In an article published in Policy Options before Canada’s federal election, I described future greenhouse gas emissions pathways that would give Canada a chance of doing its fair share to avoid different levels of global warming (see figure). This post explains the methods used in that analysis. A second post answers frequently asked questions about the analysis.

For this work, I developed a range of future greenhouse gas emissions trajectories for Canada that are consistent with the proposed different temperature limits. The analysis follows from the commonly used “cumulative emissions” framework. The cumulative CO₂ emissions over time can roughly predict the amount of long-term warming of the climate system.

Cumulative remaining CO₂ budgets consistent with a likely (67%) chance of avoiding 1.5°C of warming are available in Chapter 2 of the Intergovernmental Panel on Climate Change’s Special Report on Global Warming of 1.5°C (Table 2.2). In order to conservative, I used the values for the upper end of the uncertainty range. The remaining carbon budget for 3°C and 4°C were computed using the relationship between remaining carbon budget and mean temperature change in Table 2.2 (for the upper end of the uncertainty range: remaining budget = [1500 *Warming level] – 1680).

Calculating Canada’s portion of the remaining budget

The next step was to apportion some of that remaining carbon budget to Canada. I calculated the remaining budget for Canada based on Canada’s current fraction of the world’s population (0.49%, based on latest available data from Statistics Canada and the CIA World Factbook). An alternative approach would have been to apportion the budget based on Canada’s fraction of the world’s emissions (1.59%, based on most recent five-year average of CO₂-only emissions from the Global Carbon Project). See an earlier analysis and article in Policy Options for a comparison of these approaches.

Why use the population approach here? Two reasons – one ethical, and one practical. A core principle of international climate agreements is that the developed world, which is historically more responsible for greenhouse gas emissions, should take the lead in reducing emissions. This is the principle of “common but differentiated responsibilities.” Second, even if you reject the above principle, an equitable distribution may be the only one that works.  As I mention in the Policy Options piece, if high-emitting countries like Canada claim a portion of the carbon budget based on their current emissions, rather than their population, there will be little space for the developing world. It is not a tenable approach to staying within the budget. This is a collective action problem: sure, countries like Canada could argue we need a greater slice of the pie in order to sustain our economy, but if we do so, the world is unlikely to stay within the budget.

The IPCC budget values were computed for January 1, 2018 onwards. Since emissions data is not yet available for 2018 and 2019, I estimated the remaining budgets for Canada assuming CO₂ emissions in 2018 and 2019 were the same as 2017, the most recent year with data currently available (Canada’s 2017 National Inventory Report). Values excluding emissions from land use, land use change, and forestry were used, following convention in federal government calculation of the future emissions targets and in national reports to the United Nations.

Calculating the future emission trajectories

I calculated the future emissions trajectories using logistic or S-shaped curves, as in the previous report (pdf) and in most research on future emissions trajectories over the past decade. Multiple possible trajectories consistent with each emissions budget were created by varying the year that emissions begin to decline (lag of 0-10 years) and varying the parameter t₀ in the logistic equation below (from 2050 to 2190, with increments of 20 years).

With each set of assumptions, the equation was solved iteratively for k such that the cumulative emissions by year were equal to the available budget. This method created up to 36 possible trajectories for each temperature limit. The number of compatible trajectories is higher for higher temperature limits (1.5°C – 14 trajectories, 2°C – 21 trajectories, 3°C – 30 trajectories, 4°C – 36 trajectories) because of the greater possible time lags and later midpoints.

The final step was scaling the CO₂ emissions trajectories to trajectories for all greenhouse gas emissions (i.e., CO₂-equivalent, including methane and other gases) so that the results are comparable to Canada’s emissions targets and federal policy proposals – all of which focus on total greenhouse gas emissions or CO₂e. I scaled each of the trajectories from CO₂-only to CO₂-equivalent by assuming that CO₂ emissions will continue to represent 79.8% of all Canada’s greenhouse gas emissions, the value for 2017.

The assumption is reasonable given that CO₂ has represented a consistent fraction (79.0%-80.6%) of total Canadian greenhouse gas emissions since 2005, Canada’s baseline for policy. It is important to note that this simple linear scaling comes with caveats: it ignores the effect of the different residence time of gases like methane and of likely future reduction in aerosol cooling on the size of the remaining greenhouse gas budget (see SR1.5, Chapter 2, Section 2.2.2.2).

Finally, the figure shown above and that appears in Policy Options presents the 5^th to 95^th percentile range from the computed greenhouse gas emissions trajectories (in CO₂e) for each of the temperature limits.

Up next: Frequently Asked Questions on Canada’s remaining carbon budget