Exploring Arctic Ice Minima

Every year 2007-2013 had a lower Arctic sea ice extent than every year before 2007.  2014 seems likely to continue this record.  I'll also suggest below that maybe the Arctic has entered a 'new normal', with September ice extents bouncing around 4.7 million km^2. 

For some data to work with further, I pulled the NSIDC September figures.  It's a small, simple text file, so you can check yourself what follows.  First up, let's draw a figure of what we're looking at -- but don't connect the observation dots.  Our eyes tend to be led to conclusions by the superposed lines.

You can check some of the sources for ice before 1979 and see that figures below 5.5 million km^2 are unprecedented in the longer records as well.  To have data precision and consistency, though, I'll stay with the 1979-present.

What else can we say from eyeballing the data?  Since the 1979 starting point:

• There have been 2 record highs (1980 and 1996)
• There have been 8 record lows (1984, 1985, 1990, 1995, 2002, 2005, 2007, 2012)
• There have been more record lows in the last 10 years (3) than record highs in the full 35 year record
• 1996 is about the last year one could say there was no trend in the data
• Versus eyeball curve fitting, 1996 is the most exceptionally high year (not just an absolute record, but even higher above smooth curves we'd try to fit to the data than any other year).
• More recent years look like they have more scatter than the earlier years
• It looks like we might want to divide the period in to 3 intervals -- 1979-1996 (the longest arguably trendless span), 1997-2006 (an intermediate with at least some overlap on the earlier figures) and 2007-present (entirely outside the range of the previous years)

But maybe your eyeballs disagree with mine, and perhaps the appearances are deceiving.  So on to working with numbers, which will also lead us to some additional ideas.
First, I'll put in the lines between data points and ask you to reconsider what leaps out to your eyes.  One change for me is that 1997-2006 look less disconnected from 1979-1996 than with just the data points.

Now a bit of spreadsheet computation.  I'll make up 4 periods -- the 3 I mentioned before, plus adding in 1979-2006.

Span	stdev	intercept	slope
1979-1996	0.515	7.467	-0.036
1997-2006	0.379	8.484	-0.100
2007-2013	0.614	4.498	+0.007
1979-2006	0.651	7.642	-0.060

For doing this, I just used the spreadsheet functions stdev, intercept, slope.  For research purposes, I wouldn't, as there are some subtleties in how the computations should be done that spreadsheets don't necessarily respect.  My eyeball notion of increased variability in the recent span doesn't seem to hold up.  Oh well, onwards.

The intercept and slope show 2007-2013 to be wildly, drastically, spectacularly different from the prior periods.  We already pretty much knew that, but this gives another way of seeing it.  Intercept and slope give us straight lines.  The intercept is the sea ice extent for 1979 (it was actually 7.20, with 1980 being 7.85), and then the slope says how much less ice (if negative) there is year by year after that.  I'll plot all three of these lines on the data:

 The line for 2007-2013 is far below all prior observations.  It shows a very small upwards trend, so small that it's almost certainly meaningless statistically.  (It would take 300+ years to get ice cover back to the range of the first span of data; nevertheless, start your stopwatches for someone to claim Arctic ice is 'recovering').  It intersects with the line from the middle period in 2016, at about 4.78 million km^2.  The scattering of observations above and below the line, and essentially zero slope, in this period suggest the hypothesis "Arctic ice entered a new normal with the year 2007, where the September minimum averages 4.71 million km^2"

The two years which stand out most from the fitted lines are 1996, which is indeed the most drastically above the lines, and 2012, which is the most drastically below.  So, not exactly a hypothesis, but data-driven research questions -- What happened in 1995-1996, 2011-2012 to make for such extraordinary changes in the sea ice pack?

Since 2007 is the first year of the 'new normal', what happened in 2006-2007 to make that change of normals?

Looking at the line for the middle period (1997-2006), we see that as you look backwards in time, it is rising spectacularly fast.  By the early 1970s, it is far above anything previously seen.  One thing this says is that whatever was causing the decline in this period, it hasn't operated for long before.  If it had for more than a decade or two (1-2 million km^2 changes), the prior observations wouldn't look anything like they do (around the 7-8 million km^2 range, give or take).  This line is a little below 2013's figure, which suggests it isn't entirely out to lunch for present and future considerations.  If we run it straight forward, it hits zero in 2064.  You could apply my earlier idea on how to estimate the disappearance time of sea ice to this straight line instead of my more complex curve from then to get a statistical range and confidence levels for when the Arctic ice pack might go away. 

Finally, let's look at the first line.  It has a relatively shallow slope, enough so that if we run it back in time, it doesn't get outrageously high (I'll define that as 9 million km^2) for a longish time (1936, it turns out).  So it has at least some plausibility for telling us about earlier times.  Whenever we fit a line to data, the data should sometimes be above, and sometimes below the line.  Further, the points should be on both sides of the line in both the early and late period of the line.  For the first line, the last time data goes above the line is 2001.  (we aren't happy about the fact that all 4 years before 2001 are below the line, and 2001 is only marginally above, but it's a start.)  This is more recent than the 1996 I had stopped with earlier.  By eye, it also looks like we might be able to put a line through the data 2002-2013.  One benefit to this is that then we only have two lines instead of three.  If we're arguing that something changed in the Arctic system (which I'm not yet, but might want to later), it's easier to explain 1 change than 2 (or 3, or ...).

Ok, I can't say I'm excited by this version.  The early line, with its additional 5 years, is a little different, but still entirely out to lunch past its last data point (2001).  And it's now dropping more steeply, so becomes unreasonable a decade earlier in the past (per above definition of 'unreasonable').  The line for the more recent (2002-2013) period doesn't look too bad, though.  At least it remains plausible back to 1996, maybe 1992, 6-10 years before its starting date, and observations in the more recent period bounce to either side of the line.  Sending the line forward, it passes zero in about 2042, which is in the range of other people's estimates (as is the 2064).

What have I proven?  Nothing, this is science after all.  It's mathematicians who get to prove things.  But even in the more casual usage of 'prove', nothing except that with only 35 data points I can write quite a lot of words.  Not news to anyone who's been here before or otherwise knows me :-)

This is, as advertised, an exploration.  The purpose of exploration is to see what's going on and get ideas for future research.  I'll take this up in additional posts.  You've noticed a number of question marks and hypotheses above.  These are all items to look in to, yourself or me.  There are several years which seem to be particularly interesting, in that they don't fit nicely on the curves (lines for now), and the transition times between lines.  Was anything unusual happening meteorologically then?  Oceanographically?  Somewhere else?  Could they have caused what we saw in the sea ice?  Was it instead that something happened in the data source, not in nature?  Have we really hit a new normal, or is the ice still declining?  How would we tell the difference?

Applying my 'new normal' hypothesis gives a guess for 2014 of 4.71 million km^2.  It looks likely that this won't be very close.  But it shouldn't be too bad compared to other methods.  Again, more later.