Sea Ice Extent Dynamics

[Dundee]

I am only recently registered here but have been following the subject and the forum for years. I am a retired quantitative analyst (and nuclear submariner, and geologist, and radar designer, and day-trader, and a few other things) who finally gave in to temptation a few days ago and started downloading data.

I was looking to pry into a particular topic, but got side tracked while working up a useable data set. First cul de sac - moving averages are helpful, but large daily spikes in data still leave visible jitters in the annual graphs. In a graph they are simply unaesthetic but I am looking specifically the rate of change in the daily numbers.  When you drill down to these, even small jitters generate a huge amount of noise.

Many financial analysts started using digital signal processing techniques in preference to moving averages some time ago, and a 30 day low pass filter appears to work just fine on ice data. I used a FIT filter that preserves frequencies 30 days and up while suppressing frequencies shorter than 15 days by a factor of 30,000. If anyone familiar with actual periodicities in arctic weather patterns (who can follow what I am doing with the filter) would like to talk filter parameters, please start a thread - to be honest I was eyeballing it.

I started with IJIS data and quickly found another rathole too curious to not poke around in. Attached is a graph of the rate of change for SIE, which amounts to the slope (derivative) of the familiar SIE plot. Generally, these lines cross zero at the annual maximum and minimum, the bigger the absolute value the faster SIE is changing. The relatively constant melt rate from mid April through May is apparent (it was discussion of the "May Pause" that got me going with this).

What I found striking is the smooth curve from early July through  mid October. I was amazed at how, as decades pass, SIE consistently gets on the curve sooner and stays with it longer. The tight grouping through September is remarkable.   

I believe I know what drives a number of the characteristics of these lines but have a lot of work to do before I'll commit to anything beyond "Gee, isn't that interesting?"

I'm curious what others think. Also, if this dynamic behavior is a well studied thing that I simply haven't stumbled over (I absolutely do not have formal training or qualifications in the field) I'd appreciate being pointed in the direction of prior art.

[Tor Bejnar]

This reminds me of something I attempted to look at a few years ago (but didn't know how to post a graph then).  Your several curve peaks appear to increase at a regular rate.  Do the annual graph equivalents stack up at all as nicely as the decadal averages?  My graphs (I'll share if I can find them) suggested to me that there was an approximately linear progression that might be a reasonable projection tool. 

[Tealight]

I absolutely do not have formal training or qualifications in the field

I see it as a positive thing because you might know techniques a formally trained climate scientist has never heard of. At least I haven't heard of it during my few month of meteorology study.

Not sure how useful this 30 day filter is and for which application exactly. At least it isn't fixed at specific dates like monthly averages.

I could quickly make a 30 day average daily area change graph which looks similar. So your finding isn't restricted to IJIS data.

[theoldinsane]

Many financial analysts started using digital signal processing techniques in preference to moving averages some time ago, and a 30 day low pass filter appears to work just fine on ice data. I used a FIT filter that preserves frequencies 30 days and up while suppressing frequencies shorter than 15 days by a factor of 30,000. If anyone familiar with actual periodicities in arctic weather patterns (who can follow what I am doing with the filter) would like to talk filter parameters, please start a thread - to be honest I was eyeballing it.

Are you talking about MACD or some variation of this technical indicator for the stock market?

http://www.investopedia.com/terms/m/macd.asp

[crandles]

The top of the smooth curves are gains in extent. The lower the extent goes in summer the more there is to recover. It takes to a later date to recover because there is more heat stored in the ocean which has to be given up before ice starts forming.

Does seems surprising how close the curves are all the way up that upslope which includes both losses and gains in extent.

The sun reliably changes to lower angles which might causes losses in extent to decline in a steady predictable manner. However over such a long time range you could argue that the ice remaining towards end of period get harder to melt out as the easy ice to melt has already melted out. Against this larger area ice free means more heat can build up in the ocean for bottom melt. When we get on to gains in extent in fall, from a lower extent more area wants to freeze over given the insolation but there is more heat in the oceans.

Thus seems surprising that these competing factors balance out and keep the line surprisingly steady in the same position.

[ktonine]

What we see is the huge effect a 6 month summer, 6 -month winter cycle has on the ice.  Insolation is more variable in spring and summer because weather in the form of clouds can interrupt the amount of insolation the ice sees, but in fall/winter the absence of the sun is not much affected by clouds until the ice has all refrozen.  Cold is more reliable than warmth.

[Dundee]

Are you talking about MACD or some variation of this technical indicator for the stock market?

No, not MACD (which works with multiple moving averages). This is not so much in the consumer investor press as under the hood. Off topic, but some years back financial firms began looking harder at applied mathematicians (often at the PhD level) rather than business types to manage trading.

I think it fair to say you would have trouble putting together an automated trading system without DSP techniques, and these systems direct most of today's trading volume. Where stock analysis used to begin with a balance sheet, it often starts today with a Fast Fourier Transform (to identify all periodicity in a stock's history).

The dice have no memory, and studying the history of a random process gains you nothing. If you can say for certain that a particular break in a stock price is noise overlaid on an underlying pattern, you can begin making money. The more you understand the patterns (and the nature of noise - a key topic in information science), the better you are positioned to predict what comes next. In the markets, you don't need inside information to analyze patterns but it certainly helps. WRT sea ice, you can find patterns by analysis, but when you can connect those to underlying physics, things get a lot more interesting.

[Dundee]

Below are a couple of Epsens's periodic graphs that show what that tight late summer grouping means. At the minimum, the lines rarely cross and are in general smooth, consistent curves. At the maximum, the plot is tangled chaos, and most lines have significant disruptions.

To put this in context, though insolation is decreasing in one case and increasing in the other, the daily solar energy flow is similar. Fractionally, the maximum has changed the least over the years and the minimum the most (declining by nearly half since the 80's). So how (given that the margin geography at minimum has changed radically in the last 35 years and is often strikingly different year to year) has the specific number of km2 melted and frozen each day of this period managed to remain so consistent? This period of time runs after the stable period in >80N temperatures. Given the annual suspense as we pass through the minimum (arguably more exciting than the max, at least in most years) I did not expect to see underlying stability in this of all parts of the annual cycle.

Again I have more work to do (with annual, rather than decadal average)  before I am willing to think out loud about causes - at this point I am looking for other's impressions.

[theoldinsane]

Are you talking about MACD or some variation of this technical indicator for the stock market?

No, not MACD (which works with multiple moving averages). This is not so much in the consumer investor press as under the hood. Off topic, but some years back financial firms began looking harder at applied mathematicians (often at the PhD level) rather than business types to manage trading.

I think it fair to say you would have trouble putting together an automated trading system without DSP techniques, and these systems direct most of today's trading volume. Where stock analysis used to begin with a balance sheet, it often starts today with a Fast Fourier Transform (to identify all periodicity in a stock's history).

The dice have no memory, and studying the history of a random process gains you nothing. If you can say for certain that a particular break in a stock price is noise overlaid on an underlying pattern, you can begin making money. The more you understand the patterns (and the nature of noise - a key topic in information science), the better you are positioned to predict what comes next. In the markets, you don't need inside information to analyze patterns but it certainly helps. WRT sea ice, you can find patterns by analysis, but when you can connect those to underlying physics, things get a lot more interesting.

Thank You! This is maybe one of the moments when different knowledge put together will render new knowledge and better understanding. I look forward to your analysis and achievements.

[Rob Dekker]

Dundee/Tealight,
These are very interesting finds.
It is less apparent in Dundee's graphs than it is in Tealight's graph, but both seem to suggest that melt started earlier, but then the RATE of melt did not change much over the decades, at least not during the June-Sept main melting season.
Or is that a side-effect of taking the 30-day average ?

[Dundee]

Remember "melt starts" at the Spring zero crossing and ends at the Autumn crossing, so no, the charts do not suggest a change in timing of melt. Likewise, drops in both maximums and minimums would (all else being equal - which they are not) mean lower daily change rate magnitudes rather than higher. It is tough to eyeball the effect of the rate chart on the amount of sea ice.

The Spring zero crossing is chaotic, the Autumn (weather filtered out) is strikingly consistent. There has been a lot of discussion the last few years over whether peaks are earlier or later than the past. Provisionally, I believe neither has changed markedly. The excitement comes because a weather change can readily skew the peak by a week or two - given the fundamental rate of change at maximum and minimum is small compared to the rate of change a large weather blip can create. A few of these in a row can look like a trend, even when they are not.

The charts below are from the full NSIDC record, filtered to essentially exclude changes with a "period" of less than 15 days while creating minimal distortion (visible in the last graphs I posted earlier, if you look for it - I've modified the filter) in changes with periods greater than 30 days. The first is an enlargement of a random chunk of the record, to clarify the annual detail. The second shows the entire record.

I can generalize that every year, for many years, the daily rate moves from peak melting to peak freezing in a smooth fashion at a brisk and increasing rate. The fall in rate is slower and much more chaotic - at this level of smoothing all you can say about the shape is that it takes much longer than the rise in rate did. If you look closely, this pattern is visible every single year, always chaotic from peak freeze to peak melt and with at most a glitch or two through the period in "the groove" from peak melt to peak freeze.

As an aside, the plots of summary charts seemed to indicate that, over the years, the rate settles down onto "the groove" sooner and stays with it longer before becoming unstable. I caution this is wild conjecture until I look a lot harder at individual years.

This is premature, but I'll throw out two of the factors I believe are involved. The first is geography. The smooth part of the curve roughly correlates with the period when the action is happening in the Arctic Ocean proper, away from land (other than the CAA, which in the old days never melted anyway). The next rough correlation should be near and dear to Rob's heart - and he knows a lot more about it than I do. I believe it is fair to say that in the smooth part of the curve, most of the sun that falls on the annulus of active extent decrease is falling on water - not snow, land, or ice, but water. In the chaotic portion the opposite is true.

The sunlight to the atmosphere is identical on the two equinoxes. I don't know enough about cloud climate to know about the sun hitting the ground, but speculate it is not radically different either. In the Spring however most of the sun falls on ice or snow, minimizing its contribution to the heat balance. In the Autumn, most sun falls on water - its contribution dominates the heat balance. In short, the chaotic portion of the annual trend is controlled by heat arriving with ocean currents and air/humidity in weather systems, which are of course as fickle as the weather. The smooth portion is dominated by insolation, which is (astronomically) dead consistent. The mismatch between the peaks in the curve and the solar equinox calendar is driven by geography and melting - until the sun is consistently heating water, it can't drive the problem (wresting the reins from weather).

I have not seen a formal heat balance of the Arctic (even on crude terms) but suspect it will eventually have a lot to say about the shape and timing of the daily rate curve.

FWIW, global warming affects both the ocean/atmospheric and solar heat inputs directly. And again, I as I conjectured, it may affect the timing (changing the date at which snow, land, and melt ponds take their part in the process). The effect of the latter on SIE overall may be one of those non-linearities we've been looking for WRT CO2 forcing.

I don't think we will ever be able to predict how deep next year's jet stream waves will be or where on the ice map they fall. I fear we will increasingly be able to predict changes in melting within the Arctic basin proper (which will become more and more of the ice year).

So, Rob, I am intensely interest in where you have been going. I suspect that if enough data exists to put a statistically effective "years through time" factor (regressing wrt year rather than averaging across years) into each term of your equation from July of 2013, you may find something that works more rather than less well as years progress. It is also possible this "snow/extent/area" approach may yield an effective prediction sooner and sooner in the year.

One thing I've been scratching my head over is "extent". I can see consistency in ice volume rate (linearly related to heat movement), but why we see such consistency in extent rate (at extent minimum), given the enormous (annual and trending) changes in the size of geographic area where the extent change occurs (roughly proportional to perimeter length of the MIZ) and thickness of ice at and approaching the edge has me buffaloed. Robust statistical trends are lovely, but in physical systems they have to have physical explanations . . .

[Rob Dekker]

Remember "melt starts" at the Spring zero crossing and ends at the Autumn crossing, so no, the charts do not suggest a change in timing of melt.

You are right. That was poorly worded.
What I wanted to say is that the main rate of loss of ice seems to accelerate in spring, while it seems to be unchanged during the rest of the season.
That I find surprising and interesting.

[Rob Dekker]

FWIW, global warming affects both the ocean/atmospheric and solar heat inputs directly. And again, I as I conjectured, it may affect the timing (changing the date at which snow, land, and melt ponds take their part in the process). The effect of the latter on SIE overall may be one of those non-linearities we've been looking for WRT CO2 forcing.

I've been thinking about these non-linearities a lot. But over the years I've been surprised how 'linear' the decline has been. Both for SIE as well as volume.
It may be related to the albedo-amplification factor (caused by snow and ice extent decline) during the melting season. If that factor is constant (as kind of could be expected), then the decline in sea ice volume will be linear. And if the ice thickness of the ice that melts out (mostly FYI) does not differ that much, then SIE will also decline linearly.

I still expect some non-linearity once ice volume gets really low, as best shown in this graph by Chris Reynolds :



Since there is no physical reason why volume would not continue to decline linearly, there will come a point that SIE will decline rapidly, and non-linearly.
As prof. Wadhams once stated : "In the end, it will just melt away quite suddenly. ".

[Dundee]

I've found lots of things that didn't pan out . . . I'm not stumped yet, but since I will be away from my computer for a while, I'll post where I am so far.

First, we can all agree there is a declining trend in ice. We also know minimums are declining faster than maximums. I took the Wipneus NSIDC-like data, lined it up to the Winter Solstice (Leap Years are a bitch - the effect is not large, but it always seems to be annoyingly present, and at just the wrong times), and regressed it daywise. In effect, I took the first derivative (to daily melt/freeze rate) and applied a low pass filter to remove weather noise. It turns out it did not matter what order these are done (which probably should have been obvious, but I spent about a week saying Gee, this graph looks just like that one).

I toyed with the filter parameters - too little and obvious weather bumps propagate into far future predictions (which doesn't make sense) but too little inserts a definite lag into higher order views.

The first charts are views of the regression model over a century, unfiltered and filtered. Next is an indication of how much of the variability in SIE is due to the long term trend - half or more. For most of the year RMS "unpredictability" is 300,000 km² or less, which is not bad. We are used to seeing days near or outside the -2SD side of the envelope, but most of this is because we are comparing to an average centered years in the past. The 2015 minimum numbered in the lowest measured and by Chartic is out of the envelope but, taking into account the long term trend, 2015 was a very well behaved year.

[Dundee]

If that were all there is to it, I'd note that minimums hit 1 million is 2058, or between 2051 and 2063 to one sigma. It hits zero in 2069 (62-75). All there is left is to vote in the polls and call it a day, right?

As it happens, the minimum is the most unpredictable time of year for ice. Minimums also have a habit of being much lower than they should be, for no apparent reason. So what is going on?

What led me into this was the behavior of the daily rate of change in SIE. From peak melting to peak freezing, things appeared to be remarkably well organized. From peak freezing to peak melting, remarkably chaotic. Surely there was something to be made of this. I had expected to be able to make projections based on extent trends during most of the year and exploit rate consistency to aid prediction around the minimum, but is turns out "visually well organized" does not translate to "exploitable statistics".  I am still convinced there is something there, but don't have any idea what. Here is where I am at so far.

The SIE year appears to have two parts. From November through early June, extent is well behaved and can be fairly described by linearly decreasing trendlines. From August through September there is a well organized (but, as it turns out, not particularly predictable) shift from maximum melting to maximum freezing. Despite this apparent consistency, this period has large average anomalies as well as residuals vs trend.  The linearity of extent over time also degrades - the minimum in particular seems to be dropping at a greater than linear rate. Surprise minimums have been cropping up regularly for decades, and they are getting lower and lower with respect to a postulated linear trend.

Although I can project out long term trends (and, for most of the year, expect SIE to follow them) I have little confidence in them from roughly August through October. To the contrary - I can't explain or justify my impression, but I firmly believe we will see more and deeper surprise minimums, and that "ice free" will happen long before the basic statistics would have us expect. In effect, there is a well in the long term trend sheet that splices into an otherwise well behaved picture. I don't have a handle on how the well works yet, but I think I can say the points it splices into the rest of the year are getting broader over time, and the peak melt and freeze rates and depth of the well at minimum are becoming more and more dramatic.

The shift in SIE behavior (from linearly declining to something else) is inconsistent from year to year. If a shift between two distinct regimes is occurring, I can't (at the moment) say whether it happens every year or is only a feature of outlying years (2007, 2012 . . .).  I was hoping it could be correlated with either the period of widespread surface water and resulting albedo loss or with the movement of the melting front away from land (and into the Arctic Basin proper) but neither of these quite fit.

Things in the physical world have physical explanations, so there must be information out there that will help make sense of this, but I am still looking for it.

I think my next step is to look at area (and, along the way, extent-area relationships). I am also tempted to repeat the extent projection process with '"obvious" outlying years removed, and again based only on outlying years, but fear that may be a waste of time (and brings the problem of defining with rigor which years are normal and which are not).

I'd also like to see an approachable data set that reduces snow, ice, surface melt, and cloud cover to a single albedo term, ideally daily, for at least 30 years, and at a minimum by latitude with perhaps 5 degree resolution.  I can't help think there is something there to be found.

I'll toss out one chart before I go, the standard deviation in SIE daily rate of change plotted with the standard deviation in published SIE anomaly for context (nothing here from other models or regressions). I think the two peaks in rate SD represent the period of transition between melting regimes, but (as I said) have not found a practical way to use the consistency that develops beginning in July to improve predictions of the minimum.

As an aside, the current rate of posting in the "2016 melting season" thread is in part explained here - average melting rates this time of year are about 50,000 km²/day with a standard deviation of roughly 65,000, so it stands to reason June is "interesting times".

[ktonine]

Dundee, it might be interesting to detrend the data and then do an FFT analysis.  I know when I was looking at annual numbers there appeared to be some cycles, but I never got around to analyzing the dataset properly.

As for detrending, I'm not sure what I'd use as the baseline period or what I'd use for the linear approximation.  My initial thought was to do piecewise linear approximations, but -- as I said --  I just dropped it.

[Dundee]

It has been a while since I’ve downloaded ice data – the nature of what I was doing with it is long term, and there wasn’t much gain likely without a lot more data. It’s been about five years, and even better, there are more than forty years of NSIDC ice index to work with.

A key answer I was looking for was whether or not ice was decreasing at an increasing or decreasing rate. I had a couple of analysis paths in mind, but thought I’d start with something quick and dirty. I’m not a big fan of moving averages but they are easy to compute, so why not look at them?

This is a chart of very long term moving averages of the NSIDC index. My first impression was just how noisy a one year average is. When I last swam through the data, I filtered out short term noise – looking at longer averages, it is clear that “weather noise” affecting the ice pack is not days or weeks long, but years.

A ten year window begins to smooth things out. A 20 year window begins to look like there might be an accelerating trend. The thirty year moving average (barely twelve years long) however, is remarkably flat.

I’m not sure enough data exists to say much more than that with confidence. One hundred or, better, five hundred years of data would be nice to have. Sadly, with the state of space investment in the U.S., it is far from certain we will ever have a lot more to work with. The NSIDC index certainly has warts, but its value is that it has been done the same way for many years. It is not hard to imagine an end to it as spacecraft die and no comparable sensors go in orbit to continue the series.

I put this out there as food for thought. I welcome suggestions on things to do (short of building satellites) while waiting for another five years worth of data.

[uniquorn]

A 22yr average might coincide with solar cycles.

[johnm33]

I've often wondered what overlapping 11year averages would look like, 70-80,75-85, etc.

[oren]

Nice chart indeed.

[Dundee]

Solar irradiance varies (it is thought - instrument precision is of the same order as  the variation) something like 0.1% across a typical solar cycle, which should not have a noticeable affect on Arctic ice.

That said, moving averages are easy to generate. The harder part was shoehorning all the data into one graph, ice people and sunspot people have markedly different data habits. When the smoke clears, it looks like below. I've included an 11 year window, a 22 year window (which should largely smooth out any solar cycle variation), a 6 year window (which should strongly reflect any solar cycle variation), and raw and smoothed NOAA sunspot numbers (SSN, SmSSN).

I don't eyeball any consistent influence of SSN on Ice Index.

To be completely fair, the effectiveness of a sliding window is best if the underlying cycle is dead consistent - even year windows against the NSIDC index work very well, because the length of a year is exact. In contrast,he length of the solar cycle varies by nearly three years. The three complete cycles in our view are 9.9, 12.3, and 11.0 years long (oddly, the ONLY observed solar cycle that was exactly 11 years long). The "11 year" part is very nominal. This means there will be significant residuals hanging on the edges of the moving averages, confounding the picture a bit. Even so, my Mark I eyeball does not detect any sign the solar cycle is a driver.

I do find it interesting to see the 22 year index is essentially flat to about the millennium, and then seems to steepen a bit.

My last detailed analysis used daywise linear regressions, essentially assuming the rate of decline to be constant. I am very interested in whether it is concave up, or concave down. If linear, we are looking at the end of arctic summer ice in about 2060, plus or minus many years based on observed annual variation (and the likelihood that at some level probably significantly larger than zero, the ice will simply collapse - think "goodbye waves" across the basin). If it is concave down, the end could be a couple of decades sooner.

The most reliable indicator I have computed so far (30yr moving average) says "roughly linear". the 22 year average (which reflects 4 years more recent history) says "it may be getting a little worse". If you extend either the 22 or 30 year lines, the early years and the late years of the satellite record tend to fall below them - my gut says definitely concave down, but it doesn't trip (admitedly crude - I may be a quantitative analyst but I've always been able to to my job with very unsophisticated stat tools and am far from a guru) statistical measures to a high degree of confidence.

All in all, no good news. Not unexpected, based on how we think the irradiation budget is changing. There was a good stretch in the 1990's, countered by a bad stretch in the 2000's, but writ large sea ice is not looking good.

I have several other things to try (the max and minimum seasons over time, and Fourier - as was suggested long ago but which did not really yield anything last time I looked). I'm open to suggestions, even long shots.

(ps - I have not included a scale for sunspots but rather scaled for best visibility - they vary from roughly zero to roughly 285. Annual average solar irradiance appears to track smoothed SSN, but varies narrowly between roughly 1365.5 and 1366.7 watts per square meter at the top of the atmosphere).

[uniquorn]

Thanks for that detailed analysis Dundee. I think it was the 10yr that caught my eye but I'm aware of a ~22yr from A-Teams recent posts

[Glen Koehler]

<snip> Annual average solar irradiance appears to track smoothed SSN, but varies narrowly between roughly 1365.5 and 1366.7 watts per square meter at the top of the atmosphere.

      I enjoy your work and your approach to it Dundee.  I'll save a rant about the value of simplicity for a less mission-critical thread.  Just wanted to say thanks.  My amateur look at the solar radiance cycle for other purposes came to exactly the same conclusion about the range between top and bottom values.  By posting your observations you have also provided informal support for that unrelated work.  While "The plural of anecdote is not data." ~ Roger Brinner, it helps to have company!

[kassy]

The dice have no memory, and studying the history of a random process gains you nothing. If you can say for certain that a particular break in a stock price is noise overlaid on an underlying pattern, you can begin making money. The more you understand the patterns (and the nature of noise - a key topic in information science), the better you are positioned to predict what comes next. In the markets, you don't need inside information to analyze patterns but it certainly helps. WRT sea ice, you can find patterns by analysis, but when you can connect those to underlying physics, things get a lot more interesting.

One problem is the dataset. SIE is mainly a surface metric it melts in summer and refreezes in winter until it does not.

When we look at older historical data it does not reflect changes such as atlantification or the heat build up from pacific waters. Old data also does not account for the more fractured state of the ice overall or the fact the ice pack is not clinging to land like it used to or it is not compacted into coast like it used to.

We also have another thread which features trends on volume, extent and thickness which don´t finish on the same year. If you look at it in a simple way you need some volume of ice to grow extent. If you zoom out a little open waters will bring mixing of water layers from below while the Arctic climate system itself is changing from an Arctic desert to a system with more water vapour in the atmosphere.

So basically historical SIE data is not going to tell you when the Arctic sea ice is going to crash.

[uniquorn]

This got me interested enough to want to see the data in more detail so here is a larger chart of NSIDC extent  where the total extent is divided by the number of years. Data to 1987-08-18 is only every other day so I suppose that is why the saw tooth is flattened. I'm not looking for solar cycle influence but 11 seemed as good as any other and 33yr gives a reasonably long trend.

Data up to 1987-08-18 was duplicated

[Dundee]

So, Fourier analysis has cropped up in discussion a few times, the goal being to detect (otherwise unrecognized) periodicity.

For large data sets, this is usually done with Fast Fourier Transforms, which always seem to work out neatly in textbook examples. Challenges include a data limit of 4096 points (and requirement that the data points are an even power of 2) and the lack of any relationship between 365 and even powers of two.

I took every fifth day of a little over 15,000 daily values of the Ice Index (shouldn't be a problem, the five day average already removed very high frequency noise - every fourth day worked out badly, four does not go into 365 evenly) and padded it out to 4096 points (smoothly blending to the annual average). The rub is, this means exactly 365 days does not end up as a bin - the result is the annual peak bleeds out into other bins as well as harmonics. It is possible that clever down-selecting, windowing, padding could minimize this but if I tried it would be a stab in the dark - I'm not that clever. If anyone has tools to do an FFT on 16K data points (and the wisdom to pad the thousand empty values without inducing artifacts) let me know.

So, other than the 365 day peak (slightly off center in a 365.7 day bin) visibly creating a peak to the left and dip to the right, and small harmonics (presumably artifacts) at even fractions of a year, what it there to see?

First, there is no definite sign of any periodicity of less than a year, and anything greater than a year is buried in noise (and increasingly wider bins, in terms of period). I do note that 11 and (about) 6.5 years are aligned near local minimums - if the solar cycle is inducing periodicity, it is well below the noise level in the data. To be honest, no real surprises.

The amplitude units are arbitrary, the x-axis (rather than frequency) is labeled with period in days.

[binntho]

Excellent work Dundee!

[Aluminium]

First, there is no definite sign of any periodicity of less than a year, and anything greater than a year is buried in noise (and increasingly wider bins, in terms of period). I do note that 11 and (about) 6.5 years are aligned near local minimums - if the solar cycle is inducing periodicity, it is well below the noise level in the data. To be honest, no real surprises.

I tried it 3.5 years ago, nice to see confirmation of my results. Results are still boring though.