Transient climate response

Calculation

Formulas

The TCRE can be 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 how sensitive the climate is to carbon dioxide 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:

${\displaystyle TCRE=△T/E_T=(△T/△C_A)\times (△C_A/E_T)}$

where,

• ΔT = average global temperature change (°C)
• E_T = cumulative carbon dioxide emissions (Tt C)
• ΔC_A = change in atmospheric carbon (Tt C)

and, 1Tt C = 3.8 Tt CO₂

TCRE can also be defined not in terms of temperature response to emitted carbon, but in terms of temperature response to the change in radiative forcing:

${\displaystyle TCRE=△T/RF}$

where,

• 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.

Modeling

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.