5.9 What's the relationship between emission reduction targets, global carbon budgets and global temperature increase?

This depends on ‘climate sensitivity’, the time of peak emissions and the rate of decline thereafter. Because CO2 has a residence time of 100 years in the atmosphere, what matters is the total amount of carbon emitted.

The answer to ‘So how much warming is likely?’ (Section 5.6) gives some insight to the question here.

Current policy time horizons don't look beyond 2100, but a number of papers point to CO2 emitted by human activity influencing global climate for thousands of years. Once CO2 concentrations reach a particular point at any time from now on, even if emissions were then shut down completely the concentration would not reduce. Inertia in the climate system means that the CO2 concentration could stay at that level for hundreds of years at least.

Targets are an important way to communicate the complexity of a carbon budget. Even though they focus attention on a particular year (e.g. 50% by 2050), behind that lie calculations linking probable temperature ranges to concentrations of greenhouse gases in the atmosphere and the associated total emissions of greenhouse gases due to human activity. This gives a carbon budget. Like any budget, it can be profiled over the budget period to give the amount of carbon that can be released in any one year to remain within budget. If you overshoot in one year, then you have to find savings in subsequent years to get back within budget. For any plot of emissions over time (whether historical or projected) it is the area under the curve that represents the cumulative emissions (i.e. the carbon budget). This is the key number.

But there are limits to this financial analogy. One important difference is that early carbon savings are likely to be more valuable than emission reductions later in the budget period. This is because avoiding emissions sooner means that carbon doesn't get into the atmosphere where it remains for a long time with the potential to trigger positive feedbacks.

What matters most is the global carbon budget.

5.8 How do you compare different emission reduction targets and carbon budgets?

5.10 How do you work out a carbon budget?