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FIGURE 1: EMPIRICAL SENSITIVITY VALUES 1880-2018: BY LOCATION

FIGURE 2: EMPIRICAL SENSITIVITY VALUES 1880-2018: BY DATA SOURCE

FIGURE 3: CORRELATION ANALYSIS 1880-2018

FIGURE 4: CLIMATE SENSITIVITY SUMMARY TABLE

FIGURE 5: CORRELATION ANALYSIS: SUMMARY TABLE

FIGURE 6: CLIMATE SENSITIVITY IN A MOVING 60-YEAR WINDOW

FIGURE 7: 1959-2018: SENSITIVITY & CORRELATION

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1. The science of climate change by human activity in the industrial economy in terms of the combustion of fossil fuels rests on two relationships. The first is that the observed rise in atmospheric CO2 concentration is driven by CO2 emissions from fossil fuels; and the second is that the observed rise in surface temperature is driven by the higher levels of atmospheric CO2 thus created. The relationship between atmospheric CO2 concentration and surface temperature is thought to be governed by the so called “greenhouse effect” which implies that surface temperature is responsive to the logarithm of atmospheric CO2 concentration in a positive relationship such that higher atmospheric CO2 concentration generates higher surface temperature. This relationship is expressed as “climate sensitivity” and computed as the the increase in surface temperature in Celsius units for each doubling of atmospheric carbon dioxide. The first of these two critical relationships in the science of climate change is discussed in a related post on this site [LINK] . This post is a presentation of the second relationship in the form of an empirical test with global mean temperature reconstructions. This relationship has been studied in prior posts on this site  [LINK]  [LINK]  [LINK]  [LINK] .
2. Although climate models deliver robust and consistent values for the climate sensitivity parameter λ across time spans and forcing conditions, climate science acknowledges an “uncertainty problem” in the matter of the testable implication of the climate sensitivity hypothesis in empirical temperature data. Long term empirical data for global mean temperature prior to the satellite er are available only as temperature reconstructions from the instrumental record over long time spans greater than a century. Direct observations of lower troposphere temperature in the satellite era are available since 1979. A comparison of  climate sensitivities for the direct observations in the satellite era with those in temperature reconstructions and climate models in the 40-year sample period 1979-2018 is presented in a related posts on this site  [LINK]  [LINK] . These comparison shows gross unexplained differences in climate sensitivities among direct observations, temperature reconstructions, and climate models.
3. It is claimed that a weakness of the 40-year study 1979-2018 may lie in terms of the brief span of the sample period  if the climate sensitivity mechanism works over longer time spans. This argument contains a serious weakness in terms of inconsistency such that climate scientists themselves, faced with large uncertainties in climate sensitivity over the longer time spans of temperature reconstructions now claim that the climate sensitivity theory can be empirically validated at much lower uncertainty “since the 1970s” [LINK] and “in the last 35 years” [LINK] .
4. Extending the time span of the study to the time prior to the satellite era comes at the cost of of losing access to direct observations of global mean temperature and thereby being restricted to reconstructions of global mean temperature the weaknesses of which is demonstrated in related works [LINK]  [LINK].  These weaknesses imply that temperature reconstructions may contain built-in circular reasoning in terms of empirical tests of climate sensitivity if climate sensitivity was assumed in their construction. This study of climate sensitivity over longer time spans with temperature reconstructions is therefore presented with the caveat that the data exhibit significant differences from direct observations in the common 40-year period 1979-2018 [LINK] .
5. Four temperature data sets are studied in the common 139-year sample period 1880-2018. The datasets include three temperature reconstructions (HAD=Hadley Centre HadCRUT4, GIS=GISTEMP land and ocean global mean, and BRK=Berkeley Earth Surface Temperatures) and one climate model construction with CMIP5 forcings (RCP=RCP8.5 business as usual temperature prediction according to the CO2 theory of warming). The temperature reconstructions are provided as temperature anomalies for each calendar month while the theoretical climate model series is provided in actual temperatures for each calendar month. All four temperature time series are tabulated in Celsius units.
6. The methodology used consists of simply comparing the climate sensitivities and the correlations with Ln(CO2) of the four temperature series needed to validate the computed sensitivity. These tests are carried out at the full span of the available data as well as for the first half, second half, and middle half of the data series as a way of testing the stability and robustness of the empirical value of climate sensitivity. In addition we look at the stability and robustness of the climate sensitivity in a moving 60-year window that moves through the time series one year at a time. The 60-year period was selected as twice the 30-year span described by the WMO as the minimum time span needed to aggregate weather data into a statement about climate (“Climate is thirty years of weather.”).
7. A separate comparative analysis is presented for the last 60 years 1958-2018. The unique property of the last 60 years is that high quality direct observations of monthly mean atmospheric CO2 concentration are available from the relatively isolated Mauna Loa measurement station. By contrast, studies of older temperatures are forced to rely on atmospheric CO2 concentration reconstructions from the Law Dome ice core study. All analyses are carried out separately for the twelve calendar months. The atmospheric CO2 concentration data prior to 1958 from the Law Dome dataset and are available only as annual means. These annual means are used for each calendar month as an approximation.  The separate analysis of the last 60 years derives its significance in terms of the availability of better quality monthly mean CO2 data.
8. Figure 1 and Figure 2 display the empirical climate sensitivity values computed from the four temperature series labeled as HAD, GIS, BRK, and RCP. Four sensitivity values are computed for each temperature time series at different locations within the sample period and color coded. The charts are labeled as FULL SPAN (1880-2018), 1st HALF (1880-1949), 2nd HALF (1949-2018), MID-HALF (1915-1983). Each sensitivity chart shows twelve sensitivity values, one for each calendar month. Each of Figure 1 and Figure 2 consists of four charts. The results in these charts are as follows:
9. Figure 1: The top left chart shows that the full span climate sensitivity values for the four temperature series and twelve calendar months are tightly distributed within a range of  FULLSPAN λ=2.0<λ<2.7  with a mean of λ=2.4 and median of λ=2.3. The variance represents mostly differences among data sources with little or no variance among calendar months. The annual means for the four data sources are λ[HAD,GIS,BRK,RCP]=[2.1,2.3,2.5,2.5]. These results taken in isolation appear to indicate  that …
10. (1) a robust, stable, and statistically significant value of climate sensitivity is found in the empirical data as λ=2.4
11. (2) the value of the sensitivity parameter is highest for the theoretical climate model derived RCP8.5 series at λ=2.5 and lowest in the HadCRUT4 temperature reconstructions at λ=2.1 with minor differences among the calendar months. The mean value of λ=2.4 is a significant departure from the Charney/IPCC value of λ=3 but within the large IPCC uncertainty range of [1.5<λ<4.5].
12. Figure 1: The top right chart shows that the half span climate sensitivity values in the most recent period 1949-2018 for the four temperature series and twelve calendar months are are in close agreement with the full span values but with somewhat greater variance with 2ndHALF λ=1.9<λ<2.9  with a mean of λ=2.4 and median of λ=2.4. This portion of the split half test appears to provide strong support for the stability of the mean full span sensitivity of λ=2.4.
13. Figure 1: The bottom left chart shows that the half span climate sensitivity values in the the first half of the data series 1880-1949 for the four temperature series and twelve calendar months show a gross departure from the full span values with much greater variance. Here we find climate sensitivity values of 1stHALF λ=1.8<λ<5.6  with a mean of λ=3.5 and median of λ=3.7 and with much larger variance among the calendar months. This portion of the split half test does not provide support for the stability of the mean full span sensitivity of λ=2.4 and implies instead that the sensitivity mean value seen in the full span is not supported in terms of statistical stability.
14. Figure 1: The bottom right chart shows that the half span climate sensitivity values in the the middle half of the data 1915-1983 for the four temperature series and twelve calendar months also show a gross departure from full span sensitivities but toward much lower values. Here we find climate sensitivity values of MIDHALF λ=1.0<λ<2.7  with a mean of λ=1.9 and median also of λ=1.9. A much larger variance among the calendar months is seen when compared with the full span and 2ndHALF values. This portion of the split half test does not provide support for the stability of the mean full span sensitivity of λ=2.4 and implies instead that the sensitivity mean value seen in the full span is not supported in terms of statistical stability.
15. The sensitivity values displayed in Figure 1 also appear in Figure 2 but differently arranged. The empirical sensitivity values are grouped according to location along the time series in Figure 1 with each chart showing all four data series for a given location. In Figure 2 they are grouped according to data source with each chart showing all four locations for a given data source. The sensitivity values and their statistical properties are tabulated in Figure 4.
16. A further investigation of the stability and reliability of these empirical climate sensitivity values is presented as a correlation analysis in Figure 3 where the correlation between temperature and Ln(CO2) implied by the theory of climate sensitivity is examined. There are eight charts. The top four charts show correlations in the source data while the bottom four show the corresponding detrended correlation. Source data correlation includes a contribution to correlation from shared long term trends while detrended correlations show only the responsiveness at an annual time scale.
17. The first row of charts of Figure 3 shows that the theoretical series RCP8.5 derived from climate models contains a strong and near perfect correlation of ρ=0.96 for the full span and 2nd half of the time series. This correlation mostly survives into the detrended series at ρ=0.81 for the full span and an even stronger ρ=0.89 for the 2nd half as shown in the third row of charts. These strong correlations and their high survival rate into the detrended series constitute strong evidence for the validity and reliability of the observed full span and 2nd half sensitivity values for the RCP8.5 series shown in Figure 1. It is noted that these correlations are the same for all twelve calendar months with no obvious variation among calendar months..
18. The corresponding correlations for the temperature reconstructions are considerably lower and with a distinctive pattern of differences among the calendar months not seen in the temperatures generated by climate models. The pattern indicates generally higher correlations in summer than in winter. The first row of charts in Figure 3 show that the source data correlations for the full span and 2nd half are close to but less than the RCP8.5 climate model correlations with full span summer correlations of ρ=[0.90-0.92] and winter correlations lower at ρ=[0.82-0.87]. The corresponding values for the 2nd half are are similar with summer ρ=[0.88-0.92] and winter ρ=[0.78-0.89]. Among the three reconstruction sources, GIS and BRK show higher correlations than HAD in the full span and GIS shows higher correlations than BRK and HAD in the 2nd half. However all correlations in both the full span and 2nd half are strong and statistically significant. 
19. The detrended correlations of temperature reconstructions for the full span and 2nd half are found in the third row of correlation charts of Figure 3. They show a significant loss in correlation when the series are detrended particularly in the winter months but statistically significant correlations are found in the summer months ranging from ρ=[0.49-0.68] for the full span and even stronger correlations of ρ=[0.58-0.78] in the 2nd half of the sample period. All of these detrended correlations are statistically significant. We conclude from these results that the full span and 2nd half climate sensitivity values of λ=[2.0<λ<2.7]  and λ=[1.9<λ<2.9] respectively are supported by correlation analysis as stable and statistically valid and reliable. 
20. The correlation analysis for the first half of the sample period 1880-1949 and the mid-half of the sample period 1915-1983 are displayed in the second and fourth rows of Figure 3. Here we find that for the climate model temperature series RCP8.5, the source data correlation is a strong and steady ρ=[0.84-0.87] across all twelve calendar months and that the corresponding detrended correlations fall to the much lower but still statistically significant values of ρ=[0.43-0.68] . However, the temperature reconstructions do not fare as well. Here the source data correlations of ρ=[0.33-0.70] collapse to mostly statistically insignificant values of ρ=[Zero-0.52] in the detrended series. The highest detrended correlations are found in the GIS reconstructions from NASA-GISS which was flagged in a prior study [LINK] as an outlier among temperature reconstructions in its conformance with the GHG theory. This odd behavior of the GIS reconstruction raises the possibility that GHG forcing may have been assumed in its construction. 
21. Figure 6 shows the observed climate sensitivity in a moving 60-year window that moves one year at a time from end-year 1938 to the end of the data series in 2018. There are four charts one for each temperature series HAD, GIS, BRK, and RCP. Each chart contains twelve curves one for each calendar month. The charts show a common pattern of 60-year climate sensitivities for the three temperature reconstruction series with the the sensitivity values initially rising from end-year 1938 [HAD (2-4), GIS (0.5-2), and BRK (2.5-5)] to a high at end-year 1965 [HAD (5-6.5), GIS (4-6), and BRK (6-8)]. Thereafter, there is a sharp decline to end-year 1985 [HAD (0-2), GIS (0.5-2.5), and BRK (0-2)] followed by a gradual increase until end-year 2018 [HAD=2, GIS (2.5), and BRK (2.5)]. A great variability among calendar months seen in the earlier periods narrows progressively from 1985 such that a tight and narrow range of sensitivity values among calendar months is seen in end-year 2018. These results generalize the findings in the split half studies above as further evidence of an unacceptable level of instability and uncertainty in the estimation of climate sensitivity in empirical data for the data to serve as empirical evidence of climate sensitivity.
22. The comparatively low spread of sensitivities among calendar months very close to the value of λ=2 in the last 60-year period suggested a more detailed study of the period 1959-2018. The results are summarized in Figure 7. Here, the empirical sensitivity values plotted on the top frame for the four temperature series against the calendar months numbered from 1 to 12. The theoretical RCP temperature series shows a narrow range of values from λ=2.79 to λ=3.18 with a mean of λ=2.94 close to the theoretical value of λ=3 that was used to construct the series. Of the three temperature reconstructions, GIS sensitivity values are closest to theory with sensitivities for calendar months ranging from λ=2.29 to λ=2.73 and a mean of λ=2.48, somewhat lower than RCP but in a tight range. Sensitivity values for the other two reconstructions are at a greater distance from the theoretical RCP values with BRK [λ=2.16 to λ=2.64 mean λ=2.41] and HAD [λ=1.93 to λ=2.45 mean λ=2.17]. The range of values for all three reconstructions is larger with λ=1.93 to λ=2.73. 
23. A correlation analysis for these sensitivities is displayed in the middle frame of Figure 7. It shows strong detrended correlations for the theoretical RCP series ρ=[0.74-0.81] with a mean of ρ=0.78. Among the temperature reconstructions the detrended correlations from highest to lowest are HAD: ρ=[0.24-0.60] with a mean of ρ=0.48, HAD: ρ=[0.24-0.60] with a mean of ρ=0.48, GIS: ρ=[0.28-0.58] with a mean of ρ=0.39, and BRK: ρ=[0.41-0.63] with a mean of ρ=0.47. Although much lower than the theoretical RCP series, the mean detrended correlations are statistically significant. It is therefore safe to conclude that these detrended correlations support the sensitivity of the temperature reconstructions to atmospheric CO2 in accordance with the GHG theory of global warming in the 60-year period 1959-2018 but with some differences among the four temperature series in the magnitude of the sensitivity value which ranges from λ=2.17 to λ=3.28. 
24. CONCLUSION: A study of empirical climate sensitivity values in global mean temperature reconstructions 1880-2018 shows significant evidence of an unstable and unreliable relationship between atmospheric CO2 concentration and surface temperature with significant differences between theoretical and reconstruction temperature series. The findings do not provide good evidence for the existence of a climate sensitivity parameter that determines surface temperature according to atmospheric CO2 concentration over a study period from pre-industrial times to the present. Though the evidence for climate sensitivity is much stronger in the last 60-year period 1959-2018, evidence for the stability of this value over the generally accepted climate change study period is not found.

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ECS Bibliography

1. 2018: Dessler, A. E., and P. M. Forster. “An estimate of equilibrium climate sensitivity from interannual variability.“Journal of Geophysical Research: Atmospheres (2018). Estimating the equilibrium climate sensitivity (ECS; the equilibrium warming in response to a doubling of CO2) from observations is one of the big problems in climate science. Using observations of interannual climate variations covering the period 2000 to 2017 and a model‐derived relationship between interannual variations and forced climate change, we estimate ECS is likely 2.4‐4.6 K (17‐83% confidence interval), with a mode and median value of 2.9 and 3.3 K, respectively. This analysis provides no support for low values of ECS (below 2 K) suggested by other analyses. The main uncertainty in our estimate is not observational uncertainty, but rather uncertainty in converting observations of short‐term, mainly unforced climate variability to an estimate of the response of the climate system to long‐term forced warming.: Plain language summary: Equilibrium climate sensitivity (ECS) is the amount of warming resulting from doubling carbon dioxide. It is one of the important metrics in climate science because it is a primary determinant of how much warming we will experience in the future. Despite decades of work, this quantity remains uncertain: the last IPCC report stated a range for ECS of 1.5‐4.5 deg. Celsius. Using observations of interannual climate variations covering the period 2000 to 2017, we estimate ECS is likely 2.4‐4.6 K. Thus, our analysis provides no support for the bottom of the IPCC’s range.
2. 2018: Cox, Peter M., Chris Huntingford, and Mark S. Williamson. “Emergent constraint on equilibrium climate sensitivity from global temperature variability.” Nature 553.7688 (2018): 319. Equilibrium climate sensitivity (ECS) remains one of the most important unknowns in climate change science. ECS is defined as the global mean warming that would occur if the atmospheric carbon dioxide (CO₂) concentration were instantly doubled and the climate were then brought to equilibrium with that new level of CO₂. Despite its rather idealized definition, ECS has continuing relevance for international climate change agreements, which are often framed in terms of stabilization of global warming relative to the pre-industrial climate. However, the ‘likely’ range of ECS as stated by the Intergovernmental Panel on Climate Change (IPCC) has remained at 1.5–4.5 degrees Celsius for more than 25 years¹. The possibility of a value of ECS towards the upper end of this range reduces the feasibility of avoiding 2 degrees Celsius of global warming, as required by the Paris Agreement. Here we present a new emergent constraint on ECS that yields a central estimate of 2.8 degrees Celsius with 66 per cent confidence limits (equivalent to the IPCC ‘likely’ range) of 2.2–3.4 degrees Celsius. Our approach is to focus on the variability of temperature about long-term historical warming, rather than on the warming trend itself. We use an ensemble of climate models to define an emergent relationship²between ECS and a theoretically informed metric of global temperature variability. This metric of variability can also be calculated from observational records of global warming, which enables tighter constraints to be placed on ECS, reducing the probability of ECS being less than 1.5 degrees Celsius to less than 3 per cent, and the probability of ECS exceeding 4.5 degrees Celsius to less than 1 per cent.
3. 2018: Schurgers, Guy, et al. “Climate sensitivity controls uncertainty in future terrestrial carbon sink.” Geophysical Research Letters 45.9 (2018): 4329-4336. For the 21st century, carbon cycle models typically project an increase of terrestrial carbon with increasing atmospheric CO₂ and a decrease with the accompanying climate change. However, these estimates are poorly constrained, primarily because they typically rely on a limited number of emission and climate scenarios. Here we explore a wide range of combinations of CO₂ rise and climate change and assess their likelihood with the climate change responses obtained from climate models. Our results demonstrate that the terrestrial carbon uptake depends critically on the climate sensitivity of individual climate models, representing a large uncertainty of model estimates. In our simulations, the terrestrial biosphere is unlikely to become a strong source of carbon with any likely combination of CO₂ and climate change in the absence of land use change, but the fraction of the emissions taken up by the terrestrial biosphere will decrease drastically with higher emissions.
4. 2018: Wagner, Gernot, and Martin L. Weitzman. “Potentially large equilibrium climate sensitivity tail uncertainty.” Economics Letters 168 (2018): 144-146. Equilibrium climate sensitivity (ECS), the link between concentrations of greenhouse gases in the atmosphere and eventual global average temperatures, has been persistently and perhaps deeply uncertain. Its ‘likely’ range has been approximately between 1.5 and 4.5 degrees Centigrade for almost 40 years (Wagner and Weitzman, 2015). Moreover, Roe and Baker (2007), Weitzman (2009), and others have argued that its right-hand tail may be long, ‘fat’ even. Enter Cox et al. (2018), who use an ‘emergent constraint’ approach to characterize the probability distribution of ECS as having a central or best estimate of 2.8  °C with a 66% confidence interval of 2.2–3.4  °C. This implies, by their calculations, that the probability of ECS exceeding 4.5  °C is less than 1%. They characterize such kind of result as “renewing hope that we may yet be able to avoid global warming exceeding 2[°C]”. We share the desire for less uncertainty around ECS Weitzman (2011), Wagner and Weitzman (2015). However, we are afraid that the upper-tail emergent constraint on ECS is largely a function of the assumed normal error terms in the regression analysis. We do not attempt to evaluate Cox et al. (2018)’s physical modeling (aside from the normality assumption), leaving that task to physical scientists. We take Cox et al. (2018)’s 66% confidence interval as given and explore the implications of applying alternative probability distributions. We find, for example, that moving from a normal to a log-normal distribution, while giving identical probabilities for being in the 2.2–3.4 °C range, increases the probability of exceeding 4.5 °C by over five times. Using instead a fat-tailed Pareto distribution, an admittedly extreme case, increases the probability by over forty times. (blogger’s comment: some statistical issues in the treatment of ECS by climate scientists.)
5. 2018: Jonko, Alexandra, Nathan M. Urban, and Balu Nadiga. “Towards Bayesian hierarchical inference of equilibrium climate sensitivity from a combination of CMIP5 climate models and observational data.” Climatic Change 149.2 (2018): 247-260. Despite decades of research, large multi-model uncertainty remains about the Earth’s equilibrium climate sensitivity to carbon dioxide forcing as inferred from state-of-the-art Earth system models (ESMs). Statistical treatments of multi-model uncertainties are often limited to simple ESM averaging approaches. Sometimes models are weighted by how well they reproduce historical climate observations. Here, we propose a novel approach to multi-model combination and uncertainty quantification. Rather than averaging a discrete set of models, our approach samples from a continuous distribution over a reduced space of simple model parameters. We fit the free parameters of a reduced-order climate model to the output of each member of the multi-model ensemble. The reduced-order parameter estimates are then combined using a hierarchical Bayesian statistical model. The result is a multi-model distribution of reduced-model parameters, including climate sensitivity. In effect, the multi-model uncertainty problem within an ensemble of ESMs is converted to a parametric uncertainty problem within a reduced model. The multi-model distribution can then be updated with observational data, combining two independent lines of evidence. We apply this approach to 24 model simulations of global surface temperature and net top-of-atmosphere radiation response to abrupt quadrupling of carbon dioxide, and four historical temperature data sets. Our reduced order model is a 2-layer energy balance model. We present probability distributions of climate sensitivity based on (1) the multi-model ensemble alone and (2) the multi-model ensemble and observations.
6. 2018: Skeie, Ragnhild Bieltvedt, et al. “Climate sensitivity estimates–sensitivity to radiative forcing time series and observational data.” Earth System Dynamics 9.2 (2018): 879-894. . Inferred effective climate sensitivity (ECSinf) is estimated using a method combining radiative forcing (RF) time series and several series of observed ocean heat content (OHC) and near-surface temperature change in a Bayesian framework using a simple energy balance model and a stochastic model. The model is updated compared to our previous analysis by using recent forcing estimates from IPCC, including OHC data for the deep ocean, and extending the time series to 2014. In our main analysis, the mean value of the estimated
   ECSinf is 2.0 ◦C, with a median value of 1.9 ◦C and a 90 % credible interval (CI) of 1.2–3.1 ◦C. The mean estimate has recently been shown to be consistent with the higher values for the equilibrium climate sensitivity estimated by climate models. The transient climate response (TCR) is estimated to have a mean value of 1.4 ◦C
   (90 % CI 0.9–2.0 ◦C), and in our main analysis the posterior aerosol effective radiative forcing is similar to the range provided by the IPCC. We show a strong sensitivity of the estimated ECSinf to the choice of a priori RF time series, excluding pre-1950 data and the treatment of OHC data. Sensitivity analysis performed by merging the upper (0–700 m) and the deep-ocean OHC or using only one OHC dataset (instead of four in the main analysis) both give an enhancement of the mean ECSinf by about 50 % from our best estimate. FULL TEXT PDF
7. 2018: Qu, Xin, et al. “On the emergent constraints of climate sensitivity.” Journal of Climate 31.2 (2018): 863-875. Differences among climate models in equilibrium climate sensitivity (ECS; the equilibrium surface temperature response to a doubling of atmospheric CO₂) remain a significant barrier to the accurate assessment of societally important impacts of climate change. Relationships between ECS and observable metrics of the current climate in model ensembles, so-called emergent constraints, have been used to constrain ECS. Here a statistical method (including a backward selection process) is employed to achieve a better statistical understanding of the connections between four recently proposed emergent constraint metrics and individual feedbacks influencing ECS. The relationship between each metric and ECS is largely attributable to a statistical connection with shortwave low cloud feedback, the leading cause of intermodel ECS spread. This result bolsters confidence in some of the metrics, which had assumed such a connection in the first place. Additional analysis is conducted with a few thousand artificial metrics that are randomly generated but are well correlated with ECS. The relationships between the contrived metrics and ECS can also be linked statistically to shortwave cloud feedback. Thus, any proposed or forthcoming ECS constraint based on the current generation of climate models should be viewed as a potential constraint on shortwave cloud feedback, and physical links with that feedback should be investigated to verify that the constraint is real. In addition, any proposed ECS constraint should not be taken at face value since other factors influencing ECS besides shortwave cloud feedback could be systematically biased in the models.
8. 2018: Rohling, Eelco J., et al. “Comparing climate sensitivity, past and present.” Annual review of marine science 10 (2018): 261-288. Climate sensitivity represents the global mean temperature change caused by changes in the radiative balance of climate; it is studied for both present/future (actuo) and past (paleo) climate variations, with the former based on instrumental records and/or various types of model simulations. Paleo-estimates are often considered informative for assessments of actuo-climate change caused by anthropogenic greenhouse forcing, but this utility remains debated because of concerns about the impacts of uncertainties, assumptions, and incomplete knowledge about controlling mechanisms in the dynamic climate system, with its multiple interacting feedbacks and their potential dependence on the climate background state. This is exacerbated by the need to assess actuo- and paleoclimate sensitivity over different timescales, with different drivers, and with different (data and/or model) limitations. Here, we visualize these impacts with idealized representations that graphically illustrate the nature of time-dependent actuo- and paleoclimate sensitivity estimates, evaluating the strengths, weaknesses, agreements, and differences of the two approaches. We also highlight priorities for future research to improve the use of paleo-estimates in evaluations of current climate change.
9. 2017: Feldman, Daniel, et al. “How Continuous Observations of Shortwave Reflectance Spectra Can Narrow the Range of Shortwave Climate Feedbacks.” AGU Fall Meeting Abstracts. 2017. Shortwave feedbacks are a persistent source of uncertainty for climate models and a large contributor to the diagnosed range of equilibrium climate sensitivity (ECS) for the international multi-model ensemble. The processes that contribute to these feedbacks affect top-of-atmosphere energetics and produce spectral signatures that may be time-evolving. We explore the value of such spectral signatures for providing an observational constraint on model ECS by simulating top-of-atmosphere shortwave reflectance spectra across much of the energetically-relevant shortwave bandpass (300 to 2500 nm). We present centennial-length shortwave hyperspectral simulations from low, medium and high ECS models that reported to the CMIP5 archive as part of an Observing System Simulation Experiment (OSSE) in support of the CLimate Absolute Radiance and Refractivity Observatory (CLARREO). Our framework interfaces with CMIP5 archive results and is agnostic to the choice of model. We simulated spectra from the INM-CM4 model (ECS of 2.08°K/2xCO2), the MIROC5 model (ECS of 2.70 °K/2xCO2), and the CSIRO Mk3-6-0 (ECS of 4.08 °K/2xCO2) based on those models’ integrations of the RCP8.5 scenario for the 21st Century. This approach allows us to explore how perfect data records can exclude models of lower or higher climate sensitivity. We find that spectral channels covering visible and near-infrared water-vapor overtone bands can potentially exclude a low or high sensitivity model with under 15 years’ of absolutely-calibrated data. These different spectral channels are sensitive to model cloud radiative effect and cloud height changes, respectively. These unprecedented calculations lay the groundwork for spectral simulations of perturbed-physics ensembles in order to identify those shortwave observations that can help narrow the range in shortwave model feedbacks and ultimately help reduce the stubbornly-large range in model ECS
10. 2017: Schneider, Tapio, et al. “Climate goals and computing the future of clouds.” Nature Climate Change 7.1 (2017): 3. How clouds respond to warming remains the greatest source of uncertainty in climate projections. Improved computational and observational tools can reduce this uncertainty. Here we discuss the need for research focusing on high-resolution atmosphere models and the representation of clouds and turbulence within them
11. 2016: Ullman, D. J., A. Schmittner, and N. M. Urban. “A new estimate of climate sensitivity using Last Glacial Maximum model-data constraints that includes parametric, feedback, and proxy uncertainties.” AGU Fall Meeting Abstracts. 2016. The Last Glacial Maximum (LGM) provides potentially useful constraints on equilibrium climate sensitivity (ECS) because it is the most recent period of large greenhouse gas and temperature change. In addition, the wealth of proxy data from ice cores, ocean cores, and terrestrial records during this time period helps to test the relationship between greenhouse gas concentrations and temperature. A previous study (Schmittner et al., 2011) has estimated probability distributions of ECS using a small ensemble of model simulations that varies model sensitivity to atmospheric CO2 concentrations by changing only one model parameter. However, that estimate neglected cloud feedbacks, although they are the largest source of uncertainty in comprehensive climate models. Here, we provide a new estimate of ECS using a much larger ensemble of simulations (>1000) including cloud feedbacks and other uncertainties. We apply a new method to diagnose separately shortwave and longwave cloud feedbacks from comprehensive models and include them in the University of Victoria Earth System Climate Model (UVic-ESCM). We also explore parametric uncertainties in dust forcing, snow albedo, and atmospheric diffusivities, which all influence important feedbacks in UVic-ECSM. Finally, we use Bayesian statistics to compare LGM proxy data with this new model ensemble and to provide a new probabilistic estimate of ECS that better includes dominant sources of model and data uncertainty.
12. 2016: Marvel, Kate, et al. “Implications for climate sensitivity from the response to individual forcings.” Nature Climate Change 6.4 (2016): 386. Climate sensitivity to doubled CO₂ is a widely used metric for the large-scale response to external forcing. Climate models predict a wide range for two commonly used definitions: the transient climate response (TCR: the warming after 70 years of CO₂ concentrations that rise at 1% per year), and the equilibrium climate sensitivity (ECS: the equilibrium temperature change following a doubling of CO₂ concentrations). Many observational data sets have been used to constrain these values, including temperature trends over the recent past inferences from palaeoclimate and process-based constraints from the modern satellite era However, as the IPCC recently reported, different classes of observational constraints produce somewhat incongruent ranges. Here we show that climate sensitivity estimates derived from recent observations must account for the efficacy of each forcing active during the historical period. When we use single-forcing experiments to estimate these efficacies and calculate climate sensitivity from the observed twentieth-century warming, our estimates of both TCR and ECS are revised upwards compared to previous studies, improving the consistency with independent constraints
13. 2015: Ullman, D. J., A. Schmittner, and N. M. Urban. “Incorporating feedback uncertainties in a model-based assessment of equilibrium climate sensitivity using Last Glacial Maximum temperature reconstructions.” AGU Fall Meeting Abstracts. 2015. As the most recent period of large climate change, the Last Glacial Maximum (LGM) has been a useful target for analysis by model-data comparison. In addition, significant changes in greenhouse gas forcing across the last deglaciation and the relative wealth of LGM temperature reconstructions by proxy data provide a potentially useful opportunity to quantify equilibrium climate sensitivity (ECS), the change in global mean surface air temperature due to a doubling of atmospheric CO2. Past model-data comparisons have attempted to estimate ECS using the LGM climate in two ways: (1) scaling of proxy data with results from general circulation model intercomparisons, and (2) comparing data with results from an ensemble of ECS-tuned simulations using a single intermediate complexity model. While the first approach includes the complexity of climate feedbacks, the sample size of the ECS-space may be insufficiently large to assess climate sensitivity. However, the second approach may be model dependent by not adequately incorporating uncertainty in climate feedbacks. Here, we present a new LGM-based assessment of ECS using the latter approach along with a simple linear parameterization of the longwave and shortwave cloud feedbacks derived from the CMIP5/PMIP3 results applied to the University of Victoria Earth System intermediate complexity model (UVIC). Cloud feedbacks are found to be the largest source of variability among the CMIP5/PMIP3 simulations, and our parameterization emulates these feedbacks in the UVIC model. In using this parameterization, we present a new ensemble of UVIC simulations to estimate ECS based on a Bayesian comparison with LGM temperature reconstructions that determines a probability distribution of optimal overlap between data and model results.
14. 2015: Lewis, Nicholas, and Judith A. Curry. “The implications for climate sensitivity of AR5 forcing and heat uptake estimates.” Climate dynamics 45.3-4 (2015): 1009-1023. Energy budget estimates of equilibrium climate sensitivity (ECS) and transient climate response (TCR) are derived using the comprehensive 1750–2011 time series and the uncertainty ranges for forcing components provided in the Intergovernmental Panel on Climate Change Fifth Assessment Working Group I Report, along with its estimates of heat accumulation in the climate system. The resulting estimates are less dependent on global climate models and allow more realistically for forcing uncertainties than similar estimates based on forcings diagnosed from simulations by such models. Base and final periods are selected that have well matched volcanic activity and influence from internal variability. Using 1859–1882 for the base period and 1995–2011 for the final period, thus avoiding major volcanic activity, median estimates are derived for ECS of 1.64 K and for TCR of 1.33 K. ECS 17–83 and 5–95 % uncertainty ranges are 1.25–2.45 and 1.05–4.05 K; the corresponding TCR ranges are 1.05–1.80 and 0.90–2.50 K. Results using alternative well-matched base and final periods provide similar best estimates but give wider uncertainty ranges, principally reflecting smaller changes in average forcing. Uncertainty in aerosol forcing is the dominant contribution to the ECS and TCR uncertainty ranges.
15. 2014: Sherwood, Steven C., Sandrine Bony, and Jean-Louis Dufresne. “Spread in model climate sensitivity traced to atmospheric convective mixing.” Nature 505.7481 (2014): 37.  Equilibrium climate sensitivity refers to the ultimate change in global mean temperature in response to a change in external forcing. Despite decades of research attempting to narrow uncertainties, equilibrium climate sensitivity estimates from climate models still span roughly 1.5 to 5 degrees Celsius for a doubling of atmospheric carbon dioxide concentration, precluding accurate projections of future climate. The spread arises largely from differences in the feedback from low clouds, for reasons not yet understood. Here we show that differences in the simulated strength of convective mixing between the lower and middle tropical troposphere explain about half of the variance in climate sensitivity estimated by 43 climate models. The apparent mechanism is that such mixing dehydrates the low-cloud layer at a rate that increases as the climate warms, and this rate of increase depends on the initial mixing strength, linking the mixing to cloud feedback. The mixing inferred from observations appears to be sufficiently strong to imply a climate sensitivity of more than 3 degrees for a doubling of carbon dioxide. This is significantly higher than the currently accepted lower bound of 1.5 degrees, thereby constraining model projections towards relatively severe future warming.

1. 1963: Möller, Fritz. “On the influence of changes in the CO2 concentration in air on the radiation balance of the earth’s surface and on the climate.” Journal of Geophysical Research68.13 (1963): 3877-3886. The numerical value of a temperature change under the influence of a CO₂ change as calculated by Plass is valid only for a dry atmosphere. Overlapping of the absorption bands of CO₂ and H₂O in the range around 15 μ essentially diminishes the temperature changes. New calculations give ΔT = + 1.5° when the CO₂ content increases from 300 to 600 ppm. Cloudiness diminishes the radiation effects but not the temperature changes because under cloudy skies larger temperature changes are needed in order to compensate for an equal change in the downward long‐wave radiation. The increase in the water vapor content of the atmosphere with rising temperature causes a self‐amplification effect which results in almost arbitrary temperature changes, e.g. for constant relative humidity ΔT = +10° in the above mentioned case. It is shown, however, that the changed radiation conditions are not necessarily compensated for by a temperature change. The effect of an increase in CO₂ from 300 to 330 ppm can be compensated for completely by a change in the water vapor content of 3 per cent or by a change in the cloudiness of 1 per cent of its value without the occurrence of temperature changes at all. Thus the theory that climatic variations are effected by variations in the CO₂ content becomes very questionable.
2. 1964: Manabe, Syukuro, and Robert F. Strickler. “Thermal equilibrium of the atmosphere with a convective adjustment.” Journal of the Atmospheric Sciences 21.4 (1964): 361-385. The states of thermal equilibrium (incorporating an adjustment of super-adiabatic stratification) as well as that of pure radiative equilibrium of the atmosphere are computed as the asymptotic steady state approached in an initial value problem. Recent measurements of absorptivities obtained for a wide range of pressure are used, and the scheme of computation is sufficiently general to include the effect of several layers of clouds. The atmosphere in thermal equilibrium has an isothermal lower stratosphere and an inversion in the upper stratosphere which are features observed in middle latitudes. The role of various gaseous absorbers (i.e., water vapor, carbon dioxide, and ozone), as well as the role of the clouds, is investigated by computing thermal equilibrium with and without one or two of these elements. The existence of ozone has very little effect on the equilibrium temperature of the earth’s surface but a very important effect on the temperature throughout the stratosphere; the absorption of solar radiation by ozone in the upper and middle stratosphere, in addition to maintaining the warm temperature in that region, appears also to be necessary for the maintenance of the isothermal layer or slight inversion just above the tropopause. The thermal equilibrium state in the absence of solar insulation is computed by setting the temperature of the earth’s surface at the observed polar value. In this case, the stratospheric temperature decreases monotonically with increasing altitude, whereas the corresponding state of pure radiative equilibrium has an inversion just above the level of the tropopause. A series of thermal equilibriums is computed for the distributions of absorbers typical of different latitudes. According to these results, the latitudinal variation of the distributions of ozone and water vapor may be partly responsible for the latitudinal variation of the thickness of the isothermal part of the stratosphere. Finally, the state of local radiative equilibrium of the stratosphere overlying a troposphere with the observed distribution of temperature is computed for each season and latitude. In the upper stratosphere of the winter hemisphere, a large latitudinal temperature gradient appears at the latitude of the polar-night jet stream, while in the upper statosphere of the summer hemisphere, the equilibrium temperature varies little with latitude. These features are consistent with the observed atmosphere. However, the computations predict an extremely cold polar night temperature in the upper stratosphere and a latitudinal decrease (toward the cold pole) of equilibrium temperature in the middle or lower stratosphere for winter and fall. This disagrees with observation, and suggests that explicit introduction of the dynamics of large scale motion is necessary.
3. 1967: Manabe, Syukuro, and Richard T. Wetherald. “Thermal equilibrium of the atmosphere with a given distribution of relative humidity.” Journal of the Atmospheric Sciences 24.3 (1967): 241-259. [ECS=2]
4. 1969: Budyko, Mikhail I. “The effect of solar radiation variations on the climate of the earth.” tellus 21.5 (1969): 611-619. It follows from the analysis of observation data that the secular variation of the mean temperature of the Earth can be explained by the variation of short-wave radiation, arriving at the surface of the Earth. In connection with this, the influence of long-term changes of radiation, caused by variations of atmospheric transparency on the thermal regime is being studied. Taking into account the influence of changes of planetary albedo of the Earth under the development of glaciations on the thermal regime, it is found that comparatively small variations of atmospheric transparency could be sufficient for the development of quaternary glaciations.
5. 1969: Sellers, William D. “A global climatic model based on the energy balance of the earth-atmosphere system.” Journal of Applied Meteorology 8.3 (1969): 392-400. A relatively simple numerical model of the energy balance of the earth-atmosphere is set up and applied. The dependent variable is the average annual sea level temperature in 10° latitude belts. This is expressed basically as a function of the solar constant, the planetary albedo, the transparency of the atmosphere to infrared radiation, and the turbulent exchange coefficients for the atmosphere and the oceans. The major conclusions of the analysis are that removing the arctic ice cap would increase annual average polar temperatures by no more than 7C, that a decrease of the solar constant by 2–5% might be sufficient to initiate another ice age, and that man’s increasing industrial activities may eventually lead to a global climate much warmer than today.
6. 1971: Rasool, S. Ichtiaque, and Stephen H. Schneider. “Atmospheric carbon dioxide and aerosols: Effects of large increases on global climate.” Science 173.3992 (1971): 138-141. 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. For aerosols, however, the net effect of increase in density is to reduce the surface temperature of Earth. Because of the exponential dependence of the backscattering, the rate of temperature decrease is augmented with increasing aerosol content. An increase by only a factor of 4 in global aerosol background concentration may be sufficient to reduce the surface temperature by as much as 3.5 ° K. If sustained over a period of several years, such a temperature decrease over the whole globe is believed to be sufficient to trigger an ice age.
7. 1975: Manabe, Syukuro, and Richard T. Wetherald. “The effects of doubling the CO2 concentration on the climate of a general circulation model.” Journal of the Atmospheric Sciences 32.1 (1975): 3-15. 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. This model contains the following simplifications: a limited computational domain, an idealized topography, no beat transport by ocean currents, and fixed cloudiness. Despite these limitations, the results from this computation yield some indication of how the increase of CO2 concentration may affect the distribution of temperature in the atmosphere. It is shown that the CO2 increase raises the temperature of the model troposphere, whereas it lowers that of the model stratosphere. The tropospheric warming is somewhat larger than that expected from a radiative-convective equilibrium model. In particular, the increase of surface temperature in higher latitudes is magnified due to the recession of the snow boundary and the thermal stability of the lower troposphere which limits convective beating to the lowest layer. It is also shown that the doubling of carbon dioxide significantly increases the intensity of the hydrologic cycle of the model. 
8. 1976: Cess, Robert D. “Climate change: An appraisal of atmospheric feedback mechanisms employing zonal climatology.” Journal of the Atmospheric Sciences 33.10 (1976): 1831-1843. The sensitivity of the earth’s surface temperature to factors which can induce long-term climate change, such as a variation in solar constant, is estimated by employing two readily observable climate changes. One is the latitudinal change in annual mean climate, for which an interpretation of climatological data suggests that cloud amount is not a significant climate feedback mechanism, irrespective of how cloud amount might depend upon surface temperature, since there are compensating changes in both the solar and infrared optical properties of the atmosphere. It is further indicated that all other atmospheric feedback mechanisms, resulting, for example, from temperature-induced changes in water vapor amount, cloud altitude and lapse rate, collectively double the sensitivity of global surface temperature to a change in solar constant. The same conclusion is reached by considering a second type of climate change, that associated with seasonal variations for a given latitude zone. The seasonal interpretation further suggests that cloud amount feedback is unimportant zonally as well as globally. Application of the seasonal data required a correction for what appears to be an important seasonal feedback mechanism. This is attributed to a variability in cloud albedo due to seasonal changes in solar zenith angle. No attempt was made to individually interpret the collective feedback mechanisms which contribute to the doubling in surface temperature sensitivity. It is suggested, however, that the conventional assumption of fixed relative humidity for describing feedback due to water vapor amount might not be as applicable as is generally believed. Climate models which additionally include ice-albedo feedback are discussed within the framework of the present results.
9. 1978: Ramanathan, V., and J. A. Coakley. “Climate modeling through radiative‐convective models.” Reviews of geophysics16.4 (1978): 465-489. We present a review of the radiative‐convective models that have been used in studies pertaining to the earth’s climate. After familiarizing the reader with the theoretical background, modeling methodology, and techniques for solving the radiative transfer equation the review focuses on the published model studies concerning global climate and global climate change. Radiative‐convective models compute the globally and seasonally averaged surface and atmospheric temperatures. The computed temperatures are in good agreement with the observed temperatures. The models include the important climatic feedback mechanism between surface temperature and H₂O amount in the atmosphere. The principal weakness of the current models is their inability to simulate the feedback mechanism between surface temperature and cloud cover. It is shown that the value of the critical lapse rate adopted in radiative‐convective models for convective adjustment is significantly larger than the observed globally averaged tropospheric lapse rate. The review also summarizes radiative‐convective model results for the sensitivity of surface temperature to perturbations in (1) the concentrations of the major and minor optically active trace constituents, (2) aerosols, and (3) cloud amount. A simple analytical model is presented to demonstrate how the surface temperature in a radiative‐convective model responds to perturbations.
10. 1985: Wigley, Thomas ML, and Michael E. Schlesinger. “Analytical solution for the effect of increasing CO2 on global mean temperature.” Nature 315.6021 (1985): 649. Increasing atmospheric carbon dioxide concentration is expected to cause substantial changes in climate. Recent model studies suggest that the equilibrium warming for a CO2 doubling (Δ T2×) is about 3–4°C. Observational data show that the globe has warmed by about 0.5°C over the past 100 years. Are these two results compatible? To answer this question due account must be taken of oceanic thermal inertia effects, which can significantly slow the response of the climate system to external forcing. The main controlling parameters are the effective diffusivity of the ocean below the upper mixed layer (κ) and the climate sensitivity (defined by Δ T2×). Previous analyses of this problem have considered only limited ranges of these parameters. Here we present a more general analysis of two cases, forcing by a step function change in CO2 concentration and by a steady CO2 increase. The former case may be characterized by a response time which we show is strongly dependent on both κ and Δ T2×. In the latter case the damped response means that, at any given time, the climate system may be quite far removed from its equilibrium with the prevailing CO2 level. In earlier work this equilibrium has been expressed as a lag time, but we show this to be misleading because of the sensitivity of the lag to the history of past CO2 variations. Since both the lag and the degree of disequilibrium are strongly dependent on κ and Δ T2×, and because of uncertainties in the pre-industrial CO2 level, the observed global warming over the past 100 years can be shown to be compatible with a wide range of CO2-doubling temperature changes.
11. 1991: Lawlor, D. W., and R. A. C. Mitchell. “The effects of increasing CO2 on crop photosynthesis and productivity: a review of field studies.” Plant, Cell & Environment 14.8 (1991): 807-818. Only a small proportion of elevated CO₂ studies on crops have taken place in the field. They generally confirm results obtained in controlled environments: CO₂increases photosynthesis, dry matter production and yield, substantially in C₃ species, but less in C₄, it decreases stomatal conductance and transpiration in C₃ and C₄ species and greatly improves water‐use efficiency in all plants. The increased productivity of crops with CO₂ enrichment is also related to the greater leaf area produced. Stimulation of yield is due more to an increase in the number of yield‐forming structures than in their size. There is little evidence of a consistent effect of CO₂ on partitioning of dry matter between organs or on their chemical composition, except for tubers. Work has concentrated on a few crops (largely soybean) and more is needed on crops for which there are few data (e.g. rice). Field studies on the effects of elevated CO₂ in combination with temperature, water and nutrition are essential; they should be related to the development and improvement of mechanistic crop models, and designed to test their predictions.
12. 2009: Danabasoglu, Gokhan, and Peter R. Gent. “Equilibrium climate sensitivity: Is it accurate to use a slab ocean model?.” Journal of Climate 22.9 (2009): 2494-2499. The equilibrium climate sensitivity of a climate model is usually defined as the globally averaged equilibrium surface temperature response to a doubling of carbon dioxide. This is virtually always estimated in a version with a slab model for the upper ocean. The question is whether this estimate is accurate for the full climate model version, which includes a full-depth ocean component. This question has been answered for the low-resolution version of the Community Climate System Model, version 3 (CCSM3). The answer is that the equilibrium climate sensitivity using the full-depth ocean model is 0.14°C higher than that using the slab ocean model, which is a small increase. In addition, these sensitivity estimates have a standard deviation of nearly 0.1°C because of interannual variability. These results indicate that the standard practice of using a slab ocean model does give a good estimate of the equilibrium climate sensitivity of the full CCSM3. Another question addressed is whether the effective climate sensitivity is an accurate estimate of the equilibrium climate sensitivity. Again the answer is yes, provided that at least 150 yr of data from the doubled carbon dioxide run are used.
13. 2010: Connell, Sean D., and Bayden D. Russell. “The direct effects of increasing CO2 and temperature on non-calcifying organisms: increasing the potential for phase shifts in kelp forests.” Proceedings of the Royal Society of London B: Biological Sciences (2010): rspb20092069. Predictions about the ecological consequences of oceanic uptake of CO₂ have been preoccupied with the effects of ocean acidification on calcifying organisms, particularly those critical to the formation of habitats (e.g. coral reefs) or their maintenance (e.g. grazing echinoderms). This focus overlooks the direct effects of CO₂ on non-calcareous taxa, particularly those that play critical roles in ecosystem shifts. We used two experiments to investigate whether increased CO₂ could exacerbate kelp loss by facilitating non-calcareous algae that, we hypothesized, (i) inhibit the recovery of kelp forests on an urbanized coast, and (ii) form more extensive covers and greater biomass under moderate future CO₂ and associated temperature increases. Our experimental removal of turfs from a phase-shifted system (i.e. kelp- to turf-dominated) revealed that the number of kelp recruits increased, thereby indicating that turfs can inhibit kelp recruitment. Future CO₂ and temperature interacted synergistically to have a positive effect on the abundance of algal turfs, whereby they had twice the biomass and occupied over four times more available space than under current conditions. We suggest that the current preoccupation with the negative effects of ocean acidification on marine calcifiers overlooks potentially profound effects of increasing CO₂and temperature on non-calcifying organisms.
14. 2011: Schmittner, Andreas, et al. “Climate sensitivity estimated from temperature reconstructions of the Last Glacial Maximum.” Science 334.6061 (2011): 1385-1388. 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.
15. 2012: Fasullo, John T., and Kevin E. Trenberth. “A less cloudy future: The role of subtropical subsidence in climate sensitivity.” science 338.6108 (2012): 792-794. An observable constraint on climate sensitivity, based on variations in mid-tropospheric relative humidity (RH) and their impact on clouds, is proposed. We show that the tropics and subtropics are linked by teleconnections that induce seasonal RH variations that relate strongly to albedo (via clouds), and that this covariability is mimicked in a warming climate. A present-day analog for future trends is thus identified whereby the intensity of subtropical dry zones in models associated with the boreal monsoon is strongly linked to projected cloud trends, reflected solar radiation, and model sensitivity. Many models, particularly those with low climate sensitivity, fail to adequately resolve these teleconnections and hence are identifiably biased. Improving model fidelity in matching observed variations provides a viable path forward for better predicting future climate.
16. 2012: Andrews, Timothy, et al. “Forcing, feedbacks and climate sensitivity in CMIP5 coupled atmosphere‐ocean climate models.” Geophysical Research Letters 39.9 (2012). We quantify forcing and feedbacks across available CMIP5 coupled atmosphere‐ocean general circulation models (AOGCMs) by analysing simulations forced by an abrupt quadrupling of atmospheric carbon dioxide concentration. This is the first application of the linear forcing‐feedback regression analysis of Gregory et al. (2004) to an ensemble of AOGCMs. The range of equilibrium climate sensitivity is 2.1–4.7 K. Differences in cloud feedbacks continue to be important contributors to this range. Some models show small deviations from a linear dependence of top‐of‐atmosphere radiative fluxes on global surface temperature change. We show that this phenomenon largely arises from shortwave cloud radiative effects over the ocean and is consistent with independent estimates of forcing using fixed sea‐surface temperature methods. We suggest that future research should focus more on understanding transient climate change, including any time‐scale dependence of the forcing and/or feedback, rather than on the equilibrium response to large instantaneous forcing.
17. 2012: Bitz, Cecilia M., et al. “Climate sensitivity of the community climate system model, version 4.” Journal of Climate 25.9 (2012): 3053-3070.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.
18. 2012: Rogelj, Joeri, Malte Meinshausen, and Reto Knutti. “Global warming under old and new scenarios using IPCC climate sensitivity range estimates.” Nature climate change 2.4 (2012): 248. Climate projections for the fourth assessment report¹ (AR4) of the Intergovernmental Panel on Climate Change (IPCC) were based on scenarios from the Special Report on Emissions Scenarios² (SRES) and simulations of the third phase of the Coupled Model Intercomparison Project³ (CMIP3). Since then, a new set of four scenarios (the representative concentration pathways or RCPs) was designed⁴. Climate projections in the IPCC fifth assessment report (AR5) will be based on the fifth phase of the Coupled Model Intercomparison Project⁵ (CMIP5), which incorporates the latest versions of climate models and focuses on RCPs. This implies that by AR5 both models and scenarios will have changed, making a comparison with earlier literature challenging. To facilitate this comparison, we provide probabilistic climate projections of both SRES scenarios and RCPs in a single consistent framework. These estimates are based on a model set-up that probabilistically takes into account the overall consensus understanding of climate sensitivity uncertainty, synthesizes the understanding of climate system and carbon-cycle behaviour, and is at the same time constrained by the observed historical warming.
19. 2014: Sherwood, Steven C., Sandrine Bony, and Jean-Louis Dufresne. “Spread in model climate sensitivity traced to atmospheric convective mixing.” Nature 505.7481 (2014): 37. Equilibrium climate sensitivity refers to the ultimate change in global mean temperature in response to a change in external forcing. Despite decades of research attempting to narrow uncertainties, equilibrium climate sensitivity estimates from climate models still span roughly 1.5 to 5 degrees Celsius for a doubling of atmospheric carbon dioxide concentration, precluding accurate projections of future climate. The spread arises largely from differences in the feedback from low clouds, for reasons not yet understood. Here we show that differences in the simulated strength of convective mixing between the lower and middle tropical troposphere explain about half of the variance in climate sensitivity estimated by 43 climate models. The apparent mechanism is that such mixing dehydrates the low-cloud layer at a rate that increases as the climate warms, and this rate of increase depends on the initial mixing strength, linking the mixing to cloud feedback. The mixing inferred from observations appears to be sufficiently strong to imply a climate sensitivity of more than 3 degrees for a doubling of carbon dioxide. This is significantly higher than the currently accepted lower bound of 1.5 degrees, thereby constraining model projections towards relatively severe future warming.
20. 2015: Mauritsen, Thorsten, and Bjorn Stevens. “Missing iris effect as a possible cause of muted hydrological change and high climate sensitivity in models.” Nature Geoscience 8.5 (2015): 346. Equilibrium climate sensitivity to a doubling of CO₂ falls between 2.0 and 4.6 K in current climate models, and they suggest a weak increase in global mean precipitation. Inferences from the observational record, however, place climate sensitivity near the lower end of this range and indicate that models underestimate some of the changes in the hydrological cycle. These discrepancies raise the possibility that important feedbacks are missing from the models. A controversial hypothesis suggests that the dry and clear regions of the tropical atmosphere expand in a warming climate and thereby allow more infrared radiation to escape to space. This so-called iris effect could constitute a negative feedback that is not included in climate models. We find that inclusion of such an effect in a climate model moves the simulated responses of both temperature and the hydrological cycle to rising atmospheric greenhouse gas concentrations closer to observations. Alternative suggestions for shortcomings of models — such as aerosol cooling, volcanic eruptions or insufficient ocean heat uptake — may explain a slow observed transient warming relative to models, but not the observed enhancement of the hydrological cycle. We propose that, if precipitating convective clouds are more likely to cluster into larger clouds as temperatures rise, this process could constitute a plausible physical mechanism for an iris effect.
21. 2015: Schimel, David, Britton B. Stephens, and Joshua B. Fisher. “Effect of increasing CO2 on the terrestrial carbon cycle.” Proceedings of the National Academy of Sciences 112.2 (2015): 436-441. Feedbacks from terrestrial ecosystems to atmospheric CO₂ concentrations contribute the second-largest uncertainty to projections of future climate. These feedbacks, acting over huge regions and long periods of time, are extraordinarily difficult to observe and quantify directly. We evaluated in situ, atmospheric, and simulation estimates of the effect of CO₂ on carbon storage, subject to mass balance constraints. Multiple lines of evidence suggest significant tropical uptake for CO₂, approximately balancing net deforestation and confirming a substantial negative global feedback to atmospheric CO₂ and climate. This reconciles two approaches that have previously produced contradictory results. We provide a consistent explanation of the impacts of CO₂ on terrestrial carbon across the 12 orders of magnitude between plant stomata and the global carbon cycle.
22. 2016: Tan, Ivy, Trude Storelvmo, and Mark D. Zelinka. “Observational constraints on mixed-phase clouds imply higher climate sensitivity.” Science 352.6282 (2016): 224-227. How much global average temperature eventually will rise depends on the Equilibrium Climate Sensitivity (ECS), which relates atmospheric CO₂ concentration to atmospheric temperature. For decades, ECS has been estimated to be between 2.0° and 4.6°C, with much of that uncertainty owing to the difficulty of establishing the effects of clouds on Earth’s energy budget. Tan et al. used satellite observations to constrain the radiative impact of mixed phase clouds. They conclude that ECS could be between 5.0° and 5.3°C—higher than suggested by most global climate models.
23. 2018: Watanabe, Masahiro, et al. “Low clouds link equilibrium climate sensitivity to hydrological sensitivity.” Nature Climate Change (2018): 1. Equilibrium climate sensitivity (ECS) and hydrological sensitivity describe the global mean surface temperature and precipitation responses to a doubling of atmospheric CO₂. Despite their connection via the Earth’s energy budget, the physical linkage between these two metrics remains controversial. Here, using a global climate model with a perturbed mean hydrological cycle, we show that ECS and hydrological sensitivity per unit warming are anti-correlated owing to the low-cloud response to surface warming. When the amount of low clouds decreases, ECS is enhanced through reductions in the reflection of shortwave radiation. In contrast, hydrological sensitivity is suppressed through weakening of atmospheric longwave cooling, necessitating weakened condensational heating by precipitation. These compensating cloud effects are also robustly found in a multi-model ensemble, and further constrained using satellite observations. Our estimates, combined with an existing constraint to clear-sky shortwave absorption, suggest that hydrological sensitivity could be lower by 30% than raw estimates from global climate models.