Optimal carbon mitigation strategy under non-linear feedback effects and in the presence of permafrost release trigger hazard

Abstract

The threat of release of methane sequestered in the circumpolar Arctic regions of the world creates the possibility of triggering additional feedback effects from the terrestrial and the deep ocean systems which could potentially add large amounts of carbon (C) into the atmosphere. This paper analyses the implications for C mitigation policy under the threats of a substantial permafrost methane release. Several insights emerge from the analysis. First, the presence of non-linear feedbacks creates a bifurcation zone in the C emissions-stock space, on one side of which large accumulations of atmospheric C materialize leading to significant damages. Second, the bifurcation line does not have a steep slope, implying that it would be possible to avoid falling on the wrong side of this zone even if the current atmospheric stock of C were higher than what they are today. Third, when the release of permafrost C is uncertain, there is benefit in reducing anthropogenic C more than what would be optimal under a certain release of the same. Fourth, higher abatement cost scenarios do not necessarily imply significantly reduced abatement efforts. On the contrary, abatement efforts, which are only reduced marginally under this scenario, ensure that long run carbon path is stabilized. This is done in order to avoid incurring substantial costs of abatement in the future when non-linear feedback effects kick in.

Appendix: model calibration

1.1 Carbon feedback

Estimates of positive feedback to the atmospheric C from higher temperatures vary in the literature. Friedlingstein et al. (2001) obsaerve that climate change could potentially reduce land uptake of CO₂ by 50 percent. For large climate sensitivities and large anthropogenic GHG emissions, the feedback could be around a factor of two (Harvey and Huang 1995; Archer and Buffett 2005). Based upon the above, we assume that, when atmospheric CO₂ concentration is double the preindustrial levels of 280 ppm, non-linear feedback is 1 ppm, when atmospheric concentration is three times, feedback is 4 ppm and it is 5 ppm at four times the pre-industrial level. The calibrated parameter values for this relationship, specified in equation (1), are (see Fig. 9): ${\eta_s}=4.8,\,a=8.96,\,b=2500$

Fig. 9

Feedback effect calibrated as a function of the ratio of current concentrations to the pre-industrial concentrations of atmospheric C

1.2 Hazard function

The IPCC Fifth Assessment Report relies on four representative concentration pathways (RCP) which refer to the level of radiative forcing (in W/m²) brought about by the accumulation of C in the atmosphere by 2100. Schuur and Abbot (2011) derive low and high estimates of permafrost release based upon the RCP scenarios. These estimates are derived from a survey of 41 international scientists working on permafrost. The high warming scenario leads to a release of 63GT CO₂ by 2040, 380GT CO₂ by 2100 and 865GT CO₂ by 2300. The low warming scenario leads to a release of 30GT CO₂ by 2040, 232 GT CO₂ by 2100 and 549GT CO₂ by 2300.

While these estimates are deterministic, there is still a significant degree of uncertainty associated with the timing and extent of permafrost release. In this paper we also calibrate the risk of permafrost release through a hazard event. The hazard event represents a possibility of an additional release of 2 gtc emissions through melting of the permafrost.

Imagine if the CO₂ stock remained fixed at 391 ppm, what would be the probability of the event happening in a century? If the stock were fixed at 560 ppm, what would be the probability of the event then? Based upon this criteria, the relationship between the probability, stock of C and hazard rate is derived as: $p(s)=1-\exp \left( { - 100 \cdot h(s)} \right)$ where h(s) is calibrated at three levels of stocks of C: when the current ppm is 2 times, 2.5 and 3 times the pre-industrial levels, the probability of release by 2050 is assumed to be 0.75, 0.85 and 0.95. The hazard rate is calibrated to the functional form presented in equation (4). The calibrated parameter values are (see Fig. 10):

Fig. 10

Hazard rate of permafrost methane release calibrated as a function of the ratio of current concentrations to the pre-industrial concentrations stock of atmospheric carbon

$$ {\eta_{hzd }}=6.12,{a_{hzd }}=5.56,{b_{hzd }}=62000,d=.028 $$

1.3 Damage function

The damage function is assumed sigmoid in the stock of C. It is calibrated in a way so that the doubling, tripling and quadrupling of the stock of C leads to 10, 30 and 40 percent loss in gdp respectively (see Fig. 11). Damage function is assumed to taper off to a level equal to 40 percent of the GDP at high levels of concentration to reflect the possibility that maximum possible damages to the GDP are less than 100 percent. The range of damages chosen here is higher than that shown in the IPCC working group II estimates, where a six degree increase in temperatures from the pre-industrial levels leads to about 15 percent of GDP loss (IPCC 2007b). The calibrated parameters based upon the functional form presented in equation (5) are:

Fig. 11

Percent damages to the gdp calibrated as a function of the ratio of current concentrations to the pre-industrial concentrations of atmospheric carbon

$$ d(s)={\eta_d}\cdot \frac{{{s^{d1 }}}}{{{s^{d1 }}+{d_2}}},\,\mathrm{where}\,{\eta_d}=42.1,\ {d_1}=6.58,{d_2}=440 $$

We also consider a milder damage scenario (where the doubling, tripling and quadrupling of the stock of C leads to 10, 20 and 30 percent loss in gdp respectively). The calibrated function for this scenario is:

$$ d(s)={\eta_d}\cdot \frac{{{s^{d1 }}}}{{{s^{d1 }}+{d_2}}},\,\mathrm{where}\,{\eta_d}=30,{d_1}=4.942,{d_2}=80 $$

1.4 Abatement cost function

For the purposes of empirical estimation of abatement cost, abatement effort is measured not as a percentage of emissions but in absolute terms. Abatement cost estimates are derived, based upon the information in Table 1, so that cutting emissions by x ppm will lead to a cost of c(x) trillion dollars. Abatement cost function is calibrated as sigmoid to reflect possible cost savings from technological progress in future (see Fig. 12):

Table 1 Abatement cost estimates calibrated from various sources in the literature (Enkvist et al. 2007; Dietz and Stern 2008; Weyant 2008)

Fig. 12

Abatement costs in trillions of USD calibrated as a function of abatement

$$ c(x)={\eta_a}\cdot \frac{{{x^{a1 }}}}{{{x^{a1 }}+{a_2}}},\,{\eta_a}=6,{a_1}=5.22,{a_2}=1800. $$

(6)

For the scenario where costs are assumed twice the above estimates, the parameter values are: ${\eta_a}=4.3,\ {a_1}=10.35,\ {a_2}=400$