Compendium

Climate Sensitivity and Feedbacks

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Climate Sensitivity and Feedbacks

Climate sensitivity is the single most consequential parameter in geophysics: how much does global surface temperature change for a given perturbation to Earth’s radiation budget? The dominant framing — equilibrium climate sensitivity (ECS) for doubled atmospheric CO2 — was operationalised by the Charney Committee in 1979 (“Carbon Dioxide and Climate: A Scientific Assessment”, National Research Council; chaired by Jule Charney) with the now-classic estimate of 3 °C ± 1.5 °C. Forty-five years later the answer has barely narrowed in headline range and yet has been transformed in its underlying confidence structure. IPCC AR6 (Forster-Storelvmo-Armour-Collins-Dufresne-Frame-Lunt-Mauritsen-Palmer-Watanabe-Wild-Zhang 2021, WG1 Ch 7) gave best estimate 3 °C, likely range 2.5–4 °C, very likely range 2–5 °C — substantially narrower than AR5 (Collins et al. 2013) 1.5–4.5 °C. The narrowing reflects independent constraints from process understanding, the instrumental record, and paleoclimate combining via Bayesian synthesis (Sherwood-Webb-Annan-Armour-Forster-Hargreaves-Hegerl-Klein-Marvel-Rohling-Watanabe-Andrews-Braconnot-Bretherton-Foster-Hausfather-vonderHeydt-Knutti-Mauritsen-Norris-Proistosescu-Rugenstein-Schmidt-Tokarska-Zelinka 2020, “An assessment of Earth’s climate sensitivity using multiple lines of evidence”, Reviews of Geophysics) — the WCRP-sponsored synthesis that anchors AR6. This note compiles the definitions, the feedback decomposition, the paleoclimate and instrumental constraints, the central role of cloud feedbacks and the pattern effect, and the recent (2023+) controversies around accelerating warming.

1. Definitions

1.1 Equilibrium Climate Sensitivity (ECS)

The equilibrium global mean surface temperature change for a doubling of atmospheric CO2 concentration once the entire climate system (atmosphere, ocean, sea ice) has equilibrated:

ECS = − F_2x / lambda

where F_2x is the effective radiative forcing for CO2 doubling (~3.7 W m-2 traditional, ~3.93 W m-2 in AR6 Smith 2020 update) and lambda is the climate feedback parameter (W m-2 K-1, negative for stabilising). Strictly, ECS in coupled models is approached over ~1 000–3 000 yr; in practice estimated from the Gregory-Ingram-Williams 2004 method (regression of TOA net radiation imbalance N versus temperature anomaly T in abrupt-4xCO2 experiments, intercept divided by 2 gives “effective ECS”). Effective ECS differs from true ECS (the latter incorporates slow ocean warming pattern feedback; Andrews-Webb 2018).

1.2 Transient Climate Response (TCR)

The global temperature change at the time of CO2 doubling under a 1 %/yr CO2 increase (~70-yr ramp). Captures the ocean-uptake-modulated transient response:

TCR ≈ F_2x / (lambda + kappa)

where kappa is the ocean-heat-uptake efficiency (~0.7 W m-2 K-1). IPCC AR6 TCR best estimate 1.8 °C, likely range 1.4–2.2 °C, very likely 1.2–2.4 °C.

1.3 Earth System Sensitivity (ESS)

Includes slow Earth-system feedbacks (ice-sheet retreat, vegetation shifts, methane release from permafrost, ocean carbon cycle response). Typically 1.3–2× ECS over centennial-to-millennial timescales (Knutti-Hegerl 2008; PALAEOSENS 2012 Nature). Paleoclimate combination of ESS and ECS depends on assumed slow-feedback contribution.

1.4 ZEC, TCRE

  • Zero Emissions Commitment (ZEC, MacDougall-Frölicher-Jones-Rogelj-Matthews-Zickfeld-Arora-Barrett-Brovkin-Burger-Eby-Eliseev-Hajima-Holden-Jeltsch-Thömmes-Koven-Mengis-Menviel-Michou-Mokhov-Oka-Schwinger-Séférian-Shaffer-Sokolov-Tachiiri-Tjiputra-Wiltshire-Ziehn 2020 Biogeosciences): temperature change after emissions cease; ~0 °C in most ESMs over decades.
  • Transient Climate Response to Cumulative Emissions (TCRE, Matthews-Gillett-Stott-Zickfeld 2009 Nature): K per TtC of cumulative carbon emitted. IPCC AR6 TCRE 0.27–0.63 °C per 1000 GtCO2 (very likely), 0.45 °C central — the basis of carbon budgets for 1.5 °C / 2 °C targets.

2. The feedback decomposition

In linearised feedback analysis the change in TOA net energy budget is:

N = F + lambda · T, lambda = sum_i lambda_i

For doubling, lambda · ECS = − F_2x. Standard feedback partition (Soden-Held 2006; Soden-Held-Colman-Shell-Kiehl-Shields 2008; AR6 Forster 2021):

Feedbacklambda_i (W m-2 K-1)Comment
Planck (blackbody)−3.20 ± 0.04Stefan-Boltzmann; warming radiates more
Water vapour+1.30 ± 0.12Constant RH assumption (Manabe-Wetherald 1967)
Lapse rate−0.50 ± 0.20Tropical amplified upper-tropospheric warming
WV+LR combined+0.85 ± 0.10Anti-correlated; combine cleanly (Held-Shell 2012)
Surface albedo (snow/ice)+0.35 ± 0.10Arctic + boreal snow
Cloud (total)+0.42 ± 0.35Dominant uncertainty (AR6 better constrained)
Cloud (SW component)+0.32 ± 0.30Tropical low cloud + extratropical SW
Cloud (LW component)+0.10 ± 0.10High-cloud, FAT
Net non-Planck+1.62 ± 0.40
Net total lambda−1.58 ± 0.40
Implied ECS3.0 K (1.9–5.5)F_2x = 3.93 W m-2

(AR6 Table 7.10; updated with Sherwood 2020 process-based estimates.)

2.1 Planck feedback

Stefan-Boltzmann thermal-radiation increase with surface warming, ~3.2 W m-2 K-1 globally. This is the irreducible baseline negative feedback that keeps Earth stable. If only Planck operated, ECS would be ~1.2 °C.

2.2 Water-vapour feedback

Saturation vapour pressure rises ~6.5 %/K (Clausius-Clapeyron). Under near-constant relative humidity (well supported in observations and models, Held-Soden 2000; Dessler 2010), specific humidity increases, amplifying greenhouse trapping particularly in upper troposphere where IR emission to space originates. WV feedback +1.3 to +2.0 W m-2 K-1, well constrained (Soden-Held 2006; Dessler-Sherwood 2009; Liu-Mauritsen 2020).

2.3 Lapse-rate feedback

Moist adiabat steepens less than dry adiabat with warming (latent-heat release aloft). Tropical upper-troposphere warms ~2× surface (“tropical amplification”, “hot spot”), increasing lapse rate (more uniform vertical T profile relative to surface), enhancing OLR per surface K → negative feedback (~−0.5 W m-2 K-1 globally). Anti-correlates with water-vapour feedback geographically; combined WV+LR ≈ +0.85 W m-2 K-1 with much less uncertainty than separately (Held-Shell 2012; Po-Chedley-Fu 2012).

2.4 Surface-albedo feedback

Snow and sea-ice loss exposes darker surfaces. Estimates: Hall-Qu 2006 used seasonal-cycle observed albedo response as constraint on NH snow feedback (~+0.30 W m-2 K-1 NH, ~+0.20 globally). Arctic-amplification is consequence rather than cause of sea-ice loss (Pithan-Mauritsen 2014 Nature Geosci).

2.5 Cloud feedback — the central uncertainty

Bony-Dufresne-LeTreut-Morcrette-Senior 2004 first showed that cloud feedback uncertainty dominates inter-model ECS spread in CMIP3. Andrews-Gregory-Webb 2012 confirmed for CMIP5; Zelinka-Myers-McCoy-Po-Chedley-Caldwell-Ceppi-Klein-Taylor 2020 (GRL) showed CMIP6 high-ECS models are driven by extratropical SW cloud feedback. Decomposition (Zelinka 2013 cloud-radiative kernels):

  • Tropical low cloud (subtropical Sc, stratocumulus over SE Pacific, SE Atlantic, off California, off Namibia): inversion-topped boundary-layer clouds. Sherwood-Bony-Dufresne 2014 (Nature) identified lower-tropospheric mixing index as emergent constraint; high-mixing models lose more low cloud, higher ECS. Cesana-DelGenio 2021 satellite analysis constrained tropical SW feedback +0.21 W m-2 K-1. Myers-Scott-Zelinka-Klein-Norris-Caldwell 2021 Nature Climate Change combined CALIPSO observations + LES to constrain low-cloud feedback +0.19 ± 0.12 W m-2 K-1.
  • Tropical high cloud (cirrus anvil): FAT (Fixed Anvil Temperature) hypothesis (Hartmann-Larson 2002) — anvil tops remain at constant temperature (~200 K) as troposphere warms, so anvil altitude rises, OLR from anvil unchanged → strong positive LW feedback ~+0.20 W m-2 K-1. Mixing of FAT with PHAT (Proportionately Higher Anvil Temperature, Zelinka-Hartmann 2010) refinement. Anvil-area changes possibly negative iris effect (Lindzen 2001 controversial).
  • Extratropical SW: mid-latitude oceanic cloud-cover and optical-thickness changes. CMIP6 high-sensitivity models (CESM2, UKESM, HadGEM3, CanESM5, E3SM) show strongly positive extratropical low-cloud feedback driven by treatment of mixed-phase clouds — supercooled liquid converts to ice less efficiently with warming, increasing reflective liquid (Tan-Storelvmo-Zelinka 2016 Science). Bock-Lauer-Schlund-Barreiro-Bellouin-Jones-Meehl-Predoi-Roberts-Eyring 2020 documented CMIP6 mean ECS jump to 3.7 °C from CMIP5 3.3 °C, largely traced to cloud-treatment changes. Subsequent observational constraints (Sherwood 2020) reduced the apparent ECS rise.
  • Mixed-phase cloud transition: as -38 to 0 °C clouds warm, fraction of liquid increases → higher albedo (Mitchell-Garnier 2017; Bjordal-Storelvmo-Alterskjær-Carlsen 2020).

2.6 Effective radiative forcing (ERF) and rapid adjustments

Bony-Colman-Kattsov-Allan-Bretherton-Dufresne-Hall-Hallegatte-Holland-Ingram-Randall-Soden-Tselioudis-Webb 2006 (J Climate) review distinguished “feedbacks” (T-mediated radiative responses) from “rapid adjustments” (atmospheric responses that occur before significant surface T change — e.g., stratospheric cooling adjusts ~3 mo). ERF (Sherwood-Bony-Boucher-Bretherton-Forster-Gregory-Stevens 2015) incorporates rapid adjustments into forcing, providing cleaner separation. AR6 adopts ERF as the standard forcing metric — F_2x_CO2 ERF ≈ 3.93 W m-2 (vs ~3.71 W m-2 instantaneous).

3. Paleoclimate constraints

3.1 Last Glacial Maximum (LGM, 21 ka)

LGM global mean cooling 4–7 °C below pre-industrial; CO2 ~190 ppm (−95 ppm forcing -2.0 W m-2); ice sheets + lower vegetation albedo (−3 W m-2); aerosols + lapse rate adjustments — net forcing ~−8.5 W m-2 (Annan-Hargreaves 2013 model-data assimilation, found cooling 4.0 °C). Tierney-Zhu-King-Malevich-Hakim-Poulsen 2020 (Nature) data-assimilation reconstruction found 6.1 °C cooling (5.7–6.5 °C 95 % CI), inferring ECS 3.4 °C (2.4–4.5 °C 95 %). PMIP3/PMIP4 model ensembles. Sherwood 2020 synthesis used LGM as one anchor.

3.2 Mid-Pliocene Warm Period (mPWP, 3.3–3.0 Ma)

CO2 ~400 ppm; global mean ~2–3 °C warmer than pre-industrial; sea level +10–20 m. PlioMIP / PlioMIP2 (Haywood-Hill-Dolan-Otto-Bliesner-Bragg-Chan-Chandler-Contoux-Dowsett-Jost-Kamae-Lohmann-Lunt-Abe-Ouchi-Pickering-Ramstein-Rosenbloom-Salzmann-Sohl-Stepanek-Ueda-Yan-Zhang 2013, 2020). Pliocene constrains ESS and equilibrium response at moderate CO2 — used as the “high-CO2 not too-high” anchor (Burton-Sippola-Foster-Lear-Burton-Edgar-Ridgwell-Foster 2023).

3.3 PETM (Paleocene-Eocene Thermal Maximum, 56 Ma)

~5 °C warming from massive carbon release (3 000–7 000 GtC); ECS estimated 3.5–6 °C (Zeebe-Ridgwell-Zachos 2016; Tierney 2022).

3.4 PALAEOSENS

PALAEOSENS-Project Members 2012 (Nature) synthesised paleoclimate ECS over Cenozoic — best estimate 2.2–4.8 °C; included Eocene-Oligocene boundary, Miocene, Pliocene, Pleistocene anchors.

4. Instrumental / energy-budget constraints

4.1 Method

ECS_inst = F · T_obs / (F − N)

where F is anthropogenic forcing since pre-industrial, T_obs is observed temperature change, N is current TOA imbalance (CERES + Argo). Otto-Otto-Boucher-Church-Hegerl-Forster-Gillett-Gregory-Johnson-Knutti-Lewis-Lohmann-Marotzke-Myhre-Shindell-Stevens-Allen 2013 (Nature Geosci) inferred ECS 2.0 °C (1.2–3.9 °C).

4.2 The “pattern effect”

Andrews-Gregory-Webb 2015; Stevens-Sherwood-Bony-Webb 2016; Andrews-Forster-Gregory-Andrews-Mauritsen 2018 (JGR); Andrews-Gregory-Paynter-Silvers-Zhou-Mauritsen-Webb-Armour-Forster-Titchner 2018: present-day SST warming pattern (relatively cold E Pacific + Southern Ocean, warm W Pacific warm-pool) drives anomalously high low-cloud cover and thus stronger negative feedback than equilibrium pattern — so observed lambda is more negative (less sensitive) than equilibrium lambda. Means energy-budget ECS estimates are biased low. Recent estimates:

  • Lewis-Curry 2018: ECS 1.5 (1.05–2.45) °C and TCR 1.20 (0.9–1.7) °C, low end.
  • Sherwood 2020 process-based: ECS 2.6–3.9 °C (66 % range), much higher.
  • Mauritsen-Bader-Becker-Behrens-Bittner-Brokopf-Brovkin-Claussen-Crueger-Esch-Fast-Fiedler-Fläschner-Gayler-Giorgetta-Goll-Haak-Hagemann-Hedemann-Hohenegger-Ilyina-Jahns-Jiménez-de-la-Cuesta-Jungclaus-Kleinen-Kloster-Kracher-Kinne-Kleberg-Lasslop-Kornblueh-Marotzke-Matei-Meraner-Mikolajewicz-Modali-Möbis-Müller-Nabel-Nam-Notz-Nyawira-Paulsen-Peters-Pincus-Pohlmann-Pongratz-Popp-Raddatz-Rast-Redler-Reick-Rohrschneider-Schemann-Schmidt-Schnur-Schulzweida-Six-Stein-Stemmler-Stevens-vonStorch-Tian-Voigt-Vrese-Wieners-Wilkenskjeld-Winkler-Roeckner 2019 (JAMES) MPI-ESM tuning + ECS targeting discussion.
  • Forster-Andrews-Good-Gregory-Jackson-Zelinka 2021 review.

The “pattern effect” magnitude is uncertain — Watanabe-Iwakiri-Dong-Mauritsen-Sherwood-Sun-Zhang 2024 (Nature) recent paper.

5. ML emulators and emergent constraints

5.1 Emergent constraints

Out-of-sample regression where ECS in models correlates with an observable. Used:

  • Hall-Qu 2006: NH snow-albedo seasonal-cycle constrains snow-albedo feedback.
  • Sherwood-Bony-Dufresne 2014: lower-tropospheric mixing constrains tropical cloud feedback.
  • Brient-Schneider 2016: tropical SW cloud variability constrains feedback.
  • Cox-Huntingford-Williamson 2018 Nature: global T variability emergent constraint on ECS (later critiqued by Po-Chedley-Proistosescu-Armour-Santer 2018, Brown-Stolpe-Caldeira 2018).
  • Caldwell-Bretherton-Zelinka-Klein-Santer-Sanderson 2018 review of EC pitfalls.

5.2 Machine learning emulators

  • Mansfield-Nowack-Kasoar-Everitt-Collins-Voulgarakis 2020 (Nature Comms): random forest + deep-learning emulator of ECS from CMIP outputs.
  • Eyring-Cox-Flato-Gleckler-Abramowitz-Caldwell-Collins-Gier-Hall-Hoffman-Hurtt-Jahn-Jones-Klein-Krasting-Kwiatkowski-Lorenz-Maloney-Meehl-Pendergrass-Pincus-Ruane-Russell-Sanderson-Santer-Sherwood-Simpson-Stouffer-Williamson 2019 (Nature Climate Change) “Taking climate model evaluation to the next level”.
  • Karpatne-Atluri-Faghmous-Steinbach-Banerjee-Ganguly-Shekhar-Samatova-Kumar 2017 climate informatics review.

5.3 Downscaling

GAN-based statistical downscaling (Stengel-Glaws-Hettinger-King 2020 PNAS); transformer architectures emerging (cross-ref ai-and-machine-learning-for-climate).

6. Non-CO2 and Earth-system feedbacks

6.1 Carbon-cycle feedbacks

  • Ocean acidification reduces buffering capacity; ocean sink efficiency declines from ~0.45 of emissions today (Friedlingstein 2023 Global Carbon Budget).
  • Tropical land carbon → carbon source under warming (Amazon dieback, Cox-Betts-Jones-Spall-Totterdell 2000 controversial).
  • Boreal soil decomposition speeds — Crowther-Todd-Carey-Maynard-Wang-Caldararu 2016 (Nature) found ~55 PgC release for 1 °C surface warming over 35 yr.

6.2 Permafrost

~1 460–1 600 PgC stored in northern circumpolar permafrost (Schuur-McGuire-Schädel-Grosse-Harden-Hayes-Hugelius-Koven-Kuhry-Lawrence-Natali-Olefeldt-Romanovsky-Schaefer-Turetsky-Treat-Vonk 2015 Nature). PCN (Permafrost Carbon Network) projections: ~150 PgC release by 2100 RCP 8.5 (Schaefer-Lantuit-Romanovsky-Schuur-Witt 2014). Methane fraction of release uncertain; abrupt thaw (thermokarst, taliks) accelerates (Turetsky 2020 Nature Geosci).

6.3 Wetland methane

Wetland CH4 emissions ~150–180 Tg yr-1 (Saunois 2020 Global Methane Budget). Increase under warming + precipitation changes — IPCC AR6 medium confidence in positive feedback.

6.4 Fire emissions

Wildfire C release ~2 PgC yr-1; CC + land-use intensification drive trends (van der Werf 2017 GFED). Pyrogenic carbon partly stable (charcoal).

6.5 BVOCs

Biogenic VOC emissions (isoprene, monoterpenes) increase with T and CO2; produce secondary organic aerosol (Carslaw-Boucher-Spracklen-Mann-Rae-Woodward-Kulmala 2010 ACP; Pacifico-Folberth-Sitch-Haywood-Rizzo-Malavelle-Artaxo 2015). Net forcing sign uncertain (cooling from SOA, warming from O3).

6.6 AMOC

Atlantic Meridional Overturning Circulation slowdown weakens northward heat transport; warming N Atlantic less than uniform. Caesar-Rahmstorf-Robinson-Feulner-Saba 2018 (Nature) and Boers 2021 (Nature Climate Change) found evidence of weakening + bistability indicators. Rahmstorf 2024 update. Collapse risk debated but Ditlevsen-Ditlevsen 2023 (Nature Comms) projected critical transition between 2025–2095. Slowdown shifts ITCZ southward, weakens monsoons.

6.7 Ice sheets

Multi-millennial response; West Antarctic + Greenland marine-terminating glaciers susceptible to marine ice-sheet instability (Joughin-Smith-Medley 2014). Slow Earth-system feedback — included in ESS, not ECS. DeConto-Pollard 2016 ice-cliff hypothesis controversial but increased Antarctic SLR projections.

7. Aerosol forcing and aerosol-cloud interactions

7.1 Aerosol direct effect

Scattering (sulfate, OC) cools; absorbing (BC) warms. AR6 aerosol direct ERF -0.22 ± 0.20 W m-2 (low confidence).

7.2 Twomey effect (first indirect)

Twomey 1977: at constant LWP, more CCN → more, smaller drops → higher cloud albedo.

7.3 Albrecht effect (second indirect)

Albrecht 1989: more CCN → less drizzle → longer-lived clouds → higher cover/LWP.

7.4 Total aerosol-cloud forcing

AR6 ERF aerosol-cloud -1.0 W m-2 (-1.7 to -0.3, low confidence) — major source of historical-record ECS estimate uncertainty. Stevens-Feingold 2009 (Nature) on the buffering of cloud systems against perturbations. Sorooshian-Nenes-Flagan-Seinfeld-Macfarquhar 2010 precipitation susceptibility.

7.5 GeoMIP

Geoengineering Model Intercomparison Project (Kravitz-Robock-Boucher-Schmidt-Taylor-Stenchikov-Schulz 2011 + ongoing) explores SAI, MCB, cirrus thinning radiative forcing (cross-ref solar-geoengineering-and-cdr).

8. CMIP6 ECS range and the “hot model” question

CMIP6 archive shows ECS range 1.83 °C (INM-CM4-8) to 5.65 °C (CanESM5) — wider than CMIP5 1.5–4.7 °C. Sherwood 2020 + Tokarska-Stolpe-Sippel-Fischer-Smith-Lehner-Knutti 2020 (Science Advances) showed high-ECS models warm too fast vs observations; recommended ECS-weighted multimodel mean. Hausfather-Marvel-Schmidt-Nielsen-Heede 2022 (Nature) called for screening “hot models” — IPCC AR6 already used assessed-range ECS (3 °C central) rather than raw CMIP6 mean (3.74 °C).

9. Recent developments (2023–2024)

9.1 2023–24 record warming

2023 was warmest year on record (+1.46 °C above 1850–1900 mean, Copernicus C3S Jan 2024); 12-month running mean exceeded 1.5 °C Feb 2023 – Jan 2024. Surprise magnitude — possible contributions: solar maximum, Hunga Tonga 2022 stratospheric water vapour, IMO 2020 shipping fuel sulfur regulations reducing N Atlantic + N Pacific cooling aerosol forcing (Schmidt 2023 commentary; Diamond-Wood 2024 GRL). Hansen-Kharecha-Sato-vonSchuckmann-Carlson-Cazenave-Cescatti-Cuevas-Domingues-Forster-Foster-Goyal-Hakkinen-Hamlington-Hausfather-Hicks-Karim-Khazendar-Kondrashov-Lee-Loeb-Magnani-Mauritsen-Nivet-OConnell-Pesnell-Quesada-Rahmstorf-Rye-Sato-Stuhne-Sun-Tselioudis-Velicogna-vonderHeydt-vonHeydt-vonStorch-Wieczorek-Williams-Willis-Zhao 2023 (“Global warming in the pipeline”, Oxford Open Climate Change): controversially raised ECS to 4.8 °C (3.6–6 °C) based on paleo + interpreting recent warming as evidence of higher sensitivity; widely disputed (Schmidt 2023 commentary).

9.2 Committed warming and net-zero

Hausfather-Forster 2023: committed warming from existing GHGs is consistent with stabilising at current levels when emissions reach net zero (ZEC ≈ 0). Distinguishes from earlier framing of large “warming in the pipeline”.

9.3 AR6 narrowing — significance

The Sherwood 2020 + AR6 narrowing from 1.5–4.5 °C to 2.5–4 °C eliminates the long tail of low sensitivity but extends the high-end concern; reflects independent corroboration across paleo, process, and instrumental lines.

9.4 Forster-Smith-Gulev-Jenkins-Cain-MacDougall-Allen-Andrews-Betts-Boyer-Bradshaw-Cheng-Collins-Cowtan-Dennig-Doutriaux-Hall-Hartmann-Hawkins-Hodnebrog-Hong-vonKlein-Knutti-Lawrence-Loeb-Marotzke-Meinshausen-Myhre-Norris-OGorman-Rohling-Rohrschneider-Sallée-Schmidt-Sherwood-Smith-Stevens-Tett-Trewin-vonSchuckmann-Wild 2024 (“Indicators of Global Climate Change 2023”) annual update tracking forcing, warming, and remaining carbon budgets

10. Implications

  • ECS likely 2.5–4 °C means 2× CO2 from pre-industrial (560 ppm; reached ~2070 on current emissions) produces 2.5–4 °C warming. Currently ~423 ppm in 2024 + non-CO2 GHGs → effective CO2-eq ~525 ppm.
  • 1.5 °C carbon budget (50 % probability): ~250 GtCO2 from 2024 (Forster 2024 update); at ~40 GtCO2 yr-1 emissions, exhausted by ~2030.
  • 2 °C carbon budget (67 % probability): ~900 GtCO2 from 2024.
  • Higher pattern-effect-corrected ECS implies less time / more aggressive mitigation needed.

11. Forcing inventory

11.1 IPCC AR6 ERFs (1750–2019, central + 90 % CI, W m-2)

AgentERF (W m-2)Confidence
CO2+2.16 (1.90 to 2.41)High
CH4+0.54 (0.43 to 0.65)High
N2O+0.21 (0.18 to 0.24)High
Halogens (CFCs, HCFCs, HFCs)+0.41 (0.33 to 0.49)High
Tropospheric O3+0.47 (0.24 to 0.71)Medium
Stratospheric O3−0.02 (−0.15 to 0.11)Medium
Stratospheric H2O from CH4+0.05 (0.00 to 0.10)Medium
Land use (albedo + irrigation)−0.20 (−0.30 to −0.10)Medium
Aerosol-radiation−0.22 (−0.47 to +0.04)Medium
Aerosol-cloud−0.84 (−1.45 to −0.25)Low
Surface BC on snow+0.08 (0 to 0.18)Low
Contrails + aviation cirrus+0.06 (0.02 to 0.11)Low
Solar irradiance+0.01 (−0.06 to +0.08)Medium
Volcanic stratospheric aerosol~0 (highly variable)High
Total anthropogenic ERF+2.72 (1.96 to 3.48)Medium

11.2 Pre-industrial baseline

1750 reference, but pre-industrial era extends to ~1850 for temperature baselines (1850–1900 average). CMIP6 piControl runs equilibrium pre-industrial state.

11.3 Volcanic forcing

Major eruptions reduce ERF temporarily: Pinatubo 1991 ~−3 W m-2 peak; Tambora 1815 ~−5 W m-2; Krakatoa 1883 ~−2 W m-2. Hunga Tonga-Hunga Ha’apai Jan 2022 was unusual — small SO2 (~0.4 Tg) but massive stratospheric water vapour injection (~150 Tg), giving small NET warming forcing ~+0.012 W m-2 (Jenkins-Smith-Allen-Grainger 2023 J Climate; Zhu-Bardeen-Tilmes-Mills-Wang-Harvey-Taha-Kinnison-Portmann-Yu-Rosenlof-Avery-Kloss-Li-Glanville-Millán-Deshler-Krotkov-Toon 2022 Comms Earth Env).

12. Hierarchy of climate models

12.1 Energy balance models (EBMs)

Budyko 1969 + Sellers 1969 zero-dimensional + one-dimensional latitudinal EBMs; first quantitative ice-albedo feedback investigations.

12.2 Radiative-convective equilibrium (RCE)

Manabe-Wetherald 1967 1-D vertical column with prescribed lapse rate; landmark first ECS estimate at 2 °C for CO2 doubling. Modern RCE: Held 2014 review; CRMs (cloud-resolving models) under doubled CO2.

12.3 Earth System Models of Intermediate Complexity (EMICs)

UVic, CLIMBER-2 (Brovkin), GENIE-1, Bern2.5D. Used for paleoclimate + long timescale.

12.4 Coupled Atmosphere-Ocean GCMs

CMIP6 generation: ~50 modelling centres. Resolution typically 1° atmosphere + 1° ocean; high-res tier 0.25° + 0.1° ocean (HighResMIP, Haarsma-Roberts-Vidale-Senior-Bellucci-Bao-Chang-Corti-Fuckar-Guemas-vonHardenberg-Hazeleger-Kodama-Koenigk-Leung-Lu-Luo-Mao-Mizielinski-Mizuta-Nobre-Satoh-Scoccimarro-Semmler-Small-vonStorch 2016).

12.5 ESMs (Earth System Models)

CMIP6 ESMs add interactive carbon + nitrogen cycles, vegetation, atmospheric chemistry. CESM2, GFDL-ESM4, UKESM1, MPI-ESM1.2, NorESM2, ACCESS-ESM1.5, EC-Earth3, IPSL-CM6A-LR, CanESM5, CNRM-ESM2, E3SM, CESM2-WACCM (chem-climate).

12.6 Cloud-resolving + LES

Global storm-resolving models (GSRMs) at ~3 km resolution emerging: ICON-LEM, NICAM, X-SHiELD, IFS-FVM, MPAS-A. DYAMOND project (Stevens 2019 PEPS) intercomparison.

ML emulators (NeuralGCM, GraphCast, Pangu-Weather): cross-ref ai-and-machine-learning-for-climate.

13. Detection and attribution

13.1 Detection

Demonstrating that observed change is unlikely to be due to natural variability alone. Optimal fingerprinting (Hasselmann 1979, 1997; Allen-Stott 2003) projects observations onto model-derived response patterns.

13.2 Attribution

Apportioning the detected change among multiple forcings (GHG, aerosol, natural). Stott 2003 (Geophys Res Lett) attributed >50 % of late 20th C warming to GHG; AR6 strengthened: virtually all observed warming since 1850 is human-caused, with central estimate human contribution +1.07 °C (likely range 0.8 to 1.3 °C) vs observed +1.07 °C.

13.3 Hindcast evaluation

Hausfather-Drake-Abbott-Schmidt 2020 (GRL) evaluated 1970s–2007 climate-model projections of global temperature against observations; 14 of 17 projections within observational uncertainty.

14. Geographical patterns

14.1 Arctic amplification

NH high-latitude warming 2–4× global mean. Mechanisms (Pithan-Mauritsen 2014; Stuecker-Bitz-Armour-Proistosescu-Kang-Xie-Kim-McGregor-Zhang-Zhao-Cai-Dong-Jin 2018 Nature Climate Change): surface albedo (sea ice), Planck (cold base, weaker), lapse rate (positive Arctic, T-inversion → warming aloft is less than surface), enhanced ocean heat transport, atmospheric energy convergence.

14.2 Antarctic delayed warming

Surface temperature in Southern Ocean has cooled or warmed less than expected — “Southern Ocean cooling enigma” (Armour-Marshall-Scott-Donohoe-Newsom 2016 Nature Geosci). Mechanism: deep mixing of heat downward + N transport from sea ice.

14.3 Tropical amplification aloft

Upper-tropospheric tropical warming ~2× surface (moist adiabatic). Observed signal weaker than models predicted (“tropical hot spot” debate); Mitchell-Lo-Seviour-Haimberger-Polvani 2020 found observations now consistent with models after reanalysis corrections.

14.4 Land-sea contrast

Land warms ~1.4× ocean due to lower thermal inertia + soil-moisture feedback (Sutton-Dong-Gregory 2007).

15. Carbon-cycle feedback quantified

C4MIP (Coupled Climate-Carbon Cycle Model Intercomparison, Friedlingstein-Cox-Betts-Bopp-vonBloh-Brovkin-Cadule-Doney-Eby-Fung-Bala-John-Jones-Joos-Kato-Kawamiya-Knorr-Lindsay-Matthews-Raddatz-Rayner-Reick-Roeckner-Schnitzler-Schnur-Strassmann-Weaver-Yoshikawa-Zeng 2006). AR6 carbon-cycle feedback parameters:

  • beta = sensitivity of land + ocean C uptake to atmospheric CO2 (positive, takes more C as CO2 rises).
  • gamma = sensitivity to temperature (negative; warming reduces uptake).

CMIP6 gamma_land ~−45 GtC K-1; gamma_ocean ~−17 GtC K-1.

16. Specific feedback observations

16.1 CERES observations

Clouds and Earth’s Radiant Energy System (CERES) instruments on Terra (1999+), Aqua (2002+), Suomi NPP (2011+), NOAA-20 (2017+), NOAA-21 (2022+). Edition 4 EBAF (Energy Balanced and Filled, Loeb-Doelling-Wang-Su-Thorsen-Smith-Kato 2018 J Climate) ties TOA to surface energy. Provides observed dTOA / dT for direct feedback estimation. Loeb-Wang-Allan-Andrews-Armour-Bellucci-Doelling-Forster-Frenger-Frölicher-Gettelman-Goyal-Lyman-Mauritsen-Newsom-Olonscheck-Rabbette-Stevens-Stuecker-Trenberth-Wing-Wong-Zhang-Zhao 2021 (J Climate) “Toward a consistent definition between satellite and model clear-sky radiative fluxes”.

16.2 OLR and ASR partitioning

Outgoing Longwave Radiation: cloud LW, water-vapour LW, lapse-rate LW, surface LW, GHG LW. Absorbed Shortwave Radiation: cloud SW, surface albedo SW, gas absorption SW.

16.3 Cloud feedback observational constraints

  • Norris-Allen-Evan-Zelinka-O’Dell-Klein 2016 Nature: observed cloud cover decreased in midlatitudes consistent with model-projected positive feedback.
  • McCoy-Hartmann-Zelinka-Ceppi-Grosvenor 2015 high-resolution observation of mid-latitude oceanic cloud optical depth + LWP.
  • Ceppi-Brient-Zelinka-Hartmann 2017 WIREs Climate Change cloud-feedback review.

16.4 PALEOSENS multi-temporal

Köhler-vanderHeydt-PALAEOSENS 2015 (Clim Past) found state-dependent ECS — sensitivity rises 25 % for warmer baselines. AR6 acknowledged ECS may depend on background state (not strict linearity).

17. ECS in the political conversation

ECS lies at the heart of carbon-budget calculations driving NDCs + net-zero pathways. The narrowing of ECS likely range from AR5 (1.5–4.5 °C) to AR6 (2.5–4 °C) ruled out very-low-sensitivity reassurance and tightened the urgency. Higher ECS in AR6 implies:

18. Outlook

  • AR7 WG1 (due 2028) will narrow ECS further; pattern-effect physics + improved cloud constraints likely.
  • Hyper-resolution climate models (k-scale) operational late 2020s — DYAMOND + EERIE.
  • Solar geoengineering modelling (cross-ref solar-geoengineering-and-cdr) increasingly integrated.
  • ML emulators reducing time-to-attribution.
  • Process understanding of pattern effect + Southern Ocean dynamics priority.

19. Climate sensitivity timeline

  • 1896: Arrhenius “On the influence of carbonic acid in the air upon the temperature of the ground” (Phil Mag) — first quantitative ECS at 5–6 °C (used overestimated CO2 absorption).
  • 1938: Callendar “The artificial production of carbon dioxide and its influence on temperature” Q J R Meteorol Soc — linked fossil-fuel CO2 to observed warming.
  • 1956: Plass “The carbon dioxide theory of climatic change” Tellus.
  • 1967: Manabe-Wetherald J Atmos Sci — 1D radiative-convective ECS 2.4 °C.
  • 1975: Manabe-Wetherald 3D GCM ECS 2.93 °C.
  • 1979: Charney Report ECS 1.5–4.5 °C (NRC US National Academy of Sciences).
  • 1990: IPCC FAR same range.
  • 1995: SAR same range.
  • 2001: TAR same range.
  • 2007: AR4 ECS 2–4.5 °C likely, best 3 °C.
  • 2013: AR5 ECS 1.5–4.5 °C likely, no best estimate.
  • 2020: Sherwood et al. ECS 2.6–3.9 °C likely (66 %).
  • 2021: AR6 ECS 2.5–4 °C likely, best 3 °C, very likely 2–5 °C.

Adjacent

Graph View