**Estimation
of the Radiative Forcing
for CO2 Doubling**

by Peter Dietze

**The additional IR absorption
for CO2 doubling is the energy
source for global warming. HITRAN transmission spectra – the fringes being
by no means saturated yet – can be used to evaluate this absorption, mostly
occurring near ground. A simple radiative energy equilibrium model of the
troposphere yields an IPCC-conforming radiative forcing which is here defined
as the additional energy re-radiated to ground. Coping with water vapor
overlap on the low frequency side of the 15 µm band, the clear sky
CO2 forcing is considerably reduced
to 1.9 W/m². With vapor feedback and for cloudy sky the ground warming
will be about 0.4 to 0.6 °C only – a factor 4 to 6 less than IPCC's
'best guess'.**

The radiative forcing caused by a prescribed doubling of the pre-industrial (or present or any) CO2 concentration is the imbalance in the Earth's radiation budget that is supposed to cause global warming. More CO2 means more absorption of the infrared (IR) re-radiation which the Earth emits to space to compensate for the solar short wave irradiation. To restore the radiative equilibrium between warming and cooling, the average 15 °C ground which sends most of the thermal black body Planck emission directly to space, has to warm up slightly until the withheld energy – i.e. in our definition the increased back-radiation – is re-emitted.

The IPCC used the following definition, focusing on topopause level conditions:

"The radiative forcing of the surface-troposphere system (due to a change, for example, in greenhouse gas concentration) is the change in net (solar plus longwave irradiance) in W/m² at the tropopause AFTER allowing the stratospheric temperatures to re-adjust to radiative equilibrium, but with surface and tropospheric temperature and state held fixed at the unperturbed values".

The often quoted additional absorption for CO2 doubling within the troposphere is not the forcing itself, as formerly often (mis)understood by non-specialists, but it is the source of the (thermal) re-emission to ground which is based on the atmospheric energy equilibrium. This means, the re-emission at tropopause level plus the re-emission to ground (which causes the warming) is equal to the additionally absorbed energy.

Using HITRAN-1996 CO2 transmission
spectra from *Jack Barrett*, an Excel diagram (Fig.1) was prepared
for a range of 300 cm^-1 and 560 intervals. It shows the transmission,
i.e. the intensity ratio T=I/Io
of an IR beam travelling from ground to the top of the troposphere, which
would be a layer of 6800 m for ground pressure. T depends strongly on the
wavenumber per cm (for example 15 µm means a wavenumber of 1/15*10^4=667/cm).
The area of the integrated absorption A=1-T of the yellow spectrum for
the total troposphere (without coping with water
vapor) is 196 cm^-1. This is about 74 W/m² when multiplied
with a medium Planck radiation of 0.38 W/m²/cm^-1 for 288 K in the
range around 15 µm. The exact method would be to take the A value
of each interval, multiply with the interval length (here 15/28 cm^-1)
and with the individual Planck radiation at the interval, and integrate
over the whole range, here 560 intervals. The residual area in Fig.1 (difference
between the yellow (1*CO2) and
green (2*CO2) spectra = CO2
doubling absorption) was integrated to 16.8 cm^-1, which is **6.4
W/m²** when multiplied with the Planck radiation.

This absorbed energy depends very little on the layer
thickness (optical density) and is thus not at all sensitive to the accuracy
of absorption within the troposphere (which was here simply powered up
according to the Lambert-Beer law, based on a 139 m equivalent probe, to
show the layer characteristics). The red spectrum for a 1000 m layer (related
to ground pressure) is quite exactly the same as the one published by *E.
Raschke et al.* **[see H. Hug,
Chemische Rundschau (19 Feb 1999)]**. Though no adaptions
for pressure or temperature changes in the atmosphere were made, the residual
result was within 0.1 W/m² conforming with another data set for the
whole troposphere. Let us assume the residual absorption for CO2
doubling to be

**Fig. 1: HITRAN transmission
diagram based on data for 5% CO2
and 100 cm at ground pressure**

The absorbed radiation is nearly completely thermalized
and dissipated (acc. to *J. Barrett* and *H. Hug*). In thermal
equilibrium this energy is re-radiated by atmospheric components as CO2
(double density yields double emission for the same temperature) and partly
by other GHGs – the latter only in case the temperature profile shifts,
contradicting the IPCC definition. In this case convective and latent heat
processes would become involved in additional vertical energy transport.
All these have to end up in thermal re-emission at tropopause level, directed
to both sides, space and ground. Whereas the
lower atmosphere warms, the upper atmosphere
is cooling (thus increasing
the lapse rate) – here doubled CO2 takes over
a part of the emission from the other GHGs.

As all re-emission has to be considered as being
bidirectional, we can assume in first approximation that half the total
re-emission goes to space and half goes to ground. So we yield the new
(by 15% reduced) IPCC TAR forcing of **3.7
W/m²**, as shown in Fig.2. But the emission depends
on the 4th power of the absolute temperature. So if
we assume the bulk radiation temperature near ground (500m) as 285 K and
in the upper troposphere (5500m) as 255 K, the upper emission should be
only 64%. On the other hand we find very little water vapor in the upper
troposphere, whereas the vapor near ground considerably absorbs the CO2
emission. As we have a mixture of up and down radiation, absorption and
thermal re-emission, and only the sum of re-radiation is known, the correct
ratio of the two emissions cannot easily be determined. So it seems reasonable
to assume that the total emission is split about 1:1.

Important to mention that IPCC's forcing *for
clear sky conditions* is meant for *well
mixed* GHGs, i.e. without water vapor overlap **[ G.
Myhre, J. Highwood, P. Shine, F. Stordal in Geophs. Res. Letters 25,
2715-2718 (July 15, 1998)]**. IPCC argues that at tropopause
level the water vapor density is negligible, which is true – but in reality
the forcing stems from absorption and back-radiation within the

**Fig. 2: Radiative fluxes
and forcing for CO2 doubling,
atmospheric thermal equilibrium model**

Now the IPCC errors become very obvious. Using the
former forcing of 4.3 W/m² for tropopause level, application of the
differential form of the Stefan-Boltzmann law **dT/T=1/4*dS/S**,
with S=240 W/m² and T=255 K, yielded a temperature increment of dT=1.14
K (which is now reduced to 0.98 K with 3.7 W/m²). The IPCC
assumed that this increment would be transmitted 1:1 down to the ground,
based on a constant lapse rate. Because water vapor is a strong greenhouse
gas, the IPCC then used a factor of 2.2 as the effect of water
vapor feedback – neglecting that on the other hand vapor should
also *reduce* the radiative CO2
forcing – and thus obtained a warming of 2.5 °C
for CO2 doubling, the 'best guess' – so called by
*T. Wigley* and *S. Raper* in a review paper **[Nature
357, 293-300 (1992)]**). *D. Rind* titled his article
about the feedback approach "Just add Water
Vapor" **[Science 281,
1152 (21 Aug 1998)]**.

But as observations did not support the exaggerated warming, the IPCC assumed, the discrepancy was an effect of aerosol cooling while other effects (e.g. amplification of solar forcing) were considered to be insignificant. Their exaggerated aerosol cooling and the gain in parameter variability was ideal to maintain a far too high CO2 climate sensitivity, thus compensating for missing solar forcing amplification and any other model discrepancies, just as required.

Of course, the argument exists that the amount of
near ground moisture will increase with warming, and water vapor is a strong
greenhouse gas. This argument depends on IPCC's questionable assumptions
of total transfer of the upper troposphere warming to the lower atmosphere,
and a strong water vapor feedback. But
here we have to consider a feedback damping
because the more IR is absorbed around 15 µm by water vapor, the
less remains for CO2 to be absorbed in the same overlapping
bands, and the water vapor absorbtion capability is mostly saturated in
this region of the IR spectrum, though not in other parts. According to
a mean ratio of 1.34 between clear sky and cloudy
sky forcing **[Tab.1 and Tab.2 in G. Myhre et al.
(1998), see above]** we can adapt our forcing of 1.9 W/m²
to

Btw., the solar
fraction analysis sensitivity is by a factor three
less than IPCC's 2.5 K. If we would assume a factor 2.2 for water vapor
feedback, our doubling sensitivity would become **0.57
K**, still 33% less than the solar fraction analysis figure.
These values do not require an assumption of enforced aerosol cooling because
they provide better agreement with observations than IPCC's 'best guess'
sensitivity. Additionally, a CO2 doubling can hardly
occur because of increasing sink flows and limited
fossil reserves. Even if 1.500 GtC would be burnt until 2100 according
to the *business as usual* scenario IS92a (instead
of the reasonable estimate of 1.300 GtC that could and would be used),
the concentration would only increase to about **570
ppm** (see Tab.1 in this German carbon
model paper – for 1.300 GtC burnt by 2090, the concentration only reaches
**548 ppm**). Therefore,
the harmless temperature increment from doubled CO2
concentration is a probable maximum rise in mean global temperature from
anthropogenic CO2 greenhouse effect.

As most of the absorption for CO2
doubling occurs near ground – a doubling test for
139 m already yielded 6.5 W/m² (88% of
7.4 W/m²) – the water vapor overlap should mostly cancel
the left residual (and btw. some fraction of the right one as well).
*H. Fischer* has shown this in a graph of a position
paper of the German Meteorological Association (DMG), which advocates
the greenhouse effect. The "residuals" are the differences in
transmission between 1*CO2 and
2*CO2 (Fig.3). We can estimate
the cm^-1 area of the right residual (the left was cancelled because the
water vapor transmission is very small here) and multiply with the associated
Planck radiation per cm^-1. The radiative clear sky forcing represented
by this DMG residual is **1.7 W/m²**
only, of which 0.3 W/m² stems from the hot band around 960 cm^-1.
So our **1.9 W/m²**
forcing in Fig.2 is likely. *H. Fischer* used HITRAN data and apart
from water vapor overlap he coped with other greenhouse gases and with
thermal CO2 emission depending on atmosphere temperatures.

**Fig. 3: German DMG residual
(H. Fischer, IMK Karlsruhe 1999)**

IPCC authors so far refused to disclose details about
the modelling assumptions and computation of their core parameter, demanding
us to believe in their results – which is an unprecedented offence against
rules in public funded science, and the TAR again follows this line. A
graph about radiative forcing of the 1994 IPCC report is shown in Fig.4.
As the left residual is not cancelled, here obviously water vapor overlap
has hardly been considered, contrary to the statement in the note on p.174
and the approach of *H. Fischer*. Each residual area in W/m²
from net irradiance at tropopause level roughly matches the one in Fig.3
when logarithmically adapted to CO2 doubling, though
IPCC claims having even coped with cloud effects. *R.D. Chess et al.*
state in **[Uncertainies in CO2
Radiative Forcing in Atmospheric GCMs, Science 262, 1252 (19 Nov 1993)]**
"The forcing is substantially reduced through
radiative overlap of the CO2 absorption bands by the
absorption of water vapor" and "Clouds
also reduce the forcing".

Surprisingly the IPCC residuals (Fig.4c) come together
at 15 µm, whereas in Fig.3 they would be about 70 cm^-1 apart from
each other. The IPCC residuals were calculated with radiative transfer
equations, using the standard narrow band code of *P. Shine* 1991
- both not been published by IPCC and obviously available within the 'community'
only. Residuals show a broad gap inbetween when only absorption is considered.
Coping with thermal emission, they are shifted towards the 15 µm
center – the more, if only a fractional layer (e.g.
upper troposphere) is evaluated. Their area (which is important)
keeps mostly unchanged.

**Fig. 4: IPCC 1994 p.175
radiative forcing figure 4.1**

The linestrengths in
Fig.4b are not explained and easily misinterpreted. The data from HITRAN
(high resolution transmission molecular absorption database by *L.S.
Rothman et al.*) are extinctions (line intensities
or linestrengths) given per CO2 molecule for
each individual peak wavenumber. The resolution is extremely precise, about
0.0005 cm^-1. To cope with the optical density, the molecular extinction
is multiplied by the number of molecules (the troposphere contains about
4.1 kg CO2/m²). The lines are then integrated
over an interval (e.g. 1/560 of the diagram range of 300 cm^-1, see Fig.1),
coping with the peak shape, pressure broadening and temperature dependency.
IPCC's linestrengths in Fig.4b are extinctions E=-log(T) for the whole
troposphere, integrated over 10 cm^-1 for smoothing purposes, and divided
by ten (the integration interval) to get cm^-1 related values. To prepare
transmission diagram data, each interval T value is calculated as T=10^-E
for the specific wavenumber (which is done by HITRAN). As T is a nonlinear
function of E, the smoothing of E may have some effect on T. *H. Hug*
proved the HITRAN assumption to be flawed, that nitrogen is neutral with
respect to the IR absorption of CO2 **[CHEMKON
7, 6-14 (Jan 2000)]**. With presence of atmospheric N2
the IR absorption increased to double (!)
of the one for CO2 alone in a lab measurement.

Using the triangular section of IPCC's linestrengths in Fig.4b between 450 and 900 cm^-1, the decadal exponent of E can be expressed as two linear functions of the wavenumber. So transmissions have been calculated analytically in order of a comparative test for the tropospheric 6800 m layer (at ground pressure) and a layer of 2.5 m only, as well as residuals for CO2 doubling absorption (without thermal emission). In Fig.5 the obtained diagram is shown for a wavenumber range of 400 cm^-1, with 560 intervals of 5/7 cm^-1 each.

**Fig. 5: Transmission and
absorption calculated using IPCC 1994 linestrengths**

The purple T curve computed from IPCC's linestrengths, fits the bulk of the blue 6800 m HITRAN transmission spectrum (except for the outer ranges). The green residual curve for additional absorption for CO2 doubling within the very thin 2.5 m layer looks similar to what IPCC had calculated for the forcing at tropopause level. The unit is 200 mW/m²/cm^-1, the 2*CO2 residual absorption for the 2.5 m layer is already 5.0 W/m².

In Fig.4a IPCC did not correctly model the emission characteristic to be seen in satellite measurements (satellite spectrum here) which does not show a zero emission at the bottom of the funnel around 15 µm, but a thermal emission of about 0.12 W/m²/cm^-1 (any steradian-related figure has to be multiplied by p though one would expect it to be 2p). This left out emission – it is about 4 W /m² for the 1*CO2 base case – results in a too high radiative forcing as it causes an increased part of the radiative energy being withheld at tropopause level in case of CO2 doubling.

For a long time we had a controversial discussion
about discrepancies between satellite MSU measurements (about
1-5 km height, indicating hardly any warming trend), and ground
station readings, see as well http://www.john-daly.com/graytemp/surf-msu.htm#Dietze1.
Using IPCC's flexible aerosols, *Ben Santer, Tom Wigley et al.* tried
to model-experiment away and downplay this problem **[Science
287, 1227-1232 (18 Feb 2000), see as well D.E. Parker on p.1216]**.
The warming effect from radiative CO2 forcing occurs
mostly near ground. So the GCMs which assume a parallel
shift of the troposphere temperature profile (as e.g.

Even the TAR draft Ch.6 p.6, line 52-54 still says that surface and troposphere are closely coupled, the thermal structure being determined by a nominal lapse rate, all thus behaving as a single thermodynamical system. Because of the increasing lapse rate satellites measure a mix of cooling and warming and thus can principally not replicate the ground temperature trend.

Even if most of the error sources in ground temperature series (not to forget ocean measurements) would be eliminated, the trend should still not be (mis)used as a "proof" for the correctness of the CO2 sensitivity parameter the IPCC model results were based on. The estimation of radiative forcing done here and previously in the solar fraction analysis show that the CO2 climate sensitivity has indeed to be reduced considerably, just resulting in a rather harmless (if not beneficial) warming till 2100 – when fossil reserves become rare and mankind may turn to bulk power production from thorium breeders and fusion reactors anyway.

17 April 2000, **Dipl.-Ing.
Peter Dietze
**Phone & Fax: +49/9133-5371

e-mail: 091335371@t-online.de

this paper: http://www.john-daly.com//forcing/forcing.htm

**Comments and reviews on the above paper are
available at the following link:
`Open Review'**

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