How polar ice is modulated by the sun
What follows here is a demonstration of how earth orbit shapes Arctic ice and in a later post I intend to show how this may well relate to palaeoclimatology shown in ice cores.
You will have seen the plots of Arctic sea ice. I am going to use one dataset here, which one is unimportant, others give the same answer.
Arctic sea ice extent, monthly data
I can model that very closely using a single function plus a fixed offset, which is unimportant.
Model data matched to the ice data
Now here is one overlaying the other.
Data and model overlay
The match is r2=0.96
Here is the remainder, subtract the model from the data
Remainder not accounted by the model
Now lets switch to showing you the details.
Model and underlying sine
The function is trivially simple, a pure sine wave with a period of 2 years which has been made single polarity.
Here are the spectra
And it ought to be no surprise given this
Why does the ice amount follow that exact law?
Superimposed the earth sun distance variation
The data from the SORCE satellite which measures TSI also includes data for 1AU distance i.e. earth/sun distance and this primarily shows the variation in solar irradiation during earth orbit.
Look carefully, minimum ice occurs when solar irradiation is highest and the converse. Perhaps the surprise is the almost exact sine/cosine shape but that is a pure rotating vector… and so is a near circular planet orbit, ours.
My critical point here is the creation of a unipolar signal from a bipolar stimulation. This is a non-linearity and creates an otherwise unexpected harmonic structure. I point out that the sunspot cycle is something similar, can only but appearing sunspots, never negative spots! (the solar magnetics tell a different story and why there is an underlying slower magnetic cycle)
SORCE 1AU
Commentary.
In fact the earth has an inclined axis, not quite the same thing as the TSI variation, but the SORCE data is a very accurate measurement. (the shown curve is from a model derived from 3 hourly data)
You will notice the phase of the ice variation and the phase of TSI differ slightly. The exact projection used by the the sea ice data providers influences this, JAXA/IJIS is slightly different. (same result, yes)
The same effect does not occur for the Antarctic which is land surrounded by sea ice instead of sea ice surrounded by land as it is for the Arctic.
From a palaeoclimatology point of view the elliptical earth orbit is not contant.
This like says a little about this with more detail than usual in general texts
http://www.personal.soton.ac.uk/ejr/DarkMed/ch5.html
I will leave it at that for the moment.
NOAA and SORCE are both very well known datasets, I give no links.
Deadal Earth 
Not so sure about the rectified sine model. Does not look much like it when you get close up.
You may do better with a sin^2 rather than |sin| , there’s more chance that you may get a physically meaning model that way as well: cos(inclination)*(distance), variation in distance also being sine like.
The only reason that looks like a rect sine is the monthly sampling. This is my old the runny mean coming in again.
12 monthly means are basically identical to 12 evenly spaced samples from a 30 day running mean (with all the distortions that implies). The trouble is added to by the fact that no anti-alias filter has been applied before doing the sub-sampling. Unless you want to pretend that your anti-alias is the running mean which is probably about the crappiest choice to make.
So runny mean introduces lots of spurious distortions then it get sub sampled without proper Nyquist filtering. What’s not to like.
Averaging is a valid means of removing _random_ normally distributed noise. It is a very bad way to remove non random probably cyclic signals that may (or will) alias with the length of the average.
Sadly scientists seem blissfully ignorant of basic signal processing. This is a friggin ubiquitous problem.
Here I used daily data and gaussian filters.
https://daedalearth.wordpress.com/2011/04/30/how-polar-ice-is-modulated-by-the-sun/
I suggest if you look into this again you do you spectral analysis on the daily data. I’m pretty sure a sin^2 model will be closer.
BTW same applies to sun spots. Ray Dome (?) suggested from the nature of the noise that taking the square root made it “better” for his processing.
I was pretty critical of doing that arbitrarily but what he noted about the noise may well indicate SSN is a manifestation of an underlying sinusoidal process which is proportional to its square.
Anyway, thanks for pointing me to this post. I had not spotted the sin^2 shape, I’d just concluded it was a slightly distorted sine. Since both inclination and distance will be something like sine and will modulate each other, this makes a reasonable first approximation.
oops, wrong link, of course I meant this : http://i49.tinypic.com/xudsy.png
Any thoughts on where the 5.42y cycle may be from ?
I wasn’t expecting comments here, oh well, no harm.
As I recall, not looked at this stuff for some time, the fit is excellent, so it ought to be, it is a law, apart from the minor spoilers. I wrote it up in the hope it gives a clear explanation which is not provided by those paid to do so.
Lot of history over daily data, won’t go into that now. In this case I specifically used the monthly since it is the one widely promoted. It will look different from amsu or (defunct) NASA Stereo, which provides 2 day then daily from 1978 through to 2007. (go figure and emails show a refusal to carry on)
Memory just called, something on this blog with long daily, I figured out the join. Seemed to be mainly geometric, probably a different orbit.
https://daedalearth.wordpress.com/arctic-sea-ice/
“Sadly scientists seem blissfully ignorant of basic signal processing. This is a friggin ubiquitous problem.” and sampling laws. Even after that we get things like truncating data instead of dither, destroying any buried data. All rather annoying.
There is another problem, in statistics, why bad confidence is given. The data is not normal, **in time**, not for here and now.
There has been various discussion on the cause of minor cyclic changes in the Arctic, often mentioning arriving as water. I’ve no real opinion on that, I tend to keep away from the various index. I have though wondered about a very short wavelength solar change which might correlate with the longer wave, bit of a story there. (I think plots are on a low bandwidth server, not very useful because this is science, data ceases)
There is a twist which is discussions on the Talkshop. Someone suggested there had been a change in the annual cycle. I looked and confirm that is the case for Arctic extent (not looked at area, usually the same).
I haven’t followed this up, got hacked off with the stuff I was uncovering, time to walk away from meddlers.
Something fundamental changed. My guess is with the data but of course sit on hands instead of coming clean and direct.
Okay, click, click, got a new dataset from the nasty format. Twiddle, take a guess, twiddle. Yep got it.
I am seeing ouch. Didn’t want a side track. Better write up something.
” the fit is excellent, so it ought to be, it is a law” What law is that?
“I specifically used the monthly since it is the one widely promoted”. OK, but that does not mean it is a good choice. I would always tend to go with the best resolution available and re-sample (after appropriate filtering) if necessary.
Monthly averages are ubiquitous in climate data (data volume convenience ) but with the various lunar and tidal cycles close to this really bad for the reasons I pointed out above.
As you can see it can easily lead you fit a rectified sine when a sin^2 is a more reasonable physical model.
This actually provides me with another good example of what is wrong with running means and averaging non random errors. The distortion caused by taking monthly means actually meant that your rectified sine fitted pretty well to data does not have any such polarity flip.
In fact it surely fits better than sin^2 to the monthly data.
Given the intent of the article using do2135 is sufficient, is most familiar to readers, covers the whole satellite era.
Sine squared? You can see the plot of residual. Maybe try plotting sine squared.
Daily data? Same result.
Dug this out of an old work. Using the unipolar on daily.
That was more about UAH TLT Arctic, it follows. Can’t remember if there was anything public to do with that one but some time ago was discussed in private.
In practice on daily there is no advantage in using unipolar over straight Fourier given I have the tools. The point of this article is demonstrating the Arctic ice follows an orbital law.
Antarctic does but to a much lesser extent because it is an annulus of sea ice which sees much less insolation change.
Tim: “There is a twist which is discussions on the Talkshop. Someone suggested there had been a change in the annual cycle. I looked and confirm that is the case for Arctic extent ”
There was a distinct change in behaviour from 1997-2007, that is what my graph was all about. What has not been recognised anywhere that I can find is that the earlier pattern had been re-established since 2007.
Everyone is still wailing about the “catastrophic” collapse of Arctic sea ice , when in truth it has stabilised
I think I’ve answered my own question to some extent about 5.42y seems to be a dominant cycle in N.Pacfic that also is present at about 50% in N. Atl.
There seems to be about 50% of Atlantic signal is determined by Pacific. But, at around 35 years lag, when pacific is decorrelated, we see that N. Atl is quite a clean form. I see five peaks in 45 years, a period of 9y that is close to the 9.1y lunar cycle detected extraterrestrial factors by Scaffeta.
The most obvious short cycle in N.P. is 22/4 =5.5 y ; there seems to be an obvious beat of two close cycles, I estimated the null to be about 36.7y but looking again I’d say it’s a bit short.
So 5.2 and 6.1y in N.P. based on 36.7y.
A better estimate of 38y null would give 6.33y and 5.43y cycles in N.Pacific.
The autocorrelation was based on data ending in 2005, so for the phase the null point would be about 1975, near the beginning of satellite based Ice area data.
Rate of change sea ice with N. Atlantic SST (this is incorrectly labelled AMO, it was the NON-detrended AMO version, ie true SST)
Not much cyclic correlation but clear evidence that the Arctic ice cover has adapted to the still warmer SST. Strong evidence of a neg. feedback, not positive feedback “tipping points”.
5.4y cycle seems to be either driven by N. Pacific SST or to be driven by the same thing as N. Pacific .
I mentioned a possible connection with very short wavelength solar, we are talking about the same region of the record.
Here is a PDF of part of something else, a lot of background I don’t want to talk about, would take a lot of explaining. Part of the tale is finding something strange in a totally different field and going looking for any possible cause, arriving at this
Click to access mgii-ice-2.pdf
I still don’t know whether there was a fault, whether it it real, change, wrong, etc.
Take as a curiosity.