Simple Explanation of Why Greenhouse Gases Do Not Warm the Earth's Surface

This is a simple explanation why an essential claim of greenhouse gas theory or the catastrophic man-made global warming hypothesis is very wrong.  That theory believes that back-radiation from the atmosphere to the surface is about the same as the total solar radiation incident upon the top of the Earth's atmosphere.  For a much longer exposition of many of the problems with this theory you might examine my earlier and much-updated post

AGW Theory: Back Radiation Insignificant for Surface Temperature

This post is comparatively very short and will only discuss a simple explanation of the cornerstone argument of huge back-radiation to the surface.  Indeed, I will show why that back-radiation is virtually zero.  Because it is nearly zero, the catastrophic man-made global warming hypothesis is shown to be nonsense.  There is no excuse for governments acting to force individuals and companies to reduce their carbon dioxide emissions.  Doing so is very expensive, causes energy reliability problems, and puts people out of work.  Causing these miseries in the name of a failed hypothesis is a very serious injustice to mankind.

Let us examine a current NASA depiction of the huge role the catastrophic AGW hypothesis gives to back-radiation:

Now notice that the emitted surface radiation is 117% of the top of the atmosphere average radiation from the sun and back-radiation is 100% of the top of the atmosphere incident solar radiation.  Notice also that only 48% of the total solar radiation was ever absorbed by the Earth's surface.  Of the 48% of the total solar incident energy absorbed by the surface, 25% is lost by evaporation of water and 5% by convection loss, leaving only 18% to be emitted by radiation.  Now the proponents of the large greenhouse warming effect claim that the 18% is just a net difference between a larger surface radiation emission rate and a large back-radiation rate.  In this case the difference of 117% - 100% = 17%, which is about 18%.  We are going to evaluate this claim.

Consider the surface of the Earth for a moment.  The density of atoms per cubic meter in the surface is about 1 gram per cubic centimeter for the water that covers about 71% of the Earth's surface and even greater for land materials or if considering the salts in the oceans.  Expressed as a density per cubic meter of water, this is 1000 kg per cubic meter.   A cubic meter of water has 3.34 x 10²⁸ water molecules.  Infra-red emission and absorption in a surface occurs in the outer 2 micrometers of the surface.  Consequently, there are about 6.7 x 10²² water molecules emitting infra-red at most from the surface.  When infra-red radiation is incident upon the surface, these are the same water molecules that would be able to absorb that radiation.

The density of the atmosphere near the surface at sea level is 1.225 kg per cubic meter in the U.S. Standard Atmosphere at a temperature of 288.15K.  Adding water vapor very slightly decreases that density.  The number of molecules per cubic meter at sea level in the U.S. Standard Atmosphere is 2.55 x 10²⁵/m³.  The important infra-red active gas near the surface is water vapor and its density per cubic meter is commonly between 10 g/kg to 14 g/kg of air as shown in Fig. 1. below.  At a specific humidity of 12 g/kg, the number of water molecules/m³ of air is about 4.9 x 10²³.  Therefore, there are more water molecules in the first cubic meter of air above 1 m² of water surface emitters by a factor of 7.3.  This should mean that radiation that can be absorbed by water vapor will be absorbed in the first meter of air above the surface at a humidity near the Earth average humidity.  There is a report that the average mean free length for water vapor absorption in the atmosphere is as long as 8 m.  If it actually is that long, then the result I get below on the amount of back-radiation can be multiplied by a factor of 8.  That number will still be most unimpressive.

Fig. 1. The average specific humidity of air is shown as a function of latitude.  The specific humidity is the weight of water in grams in one kilogram of air.

In comparison, at 400 ppm of carbon dioxide, there are 1.0 x 10²² molecules of CO₂ /m³.  There are 49 water vapor molecules for every carbon dioxide molecule at a specific humidity of 12 g/kg.  In addition, the emissivity of CO₂ molecules is less than 40% that of water vapor molecules.  Since many of the carbon dioxide molecule absorption peaks are largely or mostly already absorbed by overlapping water vapor absorption lines, the effect of CO₂  near the surface is very minimal compared to that of water vapor.  This is less true at altitudes above 4 km where the concentration of water vapor drops greatly and the carbon dioxide remains in proportion to nitrogen and oxygen, but such altitudes have nothing to do with the back-radiation to the surface issue.

Returning to the back-radiation caused by water vapor, we find that the temperature difference over the 1 meter absorption range according to the U.S. Standard Atmosphere is only about 0.0065 K/m.  For humid air, the temperature gradient is even less.  So if the water surface and the water vapor in the first meter of air above the surface are treated as gray bodies, we have a power transfer from the surface to the water vapor in the atmosphere of P_W

P_W = σ (ε_s T_s⁴ – ε_a T_a⁴) , 

for the surface s and the atmosphere water vapor a and if we take the emissivities to be a high value of 0.95 often used by the catastrophic man-made global warming promoters, this is equal to 0.033 W/m².

This is actually an over-estimate because we have ignored the fact that some of the heat energy in the surface is used to evaporate water and some is lost to the air by means of air molecule collisions with the surface.  Much of the solar radiation absorbed by the surface is actually transferred out of the surface by evaporation and by conduction.  Of the 48% of solar radiation absorbed by the surface according to the above NASA schematic, a total of 30% is removed from the Earth's surface by evaporation and convection/conduction.  This leaves only about 18% to be radiated away from the surface.  So if the Earth's surface was an interface directly with vacuum, the 48% of solar radiation absorbed would be radiated in its entirety.  But other processes, evaporation and conduction, remove most of this energy, leaving a fraction of only 18%/48% = 0.375 of the total energy flux to be removed by radiation.

But water vapor does not absorb infra-red across the entire surface emission spectrum.  It actually absorbs only about 65% of it.  At least 28% of the surface emission is into the atmospheric window where no atmospheric gases absorb the infra-red radiation.  See the transmission spectrum of the Earth's infra-red surface emissions taken by Nimbus IV in 1970 near Guam below:

This points out one of many flaws in the NASA depiction of the Earth Energy Budget above.  Taking the two atmospheric windows at higher wave numbers than the peak of the Earth emission spectrum, the infra-red radiated into them is about 28%.  28% of the 117% surface infra-red emission claimed by NASA is 33%, not the 12% quantity their schematic assigns to the atmospheric window radiation lost directly into space from the surface.  The direct loss to space of surface emission with the NASA depicted 117% surface emission should be 2.75 times what NASA puts in its Earth Energy Budget schematic diagram at the start of this article.  This inconsistency suggests that the surface emission radiation is actually much less than the 117% claimed.  If that emission is much less, then the back-radiation would also have to be much less.

So the actual water vapor absorbed infra-red radiation is only about 

P_W =  (0.375) (0.65) (0.033 W/m²) = 0.0080 W/m².

But because of the 6.9 x 10⁹ collisions/s in air near sea level, most of this energy is transferred to non-radiating nitrogen, oxygen, and argon.  Only about 20% is re-radiated and half of that is radiated toward space.  Consequently, the total back-radiation which can be absorbed by the surface, P_B, is about

P_B = (0.2) (.5) (0.0080 W/m²) = 0.00080 W/m²

Thus, the absorbed back-radiation has an upper limit of about 0.00023% of the average solar insolation at the top of the atmosphere (342 W/m²)!  For all intents and purposes, the absorbed back-radiation is zero.  This value should be multiplied by the mean free path for absorption by water vapor, which may be as large as 8 m on average.

I just proceeded down the true path of analysis dictated by the use of Occam's Razor.  Let us assume that NASA is right that 117% of the solar incident radiation at the top of the atmosphere actually is emitted from the surface due to some unknown extra input energy that lifts the 48% of the solar absorbed energy flux at the surface by 117% + 25% + 5% - 48% = 99% so that one can have 117% radiation, 25% evaporation, and 5% conduction cooling mechanisms at work.  Is it possible for that 99% warming source to be back-radiation?

The 117% radiation is greater than the 18% upon which I performed the Occam's Razor version of the calculation.  In fact, the back-radiation per meter of mean free path is then 117% / 18% = 6.5 times greater than the value I calculated.  So, if we assume that the average water vapor mean free path is 8m, we get 8 (6.5) (0.00023%) = 0.012%, which does not look at all like the 100% claimed by NASA.


Because back-radiation to the surface is insignificant compared to the claims made by the proponents of catastrophic man-made global warming, the mechanism upon which that theory stands is wrong.  Indeed, adding carbon dioxide to the atmosphere will actually cause more incoming solar radiation to be absorbed by the atmosphere before it reaches the surface.  This results in a cooling of the surface.  In addition, more CO2 in the atmosphere near the surface will also cause the temperature gradient in the atmosphere to become slightly smaller, just as infra-red absorbing water vapor makes it smaller.  This is because radiation transport effects operate at the speed of light, which is faster than evaporation/condensation transport or conduction/convection transport of energy.  Since all remove energy from the surface, they are all cooling effects.  As a result, adding CO2 to the atmosphere actually causes a very slight cooling of the surface, contrary to the claims of a substantial warming effect.

The primary sources of CO2 in the atmosphere are warming oceans, decaying plant life, and heat vents and volcanic emissions.  Since CO2 in the atmosphere creates a slight cooling of the surface, it acts as a negative feedback to the warming oceans that cause it to increase and it slightly cools the decaying plants to slow down the further generation of CO2 from that source.  Of course volcanic and heat vent sources of CO2 are also providing heating, so carbon dioxide as an surface coolant acts to stabilize the Earth's temperature much as water vapor does.  It has negative feedback effects.  It is no more subject to the sort of tipping point catastrophes that global warming alarmists put out than is water vapor, though its effects are much, much weaker.

This article was last updated on 29 July 2014. 

[The fact that back-radiation itself is insignificant in explaining the 33C warming of the surface claimed by the proponents of catastrophic AGW is not at all to say that the effects of water vapor on the surface temperature are without significance.  During the day the evaporation of water is an important surface cooling effect and during the night its condensation can be an important warming effect.  During the day, the infra-red active gases absorb a portion of the incoming solar radiation and prevent it from being absorbed by the surface.  At night, fog and clouds scatter, reflect, and absorb the infra-red radiation emitted from the surface.  Also at night, the small true back-radiation effect is not off-set by the absorption of incoming solar radiation by the same infra-red active molecules in the atmosphere.  There is a very important moderation of the surface temperature between day and night due to these effects.  This note was added on 13 November 2014 to remind people of the context in which my criticism of the usual greenhouse gas theory is framed.]

Revised State Real GDP Changes in 2013

According to the U.S. Bureau of Economic Analysis, the percentage change of real GDP in 2013 was:

Now recall that real GDP is under-corrected for inflation due to the government insistence in leaving such volatile, but clearly more rapidly increasing cost, items such as food and energy are not included in the cost of living index.  Then also recall that one should really be looking at real per capita GDP since that tells us whether our standard of living is actually increasing.  If the GDP increases by less than the rate of growth of the population, then our standard of living actually falls.  The average US population growth rate was 0.9% from 2001 to 2010, so real GDP increases of 0.9% provides a stagnant standard of living.

New York state which is running ads nationally claiming to be the second best job creator state in the nation clearly underperformed in 2013 with a state GDP that grew by a mere 0.7%.  The state of Maryland, whose Governor O'Malley believes himself ready to run for the presidency, had a 0.0% growth rate.  Yes, preventing the growth of one's own state's GDP now qualifies a politician well for the Democrat Party nomination for the presidency!

Most of the high growth states in the US are in the center of the nation.  The Dakotas, the Rocky Mountain states, Nebraska, Oklahoma, Texas, and West Virginia are the heroic states for those who wish to earn a living.

Maintaining Climate Change Alarmism: Replacing Cool Weather Station Data with Warm Station Data

Steven Goddard at Real Science has lately had a series of posts on the effects of a very large reduction of temperature data reported from many weather stations since 1990.  The effect of the data loss and its replacement with massaged data, turns out to be a considerable artificial warming effect.  His most recent post is here.

The following plot by Steven Goddard of the older and generally complete temperature data in the USHCN temperature record kept by National Oceanic and Atmospheric Administration (NOAA) until 1990 shows the separated data from the stations still reporting complete data and compares that to the temperature data, then complete, of the stations which are missing much of their temperature data since 1990:

Clearly the stations reporting complete data since 1990 are the stations that were warmer prior to 1990 than those which have been reporting incomplete data since 1990.  The temperature differences between the two data sets prior to 1990 are very substantial.

In an earlier post, Goddard presented the percentage of the NOAA USHCN temperature data for which there was no raw data in the record by year:

Note the increase in the missing raw temperature data since 1990, which became a particularly rapid increase in lost raw temperatures after 1994.  The rate of loss of raw data is really remarkable in the recent years of stagnant temperature reports, indicating that there is a greater and greater need by the alarmists to hide the cooling that must really be going on of late.

Steven Goddard then presents the data as reported since 1990 from these same two sets of stations on the basis of the raw data that actually was reported in the raw data record.

So it becomes very clear that NOAA is preferentially losing the raw temperature data since 1990 from the cooler stations.  The final massaged data that they report to everyone replaces the missing cooler temperatures with temperatures interpolated geographically from the warmer data from the stations with complete raw temperature data records.  That is, NOAA is not just losing cooler raw temperatures, but it is adding in warmer temperatures as though that comes from the cooler stations!

It is clear that many of the NOAA warm stations are warm because of urban and suburban locations, airport locations, and massive heat absorbing or even heat-emitting objects at the immediate site.  The Urban Heat Island Effect has corrupted much of the NOAA weather station network data.  Far from correcting the data from overly warm sites downward, NOAA is correcting the cooler and usually better station data upward.  See Anthony Watts' recent evaluation of the USHCN weather stations.

Over and over, I am asked scornfully by believers in the catastrophic man-made global warming hypothesis if I believe that the government and many climate alarmist scientists are lying to us.  There are many temperature records that have clearly been adjusted with great bias of heart to exaggerate or manufacture a warming trend to support this hypothesis.  I have discussed this in many prior posts.  This very interesting sleuthing by Steven Goddard into the NOAA USHCN temperature data and what NOAA has villainously and corruptly done to the temperature record makes it very clear that our government and its scientists are very determinedly lying to us.  Apparently, the lust for power is overwhelming for many government scientists and for many scientists funded by the power lusting government.

Our Mind-Closing Universities and Conformity

A short post by William Murchison entitled When Higher Ed Shuts the Door on Taxpayer's Right to Know discusses the increasing trend to secrecy on the part of university boards and presidential selection committees.  Murchison says:

The Columbia Journalism Review scores the “increasingly closed-door culture” of university boards, such as Kent State University’s, which not only conducted a secret presidential search recently but “admitted to shredding documents to cover their tracks.”  How about the boards of Wayne State University and the University of Michigan, which not only kept their searches secret but suppressed the names of the finalists until both were hired. Then they told the world!

One can see that given the state of commitment to Progressive Elitism and to political correctness on college campuses that it must be very nearly impossible to conduct the managerial affairs of a public college in the open.  If the board and selection committees maintain political correctness and promote Progressive Elitism as they are expected to by student activists and most faculty members, many taxpayers will be appalled to see what is going on.  If the board and other college controlling committees do not do as expected by student activists and faculty, they are also in very hot water.  Nay, boiling water surrounded by drooling cannibals on most campuses.  Given the culture of the college campus today, such public institutions of Progressive Elitist indoctrination are in a dilemma in all but the most socialistic of states.

Private universities generally only need to satisfy their alumni, students, and faculty, despite raking in huge sums of research grants from the taxpayers.  This is a less tough nut to crack, especially in the Ivy League and equivalent schools, where the alumni have long been very successfully indoctrinated in the Progressive Elitist viewpoint.  These Ivy League schools are very assured that virtually all of their graduates are fully committed to Progressive Elitism, partly because they select for that in their admissions and partly because the on-campus commitment to this indoctrination has long been so thorough.

So how did I escape becoming a Progressive Elitist at Brown University?  By never tiring of pitched debates with up to a dozen Progressive Elitists at a time.  By never being intimated, because I was able to shake the very foundations of their belief, at least for a few hours.  After which they would return as though the discussion never occurred, but with no better ideas than those ideas that had failed so miserably but hours earlier.  Progressive Elitism is definitely a religion for almost all such persons and they refuse to allow that religion to be evaluated and assessed by reason.  But being fully committed to reason, I at least was not susceptible to their religious conformity.

Just as most people in many communities become captured by their desire to belong to a particular dominant religion, whether Christian, Hindi, Islam, or Buddhism, so too do most people in a community dominated by the Progressive Elitist religion just have to be Progressive Elitists so they will belong.  So while people are complex and highly differentiated individuals, most still have a great desire to conform so they will be accepted into a community of people.  If this means denying reality, including their own natures, well then reality will generally be denied.  The human suffering that results knows few bounds, which is why our culture has become more and more cheerless and more and more nihilistic.

Only a community committed to reality, reason, productivity, and individuality can achieve man's greatest needs of security, freely given and valued friendships, real cooperation in mutual endeavors and relationships, the freedom to pursue our highly differentiated values generally according to our individual natures, and hence the freedom to pursue our own happiness.  Such a community is rich in its choices and possibilities.

Unfortunately, those people with already low self-esteem are fearful of that very richness of choices and possibilities.  The less free a society becomes, the larger the number of people with such low self-esteem and the more fearful the society becomes of individuality, choices, and possibilities.  Universities, far from opening young people's eyes to the joy of pursuing life in such a rich, reality-driven society, have long been indoctrinating them to choose a conforming, low-choice, hierarchically managed society that denies them their very individuality.