Transient climate response

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:

$TCRE\; =\; \backslash bigtriangleup\; T/E\_T\; =\; (\backslash bigtriangleup\; T/\backslash bigtriangleup\; C\_A)\backslash times(\backslash bigtriangleup\; C\_A/E\_T)$

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 = 3.7 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:{{Cite journal|last1=Myhre|first1=Gunnar|last2=Boucher|first2=Olivier|last3=Bréon|first3=François-Marie|last4=Forster|first4=Piers|last5=Shindell|first5=Drew|date=March 2015|title=Declining uncertainty in transient climate response as CO2 forcing dominates future climate change|journal=Nature Geoscience|volume=8|issue=3|pages=181–185|doi=10.1038/ngeo2371|issn=1752-0908|url=http://eprints.whiterose.ac.uk/85097/1/14970_3_merged_1421254578.pdf}}

$TCRE\; =\; \backslash bigtriangleup\; T/\; RF$

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.

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).{{Cite journal|last1=Williams|first1=Richard G.|last2=Goodwin|first2=Philip|last3=Roussenov|first3=Vassil M.|last4=Bopp|first4=Laurent|date=2016|title=A framework to understand the transient climate response to emissions|journal=Environmental Research Letters|volume=11|issue=1|pages=015003|doi=10.1088/1748-9326/11/1/015003|issn=1748-9326|doi-access=free}} Since these experiments all start from the same initial atmospheric concentration of CO₂ (around 285 ppm{{Cite journal|last1=Gillett|first1=Nathan P.|last2=Arora|first2=Vivek K.|last3=Matthews|first3=Damon|last4=Allen|first4=Myles R.|date=2013-09-09|title=Constraining the Ratio of Global Warming to Cumulative CO2Emissions Using CMIP5 Simulations*|journal=Journal of Climate|volume=26|issue=18|pages=6844–6858|doi=10.1175/jcli-d-12-00476.1|s2cid=129808331 }}), 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;{{Cite journal|last1=Frölicher|first1=Thomas L.|last2=Paynter|first2=David J.|date=2015|title=Extending the relationship between global warming and cumulative carbon emissions to multi-millennial timescales|journal=Environmental Research Letters|volume=10|issue=7|pages=075002|doi=10.1088/1748-9326/10/7/075002|issn=1748-9326|doi-access=free|hdl=20.500.11850/108132|hdl-access=free}} 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.{{Cite journal|last1=Frame|first1=David J.|last2=Macey|first2=Adrian H.|last3=Allen|first3=Myles R.|date=2014-09-21|title=Cumulative emissions and climate policy|journal=Nature Geoscience|volume=7|issue=10|pages=692–693|doi=10.1038/ngeo2254}} The IPCC Sixth Assessment Report, which is the most thorough estimate as of 2021, suggests a likely TCRE of 1.4 °C–2.2 °C per Tt C (or 1000 Pg C), a narrowing of the 0.8° to 2.5 °C per Tt C range estimated by the IPCC in 2013.

Though the global average temperature response to cumulative emissions is approximately linear, this response is not uniform throughout the globe.{{Cite journal|last1=Partanen|first1=Antti-Ilari|last2=Leduc|first2=Martin|last3=Matthews|first3=H. Damon|date=2017|title=Seasonal climate change patterns due to cumulative CO 2 emissions|journal=Environmental Research Letters|volume=12|issue=7|pages=075002|doi=10.1088/1748-9326/aa6eb0|issn=1748-9326|doi-access=free}} 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 because the ocean absorbs much of the heat.{{Cite journal|last1=Bryan|first1=K.|last2=Komro|first2=F.G.|last3=Manabe|first3=S.|last4=Spelman|first4=M.J.|date=January 1, 1982|title=Transient climate response to increasing atmospheric carbon dioxide|journal=Science|volume=215|issue=4528|pages=56–58|doi=10.1126/science.215.4528.56|pmid=17790468|s2cid=10552825 }}

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.

{{main|Carbon budget}}

The observed and calculated linear TCRE leads to the notion of a carbon budget.{{Cite journal|author1-link=Joeri Rogelj|last1=Rogelj|first1=Joeri|last2=Forster|first2=Piers M.|last3=Kriegler|first3=Elmar|last4=Smith|first4=Christopher J.|last5=Séférian|first5=Roland|date=2019-07-18|title=Estimating and tracking the remaining carbon budget for stringent climate targets|journal=Nature|language=en|volume=571|issue=7765|pages=335–342|doi=10.1038/s41586-019-1368-z|pmid=31316194 |s2cid=197542084 |issn=0028-0836|doi-access=free|hdl=10044/1/78011|hdl-access=free}} A carbon budget is “the maximum amount of cumulative net global anthropogenic carbon dioxide (CO₂) emissions that would result in limiting global warming to a given level with a given probability, taking into account the effect of other anthropogenic climate forcers”.

{{Portal|Global warming|Environment}}

• Climate sensitivity
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Category:Climatology

Category:Carbon emissions