There’s some consideration in the blogosphere about whether we’ve recently seen some weather and climate events so extreme, so unusual compared to past records, that they are properly said to be caused by anthropogenic global warming, or AGW. See, for example, Michael Tobis, Gareth, and Roger Pielke Jr. for various perspectives. Gareth and Piekle Jr. notes that other sources (such as the World Meteorological Organization) are not merely considering it, they’re explicitly drawing the connection.
Up to this point, the one thing everybody has agreed upon, albeit grudgingly, is that no single weather event can be attributed to AGW. But that’s not really true. Weather is chaotic, which means (among other things) that a small perturbation to the atmosphere grows over time, becoming progressively more noticeable and influencing other weather phenomena in a chain of causality so that eventually (in two to three weeks or so) the weather is totally unlike what it would have been without that small perturbation, even though the climate is unaffected.
Dirce Beauty (Colobura dirce)
Photo: Richard Bartz, from Wikimedia
Philip Merilees summarized this concept in the title of a talk by Edward Lorenz, the pioneer of chaos theory and its application to the atmospere. The title was, “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” The answer, it turns out, is yes. In a very real sense, the weather that we are experiencing now is a consequence of everything that has happened to the atmosphere since the dawn of the Earth up until a few days ago. If something different had happened, today’s weather would have been different.
It’s also correct to say that this year’s Hurricane Alex would not have happened the way it did if I hadn’t coughed outdoors on March 18, 2005, and Hurricane Ike may not have existed at all if it wasn’t for some idiot in Seattle running a red light in October 1992. So, for that matter, the addition of extra greenhouse gases to the atmosphere has perturbed the weather. Probably none of the recent extreme weather events would have happened if it wasn’t for AGW. Likewise, none of the recent extreme weather events would have happened if Archduke Franz Ferdinand had not been assassinated.
But it’s likely that we would have had a different set of extreme weather events to talk about instead.
So, asking whether a weather event was caused by global warming is the wrong question. It leads to the useless answer: yes, it was caused by global warming, and it was caused by everything else too.
The opposite approach, focusing on climate, isn’t much more satisfying. Greenhouse gases are a major player these days, but their climate impacts are still somewhat unpredictable. There are potential nonlinearities and chaotic behaviors in particular aspects of the climate system (ocean circulation, ice, and vegetation/fire come to mind) that would prevent a perfect projection of climate change even if we knew all the external forcings precisely. But it is safe to say that greenhouse gas increases probably caused a large part of the warming over the past several decades and will probably cause even greater warming in the future.
It’s also reasonable to consider the consequences of that warming on the probability of extreme events. For example, if temperatures are warmer due to AGW, the probability of extremely warm temperatures is larger than the probability of extremely cold temperatures.
Temperature’s a simple one, though; other extreme impacts are more complicated. For example, both models and theory predict that heavy rainfall events should become more common with warmer temperatures. Does that mean that you should expect more heavy rainfall events where you live? (Or in Pakistan?) Not necessarily, because there will also be changes in average precipitation; if AGW causes a reduction of rainfall at a particular place, the frequency of heavy rainfall events might likewise decline there. Pakistan happens to be one of those places where some models project an increase in summertime precipitation, while others predict a decrease. So we can’t even say for sure that floods in Pakistan should become more likely due to AGW.
In between these two extremes, where AGW in a sense causes everything and AGW changes the probabilities but doesn’t in a sense cause anything in particular, there are, I think, two possibilities for ways in which we can assign a portion of the blame to AGW if appropriate.
The first way is to consider the direct effect of AGW on the mean state of the atmosphere, and consider that change to the mean state as AGW’s contribution to individual weather events. I’ll call this the “additive effect” approach. Here, it’s not fair to consider greenhouse gases in isolation because, for example, anthropogenic aerosols have made temperatures cooler in many places than they would be otherwise. It doesn’t make sense to me to consider the impact of an imaginary scenario (only greenhouse gases have changed) on a real-world event.
So, for example, temperatures in large parts of Russia are averaging 6 C or more above normal. At this point, climate change (from all anthropogenic causes), according to best estimates, has produced about 1 C of warming in the area. So it would be fair to say that man has turned what would have been a 5 C heat wave into a 6 C heat wave. Climate change has added one degree to the heat wave.
This sounds like a small impact, but it’s not appropriate to attribute 1/6 of the impacts to anthropogenic climate effects. Deaths, fires, and the like increase nonlinearly with the severity of a heat wave, so anthropogenic effects have made this heat wave lots more than 20% more severe than it would have been otherwise.
(This is meant to be an illustration, not a rigorously quantitative attribution.)
The second way is to consider the estimated effect of AGW on the probability of extreme events. I’ll call this the “probabilistic approach”. As I mentioned earlier for temperature, warmer temperatures (with temperature variability held fixed) increase the chances of extreme warm temperatures and decreases the chances of extreme cold temperatures. The graph below shows how big this effect is.
Blue: Normal temperature distribution, sd=4. Green: New temperature distribution with AGW, mean=+2. Purple: Fractional change in probabilities (new/normal). Black: Fractional change in exceedance probability (new/normal). Yellow: Fractional change in non-exceedance probatility (new/normal).
I’ve created this graph by assuming current temperatures have a Gaussian distribution with a mean departure from normal of zero and a standard deviation of four degrees. (Different assumptions change the graphs and numbers but do not affect the argument.) This is shown by the blue curve. Now suppose AGW produces an average warming of 2C. The new probability distribution for temperatures is shown by the green curve.
To get the purple curve, I divided the green curve by the blue curve. This is the factor by which the probabilities have changed under AGW. The purple curve equals 1 at 1 C, which had the same probability of occurring before AGW (one degree above normal) and after AGW (one degree below the new normal). All colder temperatures are less likely under AGW, all warmer temperatures are more likely.
Note that temperatures 8 C above the old normal are now more than twice as likely as before in this example. But that’s not quite what we want to know. For extreme events, we want to know how often a certain threshold is crossed. For extreme heat, we want to know how much more often temperatures will exceed certain values. In my graph, this is shown in black. Conversely, the change in the chances that temperatures will fall below a certain value is shown in yellow.
The black curve tells us that, in this example, a heat wave of 8 C is about 2.5 times more likely if the mean temperature rises by 2 C. What used to happen only 2.3% of the time now happens 5.5% of the time. A 10 C heat wave, two and a half standard deviations above the old mean, would now happen three times as often, 1.8% of the time versus 0.6% of the time. And a day so warm that would only happen once every hundred years during the summer months (probability 1 in (100*90), or 0.011%), would now be expected to happen four or five times as frequently.
How much more frequent does an event have to become due to AGW before we can say that it is being caused by AGW? I propose an arbitrary threshold of 3. If the probability of occurrence of an event has tripled, it’s reasonable to say that each occurrence of the event is likely caused by AGW.
In reality, if such an event occurs three times, one of them would have happened anyway and two of them are extra occurrences caused by AGW. So each individual event has a 67% chance of being caused by AGW. The IPCC’s definition of likely is 67% to 90%. So, to correctly say that an individual event was likely caused by AGW, its probability of occurrence would need to have increased, because of AGW alone, by a factor of 3 or more over pre-AGW conditions.
To that uncertainty would be added the challenge of estimating the correct change in the probability of occurrence, as well as attribution of that change. One could always add a conditional, such as: “If climate model projections are correct regarding [insert phenomenon here], this event was likely caused by AGW.”
Of course, climate change would not merely affect the center of the probability distribution. Its shape would be expected to change too, and changes in both shape and center could be rather large at particular locations if, for example, climate change induces changes in circulation patterns or one of those chaotic climate responses I spoke of earlier. People are speculating that the Moscow heat might be a reflection of one of those major PDF changes.
Black swan (Cygnus atratus)
Photo: Mike Lehmann, Wikimedia
Maybe so, maybe not. But my probabilistic approach works fine for complicated, major PDF changes. All you have to do is figure out, somehow, how the PDF would be expected to change due to AGW. But it’s not sufficient to simply argue, as Tamino has done, that such an event was extremely unlikely in a pre-AGW world, and therefore that AGW had something to do with it. To me, such an explanation sounds a lot like a black swan fallacy.
I hereby assert that this probabilistic approach is legitimate and appropriate, and provides us with a way of attributing specific weather events to anthropogenic global warming. Or not, as the case may be.