{"id":280663,"date":"2023-09-27T12:43:19","date_gmt":"2023-09-27T10:43:19","guid":{"rendered":"https:\/\/climatescience.press\/?p=280663"},"modified":"2023-09-27T12:43:23","modified_gmt":"2023-09-27T10:43:23","slug":"causality-and-climate","status":"publish","type":"post","link":"https:\/\/climatescience.press\/?p=280663","title":{"rendered":"Causality and climate"},"content":{"rendered":"\n
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From Climate Etc.<\/a><\/p>\n\n\n\n

\u00a0September 26, 2023<\/a>\u00a0by\u00a0curryja<\/a><\/p>\n\n\n\n

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Guest post by Antonis Christofides, Demetris Koutsoyiannis, Christian Onof and Zbigniew W. Kundzewicz<\/p>\n\n\n\n

On the chicken-and-egg problem of CO2 and temperature.<\/p>\n\n\n\n

Bare facts vs. mechanism<\/strong><\/h2>\n\n\n\n

A car is travelling at 80 km\/h, and a ray of light is travelling parallel to the car, in the same direction. Its speed relative to the Earth is 300,000 km\/s. What is its speed relative to the car? Today we know that the answer \u201c300,000 km\/s minus 80 km\/h\u201d is wrong. But in 1887, people thought that it was self-evident and undisputable\u2014after all, it\u2019s basic logic and simple arithmetic. At that time, physicists Michelson and Morley had devised a method with sufficient accuracy to measure the small differences in the speed of light, and in an effort to discover details about its movement, they conducted one of the most famous experiments in the history of science. The results were baffling. The speed of light was constant in all directions\u2014the direction of the Earth\u2019s movement, the opposite direction, and the perpendicular direction. There was no explanation for that\u2014it defied all logic.<\/p>\n\n\n\n

However, we have to look at the bare facts, regardless how impossible they seem. Michelson and Morley did not feel compelled to provide an alternative theory of light, or of anything. They concluded that their results \u201crefute Fresnel\u2019s explanation of aberration\u201d and that Lorentz\u2019s theory \u201calso fails.\u201d Had they written \u201cwe have no idea what\u2019s going on\u201d it would have been the same. Making their negative results public opened the road to further research. It was a long road, and it took almost twenty years of work by distinguished scientists before arriving at the theory of relativity.<\/p>\n\n\n\n

It goes without saying that this is hardly the first or the last mystery in the history of science. One that is still unsolved is the changing mass of the International Prototype of the Kilogram. Until a few years ago, the kilogram was defined as the mass of a platinum-iridium object stored in the International Bureau of Weights and Measures in Paris. It has been found that its mass changes over time by something like 0.000005% per century, and no-one knows why exactly. That no-one knows the mechanism does not alter the fact that the mass does change.<\/p>\n\n\n\n

How a clear case of causality can become a noisy mess<\/strong><\/h2>\n\n\n\n

Imagine a beach being hit by small waves. Once in a while, a series of noticeably larger waves arrive. There\u2019s a port 10 km further, and ships are departing from it. We might notice that the departures of the ships are correlated to the instances of larger waves, and suspect that there could be a causal relationship.<\/p>\n\n\n\n

In reality, in this case we understand the mechanism through which the ships cause the waves; but if we assume we don\u2019t, here is how we might try to investigate: we might draw a chart like the following, where the horizontal axis is time, the orange line shows ship departures (the vertical axis showing the size of the ship) and the blue line shows sea level. If every departure was reliably followed by a temporary increase in wave height, we could conclude that the departures of the ships potentially cause the increase in wave height, especially if we noticed that the size of the ship is correlated to the size of the increase in wave height.<\/p>\n\n\n\n

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We say \u201cpotentially\u201d because we can never be certain about causation. It could be that the departures and the waves both have a common cause. Even if someone was shot in the head, we can\u2019t be certain it was the bullet that killed him\u2014he might have suffered a stroke just before the bullet entered his brain (Agatha Christie\u2019s Poirot has resolved several mysteries of similar type). So we can hardly be 100% certain that X causes Y. One thing is clear, however: the waves do not cause the ships to depart. The reason is that first the ship departs and later the waves hit the beach. The effect cannot precede the cause.<\/p>\n\n\n\n

Even in this simple case where there\u2019s an impulse (the departing ship) followed by a response, things can quickly get complicated. Ships could be going in many different directions, and the response would not always appear in an equal time interval after the impulse. For some impulses the response could be totally absent (e.g. for ships that depart in a direction away from the beach). The interval between departures could be smaller than the time it takes for the response to arrive, and the intertwining of impulses and responses could be confusing. Sometimes responses might appear out of the blue, without impulse (for example, there could be arriving ships that cause that, which we might not have taken into account). It might not be as easy to distinguish the wave response from the other waves if the sea is rough. Add all these factors together, and the blue line could be a big noisy mess.<\/p>\n\n\n\n

And in a real world example, like in the question of whether CO\u2082 concentration affects the temperature, both lines can be a big noisy mess.<\/p>\n\n\n\n

Investigating potential causes<\/strong><\/h2>\n\n\n\n

So here is the question: given two processes, how can we determine if one is a potential cause of the other? We deal with this question in two papers we published last year in the Proceedings of the Royal Society A (PRSA): Revisiting causality using stochastics: 1. Theory<\/a> (preprint<\/a>); 2. Applications<\/a> (preprint<\/a>). We reviewed existing theories of causation, notably probabilistic theories, and found that all of them have considerable limitations.<\/p>\n\n\n\n

For example, Granger\u2019s theory and statistical test have already been known to be identifying correlation (for making predictions), not causation, despite the popular term \u201cGranger causality\u201d. What is more, they ignore the fact that processes exhibit dependence in time. Hence, formally testing hypotheses in geophysics by such tests can be inaccurate by orders of magnitude due to that dependence.<\/p>\n\n\n\n

As another example, Pearl\u2019s theories make use of causal graphs, in which the possible direction of causation is assumed to be known a priori<\/em>. This implies that we already have a way of identifying causes. Moreover, insofar as those theories assume, in their use of the chain rule for conditional probabilities, that the causality links in the causal graphs are of Markovian type, their application to complex systems is problematic.<\/p>\n\n\n\n

Another misconception in some of earlier studies is the aspiration that by using a statistical concept other than the correlation coefficient (e.g. a measure of information) we can detect genuine causality.<\/p>\n\n\n\n

Having identified the weaknesses in existing theories and methodologies, we proceeded to develop a new method to study the question whether process X is a potential cause of process Y, or the other way round. This has several key characteristics which distinguish it from existing methods.<\/p>\n\n\n\n