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Ice Cool Kim

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Arctic area acceleration
« on: April 28, 2013, 07:19:00 PM »
Following some discussion of rate of change and various opinions as to how that could be interpreted in terms of whether various periods could be described as showing accelerated melting, I thought it may be informative to look at acceleration directly.

It was quite a surprise.

I'm sure ChrisReynolds will recognise this as quickly as I did. There is an obvious beats pattern as is produced by two or more harmonic signals of similar frequency.

For those not familiar with the phenomenon:
http://en.wikipedia.org/wiki/Beat_%28acoustics%29


It was obvious to me from the rate of change plots that there was some repetitive patterns but I did not expect it to be this regular.

The filter used here is a triple running mean that avoids the usual distortions of running mean filters and has a zero in the frequency response at 365 days. In short it removes the residual annual signal that gets past the "anomaly" processing as supplied by Cryo Today. [Normal since annual variations are not constant across the record and a significant annual residual is still present. ]

Other than the cyclic aspects I can't find any obvious sign of either acceleration or deceleration in the record, which is another surprise. I'd expected something one way or the other.

I have done the mean over a few period that are usually discussed and found nothing that is distinguishable from zero.

That would suggest that any ideas of acceleration in the time series are just the result of these various accelerating and deceleration oscillations.

NB. this does not say anything about the value of the net rate of change in the record, just that its not getting worse or better.

PS the main frequencies are probably close to and either side of two years.

This would probably tie in with the recognised one year anti-correlation that I believe crandles brought up at some point. It also explains why a simple annual alternation only holds for a limited duration then skips. It is not a simple two year variation.

The alternation can be seen in examination of duration of melting/freezing seasons:
https://forum.arctic-sea-ice.net/index.php/topic,174.msg2880.html#msg2880


Here's the acceleration plot:
« Last Edit: April 29, 2013, 12:55:18 PM by Ice Cool Kim »

mhampton

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Re: Arctic area acceleration
« Reply #1 on: April 28, 2013, 10:51:41 PM »
Could you describe what you did a little more precisely?  I plotted the same data in a couple of different ways and I am getting quite different plots.  I'm a little skeptical that there is a really a clean mixture of two sharply defined frequencies in there.

Ice Cool Kim

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Re: Arctic area acceleration
« Reply #2 on: April 28, 2013, 11:46:20 PM »
Firstly, in view of the deviations, it's clearly a bit more than just two frequencies, but the general form is as described. A closer look at freq. spect would be interesting.

explanation: first difference, done twice on daily data. Then triple running mean.
 triple running mean :  365  273  204 days.

[technical detail]
freq resp of running mean (sinc fn)  has a negative lobe, that badly distorts the result, at tan(x)=pi ; x=1.3371

so each stage is 1.3371 times shorter than the previous one. This removes the neg. lobes and gives a profile similar to gaussian filter but with a true zero at 365, which is better than gaussian for removing a specific fixed frequency.


You say you did the same thing. What did you do for 3RM ?

I also had to 'correct' erratic dates in Cryo Today's data. They are within a day but all over the place with loads of dupes. Esp. leap years but elsewhere too.

[Edit: "all over the place" probably gives false impression. Most intervals are one of two close values but there are a significant number duplicate dates (which thus give infinite rate of change) most but not all of which are related to not correctly processing leap years. There are other irregularities, especially at end of 1980s which is rather messy. None of this too visible if you just look at the time series but needs to be resolved before doing the first difference calculation. Or any other processing, for that matter. Such as filtering with a convolution filter (even a crude running mean) that assumes constant sampling intervals. ]

There are the correct number of data in each year so the best I could do (since they do not answer questions about why their dates are erratic) was to renumber with equally spaced dates.

I would rather have them correct or explain it but in absence of any response it seems a reasonable solution.

I don't think such a result is likely to be the result of my mangling the data but all such questions are fair game.

Does that adequately answer your question ?
Are you now able to get something similar?
 8)



« Last Edit: April 29, 2013, 09:59:47 AM by Ice Cool Kim »

Ice Cool Kim

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Re: Arctic area acceleration
« Reply #3 on: April 30, 2013, 01:14:49 PM »
Well I had a quick look at freq spectrum and it's not two but three close frequencies that give rise to this pattern. What is even more interesting is that they form a triplet of frequencies that correspond to amplitude modulation: a central frequency and two equally spaced 'sideband' frequencies. Again I'm sure Chris will know what this is about, but for others not so well versed in electronics and radio theory:

http://www.radio-electronics.com/info/rf-technology-design/am-amplitude-modulation/theory-equations.php

It is fairly easy to convert the frequencies of the triplet back into the base frequencies that would cause the same pattern.  It gives 2.006 and 12.83 years.

The frequencies were with 0.3% of the perfect theoretical spacing for A.M., so this is a legitimate interpretation, not just a close coincidence or me twisting the data to fit because I like it.

If I quickly reconstruct a pure cosine function of these three, with the amplitudes found, and superimpose it on the data, it's quite a good fit all on it's own. It would account for a large amount of the inter-annual variation and captures a lot of the key features, even matching almost perfectly the dramatic swing in 2007.

Now I'm ignoring the rest of the spectrum and there are at least a couple of other major peaks that contribute so the model does not explain all the variation. But it is very interesting because of the A.M. pattern it shows.

What this means physically is probably that an internal tendency to alternate between up and down (which crandle suggested could be caused by snow cover changes) is being modulated in amplitude by something that has a period of 12.83 years.

I will just mention in passing that N. Atlantic SST also shows a periodicity very close to that. One obvious possibility is a direct affect of Atlantic SST on Arctic ice area. Another is that whatever causes that variation in N. Atl also affects arctic ice.

It is interesting to see what a bit of basic signal processing can tell us about sea ice variations.

What becomes clear is that what some people dismiss as 'chaotic', 'stochastic' or 'random' variation is in fact just complex, and a little effort can help understand a lot of the structure behind what is happening.

If these variations can be characterised and then removed we will get a clearer picture of what else is happening and a clearer view of longer term variability.

Here's the plot:


« Last Edit: April 30, 2013, 01:20:20 PM by Ice Cool Kim »

Ice Cool Kim

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Re: Arctic area acceleration
« Reply #4 on: April 30, 2013, 05:35:52 PM »
Power spectrum of 100 years of N. Atlantic SST.

That the other stronger peaks do not seem to be reflected in ice area changes may lend weight to the idea of a common cause for 12.86 year influence rather than a direct influence of SST being responsible. Unless, for some reason the Arctic basin is resonant to this period and does not respond to 9 and 10.6 year variations.

There is also a strong 66 year peak  in SST, off scale here, for which the ice record is too short for spectra analysis to pick up.


major peaks (more accurately read at enhanced scale):
9.07, 10.58, 12.86, 21.46, 65.8 years.

[Note: shorter period peaks are attenuated by filter so would be stronger]

The similarity between the period reflected by the A.M. triplet in ice area and that in SST seems too close for it to be coincidental.
« Last Edit: April 30, 2013, 06:14:59 PM by Ice Cool Kim »