Six Sigma Deviation for Antarctic Sea Ice | Hacker News Reader

Six Sigma Deviation for Antarctic Sea Ice

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44 pointsrene_d32 comments

It's clearly a signal of ongoing warming, but the assumption of a Gaussian probability distribution of annual ice extent- something we only have a few tens of years of data to estimate - seems peculiar.

I’m not a statistician, but I’ve read somewhere the argument that the gaussian is the distribution that assumes the least about its data (just that there’s a mean and non-infinite variance) so it is typically safe to use when you know little about the real distribution.

(I’m just commenting to compel someone to correct me and expand on this subthread really :) )

Good tactic!

> so it is typically safe to use when you know little about the real distribution.

That was what the quants doing risk assessment at the big banks thought pre-2008, which is the other context I associate with the n-sigma notation for probability

So what OP is missing is the central limit theorem[1]. According to which any sum diatribution of independently-identically-distributed random variables in the limit becomes gaussian distributed.

So taking it apart, given some restrictions, any sum of randomly distributed data is gaussian distributed.

If you take an average of some value. E.g. sea ice extent at fixed date x, e.g. January 1st every year, you have a sum distribution.

So you're not talking about the random distribution of any date, but of the random distribution of the average value. Only this has the Gaussian distribution.

Now there are some restrictions IID - independently identically distributed. This is the part the quants got wrong. Identical distribution is usually not the issue, we can, for a certain timespan, assume that the random distribution stays roughly the same.

But independent was the issue. If one event is correlated with the next, the central limit theorem may hold for a bit, but if the correlation is, too extreme will break down, like in the quant models of yore.

Their estimates for the housing market risk were ok as long as the credit defaults were not highly correlated, but as soon as the crisis started some vicious cycles formed between the foreclosures and tumbling house prices causing more foreclosures.

The models broke down.

Back to the ice sheats, if we assume the melting of the ice sheats won't increase (or decrease) the melting of the ice sheats we're good. I don't know about causative mechanisms here, but it could be that the models do break down in these times of extreme change.

That doesn't mean that the extreme change is nothing to worry about, since only by being extreme might it break the models.

[1] https://en.m.wikipedia.org/wiki/Central_limit_theorem

Maybe you can make an argument that, in the absence of any information, your best bet is assuming a Gaussian distributon, but it definitely is not safe to assume so. Your data might not be symmetrically or even unimodally distributed and making these assumption can lead to completely wrong conclusions.

If you know that your data has a well-defined mean and standard deviation but you know nothing else about it then you start with a Gaussian distribution. This isn't an assumption. The Gaussian distribution has the highest entropy and hence encodes the least information possible about the data. Then as you learn more about your data, you would update this distribution using Bayes' theorem. This could give rise to skew or multiple maxima.

I would consider a well-defined mean and standard deviation an assumption. The distribution of maximum entropy is determined by the constraints. Those constraints have to be assumed. If you constrain your problem to only have nonzero probabilities in a fixed interval, then a uniform distribution will have maximum entropy.

I agree that there is an assumption that the data are well described by a distribution on R instead of some interval [a,b]. I don't know how well justified this is. The assumption of well defined mean and stddev is weak and better supported each time you collect more data. If your stddev is ill defined then you'll find your sample stddev will diverge (increase) as you add more data points.

In this case, as each day is highly correlated to the previous one, it is safe to say that the distribution of daily sea ice variation is probably not Gaussian? (Though obviously, this is very bad...)

The comparison is between ice extent measurements at the same date, at differing years, so the day-to-day correlation is not the relevant metric here, but the year-to-year correlation, which should be very low.

There's still something funny about quoting tail probabilities converted to once in X years, though, isn't there? Maybe I'm thinking about this wrong...

Thirty years of antartic sea ice extent varied in a Gaussian fashion - with a fairly tight std deviation.

The last few years have been further and further from the [1981 - 2010] "normal flux cycle".

This may help visualise the data better:

https://nsidc.org/arcticseaicenews/charctic-interactive-sea-...

( click the antartic button to switch poles; the default is to grey the thrirty year normal data band and to only show last year and this year, other choices can be made by selection on the data table )

So we're fucked at this point, and nobody is saying anything about it.

Don't Look Up was right. We're dumb idiots of a species.

The fun thing is, we cannot recognise this kind of danger. Our regular animalistic detection mechanism cannot be triggered by this, so we're kind of aware but nothing in us tells us to get away from the problem. Even as you write this, you probably don't truly believe that this could very well be the end. For once the slowly boiled frog thing is actually true.

I certainly have had my panicky days about this, so something inside me is getting at least part of the picture.

Unfortunately the people who can actually do anything about this lack the parts of their brain that could ever hope to understand.

It seems a bit like dying of a radiation overdose - a lethal exposure can take just moments, and you will go on as though nothing happened for a time, but the damage is done and irreversible.

like cigarettes, another dumb behavior of humans

over 20 years I completely recognized a warming, and I'm doing my best (no car, minimal consumption/spending, CO2eq footprint about 5% of average person in Western Europe), not many people are doing this, but there are plently benefits, not just environmental

It’s noneoftheabove that stands above the don’t look up.

Practically speaking, unverifiable and unfalsifiable.

They say once in 7.5 million years, so why don’t they show the previous 7.5 million years?

If that's not possible, and we only have 1989-2023 data, then the 7.5 million year comment is particularly ridiculous, as is making any generalization with data for only 0.0001% of the time span in question.

The timespan is just a more easily digested framing of the odds. It's meant to be easier for a layman to understand, and doesn't actually have anything to do with what things would look like over 7.5 million years. That would take models with an impossible level of detail about planet scale dynamics.

The quote from one researcher here:

Antarctic sea ice levels dive in 'five-sigma event' (abc.net.au)

https://www.abc.net.au/news/2023-07-24/antarctic-sea-ice-lev...

34 points by adrian_mrd 1 day ago https://news.ycombinator.com/item?id=36839757

has it a bit over five sigma and easily less than six.

Still hella significant.

I want to make clear up front that I take global warming absolutely seriously, that it is undoubtedly human-caused, and that it is progressing faster than consensus models have predicted.

But the interpretations given to 34 years of highly-correlated time-series data are highly questionable and largely unwarranted.

Put briefly, we have very little long-term global remote-sensing data largely because remote sensing didn't exist until the 1960s, and largely came of age long after then. As with this data series which begins in 1989.

We *ABSOLUTELY DO* have many other long-term data series showing tremendous changes and associated climatic conditions: ice-core data going back 800,000 years, sea-level measurements going back a billion+ years (at which point plate tectonics are a major confounding factor), plant growth distributions and patterns dating back millions of years, and global temperature inferences also dating back on the order of a billion years or more.

And yes, assuming a normal distribution, a six-sigma event is extraordinarily rare. But to make accurate inferences of such extreme-outlier events based on 34 measurements is statistical malpractice.

Call this "unprecedented in the data record". Call it "extremely concerning". Find other data series with which this pattern can be correlated and from which stronger inferences might be drawn.

(Note that ice-field extant data before the age of satellite observation are very thin, though outlier events such as bergs being sited in temperate waters might well occur, and that shipping logs do tend to record numerous events of interest and date back about 500 years over a fairly wide area. Indigenous records from, say, Tierra del Fuego might also note sitings over a longer period.)

Sources: three years of stats courses at uni, work in stats and data reporting professionally and at an amateur level, though not an actual statistician.

Well bite me for not chiming in with some rehash of the Earths-heating-be-very-afraid greenhouse dogma, but specifically

( https://www.nature.com/articles/s41598-022-05449-8 ) Persistent extreme ultraviolet irradiance in Antarctica despite the ozone recovery onset ?

That is an Earth change I could sink my teeth into because our measurements of ozone are first rate, the crisis continues and Antarctica is a known target of the phenomenon.

Where are those persons saying that with global warming Antarctica would actually get cooler?

It is incredibly easy to bash something, very hard to come up with your own ideas.

To show this, reader, try to do a small experiment yourself - something your interested in - but make it really, really small. Can be testing products you use often to see which is the best for you.

It is REALLY hard! And it's extremely easy for people to pick it apart. "Oh, you know more than the guys who wrote the standards?" "I've been using that for years, you're just using it wrong" "Here's a picture of me doing xyz it works fine"

They spent two seconds, you almost certainly spent days and days on your really small test.

This is why you won't see people back up these claims. They didn't spend time or effort getting there, and they won't spend that time or effort backing them up.

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