HISTORY
In the middle of 1890's the scientist Svante Arrhenius proposed that the use of fossil fuel would change the climate. Carbon dioxide and some other greenhouse gases works like clothing for earth. The sun is heating up earth surface and the greenhouse gases stop some of the heat radiation to vanish back in space. More clothing make the surface warmer.
At that time science had discovered that earth previously had several periodical times of extended polar glaciation. A great deal of northern Europe and northern America had some 20 thousand years ago been covered by ice of great depth. And seemingly, the start of the next glaciation was rather close in time, perhaps in 10 thousand years. Arrhenius thought that the use of coal and petrol most probably would prohibit the next glaciation.
Fossil fuel comes from underground rests of ancient plants and animals. The carbon of the fuel had once been a part of a biosphere with a completely different climate. For hundreds of million years carbon has vanished from the biosphere, decreasing the rate of atmospheric carbon dioxide and decreasing the global mean temperature.
About one million years ago the era of periodic glaciations started with about one glaciation in hundred thousand years. When the sea become colder it resolves carbon dioxide better and when it get warmer it release carbon dioxid to the atmosphere. As in the case with sparkling water. An idea of Arrhenius was that the pendling migration of carbon dioxide between sea and atmosphere caused the periodic glaciations. When the atmospheric carbon dioxide was minimal at about 180 ppm, the temperature was as lowest. Without greenhouse gases earth would be totally covered with ice.
Since the fossil process naturally goes in one direction, it would be less and less carbon dioxide in the biosphere. So in a way the fossil fuel is an asset not only for energy but also for climate regulation. At the time of Arrhenius the use of fossil fuels was just a small fraction of what we use today. Arrhenius supposed that the emission of carbon dioxide wouldn't extend today emission in thousand years. He couldn't then foresee the rapid evolution of modern society. Slower emissions of carbon dioxide would have been possible to manage without the risk of global disaster.
CALCULATIONS
Arrhenius deduced a law for the relation between the content of carbon dioxide and the global warming from Stefan-Boltzmanns law of thermal equilibrium:
a certain increase of temperature correspond to a doubling of the content of carbon dioxid i the atmosphere.
Or as a formula: T2-T1=aλ*ln(C2/C1), a≈5.35 and λ is a value called climate sensitivity, estimated to be λ≈0.8.
Normally the mean temperature and the mean content from 1850-1900 is used as T1 and C1 and C1≈290 ppm. Today content of CO2: C2≈410 ppm, which gives
T2-T1≈ 5.35*0.8*ln(410/290)≈5.35*0.8*0.35≈1.5 °C
Due to IPCC T2-T1=1.0±0.2 °C only, but Arrhenius formula assume that earth surface is a rigid body, while 70 % of the surface is actually sea water. The sea is accumulating about 90 % of the energy from the insolation and deep sea levels are warming up. At land the insolation is only warming some few decimeters down. Therefore the surface of the sea is cooler than the surface of land. The result of the formula should be multiplied with 2/3 to correspond with the real values from 70 % sea surface globe.
Also due to IPCC the best scenario (Paris agreement) for year 2100 is about 550 ppm and the worst scenario (go on like now) is about 900 ppm. (See diagram above). Calculus as above gives:
Best case: T2-T1≈5.35*0.8*ln(550/290)*2/3≈1.8 °C.
Worst case: T2-T1≈5.35*0.8*ln(900/290)*2/3≈3.25 °C.
MODERN VIEW
Milutin Milaković hypothesized in 1920 that variations in eccentricity, axial tilt, and precession of the Earth's orbit resulted in cyclical variation in the solar radiation reaching the Earth, and that this orbital forcing caused the periodical glaciations.
The surface temperature on earth depends on the heating effect from the sun (W/m2) and the isolating effect from the greenhouse gases. In the last 5 thousand years the heating effect from the sun had decreased due to the Milankovitch cycles. Unless there are big enough unknown effects, the latest sequel of global warming must be caused by the isolation effects of greenhouse gases.
Since there is an abnorm contribution of extra carbon dioxide from the use of fossil fuel, there must be a warming effect from that. And since the warming has accelerated extra the last 40-50 years as the emission has increased exponentially, there are no serious reasons to deny the conclusion from science: human being cause a global warming of 0.2 °C per decade.
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