Falsi cation Of arXiv:0707.1161v3 [physics.ao-ph] 11 Sep 2007 The Atmospheric CO2 Greenhouse E ects Within The Frame Of Physics Version 3.0 (September 9, 2007) replaces Version 1.0 (July 7, 2007) and later Gerhard Gerlich Institut fur Mathematische Physik Technische Universitat Carolo-Wilhelmina Mendelssohnstrae 3 D-38106 Braunschweig Federal Republic of Germany g.gerlich@tu-bs.de Ralf D. Tscheuschner Postfach 60 27 62 D-22237 Hamburg Federal Republic of Germany ralfd@na-net.ornl.gov Gerhard Gerlich and Ralf D. Tscheuschner Abstract The atmospheric greenhouse e ect, an idea that authors trace back to the traditional works of Fourier 1824, Tyndall 1861, and Arrhenius 1896, and which is still supported in global climatology, essentially describes a ctitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist. Nevertheless, in almost all texts of global climatology and in a widespread secondary literature it is taken for granted that such mechanism is real and stands on a rm scienti c foundation. In this paper the popular conjecture is analyzed and the underlying physical principles are clari ed. By showing that (a) there are no common physical laws between the warming phenomenon in glass houses and the ctitious atmospheric greenhouse e ects, (b) there are no calculations to determine an average surface temperature of a planet, (c) the frequently mentioned di erence of 33 C is a meaningless number calculated wrongly, (d) the formulas of cavity radiation are used inappropriately, (e) the assumption of a radiative balance is unphysical, (f) thermal conductivity and friction must not be set to zero, the atmospheric greenhouse conjecture is falsi ed. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 3 Contents Abstract 2 1 Introduction 6 1.1 Problembackground ................................ 6 1.2 Thegreenhousee ecthypothesis ......................... 11 1.3 Thispaper...................................... 14 2 The warming mechanism in real greenhouses 16 2.1 RadiationBasics .................................. 16 2.1.1 Introduction ................................. 16 2.1.2 Thein nitesimalspeci cintensity. . . . . . . . . . . . . . . . . . . . . 16 2.1.3 Integration ................................. 18 2.1.4 TheStefan-Boltzmannlaw ......................... 19 2.1.5 Conclusion.................................. 20 2.2 TheSunasablackbodyradiator ......................... 21 2.3 Theradiationonaveryniceday ......................... 23 2.3.1 Thephenomenon .............................. 23 2.3.2 Thesunshine ................................ 23 2.3.3 Theradiationoftheground ........................ 25 2.3.4 Sunshineversusgroundradiation ..................... 27 2.3.5 Conclusion.................................. 29 2.4 HighSchoolExperiments.............................. 29 2.5 ExperimentbyWood ................................ 32 2.6 Glasshousesummary................................ 34 3 The ctitious atmospheric greenhouse e ects 35 3.1 Problemde nition ................................. 35 3.2 Scienti cerrorversusscienti cfraud ....................... 35 3.3 Di erent versions of the atmospheric greenhouse conjecture . . . . . . . . . . . 38 3.3.1 Atmospheric greenhouse e ect after Moller (1973) . . . . . . . . . . . . 38 3.3.2 Atmospheric greenhouse e ect after Meyer's encyclopedia (1974) . . . . 38 3.3.3 Atmospheric greenhouse e ect after Schonwiese (1987) . . . . . . . . . 38 3.3.4 Atmospheric greenhouse e ect after Stichel (1995) . . . . . . . . . . . . 39 3.3.5 Atmospheric greenhouse e ect after Anonymous 1 (1995) . . . . . . . . 39 3.3.6 Atmospheric greenhouse e ect after Anonymous 2 (1995) . . . . . . . . 40 3.3.7 Atmospheric greenhouse e ect after Anonymous 3 (1995) . . . . . . . . 40 3.3.8 Atmospheric greenhouse e ect after German Meteorological Society (1995) 40 Gerhard Gerlich and Ralf D. Tscheuschner 3.3.9 Atmospheric greenhouse e ect after Gral (1996) . . . . . . . . . . . . 41 3.3.10 Atmospheric greenhouse e ect after Ahrens (2001) . . . . . . . . . . . . 41 3.3.11 Atmospheric greenhouse e ect after Dictionary of Geophysics, Astrophysics,andAstronomy(2001) ...................... 42 3.3.12 Atmospheric greenhouse e ect after Encyclopaedia of Astronomy and Astrophysics(2001)............................. 42 3.3.13 Atmospheric greenhouse e ect after Encyclopaedia Britannica Online (2007) .................................... 43 3.3.14 Atmospheric greenhouse e ect after Rahmstorf (2007) . . . . . . . . . . 43 3.3.15 Conclusion.................................. 44 3.4 TheconclusionoftheUSDepartmentofEnergy . . . . . . . . . . . . . . . . . 44 3.5 Absorption/EmissionisnotRe ection ...................... 45 3.5.1 An inconvenient popularization of physics . . . . . . . . . . . . . . . . 45 3.5.2 Re ection .................................. 47 3.5.3 AbsorptionandEmission.......................... 48 3.5.4 Re-emission ................................. 48 3.5.5 TwoapproachesofRadiativeTransfer . . . . . . . . . . . . . . . . . . 49 3.6 The hypotheses of Fourier, Tyndall, and Arrhenius . . . . . . . . . . . . . . . 51 3.6.1 Thetraditionalworks............................ 51 3.6.2 Modernworksofclimatology ....................... 57 3.7 Theassumptionofradiativebalance ....................... 58 3.7.1 Introduction ................................. 58 3.7.2 Anoteon\radiationbalance"diagrams . . . . . . . . . . . . . . . . . 58 3.7.3 Thecaseofpurelyradiativebalance. . . . . . . . . . . . . . . . . . . . 60 3.7.4 The average temperature of a radiation-exposed globe . . . . . . . . . . 62 3.7.5 Non-existence of the natural greenhouse e ect . . . . . . . . . . . . . . 64 3.7.6 Anumericalexample ............................ 65 3.7.7 Non-existenceofaglobaltemperature . . . . . . . . . . . . . . . . . . 66 3.7.8 Therotatingglobe ............................. 67 3.7.9 Theobliquelyrotatingglobe ........................ 68 3.7.10 Theradiatingbulk ............................. 69 3.7.11 ThecomprehensiveworkofSchack .................... 70 3.8 Thermal conductivity versus radiative transfer . . . . . . . . . . . . . . . . . . 72 3.8.1 Theheatequation ............................. 72 3.8.2 Heattransferacrossandnearinterfaces. . . . . . . . . . . . . . . . . . 74 3.8.3 In the kitchen: Physics-obsessed housewife versus IPCC . . . . . . . . . 74 3.9 Thelawsofthermodynamics............................ 75 3.9.1 Introduction ................................. 75 Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 5 3.9.2 Diagrams .................................. 76 3.9.3 Aparadox .................................. 77 3.9.4 Possibleresolutionoftheparadox ..................... 78 4 Physical Foundations of Climate Science 80 4.1 Introduction ..................................... 80 4.2 The conservation laws of magnetohydrodynamics . . . . . . . . . . . . . . . . 81 4.2.1 Overview .................................. 81 4.2.2 Electricchargeconservation ........................ 82 4.2.3 Massconservation.............................. 82 4.2.4 Maxwell'sequations ............................ 82 4.2.5 Ohm'slawformovingmedia........................ 83 4.2.6 Momentumbalanceequation........................ 83 4.2.7 Totalenergybalanceequation ....................... 83 4.2.8 Poynting'stheorem ............................. 83 4.2.9 Consequencesoftheconservationlaws . . . . . . . . . . . . . . . . . . 84 4.2.10Generalheatequation ........................... 84 4.2.11Discussion.................................. 85 4.3 ScienceandGlobalClimateModelling ...................... 86 4.3.1 ScienceandtheProblemofDemarcation . . . . . . . . . . . . . . . . . 86 4.3.2 Evaluation of Climatology and Climate Modelling . . . . . . . . . . . . 89 4.3.3 Conclusion.................................. 90 5 Physicist's Summary 92 Acknowledgement 95 List of Figures 96 List of Tables 99 References 100 6 Gerhard Gerlich and Ralf D. Tscheuschner 1 Introduction 1.1 Problem background Recently, there have been lots of discussions regarding the economic and political implications of climate variability, in particular global warming as a measurable e ect of an anthropogenic, i.e. human-made, climate change [1{13]. Many authors assume that carbon dioxide emissions from fossil-fuel consumption represent a serious danger to the health of our planet, since they are supposed to in uence the climates, in particular the average temperatures of the surface and lower atmosphere of the Earth. However, carbon dioxide is a rare trace gas, a very small part of the atmosphere found in concentrations as low as 0, 03 Vol % (cf. Table 1 and 2, see also Ref. [16]).1 Date CO2 concentration Source [ppmv] March 1958 315:56 Ref. [14] March 1967 322:88 Ref. [14] March 1977 334:53 Ref. [14] March 1987 349:24 Ref. [14] March 1996 363:99 Ref. [14] March 2007 377:3 Ref. [15] Table 1: Atmospheric concentration of carbon dioxide in volume parts per million (1958 2007) A physicist starts his analysis of the problem by pointing his attention to two fundamental thermodynamic properties, namely the thermal conductivity , a property that determines how much heat per time unit • and temperature di erence ows in a medium; • the isochoric thermal di usivity av, a property that determines how rapidly a temperature change will spread, expressed in terms of an area per time unit. 1In a recent paper on \180 Years accurate CO2 Gas analysis of Air by Chemical Methods” the German biologist Ernst-Georg Beck argues that the IPCC reliance of ice core CO2 gures is wrong [17, 18]. Though interesting on its own that even the CO2 data themselves are subject to a discussion it does not in uence the rationale of this paper which is to show that CO2 is completely irrelevant. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. Gas Formula U.S. Standard 1976 Ref. [14] [Vol %] Hardy et al. 2005 Ref. [8] [Vol %] Working hypothesis [Vol %] Nitrogen Oxygen Argon Carbon dioxide N2 O2 Ar CO2 78:084 20:9476 0:934 0:0314 78:09 20:95 0:93 0:03 78:09 20:94 0:93 0:04 Table 2: Three versions of an idealized Earth's atmosphere and the associated gas volume concentrations, including the working hypothesis chosen for this paper Both quantities are related by . av = (1) %cv the proportionality constant of the heat equation @T = av · T (2) @t whereby T is the temperature, . the mass density, and cv the isochoric speci c heat. To calculate the relevant data from the gaseous components of the air one has to use their mass concentrations as weights to calculate the properties of the mixture \air” according to Gibbs thermodynamics [19, 20].2 Data on volume concentrations (Table 2) can be converted into mass concentrations with the aid of known mass densities (Table 3). A comparison of volume percents and mass percents for CO2 shows that the current mass concentration, which is the physically relevant concentration, is approximately 0:06% and not the often quoted 0:03 % (Table 4). 2The thermal conductivity of a mixture of two gases does not, in general, vary linearly with the composition of the mixture. However for comparable molecular weight and small concentrations the non-linearity is negligible [21]. Gerhard Gerlich and Ralf D. Tscheuschner Gas Formula mass density . [kg=m3] Source Nitrogen N2 1:1449 Ref. [14] Oxygen O2 1:3080 Ref. [14] Argon Ar 1:6328 Ref. [14] Carbon Dioxide CO2 1:7989 Ref. [14] Table 3: Mass densities of gases at normal atmospheric pressure (101.325 kPa) and standard temperature (298 K) Gas Formula xv [Vol %] . (298 K) [kg=m3] xm [Mass %] Nitrogen Oxygen Argon Carbon dioxide N2 O2 Ar CO2 78:09 20:94 0:93 0:04 1.1449 1.3080 1.6328 1.7989 75:52 23:14 1:28 0:06 Table 4: Volume percent versus mass percent: The volume concentration xv and the mass concentration xm of the gaseous components of an idealized Earth's atmosphere From known thermal conductivities (Table 5), isochoric heat capacities, and mass densities the isochoric thermal di usivities of the components of the air are determined (Table 6). This allows to estimate the change of the e ective thermal conductivity of the air in dependence of a doubling of the CO2 concentration, expected to happen within the next 300 years (Table 7). It is obvious that a doubling of the concentration of the trace gas CO2, whose thermal conductivity is approximately one half than that of nitrogen and oxygen, does change the thermal conductivity at the most by 0, 03 % and the isochoric thermal di usivity at the most by 0:07 %. These numbers lie within the range of the measuring inaccuracy and other uncertainties such as rounding errors and therefore have no signi cance at all. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. Gas Formula (200 K) [W=mK] Ref. [14] (298 K) [W=mK] (interpolated) (300 K) [W=mK] Ref. [14] (400 K) [W=mK] Ref. [14] Nitrogen Oxygen Argon Carbon dioxide N2 O2 Ar CO2 0.0187 0.0184 0.0124 0.0096 0.0259 0.0262 0.0178 0.0167 0.0260 0.0263 0.0179 0.0168 0.0323 0.0337 0.0226 0.0251 Table 5: Thermal conductivities of the gaseous components of the Earth's atmosphere at normal pressure (101:325 kPa) Gas cp [J=kg K] Mr [g=mol] R=Mr [J=kg K] cv [J=kg K] . [kg=m3] . [Js=mK] av [m2=s] N2 1039 28.01 297 742 1.1489 0.0259 3:038 · 10..5 O2 919 32.00 260 659 1.3080 0.0262 3:040 · 10..5 Ar 521 39.95 208 304 1.6328 0.0178 3:586 · 10..5 CO2 843 44.01 189 654 1.7989 0.0167 1:427 · 10..5 Table 6: Isobaric heat capacities cp, relative molar masses Mr, isochoric heat capacities cv ˜ cp - R=Mr with universal gas constant R =8:314472 J=mol K, mass densities %, thermal conductivities , and isochoric thermal di usivities av of the gaseous components of the Earth's atmosphere at normal pressure (101:325 kPa) Gerhard Gerlich and Ralf D. Tscheuschner Gas xm Mr cp cv . . av [Mass %] [g=mol] [J=kg K] [J=kg K] [kg=m3] [Js=mK] [m2=s] N2 75.52 28.01 1039 742 1.1489 0.0259 3:038 · 10..5 O2 23.14 32.00 929 659 1.3080 0.0262 3:040 · 10..5 Ar 1.28 39.95 512 304 1.6328 0.0178 3:586 · 10..5 CO2 0.06 44.01 843 654 1.7989 0.0167 1:427 · 10..5 Air 100.00 29.10 1005 719 1.1923 0.02586 3:0166 · 10..5 Gas xm Mr cp cv . . av [Mass %] [g=mol] [J=kg K] [J=kg K] [kg=m3] [Js=mK] [m2=s] N2 75.52 28.01 1039 742 1.1489 0.0259 3:038 · 10..5 O2 23.08 32.00 929 659 1.3080 0.0262 3:040 · 10..5 Ar 1.28 39.95 512 304 1.6328 0.0178 3:586 · 10..5 CO2 0.12 44.01 843 654 1.7989 0.0167 1:427 · 10..5 Air 100.00 29.10 1005 719 1.1926 0.02585 3:0146 · 10..5 Table 7: The calculation of the isochoric thermal di usivity av = =(%cv) of the air and its gaseous components for the current CO2 concentration (0:06 Mass %) and for a ctitiously doubled CO2 concentration (0:12 Mass %) at normal pressure (101:325 kPa) Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 11 1.2 The greenhouse e ect hypothesis Among climatologists, in particular those who are aliated with the Intergovernmental Panel of Climate Change (IPCC)3, there is a \scienti c consensus” [22], that the relevant mechanism is the atmospheric greenhouse e ect, a mechanism heavily relying on the assumption, that radiative heat transfer clearly dominates over the other forms of heat transfer such as thermal conductivity, convection, condensation et cetera [23{30]. In all past IPCC reports and other such scienti c summaries the following point evocated in Ref. [24], p. 5, is central to the discussion: \One of the most important factors is the greenhouse e ect; a simpli ed explanation of which is as follows. Short-wave solar radiation can pass through the clear atmosphere relatively unimpeded. But long-wave terrestrial radiation emitted by the warm surface of the Earth is partially absorbed and then re-emitted by a number of trace gases in the cooler atmosphere above. Since, on average, the outgoing long-wave radiation balances the incoming solar radiation, both the atmosphere and the surface will be warmer than they would be without the greenhouse gases ::. The greenhouse e ect is real; it is a well understood e ect, based on established scienti c principles.” To make things more precise, supposedly, the notion of radiative forcing was introduced by the IPCC and related to the assumption of radiative equilibrium. In Ref. [27], pp. 7-6, one nds the statement: \A change in average net radiation at the top of the troposphere (known as the tropopause), because of a change in either solar or infrared radiation, is de ned for the purpose of this report as a radiative forcing. A radiative forcing perturbs the balance between incoming and outgoing radiation. Over time climate responds to the perturbation to re-establish the radiative balance. A positive radiative forcing tends on average to warm the surface; a negative radiative forcing on average tends to cool the surface. As de ned here, the incoming solar radiation is not considered a radiative forcing, but a change in the amount of incoming solar radiation would be a radiative forcing ::. For example, an increase in atmospheric CO2 concentration leads to a reduction in outgoing infrared radiation and a positive radiative forcing.” However, in general \scienti c consensus” is not related whatsoever to scienti c truth as countless examples in history have shown. \Consensus” is a political term, not a scienti c 3The IPCC was created in 1988 by the World Meteorological Organization (WHO) and the United Nations Environmental Programme (UNEP). Gerhard Gerlich and Ralf D. Tscheuschner term. In particular, from the viewpoint of theoretical physics the radiative approach, which uses physical laws such as Planck's law and Stefan-Boltzmann's law that only have a limited range of validity that de nitely does not cover the atmospheric problem, must be highly questioned [31{35]. For instance in many calculations climatologists perform calculations where idealized black surfaces e.g. representing a CO2 layer and the ground, respectively, radiate against each other. In reality, we must consider a bulk problem, in which at concentrations of 300 ppmv at normal state still N ˜ 3 · 10..4 · V · NL ˜ 3 · 10..4 · (10 · 10..6)3 · 2:687 · 1025 ˜ 3 · 10..4 · 10..15 · 2:687 · 1025 ˜ 8 · 106 (3) CO2 molecules are distributed within a cube V with edge length 10 m, a typical wavelength of the relevant infrared radiation.4 In this context an application of the formulas of cavity radiation is sheer nonsense. It cannot be overemphasized that a microscopic theory providing the base for a derivation of macroscopic quantities like thermal or electrical transport coecients must be a highly involved many-body theory. Of course, heat transfer is due to interatomic electromagnetic interactions mediated by the electromagnetic eld. But it is misleading to visualize a photon as a simple particle or wave packet travelling from one atom to another for example. Things are pretty much more complex and cannot be understood even in a (one-)particle-wave duality or Feynman graph picture. On the other hand, the macroscopic thermodynamical quantities contain a lot of information and can be measured directly and accurately in the physics lab. It is an interesting point that the thermal conductivity of CO2 is only one half of that of nitrogen or oxygen. In a 100 percent CO2 atmosphere a conventional light bulb shines brighter than in a nitrogen- oxygen atmosphere due to the lowered thermal conductivity of its environment. But this has nothing to do with the supposed CO2 greenhouse e ect which refers to trace gas concentrations. Global climatologists claim that the Earth's natural greenhouse e ect keeps the Earth 33 C warmer than it would be without the trace gases in the atmosphere. 80 percent of this warming is attributed to water vapor and 20 percent to the 0.03 volume percent CO2. If such an extreme e ect existed, it would show up even in a laboratory experiment involving concentrated CO2 as a thermal conductivity anomaly. It would be manifest itself as a new kind of `superinsulation’ violating the conventional heat conduction equation. However, for CO2 such anomalous heat transport properties never have been observed. Therefore, in this paper, the popular greenhouse ideas entertained by the global climatology community are reconsidered within the limits of theoretical and experimental physics. 4NL is determined by the well-known Loschmidt number [36]. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. Authors trace back their origins to the works of Fourier [37,38] (1824), Tyndall [39{43] (1861) and Arrhenius [44{46] (1896). A careful analysis of the original papers shows that Fourier's and Tyndall's works did not really include the concept of the atmospheric greenhouse e ect, whereas Arrhenius's work fundamentally di ers from the versions of today. With exception of Ref. [46], the traditional works precede the seminal papers of modern physics, such as Planck's work on the radiation of a black body [33, 34]. Although the arguments of Arrhenius were falsi ed by his contemporaries they were picked up by Callendar [47{53] and Keeling [54{60], the founders of the modern greenhouse hypothesis.5 Interestingly, this hypothesis has been vague ever since it has been used. Even Keeling stated 1978 [57]: \The idea that CO2 from fossil fuel burning might accumulate in air and cause warming of the lower atmosphere was speculated upon as early as the latter the nineteenth century (Arrhenius, 1903). At that time the use of fossil fuel was slight to expect a rise in atmospheric CO2 to be detectable. The idea was convincingly expressed by Callendar (1938, 1940) but still without solid evidence rise in CO2.” The in uence of CO2 on the climate was also discussed thoroughly in a number of publications that appeared between 1909 and 1980, mainly in Germany [61{88]. The most in uential authors were Moller [69,80{86], who also wrote a textbook on meteorology [89,90], and Manabe [73{77,85]. It seems, that the joint work of Moller and Manabe [85] has had a signi cant in uence on the formulation of the modern atmospheric CO2 Greenhouse conjectures and hypotheses, respectively. In a very comprehensive report of the US Department of Energy (DOE), which appeared in 1985 [91], the atmospheric greenhouse hypothesis had been cast into its nal form and became the cornerstone in all subsequent IPCC publications [23{30]. Of course, it may be, that even if the oversimpli ed picture entertained in IPCC global climatology is physically incorrect, a thorough discussion may reveal a non-neglible in uence of certain radiative e ects (apart from sunlight) on the weather, and hence on its local averages, the climates, which may be dubbed the CO2 greenhouse e ect. But then three key questions will remain, even if the e ect is claimed to serve only as a genuine trigger of a network of complex reactions: 1. Is there a fundamental CO2 greenhouse e ect in physics? 2. If so, what is the fundamental physical principle behind this CO2 greenhouse e ect? 3. Is it physically correct to consider radiative heat transfer as the fundamental mechanism controlling the weather setting thermal conductivity and friction to zero? 5Recently, von Storch critized the anthropogenic global warming scepticism by characterizing the discussion as \a discussion of yesterday and the day before yesterday” [1]. Ironically, it was Calendar and Keeling who once reactivated \a discussion of yesterday and the day before yesterday” based on already falsi ed arguments. 14 Gerhard Gerlich and Ralf D. Tscheuschner The aim of this paper is to give an armative negative answer to all of these questions rendering them rhetoric. 1.3 This paper In the language of physics an e ect is a not necessarily evident but a reproducible and measurable phenomenon together with its theoretical explanation. Neither the warming mechanism in a glass house nor the supposed anthropogenic warming is due to an e ect in the sense of this de nition: • In the rst case (the glass house) one encounters a straightforward phenomenon. • In the second case (the Earth's atmosphere) one cannot measure something; rather, one only makes heuristic calculations. The explanation of the warming mechanism in a real greenhouse is a standard problem in undergraduate courses, in which optics, nuclear physics and classical radiation theory are dealt with. On this level neither the mathematical formulation of the rst and second law of thermodynamics nor the partial di erential equations of hydrodynamics or irreversible thermodynamics are known; the phenomenon has thus to be analyzed with comparatively elementary means. However, looking up the search terms \glass house e ect", \greenhouse e ect", or the German word \Treibhause ekt” in classical textbooks on experimental physics or theoretical physics, one nds -possibly to one's surprise and disappointment -that this e ect does not appear anywhere -with a few exceptions, where in updated editions of some books publications in climatology are cited. One prominent example is the textbook by Kittel who added a \supplement” to the 1990 edition of his Thermal Physics on page 115 [92] : "The Greenhouse E ect describes the warming of the surface of the Earth caused by the infrared absorbent layer of water, as vapor and in clouds, and of carbon dioxide on the atmosphere between the Sun and the Earth. The water may contribute as much as 90 percent of the warming e ect.” Kittel \supplement” refers to the 1990 and 1992 books of J.T. Houghton et al. on Climate Change, which are nothing but the standard IPCC assessments [23, 25]. In general, most climatologic texts do not refer to any fundamental work of thermodynamics and radiation theory. Sometimes the classical astrophysical work of Chandrasekhar [93] is cited, but it is not clear at all, which results are applied where, and how the conclusions of Chandrasekhar t into the framework of infrared radiation transfer in planetary atmospheres. There seems to exist no source where an atmospheric greenhouse e ect is introduced from fundamental university physics alone. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. Evidently, the atmospheric greenhouse problem is not a fundamental problem of the philosophy of science, which is best described by the Munchhausen trilemma6, stating that one is left with the ternary alternative7 in nite regression -dogma -circular reasoning Rather, the atmospheric Greenhouse mechanism is a conjecture, which may be proved or disproved already in concrete engineering thermodynamics [95{97]. Exactly this was done well many years ago by an expert in this eld, namely Alfred Schack, who wrote a classical textbook on this subject [95]. 1972 he showed that the radiative component of heat transfer of CO2, though relevant at the temperatures in combustion chambers, can be neglected at atmospheric temperatures. The in uence of carbonic acid on the Earth's climates is de nitively unmeasurable [98]. The remaining part of this paper is organized as follows: • In Section 2 the warming e ect in real greenhouses, which has to be distinguished strictly from the (in-) famous conjecture of Arrhenius, is discussed. • Section 3 is devoted to the atmospheric greenhouse problem. It is shown that this e ect neither has experimental nor theoretical foundations and must be considered as ctitious. The claim that CO2 emissions give rise to anthropogenic climate changes has no physical basis. • In Section 4 theoretical physics and climatology are discussed in context of the philosophy of science. The question is raised, how far global climatology ts into the framework of exact sciences such as physics. • The nal Section 5 is a physicist's summary. 6The term was coined by the critical rationalist Hans Albert, see e.g. Ref. [94]. For the current discussion on global warming Albert's work may be particularly interesting. According to Albert new insights are not easy to be spread, because there is often an ideological obstacle, for which Albert coined the notion of immunity against criticism. 7Originally, an alternative is a choice between two options, not one of the options itself. A ternary alternative generalizes an ordinary alternative to a threefold choice. 16 Gerhard Gerlich and Ralf D. Tscheuschner 2 The warming mechanism in real greenhouses 2.1 Radiation Basics 2.1.1 Introduction For years, the warming mechanism in real greenhouses, paraphrased as \the greenhouse effect", has been commonly misused to explain the conjectured atmospheric greenhouse e ect. In school books, in popular scienti c articles, and even in high-level scienti c debates, it has been stated that the mechanism observed within a glass house bears some similarity to the anthropogenic global warming. Meanwhile, even mainstream climatologists admit that the warming mechanism in real glass houses has to be distinguished strictly from the claimed CO2 greenhouse e ect. Nevertheless, one should have a look at the classical glass house problem to recapitulate some fundamental principles of thermodynamics and radiation theory. Later on, the relevant radiation dynamics of the atmospheric system will be elaborated on and distinguished from the glass house set-up. Heat is the kinetic energy of molecules and atoms and will be transferred by contact or radiation. Microscopically both interactions are mediated by photons. In the former case, which is governed by the Coulomb resp. van der Waals interaction these are the virtual or o -shell photons, in the latter case these are the real or on-shell photons. The interaction between photons and electrons (and other particles that are electrically charged or have a nonvanishing magnetic momentum) is microscopically described by the laws of quantum theory. Hence, in principle, thermal conductivity and radiative transfer may be described in a uni ed framework. However, the non-equilibrium many body problem is a highly non-trivial one and subject to the discipline of physical kinetics unifying quantum theory and non-equilibrium statistical mechanics. Fortunately, an analysis of the problem by applying the methods and results of classical radiation theory already leads to interesting insights. 2.1.2 The in nitesimal speci c intensity In classical radiation theory [93] the main quantity is the speci c intensity I. It is de ned in terms of the amount of radiant energy dE. in a speci ed frequency interval [, . + d] that is transported across an area element dF1 in direction of another area element dF2 during a time dt: (r dF1)(r dF2) dE. = I. d. dt (4) jrj4 where r is the distance vector pointing from dF1 to dF2 (Figure 1). Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. Figure 1: The geometry of classical radiation: A radiating in nitesimal area dF1 and an illuminated in nitesimal area dF2 at distance r. For a general radiation eld one may write I. = I(x, y, z; l, m, n; t) (5) where (x, y, z) denote the coordinates, (l, m, n) the direction cosines, t the time, respectively, to which I. refers. With the aid of the de nition of the scalar product Equation (4) may be cast into the form dE. = I. d. dt (cos #1 dF1) · 2 (cos #2 dF2) (6)· rA special case is given by #2 :=1 (7) With . := #1 ds := dF1 d. := dF2=r2 (8) Equation (6) becomes dE. = I. d. dt cos . ds d. (9) de ning the pencil of radiation [93]. Equation (6), which will be used below, is slightly more general than Equation (9), which is more common in the literature. Both ones can be simpli ed by introducing an integrated intensity . 1 I0 = I. d. (10) 0 18 Gerhard Gerlich and Ralf D. Tscheuschner and a radiant power dP . For example, Equation (6) may be cast into the form dP = I0 · (cos #1 dF1) · 2 (cos #2 dF2) (11) r 2.1.3 Integration When performing integration one has to bookkeep the dimensions of the physical quantities involved. Usually, the area dF1 is integrated and the equation is rearranged in such a way, that there is an intensity I (resp. an intensity times an area element IdF ) on both sides of the equation. Three cases are particularly interesting: (a) Two parallel areas with distance a. According to Figure 2 one may write Figure 2: Two parallel areas with distance a. #1 = #2 =: . (12) By setting one obtains Iparallel areas r 2 = r 2 0 + a 2 2rdr = 2r0dr0 cos . = a r = . 2p 0 . R0 0 I0 (cos #)2 r2 r0dr0d. (13) (14) (15) . 2p . R0 a2 = I0 r0dr0d. 4 00 r 2 2 . 2p . pR0 2+aa = I0 rdrd. 0 a r4 Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. . pR 2 0 +a 2 1 = 2I0 · a 2 · dr · a r3 pR 2 0 +a 2 1 2 = 2I0  · a - 2r2 a 11 2 = p · I0 · a 2 · a2 - R0 2 + a R2 = p · I0 · R0 2 + 0 a2 (16) (b) Two parallel areas with distance a 0 . If the distance a is becoming very small whereas R0 is kept nite one will have R2 Iparallel areas (a0) = lim I0 · 0 2 = I0 (17) !a!0 · R0 2 + a This relation corresponds to the total half-space intensity for a radiation from a unit surface. (c) The Earth illuminated by the Sun With I0 Sun being the factor I0 for the Sun the solar total half-space intensity is given by ISun's surface = I0 Sun (18) · Setting a =REarth's orbit (19) R0 =RSun (20) one gets for the solar intensity at the Earth's orbit R2 IEarth's orbit · 0 · R2 +R2 = ISun Sun Sun Earth's orbit R2 = ISun's surface · Sun R2 +R2 Sun Earth's orbit R2 = ISun's surface · R2 Sun Earth's orbit 1 = ISun's surface · (215)2 (21) 2.1.4 The Stefan-Boltzmann law For a perfect black body and a unit area positioned in its proximity we can compute the intensity I with the aid of the the Kirchho -Planck-function, which comes in two versions 2h3 ". h. !#..1 B. (T )= c2 exp - 1 (22) kT 2hc2 ". hc !#..1 B(T )= 5 exp kT - 1 (23) Gerhard Gerlich and Ralf D. Tscheuschner that are related to each other by d. c B(T ) d. =B(T ) d. = ..B(T ) d. =: ..B(T ) d. (24) d. 2 with . = c=. (25) where c is the speed of light, h the Planck constant, k the Boltzmann constant, . the wavelength, . the frequency, and T the absolute temperature, respectively. Integrating over all frequencies or wavelengths we obtain the Stefan-Boltzmann T 4 law I = p · 0 8 B. (T ) d. = p · 0 8 B(T ) d. = T 4 (26) with 24k4 W s = p =5:670400 10..8 (27) · 15c2h3 · m2K4 One conveniently writes 4 T W s =5:67 2K4 (28) · 100 mThis is the net radiation energy per unit time per unit area placed in the neighborhood of a radiating plane surface of a black body. 2.1.5 Conclusion Three facts should be emphasized here: • In classical radiation theory radiation is not described by a vector eld assigning to every space point a corresponding vector. Rather, with each point of space many rays are associated (Figure 3). This is in sharp contrast to the modern description of the radiation eld as an electromagnetic eld with the Poynting vector eld as the relevant quantity [99]. Figure 3: The geometry of classical radiation: Two surfaces radiating against each other. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. • The constant s appearing in the T 4 law is not a universal constant of physics. It strongly depends on the particular geometry of the problem considered.8 • The T 4-law will no longer hold if one integrates only over a ltered spectrum, appropriate to real world situations. This is illustrated in Figure 4 . Figure 4: Black body radiation compared to the radiation of a sample coloured body. The non-universal constant s is normalized in such a way that both curves coincide at T = 290 K. The Stefan-Boltzmann T 4 law does no longer hold in the latter case, where only two bands are integrated over, namely that of visible light and of infrared radiation from 3 m to 5 m, giving rise to a steeper curve. Many pseudo-explanations in the context of global climatology are already falsi ed by these three fundamental observations of mathematical physics. 2.2 The Sun as a black body radiator The Kirchho -Planck function describes an ideal black body radiator. For matter of convenience one may de ne Bsunshine =BSun RSun 2 =BSun 1 (29) .  · REarth's orbit 2 · (215)2 Figure 5 shows the spectrum of the sunlight, assuming the Sun is a black body of temperature T = 5780 K. 8For instance, to compute the radiative transfer in a multi-layer setup, the correct point of departure is the in nitesimal expression for the radiation intensity, not an integrated Stefan-Boltzmann expression already computed for an entirely di erent situation. Gerhard Gerlich and Ralf D. Tscheuschner Figure 5: The spectrum of the sunlight assuming the sun is a black body at T = 5780 K. To compute the part of radiation for a certain wave length interval [1;2] one has to evaluate the expression . 2 Bsunshine(5780) d 1  . 08 Bsunshine . (30) (5780) d. Table 8 shows the proportional portions of the ultraviolet, visible, and infrared sunlight, respectively. Band Range Portion [nm] [%] ultraviolet 0 - 380 10.0 visible 380 - 760 44,8 infrared 45,2 760 ..8 Table 8: The proportional portion of the ultraviolet, visible, and infrared sunlight, respectively. Here the visible range of the light is assumed to lie between 380 nm and 760 nm. It should be mentioned that the visible range depends on the individuum. In any case, a larger portion of the incoming sunlight lies in the infrared range than in the visible range. In most papers discussing the supposed greenhouse e ect this important fact is completely ignored. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 23 2.3 The radiation on a very nice day 2.3.1 The phenomenon Especially after a year's hot summer every car driver knows a sort of a glass house or greenhouse e ect: If he parks his normally tempered car in the morning and the Sun shines into the interior of the car until he gets back into it at noon, he will almost burn his ngers at the steering wheel, if the dashboard area had been subject to direct Sun radiation. Furthermore, the air inside the car is unbearably hot, even if it is quite nice outside. One opens the window and the slide roof, but unpleasant hot air may still hit one from the dashboard while driving. One can notice a similar e ect in the winter, only then one will probably welcome the fact that it is warmer inside the car than outside. In greenhouses or glass houses this e ect is put to use: the ecologically friendly solar energy, for which no energy taxes are probably going to be levied even in the distant future, is used for heating. Nevertheless, glass houses have not replaced conventional buildings in our temperate climate zone not only because most people prefer to pay energy taxes, to heat in the winter, and to live in a cooler apartment on summer days, but because glass houses have other disadvantages as well. 2.3.2 The sunshine One does not need to be an expert in physics to explain immediately why the car is so hot inside: It is the Sun, which has heated the car inside like this. However, it is a bit harder to answer the question why it is not as hot outside the car, although there the Sun shines onto the ground without obstacles. Undergraduate students with their standard physical recipes at hand can easily \explain” this kind of a greenhouse e ect: The main part of the Sun's radiation (Figure 6) passes through the glass, as the maximum (Figure 7) of the solar radiation is of bluegreen wavelength bluegreen =0:5 m (31) which the glass lets through. This part can be calculated with the Kirchho -Planck-function. Evidently, the result depends on the type of glass. For instance, if it is transparent to electromagnetic radiation in the 300 nm -1000 nm range one will have . 0 1 :3   m m Bsunshine . (5780) d. . 08 Bsunshine . (5780) d. = 77, 2 % (32) In case of a glass, which is assumed to be transparent only to visible light (380 nm -760 nm) one gets . 0:760 m Bsunshine(5780) d 0:380 m  . 08 Bsunshine . (5780) d. = 44, 8 % (33) Because of the Fresnel re ection [99] at both pane boundaries one has to subtract 8 -10 percent and only 60 -70 percent (resp. 40 percent) of the solar radiation reach the interior Gerhard Gerlich and Ralf D. Tscheuschner Figure 6: The un ltered spectral distribution of the sunshine on Earth under the assumption that the Sun is a black body with temperature T = 5780 K (left: in wave length space, right: in frequency space). Figure 7: The exact location of the zero of the partial derivatives of the radiation intensities of the sunshine on Earth (left: in wave length space, right: in frequency space). Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. of the vehicle. High performance tinted glass which is also referred to as spectrally selective tinted glass reduces solar heat gain typically by a factor of 0:50 (only by a factor of 0:69 in the visible range) compared to standard glass [100]. 2.3.3 The radiation of the ground The bottom of a glass house has a temperature of approximately 290 K (Figure 8). The maximum of a black body's radiation can be calculated with the help of Wien's displacement law (cf. Figure 9 and Figure 10) Figure 8: The un ltered spectral distribution of the radiation of the ground under the assumption that the earth is a black body with temperature T = 290 K (left: in wave length space, right: in frequency space). max(T ) · T = const. (34) giving 6000 K max(300 K) = 300 K · max(6000 K) = 10 m (35) This is far within the infrared wave range, where glass re ects practically all light, according to Beer's formula [101]. Practically 100 percent of a black body's radiation at ground temperatures lie above the wavelengths of 3.5 m. The thermal radiation of the ground is thus \trapped” by the panes. According to Wien's power law describing the intensity of the maximum wave-length Bmax(T ) . T 5 (36) the intensity of the radiation on the ground at the maximum is T 5 60005 T 5 Sun ˜ 3005 = 205 =3:2 · 106 (37) Earth's ground 26 Gerhard Gerlich and Ralf D. Tscheuschner Figure 9: The radiation intensity of the ground and its partial derivative as a function of the wave length . (left column) and of the frequency . (right column). Figure 10: Three versions of radiation curve families of the radiation of the ground (as a function of the wave number k, of the frequency , of the wave length , respectively), assuming that the Earth is a black radiator. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. times smaller than on the Sun and T 5 R2 1 T 5 Sun · R2 Sun ˜ 205 · 2152 ˜ 70 (38) Earth's ground Earth's orbit times smaller than the solar radiation on Earth. The total radiation can be calculated from the Stefan-Boltzmann law Btotal(T )= T 4 (39) · Hence, the ratio of the intensities of the sunshine and the ground radiation is given by T 4 R2 1 T 4 Sun · R2 Sun ˜ 204 · 2152 ˜ 3:46 (40) Earth's ground Earth's orbit Loosely speaking, the radiation of the ground is about four times weaker than the incoming solar radiation. 2.3.4 Sunshine versus ground radiation To make these di erences even clearer, it is convenient to graphically represent the spectral distribution of intensity at the Earth's orbit and of a black radiator of 290 K, respectively, in relation to the wavelength. (Figures 11, 12, and 13) To t both curves into one drawing, Figure 11: The un ltered spectral distribution of the sunshine on Earth under the assumption that the Sun is a black body with temperature T = 5780 K and the un ltered spectral distribution of the radiation of the ground under the assumption that the Earth is a black body with temperature T = 290 K, both in one diagram (left: normal, right: super elevated by a factor of 10 for the radiation of the ground). one makes use of the technique of super-elevation and/or applies an appropriate re-scaling. It becomes clearly visible, Gerhard Gerlich and Ralf D. Tscheuschner Figure 12: The un ltered spectral distribution of the sunshine on Earth under the assumption that the Sun is a black body with temperature T = 5780 K and the un ltered spectral distribution of the radiation of the ground under the assumption that the Earth is a black body with temperature T = 290 K, both in one semi-logarithmic diagram (left: normalized in such a way that equal areas correspond to equal intensities, right: super elevated by a factor of 10 for the radiation of the ground). Figure 13: The un ltered spectral distribution of the sunshine on Earth under the assumption that the Sun is a black body with temperature T = 5780 K and the un ltered spectral distribution of the radiation of the ground under the assumption that the Earth is a black body with temperature T = 290 K, both in one semi-logarithmic diagram (left: normalized in such a way that equal areas correspond to equal intensities with an additional re-scaling of the sunshine curve by a factor of 1=3:5, right: super elevated by a factor of 68 for the radiation of the ground). Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 29 • that the maxima are at 0.5 m or 10 m, respectively; • that the intensities of the maxima di er by more than an order of ten; • that above 0.8 m (infrared) the solar luminosity has a notable intensity. Figure 13 is an obscene picture, since it is physically misleading. The obscenity will not remain in the eye of the beholder, if the latter takes a look at the obscure scaling factors already applied by Bakan and Raschke in an undocumented way in their paper on the so- called natural greenhouse e ect [102]. This is scienti c misconduct as is the missing citation. Bakan and Raschke borrowed this gure from Ref. [103] where the scaling factors, which are of utmost importance for the whole discussion, are left unspeci ed. This is scienti c misconduct as well. 2.3.5 Conclusion Though in most cases the preceding \explanation” suces to provide an accepted solution to the standard problem, presented in the undergraduate course, the analysis leaves the main question untouched, namely, why the air inside the car is warmer than outside and why the dashboard is hotter than the ground outside the car. Therefore, in the following, the situation inside the car is approached experimentally. 2.4 High School Experiments On a hot summer afternoon, temperature measurements were performed with a standard digital thermometer by the rst author [104{108] and were recently reproduced by the other author. In the summertime, such measurements can be reproduced by everyone very easily. The results are listed in Table 9. Thermometer located . . . Temperature inside the car, in direct Sun inside the car, in the shade next to the car, in direct Sun, above the ground next to the car, in the shade, above the ground in the living room 71 C 39 C 31 C 29 C 25 C Table 9: Measured temperatures inside and outside a car on a hot summer day. Gerhard Gerlich and Ralf D. Tscheuschner Against these measurements one may object that one had to take the dampness of the ground into account: at some time during the year the stones certainly got wet in the rain. The above mentioned measurements were made at a time, when it had not rained for weeks. They are real measured values, not average values over all breadths and lengths of the Earth, day and night and all seasons and changes of weather. These measurements are recommended to every climatologist, who believes in the CO2-greenhouse e ect, because he feels already while measuring, that the just described e ect has nothing to do with trapped thermal radiation. One can touch the car's windows and notice that the panes, which absorb the infrared light, are rather cool and do not heat the inside of the car in any way. If one holds his hand in the shade next to a very hot part of the dashboard that lies in the Sun, one will practically feel no thermal radiation despite the high temperature of 70 C, whereas one clearly feels the hot air. Above the ground one sees why it is cooler there than inside the car: the air inside the car \stands still", above the ground one always feels a slight movement of the air. The ground is never completely plain, so there is always light and shadow, which keep the circulation going. This e ect was formerly used for many old buildings in the city of Braunschweig, Germany. The south side of the houses had convexities. Hence, for most of the time during the day, parts of the walls are in the shade and, because of the thus additionally stimulated circulation, the walls are heated less. In order to study the warming e ect one can look at a body of speci c heat cv and width d, whose cross section F is subject to the radiation intensity S (see Figure 14). One has Figure 14: A solid parallelepiped of thickness d and cross section F subject to solar radiation . F d cv dT dt = FS (41) or, respectively, dT dt = S . cv d (42) Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. which may be integrated yielding S T = T0 + %cv d(t - t0) (43) In this approximation, there is a linear rise of the temperature in time because of the irradiated intensity. One sees that the temperature rises particularly fast in absorbing bodies of small diameter: Thin layers are heated especially fast to high temperatures by solar radiation. The same applies to the heat capacity per unit volume: • If the heat capacity is large the change of temperature will be slow. • If the heat capacity is small the change in temperature will be fast. Thus the irradiated intensity is responsible for the quick change of temperature, not for its value. This rise in temperature is stopped by the heat transfer of the body to its environment. Especially in engineering thermodynamics the di erent kinds of heat transfer and their interplay are discussed thoroughly [95{97]. A comprehensive source is the classical textbook by Schack [95]. The results have been tested e.g. in combustion chambers and thus have a strong experimental background. One has to distinguish between Conduction • Convection • Radiation • • Transfer of latent heat in phase transitions such as condensation and sublimation9 Conduction, condensation and radiation, which slow down the rise in temperature work practically the same inside and outside the car. Therefore, the only possible reason for a di erence in nal temperatures must be convection: A volume element of air above the ground, which has been heated by radiation, is heated up (by heat transfer through conduction), rises and is replaced by cooler air. This way, there is, in the average, a higher di erence of temperatures between the ground and the air and a higher heat transmission compared to a situation, where the air would not be replaced. This happens inside the car as well, but there the air stays locked in and the air which replaces the rising air is getting warmer and warmer, which causes lower heat transmission. Outside the car, there is of course a lot more cooler air than inside. On the whole, there is a higher temperature for the sunlight absorbing surfaces as well as for the air. 9Among those phenomena governed by the exchange of latent heat there is radiation frost, an striking example for a cooling of the Earth's surface through emission of infrared radiation. 32 Gerhard Gerlich and Ralf D. Tscheuschner Of course, the exposed body loses energy by thermal radiation as well. The warmer body inside the car would lose more heat in unit of time than the colder ground outside, which would lead to a higher temperature outside, if this temperature rise were not absorbed by another mechanism! If one considers, that only a small part of the formerly reckoned 60 -70 percent of solar radiation intensity reaches the inside of the car through its metal parts, this e ect would contribute far stronger to the temperature outside! The \explanation” of the physical greenhouse e ect only with attention to the radiation balance would therefore lead to the reverse e ect! The formerly discussed e ect of the \trapped” heat radiation by re ecting glass panes remains, which one can read as hindered heat transmission in this context. So this means a deceleration of the cooling process. However, as this heat transmission is less important compared to the convection, nothing remains of the absorption and re ection properties of glass for infrared radiation to explain the physical greenhouse e ect. Neither the absorption nor the re ection coecient of glass for the infrared light is relevant for this explanation of the physical greenhouse e ect, but only the movement of air, hindered by the panes of glass. Although meteorologists have known this for a long time [109,110], some of them still use the physical greenhouse e ect to explain temperature e ects of planetary atmospheres. For instance in their book on the atmospheric greenhouse e ect, Schonwiese and Diekmann build their arguments upon the glass house e ect [111]. Their list of references contains a seminal publication that clearly shows that this is inadmissable [91]. 2.5 Experiment by Wood Although the warming phenomenon in a glass house is due to the suppression of convection, say air cooling10, it remains true that most glasses absorb infrared light at wavelength 1 m and higher almost completely. An experimentum crucis therefore is to build a glass house with panes consisting of NaCl or KCl, which are transparent to visible light as well as infrared light. For rock salt (NaCl) such an experiment was realized as early as 1909 by Wood [112{115]: \There appears to be a widespread belief that the comparatively high temperature produced within a closed space covered with glass, and exposed to solar radiation, results from a transformation of wave-length, that is, that the heat waves from the Sun, which are able to penetrate the glass, fall upon the walls of the enclosure and raise its temperature: the heat energy is re-emitted by the walls in the form of much longer waves, which are unable to penetrate the glass, the greenhouse acting as a radiation trap. I have always felt some doubt as to whether this action played any very large part 10A problem familiar to those who are involved in PC hardware problems. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. in the elevation of temperature. It appeared much more probable that the part played by the glass was the prevention of the escape of the warm air heated by the ground within the enclosure. If we open the doors of a greenhouse on a cold and windy day, the trapping of radiation appears to lose much of its ecacy. As a matter of fact I am of the opinion that a greenhouse made of a glass transparent to waves of every possible length would show a temperature nearly, if not quite, as high as that observed in a glass house. The transparent screen allows the solar radiation to warm the ground, and the ground in turn warms the air, but only the limited amount within the enclosure. In the \open", the ground is continually brought into contact with cold air by convection currents. To test the matter I constructed two enclosures of dead black cardboard, one covered with a glass plate, the other with a plate of rock-salt of equal thickness. The bulb of a thermometer was inserted in each enclosure and the whole packed in cotton, with the exception of the transparent plates which were exposed. When exposed to sunlight the temperature rose gradually to 65 C, the enclosure covered with the salt plate keeping a little ahead of the other, owing to the fact that it transmitted the longer waves from the Sun, which were stopped by the glass. In order to eliminate this action the sunlight was rst passed through a glass plate. There was now scarcely a di erence of one degree between the temperatures of the two enclosures. The maximum temperature reached was about 55 C. From what we know about the distribution of energy in the spectrum of the radiation emitted by a body at 55 C, it is clear that the rock-salt plate is capable of transmitting practically all of it, while the glass plate stops it entirely. This shows us that the loss of temperature of the ground by radiation is very small in comparison to the loss by convection, in other words that we gain very little from the circumstance that the radiation is trapped. Is it therefore necessary to pay attention to trapped radiation in deducing the temperature of a planet as a ected by its atmosphere? The solar rays penetrate the atmosphere, warm the ground which in turn warms the atmosphere by contact and by convection currents. The heat received is thus stored up in the atmosphere, remaining there on account of the very low radiating power of a gas. It seems to me very doubtful if the atmosphere is warmed to any great extent by absorbing the radiation from the ground, even under the most favourable conditions. I do not pretend to have gone very deeply into the matter, and publish this note merely to draw attention to the fact that trapped radiation appears to play but a very small part in the actual cases with which we are familiar.” 34 Gerhard Gerlich and Ralf D. Tscheuschner This text is a recommended reading for all global climatologists referring to the greenhouse e ect. 2.6 Glass house summary It is not the \trapped” infrared radiation, which explains the warming phenomenon in a real greenhouse, but it is the suppression of air cooling.11 11As almost everybody knows, this is also a standard problem in PCs. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 35 3 The ctitious atmospheric greenhouse e ects 3.1 Problem de nition After it has been thoroughly discussed, that the physical greenhouse e ect is essentially the explanation, why air temperatures in a closed glass house or in a closed car are higher than outside, one should have a closer look at the ctitious atmospheric greenhouse e ects. Meanwhile there are many di erent phenomena and di erent explanations for these e ects, so it is justi ed to pluralize here. Depending on the particular school and the degree of popularization, the assumption that the atmosphere is transparent for visible light but opaque for infrared radiation is supposed to lead to • a warming of the Earth's surface and/or • a warming of the lower atmosphere and/or • a warming of a certain layer of the atmosphere and/or • a slow-down of the natural cooling of the Earth's surface and so forth. Unfortunately, there is no source in the literature, where the greenhouse e ect is introduced in harmony with the scienti c standards of theoretical physics. As already emphasized, the \supplement” to Kittel's book on thermal physics [92] only refers to the IPCC assessments [23, 25]. Prominent global climatologists (as well as \climate sceptics") often present their ideas in handbooks, encyclopedias, and in secondary and tertiary literature. 3.2 Scienti c error versus scienti c fraud Recently, the German climatologist Gral emphasized that errors in science are unavoidable, even in climate research [116]. And the IPCC weights most of its ocial statements with a kind of a \probability measure” [2]. So it seems that, even in the mainstream discussion on the supposed anthropogenic global warming, there is room left for scienti c errors and their corrections. However, some authors and lmmakers have argued that the greenhouse e ect hypothesis is not based on an error, but clearly is a kind of a scienti c fraud. Five examples: • As early as 1990 the Australian movie entitled \The greenhouse conspiracy” showed that the case for the greenhouse e ect rests on four pillars [117]: Gerhard Gerlich and Ralf D. Tscheuschner 1. the factual evidence, i.e. the climate records, that supposedly suggest that a global warming has been observed and is exceptional; 2. the assumption that carbon dioxide is the cause of these changes; 3. the predictions of climate models that claim that a doubling of CO2 leads to a predictable global warming; 4. the underlined physics. In the movie these four pillars were dismantled bringing the building down. The speaker states: \In a recent paper on the e ects of carbon dioxide, Professor Ellsaesser of the Lawrence Livermore Laboratories, a major US research establishment in California, concluded that a doubling of carbon dioxide would have little or no e ect on the temperature at the surface and, if anything, might cause the surface to cool.” The reader is referred to Ellsaesser's original work [118]. • Two books by the popular German meteorologist and sociologist Wolfgang Thune, entitled The Greenhouse Swindle (In German, 1998) [119] and Aquittal for CO2 (In German, 2002) [120] tried to demonstrate that the CO2 greenhouse e ect hypothesis is pure nonsense. • A book written by Heinz Hug entitled Those who play the trumpet of fear (In German, 2002), elucidated the history and the background of the current greenhouse business [121] • Another movie was shown recently on Channel 4 (UK) entitled \The great global warming swindle” supporting the thesis that the supposed CO2 induced anthropogenic global warming has no scienti c basis [122]. • In his paper \CO2: The Greatest Scienti c Scandal of Our Time” the eminent atmospheric scientist Jaworowski made a well-founded statement [12]. On the other hand, Sir David King, the science advisor of the British government, stated that \global warming is a greater threat to humanity than terrorism” (Singer)12, other individuals put anthropogenic global warming deniers in the same category as holocaust deniers, and so on. In an uncountable number of contributions to newspapers and TV shows in Germany the popular climatologist Latif13 continues to warn the public about the consequences of rising 12cf. Singer's summary at the Stockholm 2006 conference [1]. 13Some time ago one of the authors (R.D.T.) was Mojib Latif's teaching assistant in the physics lab. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. greenhouse gas (GHG) emissions [123]. But until today it is impossible to nd a book on non-equilibrium thermodynamics or radiation transfer where this e ect is derived from rst principles. The main objective of this paper is not to draw the line between error and fraud, but to nd out where the greenhouse e ect appears or disappears within the frame of physics. Therefore, in Section 3.3 several di erent variations of the atmospheric greenhouse hypotheses will be analyzed and disproved. The authors restrict themselves on statements that appeared after a publication by Lee in the well-known Journal of Applied Meteorology 1973, see Ref. [109] and references therein. Lee's 1973 paper is a milestone. In the beginning Lee writes: \The so-called radiation `greenhouse’ e ect is a misnomer. Ironically, while the concept is useful in describing what occurs in the earth's atmosphere, it is invalid for cryptoclimates created when space is enclosed with glass, e.g. in greenhouses and solar energy collectors. Speci cally, elevated temperatures observed under glass cannot be traced to the spectral absorbtivity of glass. The misconception was demonstrated experimentally by R. W. Wood more than 60 years ago (Wood, 1909) [112] and recently in an analytical manner by Businger (1963) [124]. Fleagle and Businger (1963) [125] devoted a section of their text to the point, and suggested that radiation trapping by the earth's atmosphere should be called `atmosphere e ect’ to discourage use of the misnomer. Munn (1966) [126] reiterated that the analogy between `atmosphere’ and `greenhouse’ e ect `is not correct because a major factor in greenhouse climate is the protection the glass gives against turbulent heat losses'. In one instance, Lee (1966) [127], observed that the net ux of radiant energy actually was diminished be pore than 10 % in a 6-mil polyvinyl enclosure. In spite of the evidence, modern textbooks on meteorology and climatology not only repeat the misnomer, but frequently support the false notion that `heatretaining behavior of the atmosphere is analogous to what happens in a greenhouse’ (Miller, 1966) [128], or that `the function of the [greenhouse] glass is to form a radiation trap’ (Peterssen, 1958) [129]. (see also Sellers, 1965, Chang, 1968, and Cole, 1970) [130{132]. The mistake obviously is subjective, based on similarities of the atmosphere and glass, and on the `neatness’ of the example in teaching. The problem can be recti ed through straightforward analysis, suitable for classroom instruction.” Lee continues his analysis with a calculation based on radiative balance equations, which are physically questionable. The same holds for a comment by Berry [110] on Lee's work. Nevertheless, Lee's paper is a milestone marking the day after every serious scientist or science 38 Gerhard Gerlich and Ralf D. Tscheuschner educator is no longer allowed to compare the greenhouse with the atmosphere, even in the classroom, which Lee explicitly refers to. 3.3 Di erent versions of the atmospheric greenhouse conjecture 3.3.1 Atmospheric greenhouse e ect after Moller (1973) In his popular textbook on meteorology [89, 90] Moller claims: \In a real glass house (with no additional heating, i.e. no greenhouse) the window panes are transparent to sunshine, but opaque to terrestrial radiation. The heat exchange must take place through heat conduction within the glass, which requires a certain temperature gradient. Then the colder boundary surface of the window pane can emit heat. In case of the atmosphere water vapor and clouds play the role of the glass.” Disproof: The existence of the greenhouse e ect is considered as a necessary condition for thermal conductivity. This is a physical nonsense. Furthermore it is implied that the spectral transmissivity of a medium determines its thermal conductivity straightforwardly. This is a physical nonsense as well. 3.3.2 Atmospheric greenhouse e ect after Meyer's encyclopedia (1974) In the 1974 edition of Meyer's Enzyklopadischem Lexikon one nds under \glass house e ect” [133]: \Name for the in uence of the Earth's atmosphere on the radiation and heat budget of the Earth, which compares to the e ect of a glass house: Water vapor and carbon dioxide in the atmosphere let short wave solar radiation go through down to the Earth's surface with a relative weak attenuation and, however, re ect the portion of long wave (heat) radiation which is emitted from the Earth's surface (atmospheric backradiation).” Disproof: Firstly, the main part of the solar radiation lies outside the visible light. Secondly, re ection is confused with emission. Thirdly, the concept of atmospheric backradiation relies on an inappropriate application of the formulas of cavity radiation. This will be discussed in Section 3.5 3.3.3 Atmospheric greenhouse e ect after Schonwiese (1987) The prominent climatologist Schonwiese states [111]: Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 39 \::. we use the picture of a glass window that is placed between the Sun and the Earth's surface. The window pane lets pass the solar radiation unhindered but absorbs a portion of the heat radiation of the Earth. The glass pane emits, corresponding to its own temperature, heat in both directions: To the Earth's surface and to the interplanetary space. Thus the radiative balance of the Earth's surface is raised. The additional energy coming from the glass pane is absorbed almost completely by the Earth's surface immediately warming up until a new radiative equilibrium is reached.” Disproof: That the window pane lets pass the solar radiation unhindered is simply wrong. Of course, some radiation goes sidewards. As shown experimentally in Section 2.4, the panes of the car window are relatively cold. This is only one out of many reasons, why the glass analogy is unusable. Hence the statement is vacuous. 3.3.4 Atmospheric greenhouse e ect after Stichel (1995) Stichel (the former deputy head of the German Physical Society) stated once [134]: \Now it is generally accepted textbook knowledge that the long-wave infrared radiation, emitted by the warmed up surface of the Earth, is partially absorbed and re-emitted by CO2 and other trace gases in the atmosphere. This e ect leads to a warming of the lower atmosphere and, for reasons of the total radiation budget, to a cooling of the stratosphere at the same time.” Disproof: This would be a Perpetuum Mobile of the Second Kind. A detailed discussion is given in Section 3.9. Furthermore, there is no total radiation budget, since there are no individual conservation laws for the di erent forms of energy participating in the game. The radiation energies in question are marginal compared to the relevant geophysical and astrophysical energies. Finally, the radiation depends on the temperature and not vice versa. 3.3.5 Atmospheric greenhouse e ect after Anonymous 1 (1995) \The carbon dioxide in the atmosphere lets the radiation of the Sun, whose maximum lies in the visible light, go through completely, while on the other hand it absorbs a part of the heat radiation emitted by the Earth into space because of its larger wavelength. This leads to higher near-surface air temperatures.” Disproof: The rst statement is incorrect since the obviously non-neglible infrared part of the incoming solar radiation is being absorbed (cf. Section 2.2). The second statement is falsi ed by referring to a counterexample known to every housewife: The water pot on the stove. Without water lled in, the bottom of the pot will soon become glowing red. Water is 40 Gerhard Gerlich and Ralf D. Tscheuschner an excellent absorber of infrared radiation. However, with water lled in, the bottom of the pot will be substantially colder. Another example would be the replacement of the vacuum or gas by glass in the space between two panes. Conventional glass absorbs infrared radiation pretty well, but its thermal conductivity shortcuts any thermal isolation. 3.3.6 Atmospheric greenhouse e ect after Anonymous 2 (1995) \If one raises the concentration of carbon dioxide, which absorbs the infrared light and lets visible light go through, in the Earth's atmosphere, the ground heated by the solar radiation and/or near-surface air will become warmer, because the cooling of the ground is slowed down.” Disproof: It has already been shown in Section 1.1 that the thermal conductivity is changed only marginally even by doubling the CO2 concentration in the Earth's atmosphere. 3.3.7 Atmospheric greenhouse e ect after Anonymous 3 (1995) \If one adds to the Earth's atmosphere a gas, which absorbs parts of the radiation of the ground into the atmosphere, the surface temperatures and near-surface air temperatures will become larger.” Disproof: Again, the counterexample is the water pot on the stove; see Section 3.3.5. 3.3.8 Atmospheric greenhouse e ect after German Meteorological Society (1995) In its 1995 statement, the German Meteorological Society says [135]: \As a point of a departure the radiation budget of the Earth is described. In this case the incident unweakened solar radiation at the Earth's surface is partly absorbed and partly re ected. The absorbed portion is converted into heat and must be re-radiated in the infrared spectrum. Under such circumstances simple model calculations yield an average temperature of about ..18C at the Earth's surface ::. Adding an atmosphere, the incident radiation at the Earth's surface is weakened only a little, because the atmosphere is essentially transparent in the visible range of the spectrum. Contrary to this, in the infrared range of the spectrum the radiation emitted form the ground is absorbed to a large extent by the atmosphere ::. and, depending on the temperature, re-radiated in all directions. Only in the so-called window ranges (in particular in the large atmospheric window 8 -13 m) the infrared radiation can escape into space. The infrared radiation that is emitted downwards from the atmosphere (the so-called back-radiation) raises the energy supply of the Earth's surface. A state of equilibrium can adjust itself if Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 41 the temperature of the ground is rises and, therefore, a raised radiation according to Planck's law is possible. This undisputed natural Greenhouse e ect gives rise to an increase temperature of the Earth's surface.” Disproof: The concept of an radiation budget is physically wrong. The average of the temperature is calculated incorrectly. Furthermore, an non-neglible portion of the incident solar radiation is absorbed by the atmosphere. Heat must not be confused with heat radiation. The assumption that if gases emit heat radiation, they will emit it only downwards is rather obscure. The described mechanism of re-calibration to equilibrium has no physical basis. The laws of cavity radiation do not apply to uids and gases. 3.3.9 Atmospheric greenhouse e ect after Gral (1996) The former director of the World Meteorological Organization (WMO) climate research program, Professor Hartmut Gral, states [136]: \In so far as the gaseous hull [of the Earth] obstructs the propagation of solar energy down to the planet's surface less than the direct radiation of heat from the surface into space, the ground and the lower atmosphere must become warmer than without this atmosphere, in order to re-radiate as much energy as received from the Sun.” Disproof: This statement is vacuous, even in a literal sense. One cannot compare the temperature of a planet's lower atmosphere with the situation where a planetary atmosphere does not exist at all. Furthermore, as shown in Section 2.2 the portion of the incoming infrared is larger than the portion of the incoming visible light. Roughly speaking, we have a fty- fty relation. Therefore the supposed warming from the bottom must compare to an analogous warming from the top. Even within the logics of Gral's oversimpli ed (and physically incorrect) conjecture one is left with a zero temperature gradient and thus a null e ect. 3.3.10 Atmospheric greenhouse e ect after Ahrens (2001) In his textbook \Essentials in Meteorology: In Invitation to the Atmosphere” the author Ahrens states [137]: \The absorption characteristics of water vapor, CO2, and other gases such as methane and nitrous oxide ::. were, at one time, thought to be similar to the glass of a orists greenhouse. In a greenhouse, the glass allows visible radiation to come in, but inhibits to some degree the passage of outgoing infrared radiation. For this reason, the behavior of the water vapor and CO2, the atmosphere is popularly Gerhard Gerlich and Ralf D. Tscheuschner called the greenhouse e ect. However, studies have shown that the warm air inside a greenhouse is probably caused more by the airs inability to circulate and mix with the cooler outside air, rather than by the entrapment of infrared energy. Because of these ndings, some scientists insist that the greenhouse e ect should be called the atmosphere e ect. To accommodate everyone, we will usually use the term atmospheric greenhouse e ect when describing the role that water vapor and CO2, play in keeping the earths mean surface temperature higher than it otherwise would be.” Disproof: The concept of the Earth's mean temperature is ill-de ned. Therefore the concept of a rise of a mean temperature is ill-de ned as well. 3.3.11 Atmospheric greenhouse e ect after Dictionary of Geophysics, Astrophysics, and Astronomy (2001) The Dictionary of Geophysics, Astrophysics, and Astronomy says [138]: \Greenhouse E ect: The enhanced warming of a planets surface temperature caused by the trapping of heat in the atmosphere by certain types of gases (called greenhouse gases; primarily carbon dioxide, water vapor, methane, and chloro uorocarbons). Visible light from the sun passes through most atmospheres and is absorbed by the body's surface. The surface reradiates this energy as longer- wavelength infrared radiation (heat). If any of the greenhouse gases are present in the body's troposphere, the atmosphere is transparent to the visible but opaque to the infrared, and the infrared radiation will be trapped close to the surface and will cause the temperature close to the surface to be warmer than it would be from solar heating alone.” Disproof: Infrared radiation is confused with heat. It is not explained at all what is meant by `the infrared radiation will be trapped". Is it a MASER, is it \superinsulation", i.e. vanishing thermal conductivity, or is it simple thermalization? 3.3.12 Atmospheric greenhouse e ect after Encyclopaedia of Astronomy and Astrophysics (2001) The Encyclopaedia of Astronomy and Astrophysics de nes the greenhouse e ect as follows [139]: \The greenhouse e ect is the radiative in uence exerted by the atmosphere of a planet which causes the temperature at the surface to rise above the value it would normally reach if it were in direct equilibrium with sunlight (taking Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. into account the planetary albedo). This e ect stems from the fact that certain atmospheric gases have the ability to transmit most of the solar radiation and to absorb the infrared emission from the surface. The thermal (i.e. infrared) radiation intercepted by the atmosphere is then partially re-emitted towards the surface, thus contributing additional heating of the surface. Although the analogy is not entirely satisfactory in terms of the physical processes involved, it is easy to see the parallels between the greenhouse e ect in the atmosphere-surface system of a planet and a horticultural greenhouse: the planetary atmosphere plays the role of the glass cover that lets sunshine through to heat the soil while partly retaining the heat that escapes from the ground. The analogy goes even further, since an atmosphere may present opacity `windows’ allowing infrared radiation from the surface to escape, the equivalent of actual windows that help regulate the temperature inside a domestic greenhouse.” Disproof: The concept of the \direct equilibrium with the sunlight’ is physically wrong, as will be shown in detail in Section 3.7. The description of the physics of a horticultural greenhouse is incorrect. Thus the analogy stinks. 3.3.13 Atmospheric greenhouse e ect after Encyclopaedia Britannica Online (2007) Encyclopaedia Britannica Online explains the greenhouse e ect in the following way [140]: \The atmosphere allows most of the visible light from the Sun to pass through and reach the Earth's surface. As the Earth's surface is heated by sunlight, it radiates part of this energy back toward space as infrared radiation. This radiation, unlike visible light, tends to be absorbed by the greenhouse gases in the atmosphere, raising its temperature. The heated atmosphere in turn radiates infrared radiation back toward the Earth's surface. (Despite its name, the greenhouse e ect is di erent from the warming in a greenhouse, where panes of glass transmit visible sunlight but hold heat inside the building by trapping warmed air.) Without the heating caused by the greenhouse e ect, the Earth's average surface temperature would be only about ..18 C (0 F).” Disproof: The concept of the Earth's average temperature is a physically and mathematically ill-de ned and therefore useless concept as will be shown in Section 3.7. 3.3.14 Atmospheric greenhouse e ect after Rahmstorf (2007) The renowned German climatologist Rahmstorf claims [141]: 44 Gerhard Gerlich and Ralf D. Tscheuschner \To the solar radiation reaching Earth's surface ::. the portion of the long-wave radiation is added, which is radiated by the molecules partly downward and partly upward. Therefore more radiation arrives down, and for reasons of compensation the surface must deliver more energy and thus has to be warmer (+15 C), in order to reach also there down again an equilibrium. A part of this heat is transported upward from the surface also by atmospheric convection. Without this natural greenhouse e ect the Earth would have frozen life-hostilely and completely. The disturbance of the radiative balance [caused by the enrichment of the atmosphere with trace gases] must lead to a heating up of the Earth's surface, as it is actually observed.” Disproof: Obviously, re ection is confused with emission. The concept of radiative balance is faulty. This will be explained in Section 3.7. 3.3.15 Conclusion It is interesting to observe, • that until today the \atmospheric greenhouse e ect” does not appear – in any fundamental work of thermodynamics, – in any fundamental work of physical kinetics, – in any fundamental work of radiation theory; • that the de nitions given in the literature beyond straight physics are very di erent and, partly, contradict to each other. 3.4 The conclusion of the US Department of Energy All ctitious greenhouse e ects have in common, that there is supposed to be one and only one cause for them: An eventual rise in the concentration of CO2 in the atmosphere is supposed to lead to higher air temperatures near the ground. For convenience, in the context of this paper it is called the CO2-greenhouse e ect. 14 Lee's 1973 result [109] that the warming phenomenon in a glass house does not compare to the supposed atmospheric greenhouse e ect was con rmed in the 1985 report of the United States Department of Energy \Projecting the climatic e ects of increasing carbon dioxide” [91]. In this comprehensive pre-IPCC publication MacCracken explicitly states that the terms \greenhouse gas” and \greenhouse e ect” are misnomers [91,142]. A copy of the last paragraph of the corresponding section on page 28 in shown in Figure 15. It should be emphasized: 14The nomenclature naturally extents to other trace gases. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. Figure 15: An excerpt from page 28 of the DOE report (1985). • The warming phenomenon in a glass house and the supposed atmospheric greenhouse e ects have the same participants, but in the latter case the situation is reversed. • Methodically, there is a huge di erence: For the physical greenhouse e ect one can make measurements, look at the di erences of the instruments readings and observe the e ect without any scienti c explanation and such without any prejudice. For the ctitious atmospheric greenhouse e ect one cannot watch anything, and only calculations are compared with one another: Formerly extremely simple calculations, they got more and more intransparent. Nowadays computer simulations are used, which virtually nobody can reproduce [143]. In the following the di erent aspects of the physics underlying the atmospheric situation are discussed in detail. 3.5 Absorption/Emission is not Re ection 3.5.1 An inconvenient popularization of physics Figure 16 is a screenshot from a controversial award-winning \documentary lm” about \climate change", speci cally \global warming", starring Al Gore, the former United States Vice President, and directed by Davis Guggenheim [144, 145]. This movie has been supported by managers and policymakers around the world and has been shown in schools and in outside events, respectively. Lewis wrote an interesting \A Skeptic's Guide to An Inconvenient Truth” evaluating Gore's work in detail [146]. From the view of a trained physicist, Gore's movie is rather grotesque, since it is shockingly wrong. Every licensed radio amateur15 knows that what is depicted in Figure 16 would be 15Callsign of R.D.T.: DK8HH Gerhard Gerlich and Ralf D. Tscheuschner Figure 16: A very popular physical error illustrated in the movie \An Inconvenient truth” by Davis Guggenheim featuring Al Gore (2006). true only, • if the radiation graphically represented here was long wave or short wave radiation; • if the re ecting sphere was a certain layer of the ionosphere [147]. Short waves (e.g. in the 20 m/14 MHz band) are re ected by the F layer of the ionosphere (located 120 -400 km above the Earth's surface) enabling transatlantic connections (QSOs). Things depend pretty much on the solar activity, i.e. on the sun spot cycle, as every old man (OM) knows well. The re ective characteristics of the ionosphere diminish above about 30 MHz. In the very high frequency (VHF) bands (e.g. 2 m/144 MHz band) one encounters the so called Sporadic-E clouds (90 -120 km above the Earth's surface), which still allow QSOs from Germany to Italy, for example. On the other hand at the extremely low frequencies (ELF, i.e. frequency range 3 -30 Hz) the atmosphere of the Earth behaves as a cavity and one encounters the so called Schumann resonances [148]. These may be used to estimate a lower bound for the mass of the photon16 and, surprisingly, appear in the climate change discussion [149]. However, the radio signal of Al Gore's cellular phone (within the centimeter range) does not travel around the world and so does not Bluetooth, Radar, microwave and infrared radiation (i.e. electromagnetic waves in the sub millimeter range). Ionosphere Radars typically work in the 6 m Band, i.e. at 50 MHz. Meteorological Radars work in the 0.1 -20 cm range (from 90 GHz down to 1.5 GHz), those in the 3 -10 cm range (from 10 GHz down to 3 GHz) are used for wind nding and weather watch [150]. It is obvious, that Al Gore confuses the ionosphere with the tropopause, the region in the atmosphere, that is the 16As a teaching assistant at Hamburg University/DESY, R.D.T. learned this from Professor Herwig Schop per. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 47 boundary between the troposphere and the stratosphere. The latter one is located between 6 km (at the poles) and 17 km (at the equator) above the surface of the Earth.17 Furthermore, Al Gore confuses absorption/emission with re ection. Unfortunately, this is also done implicitly and explicitly in many climatologic papers, often by using the vaguely de ned terms \re-emission", \re-radiation” and \backradiation". 3.5.2 Re ection When electromagnetic waves move from a medium of a given refractive index n1 into a second medium with refractive index n2, both re ection and refraction of the waves may occur [151]. In particular, when the jump of the refractive index occurs within a length of the order of a wavelength, there will be a re ection. The fraction of the intensity of incident electromagnetic wave that is re ected from the interface is given by the re ection coecient R, the fraction refracted at the interface is given by the transmission coecient T . The Fresnel equations, which are based on the assumption that the two materials are both dielectric, may be used to calculate the re ection coecient R and the transmission coecient T in a given situation. In the case of a normal incidence the formula for the re ection coecient is 2 R = n2 - n1 (44) n2 + n1 In the case of strong absorption (large electrical conductivity ) simple formulas can be given for larger angles . of incidence, as well (Beer's formula): (n2 - n1 cos )2 + n22 2 Rs = (45) (n2 + n1 cos )2 + n22 2 and (n1 - n2 cos )2 + n22 cos2 . Rp = (n1 + n2 cos )2 + n22 2 2 cos2 . (46) When the jump of the refractive index occurs within a length of the order of a wavelength, there will be a re ection, which is large at high absorption. In the case of gases this is only possible for radio waves of a comparatively long wave length in the ionosphere, which has an electrical conductivity, at a diagonal angle of incidence. There is no re ection in the homogeneous absorbing range. As already elucidated in Section 3.5.1 this has been well- known to radio amateurs ever since and a ects their activity e.g. in the 15 m band, but never in the microwave bands. On the other hand, most glasses absorb the infrared light almost completely at approximately 1 m and longer wavelength: therefore, the re ection of the infrared waves for normal glasses is very high. For dielectric media, whose electrical conductivity is zero, one cannot use Beer's formulas. This was a severe problem in Maxwell's theory of light. 17Some climatologists claim that there is a CO2 layer in the troposphere that traps or re ects the infrared radiation coming from the ground. 48 Gerhard Gerlich and Ralf D. Tscheuschner 3.5.3 Absorption and Emission If an area is in thermodynamical equilibrium with a eld of radiation, the intensity E. (resp. E) emitted by the unit solid angle into a frequency unit (resp. a wavelength unit) is equal to the absorptance A. (resp. A) multiplied with a universal frequency function B. (T ) (resp. a wavelength function B(T )) of the absolute temperature T . One writes, respectively, E. =A. B(T ) (47) · E. =A. · B(T ) (48) This is a theorem by Kirchho . The function B(T ) (resp. B(T )) is called the Kirchho - Planck-function. It was already considered in Section 2.1.4. The re ectance is, respectively, R. =1 - A. (49) R. =1 - A. (50) and lies between zero and one, like the absorptance A. . If R is equal to zero and A is equal to one, the body is called a perfect black body. The emissivity is largest for a perfect black body. The proposal to realize a perfect black body by using a cavity with a small radiating opening had already been made by Kirchhoff and is visualized in Figure 17. For this reason, Figure 17: A cavity realizing a perfect black body. the emission of a black body for A. = 1 (resp. A. = 1) is called cavity radiation. The emitted energy comes from the walls, which are being held at a xed temperature. If this is realized with a part of a body's surface, it will become clear, that these points of view will only be compatible, if the electromagnetic radiation is emitted and absorbed by an extremely thin surface layer. For this reason, it is impossible to describe the volumes of gases with the model of black cavity radiation. Since thermal radiation is electromagnetic radiation, this radiation would have to be caused by thermal motion in case of gases, which normally does not work e ectively at room temperatures. At the temperatures of stars the situation is di erent: The energy levels of the atoms are thermally excited by impacts. 3.5.4 Re-emission In case of radiation transport calculations, Kirchho 's law is \generalized” to the situation, in which the corresponding formula for the emission, or respectively, for the absorption (per Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 49 unit length along the direction ds) is supposed to be applicable ". ds = ds B. (T ) (51) · The physical meaning of this \generalization” can be seen most easily, if the above mentioned Kirchhoff law is mathematically extracted out of this formula. For this, one may introduce ". =E. (s - s0) (52) . =A. (s - s0) (53) with a -density localized at the interface. Physically, this means that all of the absorption and emission comes out of a thin super cial plane. Just like with the correct Kirchhoff law, use is made of the fact, that all absorbed radiation is emitted again, as otherwise the volume area would raise its temperature in thermal balance. This assumption is called the assumption of Local Thermodynamical Equilibrium (LTE). Re-emission does never mean re ection, but, rather, that the absorption does not cause any rise of temperature in the gas. An important physical di erence to the correct Kirchhoff law lies in the fact, that there is no formula for the absorption per linear unit analogous to R. =1 - A. (54) With . being the density of the medium one can de ne a absorption coecient . and an emission coecient j. , respectively, by setting . = . . (55) ". = j. (56) The ratio of the emission to the absorption coecient j S. = (57) . describes the re-emission of the radiation and is called the source function. 3.5.5 Two approaches of Radiative Transfer In a gas the radiation intensity of an area changes in the direction of the path element ds according to dI. - ds = . I. - ". (58) With the aid of the functions introduced in Equations (55) -(57) this can be expressed as 1 dI. =I. - S. (59) . ds Gerhard Gerlich and Ralf D. Tscheuschner This equation is called the radiative transfer equation. Two completely di erent approaches show that this emission function is not just deter mined by physical laws [93]: 1. The usual one, i.e. the one in case of LTE, is given by the ansatz S. (x, y, z; l, m, n)=B. (T(x, y, z; l, m, n)) (60) where the coordinates (x, y, z) and the direction cosines (l, m, n) de ne the point and the direction to which S. and B. (resp. T ) refer. This approach is justi ed with the aid of the Kirchho -Planck-function B. and the \generalized” Kirchhoff law introduced in Equation (51). This assumption of Local Thermodynamical Equilibrium (LTE) is ruled out by many scientists even for the extremely hot atmospheres of stars. The reader is referred to Chandrasekhar's classical book on radiative transfer [93]. LTE does only bear a certain signi cance for the radiation transport calculations, if the absorption coecients were not dependent on the temperature, which is not the case at low temperatures. Nevertheless, in modern climate model computations, this approach is used unscrupulously [91]. 2. Another approach is the scattering atmosphere given by 1 . p . 2p S. = p(#, '; #0;'0)I(#0;'0) sin #0d#0d'. (61) 4p 00 These extremely di erent approaches show, that even the physically well-founded radiative transfer calculations are somewhat arbitrary. Formally, the radiative transfer Equation (59) can be integrated leading to s I. (s)=I(0) exp(..t (s, 0))+ S. (s0) exp(..(s, s0)). ds. (62) 0 with the optical thickness s (s, s0)= . . ds0. (63) s. The integrations for the separate directions are independent of one another. In particular, the ones up have nothing to do with the ones down. It cannot be overemphasized, that di erential equations only allow the calculation of changes on the basis of known parameters. The initial values (or boundary conditions) cannot be derived from the di erential equations to be solved. In particular, this even holds for this simple integral. If one assumes that the temperature of a volume element should be constant, one cannot calculate a rising temperature. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 51 3.6 The hypotheses of Fourier, Tyndall, and Arrhenius 3.6.1 The traditional works In their research and review papers the climatologists refer to legendary publications of Svante August Arrhenius (Feb. 19th 1859 -Oct. 2nd 1927), a Nobel Prize winner for chemistry. Arrhenius published one of the earliest, extremely simple calculations in 1896, which were immediately -and correctly -doubted and have been forgotten for many decades [44{46]. It is a paper about the in uence of carbonic acid in the air on the Earth's ground temperature. In this quite long paper, Arrhenius put the hypothesis up for discussion, that the occurrences of warm and ice ages are supposed to be explainable by certain gases in the atmosphere, which absorb thermal radiation. In this context Arrhenius cited a 1824 publication by Fourier18 entitled \Memoire sur les temperatures du globe terrestre et des espaces planetaires” [37, 38]. Arrhenius states incorrectly that Fourier was the rst, who claimed that the atmosphere works like a glass of a greenhouse as it lets the rays of the Sun through but keeps the so-called dark heat from the ground inside. The English translation of the relevant passage (p. 585) reads: We owe to the celebrated voyager M. de Saussure an experiment which appears very important in illuminating this question. It consists of exposing to the rays of the Sun a vase covered by one or more layers of well transparent glass, spaced at a certain distance. The interior of the vase is lined with a thick envelope of blackened cork, to receive and conserve heat. The heated air is sealed in all parts, either in the box or in each interval between plates. Thermometers placed in the vase and the intervals mark the degree of heat acquired in each place. This instrument has been exposed to the Sun near midday, and one saw, in diverse experiments, the thermometer of the vase reach 70, 80, 100, 110 degrees and beyond (octogesimal division). Thermometers placed in the intervals acquired a lesser degree of heat, and which decreased from the depth of the box towards the outside. Arrhenius work was also preceded by the work of Tyndall who discovered that some gases absorb infrared radiation. He also suggested that changes in the concentration of the gases could bring climate change [39{43]. A faksimile of the front pages of Fourier's and Arrhenius often cited but apparently not really known papers are shown in Figure 18 and in Figure 19, respectively. 18There is a misprint in Arrhenius’ work. The year of publication of Fourier's paper is 1824, not 1827 as stated in many current papers, whose authors apparently did not read the original work of Fourier. It is questionable whether Arrhenius read the original paper. Gerhard Gerlich and Ralf D. Tscheuschner Figure 18: The front page of Fourier's 1824 paper. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. Figure 19: The front page of Arrhenius’ 1896 paper. Gerhard Gerlich and Ralf D. Tscheuschner In which fantastic way Arrhenius uses Stefan-Boltzmann's law to calculate this \e ect", can be seen better in another publication, in which he defends his ice age-hypothesis [46]. see Figure 20. Figure 20: Excerpt (a) of Arrhenius’ 1906 paper. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. First, Arrhenius estimates that 18:7 % of the Earth's infrared radiation would not be emitted into space because of its absorption by carbonic acid. This could be taken into account by reducing the Earth's e ective radiation temperature Teff to a reduced temperature Treduced. Arrhenius assumed Teff = 15 C = 288 K (64) and, assuming the validity of the Stefan-Boltzmann law, made the ansatz s · T 4 = (1 - 0:187) · I0 (65) reduced T 4 s eff I0 · yielding 4 Treduced = Teff p1 - 0:187 (66) and 4 Treduced = p0:813 288 = 273:47 (67) · which corresponds to a lowering of the Earth's temperature of 14:5 C. As one would probably not think that such an absurd claim is possible, a scan of this passage is displayed in Figures 21 and 22. Figure 21: Excerpt (b) of Arrhenius’ 1906 paper. Gerhard Gerlich and Ralf D. Tscheuschner Figure 22: Excerpt (c) of Arrhenius’ 1906 paper. The English translation reads: \This statement could lead to the impression, that I had claimed that a reduction of the concentration of carbonic acid in the atmosphere of 20 % would be su cient to cause ice-age temperatures, i.e. to lower the Europe's average temperature about four to ve degrees C. To keep such an idea from spreading, I would like to point out that according to the old calculation a reduction of carbonic acid of 50 % would cause the temperature to fall for 4 (1897) or, respectively, 3:2 (1901) degrees. The opinion that a decrease of carbonic acid in the air can explain ice-age temperatures is not proved wrong until it is shown, that the total disappearance of carbonic acid from the atmosphere would not be sucient to cause a lowering of temperatures about four to ve degrees. It is now easy to estimate how low the temperature would fall, if the Earth's radiation rose in the ratio of 1 to 0:775, i.e. for 29 %, which matches the data of Messrs. Rubens and Ladenburg. An increase of emissions of 1 % would be equivalent to a decrease of temperatures of 0:72 C, as the average absolute temperature of the Earth is taken to be 15 C = 288C. Therefore, one could estimate a lowering of the temperatures about 20, 9 C as a result of the disappearance of carbonic acid from the atmosphere. A more exact calculation, which takes into Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 57 account the small amount of radiation of the carbonic acid and of which I have given details in my paper of 1901, leads to slightly lower numbers. According to this calculation, 3:8 % out of the 22:5 % of terrestrial radiation, which are being absorbed by the carbonic acid in the atmosphere at its current state, are emitted into space by the carbonic acid, so the real decrease of terrestrial radiation would be 18:7 %. After the disappearance of the carbonic acid, instead of the current temperature of 15 C = 288 K, there would be an absolute temperature T , which is: T 4 : 2884 = (1 - 0, 187) : 1 (68) being T = 273, 4K = 0, 4 C. (69) The current amount of carbonic acid would therefore raise the temperature of the Earth's surface for 14, 6 C its disappearance from the atmosphere would result in a lowering of temperatures about three times as strong as the one, which caused the ice ages. I calculate in a similar way, that a decrease in the concentration of carbonic acid by half or a doubling would be equivalent to changes of temperature of ..1, 5 C or +1, 6 C respectively.” It is an interesting point that there is an inversion of the burden of proof in Arrhenius’ paper, which is typeset in boldface here, because it winds its way as a red thread through almost all contemporary papers on the in uence of CO2 of the so-called global climate. 3.6.2 Modern works of climatology Callendar [47{53] and Keeling [54{60], the founders of the modern greenhouse hypothesis, recycled Arrhenius’ \discussion of yesterday and the day before yesterday"19 by perpetuating the errors of the past and adding lots of new ones. In the 70s and 80s two developments coincided: A accelerating progress in computer technology and an emergence of two contrary policy preferences, one supporting the development of civil nuclear technology, the other supporting Green political movements. Suddenly the CO2 issue became on-topic, and so did computer simulations of the climate. The research results have been vague ever since: • In the 70s, computer simulations of the \global climate” predicted for a doubling of the CO2 concentration a global temperature rise of about 0.7 -9.6 K [152]. • Later, computer simulations pointed towards a null e ect20: 19a phrase used by von Storch in Ref. [1] 20G.G. is indebted to the late science journalist Holger Heuseler for this valuable information [153]. 58 Gerhard Gerlich and Ralf D. Tscheuschner – In the IPCC 1992 report, computer simulations of the \global climate” predicted a global temperature rise of about 0.27 -0.82 K per decade [25]. – In the IPCC 1995 report, computer simulations of the \global climate” predicted a global temperature rise of about 0.08 -0.33 K per decade [28]. • Two years ago (2005), computer simulations of the \global climate” predicted for a doubling of the CO2 concentration a global temperature rise of about 2 -12 K, whereby six so-called scenarios have been omitted that yield a global cooling [154]. The state of the art in climate modeling 1995 is described in Ref. [155] in detail. Today every home server is larger than a mainframe at that time and every amateur can test and modify the vintage code [156]. Of course, there exist no realistic solvable equations for the weather parameters. Meanwhile, \computer models” have been developed which run on almost every PC [154, 156] or even in the internet [157]. To derive a climate catastrophe from these computer games and scare mankind to death is a crime. 3.7 The assumption of radiative balance 3.7.1 Introduction Like the physical mechanism in glass houses the CO2-greenhouse e ect is about a comparison of two di erent physical situations. Unfortunately, the exact de nition of the atmospheric greenhouse e ect changes from audience to audience, that is, there are many variations of the theme. Nevertheless, one common aspect lies in the methodology that a ctitious model computation for a celestial body without an atmosphere is compared to another ctitious model computation for a celestial body with an atmosphere. For instance, \average” temperatures are calculated for an Earth without an atmosphere and for an Earth with an atmosphere. Amusingly, there seem to exist no calculations for an Earth without oceans opposed to calculations for an Earth with oceans. However, in many studies, models for oceanic currents are included in the frameworks considered, and radiative \transport” calculations are incorporated too. Not all of these re nements can be discussed here in detail. The reader is referred to Ref. [156] and further references therein. Though there exists a huge family of generalizations, one common aspect is the assumption of a radiative balance, which plays a central role in the publications of the IPCC and, hence, in the public propaganda. In the following it is proved that this assumption is physically wrong. 3.7.2 A note on \radiation balance” diagrams From the de nition given in Section 2.1.2 it is immediately evident that a radiation intensity I. is not a current density that can be described by a vector eld j(x;t). That means Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. that conservation laws (continuity equations, balance equations, budget equations) cannot be written down for intensities. Unfortunately this is done in most climatologic papers, the cardinal error of global climatology, that may have been overlooked so long due to the oversimpli cation of the real world problem towards a quasi one-dimensional problem. Hence the popular climatologic \radiation balance” diagrams describing quasi-one-dimensional situations (cf. Figure 23) are scienti c misconduct since they do not properly represent the mathematical and physical fundamentals. Figure 23: A schematic diagram supposed to describe the global average components of the Earth's energy balance. Diagrams of this kind contradict to physics. Diagrams of the type of Figure 23 are the cornerstones of \climatologic proofs” of the supposed Greenhouse e ect in the atmosphere [142]. They are highly suggestive, because they bear some similarity to Kirchhoff rules of electrotechnics, in particular to the node rule describing the conservation of charge [158]. Unfortunately, in the literature on global climatology it is not explained, what the arrows in \radiation balance” diagrams mean physically. It is easily veri ed that within the frame of physics they cannot mean anything. Climatologic radiation balance diagrams are nonsense, since they 1. cannot represent radiation intensities, the most natural interpretation of the arrows depicted in Figure 23, as already explained in Section 2.1.2 and Section 2.1.5 ; 2. cannot represent sourceless uxes, i.e. a divergence free vector elds in three dimensions, since a vanishing three-dimensional divergence still allows that a portion of the eld goes sidewards; 60 Gerhard Gerlich and Ralf D. Tscheuschner 3. do not t in the framework of Feynman diagrams, which represent mathematical expressions clearly de ned in quantum eld theory [159]. 4. do not t in the standard language of system theory or system engineering [160]. Kirchho -type node rules only hold in cases, where there is a conserved quantity and the underlying space may be described by a topological space that is a one-dimensional manifold almost everywhere, the singularities being the network nodes, i.e. in conventional electric circuitry [158], in mesoscopic networks [161], and, for electromagnetic waves, in waveguide networks21 [163,164]. However, although Kirchho 's mesh analysis may be successfully applied to microwave networks, the details are highly involved and will break down if dissipation is allowed [163,164]. Clearly, neither the cryptoclimate of a glass house nor the atmosphere of the Earth's does compare to a waveguide network e.g. feeding the acceleration cavities of a particle accelerator. Therefore, the climatologic radiation balance diagrams are inappropriate and misleading, even when they are supposed to describe averaged quantities. 3.7.3 The case of purely radiative balance If only thermal radiation was possible for the heat transfer of a radiation-exposed body one would use Stefan-Boltzmann's law S(T )= T 4 (70) to calculate the ground temperature determined by this balance. The irradiance S has dimensions of a power density and s is the Stefan-Boltzmann constant given by 25k4 W . T 4 W s = 15c2h3 =5:670400 · 10..8 m2K4 ˜ 5:67 · 100 m2K4 (71) For example, the energy ux density of a black body a room temperature 300 K is approximately S( T =300K) = 459 W=m 2 (72) One word of caution is needed here: As already emphasized in Section 2.1.5 the constant s appearing in the T 4 law is not a universal constant of physics. Furthermore, a grey radiator must be described by a temperature dependent (T ) spoiling the T 4 law. Rigorously speaking, for real objects the Equation (70) is invalid. Therefore all crude approximations relying on T 4 expressions need to be taken with great care. In fact, though popular in global climatology, they prove nothing! 21The second and the third type are beautifully related by the correspondence of the v. Klitzing resistance RvK ˜ 25, 813 kO with the characteristic impedance Z0 ˜ 376, 73 O via the Sommerfeld ne structure constant a =Z0=2RvK ˜ 1=137, 036 [162]. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. In the balance equation R2 T 4 = T 4 Sun (73) · Earth's ground · Sun · R2 Earth's orbit one may insert a general phenomenological normalization factor . at the right side, leaving room for a ne tuning and inclusion of geometric factors.22 Thus one may write T 4 = s 57804 1= . 1368 W=m 2 = . s (74) · Earth's ground · · 46225 · which yields TEarth's ground 4p215 4· = p. 5780 K= p. 394:2 K (75) s is the solar constant. With the aid of Equation (75) one calculates the values displayed in Table 10. TEarth'sground[K]TEarth'sground[C] 1:00394:2121:20:70360:687:60:62349:876:8 Table 10: E ective temperatures TEarth's ground in dependence of the phenomenological normalization parameter . Only the temperature measured in the Sun inside the car bears some similarity with the three ones calculated here. Therefore, the radiation balance does not determine the temperature outside the car! In contrast to this, Table 11 displays the \average e ective” temperatures of the ground, which according to climatological consensus are used to \explain” the atmospheric greenhouse e ect. The factor of a quarter is introduced by \distributing” the incoming solar radiation seeing a cross section Earth over the global surface Earth Earth = p · REarth 2 = 1 (76) Earth 4p REarth 2 4 · The ctitious natural greenhouse e ect is the di erence the \average e ective” temperature of ..18 C and the Earth's \observed” average temperature of +15 C. 22The factor e is related to the albedo A of the Earth describing her re ectivity: A =1 - ". In the earlier literature one often nds A =0:5 for the Earth, in current publications A =0:3. The latter value is used here. Gerhard Gerlich and Ralf D. Tscheuschner . TEarth's ground [K] TEarth's ground [C] 0:25 · 1:00 278:7 5:7 0:25 · 0:70 255:0 ..18:0 0:25 · 0:62 247:4 ..25:6 Table 11: E ective \average” temperatures Tground in dependence of the phenomenological normalization parameter . incorporating a geometric factor of 0:25. In summary, the factor 0.7 will enter the equations if one assumes that a grey body absorber is a black body radiator, contrary to the laws of physics. Other choices are possible, the result is arbitrary. Evidently, such an average value has no physical meaning at all. This will be elucidated in the following subsection. 3.7.4 The average temperature of a radiation-exposed globe Figure 24: A radiation exposed static globe. For a radiation exposed static globe (cf. Figure 24) the corresponding balance equation must contain a geometric factor and reads therefore . T 4 = . . · S · cos . = . · s · 57804=2152 · cos . if 0 = . = =2 (77)· . 0 if =2 = . = p It is obvious that one gets the e ective temperatures if the right side is divided by . This in turn will determine the formerly mentioned \average” e ective temperatures over the global surface. 1 T 4 = T 4 d eff 4p surface Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 1 . 2p . p = T 4 sin . d. d. 4p 00 = 1 . 2p . ..1 T 4d(- cos #) d. 4p 01 1 . 2p . 1 = T 4d(cos #) d. (78) 4p 0 ..1 De ning µ := cos . (79) one gets 1 . 2p . 1 T 4 = T 4 dµ d. eff 4p 0 ..1 1 . 2p . 1 S = . dd. 4p 00 · s · 1S . 1 = . dµ 2 · s · 0 1 S 4 · s 1 = . (394:2)4 K4 (80) 4 · This is the correct derivation of the factor quarter appearing in Equation (76). Drawing the fourth root out of the resulting expression . S Teff = 4 4 · s = 4 394:2K 4 · 4 = (1=p2) p. 394:2K · 4 =0:707 p. 394:2 K (81) · Such a calculation, though standard in global climatology, is plainly wrong. Namely, if one wants to calculate the average temperature, one has to draw the fourth root rst and then determine the average, though: 1 . 2p . 1 Tphys = T dµ d. 4p 0 ..1. 1 . 2p . 1 S 4 = . µ dd. 4p 00 · s · 4 4 = 21 · . · s S · . 0 1 pµ dµ 1 S4 4 2 · s · 5 2S 4 = . (82) 5 · s Gerhard Gerlich and Ralf D. Tscheuschner nally yielding 4 Tphys = 52 p. · 394:2K 4 =0:4 p. 394:2 K (83) · Now the averaged temperatures Tphys are considerably lower than the absolute temperature's fourth root of the averaged fourth power (cf. Table 12). . Teff [C] Tphys [C] 1:00 5:7 ..115 0:70 ..18:0 ..129 0:62 ..25:6 ..133 Table 12: Two kinds of \average” temperatures Teff and Tphys in dependence of the emissivity parameter . compared. This is no accident but a consequence of Holder's inequality [165{168] . . 1=p . 1=q fg dµ = fp dµ · gq dµ (84) X X X for two non-negative measurable functions f, g and non-negative integers p, q obeying 1 1 + = 1 (85) p q In the case discussed here one has p = 4, q = 4=3, g(x) = 1 (86) and f = T (87) 3.7.5 Non-existence of the natural greenhouse e ect According to the consensus among global climatologists one takes the ..18C computed from the T 4 average and compares it to the ctitious Earth's average temperature of +15 C. The di erence of 33 C is attributed to the natural greenhouse e ect. As seen in Equation (83) a correct averaging yields a temperature of ..129 C. Evidently, something must be fundamentally wrong here. In global climatology temperatures are computed from given radiation intensities, and this exchanges cause and e ect. The current local temperatures determine the radiation Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. intensities and not vice versa. If the soil is warmed up by the solar radiation many di erent local processes are triggered, which depend on the local movement of the air, rain, evaporation, moistness, and on the local ground conditions as water, ice, rock, sand, forests, meadows, etc. One square meter of a meadow does not know anything of the rest of the Earth's surface, which determine the global mean value. Thus, the radiation is locally determined by the local temperature. Neither is there a global radiation balance, nor a global radiation budget, even in the mean- eld limit. While it is incorrect to determine a temperature from a given radiation intensity, one is allowed to compute an e ective radiation temperature Teff rad from T 4 averages representing a mean radiation emitted from the Earth and to compare it with an assumed Earth's average temperature Tmean Holder's inequality says that the former is always larger than the latter Teff rad >Tmean (88) provided sample selection and averaging (probability space) remain the same. For example, if n weather stations distributed around the globe measure n temperature values T1, ... Tn, an empirical mean temperature will be de ned as n Tmean = Ti (89) n i=1 For the corresponding black body radiation intensity one can approximately set n 1 1 T 4 =: T 4 i eff rad (90) Smean = n i=1 de ning an e ective radiation temperature 1 Teff rad = Smean (91) s One gets immediately n 4 n i=1 Holder's inequality shows that one always has Teff rad >Tmean (93) 3.7.6 A numerical example From Equation (92) one can construct numerical examples where e.g. a few high local temperatures spoil an average built from a large collection of low temperatures. A more realistic distribution is listed in Table 13. The e ective radiation temperature Teff rad is slightly higher 1 T 4 i Teff rad (92) = Gerhard Gerlich and Ralf D. Tscheuschner Weather Station Instruments Reading Ti [C] Absolute Temperature Ti [K] 4th Power T 4 i 4th Root of 4th Power Mean Teff rad [K] 4th Root of 4th Power Mean Teff rad [C] 1 2 3 4 5 6 Mean 0.00 10.00 10.00 20.00 20.00 30.00 15.00 273.15 283.15 283.15 293.15 293.15 303.15 288.15 5566789756 6427857849 6427857849 7385154648 7385154648 8445595755 6939901750 288,63 15.48 Table 13: An example for a measured temperature distribution from which its associated e ective radiation temperature is computed. The latter one corresponds to the fourth root of the fourth power mean. than the average Tmean of the measured temperatures. According to Holder's inequality this will always be the case. Thus there is no longer any room for a natural greenhouse e ect, both mathematically and physically: • Departing from the physically incorrect assumption of radiative balance a mathematically correct calculation of the average temperature lets the di erence temperature that de nes the natural greenhouse e ect explode. • Departing from the mathematically correct averages of physically correct temperatures (i.e. measured temperatures) the corresponding e ective radiation temperature will be always higher than the average of the measured temperatures. 3.7.7 Non-existence of a global temperature In the preceding sections mathematical and physical arguments have been presented that the notion of a global temperature is meaningless. Recently, Essex, McKitrick, and Andresen showed [169]: \that there is no physically meaningful global temperature for the Earth in the context of the issue of global warming. While it is always possible to construct statistics for any given set of local temperature data, an in nite range of such statistics is mathematically permissible if physical principles provide no explicit Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 67 basis for choosing among them. Distinct and equally valid statistical rules can and do show opposite trends when applied to the results of computations from physical models and real data in the atmosphere. A given temperature eld can be interpreted as both `warming’ and `cooling’ simultaneously, making the concept of warming in the context of the issue of global warming physically ill-posed.” Regardless of any ambiguities, a global mean temperature could only emerge out of many local temperatures. Without knowledge of any science everybody can see, how such a changing average near-ground temperature is constructed: There is more or less sunshine on the ground due to the distribution of clouds. This determines a eld of local near-ground temperatures, which in turn determines the change of the distribution of clouds and, hence, the change of the temperature average, which is evidently independent of the carbon dioxide concentration. Mathematically, an evolution of a temperature distribution may be phenomenologically described by a di erential equation. The averages are computed afterwards from the solution of this equation. However, one cannot write down a di erential equation directly for averages. 3.7.8 The rotating globe Since the time when Fourier formulated the heat conduction equation, a non-linear boundary condition describing radiative transfer of a globe with a sun-side and a dark side has never belonged to the family of solvable heat conduction problems, even in the case of a non-rotating globe. Regardless of solvability, one can write down the corresponding equations as well as their boundary conditions. If a rotating globe (Fig. 25) was exposed to radiation and only radiative Figure 25: The rotating globe heat transfer to its environment was possible, the initial problem of the heat conduction Gerhard Gerlich and Ralf D. Tscheuschner equation would have to be solved with the following boundary condition = 8. . T 4 - S sin . cos(. - !dt) if ..=2 = . - !dt = =2 · T 4 if =2 = . - !dt = 3=2 (94) @T - . @n where . @n = n · . (95) denotes the usual normal derivative at the surface of the sphere and !d the angular frequency associated with the day-night cycle. By de ning an appropriate geometry factor (#, ', !d, t) = sin . cos(. - !dt) and the corresponding Sun side area (96) A = f(', #) | (#, ', !d, t) = 0} one can rewrite the expression as (97) = 8. . T 4 - S (#, ', !d;t) if(', #) . A · T 4 if (', #) 6 . A (98) @T - . @n 3.7.9 The obliquely rotating globe The result obtained above may be generalized to the case of an obliquely rotating globe. Figure 26: An obliquely rotating globe For an obliquely rotating globe (Fig. 26) one has @T = 8. . T 4 - S (#0, #, ', !y;!d;t) if(', #) . A · T 4 if (', #) 6 . A (99) - . @n Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. where @=@n denotes the usual normal derivative on the surface of the sphere and !y, !d the angular frequencies with the year cycle and the day-night cycle, respectively.23 The geometry factor now reads (#0, #, ', !y;!d;t) = [ sin(!yt) cos(!dt) + cos(!yt) sin(!dt) cos #0] sin . cos . +[- sin(!yt) sin(!dt) + cos(!yt) cos(!dt) cos #0] sin . sin . - [ cos(!yt) sin #0 ] cos . (100) and the expression for the sun-side surface is given by A = f(', #) | (#0, #, ', !y, !d, t) = 0} (101) Already the rst unrealistic problem will be too much for any computer. The latter more realistic model cannot be tackled at all. The reasons for this is not only the extremely di erent frequencies !y and !d but also a very non-physical feature which a ects the numeric as well: According to a famous law formulated by Wiener, almost all particles in this mathematical model which cause the di usion, move on paths at in nitely high speeds [170, 171]. Rough estimates indicate that even these oversimpli ed problems cannot be tackled with any computer. Taking a sphere with dimensions of the Earth it will be impossible to solve this problem numerically even in the far future. Not only the computer would work ages, before a \balanced” temperature distribution would be reached, but also the correct initial temperature distributions could not be determined at all. 3.7.10 The radiating bulk The physical situation of a radiating volume where the radiation density S(T )= T 4 (102) emitted through the surface shell originates from the volume's heat content, cannot be realized easily, if at all. However, it is interesting to study such a toy model in order to get a feeling about radiative equilibration processes which are assumed to take place within a reasonable time interval. With disregard to the balancing processes inside, one gets the di erential equation dT V%cv = ..O T 4 (103) dt with V denoting the volume, . the density, cv the isochoric speci c heat, O the surface of the body. By de ning O . = (104) V 23Here sidereal time is used [138,139]. Gerhard Gerlich and Ralf D. Tscheuschner the above equation can be rewritten as dT s dt = ..%cv · T 4 (105) For a cube with an edge length of a one has . =6=a, for a globe with radius r one has . =3=r instead. For bodies with unit volumes . =6 or . =4:8, respectively. The di erential equation is easily solvable. The solution reads vuut 3T ()= T=t0 1+ 3 . T 0 3 %cv t (106) At an initial temperature of 300 K with the values of . and cv for air, one gets one half of the temperature value within three seconds for the standard cube (cf. Figure 27) For iron the Figure 27: The cooling curve for a radiating standard cube isochoric thermal di usivity av = %cv (107) is about 3000 times higher than for air, the half time for the temperature decrease is approximately three hours. For air, even if only one of the cube's planes were allowed to radiate, one would get a fall in temperatures of seventy degrees within the rst three seconds, and almost 290 degrees within ten hours -a totally unrealistic cooling processes. Hence, this simple assessment will prove that one has to be extremely careful, if the radiation laws for black-body radiation, where the energy comes from the heated walls of the cavity, are to be used for gases, where the emitted electromagnetic radiation should originate from the movements of the gas molecules (cf. Section 3.5). 3.7.11 The comprehensive work of Schack Professor Alfred Schack, the author of a standard textbook on industrial heat transfer [95], was the rst scientist who pointed out in the twenties of the past century that the infrared Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. light absorbing re gas components carbon dioxide (CO2) and water vapor (H2O) may be responsible for a higher heat transfer in the combustion chamber at high burning temperatures through an increased emission in the infrared. He estimated the emissions by measuring the spectral absorption capacity of carbon dioxide and water vapor. In the year 1972 Schack published a paper in Physikalische Blatter entitled \The in uence of the carbon dioxide content of the air on the world's climate". With his article he got involved in the climate discussion and emphasized the important role of water vapor [98]. Firstly, Schack estimated the mass of the consumed fossil fuels up mburned =5 1012 kg = 5 GtC (108) · per anno. Since 1 kg produces 10 m3 waste gas with 15 % CO2, a volume of VCO2 =7:5 1012 m 3 (109) · is blown into the Earth's atmosphere, whose total volume under normal conditions (0 C and 760 mm Hg) is Vatmosphere =4 1018 m 3 (110) · It follows immediately that the increase of the CO2 concentration is approximately 1:9 10..6 · per anno. About one half is absorbed by the oceans, such that the increase of CO2 is reduced to VCO2 =0:95 10..6 (111) VCO2 · per anno. With the \current” (1972) atmospheric CO2 volume concentration of 0:03%=300 10..6 (112) · and an relative annual increase of 0:95 10..6 0:32% = · (113) 300 10..6 · the CO2 concentration in the atmosphere would rise by one third of current concentration within 100 years, supposed the fossil fuel consumption will remain constant. Schack then shows that CO2 would absorb only one seventh of the ground's heat radiation at most, if the water vapor had not already absorbed the infrared light in most situations. Furthermore, a doubling of the CO2-content in the air would only halve the radiation's characteristic absorption length, that is, the radiation would be absorbed at a length of 5 km instead of at a length of 10 km, for example. Schack discussed the CO2 contribution only under the aspect that CO2 acts as an absorbent medium. He did not get the absurd idea to heat the radiating warmer ground with the radiation absorbed and re-radiated by the gas. 72 Gerhard Gerlich and Ralf D. Tscheuschner In a comment on an article by the science journalist Rudzinski [172] the climatologist Oeschger objectioned against Schack's analysis of the in uence of the CO2 concentration on the climate that Schack had not calculated thoroughly enough [173]. In particular, he referred to radiation transport calculations. However, such calculations have formerly been performed only for the atmospheres of stars, because the processes in planetary atmospheres are far too complicated for such simple models. The goal of astrophysical radiation transport calculations is to calculate as many absorption lines as possible with one boundary density distribution and one temperature dependency with respect to the height with Saha's equation and many other additional hypotheses [174]. However, the boundary density of the radiation intensity cannot be derived from these calculations. One should emphasize that Schack was the rst scientist to take into account the selective emission by the infrared light absorbing re-gases for combustion chambers. Therefore one is driven to the verge of irritation when global climatologists blame him for not calculating complicatedly enough, simply because he saw the primitive physical concepts behind the equations for the radiation transfer. 3.8 Thermal conductivity versus radiative transfer 3.8.1 The heat equation In many climatological texts it seems to be implicated that thermal radiation needs not be taken into account when dealing with heat conduction, which is incorrect [175]. Rather, always the entire heat ow density q must be taken into account. This is given by the equation q = ... grad T (114) · in terms of the gradient of the temperature T . It is inadmissible to separate the radiation transfer from the heat conduction, when balances are computed. In the following, a quasi one-dimensional experimental situation for the determination of the thermal conductivity is considered (Fig. 28). With F being the cross section, d the Figure 28: A simple heat transport problem. distance between the two walls, and Q being the heat per time transported from 1 to 2, such Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. that, qx = Q F (115) we have Q = F · qx = ... · F · @T @x = ... · F · T2 - T1 d = . · F · T1 - T2 d (116) in case of a stationary temperature distribution. Q is produced and measured for the stationary situation by Joule heat (i.e. electric heat) at the higher temperature. The heat transfer by radiation cannot be separated from the heat transfer of kinetic energy. Of course, one tries to avoid the heat convection by the experimental arrangement. Hence any e ects of the thermal radiation (long wave atmospheric radiation to Earth) are simply contained in the stationary temperatures and the measured Joule heat. In the non-stationary case the divergence of the heat ow no longer vanishes, and we have for constant thermal conductivity @T div q = ... div grad T = ... T = ..%cv · (117) · @t where T is the Laplacean of the temperature and %cv the speci c heat of unit volume. We nally obtain @T . =T (118) @t %cv It is important to note, that the thermal conductivity is divided by %cv, which means that the isochoric thermal di usivity . av = (119) %cv of gases and metals can be of the the same order of magnitude, even if the thermal conductivities . are completely di erent. Unfortunately, the work on even the simplest examples of heat conduction problems needs techniques of mathematical physics, which are far beyond the undergraduate level. Because a concise treatment of the partial di erential equations lies even outside the scope of this paper, the following statements should suce: Under certain circumstances it is possible to calculate the space-time dependent temperature distribution with given initial values and boundary conditions. If the temperature changes have the characteristic length Lchar, the characteristic time for the heat compensation process is 1 . 1 tchar = %cv · Lchar 2 (120) If the radius of the Moon were used as the characteristic length and typical values for the other variables, the relaxation time would be equivalent to many times the age of the universe. Therefore, an average ground temperature (over hundreds of years) is no indicator at all that 74 Gerhard Gerlich and Ralf D. Tscheuschner the total irradiated solar energy is emitted. If there were a di erence, it would be impossible to measure it, due to the large relaxation times. At long relaxation times, the heat ow from the Earth's core is an important factor for the long term reactions of the average ground temperature; after all, according to certain hypotheses the surfaces of the planetary bodies are supposed to have been very hot and to have cooled down. These temperature changes can never be separated experimentally from those, which were caused by solar radiation. 3.8.2 Heat transfer across and near interfaces In the real world things become even more complex through the existence of interfaces, namely • solid-gas interfaces • solid-liquid interfaces • liquid-gas interfaces for which a general theory of heat transport does not exist yet. The mechanisms of air cooling and water cooling and the in uence of radiation have been studied in engineering thermodynamics [95{97] and are of practical interest e.g. in solar collectors, re research, chemistry, nuclear engineering, electronic cooling, and in constructing reliable computer hardware [176, 177]. Obviously, there are of utmost importance in geophysics and atmospheric physics as well. Since they add an additional degree of complexity to the problem discussed here, they are not discussed further in this context. 3.8.3 In the kitchen: Physics-obsessed housewife versus IPCC In Section 3.3.5 it was indicated how simple it is to falsify the atmospheric greenhouse hypotheses, namely by observing a water pot on the stove: Without water lled in, the bottom of the pot will soon become glowing red. However, with water lled in, the bottom of the pot will be substantially colder. In particular, such an experiment can be performed on a glass-ceramic stove. The role of the Sun is played by the electrical heating coils or by infrared halogen lamps that are used as heating elements. Glas-ceramic has a very low heat conduction coecient, but lets infrared radiation pass very well. The dihydrogen monoxide in the pot, which not only plays the role of the \greenhouse gas” but also realizes a very dense phase of such a magic substance, absorbs the infrared extremely well. Nevertheless, there is no additional \backwarming” e ect of the bottom of the pot. In the opposite, the ground becomes colder. There are countless similar experiments possible that immediately show that the atmospheric greenhouse picture is absolutely ridiculous from an educated physicist's point of view or from the perspective of a well-trained salesman o ering high performance tinted glass that reduces solar heat gain mainly in the infrared [100]: Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 75 \Daylight and view are two of the fundamental attributes of a window. Unfortunately, windows are also the source of signi cant solar heat gain during times when it is unwanted. Traditional solutions to reducing solar heat gain such as tinted glazing or shades mean that the amount of light is reduced as well. New glazings with low-solar-gain Low-E (spectrally selective) coatings can provide better solar heat gain reduction than tinted glass, with a minimal loss of visible light. This also means that views can be clearer and unobstructed.” Ironically, this works already in the case of dihydrogen monoxide. Such experiments can be performed easily on every overhead projector, showing that the absorption of the infrared portion of the incoming radiation by water is a non-neglible and leads to a drop of the temperature of the illuminated surface dressed by an infrared absorbing layer that is transparent to visible light. 3.9 The laws of thermodynamics 3.9.1 Introduction At the time of Fourier's publication [37, 38] the two fundamental laws of classical thermodynamics were not known. For each law two equivalent versions as formulated by Rudolf Clausius (January 2, 1822 -August 24, 1888), the founder of axiomatic thermodynamics, are given by [178, 179]: • First law of thermodynamics: – In all cases, when work is transformed into heat, an amount of heat in proportion to the produced work is used up, and vice versa, the same amount of heat can be produced by the consumption of an equal amount of work. – Work can be transformed into heat and vice versa, where the amount of one is in proportion to the amount of the other. This is a de nition of the mechanical heat equivalent. • Second law of thermodynamics: – Heat cannot move itself from a cooler body into a warmer one. – A heat transfer from a cooler body into a warmer one cannot happen without compensation. A ctitious heat engine which works in this way is called a perpetuum mobile of the second kind. Clausius examines thoroughly, that the second law is relevant for radiation as well, even if image formations with mirrors and lenses are taken into account [178, 179]. 76 Gerhard Gerlich and Ralf D. Tscheuschner 3.9.2 Diagrams It is quite useful to clarify the second law of thermodynamics with (self-explaining) diagrams. • A steam engine works transforming heat into mechanical energy, whereby heat is transferred from the warmth to the cold (see Figure 29). Figure 29: A steam engine works transforming heat into mechanical energy. • A heat pump (e.g. a refrigerator) works, because an external work is applied, whereby heat is transferred from the the cold to the warmth (see Figure 30). Figure 30: A heat pump (e.g. a refrigerator) works, because an external work is applied. • In a perpetuum mobile of the second kind heat is transferred from the cold to the warmth without external work applied (see Figure 31). Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. Figure 31: Any machine which transfers heat from a low temperature reservoir to a high temperature reservoir without external work applied cannot exist: A perpetuum mobile of the second kind is impossible. 3.9.3 A paradox The use of a perpetuum mobile of the second kind can be found in many modern pseudo- explanations of the CO2-greenhouse e ect. Even prominent physicists have relied on this argumentation. One example was the hypothesis of Stichel already discussed in Section 3.3.4 [134]. The renowned German climatologist Rahmstorf has claimed that greenhouse e ect does not contradict to the the second law of thermodynamics [141]: \Some `sceptics’ state that the greenhouse e ect cannot work since (according to the second law of thermodynamics) no radiative energy can be transferred from a colder body (the atmosphere) to a warmer one (the surface). However, the second law is not violated by the greenhouse e ect, of course, since, during the radiative exchange, in both directions the net energy ows from the warmth to the cold.” Rahmstorf's reference to the second law of thermodynamics is plainly wrong. The second law is a statement about heat, not about energy. Furthermore the author introduces an obscure notion of \net energy ow". The relevant quantity is the \net heat ow", which, of course, is the sum of the upward and the downward heat ow within a xed system, here the atmospheric system. It is inadmissible to apply the second law for the upward and downward heat separately rede ning the thermodynamic system on the y. A similar confusion is currently seen in the German version of Wikipedia [180]: \Some have problems with the energy that is radiated by the greenhouse gases towards the surface of the Earth (150 W=m2 -as shown above) because this energy Gerhard Gerlich and Ralf D. Tscheuschner Figure 32: A machine which transfers heat from a low temperature reservoir (e.g. stratosphere) to a high temperature reservoir (e.g. atmosphere) without external work applied, cannot exist -even if it is radiatively coupled to an environment, to which it is radiatively balanced. A modern climate model is supposed to be such a variant of a perpetuum mobile of the second kind. ows from a colder body (approx. ..40 C) to a warmer one (Earth's ground approx. +15 C) apparently violating the second law of thermodynamics. This is a wrong interpretation, since it ignores the radiation of the Sun (even 6000 K). With respect to the total balance the second law is obeyed indeed.” Obviously, the authors are confusing energy with heat. Furthermore, the system in question here is the atmospheric system of the Earth including the Earth's ground. Since this system is assumed to be in radiative balance with its environment, and any other forms of energy and mass exchange with its environment are strictly prohibited, it de nes a system in the sense of thermodynamics for which the second law holds strictly. The di erence between heat, energy and work is crucial for the understanding of thermodynamics. The second law is a statement about this di erence. 3.9.4 Possible resolution of the paradox It may be due to the following approximation that something is possible in climate models, which contradicts the second law of thermodynamics. In the eld theoretical description of irreversible thermodynamics, the second law is found in the statement, that the heat ow density and the gradient of the temperature point into opposite directions q = ... grad T (121) · Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. In this formula, the heat conduction necessarily is a positive de nite tensor. In climate models it is customary to neglect the thermal conductivity of the atmosphere, which means to set it to zero [181]. . = 0 (122) This could explain, why the numerical simulations could produce small e ects in contradiction to the second law of thermodynamics. To set the heat conduction to zero would not be a real violation of the second law of thermodynamics as it corresponds to an approximation of an ideal system: In spite of the temperature di erences no heat ow could move from a warmer area to a colder one. It would be in accordance to the second law, if there were no temperature rise. In the past, the \predictions” of the climate models were pointing sometimes in this direction, as was shown in detail in Section 3.6.2. 80 Gerhard Gerlich and Ralf D. Tscheuschner 4 Physical Foundations of Climate Science 4.1 Introduction A fundamental theory of the weather and its local averages, the climates, must be founded on a reasonable physical theory. Under the premise that such a theory has already been formulated there are still two basic problems left unresolved, namely • the embedding of the purely physical theory in a much more wider framework including the chemical and biological interactions within the geophysical realm, • the correct physical account of a possible non-trivial radiative e ect, which must go far beyond the famous black body approach, which is suggestive but does not apply to gases. A review of the issues of chemistry and biology such as the carbon cycle lies outside the perspective of this paper, but it must not be neglected. In his criticism of global warming studies by means of computer models the eminent theoretical physicist Freeman J. Dyson stated [182]: \The models solve the equations of uid dynamics, and they do a very good job of describing the uid motions of the atmosphere and the oceans. They do a very poor job of describing the clouds, the dust, the chemistry and the biology of elds and farms and forests. They do not begin to describe the real world that we live in. The real world is muddy and messy and full of things that we do not yet understand. It is much easier for a scientist to sit in an air-conditioned building and run computer models, than to put on winter clothes and measure what is really happening outside in the swamps and the clouds. That is why the climate model experts end up believing in their own models.” However, it can be shown that even within the borders of theoretical physics with or without radiation things are extremely complex so that one very quickly arrives at a point where veri able predictions no longer can be made. Making such predictions nevertheless may be interpreted as an escape out of the department of sciences, not to say as a scienti c fraud. In the following the conservation laws of magnetohydrodynamics are reviewed. It is generally accepted that a Navier-Stokes-type approach or a simpli ed magnetohydrodynamics provides the backbone to climatological computer simulations [156,183,184]. In these frameworks neither the radiative budget equations can be derived, nor is it possible to integrate radiative interactions in a consistent way. Therefore it would conceptually be necessary to go into the microscopic regime, which is described by non-equilibrium multi-species quantum electrodynamics of particles incorporating bound states with internal degrees of freedom, Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 81 whereby the rich structure and coexistence of phases have to be taken into account in the discussion of natural situations. From these only formally sketchable microscopic ab initio approaches there is no path known that leads to a family of more realistic phenomenological climate models [185]. 4.2 The conservation laws of magnetohydrodynamics 4.2.1 Overview The core of a climate model must be a set of equations describing the equations of uid ow, namely the Navier-Stokes equations [183, 184]. The Navier-Stokes equations are nonlinear partial di erential equations, which, in general, are impossible to solve analytically. In very special cases numerical methods lead to useful results, but there is no systematics for the general case. In addition, the Navier-Stokes approach has to be extended to multi-component problems, which does not simplify the analysis. Climate modelers often do not accept that \climate models are too complex and uncertain to provide useful projections of climate change” [186]. Rather, they claim that \current models enable [them] to attribute the causes of past climate change and predict the main features of the future climate with a high degree of con dence” [186]. Evidently, this claim (not specifying the observables subject to the prediction) contradicts to what is well-known from theoretical meteorology, namely that the predictability of the weather forecast models is (and must be) rather limited (i.e. limited to a few days) [187]. The non-solvability of Navier-Stokes-type equations is related (but not restricted) to the chaotic character of turbulence. But this is not the only reason why the climate modeling cannot be built on a solid ground. Equally importantly, even the full set of equations providing a proper model of the atmospheric system (not to say atmospheric-oceanographic system) are not known (and never will) to a full extent. All models used for \simulation” are (and have to be) oversimpli ed. However, in general a set of oversimpli ed nonlinear partial di erential equations exhibits a totally di erent behavior than a more realistic, more complex system. Because there exist no strategy for a stepwise re nement within the spirit of the renormalization (semi-)group, one cannot make any useful predictions. The real world is too complex to be represented properly by a feasable system of equations ready for processing [185]. The only safe statement that can be made is that the dynamics of the weather is probably governed by a generalized Navier-Stokes-type dynamics. Evidently, the electromagnetic interactions have to be included, leading straightly to the discipline of Magnetohydrodynamics (MHD) [188{191]. This may be regarded as a set of equations expressing all the essential physics of a uid, gas and/or plasma. In the following these essential equations are reviewed. The purpose is twofold: 82 Gerhard Gerlich and Ralf D. Tscheuschner • Firstly, it should be made a survey of what budget relations really exist in the case of atmospheric physical systems. • Secondly, the question should be discussed at what point the supposed greenhouse mechanism does enter the equations and where the carbon dioxide concentration appears. Unfortunately, the latter aspect seems to be obfuscated in the mainstream approaches of climatology. 4.2.2 Electric charge conservation As usual, electric charge conservation is described by the continuity equation @%e + . · j = 0 (123) @t where %e is the electrical (excess) charge density and j is the electrical (external) current density. 4.2.3 Mass conservation The conservation of mass is described by another sort of continuity equation @. + . · (. v) = 0 (124) @t where . is the mass density and . v is the density of the mass current. 4.2.4 Maxwell's equations The electromagnetic elds are described by Maxwell's eld equations that read . · D = %e (125) @B . × E = - @t (126) (127) . · B = 0 (128) @D . × H = j + @t (129) where the standard notation is used. They have to be supplemented by the material equations D = ""0 E (130) B = 0 H (131) where e and µ are assumed to be constant in space and time, an assumption that was already made by Maxwell. Falsi cation Of The Atmospheric CO2 Greenhouse E ects . . . 83 4.2.5 Ohm's law for moving media Electric transport is described by Ohm's law for moving media j - %ev = s (E + v × B) (132) with s being the electrical conductivity tensor. Expressed in terms of the resistivity tensor . this reads (j - %ev)= E + v × B (133) 4.2.6 Momentum balance equation Conservation of momentum is described by a momentum balance equation, also known as Navier-Stokes equation, . (. v)+ . · (. v . v)= ..rp - . r+ %eE + j × B + . · R + Fext (134) @t where v is the velocity vector eld, p the pressure eld, F the gravitational potential, R the friction tensor, and Fext are the external force densities, which could describe the Coriolis and centrifugal accelerations. 4.2.7 Total energy balance equation The conservation of energy is described by @. 11 @t 2jvj2 + 2 H · B + 2 E · D + . + %u + +. · . 2jvj2 v + E × H + . F v + %u v + p v - v · R + . · rT = @F = . + Fext · v + Q (135) @t where u is the density of the internal energy, T is the temperature eld, and . the thermal conductivity tensor, respectively. Furthermore a term Q has been added which could describe a heat density source or sink distribution. 4.2.8 Poynting's theorem From Maxwell's equation with space-time independent e and µ one obtains the relation . 11 @t 2 H · B + 2 E · D + . · (E × H)= - j · E (136) This relation is a balance equation. The Pointing vector eld E × H may be interpreted as an energy current density of the electromagnetic eld. 84 Gerhard Gerlich and Ralf D. Tscheuschner 4.2.9 Consequences of the conservation laws Multiplying Ohm's law for moving media (Equation 133) with (j - %e v) one gets (j - %ev) (j - %ev)= jE + j (v × B) - %e vE · · = jE - v (j × B) - %e vE (137) · · which may be rewritten as jE =(j - %ev) (j - %ev)+ v (j × B)+ %e vE (138) · · Inserting this into Poynting's theorem (Equation 136) one obtains . 11 @t 2 H · B + 2 E · D + . · (E × H)= = - (j - %ev) (j - %ev) - v (%e E + j × B) (139) · On the other hand, if one applies the scalar product with v on the momentum balance equation (134) one gets @. 2 . 2 @t 2 jvj+ . · 2 jvjv = = ..v · rp - . v · r+ v (%eE + j × B)+ v (. · R)+ vFext (140) · · Replacing v (%eE + j × B) with Equation (139) and doing some elementary manipulations · one nally obtains @. 2 11 @t 2jvj+ 2 H · B + 2 E · D + . + +. · 2jvj2 v + E × H - v · R + p v + . F v = = p . · v + . @ @t F - Tr((. . v) R) - (j - %ev) (j - %ev)+ Fext · v (141) · Hence, this relation is a consequence of the fundamental equations of magnetohydrodynamics. The heat density source term Q, the internal energy density u, and the divergence of the heat current density q are missing here. 4.2.10 General heat equation With p du = d. + T ds (142) %2 for reversible processes one can substitute the density of the internal energy u by the density of the entropy s. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. With the aid of Equations (135) and (136) one derives a di erential equation for the entropy density s: @(%s) + . · (%s v)= @t = 1 Tr((. . v) R)+ 1(j - %ev) (j - %ev) T · T 1 Q - T . · (. · rT )+ T (143) This is the generalized form of the heat equation. Only with arti cial heat densities Q in Equation (143) one can incorporate a hypothetical warming by radiation. There is no term that depends on the carbon dioxide concentration. 4.2.11 Discussion The equations discussed above comprise a system of one- uid equations only. One can (and must) write down many- uid equations and, in addition, the averaged equations describing the turbulence. To get a realistic model of the real world, the above equations must be generalized to take into account • the dependency of all relevant coecients on space and time; • the presence and coexistence of various species of uids and gases; • the inhomogenities of the media, the mixture and separation of phases. In principle such a generalization will be feasable, if one cuts the domains of de nition into pieces and treats the equations by a method of patches. Thus the nal degree of complexity may be much larger than originally expected arriving at a system of thousands of phenomenological equations de ning non-linear three-dimensional dynamics and heat transfer [192{194]. It cannot be overemphasized that even if these equations are simpli ed considerably, one cannot determine numerical solutions, even for small space regions and even for small time intervals. This situation will not change in the next 1000 years regardless of progress made in computer hardware. Therefore, global climatologists may continue to write updated research grant proposals demanding next-generation supercomputers ad in nitum. As the extremely simpli ed one- uid equations are unsolvable, the many- uid equations would be more unsolvable, the equations that include the averaged equations describing the turbulence would be still more unsolvable, if \unsolvable” had a comparative. Regardless of the chosen level of complexity, these equations are supposed to be the backbone of climate simulations, or, in other words, the foundation of models of nature. But even this is not true: In computer simulations heat conduction and friction are completely neglected, since they are mathematically described by second order partial derivatives that 86 Gerhard Gerlich and Ralf D. Tscheuschner cannot be represented on grids with wide meshes. Hence, the computer simulations of global climatology are not based on physical laws. The same holds for the speculations about the in uence of carbon dioxide: • Although the electromagnetic eld is included in the MHD-type global climatologic equations, there are no terms that correspond to the absorption of electromagnetic radiation. • It is hard if not impossible to nd the point in the MHD-type global climatologic equations, where the concentration of carbon dioxide enters the game. • It is impossible to include the radiative transfer equation (59) into the MHD-type climatologic equations. • Apparently, there is no reference in the literature, where the carbon dioxide concentration is implemented in the MHD-type climatologic equations. Hence, one is left with the possibility to include a hypothetical warming by radiation by hand in terms of arti cial heat densities Q in Equation (143). But this would be equivalent to imposing the \political correctly” requested anthropogenic rise of the temperature even from the beginning just saving an additional trivial calculation. In case of partial di erential equations more than the equations themselves the boundary conditions determine the solutions. There are so many di erent transfer phenomena, radiative transfer, heat transfer, momentum transfer, mass transfer, energy transfer, etc. and many types of interfaces, static or moving, between solids, uids, gases, plasmas, etc. for which there does not exist an applicable theory, such that one even cannot write down the boundary conditions [176, 177]. In the \approximated” discretized equations arti cial unphysical boundary conditions are introduced, in order to prevent running the system into unphysical states. Such a \calculation", which yields an arbitrary result, is no calculation in the sense of physics, and hence, in the sense of science. There is no reason to believe that global climatologists do not know these fundamental scienti c facts. Nevertheless, in their summaries for policymakers, global climatologists claim that they can compute the in uence of carbon dioxide on the climates. 4.3 Science and Global Climate Modelling 4.3.1 Science and the Problem of Demarcation Science refers to any system of objective knowledge, in particular knowledge based on the scienti c method as well as an organized body of knowledge gained through research [195,196]. There are essentially three categories of sciences, namely Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. • formal sciences (mathematics), • natural sciences (physics, chemistry, biology) social sciences • In natural sciences one has to distinguish between • a theory: a logically self-consistent framework for describing the behavior of certain natural phenomena based on fundamental principles; • a model: a similar but weaker concept than a theory, describing only certain aspects of natural phenomena typically based on some simpli ed working hypothesis; • a law of nature: a scienti c generalization based on a suciently large number of empirical observations that it is taken as fully veri ed; • a hypothesis: a contention that has been neither proved nor yet ruled out by experiment or falsi ed by contradiction to established laws of nature. A consensus, exactly speaking a consensus about a hypothesis is a notion which lies outside natural science, since it is completely irrelevant for objective truth of a physical law: Scienti c consens(us) is scienti c nonsense. The problem of demarcation is how and where to draw lines around science, i.e. to distinguish science from religion, from pseudoscience, i.e. fraudulent systems that are dressed up as science, and non-science in general [195,197]. In the philosophy of science several approaches to the de nition of science are discussed [195, 196]: • empirism24 (Vienna Circle): only statements of empirical observations are meaningful, i.e. if a theory is veri able, then it will be scienti c; • falsi cationism (Popper): if a theory is falsi able, then it will be scienti c; • paradigm shift (Kuhn): within the process of normal science anomalies are created which lead eventually to a crisis nally creating a new paradigm; the acceptance of a new paradigm by the scienti c community indicates a new demarcation between science and pseudoscience; • democratic and anarchist approach to science (Feyerabend): science is not an autonomous form of reasoning but inseparable from the larger body of human thought and inquiry: \Anything goes". 24also logical positivism or veri cationism Gerhard Gerlich and Ralf D. Tscheuschner Super cially, the last point provides a nice argument for computer modelers in the framework of global climatology. However, it is highly questionable whether this ts into the frame of physics. Svozil remarked that Feyerabend's understanding of physics was super cial [198]. Svozil emphasizes: \Quite generally, partly due to the complexity of the formalism and the new challenges of their ndings, which left philosophy proper at a loss, physicists have attempted to develope their own meaning of their subject.” Physics provides a fundament for engineering and, hence, for production and modern economics. Thus the citizen is left with the alternative (in the sense of a choice between two options) (a) either to accept the derivation of political and economical decisions from an anarchic standpoint that eventually claims that there is a connection to experiment and observation, and, hence, the real world, when there is no such connection; (b) or to call in the derivation of political and economical decisions from veri able research results within the frame of physics, where there is a connection to experiment and observation, and hence, the real world. Evidently, the option (b) de nes a pragmatic approach to science, de ning a minimum of common features, such that engineers, managers and policymakers have something to rely on: Within the frame of exact sciences a theory should (a) be logically consistent; (b) be consistent with observations; (c) have a grounding in empirical evidence; (d) be economical in the number of assumptions; (e) explain the phenomena; (f) be able to make predictions; (g) be falsi able and testable; (h) be reproducible, at least for the colleagues; (i) be correctable; (j) be re nable; Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 89 (k) be tentative; (l) be understandable by other scientists. Can these criteria ever be met by a computer model approach of global climatology? 4.3.2 Evaluation of Climatology and Climate Modelling In contrast to meteorology climatology studies the averaged behavior of the local weather. There are several branches, such as paleoclimatology, historical climatology, and climatology involving statistical methods which more or less t into the realm of sciences. The problem is, what climate modelling is about, especially if it does refer to chaotic dynamics on the one hand, and the greenhouse hypothesis on the other. The equations discussed in Section 4.2 may give an idea what the nal de ning equations of the atmospheric and/or oceanic system may look like. It has been emphasized that in a more realistic albeit phenomenological description of nature the system of the relevant equations may be huge. But even by simplifying the structure of equations one cannot determine solutions numerically, and this will not change, if one does not restrict oneself on small space- time domains. There are serious solvability questions in the theory of non-linear partial di erential equations and the shortage of numerical recipes leading to sucient accurate results will remain in the nearer or farer future -for fundamental mathematical reasons. The Navier-Stokes equations are something like the holy grail of theoretical physics, and a brute force discretization with the aid of lattices with very wide meshes leads to models, which have nothing to do with the original puzzle and thus have no predictability value. In problems involving partial di erential equations the boundary condition determine the solutions much more than the di erential equations themselves. The introduction of a discretization is equivalent to an introduction of arti cial boundary conditions, a procedure, that is characterized in von Storch's statement \The discretization is the model” [199]. In this context a correct statement of a mathematical or theoretical physicist would be: \A discretization is a model with unphysical boundary conditions.” Discretizations of continua problems will be allowed if there is a strategy to compute stepwise re nements. Without such a renormalization group analysis a nite approximation does not lead to a physical conclusion. However, in Ref. [199] von Storch emphasized that this is by no means the strategy he follows, rather he takes the nite di erence equations are as they are. Evidently, this would be a grotesque standpoint, if one considered the heat conduction equation, being of utmost relevance to the problem and being a second order partial di erential equation, that cannot be replaced by a nite di erence model with a lattice constant in the range of kilometers. Generally, it is impossible to derive di erential equations for averaged functions and, hence, an averaged non-linear dynamics. 90 Gerhard Gerlich and Ralf D. Tscheuschner Thus there is simply no physical foundation of global climate computer models, for which still the chaos paradigma holds: Even in the case of a well-known deterministic dynamics nothing is predictable [200]. That discretization has neither a physical nor a mathematical basis in non-linear systems is a lesson that has been taught in the discussion of the logistic di erential equation, whose continuum solutions di er fundamentally from the discrete ones [201,202]. Modern global climatology has confused and continues to confuse fact with fantasy by introducing the concept of a scenario replacing the concept of a model. In Ref. [29] a clear de nition of what scenarios are is given: Future greenhouse gas (GHG) emissions are the product of very complex dynamics systems, determined by driving forces such as demographic development, socioeconomic development, and technological change. Their future evolution is highly uncertain, Scenarios are alternative images of how the future might unfold and are an appropriate tool with which to analyze how driving forces may in uence future emission outcomes and to access the associated uncertainties. They assist in climate change analysis, including climate modeling and the assessment of impacts, adaptation and mitigation. The possibility that any single emissions path will occur as described in scenarios is highly uncertain. Evidently, this is a description of a pseudo-scienti c (i.e. non-scienti c) method by the experts at the IPCC. The next meta-plane beyond physics would be a questionnaire among scientists already performed by von Storch [203] or, nally, a democratic vote about the validity of a physical law. Exact science is going to be replaced by a sociological methodology involving a statistical eld analysis and by \democratic” rules of order. This is in harmony with the de nition of science advocated by the \scienti c” website RealClimate.org that has integrated in ammatory statements, personal attacks and o enses against authors as a part of their \scienti c” work ow. 4.3.3 Conclusion A statistical analysis, no matter how sophisticated it is, heavily relies on underlying models and if the latter are plainly wrong then the analysis leads to nothing. One cannot detect and attribute something that does not exist for reason of principle like the CO2 greenhouse e ect. There are so many unsolved and unsolvable problems in non-linearity and the climatologists believe to beat them all by working with crude approximations leading to unphysical results that have been corrected afterwards by mystic methods, ux control in the past, obscure ensemble averages over di erent climate institutes today, by excluding accidental global cooling results by hand [154], continuing the greenhouse inspired global climatologic tradition Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. of physically meaningless averages and physically meaningless applications of mathematical statistics. In conclusion, the derivation of statements on the CO2 induced anthropogenic global warming out of the computer simulations lies outside any science. 92 Gerhard Gerlich and Ralf D. Tscheuschner 5 Physicist's Summary A thorough discussion of the planetary heat transfer problem in the framework of theoretical physics and engineering thermodynamics leads to the following results: 1. There are no common physical laws between the warming phenomenon in glass houses and the ctitious atmospheric greenhouse e ect, which explains the relevant physical phenomena. The terms \greenhouse e ect” and \greenhouse gases” are deliberate misnomers. 2. There are no calculations to determinate an average surface temperature of a planet • with or without an atmosphere, • with or without rotation, • with or without infrared light absorbing gases. The frequently mentioned di erence of 33 C for the ctitious greenhouse e ect of the atmosphere is therefore a meaningless number. 3. Any radiation balance for the average radiant ux is completely irrelevant for the determination of the ground level air temperatures and thus for the average value as well. 4. Average temperature values cannot be identi ed with the fourth root of average values of the absolute temperature's fourth power. 5. Radiation and heat ows do not determine the temperature distributions and their average values. 6. Re-emission is not re ection and can in no way heat up the ground-level air against the actual heat ow without mechanical work. 7. The temperature rises in the climate model computations are made plausible by a perpetuum mobile of the second kind. This is possible by setting the thermal conductivity in the atmospheric models to zero, an unphysical assumption. It would be no longer a perpetuum mobile of the second kind, if the \average” ctitious radiation balance, which has no physical justi cation anyway, was given up. 8. After Schack 1972 water vapor is responsible for most of the absorption of the infrared radiation in the Earth's atmosphere. The wavelength of the part of radiation, which is absorbed by carbon dioxide is only a small part of the full infrared spectrum and does not change considerably by raising its partial pressure. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 9. Infrared absorption does not imply \backwarming". Rather it may lead to a drop of the temperature of the illuminated surface. 10. In radiation transport models with the assumption of local thermal equilibrium, it is assumed that the absorbed radiation is transformed into the thermal movement of all gas molecules. There is no increased selective re-emission of infrared radiation at the low temperatures of the Earth's atmosphere. 11. In climate models, planetary or astrophysical mechanisms are not accounted for properly. The time dependency of the gravity acceleration by the Moon and the Sun (high tide and low tide) and the local geographic situation, which is important for the local climate, cannot be taken into account. 12. Detection and attribution studies, predictions from computer models in chaotic systems, and the concept of scenario analysis lie outside the framework of exact sciences, in particular theoretical physics. 13. The choice of an appropriate discretization method and the de nition of appropriate dynamical constraints ( ux control) having become a part of computer modelling is nothing but another form of data curve tting. The mathematical physicist v. Neumann once said to his young collaborators: \If you allow me four free parameters I can build a mathematical model that describes exactly everything that an elephant can do. If you allow me a fth free parameter, the model I build will forecast that the elephant will y.” (cf. Ref. [185].) 14. Higher derivative operators (e.g. the Laplacian) can never be represented on grids with wide meshes. Therefore a description of heat conduction in global computer models is impossible. The heat conduction equation is not and cannot properly be represented on grids with wide meshes. 15. Computer models of higher dimensional chaotic systems, best described by non-linear partial di erential equations (i.e. Navier-Stokes equations), fundamental di er from calculations where perturbation theory is applicable and successive improvements of the predictions -by raising the computing power -are possible. At best, these computer models may be regarded as a heuristic game. 16. Climatology misinterprets unpredictability of chaos known as butter y phenomenon as another threat to the health of the Earth. In other words: Already the natural greenhouse e ect is a myth albeit any physical reality. The CO2-greenhouse e ect, however is a \mirage” [204]. The horror visions of a risen sea level, melting pole caps and developing deserts in North America and in Europe are ctitious Gerhard Gerlich and Ralf D. Tscheuschner consequences of ctitious physical mechanisms as they cannot be seen even in the climate model computations. The emergence of hurricanes and tornados cannot be predicted by climate models, because all of these deviations are ruled out. The main strategy of modern CO2-greenhouse gas defenders seems to hide themselves behind more and more pseudo- explanations, which are not part of the academic education or even of the physics training. A good example are the radiation transport calculations, which are probably not known by many. Another example are the so-called feedback mechanisms, which are introduced to amplify an e ect which is not marginal but does not exist at all. Evidently, the defenders of the CO2-greenhouse thesis refuse to accept any reproducible calculation as an explanation and have resorted to unreproducible ones. A theoretical physicist must complain about a lack of transparency here, and he also has to complain about the style of the scienti c discussion, where advocators of the greenhouse thesis claim that the discussion is closed, and others are discrediting justi ed arguments as a discussion of \questions of yesterday and the day before yesterday"25 . In exact sciences, in particular in theoretical physics, the discussion is never closed and is to be continued ad in nitum, even if there are proofs of theorems available. Regardless of the speci c eld of studies a minimal basic rule should be ful lled in natural science, though, even if the scienti c elds are methodically as far apart as physics and meteorology: At least among experts, the results and conclusions should be understandable or reproducible. And it should be strictly distinguished between a theory and a model on the one hand, and between a model and a scenario on the other hand, as clari ed in the philosophy of science. That means that if conclusions out of computer simulations are to be more than simple speculations, then in addition to the examination of the numerical stability and the estimation of the e ects of the many vague input parameters, at least the simpli cations of the physical original equations should be critically exposed. Not the critics have to estimate the e ects of the approximation, but the scientists who do the computer simulation. \Global warming is good ::. The net e ect of a modest global warming is positive.” (Singer).26 In any case, it is extremely interesting to understand the dynamics and causes of the long-term uctuations of the climates. However, it was not the purpose of this paper to get into all aspects of the climate variability debate. The point discussed here was to answer the question, whether the supposed atmospheric e ect has a physical basis. This is not the case. In summary, there is no atmospheric greenhouse e ect, in particular CO2-greenhouse e ect, in theoretical physics and engineering thermodynamics. Thus it is illegitimate to deduce predictions which provide a consulting solution for economics and intergovernmental policy. 25a phrase used by von Storch in Ref. [1] 26cf. Singer's summary at the Stockholm 2006 conference [1]. Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. Acknowledgement This work is dedicated (a) to the late Professor S. Chandrasekhar, whom R.D.T. met in Chicago in 1991, (b) to the late Professor C. F. v. Weizsacker, a respected discussion partner of both authors, and (c) the late investigative science journalist H. Heuseler, whom G.G. owes valuable information on the topic. Both authors would like to thank many people for discussions, email exchanges, and support at various stages of this work, in particular StD Dipl.-Biol. Ernst-Georg Beck, H. J. Labohm, Professor B. Peiser, H. Thieme, Dr. phil. Wolfgang Thune, and Professor A. Zichichi for sending them the manuscript of his talk presented at the Vatican conference. Mrs. S. Feldhusen's rst translation of Ref. [104] is greatly appreciated. Gerhard Gerlich would like to express his gratitude to all those who contributed to this study either directly or indirectly: Students, Staff Members, Research and Teaching Assistants, even collegues, who listened to his lectures and talks, who read his texts critically, who did some successful literature search. In particular, he is indebted to the Diploma Physicists (Diplomphysiker) Dr. V. Blahnik, Dr. T. Dietert, Dr. M. Guthmann, Dr. G. Linke, Dr. K. Pahlke, Dr. U. Schomacker, H. Bade, M. Behrens, C. Bollmann, R. Flogel, StR D. Harms, J. Hauschildt, F. Ho mann, C. Mangelsdorf, D. Osten, M. Schmelzer, A. Sohn, and G. Toro, the architects P. Bossart and Dipl.-Ing. K. Fischer. Gerhard Gerlich extends his special gratitude to Dr. G.-R. Weber for very early bringing his attention to the outstanding DOE 1985 report [91] to which almost no German author contributed. Finally, he is pleased about the interest of the many scienti c laymen who enjoyed his talks, his letters, and his comments. Ralf D. Tscheuschner thanks all his students who formulated and collected a bunch of questions about climate physics, in particular Elvir Donlc. He also thanks Professor A. Bunde for email correspondence. Finally he is indebted to Dr. M. Dinter, C. Kloe, M. Kock, R. Schulz for interesting discussions, and Professor H. Grassl for an enlightening discussion after his talk on Feb. 2, 2007 at Planetarium Hamburg. A critical reading by M. Mross and Dr. M. Dinter and a translation of Fourier's 1824 paper in part by M. Willer's team and by Dr. M. Dinter are especially acknowledged. The authors express their hope that in the schools around the world the fundamentals of physics will be taught correctly and not by using award-winning \Al Gore” movies shocking every straight physicist by confusing absorption/emission with re ection, by confusing the tropopause with the ionosphere, and by confusing microwaves with shortwaves. Gerhard Gerlich and Ralf D. Tscheuschner List of Figures 1 The geometry of classical radiation: A radiating in nitesimal area dF1 and an illuminated in nitesimal area dF2 at distance r. . . . . . . . . . . . . . . . . . 17 2 Two parallel areas with distance a. . . . . . . . . . . . . . . . . . . . . . . . . 18 3 The geometry of classical radiation: Two surfaces radiating against each other. 20 4 Black body radiation compared to the radiation of a sample coloured body. The non-universal constant s is normalized in such a way that both curves coincide at T = 290 K. The Stefan-Boltzmann T 4 law does no longer hold in the latter case, where only two bands are integrated over, namely that of visible light and of infrared radiation from 3 m to 5 m, giving rise to a steeper curve. 21 5 The spectrum of the sunlight assuming the sun is a black body at T = 5780 K. 22 6 The un ltered spectral distribution of the sunshine on Earth under the assumption that the Sun is a black body with temperature T = 5780 K (left: in wave length space, right: in frequency space). . . . . . . . . . . . . . . . . . . 24 7 The exact location of the zero of the partial derivatives of the radiation intensities of the sunshine on Earth (left: in wave length space, right: in frequency space). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 8 The un ltered spectral distribution of the radiation of the ground under the assumption that the earth is a black body with temperature T = 290 K (left: in wave length space, right: in frequency space). . . . . . . . . . . . . . . . . . 25 9 The radiation intensity of the ground and its partial derivative as a function of the wave length . (left column) and of the frequency . (right column). . . . 26 10 Three versions of radiation curve families of the radiation of the ground (as a function of the wave number k, of the frequency , of the wave length , respectively), assuming that the Earth is a black radiator. . . . . . . . . . . . 26 11 The un ltered spectral distribution of the sunshine on Earth under the assumption that the Sun is a black body with temperature T = 5780 K and the un ltered spectral distribution of the radiation of the ground under the assumption that the Earth is a black body with temperature T = 290 K, both in one diagram (left: normal, right: super elevated by a factor of 10 for the radiation of the ground). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. 12 The un ltered spectral distribution of the sunshine on Earth under the assumption that the Sun is a black body with temperature T = 5780 K and the un ltered spectral distribution of the radiation of the ground under the assumption that the Earth is a black body with temperature T = 290 K, both in one semi-logarithmic diagram (left: normalized in such a way that equal areas correspond to equal intensities, right: super elevated by a factor of 10 for the radiationoftheground). .............................. 28 13 The un ltered spectral distribution of the sunshine on Earth under the assumption that the Sun is a black body with temperature T = 5780 K and the un ltered spectral distribution of the radiation of the ground under the assumption that the Earth is a black body with temperature T = 290 K, both in one semi-logarithmic diagram (left: normalized in such a way that equal areas correspond to equal intensities with an additional re-scaling of the sunshine curve by a factor of 1=3:5, right: super elevated by a factor of 68 for the radiationoftheground). .............................. 28 14 A solid parallelepiped of thickness d and cross section F subject to solar radiation 30 15 Anexcerptfrompage28oftheDOEreport(1985). . . . . . . . . . . . . . . . 45 16 A very popular physical error illustrated in the movie \An Inconvenient truth” byDavisGuggenheimfeaturingAlGore(2006). . . . . . . . . . . . . . . . . . 46 17 Acavityrealizingaperfectblackbody....................... 48 18 ThefrontpageofFourier's1824paper. ...................... 52 19 ThefrontpageofArrhenius'1896paper. ..................... 53 20 Excerpt(a)ofArrhenius'1906paper. ....................... 54 21 Excerpt(b)ofArrhenius'1906paper........................ 55 22 Excerpt(c)ofArrhenius'1906paper. ....................... 56 23 A schematic diagram supposed to describe the global average components of the Earth's energy balance. Diagrams of this kind contradict to physics. .. 59 24 Aradiationexposedstaticglobe. ......................... 62 25 Therotatingglobe ................................. 67 26 Anobliquelyrotatingglobe ............................ 68 27 Thecoolingcurveforaradiatingstandardcube . . . . . . . . . . . . . . . . . 70 28 Asimpleheattransportproblem. ......................... 72 29 A steam engine works transforming heat into mechanical energy. . . . . . . . . 76 30 A heat pump (e.g. a refrigerator) works, because an external work is applied. . 76 31 Any machine which transfers heat from a low temperature reservoir to a high temperature reservoir without external work applied cannot exist: A perpetuum mobile of the second kind isimpossible. ...................... 77 98 Gerhard Gerlich and Ralf D. Tscheuschner 32 A machine which transfers heat from a low temperature reservoir (e.g. stratosphere) to a high temperature reservoir (e.g. atmosphere) without external work applied, cannot exist -even if it is radiatively coupled to an environment, to which it is radiatively balanced. A modern climate model is supposed to be such a variant of a perpetuum mobile of the second kind. . . . . . . . . . . . . 78 Falsi cation Of The Atmospheric CO2 Greenhouse E ects ::. List of Tables 1 Atmospheric concentration of carbon dioxide in volume parts per million (1958 -2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Three versions of an idealized Earth's atmosphere and the associated gas volume concentrations, including the working hypothesis chosen for this paper . . 7 3 Mass densities of gases at normal atmospheric pressure (101.325 kPa) and standard temperature (298 K) . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4 Volume percent versus mass percent: The volume concentration xv and the mass concentration xm of the gaseous components of an idealized Earth's atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 Thermal conductivities of the gaseous components of the Earth's atmosphere at normal pressure (101:325 kPa) . . . . . . . . . . . . . . . . . . . . . . . . . 9 6 Isobaric heat capacities cp, relative molar masses Mr, isochoric heat capacities cv ˜ cp - R=Mr with universal gas constant R = 8:314472 J=mol K, mass densities %, thermal conductivities , and isochoric thermal di usivities av of the gaseous components of the Earth's atmosphere at normal pressure (101:325 kPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 7 The calculation of the isochoric thermal di usivity av = =(. cv) of the air and its gaseous components for the current CO2 concentration (0:06 Mass %) and for a ctitiously doubled CO2 concentration (0:12 Mass %) at normal pressure (101:325 kPa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 8 The proportional portion of the ultraviolet, visible, and infrared sunlight, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 9 Measured temperatures inside and outside a car on a hot summer day. . . . . . 29 10 E ective temperatures TEarth's ground in dependence of the phenomenological normalization parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 11 E ective \average” temperatures Tground in dependence of the phenomenological normalization parameter . incorporating a geometric factor of 0:25. . . . . 62 12 Two kinds of \average” temperatures Teff and Tphys in dependence of the emissivity parameter . compared. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 13 An example for a measured temperature distribution from which its associated e ective radiation temperature is computed. 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