Transient climate response to cumulative carbon emissions
The transient climate response to cumulative carbon emissions (TCRE) is the ratio of the globally averaged surface temperature change per unit carbon dioxide (CO2) emitted. As emitted CO2 exhibits atmospheric lifetimes on millennial timescales, this response is conceived as the amount that global temperature changes per the amount of total carbon dioxide in the atmosphere. With respect to cumulative CO2 emissions over time, global temperature is reasonably estimated to change linearly regardless of the path taken to reach peak CO2 emissions. This means that for specific amount of cumulative CO2 emissions, a known global temperature change (within a range of uncertainty) can be expected, which indicates that holding global temperature change to below specific thresholds is a problem of limiting cumulative CO2 emissions, leading to the idea of a carbon budget.
The TCRE is calculated based on a formula for the ratio of temperature change to cumulative carbon emissions (measured as CO2), which is the net carbon remaining in the atmosphere after accounting for relevant sources and sinks. As a measure of atmospheric carbon change, the TCRE parameterizes climate sensitivity and carbon sensitivity to formulate a value that is the temperature change (°C) per trillion tonnes of carbon emitted (Tt C). This is represented via the following formula from Matthews et al., 2009:
- ΔT = average global temperature change (°C)
- ET = cumulative carbon dioxide emissions (Tt C)
- ΔCA = change in atmospheric carbon (Tt C)
and, 1Tt C = 3.7 Tt CO2
- RF = radiative forcing (W/m2) taken at the top of the atmosphere (TOA)
Here TCRE is used to assess the assumed linear effect radiative forcing has on temperature change in an historical analysis.
TCRE is modeled using climate models that simulate carbon emissions by increasing CO2 emissions by 1% per year from pre-industrial levels until the concentration of CO2 in the atmosphere is doubled (2 x CO2) or quadrupled (4 x CO2). Since these experiments all start from the same initial atmospheric concentration of CO2 (around 285 ppm), the doubling and quadrupling occur at 70 and 140 years respectively. Different modelling parameterizations of TCRE include: holding CO2 emissions constant after quadrupling; modelling net negative emissions after doubling or quadrupling; stopping emissions after doubling and continuing the model for up to 10,000 years; or running extended RCP scenarios and assessing temperature change per cumulative emissions at high CO2 concentrations.
Global temperature change is approximately linearly proportional to cumulative carbon emissions. This means that for a given amount of carbon emissions, a related amount of global warming can reasonably be expected. Model data synthesized by the IPCC Fifth Assessment Report from available studies suggests a likely TCRE of 0.8° to 2.5 °C per Tt C (or 1000 Pg C). In a TCRE focus review, Matthews et al. (2018) estimate TCRE as 0.8° to 2.4 °C per Tt C and suggest an observationally-constrained best estimate of 1.35 °C per Tt C.
Though the global average temperature response to cumulative emissions is approximately linear, this response is not uniform throughout the globe. Calculations by Leduc et al., (2016) of the geographical pattern of temperature response (the regional TCRE, or RTCRE) show values of low temperature change over equatorial and tropical ocean regions and high values of temperature change exceeding 4 °C/Tt C in the Arctic. Likewise, they show a pronounced temperature response difference between the land and ocean, which is largely the result of ocean heat cycling.
Regional precipitation response
Unlike the positive regional temperature response, regional precipitation change to cumulative emissions are positive or negative, depending on location. Partanen et al., (2017) show a strong positive precipitation response in the Arctic with negative responses (meaning reduced precipitation) in parts of Southern Africa, Australia, North and South America.
The observed and calculated linear TCRE and RTCRE leads to the notion of a carbon budget. A carbon budget is the cumulative amount of CO2, emitted anthropologically as a globe, that leads to a set limit of global warming. The IPCC estimates the CO2-only carbon budget (with a 50% chance) for staying below 2 °C at 1210 PgC (or 1.21 Tt C). Accounting for the 515 PgC of CO2 emitted between 1870 and 2011, this leaves a CO2-only carbon budget of 695 PgC, for a 50% chance of staying below a global average temperature change of 2 °C.
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