deviate from the deterministic trajectory trend in one direction or the other, and the net present value of damages plotted in Fig. It should be noted, though, that this temperature persistence does not directly translate into higher risk premia for aleatory uncertainty in our analysis. The damage function and the social welfare function have no memory. It therefore only matters how the shape of the temperature distribution evolves over time, but it does not matter what the individual temperature trajectories look like that make up that evolving distribution.

For the social planner envisioned by these integrated assessment models, then, the degree of autocorrelation of temperatures is largely irrelevant. The simple integrated assessment models were built with a deterministic climate in mind, of course, so it is not entirely surprising that they are poorly equipped to deal with the consequences of temperature autocorrelation.

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But if societies lack the foresight to plan for longer periods of extreme climatic conditions, seven consecutive years of drought may be much more difficult to endure than if they were interspersed with years of plenty. In the story of Joseph, let us not forget, civilisation is saved only thanks to a divine prophecy. If, in reality, more strongly autocorrelated temperatures produce greater damages, then the true cost of temperature variability is likely to be substantially larger than we estimate here.

More concretely, a country like Syria may be reasonably successful at containing the damage of a 1-year or even 2-year drought, but collapse under the weight of a 3-year drought, having far-reaching and disproportionate consequences.

The combination of anthropogenic forcing and autocorrelated natural variability makes such severe droughts much more likely An important challenge in the years to come will be to pin down how damages accumulate during longer periods of extreme climate, so that these effects can be incorporated into future assessments of the economic damages from climate change. Fredriksen, H.

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