New paper finds climate sensitivity to CO2 significantly less than claimed by IPCC; low-sensitivity paper #37

A new paper published in Earth System Dynamics finds equilibrium climate sensitivity [ECS] to doubled CO2 levels is 1.8C, about 44% less than claimed by the IPCC AR5 report. The paper adds to at least 36 other peer-reviewed papers finding climate sensitivity to be significantly less than the IPCC mean modelled estimate of 3.2C [range 1.5 - 4.5C].

Excerpt from globalwarming.org: The IPCC’s 2007 Fourth Assessment Report (AR4) estimated a “likely” ECS range of 2°C-4.5°C, with a “best estimate” of 3°C. Since 2011, however, the warming pause and the growing divergence of model predictions and observed global temperatures have been the impetus for several studies finding that IPCC sensitivity estimates are too hot.

Cato Institute scientists Patrick Michaels and Chip Knappenberger maintain a growing list of such studies, which totaled 18 as of February 2014:

The average sensitivity estimate of the 18 studies compiled by Michaels and Knappenberger is just under 2°C. In other words, the IPCC AR4 “best estimate” of 3°C is 50% higher than the mean estimate of the new studies. That may be why the IPCC’s 2013-2014 Fifth Assessment Report (AR5) declines to offer a “best estimate.”

A new “best estimate” of 2°C would deflate the scary climate change impacts featured elsewhere in AR5, but recycling the same old 3°C “best estimate” would deflate the IPCC’s claim to be an honest broker. So instead the IPCC chose to lower the low end of the “likely” sensitivity range. Whereas the “likely” range in AR4 was 2°C-4.5°C, in AR5 it is 1.5°C-4.5°C.

That small concession, however, does not dispel the growing challenge to consensus climatology. As indicated in the Michaels and Knappenberger chart above, the average sensitivity of the climate models used in AR5 is 3.2°C. That is 60% higher than the mean of recent estimates (< 2°C).

An additional 21 peer-reviewed papers based upon observations and compiled by the Hockey Schtick find even lower ECS estimates of < 1C, about 7 times less than claimed by the IPCC. In total, there are now at least 37 published, peer-reviewed studies compiled by Michaels, Knappenberger, and the HS finding climate sensitivities significantly less than claimed by the IPCC. In contrast, there is a drought of studies finding climate sensitivities higher than claimed by the IPCC AR5 mean modelled estimate of 3.2C. 

The new paper below finds an ECS of 1.8C, but does not consider natural changes in ocean oscillations, cloud cover, global "brightening" & "dimming," which can alone explain all of the post-1950 warming. The paper also uses long-term ocean heat content [OHC] data as the basis of the ECS calculation, but the OHC trends have been determined to be exaggerated due to sampling biases in a paper published this week. The paper also does not consider the possibility of solar amplification mechanisms, which can explain 95% of climate change over the past 400 years. Consideration of these 4 factors would further lower the ECS estimates significantly. 

A description of the paper from the Swedish Stockholm Initiative site is below [Google translation], followed by the abstract and full paper in English. 

Norwegian research team got climate sensitivity (ECS) between 0.9 and 3.2 degrees C

31/10/2014 by Pehr Björnbom .

72 Comments

The Norwegian research team consists of climate scientists and statistical mathematician. They have used every conceivable observations, together with a relatively simple climate model, a so-called energy balance model in which climate sensitivity is one of the input parameter values. They have adjusted the parameter values ​​of the climate model to observations using Bayesian statistics. They were then equilibrium climate sensitivity (ECS = Equilibrium Climate Sensitivity) to 1.8 degrees C (0.9 to 3.2 degrees C with 90% probability) for the doubling of carbon dioxide levels.

The article of Skeie et al. (2014) is published in the geosciences journal Earth System Dynamics.Three of the authors belong climate research center CICERO, University of Oslo, Terje Berntsen ,Gunnar Myhre and Ragnhild Bieltvedt Skeie . The other two authors are statistical mathematician belonging Norsk Regnesentral, Marit Holden and Magne Aldrin .

It inspires confidence that climate scientists here collaborates with statistical mathematician who is proficient in Bayesian statistics . The idea is to use a climate model that includes climate sensitivity as a parameter and to find out the value of climate sensitivity by adapting the model to the observed data. To do this properly with Bayesian statistics needed the expertise of statistical mathematics.

Magne Aldrin (2010) has given a presentation of the methods that they use at a workshop in Cambridge, UK in 2010. The simple climate model is not of the simplest kind, the atmosphere is divided into northern and southern hemispheres. The model ocean is still more complicated and divided into the southern polar ocean, the southern hemisphere's main body, the northern hemisphere's body and the northern polar ocean. The following figure gives an approximate schedule for this climate model (the dimensions listed are only possible examples).

This simple climate model , according to previous studies cited in Skeie et al. (2014) have been able to reproduce the simulations with advanced climate models. The reason for for this kind of adaptation of the model parameters to the observed data are not using an advanced climate model directly, is that such models are very complex and require too much computing power. One way to solve this problem is to do what the writers have done, using a simple model that has been confirmed by simulation can reproduce sophisticated climate model results.

Climate model includes climate sensitivity at equilibrium (ECS = Equilibrium Climate Sensitivity) as an unknown parameter, and six additional parameters related to the heat flows into the ocean to do. You also need radiation exchange between the atmosphere and the upper and solar. This type of data is called "radiative forcing" and that climate science has devoted considerable effort to determine, but the uncertainties in the data are still large. As is known, the impact of increased levels of greenhouse gases in the atmosphere, which mainly affects the "radiative forcing" and that they have pretty good data as well as changed aerosol influence and where the uncertainty is much larger.

Has values ​​of these seven parameters and a graph of how the "radiative forcing" has varied with time since pre-industrial times so this simple climate model to figure out how the temperature has varied in both the northern and southern hemispheres, and how the heat content of the ocean has changed. You can then modify the parameter values, whereby man is above all interested in climate sensitivity, within the possible limits of error, and also vary the "radiative forcing" within their error limits. In this way, one can see for what combinations of parameter values ​​to obtain curves for the temperatures and ocean heat content, which agrees with observations. This is what is called the parameter adjustment .

It's such a parameter adjustment statistical mathematician can help with making in a professional manner and really exploit the knowledge of Bayesian methods to get the best possible results. In this way one can determine a probability interval for climate sensitivity, in this case one can say about the ECS that the most likely value is 1.8 degrees C for a doubling of carbon dioxide and that with 90% probability value lies between 0.9 and 3.2 degrees C (compared to the UN Climate Change (IPCC) range to the 66-100% probability value lies between 1.5 and 4.5 degrees C).

The observations that the authors have used for their study is part six temperature series: HadCRUT3, NCDC and GISS for the northern and southern hemisphere (there is a significant body of scientific work that has taken a long time to implement, why not HadCRUT4 been used throughout, but only for a supplemental analysis ), and data for ocean heat content from Levitus research team at NOAA and two other research groups. So it is incredibly much data as adapting the model parameters to. It has also, as is possible in a Bayesian analysis, taken with data for ocean parameters based on independent observations as input data (so-called "prior probability distribution").

The result for the equilibrium sensitivity ECS is low, 1.8 degrees C for a doubling of carbon dioxide levels, but especially noteworthy is that the uncertainty interval, 0.9 to 3.2 degrees C, is shorter than in other similar studies. Compare, for example, with the much talked about recently published study by Lewis and Curry who were 1-4 degrees C.

The authors therefore studied how the results varied with the data ended. If they used data only up to 2000, they received a slightly higher climate sensitivity, but above all was the uncertainty range for much longer.

They suggest thereof an explanation of why this is so. This is partly due to "radiative forcing" has risen significantly during the past decade, so that the relative error of this has diminished. The second contributing factor is the availability of data for the heat content of the ocean has increased by 20% (depending on the test series starting about 1950). They say not to the reduced length of the uncertainty interval would have to do with heating the break.

The transient climate sensitivity is also of interest because it is this which, in theory, primarily determines the temperature will increase with increased greenhouse gas concentrations within 50 to 100 years. It uses as a measure of the climate sensitivity of the temperature increase due to how the temperature is affected by a change in the carbon content of 1% per year (ie 400 ppm increase in one year to 404 ppm). Climate sensitivity measure is called TCR (Transient Climate Response) and indicates the temperature rise at the time when carbon dioxide levels doubled, with 1% annually takes about 70 years.

Skeie et al. got the TCR value 1.4 degrees C with 90% probability that the value is in the range 0.8-2.2 degrees C. Even in this case was the uncertainty interval longer, almost 70% increase, if only the data up to 2000 were used .

The most exciting aspect of this very reassuring study, I think, is the already mentioned comparison with the UN climate panel climate sensitivity range, ie that climate sensitivity is likely, with 66-100% probability, is between 1.5 and 4.5 degrees Celsius . The latest scientific summary for policy makers (Summary for Policymakers, SPM) writes more accurately:

Equilibrium climate sensitivity is likely in the range 1.5 ° C to 4.5 ° C (high confidence), Extremely Unlikely less than 1 ° C (high confidence), and very Unlikely Greater Than 6 ° C (medium confidence).

(Likely = 66-100% probability, Extremely Unlikely = 0-5%, Very Unlikely = 0-10%).

This present study has instead concluded that with 90% probability is climate sensitivity between 0.9 and 3.2 ° C . The difference from the UN Climate Panel range of 1.5-4.5 degrees C is remarkable.

References

Skeie RB, Berntsen T, Aldrin M, Holden M, Myhre G (2014) A lower and more constrained estimate of climate sensitivity using updated observations and detailed radiative forcing time series . Earth Syst Dyn 5: 139-175. doi: 10.5194 / esd-5-139-2014

Aldrin M. (2010) Bayesian estimation of the climate sensitivity based on a simple climate model fitted to global temperature observations . Cambridge Workshop, December 2010.

Earth Syst. Dynam., 5, 139-175, 2014 www.earth-syst-dynam.net/5/139/2014/ doi:10.5194/esd-5-139-2014 A lower and more constrained estimate of climate sensitivity using updated observations and detailed radiative forcing time series

R. B. Skeie¹, T. Berntsen^1,2, M. Aldrin^3,4, M. Holden³, and G. Myhre^1
1Center for International Climate and Environmental Research – Oslo (CICERO), Oslo, Norway
²Department of Geosciences, University of Oslo, Oslo, Norway
³Norwegian Computing Center, Oslo, Norway
⁴Department of Mathematics, University of Oslo, Oslo, Norway
Abstract. Equilibrium climate sensitivity (ECS) is constrained based on observed near-surface temperature change, changes in ocean heat content (OHC) and detailed radiative forcing (RF) time series from pre-industrial times to 2010 for all main anthropogenic and natural forcing mechanism. The RF time series are linked to the observations of OHC and temperature change through an energy balance model (EBM) and a stochastic model, using a Bayesian approach to estimate the ECS and other unknown parameters from the data. For the net anthropogenic RF the posterior mean in 2010 is 2.0 Wm⁻², with a 90% credible interval (C.I.) of 1.3 to 2.8 Wm⁻², excluding present-day total aerosol effects (direct + indirect) stronger than −1.7 Wm⁻². The posterior mean of the ECS is 1.8 °C, with 90% C.I. [confidence interval] ranging from 0.9 to 3.2 °C, which is tighter than most previously published estimates. We find that using three OHC data sets simultaneously and data for global mean temperature and OHC up to 2010 substantially narrows the range in ECS compared to using less updated data and only one OHC data set. Using only one OHC set and data up to 2000 can produce comparable results as previously published estimates using observations in the 20th century, including the heavy tail in the probability function. The analyses show a significant contribution of internal variability on a multi-decadal scale to the global mean temperature change. If we do not explicitly account for long-term internal variability, the 90% C.I. is 40% narrower than in the main analysis and the mean ECS becomes slightly lower, which demonstrates that the uncertainty in ECS may be severely underestimated if the method is too simple. In addition to the uncertainties represented through the estimated probability density functions, there may be uncertainties due to limitations in the treatment of the temporal development in RF and structural uncertainties in the EBM.

Citation: Skeie, R. B., Berntsen, T., Aldrin, M., Holden, M., and Myhre, G.: A lower and more constrained estimate of climate sensitivity using updated observations and detailed radiative forcing time series, Earth Syst. Dynam., 5, 139-175, doi:10.5194/esd-5-139-2014, 2014.

Related:

Three new studies demonstrate climate sensitivity to CO2 is very low

New paper finds transient climate sensitivity to doubled CO2 levels is only about 1C

A new paper published in Ecological Modelling finds climate sensitivity to doubled CO2 concentrations is significantly lower than estimates from the IPCC and climate models which "utilize uncertain historical data and make various assumptions about forcings." The author instead uses a 'minimal model' with the fewest possible assumptions and least data uncertainty to derive a transient climate sensitivity of only 1.093C:

"A minimal model was used that has the fewest possible assumptions and the least data uncertainty. Using only the historical surface temperature record, the periodic temperature oscillations often associated with the Pacific Decadal Oscillation and Atlantic Multidecadal Oscillation were estimated and subtracted from the surface temperature data, leaving a linear warming trend identified as an anthropogenic signal. This estimated rate of warming was related to the fraction of a log CO2 doubling from 1959 to 2013 to give an estimated transient sensitivity of 1.093 °C (0.96–1.23 °C 95% confidence limits) and equilibrium climate sensitivity of 1.99 °C (1.75–2.23 °C). It is argued that higher estimates derived from climate models are incorrect because they disagree with empirical estimates."

Otto et al find equilibrium climate sensitivity [over the next several centuries] is only ~1.3 times greater than transient climate sensitivity, thus the estimate of 1.093C transient sensitivity could be associated with as little as 1.4C equilibrium sensitivity, less than half of the implied IPCC central estimate in AR5 of ~3.3C.

Moreover, this paper does not assume any solar forcing or solar amplification mechanisms. The integral of solar activity plus ocean oscillations explain ~95% of global temperature change over the past 400 years. Including potential solar forcing into the 'minimal model' could substantially reduce estimated climate sensitivity to CO2 to a much greater extent. 

A minimal model for estimating climate sensitivity

• Craig Loehle

•

Empirical estimates of climate sensitivity are highly uncertain.

•

Anthropogenic warming was estimated by signal decomposition.

•

Warming and forcing were equated in the time domain to obtain sensitivity.

•

Estimated sensitivity is 1.093 °C (transient) and 1.99 °C (equilibrium).

•

Empirical study sensitivity estimates fall below those based on GCMs [Global Circulation Models].

---

Abstract

Climate sensitivity summarizes the net effect of a change in forcing on Earth's surface temperature. Estimates based on energy balance calculations give generally lower values for sensitivity (< 2 °C per doubling of forcing) than those based on general circulation models, but utilize uncertain historical data and make various assumptions about forcings. A minimal model was used that has the fewest possible assumptions and the least data uncertainty. Using only the historical surface temperature record, the periodic temperature oscillations often associated with the Pacific Decadal Oscillation and Atlantic Multidecadal Oscillation were estimated and subtracted from the surface temperature data, leaving a linear warming trend identified as an anthropogenic signal. This estimated rate of warming was related to the fraction of a log CO₂ doubling from 1959 to 2013 to give an estimated transient sensitivity of 1.093 °C (0.96–1.23 °C 95% confidence limits) and equilibrium climate sensitivity of 1.99 °C (1.75–2.23 °C). It is argued that higher estimates derived from climate models are incorrect because they disagree with empirical estimates.

h/t Die Kalte Sonne

Why the basic global warming hypothesis is wrong; CO2 climate sensitivity exaggerated 21X

Kyoji Kimoto, a Japanese chemist, scientist, and fuel-cell computer modeler & inventor, has a new essay below explaining why the basic anthropogenic global warming hypothesis is wrong and leads to highly exaggerated climate sensitivity to doubled CO2. Kimoto finds climate sensitivity of only 0.14C, a factor of 21 times smaller than the IPCC canonical climate sensitivity estimate of ~3C per doubled CO2. 

See prior posts by Kimoto here. 

Basic global warming hypothesis is wrong

by Kyoji Kimoto 

1. Activities of four eminent modelers

The central dogma in anthropogenic global warming (AGW) theory is that zero feedback climate sensitivity (Planck response) is 1.2~1.3 K. This gives climate sensitivity when multiplied by feedbacks (Hansen et al., 1984).

Until Kimoto (2009), theoretical discussions concentrated on the feedback issue. However, it is impossible to accurately determine the feedbacks caused by the variable nature of water in the perturbed atmosphere with CO2 doubling. This problem has resulted in speculative discussions for a long time.

However, rigorous discussions are possible for the zero feedback climate sensitivity (Planck response) based on mathematics and physics. The Planck response of 1.2 K for GCMs comes from one-dimensional radiative convective equilibrium models (1DRCM) that assume the fixed lapse rate of 6.5 K/km (FLRA) and use the mathematical method of Cess (1976), equation (3).

The work of the following eminent modelers are mainly concerned with the central dogma of the AGW theory.

Dr. S. Manabe:

Manabe & Wetherald (1967) used the FLRA for the CO₂ mixing ratio of 300 ppm (1xCO₂) and that of 600 ppm (2xCO₂) in the atmosphere, and obtained the zero feedback climate sensitivity CS(FAH) of 1.3 K in their 1DRCM study. Regarding lapse rate, Manabe & Strickler (1964) wrote,

“The observed tropospheric lapse rate of temperature is approximately 6.5 K/km. The explanation for this fact is rather complicated. It is essentially the result of a balance between (a) the stabilizing effect of upward heat transport in moist and dry convection on both small and large scales and (b), the destabilizing effect of radiative transfer. Instead of exploring the problem of the tropospheric lapse rate in detail, we here accept this as an observed fact and regard it as a critical lapse rate for convection.”

In the farewell lecture held on October 26, 2001, in Tokyo, Manabe told about his research,

“Research funds have been 3 million dollars per year and 120 million dollars for the past 40 years. It is not clever to pursue the scientific truth. Better way is choosing the relevant topics to the society for the funds covering the staff and computer cost of the project.”

Dr. J. Hansen:

(a) Hansen obtained the zero feedback climate sensitivity CS(FAH) of 1.2 K with the FLRA for 1xCO₂ and 2xCO₂ in his 1DRCM study.

(b) Although Hansen alarmed society about tipping points of catastrophic AGW many times, he showed no confidence in his model studies:

“The 1DRCM study is a fudge because obtained results strongly depend on the lapse rate assumed.”

https://www.aip.org/history-programs/niels-bohr-library/oral-histories/24309-1

“Observations Not Models”

http://www.worldclimatereport.com/index.php/2004/04/14/observations-not-models/

“James Hansen Increasingly Insensitive”

http://www.worldclimatereport.com/index.php/2005/04/28/james-hansen-increasingly-insensitive/

Dr. M. Schlesinger:

Schlesinger was an AGW denier in the early 1980s as shown by Gates et al. (1981) which calculated a climate sensitivity of 0.3 K when the sea surface temperature is held in climatological values for 2xCO_2. In order to get plentiful funds, he has become the top alarmist of catastrophic AGW. He calculated the central dogma of AGW theory as follows:

(a) He obtained the zero feedback climate sensitivity of 1.3 K with the FLRA for 1xCO₂ and 2xCO₂ in his 1DRCM study (Schlesinger, 1986).

(b) Unfairly, he utilized the Cess method without referring to Cess (1976) to obtain his equation (6) for the Planck response of 1.2 K (Schlesinger, 1986). Kimoto (2009) pointed out that it is only a transformation of Cess equation (4) as shown in Section 3.

Dr. D. Randall:

Randall obtained the zero feedback climate sensitivity of 1.2 K utilizing equation (3) in his lecture (2011) here. https://www.youtube.com/watch?v=FjE4GDC7afQ

However, his calculation contains a mathematical error as shown in Section 4.

2. Failure of the fixed lapse rate assumption of 6.5 K/km (FLRA)

Modern AGW theory began from the 1DRCM studies with fixed absolute and relative humidity utilizing the FLRA for 1xCO₂ and 2xCO₂ (Manabe & Strickler, 1964; Manabe & Wetherald, 1967; Hansen et al., 1981).

Table 1 shows the climate sensitivities for 2xCO₂ obtained in these studies, where the climate sensitivity with the fixed absolute humidity CS (FAH) is 1.2 to 1.3 K (Hansen et al., 1984).

Schlesinger (1986) confirmed these results by obtaining the CS (FAH) of 1.3 K and the radiative forcing of 4 W/m2 for 2xCO₂ in his 1DRCM study.

The ratio of the climate sensitivity with fixed relative humidity CS (FRH) to the zero feedback climate sensitivity CS (FAH) is water vapor feedback WVF by (1), which is 1.6 ~ 1.8 as shown in Table 1.

CS (FRH) = CS (FAH) x WVF=CS (FAH) x 1.6 ~ 1.8              (1)

In the 1DRCM studies, the most basic assumption is the FLRA. The lapse rate of 6.5 K/km is defined for 1xCO₂ in the U.S. Standard Atmosphere (1962) (Ramanathan & Coakley, 1978). There is no guarantee, however, for the same lapse rate maintained in the perturbed atmosphere with 2xCO₂ (Chylek & Kiehl, 1981; Sinha, 1995).

Therefore, the lapse rate for 2xCO₂ is a parameter requiring a sensitivity analysis to check the validity of the modeled results as shown in Fig.1. In the figure, line B shows the FLRA gives a uniform warming for the troposphere and the surface. Since CS (FAH) greatly changes with a minute variation of the lapse rate for 2xCO₂, the results of the 1DRCM studies in Table 1 are theoretically meaningless.

Further, Fig.1 shows the failure of the FLRA in 1DRCM studies, which were initiated by Manabe & Strickler (1964) who used an invalid assumption about how doubling CO2 perturbs the atmosphere, shown in Section 1.

Fig. 1 Parameter sensitivity analysis of the lapse rate for 2xCO2. CS (FAH): Climate sensitivity with the fixed absolute humidity.

In IPCC’s AGW theory, the CS (FAH) of 1.2 ~ 1.3 K is called as Planck response (Bony et al., 2006). The FLRA in the 1DRCM is extended to the Planck response of 1.2 K with the uniform warming throughout the troposphere in the GCMs studies (Hansen et al., 1984; Soden & Held, 2006; Bony et al., 2006). Climate sensitivity for 2xCO₂ is expressed by (2) in the 14 GCMs studies for the IPCC AR4 as the extension of (1) (Soden & Held, 2006; Bony et al., 2006).

Climate sensitivity = Planck response x Feedbacks (wv, al, cl, lr)

= 1.2 K x 2.5 = 3 K                                    (2)

Feedbacks are water vapor, ice albedo, cloud and lapse rate feedback.

The theoretical 1DRCM studies with the FLRA have failed, as shown in Fig. 1. Therefore, the canonical climate sensitivity of 3 K claimed by the IPCC is theoretically meaningless since it is used the 1DRCM studies in Table 1 in its GCMs.

Therefore, the cause of the AGW debate for the past 50 years is the lack of the parameter sensitivity analysis in the 1DRCM studies by Manabe & Wetherald (1967), Hansen et al. (1981) and Schlesinger (1986). Such sensitivity analysis is a standard scientific procedure to check the validity of the obtained results.

If sensitivity analysis were performed in the above studies, the result would show AGW will cause no huge economic loss. Also, the Fukushima nuclear disaster might not have occurred without the Kyoto protocol that promoted nuclear power.

3. Mathematical error in Cess (1976)

In 1976, Cess obtained – 3.3 (W/m2)/K for the Planck feedback parameter  utilizing the modified Stefan-Boltzmann equation (3), which gives the Planck response of 1.2 K with the radiative forcing RF of 4 W/m2 for 2xCO₂ as follows (Cess, 1976).

OLR =   T_s⁴                                                                             (3)

 = – dOLR/dT_s = – 4   T_s³ = – 4 OLR/T_s = – 3.3 (W/m2)/K                (4)

Planck response = – RF/ = 4(W/m2)/ 3.3 (W/m2)/K = 1.2 K                  (5)

Where,

OLR (Outgoing long wave radiation at the top of the atmosphere) = 233 W/m2

: the effective emissivity of the surface-atmosphere system

: Stefan-Boltzmann constant

T_s: the surface temperature of 288 K

Coincidently, the Planck response of 1.2 K in (5) is the same as the zero feedback climate sensitivities of 1.2 to 1.3 K obtained from the 1DRCM studies in Table 1. Therefore, many researchers followed the Cess method. Their results are in the 14 GCMs studies for the IPCC AR4. AR4 shows the theoretical basis of IPCC’s claim that the Planck response is 1.2 K (Schlesinger, 1986; Wetherald & Manabe, 1988; Cess et al., 1989; Cess et al., 1990; Tsushima et al., 2005; Soden & Held, 2006; Bony et al., 2006).

However, the above derivation is apparently a mathematical error since it is not a constant enabling us to differentiate (3) as shown in (4) (Kimoto, 2009). Schlesinger (1986) proposed a different equation (6) to give the Planck response of 1.2 K, which is only a transformation of (4) as follows (Kimoto, 2009).

– 1/ =  = T_s/ (1 –  ) S₀ = 0.3 K / (W/m2)                     (6)

Here,

surface albedo  = 0.3 and solar constant S₀ = 1370 W/m2.

At the equilibrium,

OLR = (S₀/4) (1 – )

From (4),

 = – 4OLR/T_s = – 4x (S₀/4) (1 – )/T_s

Then,

– 1/ =  = T_s/ (1 – ) S₀

Further, the combination of T_s=288 K and OLR=233 W/m2 is not in accordance with Stefan-Boltzmann law in (4) (Bony et al., 2006; Kimoto, 2009). Since (3) can be rewritten as

 = OLR/T_s⁴,

 is the ratio of OLR to the radiation flux at the surface. There are, however, fluxes from evaporation and thermal conduction in addition to the radiation flux at the surface in Fig. 3. Therefore, (3) cannot be a theoretical basis of the AGW theory because it is against the physical reality of nature.

4. Mathematical error in Randall lecture (2011)

https://www.youtube.com/watch?v=FjE4GDC7afQ

Randall shows the following equation series in his lecture.

(1 – )S  a² =  ( T_s⁴) 4  a²

(1 – )S = 4  ( T_s⁴)

0 = 4( ) ( T_s⁴) + 4 (4  T_s³  T_s)

 Ts = – (T_s/4) ( /)

 ( T_s⁴) = 240 W/m2

( ) ( T_s⁴) = – 4 W/m2

This is a mathematical error as shown below.

 / = – 4/240

Ts = 288 K

 Ts = – (T_s/4) (  /  ) = (- 288/4) (- 4/240) = 1.2 K

Kimoto critique:

The following equation is obtained when Cess’s eq.

OLR =  ( T_s⁴

is differentiated with CO2 concentration C.

 OLR/ C = ( / C) ( T_s⁴) + 4  ( T_s³) ( Ts/  C)

Radiative forcing is 4 W/m2 when  C is 2xCO2.

– 4 W/m2 =   ( T_s⁴) + 4  ( T_s³) Ts

Randall lecture (2011) neglects the second term to obtain the tricky equation above.

5. Physical reality of the response to 2xCO₂

In the orthodox AGW theory based on the radiation height change by Mitchell (1989) and Held & Soden (2000), the radiation height increases from point a to point b in Fig. 2 due to the increased opaqueness when CO₂ is doubled. This decreases the temperature at the effective radiation height of 5 km which causes an energy imbalance between the absorbed solar radiation (ASR) of 239 W/m2 and the outgoing long wave radiation (OLR) in Fig. 3.

In order to recover the balance of energy, the radiation temperature increases from point b to point c. A 1 K warming at the effective radiation height is enough to recover the energy imbalance caused by the radiative forcing of 3.7 W/m2 for 2xCO₂ from Stefan-Boltzmann law as shown in Fig.2. Under the FLRA, the surface temperature increases in the same degree of 1 K from T_s1 to T_s2 in Mitchell (1989) and Held & Soden (2000). However, it is erroneous since the FLRA failed in Section 2.

Fig. 2. Global warming theory based on the radiation height change. Physical reality: The surface temperature increase is 0.1 ~ 0.2 K with the slightly decreased lapse rate of 6.3 K/km from 6.5 K/km.

In reality, the bold line in Fig.2 shows the surface temperature increases as much as 0.1~0.2 K with the slightly decreased lapse rate from 6.5 K/km to 6.3 K/km. Since the zero feedback climate sensitivity CS(FAH) is negligibly small at the surface, there is no water vapor or ice albedo feedback which are large positive feedbacks in the GCMs studies of the IPCC. The following data support the above picture.

(A) Kiehl & Ramanathan (1982) show the following radiative forcing for 2xCO₂.

Radiative forcing at the tropopause: 3.7 W/m2.

Radiative forcing at the surface: 0.55 ~ 1.56 W/m2 (averaged 1.1 W/m2).

The surface radiative forcing is greatly reduced by the IR absorption overlap with water vapor plentifully existing at the surface. This denies the FLRA giving the uniform warming throughout the troposphere in the 1DRCM and the GCMs studies.

(B) Newell & Dopplick (1979) obtained a climate sensitivity of 0.24 K considering the evaporation cooling from the surface of the ocean.

(C) Ramanathan (1981) shows the surface temperature increase of 0.17 K with the direct heating of 1.2 W/m2 for 2xCO₂ at the surface.

(D) The surface climate sensitivity is calculated from the energy budget of the earth in Fig. 3 and the surface radiative forcing of 1.1W/m2 as follows.

Natural greenhouse effect:     289 K – 255 K = 34 K

Natural greenhouse energy:    E_b – E_s = 333 – 78 (W/m2) = 255 (W/m2)

Climate sensitivity factor :     34 K/255 (W/m2) = 0.13 K/ (W/m2)

Surface radiative forcing:         0.55 ~ 1.56 W/m2 (averaged 1.1 W/m2 )

Surface climate sensitivity:        0.13K/(W/m2) x 1.1 (W/m2) = 0.14 K

Fig. 3. Energy budget of the earth adapted from Trenberth et al. (2009).

Conclusions

Four eminent modelers formed the central dogma of the IPCC AGW theory. Their theory claims the zero feedback climate sensitivity (Planck response) is 1.2 ~ 1.3 K for 2xCO2. When multiplied by the feedback factor of 2.5, this gives the canonical climate sensitivity of 3 K claimed by the IPCC .

However, this IPCC dogma fails due to the lack of parameter sensitivity analysis of the lapse rate for 2xCO2 in the one dimensional model (1DRCM). The dogma also contains a mathematical error in its derivation of the Planck response by Cess (1976). Therefore, the IPCC AGW theory and its canonical climate sensitivity of 3 K for 2xCO2 are invalid.

This study derives a climate sensitivity of 0.14 K from the energy budget of the earth.

References

Bony, S., Colman, R., Kattsov, V.M., Allan, R.P., Bretherton, C.S., Dufresne, J.L., Hall, A., Hallegatte, S., Holland, M.M., Ingram, W., Randall, D.A., Soden, B.J., Tselioudis, G., Webb, M.J., 2006. Review article: How well do we understand and evaluate climate change feedback processes?  J. Climate 19, 3445-3482.

Cess, R.D., 1976. An appraisal of atmospheric feedback mechanisms employing zonal climatology. J.Atmospheric Sciences 33, 1831-1843.

Cess, R.D., Potter, G.L., Blanchet, J.P., Boer, G.J., Ghan, S.J., Kiehl, J.T., Le Treut, H., Li, Z.X., Liang, X.Z., Mitchell, J.F.B., Morcrette, J.J., Randall, D.A., Riches, M.R., Roeckner, E., Schlese, U., Slingo, A., Taylor, K.E., Washington, W.M., Wetherald, R.T., Yagai, I., 1989. Interpretation of cloud-climate feedback as produced by 14 atmospheric general circulation models. Science 245, 513-516.

Cess, R.D., Potter, G.L., Blanchet, J.P., Boer, G.J., DelGenio, A.D., Deque, M., Dymnikov, V., Galin, V., Gates, W.L., Ghan, S.J., Kiehl, J.T., Lacis, A.A., LeTreut, H., Li, Z.X., Liang, X.Z., McAvaney, B.J., Meleshko, V.P., Mitchell, J.F.B., Morcrette, J.J., Randall, D.A., Rikus, L., Roeckner, E., Royer, J.F., Schlese, U., Sheinin, D.A., Slingo, A., Sokolov, A.P., Taylor, K.E., Washington, W.M. and Wetherald, R.T., 1990.  Intercomparison and interpretation of climate feedback processes in 19 Atmospheric General Circulation Models.  J. Geophysical Research 95, 16,601-16,615.

Chylek, P., Kiehl, J.T., 1981. Sensitivities of radiative-convective climate models. J. Atmospheric Sciences 38, 1105-1110.

Gates, W.L., Cook, K.H., Schlesinger, M.E., 1981: Preliminary analysis of experiments on the climatic effects of increased CO2 with an atmospheric general circulation model and a climatological ocean. J. Geophysical Research 86, 6385-6393.

Hansen, J., Johnson, D., Lacis, A., Lebedeff, S., Lee, P., Rind, D., Russell, G., 1981. Climate impact of increasing atmospheric carbon dioxide. Science 213, 957-966.

Hansen, J., Lacis, A., Rind, D., Russell, G., Stone, P., Fung, I., Ruedy, R., Lerner, J., 1984. Climate sensitivity: Analysis of feedback mechanisms. in Climate Processes and Climate Sensitivity, J.E. Hansen and T. Takahashi, Eds. (American Geophysical Union, Washington, D.C., 1984), pp. 130-163.

Held, I.M., Soden, B.J., 2000. Water vapor feedback and global warming. Annu. Rev. Energy Environ. 25, 441-475.

Kiehl, J.T., Ramanathan, V., 1982. Radiative heating due to increased CO₂: The role of H₂O continuum absorption in the 12-18 micron region. J. Atmospheric Sciences 39, 2923-2926.

Kimoto, K., 2009. On the confusion of Planck feedback parameters. Energy & Environment 20, 1057-1066.

Manabe, S., Strickler, R.F., 1964. Thermal equilibrium of the atmosphere with a convective adjustment. J. Atmospheric Sciences 21, 361-385.

Manabe, S., Wetherald, R.T., 1967. Thermal equilibrium of the atmosphere with a given distribution of relative humidity. J. Atmospheric Sciences 24, 241-259.

Mitchell, J.F.B., 1989. The greenhouse effect and climate change. Reviews of Geophysics 27, 115-139.

Newell, R.E., Dopplick, T.G., 1979. Questions concerning the possible influence of anthropogenic CO₂ on atmospheric temperature. J. Applied Meteorology 18, 822-825.

Ramanathan, V., Coakley, Jr.J.A., 1978. Climate modeling through radiative-convective models. Reviews of Geophysics and Space Physics 16, 465-489.

Ramanathan, V., 1981. The role of ocean-atmosphere interactions in the CO₂ climate problem. J. Atmospheric Sciences 38, 918-930.

Schlesinger, M.E., 1986. Equilibrium and transient climatic warming induced by increased atmospheric CO₂. Climate Dynamics 1, 35-51.

Sinha, A., 1995. Relative influence of lapse rate and water vapor on the greenhouse effect. J. Geophysical Research 100, 5095-5103.

Soden, B.J., Held, I.M., 2006. An assessment of climate feedbacks in coupled ocean-atmosphere models. J. Climate 19, 3354-3360.

Trenberth, K.E., Fasullo, J.T., Kiehl, J., 2009. Earth’s global energy budget. BAMS March 2009, 311-323.

Tsushima, Y., Abe-Ouchi, A., Manabe, S., 2005. Radiative damping of annual variation in global mean temperature: comparison between observed and simulated feedbacks. Climate Dynamics 24, 591-597.

Wetherald, R.T., Manabe, S., 1988. Cloud Feedback Processes in a General Circulation Model. J. Atmospheric Science 45, 1397-1415.