The Most Essential Physics of the Earth's Temperature

The Most Essential Physics of the Earth's Temperature

and Why Carbon Dioxide is No Threat

Charles R. Anderson, Ph.D., Physics

This post is a summary of the major conclusions and viewpoints of my much longer and more technical paper:

Infrared-Absorbing Gases and the Earth's Surface Temperature:

A Relatively Simple Baseline Evaluation of the Physics

Readers with a desire to understand more about whether the catastrophic man-made global warming hypothesis due to carbon dioxide emissions is true or false may examine the longer paper for my arguments.  That hypothesis is false.  This note will summarize the essential physics of  the Earth's equilibrium surface temperature and the reasons why higher carbon dioxide atmospheric concentrations in the past have not and in the future will not cause a catastrophic warming of the Earth's surface, where we live.

I will show that the essential physics can be summarized as:

• Infra-red active (so-called greenhouse) gases absorb a substantial portion of the incoming solar radiation in the infrared portion of its spectrum with the result that additions to their concentrations have a cooling effect
• The Earth's surface is not a black body radiator, so it takes much less absorbed solar radiation to warm it to 287.65K or 14.5ºC than the alarmist greenhouse gas theories claim.  In fact, the Earth's surface is only half as efficient an infrared radiator as is a black body.
• The Stefan-Boltzmann law of radiation applies to a surface radiating into vacuum, not into an atmosphere able to provide competing cooling processes due to air conduction, air convection, and water evaporation.  This Stefan-Boltzmann radiation equation provides the total cooling power from a surface at a given temperature.  This will all be in the form of radiation in the case of the surface interfaced to vacuum.  Due to energy conservation, the radiation resulting when interfaced to an atmosphere will be that total power minus all of the cooling by other competing cooling mechanisms.  The alarmists add the other cooling mechanism's power to that of a 100% efficient black body radiator.  They then seek a convoluted reason to provide more counteracting warming to this excessive surface cooling.
• At the Earth's surface, the sum of evaporative, conductive, and convective cooling exceed radiative cooling, contrary to the usual alarmist theory.
• A short distance of 100 or 200 meters above the surface, the 65% of the surface infrared radiation that can be absorbed by IR-active gases has been absorbed already due to short mean free path lengths and the energy has been distributed to the non-radiating molecules of the atmosphere due to extremely high collision rates.  Only the 35% of surface radiation into the atmospheric window continues on into space under rapid radiative transport.  This is 35% of a much smaller amount of surface radiation than posited by the alarmist theory.
• The atmosphere near the surface is mostly characterized by slow energy transport mechanisms, not by extremely fast radiative cooling mechanisms imagined by the alarmist theory.  Energy transport here is almost entirely upward.  Radiation transport is just in very short hops between layers of air usually differing very little in temperature.  This lower part of the troposphere is critically and fortunately not in radiative equilibrium with space.
• Most of the radiation into space is from the upper zone of substantial water vapor concentrations.  The difference is radiation from the surface into the atmospheric window.  The weighted mean altitude between the water vapor radiative emission into space and the smaller surface emission is the altitude with a temperature of 255K.  This is the effective temperature of the Earth as a unitary radiator seen from space, although only in that it would generate the right amount of total energy as a black body radiator.  This temperature is such that it balances the Earth's total absorbed radiation from the sun with an equal cooling radiation into space.
• The gravitational field of the Earth and the Conservation of Energy for static air produce a temperature gradient in the lower atmosphere, the troposphere, which is linear with altitude.  In the lowest 5000 m, this decreasing temperature gradient with increasing altitude is about 6.49K/km.  The altitude of effective radiative equilibrium with space at a temperature of 255K  is about 5100 meters.  Starting from there with a gradient of 6.49K/km produces a temperature at the bottom of the atmosphere of 288.15K.  This matches the temperature of the solar radiation warmed surface.
• The lower atmosphere always has some rising, non-static air due to convection. This rising air expands due to the dropping pressure and cools as it does so.  Depending upon the amount of rising convection, the temperature gradient in the troposphere may become as large as 9.78K/km in the bottom 5 km of the atmosphere.  The gradient will then be between 6.49 and 9.78K/km depending on the amount of upward air convection.  This applies unless winds carry air from areas receiving very different amounts of solar insolation to disturb the area.

I will explain why additions of carbon dioxide are relatively unimportant.

• Added carbon dioxide in the alarmist theory causes an increase in back radiation, or in radiation from the Earth's surface being returned to it.  But the alarmists overstate the radiation emitted from the Earth by a factor of two and they overstate the radiation returned to the Earth's surface hugely.
• The limited radiation from the Earth's surface that can be absorbed by carbon dioxide is almost entirely absorbed within 100 or 200 meters from the surface.  The heat transported by radiation is quickly spread to non-radiating nitrogen and oxygen molecules and to argon atoms that make up 99.97% of the air due to the 6.9 billion collisions per second of molecules.  This adds to the slow convective transfer of heat upward.
• Carbon dioxide molecules in the air will radiate infrared radiation, but it will be at the energy level of the temperature of the surrounding air molecules.  Thus they radiate toward the surface as cooler molecules and upward as warmer molecules given the normal temperature gradient in the air with altitude.  Consequently, carbon dioxide emitted radiation speeds the transfer of heat toward higher altitudes slightly and only under relatively infrequent conditions can supply the surface with added heat.  Carbon dioxide is only about 0.04% of the molecules in the air, placing a limit on amount of heat transfer at particular wavelengths by so few molecules.
• When the relatively infrequent conditions exist that the emitting carbon dioxide molecules in the air above the surface are warmer than the surface, carbon dioxide emitted radiation is less effectively absorbed by the surface than is that from water vapor.  This is because some of the characteristic radiation frequencies of carbon dioxide are not as likely absorbed by water that covers 71% of the planet or by plants based on a water-rich chemistry or by soils and minerals with their commonly high water content.
• Incoming solar radiation is about 49% infrared radiation.  Some of this is absorbed in the atmosphere by added carbon dioxide before it can reach the surface and warm it.  This results in a cooler surface.
• Carbon dioxide mostly emits radiation into space from altitudes exceeding 9 km and extending to 20 km.  From 11 to 20 km there is no temperature change, there being a uniform temperature of about 217K.  There is a version of the carbon dioxide warming theory that more carbon dioxide emitters at this altitude decrease the cooling efficiency of the Earth and that warms the atmosphere below it.  Adding carbon dioxide at these altitudes does almost nothing to change the temperature of the emitting molecules since they are already mostly emitting in the constant 217K zone.  What is more, fast radiative cooling has already become the almost exclusive mode of moving heat to higher altitude and to space due to the water-rich radiation zone at much lower altitudes.  More carbon dioxide absorbers at a higher altitude just simply re-emit the radiation quickly into space due to the low gas molecule collision rates.  Any radiation directed downward is quickly turned around and also sent into space.
• Even with the considerable very bad physics used to justify a warming effect by carbon dioxide, the warming effect wrongly claimed by the IPCC was only 1.2K upon doubling the amount of carbon dioxide.  They then invoked a claimed stronger reinforcing warming due to increased water vapor to make a total warming of 5.4K.  Experimental measurements, eons of relatively stable climate, and the expectation of additional cloud cooling and additional solar radiation absorption in the atmosphere due to added water vapor all indicate that increased water vapor would actually provide a negative feedback or a counteracting cooling effect even it added CO2 were to produce a slight warming.  Actually, it would produce a slight cooling effect.
• The health of plants, upon which we humans and other animals are so dependent, is improved with higher concentrations of carbon dioxide.  Carbon dioxide is essential plant food.  The improved growth of plants uses up a good portion of any additional carbon dioxide added to the atmosphere.
• Increased greenhouse gases tend to moderate the temperature variations of night and day. This is a good thing.

Consequently, it is unreasonable to believe that increased carbon dioxide in the atmosphere will cause the Earth's surface temperature to increase either measurably or catastrophically.  The effect is actually more likely to be a slight cooling effect, though this will prove difficult to measure.  The so-called settled science viewpoint of catastrophic man-made global warming due to added carbon dioxide is nonsense.  The many scientific organizations that have backed this claim have acted disgracefully.  Many politicians have been eager to bribe scientists to do this bad science with government research funding conditional upon findings of catastrophic man-made global warming. They are corrupt and power-hungry politicians looking for every excuse to gain more control over our lives, our economy, and our standard of living.

Updated on 17 March 2013.