Why the scientific basis of greenhouse gas warming is incorrect

Late Prof. Richard Schwartz was an astrophysicist, and had his article entitled “An Astrophysicist Looks at Global Warming” published posthumously by the Geophysical Society of America in GSA Today, 22(1), 44-45 (January 2012).  Schwartz demanded in the article “most important, contrarians must show why the scientific basis of greenhouse gas warming is incorrect.”

This question does deserve an answer.  Let’s answer the question by addressing what Schwartz considered the scientific basis of greenhouse gas warming was. 

First of all, Schwartz employed the planetary mean temperature for the Venus, the Mars and the Earth to interpret the greenhouse gas warming effect; the total atmospheric greenhouse gas warming raised the temperature by 33 °C for the Earth, 6°C for the Mars and 460°C for the Venus.

To explain why this interpretation is incorrect, we need to examine how the 33°C greenhouse effect for the Earth is obtained.  33°C = 15°C – (-18°C).  The -18°C is obtained by radiative equilibrium between incoming absorbing radiant flux from the Sun and outgoing emitting radiant flux from the Earth:

(1)     p r² (1-a) S₀ = 4 p r2 ε σ T⁴

where, r, is radius of the Earth, and T earth’s mean surface temperature; α is albedo and S₀ is the solar constant representing the incoming solar radiation energy per unit area and unit time with its value being around 1368 W/m²; σ is the Stefan-Boltzmann constant equal to 5.670373 x 10^-8 (W/m²K⁴), and ε is the emissivity of the earth surface.

In current climate research, ε is either missing in the equation or is assumed to be unit.  Inserting the value of α = 0.3 and ε = 1 into and rearranging Eq. (1) leads to:

(2)     T = 254.9 (K) @ 255 (K) @ -18°C        

However, by adopting ε = 1, one has assumed that the earth surface is a black-body surface, which of course can not be true.  If ε is not 1, but 0.9, 0.8, 0.7 and 0.6, T would be -11.5°C, -3.6°C, 5.5°C or 16.5°C respectively.  This -18°C is simply a result of technical error.

On the other hand, the Earth’s mean near-surface air temperature, as measured by global weather stations, is around 15°C (@ 288K).  Another widely spread technical error is to use this 15°C to subtract the -18°C.  To explain why, it is essential to decode highly symbolised notions “surface” and “surface temperature T” of the Stefan-Boltzmann law to extract true physical meanings for the case of earth-atmosphere system. 

If there is no atmosphere, the surface means the land and water ground surface of the Earth, and T represents the mean temperature of the ground surface.  If there is atmosphere that are all of nitrogen and oxygen, the surface is still the ground surface, and T still the mean temperature of the ground surface, regardless what the temperature of nitrogen and oxygen may be.  This is because nitrogen and oxygen are non-radiative (literally ε = 0 for transparent and white bodies).  0 multiplying anything leads to 0.   

The real earth-atmosphere system consists of the ground surface, non-radiative gases as well as radiative gases such as water vapour and carbon dioxide.  In this case the earth surface is not straightforward any more: over the absorption bands of water vapour and carbon dioxide (e.g. the absorption band 15 μm for CO₂), the surface is a layer of atmosphere starting from the top of atmosphere (TOA) with thickness equal to absorption depth, and the temperature is the mean temperature of CO₂ in this air layer, T_co2(h).  One can similarly find out the surface and surface temperature for any other absorbing bands of radiative gases.  For the rest of infrared bands, the surface and surface temperature are the ground surface and its mean temperature, T_GSurf.  What T stands for in Equation (1) is the mean temperature averaged over all the infrared bands.  Figure 1 shows that over the 15 μm infrared band, the earth surface and surface temperature are the top layer of the atmosphere and the temperature of CO₂ in this layer respectively.   

Figure 1  An illustration showing what surface and surface temperature should be over the CO₂ absorption band 15 μm.  For infrared bands transparent to the atmosphere, the surface and surface temperature are the ground surface and ground surface temperature, T_GSurf

The global mean surface temperature 15°C is measured by weather stations using thermometers, and can be denoted T_air(h).  Obviously, T_air(h) is the mean temperature of T_n2o2(h), T_co2(h) and temperature of water vapour etc., averaged in terms of heat capacity.  As such the 15°C is largely of the temperature of nitrogen and oxygen gases that consist of 99% dry air.  Therefore, it is not physically meaningful to subtract -18°C from this 15°C.

In calculation of Mars planetary mean temperature using the Stefan-Boltzmann equation, climate scientists made the same error as they did in calculation of the earth mean temperature, i.e. they falsely assumed the Mars has a black-body surface.  If this error is corrected, one obtains the mean surface temperature for Mars -47.13°C, which is in agreement with measurements -47°C. http://www.ucar.edu/learn/1_1_2_1t.htm

When there is a net heating source on a planet, we’ll not be able to calculate its planetary mean temperature any more from radiative equilibrium.  For example, the incoming radiation energy for the Sun is almost 0, while its outgoing radiation energy is still εσT⁴, with ε @ 1 and T = 5778 K, which is a result of its energy generation due to nuclear fusion of hydrogen nuclei into helium.

The Venus has almost same temperature day and night in spite of the fact that a venusian day is as long as 243 earthly days.  This is an indication that there are heat generating sources, most likely magma covering generated by volcanoes on the Venus. 

Clearly, how to apply and interpret the Stefan-Boltzmann’s law is the problem that has led to a misunderstanding of the greenhouse gas warming effect.

In explaining the molecular mechanism of greenhouse gases warming, Schwartz stated:

“When a greenhouse molecule absorbs an infrared photon, the molecule rotates or vibrates faster and is said to be in an “excited” state.  At low gas densities, an excited greenhouse gas molecule will spontaneously (by the rules of quantum mechanics) reradiate an infrared photon, which may escape the atmosphere into space and produce no net warming.

“At the higher densities of Earth’s atmosphere, the excited molecule will bump into (collide with) another molecule (any molecule in the atmosphere).  In the collision, the energized greenhouse gas molecule loses its rotational energy, which is transferred to the kinetic energy of the molecule it collides with (this is called collisional de-excitation).  The increased kinetic energies of the colliding molecules means that the molecules are moving faster than they were prior to the collision, and the increased velocities of such molecules represents a direct measure of increased atmospheric temperature.

“’Greenhouse gas’ warming occurs because the collisional de-excitation time for greenhouse molecules in Earth’s lower atmosphere is much shorter than the radiation lifetime of excited molecular states.  This is the basic science of greenhouse gas warming.”

A paper by Prof. Pierrehumbert (Pierrehumbert, R.T., 2011, Infrared radiation and planetary temperature: Physics Today, v.64, p.33–38.) specifies radiation lifetime ranging from a few milli-seconds to a few tenth of a second, and collisional time 10^-7 s, implying that the thermal transfer process between N₂O₂ and CO₂/H₂O by molecular collisions is far faster than the heat loss/gain by radiation for CO₂/H₂O. 

Unfortunately, wrong physics has been employed to explain the thermal absorption and in particular emission phenomena of radiative gases.  De-excitation occurs only after excitation; however, emission occurs 24/7 to a non-white/transparent object as long as temperature of the object is not 0 K (-273.15°C), regardless whether it absorbs or not. 

The kinetics of heat transfer by radiation is determined by the equation εσT⁴ (or I = a I₀) that measures the heat energy gained/lost per unit area and unit time for an object.  Assuming the total surface area, S, mass, M, and specific heat capacity, c_p, for the object, one can readily convert absorption/emission energy to temperature rise/drop for the object.  The emission rate will be 10¹² times faster at 1000 K than that at 1 K.  On the other hand, the collision time of 10^-7 s, which is related to the mean free path of air molecules, does not mean that air homogenizes its temperature in 10^-7 s time scale.  In fact air is a thermal insulator because thermal transfer for air by molecular collision is slow.  Industrial examples of taking advantage of air’s thermal insulation property include: double glass windows for trains and hollow synthetic fibres etc.

Hopefully, this article is comprehensive enough and does answer late Schwartz’s question.

Why the theory of AGW is fundamentally wrong in a nutshell

Two most fatal technical errors in current climate research that have led to the false illusion of global warming are comprehensively briefed as follows:

1)  False assumption of a black-body earth surface

Thermal radiation energy per unit time and unit area the Earth emits into space is written as ε σT⁴ , where T is the mean temperature of the earth surface, and σ the Stefan-Boltzmann constant equal to 5.67 x 10^-8 (W/m²K⁴).  

The symbol ε denotes emissivity which has a value between 0 and 1; 0 is for white and transparent bodies, and 1 for black bodies.  Most substances are grey bodies with 0 < ε < 1.  In current climate research, ε is either missing or asserted to be a unit, implying a black-body earth surface.  Truly this is illogically wrong. 

2)         Omission of the thermal emission property of CO₂

We all know that CO₂ absorbs significant amount of earth’s outgoing radiation.  However, this is only half of the story for CO₂.  According to the Kirchhoff’s law of 19^th century physics, an object that absorbs emits.  As a result of emission of thermal radiation, CO₂ is cooler than, gains heat by molecular collision from, and dissipates heat by radiation for nitrogen and oxygen.  It is N₂ and O₂ that award the Earth a warm liveable atmosphere. 

The kingdoms of plantae and animalia, must share the earth atmosphere.  CO₂ is never a pollutant, but a necessity for life.  Increased level of CO₂ concentration is ecologically beneficial, with improved agriculture yields and a greener earth surface coverage due to enhanced efficiency for photosynthesis. (by Dr. J. Cao, Australia)

Heat Death of the Universe and Global Warming

The second law of thermodynamics states the entropy of an isolated system increases always with time towards its maximum.  William Thomson (Lord Kelvin), one of the most brilliant minds in the field of thermodynamics in the 19^th century, applied the law to the case of the universe and formulised a hypothesis that says: when the maximum entropy is reached the universe will have no thermodynamic free energy any more to sustain motion or life – ultimate fate of the universe is heat death.  The theory has been further developed since, and cosmological research suggests eventually all matters will decay into iron, and collapse into black holes in some remote future of 10’s 3 digits power (>10^100) years from now.  Presumably this is the scariest projection our human minds are capable to image.

A century after Lord Kelvin, another scary projection is formulised by climate scientists.  Instrumental observations have found that atmospheric carbon dioxide absorbs significant amount of earth outgoing radiation.  It is then believed that atmospheric carbon dioxide traps heat and warms up the atmosphere.  With the concentration of CO2 increasing more and more, the Earth will get warmer and warmer, ice melts, sea level rises, leading to catastrophic climate change that will destroy the living environment of the mother Earth.  "Earth 2100," as an ABC television program forecasts, is the "Final Century of Civilization."

Unlike the theory of heat death of the universe that is only studied by academics, the theory of global warming has alarmed and mobilised our mankind.  We’ve spent trillions of dollars trying to combat global warming.  From the Kyoto Protocol to the Copenhagen Climate Summit COP15 to the current Durban conference COP17, world leaders have shown how they are convinced that carbon dioxide is causing global warming.  Australian parliament even passed recently a carbon tax law upon its citizens.

While the theory of heat death of the universe remains a valid scientific hypothesis, the theory of global warming, fortunately and unfortunately, has been found to be a false illusion due to technical errors.  Physical analysis of carbon dioxide, oxygen and nitrogen molecules shows carbon dioxide is cooler than, gains heat by molecular collision from, and dissipates heat by radiation for nitrogen and oxygen gases. 

CO₂ is a cooling agent for the atmosphere; nitrogen and oxygen gases secure the Earth a warm liveable near surface atmosphere.  In the thermosphere where CO₂ is sorted out due to heavier molecular weight, the temperature of residual air is well above 100°C, goes higher and higher with altitude reaching a value exceed 1000°C.

False assumption of black-body earth surface leading to false illusion of global warming

The false assumption that the earth surface is a black body surface has been identified being a fatal technical error leading to false illusion of global warming.

The Stefan-Boltzmann law states that a black-body object with surface temperature, T, emits energy σT⁴ per unit time and unit surface area, where σ is the Stefan-Boltzmann constant equal to 5.670373 x 10^-8 (W/m²K⁴).  For an object with any surface, it emits ε σT⁴, where ε is surface emissivity of the object.  ε is a value between 0 and 1; 0 is literally for white and transparent bodies, and 1 for black bodies.  Most substances are grey bodies with 0 < ε < 1. 

When the Stefan-Boltzmann law is applied to calculate the Earth’s outgoing emission flux, Q_e, one shall write:

     Q_e  =  4pr²  ε  σT⁴

where, r, is radius of the Earth,  and T is the Earth’s mean surface temperature; 4pr² constitutes of the surface area of the Earth.

  

In current climate research, ε is either missing in the expression or asserted to be unit.  By taking ε = 1, one has assumed the earth surface a black-body surface, which means that almost everything on the earth surface ¾ ocean, soil, snow and vegetations etc are all objects with black-body surface!  Truly this is illogically wrong. 

For a given outgoing flux, Q_e, the calculated mean earth surface temperature T for ε = 1.0 becomes lower than that for ε < 1.0.    

This technical error has led to a widely spreading misunderstanding that the Earth would be much colder should there is no greenhouse gas effect.  With ε = 1.0, one obtains T = -18°C, which is then compared with actual mean near surface air temperature 15°C.  The difference 33°C has been considered a common measure of the greenhouse effect [e.g. Lucis et al. “Atmospheric CO₂: Principal Control Knob Governing Earth’s Temperature” Science 33, 356-359 (2010)].

Numerous documents have made similar statements without realising the value of -18°C is incorrect.  The Joint Science Academies’ Statement: Global Response to Climate Change (2005) by academies of Brazil, Canada, China, France, Germany, India, Italy, Japan, Russia, UK and USA stated:

“The existence of greenhouse gases in the atmosphere is vital to life on Earth – in their absence average temperatures would be about 30 centigrade degrees lower than they are today.”

CSIRO’s Science and Solutions for Australia – Climate Change (2010) writes:

“The surface of the planet would be more than 30°C cooler than it is now without this natural greenhouse effect, and life as we know it would not be possible.”

After quoting the Science paper, the Australian Climate Commission Report – The Critical Decade (2011) continues:

“In fact, without these long-lived greenhouse gases, the Earth’s temperature would drop rapidly and drive the planet into an ice-bound state.”

It is a collective error in current climate research.  One can find the error in peer reviewed academic publications as well as in climate science textbooks.  It may prove to be the most expensive technical error we ever had in the human history.  (By Dr. J. Cao, Australia)

Physical analysis shows CO2 is a coolant for the atmosphere

There is a fallacy dominating the way of our thinking in current climate research that radiative gases such as carbon dioxide and water vapour are regarded greenhouse gases that trap heat and warm up the atmosphere.  Physics analysis of carbon dioxide, oxygen and nitrogen molecules, however, tells a different story: carbon dioxide is cooler than, gains heat by molecular collision from, and dissipates heat by radiation for nitrogen and oxygen.  Indeed, CO₂ is a coolant of the atmosphere, and it is nitrogen and oxygen gases that award the Earth a warm liveable near surface atmosphere. 

The physical principle behind the analysis lies in the Kirchhoff’s law of 19^th century radiation physics, which can be restated in plain English as: an object that absorbs emits and an object that emits absorbs.   Absorption and emission are two inseparable equivalent identities of the same physical essence.  Carbon dioxide absorbs infrared therefore it emits as well thermal radiation.  Nitrogen and oxygen do not absorb, therefore do not emit.  CO₂ approaches 0 K because of its emission if there is no radiation source; absorption of the thermal radiation from the earth ground surface rises CO₂ temperature from -273.15°C to -78°C only.  CO₂ gains heat by colliding with warmer nitrogen and oxygen to rise its temperature further, which can be measured by spectroscopy.   

We will have a better understanding of the physical principle if one notices that a computer case is often designed black.  This is because a black surface emits more heat out so the computer will be cooler.  On the other hand, an industrial boiler is usually painted silver to reduce thermal emission to reserve heat. 

With this alternative interpretation, we have a better explanation of the temperature-altitude profile of the atmosphere; in particular, a better explanation of the existence of the thermosphere where the molecular temperature of residual oxygen gas is well above 100°C ¾ CO₂ gas is sorted out in the thermosphere due to its heavier molecular weight. 

A PDF file of the full manuscript entitled “Role of heat reservation of N₂ and O₂ and the role of heat dissipation of CO₂ and water vapour” is available to download if interested.

http://www.tech-know-group.com/papers/JCao_N2O2GreenGases_Blog.pdf

(By Dr. J. Cao, Australia)