Equilibrium Climate Sensitivity (ECS) is the most critical value for any assessment of human impact on climatic variatio
Equilibrium Climate Sensitivity An estimate based on a simple radiative forcing and feedback system © 2012 - 2016, Michel de Rougemont Equilibrium Climate Sensitivity (ECS) is the most critical value for any assessment of human impact on climatic variations. It relates the global temperature response to a doubling of the concentration of CO2, the greenhouse gas produced by carbon containing fuels. From it derives the now generally admitted belief that the almost solely cause of the warming of the climate is of anthropogenic nature; and ambitious emission reduction programs are put in place to mitigate these effects in the future. It is therefore of utmost importance to have a high confidence in estimated ECS values. This paper presents a simple and verifiable method to determine it on the basis of primary radiative forcing and the subsequent feedback response of the global climate system. The obtained result, ECS = 0.53 K [0.42 to 0.73], differs widely from the ECS values estimated as likely by the Intergovernmental Panel on Climate Change (IPCC). This due to a gross mistake in the modelling retained by IPCC. ECS cannot be estimated from available observation data because too many other parameters and disturbances interfere to enable a clear causal and quantitative attribution. Reliable instrumental measurements span over a too short period of time as compared with climatic variations to enable valid correlation. In addition, the paleo-climatic CO2 concentration range estimated over the past 400’000 years (1) lies between 180 and 300 ppm, and during the past millennium, before the start of the industrial era in the 19th century, it was narrowly oscillating around 280 ppm (2). This is an insufficient basis to allow for extrapolation to 400 ppm (the current 43% increase), or doubling or trebling such concentration. Therefore, and with these limitations, the only way to ascertain what ECS may be, is to estimate it with the help of models.
Radiative Forcing Radiative forcing resulting from the absorption by carbon dioxide (CO2) of electromagnetic radiations in the infrared range is approximated with the practical formula of Myhre (3): 𝐶
𝐹𝐶𝑂2 = 5.35 ∙ ln( 1 ) 𝐶0
(equation 1)
Where FCO2 = radiative forcing caused by CO2 [W m-2] C0 and C1 = initial and final CO2 concentration [ppmV or mol%] Thus, according to Myhre, if the CO2 concentration doubles: F2xCO2 = 3. 71 W m-2.
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Feedback system As primary radiative forcing is taking place due to an elevation of the concentration of so-called greenhouse gases, the system responds by an elevation of the atmospheric temperature, and subsequently by a series of feedbacks. At the equilibrium, the system can be described by the following block diagram.
Figure 1
Simplified block diagram of climate response to radiative forcing caused by a greenhouse gas.
Where: FGHG = Forcing resulting from the absorption of long wave radiations by greenhouse gases FF = Forcing resulting from feedback mechanisms [W m-2] Fall = FGHG + FF ∆T= Surface temperature variation resulting from the total forcing [K] GS = Primary system response = ∆T/Fall [K W-1 m2] GF = System feedback response = FF/∆T [W m-2 K-1] Applying the transfer functions GS and GF, and resolving for ∆T: ∆T = GS· Fall FF = GF· ΔT Fall = FGHG + FF = FGHG + GF· ∆T ∆T/GS = FGHG + GF·∆T ∆T·(1- GF·GS)= GS· FGHG
∆𝑇 =
𝐺𝑆 (1−𝐺𝑆 ∙𝐺𝐹 )
∙ 𝐹𝐺𝐻𝐺
(equation 2)
The primary transfer function GS of the system is given by the derivative of the Stefan Boltzman equation:
2
F = ε·σ·T4 or T = (F/(ε·σ))0.25
(equation 3)
Where: ε is the emissivity, σ the Stefan Boltzmann constant. Thus:
(equation 4) This derivative is dependent of the radiation intensity which at its turns is a function of temperature, as seen on Figure 2, calculated with ε = 1.
Figure 2
Transfer function GS at Earth surface temperature
To simplify, around 285-289 K (12 -16 °C), the average Earth surface temperature, this transfer function can be linearized at: GS = 0.187 K W-1 m2. According to equation 3, the stability of such a feedback system is no more given when the product GS·GF, also called feedback factor, approaches 1. Thus, in the present case, GF should remain significantly inferior to +5.3 W m-2 K-1.
Figure 3
Stability and feedback factor GS·GF
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Feedback phenomena The feedback transfer function GF is taken as the sum of the average individual values summarized on table 9.5 of the 5th IPCC report (4). The associated phenomena are: Planck: As temperature increases, the radiative energy emitted will also increase according to Planck law. While losing this energy, the temperature of the emitting material will decrease. Part of the temperature increase contributes therefore to eliminate the forcing, and to dampen the temperature rise. Thus, Planck response is a negative, attenuating, feedback: λP = -3.21 [-3.3 – -3.1] W m-2 K-1 Water Vapour: More water will evaporate when temperature is increasing. The higher air humidity will absorb more radiative energy and contribute to amplifying the forcing. This is a positive, amplifying, feedback: λWV = +1.63 W m-2 K-1 , in a range of1.4 to 1.9 However, the evaporation-condensation of water, with its large latent heat (2444 J g-1 at surface temperature), was not considered in this parameter. Another model would be required to reflect this. Lapse Rate: The lapse rate is the temperature gradient that establishes itself from the surface up to the top of the troposphere. When the overall temperature increases, the structure of the atmosphere will change, convective force will move warmer air upwards and the gradient will change: it will tend to be less pronounced in tropical latitudes (negative feedback) and more pronounced in midlatitudes (positive feedback). Overall it results to be a negative feedback, with a large uncertainty: λLR = -0.60 W m-2 K-1 [-1 to -0.2] Albedo: The reflectivity of the sunlight depends on the type and on the extent of the surface that is reflecting it. In particular, there is a large difference between ice and water. With higher temperature, less ice or snow coverage is expected, resulting in less reflection. This is a positive feedback: λA = +0.31 W m-2 K-1 [0.2 to 0.4] Clouds: Clouds show two different feedbacks. With higher temperature, water will evaporate and more clouds will be formed. With a larger reflective surface, cloud albedo will increase, more sunlight will be reflected back to the outer space, a negative feedback. But at higher altitude the clouds will contribute to more radiative forcing in the IR range. Overall the current estimate is that it is a positive feedback, albeit with a high uncertainty (300%): λC = 0.28 W m-2 K-1 [-0.4 to +1.2] Overall, these factors are additive, resulting in a negative feedback: λ = λP + λWV + λLR + λA + λC = -3.21 + 1.63 – 0.60 + 0.31 + 0.28 = -1.59
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and by adding the error ranges from the individual model estimations: GF = λ = -1.59 W m-2 K-1 , in a range of -3.10 to +0.20 The overall negative value of the feedback GF indicates a dampening of the system in response to the primary radiative forcing.
Figure 4
The five prevalent feedback factors as calculated from models reviewed by IPCC
The calculated ∆T in relation with CO2 concentration is shown in Figure 5:
Figure 5
Calculated temperature sensitivity to CO2. 280 ppm taken as the pre-industrial concentration. The grey area indicates the range of uncertainty of the feedback factor GF.
Thus, Equilibrium Climate Sensitivity, in the sense given to this expression by IPCC (temperature increase resulting from doubling of the CO2 concentration), is calculated as: ECS = 0.53 K [0.42 to 0.73] 5
According to F.K. Reinhart (5) the parameter 5.35 in equation 1 could be reduced to 1.88; then ECS would be reduced to 0.19 K.
Exhaustion of World fossil reserves: Extrapolating to a hypothetical burning of 3 times the proved fossil reserves (6), having as consequence that the CO2 concentration would reach approximately 925 ppm, would imply a warming of: ΔT = 0.92 K [0.73 to 1.26], since the beginning of the industrial era.
Comparison with the IPCC published view. In the IPCC report (4, page 920), ECS is defined as:
ECS = F2.CO2/
(equation 5)
Where: F2.CO2 is the calculated forcing for doubling [CO2], thus 3.71 Wm-2, as FGHG above =-λ Thus, according to the model adopted by IPCC, ECS is calculated as: ECSIPCC = 3.71/1.59 = 2.33 K which lies well in the midst of the claimed likely range of 1.5 to 4.5 K. But ECS response to is an indeterminate infinite value if it tends to be nil; or even a cooling would occur if the overall feedback would be amplifying ( negative, λ positive). 50 40
=
=
2
3
30
20 -3.10; 1.20
-1.59; 2.33
10
-5
-4
-3
-2
-1
-10
0
1
5
λ [W m-2 K-1]
-20
-30
4
0.20; -18.55
-40 -50
Figure 6
Hyperbolic climate response for feedback values λ in the range considered by IPCC
As zero or a negative value for are within the possible range of the model estimates reviewed by IPCC in its report, a physically impossible situation could result.
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Thus, IPCC does not consider any feedback as standard engineering practices require, as in figure 1. Apparently, and it is not explained in details in the report, an additive succession is built from primary forcing to overall climate response which results in equation 4. This wrong and impossible model has three dramatic consequences: a) Instilling the belief that sudden and high instabilities may occur; b) Attributing most of the warming since the beginning of the industrial era to greenhouse gases, thus accrediting the belief in the anthropogenic culprit; c) Totally false [catastrophic] projections calculated with any emission scenario for the future; with the associated activism for global mobilization against fossil fuels (that represent 87% of the World energy consumption). The climate response experienced after significant perturbations, such as large volcanic eruptions or successions of warm periods and little ice ages, lets infer that the system is not prone to such an instability. It is difficult to understand IPCC’s persistence with its invalid appreciation of ECS. Questioned more than once about this evident blunder, Thomas Stocker, the lead author of the IPCC report (4) who teaches climate modelling (7) with equation 5 at the University of Bern, Switzerland, has not found necessary to respond.
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References (1)
NOAA Paleoclimatology www.ncdc.noaa.gov/paleo/globalwarming/temperature-change.html
(2)
Carbon Dioxide Information Analysis Center cdiac.ornl.gov/trends/co2/graphics/lawdome.gif
(3)
Myhre et al. New estimates of radiative forcing due to well mixed greenhouse gases. Geophysical Research Letters, Vol. 25, No.14, pages 2715-2718, July 15, 1998 folk.uio.no/gunnarmy/paper/myhre_grl98.pdf
(4)
IPCC, 2013: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.). Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 1535 pp. Feedback factors are summarized on Table 9-5, page 818. ECS is defined on Page 920.
(5)
F. K. Reinhart, www.eike-klima-energie.eu/uploads/media/Infrared_absorption_capability_of_atmospheric_carbon_dioxide.pdf.
(6)
BP Statistical Review of World Energy, June 2014, http://bp.com/statisticalreview
(7)
Stocker, T., Lecture notes: Einführung in die Klima Modellierung. http://www.climate.unibe.ch/~stocker/papers/stocker08EKM.pdf
Conflict of interest: Michel de Rougemont has no conflict of interest. Financial support: None. Author address:
[email protected] Internet links of the author: www.mr-int.ch
blog.mr-int.ch
climate.mr-int.ch
A calculator (Excel spreadsheet) integrating the present evaluation with a simple energy balance model can be downloaded here.
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