This page contains two calculations, one for an Earth without greenhouse gases and the other for an Earth completely devoid of any atmosphere. They show in both cases that the planet would resemble a snowball


The radiative temperature of the Earth is 253.7 K, based on the measured flux of radiation to space. This is measured to be 235 W m-2 and the apparent temperature follows from the Stefan-Boltzmann equation:

E = esT4

The emissivity e, is equal to 1 for a blackbody radiator, but the Earth is not a perfect blackbody. The average surface temperature of the Earth is considered to be 288 K, thus we enjoy ~34.5 K of global warming. Without the greenhouse gases the reduced temperature would lead to the freezing of the oceans, and clouds would be minimal if there were any at all. This would imply a much higher albedo, since snow and ice are very good reflectors of sunlight [they are white or transparent]. There would be no life, no greenery. An Earth without an atmosphere would have a much lower surface temperature. In both cases the Earth would be a snowball. But, what would its temperature be? The figure below is a block diagram that shows the basis of the calculation of the surface temperature of an Earth without greenhouse gases.


The atmosphere would still scatter some radiation to space [say, 42 W m-2] and the icy surface, with an albedo of 0.8 would reflect another 240 W m-2 leaving only 60 W m-2 to warm the surface. The surface would emit 60 W m-2 to space to maintain radiative equilibrium and, assuming an emissivity of 0.95 for ice and snow, the surface temperature would have to be 183 K or -90C.

            If there were no atmosphere at all there would be no scattering to space and the calculation alters slightly. The corresponding energy budget is shown in the next figure.



There would be slightly more solar radiation absorbed by the surface and to maintain radiative balance would have a temperature of 188 K or -85C. Thus, the surface would be slightly warmer without an atmosphere than with an atmosphere devoid of greenhouse gases. It would still be very cold!

There are suggestions that a real snowball Earth actually happened some long time ago. The problem with that is there seems to be no strong evidence for a real snowball and there are difficulties in deciding if one were to occur the way out is not at all clear.

One paper shows that even with the possibly exaggerated sensitivity of a general circulation model of the system a concentration of CO2 of some 10% would be required if the warming from that gas was to allow the escape from the snowball to a liquid ocean. Other explanations refer to the ending of ice ages by some orbital changes that increase the sun's radiation hitting the surface and the possibility of considerable volcanic action to spread dark ash over the surface so that the albedo value decreases, again increasing the effectiveness of solar radiation.

Such ice age endings would then be bolstered by the degassing of the oceans causing the concentrations of the greenhouse gases to increase. This would be followed by an increase in surface temperature allowing even more degassing to occur and thus a general warming would ensue. This would continue until balance was achieved by the operation of the water evaporation thermostat.