The Plateau Hypothesis

[DavidR]

I’ve posted this to clarify the hypothesis mentioned in various places on the forum for anyone who is interested.

I define the plateau as the period when the sea ice remains within a set range of the maximum extent for the year. The plateau commences when the ice first reaches that level and ends when the ice is last within that range. The period will change depending on the measure used, extent or area; the source of the data eg IJIS , NSIDC; and the length of the measure 1 day, 2 day or 5 day averages.

The objective of the hypothesis is to determine whether the duration of the near maximum conditions is an indicator of the likely fall of extent over the year. Other readers have argued that the peak itself is not a good indicator. My initial idea was that a short sharp peak could indicate significant melt while a long duration could indicate consolidation of the ice and therefore a smaller melt.

To test the hypothesis I first checked the NSIDC extent using a 200K loss as the plateau, for the period from 2006. In all cases with NSIDC and CT Area I use the 5 day average not the daily peak.

This was exactly the reverse of my original idea. The graph suggests that the longer the duration of the plateau the greater the extent loss in that year. Over 44K per day according to the graph. As the plateau lasted 51 days this year, this would have disturbing implications for 2015.

When I first put the idea up, one criticism was that the period was too short and my choice of extent and the 200K range was arbitrary. With the assistance of other members of the forum we gathered figures for the same period, covering  CTArea, IJIS/Jaxa, and extending the 200K level  to 300K for NSIDC extent. The relationship held up for all the measures we used, however there was still the issue of the relatively  short time frame.

Extending the time frame back to 1979 produced quite a different story.

Over the entire 36 year period of the NSIDC there is a very slight correlation the other way, almost 5K km^2 smaller loss per day of the duration.

While that would normally be sufficient to suggest that the short term correlation is only a statistical blip I decided to investigate the variations over the 36 years. 

I decided to use 15 year periods and calculate the coefficient of change for each  15 year  period.  For simplicity I have plotted them below against  the mid year of the 15 year period.

What we can see here is that for 13 years up until 1998 the coefficient was very stable. 

Y = - 0.013X +/- 0.0018. 

However following 1998 the coefficient  changed dramatically. It has switched from negative to positive and steadily increased. For the last  15 year period the graph shows a coefficient of +0.396 that  is ~ 29 standard deviations from the 13 year trend prior to 1998.

I can’t help but think that this is a little more than statistical noise and bears watching to  determine if 1998  really  was the tipping point in the relationship  between the duration of the maximum plateau and the loss of extent.

For the record the four plateaus I have, based on the relatively short past 8 years, predict:

CT Area 200K  : 2.333 M km^2
NSIDC extent 200K    : 3.191 M km^2
NSIDC extent 300K    : 3.181 M km^2 (assumes another 6 days above 300K)
IJIS/jaxa                     : 3.503 M km^2

Even with a std deviation around the trend of 600K km^2 the prediction is definitely placing the final minimum in the lowest 2 on record. 

[Neven]

Thanks for opening a separate topic for this interesting theory, DavidR!

[pikaia]

The difference between the first two graphs is surely due to the small sample size of the first. If you ignore the leftmost point on the first graph then the slope of the line falls to almost zero. The extreme points in a range can have a disproportionate effect and should be treated with caution. The slope of the second line is too small to be very significant, and could merely be due to statistical noise, as you say.

[Nightvid Cole]

I’ve posted this to clarify the hypothesis mentioned in various places on the forum for anyone who is interested.

I define the plateau as the period when the sea ice remains within a set range of the maximum extent for the year. The plateau commences when the ice first reaches that level and ends when the ice is last within that range. The period will change depending on the measure used, extent or area; the source of the data eg IJIS , NSIDC; and the length of the measure 1 day, 2 day or 5 day averages.

The objective of the hypothesis is to determine whether the duration of the near maximum conditions is an indicator of the likely fall of extent over the year. Other readers have argued that the peak itself is not a good indicator. My initial idea was that a short sharp peak could indicate significant melt while a long duration could indicate consolidation of the ice and therefore a smaller melt.

To test the hypothesis I first checked the NSIDC extent using a 200K loss as the plateau, for the period from 2006. In all cases with NSIDC and CT Area I use the 5 day average not the daily peak.

This was exactly the reverse of my original idea. The graph suggests that the longer the duration of the plateau the greater the extent loss in that year. Over 44K per day according to the graph. As the plateau lasted 51 days this year, this would have disturbing implications for 2015.

When I first put the idea up, one criticism was that the period was too short and my choice of extent and the 200K range was arbitrary. With the assistance of other members of the forum we gathered figures for the same period, covering  CTArea, IJIS/Jaxa, and extending the 200K level  to 300K for NSIDC extent. The relationship held up for all the measures we used, however there was still the issue of the relatively  short time frame.

Extending the time frame back to 1979 produced quite a different story.

Over the entire 36 year period of the NSIDC there is a very slight correlation the other way, almost 5K km^2 smaller loss per day of the duration.

While that would normally be sufficient to suggest that the short term correlation is only a statistical blip I decided to investigate the variations over the 36 years. 

I decided to use 15 year periods and calculate the coefficient of change for each  15 year  period.  For simplicity I have plotted them below against  the mid year of the 15 year period.

What we can see here is that for 13 years up until 1998 the coefficient was very stable. 

Y = - 0.013X +/- 0.0018. 

However following 1998 the coefficient  changed dramatically. It has switched from negative to positive and steadily increased. For the last  15 year period the graph shows a coefficient of +0.396 that  is ~ 29 standard deviations from the 13 year trend prior to 1998.

I can’t help but think that this is a little more than statistical noise and bears watching to  determine if 1998  really  was the tipping point in the relationship  between the duration of the maximum plateau and the loss of extent.

For the record the four plateaus I have, based on the relatively short past 8 years, predict:

CT Area 200K  : 2.333 M km^2
NSIDC extent 200K    : 3.191 M km^2
NSIDC extent 300K    : 3.181 M km^2 (assumes another 6 days above 300K)
IJIS/jaxa                     : 3.503 M km^2

Even with a std deviation around the trend of 600K km^2 the prediction is definitely placing the final minimum in the lowest 2 on record.

This is quite a strange way of examining the data. Why do you not give a P-value?

[viddaloo]

Great thread, DavidR! I'm sure it will be interesting to follow, and interesting to verify the hypothesis.

BTW, I'll release graphs for PIOMAS plateaus when they publish new data in mid–April.

[Peter Ellis]

David- can you run the same "windowed" analysis, but leaving out the single year of 2006, to see if the results still hold.

As pikaia points out, this year is the single outlier at the bottom left of the 2006-2015 graph which essentially dictates the trend.  It has both an unusually narrow peak (one of the narrowest on record), and also an unusually small yearly loss for recent years.

This means that in _any_ graph of a small number of recent years, such as the 15-year windowing exercise, 2006 will appear an outlier in the lower left and give a spurious trend. In this light, it is interesting that the red line in the graph starts climbing from  ~1998 onwards - i.e. exactly those years when 2006 is included within the window.

Finally, looking at the Charctic plot for 2006 (http://nsidc.org/arcticseaicenews/charctic-interactive-sea-ice-graph/), I do not find the narrow peak for this year at all convincing - it's simply a couple of days' upwards "blip" within a much broader and flatter overall peak.  However, this objection applies more generally, and I'm unconvinced that "peak width" is a remotely meaningful measurement.  If it has any real basis, then it ought to be robust to your choice of measure of peak width, so another good exercise would be to repeat all these plots using thresholds of 100, 200, 300 and 400K to define the peak width.

[jdallen]

Interesting points, all.

I think it is also worthwhile to point out, that the over-all behavior of the system has changed.  Picking a semi arbitrary point - say 1997 - I think we'd find the behavior quite different between the two ensembles.

It may be a better point than pre/post 2000, as there *is* a distinct break in what climate was doing at that time - we shifted into a "super" El Nino about that point, and things haven't been the same since, pretty much.  It may represent a minor "tipover" point in the total enthalpy in the system.

[Peter Ellis]

I think it is also worthwhile to point out, that the over-all behavior of the system has changed

That's the point: I don't think it has.  I think there is one outlier point in 2006 which is entirely responsible for the apparent change in the behaviour, and if you drop that point, the effect will more or less disappear.

Moreover, that outlier itself hinges on a very transient upward "blip", which will vanish if different definitions of "plateau" are chosen.

[Steven]

In the above graph, you used a threshold of 200k km^2 to define the plateaus.  Using a threshold of 300k km^2 (rather than 200k), the above graph changes as follows:




So with threshold 300k km^2, the correlation between "length of plateau" and "yearly extent loss" becomes very weak.  In fact the correlation is slightly negative: r = -0.02, using 2000-2014 data.

I repeated the same calculation for some other values of plateau threshold: 150k, 250k, 300k, 350k km^2 etc.  Here are the corresponding values for the correlation coefficient, calculated in the same way as above:

Threshold       Correlation
100k km^2     0.14                 
150k km^2     0.52
200k km^2     0.49
250k km^2     0.36
300k km^2    -0.02
350k km^2    -0.04
400k km^2     0.02
450k km^2    -0.06
500k km^2    -0.08

So the correlation is very weak, except when the threshold is close to 200k km^2.

[DavidR]

Pikaia, if I drop 2006 the coefficient drops to 0.0239, this is still positive and a long way from that for the 15 year trends up until 1998.

Peter Ellis, 2006 is an outlier and its impact is to raise the trend line. However removing it only eliminates a small part of the change since 1998. The 2000- 2014 trend remains above 0.030. We could equally choose to remove 2014 which has a very similar behaviour to 2006 and that would increase the trend. Removing individual years is highly inappropriate which is why the trends I am interested are the sequence of 15 year trends.

You are right about 2006 being a little odd. It had the shortest 200K plateau, (10 days) but a much longer 300K (38 days) plateau. However taking 2006 out does not have a significant impact on the change since 1998. Sure it drops the coefficient from +0.04 to +0.03, However when we are looking at a shift from a consistent trend of -0.013 +/- 0.0018 we are still seeing a significant change.


Steven, your analysis indicating that only plateaus between 150 & 250 K have predictive value is useful in setting boundaries on the predictive value of the hypothesis. In my definition of the plateau I allowed for any value for the decline, however that doesn’t mean that all values will or should have the same predictive capabilities.

I am not suggesting that this correlation, if it exists, will give us a way of predicting accurately the minimum in September. With a trend decline of only 0.04 M km^2 and a standard deviation of about 0.6 in loss of extent, that would be far too much to hope for. There are far too many factors involved in the final melt for any single predictor to be highly accurate. Identifying factors that contribute to the prediction is the objective here.
It is interesting to observe how much the predictive values have changed since 1998 and to observe whether the change continues into the future.

[seaicesailor]

Typical rule says one needs at least 25 samples to get the standard deviation of a mean within a 10%. For two dimensions, the sample size N goes with 25^2 = 625 for the same degree of confidence in the deviation of the slope

http://en.wikipedia.org/wiki/Regression_analysis#Power_and_sample_size_calculations

Still, I find plausible the physical explanations given by Vid and David. Thin ice at the boundary of the ice cap may fluctuate (melt and refreeze) near the maximum for more number of days  compared to pre-2000 years, when the ice boundary lied at lower latitudes. At lower latitudes, Spring weather and sunlight would shift the growth to retreat more quickly.

The correlation is not causal (  both longer plateau and larger extent loss are caused by a weaker Arctic ice, but one thing would not cause the other).

Hope this explanation makes some sense
 :-)

[Peter Ellis]

The standard climatological period used is 30 years: calculating trends over shorter periods just isn't a valid exercise.  If it's not valid for temperature trends, it's not valid for these trends either.  It's interesting that the trend in recent years doesn't depend entirely on 2006, but since it's not robust to changes in the threshold for defining "plateau" I don't think it'll be a useful observation.

Dropping individual years is an entirely valid thing to do - and in fact a necessary test to ensure your findings aren't being unduly skewed by any individual year.  The systematic way to do it would be to recompute the data set multiple times, leaving out one year each time, and see if there's any specific anomalous year that dictates the trend.  If you find that the observation holds up no matter which single year you leave out, you can be sure it's not just down to one rogue outlier.  However, you really also need to be using a minimum of 30 years to start with.


edit:  Another thing you should do is to calculate the p value for your trends (i.e. whether the trend really is statistically significantly different from zero for each period).

[DavidR]

Peter,
I  did as you suggested and removed every year  in the 2000-2014 period individually.  None of them had a large impact on the result. The x coefficient remained between +0.030 and 0.050.

2006  causes a large drop in R^2 but it  stays between a range 0f 0.12- 0.35 for all calculations.  When we compare the 36 year  values for this we see quite a different pattern for both.

In this case we see R^2 drop to virtually zero as the trend changes from negative to positive.  At the end of the 36  year the 15 year trend is as good a predictor as at the start of the period however the trend has reversed.

I am having trouble working out a suitable way of calculating the p value for the change, if you  can suggest a suitable probability function to  use I'll have a look at it.  A simple binomial distribution would be unacceptable obviously but my ability in stats doesn't stretch to identifying the appropriate measure to use here.

I see the 15 year trends as a useful way of looking for predictors of change in an area where change is clearly occurring. When we only have 36 years of data, relying on a thirty year trend measurement is not providing us with sufficient observations outside the 30 year range to make any definitive statements. So I wouldn't stake the house on this observation being correct, however I see a significant change in the data, which is worth watching.

I don't accept that the plateau has to be a good predictor at any measure of loss. Once the measure goes beyond about 250K below the maximum there is no plateau behaviour, extent is either increasing or decreasing rapidly at above 35K / day so the range becomes more consistent. 

[Peter Ellis]

http://www.oneonta.edu/faculty/vomsaaw/w/psy220/files/SignifOfCorrelations.htm

This gives you the significance of correlations depending on r^2 and n.  The column headings are for single-tailed probabilities, while for this purpose we should be using two-tailed probabilities (we have no a priori reason to suppose that a correlation between winter plateau length and summer extent should be positive or negative). So we need to double the numbers at the top of the columns.

For an n of 15, then for statistical significance at the p=0.05 level, we need an r^2 of at least 0.51

Therefore none of the observed correlations are statistically significant - and indeed they are not significant at the p=0.1 level either.

[plinius]

...apart from the typical failure here to detrend data (quadratically) in time/global temperature.

[AbruptSLR]

The standard climatological period used is 30 years: calculating trends over shorter periods just isn't a valid exercise.

As the world has now entered a period of strongly non-stationary conditions I very much doubt that for a few centuries to come that one will be able to find any 30-year period with common climate conditions (particularly in the Arctic).  Thus either we are left with gut opinions based on non-linear projections of a hand-full of recent data; or we will need to wait 3 to 10-years until state of the art Earth System Models, such as the DOE's ACME projections become available.

[Steven]

http://www.oneonta.edu/faculty/vomsaaw/w/psy220/files/SignifOfCorrelations.htm

This gives you the significance of correlations depending on r^2 and n.  The column headings are for single-tailed probabilities, while for this purpose we should be using two-tailed probabilities (we have no a priori reason to suppose that a correlation between winter plateau length and summer extent should be positive or negative). So we need to double the numbers at the top of the columns.

For an n of 15, then for statistical significance at the p=0.05 level, we need an r^2 of at least 0.51

Not quite.  That website uses r, rather than r^2.

So if the sample size n=15, then for statistical significance at the 0.05 level, the correlation coefficient r needs to be at least 0.51, in absolute value.  Equivalently, r^2 needs to be at least 0.26.

BTW, here is an online calculator for calculating p-values.  (The two-tailed probabilities are the most relevant in this context, as you mentioned).

[Peter Ellis]

Thanks for catching the r^2 versus r mistake there, Steven.  For some reason none of the plots in this thread are loading for me except the most recent one, which is showing as a low-res thumbnail only.  However from what I can make out it looks as though the trends are still below significance.  Can anyone confirm?

[DavidR]

Peter, sorry about the plots I  will  see if I  can get better copies. I  am referencing images in google photos and though they look ok there some of them don't translate well. 

I  think the probability functions you  and Steven are suggesting are assuming that this   is a simple two variable problem where we are trying to identify if a causes b. In reality this is an issue with a large number of variables and we need to  tease out  if any of them are useful predictors of the final melt. 

No  single variable is going to  give us that  and there are many variables involved  just  in determining the duration of the 'plateau'.  Let alone the number involved in the actual melt. In this situation an R^2  value of 0.25 can actually indicate that this correlation is strong enough to  be useful. 

Obviously a 30  year trend would give me greater confidence which  is why  I only  rate this as an hypothesis. It is an interesting observation, that a change seems to have occurred whether it is a significant change remains to be seen.  I  expect it  would take a considerable amount of effort just to identify a suitable statistical technique for assessing the issue.
 
The online calculator Steven uses a Pearson chi-square test which isn't relevant itself, but it provides a link to a test for significance of two slopes which I will explore later.

[Steven]

For some reason none of the plots in this thread are loading for me except the most recent one, which is showing as a low-res thumbnail only.  However from what I can make out it looks as though the trends are still below significance.  Can anyone confirm?

Currently, the graphs in this thread are not loading for me either, except the two graphs in Reply #12 and the second one in Reply #8.  My browser shows empty space at the places where the other graphs are supposed to be, e.g. in the topmost post of the thread.  A few days ago I could see all the graphs but now they seem to have disappeared.

Anyway, I did some calculations a few days ago.  If the time period is 2000-2014 (so n=15) and the threshold for defining the plateaus is selected to be 150k km^2, then the corresponding p-value (two-tailed) is 0.046.  So in this case the result is statistically significant (barely) at the p<0.05 level. 

But for all other values that I used for the plateau threshold and time period, the resulting p-values are greater than 0.05 and so the corresponding results are not statistically significant at that level.

Moreover, playing around with several parameter values increases the risk of finding spurious relationships.  I guess that this is the case here.

[DavidR]

I think I  have my posts fixed, unfortunately any post  that  has copied them I  can't fix.  It  was a google+ setup thing.

[Rubikscube]

I think I  have my posts fixed, unfortunately any post  that  has copied them I  can't fix.  It  was a google+ setup thing.

Thanks, it easier to see what you mean now.

[DavidR]

Now that the plateaus for all the measures are completed the predictions from each measure are listed below.

Measure	Duration (days)	Prediction (Mkm^2)	Std Dev (Mkm^2)	R^2	Record (Mkm^2)
Jaxa Daily Extent 200K	47	3.503	0.614	0.0652	3.177
NSIDC 5 Day Extent 200K	51	3.191	0.634	0.3766	3.399
NSIDC 5 Day Extent 300K	60	3.285	0.670	0.3036	3.399
CT Area 5 Day Ave 200K	49	2.275	0.436	0.1300	2.234
The figures above are based on the	9 year trend from 2006
The following figure is based on the	15 year trend line:
NSIDC 5 Day Extent 200K	51	3.643		0.2352	3.399

The NSIDC 200K predictor is considered the 'most reliable', which fits in with Steven's analysis that plateaus of 150-250 K are the most predictive.
Three of the first four predictions suggest a new record is about a 50% probability and they all indicate that first or second position is highly likely.

On the other hand the entire hypothesis could just be a consequence of a statistical blip.

[Peter Ellis]

With 9 data points you need r > 0.667 (r^2 > 0.445) to mean anything at the p < 0.05 significance level. On top of that, since you're testing at least 4 different data sources and 2 thresholds, you need to correct for multiple testing, so you should really be looking for p < 0.01 or lower (r^2 < 0.637).

This doesn't even qualify as a statistical blip, since there is no observation in the first place that requires explanation.

[DavidR]

Peter,
If I  was claiming that the duration of the plateau was the cause of the decline your criticism would have some merit however this isn't that  sort of observation.

There are a whole host of factors that cause the winter ice extent maximum and go on to cause the summer ice minimum.  In a situation where there a wide range of variables, the impact of any one variable is never going to be that  strong.

What we need is some reliable  indicators of the summer melt. This might be one.

We only have 36 individual data points on this measure and  22, 15 year trends. What we can see is that a very stable measure that was consistent for 13 successive measurements has in the last 8 measures swung wildly and consistently in the opposite direction.  Its not caused by  one outlier year as I demonstrated earlier. 

Your approach  is as simplistic as those who  claim that AGW isn't occurring because there isn't an exact correlation between CO2 levels and global temperatures.

At this stage all we can look for is insight not answers.

[dnem]

Long time lurker here.  I'm sorry, I'm just a biologist, so what the hell do I know?  Other than, if I took the Plateau Hypothesis to my advisor's office, he would have smacked me in the head and sent me away without further comment.  Too short a time series, criteria too arbitrary, too little physical explanation underlying the "analysis".  Sorry - just not seeing it. 

[viddaloo]

If I  was claiming that the duration of the plateau was the cause of the decline your criticism would have some merit however this isn't that  sort of observation.

There are a whole host of factors that cause the winter ice extent maximum and go on to cause the summer ice minimum.  In a situation where there a wide range of variables, the impact of any one variable is never going to be that  strong.

What we need is some reliable  indicators of the summer melt. This might be one.

Fair point, and very well explained, DavidR. Sometimes negativists are guilty of more errors than positivists, and their errors are a lot more glaring and simplistic than ours, at least to people who understand what the discussion is about.

What I miss the most in discussions about the plateaus as indicators of strong melt, is calm and scientific discussion about the causes of the increasingly long plateaus. Are they long (and low) because of more ocean heat, or something else? Instead of this we get (willfully?) misunderstood discussions about whether a numerically long plateau is the one and only cause of ice–melt, which is unhelpful and quite depressing. A forum like this could do better than that, IMO.

I suspect the reasons for such an unhelpful discussion have a lot to do with basic human psychology in particular as it relates to conservatism and opposition to all kinds of new ideas and approaches. In a float diagram the most basic and simplistic reasoning would go something like this:

Code: [Select]

Is this idea new? => Then it must be wrong!

[Nightvid Cole]

Peter,
If I  was claiming that the duration of the plateau was the cause of the decline your criticism would have some merit however this isn't that  sort of observation.

There are a whole host of factors that cause the winter ice extent maximum and go on to cause the summer ice minimum.  In a situation where there a wide range of variables, the impact of any one variable is never going to be that  strong.

What we need is some reliable  indicators of the summer melt. This might be one.

We only have 36 individual data points on this measure and  22, 15 year trends. What we can see is that a very stable measure that was consistent for 13 successive measurements has in the last 8 measures swung wildly and consistently in the opposite direction.  Its not caused by  one outlier year as I demonstrated earlier. 

Doesn't change the fact that the P-values do not suggest significance after adjusting for multiple testing. You have a situation in which you are within a range that can be reasonably expected for random noise, hence the data simply do not support the hypothesis.

This is not a matter of opinion, it is a demonstrable fact from the data that you are not observing anything distinguishable from noise.

Your approach  is as simplistic as those who  claim that AGW isn't occurring because there isn't an exact correlation between CO2 levels and global temperatures.

Sorry, but that's just ridiculous. The global warming trend is significant, as can be shown by calculating a P-value. Yours is not. There is simply no comparison.

At this stage all we can look for is insight not answers.

Huh? Either you can reject the null hypothesis or you can't. It has nothing to do with insight or attitude - we have hard numbers which either exceed the threshold or they don't.

[Peter Ellis]

Your approach  is as simplistic as those who  claim that AGW isn't occurring because there isn't an exact correlation between CO2 levels and global temperatures.

Sorry, but that's just ridiculous. The global warming trend is significant, as can be shown by calculating a P-value. Yours is not. There is simply no comparison.

[...]

Either you can reject the null hypothesis or you can't. It has nothing to do with insight or attitude - we have hard numbers which either exceed the threshold or they don't.

Quite so.  This plateau hypothesis has much more in common with the other "plateau hypothesis", i.e. the denialists' claim that global warming has stopped because if they take just the right set of recent years they can show that the trend appears to have changed (if you don't bother to calculate the p values and error bars). Mathturbation is fruitless no matter which side of the debate is engaged in it.

There is no significant trend in the length of plateau: it is not changing over time.
There is no significant association between plateau length and amount of melting.

These observations are not disputable, they are mathematical fact.

[ktonine]

The plateau hypothesis is a non-starter for me because it fails basic logic.

The longest plateau would last 365 days.  The entire year would be one flatline with no melt at all.

[DavidR]

What I miss the most in discussions about the plateaus as indicators of strong melt, is calm and scientific discussion about the causes of the increasingly long plateaus. Are they long (and low) because of more ocean heat, or something else? Instead of this we get (willfully?) misunderstood discussions about whether a numerically long plateau is the one and only cause of ice–melt, which is unhelpful and quite depressing. A forum like this could do better than that, IMO.

Vid,
There is no long term trend to a longer plateau. I calculated a 10 year average over the entire satellite record and the current values are very similar to the earliest values. Values through  the 1990s rose about 10 days, from below 30 to almost 40 but then it dropped back to below 30 by  2005.

 

[DavidR]

Your approach  is as simplistic as those who  claim that AGW isn't occurring because there isn't an exact correlation between CO2 levels and global temperatures.

Sorry, but that's just ridiculous. The global warming trend is significant, as can be shown by calculating a P-value. Yours is not. There is simply no comparison.

[...]

Either you can reject the null hypothesis or you can't. It has nothing to do with insight or attitude - we have hard numbers which either exceed the threshold or they don't.

Quite so.  This plateau hypothesis has much more in common with the other "plateau hypothesis", i.e. the denialists' claim that global warming has stopped because if they take just the right set of recent years they can show that the trend appears to have changed (if you don't bother to calculate the p values and error bars). Mathturbation is fruitless no matter which side of the debate is engaged in it.

There is no significant trend in the length of plateau: it is not changing over time.
There is no significant association between plateau length and amount of melting.

These observations are not disputable, they are mathematical fact.

Peter,
I absolutely accept that there is no statistically significant trend in the data for individual years. However given that we have only 36 years of data any 30 year trend line  covers practically  all the data.

What is interesting is the change in the 15 year trend values.  Lets be clear that scientists didn't just dismiss the deniers claims about the 15 year 'hiatus'; they demonstrated that there are a whole series of factors the contribute to the rate of warming and when these are taken in to  account there is no 'hiatus'.

In this hypothesis we see a constant 13 year period trend with very low std dev of just 0.0018  switching to a value that is more than 25 std deviations away and with the opposite gradient in just 10  years.  There is no obvious reason for this, certainly no year or group of years that effect it, such as we saw with the temperature record in 1998.   

Even if we treat the 15 year trend values as independent measures we get a mean of  -0.00268 and a std dev of 0.0162 putting the P-value for the latest 15 year trend value at 0.0047.

However I don't think any of the statistical values provided are suitable for the problem of assessing a change in trend so I  make no assertions at all about the statistical significance of the observations.

They are just interesting observations that I find are worth watching.  As we don't have any good predictors of the melt, I am keeping an open mind about anything that  might provide an insight.  Its not even worth doing multivariate analysis of the problem if we have no idea of what the relevant variables are.

[Nightvid Cole]

Your approach  is as simplistic as those who  claim that AGW isn't occurring because there isn't an exact correlation between CO2 levels and global temperatures.

Sorry, but that's just ridiculous. The global warming trend is significant, as can be shown by calculating a P-value. Yours is not. There is simply no comparison.

[...]

Either you can reject the null hypothesis or you can't. It has nothing to do with insight or attitude - we have hard numbers which either exceed the threshold or they don't.

Quite so.  This plateau hypothesis has much more in common with the other "plateau hypothesis", i.e. the denialists' claim that global warming has stopped because if they take just the right set of recent years they can show that the trend appears to have changed (if you don't bother to calculate the p values and error bars). Mathturbation is fruitless no matter which side of the debate is engaged in it.

There is no significant trend in the length of plateau: it is not changing over time.
There is no significant association between plateau length and amount of melting.

These observations are not disputable, they are mathematical fact.

Peter,
I absolutely accept that there is no statistically significant trend in the data for individual years. However given that we have only 36 years of data any 30 year trend line  covers practically  all the data.

What is interesting is the change in the 15 year trend values.  Lets be clear that scientists didn't just dismiss the deniers claims about the 15 year 'hiatus'; they demonstrated that there are a whole series of factors the contribute to the rate of warming and when these are taken in to  account there is no 'hiatus'.

In this hypothesis we see a constant 13 year period trend with very low std dev of just 0.0018  switching to a value that is more than 25 std deviations away and with the opposite gradient in just 10  years.  There is no obvious reason for this, certainly no year or group of years that effect it, such as we saw with the temperature record in 1998.   

Even if we treat the 15 year trend values as independent measures we get a mean of  -0.00268 and a std dev of 0.0162 putting the P-value for the latest 15 year trend value at 0.0047.

However I don't think any of the statistical values provided are suitable for the problem of assessing a change in trend so I  make no assertions at all about the statistical significance of the observations.

They are just interesting observations that I find are worth watching.  As we don't have any good predictors of the melt, I am keeping an open mind about anything that  might provide an insight.  Its not even worth doing multivariate analysis of the problem if we have no idea of what the relevant variables are.

These values you give for the standard deviation and P-value are totally inconsistent with the data you gave earlier. What gives?

(See Reply #13)

[DavidR]

In this hypothesis we see a constant 13 year period trend with very low std dev of just 0.0018  switching to a value that is more than 25 std deviations away and with the opposite gradient in just 10  years.  There is no obvious reason for this, certainly no year or group of years that effect it, such as we saw with the temperature record in 1998.   

Even if we treat the 15 year trend values as independent measures we get a mean of  -0.00268 and a std dev of 0.0162 putting the P-value for the latest 15 year trend value at 0.0047.

These values you give for the standard deviation and P-value are totally inconsistent with the data you gave earlier. What gives?

(See Reply #13)

NightVid,
In my original post  I stated that in relation to the 15 year trends:
"What we can see here is that for 13 years up until 1998 the coefficient was very stable.
Y = - 0.013X +/- 0.0018. 
However following 1998 the coefficient  changed dramatically. It has switched from negative to positive and steadily increased. For the last  15 year period the graph shows a coefficient of +0.396 that  is ~ 29 standard deviations from the 13 year trend prior to 1998.".

All I  have done in the calculation you quote above is take the entire dataset of 22, 15 year trends, treat them as independent variables and calculate the mean and standard deviation.  The fact that  the 2014 , 15 year mean is 2.6 std deviations from the mean gives it a P - value of 0.0047.  2012 and 2013 were both close to 2 std devs from the mean also.

However let  me repeat "I don't think any of the statistical values [used in this thread] are suitable for the problem of assessing a change in trend"



 

[Peter Ellis]

You can't treat them as independent variables, because one 15-year trend shares 14/15 of its data with the next-door 15-year trend. Even if individual years were uncorrelated (they're not), then from a 30-year dataset you can only get TWO independent 15-year trends.

[DavidR]

You can't treat them as independent variables, because one 15-year trend shares 14/15 of its data with the next-door 15-year trend. Even if individual years were unvote elated (they're not), then from a 30-year dataset you can only get TWO independent 15-year trends.

Peter,
Of  course you  can't treat them as independent variables. 

Let  me reiterate, this is an interesting observation NOT something  supported or contradicted by statistics.  You  are claiming that  I  should use some sort of simplistic statistical calculation to  justify my  position. I  don't make that  claim!!   I  don't make any  claims for statistical  significance. If you are only  interested in observations that  are statistical significant using a simplistic evaluation then this is not the hypothesis for you.

Suggest a method of evaluating the change and that would be interesting.   But I  don't think even that  is statistically  significant at this stage. The data set is too short!  It is not 'wrong' it is just  too  short. It  could fly or it could crash it is just an interesting observation.

[Nightvid Cole]

You can't treat them as independent variables, because one 15-year trend shares 14/15 of its data with the next-door 15-year trend. Even if individual years were unvote elated (they're not), then from a 30-year dataset you can only get TWO independent 15-year trends.

Peter,
Of  course you  can't treat them as independent variables. 

Let  me reiterate, this is an interesting observation NOT something  supported or contradicted by statistics.  You  are claiming that  I  should use some sort of simplistic statistical calculation to  justify my  position. I  don't make that  claim!!   I  don't make any  claims for statistical  significance. If you are only  interested in observations that  are statistical significant using a simplistic evaluation then this is not the hypothesis for you.

Suggest a method of evaluating the change and that would be interesting.   But I  don't think even that  is statistically  significant at this stage. The data set is too short!  It is not 'wrong' it is just  too  short. It  could fly or it could crash it is just an interesting observation.

If you understand that they are not independent, then how can you base a Gaussian distribution on them via the raw standard deviation and then assert that a later period is 2.6 standard deviations away and thus has a P-value of .0047, as you did in Reply #33?

[DavidR]

I  don't think even that  is statistically  significant at this stage. The data set is too short!  It is not 'wrong' it is just  too  short. It  could fly or it could crash it is just an interesting observation.

If you understand that they are not independent, then how can you base a Gaussian distribution on them via the raw standard deviation and then assert that a later period is 2.6 standard deviations away and thus has a P-value of .0047, as you did in Reply #33?

Let  me repeat again "I don't think any of the statistical values [used in this thread] are suitable for the problem of assessing a change in trend"

[crandles]

There are a whole host of factors that cause the winter ice extent maximum and go on to cause the summer ice minimum.  In a situation where there a wide range of variables, the impact of any one variable is never going to be that  strong.

What we need is some reliable  indicators of the summer melt. This might be one.

If there are a whole host of factors, what is needed is a factor that picks up some predictability that other factors miss. So I would suggest testing for correlation with the residual from this method:
http://neven1.typepad.com/blog/2013/07/problematic-predictions-2.html

If it doesn't do better than say 'April+May' decline in area then it may be time to decide it doesn't appear to be a useful indicator.

I am thinking that last year is telling us the methods are generally over-confident and by trying to find factors that further narrow the range of the estimates, we are making this problem worse. We just cant predict it that well with the information available.

[viddaloo]

It's hard to see how trying to find better indicators for seasonal melt can make the problem worse, unless trying to find better indicators is auto–translated to trying to find worse indicators for seasonal melt.

To illustrate: Let's say DavidR has found a reasonably good indicator for seasonal melt. How does that make the problem of Arctic unpredictability worse? IMO we just have to keep trying.

[crandles]

If the indicators are better yes it should give better result. But if it is from looking at too many indicators that mean that some will appear to have corellations but they are just spurious then you get overconfident narrow ranges.

From SEARCH what do we find?

Beckwith, 3.25 (2.75-3.75), Heuristic
Kauker et al., (AWI/OASys); 3.72 (3.30-4.14), Modeling
Andersen, 4.00 (3.80-4.00), Statistical/Heuristic
Reynolds (Public), 4.06 (3.49-4.63), Statistical/Heuristic
Hamilton, 4.10 (3.10-5.10), Statistical
Met Office (Peterson et al), 4.10 (3.10-5.10), Modeling
Naval Research Lab (Posey et al), 4.20 (3.70-4.70), Modeling
Blanchard-Wrigglesworth et al., 4.39 (3.89-4.89), Modeling
Dekker (Public), 4.60, (4.15-5.05 standard deviation range), Statistical
Zhang and Lindsay, 4.60 (4.00-5.20), Modeling

Wang, 6.31 (5.84-6.78), Modeling

10 range entirely below actual 5.3, possibly as many as 16 where 5.3 is in the range though some don't give ranges, and 1 with range entirely above actual.

I would expect some variation so that you don't get 95% of ranges covering the actual value but it isn't totally clear that 50% of estimates manage to cover the actual value.

One approach to this is to just say the ranges given are too narrow. Arguably it may be better to try and get people to drop spurious correlations so the predictors used are more soundly based. This should result in less claimed accuracy and a higher proportion of the ranges covering the actual value.

[viddaloo]

Last year's melt season was dominated by record wildfires, as documented by Box and largely ignored in this forum. No–one could predict or foresee that early in spring 2014.

An extended Plateau Hypothesis would probably have to incorporate the risk of more wildfires when the ocean is hot enough to stop refreeze at such a low level for such a long time. Plus how long will wildfires be a factor? If outside of peak insolation it would act as a positive feedback, thus making the extended PH a lot more complicated.

[dnem]

Again, as someone with no experience in this arena whatsoever, but a decent amount of experience with complex systems, my take is that the arctic is quite clearly in the midst of a state change from one stable (yet still dynamic) equilibrium to another.  Systems often display enhanced variability while undergoing a state change, as the arctic has been doing over the past decade or so. I would expect continued enhanced variability as we transition to an ice-free summer state, making predictions (especially within year) all but impossible.  I suppose there's no real harm in trying, but I'd be very suspicious of attributing any model's (or educated guess's) success in any given year to much more than luck. 

[Peter Ellis]

So, now we have another hypothesis: that the amount and date of wildfires affects the summer melt.  So go and test it! Find the historical data on wildfires, and see if incorporating that gives better prediction than just using April and May ice extent data  - e.g. by showing an improved correlation, together with something like AIC (Akaike information criterion) to demonstrate that the added variables in your model are useful. 

If so, congratulations, you just added to the sum of human knowledge. 

Until then, you're just asserting one unproven and untested hypothesis as the reason why another unproved hypothesis fails when actually tested - which isn't how you do science.

[viddaloo]

So, now we have another hypothesis: that the amount and date of wildfires affects the summer melt.

No, we don't, you're not reading that properly, <sarcasm snip>, we don't have a new hypothesis, but an extended Plateau Hypothesis would probably have to incorporate the risk of more wildfires when the ocean is hot enough to stop refreeze at such a low level for such a long time.

<sarcasm snip>

[Peter Ellis]

Uh.  Whether you realise it or not, you're putting forward another hypothesis - in fact two of them.

Plateau hypothesis:  That a wide/flat peak to the melt season in Feb/March is predictive of a severe melt

Wildfire hypothesis (a):  That high levels of wildfires during peak insolation season retard the summer melt
Wildfire hypothesis (b): That high levels of wildfires during earlier parts of the melt season will increase summer melt.

You can weld all of these into one giant uber-hypothesis if you like, but each part of it should be testable individually by getting the data and doing the necessary work.

Remember that just adding more variables will always make it easier to fit the existing data, hence the need for something like AIC to see if the  variable is genuinely useful in modelling the melt.

[viddaloo]

Uh.  Whether you realise it or not, you're putting forward another hypothesis - in fact two of them.

No. I'm saying the existing PH probably won't work that well because of a major complicating factor. That's different from launching 1 or 2 or 3 new hypotheses for which you feel I should have already done absolutely all the math. <sarcasm snip>

And Peter, I'm not entirely sure I agree with you that the tremendous amount of fear you constantly induce in people of being wrong or lacking or in error in some way is the most fruitful way of collaborating in learning more about sea ice and the Arctic. I see some people declaring all the time pompously that they're 'here to learn', of course we are, all of us, it's not something you have to say in every paragraph every day, but IMO we don't learn very well while being scared out of our wits of being wrong and getting the Peter treatment of ridicule and vitriol.

I've been around the block a few times, and I know that when 'critics' — to use a very kind word — don't even wait for you to make mistakes, but rather invent the mistakes for you, and go on to criticise those mistakes, that you haven't even made yet, and maybe would never make, then those 'critics' have entered into a roam of ideological resistance to new thought or to a particular subject. Their use of 'straw men' is indicative of this hostile environment, where the straw men are the invented mistakes not even made by their opponents.

I'm not a 100% sure why ideology — or what sort of ideology — would be involved in relation to sea ice and the Arctic, but as we know, the whole topic of climate change is a highly contested and bitter battlefield, and ideology, activism, business interests etc are mixed into this soup, making it less of an open academic and friendly discussion, and more of a lethal war zone, with very much at stake for a host of different groups. In any case it seems very strange to be so angry at total strangers who propose something as harmless as an early indicator for sea ice melt.

And maybe wildfires could play a role? I guess, but do I have the guts to say it out loud and be viciously ridiculed and attacked for it in the months or years it would take to verify such a role absolutely? We shouldn't have to be afraid every day to discuss factors that influence the melting or freezing of ice. Fear seldom brings out the best in us, so if the stated intention is to work together to learn more about the ice and the Arctic, then I honestly don't know what all the anger and ridicule and abuse is doing in this forum.

[Michael Hauber]

Peter has been quite polite and reasonable and I cannot see how he has contributed to a ' tremendous amount of fear... of being wrong'.

Unless you are trying to say that no one is allowed to disagree with you because it will make you afraid.  Is there a nicer way that Peter could have stated his disagreement?

If this forum is going to be a scientific discussion and not just an echo chamber then all participants need to be prepared to have their ideas disagreed with and criticized. 

[DavidR]

Peter has been quite polite and reasonable and I cannot see how he has contributed to a ' tremendous amount of fear... of being wrong'.

If this forum is going to be a scientific discussion and not just an echo chamber then all participants need to be prepared to have their ideas disagreed with and criticized.

I have found most  of the comments here to  be constructive and reasonable.

Although there are numerous variables that effect the decline,  variables can't just be thrown together just on the off chance that they are related. This hypothesis is about nothing  more than the relationship between the duration of the 'plateau' and the extent of the decline.

It may be possible to link wild fires to either the decline, or the plateau but that  should be done separately; only when a link has been identified should the variables be considered together.  The purpose of this thread was to examine one variable, which although it is not statistically  significant in its own right, does show an increasing correlation with melt.  I  would prefer to investigate whether the plateau is a consequence of particular conditions rather than throw in an apparently unrelated variable.

[Neven]

Fear seldom brings out the best in us, so if the stated intention is to work together to learn more about the ice and the Arctic, then I honestly don't know what all the anger and ridicule and abuse is doing in this forum.

That's your interpretation, Vid, and that's where things go wrong. You propose a theory, people criticize it, you lash out at them with sarcasm and arrogance, they get angry, lash back, you feel persecuted and go berserk. Result: conflict, spoilt atmosphere, waste of Neven's time (who has other things to do).

It's at the third step where the problems start. Only you can change that, or I can snip the sarcasm out of your comments for you, which I won't be doing for very long.

The Plateau Hypothesis is interesting (and I really appreciate DavidR's polite replies to criticism), but it looks like it's difficult to prove the case as there is not enough evidence. That's okay, that's how science works. Oh, we want it to prove that there is a catastrophe going on in the Arctic? No need for that, it's bad and alarming enough as it is, even if all the ice won't melt out by 2020.