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By Charles Rhodes, P.Eng., Ph.D.


The average temperature at any point on the Earth's surface is determined by the following parameters:
1. The solar radiation intensity at the Earth's orbit (Solar Irradiance);
2. The fraction of incident solar radiation reflected from the Earth (bond albedo);
3. The near spherical shape of the Earth;
4. The latitude of the observer;
5. The angle of the Earth's axis with respect to a straight line between the Earth and the sun;
6. The local ocean surface temperature which sets the local average atmospheric partial pressure of water vapor at sea level;
7. The atmospheric partial pressure of CO2 at sea level;
8. The amounts and vertical distributions of other greenhouse gases in the atmosphere;
9. The local heat absorption by the heat capacity of the ocean, by the latent heat of fusion of water or by the latent heat of vaporization of water;
10. Thermal convection via wind or ocean currents;
11. Condensation of water vapor which transfers its latent heat of vaporization to neighboring gas molecules;
12. Freezing of liquid water which releases its latent heat of fusion as thermal infrared radiation;
13. Thermal infrared radiative emission from the Earth's surface;
14. Wavenumber dependent filtering of thermal infrared radiation by upper atmosphere greenhouse gases;
15. Net emission of thermal infrared radiation into space.

In order to understand the global warming calculations it is necessary to have a rudimentary understanding of radiation physics. All objects absorb and emit thermal electromagnetic radiation. The emitted thermal radiation power per unit area increases in proportion to the fourth power of the object's absolute surface temperature. Most of the emitted thermal radiation is concentrated near a wavenumber that is proportional to the object's absolute temperature.

Thermal radiation from the sun is known as solar radiation. The earth, in a nearly circular orbit around the sun, is subject to a nearly constant flux of solar radiation. Solar radiation has a broad intensity peak spanning visible wavelengths. At visible wave lengths the earth's atmosphere is relatively transparent. Part of the solar radiation is reflected into space. The remaining solar radiation is absorbed by the earth. Reference: The Atmospheric Absorption Spectrum

Bond Albedo is defined as the fraction Fr of the total solar radiation power, that is incident on the Earth, which is reflected into space. Local albedo is subject to geographic and time variation due to changing cloud cover, changing snow cover, changing ice cover and changing vegetation color. The average value of the Earth's bond albedo measured during the period late 1998 to early 2001 was found to be about 0.297 +/- 0.005

At long term steady state conditions the energy flux of solar radiation that is absorbed by the Earth is balanced by the net infrared thermal radiation flux that is emitted by the Earth. Certain gases in the Earths upper atmosphere such as water vapor, carbon dioxide, ozone, methane and nitrous oxide, known as greenhouse gases, exhibit wavenumber dependent infrared radiation scattering. This infrared radiation scattering reduces the Earth's emissivity Ft and hence causes the average temperature at the Earth's surface to be warmer than it would be if there was no atmosphere but the same bond albedo. This warming mechanism is known as the greenhouse effect.

The greenhouse effect traps heat in the lower atmosphere. The warm air rises causing convection that distributes the heat vertically. Wind distributes this heat horizontally over the earth's surface. Most of the heat is eventually radiated out into space. The warmed atmosphere also loses heat in cold polar and glacier regions, where this heat contributes to melting of otherwise permanent ice.

Existing life on earth evolved at an atmospheric carbon dioxide concentration of about 280 ppmv (parts per million by volume).

Combustion of fossil fuels by mankind increases the atmospheric carbon dioxide concentration and hence increases the greenhouse effect. The consequent warming increases the ocean surface temperature which in turn increases the average atmospheric water vapor pressure. The increase in atmospheric water vapor concentration further increases the greenhouse warming. The increase in atmospheric water vapor concentration also increases cloud cover, which increases the bond albedo Fr. This increase in Fr partially off sets greenhouse warming.

Improper or incomplete combustion of fuels can also lead to release to the atmosphere of methane and nitrous oxide that further increase the greenhouse warming. The total inland average dry ground temperature increase measured far from any fossil CO2 emitter, due to man made greenhouse gases, is known as "global warming".

During the 40 year period January 1, 1965 to December 31, 2004 the atmospheric carbon dioxide concentration measured at Mauna Loa, Hawaii increased from 319.44 ppmv to 377.48 ppmv. Mauna Loa is a remote place in the middle of the Pacific Ocean, so the measurements of increased atmospheric carbon dioxide concentration made at Mauna Loa are considered indicative of the increase in average atmospheric carbon dioxide concentration that is the principal cause of global warming. During this January 1, 1965 to December 31, 2004 period the annual average ground level atmospheric warming, measured at the Toronto International Airport, was 2.44 degrees C.

At dry inland locations such as inland airports in desert areas there is no opportunity for local cooling via evaporation of water, melting of ice or heat absorption by the ocean. At such locations the experimentally measured long term increase in annual average temperature is a good indicator of the amount of global warming.

The theoretical relationship between the increase in atmospheric carbon dioxide concentration and the amount of dry land temperature warming can be obtained by analysis of the earth's thermal emission spectrum as recorded by a spacecraft borne thermal emission spectrometer. This data can be used to calculate the amount of warming caused by a change from one atmospheric carbon dioxide concentration to another atmospheric carbon dioxide concentration. Alternatively, if the temperature change is known and one of the atmospheric carbon dioxide concentrations is known the other atmospheric carbon dioxide concentration can be calculated.

The analysis of thermal emission data presented herein indicates that doubling the atmospheric carbon dioxide concentration causes an average dry land temperature increase of about 3.15 degrees C. An average temperature increase of 3.15 degrees C will cause of major environmental change in Canada. Melting of snow and ice reduces reflection of sunlight (albedo) causing further warming. In more equitorial countries an average temperature increase of 3.15 degrees C makes large areas uninhabitable.

Extrapolation of a plot of the measured atmospheric carbon dioxide concentration as a function of time indicates that the average atmospheric carbon dioxide concentration will be twice its historic value by about the year 2065. Close to carbon dioxide emitters, such as fossil fuelled electricity generating stations, the carbon dioxide concentration and hence the dry land temperature increase will be higher.

The direct effects of dry land temperature increase on agriculture are to reduce mountain snowpacks and to increase soil evaporation. The reduction in mountain snow packs reduces the amount of fresh water that is available for crop irrigation in the dry season. The increase in soil evaporation increases the required amounts of irrigation water and irrigation pumping energy per unit of crop output.

The consequent reduction in agricultural production in combination with the presently increasing human population and increasing demand for agricultural products to displace fossil fuels, is leading to global starvation. The only ways to mitigate this problem are to replace fossil fuel energy with non-fossil fuel energy, reduce the human population and reduce the average per capita energy consumption.

The relationship between the increase in atmospheric carbon dioxide concentration and the amount of net heat absorbed by the oceans can be obtained by measurement of the increase in annual average inland dry ground temperature or by analysis of the earth's thermal emission spectrum as recorded by a spacecraft borne thermal emission spectrometer. The net heat absorbed by the oceans warms ocean surface water, decreasing its density. This warm lower density water is conveyed by natural circulation to the polar regions. When this circulating warm lower density water contacts floating ice the circulating water temperature drops and the ice melts. The circulating water, now denser due to cooling, sinks in the ocean, driving the natural circulation. The net ocean heat capture rate places an upper limit on the rate of polar ice melting.

In the very near term the rate of polar ice melting has little immediate direct consequence because melting of old floating ice causes no change in sea level. However, in the longer term polar ice melting has major consequences because once the old floating ice has melted new floating ice will form from the glacier bottom discharge streams from Greenland and Antarctica. Formation and melting of this new floating ice will cause a rise in sea level that will be impossible to stop until the Earth's atmosphere loses its excess CO2. The only way to mitigate this sea level rise problem is to immediately cease use of fossil fuels to allow the excess CO2 concentration in the atmosphere to naturally decay and the oceans to cool before the old floating polar ice melts. Ceasing use of fossil fuels has major implications on transportation, electricity generation, comfort heating and agriculture.

As indicated herein, as the ocean surface temperature changes the average atmospheric partial pressure of water vapor changes, which in turn causes changes in the Earth's infrared emissivity Ft and the bond albedo Fr. Changes in Ft and Fr in turn affect the net heat absorbed or emitted by the Earth and hence eventually affect the bulk ocean temperature. It is likely that this ocean temperature feedback control mechanism has a zone of instability that causes long term average Earth surface temperature oscillations that manifest themselves as ice ages. Mankind's addition of excess CO2 to the atmosphere significantly changes Ft which may in turn significantly change the current interglacial period. However, since the interglacial period is generally over 10,000 years this issue is thought to have little relevance to those now living and is not further addressed on this website.


This web page last updated November 12, 2015.

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