Annual Average Thread

[viddaloo]

Edit December 2014: This thread follows particularly the development of the Annual Average Volume, as calculated from PIOMAS volume data from 1979 to 2014. The use of the word 'average' is based on the everyday sense of the word, as defined by Wikipedia: The sum of a list of numbers divided by the size of the list, in other words the arithmetic mean.

Inherent in this thread and in the following summary graph is the claim that the annual average volume is the most telling or central statistic for the state of the Arctic sea ice.

Perhaps even for the Earth's climate as a whole? In any case, following the AAV is exciting!



The following below this line are earlier versions of this top post.

Edit: I changed the name of this thread, as the focus shifted from the 365 Day Mean volume to the 5 Year Cycle of both extent and volume. This graph took some time ironing out, but it got there, and it's both scary and impressive:



What follows is the original start of the thread:

I wanted to strip away all seasonal variation from the graph, to get rid of the wave shape. How to do it? Just calculate the daily 365 day mean for the date. This is what I got.

[viddaloo]

As you can see, 2012's main achievement is to start low (and go slightly lower). Unlike 2007, 2010 and 2011, that really melt away a great deal of ice from their starting points. 2007 is still the leader in this respect, followed by 2010.

[viddaloo]

Because a mean of 365 days is calculated for each data point, the graph is pretty stable and one–directional. It doesn't go up and down from day to day, as that would mean that the ice volume of a day would be higher than last year one day of a week, and then lower than last year the next. Naturally, that doesn't happen very often. This means that the graph in the top post really only changes direction (down to up, or up to down) about 5 times:

After descending since (at least*) January 2007, the mean ice volume starts ascending in January 2008, then it grows until March 2009, when a major shift happens that will last more than 2 ½ years and remove almost 3000 km³ of Arctic sea ice from the 365 day mean volume. This amounts to a loss of 18% of the mean ice mass during the record descent period of 33 months from March 2009 to December 2011. Then ice packs for ½ year until May 31st 2012, where a shift in early June starts the 8 month descent down to May 13th 2013 (a record low 365 day mean volume of 13395 km³), which also includes the all–time low minimum volume of 3673 km³ on September 18th 2012. Since mid–May 2013 it's been up–up, packing–packing, more and more ice. So we're still waiting for the graph to turn into a new descent. The previous one brought an all–time low minimum, just like the one before that, in fact, all the descents from 2007 forward have given all–time low minima records at that time, each of them even lower than the previous descent.

Whatever happens on March 14th 2009 lasts 1006 days, to December 14th 2011, exactly 33 months to the day, melts almost 3000 km³ from the Arctic sea ice and sets 2 new all-time low minimums, on September 15th 2010 and September 10th 2011. This huge 1006 day melt was also highly instrumental for the current all-time low minimum of September 18th 2012.

*) Actually, the 2007 major ice loss event starts as early as March 2002, lasts until January 2008, 70 months, and melts even more ice, nearly 5000 km³, than the 2010 event (2009–2012).

[viddaloo]

Thanks. The averages are not centered, but 365 days almost a year ago till the date in the graph.

[viddaloo]

One last graph for the day, even though it is of course preliminary for 2014, not final.

This one shows the yearly mean volumes for each calendar year. For 2014 it shows the average for the year so far, plus the rest of the year (as an estimate) from last year. This means the 2014 data point at the end of the graph could go a bit higher — or lower — when real data arrive.

As the graph highlights average volume during a year — which is of course higher than the yearly minimum in September — future ice–free September minima could very well come in a 12 000 km³ average year. Average doesn't have to be zero for Autumn to hit zero. However, when the X axis is extended to the right, into the future, it shows the yearly mean volume hitting zero in 2031.

Yup. That means no Arctic sea ice at all on any day of the year by 2031. Not even in the CAA.

[viddaloo]

I changed the name of this thread, as the focus shifted from the 365 Day Mean volume to the 5 Year Cycle of both extent and volume. This graph took some time ironing out, but it got there, and it's both scary and impressive:



We're at the start of a big, 1000–day, descent in yearly average ice extent. At least that's the working hypothesis!

[Rick Aster]

The five-year cycle is a reasonable hypothesis and certainly something I will want to watch for.

[viddaloo]

We are so much lower on average ice now, that even the (then) record low September 2010 (blue line, end of Year4) is way above the current 2014 yearly average. A 1000 day long descent now will mean a crash for Summer ice.

[jdallen]

Intriguing hypothesis. Last years numbers during the freeze spent disturbing lengths of time in the bottom three low years.

[kingbum]

Just a fresh idea I have....maybe this 5-year cycle actually follows the ebb and flow of the 11 year solar cycle....its a possible relationship worth investigating I think...

[viddaloo]

OK? But if so, why would it have two heat maxima during those 11 years?

[jdallen]

OK? But if so, why would it have two heat maxima during those 11 years?

Very doubtful it could.  There's no clear mechanism(s) to explain the changes in heat flow and weather.  I don't see the changes in insolation being significant enough.

[carmiac]

Dumb question: Would it be possible to go back from the 5 year cycle prediction to a daily number? To see if it looks at all realistic?

[viddaloo]

Absolutely, carmiac! And that will be my next new coding project; today's rainy in Hardanger and thus perfect for such activities. Plus, I need to rest after visiting my local alpine glacier yesterday

[viddaloo]

Low (IJIS) Extent Years, Including 5YC Forecasts.

[carmiac]

Thanks! I think this is an interesting analysis.

That's a completely reasonable looking 2015. Let's see how it goes!

[ChrisReynolds]

I don't think there is a five year cycle. There are two events, the lows of 2007 and 2012 which drive the lows of the claimed cycle. There is no evidence that 2007 and 2012 were periodic events.

Sorry.

The following plot shows NSIDC extent data from 2000, with a lagging 365 day running mean applied from 30/12/2000, the five year periods 2007 to 2011 and 2012 onwards are shown in different colours.

[idunno]

Hi everybody,

(Sorry real life has prevented me from paying proper attention for some time. I've been lurking sporadically.)

I am rather dubious also that 2 repetitions of a low would constitute a cycle.

I DO think that a 365 day average of the data is a very excellent idea.

Perhaps one could posit that the possibility that any one year is now going to see a spectacular crash is round about 20%? So about 2 per decade, with, I would assume at present, higher odds as time goes on that any one particular crash year might actually result in a seasonally ice free Arctic?

At any rate, removing the seasonal component in the data is, imho, an excellent idea.

[viddaloo]

That's perfectly all right, folks. This thread is for discussing whether there is a cycle, and if so, what causes it.

At the moment, I'm only looking at the statistics of it, I really have no idea why there seems to be such a pattern.

[viddaloo]

The following plot shows NSIDC extent data from 2000, with a lagging 365 day running mean applied from 30/12/2000, the five year periods 2007 to 2011 and 2012 onwards are shown in different colours.

I'm assuming some sort of regime change in the pack ice around the time iPhone was first introduced, a new level of ice loss, hence the start of the first cycle in 2007. I've laid out in previous posts that the descent that ended in the 2007 minimum record lasted 70 months and started as early as 2002, so I'm not ignoring the past. In fact, one of my main points has been that yearly mean descents are very long–lasting, and that we can expect a 1000 days when it finally gets going. Per 2002 to 2007, of course, way more than 1000 days.

Until 2007, it was unheard of for walruses to leave the sea ice for dry land for prolonged periods of time. But the retreat of sea ice has seen “drastic changes” in behaviour, Jay said. Walruses have struck out for beaches in six of the last eight years.

I DO think that a 365 day average of the data is a very excellent idea. [...] At any rate, removing the seasonal component in the data is, imho, an excellent idea.

Thanks, idunno, I thought so, too!

We'll see what applications can be built from that starting point. A sort of half–reliable prediction of a record minimum one year in advance seemed too cool to NOT try

That's a completely reasonable looking 2015. Let's see how it goes!

Maybe too reasonable?! Unfortunately, there was an error in my equation, producing the smooth 2015 graph I posted yesterday. It looked so right and reasonable that I didn't bother to control the calculations made by the script.

In real life, it's more of a bumpy ride, I'm afraid. Some of the drops and gains imposed by the yearly mean cyclic model are impossible for the ice to carry out in the real world. You can get a general idea, though, from this graph:

[crandles]

This seems to show some similarity of pattern.

Here is PIOMAS 365 day trailing average shown similarly:

Piomas5yearcycle by crandles2011, on Flickr

This is nowhere near as much of a pattern match. If it was the other way around that PIOMAS showed a similar pattern but extent less so, then I might be more inclined to believe there is a possible pattern to watch out for.

Don't think we are in a position to conclude the extent pattern match is not just random chance:

You could try to characterise the shape as having 2 three way choices: Firstly change over year being increase, decrease or similar. Secondly is there a hump, trough or nothing much in the middle of the year compared to the general trend of the year. If with 3 years of overlap, all 6 features matched would this be a 1 in 3^6 (1 in 729) chance of happening by chance? I don't think so. There is the choice of how many years before the cycle repeats so the first year is bound to match or we wouldn't be doing this analysis. So forget first year. Second year does have increase over the year but 2013 has a dip relative to that which 2008 didn't. 2010 and 2014 look fairly similar so far but it is possible that the decline over the year will be larger than the extent decline of 2012. Therefore to say 3 out of 4 1 in 3 chances appears to me to be pushing it and there is a 9.8% chance of that happening by chance. So I don't think we can rule out the similarities just being chance.


BTW the red and blue vary in distance between each other but end with the gap about the same. Why does the orange '5 year cycle prognosis' line then decline at a faster rate than the blue line to about double the size of the gap? Shouldn't it follow the blue line?

[viddaloo]

Thanks, crandles, I'll be making a similar 5-year view when(**) the PIOMAS data arrives. PIOMAS was where this thing started, by the way, and I checked out the possible extent similarity to this pattern only in frustration that the volume data wasn't daily, but monthly. I was amazed to find the same pattern in the extent data.

PS: I guess the answer to your question about the increasing gap, is that the gap has been increasing for about a year now, and that I've built this into the prognosis. So the Cycle is the basis of the prognosis, but realism and basis in the data means the gap will grow. The starting point of the prognosis will always be the latest day of data, so if the gap was to decrease in the observations, that would also propagate down into the prognosis period.

** Make that an IF, not a When. Issues over at NCEP continue to be uncertain, and no official date (or explanation) has yet been given for a return of the input data for the PIOMAS model.

[viddaloo]

I guess the big gap is interesting whether or not you believe the 5-year cycle to be real? Note how the 2012-2016 curve is consistently lower than the 2007-2011 curve, and how that implies that any prolonged descent from this starting point - comparable to the 2009-2011 descent - is likely to end up very, very low. And being very low in average ice extent means pretty big chances of a total meltdown  in Autumn.

In this way, making these 5-year cycle graphs is a bit like making 5-year average Autumn minimum plots or decade average plots for the Autumn minimum, in that you clearly see the steady and relentless decline as time goes by. The seasonal wave-shape element kind of clouds this insight, and the clarity disappears, as seasonal variations are so overwhelming compared to the tiny ups and downs of each year in that wavy seasonal curve.

I'm sure improvements and variations can be made. For instance, you could make a plot where each year starts on zero on January 1st, "forgetting" the extent level that the previous year delivered to it. That way you might see even more clearly how each new year performs, if it melts or builds ice, relative to the other years.

That said, I still "believe" the 2014 to 2016 descent will be dramatic and widen the gap even more to the 2009 to 2011 descent. Close-up views of this descent compared to 5 years ago is something I want to make later in the month, once certain hardware issues are resolved.

[viddaloo]

Yearly Mean Volume is up 3.8 km³/day, up 27 km³/week and up 122 km³/month per September 30th. This means no yearly average descent has started yet for ice volume, even though daily deltas are trending towards zero.

Yearly Mean Extent is down 985 km²/day, down 4677 km²/week and down 1954 km²/month. Daily deltas for extent are also trending downwards, meaning more negative, increasing the size of the descent.

[viddaloo]

At 1054 km² down on October 8th, the yearly mean extent is for the first time breaking the 1000 km² per day limit during this descent. Following the Big Descent closely, it will be exciting to see how big these daily drops will get, as we go further down the 1000 day slope.

Yearly Mean Extent is down 1054 km²/day, down 5111 km²/week and down 3461 km²/month. Daily deltas for extent are still trending downwards, meaning towards more negative daily deltas, increasing the size and speed of the descent.

[viddaloo]

I've added the very first 1000–Day Descent in the IJIS data series, so that the graph now covers all the data in IJIS. (Half the first year, 2002, has only -9999 error values, and so you need a whole year of real values after that before you can get a yearly average value.)

Looks like we're in for the Big Melt, folks! I am pretty sure this is the first time in recorded history that A MILLION km² disappears from the average in one single melt/descent period.

[crandles]

Don't you think that makes that widening gap look even more unlikely?

The red to orange gap looks to start and end at about 0.3. The gap goes narrower, wider, narrower then wider again. Why would you think the last wider again is the only pattern to follow? That makes no sense to me (and smells of inappropriate cherry picking a short period to give the result you want to me).

(Also why start the blue line half way through the second year?)

[viddaloo]

Don't you think that makes that widening gap look even more unlikely?

The red to orange gap looks to start and end at about 0.3. The gap goes narrower, wider, narrower then wider again. Why would you think the last wider again is the only pattern to follow? That makes no sense to me (and smells of inappropriate cherry picking a short period to give the result you want to me).

As I've already explained that, I am more than happy to repeat (paste):

«I guess the answer to your question about the increasing gap, is that the gap has been increasing for about a year now, and that I've built this into the prognosis. So the Cycle is the basis of the prognosis, but realism and basis in the data means the gap will grow. The starting point of the prognosis will always be the latest day of data, so if the gap was to decrease in the observations, that would also propagate down into the prognosis period.»

(Also why start the blue line half way through the second year?)

As I've already explained that, too, I am more than happy to repeat (paste):

«(Half the first year, 2002, has only -9999 error values, and so you need a whole year of real values after that before you can get a yearly average value.)»

[crandles]

(Also why start the blue line half way through the second year?)

As I've already explained that, too, I am more than happy to repeat (paste):

«(Half the first year, 2002, has only -9999 error values, and so you need a whole year of real values after that before you can get a yearly average value.)»

Sorry missed that.

(You could use NSIDC
ftp://sidads.colorado.edu/DATASETS/NOAA/G02135/north/daily/data/ )

Don't you think that makes that widening gap look even more unlikely?

As I've already explained that, I am more than happy to repeat (paste):

I had seen that explanation, but didn't think your explanation was adequate and thought the extra blue line made the criticism even more obvious and worth repeating.

Why use 'last year' when you can use last 3 years? Using just 1 year is likely to be open to causing large spurious trend, when using 3 years would be much less susceptible to such a problem.

Alternately use average of red and blue lines' movements would also seem a sensible possibility given the way they stay pretty parallel.

[viddaloo]

I had seen that explanation, but didn't think your explanation was adequate and thought the extra blue line made the criticism even more obvious and worth repeating.

Why use 'last year' when you can use last 3 years? Using just 1 year is likely to be open to causing large spurious trend, when using 3 years would be much less susceptible to such a problem.

Alternately use average of red and blue lines' movements would also seem a sensible possibility given the way they stay pretty parallel.

I assumed that in your world an extra thousand days repeating the same pattern would increase the criticism and make the 5–Year Cycle hypothesis seem more unlikely. I think this may be another issue where you and I should rather agree to disagree, instead of trying to explain to each other why 1000 extra days is more/less reaffirming. The other thing of course being the utter unlikeliness of any more sea ice ever melting again in the future, compared to 2010-2012. We obviously come from differing traditions of thought and logic.

For the "1000–Day Forecast" I think we'll just wait it out and see what happens. It could be accurate or less accurate. So far it's been overwhelmingly successful and over-performing compared to the initial prognosis. I expect it to turn the other way and narrow the gap, too, at some point. It will be exciting to follow as we go into 2015 and 2016!

[viddaloo]

For the record: I expect Yearly Average Extent to drop for a long time, about a 1000 days, I don't expect 2015–2019 to be an exact replica of 2010–2014. I'm also ready to throw the whole Five Year Cycle hypothesis in the bin the minute someone can show me a more plausible 5–year outlook.

The fact that 2012 followed 5 years after 2007, and that 2008–2010 YAE was higher than 2007 YAE and 2013-2014 YAE higher than 2012 YAE may be random, but 2007 and 2012 are the only such events in the IJIS series.

I'd say we could just as likely have an 07/12 event in 2016 as in 2017, but for now we only have 2 such events, and the years after them seem to follow in some sort of 'after–shock'.

What causes the whole system to leave an all–time low YAE in 2006 to go to a new low in 2007 and then higher than 2006 in 2008 and 2009 before ending up roughly equal to 2006 in 2010, would be fun to hear thoughts about. To a complete amateur it seems like the 'price' of having a record year like 2007 is 'three steps back', as in one step forward and three steps back, but that 2011 ends up much lower than 2006 in YAE, before the whole pattern starts over.

However, I'm assuming that as we go so low as the 5–Year Cycle Prognosis for 2015 indicates, there will be a change in patterns. Something will break, and I'm thinking of another extreme melt event, as 2015 YAE will be the lowest we've been ever.

[viddaloo]

Some day during October or November I'm expecting a drop to start even in Yearly Average Volume — it usually follows extent for most years — but 2014 is NOT like most years.

Will be exciting to see in 2 weeks.

[viddaloo]

Here is PIOMAS 365 day trailing average shown similarly:

This plot is more complete for Average Volume:



Data points for October are of course estimated values.

[Rubikscube]

What causes the whole system to leave an all–time low YAE in 2006 to go to a new low in 2007 and then higher than 2006 in 2008 and 2009 before ending up roughly equal to 2006 in 2010, would be fun to hear thoughts about.

This effect is most certainly caused by the low winter extent in 2006 and 2007. Why 2006 in particular had such a low extent throughout the entire winter is not easy to answer, and it might perhaps be random. Extent in Bering can be PDO related, which may explain some of the recent rebound in winter extent, but this rebound is also partly caused by Baffin/Newfoundland. It might be a little bit far fetched to relate that region's winter extent to increased freshwater runoff from glaciers (both CAA and Greenland), I don't know how much difference it could really make.

[viddaloo]

Thanks, Rubik. I'm thinking of it in terms of "sustained decline, only broken by 2007+2 years and 2012+2 year". Sounds silly, but it's the best way I can put it right now:



I see 2006 as low because it follows 2005, 2004, 2003 which are all going fast downhill. Then 2007 breaks every record the year after. But the dramatic way in which this 2007 thing happens, causes 2008 and 2009 to go way back up again (higher than 4 years ago, but not higher than 5 years ago).

I wouldn't be as curious to find out what part of the 2007 event that causes the 2008/09 rebound, if it wasn't for the fact that we see a similar thing happen with 2012 and 2013/14.

I would say the 5 years between 2007 and 2012 is random, but my gut feeling says the 2 following rebound years are caused by the sharp drops (and/or the whole 4–year decline that ends with 2007/12).

As a total amateur on the physical side of things, I'm only guessing what the causes may be, for instance the Beaufort Gyre changing direction, so I definitely need everyone's help here! 

[viddaloo]

New plot using all the yearly averages you can get from the PIOMAS series.

[viddaloo]

A little intro to my (admittedly) *speculative* 5–Year Cycle prognosis:

The 5YC prognosis assumes that the delta between the attached gap in annual extent and the corresponding gap 5 years ago, stays the same for the rest of the 5–year period (end 2016).

Yesterday, the 2014/13 gap was 85152 km², and a corresponding gap ~5 years ago will not be this big until June 6th, according to the script, meaning we're 196 days 'ahead of schedule'.

Another way of putting this is to say that we're losing sea ice extent much faster in 2014 than we did 5 years ago.

[jdallen]

New plot using all the yearly averages you can get from the PIOMAS series.

Quick thought - yearly annual volume does strike me as a good reflection of system enthalpy and the annual arctic heat budget.

[viddaloo]

It is, but the difference from volume (attached) to extent (see above) kind of suggests we're looking at a different heat budget for the CAB from that of the Southern oceans.

[jdallen]

It is, but the difference from volume (attached) to extent (see above) kind of suggests we're looking at a different heat budget for the CAB from that of the Southern oceans.

Without question, for reasons both orbital and topographic.  The orbital effect is to make southern hemisphere summers slightly warmer, and southern hemisphere winters slightly cooler.

The additional twist is in the fact that the south pole is a land mass surrounded by water, whereas the north is water surrounded by land mass.  The permanent ice on the south pole, combined with the isolation provided by stronger circumpolar circulation pretty much guarantees less heat will be taken up during summer.

[viddaloo]

It is, but the difference from volume (attached) to extent (see above) kind of suggests we're looking at a different heat budget for the CAB from that of the Southern oceans.

Without question, for reasons both orbital and topographic.  The orbital effect is to make southern hemisphere summers slightly warmer, and southern hemisphere winters slightly cooler.

The additional twist is in the fact that the south pole is a land mass surrounded by water, whereas the north is water surrounded by land mass.  The permanent ice on the south pole, combined with the isolation provided by stronger circumpolar circulation pretty much guarantees less heat will be taken up during summer.

Umm, let me rephrase that: It is, but the difference from volume (attached) to extent (see above) kind of suggests we're looking at a different heat budget for the CAB from that of the Southern Arctic oceans.

[jdallen]

It is, but the difference from volume (attached) to extent (see above) kind of suggests we're looking at a different heat budget for the CAB from that of the Southern oceans.

Without question, for reasons both orbital and topographic.  The orbital effect is to make southern hemisphere summers slightly warmer, and southern hemisphere winters slightly cooler.

The additional twist is in the fact that the south pole is a land mass surrounded by water, whereas the north is water surrounded by land mass.  The permanent ice on the south pole, combined with the isolation provided by stronger circumpolar circulation pretty much guarantees less heat will be taken up during summer.

Umm, let me rephrase that: It is, but the difference from volume (attached) to extent (see above) kind of suggests we're looking at a different heat budget for the CAB from that of the Southern Arctic oceans.

AH!, yes, that makes a considerable difference 

I'll need to ponder that a bit.

[viddaloo]

Umm, let me rephrase that: It is, but the difference from volume (attached) to extent (see above) kind of suggests we're looking at a different heat budget for the CAB from that of the Southern Arctic oceans.

AH!, yes, that makes a considerable difference 

I'll need to ponder that a bit.

Please do. Compared to 5 years ago, this gap is as big as it was on April 25th — meaning average volume is 213 days 'late'. While average extent has a gap the size of June 8th, 196 days 'early'.

It seems to me that not only is extent exceptionally early — meaning it disappears faster than expected — volume is also exceptionally late — meaning it probably has it coming — giving a total distance of 409 days between the two.

Some sort of leveling is to be expected, and with the exceptionally warm Southern Arctic oceans, I expect that leveling to happen mostly in the CAB.

[viddaloo]

Annual volume gap to last year is now +881 km³, similar to April 29 five years ago +217 days.
Annual extent gap is –96015 km², similar to June 13 four years ago –193 days.

With a 410 day diff between volume and extent, this means the annual average volume gap is contributing the most to the growing diff, while the negative extent gap is narrowing, in terms of days. You could say the extent anomaly is being normalized, which is also supported by extent being up +60217 km² during December compared to the 2002—2013 average.

The annual average volume gap is getting smaller in terms of km³, but not as fast as five years ago, which is why it's up from 213 days a week ago to 217 yesterday.

[viddaloo]

I've reconsidered (based largely on feedback from this forum and new data from the Arctic) and made a new auto–zoom function for the annual average graphs. This means you are now zoomed straight to the center of the action, with yesterday always centered on the chart.

Among the features is an automatic choice of year for comparisons. These days the zoom chooses 2010, as the 2010 graph is both below 2014 in annual average volume, and above 2014 in annual average extent. This makes it ideal for visual comparisons, which is the focus here.

Theoretically, at least, the 'gold standard' year for comparisons could change every day, but it always stays the same for extent and volume: They choose the year closest to both of them in common. Also, in real life, it won't change very often, probably about once a year.

This also means I've ditched the old '5–year Cycle' thing for comparisons (yey!), as its merits were frankly limited. I'm hoping the new closer and more visual reference will make it easier to see how today's annual extent/volume is developing, and co–developing.

Currently, we have an average extent similar to that in 2010 + 43 days (Jan 16), and an average volume similar to Aug 10 2010 (116 days).

The extent gap is decreasing (by 1 day since yesterday) and the volume gap increasing (also by 1 day per day). The total diff between the two on the new 2010 scale is 159 days. If annual extent wasn't so low (because of quicker meltout in the periferal seas) and volume so high (because of slower melt in the CAB), you'd expect this diff to be about zero.

Other automatic features of the new graphs: They automatically include all the relevant years that are 'in the area' of the plot, not just the ones I remember! For instance, 2006 is featuring strong on the extent graph, soon to morph into record–breaking 2007.

The lines are also automatically coloured through the Google Charts scheme, meaning orange is 3rd lowest, green 4th, purple 5th etc, even though the bottom 2 years are still not in our zoomed view at this moment.

And besides, all the tags and annotations are also added automatically and driven by the data (that goes for chart heading as well — nothing is written by hand or manually).

Basically, the width or horizontal scope of the graph is determined by the gap between the current year and the 'gold standard' year, in our case 2010, so that the day it levels with the current year is always in view. Vertical scope is also determined by these two years that are being compared, and all other years are just shown simply because they are 'in the area'.

It was fun coding it! Hope you will enjoy the new posting series, too

[viddaloo]

Great (and sufficiently clear for my use) comment and questions, Peter.

I don't know why many of you assume such things. IMO none of you have explained this sufficiently. In 2013 you had 365 days. Each of those days had their total ice volume figure. Add day 1 + day 2 ... + day 365 into a year total and divide by 365. Et voila!

Yes, but you are then projecting that forward, and you need to be clear in your own mind (and in your posts) about what that projection entails. When you predict that (say) 2020 will be 3.5x10^6 km^3 lower than 2015, how is that actually playing out in terms of day to day volume?

As the Roadmap shows we're at about 15.2 thousand km³ yesterday, going to a 2020 3.5 million km³ lower will be a tough one. Frankly, I don't think it's physically possible, as that would entail huge areas with thousands of km³ of negative packice! 

(OK, that was the humorous short answer — I will return with a longer and serious one tonight.)

[Peter Ellis]

Sorry, I had millions instead of thousands.

Since the summer minimum is of the order of a few thousand, then lowering everything by (say) three thousand across the board is possible, and corresponds to an ice-free summer.

However, lowering everything by 14 thousand across the board is not possible, since that corresponds to a summer volume of -10 thousand!  Ergo in order for the annual average to go down by 14 thousand (which is what you're projecting by 2031), then the summer and winter must both drop to zero - a loss of  a few thousand km^3 of summer ice and tens of thousands of km^3 of winter ice.

[crandles]

If your objection is about the trendline, then please suggest a different sort of trendline that you believe is more plausible, plus the reasoning behind this.

How about we start with reasoning rather than trendline. From Lindsay and Zhang 2004:


1. Preconditioning. During this period, 1948 to approximately 1989, warming winter air temperatures reduced the thickness of undeformed ice while the thickness of ridged ice increased. Undeformed ice is that which has thickened thermodynamically, as heat is lost through the ice to the atmosphere new ice grows on the underside of ice floes. Critical to this ice formation is the heat flux through the ice which is set by the temperature difference between the ice/ocean boundary at the underside of the ice (freezing point) and the temperature of the atmosphere at the ice surface, changes in atmospheric temperature dictate thermodynamic freezing. Ridged (or deformed) ice thickens as mechanical compression of ice causes the ice to buckle under compression and form ridges. So as the air warmed over this early period it reduced the thickening of ice over winter by reducing heat flux through the ice and reducing growth of new ice.

2. Trigger: (Approximately 1990 to 1995) During the 1990s the Arctic Oscillation and Pacific Decadal Oscillation lead to a shift in the strength and centre of action of the Beaufort Gyre, from 1990 this lead to larger amounts of open water in summer. Due to export of ice through the Fram Strait (as noted by other authors, e.g. Rigor et al) there is a large drop in deformed ice thickness as multi-year ice North of Greenland and the Canadian Arctic Archipelago (CAA) was reduced by large volumes exporting out of the Fram Strait. This period can be seen in the first graphic of this post as a succession of large interannual variations in NSIDC sea ice extent.

3. Feedback. (Approximately 1996 onwards) Following the thinning of the pack in the Preconditioning and Trigger phases, the stage was set for ice albedo feedback to take effect. Ice was thin enough such that in the marginal oceans summer thinning was able to open up more open water and lower concentrations of ice, allowing heat gain within the open water.

Other papers have then noted
4. Failure of 'Beaufort gyre flywheel'
This lead to larger areas of open waters in Chukchi and East Siberian Sea which set the stage for multi-year ice (MYI) to fail to survive passage around the Beaufort Gyre. This lead to both a rapid loss of MYI area and to thinning of the MYI towards just 2m thick.

5. 2008 to 2014 or a few years beyond.
The rapid loss of thick MYI above 2m has to come to an end as the volume of ice above 2m thick runs out. Even if an area ceases to be MYI the winter is cold and long enough for FYI nearly that thick to form each year. So the fast rate of loss during 1996 to 2007 starts to slow down. Instead of having both loss of thick MYI above 2m and slow decrease in thickness of FYI, the rate slows down to just the effect of slow decrease in thickness of FYI.

So there is some of the reasoning. This leads to a trendline that not only accelerates downwards (1996 - 2007) but also subsequently becomes less steep. (Something like graph I have previous posted.)

Maybe you would prefer a simpler story that allows you to construct and defend a trendline that just gets steeper. Unfortunately reality is likely to be a little more complicated.

[Unmex Chingon]

"If your objection is about the trendline, then please suggest a different sort of trendline that you believe is more plausible, plus the reasoning behind this."

I am by no means a mathematician thus can't give you a trendline.  However, I am a basic logical person.  As you say - humans make mistakes and I as well as you are human. 

I believe we are discussing ANNUAL average and not ONE day of ZERO Ice, correct?   Then it is my opinion that even IF there were 6 months of ZERO ice - there would be a winter refreeze.  If I were to follow your projection under this scenario:

I would have to ascertain what your model would have as the lowest amount of winter ice.
I would guess you would have Zero for summer ice.
Then combine these 2 to make a limit line above zero.

[viddaloo]

Sorry, I shouldn't have said anything. My mistake.