Boston’s astounding month of snow a 1-in-26,315 year occurrence
washingtonpost.com
washingtonpost.com
Source: http://xkcd.com/1225/
In that case, a +10 sigma event will occur with probability 4.26361e-81. Each year consists of about 3.1536e+22 femtoseconds, which are 1e-6 the length of a nanosecond, which is the smallest unit of time I've ever heard mentioned in Finance. So, even on that time scale, and with millions of derivatives and securities, I'm not seeing much possibility for a 10 sigma event.
For snow to fall you want warmer temperatures (relatively) which allow large amounts of atmospheric moisture. Ideally striking a cold air mass which then causes snow to fall. Most notably in the U.S. in the form of "lake effect snow", where warmer, moister air over the Great Lakes moves (typically NW to SE) over colder land, and dumps often major amounts of precipitation:
http://eoimages.gsfc.nasa.gov/images/imagerecords/17000/1777...
For snow to accumulate you need annual temperatures which remain below freezing. In this case, even with modest amounts of annual precipitation you can achieve large ice sheets. The annual precipitation over the Antarctic is quite low: "As strange as it sounds, however, Antarctica is essentially a desert. The average yearly total precipitation is about two inches."
http://www.antarcticconnection.com/shopcontent.asp?type=weat...
But with an annual average temperature well below freezing, any snow which falls will accumulate.
The daily high temperature in Boston is above freezing every month of the year, and the low from mid March to early December. Odds of Boston being covered in kilometer-thick ice sheets any time in the near future are exceedingly low.
https://weatherspark.com/averages/29794/Boston-Massachusetts...
As another response notes tongue-in-cheek, this is better than some financial models, though my understanding is that many of those were trained with very recent and short-term data, the figure "14 years" is lodged in my memory though I've been unable to turn it up (possibly discussed by Krugman, Stiglitz, or Taleb).
A lesson is that long-term secular trends, or nonlinear breaks, can render statistical modeling invalid or inaccurate. That's actually a really powerful lesson to be aware of, and accounts for much if not all of the disagreement between demographic trends, say, produced by United Nations demographers or people such as Hans Rosling, and the decidedly more pessimistic estimates of the Club of Rome, Dennis Meadows, et al. Demographers are extrapolating statistical models in which past data observations have been fitted to curves, while the systems modelers such as Meadows are looking at dynamics between multiple real-world factors and looking at their interactions and consequences.
And while I don't want to get into a long debate on the validity or lack of LTG models, I'll note that:
1. The are models not projections, and that a set of multiple scenarios, including one with no resource restraints, have been run.
2. That following a breaking point in the default "World 3" model, further predictive value is considered low -- the system is too chaotic to make further valid inference. Meadows has spoken on this multiple times.
Which raises another further set of points:
1. Inference based on a limited set of data is limited. For climate, we're aware of significant changes in widespread climatic patterns over the past 3,000 to 6,000 years. Some reflected in historical records (e.g., the "Little Ice Age" and "Medieval Warm Period"), some only available from indirect metrics (tree ring data, ice cores, pollen counts).
2. The experience in the American North East points to dramatic shifts away from the recent past historical reference in climate. The times, they are a-changing, as someone said.
Many of the Cascade ski resorts are either fully or partially closed. Further inland things haven't been much better in terms of snowfall[1]. We moved into a house in Idaho this summer with a long driveway that typically has 1'-3' of snow for a month or two every winter, but I took the plow off our UTV 3 weeks ago, after only having used it once (on about 4" of snow) the entire winter.
While of course climate isn't equal to weather one interesting side effect is that I've heard quite a few people say things along the lines of "Ok, I believe in global warming now." I'd imagine the reaction has been quite different in Boston.
[1] http://www.wcc.nrcs.usda.gov/ftpref/data/water/wcs/gis/maps/...
http://cliffmass.blogspot.com/2015/02/why-is-northwest-warm-...: "It is quite easy to explain the proximate cause of the warmth over the Northwest, the drought over California, and the cold/snow over the eastern U.S. They are all caused by the same basic phenomenon: a high amplitude upper level pattern with a persistent ridge over the West Coast and a trough over the eastern U.S."
We all know that hot air rises, and cold air sinks. Therefore if you heat one place and cool another, air will rise in the one, move to the other, and then sink. The Earth is heated up near the equator, and cooled near the poles, so we show that pattern. It actually repeats several times, and the result are the Hadley cells. See http://en.wikipedia.org/wiki/Hadley_cell for confirmation of this.
However in the Earth there is a complication. We are rotating. When air rises, then moves towards the pole, it maintains its angular momentum, and now goes a lot faster than the ground. Thus the air that is about to come back down is going very fast. We call this the jet stream. (There are actually a few jet streams at different latitudes.) When it comes down, the ground slows it down, but it results in a prevailing wind. Over the oceans those winds are called the trade winds because sailing ships used to follow routes that used them. The one over the US goes from west to east, and that is why many major storms tend to do that.
Next piece of information. The nice symmetrical structure I've drawn so far is unstable. It is prone to develop kinks and bends, which then grow. Around the world the overall average latitude is reasonably well fixed, just not the exact latitude at a specific spot. The result is that the jet stream tends to develop fairly large standing waves which are fairly long-lasting but do move around.
Now go get a globe and look on it. North America turns out to be roughly half a wavelength for one of these standing waves. So if the jet stream goes north on the Pacific side, it will go south by the Atlantic. This is our current pattern and it results in a mild winter on one side of the country and a severe one on the other. If the wave is flipped in another year, the pattern reverses. Or you can have a phase shift and both coasts can be average and the interior can be either warm or cold.
This has been known for decades and has nothing directly to do with global warming. (I learned it all from a fluid mechanics course that I took in 1992.)
That said, the locations of the Hadley cells changes depending on how much heat is stored in the system, and adjustments to this is part of the whole El Niño, La Niña cycle. As you increase the rate of energy storage, this results in various chaotic changes, that can increase extreme events.
But the real problem with the rarity of the event is that you arrive at that figure by a probability model assuming independent storms, probably with a Poisson model for frequency. However storms are not actually independent events. If you have a stable pattern that results in many storms following the same track to Boston, the odds of an extreme event are way higher than the naive probability model would have suggested.
Crazy weather. There's a reason the scientific community uses the term "climate change" rather than "global warming". Because as PNW heats up, the east cost gets significantly colder.
It struck a chord with me back then. It reverberates now as I look around CA reservoirs and see the drought rings.
If I had to narrow things down to one primary issue, though, I would have to say it is the total failure of the public transit system, the MBTA. Things wouldn't be nearly as bad if the T was running smoothly, but even now the commuter rail is running on a reduced schedule (which results in completely packed trains that are often late) and various subways trains break down on a daily basis.
Not fun.
How could someone even go about calculating these odds on something so dynamic. Boston was literally under ice 20K years ago and will probably be completely under water in another 20K years.
But I think the point of the article is that even taking into account recent climate changes, this is still a super unlikely string of storms, and there's a lot of chance and coincidence involved.
What do you all do to avoid going stir-crazy when the snow leaves you stuck inside the house for days?
[1]http://www.wbur.org/2015/02/23/space-saver-enforcement [2]http://www.wbur.org/2015/01/28/space-savers-boston
PS: Also, these are not independent events so those long tail odds are likely way off base.
Using 1 as the first number in the ratio makes people think of it like a comet, once you see it you won't see it again for the given period (and will not live to see another).
Using 4 in 100,000 would be an attempt to get more people to reason clearly about what the odds mean.
Rates like HDD failures, Diseases, Homicides, Accidents, are often described as X:100,000.
Odds on the other hand apply to specific events such as the Redskins winning the next Supper Bowl. The difference is when talk about a wide range of things you speak in terms of rates. Thus, the odds of getting this much snow next year that's ~1:26,000. But, the rate of years with this much snow is better described as 4 per 100,000 years.
In the end it's because they described it as events:years they should use a round number of years. But if they had said said the odds that this happens next year then 1:X should be reasonable.
In the years to come, I'm expecting headlines like this (ridiculous odds about odd weather) to become perfectly normal.
Depending on your politics you can now accuse me either of making excuses for "the hiatus", or of being a Denialist, but all I'm really doing is pointing out that the public's expectations of climate models is both too high ("the science is settled") and too low ("global warming is a hoax!")
There is a middle way between these extremes, one that acknowledges the uncertainty of the models (which are large) while at the same time recognizing that there is no physically reasonable way to double the CO2 content of the Earth's atmosphere without adding about 1 W/m2 to the heat budget.
That we don't have a very good idea of how the Earth's climate will respond to that additional heating is not something we should find reassuring, and while there are plenty of good reasons for investing in nuclear, solar and other alternative power sources, there are also good reasons to invest in climate robustness: ensuring that our cities aren't entirely shut down by a rare snowfall, investing to protect the most vulnerable populations from climate variation from any source, and so on.
Our economies are highly tuned up for the climate of the past 100 years, which was unusually stable. We should be aware that the kind of forward planning our parent's and grandparent's generations did based on the assumption of climate stability is not likely to be viable in future as the climate returns to its state of natural volatility, almost certainly helped along by anthropogenic contributions.
Nicely put.
To be honest, when I'm having these conversations I don't go near the whole debate of global warming / we did it / co2 / etc.
I think its simply important to acknowledge the climate is changing, and we need to get with the program. Why it's changing is a whole other thing for another day.
Until next year!