Sunday, June 3, 2007

Cold Facts On Global Warming (and Carbon Dioxide)

The case against carbon dioxide causing global warming just keeps building and growing stronger by the day.........consider this:

Cold Facts on Global Warming
What is the contribution of anthropogenic carbon dioxide to global warming? This question has been the subject of many heated arguments, and a great deal of hysteria. In this article, we will consider a simple calculation, based on well-accepted facts, that shows that the expected global temperature increase caused by doubling atmospheric carbon dioxide levels is bounded by an upper limit of 1.4-2.7 degrees centigrade. This result contrasts with the results of the IPCC's climate models, whose projections are shown to be unrealistically high.

The Greenhouse Effect
There is general agreement that the Earth is naturally warmed to some extent by atmospheric gases, principally water vapor, in what is often called a "greenhouse effect". The Earth absorbs enough radiation from the sun to raise its temperature by 0.5 degrees per day, but is theoretically capable of emitting sufficient long-wave radiation to cool itself by 5 times this amount. The Earth maintains its energy balance in part by absorption of the outgoing longwave radiation in the atmosphere, which causes warming.
On this basis, it has been estimated that the current level of warming is on the order of 33 degrees C [1]. That is to say, in the absence of so-called greenhouse gases, the Earth would be 33 degrees cooler than it is today, or about 255 K (-0.4° F) [2]. Of these greenhouse gases, water is by far the most important. Although estimates of the contribution from water vapor vary widely, most sources place it between 90 and 95% of the warming effect, or about 30-31 of the 33 degrees [3]. Carbon dioxide, although present in much lower concentrations than water, absorbs more infrared radiation than water on a per-molecule basis and contributes about 84% of the total non-water greenhouse gas equivalents [4], or about 4.2-8.4% of the total greenhouse gas effect.
Of course, this 33 degree increase in temperature is not caused simply by absorption of radiation by the gases themselves. Much of the 33 degree effect is caused by the Earth's adaptation to higher temperatures, which includes secondary effects such as increased water vapor, cloud formation, and changes in albedo or surface reflectivity caused by melting and aging of snow and ice. Accurately calculating the relative contribution of each of these components presents major difficulties.

Global Warming Potential (GWP)
Traditionally, greenhouse gas levels are presented as dimensionless numbers representing parts per billion (ppb) multiplied by a scaling factor (global warming potential or GWP) that allows their relative efficiency of producing global temperature increases to be compared. For carbon dioxide, this scaling factor is 1.0. The factors for methane and nitrous oxide are 21 and 310, respectively, while sulfur hexafluoride is 23,900 times more effective than carbon dioxide [5]. The GWP from carbon dioxide is primarily due to the position of its absorption bands in the critical longwave infrared region at 2, 3, 5, and 13-17 micrometers.
Methane, nitrous oxide, ozone, CFCs and other miscellaneous gases absorb radiation even more efficiently than carbon dioxide, but are also present at much lower concentrations. Their high GWP results from their molecular structure which makes them absorb strongly and at different wavelengths from water vapor and carbon dioxide. For example, although ozone is usually thought of as an absorber of ultraviolet radiation, it also absorbs longwave infrared at 9.6 micrometers. These gases account for another 1.3% of the natural greenhouse gas effect. The increase in the global energy balance caused by greenhouse gases is called "radiative forcing".
The GWP of a greenhouse gas is the ratio of the time-integrated radiative forcing from 1 kg of the gas in question compared to 1 kg of carbon dioxide. These GWP values are calculated over a 100 year time horizon and take into consideration not only the absorption of radiation at different wavelengths, but also the different atmospheric lifetimes of each gas and secondary effects such as effects on water vapor. For example, methane contributes indirectly to the production of tropospheric ozone and stratospheric water vapor. For some gases, the GWP is too complex to calculate because the gas participates in complex chemical reactions. Most researchers use the GWPs compiled by the World Meteorological Organization (WMO).
Even though most of the so-called greenhouse effect is caused by water vapor, about 1-2 degrees of our current empirically-measured temperature of roughly 288 K (59° F) can be attributed to carbon dioxide. Water vapor at least 99.99% of 'natural' origin, which is to say that no amount of deindustrialization could ever significantly change the amount of water vapor in the atmosphere. Thus, climatologists have concentrated mostly on carbon dioxide and methane.

Carbon Dioxide Levels
Figures from the U.S. Department of Energy show that the pre-industrial baseline of carbon dioxide is 288,000 ppb. The total current carbon dioxide is 368,400 parts per billion, or 0.0368% of the atmosphere.
The ocean and biosphere possess a large buffering capacity, mainly because of carbon dioxide's large solubility in water. Because of this, it is safe to conclude that the anthropogenic component of atmospheric carbon dioxide concentration will continue to remain roughly proportional to the rate of carbon dioxide emissions. In other words, the carbon dioxide buffers are in dynamic equilibrium with atmospheric carbon dioxide and are not in any danger of being saturated, which would allow all the emitted carbon dioxide to go into the atmosphere. This means:
The percentage of emitted carbon dioxide that ends up in the atmosphere can be treated as approximately constant. This percentage is about 50% [6].
The effects of carbon dioxide emissions are not cumulative. That is, lowering carbon dioxide would produce an almost instantaneous reduction (on a climatological scale) in any warming effect that it was producing.
If fossil fuel use increases or decreases, atmospheric carbon dioxide will also increase or decrease proportionately.

Amplification and Dampening
Of course, climate, like weather, is complex, nonlinear, and perhaps even chaotic. Increased solar irradiation can lower the albedo, which would amplify any effect caused by changes in solar flux, making the relation between radiation and temperature greater than linear. Increased temperatures also cause increased evaporation of sea water, which can cause warming because of water's greenhouse effect, and also can affect the radiation flux by creating additional clouds. On the other hand, increased plant growth, especially in the oceans, would tend to extract carbon dioxide from the atmosphere, making the fraction of emitted carbon dioxide that stays in the atmosphere lower. Thus, higher emissions would probably cause a slightly smaller proportion of carbon dioxide to remain in the atmosphere than is currently the case, tending to make the relation less than linear.

Absorption of Infrared Radiation
The arithmetic of absorption of infrared radiation also works to decrease the linearity. Absorption of light follows a logarithmic curve (Figure 1) as the amount of absorbing substance increases. It is generally accepted that the concentration of carbon dioxide in the atmosphere is already high enough to absorb almost all the infrared radiation in the main carbon dioxide absorption bands over a distance of only a few km. Thus, even if the atmosphere were heavily laden with carbon dioxide, it would still only cause an incremental increase in the amount of infrared absorption over current levels. This means that a situation like Venus could not happen here. The atmosphere of Venus is 90 times thicker than Earth's and is 96% carbon dioxide, making the atmospheric carbon dioxide concentration on Venus 300,000 times higher than on Earth. Even so, the high temperatures on Venus are only partially caused by carbon dioxide; a major contributor is the thick bank of clouds containing sulfuric acid [7]. Although these clouds give Venus a high reflectivity in the visible region, the Galileo probe showed that the clouds appear black at infrared wavelengths of 2.3 microns due to strong infrared absorption [8]. The infrared absorption lines by carbon dioxide are also broadened by the high pressure on Venus [9]. Fig.1. Transmitted light is a logarithmic function of concentration. This curve is the familiar Beer's Law.

Very little of the radiation from the sun at the wavelengths at which carbon dioxide absorbs reaches the surface of the Earth directly (see Figure 2) [10]. Similarly, very little of the radiation at these wavelengths that originates at the surface makes it all the way to space. Most of the infrared at these wavelengths is produced by black body radiation from objects that have been heated up by absorbing radiation at shorter wavelengths. This means that even if the carbon dioxide levels increase, it will have little effect on the total amount of infrared radiation that is absorbed from the sun. The main effect would be to trap radiation originating at the surface at lower levels in the atmosphere than before, where it would be slightly more difficult for the heat to be re-radiated back into space. This is the principle on which most of the global warming predictions are based.

[note added 6/10/2006:] Many people do not understand this important concept. To put it more simply, shortwave radiation (such as light and short-wavelength infrared) is not absorbed by CO2 and therefore reaches the earth's surface. At the surface, it is absorbed and then re-radiated at longer wavelengths (as "heat"). Some of this heat radiation is in the carbon dioxide absorption bands. This portion does not make it back to space, but is absorbed by water vapor, CO2 and other gases on its way up. More CO2 or water vapor will cause it to be absorbed at a slightly lower altitude than before. This absorbed energy will be re-emitted by the carbon dioxide molecules at even longer wavelengths (for example, around 30-40 microns). Even though the total amount of absorption is still nearly 100%, the whole process is dynamic. This means it takes a certain amount of time, while other things, such as transitions from night to day, are also happening. Therefore, it is theoretically possible for increases in CO2 to cause increases in surface temperature. The question is, is the amount of warming enough to be significant?

CO2 is more evenly distributed than water, so if CO2 caused warming it would have a proportionately greater effect in areas where there is little water vapor (such as deserts and in very cold regions), while in areas with a lot of water, the effect of CO2 may be insignificant compared to the effect of water vapor. This is one of many factors that mitigate against the idea of a "climate catastrophe."

Fig.2. Absorption of ultraviolet, visible, and infrared radiation by various gases in the atmosphere. Most of the ultraviolet light (below 0.3 microns) is absorbed by ozone (O3) and oxygen (O2). Carbon dioxide has three large absorption bands in the infrared region at about 2.7, 4.3, and 15 microns. Water has several absorption bands in the infrared, and even has some absorption well into the microwave region. There is already sufficient CO2 in the atmosphere to absorb almost all of the radiation from the sun or from the surface of the earth in the principal CO2 absorption bands. (Data from ref. [1], page 93).

The net effect of all these processes is that doubling carbon dioxide would not double the amount of global warming. In fact, the effect of carbon dioxide is roughly logarithmic. Each time carbon dioxide (or some other greenhouse gas) is doubled, the increase in temperature is less than the previous increase. The reason for this is that, eventually, all the longwave radiation that can be absorbed has already been absorbed. It would be analogous to closing more and more shades over the windows of your house on a sunny day -- it soon reaches the point where doubling the number of shades can't make it any darker.

The analogy with a greenhouse would be that the glass in the roof becomes slightly thicker. The effect of warming also depends on the conditions inside the greenhouse. If the greenhouse were full of ice at exactly -0.01 degrees Celsius, making the glass slightly thicker just might be enough to melt all the ice and flood the greenhouse. But if the greenhouse had some regions that were hot and some that were very cold (as the planet Earth does), it would have a very small overall effect.

As an aside, the term "greenhouse effect" is actually a misnomer. In greenhouses, most of the warming that is observed is not caused by carbon dioxide, or by absorption of infrared radiation by the glass as many people think, but by reduction in convection [11].

Linear Climate Projections
From the above numbers, it is easy to calculate, assuming a linear dependence of temperature on greenhouse gas concentrations, that a doubling of atmospheric carbon dioxide would produce an additional warming of (0.042 to 0.084) x 33 = 1.38 to 2.77 degrees centigrade. This is probably an upper limit, because sulfate aerosols, which are typically emitted along with carbon dioxide, tend to counteract the warming effect.

It is important to realize that the original factor of 0.042 to 0.084 represented the incremental fraction of the total global warming, taken as a holistic phenomenon, initiated by carbon dioxide. In other words, in the absence of carbon dioxide, the present average temperature of the Earth after adaptation to the loss would be 1.4-2.7 degrees cooler. This means that the calculation automatically includes the secondary and amplification effects caused by increased water vapor, changes in albedo, and so forth, caused by including the Earth's adaptation to the increment of carbon dioxide.

The linear projection shown here, while obviously simplistic, is a more straightforward argument than those used in climate models, because it does not treat the radiative forcing caused by carbon dioxide separately from the planet's adaptation to it. In other words, we did not just build a model and add carbon dioxide, but instead took numbers that are based on empirical measurements and extended them by a small percentage. If, on the other hand, we had postulated an increase in solar radiation, or if we wished to do an ab initio calculation like those attempted by some climate researchers, it would not be so simple. In this case it would have been necessary to calculate secondary effects like changes in albedo and water vapor. This would require an enormously complex computer model, similar to the models many climatologists have created.

Fig.3. Estimated greenhouse gas-induced global warming plotted against greenhouse gas concentrations expressed as a percentage of current-day values. The black curve is a linear extrapolation calculated from the DOE estimates of total current greenhouse gases. The sharp jump at the right is the data point from one computer model that predicts a nine degree increase from doubling current levels of carbon dioxide. Marked, unphysical deviations from linearity resulting in thermal runaway (red curve) are required to fit this data point with the two known points. Such a strong nonlinear effect is difficult to reconcile with our current understanding of climate.

Our calculation also assumes that the increase in temperature is linearly proportional to the greenhouse gas levels. However, as indicated above, the relationship is not linear, but logarithmic. A plot of temperature vs. gas concentration (expressed as a percentage of current-day levels) would be a convex curve, something like the blue curve in Figure 3. Thus, 1.4-2.7 degrees is an upper bound, and depending on the exact shape of the blue curve, could be an overestimate of the warming effect.

This estimate of 1.4-2.7 degrees is comparable to the estimate of 1.4 degrees associated with the "empiricist" school of the University of Delaware, University of Virginia, and Arizona State University. An increase of 1.4 degrees was also predicted by P.J. Michaels and R.C. Balling using the NCAR Community Climate Model 3 model, after the large increases in projected carbon dioxide in the original paper in which the model was described were replaced with more realistic ones.

Comparison with IPCC projections
These modest increases are quite different from the results of climate models endorsed by the IPCC. Their climate models predict temperature increases from a doubling of carbon dioxide ranging from 3 to as much as 9 degrees! Which is correct?
It goes without saying that the results shown here depend on the accuracy of the original 33 degree estimate and the validity of extrapolating of the existing curve by an additional increment. However, we can check the plausibility of the IPCC's result by asking the following question: Instead of 33 degrees, what number would result if we calculated backwards from the IPCC estimates?

Using the same assumption of linearity, if a 9 degree increase resulted from the above-mentioned increase of greenhouse gas levels, the current greenhouse gas level (which is by definition 100%) would be equivalent to a greenhouse gas-induced temperature increase of at least 107 degrees C. This means the for the 9 degree figure to be correct, the current global temperature would have to be at least 255 + 107 - 273 = 89 degrees centigrade, or 192° Fahrenheit! A model that predicts a current-day temperature well above the highest-ever observed temperature is clearly in need of serious tweaking. Even a 5 degree projection predicts current-day temperatures of 41°C (106°F). These results clearly cannot be reconciled with observations.

In order for the 9 degree estimate to make sense from a physical standpoint, we are forced to draw an exponential curve through the graph above (shown in red) through the three points instead of a straight line. However, this curve creates an even worse result: it predicts a thermal runaway. A thermal runaway is a reaction that suddenly switches from a smooth curve and goes wildly out of control. For example, in an electronic circuit, if a transistor gets too hot, the chemical properties of the silicon can change and its resistance decreases, causing more and more current to flow, which causes it to burn up. Similarly, for the the nine-degree climate model to fit the observations, the curve that we must draw predicts that a 10 or 20% increase in greenhouse gases above their current levels would cause an infinite increase in temperature! Of course, some other factor (such as explosion of the Earth in a supernova-type explosion) would undoubtedly kick in to save us before an infinite temperature could be reached. But even so, it can be seen that an above-linear increase in temperature with increasing gas concentration is not only unphysical, but inconsistent with observations.

In order to prevent absurd conclusions from the IPCC projections, it is necessary to make some additional assumption -- for example, assuming that the dependence of radiative forcing on gas concentration depends critically on the exact percentage of each component of greenhouse gases as a function of altitude, or perhaps that the relationship between gas concentration and temperature is sigmoidal, and levels off at some point above the predicted increase. Yet no physical basis for such a sigmoidicity has been proposed. This means that these projections of extreme climate changes are unlikely to be accurate, or at the very least, worthy of great skepticism.

Although the estimates of global warming made by the IPCC and the predictions of "environmental catastrophe" made by environmental groups have gradually creeping back down as climate models gradually improve, environmentalists still worry that temperatures could increase by as much as 3 to 5 degrees over the next century.
However, as shown above, even a 5 degree increase in temperature would constitute a significant departure from the previous rates of increase. It is clear from Figure 3 that this too would be a marked deviation from the curve. Such strong nonlinear effects, especially when they are in the wrong direction from a physical standpoint, are difficult to reconcile with our current understanding of climate.

Although carbon dioxide is capable of raising the Earth's overall temperature, the IPCC's predictions of catastrophic temperature increases produced by carbon dioxide have been challenged by many scientists. In particular, the importance of water vapor is frequently overlooked by environmental activists and by the media. The above discussion shows that the large temperature increases predicted by many computer models are unphysical and inconsistent with results obtained by basic measurements. Skepticism is warranted when considering computer-generated projections of global warming that cannot even predict existing observations.

[1]. Peixoto, J.P. and Oort, A.H., Physics of Climate Springer, 1992, p. 118.[2]. Thomas, G.E. and Stamnes, K Radiative Transfer in the Atmosphere and Ocean. Cambridge University Press, 1999, p. 441.[3] 95% = Michaels, P.J. and Balling, R.C., The Satanic Gases. Cato Institute, 2000 p.25. 93% =; Secretary General of the International Association for Physical Science in the Ocean.90% = Most current global warming models predict a significant water vapor chain reaction, accounting for as much as 90 percent of the warming; Ian Folkins of Dalhousie University in Nova Scotia98% = Global Warming: The Origin and Nature of the Alleged Scientific Consensus Richard S. Lindzen = Norman J. Macdonald Carbon dioxide is about 5 percent, water vapor 90. [4]. U.S. Climate Action Report 2000, US Environmental Protection Agency, page 38. [5]. Houghton, J.T. et al, eds. Climate Change 1995: The Science of Climate Change (IPCC report), 1996, Cambridge University Press.>[6]. Peixoto, J.P. and Oort, A.H., Physics of Climate Springer, 1992, p. 436.[7].[8].[9]. Ma, Q., and R.H. Tipping, J. Chem. Phys., 96, 8655-8663, 1992.[10]. [note added Feb 15, 2007] This can be easily calculated from the absorption of gaseous carbon dioxide. See Phys. Rev. 41, 291 - 303 (1932) P. E. Martin and E. F. Barker "The Infrared Absorption Spectrum of Carbon Dioxide".
Thomas and Stamnes (ref. 2, page 91) that shows 0% transmittance at 22 km and below for the 15 micron CO2 band. This section discusses the "opaque region" and also gives a very clear discussion of line broadening, which is an additional point that many people are unfamiliar with.
Schneider, Kucerovsky, and Brannen (Appl. Opt. 28:5, 1998) give an absorption coefficient at 9.90 ± 1.49 cm-1 atm-1 for low concentrations of CO2 in a 1-atm nitrogen atmosphere at 4.2 microns. This works out to 376 absorbance units per km for 380 ppm CO2, which is about as close to 100% absorption as you can get. Heinz Hug, a global warming skeptic, measured a similar value (0.03 absorbance units/10 cm for 357 ppm at 15 u) (
[11]. Peixoto, J.P. and Oort, A.H., Physics of Climate Springer, 1992, p. 30. The Satanic Gases. Cato Institute,
2000, p. 36.-->


lpeluso22 said...

Thanks, Pete. I was in an MS program in Cell Biology the last few years and had to stop and read about global warming. I had to understand. Your article makes sense and clears up a lot re CO2 and atmospheric warming. I have questions. I am concerned about the acidification of the oceans by high CO2. I wonder if there are enough other gases (higher absorbers) and reaction products of them to produce additional warming. I wonder what the causes are of the increase in water vapor partial pressure over the oceans and whether the increase is significant. I am concerned about the changes in weather patterns, particularly rainfall, that could come from the 4 degree F rise in temperature. And I am concerned about the fate of the fresh water supply, with the precious aquifer reserves of potable water being used for agriculture and industry resulting in rapid depletion. The danger now is that the new administration will set out to tackle carbon and that this will leave the real problems undealt with until it is actually too late to reverse the life-destructive course. As a Biologist, I know that Life is in trouble. As a Geoscientist and Energy Scientist, I hope to learn why. As a lawyer and citizen, I hope we can act accurately and energetically enough.

Larry Peluso, in California

Anonymous said...

I don't see any mention of amplification due to positive feedbacks. A warming atmosphere increases the evaporation rate, thus adding more water vapor to the atmosphere and amplifying the warming. A warming atmosphere will also result in a decrease in the areal extent of glaciers and sea ice, thus decreasing the average albedo of the Earth.

Anonymous said...

Responding to the comment on Amplification and asking about ocean acidification:

Regarding positive feedback from decreased albedo, etc. and from increased water pressure:

Right. Does the 4 degree C increase account for these factors? Does it account for the increased water vapor which is known to be the main factor in warming?

Also, warming will trigger an acceleration of carbon and methane release as tundra melts and ocean methane crystals may also melt and release gas. Methane is an important factor. Manure yards and other sources of methane and other greenhouse gases may also contribute to warming. And with decreased forest cover, the earth's ability to process more CO2 will decrease.

Beyond the concern over warming, carbon dioxide increases appear to have already half-saturated the ocean CO2 buffer capacity. More and more acidic oceans will harm marine life and that also will decrease CO2 processing capacity, and slow the food production chain.