How did you calculate the atmospheric cooling that happened between 1940 and 1980 using that formula?
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There's only one answer for the heating effects of the planet in your mind but there's so many other reasons for the cooling. I get it. Thanks Jeff!
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If your temperature records were completely accurate, then your question is a valid one. There's no evidence to support that your anthropogenic calculations are accurate. Despite some discrepancies between various data sets, the global temperature differences between 1942 and 1997 are small to none – except for land-based thermometer data outside the U.S. This disparity with your CO2 warming premise demands an explanation – as do the much larger in trends of the Northern Hemisphere compared to the Southern Hemisphere. Both satellite data and independent balloon data show a near-zero trend from 1979 to 1997. We all know what happened in the El Nino year of 1998.
Specific calculations on anthropogenic increases and the forcing effect of CO2 can also be found here : http://www.biocab.org/Radiative_Forcing_and_Heat_Stored.html
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Lest we forget that the past 10 years has shown no increase of temperatures. So now we are talking about a period between 1998 and 2003 of warming where the residual effects of an El Nino event may come into play. It's fair to say that there is hardly any additional warming due to the increase of CO2 in our atmosphere.
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The relatively minor warming of the ocean surface (71% of the Earth surface), stands in contrast to the reported global warming between 1970 and 2000. It suggests that land surface warming has been greatly over-estimated.
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A fact well known to all scientists is that the absorptivity-emissivity thermal property of carbon dioxide diminishes as its density increases and as the temperature augments. This happens because the infrared radiation absorption margin is very narrow (wavelengths from 12-18 micrometers) and so the opacity of carbon dioxide to infrared radiation increases with altitude. As the column of CO2 gains height, the opacity to infrared radiation increases.
Heat always moves from places of higher density of heat to places of lower density of heat. Thus states the Second Law of Thermodynamics. In daylight, air is always colder than soil; consequently, heat is transferred from the soil to the air, not vice versa. By the same physical law, the heat emitted by the Sun –a source of heat- is transferred to the Earth, which is a colder system.
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CO2 warming is enhanced by all of the other gases warming in our atmosphere and therefore it is not logarithmic. Doesn't matter what frequency or wavelength it receives radiation (energy) from. Your problem is that you think that CO2 and methane are the dominant heating gases. Of course they hold heat, but the heat in the atmosphere is generated by many gases. Oxygen and nitrogen also generate heat. How do you compensate for the "heat factor from other gases" in your formula? CO2 acts more like a thermostat and not the fuel for the fire.