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Jul 26 2006

Global warming-2: Understanding the problem

Understanding global climate concerns is not easy because it is a complex issue which involves many factors and theories, is based on data that span millennia and is not easy to extract, involves sophisticated theories and computer modeling, and requires long chains of inferential reasoning to arrive at conclusions. Compared to it, evolution, that other anathema of Bush and his anti-science Christian base, is a model of clarity.

At least with evolution, the progression shows a clear pattern, with life evolving from simple single cell organisms to the wide array of complex multi-cell systems we see today. If we started discovering anomalous organisms that seem to violate that temporal ordering, that would require a major restructuring of evolutionary theory.

With global warming, on the other hand, there isn’t such a steady progression. It is not as if global warming implies that the temperature at each and every location on the Earth rises steadily with time. If it did, then people might be more easily convinced. But that is not how it works. Instead, the relevant data always deal with averages that are calculated (1) over very long time scales (involving tens and hundreds and thousands and even millions of years) and (2) over the whole planet or at least large areas of it.

It is quite possible to have wide fluctuations over shorter time periods and in localized areas that go counter to the long-term trend. Unfortunately, this means that there are plenty of opportunities for those who either do not understand that only averages are relevant, or who are deliberately trying to mislead others, to seize upon these fluctuations to argue that global warming is either not occurring or is not a serious problem. I can surely predict that if, for example, the next winter is colder than average in Cleveland, there will be many snickering comments to the effect that this ‘proves’ that global warming is a myth. Similarly, the current heat wave in France and California cannot, by themselves, be used, to argue in favor of global warming either. Scientists’ conclusions will be unaffected since they know that data from a single year or location has only a tiny effect on averages.

These are the questions that need to be considered when we evaluate whether global warming is serious or not.

1. Is warming occurring? In other words, are average temperatures rising with time?

2. If so, is it part of normal cyclical warming/cooling trends that have occurred over geologic time or is the current warming going outside those traditional limits?

3. Are the consequences of global warming such that we can perhaps live with them (slightly milder winters and warmer summers) or are they going to be catastrophic (causing massive flooding of coastal areas due to rising ocean levels, severe droughts, blistering heat waves, total melting of the polar regions, widespread environmental and ecological damage)?

4. How reliable are the theories and computer models that are being used study this question?

5. What are the causes of global warming? Is human activity responsible and can the process be reversed?

My own ideas on this issue have changed over time. I started out by being somewhat neutral on this issue, not sure whether warming was occurring or not. Like most people, I didn’t really understand questions about climate and tended to make the mistake of equating climate with weather. My understanding of weather was strongly influenced by the one feature about weather that we all grow up with, and that is its variability and unpredictability. This tends to create a strongly ingrained belief that we cannot really predict weather and I am sure this spills over into thinking that climate is also highly variable and so should not worry too much about warming since it might just as easily reverse itself.

But the key difference between weather and climate is that while weather systems are chaotic, climate change is not, at least as far as I am aware. In everyday language, chaos means just mess and disorder and confusion. But chaos, in science, is a technical term with a precise meaning. A chaotic system is one that progresses according to particular kinds of mathematical equations, usually coupled non-linear ones, such that the end state of the system is highly sensitive to initial conditions.

With non-chaotic systems, like a thrown ball, a small change in the initial conditions results in small changes in the final state. If I throw the ball slightly faster or at a slightly different angle, the end point of its trajectory will be only slightly different as well. This is what enables us to have expert athletes in any sport involving thrown or struck balls, because based on previous attempts, the professionals know how to make slight adjustments to hit a desired target. The reason that they can do so is because the ball’s trajectory obeys non-chaotic dynamical equations.

But with a chaotic system, that is no longer true. A change in the initial conditions, however small, can result in the end state being wildly different, with the divergence increasing with time. But in order to predict the future of any system, we need to specify the current conditions. Since we can never know the initial conditions with perfect accuracy, this means that reliable long-term predictions are impossible. An analogy of a chaotic system might be river rapids. If you place a leaf at one point in the rapids, it might end up at some point further down the river. But making even a tiny change in your initial position will result in you ending up in a completely different place, even if the river flow itself is unchanged.

For example, suppose the mathematical quantity pi enters into a calculation. We know that the value of pi=3.1415927. . . , a sequence that goes on forever. But in performing actual calculations we cannot punch in an infinite sequence of digits into our computers and need to truncate the sequence. Usually for most problems (which are non-chaotic) we can treat pi as being equal to 3.14 or 22/7 or even just 3 and get fairly good results. We can adjust the precision of this input depending on the required precision of the output. But if pi was a particular part of a chaotic system of equations, then using 3.1415927 or rounding up to 3.141593 would give wildly different results. This is why this kind of chaos is better described as “extreme sensitivity to initial conditions.”

Weather is thought to obey a chaotic system of equations. This is why, despite “Doppler radar” and other innovations that can give quite accurate measures of the state of weather-related parameters at any given time, weather forecasts become notoriously unreliable after three or four days, or even fewer. There is a reason that your local TV newscasts do not go beyond five-day weather forecasts. They are at the limits of predictability and already pushing their luck.

But the equations that drive climate calculations are not believed to be chaotic. Hence, given a model, one can hope to make reasonable predictions about global temperatures in the next century with some confidence in their reliability, even though one does not know if it is going to rain next week.

(In the terminology of chaos theory, sometimes climate is referred to as a “strange attractor” of the weather system, or a “boundary value problem,” whereas weather is an “initial value problem.” Basically, weather and climate are thought to evolve according to different kinds of mathematics.)

It is important to realize that the predictability of the results is possible only once a particular model of climate change has been chosen. One could get different results by choosing a different model altogether, although the range of possible models is strongly limited because they have to conform to the fundamental laws of science and be compatible with what we know about the behavior of related systems. The difference with weather is that with weather one can very different results while using the same model, simply because of our inability to specify exactly the initial values of the problem.

Next: The emerging scientific consensus over global warming.

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