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==Skepticism about global climate change and its anthropogenic origin==
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Although the national science academies of many countries accept the IPCC's conclusion that future man-made climate change is likely,<ref name="academies"/> there is a minority of skeptical scientists and others who believe that the present climate change, if it exists at all, is not man-made and is unavoidable. These sketics dispute any immediate danger and see no need for large reductions of man-made CO<sub>2</sub> emissions. The dispute will continue because of the difficulty of the underlying science and the uncertainty of the climate data. The latter is acknowledged and accounted for by the IPCC as much as possible.
 
There is a tendency to downplay the number of skeptical scientists or to ignore them. For example, when an FPS (Forum on Physics & Society) editor of the American Physical Society wrote: "There is a considerable presence within the scientific community of people who do not agree with the IPCC conclusion that anthropogenic CO<sub>2</sub> emissions are very probably likely to be primarily responsible for the global warming that has occurred since the Industrial  Revolution",<ref>[http://www.aps.org/units/fps/newsletters/200807/editor.cfm Editor's Comment, Forum on Physics & Society of the American Physical Society, July 2008]</ref> the FPS Executive Committee hastened to declare that his statement does not represent their views.<ref>[http://www.aps.org/units/fps/newsletters/200807/ Forum on Physics & Society of the American Physical Society, July 2008]</ref> Clearly, any suggestion of a "considerable presence" of scientists disagreeing with the IPCC is politically undesirable.
None-the-less, over 400 prominent scientists from more than two dozen countries, testifying before a U.S. Senate committee in 2007, voiced objections to major aspects of the so-called "consensus" on man-made global warming. Many of those scientists were participants in the IPCC.<ref>
[http://epw.senate.gov/public/index.cfm?FuseAction=Files.View&FileStore_id=bba2ebce-6d03-48e4-b83c-44fe321a34fa U. S. Senate Report: Over 400 Prominent Scientists Disputed Man-Made Global Warming Claims in 2007]</ref>.
 
===The complexities and problems of climate change science===
 
All participants in the dispute, between those who agree with the IPPC's conclusions and those who do not agree, recognize that ''climate change'' science involves difficult problems. Some of the skeptical scientists believe that many of those problems are too difficult to be solvable. In the first place, it is an observational science (like astronomy), meaning that experiments  cannot be performed or verify or disprove certain hypotheses.
 
In the second place, the Earth's climate is an extremely complex system, much more complex than physical scientists usually dare to tackle. Most of the physical sciences is based on a [[reductionism|reductionistic approach]], in which systems are reduced to smaller ones that are easier to understand but still possess their essential characteristics. In climate science,  such an approach is impossible because the atmosphere, the oceans, and the land masses are tightly coupled subsystems and consequently the energy and mass exchanges between those three major subsystems of the Earth must be studied simultaneously and cannot be be reduced to separate smaller systems. Further, the electromagnetic radiation balance (i.e., insolation of solar irradiation) between energy absorption and back radiation by the Earth plays a crucial role and cannot be omitted, which means that the Earth's climate system  itself is not a closed system.
 
Third, there exists no encompassing theory, like [[Newton]]'s equations in [[classical mechanics]], that predicts the characteristics of the climate and of which the truth is accepted by all climatologists. Theories are ad-hoc and taken from many different (and not the simplest) areas of applied physics: turbulent and dissipative systems, convective and radiative transport phenomena, non-linear (chaotic) systems and their inherent sensitivity to initial conditions, and so on. Further, there is a paucity of reliable data to evaluate the existing climate models. Hence, even models that try to explain the ''present'' world climate are based on subjective choices open to criticism. The problems are compounded for predictions of  world-wide ''climate changes''. So, it is no surprise that many climate scientists do not have much faith in the ability of climate models to predict the future.<ref>[http://coast.gkss.de/staff/storch/pdf/070511.bray.GKSS.pdf Climate Scientists’ Perceptions of Climate Change Science] Interviews among 558 scientists working in the field of climate change (mainly climatologist and meteorologists) by Dennis Bray and Hans von Storch</ref>
 
Another problem is the use of ''proxy data'' (i.e., indirect data such as tree rings and the isotopic content of arctic and antarctic ice) used to determine past temperatures of the Earth. Proxy data are used to construct historical temperature profiles, yielding, for instance, the [[hockey stick model|hockey stick shaped]] graph.<ref> [http://www.caenvirothon.com/Resources/Mann,%20et%20al.%20Global%20scale%20temp%20patterns.pdf M. E. Mann et al. (1998),  Nature, vol. '''392''', pp. 779-787.] A famous plot of mean temperature over the last 1,000 years which is flat on average from the years 1000 to 1900. The flat part forms the hockey stick's ''shaft''. After 1900, and especiallly after 1980, temperatures appear to shoot up, forming the hockey stick's''blade''.</ref> Some scientists question the reliability of the past temperature profiles based on proxy data and doubt the uniqueness of the present global warming. They argue that the Earth has had warm periods before, without human intervention. They refer to the discovery of Greenland by the Vikings around the year 1000  when Greenland was green, and the era of the dinosaurs when the Earth was green.
 
Other scientist question the validity of the computer models predicting the climate a few decades ahead, referring to the  inability of current computer models to predict the weather for more than 10 days in advance. 
 
The majority of skeptical scientists admit a definite increase of CO<sub>2</sub> in the atmosphere, due to the  growing use of fossil fuels, but question that the increase in cO<sub>2</sub> concentration will lead to a world-wide catastrophe.
 
===Open letter to the UN Secretary-General from skeptical scientists===
During the [[United Nations]] Climate Conference on the Indonesian island of [[Bali]] in December 2007, more than 100 scientists (climatologists, physicists, biologists, meteorologists, statisticians, and others) wrote an open letter to [[Ban Ki-Moon]], the Secretary-General of the United Nations.<ref>[http://www.nationalpost.com/news/story.html?id=164002 Letter to Ban Ki-Moon]</ref> The letter expressed their opinion that "the 2007 UN climate conference [is] taking the World in entirely the wrong direction". They recognized that a climate change is occurring but they state that it is a natural phenomenon which is impossible to stop and express their doubts that "it is possible to significantly alter global climate through cuts in human greenhouse gas emissions."
 
The open letter casts doubt on the procedure of writing the IPCC  Assessment Reports of 2001 and 2007. The letter stated that "the reports are prepared  by a relatively small core writing team with the final drafts approved line-by-line by ­government representatives". It further states that "the great ­majority of IPCC contributors and ­reviewers, and the tens of thousands of other scientists who are qualified to comment on these matters, are not involved in the preparation of these documents. The summaries therefore cannot properly be represented as a consensus view among experts".
 
===Climate sensitivity===
In a contribution to the APS Forum on Physics & Society of July 2008,<ref>[http://www.aps.org/units/fps/newsletters/200807/monckton.cfm Christopher Monckton of Brenchley, Forum on Physics & Society of the American Physical Society, July 2008]</ref>  [[Christopher Monckton, 3rd Viscount Monckton of Brenchley |Christopher Monckton]], a known critic of anthropogenic causes of global warming, takes issue with the 2007 IPCC report.  Moncktons' contribution  will now be given some attention, because it follows closely the arguments of the IPCC report and yet comes to different conclusions.  A review of Monckton's criticism, which is mainly directed at climate sensitivity, gives us a chance to delve deeper into IPCC's scientific reasonings and to  give a discussion that is more quantitative than presented earlier in this article. The main purpose  of this section is to illustrate that, even when the very same physical effects are accounted for, different estimates of the same parameters lead to different conclusions. Of course, the IPCC is very much aware of this and discusses likelihoods of parameter values wherever possible, but still it is of interest to see how different parameter choices work out in practice. We present Monckton's and IPCC's values vis-à-vis, but we  do not phrase opinions about which of the opposing parties is likely to be correct.
 
Monckton begins with presenting  data  plots showing that the globally averaged land and sea surface absolute temperature (''T''<sub>S</sub>) has not risen since 1998<ref> Opponents of Monckton point out that 1998 is not a good reference year because it was unusually warm with the strongest El Nino on record.</ref>  and may have fallen since late 2001, in contrast to the prediction of further rapid warming by the IPCC. 
 
After having made this introductory point, he  directs his criticism at the value of [[climate sensitivity]] found by the IPCC. The concept of climate sensitivity arose when the IPCC members asked themselves the question how much the temperature on Earth would change by an increase of CO<sub>2</sub> in the atmosphere. To give a quantitative answer, it is necessary to define a reference concentration and a quantitative amount of increase of CO<sub>2</sub>. The IPCC accepted the following formal definition: ''Climate sensitivity is the equilibrium temperature change, <math>\scriptstyle \Delta T_\lambda</math>, in the surface temperature, T<sub>''S''</sub>,  caused by the doubling of the pre-industrial CO<sub>2</sub> concentration.'' That is, as the reference increase in CO<sub>2</sub> they take a doubling with respect to the concentration at the  start of the [[Industrial Revolution]] (1750).
 
The IPCC gives an estimate of  3.26 °C for climate sensitivity,  the Earth's temperature response to a possible CO<sub>2</sub> concentration doubling since 1750. In contrast, Monckton gives detailed arguments that 0.58 °C is the more reliable value.
 
The concept of [[radiative forcing]] plays an important role in the discussion of climate sensitivity. Basically, this is the gross amount of solar radiation absorbed by  CO<sub>2</sub> in the atmosphere. As for the climate sensitivity, it is more expedient to give a relative value, &Delta;F, i.e., an increase or decrease in absorption, rather than the absolute value ''F'' of the absorption  itself. The IPCC assumes a logarithmic dependence on concentration and relates the concentration ''C'' of CO<sub>2</sub> in the atmosphere  to radiative forcing, &Delta;F, by several formulas, the following being the simplest,
:<math> \scriptstyle
\Delta F_\mathrm{CO_2} = 5.35 \, \ln(C/C_0), \qquad\qquad\qquad\qquad(1)
</math>
where  C<sub>0</sub> is the CO<sub>2</sub> concentration before the Industrial Revolution.
The factor 5.35 has dimension W/m<sup>2</sup> (solar energy  absorbed per second per square meter by carbondioxide) and plays a pivotal role in the discussion. Note that &Delta;''F''<sub>CO<sub>2</sub></sub>  represents  a ''gross'' absorption: back radiation of the Earth into space and feedback effects (evaporation of water, etc., see earlier in this article) are not yet included.
 
By means of equation (1)  changes in CO<sub>2</sub> concentration can be expressed in the unit of &Delta;''F''<sub>CO<sub>2</sub></sub> (W/m<sup>2</sup>).  At this point Monckton remarks that at 1990 the total &Delta;F<sub>CO<sub>2</sub></sub> was ~27 W/m<sup>2</sup> and that from 1995-2005, the CO<sub>2</sub> concentration rose  from 360 to 378 W/m<sup>2</sup>, with a consequent increase in radiative forcing of  0.26 W/m<sup>2</sup>, which is less than  1% of the 1990 value of ~27 W/m<sup>2</sup>. The 2007 IPCC report states:  "The CO<sub>2</sub> radiative forcing increased by 20% in the last 10 years (1995-2005)".  Monckton, noticing that the true value is one-twentieth of the value given by the IPCC, states:
:The absence of any definition of radiative forcing in the 2007 IPCC Summary, led many to believe that the effect of CO<sub>2</sub> on ''T''<sub>S</sub>  had increased by 20% in 10 years. The IPCC – despite requests for correction – retained this confusing statement in its report.
 
By equation (1) a doubling of CO<sub>2</sub> concentration gives  a radiative forcing of  <math>\scriptstyle \Delta F_{2x}</math> = 5.35 ln2 = 3.71  W/m<sup>2</sup>.  When this value is corrected for  aerosols etc., it becomes slightly smaller  <math>\scriptstyle \Delta F_{2x}</math> = 3.405 W/m<sup>2</sup> [see Table 1 in Monckton (2008)].
 
In his explanation of the origin of the factor 5.35 in equation (1), Monckton shows  plots of different models  considered by the IPCC for relative warming rates of the atmosphere as a function of altitude and latitude. All these plots show  a strong dependence of warming rate on altitude and in particular they exhibit a tropical mid-troposphere "hot-spot".  Monckton argues that observations from satellites and by  radiosondes do not show this hot-spot: they show that not only absolute temperatures but also warming rates decline with altitude. Therefore he concludes: "Since the great majority of the incoming solar radiation incident upon the Earth strikes the tropics, any reduction in tropical radiative forcing has a disproportionate effect on mean global forcings. On the basis of Lindzen (2007),<ref>R.S. Lindzen, ''Taking greenhouse warming seriously.'' Energy & Environment vol. '''18''' pp. 937-950 (2007)</ref> the anthropogenic radiative forcing as established is divided by 3 to take account of the observed failure of the tropical mid-troposphere to warm as projected by the models". Accepting the corrected value of 3.405 he arrives at a readjusted value of radiative forcing:  <math>\scriptstyle \Delta F_{2x}</math> = 1.135 W/m<sup>2</sup>. Hence, the allegedly observed absence of hot-spots in the troposphere gives a diminishing of IPCC's climate sensitivity (predicted temperature change) by a factor 3.
 
Obviously a certain amount of radiation is transmitted back: the Earth is a source of [[blackbody radiation]]. Deviating in a non-essential way from the IPCC report, Monckton introduces a parameter &kappa; that gives the fraction of the absorbed solar radiation  that is re-emitted by the Earth in the form of blackbody (infra-red) radiation. The parameter &kappa; is referred to as ''climate sensitivity parameter'' and is introduced as a multiplying factor. If, e.g., &kappa; = 0.3, it means that effectively 70% of the insolation is radiated back into space. Some basic laws of physics state that the energy content of black-body radiation depends on absolute temperature,  meaning that &kappa;  is a function of absolute  temperature [see equation (21) of Monckton].
 
To give an estimate of the value of &kappa; one may note that at the Earth’s surface, ''T''<sub>S</sub> &asymp; 288 K (kelvin) &asymp; 15 °C, implying the surface value  &kappa;<sub>S</sub> = 0.185 K·m<sup>2</sup>/W. At the characteristic altitude at which incoming and outgoing radiative fluxes balance, the temperature ''T''<sub>C</sub> &asymp; 254 K &asymp; &minus;19 °C, giving &kappa;<sub>C</sub> = 0.269 K·m<sup>2</sup>/W. Monckton then writes:  "The IPCC’s value for &kappa; is dependent upon temperature at the surface and radiant-energy flux at the tropopause, so that its implicit value &kappa; &asymp; 0.313 K·m<sup>2</sup>/W is considerably higher than either &kappa;<sub>S</sub> or &kappa;<sub>C</sub>". Then some papers  quoted by the IPCC are mentioned by Monckton and he continues:  "None of these papers provides any theoretical or empirical justification for a value as high as the &kappa; &asymp; 0.313 K·m<sup>2</sup>/W chosen by the IPCC".
 
Monckton then proceeds to give an alternative estimate of &kappa;, but since he needs the feedback factor ''f'' for this, we digress and consider feedback first.
 
The effect of solar absorption is strengthened by feedback mechanisms, such as water evaporation, etc., see earlier in this article. To account for these effects the radiative forcing is multiplied by a dimensionless feedback factor ''f'' > 1.  Typical values of ''f'' are 2.095 or 3.077 (roughly doubling or tripling the effect of the solar absorption, as estimated by Monckton and the IPCC, respectively).
 
The following equation for ''f'' is presented  in the IPCC report:
:<math>
f = \frac{1}{(1 - b\kappa)}, \qquad\qquad\qquad\qquad\qquad(2)
</math>
where ''b'' is the sum of all climate-relevant temperature feedbacks.  Equation (2) is taken from linear feedbacks  for electronic circuits.<ref>{{cite book|author=Hendrick W. Bode|title=Network analysis and feedback amplifier design|edition=1st Edition|publisher=D. Van Nostrand Inc.|year=1945 |id=OCLC No. 1692825}}</ref> Obviously, the value of ''f'' is as important as the values of <math>\scriptstyle \Delta F_{2x}</math> and &kappa;.  Monckton observes that equation (2) is of "questionable utility because it was not designed to model feedbacks in non-linear objects such as the climate".
 
Equation (2) gives a singularity (infinite value) for ''f'' and  a corresponding blow up  for the climate sensitivity  <math>\scriptstyle \Delta T_{\lambda}</math>, when ''b'' = 1/&kappa; = 1/0.313 = 3.19 W/(m<sup>2</sup>·K). (Note that  0.313 is IPCC's implicit value  for &kappa;.)  The IPCC estimates an upper limit ''b''<sub>max</sub> = 3.38 W/(m<sup>2</sup>·K), which is close to the singularity. Monckton argues that it is very unlikely that ''b'' will exceed the value 3.19 W/(m<sup>2</sup>·K), because of its runaway temperature effect that even not has occurred in the Cambrian atmosphere. During that period the CO<sub>2</sub> concentration approached 20 times today’s,  with an inferred mean global surface temperature no more than 7 °C higher than today’s. He adds that "a runaway greenhouse effect would occur even in today’s climate when ''b'' &ge;  3.2 W/(m<sup>2</sup>·K),  but has not occurred"  and:  "The IPCC’s high-end estimates of the magnitude of individual temperature feedbacks are very likely to be excessive, implying that its central estimates are also likely to be excessive".  After a few more critical comments Monckton concludes that it is "prudent and conservative" to restore ''f'' to the 50 % lower value ''f'' &asymp; 2.08 that is implicit in the 2001 IPCC report. He  adjusts its value a little to maintain consistency with his earlier equations and proposes the value ''f'' = 2.095.
 
After this digression to the feedback, we return to the climate sensitivity parameter.
The value of &kappa; cannot be directly observed. In order to obtain an empirical estimate, Monckton rewrites &kappa; as
:<math>
\kappa = \frac{\Delta T_\lambda}{\Delta F_{2x} + b\,\Delta T_\lambda} \qquad\qquad\qquad\qquad(3)
</math>
by means of equation (2).
Now, &kappa; can be computed by equation (3), provided the three parameters, appearing in its right hand side, over a given period are known. Monckton compares the years 1980 and 2005 giving a spread of a quarter of a century.  After discussing  his choices for these parameters, Monckton arrives at &kappa; = 0.242 K·m<sup>2</sup>/W. This value is bracketed by the values deduced from atmospheric temperatures: &kappa;<sub>S</sub> = 0.185 and &kappa;<sub>C</sub> = 0.269 K·m<sup>2</sup>/W, which adds to its credibility.
 
====Conclusion about climate sensitivity====
Following Monckton and slightly deviating from the IPCC, we wrote implicitly the climate sensitivity as a product
:<math>  \scriptstyle
\Delta T_\lambda = \Delta F_{2x} \cdot \kappa\cdot f .
</math>
The climate sensitivity, from the 2007 IPCC parameters that were discussed above,  is:
:<math>  \scriptstyle
\Delta T_\lambda = 3.405 \times 0.313 \times 3.077 = 3.28\,\, ^0\mathrm{C}
</math>.
The IPCC (2007) reports<ref>[http://www.ipcc.ch/pdf/assessment-report/ar4/syr/ar4_syr.pdf Climate Change 2007: Synthesis Report] (p. 38; pdf-page 16)</ref> a likely range of <math>\scriptstyle \Delta T_{\lambda}</math> of 2.0 to 4.5 ºC, with a  best estimate of about 3 °C, demonstrating that Monckton has faithfully replicated IPCC’s method with IPCC's parameters. The IPCC report adds that a value of less than 1.5 ºC is very unlikely (probability less than 10%).
 
Using his own revised values, Monckton gives the following final estimate for the climate sensitivity
:<math> \scriptstyle
\Delta T_\lambda = 1.135 \times 0.242 \times 2.095 = 0.58\,\, ^0\mathrm{C},
</math>
which is in the range considered to be very unlikely by the IPCC.
Monckton concludes:
:If this equation is correct, the IPCC’s estimates of climate sensitivity must have been very much exaggerated. There may, therefore, be a good reason why, contrary to the projections of the models on which the IPCC relies, temperatures have not risen for a decade and have been falling since the phase-transition in global temperature trends that occurred in late 2001. Perhaps real-world climate sensitivity is very much below the IPCC’s estimates. Perhaps, therefore, there is no "climate crisis" at all. At present, then, in policy terms there is no case for doing anything. The correct policy approach to a non-problem is to have the courage to do nothing.
 
Since Monckton includes faithfully the very same physical effects as the IPCC, but differs in well-argued choices of parameters, this discussion of climate sensitivity illustrates that serious workers can have different interpretations of the same observations on climate.

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