The amount of climate change we should expect in the coming decades and centuries depends on how the climate will respond to continuing human activities and natural events (a scientific matter) and the extent of future greenhouse gas emissions (a matter of technological development, economic growth, and policy choices).
Recently, scientists have identified a convenient way to think about the connection between emissions and warming without relying upon competing assumptions about economic and technological trends. For as long as CO2 emissions continue, we can expect the average increase in temperature to be proportional to the total amount of CO2 released into the atmosphere since large scale emissions began in the 18th century.
The increase in surface temperature compared to the total amount of CO2 emitted since 1870, calculated with climate models. The black line shows averaged model results through 2005, where historical emissions are known. The blue, orange, red lines show different scenarios for CO2 emissions in the 21st century, (the Representative Concentration Pathways). Circles show the average temperature in each decade. The grey band shows the temperature evolution when only CO2 is increased in a model. Source: IPCC Assessment Report 5, Summary for Policymakers
Of course, because we cannot predict how society will evolve over the 21st century and beyond, we cannot forecast future emission levels with high confidence. Instead, scientists and energy experts have developed different scenarios for what CO2 concentrations and other human activities may be in the future—scenarios called Representative Concentration Pathways (RCPs)—reflecting different possible futures for human influence on the climate. In the highest emissions case (RCP8.5, shown by red line in figure 4) temperatures increase by an additional 2.6-4.8 °C by 2100, and continue to increase thereafter. In the lowest emissions case (RCP2.6, shown by dark blue line in figure 4) temperatures increase by 0.3-1.7 °C and do not rise much further thereafter.
Uncertainties regarding these projections still exist as demonstrated by the fairly wide range of temperature change projected by models for any amount of total emissions. The most important of which relate to what fraction of CO2 emissions accumulates in the atmosphere rather than being sequestered in plants, trees, soils, or the oceans (an issue known as airborne fraction), and the temperature increase that follows from increased CO2 concentrations in the atmosphere (an issue known as climate sensitivity). Both the airborne fraction and the climate sensitivity are important topics of continuing inquiry in climate research.[1] The public debate about climate projections, however, has focused almost entirely on the correct value of climate sensitivity.[2]
This presumed proportional relationship between temperature and total CO2 emissions implies that, to prevent warming over a threshold—for example the 2 °C goal adopted in the Paris Climate Accord—only a finite amount of CO2 can be emitted. That number is commonly referred to as the remaining carbon budget. Given the present range of estimates in warming projected by models, the Paris goal would require limiting total emissions to about 3700 GtCO2, more than half of which has already been emitted. Presently, global emissions from fossil fuels and deforestation are just about 40 GtCO2 per year, allowing for about 4 decades at today’s emissions levels. The presence of other human climate influences means that budget is probably more like three decades, if the standard estimates of climate sensitivity are correct.
The range of future warming exhibited by climate models approaches 2 °C for all of the emission scenarios considered by the IPCC and other groups. In low emissions scenarios, temperatures approach that level toward the end of the century. In high emissions scenarios, temperatures pass through 2 °C sometime in the middle to late 21st century. And insofar as the global surface temperature is an indicator of change in other parts of the climate system— e.g. changes in temperature extremes, global amounts of precipitation, and sea level rise—further changes should be expected in them as well.
See Question: Are climate models too sensitive?