Global Warming Has Accelerated - Hansen 0125.pdf
Hansen et al. make the case that the IPCC's 3°C central estimate of (ECS) climate sensitivity (warming per doubling of CO2 level) is an underestimate, that it should be 4.5°C or higher. The mistake comes from 1) an underestimate of particulate (sulfate) pollution, which has been failed to be measured by satellites, and 2) an underestimate of cloud effects.
In particular, climate sensitivities of 4.5 and 6.0°C better match the patterns in the observational data, including considerable warming in 2023 and 2024, especially when tied to the reduction in sulfates from ships, which is pronounced in open ocean areas that had so little other sulfate pollution, thanks to the rules promulgated by international shipping organization starting in 2020.
Climate Sensitivity - Where the Numbers Come from - Vorang 0626.rtf available here and excerpted at length below.
Figure 1. Global mean surface temperature versus atmospheric CO2 across 66 million years of paleoclimate data, the modern instrumental record, and the SSP2-4,5 projection through 2100. The 5 paleoclimate regression fits (Clark, Snyder, EPICA York, Judd, EPICA OLS) cluster in the 8.2-9.9 K per doubling range - the AESS tier. Snyder (2016) is the high-side fit at 9.9; the AESS band quoted in the text and in Figure 2 (8.2-9.1) excludes it as an outlier and is taken from the other 4 regressions. The modern instrumental record sits in a distinct lower tier: the 1850-2025 OLS fit gives 2.37 K per doubling; the 1975-2025 fit gives 2.93 K per doubling. The 2 tiers are separated by an unfilled gap that the 4-tier framework predicts - the transient response sits well below the equilibrium response, and the gap closes as forcing accumulates and slow feedbacks express. Data sources: Bereiter et al. 2015, Berkeley Earth, Judd et al. 2024, Snyder 2016, Clark et al. 2024, Meinshausen et al. 2020 (CMIP6/AR6 SSP2-4.5).
Figure 2. The climate system’s response to abrupt CO2 doubling, plotted as temperature anomaly versus time (log scale). The blue curve is an illustrative 3-component response model, tuned to pass through TCR ~ 1.8°C at year 70, ECS ~ 3.0°C at centuries, and ESS ~ 6°C at millennia. 2 empirical bands flank the curve; the AESS band at the top (8.2-9.1°C, from 4 paleoclimate regressions) and the modern record band at the bottom (2.37-2.93 K per doubling, from OLS fits to the 1850-2025 and 1975-2025 instrumental records shown in Figure 1). The Planck no-feedback response at 1.2°C is shown as a dashed reference. Background shading marks the timescales over which different categories of feedbacks operate. ECS is shown at the AR6 assessed central estimate of 3.0°C; the Appendix walks through how a single-stream feedback calculation gives 3.4°C, and why the 4-stream assessed value is lower. Adapted from PALAEOSENS Project 2012 and National Academies 2016.
Two quantities in climate sensitivity come closest to falling out of pencil-and-paper physics.
1) The radiative forcing from doubled CO2 (~3.7 W/m²). This is calculated from line-by-line radiative transfer through a known atmospheric profile. Not pencil-and-paper exactly — the calculation needs computational integration across thousands of spectral lines — but anchored to spectroscopy measured in the laboratory for more than a century. The Tyndall-Foote tradition, continued. The current best estimate has roughly 10% uncertainty, depending on the assumed atmospheric water vapor profile and other inputs.
2) The Planck response (~1.2°C). What the surface would warm by if the atmosphere had no feedbacks at all — only the adjustment of outgoing thermal radiation as the surface heats up. Derivable in closed form from Stefan-Boltzmann equation (a warm body radiates more), with one caveat: the exact value depends on what you hold constant. The conventional value is 1.2°C per doubled CO2.
These two quantities together account for roughly 10% of the predicted long-term warming. They are the most analytically transparent values in climate science. Everything else — the path from 1.2°C to roughly 3°C, and from 3°C to roughly 8°C — comes from feedbacks expressing on different timescales. Each feedback amplifies or dampens the initial response. Their combined effect, and the time over which they express, is what produces the four sensitivity metrics.
The four sensitivity quantities are defined by what experiment is performed and when the temperature is read.
TCR (Transient Climate Response, ~1.4–2.2°C). The experiment: increase CO2 at 1% per year until it doubles (year 70), then read the average temperature for years 61–80. TCR captures water vapor feedback, lapse rate feedback, the part of cloud feedback that has expressed in 70 years, and the modest sea-ice retreat that fits in that interval. The deep ocean has barely begun to warm. Slow feedbacks (ice sheets, vegetation) have not started.
ECS (Equilibrium Climate Sensitivity, AR6 likely range 2.5–4.0°C, central estimate ~3.0°C). The experiment: hold CO2 at 2× preindustrial and wait until the system stops adjusting. In practice, models quadruple CO2, run for 150–300 years, and extrapolate to equilibrium. ECS includes everything in TCR plus full cloud feedback, full sea-ice response, and the deep ocean’s slow warming. It still excludes ice sheets, vegetation, and the slow carbon cycle by definition.
ESS (Earth System Sensitivity, ~5–8°C). The experiment: hold CO2 at 2× preindustrial and wait longer — millennia. Now ice sheets retreat, boreal forests march north, soil and vegetation reorganize, and ocean carbonate chemistry adjusts. All of this further amplifies warming. ESS is harder to estimate than ECS, because the experiment is harder to model. Coupled ice-sheet and dynamic-vegetation models are newer and less well-validated than the atmosphere-ocean models used for ECS.
AESS (Apparent Earth System Sensitivity, ~8–9°C). The experiment: don’t run a model at all. Plot atmospheric CO2 against global temperature for the available paleoclimate data and measure the slope. This is the equilibrium relationship visible in Figure 1, traced out over millions of years across multiple independent archives. The word apparent is doing work: the slope is what is observed, not a clean separation of CO2’s response from everything else that was changing over geological time. For the question of where the system is likely to land if a CO2 level is sustained for many millennia, AESS is the most directly observational quantity available.
The gap between ESS (~5–8°C) and AESS (~8–9°C) is real and worth naming. ESS as computed by Earth System Models captures the slow feedbacks that current models include: ice sheets, vegetation reorganization, ocean carbonate chemistry on millennial timescales. AESS captures everything that actually happened in the paleoclimate record, which includes processes operating over 100s of 1,000s of years — silicate weathering (the geological CO2 thermostat, atmospheric CO2 reacting with rocks to form carbonate minerals), full reorganization of vegetation and soil carbon pools, polar amplification effects that strengthen in sustained warm states, and state-dependent feedbacks where sensitivity itself rises in warmer climates (Anagnostou et al. 2016, Cael et al. 2026). The gap is the part of the long-term response that the modeled ESS does not yet fully capture. The reason to use AESS for paleoclimate questions is that the record measured all of it directly, regardless of whether models can yet reproduce the underlying mechanisms.
The four metrics are not four different theories of climate. They are four moments in the same response. Figure 2 shows this directly: a single curve of temperature versus time after CO2 doubling, with TCR at year ~70, ECS at centuries, ESS at millennia, and AESS as the empirical band from paleoclimate.
The shape of the curve — fast initial response, "plateau", then a second rise as slow feedbacks express — is what every climate model produces. The disagreements in the field are about the height of the plateau (the value of ECS) and the timing and magnitude of the second rise (the values and onset times of slow feedbacks). The disagreements are not about whether the structure exists.
The bands in Figure 2 are data. The top band is what 66 million years of paleoclimate record actually shows. The bottom band is what 175 years of the modern instrumental record actually shows. They are not theoretical claims about what the system ought to do. They are measurements of what it has done. The illustrative curve threading between them is one possible reconciliation — the response of the climate system as physics predicts. Whether the curve is exactly right in any detail is a separate question. The empirical bands are what they are.
Looking at the modern band specifically: it climbs. The 1850–2025 fit gives 2.37 K per doubling. The 1975–2025 fit gives 2.93 K per doubling. G. Foster (2026, Geophysical Research Letters) used changepoint analysis after removing the influence of ENSO, solar variability, and volcanic forcing. Foster found the acceleration statistically significant. P. Forster and colleagues (2025) report attributed human-induced warming has risen to 0.27°C per decade for 2015–2024 — well above the 0.18–0.20°C per decade rate of earlier decades. [0.39°C actual warming over 2015 -24 and 0.30°C over 2015-25 were even farther above 0.18-0.20°C.] The observation is consistent with what the four-tier framework predicts: as forcing accumulates and slow feedbacks begin to express, the transient slope climbs toward ECS. The recent slope sits just below the labeled ECS value on Figure 2.
Where do the IPCC’s likely ranges come from? AR6 combines evidence from four independent streams, weighted by formal Bayesian inference. Each stream alone gives a wider uncertainty than the combined estimate. The tightening of the AR6 likely range — from AR5’s 1.5–4.5°C to AR6’s 2.5–4.0°C — came from this combination.
Stream 1: Physics plus models. Start with the 3.7 W/m² forcing and the 1.2°C Planck response. Add feedbacks as parameterized in Earth System Models. Run the abrupt-2× experiment, extract ECS via linear extrapolation of the early temperature trajectory to the radiative equilibrium point (the Gregory method). Different models produce different ECS values — 1.8°C to 5.6°C across the CMIP ensemble — because they parameterize cloud and aerosol microphysics differently. The spread is honest; it is not error.
Stream 2: Observational energy budget. The CERES satellites have measured the planetary energy imbalance at the top of the atmosphere since 2000 ("currently" ±0.9 W/m² in recent years [and rising, 1.33 to 1.5 W/m² in 2020-25). Combined with the surface temperature record and best estimates of historical forcing, this gives a feedback parameter and therefore an estimate of ECS that does not require running a climate model. Earlier work using this method produced lower ECS estimates (~2.0–2.4°C). The gap turned out to be a methodological issue: the warming so far has been concentrated in regions whose cloud response does not represent the long-term equilibrium response — the so-called pattern effect. Cooper et al. (2026) corrected for pattern effects and brought observational ECS estimates to about 2.8°C, consistent with the model-based estimates. The convergence between methods, once properly calibrated, is one of the more important developments in the last decade of climate science.
Stream 3: Paleoclimate. The deep past gives independent estimates. Warm states such as the Pliocene and Eocene constrain sensitivity at elevated CO2. Glacial-interglacial cycles constrain it at lower CO2. These estimates are noisier than the modern energy budget, because both temperature proxies and CO2 reconstructions carry error bars. But the central tendency is consistent with ~3°C ECS for modern conditions, with higher values at warmer climate states. The formal framework for combining fast and slow feedbacks across paleoclimate was developed by the PALAEOSENS Project (2012, Nature).
Stream 4: Emergent constraints. Across models, certain present-day observables (cloud properties, the seasonal cycle, the response to volcanic eruptions) correlate with the model’s ECS. Apply the observed value to the model-derived relationship and you get an observationally-anchored constraint on ECS. Sherwood et al. (2020) combined multiple emergent constraints with the other streams in a formal Bayesian framework — the work that became the basis for AR6. More recent emergent-constraint work has continued to refine the picture. Wilson Kemsley et al. (2026, GRL) used satellite cloud observations to constrain cloud feedback and found it robustly positive, pushing the central ECS estimate modestly upward from AR6’s 3.0°C.
AR6’s 2.5–4.0°C likely range is what falls out when these four streams are combined. Each stream alone gives a wider uncertainty; the combination is tighter than any single stream. This is consilience working: multiple independent methods, with independent assumptions and independent failure modes, converging on overlapping ranges.
The framework’s real use is taking apart a dispute that usually arrives as a single tangled claim. James Hansen and collaborators argue for an ECS of roughly 4.5°C or higher, well above the AR6 central estimate. It is tempting to file this as Hansen using a looser definition — letting ice sheets sneak into ECS — But that is not what is happening, and the framework is precise enough to show why.
Hansen’s 4.8°C is, by his own paper’s label, a Charney (fast-feedback) sensitivity: the same experiment AR6 runs, with ice sheets and the other slow feedbacks held fixed. It is not Earth System Sensitivity, and it is not a hybrid sitting partway up the curve. It is an estimate of the same quantity AR6 puts near 3°C — and it simply disagrees about the value.
Two choices produce the higher number, both inside the fast-feedback experiment. First, Hansen reads the fast feedbacks — cloud feedback above all — at the strong end of their range. Appendix D shows the consequence directly: with cloud feedback at +0.7 W/m²/K and ice sheets held fixed, the arithmetic gives ECS ≈ 4.6°C. No slow feedback is needed to reach Hansen’s neighborhood; strong clouds alone get there. Second, he assesses historical aerosol forcing as more strongly negative than AR6 does. Aerosols mask greenhouse warming, so a larger hidden cooling means the observed warming was produced by a smaller net forcing — which implies a more sensitive system.
There is a second Hansen argument, and it is the one most often confused with the first. He reads the paleoclimate record as showing that the slow feedbacks — ice-sheet retreat in particular — and the warming already “in the pipeline” arrive faster than AR6 assumes, on the order of a century or two rather than millennia. This is a real and consequential claim. But it is a claim about how quickly ESS is realized, not about the value of ECS. One concerns the height of the fast-feedback plateau; the other, the timing of the slow rise. They are different axes, and Hansen’s critics and defenders routinely argue past each other by collapsing them into one.
The framework does not resolve whether Hansen is right on either count. On the fast-feedback value, the recent weight of evidence — the pattern-effect correction of Cooper et al. (2026), the four-stream AR6 assessment — sits near 3°C, with Hansen on the high tail rather than at the center. On the speed of the slow response, the question is genuinely open. What the framework gives the reader is the ability to say which disagreement is on the table. That alone is more than most climate writing offers.
The body of the essay treated feedbacks qualitatively. This appendix shows the bookkeeping — the governing equation, the measured parameters, the satellite constraint, and one worked example. Nothing here requires more than algebra.
A. The decomposition equation
The framework is the one electrical engineers use for amplifiers with feedback. At equilibrium, a radiative forcing F (in W/m²) is balanced by the climate system’s radiative response. Each physical process contributes a feedback parameter λi, in watts per square meter per kelvin of surface warming. The Planck response, λP = −3.2 W/m²/K, is the baseline restoring term — the extra thermal radiation a warmer surface emits. Equilibrium warming is
ΔTeq = F / ( |λP| − Σ λi )
with amplifying feedbacks entering as positive terms in the sum. Equivalently, in gain form,
ΔTeq = ΔTPlanck / (1 − g), g = Σ λi / |λP|
which any reader of Bode will recognize as a closed-loop gain. The system is stable so long as g < 1, and the paleoclimate record shows that it is. One structural consequence matters for everything downstream: 1/(1 − g) is nonlinear in g, so symmetric uncertainty in the feedbacks maps into asymmetric uncertainty in ΔTeq. This is why sensitivity estimates have always carried a fatter upper tail than lower tail (Roe & Baker 2007). The shape of the uncertainty is built into the algebra, not into anyone’s pessimism.
B. The feedback parameters
AR6 Chapter 7 central values, in W/m²/K:
Planck: −3.2. Stefan-Boltzmann applied to the observed temperature structure of the atmosphere. The best-constrained number in the set.
Water vapor: +1.8. Warmer air holds more water vapor (Clausius-Clapeyron, roughly 7% per degree), and water vapor is itself a greenhouse gas. Constrained by satellite humidity records and consistent behavior across models.
Lapse rate: −0.5. The tropical upper troposphere warms faster than the surface and radiates to space more efficiently, partially offsetting the water vapor amplification. The two are often quoted as a combined +1.3 because their uncertainties anticorrelate — the same upper-tropospheric moistening that strengthens one strengthens the offsetting other.
Surface albedo: +0.4. Retreating snow and sea ice darken the surface. Constrained by the observed retreat over the satellite era.
Cloud: +0.4 ± 0.3. The dominant uncertainty in the whole problem. Constrained by cloud-controlling-factor analyses against satellite observations; Wilson Kemsley et al. (2026) find it robustly positive.
C. What CERES actually measures
The CERES instruments have measured the net radiative imbalance N at the top of the atmosphere since 2000 — currently about +0.9 [no, +1.4] W/m². Out of equilibrium, the energy budget reads
N = F − λ ΔT
energy absorbed minus energy restored. Rearranged, λ = (F − N)/ΔT. Every term on the right is measured or independently estimated, so the feedback parameter — and from it ECS = F2×/λ — comes out of observations with no climate model in the loop. Round historical numbers (net forcing to date F ≈ 2.7 W/m², N ≈ 0.9, ΔT ≈ 1.3 °C) give λ ≈ 1.4 W/m²/K and ECS ≈ 2.6 °C — the neighborhood of the energy-budget estimates that ran below the model range for a decade. (Forster et al. 2025 estimate F closer to 2.9 W/m² for 2024, which shifts the illustrative ECS down to about 2.4 °C; the qualitative point is the same.) The largest single uncertainty in this calculation is the historical aerosol forcing — anthropogenic aerosols partially offset CO2 warming, so F is a net of greenhouse warming minus aerosol cooling, and the aerosol term is the least well-constrained piece. Beyond that, the pattern effect from Stream 2: the λ inferred from the historical warming pattern overstates the long-run restoring strength, because the warming so far has been concentrated in regions whose cloud response is unusually stabilizing. Correcting for it (Cooper et al. 2026) brings the observational estimate to about 2.8 °C.
D. A worked example
Sum the central feedbacks: Σ λi = 1.8 − 0.5 + 0.4 + 0.4 = +2.1 W/m²/K. The denominator is 3.2 − 2.1 = 1.1, and with F = 3.7 W/m² for doubled CO2,
ΔTeq = 3.7 / 1.1 ≈ 3.4 °C.
In gain form, g = 2.1/3.2 ≈ 0.66 and 1.2 °C / (1 − 0.66) gives the same answer. Two things are worth noticing. First, the single-stream feedback arithmetic lands near 3.4 °C — slightly above the AR6 assessed central of 3.0 °C shown in Figure 2. Both are correct; they answer different questions. The 3.4 °C is what one method produces from central feedback values. The 3.0 °C is the four-stream Bayesian assessed central, which pulls the estimate down and tightens the range. The difference between them is exactly what consilience does. Second, run the cloud feedback across its published ±0.3 uncertainty: at +0.1 the denominator is 1.4 and ECS ≈ 2.6 °C; at +0.7 it is 0.8 and ECS ≈ 4.6 °C. One parameter, at its published uncertainty, spans the entire AR6 likely range. That is the cloud problem in one line of arithmetic — and the reason Streams 2 through 4 exist: they constrain ECS in ways that do not require knowing the cloud feedback first.
CO2 Puts Heavier Stamp on Temperature than Previously Thought 0624.rtf - from Dutch and English researchers. From the Abstract: “.... From 15.0-0.3 Myr ago, our reconstructed pCO2 values steadily decline from 650 ± 150 to 280 ± 75 ppmv, mirroring global temperature decline. Using our new range of pCO2 values, we calculate average Earth system sensitivity and equilibrium climate sensitivity, resulting in 13.9°C and 7.2°C per doubling of pCO2, respectively. These values are significantly higher than IPCC global warming estimations, consistent [with] or higher than some recent state-of-the-art climate models, and consistent with other proxy-based estimates.”
Climate Worst-Case Scenarios May Not Go Far Enough, Cloud Data Shows 0620.rtf - Clouds provide a substantial amplifying feedback. Climate sensitivity is about 5°C for doubled CO2, not 3°.
In the the 3-panel figure below, not only do high ECS models match observations much better than low ECS models do at 35-60°S latitude (see this commentary in blue), high ECS models also match observations better at 40-60°N latitude. The high ECS model also matches observations a little better from 10 to 30°S over May to December.
Shown below are climate sensitivities (eventual temperature response to doubled CO2 levels) in 28 and 29 partially overlapping Global Climate Models (GCMs). CMIP6 GCMs are more recent and more detailed than CMIP5 models. They especially do a better job of modeling clouds in detail.
Climate sensitivities of -1 to +6[°C] are shown on the bottom axis. For 3 decades, the IPCC saw +3° as the central estimate for climate sensitivity, with a modest 1 to 1.5° error band. More recent models, below, mostly show higher sensitivities above +3°.
Abbreviations shown below, just above the -1 to +6 warming key, are TR = Tropics, EX = Extra-Tropical, both for Forcing by greenhouse gases (other than water vapor), which leads to heating. LR and RH are for Longwave Radiation and Relative Humidity.
Albedo is the % of incoming solar radiation that Earth reflects, mostly from sea ice and snow, plus a little bit from land ice. Clouds refers to the albedo (reflectivity) of clouds, directly and indirectly, from changes mostly in cloud area, altitude, and opaqueness.
Notice that more recent models, which handle clouds better, yields more heating per doubled CO2. Only 1 out of 28 shows a climate sensitivity below 2.5, while 15 of 28 show a climate sensitivity above 4°C for doubled CO2. 3 of the 28 show a climate sensitivity of almost 6°C.
(Research by Dr. Fry, this website's author, yielded a trend line (see Heat/Distant Past) for Vostok ice ice core over 440,000 years, leading to a long-run climate sensitivity of 8.6°C for CO2 doubled from 280 to 560 ppm. But it did not break out separate components for forcing from CO2 and other greenhouse gases, nor for albedo and clouds, nor for longwave radiation of relative humidity.)
Why Low-End Climate Sensitivity Can Now Be Ruled Out 0820.rtf
take 3, by some authors of the study
Why Clouds Are the Key to New Troubling Projections on Warming 0220.rtf
Newer global climate models (GCMs) do a much better job of handling clouds, for which droplet size is very important, as is large scale (10s to 100s of kilometers): micro and macro in the same model.
These newer GCMs find that clouds diminish as Earth's surface warms. See reasons in figures in the Albedo - Clouds page: How Climate Change Breaks Up Clouds.
And in the cloud graphs with trend lines, not as far above in the Albedo - Clouds section.
Taking into account the feedbacks involving cloud changes, these newer GCMs find climate sensitivity (∆°C for 2 x ppm CO2) of not ~ 3°, which has the central estimate for decades, but
4.0 to 5.6°C.
Climate modelers and the IPCC sometimes refer to these new and improved models as "hot models".
Real-world data from satellites suggests that the modelers’ predictions may already be coming true. See the 3-panel graph at the top of this Climate Sensitivity page.
"Past models have overestimated how much ice in these clouds will turn to liquid water in a warmer world — and so overestimated both the thickness of future clouds and their ability to keep us cool. Eliminating that bias, says Tan, could increase climate sensitivity by as much as 1.3°C."
For example, French scientists at the National Center for Scientific Research concluded that the new models predicted that rapid economic growth driven by fossil fuels would deliver temperature rises averaging 6 to 7°C (10.8 to 12.6°F) by the end of the century. They warned that keeping warming below 2°C was all but impossible.
2 Million Year Record Indicates 5°C Warming from 400 ppm CO2, 9° from 560 ppm 0916.rtf
- Figure below is from Hansen, also shown a little farther below.
Sensitivity and the Carbon Budget - Wasdell 0614.pdf - PDF available here.
Making Sense of Palaeoclimate Sensitivity - Hansen 1112.pdf available also here.
also above (Distant Past) and on Water page. It has climate sensitivity estimates from 38 pale-climate studies. Hansen "discards" 11 of the 38.
Below, Hansen draws Figure a from 800 K years, like Figure c (earlier, also by Hansen). Figure b is drawn from the last 20 M years, according to van der Wal. Figure d melds all 3. Slow feedbacks include albedo (reflectivity) changes due to changes in vegetation and extent of ice sheets, as well as plate tectonics, weathering, and some aspects of the carbon cycle. Fast feedbacks include cloud coverage, snow extent, sea ice, upper ocean heating, carbon emissions from permafrost and methane hydrates, and most aspects of dust and aerosol changes.
Dr. Fry's analysis and projections suggest that climate sensitivity is not one number, but increases as more ice (in sheets) is available for albedo changes (6-8°C / doubled CO2) in the heart of an ice age. Conversely, it decreases in a warmer world with less ice left to melt, until it reaches about 2° when no icde is left to melt.
Section Map: Heat