science notes
mar 17, 2003 (last updated dec 19, 2009)
Cold Facts on Global Warming
hat 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
estimate 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 1.76±0.27 degrees Celsius. This
result contrasts with the results of the IPCC's climate models, whose projections are shown to be
unrealistically high. Even though global warming has become mostly an academic concern now that the
climate has moved into a cooling phase [24], it's still important to understand what is and is not factual about
the climate.
The Greenhouse Effect
Fig. 1. Theory of global warming.
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, many sources place it between 90 and 95% of the
warming effect, or about 30-31 of the 33 degrees [3, 25]. 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.
Cold Facts on Global Warming
Cold Facts on Global Warming 1
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.
The theory of global warming is shown in Fig. 1. Infrared radiation comes from two sources: the sun and the
earth's surface. CO2 absorbs some of the infrared radiation and re-emits it in a random direction. If there is
more CO2, the radiation is absorbed closer to the source. For radiation from the sun, this theory predicts that
increased CO2 would cause cooling in the upper atmosphere and warming in the lower atmosphere.
Thermometer measurements show that the lower atmosphere was warming between about 1906 and 1944 and
between about 1976 and 1998, and either constant or cooling at other times. However, the validity of the
temperature figures is hotly disputed on both sides because the issue is highly political.
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 microns.
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 microns. 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. However, in the past few years, a few climatologists have started
talking about anthropogenic increases in atmospheric water vapor [17]. This validates suspicions that, if
environmentalists get their way with CO2, a campaign to force us to reduce water vapor could well be next.
Carbon Dioxide Levels
Cold Facts on Global Warming
The Greenhouse Effect 2
The Carbon Dioxide - Bicarbonate Equilibrium
CO2 dissolves rapidly in water, and reacts with water to form carbonic acid, which rapidly ionizes to form
bicarbonate and carbonate. Dissolved CO2 causes water to become slightly acidic; the current atmospheric
levels of CO2 are sufficient, in the absence of other factors, to cause pure water to have a pH of 5.7, which is
roughly the same pH as normal rain. However, the oceans contain many other pH buffers, including borate,
phosphate, and silicate, which tend to counteract this effect, while acid rain increases it. The pH of sea water
today is typically between 7.36 and 8.4, which is slightly basic.
Living cells contain the enzyme carbonic anhydrase, which greatly accelerates the reaction in both directions,
helping cells to get rid of excess CO2. Bicarbonate is also sequestered by plants and animals to form calcium
carbonate. The vast majority of the earth's carbon is locked in the form of limestone and other carbonate
rocks.
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 for any conceivable rate of human emission. 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]. However, the buffering capacity of the
oceans is enormous. The oceans currently contain about 50 times as much CO2 as the atmosphere
[20].
•
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.
•
Comment added 1/5/2008:
This last point has been misinterpreted by some commentators. To clarify, this means that if we were to stop
emitting carbon dioxide, the CO2 levels in the atmosphere would rapidly return to pre-industrial levels.
Geologists tell us that the residence time of CO2 in the atmosphere is on the order of five to ten years [23]. In
contrast, the IPCC says it is 50-200 years. Whatever the actual number, there is no question that emitting CO2
will cause it to accumulate over short periods. But other processes, such as sequestration, also work against it,
causing the levels to decrease rapidly over time.
This fact is the very basis of the effort among global warming advocates to lower CO2 emissions. Indeed, if
this were not true, there would be no possible benefit to reducing CO2 emissions, as CO2 levels would ratchet
up indefinitely, whether by natural or artificial means, without limit.
Cold Facts on Global Warming
Carbon Dioxide Levels 3
Amplification and Dampening
Of course, climate, like weather, is complex, nonlinear, and perhaps even chaotic. Increased solar irradiation
can lower the surface albedo (reflectivity), which could amplify any effect caused by changes in solar flux,
making the relation between radiation and temperature greater than linear. A change in albedo can occur
through several factors: (1) at the edges of snow/ice cover, where snow and ice cover bare ground or
vegetation for only part of the year; (2) as ice cover ages, its reflectivity can change; and (3) dust and dirt can
land on top of the ice, increasing absorption of light.
Increased temperatures also cause increased evaporation of sea water, which can cause warming because of
water's greenhouse effect, and also can by creating additional clouds, which reflect more radiation into space.
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
Fig.2. Transmitted light is a logarithmic function of concentration. This curve is the familiar Beer's Law.
The arithmetic of absorption of infrared radiation also works to decrease the linearity. Absorption of light
follows a logarithmic curve (Fig. 2) 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]. Thus, Venus's high
temperature might be entirely explainable by direct absorption of incident light, rather than by any greenhouse
effect. The infrared absorption lines by carbon dioxide are also broadened by the high pressure on Venus [9],
making any comparison with Earth invalid.
Cold Facts on Global Warming
Amplification and Dampening 4
Very little of the radiation from the sun at the wavelengths at which carbon dioxide absorbs reaches the
surface of the Earth directly (see Fig. 3) [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 9/30/2008:
Several readers have commented on the use of Beer's law here. I am not implying that we can use Beer's law
to calculate climate changes. As one reader pointed out, Beer's law only applies to monochromatic light (light
whose wavelength is narrow compared to the absorption peak). This reader writes:
What matters for global warming is that, as greenhouse gas concentrations go up, more and
more IR wavelengths get captured completely ("saturated absorption"). The relationship at
every wavelength is exponential, but that doesn't matter. What matters is the distribution of
absorption coefficients across the spectrum (weighted by 255K black body radiation).
Greenhouse gas emissions just recruit more and more wavelengths into saturation.
Of course, this is somewhat of an oversimplification, because a spectrophotometer never measures a single
wavelength; it always measures a band of finite width. Across that band, you always have a logarithmic
function. What this reader is actually saying is that if the concentration increases, those wavelengths at the
edges of the absorption band will absorb more energy over a given distance.
As another reader pointed out, Beer's law was derived for a single beam of light going through a gas or
solution for which the reemitted radiation does not enter the detector. Therefore, Beer's law will not fit the
situation precisely, but there is general agreement that the curve is approximately logarithmic in shape.
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 [13] 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 energy will be absorbed and re-emitted by the carbon dioxide molecules.
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 (in terms of its effect on local temperature) compared to
the effect of water vapor. This is one of many factors that mitigate against the idea of a "climate catastrophe."
[16]
Cold Facts on Global Warming
Absorption of Infrared Radiation 5
Fig.3. 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; original data are from
Howard et al [21] and Goody [22]).
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 the same as 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.
Another way of looking at it is by thinking of adding blankets to your bed on a cold night: if you have no
blankets, adding one will have a big effect. If you have a thousand blankets, adding another thousand will
have an unmeasurably small effect.
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
Cold Facts on Global Warming
Absorption of Infrared Radiation 6
think, but by reduction in convection [11].
What does 'saturation' mean?
Many people seem to be confused about the "saturation" argument. It's easy to calculate, using the known
extinction coefficients [10], that 99% of the radiation in the CO2 absorption bands is absorbed within only a
few tens to hundreds of meters of the source. These coefficients are derived from measurements in modern,
high-resolution spectrometers. But strong absorption is also found even with older, lower-resolution
instruments. So what does this mean? Is the global warming theory false? Or should older measurements not
be trusted? Here is what it means:
The "saturation" argument does not mean that global warming doesn't occur. What saturation tells us
is that exponentially higher levels of CO2 would be needed to produce a linear increase in absorption,
and hence temperature. This is basic physics. Beer's law has not been repealed.
1.
Some people have gotten the idea that water vapor, which is mainly present at lower altitudes, is
somehow necessary for the CO2 to absorb infrared radiation, and that therefore at higher altitudes,
CO2 is not anywhere near saturation. This is not true. The presence or absence of water vapor has no
bearing on whether radiation is absorbed by CO2. That is because, for all practical purposes, the
absorption bands of H2O and CO2 important for warming are different. (If they weren't, CO2
absorption would be so insignificant compared to water vapor that it wouldn't be a potential problem,
and we wouldn't be having this discussion.)
2.
CO2 is very nearly homogeneous throughout the atmosphere, so its concentration (as a percentage of
the total) is about the same at all altitudes. Although the pressure is lower at high altitudes, there is
also a much greater volume. That is why the ozone layer, which is around 30-90 km in altitude, is still
able to absorb almost all of the shortwave UV, even though its concentration is only 8-12 ppm. So the
importance of low concentrations of gases should not be underestimated. But water vapor is a red
herring: it has essentially no effect on what CO2 does. Where water vapor becomes important is in the
earth's response to CO2.
3.
Some people also think that line broadening of the CO2 absorption lines by pressure, water vapor, or
temperature provides an escape from the saturation dilemma. But in line broadening, the absorbance
is peak is only smeared out; the total amount of energy absorbed is not affected. For the same reason,
measurements with lower-resolution spectrometers, which slightly smear out the absorption lines, are
still valid.
4.
Saturation does not tell us whether CO2 can raise the atmospheric temperature, but it gives us a powerful clue
about the shape of the curve of temperature vs. concentration.
Calculating the actual temperature increase
So, what is the actual increase? Interestingly enough, that is easy to estimate--and without resorting to
complex computer models.
Because a linear increase in temperature requires an exponential increase in carbon dioxide (thanks to the
physics of radiation absorption described above), we know that the next two-fold increase in CO2 will
produce exactly the same temperature increase as the previous two-fold increase. Although we haven't had a
two-fold increase yet, it is easy to calculate from the observed values what to expect.
Between 1900 and 2000, atmospheric CO2 increased from 295 to 365 ppm, while temperatures increased
about 0.57 degrees C (using the value cited by Al Gore and others). It is simple to calculate the proportionality
constant (call it 'k') between the observed increase in CO2 and the observed temperature increase:
Cold Facts on Global Warming
What does 'saturation' mean? 7
Note added 2/12/2009: Is 'k' a constant?
Note that k takes into account all of the Earth's adaptation to the increased carbon dioxide: changes in
reflectivity due to changing ice cover, changes in cloud cover, and so on. Some might still argue, however,
that k is not a constant, but decreases with temperature. But what could cause k to decrease? All climatological
factors have already been ruled out. In order for k to be a variable, the laws of absorption of radiation would
have to be change with temperature in a fundamentally new way, and not by a small amount: k would have to
decrease by 37% to raise ∆T by even one degree. No physical process in any complex system like the
atmosphere changes this dramatically with temperature. Spectroscopists have been studying light absorption
for over 340 years. One of them would certainly have noticed such a huge temperature sensitivity by now.
Also consider that the temperature increase is only 1-2 degrees C. This is much smaller than the seasonal
variation, the variation between different locations on the Earth, or even the variation between day and night
temperatures. The laws of physics don't change when you go from New York to New Jersey. Questioning
whether k is a constant is grasping at straws. The question people should be asking is: is k equal to zero?
This shows that doubling CO2 over its current values should increase the earth's temperature by about 1.85
degrees C. Doubling it again would raise the temperature another 1.85 degrees C. Since these numbers are
based on actual measurements, not models, they include the effects of amplification, if we make the
reasonable assumption that the same amplification mechanisms that occurred previously will also occur in a
world that is two degrees warmer.
If we want to include other greenhouse gases, such as methane, in the calculation, we need to use the
"effective" CO2 concentrations instead. These effective CO2 numbers are less solid than the CO2-only
numbers, but the best estimates are that effective CO2 increased from 305 to about 450 ppm during the 20th
century[12]. Using these numbers, k becomes 0.6823 and the predicted ∆T becomes 1.02 degrees.
These estimates assume that the correlation between global temperature and carbon dioxide is causal in
nature. This remains to be proved. Therefore, the 1.02 and 1.85 degree estimates should also be regarded as
upper limits.
Refinements to the estimate
Unfortunately, the above calculations slightly overestimate the degree of warming, because they allow the
temperature to rise indefinitely. At very high CO2 levels, self-absorption would become a limiting factor. A
more accurate calculation is shown below.
A reader named Ted Ladewski made an interesting suggestion: use the 255K zero-greenhouse gas data point,
where there is zero CO2, as a data point, and fit the other points to a smooth curve. To maximize the accuracy
of the estimate, we will only use global CO2 and temperature values between 1900 and 2000 [14], about
which there is relatively little dispute, and ignore estimates of prehistoric values, which could be more
affected by changes in solar flux and other factors. This gives a total of 102 data points. These points are
shown in blue in the figure below.
Including the CO2 = 0 data point severely constrains the shape of the curve (and, interestingly, effectively
rules out any sort of hockey stick-shaped curve). It is also clear that some sort of monotonically-increasing
Cold Facts on Global Warming
Calculating the actual temperature increase 8
curve, and not a straight line, has to be used. The best fit was obtained with a hyperbola. If the 102 data points
are fitted to a hyperbola, we obtain 288.92 ±0.27K (±1 SD) for 736 ppm CO2 (red line).
The present-day value is taken as the average of the global mean temperatures between 1980 and 2000, or
287.17K. If the above estimate is correct, this means that the temperature would increase by 1.76 ±0.27°C
above the present-day value when CO2 levels double their present levels. This is very close to the 1.85°C
calculated above.
Stated differently, doubling CO2 from its pre-industrial value would increase the temperature about 1.2
degrees Celsius.
Fig. 4.
However, there is a problem with this method. The 255K data point is not just zero CO2, it is zero water vapor
as well. In reality, there would always be some water vapor present, even if there were no CO2. This means
that the actual temperature for zero CO2 would be higher than 255K, which would change the shape of the
curve. For example, if the CO2=0 value was 271 (halfway between 255 and the current temperature), the
prediction changes to 288.55K, or about a 1.39 degree increase for doubling of CO2. This can be seen in the
blue curve (see enlarged graph below). The result is not much different than the 1.76, but the important point
is that as the estimates become more realistic, the predicted temperature does not increase, but decreases
slightly.
Cold Facts on Global Warming
Refinements to the estimate 9
Fig. 5.
Fitting other curves to these data points gives similar results. For example, Ted Ladewski suggested deriving
an exponential curve from Beer's Law. Although there are obvious problems involved in applying Beer's Law
quantitatively to a transparent medium as complex as the atmosphere (as he discusses in greater detail on his
website, http://mysite.du.edu/~etuttle/weather/atmrad.htm#Spec), the equation he recommends is:
where AIo and k are constants, C is the CO2 concentration, and T is temperature. (This is also discussed in
http://www.sjsu.edu/faculty/watkins/GWnonlinear.htm )
Fitting the data to this equation, as shown in the brown curve in the figure above, gives the much lower value
of 287.62±0.07 K (±1 SD), or 0.46±0.08 °C increase above the 1980-2000 mean for a doubling of CO2 from
current values.
Although extrapolating beyond the ends of the data, as is done here and as is done with climate models, is
hazardous, it's clear that both of these curves are significantly lower than a straight linear estimate. The
hyperbola is probably closest to the actual value, because it makes the fewest assumptions about the
underlying physical processes. In any case, both estimates should be regarded as upper limits because, as
mentioned above, they assume that CO2 is the root cause of the observed changes in temperature.
How long will it take to double CO2 levels?
Another issue that people are confused about is the rate of increase of carbon dioxide. Some people think that
CO2 is rising dramatically. This is probably because of graphs like the one below.
Cold Facts on Global Warming
How long will it take to double CO2 levels? 10
Fig. 6.
However, in hard science journals, the graph above would be considered dishonest, because the y-axis starts at
290 instead of zero. This misleads the reader into thinking that CO2 levels have undergone a huge increase
when in fact, CO2 levels have only increased by 23.7% since 1900. When the data are plotted honestly, with
the y axis starting at zero, the true scope of the change becomes clear.
Cold Facts on Global Warming
How long will it take to double CO2 levels? 11
Fig. 7.
According to the US Department of Energy, about 14.8% of the total CO2 is man-made. The remainder is
caused by natural forces, such as volcanoes and forest fires [25].
At the current rate of increase, CO2 will not double its current level until 2255.
Cold Facts on Global Warming
How long will it take to double CO2 levels? 12
Fig. 8.
Some climatologists, making assumptions about ever-increasing rates of carbon dioxide production, assert
that the doubling will occur within a few decades instead of a few centuries. However, they are doing
sociology, not climatology. They are assuming that fossil fuel consumption will increase drastically over
current levels. This is very unlikely. The only honest way to estimate the change of CO2 levels is to make
predictions based on what is happening now, not what might happen in some hypothetical future society;
otherwise, we are merely inflating our predictions by indulging in speculation about future social trends.
Many people have used tricks like these to exaggerate the amount of global warming, and this has made it into
a political issue. Most people would have great difficulty feeling an increase of 0.6 degrees Celsius. Any
effects of such a small change would be slow and subtle. In general, if you are able to see or feel some
change, that means it is almost certainly not caused by CO2-induced global warming.
Secondary effects
What about secondary effects, such as ice melting, changes in albedo, and so forth? Doesn't this increase the
predicted temperature beyond the 1.39 to 1.76 degree estimate?
In short, no. Because these calculations are based on observed measurements, they automatically take into
account all of the earth's responses. Whatever way the climate adapted to past CO2 increases, whether through
melting, changes in albedo, or other effects, is already reflected in the measured temperature, and therefore it
will also be reflected in the prediction. This is because the prediction is based on an extrapolation of past
measurements that were taken after the earth adapted to the CO2 increase.
In order to get higher temperatures than those predicted above, it would be necessary to assume that a small
increase in warming causes a large change in the amplification effect that had never occurred before. In other
words, the "rules of the game" would have to drastically and abruptly change in a fundamentally new way--in
response to an increase of only one or two degrees. Such changes do not occur in the real world--only in
Cold Facts on Global Warming
Secondary effects 13
computer models. (If these so-called "tipping points" existed, random, day-to-day, and seasonal variability
would have pushed us past them a long time ago.)
This is what makes the "empirical" method superior to all the computer models, as sophisticated as they may
be. The empirical model just looks at what's happening and makes a reasonable extrapolation, with very few
prior assumptions. The only drawback of the empirical method is that it can only predict an upper limit,
because it does make one big assumption: that correlation implies causality. Therefore, although the actual
warming cannot be greater than the predicted estimate, it could be considerably less.
Masking
Some climatologists may object to the foregoing analysis, pointing out that the effects of an increase in CO2
could be masked by sulfate aerosols or other factors. For example, the eruption of Mount Pinatubo in 1991
released large amounts of volcanic aerosols that may have been responsible for a brief global cooling [18].
However, later studies showed that water vapor feedback was necessary to account for this effect [19].
Applied to global warming, the reasoning is that human sulfate emissions might "mask" warming by cooling
the atmosphere. In the future, they say, sulfate emissions might decrease while CO2 remains constant, and the
true global warming would be revealed.
The problem here is that trying to account for sulfates drags us into the morass of modeling of social trends. It
is much more reasonable to assume that, as industry shifts production to developing countries and people use
more coal and high-sulfur oil to replace dwindling supplies, that sulfate emissions will greatly increase.
Additionally, sulfates are only one factor. Many other factors, even including such things as cosmic rays, have
been shown to have potential effects on climate. Some of these hypothetical effects would cause warming and
some would cause cooling. We need to focus on what can be measured directly. The only issue is whether
CO2 is a problem. To add or subtract these myriad hypothetical effects, and claim that the actual amount of
warming that is occurring is different from the warming that can be observed, only serves to take climatology
that much closer to metaphysics.
One reader pointed out a similar factor that is sometimes mentioned: the heat absorbing capacity of the
oceans. Water has 4.13 times the heat capacity of air on a weight basis at 25°C (2.58 times on a molar basis).
The oceans contain 273 times as much mass as the atmosphere, and the top few meters alone can store as
much heat energy as the entire atmosphere. Thus, much of the extra heat is undoubtedly going into the oceans.
But what does this really mean? If the oceans masked all the warming by absorbing the heat, we would have
to multiply the time scale by about 1128 before we see the real warming. That means warming that we
thought would occur over a 250-year time period would actually take 250×1128 = 282,000 years. By then,
humans will almost certainly be getting their energy from some other source besides combustion of
hydrocarbons. And then there is the earth's crust, which can absorb additional heat over a scale of billions of
years.
Linear Climate Projections
An alternative way of calculating future temperature increases is to consider the fraction of warming that is
caused by CO2. To do this, we cannot just use the fraction of radiation that is absorbed by CO2, because that
does not take feedback processes into account.
As a first step, let us suppose that temperature increases linearly with greenhouse gas concentrations. From the
above numbers, it is easy to calculate 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 the temperature change
one would expect that if CO2 doubles over its current levels.
Cold Facts on Global Warming
Masking 14
It is important to realize that the original factor of 0.042 to 0.084 used in these calculations represents the
incremental fraction of the total global warming, taken as a holistic phenomenon, initiated by carbon dioxide.
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.
Fig. 9. 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.
However, our results are based on the assumption that the increase in temperature is linearly proportional to
the greenhouse gas levels. This is not true. The relationship is not linear, but logarithmic. If we plot
temperature vs. gas concentration (expressed as a percentage of current-day levels), we obtain a convex curve,
something like the blue curve in Fig. 9. Thus, the 1.4-2.7 degrees obtained from our linear estimate is an
upper bound, and depending on the exact shape of the blue curve, could be a large overestimate of the
warming effect.
It goes without saying that the results from this method depend on the accuracy of the 5% estimate (from ref.
[3]) and the validity of extrapolating the existing curve by an additional increment. The exact number is very
difficult to pin down.
Note added 1/5/2008:
Some authors [15] suggest that the percentage of warming attributable to CO2 is not 5%, but is closer to 26%.
Cold Facts on Global Warming
Linear Climate Projections 15
It is easy to show why the 26% estimate (and estimates similar to it) are almost certainly wrong. We know
that the total warming from greenhouse gases is 33K. If 26% of this was from CO2, then doubling CO2 would
raise temperatures by 0.26*33 or 8.6K. Since the 26% estimate is based on total radiation absorbed, and not
the amount of warming, we would have to add secondary feedback effects to this figure. This would double or
even triple the value, giving us a predicted temperature increase of up to 25° C, or a predicted global average
temperature of 40°C (104°F). Balmy!
Whether the exact number is 5% or 9%, because our estimate is based on the percentage of warming, not
percentage of radiation absorbed, that is attributable to CO2, feedbacks in the estimate here are automatically
taken into account. However, because of the large uncertainty about the actual value, the estimate from Fig. 4
(which derives an estimate from extrapolation of current trends) is probably more accurate.
However, we can also check the plausibility of the IPCC's result by asking the following question: 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 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.
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, even a 5 degree increase in temperature over the next century would constitute a significant
departure from the previous rates of increase. It is clear from Fig. 9 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.
Conclusion
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.
Cold Facts on Global Warming
Conclusion 16
References and Notes
[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] Most credible sources place the number at 95%.
95% = Michaels, P.J. and Balling, R.C., The Satanic Gases. Cato Institute, 2000 p.25.
90-95% = http://www.globalwarming.org/node/62
90% = http://www.ncpa.org/press/transcript/globalwm/global2.html Norman J. Macdonald Carbon dioxide is
about 5 percent, water vapor 90.
Here is a paper that gives a different figure:
http://www.atmo.arizona.edu/students/courselinks/spring04/atmo451b/pdf/RadiationBudget.pdf"
S.M. Freidenreich and V. Ramaswamy, Solar Radiation Absorption by Carbon Dioxide, Overlap with Water,
and a Parameterization for General Circulation Models. Journal of Geophysical Research 98(1993):7255-7264
[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. http://www.ipcc.ch/pub/sarsum1.htm
[6]. Peixoto, J.P. and Oort, A.H., Physics of Climate. Springer, 1992, p. 436.
[7]. http://www.aas.org/publications/baas/v33n3/dps2001/354.htm
[8]. http://www2.jpl.nasa.gov/galileo/slides/slide3.html
[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
15µm) ( http://www.john-daly.com/artifact.htm).
[11]. Peixoto, J.P. and Oort, A.H., Physics of Climate. Springer, 1992, p. 30.
[12]. The Satanic Gases, p.36.
[13]. Carbon dioxide is written here as CO2 instead of CO2 because using subscripts messes up the line
spacing in HTML. The Unicode character x2082 (₂ or âµµ), which normally solves this problem, doesn't
display properly in IE.
[14]. The temperature data for these calculations were obtained from
http://lwf.ncdc.noaa.gov/oa/climate/research/anomalies/anomalies.html
[15]. www.realclimate.org
[16]. One reader pointed out that the Arctic region has dew points above freezing during a significant portion
of the year. The average desert atmosphere also has a much higher water content than many people think.
[17]. However, some climatologists have tried to invoke anthropogenic increases in atmospheric water vapor:
see Santer et al., "Identification of human-induced changes in atmospheric moisture content" (Proc Natl Acad
Sci U S A. 2007 Sep 25;104(39):15248-53). Using a computer model, the authors concluded that human
activity is increasing water vapor.
[18]. Radiative Climate Forcing by the Mount Pinatubo Eruption. Minnis P, Harrison EF, Stowe LL, Gibson
GG, Denn FM, Doelling DR, Smith WL Jr. Science. 1993 Mar 5;259(5100):1411-1415.
Cold Facts on Global Warming
References and Notes 17
[19]. Global cooling after the eruption of Mount Pinatubo: a test of climate feedback by water vapor. Soden
BJ, Wetherald RT, Stenchikov GL, Robock A. Science. 2002 Apr 26;296(5568):727-30.
[20]. http://www.aip.org/history/climate/oceans.htm This is a pro-global warming website.
[21]. Howare, J.N., Burch, D.L., Williams, D (1955). Near-infrared transmission through synthetic
atmospheres. Geophys. Res. Papers No. 40, Geophys, Res. Dir., Air Force Cambridge Research Center, 244
pp.
[22]. Goody, R.M. (1964). Atmospheric Radiation: I. Theoretical Basis. Clarendon, Oxford, 436 pp.
[23]. National Academy of Sciences, Climate Research Board (1979). Carbon dioxide and climate: a
scientific assessment. National Academy of Sciences, 72pp.; cited in Ref. 1, p. 434.
[24]. See also: Steven Goddard, Divergence Between GISS and UAH since 1980 and
Oceans are cooling according to NASA (non-technical newspaper article).
[25]. Current Greenhouse Gas Concentrations (updated October, 2000) Carbon Dioxide Information Analysis
Center, U.S. Department of Energy Oak Ridge, Tennessee
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Cold Facts on Global Warming
References and Notes 18