The solid line shows the mean values and the dashed lines are the 5 and 95% confidence intervals.
The PAGE09 model.
PAGE09 is an integrated assessment model that values the impacts of climate change and the costs of policies to abate and adapt to it. PAGE09 is designed to help policy makers understand the costs and benefits of action or inaction. All results reported are from 100,000 runs of the model. The probabilistic structure of the model enables consideration of the full spectrum of risks from climate change.
PAGE09 is an updated version of the PAGE2002 integrated assessment model that has been used to value the impacts and calculate the social cost of CO2 (refs 15, 19), and to value the impacts and costs of deforestation20. PAGE09 accounts for more recent scientific and economic information, primarily in the Fourth Assessment Report of the IPCC (ref. 21). A full description of the updated treatment of the science, impact, abatement and adaptation costs in the latest default version of the model, PAGE09 v1.7, and the full set of model equations and default inputs to the model are given in the Supplementary Material of ref. 3.
PAGE09 uses simple equations to simulate the results from more complex specialized scientific and economic models, accounting for the profound uncertainty that exists around the impacts of climate change. Calculations are made for eight world regions, ten time periods to the year 2200, and four impact sectors (sea level, economic, non-economic and discontinuities), which for clarity we collect together under the description ‘economic’ in this paper. All calculations are performed probabilistically, using Latin hypercube sampling to build up probability distributions of the results. The results for two policies and the difference between them are calculated in a single run of the model, so that the incremental costs and benefits of different emissions can be found.
The sources used for the impact curve parametrization in the default PAGE09 model are of particular interest, so we present these in some detail here.
Impacts as a proportion of GDP.
The PAGE09 model values four types of climate change damage: sea level, economic, non-economic and discontinuities. In PAGE09, sea-level damages before adaptation are a polynomial function of sea-level rise, and economic and non-economic damages before adaptation are a polynomial function of the regional temperature. Economic impacts are those that are included directly in GDP, such as agricultural losses and air-conditioning costs; non-economic impacts are those that are not included directly in GDP, such as human health and ecosystem impacts. The default triangular distributions for these parameters in the focus region of the EU are shown in Supplementary Table 2.
They produce a mean impact before adaptation of just under 2% of GDP (W_S plus W_1 plus W_2) for a temperature rise of 3 °C (TCAL; ref. 22), including the associated sea-level rise of just under half a metre (SCAL; ref. 23). Sea-level impacts rise less than linearly with sea-level rise (POW_S), as land and people (and hence GDP) are concentrated in the most low-lying areas23 (Fig. 1). Economic and non-economic impacts rise on average as just over a quadratic function of temperature (POW_1 & POW_2); the same range as in ref. 24.
Supplementary Figs 6–8 show how these inputs combine to produce a range of values for the economic, non-economic and sea-level damages in the EU in the default PAGE09 model. Note the different horizontal variable and vertical scale of Supplementary Fig. 8. The amount and spread of the damages increase over time, reflecting the fact that the magnitude and potential range of temperature and sea-level rise increase over time.
Other regions are on average less vulnerable than the EU for the same sea-level and temperature rise, and at the same GDP per capita, largely because of the long coastline of the EU. The multiplicative weight factors applied to impacts in other regions for the same sea-level and temperature rise, and at the same GDP per capita, are shown in Supplementary Table 3 (ref. 23). The range of impacts is consistent with the range of 0–3% of GDP for a 2–3 °C warming, with higher costs in poor countries, quoted on page 143 of Stern (ref. 15).
Extra flexibility is introduced by allowing the possibility of initial benefits from small increases in regional temperature25, by linking impacts explicitly to GDP per capita and by letting the impacts drop below their polynomial on a logistic path once they exceed a certain proportion of the remaining GDP, to reflect a saturation in the vulnerability of economic and non-economic activities to climate change, and ensure they do not exceed 100% of GDP (ref. 26).
There is a risk of a large-scale discontinuity, such as the Greenland Ice Sheet melting, if climate change continues27. The default triangular distributions for the parameters for the risk of a possible future large-scale discontinuity are shown in Supplementary Table 2. The modal parameter values are chosen such that a large-scale discontinuity becomes possible only when the global temperature has risen by 3 °C above pre-industrial levels (TDIS; ref. 27 and Table 1 therein), with a range of 2–4 °C (ref. 15 and box 1.4 therein). For every 1 °C rise in temperature beyond this threshold, the chance of a large-scale discontinuity occurring rises by 20% (PDIS). With modal values it is 20% if the temperature is 4 °C above pre-industrial levels, 40% at 5 °C, and so on24. The ranges here are wide, as our knowledge is so limited. The upper ends of the ranges imply that a discontinuity will certainly occur if the temperature rises by about 6 °C, the lower ends imply that there is only about a 20% chance of a discontinuity for the same temperature rise27 (Table 1; ref. 15; box 1.4).
If the discontinuity occurs, the EU loses between 5 and 25% of its GDP (WDIS), and other regions lose more or less depending on their GDP per capita and weight factors. Again the range is wide because so few studies of discontinuities have been made; the lower figure is the value for a 10 m sea-level rise23, the upper figure is that assumed in ref. 28. The losses build up gradually with a mean characteristic lifetime of 90 years (DISTAU), and a range of 20–200 years, after the discontinuity is triggered. The shorter values for this lifetime are appropriate for discontinuities such as monsoon disruption and thermohaline circulation, with the longer values more appropriate to the loss of ice sheets27. PAGE09 assumes that only one discontinuity occurs, and if it occurs it is permanent.
Adaptation.
As the climate changes, there will be opportunities to adapt to the changes, either reactively, as the climate changes, or pro-actively, anticipating what future changes might occur. Supplementary Table 4 shows the default assumptions in PAGE09 about adaptation in the developed world regions (labelled EU) and the developing countries (labelled RoW).
Interpreting the values in the first row of the table, in the economic sector, adaptation means that the EU will eventually be able to tolerate a 1 °C rise in temperature (Plateau) with no impacts. It is assumed that this adaptation was started in 2000 (Pstart) and will take 20 years to take full effect (Pyears). If the temperature rises more than 1 °C, adaptation will not be fully effective, but will be able to reduce impacts by 30% (Impred); this type of adaptation starts in 2010 (Istart) and takes 20 years to reach its full effect (Iyears). It works only for the first 2 °C of temperature rise above the tolerable level (Impmax; this is 3 °C above pre-industrial); beyond that temperature rise adaptation is assumed to be ineffective.
From the second row in the table, in much of the non-economic sector, such as ecosystems, adaptation is harder, so there is no tolerable temperature rise, and the reduction in impacts is only 15%, starting in 2010 and taking 40 years to reach its full effect, which applies only for the first 2 °C of temperature rise above pre-industrial levels.
The third and fourth rows in the table reflect the common understanding that adaptation will be slower and less effective in developing countries, as they are poorer and more vulnerable.
The assumptions made here are consistent with the findings that: ‘the optimal level of adaptation varies from 0.13 to 0.34, with an average of 0.27, that is 27 percent of gross damages are reduced due to adaptation.’ (p15; ref. 29) and their table 2 showing residual damages of about 85% of damages without adaptation in 2030, and 72% in 2100 (ref. 29).
Ref. 30 finds that ‘much damage will not be adapted to over the longer term …the amount may be significant and is likely to increase over time’, but the only quantitative estimate is for agriculture, where residual impacts are estimated at about a fifth of all impacts in 2030, so that adaptation is 80% effective for this sector (p13; ref. 30).
The adaptation inputs are policy variables in PAGE09. They result from policy decisions and so are represented as single-choice values rather than probability distributions. These default assumptions in PAGE09 assume less adaptation than in earlier versions of the model, particularly in the economic sector, which was criticized for possibly being over-optimistic24.
Permafrost emissions.
Estimates of permafrost emissions were based on an ensemble of projections using the Simple Biosphere/Carnegie-Ames-Stanford Approach (SiBCASA) model for the A1B scenario7. Assuming a uniform spatial distribution of carbon frozen in permafrost, a series of projections was run from 1973 to 2200 driven by output from global climate models that ran the A1B scenario for the AR4 (ref. 7). The mean of the ensemble is the best estimate of permafrost carbon emissions and the ensemble standard deviation is the uncertainty (Fig. 1). To estimate methane emissions (Fig. 2), we assumed 2.3% of total carbon emissions will be CH4 (ref. 8). We estimated permafrost emissions for the low anthropogenic emissions scenario by scaling the fluxes from ref. 7 to the predicted global temperature increase assuming a linear increase in emissions with temperature and a ratio of Arctic to global warming of 1.622 based on the average of global climate simulations from AR4. We assume uncertainties in the thawing permafrost CO2 and CH4 emissions are perfectly correlated across gases and over time. The analysis assumes that the CO2 and CH4 from thawing permafrost have the same atmospheric residence pattern and radiative forcing effect as anthropogenic emissions. It also assumes the temperature rise from the permafrost CO2 and CH4 does not trigger additional CO2 or CH4 emissions that would not otherwise have occurred. This may result in an underestimation of the extra impacts. If permafrost releases respond linearly with respect to global mean temperature increase, the scale of the underestimate would be expected to be about the same as the proportional increase in global mean temperature in 2100, which is 0.29 ± 0.21 °C (ref. 2), or about 7.8 ± 5.7 %.