Arctic sea ice minimum early prediction

[Ned W]

I am rebuilding and improving the JAXA predict-o-matic, which performed so nicely last year.  It will do a better job of handling uncertainty.

As of today, the expected value for the 2018 minimum is 4.33, but with a very wide 95% CI of 2.67 to 6.00.  That expected value would put 2018 in 6th place, but due to the spacing of prior years' values and the wide range of uncertainty, the most probable bins for this poll are 1st-2nd place and 2nd-3rd place. 

If it seems odd that the most likely extent (4.33 x10^6 km^2) would put 2018 in 6th place, but the single most likely rank is 2nd place, it's because the latter involves integrating probabilities over a range, and the range of possible extent values for 2nd place is huge.

There are approximately equal probabilities of ending up in:

1st-2nd place (34%)
3rd-8th place (31%)
9th-16th place (33%)

Probabilities for individual ranks are as follows:

1st place   7%
2nd   27%
3rd   2%
4th   10%
5th   1%
6th   10%
7th   1%
8th   6%
9th   9%
10th   3%
11th   6%
12th   4%
13th   7%
14th   2%
15th   1%
16th   2%

[Daniel B.]

And yet, the submitted predictions are heavily skewed towards one end.

[Ned W]

And yet, the submitted predictions are heavily skewed towards one end.

I've pointed that out in previous polls, where there's a big disparity between what people "vote" for and what the statistics suggest.  But in this case, the results are actually defensibly rational.

As noted above, the most likely "bin" at this point is second place, because the range of plausible outcomes is wide and that bin covers a much larger range than some others (e.g., 3rd, 5th, 7th place are all extremely narrow). 

So from any individual's perspective, the optimal choice is either 1/2 or 2/3, given the options in the poll.  There's no reason to expect the distribution of responses to match the distribution of probabilities.

[Archimid]

Statistics are biased towards the past.

[Ned W]

... and thus they can provide a handy corrective to human psychology, which is biased towards excitement and drama.

[gerontocrat]

And yet, the submitted predictions are heavily skewed towards one end.

In the 1-2 category, I wonder how many voters thought No. 1 (i.e. < 2012) was the probability given that 2012 was 840,000 km2 below the 2nd lowest in the satellite record (2016) ?
The difference between 2nd & 3rd (2007) minima is just 50,000 km2.

Skewed votes in a skewed poll?

[jdallen]

And yet, the submitted predictions are heavily skewed towards one end.

In the 1-2 category, I wonder how many voters thought No. 1 (i.e. < 2012) was the probability given that 2012 was 840,000 km2 below the 2nd lowest in the satellite record (2016) ?
The difference between 2nd & 3rd (2007) minima is just 50,000 km2.

Skewed votes in a skewed poll?

... and 4th is only a few thousand more past that.

I was enamoured of statistical analysis at one point until I determined just how useless it is for predicting outcomes in a dynamically changing system.  The clustering of recent minima...all of which since 2007 were  5.1 million KM2 or less... and which follow a distinctly declining trend... underscore this. The differences for many lie within one another's margin of uncertainty.

Previous years totals are about as relevant to one another as year over year stock prices.  I might actually be more skillful with stocks - which is to say not really - evaluating historical data.

Skillful predictive methods and data sources lie elsewhere.

Before someone latches onto this to try and suggest we may recover or this is just natural variability, the trend, which *is* significant is distinctly down, much as total system enthalpy and CO2 levels have increased.

[Dharma Rupa]

And yet, the submitted predictions are heavily skewed towards one end.

In the 1-2 category, I wonder how many voters thought No. 1 (i.e. < 2012) was the probability given that 2012 was 840,000 km2 below the 2nd lowest in the satellite record (2016) ?
The difference between 2nd & 3rd (2007) minima is just 50,000 km2.

Skewed votes in a skewed poll?

... and 4th is only a few thousand more past that.

I was enamoured of statistical analysis at one point until I determined just how useless it is for predicting outcomes in a dynamically changing system.  The clustering of recent minima...all of which since 2007 were  5.1 million KM2 or less... and which follow a distinctly declining trend... underscore this. The differences for many lie within one another's margin of uncertainty.

Previous years totals are about as relevant to one another as year over year stock prices.  I might actually be more skillful with stocks - which is to say not really - evaluating historical data.

Skillful predictive methods and data sources lie elsewhere.

Before someone latches onto this to try and suggest we may recover or this is just natural variability, the trend, which *is* significant is distinctly down, much as total system enthalpy and CO2 levels have increased.

If one consistently voted 1st or 2nd lowest every year for the last 10 years what percentage of the time would one be right?  A harder question: what would be the expected percentage?  (I was about to say 10%, and then took pause.)

[Daniel B.]

And yet, the submitted predictions are heavily skewed towards one end.

In the 1-2 category, I wonder how many voters thought No. 1 (i.e. < 2012) was the probability given that 2012 was 840,000 km2 below the 2nd lowest in the satellite record (2016) ?
The difference between 2nd & 3rd (2007) minima is just 50,000 km2.

Skewed votes in a skewed poll?

... and 4th is only a few thousand more past that.

I was enamoured of statistical analysis at one point until I determined just how useless it is for predicting outcomes in a dynamically changing system.  The clustering of recent minima...all of which since 2007 were  5.1 million KM2 or less... and which follow a distinctly declining trend... underscore this. The differences for many lie within one another's margin of uncertainty.

Previous years totals are about as relevant to one another as year over year stock prices.  I might actually be more skillful with stocks - which is to say not really - evaluating historical data.

Skillful predictive methods and data sources lie elsewhere.

Before someone latches onto this to try and suggest we may recover or this is just natural variability, the trend, which *is* significant is distinctly down, much as total system enthalpy and CO2 levels have increased.

If one consistently voted 1st or 2nd lowest every year for the last 10 years what percentage of the time would one be right?  A harder question: what would be the expected percentage?  (I was about to say 10%, and then took pause.)

Actually 10% would be correct for 1st lowest only - 2012.  On three more occasions, the minimum was 2nd lowest; 2008, 2011, 2016, with each year knocking the previous out of second place.  Hence, the answer is 40%.  Not sure about expected percentage.

[Steven]

I am rebuilding and improving the JAXA predict-o-matic, which performed so nicely last year.  It will do a better job of handling uncertainty.

As of today, the expected value for the 2018 minimum is 4.33, but with a very wide 95% CI of 2.67 to 6.00.

Could you elaborate on the calculation?  How did you arrive at 4.33 million km2?

[jdallen]

Just to put this in perspective, 4.33 million KM2 is only 200-300000 KM2 behind the pack around 2nd/3rd/4th, which is three good melt days, or a week of smaller ones.  As Daniel B. mentioned, if you'd voted 2nd or lower the last 10 years, you would have been correct 40% of the time.  Statistical methods would not have predicted that.

The between the average and difference with 2nd is one week of melt. With 1st its about 3 weeks. With the pendulum (increased system enthalpy, warmer weather, increasing GHG in the atmosphere) lengthening each year, the probability of longer melt/more intense melt increases out of step with probability.

Thus 40% history of a low vote being accurate... rather than the < 10% it should be.

[Dharma Rupa]

Actually 10% would be correct for 1st lowest only - 2012.  On three more occasions, the minimum was 2nd lowest; 2008, 2011, 2016, with each year knocking the previous out of second place.  Hence, the answer is 40%.  Not sure about expected percentage.

OK....then is there any other guess that has a higher skill?

That is, is there any good reason for me to guess anything other than 1st or 2nd place every year?

[Dharma Rupa]

Just to put this in perspective, 4.33 million KM2 is only 200-300000 KM2 behind the pack around 2nd/3rd/4th, which is three good melt days, or a week of smaller ones.  As Daniel B. mentioned, if you'd voted 2nd or lower the last 10 years, you would have been correct 40% of the time.  Statistical methods would not have predicted that.

The between the average and difference with 2nd is one week of melt. With 1st its about 3 weeks. With the pendulum (increased system enthalpy, warmer weather, increasing GHG in the atmosphere) lengthening each year, the probability of longer melt/more intense melt increases out of step with probability.

Thus 40% history of a low vote being accurate... rather than the < 10% it should be.

Like I asked above, and how I always vote.  Is there any good reason to vote anything other than the lowest?

[jdallen]

Just to put this in perspective, ...
<snippage>
...Thus 40% history of a low vote being accurate... rather than the < 10% it should be.

Like I asked above, and how I always vote.  Is there any good reason to vote anything other than the lowest?

Increasingly, I don't think there is one. 

[Ned W]

I am rebuilding and improving the JAXA predict-o-matic, which performed so nicely last year.  It will do a better job of handling uncertainty.

As of today, the expected value for the 2018 minimum is 4.33, but with a very wide 95% CI of 2.67 to 6.00.

Could you elaborate on the calculation?  How did you arrive at 4.33 million km2?

Thanks for asking.  I'm super-busy right now but will try to give a more complete answer later.  The short version is that it's modeling each year's minimum extent as a function of that year's extent on this date.  In other words, if extent is 11.01868 x 10^6 km on 28 May, what is the ensuing minimum likely to be?  The main point is not the specific predicted values but trying to get the estimated error (uncertainty of prediction) correct.  In other words, I'm more interested in modeling how the uncertainty changes over time, as the season progresses. 

One complication I'm still dealing with is that the magnitude of the drop from date X to the September minimum isn't stationary over time -- it is bigger post-2007 than it was before, probably due to the loss of multi-year ice.  Since there's very little multi-year ice left, I'm not sure that this non-stationarity will continue into the future.

[Ned W]

Actually 10% would be correct for 1st lowest only - 2012.  On three more occasions, the minimum was 2nd lowest; 2008, 2011, 2016, with each year knocking the previous out of second place.  Hence, the answer is 40%.  Not sure about expected percentage.

OK....then is there any other guess that has a higher skill?

That is, is there any good reason for me to guess anything other than 1st or 2nd place every year?

So, first of all, I personally dislike the rank-based polls, because as we've all pointed out, the clustering vs dispersion of various years' extents means that the widths of the various ranks are wildly inconsistent.  Currently, "second place" consists of a range that's 0.84 million km2 wide.  But another 0.84 million km2 would encompass everything from 2nd to 9th (!) place.

It's much less ... fraught ... making predictions for the value of extent, rather than its historical rank relative to other years.

Having said that, over the past decade, if you used the predict-o-matic each year at this point in late May to predict the annual minimum extent, you would have had a mean absolute error (MAE) of 0.47 million km2.  If you just picked first place every time -- i.e., you picked the 2007 extent up until 2013, and then used the 2012 extent after that -- you would have a MAE of 0.96 million km2.

So just guessing the extent corresponding to 1st place would result in an error that's about twice as large as using statistics. 

If you set each year's guess to be equal to the second-largest historical extent, you'd do better (MAE 0.49) than guessing first, but still not *better* than using statistics.

As for trying to predict ranks, rather than actual extent ... it would take some tinkering to get the predict-o-matic to retroactively figure out the integrated probabilities of different ranks in the past, but if you just convert its single most likely extent value to a rank, that would give a MAE of 1.3 "places" for using stats, vs. 2.5 places for always guessing 1st place, and 1.7 places for always guessing 2nd place. 

The bottom line: 

Always guessing first place would have performed poorly over the past decade. Always guessing second place would have performed better. 

But using statistics to predict the outcome based on current extent would have performed better than either one ... and as the season goes on, its predictions tend to improve.

[Ned W]

Going forward, I'm more comfortable basing the predict-o-matic only on the data from 2007-present (i.e., after the multi-year ice is mostly gone).  That gives an expected value of 4.22 for this year's minimum, rather than the previously-quoted 4.33 (million km2).

[crandles]

Like I asked above, and how I always vote.  Is there any good reason to vote anything other than the lowest?

Of course there is:

If too many people just go for the lowest and this turns out not to be the case, then this is setting up a 'those environmentalists are always crying wolf' defence for ff companies to continue not to act. Why hand them such a defence?

[gerontocrat]

Like I asked above, and how I always vote.  Is there any good reason to vote anything other than the lowest?

Of course there is:

If too many people just go for the lowest and this turns out not to be the case, then this is setting up a 'those environmentalists are always crying wolf' defence for ff companies to continue not to act. Why hand them such a defence?

Masochists should always vote for a very improbable outcome - self-humiliation.

Benefits of having to make a prediction (on anything) could be that
- it can force one to examine the evidence and one's knowledge (or lack of) of a subject and perhaps even seek to look for the data gaps before making that prediction,
- especially when the prediction turns out to be rubbish it can force one to re-examine where that prediction came from.

Naturally an aged person such as myself knows everything that there is to know already.

ps:  a suggestion. When someone sets up a new poll on extent or volume for this year, can the deadline be on about the 8th of the month - by then the NSIDC monthly extent and the PIOMAS monthly volume analyses should be available.

[Ned W]

I agree with crandles, and also would just reiterate that picking 1st place every year would give you a mean absolute error that's about twice as high as from other methods (over the past decade). 

[...change subject ...]

Here's a graph showing (for 2018) the standard error of regression, when relating each day's extent to the ensuing minimum, based on data from 2007-2017:



It's not the full estimate of the error of prediction, which is slightly larger, but it shows the general pattern of how the uncertainty evolves over the season.

(1) From January until June there's no real improvement in the level of uncertainty. 

(2) There's an odd sort of dip in mid-June, where the daily extent values become somewhat better predictors of the eventual minimum, but after a couple weeks that breaks down again. 

(3) Then, finally, around 23 July the daily extent values start to become a much better predictor of the September minimum, with the level of uncertainty plunging rapidly through late July and August.

Ignore the spike around day 60 -- that's Feb 29, leap year.

[Ned W]

Naturally an aged person such as myself knows everything that there is to know already.

I thought it was teenagers who already know everything that there is to know.

What's the joke, "When I was 16 my parents were pretty stupid, but ten years later I was amazed at how much the old folks had learned."

[Dharma Rupa]

Like I asked above, and how I always vote.  Is there any good reason to vote anything other than the lowest?

Of course there is:

If too many people just go for the lowest and this turns out not to be the case, then this is setting up a 'those environmentalists are always crying wolf' defence for ff companies to continue not to act. Why hand them such a defence?

I am totally disinterested in the Environmentalist verses climate Denier debate, therefore your argument provides no information.  It doesn't give me any reason at all for anything.

[Dharma Rupa]

I'm very confused here.  The poll was about ranking, no matter how woefully bad ranking is as a measure.  Why are people bringing up actual measures of extent and area?

Given that the poll is RANKING and that the minimum category is 1st or 2nd, is there any good reason for me to pick anything other than the minimum category?

In essence, I am asking if predicting that there will be less ice in the future is not only a good bet, but also the best bet -- based upon historical performance.

[Ned W]

I'm very confused here.  The poll was about ranking, no matter how woefully bad ranking is as a measure.  Why are people bringing up actual measures of extent and area?

I don't think anybody has brought up "area".  I posted about extent and rank. 

Given that the poll is RANKING and that the minimum category is 1st or 2nd, is there any good reason for me to pick anything other than the minimum category?

Does "not wanting to be wrong" count as a good reason?

Using the rank bins from this poll (1/2, 2/3, 3/4, etc.) I get the following results for the past decade:

Always pick 1/2 bin: correct 4/10 times, mean absolute error 1.6 bins
Always pick 2/3 bin: correct 6/10 times, mean absolute error 1.1 bins
Use statistics [1]: correct 5/10 times,  mean absolute error 0.8 bins

Using the bins from this thread's poll, you're best off either picking "2nd/3rd place" or using statistics, depending on how you choose to measure it.

Always picking the lowest bin (1st/2nd) would have resulted in more error than either of the other options.

Does that answer your question?

[1] The fine print:  use regression model to predict minimum extent based on late-May extent, and then choose bin with 2 closest ranks to that predicted extent

[Daniel B.]

I'm very confused here.  The poll was about ranking, no matter how woefully bad ranking is as a measure.  Why are people bringing up actual measures of extent and area?

Given that the poll is RANKING and that the minimum category is 1st or 2nd, is there any good reason for me to pick anything other than the minimum category?

In essence, I am asking if predicting that there will be less ice in the future is not only a good bet, but also the best bet -- based upon historical performance.

That depends on much faith you would put in predict-o-matic value 0f 4.33.  If the predicted value is 6th lowest, would that not be a more reasonable guess, based on valid inputs?

[Ned W]

Well, I wouldn't put much faith in that prediction, and I'm the one who created it.  The main point is that it's 4.33 (or 4.22) plus or minus more than a million km2 because the uncertainty range is huge, at least until mid-July.

So it's a pretty poor predictor, but it does seem to do better than "always pick the lowest option". 

On the other hand, "always predict 3rd place" works about as well as any statistical method, as far as the past decade goes, at least this early in the season.  But that's not likely to work out this year.

[Brigantine]

I think every year now has a ~20%-25% probability of a new record, and a ~10% probability of a BOE (<1M).

I'd go a bit higher, but in the same ballpark -- about 30% and 15% respectively.

So, conditional on a minimum below 2012 (3.18 million), you both think* there's then a 40-50% chance of a further collapse all the way to 1 million this summer? That seems very ambitious to me...

* - or at least thought, 2 months ago.

[Dharma Rupa]

On the other hand, "always predict 3rd place" works about as well as any statistical method, as far as the past decade goes, at least this early in the season.  But that's not likely to work out this year.

Please explain, given that that statement at least addresses the question I asked -- even if it was not substantiated.  Over recent history what is the likelihood of being right if I predicted 3rd place every time?

Another way of putting my question:  What odds would Jimmy the Greek give?

I am asking how I ought to bet.

[Dharma Rupa]

That depends on much faith you would put in predict-o-matic value 0f 4.33.  If the predicted value is 6th lowest, would that not be a more reasonable guess, based on valid inputs?

No, it would not be if the question is (as it was) is how ought I bet if I bet the same way every time.

[oren]

I think every year now has a ~20%-25% probability of a new record, and a ~10% probability of a BOE (<1M).

I'd go a bit higher, but in the same ballpark -- about 30% and 15% respectively.

So, conditional on a minimum below 2012 (3.18 million), you both think* there's then a 40-50% chance of a further collapse all the way to 1 million this summer? That seems very ambitious to me...

* - or at least thought, 2 months ago.

Good question. The probabilities of a new record as I see them are combined of the risks of a bad year in the various regions, 2012 saw almost all regions hit a bad year simultaneously. The BOE probability is more ambiguous, as we haven't seen any BOE, but it combines the risk of the CAB having a VERY bad year. Bear in mind the CAB melting season is very short and sharp drops only start in early August. If by some fluke the season is longer by 2 weeks in some bad year, you just might get a BOE.
But 40% conditional probability does seem too high. Maybe I should revise this to 20-25% for new record, and ~5% for a BOE (growing in a decade to ~10% as the trend continues) in any given year.

[gerontocrat]

I think every year now has a ~20%-25% probability of a new record, and a ~10% probability of a BOE (<1M).

I'd go a bit higher, but in the same ballpark -- about 30% and 15% respectively.

So, conditional on a minimum below 2012 (3.18 million), you both think* there's then a 40-50% chance of a further collapse all the way to 1 million this summer? That seems very ambitious to me...

* - or at least thought, 2 months ago.

Good question. The probabilities of a new record as I see them are combined of the risks of a bad year in the various regions, 2012 saw almost all regions hit a bad year simultaneously. The BOE probability is more ambiguous, as we haven't seen any BOE, but it combines the risk of the CAB having a VERY bad year. Bear in mind the CAB melting season is very short and sharp drops only start in early August. If by some fluke the season is longer by 2 weeks in some bad year, you just might get a BOE.
But 40% conditional probability does seem too high. Maybe I should revise this to 20-25% for new record, and ~5% for a BOE (growing in a decade to ~10% as the trend continues) in any given year.

For a new record low minimum, extent loss from May 30th to minimum has to be 7.75 million km2, 0.82 million (10.6%) greater than the average of the last 10 years. Only one year in the 39 year satellite record has done that - 2012. 1 out of 39 = 2.6%.

For a BOE (<1 million km2) remaining extent loss has to be  9.93 million km, 3.00 million (30.3%) greater than the average of the last 10 years.  2012 extent loss from now to minimum, by far the greatest in the satellite record,  was 8.34 million, i.e. 1.59 million less. No year has come even remotely close to the required melt for a BOE.  As far as I can see, even 1% is a high probability for a BOE this year unless it can be shown there is something very, very different about the Arctic now compared with recent years.

"That is my view and it belongs to me"

[Peter Ellis]

That depends on much faith you would put in predict-o-matic value 0f 4.33.  If the predicted value is 6th lowest, would that not be a more reasonable guess, based on valid inputs?

No, it would not be if the question is (as it was) is how ought I bet if I bet the same way every time.

Right, so what you want to know is the distribution of yearly ranks when considering only the dataset to date.  i.e. 1979, as the first full year in the series, was by definition a new record (rank 1) even though it's now ranked 30th in the dataset.  1980 was a bit higher, so it was second lowest (rank 2) at the time even though it's now ranked 39th. 2005 was a new record at the time even though it's now ranked 12th, and so on.

Here's the stats:

Rank to date   #years with that rank
1   10
2   8
3   8
4   3
5   3
6   2
7   2
8   1
9   1
10   0
11   0
12   1


Thus, if you're betting on the rank, it always makes sense to bet in the lowest bracket.  Not particularly surprising given that there's a downward trend.  Not a lot in it though, ranks 1-3 are all quite close to each other. This indicates that the average yearly residual is about three times larger than the yearly decrease in the linear trendline.

[Peter Ellis]

Note - on checking, the overall result is pretty stable no matter whether I look at the whole dataset, just the data since 1990, or just the data since 2000.  Ranks 1 through 3 are all pretty much identical, so my advice is to pick whichever bin you like as long as it's one of the bottom two.

[Daniel B.]

That depends on much faith you would put in predict-o-matic value 0f 4.33.  If the predicted value is 6th lowest, would that not be a more reasonable guess, based on valid inputs?

No, it would not be if the question is (as it was) is how ought I bet if I bet the same way every time.

Right, so what you want to know is the distribution of yearly ranks when considering only the dataset to date.  i.e. 1979, as the first full year in the series, was by definition a new record (rank 1) even though it's now ranked 30th in the dataset.  1980 was a bit higher, so it was second lowest (rank 2) at the time even though it's now ranked 39th. 2005 was a new record at the time even though it's now ranked 12th, and so on.

Here's the stats:

Rank to date   #years with that rank
1   10
2   8
3   8
4   3
5   3
6   2
7   2
8   1
9   1
10   0
11   0
12   1


Thus, if you're betting on the rank, it always makes sense to bet in the lowest bracket.  Not particularly surprising given that there's a downward trend.  Not a lot in it though, ranks 1-3 are all quite close to each other. This indicates that the average yearly residual is about three times larger than the yearly decrease in the linear trendline.

That may be skewed due to the large drop, which started in the late 90, whereby every a new low was set every third year.  Over the last decade here are the results:

1   1
2   3
3   2
4   1
5   0
6   2
7   0
8   1

Also, those ranked 4-8 all occurred in the last five years.

[Ned W]

On the other hand, "always predict 3rd place" works about as well as any statistical method, as far as the past decade goes, at least this early in the season.  But that's not likely to work out this year.

Please explain, given that that statement at least addresses the question I asked -- even if it was not substantiated.  Over recent history what is the likelihood of being right if I predicted 3rd place every time?

[Argh ... other people are answering this while I'm writing ...]

Peter Ellis just answered this question for the whole time period, though it's problematic comparing ranks over the entire history since by definition the first year has to be ranked 1, the second year can only be 1 or 2, etc.  -- so it's biased towards ranks 1/2/3 in the early years of the series.

Over the past decade, which is what I have been referring to, there has been 1 first place, 3 second places, and 3 third places.  So always betting 2nd or 3rd would have been good.

Some people might also care how "close" a guess is, not just whether it's correct or not.  For example, if 2018 turns out to be in 2nd place, is a guess of 3rd place better than  a guess of 9th place? 

People who feel that way might prefer to evaluate the prediction methods using mean absolute error (MAE) not just "number of times correct".   If you always guessed 2nd place, but reality was 2nd place half the time and 3rd place half the time, your MAE would be 0.5.  A perfect prediction method would have an MAE of 0. 

Over the past decade, always guessing 1st has a very poor MAE of 2.5.  Always guessing 2nd gives an MAE of 1.7, and 3rd place gives an MAE of 1.5. 

So based on recent history, you'd be better off always guessing 3rd place.  It's tied with 2nd place for most exact hits, and its MAE is slightly better.

But specifically for this year, 3rd place would not be a promising choice.  I'd go with 2nd or 4th.

[Ned W]

Over the last decade here are the results:

1   1
2   3
3   2
4   1
5   0
6   2
7   0
8   1

Also, those ranked 4-8 all occurred in the last five years.

I think you're not quite right, there, DB.  No years in the past decade were ranked 4th or 8th:

1st: 2012
2nd: 2008, 2011, 2016
3rd: 2009, 2010, 2015
6th: 2013, 2017
7th: 2014

[Ned W]

So, having beaten to death the question of which ranks have been most common, I'd like to get back to the thread title ("Arctic sea ice minimum early prediction").

This is an annoyingly difficult problem (see the SIPN results from year after year).  While working on the predict-o-matic, I've tried incorporating other factors into the model:

* most recent daily PIOMAS volume (= no improvement in results)
* most recent daily CT area (= no improvement in results)
* most recent monthly Arctic Oscillation index (= no improvement in results)

No simple and easy-to-implement method seems to do better at predicting the minimum extent than simply modeling it based on day X's extent.

[Daniel B.]

Now that we are two months into the melting season, maybe we should look at where we stand.  The melt has been fairly average at 2.8 km2 from maximum, which falls right on the long term average.  An average melt season would result in a minimum around 5 km2.  Higher melt was experienced between days 120 and 130, but the rest of the season has been rather sluggish.  However, at day 150,  we are only about a quarter of the way through the melt total, and melt typically does not pick up until day 180.

[oren]

In actuality, the real melting season, that of the arctic basin proper, began less than a month ago, and the only month that can give us some real insights is June. 2012 proved beyond a shadow of a doubt that extent can drop over a cliff with barely any warning. All the statistical prediction methods would have given 2012 a comfortably high predction, until June went by.
Ask yourself this - can 2012 repeat again? I am certain it can and will. And when it does, it will be from a lower starting extent and volume and with a much more mobile and weak pack. So a new record is now much easier to achive than in 2012 itself, and ywt it did produce its record against the odds.
Nothing in 2012 was a physical fluke, it was just a confluence of factors that came together. And if the August GAC is claimed as a fluke, 2016 had one too, so it's not a one-off thing.
The first BOE will not be an average year but an extreme one, and will take many by surprise, however a downtrend coupled with high variabilty will tend to produce such outliers.
This is why my qualitative assessment of record and BOE probabilities is so "high".

[Daniel B.]

In actuality, the real melting season, that of the arctic basin proper, began less than a month ago, and the only month that can give us some real insights is June. 2012 proved beyond a shadow of a doubt that extent can drop over a cliff with barely any warning. All the statistical prediction methods would have given 2012 a comfortably high predction, until June went by.
Ask yourself this - can 2012 repeat again? I am certain it can and will. And when it does, it will be from a lower starting extent and volume and with a much more mobile and weak pack. So a new record is now much easier to achive than in 2012 itself, and ywt it did produce its record against the odds.
Nothing in 2012 was a physical fluke, it was just a confluence of factors that came together. And if the August GAC is claimed as a fluke, 2016 had one too, so it's not a one-off thing.
The first BOE will not be an average year but an extreme one, and will take many by surprise, however a downtrend coupled with high variabilty will tend to produce such outliers.
This is why my qualitative assessment of record and BOE probabilities is so "high".

No, it was not a fluke.  1999 and 2010 has had high melt during June.  What made 2012 unique, was the confluence of high melt in both June and August.  The probability that 2018 will match the high melt years for June is about 8%.  The probability that it will match 2012, with two high melt months is 0.6%.  I would call that a low probability (at least for this year).

[jai mitchell]

The probability that it will match 2012, with two high melt months is 0.6%.  I would call that a low probability (at least for this year)

how do you figure this?

[Daniel B.]

The probability that it will match 2012, with two high melt months is 0.6%.  I would call that a low probability (at least for this year)

how do you figure this?

High monthly melt (>2.5 km2) has occurred during June only three times over the past four decades, and only twice during August over that same timeframe.  One could argue that these all occurred in the last two decades, but that would increase the probability to just 1.5%.

[jai mitchell]

that would only be true if the likelihood of achieving large (>2.5km2) melt in August at the beginning of the time period was the same as today.  Since we are in a dynamic system currently experiencing great changes this is not accurate.

[jdallen]

that would only be true if the likelihood of achieving large (>2.5km2) melt in August at the beginning of the time period was the same as today.  Since we are in a dynamic system currently experiencing great changes this is not accurate.

Concur, and that's the root of my objection to using a statistical methodology to predict the melt season outcome.  There are too many factors which have shifted (example - significantly lower ice maxima and distribution of ice at maxima) such that we are actually are no longer comparing the same things.

[Steven]

Could you elaborate on the calculation?  How did you arrive at 4.33 million km2?

Thanks for asking.  I'm super-busy right now but will try to give a more complete answer later.  The short version is that it's modeling each year's minimum extent as a function of that year's extent on this date.  In other words, if extent is 11.01868 x 10^6 km on 28 May, what is the ensuing minimum likely to be?  The main point is not the specific predicted values but trying to get the estimated error (uncertainty of prediction) correct.  In other words, I'm more interested in modeling how the uncertainty changes over time, as the season progresses. 

The reason why I asked this, is that I'm unable to reproduce the 4.33 (or 4.22) million km2 that you mentioned.  I assume you used the JAXA extent for 28 May 2018, minus the average extent loss for the years 2007 to 2017 from 28 May to minimum.  But that would give an estimate of 3.96 million km2 for the 2018 minimum, rather than 4.33 million km2.  So I am wondering if you changed something to your methodology?

[Daniel B.]

that would only be true if the likelihood of achieving large (>2.5km2) melt in August at the beginning of the time period was the same as today.  Since we are in a dynamic system currently experiencing great changes this is not accurate.

Concur, and that's the root of my objection to using a statistical methodology to predict the melt season outcome.  There are too many factors which have shifted (example - significantly lower ice maxima and distribution of ice at maxima) such that we are actually are no longer comparing the same things.

True, this is only a slightly greater chance of a higher melt recently.  The average August melt in over the first decade of satellite data was 1.85 km2.  That has increased to 2.1 km2 over the past decade.  That is a 15% increase.  So, perhaps the probability can be adjusted upwards, but not by that much.

[Ned W]

The reason why I asked this, is that I'm unable to reproduce the 4.33 (or 4.22) million km2 that you mentioned.  I assume you used the JAXA extent for 28 May 2018, minus the average extent loss for the years 2007 to 2017 from 28 May to minimum.  But that would give an estimate of 3.96 million km2 for the 2018 minimum, rather than 4.33 million km2.  So I am wondering if you changed something to your methodology?

Thanks for reminding me about this, Steven.  Yes, I did change something in the methodology, relative to last year's.  But the change wasn't really deliberate, and I might go back to last year's way instead. 

The 4.33 (or 4.22) x 10^6 km2 comes from using OLS regression to predict the minimum based on the current date's extent in each year from 2003 to present (or 2007 to present).  The 3.95 comes from calculating the average drop to the minimum from the current date, and subtracting that from the current extent.  The latter is what I used last year, and I'll probably go back to that ... I think.  Actually, I'm not sure which is better conceptually.  This version has a slightly better mean absolute error over the past decade.  But I liked last year's version.

The difference between the two boils down to this: is the drop from day X to the minimum independent of whether day X's extent is unusually high/low?  I can see arguments for both sides of this question.

[Ned W]

Here's a graph showing the JAXA daily minimum, 1979-2017, with a 10-year LOESS function and 95% CI around that smoothed line (based on the variance of the residuals):



Here's the same thing, but for a 30-year LOESS function:



In the 10-year case, an extent as low as 2012's would be slightly outside the 95% CI.  In the 30-year case, it would be slightly inside the CI. 

YMMV.  My guess is that the odds of 2018 breaking 2012's record are more than 1% but less than 10%.  I also would guess that the apparent "flattening" over the past 10 years (see the 10-year LOESS) won't persist, and within a few more years we'll be on the downward track again.

[jai mitchell]

that would only be true if the likelihood of achieving large (>2.5km2) melt in August at the beginning of the time period was the same as today.  Since we are in a dynamic system currently experiencing great changes this is not accurate.

Concur, and that's the root of my objection to using a statistical methodology to predict the melt season outcome.  There are too many factors which have shifted (example - significantly lower ice maxima and distribution of ice at maxima) such that we are actually are no longer comparing the same things.

True, this is only a slightly greater chance of a higher melt recently.  The average August melt in over the first decade of satellite data was 1.85 km2.  That has increased to 2.1 km2 over the past decade.  That is a 15% increase.  So, perhaps the probability can be adjusted upwards, but not by that much.

the difference is not the base increase from zero but rather the differential between average melt and the greater than average (2.5km2) melt value.

The increase in loss of this differential value is 37.5% between decades.  in other words, the increased melt needed to reach 2.5km2 of melt in the first decade from average is 0.65km2 above the average and the increased melt needed to reach 2.5km2 of melt in the last decade from average is only 0.4km2.

I am obliged to remind you that anthropogenic aerosols (air pollution/SO2) is currently cooling the arctic between 2 and 4C and preserving over 30% of total annual sea ice loss.

[Daniel B.]

that would only be true if the likelihood of achieving large (>2.5km2) melt in August at the beginning of the time period was the same as today.  Since we are in a dynamic system currently experiencing great changes this is not accurate.

Concur, and that's the root of my objection to using a statistical methodology to predict the melt season outcome.  There are too many factors which have shifted (example - significantly lower ice maxima and distribution of ice at maxima) such that we are actually are no longer comparing the same things.

True, this is only a slightly greater chance of a higher melt recently.  The average August melt in over the first decade of satellite data was 1.85 km2.  That has increased to 2.1 km2 over the past decade.  That is a 15% increase.  So, perhaps the probability can be adjusted upwards, but not by that much.

the difference is not the base increase from zero but rather the differential between average melt and the greater than average (2.5km2) melt value.

The increase in loss of this differential value is 37.5% between decades.  in other words, the increased melt needed to reach 2.5km2 of melt in the first decade from average is 0.65km2 above the average and the increased melt needed to reach 2.5km2 of melt in the last decade from average is only 0.4km2.

I am obliged to remind you that anthropogenic aerosols (air pollution/SO2) is currently cooling the arctic between 2 and 4C and preserving over 30% of total annual sea ice loss.

Good point.