Of Distributions and Means

Weather is a chaotic stochastic system.  Outcomes that we typically like to measure – severe storms, tornadoes, hurricanes, temperatures, snowfall — all have mean or average behavior with a large bell-curve or normal distribution around that mean.

With all the talk of record snow in Washington or light snowfall in certain Olympic venues, I feel that a reminder is in order:  There is very little one can deduce about changes or drift in the mean from one or two isolated events in the tail ends of the distribution.   If a kid in your high school gets a perfect score on her SAT, does this mean that the average kid is getting higher SAT scores, that this kid’s score is a symptom of “global smartening?”  Or is this kid’s performance just an isolated event in the tail of the test score distribution?   Katrina and the Washington blizzard seem to occasion a lot of climate conclusions, when in fact I think those conclusions are virtually impossible from such events.

The only really useful role I can see that these extreme events play in the scientific debate is to weed out the credible climate commentators from the charlatans.    If an alarmist says, for example, that the heavy snows in Washington are not necessarily inconsistent with global warming, then he or she is probably relatively safe.  But run away quickly from anyone who says manmade CO2 caused Katrina or, even more incredibly, the Washington snowstorms — they are just nuts.

Of course, the argument typically morphs into folks arguing that extreme events themselves are more prevalent, in other words somehow the standard deviation of the distribution has expanded.  This, in my mind, is one of the weakest arguments in the alarmist arsenal.  The evidence for this is extremely weak (example), and a number of metrics (such as for hurricane activity and large tornadoes) have actually declines over the last decade.  What tends to happen is that the reporting frequency of such events increases, which increases the general perception of having more extreme events — but scientists are supposed to be able to see past such observation biases.

A corollary to this is that extremes in one part of the world do not necessarily mean that the world average is moving in that direction.  Those of us in the US would have sworn January was a cold month, but globally it turns out January was actually a pretty warm month, at least on the historic scale of the last 30 years.  I remember when agricultural futures were first popularized, farmers often went bankrupt forgetting just this corollary.  They would see weather in their area terrible, with terrible crop yields ahead, and they would go long on these crops in the futures markets, only to find the weather in other areas was quite good and they lost a fortune on their futures.

8 thoughts on “Of Distributions and Means”

  1. A bit of mental gymnastics- rather than trying to tease a story from the climate data -ask what we don’t see. Apply the concept of negative space.

    We are told failure to control CO2 emissions will cause an ever increasing number of calamities to befall humanity including rising seas, floods, drought, famine and disease. Given the failure in Copenhagen and the evidence that we will not control CO2 at a level below the “tipping point” one would expect to see a call for mitigation plans for a massive mobilization effort to harden our infrastructure. We should be seeing “Stimulus Money” thrown at building sea walls, flood control devices, improved water storage, bans on coastal development, etc.

    The only solution I can find to: A -the claim of near term planet wide devastation and B- the absence of any mitigation discussion is that we are seeing a solution searching for a problem. And mitigation is not in the universe of acceptable options.

    The truly desperate are always open to compromise -if they are not- then they are not desperate. The apocalyptic vision -if truly believed- should see people and leaders scrambling for shelter- for interim solutions- fall back strategies. We see none of that. Look for what you don’t see.

  2. Credit where credit is due – thank you, Mr. Meyer, for the thoughtful post. Once again I would be careful about trying to out-think the actual scientists in terms of the severity of events, but your post still serves as a good reminder about the ‘weather-vs-climate’ idea.

  3. Katrina was not a Cat 5 upon landfall, it was closer to a Cat 3 and really not outside the mean strength of landfalling hurricanes in the 20th century. In New Orleans much of the damage was due to failure in the dike system which was “designed” to handle the Cat 3 storm they got … it did plenty of damage even so but it should be looked at as an example of extreme result (bad) and not extreme weather.

  4. I wonder about how long a particular weather trend would have to last before it was judged to indicate a change of climate? In the UK we had quite a long series of very mild winters and at one point someone commented that snow in the UK would become a very rare event and would come to be regarded as a sort of cultural memory in the same way as wolves are.

    It was generally accepted that the summers would keep getting hotter and the winters would keep getting milder and surely the further along we go with this process the less likely cold weather should become.

    Yet here we are in 2010 with two colder than average summers and two colder than average winters behind us.

  5. Another element of the weather versus climate issue is how changes in climate change the distribution about the mean. This is usually referred to as changes in variability or “extremes”.

    Now, all studies I’ve seen indicate less extremes and variability if any change at all, and yet the opposite is claimed so often…

  6. A couple of comments…

    One value of these extreme climate events is to allow those who have long been skeptics to use irony and humor to rub the warmists’ noses in their own nonsense. I have seen a number of skeptic commentators (usually on the right) use these events, not as proof of anything, but as a great tease and to destroy the credibility of those who used Katrina and other events as proof of AGW.

    On Katrina…

    The hurricane rapidly lost strength as it came ashore, and shifted to the east, so that New Orleans suffered only category 1 winds. However, the storm surge contained a huge amount of momentum it had picked up from the category 5 winds and came ashore as a record storm surge (it was, in other words, a category 5 surge). It overwhelmed the levees in SE New Orleans (it was simply higher than the levees), flowed into Lake Pontchartrain (taking out a long section of the I-10 causeway) and backed into N.O from the lake.

    The system was built for a Category 3 storm surge, so the failure was inevitable, even without construction and engineering errors. There were a very large number of places where the system failed as a result.

    Before I went to bed the night it hit, I told my wife that N.O. would not be there the next day. Based on a visit to the city a year later, that was basically correct. We toured the damage area, and make a point of driving the Miss. coastline, where the brunt of the surge hit. Along that coast, every structure had been utterly obliterated. There were lots of lonely pillars upon which beach-side houses sat a year before.

  7. Here in Australia we’ve just finished a decade long drought. Unsurprisingly, it’s been dry and hot and we’ve had a disastrous bush-fire or two.

    And just like you mention, our Climate Change Minister, Penny Wong happily blamed those events on AGW.

  8. And just to follow up.

    It makes it very hard for people who aren’t convinced by the IPCC line on AGW to say: “Hey, that’s not necessarily AGW, it might just be the usual drought we have every 40 years or so” when 200 people have lost their lives and the AGW believers have claimed the “moral high ground”.

    (I’ll be discussing more of the sociological aspects of AGW in later comments)

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