Papers on climate sensitivity estimates

This is a list of papers on climate sensitivity estimates. The list is based on the “Estimates of Climate Sensitivity” by Barton Paul Levenson (2006), with some additions from John Cook’s article on climate sensitivity and from my own searches. The list is not complete, and will most likely be updated in the future in order to make it more thorough and more representative.

UPDATE (April 18, 2013): Lewis (2013), Masters (2013), and van Hateren (2012) added. Thanks to Kevin C. for pointing them out.
UPDATE (March 25, 2013): PALAEOSENS Project Members (2012) and Hargreaves et al. (2012) added.
UPDATE (March 22, 2013): Köhler et al. (2010), Pagani et al. (2010), Schmittner et al. (2011), Bitz et al. (2012) added.
UPDATE (April 2, 2012): Annan & Hargreaves (2009) added. Thanks to Barry for pointing it out.
UPDATE (June 16, 2010): Huybers (2010) added.
UPDATE (May 10, 2010): Lunt et al. (2010) added.
UPDATE (February 26, 2010): Hulburt (1931) added.
UPDATE (February 16, 2010): Lea (2004) added, thanks to Barry for pointing it out, see the comment section below.
UPDATE (November 7, 2009): Kirk-Davidoff (2009), an additional note to Schwartz (2007), and Covey et al. (1996) added, thanks to PeterPan for suggesting these.
UPDATE (November 6, 2009): I forgot to include Schwartz (2007), I added it now. I also added Schwartz’s response to critics, thanks to Paul Middents for pointing it out, see the discussion section below.

Newer papers and other papers not in Levenson’s list:

Observational estimate of climate sensitivity from changes in the rate of ocean heat uptake and comparison to CMIP5 models – Masters (2013) “Climate sensitivity is estimated based on 0–2,000 m ocean heat content and surface temperature observations from the second half of the 20th century and first decade of the 21st century, using a simple energy balance model and the change in the rate of ocean heat uptake to determine the radiative restoration strength over this time period. The relationship between this 30–50 year radiative restoration strength and longer term effective sensitivity is investigated using an ensemble of 32 model configurations from the Coupled Model Intercomparison Project phase 5 (CMIP5), suggesting a strong correlation between the two. The mean radiative restoration strength over this period for the CMIP5 members examined is 1.16 Wm⁻²K⁻¹, compared to 2.05 Wm⁻²K⁻¹ from the observations. This suggests that temperature in these CMIP5 models may be too sensitive to perturbations in radiative forcing, although this depends on the actual magnitude of the anthropogenic aerosol forcing in the modern period. The potential change in the radiative restoration strength over longer timescales is also considered, resulting in a likely (67 %) range of 1.5–2.9 K for equilibrium climate sensitivity, and a 90 % confidence interval of 1.2–5.1 K.” Troy Masters, Climate Dynamics, April 2013, DOI: 10.1007/s00382-013-1770-4.

An objective Bayesian, improved approach for applying optimal fingerprint techniques to estimate climate sensitivity – Lewis (2013) “A detailed reanalysis is presented of a ‘Bayesian’ climate parameter study (Forest et al., 2006) that estimates climate sensitivity (ECS) jointly with effective ocean diffusivity and aerosol forcing, using optimal fingerprints to compare multi-decadal observations with simulations by the MIT 2D climate model at varying settings of the three climate parameters. Use of improved methodology primarily accounts for the 90% confidence bounds for ECS reducing from 2.1–8.9 K to 2.0–3.6 K. The revised methodology uses Bayes’ theorem to derive a probability density function (PDF) for the whitened (made independent using an optimal fingerprint transformation) observations, for which a uniform prior is known to be noninformative. A dimensionally-reducing change of variables onto the parameter surface is then made, deriving an objective joint PDF for the climate parameters. The PDF conversion factor from the whitened variables space to the parameter surface represents a noninformative joint parameter prior, which is far from uniform. The noninformative prior prevents more probability than data uncertainty distributions warrant being assigned to regions where data responds little to parameter changes, producing better-constrained PDFs. Incorporating six years of unused model-simulation data and revising the experimental design to improve diagnostic power reduces the best-fit climate sensitivity. Employing the improved methodology, preferred 90% bounds of 1.2–2.2 K for ECS are then derived (mode and median 1.6 K). The mode is identical to those from Aldrin et al. (2012) and (using the same, HadCRUT4, observational dataset) Ring et al. (2012). Incorporating forcing and observational surface temperature uncertainties, unlike in the original study, widens the 90% range to 1.0–3.0 K.” Nicholas Lewis, Journal of Climate 2013, doi: http://dx.doi.org/10.1175/JCLI-D-12-00473.1.

A fractal climate response function can simulate global average temperature trends of the modern era and the past millennium – van Hateren (2012) “A climate response function is introduced that consists of six exponential (low-pass) filters with weights depending as a power law on their e-folding times. The response of this two-parameter function to the combined forcings of solar irradiance, greenhouse gases, and SO₂-related aerosols is fitted simultaneously to reconstructed temperatures of the past millennium, the response to solar cycles, the response to the 1991 Pinatubo volcanic eruption, and the modern 1850–2010 temperature trend. Assuming strong long-term modulation of solar irradiance, the quite adequate fit produces a climate response function with a millennium-scale response to doubled CO₂ concentration of 2.0 ± 0.3 °C (mean ± standard error), of which about 50 % is realized with e-folding times of 0.5 and 2 years, about 30 % with e-folding times of 8 and 32 years, and about 20 % with e-folding times of 128 and 512 years. The transient climate response (response after 70 years of 1 % yearly rise of CO₂ concentration) is 1.5 ± 0.2 °C. The temperature rise from 1820 to 1950 can be attributed for about 70 % to increased solar irradiance, while the temperature changes after 1950 are almost completely produced by the interplay of anthropogenic greenhouse gases and aerosols. The SO₂-related forcing produces a small temperature drop in the years 1950–1970 and an inflection of the temperature curve around the year 2000. Fitting with a tenfold smaller modulation of solar irradiance produces a less adequate fit with millennium-scale and transient climate responses of 2.5 ± 0.4 and 1.9 ± 0.3 °C, respectively.” J. H. van Hateren, Climate Dynamics, May 2012, DOI: 10.1007/s00382-012-1375-3. [Full text]

Can the Last Glacial Maximum constrain climate sensitivity? – Hargreaves et al. (2012) “We investigate the relationship between the Last Glacial Maximum (LGM) and climate sensitivity across the PMIP2 multi-model ensemble of GCMs, and find a correlation between tropical temperature and climate sensitivity which is statistically significant and physically plausible. We use this relationship, together with the LGM temperature reconstruction of Annan and Hargreaves (2012), to generate estimates for the equilibrium climate sensitivity. We estimate the equilibrium climate sensitivity to be about 2.5°C with a high probability of being under 4°C, though these results are subject to several important caveats. The forthcoming PMIP3/CMIP5 models were not considered in this analysis, as very few LGM simulations are currently available from these models. We propose that these models will provide a useful validation of the correlation presented here.” J. C. Hargreaves, J. D. Annan, M. Yoshimori, A. Abe-Ouchi, Geophysical Research Letters, Volume 39, Issue 24, December 2012, DOI: 10.1029/2012GL053872. [Full text]

Making sense of palaeoclimate sensitivity – PALAEOSENS Project Members (2012) “Many palaeoclimate studies have quantified pre-anthropogenic climate change to calculate climate sensitivity (equilibrium temperature change in response to radiative forcing change), but a lack of consistent methodologies produces a wide range of estimates and hinders comparability of results. Here we present a stricter approach, to improve intercomparison of palaeoclimate sensitivity estimates in a manner compatible with equilibrium projections for future climate change. Over the past 65 million years, this reveals a climate sensitivity (in K W⁻¹ m²) of 0.3–1.9 or 0.6–1.3 at 95% or 68% probability, respectively. The latter implies a warming of 2.2–4.8 K per doubling of atmospheric CO₂, which agrees with IPCC estimates.” PALAEOSENS Project Members, Nature, 491, 683–691, 29 November 2012, DOI: 10.1038/nature11574.

Climate Sensitivity of the Community Climate System Model, Version 4 – Bitz et al. (2012) “Equilibrium climate sensitivity of the Community Climate System Model, version 4 (CCSM4) is 3.20°C for 1° horizontal resolution in each component. This is about a half degree Celsius higher than in the previous version (CCSM3). The transient climate sensitivity of CCSM4 at 1° resolution is 1.72°C, which is about 0.2°C higher than in CCSM3. These higher climate sensitivities in CCSM4 cannot be explained by the change to a preindustrial baseline climate. This study uses the radiative kernel technique to show that, from CCSM3 to CCSM4, the global mean lapse-rate feedback declines in magnitude and the shortwave cloud feedback increases. These two warming effects are partially canceled by cooling because of slight decreases in the global mean water vapor feedback and longwave cloud feedback from CCSM3 to CCSM4. A new formulation of the mixed layer, slab-ocean model in CCSM4 attempts to reproduce the SST and sea ice climatology from an integration with a full-depth ocean, and it is integrated with a dynamic sea ice model. These new features allow an isolation of the influence of ocean dynamical changes on the climate response when comparing integrations with the slab ocean and full-depth ocean. The transient climate response of the full-depth ocean version is 0.54 of the equilibrium climate sensitivity when estimated with the new slab-ocean model version for both CCSM3 and CCSM4. The authors argue the ratio is the same in both versions because they have about the same zonal mean pattern of change in ocean surface heat flux, which broadly resembles the zonal mean pattern of net feedback strength.” Bitz, C. M., K. M. Shell, P. R. Gent, D. A. Bailey, G. Danabasoglu, K. C. Armour, M. M. Holland, J. T. Kiehl, 2012: Climate Sensitivity of the Community Climate System Model, Version 4. J. Climate, 25, 3053–3070. doi: http://dx.doi.org/10.1175/JCLI-D-11-00290.1.

Climate Sensitivity Estimated from Temperature Reconstructions of the Last Glacial Maximum – Schmittner et al. (2011) “Assessing the impact of future anthropogenic carbon emissions is currently impeded by uncertainties in our knowledge of equilibrium climate sensitivity to atmospheric carbon dioxide doubling. Previous studies suggest 3 kelvin (K) as the best estimate, 2 to 4.5 K as the 66% probability range, and nonzero probabilities for much higher values, the latter implying a small chance of high-impact climate changes that would be difficult to avoid. Here, combining extensive sea and land surface temperature reconstructions from the Last Glacial Maximum with climate model simulations, we estimate a lower median (2.3 K) and reduced uncertainty (1.7 to 2.6 K as the 66% probability range, which can be widened using alternate assumptions or data subsets). Assuming that paleoclimatic constraints apply to the future, as predicted by our model, these results imply a lower probability of imminent extreme climatic change than previously thought.” Andreas Schmittner, Nathan M. Urban, Jeremy D. Shakun, Natalie M. Mahowald, Peter U. Clark, Patrick J. Bartlein, Alan C. Mix, Antoni Rosell-Melé, Science 9 December 2011: Vol. 334 no. 6061 pp. 1385-1388, DOI: 10.1126/science.1203513. [Full text]

High Earth-system climate sensitivity determined from Pliocene carbon dioxide concentrations – Pagani et al. (2010) “Climate sensitivity—the mean global temperature response to a doubling of atmospheric CO2 concentrations through radiative forcing and associated feedbacks—is estimated at 1.5–4.5 °C (ref. 1). However, this value incorporates only relatively rapid feedbacks such as changes in atmospheric water vapour concentrations, and the distributions of sea ice, clouds and aerosols. Earth-system climate sensitivity, by contrast, additionally includes the effects of long-term feedbacks such as changes in continental ice-sheet extent, terrestrial ecosystems and the production of greenhouse gases other than CO2. Here we reconstruct atmospheric carbon dioxide concentrations for the early and middle Pliocene, when temperatures were about 3–4 °C warmer than preindustrial values, to estimate Earth-system climate sensitivity from a fully equilibrated state of the planet. We demonstrate that only a relatively small rise in atmospheric CO2 levels was associated with substantial global warming about 4.5 million years ago, and that CO2 levels at peak temperatures were between about 365 and 415 ppm. We conclude that the Earth-system climate sensitivity has been significantly higher over the past five million years than estimated from fast feedbacks alone.” Mark Pagani, Zhonghui Liu, Jonathan LaRiviere & Ana Christina Ravelo, Nature Geoscience 3, 27 – 30 (2010), doi:10.1038/ngeo724. [Full text]

Compensation between Model Feedbacks and Curtailment of Climate Sensitivity – Huybers (2010) “The spread in climate sensitivity obtained from 12 general circulation model runs used in the Fourth Assessment of the Intergovernmental Panel on Climate Change indicates a 95% confidence interval of 2.1°–5.5°C, but this reflects compensation between model feedbacks. In particular, cloud feedback strength negatively covaries with the albedo feedback as well as with the combined water vapor plus lapse rate feedback. If the compensation between feedbacks is removed, the 95% confidence interval for climate sensitivity expands to 1.9°–8.0°C.”

Earth system sensitivity inferred from Pliocene modelling and data – Lunt et al. (2010) “Components of the Earth’s climate system that vary over long timescales, such as ice sheets and vegetation, could have an important effect on this temperature sensitivity, but have often been neglected. Here we use a coupled atmosphere–ocean general circulation model to simulate the climate of the mid-Pliocene warm period (about three million years ago), and analyse the forcings and feedbacks that contributed to the relatively warm temperatures. Furthermore, we compare our simulation with proxy records of mid-Pliocene sea surface temperature. Taking these lines of evidence together, we estimate that the response of the Earth system to elevated atmospheric carbon dioxide concentrations is 30–50% greater than the response based on those fast-adjusting components of the climate system that are used traditionally to estimate climate sensitivity.” [Full text]

What caused Earth’s temperature variations during the last 800,000 years? Data-based evidence on radiative forcing and constraints on climate sensitivity – Köhler et al. (2010) “The temperature on Earth varied largely in the Pleistocene from cold glacials to interglacials of different warmths. To contribute to an understanding of the underlying causes of these changes we compile various environmental records (and model-based interpretations of some of them) in order to calculate the direct effect of various processes on Earth’s radiative budget and, thus, on global annual mean surface temperature over the last 800,000 years. The importance of orbital variations, of the greenhouse gases CO₂, CH₄ and N₂O, of the albedo of land ice sheets, annual mean snow cover, sea ice area and vegetation, and of the radiative perturbation of mineral dust in the atmosphere are investigated. Altogether we can explain with these processes a global cooling of 3.9 ± 0.8 K in the equilibrium temperature for the Last Glacial Maximum (LGM) directly from the radiative budget using only the Planck feedback that parameterises the direct effect on the radiative balance, but neglecting other feedbacks such as water vapour, cloud cover, and lapse rate. The unaccounted feedbacks and related uncertainties would, if taken at present day feedback strengths, decrease the global temperature at the LGM by −8.0 ± 1.6 K. Increased Antarctic temperatures during the Marine Isotope Stages 5.5, 7.5, 9.3 and 11.3 are in our conceptual approach difficult to explain. If compared with other studies, such as PMIP2, this gives supporting evidence that the feedbacks themselves are not constant, but depend in their strength on the mean climate state. The best estimate and uncertainty for our reconstructed radiative forcing and LGM cooling support a present day equilibrium climate sensitivity (excluding the ice sheet and vegetation components) between 1.4 and 5.2 K, with a most likely value near 2.4 K, somewhat smaller than other methods but consistent with the consensus range of 2–4.5 K derived from other lines of evidence. Climate sensitivities above 6 K are difficult to reconcile with Last Glacial Maximum reconstructions.” Peter Köhler, Richard Bintanja, Hubertus Fischer, Fortunat Joos, Reto Knutti, Gerrit Lohmann, Valérie Masson-Delmotte, Quaternary Science Reviews, Volume 29, Issues 1–2, January 2010, Pages 129–145, http://dx.doi.org/10.1016/j.quascirev.2009.09.026. [Full text]

On the generation and interpretation of probabilistic estimates of climate sensitivity – Annan & Hargreaves (2009) “The equilibrium climate response to anthropogenic forcing has long been one of the dominant, and therefore most intensively studied, uncertainties in predicting future climate change. As a result, many probabilistic estimates of the climate sensitivity (S) have been presented. In recent years, most of them have assigned significant probability to extremely high sensitivity, such as P(S > 6C) > 5%. In this paper, we investigate some of the assumptions underlying these estimates. We show that the popular choice of a uniform prior has unacceptable properties and cannot be reasonably considered to generate meaningful and usable results. When instead reasonable assumptions are made, much greater confidence in a moderate value for S is easily justified, with an upper 95% probability limit for S easily shown to lie close to 4°C, and certainly well below 6°C. These results also impact strongly on projected economic losses due to climate change.” J. D. Annan and J. C. Hargreaves, Climatic Change, Volume 104, Numbers 3-4, 423-436, DOI: 10.1007/s10584-009-9715-y [Full text]

On the diagnosis of climate sensitivity using observations of fluctuations – Kirk-Davidoff (2009) “It has been shown that lag-covariance based statistical measures, suggested by the Fluctuation Dissipation Theorem (FDT), may allow estimation of climate sensitivity in a climate model. Recently Schwartz (2007) has used measures of the decay of autocorrelation in a global surface temperature time series to estimate the real world climate sensitivity. Here we use a simple climate model, and analysis of archived coupled climate model output from the IPCC AR4 runs, for which the climate sensitivity is known, to test the utility of this approach. Our analysis of these archived model output data show that estimates of climate sensitivity derived from century-long time scales typically grossly underestimate the models’ true climate sensitivity.” [Full text]

Complementary observational constraints on climate sensitivity – Urban & Keller (2009) “Here we show that reducing the uncertainty about (i) oceanic heat uptake and (ii) aerosol climate forcing can—in principle—cut off this heavy upper tail of climate sensitivity estimates. Observations of oceanic heat uptake result in a negatively correlated joint likelihood function of climate sensitivity and ocean vertical diffusivity. This correlation is opposite to the positive correlation resulting from observations of surface air temperatures. As a result, the two observational constraints can rule out complementary regions in the climate sensitivity-vertical diffusivity space, and cut off the heavy upper tail of the marginal climate sensitivity estimate.” [Full text]

Insufficient forcing uncertainty underestimates the risk of high climate sensitivity – Tanaka et al. (2009) An example that shows how uncertainty in climate sensitivity estimates doesn’t necessarily mean that climate sensitivity is low. “In spite of various efforts to estimate its value, climate sensitivity is still not well constrained. Here we show that the probability of high climate sensitivity is higher than previously thought because uncertainty in historical radiative forcing has not been sufficiently considered. The greater the uncertainty that is considered for radiative forcing, the more difficult it is to rule out high climate sensitivity, although low climate sensitivity (<2°C) remains unlikely.” [Full text]

Target atmospheric CO₂: Where should humanity aim? – Hansen et al. (2008) “Paleoclimate data show that climate sensitivity is ~3°C for doubled CO₂, including only fast feedback processes. Equilibrium sensitivity, including slower surface albedo feedbacks, is ~6°C for doubled CO₂ for the range of climate states between glacial conditions and ice-free Antarctica.” [Full text]

The equilibrium sensitivity of the Earth’s temperature to radiation changes – Knutti et al. (2008) A review article. “The quest to determine climate sensitivity has now been going on for decades, with disturbingly little progress in narrowing the large uncertainty range. However, in the process, fascinating new insights into the climate system and into policy aspects regarding mitigation have been gained. The well-constrained lower limit of climate sensitivity and the transient rate of warming already provide useful information for policy makers. But the upper limit of climate sensitivity will be more difficult to quantify.” [Full text]

Aerosol radiative forcing and climate sensitivity deduced from the Last Glacial Maximum to Holocene transition – Chylek & Lohmann (2008) “We use the temperature, carbon dioxide, methane, and dust concentration record from the Vostok ice core to deduce the aerosol radiative forcing during the Last Glacial Maximum (LGM) to Holocene transition and the climate sensitivity. … This suggests a 95% likelihood of warming between 1.3 and 2.3 K due to doubling of atmospheric concentration of CO₂.”

Climate sensitivity constrained by CO₂ concentrations over the past 420 million years – Royer et al. (2007) “Here we estimate long-term equilibrium climate sensitivity by modelling carbon dioxide concentrations over the past 420 million years and comparing our calculations with a proxy record. Our estimates are broadly consistent with estimates based on short-term climate records, and indicate that a weak radiative forcing by carbon dioxide is highly unlikely on multi-million-year timescales. We conclude that a climate sensitivity greater than 1.5 °C has probably been a robust feature of the Earth’s climate system over the past 420 million years, regardless of temporal scaling.” [Full text]

Heat capacity, time constant, and sensitivity of Earth’s climate system – Schwartz (2007) See John Cook’s article for some comments on this paper. Note that in the response to critics Schwartz revises the estimated sensitivity from 1.1 K to 1.9 K. “The equilibrium sensitivity of Earth’s climate is determined as the quotient of the relaxation time constant of the system and the pertinent global heat capacity. … The resultant equilibrium climate sensitivity, 0.30 ± 0.14 K/(W m−2), corresponds to an equilibrium temperature increase for doubled CO₂ of 1.1 ± 0.5 K.” [Full text] [Link to Schwartz’s response to critics]

Using multiple observationally-based constraints to estimate climate sensitivity – Annan & Hargreaves (2006) “Climate sensitivity has been subjectively estimated to be likely to lie in the range of 1.5–4.5°C, and this uncertainty contributes a substantial part of the total uncertainty in climate change projections over the coming century. Objective observationally-based estimates have so far failed to improve on this upper bound, with many estimates even suggesting a significant probability of climate sensitivity exceeding 6°C. In this paper, we show how it is possible to greatly reduce this uncertainty by using Bayes’ Theorem to combine several independent lines of evidence. Based on some conservative assumptions regarding the value of independent estimates, we conclude that climate sensitivity is very unlikely (<5% probability) to exceed 4.5°C. We cannot assign a significant probability to climate sensitivity exceeding 6°C without making what appear to be wholly unrealistic exaggerations about the uncertainties involved. This represents a significant lowering of the previously-estimated bound.” [Full text]

Constraining Climate Sensitivity from the Seasonal Cycle in Surface Temperature – Knutti et al. (2006) “A probability density function for climate sensitivity is then calculated from the present-day seasonal cycle in reanalysis and instrumental datasets. Subject to a number of assumptions on the models and datasets used, it is found that climate sensitivity is very unlikely (5% probability) to be either below 1.5–2 K or above about 5–6.5 K, with the best agreement found for sensitivities between 3 and 3.5 K.” [Full text]

The 100 000-Yr Cycle in Tropical SST, Greenhouse Forcing, and Climate Sensitivity – Lea (2004) “Two recent advances, the development and application of proxy recorders of tropical sea surface temperature (SST) and the synchronization of the deep-sea and Antarctic ice-core time scales, make it possible to directly relate past changes in tropical SST to atmospheric carbon dioxide (CO₂) levels. The strong correspondence of a proxy SST record from the eastern equatorial Pacific and the Vostok CO₂ record suggests that varying atmospheric carbon dioxide is the dominant control on tropical climate on orbital time scales. This effect is especially pronounced at the 100 000-yr cycle. Calibration of the CO₂ influence via tropical SST variability indicates a tropical climate sensitivity of 4.4°–5.6°C (errors estimated at ± 1.0°C) for a doubling of atmospheric CO₂ concentration. This result suggests that the equilibrium response of tropical climate to atmospheric CO₂ changes is likely to be similar to the upper end of available global predictions from coupled models.” [Full text]

An Observationally Based Estimate of the Climate Sensitivity – Gregory et al. (2002) “A probability distribution for values of the effective climate sensitivity, with a lower bound of 1.6 K (5th percentile), is obtained on the basis of the increase in ocean heat content in recent decades from analyses of observed interior-ocean temperature changes, surface temperature changes measured since 1860, and estimates of anthropogenic and natural radiative forcing of the climate system.” [Full text]

Quantifying Uncertainties in Climate System Properties with the Use of Recent Climate Observations – Forest et al. (2002) “We derive joint probability density distributions for three key uncertain properties of the climate system, using an optimal fingerprinting approach to compare simulations of an intermediate complexity climate model with three distinct diagnostics of recent climate observations. On the basis of the marginal probability distributions, the 5 to 95% confidence intervals are 1.4 to 7.7 kelvin for climate sensitivity and -0.30 to -0.95 watt per square meter for the net aerosol forcing.” [Full text]

Paleoclimate data constraints on climate sensitivity: The paleocalibration method – Covey et al. (1996) “We use a new technique called paleocalibration to calculate the ratio of temperature response to forcing on a global mean scale for three key intervals of Earth history. By examining surface conditions reconstructed from geologic data for the Last Glacial Maximum, the middle Cretaceous and the early Eocene, we can estimate the equilibrium climate sensitivity to radiative forcing changes for different extreme climates. We find that the ratios for these three periods, within error bounds, all lie in the range obtained from general circulation models: 2–5 K global warming for doubled atmospheric carbon dioxide. Paleocalibration thus provides a data-based confirmation of theoretically calculated climate sensitivity.”

How Sensitive Is the World’s Climate? – Hansen et al. (1993) “But climate models are mainly a tool that helps extract information from real-world climate changes. The principal climate characteristic to be evaluated is the global climate sensitivity to a perturbing forcing, such as a change of atmospheric composition. Our most precise knowledge of climate sensitivity comes from data on ancient and recent climate changes.” [Full text]

The ice-core record: climate sensitivity and future greenhouse warming – Lorius et al. (1990) “The prediction of future greenhouse-gas-induced warming depends critically on the sensitivity of Earth’s climate to increasing atmospheric concentrations of these gases. Data from cores drilled in polar ice sheets show a remarkable correlation between past glacial–interglacial temperature changes and the inferred atmospheric concentration of gases such as carbon dioxide and methane. These and other palaeoclimate data are used to assess the role of greenhouse gases in explaining past global climate change, and the validity of models predicting the effect of increasing concentrations of such gases in the atmosphere.” [Full text]

The Temperature of the Lower Atmosphere of the Earth – Hulburt (1931) “Calculation shows that doubling or tripling the amount of the carbon dioxide of the atmosphere increases the average sea level temperature by about 4° and 7°K, respectively; halving or reducing to zero the carbon dioxide decreases the temperature by similar amounts. Such changes in temperature are about the same as those which occur when the earth passes from an ice age to a warm age, or vice versa. Thus the calculation indicates that the carbon dioxide theory of the ice ages, originally proposed by Tyndall, is a possible theory.”

Papers in Levenson’s list:

The origin of the European “Medieval Warm Period” – Goosse et al. (2006) “ECBILT-CLIO-VECODE has a relatively weak climate sensitivity, with a 1.8°C increase in global mean temperature in response to a doubling of atmospheric CO₂ concentration.” [Full text]

Climate sensitivity constrained by temperature reconstructions over the past seven centuries – Hegerl et al. (2006) “A number of observational studies, however, find a substantial probability of significantly higher sensitivities, yielding upper limits on climate sensitivity of 7.7 K to above 9 K (refs 3–8). Here we demonstrate that such observational estimates of climate sensitivity can be tightened if reconstructions of Northern Hemisphere temperature over the past several centuries are considered. … After accounting for the uncertainty in reconstructions and estimates of past external forcing, we find an independent estimate of climate sensitivity that is very similar to those from instrumental data. If the latter are combined with the result from all proxy reconstructions, then the 5–95 per cent range shrinks to 1.5–6.2 K, thus substantially reducing the probability of very high climate sensitivity.” [Full text]

An atmosphere–ocean time series model of global climate change – Stern (2005) “A time series model of the atmosphere–ocean climate system is developed, in which surface temperature (atmospheric temperature over land and sea surface temperature) moves towards a long-run equilibrium with both radiative forcing and ocean heat content, while ocean heat content accumulates the deviations from atmospheric equilibrium. … The resulting parameter estimates are closer to theoretically expected values than those of previous time series models and the estimated climate sensitivity to a doubling of carbon dioxide is 4.4 K.” [Full text]

Global Warming Simulation due to the High Resolution Climate Model by Using the Earth Simulator – Sumi (2005) “Various simulations are conducted following IPCC guidance and these results are submitted to IPCC Data Center. Warming of the global averaged surface temperature is consistent to the previous estimate.” [Full text]

Dynamical aspects of climate sensitivity – Boer & Yu (2003) “Dynamical aspects of climate feedback/sensitivity are investigated in climate change simulations with a common atmospheric general circulation model coupled to a full ocean model, which responds both dynamically and thermo-dynamically, and to a mixed-layer ocean component which responds only thermodynamically.” [Full text]

Celestial driver of Phanerozoic climate? – Shaviv & Veizer (2003) “We find that at least 66% of the variance in the paleotemperature trend could be attributed to CRF variations likely due to solar system passages through the spiral arms of the galaxy. Assuming that the entire residual variance in temperature is due solely to the CO₂ greenhouse effect, we propose a tentative upper limit to the long-term “equilibrium” warming effect of CO₂, one which is potentially lower than that based on general circulation models.” [Full text]

Climates of the Twentieth and Twenty-First Centuries Simulated by the NCAR Climate System Model – Dai et al. (2001) “The Climate System Model, a coupled global climate model without “flux adjustments” recently developed at the National Center for Atmospheric Research, was used to simulate the twentieth-century climate using historical greenhouse gas and sulfate aerosol forcing. … The projected global surface warming from the 1990s to the 2090s is 1.9°C under the BAU scenario and 1.5°C under the STA550 scenario. In both cases, the midstratosphere cools due to the increase in CO2, whereas the lower stratosphere warms in response to recovery of the ozone layer.” [Full text]

Committed warming and its implications for climate change – Wetherald et al. (2001) “Time lags between changes in radiative forcing and the resulting simulated climate responses are investigated in a set of transient climate change experiments. … Results suggest that if the radiative forcing is held fixed at today’s levels, the global mean SAT will rise an additional 1.0K before equilibrating. This unrealized warming commitment is larger than the 0.6K warming observed since 1900.” [Full text]

A transient climate change simulation with greenhouse gas and aerosol forcing: experimental design and comparison with the instrumental record for the twentieth century – Boer et al. (2000) “The Canadian Centre for Climate Modelling and Analysis (CCCma) global coupled model is used to investigate the potential climate effects of increasing greenhouse gas (GHG) concentrations and changes in sulfate aerosol loadings. … Simulations of the evolution of temperature and precipitation from 1900 to the present are compared with available observations. … IPCC 1990 estimates that the climate sensitivity falls in the range 1.5 to 4.5 °C so that the CCCma model sensitivity at 3.5 °C is in the upper half of this range.” [Full text]

Parallel climate model (PCM) control and transient simulations – Washington et al. (2000) “Results from a 300 year present-day coupled climate control simulation are presented, as well as for a transient 1% per year compound CO₂ increase experiment which shows a global warming of 1.27 °C for a 10 year average at the doubling point of CO₂ and 2.89 °C at the quadrupling point. … A 0.5% per year CO₂ increase experiment also was performed showing a global warming of 1.5 °C around the time of CO₂ doubling and a similar warming pattern to the 1% CO₂ per year increase experiment.” [Full text]

Coupled climate modelling at GFDL: Recent accomplishment and future plans – Delworth et al. (1999) (CLIVAR Exchanges 4(4), 15-20)

Transient Climate Change Simulations with a Coupled Atmosphere–Ocean GCM Including the Tropospheric Sulfur Cycle – Roeckner et al. (1999) “The time-dependent climate response to changing concentrations of greenhouse gases and sulfate aerosols is studied using a coupled general circulation model of the atmosphere and the ocean (ECHAM4/OPYC3). … As in previous experiments, the climate response is similar, but weaker, if aerosol effects are included in addition to greenhouse gases.” [Full text]

Effective thermal conduction model for estimating global warming – Wolbarst (1999) “This paper presents a simple way to approximate the dependence of the global mean air temperature at Earth’s surface on the atmospheric concentration of carbon dioxide. It treats the atmosphere as a blanket, the effective thermal conductivity of which is a decreasing function of the amount of CO₂ present, and does not involve the details of energy transport.”

Climate simulation at the secular time scale – Bertrand (1998) (Thèse de doctorat, Université catholique de Louvain, 208 pp.)

Transient Climate Change in the CSIRO Coupled Model with Dynamic Sea Ice – Gordon & O’Farrell (1997) “The CSIRO coupled model has been used in a “transient” greenhouse experiment. … The transient experiment (1% increase in CO₂ compounding per annum) gave a 2°C warming at time of CO₂ doubling. The model displayed a “cold start” effect with a (maximum) value estimated at 0.3°C.” [Full text]

Multi-fingerprint detection and attribution analysis of greenhouse gas, greenhouse gas-plus-aerosol and solar forced climate change – Hegerl et al. (1997) “A multi-fingerprint analysis is applied to the detection and attribution of anthropogenic climate change.” [Full text]

An Estimation of the Climatic Effects of Stratospheric Ozone Losses during the 1980s – MacKay et al. (1997) “Ozone perturbations at high latitudes result in a cooling of the surface–troposphere system that is greater (by a factor of 2.8) than that estimated from the change in radiative forcing resulting from ozone depletion and the model’s 2 × CO₂ climate sensitivity.” [Full text]

Geographical scenarios of greenhouse-gas and anthropogenic-sulfate-aerosol induced climate changes – Schlesinger et al. (1997) (Climate Research Group Report, Department of Atmospheric Sciences, University of illinois at Urbana Champaign, Urbana, IL, USA)

Sensitivity of Simulated Global Climate to Perturbations in Low-Cloud Microphysical Properties. Part I: Globally Uniform Perturbations – Chen & Ramaswamy (1996) “The sensitivity of the global climate to perturbations in the microphysical properties of low clouds is investigated using a general circulation model coupled to a static mixed layer ocean with fixed cloud distributions and incorporating a new broadband parameterization for cloud radiative properties. … The model’s climate sensitivity (ratio of global-mean surface temperature response to the global-mean radiative forcing) is virtually independent (to 10%) of the sign, magnitude, and the spatial pattern of the forcings considered, thus revealing a linear and invariant nature of the model’s global-mean response.” [Full text]

The Effect of Enhanced Greenhouse Warming on Winter Cyclone Frequencies and Strengths – Lambert (1995) “The extratropical winter cyclone climatologies for the Northern and Southern Hemispheres are presented for a control, or 1 × CO₂ simulation, and an enhanced greenhouse warming, or 2 × CO₂ simulation, using the second generation Canadian Climate Centre general circulation model.” [Full text]

A Global Climate Model (GENESIS) with a Land-Surface Transfer Scheme (LSX). Part II: CO₂ Sensitivity – Thompson & Pollard (1995) “The sensitivity of the equilibrium climate to doubled atmospheric CO₂ is investigated using the GENESIS global climate model version 1.02. … The global annual surface-air warming in the model is 2.1°C, with global precipitation increasing by 3.3%.” [Full text]

Response of the Météo-France climate model to changes in CO₂ and sea surface temperature – Mahfouf et al. (1993) “The climate response to an increase in carbon dioxide and sea surface temperatures is examined using the Météo-France climate model. … A 5-year simulation is performed with a doubled CO₂ concentration using, as lower boundary conditions, mean surface temperatures anomalies and sea ice limits predicted for the years 56–65 of a 100-year transient simulation performed at Hamburg with a global coupled atmosphere-ocean model. The perturbed simulation produces a global mean surface air warming of 1.4 K and an increase in global mean precipitation rate of 4%.”

Century-scale effects of increased atmospheric CO₂ on the ocean-atmosphere system – Manabe & Stouffer (1993) “A coupled ocean-atmosphere climate model is presently used to project the evolution of the world’s climate over the course of several centuries characterized by (1) a doubling and (2) a quadrupling of atmospheric CO₂. Global mean surface air temperature increases of 3.5 and 7 percent, respectively, are seen over a period of 500 years; these projections are respectively associated with sea level rises of 1 and 2 m apart from ice-sheet melting, which would make the figures much larger.”

Greenhouse Gas–induced Climate Change Simulated with the CCC Second-Generation General Circulation Model – Boer et al. (1992) “The Canadian Climate Centre second-generation atmospheric general circulation model coupled to a mixed-layer ocean incorporating thermodynamic sea ice is used to simulate the equilibrium climate response to a doubling of C0₂. … The results of the simulation indicate a global annual warming of 3.5°C with enhanced warming found over land and at higher latitudes.” [Full text]

Deriving global climate sensitivity from palaeoclimate reconstructions – Hoffert & Covey (1992) “Here we retrieve the sensitivity of two palaeoclimates, one colder and one warmer than present, by independently reconstructing both the equilibrium surface tem-perature change and the radiative forcing. Our results yield ΔT_2x = 2.3 ±0.9 °C. This range is comparable with estimates from GCMs and inferences from recent temperature observations and ocean models.”

The Response of the BMRC AGCM to a Doubling of CO₂ – McAvaney et al. (1991) (BMRC Technical Memorandum No. 3)

Sensitivity of the equilibrium surface temperature of a GCM to systematic changes in atmospheric carbon dioxide – Oglesby & Saltzman (1990) “The equilibrium response of surface temperature to atmospheric CO₂ concentration, for six values between 100 and 1000 ppm, is calculated from a series of general circulation model experiments. This response is nonlinear, showing greater sensitivity for lower values of CO₂ than for the higher values. It is suggested that changes in CO₂ concentration of a given magnitude (e.g., 100 ppm) play a larger role in the Pleistocene ice age type temperature variations, than in causing global temperature changes due to anthropogenic increases.”

C0₂ and climate: a missing feedback? – Mitchell & Ingram (1989) “Here we report results of simulations that indicate that the changes of state of cloud water may provide a substantial negative feedback on climate. The feedback is concen-trated in mid-latitudes and affects both the magnitude and distribu-tion of the climate change expected from increases in ‘greenhouse’ gases. Improved measurements and parameterizations of cloud processes are needed to quantify this process.”

The effect of doubling the CO 2 concentration on convective and non-convective rainfall in a general circulation model coupled with a simple mixed layer ocean – Noda & Tokioka (1989) (Journal of the Meteorological Society of Japan, 67, 95-110)

Design and Critical Appraisal of an Accelerated Integration Procedure for Atmospheric GCM/Mixed-Layer Ocean Models – Schlesinger et al. (1989) “The AIP was used for 1 × CO₂ and 2 × CO₂ simulations with the OSU AGCM/mixed-layer Oman model.” [Full text]

Climate sensitivity due to increased CO₂: experiments with a coupled atmosphere and ocean general circulation model – Washington & Meehl (1989) “Three simulations are run: one with an instantaneous doubling of atmospheric CO₂ (from 330 to 660 ppm), another with the CO₂ concentration starting at 330 ppm and increasing linearly at a rate of 1% per year, and a third with CO₂ held constant at 330 pm. Results at the end of 30 years of simulation indicate a globally averaged surface air temperature increase of 1.6° C for the instantaneous doubling case…”

Cloud Feedback Processes in a General Circulation Model – Wetherald & Manabe (1988) “The influence of the cloud feedback process upon the sensitivity of climate is investigated by comparing the behavior of two versions of a climate model with predicted and prescribed cloud cover. … At most latitudes the effect of reduced cloud amount in the upper troposphere overshadows that of increased cloudiness around the tropopause, thereby lowering the global mean planetary albedo and enhancing the CO₂ induced warming. On the other hand, the increase of low cloudiness in high latitudes raises the planetary albedo and thus decreases the CO₂ induced warming of climate. However, the contribution of this negative feedback process is much smaller than the effect of the positive feedback process involving the change of high cloud.” [Full text]

Simulated climate and CO₂—Induced climate change over Western Europe – Wilson & Mitchell (1987) “When atmospheric CO₂ concentrations are quadrupled, and sea surface temperatures and sea ice extents changed appropriately, the number of cold episodes is reduced and precipitation is less frequent in summer and autumn over much of Europe, and throughout the year in the south.”

An investigation of cloud cover change in response to thermal forcing – Wetherald & Manabe (1986) “This article reviews the distributions of cloud cover change from several climate sensitivity experiments conducted at the Geophysical Fluid Dynamics Laboratory of NOAA (GFDL) and other institutions. … It was found that in all five cases, clouds were decreased in the moist, convectively active regions such as the tropical and middle latitude rainbelts, whereas they increased in the stable region near the model surface from middle to higher latitudes. In addition, cloud also increased in the lower model stratosphere and generally decreased in the middle and upper troposphere for practically all latitudes.”

Volcanic, CO₂ and solar forcing of Northern and Southern Hemisphere surface air temperatures – Gilliland & Schneider (1984) “The model used here allows a direct comparison of observed and simulated temperatures from the same physical domains—over land and sea separately in each hemisphere. … The empirically derived CO₂ equilibrium doubling response for air surface temperature is 1.6 +/- 0.3°C, although the statistical significance of this result is uncertain.”

Climate sensitivity: Analysis of feedback mechanisms – Hansen et al. (1984) “We study climate sensitivity and feedback processes in three independent ways: (1) by using a three dimensional (3-D) global climate model for experiments in which solar irradiance S_o is increased 2 percent or CO₂ is doubled, (2) by using the CLIMAP climate boundary conditions to analyze the contributions of different physical processes to the cooling of the last ice age (18K years ago), and (3) by using estimated changes in global temperature and the abundance of atmospheric greenhouse gases to deduce an empirical climate sensitivity for the period 1850-1980. … Our 3-D global climate model yields a warming of ~4°C for either a 2 percent increase of S_o or doubled CO₂. … The temperature increase believed to have occurred in the past 130 years (approximately 0.5°C) is also found to imply a climate sensitivity of 2.5-5°C for doubled Cog…” [Full text]

Seasonal Cycle Experiment on the Climate Sensitivity Due to a Doubling of CO₂ With an Atmospheric General Circulation Model Coupled to a Simple Mixed-Layer Ocean Model – Washington & Meehl (1984) “A simple slab ocean of 50 m depth, which allows for seasonal ocean heat storage but no ocean heat transport, is coupled to a global spectral general circulation model with global domain, realistic geography, and computed clouds. Globally averaged, the annual mean surface air temperature increase computed over the last 3 years of an integration with a full annual cycle for 2 × CO₂ compared to the control for 1 × CO₂ is 3.5°C.”

Climate Studies with a Multi-Layer Energy Balance Model. Part II: The Role of Feedback Mechanisms in the CO₂ Problem – Chou et al. (1982) “The sensitivity of climate to a doubling of the atmospheric CO₂, content has been studied using the GLAS multi-layer energy balance model. In response to a doubled CO₂ content, tropospheric temperature lapse rate decreases at low latitudes but increases at high latitudes. Averaged over the Northern Hemisphere, the change is +2.3°C in the surface temperature and +0.47°C in the earth’s brightness temperature. … It is found that the sensitivity of surface temperature is approximately doubled at all latitudes due to the change in water vapor content.” [Full text]

Sensitivity Analysis of a Radiative-Convective Model by the Adjoint Method – Hall et al. (1982) “The adjoint method of sensitivity analysis is demonstrated on a radiative-convective climate model. … The sensitivities accurately predict the effect on surface air temperature of small variations in the model parameters. Relative sensitivities are used to rank the importance of all the parameters. Several of the sensitivities to parameters customarily considered in previous works (e.g., solar constant, surface albedo, relative humidity, CO₂ concentration) are reproduced, but the largest sensitivities are to constants used to compute the saturation vapor pressure of water.” [Full text]

Impact of coupled perturbations of atmospheric trace gases on Earth’s climate and ozone – Nicoli & Visconti (1982) “The doubling of carbon dioxide concentration has the effect of warming the troposphere and cooling the stratosphere. As a result of this cooling, the change of ozone columnar density produced by 10 ppb of chlorine amount to 9.3% as compared to –10.9% obtained without temperature feedback. Perturbation in nitrous oxide correspond to an increase in NO x of the stratosphere with consequent ozone reduction while doubling the methane concentration correspond to a slight increase in columnar density. The effect of the increased methane concentration in the stratosphere contributes to reduce the effect of CFC due to the enhanced formation of HCl. The perturbation of these two minor constituents appreciably increase the greenhouse effect to 2.30 from 1.67°, obtained when carbon dioxide alone is considered.”

The Role of Ocean-Atmosphere Interactions in the CO₂ Climate Problem – Ramanathan (1981) “The climate sensitivity question is examined from the viewpoint of surface energy balance considerations. This approach clarifies the role of ocean-atmosphere interactions in determining the surface warming to an increase in CO₂. The study uses a one-dimensional, 17-layer, coupled ocean-atmosphere model. The primary contribution to the surface warming is from the enhanced tropospheric IR emission, which is an order of magnitude greater than the direct CO₂ radiative heating at the surface. The source for this enhancement is the increased H₂O evaporation from the warmer oceans in the CO₂ rich atmosphere and, hence, ocean-atmosphere interactions play a crucial role in determining the magnitude of the surface warming as well as its transient response.” [Full text]

On the Distribution of Climate Change Resulting from an Increase in CO₂ Content of the Atmosphere – Manabe & Wetherald (1980) “A study of the climatic effect of doubling or quadrupling of CO₂ in the atmosphere has been continued by the use of a simple general circulation model with a limited computational domain, highly idealized geography, no seasonal variation of insolation, and a simplified interaction between cloud and radiative transfer. The results from the numerical experiments reveal that the response of the model climate to an increase of CO₂ content in air is far from uniform geographically.” [Full text]

The Climatological Significance of a Doubling of Earth’s Atmospheric Carbon Dioxide Concentration – Idso (1980) “The mean global increase in thermal radiation received at the surface of the earth as a consequence of a doubling of the atmospheric carbon dioxide content is calculated to be 2.28 watts per square meter. Multiplying this forcing function by the atmosphere’s surface air temperature response function, which has recently been determined by three independent experimental analyses to have a mean global value of 0.113 K per watt per square meter, yields a value of <= 0.26 K for the resultant change in the mean global surface air temperature. This result is about one order of magnitude less than those obtained from most theoretical numerical models, but it is virtually identical to the result of a fourth experimental approach to the problem described by Newell and Dopplick.”

A CO₂-climate sensitivity study with a mathematical model of the global climate – Manabe & Stouffer (1979) “An increase in the CO₂-content of the atmosphere resulting from man’s activity could have a significant effect on the climate in the near future. We describe here some new results from a study of the response of a mathematical model of the climate to an increase in the CO₂ content of the air.”

Some Experiments with a Zonally Averaged Climate Model – Ohring & Adler (1978) “When the atmospheric carbon dioxide content is doubled, the hemispheric mean surface temperature increases by 0.5°C in the absence of ice feedback, the largest increases taking place at high latitudes. Ice albedo feedback amplifies the hemispheric average temperature change by about 50%; amplifications as large as several hundred percent are obtained in polar regions. A change in mean surface temperature of ±1°C for a ±1% change in solar constant is obtained in the absence of ice feedback, but this is amplified to −1.5°C (decreased solar constant) and 1.4°C (increased solar constant) when ice feedback is included. As In the 2×CO₂ case, polar amplification factors due to ice albedo feedback are several hundred percent.” [Full text]

A Radiative-Convective Model Study of the CO₂ Climate Problem – Augustsson & Ramanathan (1977) “A radiative-convective model study of the increase in global surface temperature ΔTg due to an increase in the CO₂ concentration is presented. … The computed value of ΔTg is very sensitive to radiative-convective model assumptions regarding cloud top and relative humidity. Because of this sensitivity the estimated value of ΔTg for a doubling of the CO₂ concentration ranges from 1.98 to 3.2 K.” [Full text]

An Annual Zonally Averaged Hemispherical Climatic Model with Diffuse Cloudiness Feedback – Temkin & Snell (1976) “An annual, zonally averaged, steady-state hemispherical climatic model is developed which incorporates the diffuse thin cloud tropospheric structure of Weare and Snell as a cloudiness feedback mechanism. … The response of the model to variations in various climatic determinants is studied, including hemispherical variations in carbon dioxide, aerosol and solar constant, and also including certain zonal variations in man-made thermal energy and aerosol. … The sensitivity of the model in terms of the hemispherical mean sea level temperature is about twice that of the globally averaged model of Weare and Snell.” [Full text]

The dependence of atmospheric temperature on the concentration of carbon dioxide – Manabe (1975) A book chapter. “The effect of changes in the carbon dioxide content of the atmosphere on the average world temperature is investigated using a radiative, convective model of the atmosphere (Manabe et al., 1964, 1967). The radiative, convective equilibrium of the atmosphere obtained with the model is in good agreement with the distribution given by the U.S. standard atmosphere. Numerical computations indicate that doubling or halving the atmospheric CO₂ concentration increases or decreases the surface temperature of the atmosphere by about 2.3 deg C. Assuming a 25% increase from the 1900 concentration by the end of this century, a corresponding 0.8 deg C increase in average surface temperature is predicted.”

The Effects of Doubling the CO₂ Concentration on the climate of a General Circulation Model – Manabe & Wetherald (1975) “An attempt is made to estimate the temperature changes resulting from doubling the present CO₂ concentration by the use of a simplified three-dimensional general circulation model. … It is shown that the CO₂ increase raises the temperature of the model troposphere, whereas it lowers that of the model stratosphere.” [Full text]

A study of the sensitivity of radiativeconvective models – Ramanathan (1975) (Preprints Second Conf. Atmospheric Radiation, 1975) This probably is the referred Ramanathan (1975).

A Reassessment of the Effect of CO₂ Variations on a Simple Global Climatic Model – Sellers (1974) “A simple global climatic model described earlier is modified slightly and reapplied to the CO₂ problem. … …the average global surface temperature drops 1.64C if the amount of CO₂ in the atmosphere is halved and rises 1.32C if the amount is doubled.” [Full text]

A Diffuse Thin Cloud Atmospheric Structure as a Feedback Mechanism in Global Climatic Modeling – Weare & Snell (1974) “The sensitivity of the “climate” to variations in aerosol optical density, atmospheric carbon dioxide, and the solar constant is calculated and the results are comparable to those obtained by others using very different models. In general, our model exhibits slightly greater stability.” [Full text]

A New Global Climatic Model – Sellers (1973) “The initial carbon dioxide content of the atmosphere (250 cm) was doubled and halved without any appreciable effect on surface temperatures. Doubling the CO₂ content increased the temperature by at most 0.6C (at high northern latitudes in winter); the average increase was only 0.1C.” [Full text]

Estimates of future change of climate due to the increase of carbon dioxide concentration in the air – Manabe (1971) (Man’s Impact on the Climate, W. I-I. Matthews, W. W. Kellogg, and G. D. Robinson, Eds., Cambridge, MA: The MIT Press, 249-264)

Atmospheric Carbon Dioxide and Aerosols: Effects of Large Increases on Global Climate – Rasool & Schneider (1971) “Effects on the global temperature of large increases in carbon dioxide and aerosol densities in the atmosphere of Earth have been computed. It is found that, although the addition of carbon dioxide in the atmosphere does increase the surface temperature, the rate of temperature increase diminishes with increasing carbon dioxide in the atmosphere.”

Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity – Manabe & Wetherald (1967) “Radiative convective equilibrium of the atmosphere with a given distribution of relative humidity is computed as the asymptotic state of an initial value problem. … According to our estimate, a doubling of the CO₂ content in the atmosphere has the effect of raising the temperature of the atmosphere (whose relative humidity is fixed) by about 2C. Our model does not have the extreme sensitivity of atmospheric temperature to changes of CO₂ content which was adduced by Möller.” [Full text]

On the Influence of Changes in the CO₂ Concentration in Air on the Radiation Balance of the Earth’s Surface and on the Climate – Möller (1963) (J. Geophysical Research 68, 3877-3886) Is missing from JGR digital library.

The carbon dioxide theory of climate change – Plass (1956) “The most recent calculations of the infra-red flux in the region of the 15 micron CO₂ band show that the average surface temperature of the earth increases 3.6° C if the CO₂ concentration in the atmosphere is doubled and decreases 3.8° C if the CO₂ amount is halved, provided that no other factors change which influence the radiation balance.” [Full text]

The Artificial Production of Carbon Dioxide and Its Influence on Climate – Callendar (1938) (Quarterly J. Royal Meteorological Society 64, 223-40)

The Temperature of the Lower Atmosphere of the Earth – Hulburt (1931) “From the known amounts of the various gases of the atmosphere from sea level to about 20 km, from the observed light absorption coefficients of the gases and from the albedo of the earth’s surface the temperature of the atmosphere in radiative equilibrium is calculated on the assumption that the sunlight is the only source of energy. … Calculation shows that doubling or tripling the amount of the carbon dioxide of the atmosphere increases the average sea level temperature by about 4° and 7°K, respectively; halving or reducing to zero the carbon dioxide decreases the temperature by similar amounts. Such changes in temperature are about the same as those which occur when the earth passes from an ice age to a warm age, or vice versa. Thus the calculation indicates that the carbon dioxide theory of the ice ages, originally proposed by Tyndall, is a possible theory.”

On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground – Arrhenius (1896) “Thus if the quantity of carbonic acid increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression.” [Full text]