Monday, January 10, 2011

A few technical arguments to clear the fog surrounding the science of global warming

I did not want to write a technical post on global warming. There is plenty of information on this issue available on the Internet, and I thought that everyone with an interest in the subject would just go ahead and read. Still, after it had become clear that my discussion of this issue with Nathan in non-technical terms hit the wall, and I was accused in dismissing offhandedly the entire “scientific field of climatology”, I gave up and started researching this post. I did not intend to become an expert climatologist, but I did go as far as to read a few original research papers in peer-reviewed climatology journals such as Journal of Climate, Journal of Geophysical Research and such. I am obviously still not qualified to judge who is right in the climate change debate, the majority of the alarmist, or the minority of the skeptics, but this much I feel qualified to say: despite the vocal claims to the opposite, the science of the climate change is very far away from being fully understood and settled. Frankly speaking, I was appalled by an extremely low, by standards of my own area of science, level of argumentation and analysis of the data presented in the papers I have read. But I am running a little bit ahead of myself here, so let’s go back to basic.


The physical foundation of the global warming theory is so called “greenhouse effect”. To understand this effect one needs to realize that the solar radiation falling on the Earth comes in many different varieties: radio waves, infrared radiation, visible and ultraviolet light. All of this is essentially just electromagnetic waves, which differ from each other by their wavelengths: longest for radio waves and shortest for ultraviolet light. Waves with different wavelengths interact differently with atmosphere, oceans, ground, living organisms, etc. It is crucially important that the atmosphere is transparent to the visible light (this is why we can see it), but is not transparent to the infrared radiation. The reason for the latter is the presence in the atmosphere molecules, mainly water vapor, and to a lesser extent carbon dioxide and others, which are oblivious to other forms of electromagnetic radiation, but strongly absorb infrared waves. Therefore, the visible light travels almost unobstructed through the atmosphere, where it is either reflected back or absorbed. When electromagnetic radiation is absorbed, it is necessarily re-emitted, but in the form of infrared light, which cannot get through the atmosphere. Thus, a significant portion of the energy of light radiation remains trapped in the Earth-atmosphere system. The atmosphere still emits certain amount of infrared radiation as determined by its temperature to the outer space. This temperature is defined by the equilibrium between amount of absorbed sunlight and the emitted radiation (the Earth warms up or cools down until it emits as much energy as absorbs).


The greenhouse effect is a well-understood physical phenomenon, which plays positive and essential role for life on this planet. Without it, the temperature here would have been too low for any life to be possible. However, while being the physical foundation of the global warming theory (GWT), the greenhouse effect by itself is not part of it.


GWT can be presented in the form of three postulates


  1. The average temperature on the Earth increases

  2. This increase is due to extra amount of carbon dioxide released to the atmosphere because of human industrial activity. This extra CO2 results in more solar radiation being absorbed, and, therefore, warms up the Earth to balance out this increased absorption with more emission.

  3. Increase in temperature will result in drastic climate changes with catastrophic consequences for Earth’s ecosystem, including human population.


Let me begin with the first of these statements, which is the least controversial, and this is what most people have in mind when they talk about the overwhelming empirical evidences of global warming. I will not discuss in too many details the actual observational base of this statement, even though there is still some controversy between temperature measured by the land-based stations, and data obtained from satellites (the latter show much smaller warming). Instead, I want to focus on meaning of the concept of average temperature.


The concept of “averages” is one of the most widely used and most misunderstood ideas in natural and social sciences. One uses this concept to replace a complex set of apparently random data with a single number, which can be done with a clearly defined mathematical procedure (just add all your data together and divide by the number of entries in your data-set). What is not that obvious is the actual meaning and usability of the derived number. An example of a meaningless average is “the average temperature of patients in a hospital”. On the other hand, the average number of votes projected for a candidate for political office is an example of meaningful average. What is the difference between these examples? In the later example, winning or losing an election is determined by the cumulative effect of many voters making their choices, while in the former case there is no quantity whose value would depend on the cumulative effect of individual patient’s temperatures. I suspect that the average temperature in the context of global warming is akin to the average temperature in the hospital because none of the essential climate related quantities is determined by cumulative effects of daily, monthly or annually changing temperatures.


The climate scientists do understand this, and it seems to me that average temperature data are constructed mostly for external consumption: politicians, journalists, and political activists of all persuasions. For internal discussions, other measures of global warming are used. One of the most meaningful metrics is global heat content of the oceans. I was surprised, however, to discover that this indicator shows a lot of volatility even though one would expect the changes of the total thermal energy of the oceans to be very slow reacting only to cumulative effects. Still, these numbers are much more indicative then average temperatures, and they show that starting from about 2000 the heat content of the ocean is flat or even decreases indicating absence of warming. This point is of course being debated on both sides up to now, but the very existence of this debate shows that even with the first postulate of GWT, the situation is not as settled, as its proponents would like us to believe.


Another popular indicator used as a proof of the first postulate of GWT employs the mass of ice in Antarctic. This indicator, however, is not as clear-cut as the ocean heat content because there exist too many different phenomena that could influence melting of ice in Antarctic, such as direct sun light, ozone layer, cosmic rays and others. But even the melting phenomenon itself is not that straightforward: while the land ice in Antarctic does melt, the amount of sea ice shows unprecedented growth. It is interesting to note that the melting of Antarctic ice occurs faster than predicted by the climate models. While this fact is taken by the advocates of global warming as its even “stronger than expected” confirmation, it is really not. This fact simply shows that climate models are not reliable, their predictions are not trustworthy, and that no one really understand why the Antarctic melts.


The situation with the second postulate of the global warming theory is even worse. No one argues that industrial activity increased the amount of carbon dioxide in the atmosphere. At the same time no one also disputes the fact that the direct contribution of CO2 into greenhouse effect is very small - about one degree of centigrade for doubling of the amount of CO2, and we are still far away from this threshold. However, this small effect can be amplified through so-called feedback mechanisms. This means that rise in temperature due to small increase of CO2, which would have been otherwise negligible, stimulate additional processes, which affect the climate in a much stronger way by either enhancing the warming effect (positive feedback) or reducing it (negative feedback). The cornerstone of the global warming science is the assumption that main feedback mechanism is water vapor feedback, which is strongly positive, and, therefore, even small changes in CO2 concentration results in exponentially increasing temperature. The physical origin of this feedback lies in a simple fact that warmer air can contain more water vapor, which in its turn, absorbs more sunlight producing more warming. The problem with this picture is that this is not the only possible feedback mechanism.


Everybody agrees that clouds whose formation is affected by increased water vapor content of the atmosphere, also provide an important feedback mechanism. What scientists cannot agree upon is the type of this feedback: on one hand, clouds reflect more radiation back to space (negative feedback), but on the other hand, they trap more radiation emitted by Earth (positive feedback). Richard Lindzen of MIT argues that the cloud feedback is strongly negative so that it cancels the positive water feedback. Dessler of A&M University and others find the cloud feedback to be either positive or small negative. The uncertainty in the cloud feedback has not yet been resolved as admitted in 2010 Science article by Dessler, which makes it very difficult to know the overall feedback with any certainty.

This overall feedback determines so-called climate sensitivity, which is the crucial parameter for the GWT. If this parameter is large and positive, then the climate is indeed very sensitive to even small changes of CO2 and the humanity is in danger, but if this parameter is small or negative, we still have some hope to survive without wrecking our economy.


Another approach to determining the total feedback is based on statistical analysis of empirical data such as surface temperature and radiation imbalance (difference between incoming and outgoing radiations) in the upper atmosphere. I already mentioned that average temperature does not really measure much, and even if it does, whatever it measures depends on a number of quite arbitrary decisions, and is, therefore, highly uncertain. Given these uncertainties of the input data and a number of arbitrary assumptions unavoidable in this type of analysis, it is not surprising that different researchers come up with opposite conclusions. Therefore, I personally think than none of the results obtained with this approach can be taken seriously and that level of certainty of our knowledge of climate sensitivity implied by the Intergovernmental Panel and the media is strongly overblown.


To conclude the discussion of the 2nd postulate of GWT I want to make another point. Even if the value for the climate sensitivity provided by the Intergovernmental Panel is close to reality, the estimates of the future based on this number are seriously flawed for another reason. The whole concept of feedbacks and climate sensitivity assumes that these parameters themselves remain constant over time. This type of assumption is called linear approximation. This approximation is only valid in the close vicinity of equilibrium. When a system moves farther away from equilibrium, and this is exactly what is being implied by GWT, the linear approximation unavoidably breaks down. In order to know how far from equilibrium a system can go before this happens, we must have models going beyond the linear approximation. I am yet to find papers seriously discussing this issue, and without such a discussion, conclusions based on linear models do not worth much.


Finally, I will say just a few words about the third postulate of the GWT. It is not necessary, though, because analysis of the second postulate already has shown that Freeman Dyson was completely correct saying that the climate science is in a crappy shape. Still, I want to add a few words about long-term predictions of the climate models. Climate is a complicated nonlinear system, and if we know anything about generic nonlinear systems, it is that their dynamics is extremely sensitive to initial conditions and values of the parameters. This means that even a smallest change of one of the parameter can result in completely different predictions, and I do not mean different numbers, I mean different equilibrium states. This conclusion is a rigorous mathematical result in the theory of nonlinear dynamic systems, of which climate is one of the examples. (For those familiar with nonlinear dynamics: I do realize that situation is more complex: there are regions of parameters and initial conditions with stable behavior, as well as those with unstable; there are different types of equilibrium,or better steady states, which can be reached from different initial conditions, but these too much technicalities for this post intended for general public. I am afraid I have already bored everyone to death.) For instance, modern computer climate models include only interaction between atmosphere and oceans, but do not include effects of biosphere (trees, plants, CO2 eating plankton in the oceans, etc.). Even though, these effects appear small, over a long time interval due to the instability of the nonlinear dynamics, they can completely change the fate of the climate. How long is this long time interval? May be some climate scientists know, but they do not share this knowledge with broader public. These arguments do not mean to say that no catastrophic events can ever happen; they mean that these events are not predictable and not controllable.


To conclude, I believe I made a good point showing that the climate science does not yet have a well-established paradigm, and that its unresolved difficulties are of fundamental nature, which has to be resolved before any real paradigm can be formulated. Accordingly, I believe that it is quite irresponsible to force any political and economical actions with global consequences based on this kind of theory.