
Misconception: Without greenhouse gasses the Earth would be a frozen snowball at 18 C. 
What is the warming effect of the radiative action of the Earth atmosphere on the temperature of the surface of the Earth, the socalled
greenhouse effect?
What would thus the temperature be if the atmosphere was
fully transparent without the socalled
greenhouse gasses water vapour and CO2, thus
without effects of (infrared) radiation? This would be like an Earth with
no atmosphere.
And the other way around: What would the temperature be if the atmosphere was
fully opaque?
These questions connect to earlier posts such as
this, and
these if you want to browse. For a revelation of the mystery of black body radiation, see the web site
Computational Black Body Radiation.
The standard answer propagated by global warming alarmism is that the greenhouse effect is +
33 C. It is claimed that with a fully transparent (or no) atmosphere, the Earth would be a frozen ball at
18 C instead of the observed
+15 C with a difference of 33 C.
The presence of greenhouse gasses is thus what makes the Earth livable. The message is that the
greenhouse effect is big = 33 C and as such will lead to dangerous
global warming of 3 C upon a small increase of CO2 as the "best estimate" of IPCC, as 1/10 of an estimated big greenhouse effect.
This is the very basis of
climate alarmism demanding a stop to emission of CO2 to prevent the Earth + atmosphere passing a
tipping point into a
runaway greenhouse effect approaching the surface temperature of Venus with its atmosphere filled with CO2, that is a roaring Hell at
462 C.
This is the apocalypse waiting unless we cut down CO2 emissions from human activity to zero and form a
fossil free world following the lead of Sweden now transforming into the first fossil free welfare state as required by the
New Swedish Climate Law.
To check the alarm signal of 33 C let us recall StephanBoltzmanns radiation law for a
grey body:
connecting radiance $Q$ at temperature $T$ in Kelvin K into a background at 0 K, through Stephan Boltzmann's constant $\sigma$ with $0\le\epsilon\le 1$ a coefficient of emissivity with a black body characterised by $\epsilon =1$.
Assuming absorptivity=emissivity (according to
Kirchhoff's law), we can use the SBlaw to compute the temperature $T$ of a grey body at a certain distance $D$ from the Sun knowing that the temperature $T_S$ at the emitting surface of the Sun (acting like a black body) is 5778 Kelvin K. What is needed is the ratio $q=R/D$ with $R$ the radius of the Sun, with $q^2$ the dilution effect depending on distance/area. All grey bodies at the same distance from the Sun would then have the same surface temperature (compare with
discussion here).
For the Earth $q =0.00465047$ which gives the surface temperature $T_E$ through the following formula resulting from the above SBlaw:
 $T_E = (0.25*q^2)^{0.25}*5778 = 279$ K
with the first factor $0.25$ the ratio between projected surface to total surface of a sphere. The temperature of the Earth as a grey body with fully transparent (or no) atmosphere, would thus be
279 K or +6 C.
For
Mars with a very thin almost transparent atmosphere and with a distance to the Sun equal to 1.524 astronomical units, the formula gives
225 K, to be compared with
observed about 228 K (60 C), with then a small
3 C greenhouse effect. The two small moons
Phobos and
Deimos of Mars
are reported to have about the same temperature of 233 K.
For
Mercury essentially without atmosphere with a distance to the Sun of 0.4 au, the formula gives 440 K, just as observed with
zero greenhouse effect.
The mean value of max and min temperatures of
Ganymede, the largest of Jupiter's moons with a very thin atmosphere of Oxygen, is 125 C, which fits well with the formula with a distance of 5.2 au, again with
zero greenhouse effect.
For
Titan the largest moon of Saturn at a distance of 9.6 au the formula gives 90 K to be compared with an observed surface temperature of 94 K, thus with a very modest greenhouse effect of 4 K from an atmosphere somewhat denser than that of the Earth consisting mainly of nitrogen.
For
Pluto with average au = 40 the formula gives 44 K =  229 C in agreement with observed temperature varying between  223 and  233 C.
For the
Moon (without atmosphere) rotating once every month, it is more natural to use the formula with the factor 0.25 replaced by 1 representing maximal (instead of mean) temperature to get +121 C fitting fairly well with observed maximal temperature +127 C.
We thus see that the formula works (surprisingly or not) very well for Mercury, Mars, Ganymede, Pluto and the Moon essentially without atmospheres, and so we may expect it to serve also for an Earth without atmosphere:
The recorded mean temperature on the Earth surface is 288 C with gives a total atmosphere effect of +9 C, from fully transparent (or no) 279 K to observed 288 K with greenhouses gasses present into a semiopaque atmosphere.
The total greenhouse effect is thus at most 9 C, instead of the 33 C as the corner stone of global warming alarmism.
The observed greenhouse effect of 9 C would then represent an observation of the total effect of the atmosphere on surface temperature, including both radiation and thermodynamics with gravitational lapse rate. Observation and not speculation.
Of course, the assumption that for the Earth without atmosphere emissivity=absorptivity, can be debated, since absorption and emission occurs at vastly different light frequencies, but yet may serve to get a rough estimate of the greenhouse effect (with Mercury, Mars, Ganymede, Pluto and the Moon essentially without atmospheres as observational support of the formula).
The temperature 255 K (18 C) behind 33 C comes from an application of the SBlaw assuming absorptivity = 0.7 and emissivity = 1 with questionable logic.
We can go one step further and predict what the temperature $T_E$ would be with a fully opaque
atmosphere by extrapolation from the present observed situation with the "infrared atmospheric window" acting as fully transparent atmosphere letting through 1/6 of the total emitted (infrared) radiation from the Earth surface directly into outer space. Closing the window from 5/6 to fully shut into a fully opaque atmosphere could then have an effect of $9/5$ C, less than 2 C. This is the observed variation of temperature after the last ice age.
The ultimate effect of endless emission of CO2 into the atmosphere (without changing total density much) would thus be less than 2 C and so from any possible level (like doubling or quadrupling) the effect would be less than 1 C.
This argument thus supports an idea that climate sensitivity as the temperature increase upon doubling of CO2 from preindustrial level is less than 1 C. This is based on observation of temperature 288 K (15 C) and atmospheric window 5/6 shut combined with the SBlaw. Pretty basic and undisputable.
One can argue that the observations used in the argument include "feedback" (from convection and evaporation). This is to be compared with another common argument based on (invented) "radiative forcing without feedback" as 1 C, which is inflated to 3 C by free invention of thermodynamic feedback.
We can see the reduction of the basic greenhouse effect from 33 C to 9 C with a factor of 34, as a
reduction of the "best prediction" of climate sensitivity by IPCC of alarming 3 C into nonalarming 1 C. It may be as simple as that, to give the hope back to the people of the world.
PS1 In recent work by Nikolov and Zeller (referring to work by Volokin and ReLlez) the greenhouse effect is claimed to be whopping +90 C. A coming post will explain the origin of this utterly alarming (misleading) number. Nikolov and Zeller do not start out very promising:
Thermal enhancement of 90 K creates a logical conundrum...appears inexplicable..Stay tuned...
PS2 The infrared atmospheric window is indicated in blue in the following picture:
PS3 The thick CO2 atmosphere of Venus is fully shut, while the very high surface temperature of +462 C is a thermodynamic effect of high pressure from gravitation and not any "greenhouse effect" from CO2. For a Venus without atmosphere the grey body formula gives +60 C.