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

Earth is constantly absorbing a fraction of the incident solar radiation from the sun. Earth is constantly emitting infrared radiation into outer space. Historically, over the thousands of years prior to the industrial revolution, Earth reached a steady state condition in which the rate of solar energy absorption equalled the rate of infrared energy emission. At this steady state condition the atmospheric CO2 concentration was about 280 ppmv.

Since WWII man has been burning fossil fuels at a prodigious rate. The resulting CO2 emission has raised the atmospheric CO2 concentration which has reduced Earth's infrared emission and has significantly increased the HCO3- ion concentration in the oceans.

Combustion of fossil fuels also produces fine soot particles. The soot particles decrease the solar reflectivity snow and ice.

Global warming is cumulative net absorption of energy resulting from an increase in the rate of solar energy absorption and a decrease in the rate of infrared energy emission.

The fraction of incident solar radiation absorbed by Earth is given by:
(Fraction of incident solar radiation absorbed) = 1.00 - (Fraction of incident solar radiation reflected)
= 1.00 - (average solar reflectivity)
= 1.00 - (planetary Bond albedo)

The average solar reflectivity (AKA planetary Bond Albedo) is a strong function of the fraction of Earth's surface that is covered by white cloud (microscopic ice particles in clouds) or surface ice. The presence or absence of ice is determined by whether or not the local temperature is above or below 273.15 degrees K. Visible light photographs of Earth taken from outer space show that the local solar reflectivity is low (~ 0.10) near Earth's equator and is high (~ 0.50) near Earth's poles. The average solar reflectivity (planetary Bond albedo) measured in 1999-2000 was about 0.297 +/- 0.005. Thus melting of ice decreases solar reflectivity and increases the rate of solar energy absorption.

The decrease in local solar reflectivity (Bond albedo) with decreasing latitude and hence with increasing atmospheric temperature is clearly shown on the following photograph.

Earth From Space Apollo 17 Dec. 1972

The above photo clearly shows that as the future atmospheric temperature near Earth's poles approachs the present atmospheric temperature near Earth's equator Earth's average solar reflectivity will decrease from 0.30 to 0.10, which when Earth reaches steady state will cause an infrared emission temperature increase, as seen by an observer in outer space, of 17.5 degrees C.

However, there are other causes of a further atmospheric temperature increase.

Infrared emission is reduced by an increase in high altitude atmospheric Green House Gas (GHG) concentration. Carbon dioxide (CO2), water vapor (H2O) and methane (CH4) are all GHGs. The increase in CO2 concentration is a result of combustion of fossil fuels. The increase in water vapor and methane concentrations is a reslt of increasing ocean surface temperature.

In 1996 a spacecraft known as the Mars Global Surveyor recorded a spectrum of the far infrared radiation emitted by Earth which is shown below.

Thermal Infrared Spectrum of Earth From Space,
Mars Global Surveyor
November 24, 1996


Note the combined influence of high altitude CO2 and high altitude water vapor on this spectrum.

Note that the underlying black body shape of this spectrum indicates an emission temperature of 270 K. Due to systematic error in the spacecraft instrumentation this emission temperature was likely 270.8 K

Note that the dominant source of the emitted infrared radiation is water molecules transitioning from the liquid phase to the solid phase at 273.15 K. The photon energy at the center frequency of the radiation is the heat of fusion of water.

Note that if the atmospheric temperature at the altitude where this freezing water is located rises only 2.3 degrees K the solar reflectivity will fall and the atmospheric temperature will rapidly rise. The IR emission will then be dominated by higher temperature water vapor transitions which in the water window are much less probable than the liquid-solid transitions. The result is a decrease in IR emission at emission temperatures greater than 273.15 K.

An increase in ocean surface temperature increases the atmospheric H2O concentration and potentially triggers an increase in the atmospheric CH4 concentration.

The aforementioned warming mechanisms form a high gain positive feedback loop at a local emission temperature of 273.15 degrees K. At low atmospheric CO2 concentrations the loop gain is less than unity. Presently on average the emission temperature is less than 273.15 K and the CO2 concentration is about 400 ppmv. Presently the atmosphere is unstable as is indicated by storms but over time these storms spontaneously decay. The storm violence is greater at lower latitudes where the atmosphere is warmer than at higher latitudes where the atmosphere is cooler. If the atmospheric CO2 concentration becomes sufficiently high the thermal feedback loop gain will exceed unity, and a condition of rapid net spontaneous heat absorption known as thermal runaway will occur. Thermal runaway will cause melting of all ice on Earth and over time will cause an emission temperature rise of more than 17.5 degrees C.

Thermal runaway will cause gradual warming of the oceans which will cause the oceans to emit CO2 to the atmosphere. The resulting steady state increase in atmospheric CO2 concentration will cause the Earth to remain trapped in its "warm" state until carbonate rock and fossil fuel formation processes substantially reduce the amount of CO2 in the ocean-atmosphere pool.

About 56 million years ago, during a time period known as the PETM (Paleocene Eocene Thermal Maximum), the atmospheric CO2 concentration raapidly increased due to combustion of organic carbon and all the polar ice melted. Mass spectrometer analysis of carbon and oxygen isotopes in and adjacent to the PETM sedimentary layer at various locations around the world give us certainty regarding the occurrence of the PETM events. The PETM duration was over 200,000 years. Fossils before, during and after the PETM indicate that during the PETM there was a global extinction of all large land animals. The PETM duration and isotope ratio data indicate that the PETM was a result of combustion of accumulated organic carbon causing thermal runaway with warm state trapping.

We are quite certain that the PETM occurred as a result of the process described above. The initial event which tripped the PETM, instead of being combustion of fossil fuels by man, was likely nearby passage of another star which caused a temporary increase in solar irradiance sufficient to trigger widespread combustion of accumulated biomass and exposed fossil fuels and hence trigger thermal runaway.

Today we live in Goldilocks circumstances which permit the existence of large animal life on this planet. If mankind injects enough CO2 into the atmosphere to raise the average cloud temperature by 2.2 degrees K over subsequent years the atmospheric temperature will spontaneously rise by at least:
17.5 C + 2.2 C = 19.7 C
This temperature rise will cause a global large animal extinction.

If there is a step change in parameters which causes the absorbed solar power to exceed the emitted infrared power there is net energy accumulation by Earth.

Over dry land this energy accumulation quickly heats the surface soil, which rises in temperature. This increase in temperature quickly propagates into the atmosphere above the dry land causing an increase in atmospheric temperature, which may change the solar reflectivity of overhead cloud, and will cause an increase in thermal infrared radiation emission. Thus the net energy absorption by dry land soon stops, with the land at a slightly increased temperature.

Over the ocean the net energy accumulation heats water to a depth of about 200 feet. The resulting change in ocean surface temperature is very small and hence does not directly affect the solar reflectivity or thermal infrared emission by the ocean. However, the warm water floats on top of deeper cold water. Due to wind and ocean currents the warm water spreads over the ocean surface and eventually runs into and melts polar ice. This melting of polar ice makes a large change in the planetry reflectivity (planetary Bond albedo) which in turn causes a large increase in the absorbed solar power.

The consequential increase in net absorbed thermal power will eventually raise the ocean surface temperature which in turn will increase the atmspheric CO2 concentration and will decrease the solar reflectivity over the ocean. The decrease in solar reflectivity over the ocean will cause an extinction level temperature rise.

Thus the dominant issue affecting future temperature is a change in solar reflectivity although that change is triggered by a relatively small but prolonged increase in atmospheric CO2 concentration. The solar reflectivity data shows that this warming process will continue until the ocean surface temperature rises by about 17.5 degrees C.

This heating process will take over a century. However, from mankind's perspective the key issue is the time to when the feedback loop gain exceeds unity, after which point the thermal runaway process will be impossible to stop.

It takes centuries for an increase in net heat absorption to increase ocean temperature and hence increase the overhead cloud temperature which increases the emission temperature and hence increases the infrared radiation power emitted by the Earth. An increase in atmospheric CO2 concentration also increases the emission temperature. Over thousands of years these processes maintain an average balance between absorbed solar power and emitted infrared power. However, that balance is not true over short time spans due to the large thermal mass of the oceans and the polar ice caps.

A complicating issue is that the local solar reflectivity (local Bond albedo) has a large step discontnuity at a local emission temperature of 273.15 degrees K, the freezing point of water. This large step discontinuity gives Earth's atmosphere two semi-stable operating states.

In the "cool" state condensed water vapor in clouds is ice and the local Bond albedo (local solar reflectivity) is about 0.50. In the "warm" state condensed water vapor in clouds is liquid with a much smaller local Bond albedo. In the "warm" state in the tropics the average local bond albedo (local solar reflectivity) is about 0.10.

Today Earth's atmosphere is in the "warm" state in the tropics and is in the "cool" state in near polar regions. Today Earth's average solar reflectivity (planetary Bond albedo) is about 0.29 and the atmospheric CO2 concentration is about 400 ppmv.

The immediate effect of excess CO2 and other Green House Gases (GHGs) in the atmosphere is to cause net planetary heat absorption. In 1996 the average emission temperature was measured to be about 270 degrees K (- 3.15 degrees C) and the corresponding emissivity was about 0.80. The direct effect of doubling of the atmospheric CO2 concentration is to increase the average emission temperature by about 3.15 degrees C. However, when the emission temperature is increased so also is the atmospheric water vapor concentration. Water vapor is also a GHG. The increase in atmospheric water vapor concentration accompanying a doubling in atmospheric CO2 concentration further increases Earth's emission temperature by about 0.865 degrees C. Thus the total direct emission temperature increase causes by doubling the atmospheric CO2 concentration is:
3.15 C + 0.865 C = 4.015 C.

However, the direct increase in planetary emission temperature caused by increasing the atmospheric CO2 and H2O concentrations causes local heating which melts ice causing the latitude of the transition from the "warm" state to the "cool" state to increase. This increase in the transition latitude reduces the average solar reflectivity (planetary Bond albedo) of Earth. Hence Earth absorbs more solar radiation causing more planetary heating and hence causing the planetary emission temperature to further increase. This increase in planetary emission temperature causes yet more ice melting and causes the latitude of the "warm" state to "cool" state transition to further increase. Again Earth's solar reflectivity decreases and Earth's average emission temperature further increases. This process is assisted by ocean currents and wind that transport the extra absorbed heat from low latitude regions to high latitude regions.

If the atmospheric CO2 concentration exceeds a critical threshold Earth's entire atmosphere will progressively switch from the "cool" state to the "warm" state. This relatively rapid state change is known as thermal runaway.

The geologic isotope record shows that thermal runaway occurred on Earth 55 million years ago during a time period known as the Paleocene Eocene Thermal Maximum (PETM). During the PETM exposed organic fossil carbon burned, the polar ice caps completely melted and there was a global extinction of large land animals.

Thermal runaway is immediately followed by a phenomena known as "warm state trapping". In the "cool" state exposed ocean water tends to absorb CO2 from the atmosphere. In the "warm" state exposed ocean water tends to emit CO2 to the atmosphere. However, if the whole ocean is in the "warm" state there is no path for atmospheric CO2 concentration reduction via ocean absorption of CO2. Hence when thermal runaway occurs Earth remains trapped in the "warm" state until biochemical processes which form fossil fuels and carbonate rock reduce the CO2 concentration in the oceans and in the atmosphere sufficiently to enable a spontaneous "warm" state to "cool" state transition. During the PETM warm state trapping held Earth in the "warm" state for over 200,000 years.

Note that a local "cool" state to "warm" state transition occurs at a local emission temperature of 273.15 degrees K (0 degrees C). In 1996 Earth's average emission temperature was measured to be about 270 degrees K (- 3.15 C) indicating that tropical latitudes were already in the "warm" state and higher latitudes were still in the "cool" state. Since 1996 further injection of fossil CO2 into Earth's atmosphere has caused the latitude of the "warm" state to "cool" state transition to increase. Local transition from the "cool" state to the "warm" state has caused large changes in local average temperatue in much of northern Canada.

A major concern is that doubling of the atmospheric CO2 concentration will increase the average Earth emission temperature from 270 K to 274 K at which point water in the atmosphere no longer exists as ice. When ice micro-crystals in clouds melt the local Bond albedo sharply decreases causing local heat accumulation. Then wind and ocean current driven heat transport cause ice melting at high latitudes.

Another major concern is that the half life of non-equilibriuum excess CO2 in Earth's atmosphere is about 10 years. Hence, even if fossil fuel use is promptly halted the heat absorption by the oceans due to the excess atmospheric CO2 concentration will continue for about 16 more years. This protracted ocean heating will melt all floating ice leading to a further decrease in planetary albedo, will release large quantities of methane trapped in permafrost and will result in further sea level rise due to ocean thermal expansion.

The geologic record shows that thermal runaway has occurred in the past. The only uncertainty is the exact excess atmospheric CO2 concentration required to trigger uncontrollable thermal runaway today. The longer that there is excess CO2 in the atmosphere the warmer the ocean surface will become leading to an ever higher latitude for the "warm" state to "cool" state transition and hence a greater propensity for uncontrollable thermal runaway.

The visible light emitted by the sun can be separated into a spectrum of colors (frequencies) using a device known as a diffraction grating. Close examination of the solar spectrum shows a number of dark spectral lines. Each dark line corresponds to a frequency at which the sun's outer atmosphere is opaque (does not transmit light). These narrow dark lines arise because certain gases in the sun's outer atmosphere randomly scatter light of certain frequencies.

During the 1960s various space craft sent to the planet Venus reported that the surface temperature of Venus was far hotter than previously believed and that Venus atmosphere was primarily composed of carbon dioxide.

The reason for Venus high surface temperature is that carbon dioxide is opaque in part of the thermal infra red spectrum.

The surface temperature issues on Earth, known as the Greenhouse Effect and Global Warming, arise because the Earth's atmosphere is also opaque at certain infrared frequencies. This issue is obvious in the far infrared emission spectrum of the Earth as viewed from outer space.

The Greenhouse Effect causes Earth's cloud temperature to be warmer than it would be if the planetary Bond albedo remained the same but Green House Gases (GHGs) were not present in the Earth's atmosphere. The Green House Effect is primarily caused by carbon dioxide, water vapor, ozone, methane and certain other trace gases in the Earth's upper atmosphere.

What happens is as follows:
1. Normally about 30% of the solar radiation power incident on the Earth reflects off the Earth into outer space, unchanged in frequency. The remaining 70% of the incident solar radiation power passes through the Earth's atmosphere and is absorbed as heat by either dry land or the ocean.

2. At steady state conservation of energy requires that the average flow of infrared radiant energy emitted by the Earth into space equal to the average flow of solar energy absorbed by the Earth. However, due to the presence of CO2 and water vapor in the Earth's upper atmosphere, in certain infrared frequency bands the Earth's upper atmosphere is opaque. In these frequency bands infrared radiation is emitted into space not from clouds, but from points high in the Earth's upper atmosphere which are much colder.

3. The rate of infrared energy emission decreases with decreasing temperature. Hence the infrared radiation emission rate is much less in frequency bands where the atmosphere is opaque.

However, at steady state conservation of energy requires that the average infrared radiation emission rate must equal the average solar radiation absorption rate. Since in infrared frequency bands where the upper atmosphere is opaque the infrared radiation emission rate is reduced, in other infrared frequency bands where the atmosphere is transparent the infrared radiation emission rate must have increased. The only way for the infrared radiation emission rate to increase is for the temperature at the the point of emission to increase.

4. The Greenhouse Effect is complicated by temperature related changes in local Bond albedo. As the local temperature passes through 273.15 K in the presence of water there is a step change in local albedo from as low as 0.035 over the open ocean to 0.50 over floating sea ice. There are comparable changes in cloud albedo.

Simple Global Warming is simply an increase in the Green House Effect triggered by an increase in the Green House Gas (GHG) concentrations in the Earth's upper atmosphere. However, the consequences of the effects triggered by Global Warming on life forms on Earth should not be underestimated. During the PETM Global Warming triggered Thermal Runaway and Warm State Trapping which melted the polar ice caps and caused a global extinction of all large land animals.

1. The law of conservation of energy requires that:
(Net energy absorption by the Earth)
= (Solar radiant energy absorbed) - (infrared radiant energy emitted)

2. Prior to the industrial revolution the Earth was at a steady state condition where the average emission temperature was constant implying that:
(Solar radiant energy absorption) = (infrared radiant energy emission)

3. Experimental measurements since 1978 have shown that:
(Incident solar radiant energy per unit time) = constant +/- 0.3%.

4. About 1905 Albert Einstein discovered that:
a) Radiant energy is absorbed or emitted in energy packets known as photons.
b) Each photon has a characteristic frequency Fp.
c) The energy Ep carried by a particular photon is given by:
Ep = h Fp
h = Planck constant

5. Let Np = number of infrared photons emitted by the Earth per unit time per unit frequency
Then the total number of infrared photons emitted per unit time is given by:
Integral from Fp = 0 to Fp = infinity of:
Np dFp

6. The radiant energy emitted by the Earth per unit time is given by:
Integral from Fp = 0 to Fp = infinity of:
Np Ep dFp
Np Ep is the amplitude of the infrared spectrum at frequency Fp.

7. The black line on the following graph shows the experimentally measured amplitude (Np Ep) of the Earth's infrared emission spectrum as a function of:
Wave Number = (Fp / C),
as recorded from deep space by the Mars Global Surveyor space probe on November 24, 1996, where:
C = speed of light = 3.0 X 10^10 cm / s

8. The area under the experimentally measured black line is:
(total rate of infrared energy emission by the Earth) / C

9.Note the big notch in the center of the graph which is due to the opaqueness of the Earth's atmosphere at thermal infrared frequencies corresponding to photon scattering by carbon dioxide (CO2). In the middle of this opaque band the effective temperature at which the net infrared emission takes place is only 215 degrees K (- 58 degrees C) so Np falls by about 50%.

10. As the concentration of CO2 in the atmosphere increases the CO2 related notch in the graph becomes wider and deeper and hence the area under the black line decreases. Hence the infrared energy emission by the Earth at the notch frequencies decreases.

11. Since the rate of solar energy supply remains constant the net energy absorption by the Earth increases. This net energy absorption becomes heat which causes melting of polar ice and mountain glacier ice followed by ocean warming.

12. Water vapor (H2O) behaves in a manner analogous to CO2. Warming the ocean surface increases the concentration of atmospheric H2O, which further reduces the area under the black line on the above data graph and hence further narrows the infrared transmission window.

13. After the polar ice has melted the average ocean temperature will gradually increase which will cause the black line on the above graph on the right hand side of the CO2 notch to gradually move upwards to make the total thermal infrared power emission equal the total solar power absorption as required by the law of conservation of energy. The upward movement of the black line causes an upward movement of the red line, which corresponds to an increase in the planetary emission temperature.

Carbon dioxide alone does not cause a lot of global warming. Water vapor alone does not cause a lot of global warming. These gases have complimentary spectral windows that limit the amount of warming when these gases are individually present. However, when both of these gases are present simultaneously, each gas partially blocks the thermal infrared spectral window of the other gas, causing much more warming than the sum of the two individual gas warming contributions. Thus in the presence of water vapor the impact of raising the atmospheric CO2 concentration is more than would be the case were the water vapor not present. Similarly, the impact of raising the atmospheric water vapor concentration is more in the presence of CO2 than would otherwise be the case if the CO2 were not present. These two effects feed back on each other. Global warming denyers generally either overlook or do not understand this spectral issue.

A common misconception is related to methane and CO2. Methane alone is a strong infrared absorber on a per molecule basis. However, that absorption power has only minor direct practical effect in the Earth's atmosphere because the dominant methane absorpion band lies at the edge of the thermal infrared emission spectrum. However, over time (~ 10 years) methane spontaneously oxidizes to form more CO2, which increases the atmospheric CO2 concentration. Thus the rapid increase in the atmospheric CO2 concentration after a bulk methane release is indeed a threat to man kind. Large amounts of methane are trapped in methane hydrate (a muskeg and sea floor ice lattice called cathrate). A geophysical event that triggers rapid melting of the methane hydrate can cause a large methane release to the atmosphere which over the subsequent decade becomes a large CO2 injection.

The net radiant energy absorption causes land borne glaciers to melt and causes thermal expansion of the oceans. These two effects, if they are permitted to continue, will eventually cause an average sea level rise of about 80 m. A further problem is that in some places annual glacier melt water provides critical agricultural crop irrigation in the dry season. When the glaciers melt away, glacier melt water is no longer available for agricultural crop irrigation in the dry season.

A major implication of an increase in emission temperature is that the dry ground surface temperature increases. However, agricultural crops only grow well in a very narrow band of crop temperatures. Agricultural crops rely on evaporation of water to regulate their temperatures. As the dry ground temperature increases agricultural crops must evaporate more irrigation water to maintain the crop's optimum temperature. However, the amount of available irrigation water is primarily determined by solar energy absorption by the oceans, which might not locally increase in response to an increasing atmospheric CO2 concentration.

Viewed another way, due to increasing atmospheric CO2 concentration a lot of people in semi-arid countries and island states that presently have barely sufficient fresh water for agricultural irrigation will in the future starve to death due to insufficient fresh water for irrigation in the dry season.

An imminent danger to our grand children is that heating the cold ocean causes the ocean to release more CO2 just as heating a can of a cold soda drink causes it to release CO2. This released CO2 will further increase the atmospheric CO2 concentration and will make the CO2 notch in the above graph wider and deeper. This effect is known as a positive feedback process.

Note that the red line above corresponds to an ideal black body with a temperature of 270 degrees K. When the black line rises past the red line to a temperature of 273.15 degrees K the solar reflectivity of the clouds and of ice on Earth's surface suddenly decreases. Instead of consisting of microscopic ice crystals the clouds will consist of microscopic water droplets. Likewise ice on Earth's surface beomes liquid water. Water droplets are much less reflective of solar radiation than are ice crystals. Hence the Earth's solar reflectivity will decrease and the Earth will absorb more solar radiation and become hotter. This effect will causes an an increase in the Earth's planetary emission temperature as viewed from outer space of about 17.5 degrees C which is sufficient to make much of Earth uninhabitable. This spontaneous temperature increase is known as thermal runaway. Once thermal runaway becomes established it will be impossible to stop.

The thermal emission spectrum of the Earth indicates that uncontrollable thermal runaway likely commences at an atmospheric CO2 concentration of about 433 ppmv. The present atmospheric CO2 concentration of 400 ppm is higher than at any time since the PETM. Replacing existing fossil fuel facilities with equivalent nuclear facilities is likely at least a 60 year project. In 2013 the atmospheric CO2 concentration increased at 2.66 ppm / year. This rate of increase has tripled during the last 60 years and may further increase in the near term. It is of paramount importance to stop combustion of fossil carbon to prevent further increase in the atmospheric CO2 concentration.

Given present public behavior there is no certainty that thermal runaway and a resulting global large animal species extinction can be prevented. In some countries, particularly the USA, fossil fuel interests have enormous sway on government and most voters lack the education required to reject constant fossil fuel producer propaganda. In the USA the sense of entitlement to unlimited use of fossil fuels is very strong. It is analogous to the sense of national entitlement on the part of the German and Japanese peoples that led to WWII.

It is extremely important that persons in the Canadian government look at the Global Warming problem from the perspective of people in low elevation states and semi-arid countries. These people are not stupid. They know that if the present pattern of CO2 emissions continues it will only be a few years until they starve to death either due to sea water inundation or due to lack of irrigation water in the dry season.

This starvation is already happening in a number of semi-arid countries. Agricultural production is already reduced in Africa, USA and Australia for lack of irrigation water. From the perspective of the affected people the climate injustice brought on them by fossil CO2 emissions is huge. These people are more forgiving of China because China's per capita fossil CO2 emissions are far below the North American emissions and China is busy building numerous nuclear reactors to mitigate the problem. The Canadian and US governments worship the dollar in preference to human life in other countries. The recently adopted Canadian fossil carbon emissions tax is only about (1 / 4) of the level required to be effective at keeping fossil fuels in the ground.

One of the problems of our urban society is that most Canadians have lost sensitivity to the importance of dry season irrigation. A related issue is that neither the US nor the Canadian governments want the truth revealed to the North American voting pubic that current North American energy policies are leading to starvation in the third world. The US and Canadian governmental policies are a reflection of both short term fossil fuel interests and a scientifically illiterate electorate.

The third world people on the brink of starvation have little to lose by initiating a global conflict. North American governments blame Islamic extremists, without addressing the issue that it is North American energy policies that drive these extremists to sacrifice their own and their children's lives. It is little wonder that there is widespread public support for nuclear power in China, India, Pakistan and Iran.

This web page last updated June 6, 2017.

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