Climate change from the perspective of physics and geology Part 4. Dr.-Ing. Alexander Koewius and Prof. Dr. Christopher J. Rhodes. 3. The Greenhouse Effect (GE) as a Result from Climate Effective Trace Gases (CETG) in the Earth’s Atmosphere 3.1 Preliminary Remarks For well over 100 years, climate research has represented a growing field of activity – thanks to vastly improving insights – of such breadth and depth, that it can no longer be overlooked by anyone. This seems to be especially true for the all but small number of old as well as young people who – as educated/cultivable laymen - try for a thorough understanding of all those mechanisms which (can) exert an influence on global climate change; an understanding in the same way as that attempted (albeit solely on behalf of GE-physics) in this essay by the authors who admittedly are laymen in a “climatological” sense, however not in that of “physics” or “chemistry” . What [S. Rahmstorf, H-J Schellnhuber] said is central to this issue, namely „It is rather difficult for a today’s layman to get a profound and correct picture of the state of knowledge (state of the art) in the field of climate research“; lat alone the difficulty which faces writers who belong to the this category if they wish (in trusting their own understanding/knowledge of physics) to gain respect among the climate experts too. On the other side however the difference between a layman and an expert seems to us to be rather nebulous judging from the web-sites of many universities, government institutions or other research institutes around the world, because already the details, on which depend the complex algorithms used to arrive at climate predictions are rarely explained simply in a satisfactory manner. Nonetheless, the immense worldwide research work of the last 50 years (mainly driven by a growing concern about the fast rise of CETGs of human origin in the atmosphere) has made very clear the enormous complexity of the coupled-system which comprises earth’s atmosphere and her (life-bearing) surface, which we will call in short ‘system’ in the following discourse. It is precisely this complexity of facts and processes in the system, not seldom mirroring very subtle connections and interactions, which appears under practically every geo-scientific aspect, be it geology, biology, chemistry, or physics. A propos physics: Nearly everything of theory which this discipline offers – from (sub)micro-cosmos (atoms, molecules in a radiation field,…) to macro-cosmos (sun and planets, celestial mechanics,…) – is more or less involved in the interdisciplinary science of the climate and how it changes, in consderation the earth’s past and present behaviour. In order to carefully explain the essentials, which are orientated on the natural GE, for now we must first remain with simplified, model- concepts but which we can also find in the more specialist literature in the form of the description of globally averaged issues about climate change. Take Figure 11 (further below) as an example which shows the earth’s radiation budget expressed as flux densities in W/m2, and which is also used by several IPCC assessment reports as a familiar means of presentation. After [W. Roedel] Fig. 11 can also be understood as the result from a “zero-dimensional” energy budget model which yields only the global mean for a certain atmospheric variable, such as

MGT for example, hence not admitting regional differences. Essentially the same is true for the “radiative-convective models”, RCM, which (as principally 1-dimensional models) allow for calculating atmospheric energy fluxes only in the vertical (z-)direction, thus yielding the T-profile of the atmosphere as a function of z. However for the sake of accuracy and the regional validity of a climate model, (convective) energy fluxes in the horizontal direction must also be taken into consideration. This can in principle only be done by so-called „General Circulation Models“, GCM.

As we mentioned in part 3, there remains considerable speculation as to the validity of area-weighted global means – which significantly are part of the essence of the (relatively simple) proximate climate models - which is expressed by a number of sceptics with an academic background. In order to demonstrate how unjustified such doubts (at least on the terrestrial MGT) can be, we examined the question by means of calculating a MGT in comparison to a corresponding (Te)g for an “extra-terrestrial case”, see Annex II at the end of this part of the essay.

In view of the multitude of details to be explained within the whole complex storey-system, called ‘atmosphere’ (Figure 12), we furthermore regard it as useful and feasible when we confine ourselves to the troposphere (including the tropopause, which on average lies at z=12 km above sea level). If in the following we refer to the “Top of the Atmosphere” (= TOA), in most cases we mean the upper rim of the troposphere. There are several good reasons for a confinement of this kind: - weather, generally associated with cloud formation, occurs exclusively in the

troposphere (clouds in the skies represent a major influence on possible climate variations).

- 80 to 85 % of the mass of the entire atmosphere is contained within the troposphere. The same is true for the evenly distributed CETGs like CO2, CH4, N2O.

- Water vapour as the most important climate effective trace gas practically does not exceed the tropopause, and given the huge amounts of this gas in the lower atmosphere one can concur with [W. Roedel], that the tropospheric dry gas mixture is penetrated like by a ‘water vapour sphere’.

It need not be stressed that more exact climate models, which are in use in modern climatology, cannot neglect the climate effective processes in the stratosphere due to the presence of ozone albeit noting that gas densities/concentrations are very low there. A certain amount of the incoming solar irradiance (14 of the 67 W/m2 absorbed in total by the atmosphere, see Fig. 11), namely that in the UV part of the continuous solar spectrum, is already intercepted by absorption through stratospheric O3, thus leading to a T-rise with z, which increases until the stratopause (at z ∼ 50 km) is reached, whereupon the atmosphere again cools into the mesosphere

We were surprised that the presentation of specific knowledge in the worldwide web proved far less clear than would have been desirable (better to say: actually necessary) in the face of our endeavour to duly process the basic physical matter for a deeper understanding of the GE. For the present, such an assessment of the situation may be regarded as little more than preliminary in the light of our own investigation, which has taken many months. Thus, in the pursuit of clarity, we sometimes found ourselves putting things into a nutshell, sometimes in a way not found elsewhere. So statements can be read in specialist literature like “The energy of a radiation field which certain molecules in the air absorb, is emitted by them again to the same amount” or: “Absorption means – in contrast to scattering - , that radiation is transformed by molecules into other forms of energy; e.g. thermal energy”. “What does this mean?” the puzzled laymen will

ask himself while reading something about the impact of a CETG and, “if both statements are not false, under which conditions does one or the other apply?” “Putting something in a nutshell” means to make a simplifying, general assumption without departing too much from reality, and simultaneously not to breach the logic of an attempt at explaining the situation. But before we decide to address the assumptions involved, we must first consider some distinct physical issues referring to gases and their sub-microscopic components: The thermal energy of a gas, which consists of bi-atomic or polyatomic molecules, is not only represented by the linear motion of the molecules, i.e. by their “linear” kinetic energy m∗v2/2 (with v as a symbol for the mean translational velocity and m for the mass of a molecule), but also by rotation around their main rotational axes. Rotation means for a molecule up to three additional degrees of freedom, which add to the 3 degrees of freedom associated with uniform linear motion. We should bear in mind in this context, that (a) the temperature T of a gas is solely a function of the simple translational energy of its constituents, whereas (b) the essential translational movement of a gas particle is a continuous one; in contrast to its rotational movement, which is quantised. So the specific heat of a gas, cv or cp = cv + R in J/(g∗K), can be quantified in relation to the number of degrees of freedom in question, each of them evenly contributing to c; and c is practically a constant at around room temperature. But, as the temperature increases, the more additional degrees of freedom (so-called “inner degrees”) for a molecule come into play, thus enhancing the values of c. The underlying reason is that the atoms in a certain molecule can undergo oscillations or vibrations against one another, which occurs at various specific modes and frequencies. All in all, the so described thermal energy of a gas is also called “sensitive heat” in order to make a difference to that type of thermal energy which is called “latent heat”. The latter enters our mantle of the atmosphere when water vapour condenses to water droplets, thus forming the clouds. If a gas of any kind is heated up to temperatures lying significantly high above room temperature, say, up to well above 1000 °C, then some electrons in the shells of the atoms (bonded together in a molecule) will also be affected. Quantum leaps of electrons occur, leading to a higher energy state (so-called “electron excitation” or “excitation of the electronic state”). We see incidentally: An excitation of that kind is not only a property of high-energy photons, as textbooks of physics normally suggest! However an energy absorption process like this is less relevant for the following, but has to be mentioned here for the sake of completeness. If the molecules of the atmosphere are exposed to a radiation field, in which the high spectral frequency section is lacking – be it the solar radiation reaching the troposphere without the “hard UV” band or be it the “soft” IR radiation from the ground – then it will depend solely - of the species envisaged - whether a molecule can absorb energy quanta (photons) from such a field or not. Bearing in mind an effective absorption without any participation of an electron shell, all our considerations are to be centred around the excitation of something which is called the vibrational-rotational state (VRS, also named vibro-rotational state) of a molecule. As we will show more in detail in a special annex (Annex IV), the rotational state of a molecule and its vibrational state (at specific vibrational modes and frequencies) are usually not independent from one another, i.e. they are coupled in distinct ways being

described by quantum mechanics. So, if one of these states changes then the other one will be affected, too. We realise: The excitation of a VRS is not only a consequence of molecular collisions (their rate rises with the density and temperature of a gas), but also of an electro-magnetic field (such as terrestrial IR-radiation) provided that the molecule considered possesses a dipole moment. So do all tri-atomic molecules (like CO2, H2O, N2O,…), poly-atomic molecules (like CH4), and as well bi-atomic ones, provided that the latter combine 2 different atoms to a molecule (like in CO, for example). We thus realise that ‘the property of a dipole moment’ is a feature of every CETG (or GHG = greenhouse gas) molecule we need to consider! Now, a molecular dipole moment can be a natural one (a permanent electric dipole moment), which is present initially as a consequence of the molecule’s basic configuration, as it is the case with H2O and also ozone, which is not as symmetric as the formula O3 might suggest. Or it is “only” an induced dipole moment, resulting from a certain vibrational distortion of the basic nuclear configuration, such as it is e.g. the case for CO2, and also for CH4. Due to the natural oscillations of a molecule, dipole moments change periodically with time thus enabling the molecules to act as tiny emitters of radiation at distinctly separated frequencies (or wavelengths) in the IR portion of the spectrum of a corresponding black body radiator. In this spectrum the said emission and absorption, as well, becomes visible in the form of so-called spectral lines. So a small volume of gas, containing a considerable number of “emission centres”, sends out “secondary” radiation, which spreads evenly in all spatial directions (so-called “isotropic” radiation). If an outer “primary” electro-magnetic field participates in inducing the molecular vibrations, then energy is absorbed (prior to re-emission) from this field (see ‘terrestrial IR-radiation’), thus weakening it and – as also can be said – thus contributing to its ‘opacity’.

Last but not least there are naturally a great number of diatomic molecules, which consist of 2 atoms of the same kind, and therefore do not show any dipole moment. Such is the case with N2, O2 and in a sense Ar (as a “mono-atomic molecule”), which altogether form the main constituents (∼ 99.9 %) of our atmosphere, and which are considered to be anything else but CETGs! But, is that statement quite universally valid? For an answer it seems to us to be worthwhile citing directly from “http://chriscolose.wordpress.com” (with slight alterations), albeit being rather lengthy, for the sake of a complete understanding: >> It is often noted that the diatomic molecules like N2 cannot behave as greenhouse gases (i.e. at normal, relatively low atmospheric temperatures). However, this does not hold true for many planetary atmosphere cases, such as when the atmosphere is sufficiently dense, and collision induced absorption becomes a significant factor. This arises within the collision complex formed by two molecules in the act of colliding. When there are very frequent collisions, such as on Titan (Saturn’s largest moon) and on all the giant gas planets, diatomic molecules acquire enough of a dipole moment during the time collisions are taking place such that the electromagnetic field can interact with their transitions. This tends towards a true collisional continuum, on the way to the behaviour of a solid black body. Because of this pressure-induced opacity in a very dense atmosphere, N2 and H2 act as strong greenhouse gases on Titan, and H2 on the giant planets like Jupiter. On Titan, collisions, inter alia between N2 - N2, are responsible for its greenhouse effect (McCay et al., 1991, Science 253: 1118-1121). So this effect plays out significantly in denser atmospheres, but is not a factor on Earth.

• Methane (CH4) and nitrous oxide (N2O). Their concentrations reveal, as is true with CO2, a strong anthropogenic influence.

• tropospheric O3 (with a strong anthropogenic influence) • CFCs = Chlorofluorocarbons (with dominant anthropogenic influence)

Annotation: The H2O vapour content (averaging a concentration of about 0.25 %) is strongly dependent on temperature, T, and rises with T. Thus the content in the troposphere can be enhanced only indirectly, i.e. by an increase of the MGT. The latter process has occurred (and very probably due to human activities) since 1750 and amounts to ∼ 0.8 degrees to date. Hence the human influence on MGT can still be rated as comparatively very low. Having overviewed the general relevant atmospheric and atomic physics we would now like to present our summary assumptions/conclusions, which in general is not detailed in more specialist literature, dealing with the GE, in a similarly consistent and concise form. They read as follows: - In the face of the relatively low temperatures which prevail in the lower atmosphere,

none of the molecules existing there are capable of absorbing energy quanta by changes of state within their electron shell. The statement seems to be especially valid for the excitation of molecules (in an airy gas shell like the earth’s atmosphere) by the solar radiation, which reaches the troposphere after having been attenuated on its way through the upper regions of the atmosphere, the stratosphere included. And the statement is yet the more true for the terrestrial radiation (reflected from the earth’s surface), which occurs in the infrared.

- It is only the GHGs which – because of their usually at least tri-atomic structure – are able to transform radiative energy into thermal energy, and vice versa. The underlying mechanism is to be found in the realm of the VRS already mentioned. Changes within VRS may occur either by inter-molecular collisions (induced “from the bottom”, so-to-say) or (so-to-say “from the top”) by the absorption of energy quanta hν , which arise from an electro-magnetic field (h = Planck’s constant; ν = frequency of a line in the spectrum = something like the resonant frequency of a certain vibration mode of a molecule).

- On the other hand the homo-nuclear di-atomic species, like the atmospheric main constituents N2, O2 (besides the noble gas Ar), are not able to absorb radiative energy from that kind of radiation, which is met in the troposphere. They do however, participate in the whole process of energy transfer insofar, as they transmit (receive) kinetic energy to (from) the GHG molecules through inter-molecular collisions.

- The heating*) of the air in the troposphere by radiation does not occur immediately in a strict sense, e.g. not by radiative thrust acting on all the air particles in the direction the radiation field propagates, whereby the kinetic energy was enhanced by linear acceleration (as one could imagine it, in principal, at least). The heating by radiation is rather mediated through the VRS, as can be envisaged from the above considerations.

- The heating of the troposphere occurs by two different processes: (a) reception of thermal energy (in the form of sensible and latent heat, too) from the ( averagely warmer) ground by convection and evapo-transpiration**), and (b) absorption of solar and terrestrial radiation by CETGs within specific frequency ranges. According to Fig. 11 the atmosphere receives in total the energy (expressed by flux densities S [W/m2]): Sgross = 67 + 102 + 350 = 519, which

------------- *) On this occasion we should make ourselves conscious of the two different contexts, in which the notion “heating” (and “cooling”, as well) is used.

(a) Most likely we hereby think of an non-steady-state process, which leads – in a certain time interval – to the heating up (or cooling down) a solid body or an enclosed air volume (e.g. a room in a house) to a preset T-value lying above (or below) a given ambient temperature. (b) But, after having attained the preset value, heating (cooling) must go on (albeit to a lower extent) in order to maintain the preset temperature because of inevitable thermal fluxes, which tend to diminish the difference between the ambient and the preset temperature, as we all know. So “heating” (cooling) means just compensating for inadvertent and unavoidable outgoing (ingoing) thermal fluxes. And that again is the hallmark of a stationary state of a system (here: the constantly warm living room and the cold winter night outside, etc.), whereas “stationary state” is also called “steady state”, meaning the same as “dynamic equilibrium”. It is just in this sense we have to understand notions like “heating the atmosphere” or “radiative cooling of the atmosphere”; notions which abound in specialist literature referring to the physical aspects of the natural GE as a steady state phenomenon (as a consequence of a constant amount of CETGs in the air). *) That notion refers to the formation of water vapour due to sources on the ground, which – beside water and moist land surfaces – include the respiration activity of plants.

leads – after having subtracted the counter- (or back-) radiation of 324 – to

Snet = 519 - 324 = 195. It is just this amount, which leaves the atmosphere (‘troposphere’, as a simplification we dare to follow here) at its upper edge in the form of IR-radiation. So, in a dynamic equilibrium, the net energy, which comes in from various sources (“heating”), goes out in an equal amount (“radiative cooling”); in fact disappears into space as IR-radiation, never to be seen again!

We should, now note at least 2 macroscopic factors, which make us wonder how these can be duly described without certain mental pictures or assumptions:

The above-mentioned dynamic equilibrium, as well as the energy flux which is called counter-radiation, take place in the said amount provided that there exists a T(z)-profile within the troposphere of that kind as having been established by measurements. So in the troposphere T(z) decreases linearly from +15°C on the ground at sea level (z = 0) to some – 55 °C in the tropopause, where this value remains nearly a constant until T rises again in the stratosphere due to the absorption of solar radiation by the ozone/oxygen system, which ultimately ends-up as heat. The linear course of T(z) is governed by the equation

T = TEB + (dT/dz) ∗ z

upwards to some 10 km of height, which corresponds roughly to a mean global view. The gradient dT/dz must be < 0 as will be explained in Annex III, and as is demonstrated by Fig. 12.

Now, if Tz=0 stands for the Mean Global Temperature (MGT), which accounts for the natural GE, then we feel it is equally reasonable to assume a corresponding mean for the gradient dT/dz , too. It is dT/dz =- 6.5 °C/km, which is found at most in specialist literature (in a range of about -7 to - 6 °C/km). Considering absolute gradient values, the value is smaller than that for the DALR = Dry Adiabatic Lapse Rate, which is settled at DALR= 9.8 °C/km, see again Annex III. But let us assume that DALR would – by and large – govern the linear decrease of T with z if there were absolutely none of the CETG present in our atmosphere; hence no GE was detectable and correspondingly the ground was showing the -18 °C, which would be hostile to life. Following this logic we can understand by dT/dz < DALR,that a warming of the troposphere has taken place, respectively permanently occurs as a balance to radiative cooling during a steady state process. Now, be that as it will: the sum of IR radiation leaving from the atmosphere (troposphere) and directly from the ground to

space at the TOA [ namely SE∗(1 – a)/4 = 1367∗(1 – 0.31)/4 ≈ 235 W/m2 ] remains, of course, unaffected by all these considerations.

3.2 The natural Greenhouse Effect The vital difference between today’s MGT and a fictitious, albeit physically conceivable low temperature, namely ΔT = 15 °C – (- 18 °C) = 33 °C = MGT - (Te)g , is the topic of a later section. For the moment we are more interested in how the counter-radiation of 324 [W/m2] can be judged, which occurs mainly from the atmospheric content of water vapour and carbon dioxide, as it remains today, and which thus essentially accounts for an MGT = 15 °C (instead of -18 °C).

The flow budget diagram above is very well known and an integral part, too, of several IPCC assessment reports. It is, however, not quite understandable without additional comments unless one accepts the whole as a matter of faith. At first we want to

distinguish so-called “robust” quantities in the diagram from those, which should better be called “estimates”, in order to establish a linear equation by a differentiation like this. Our aim is to point out more clearly the influences on the counter-radiation 324, which will appear formally as the unknown w in the said equation. As (relatively) robust we may consider: (a) 235 (= 67 + 168) as the solar radiation, which effectively is available for absorption by the system, and (b) 390 as that energy, which leaves the ground in the form of IR-radiation at T = 273 + 15 °C = 288 K, whereby the Stefan-Boltzmann equation (“fourth-power law”) for a black-body radiator (like the earth or the sun) with its continuous spectrum comes into play. As ‘robust’ to a lesser extent (i.e. as more or less good ‘estimates’) are to be considered u = 67 (thus also 235 – u = 168), and v = 78 + 24 = 102. By orientation at the net energy input into the atmosphere, which corresponds to its radiative output of 195 into space, we make up the balance

u + v + 350 – w = 195, leading to w = 155 + (u + v). So w visibly cannot be smaller than 155. We should be aware of the fact that u + v = 67 + 102 = 169 must be attributed for the greater part to the water vapour content in the troposphere. On the one hand the big portion of 78 in v should be noted. On the other hand, with regard to u, we can gather from the solar spectrum, as it is received on the ground (i.e. after the sunlight has passed the entire atmosphere), that – in the near-IR-portion of this spectrum – water vapour surpasses CO2 by far in terms of absorption intensity. With regard to w we should yet bear in mind the following: In publications dealing with the GE sometimes opinions can be found, that the “secondary” IR radiation by CETGs shall leave the atmosphere (substantially the troposphere) in equal proportions to the ground and to space, as well. We cite from “Climate Protection; Answers on Popular Sceptic Arguments” by the (German) UBA (= Umwelt-Bundesamt = Environmental Federal Agency), dated from 1st of October 2005: >> This radiation ((i.e. which emerges from the ground, in total 390)) is partially ((= 350)) absorbed by CETGs, and likewise emitted by them to the same amount following the principles of quantum physics. Because of the isotropic re-radiation (which spreads from a given volume element – in the spherical air shell – evenly in all spatial directions) some 50 % of it are directed to earth’s surface as the so-called counter-radiation ((i.e. after Fig. 11: 350/2 = 175)) ….

Perhaps the following ‘picture’ may help us along, too: Imagine the said gas volume as an opaque or nebulous entity, which mildly glows in the night sky above our heads, provided that our eyes were capable of detecting ‘light’ also in the far infrared of the electro-magnetic spectrum. So, if we could see this entity from above, we would perceive a less intense glow than that which we could see from below. We could now conclude that everything has been accorded as in Fig. 11. Nevertheless we cannot easily accept this figure as the following considerations will demonstrate: The question arises whether there would also exist alternatives to some of the values indicated in FIG. 11; of course in a way which does not unduly impair the issue as a whole. There is a relation, indeed, which admits alternatives, namely for u and v as we already mentioned: u + v = 169 = const. or equally u = 169 – v. But there is another finding hidden in Fig. 11, which seems to be of interest; which we were hitting upon rather accidentally and which – at a first glance – appears to be somewhat strange; but which – at a second glance – lets us suspect perhaps something of how several numbers in that figure had been mutually adjusted. We start from the 2 radiation fluxes, which leave the atmosphere (troposphere, approximately) in both directions of z, i.e. 195 upwards and 324 downwards. These give us the proportion

f = 324/195 = 1,66154 ∼ 1.66. But, on the other hand, we get also f = 390/235 = (288 K/254 K)4 ∼ 1.66 (!) And – since we are taking also 324 = 390 - 66 and 195 = 235 - 40 into consideration – we receive by the way f = 66/40 ∼ 1.66, too (!) Now, if there is TES = 273 + 15 = 288 K that temperature, which – as a main characteristic of the natural GE – leads to SES = 390 W/m2 IR-radiation flux density emerging from the ground, then 235 would correspond to ∼ 254 K = - 19 °C on the surface, which is practically in accordance with the hypothetical reference case (i.e. the mostly quoted -18 °C) for the natural GE. For plausibility reasons we ask the question about height z, at which -19 °C may be met as a mean value within our present atmosphere. As we already mentioned at the end of section 3.1

T ∼ TEB + (dT/dz) ∗ z , hence T ∼ 15°C – 6,5 ∗ z (with z in km) can be regarded as a rather realistic mean T- course in the troposphere. Setting T = -19 °C we obtain z = 34/6.5 = 5.2 km. Values for z vary in the specialist literature between 5 and 6 km. Also dT/dz = 6 °C/km can be found there. All this is plausible within the meaning of an averaging approach. So, after [W. Roedel], such an approach actually refers to an energetic mean, which covers the entire spectral range of a thermal radiation emerging from quite different (molecular) sources, and in this sense the approach is admittedly right. But facing reality, we have to differentiate somewhat more. Citation:

>> En detail earth (her atmosphere included) does not represent an homogeneous black-body radiator, not at all. In fact the earth shows – in the various regions of wavelengths – distinct differences with regard to the height attributable to the origin of a certain radiation and to the temperature of the radiation itself.

km