Greenhouse Bulletin 121, March 1999

**Greenhouse
Warming Reduced
**by

**Vincent
R. Gray**

** Radiative
Forcing**

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.

** References**

**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.**

**Vincent
R. Gray** , M.A.,Ph.D., F.N.Z.I.C.

Climate Consultant

75 Silverstream Road

Crofton Downs

Wellington 6004,

New Zealand

Phone (FAX) (064) (04) 4795939

Email VINCEGRAY@xtra.co.nz

March 16th 1999

**Comments
- **

Subject: **Comment to Gray:
Atmospheric Carbon Dioxide**

Date: Thu, 18 Mar 1999 19:58:20 +0200

From: "**Jarl Ahlbeck**" <jarl.ahlbeck@abo.fi>

To: <daly@vision.net.au>

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.

regards,

**Jarl
Ahlbeck**, Finland

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