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Hedging the climate sensitivity risks of a temperature target


This paper addresses the problem of meeting a predetermined temperature target cost-effectively under uncertainty and gradual learning on climate sensitivity. The firstorder optimality conditions to a stochastic cost-minimization problem with a temperature constraint are first provided, portraying how marginal costs evolve with an optimal hedging strategy. Then, numerical stochastic scenarios with cost curves fitted to recent climate changemitigation scenarios are presented, illustrating both the range of possible future pathways and the effect of uncertainty to the solution. Last, the effect of several different sets of assumptions on the optimal hedging strategy are analyzed. The results highlight that the hedging of climate sensitivity risk calls for deeper early reductions, although the possibility of different assumptions prevents providing accurate policy guidance.

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Fig. 1
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Fig. 3
Fig. 4
Fig. 5


  1. If the state x τ,s is simplified to represent only temperature, T(x τ,s )=T l i m i t x τ,s .

  2. Note that T(x τ,s ) is linear by definition.

  3. Note that I s (t,τ) < 0, because I s is temperature impulse response function for an increase in emission reductions.

  4. The GWP’s used for CH4 and N2O are 21 and 310 (Schimel et al. 1996).

  5. The variance in baseline emissions in Fig. 1 is notable, and capturing this variation is not possible with single curves. However, the optimal solution of the cost-minimization problem depends on the marginal costs required to reach a given emission level. The level of baseline emissions affects the total costs, but not the optimal emission level or emission price.

  6. A convex curve translates a distribution of marginal cost with mean c onto a distribution of emissions with a mean value that is higher than the emissions corresponding to the marginal cost c.

  7. The term “prices” refers to the shadow value of CO2. In the case with capital lifetime, the shadow value can differ from the marginal cost with which emissions are reduced. For gases other than CO2, the GWP-weighted shadow value can differ from that of CO2, see e.g. Ekholm et al. (2013) for further discussion.

  8. The scenarios in Fig. 5 use low-cost curves, emissions as CO2-eq and assume no inertia.


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Correspondence to Tommi Ekholm.

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The research has been done in the project STARSHIP, funded by the Academy of Finland (Decision No. 140800).

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Ekholm, T. Hedging the climate sensitivity risks of a temperature target. Climatic Change 127, 153–167 (2014).

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  • Emission Reduction
  • Climate Sensitivity
  • Abatement Cost
  • Temperature Constraint
  • Cost Curve