Greenhouse Bulletin 121, March 1999
Vincent R. Gray
The greenhouse effect is considered to be caused by the absorption of long wave (infra red) radiation from the earth by trace gases in the atmosphere. Changes in the concentration of these gases leads to a change in the radiative energy absorbed, and thus of the temperature of the atmosphere, and of its radiation back to earth. The difference in radiation received by the earth between two defined conditions is called radiative forcing. There are two important examples. The first is the forcing thought to be caused by the combustion of fossil fuels since the large scale development of industry which is considered to be responsible for an increase in atmospheric carbon dioxide concentration over an assumed "pre-industrial" level. The second, commonly calculated by computer climate models, is the forcing produced by doubling the concentration of carbon dioxide in the atmosphere. The forcing can be converted to a mean global surface temperature change by multiplying by a "climate sensitivity" parameter which varies widely between the different models. The IPCC (Houghton et al. 1990) has amalgamated forcing and its global temperature response into a range of "temperature climate sensitivities" for the doubling of carbon dioxide concentration in the atmosphere, as estimated by the different computer climate models, for which the "Best Estimate" is 2.5°C, the "High Estimate" 4.5°C, and the "Low Estimate" 2.5°C.
Measuring the infra red absorption of the atmosphere is quite difficult. Nevertheless the pioneer of the greenhouse effect (Arrhenius 1896) obtained a value for this quantity by subtracting the infra red spectrum of the earth from that of the moon on a clear night. This method would depend on finding a part of the earth's surface that most resembles the moon, for a fair comparison.
This method is evidently not considered seriously today, although there are satellite measurements of the recent radiation behaviour of the earth. Assessment of the greenhouse effect is always made by calculations involving known measured absorption spectra of the greenhouse gases, combined with known properties (temperature, pressure) of the atmosphere at its different levels.
The major greenhouse gas is water vapour. Unfortunately, it is not "well-mixed" and its concentration and distribution over a period of time is unknown. Its radiative forcing is therefore regarded as a "feedback" and it is estimated by a procedure called parametrization where it is related to carbon dioxide or to temperature by a formula. Several other feedbacks such as aerosols and albedo changes are also related to carbon dioxide by parametrization.
The other greenhouse gases, such as methane, nitrous oxide, and CFCs are also related to carbon dioxide by being converted to "equivalent carbon dioxide". It is therefore of prime importance that procedures for calculating the radiative forcing of carbon dioxide are kept up to date.
Calculation of Forcing for Carbon Dioxide
It is well recognised that the concentration of carbon dioxide in the atmosphere is such that its infra red absorption is close to saturation, particularly with the most prominent absorption band (15mm). Further absorption with increase of concentration is considered to take place around the fringes of this band and in minor bands. The relationship between absorption and concentration at current levels in the atmosphere is very nearly logarithmic, a relationship established in the time of Arrhenius (1896) and used by him in his paper.
There is a considerable difference of opinion between various authorities making these calculations. Cess et al. (1993) found a range of calculated figures for the radiative forcing for a doubling of carbon dioxide concentration (considered on its own, without other greenhouse gases or "feedbacks") of between 3.3 and 4.8Wm-2 for fifteen models, with a mean of 4Wm-2 . This is a variability of ±0.75Wm-2 or ±19%. Since each modellist will have chosen "Best Estimate" figures for his model the actual variability of possible forcing would be larger than ±19%.
The Intergovernmental Panel on Climate Change (IPCC) in their first Report (Houghton et al 1990) gave the following formula for calculating the radiative forcing (Delta F) in Wm-2, of changes in atmospheric concentration of carbon dioxide:
Delta F = 6.3 ln (C/Co), (1)
where C is CO2 concentration in parts per million by volume and Co is the reference concentration. The formula is said to be valid below C = 1000 ppmv and there were no indications of the accuracy of the formula. The formula predicts a radiative forcing of 4.37 Wm-2 for a doubling of carbon dioxide concentration. This is 9% greater than the mean value assumed by the models (Cess et al. 1993).
This formula is said to derive from a paper by Wigley (1987), but the formula in this paper is not quite the same. Wigley's formula, derived from the model of Kiehl and Dickinson (1987), is
Delta F = 6.333 ln (C/C0) (2)
considered accurate over the range 250ppmv to 600ppmv; and "is probably accurate to about +10%"..
Removal of the extra significant figures is acceptable, but extension of the range of accuracy by the IPCC so that it will include the doubling of carbon dioxide concentration of the models seems to be less than honest.
Formula (1) has been used by the IPCC scientists for their calculations of radiative forcing "since pre-industrial times", and for their calculations of future radiative forcing (and so, temperature change) for their futures scenarios.
In the IPCC 1994 Report (Houghton et al 1994) the authors of Chapter 4 ( K.P. Shine, Y. Fouquart, V. Ramaswamy, S. Solomon, J. Srinivasan) sought to counter the prevalent belief that infra red absorption of carbon dioxide is saturated by proving an example showing the additional absorption from 1980 to 1990. Their graph (Figure 4.1, page 175) integrates to give a forcing of 0.31Wm-2 (Courtney 1999). If the Mauna Loa figures for carbon dioxide concentration of 338.52 ppmv for 1980 and 354.04 ppmv for 1990 are substituted in formula (1) you get 0.28Wm-2, 9% lower than the IPCC illustration.
A Revised Formula
A revised formula for calculation of radiative forcing from changing concentrations of carbon dioxide has recently been published (Myhre et al 1998).
Delta F = 5.35 ln (C/Co) (3)
The authors express the view that the IPCC estimates "have not necessarily been based on consistent model conditions". They carry out calculations on the spectra of the main greenhouse gases by all three of the recognised radiative transfer schemes, line by line (LBL), narrow-based model (NBM) and broad-based model (BBM). They calculate the Global Mean Instantaneous Clear Sky Radiative Forcing for 1995, for atmospheric carbon dioxide, relative to an assumed "pre-industrial" level of 280ppmv, as 1.759Wm-2 for LBL, 1.790Wm-2 for NBM and 1.800Wm-2 for BBM; a mean of 1.776Wm-2 with BBM 2.3 % greater than LBL.
The new formula gives 3.71Wm-2 for doubling carbon dioxide; 15% less than the previous formula. It is also below the mean of 4.0Wm-2 of the models (Cess 1993).
Reduced Greenhouse Warming
The replacement of the previous formula (1) for calculating radiative forcing from carbon dioxide concentrations by the revised, more accurate formula (3), means that all existing and previous estimates for future temperature rise due to the greenhouse effect, should be reduced by 15%. In particular, the "temperature climate sensitivity" (temperature change for doubling carbon dioxide) figures of 2.5°C "Best Estimate", 4.5°C "High Estimate" and 1.5°C "Low Estimate" which are the basis for most IPCC projections, should be revised to 2.1°C, 3.8°C and 1.3°C respectively..
It should be noted that Myrhe et al 1998 also give revised formulae for the other greenhouse gases. Methane remains the same, nitrous oxide is reduced, and CFCs are increased. These affect the calculation of forcing since "pre-industrial " times, but hardly affect future projections since all these gases are declining in importance.
Arrhenius, S. 1896 On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground. Phil Mag S.5 41 (251) 237-276
Cess, R.D., and 29 others, 1993. Uncertainties in Carbon Dioxide Radiative Forcing in Atmospheric General Circulation Models. Science 262, 1252-1255
Courtney, R.S. 11 Jan 1999. Private Communication (Email)
Houghton, J.T., G.J. Jenkins, and J.J. Ephraums, (Ed) 1990 Climate Change :The IPCC Scientific Assessment Cambridge University Press
Houghton, J.T., L.G. Meira Filho, J. Bruce, H. Lee, B.A. Callander, E. Haites, N. Harris and K. Maskell, 1994, Climate Change 1994. Cambridge University Press.
Keihl, J.T. and R.E. Dickinson, 1987 Study of the Radiative Effects of Enhanced Atmospheric CO2 and CH4 on Early Earth Surface Temperatures. J. Geophys. Res.92 2991-2998
Myhre, G., E.J. Highwood, K. Shine and F. Stordal, 1998. New estimates of radiative forcing due to well mixed greenhouse gases. Geophys Res Letters 25 (14) 2715-2718
Wigley, T.M.L., 1987, Relative Contributions of Different Trace Gases to the Greenhouse Effect. Climate Monitor 16 14-29.
R. Gray , M.A.,Ph.D., F.N.Z.I.C.
75 Silverstream Road
Phone (FAX) (064) (04) 4795939
March 16th 1999
Subject: Comment to Gray:
Atmospheric Carbon Dioxide
Date: Thu, 18 Mar 1999 19:58:20 +0200
From: "Jarl Ahlbeck" <firstname.lastname@example.org>
Congratulations to a good contribution ! For me there is not much in the carbon dioxide records that cannot be easily explained, it is like any industrial chemical absorber where the variations originate from :
- global temperature change
(bad temperature control)
- anthropogenic emissions (inflow of active component into the main gas)
- background noise (including measurement errors)
A small temperature change cause a small conc. change due to change of the Henry's constant. In fact, this influence can be calculated with some confidence using normal chemical equilibrium equations and assuming ocean water in the "bottle".
The simultaneous linear increase of both emissions and conc. point toward a simple diffusion-controlled absorption, see my contributions on this site. The IPCC modellers have got lost in their complicated models, this is very common in chemical process research. That's what we statisticians get money for, to take things down to reality. I am sure that these models can be improved towards more diffusion control which will make them in better agreement with measurments.
The background noise and the causes of this remain unexplained.
Jarl Ahlbeck, Finland
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