climate change from the perpective of physics and geology...aluminiumtechnik nr. 1 – märz 2008 3...

AluminiumTechnik Nr. 1 – März 2008

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Climate Change from the Perpective of Physics and Geology Authors: Dr.-Ing. Alexander Koewius and Prof. Dr. Christopher J. Rhodes Part 2 2. The facts: Measurements on the ground; their evaluation and interpretation

There has been climate change on earth for as long as there has been an atmosphere, and for as long as life has existed on this planet, living processes have been inextricably involved in this change. The recorded data measured over time which are the subject of the present discussion are (a) the CO2-content of the atmosphere (mixing ratio, k) and (b) the air temperature, T, measured at ground-level at various locations (from which a mean value, Tm, is derived by particular methods). One might ask, why have these particular parameters been chosen? What is so special about them, of all other data that might be chosen? The answer is that it is the physics of (thermal) radiation from which we can inevitably derive the conclusion that a planet’s atmosphere which contains the so-called climate-effective trace-gases (CETG) maintains – ceteris paribus – higher temperatures at the planet’s surface than would be the case if these gases were absent. This can be compared to the effect provided by those structures variously called glasshouses or greenhouses (though the mechanism of radiant heat-retention is not quite the same), which encourages plant growth in a very desirable manner. In both cases, however, the term “greenhouse effect” is used synonymously. As we are well aware from numerous newspaper articles and from other media broadcasts, CO2 – along with N2O, CH4, O3 and H2O – belongs to the family of climate-effective trace gases (i.e. greenhouse gases). 2.1 The content of carbon dioxide in the atmosphere Experiments made for the purpose of measuring the CO2-content of the atmosphere were made well back into the 19th century, but were of little more than purely academic interest for many years. Credit must be given to the Swedish physical chemist, Svante Arrhenius (1859 - 1927) who published (around 1900) his researches on the subject of quantifying the influence of CO2 on the radiation budget of the earth, including its atmosphere. Indeed it was Arrhenius who coined the term “greenhouse effect”. In consequence measurements of this kind gained greater prominence in the thinking of scientists (particularly G.S. Callendar in the 1930s) who pondered the question of whether human activities (particularly their relentlessly increased burning of fossil resources) might not become apparent in an ever rising content of atmospheric CO2. Fossil resources meant mainly all sorts of coal at that time, and subsequently a permanently increasing contribution from petroleum. Prior to the 1950s, an unequivocal answer to this question could not be given, due to the inexactness of the data available. However, this situation changed abruptly in the 1950s in consequence of the exacting work of Charles David Keeling (1928 - 2005), who was an American doctor of chemistry. The original purpose of Keeling’s measurements was as part of an investigation into the influence of atmospheric CO2 on the acidity of waters, for which it was necessary to develop pioneering analytical devices with which to measure small concentrations of a trace gas, like CO2, in an air mixture with a high degree of precision. It was at the very beginning of his investigations on atmospheric CO2-content that Keeling detected an effect, which provided a radical contradiction to the prevailing scientific knowledge of the time, namely the local independence of his readings in a natural environment. His measurements showed the same results at the shores of California and in the mountains there, provided that they had been carried out sufficiently far away from obvious sources where CO2 would be emitted, for example industrial areas etc. As time proceeded, these findings were confirmed over increasingly extended geographic regions. It was on the occasion of the International Geophysical Year in 1958, that CO2-measurements began at Mauna Loa in Hawaii. These measurements have been continued up to now (the mantle having been taken on by Keeling’s son) and are planned to be extended into the future. Also from the early beginnings of the Mauna Loa measurements, two

Translation of „Der Klimawandel aus dem Blickwinkel der Physik und der Erdge-schichte“, Teil 2, published in AluminiumTechnik (of GDA/Duesseldorf), in March 2008


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other fundamental observations were noted : (a) the seasonal oscillation of CO2-content and (b) its baseline rise year on year, see Fig. 2a. During the second half of the last century a marked development occurred worldwide of interdisciplinary climate research. As a consequence of this work, researchers were able to develop an increasingly sophisticated and quantitative model of the relationship which should exist between growing consumption of fossil energies and the constantly rising level of CO2 in the air. The entire diversity of details connected to that subject, is beyond the scope of the present discussion; however we shall return to the matter later within the framework of an alternative, rather unconventional, model. .

The annual oscillations of the CO2-content in the lower atmosphere can be perfectly interpreted phenomenologically: The reason lies in the seasonally varying activity of the flora in the northern hemisphere. Furthermore look at the dark curve seasonally adjusted: There are good reasons for its upwards bent tendency to be attributed to a constantly rising consumption of fossil resources (like coal, petroleum and natural gas). It is since 2003 that this curve is confirmed by measurements through ENVISAT, a European “environmental” satellite. On inspection of the Keeling curve in Fig. 2a a further question arises, which may be fully answered by examining geological data, e.g. from ice-core samples: namely, how may the curve be extended into the past? Initially, it is instructive to trace the curve back to the commencement of industrialization, i.e. until the point (t*) when only the “natural” (background) CO2-content would be detected? From ice core samples, cut from ice sheets some kilometres thick, which cover Greenland and Antarctica, the data represented in Fig. 2b were obtained. The beginning of the industrial age is generally assumed to have occurred in the middle of the 18th century, before when the atmospheric CO2-content was practically constant, varying only in the rather narrow range of k* = 280 +/- 5 ppm 1) during the 800 year time interval preceding the year 1750. Beyond 1750, the curve which fits all the measured points rises progressively; very slowly and almost undetectably at first, but as time passes there is a steadily increasing acceleration which achieves a level in 2006 that exceeds the “natural” (reference) level of k* = 280 ppm CO2 by 36 %. By the term “progressive”, we intend to indicate the permanently rising growth rate of measured values (like k) or of a corresponding curve due to its course over the time (t). Thus we understand that a ‘progressive’ analytical function, like k = f(t) for example, can never show details such as (relative) extremes or points of inflection or any kind of limiting line the function gradually approaches when time goes on. It is clear from Fig. 2b that k could actually be following a function like this, at least back to 256 years in the past. Thus we obtain the following equation of fit:

k = k* + a (t* - t)n ; with t


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which has the form of a parabola of the nth degree. We are thus confronted with the task of finding a satisfactory fit to the measured points in the diagram by a smooth trend-curve of this kind. Since only 2 parameters (‘fit parameters’), a and n, are to be determined we consequently need only 2 “supporting points”, i.e. the coordinates of just 2 measurements, ki at ti, in order to calculate a and n by means of equation ( I ). It is naturally understood that the selected 2 ‘supporting’ points must show a realistic time interval between them to ensure that the procedure is successful. Furthermore we establish the following criteria (see also the caption to Fig. 2b): t* corresponds to the year 1750. t = 0 means the year 2006. Both definitions lead to the relation

tc [calendar year] = 2006 – t [time-coordinate in year units] with t being


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„Gl.“ = equation


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Some general remarks with regard to the trend functions: For t we use the dimension [a], note a = (Latin) annus = year. The dimension of parameter a (or a1, a2) thus becomes [ppm / an ]. However parameter n is dimensionless. Furthermore we must stress the descriptive (i.e. non-physical!) character which befits trend functions like (I a), (I b) etc. Nevertheless parameters like a and n, if assumed to be constants, may be able to tell us something about the ‘feeding behaviour’ of a CO2-source in the past, so potentially enabling comparisons and interpretations to be made between different observed trends.. A trend curve like (I a) is also useful to obtain an initial estimate of how the atmospheric CO2-content may develop in the near future. We may wish to know, for example, in which year (t**) the said content will have doubled the number k* = 280 ppm (which it was in 1750; at t* = 256 [a], respectively). It is worth noting that an activity such as this is in the realm of the sensitivity analyses carried out by the IPCC (International Panel on Climate Change). We answer our question by determining the time interval Δt** = t** - t* on the basis of the current trend after equation (I a), setting there k = 2k*. It follows

t** - t* = - 1/t* ∗ (k*/a1)^(1/n1) (II).

Introducing in (II) our derived values we obtain Δt** = -314 [a], leading to the calendar year

2006 - (Δt** + t*) = 2006 - (-314 + 256) = 2064, for the doubling of the atmospheric CO2 concentration over that which existed in 1750.

We would like to stress again in this context, that while ‘macroscopic’ physics enables us to forecast the time behaviour of a (simple) material system according to well-known cause-effect relations (the keyword is “determinism” which makes us think of e.g. celestial mechanics), such a ‘simple truth’ is unfortunately not applicable to very complicated systems like climate on earth, since it is at least partially subject to non-deterministic influences. We may think in terms of the temporal course which climate-sensitive factors take, such as CO2 emissions from a volcanic or an anthropogenic source. Sources like these simply „behave“ (in general and over time) as non-deterministic! So trend functions may well describe what happened in the past. They may not, however, be used to predict the future. For this reason, the term “forecasting the future” has to be replaced by “future expectations/projections”, at best. In other words, we must wait and see, for only this will yield the outcome. It is precisely in this sense that we must understand/interpret any quantifying scenario in climate reports (and the extrapolation of a certain trend curve, too, for that matter). Let us spend a little time in a discussion of the Keeling curve (i.e. equation Ia). If we regard it as justified that a1 and n1 will maintain the values indicated, in the near future too, then we may predict that the volume concentration of CO2 will reach k1 = 388 ppm in 2010. Additionally equation (Ia) allows the rate of this concentration dk/dt [ppm CO2/a] to be determined at any time after 1958 thus illustrating the ever increasing rise of that rate. For this purpose we differentiate equation (I)

dk/dt = n a∗(t* - t)n-1 (III). By putting n = n1 and a = a1 we obtain

– dk1/dt = 0,85 [ppm/a] in 1958 (t = 48 a) when measurements on Mauna Loa began, and

– dk1/dt ~ 2 [ppm/a] in 2006 (t = 0 [a]), see the corresponding tangent drawn in Fig. 2b.

On pursuing the entire period from 1750 to 2006 we see that the two curves intersect in the middle of the 1950s (k1 = k2). Note, that there must not be a second intersection after 1750 for definite reasons (which, however, is guaranteed by an equation like (I) together with t* = 256 [a]). Since the 2 curves, k1 and k2, rise so differently from their point of intersection, a sharp bend exists there if we regard k = f(t) entirely within that same period.


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We may compare the above analysis with another set of data, made in the same time-period, namely that for the global annual consumption of fossil energies, dE/dt = f(t) in [SKE/a], see Fig. 3. We might expect this figure to support – together with Fig. 2b – a well-known assumption with regard to the origin of the rising CO2-content in the atmosphere, albeit that we have done it in a rather qualitative way*). Fig. 3 offers a growth process, statistically documented, which does not differ substantially from that in Fig. 2b, also if we take approximations from similar analytic trend curves into account. Proven data, as shown in Fig. 3, seem to reach back until ~ 1875. The trend curve on the left hand side (following equation (IV b)) fits the data rather well until shortly after world-war II. At its other end this curve is extrapolated back to 1750 in order to (a) fit it to CO2-emissions (Fig. 2b) for an improved comparison, and (b) additionally to take account of the fact that there was no other means available in the 18th century to meet a growing energy demand (at our northern degrees of latitude) than by adding (hard) coal to wood and charcoal as a fuel**). Coal became the dominant source of energy for North America and Europe during the 19th century. Petroleum joined coal later, in around 1900 when motorization began, and natural gas was not used until the 1940s, and then in increasing quantities . While worldwide consumption of fossil energies developed in a rather moderate way before world-war II***) this accelerated unprecedentedly thereafter. The main reason was (and remains still) a relatively peaceful common state of our worldwide community, thus allowing the production and consumption (or use) of a great variety of goods on an ever increasing scale; this unparalleled phase of global expansion and trade being supported by an extraordinary progress in the field of applied natural sciences. Indeed, many of the new technologies that provided this new direction resulted from developments of methods such as radar that were inaugurated during WW II, for example magnetic resonance spectroscopy. Despite the massive amounts of energy that all this technological innovation and expansion has incurred, its growth has managed to attain a level of accomplishment far beyond any other observed previously in human history. To the right of Fig. 3, is eloquent and impressive evidence for this. Though we cannot expect to draw here a similar curve to follow an equation of form (IV a), (see below), in order to satisfactorily fit the data over the entire period of 60 years, we may fit such a curve so that it follows well that statistical course which was observed during the last six years, and which one can reasonably expect for the very near future, at least. The equations used are: E = dE/dt [109 t SKE/a] = b∗(t* - t)m ( IV ) ; together with t


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By equating (IV a) and (IV b) we obtain the unique intersection (which exists after 1750) at ~ 60 [a], that is in 1946; in other words we have a temporal position of this point immediately after the second world-war – as we found already with k. Note: there would be no significant temporal difference in this regard between the two quantities k and dE/dt if we were to relate our analysis to the entire epoch after 1750. By inspecting the ratio of the slopes at the respective intersections (of k1 and k2, as well as of dE1/dt and E2/dt) we notice that both ratios show the same order of magnitude; the reader is invited to compare Fig. 3 to Fig. 2b. Irrespective of their somewhat qualitative character, we cannot avoid the conclusion that there is scant room remaining to doubt that the cause for an ever rising CO2-content in the atmosphere during the last centuries is anthropogenic in origin. There are many who will argue that the rise in atmospheric CO2 doesn’t depend exclusively on fossil fuel burning, and there is truth in this notion. We cannot ignore the destruction of carbon sinks, e.g. by cutting down trees in the major rain forests ****) on an ever increasing scale, which must be considered both today and in the more recent past. And we have not yet mentioned of other greenhouse trace-gases that are being released constantly into the air, such as methane. In this context we have endeavoured to derive a model-like analysis in the aim to establish a plausible quantitative relation between our relentlessly increasing release of CO2 into the air and the growing concentration of CO2 in the air. Rather than to attempt to integrate full details of this elaboration into the text now, we prefer to present them in a separate annex (Annex I) at the end of the article. We are once more reminded of the potential dramas which may await us in the future, if we persist in our “business as usual” practices, as is reflected by the graphs in Figs. 2b and 3. The last figure allows us to roughly estimate the total consumption of fossil energies between the middle of the 19th century until 2006, which amounts to E0 ~ 523 ∗109 t SKE. Of this, we may deduce that between 1946 and 2006 ~ 446 ∗109 t SKE was consumed, or 88% of the total. We may ask the question: If we actually base future development on the trend curve following equation IV a (corresponding to an unrestrained scenario which unfortunately is to be expected for the near future), how much time would it take (Δt, counted from 2006) to consume that quantity E0 again? Or E0 times z? (z = 1, 2, 3, …) For this purpose we may use the following integral:

----------------------------------- ****) Without their swift replacement by replanting them. Let us add here a citation from www.hamburger-bildungsserver.de (2008, Google search-word ‘Waldvernichtung’): >> The size of area covered by rain forests (in 1990: 19∗106 km²) decreases by ~1 % per year (~ half of the area of the Federal Republic of Germany). The reasons in particular are: (a) creating productive land for shifting cultivation and cattle breeding, and (b): the export of timber. Because exposed rain forest soils degenerate rather quickly, there will grow again – if at all – only such a vegetation which assimilates / sequestrates far less carbon (from CO2 in the air) than the earlier existing woods. If not used elsewhere, wood is commonly burned after clearing.


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which leads to the equation: For z = 1 we obtain Δt = t2 = -27 [a], hence the calendar year 2006 – (-27) = 2033. We see: A scenario is – phrased simply – merely a suggested answer to a “What would be, if..?”- question/consideration, but not very much more! However the outlook from such an answer is not completely “blind”, because it is at least based upon a number of ‘true events’ documented in the past. With regard to (future) projections we realize that the probability, of whether a future event will be in accordance with a certain scenario or not, clearly depends on how far away that moment, t2 , is from today. Our example refers to Δt = t2 = f(z). Bearing in mind the present energy situation in all its relevant details, we cannot completely rule-out that an assumption connected with z = 1 (together with equation (IV a)) appears not entirely unrealistic. To put it plainly: we may conclude from the above that a trend curve like (IV a) is most accurately designated as an “overexploitation curve”. Any other term chosen would run counter to our instinct about these matters.

~~( The end of part Two )~~

Δt = t2 – t1 = 256 – [ 256 m1+1 + z E0/b1 ∗ (m1+1)]1/(m1+1)

climate change from the perpective of physics and geology...aluminiumtechnik nr. 1 – märz 2008 3...

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