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Messages - Bill Fothergill

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Arctic sea ice / Re: The 2017 melting season
« on: July 15, 2017, 09:50:39 AM »
It was Lewis Fry Richardson who wrote...

Big whorls have little whorls
Which feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity.

... Lets honour the man with a chain limerick . Whos next? ...

Large floes break into lesser floes
Which increases their perimeter
It's like someone's taken the Arctic ice
And f***ed it with a scimitar

Arctic sea ice / Re: The 2017 melting season
« on: July 15, 2017, 01:18:37 AM »
I wonder what a 'fluid dynamics' knowledgeable person would say about those pretty swirls, and especially their opinion about any vertical mixing associated with them.

It was Lewis Fry Richardson who wrote...

Big whorls have little whorls
Which feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity.

... All this shite counts as extent. But not for long.

A wonderfully apt description. I was going to say something along the lines of "you took the words out of my mouth", but, given the context, I think I'll avoid that particular expression.

Shown below is a zoomed snapshot from NSIDC's 5-day Charctic as at 13th July. The date range covered is basically from  the 6th to 20th.

As mentioned upthread, the NSIDC daily value has dropped 516k in the last 3 days. However, it only dropped 131k over the previous 3 days. That means two of those "slow" days are still incorporated in the Charctic value for the 13th. Consequently, it is reasonable to expect that the gradient may well steepen - at least for the next couple of days.

Arctic sea ice / Re: IJIS
« on: July 13, 2017, 11:44:54 PM »
is the ijis data daily or is is one of these five day running mean finangles. interested in my pork pie prospects here! A man has to look to his food stock futures in this uncertain modern world! ;D

Actually it is neither, it is a rolling 2-day average. Here is a copy of the relevant descriptive text...

"Averaging period and the update timing of daily data : In general, sea-ice extent is defined as a temporal average of several days (e.g., five days) in order to eliminate calculation errors due to a lack of data (e.g., for traditional microwave sensors such as SMMR and SSM/I). However, we adopt the average of latest two days (day:N & day:N-1) to achieve rapid data release. Only for the processing of WindSat data (Oct. 4, 2011 to the present) the data of the day before yesterday (day:N-2) is also sometimes used to fill data gaps."

It is worthwhile taking the time to read the explanatory notes on this page...

Scroll down to beneath the graph, and there you will find the notes. The extract I pasted above is from the section marked "Method for calculating sea-ice extent".

Arctic sea ice / Re: The 2017 melting season
« on: July 13, 2017, 01:29:52 AM »
Thing is, it seems you and Bill are both missing one most simple fact of ice melting process: it accelerates much (with everything else being the same) when ice concentration drops below 50%.

Perhaps you didn't notice the bit where I said...
"The thinning (and warming) ice results in all sorts of f/b mechanisms (reduced structural integrity and mechanical strength, increased mixing with warmer water due to turbulence, wave action abrasion, loss of previously landfast MYI, greatly increased ease of transport to the killing zones, etc, etc)"

As regards the impact of GAC2012, it is worth having a look at the numbers. The first thing that should be noted is that this GAC really kicked off around August 5th, and, by that date, the NSIDC extent value was already about 300k lower than that clocked up on the equivalent 2007 date.

During 2007, the mean value of the NSIDC Sept dailies was about 1.8 million sq kms lower than the 5th August value. During 2012, the equivalent drop was 2.2 million sq kms - an increase of only around 400k.

Looking at the PIOMAS numbers for those two years can be more revealing. For 2007, the July and September average values were 12,119 kms^3 and 6,526 kms^3, giving a drop of 5,593 kms^3. The equivalent 2012 values were 9,264 kms^3 and 3,787 kms^3, giving a drop of 5,477 kms^3.

In other words, despite the effects of GAC2012, the volume drop from July to September (according to PIOMAS) was marginally less than that experienced during 2007.

I therefore think that, in order to achieve the kind of disastrous melt-out during the 2017 season that some people are anticipating, it is going to need more than just a couple of juiced up GACs .

I have appended some rough PIOMAS projections, the first using a 2nd-order polynomial trend line, and the other with a simple linear trend. It is worth having a look at when the various projections intersect the X-axis.

Arctic sea ice / Re: The 2017 melting season
« on: July 12, 2017, 11:04:20 AM »
Perhaps it's time to switch to a lower value bin (currently 4.0 - 4.5) in the poll for the Arctic SIE September average SIE. Quoting a well-known scientist speaking to the UK's Independent in an article dated 4th June...

"My prediction remains that the Arctic ice may well disappear, that is, have an area of less than one million square kilometres for September of this year,” he said.

“Even if the ice doesn’t completely disappear, it is very likely that this will be a record low year. I’m convinced it will be less than 3.4 million square kilometres [the current record low].

I think there’s a reasonable chance it could get down to a million this year and if it doesn’t do it this year, it will do it next year."

So there!

Oh, hang on a minute! That article was dated 4th June 2016.
Oh, hang on another minute! It's Peter Wadhams again!

For those readers relatively new to this topic, and therefore perhaps less familiar with the "extreme" views mooted by some of the Dramatis personæ, here is another early offering which refers to the "ice free by 2013" claim...

As there is currently only about 400k covering '07, '10, '11, '12, '13, '14, '16 & '17, a record low SIE is still certainly possible - especially in the light of last winter's lack of FDDs. However, I think the boat has well and truly sailed - at least as regards anything truly spectacular happening this year.

Although June SIE on its own has heretofore proven to have had little predictive skill as regards the annual minimum, I think that this will change one year soon. The thinning (and warming) ice results in all sorts of f/b mechanisms (reduced structural integrity and mechanical strength, increased mixing with warmer water due to turbulence, wave action abrasion, loss of previously landfast MYI, greatly increased ease of transport to the killing zones, etc, etc) and one year soon, we'll see a really low area/extent by the end of May. Given that peak insolation obviously coincides with the June solstice, that will be very bad news indeed.

There was one comment made by Prof Wadhams about a decade ago with which I have always been in total agreement...
"In the end, it will just melt away quite suddenly. It might not be as early as 2013 but it will be soon, much earlier than 2040."

The bit about "it will just melt away quite suddenly" is getting closer, but it's not going to be this year.

Arctic sea ice / Re: The 2017 melting season
« on: July 10, 2017, 04:15:04 PM »
The idea is that thickness at some point becomes so low that the influence of traditional factors (like wind, air temperature, insolation, etc) is irrelevant. When that happens across a large enough part of the ice pack, we'll have records, no matter what.

For the mechanism you talk about, i'm sure Arctic would need yet _much_ higher water temperatures during winter and spring.

I suspect that one of the mechanisms to which Neven alludes is the redistribution of "warm" water already present in the Arctic, but shielded from the under surface of the ice pack by the presence of the halocline.

The breakdown of this barrier gives yet another positive feedback mechanism.

A simple overview of this is given in Science Direct...

A far more detailed description is available here...

Arctic sea ice / Re: The 2017 melting season
« on: July 09, 2017, 06:30:59 PM »
However, if we only use data available until 2012 (forecast mode), the optimal formula changes a bit and the rebound of 2013 and 2014 is still reproduced, but not that accurately. Let me run the numbers and show you later.

Rob, correct me if I'm wrong, but I think you're using the published NSIDC September monthly averages as the "control" for your model. (As that's what the SIPN uses, I consider that to be reasonable assumption.  ;) )

A few days ago, during a dialogue with Neil on the ASIB, I posted an alternative set of results for the September average. Instead of using the NSIDC's much-criticised legacy technique of spatio-temporal averaging to derive the monthly value, the alternate approach is to simply use the arithmetic mean of the September daily values.

Unsurprisingly, the alternate version is consistently somewhat lower, but by a varying amount from year to year.

If you get bored one day, you might try a hindcast using this as a slightly modified control.

Col1=Year; Col2=published NSIDC Sept average, Col3=modified version, Col 4= difference
(All SIE values in millions of sq kms.)

1979      7.22      7.051    -0.169
1980      7.86      7.667    -0.193
1981      7.25      7.138    -0.112
1982      7.45      7.302    -0.148
1983      7.54      7.395    -0.145
1984      7.11      6.805    -0.305
1985      6.94      6.698    -0.242
1986      7.55      7.411    -0.139
1987      7.51      7.279    -0.231
1988      7.53      7.369    -0.161
1989      7.08      7.008    -0.072
1990      6.27      6.143    -0.127
1991      6.59      6.473    -0.117
1992      7.59      7.474    -0.116
1993      6.54      6.397    -0.143
1994      7.24      7.138    -0.102
1995      6.18      6.080    -0.100
1996      7.91      7.583    -0.327
1997      6.78      6.686    -0.094
1998      6.62      6.536    -0.084
1999      6.29      6.117    -0.173
2000      6.36      6.246    -0.114
2001      6.78      6.732    -0.048
2002      5.98      5.827    -0.153
2003      6.18      6.116    -0.064
2004      6.08      5.985    -0.096
2005      5.59      5.504    -0.086
2006      5.95      5.862    -0.088
2007      4.32      4.267    -0.053
2008      4.74      4.687    -0.053
2009      5.39      5.262    -0.128
2010      4.93      4.865    -0.065
2011      4.63      4.561    -0.069
2012      3.63      3.566    -0.064
2013      5.35      5.208    -0.142
2014      5.29      5.220    -0.070
2015      4.68      4.616    -0.064
2016      4.72      4.505    -0.215

It would be interesting to see if that significantly* affects the SD of the residuals. (* No pun intended, after a punishing 5 hours watching Le Tour de France, my brain could not dredge up an appropriate synonym.)

Arctic sea ice / Re: IJIS
« on: July 07, 2017, 10:08:03 AM »
It's pretty well documented that 1979 was about the "iciest" in recorded history for arctic ice extent-it was likely lower before that but the data is sparse.

"Pretty well documented"? Huh? And why is it "likely lower" prior to 1979? The Hadley dataset (top graph) shows both that 1979 was nothing special, and that sea ice has been declining since at least the mid-1950s. ...

@ Feeltheburn - As Jim P has already said, the meme that "It's pretty well documented that 1979 was about the "iciest" in recorded history for arctic ice extent" is, to say the least, highly questionable. (Except amongst those who regard the likes of Watts or Goddard as reliable sources.) It would be interesting if you could cite one, or more, of these "pretty well documented" sources.
(NB I am not in any way suggesting that you are a closet denier, merely that it would be interesting to learn how you came to that particular viewpoint.)

Here is an article on the NSIDC site which discusses pre-1979 data...

Here is a GRL article called "30-Year satellite record reveals contrasting Arctic and Antarctic decadal sea ice variability". As it was published in 2003, people can do the maths themselves.
{Oops, posted the same hyperlink twice by mistake!  :-[ }

Part of the 1979 meme is the erroneous claim that microwave study of the Arctic only began in that year. I would suggest that it can be instructive to check out the Nimbus-5 mission, especially part of the scientific payload known as ESMR.

Additionally, there is an ongoing project to digitize the thousand of photos taken during various NASA missions from the early-60's onward. There is an article on this buried somewhere in - I think - the NSIDC Icelights pages.

Arctic sea ice / Re: IJIS
« on: July 05, 2017, 01:05:44 PM »
It's a shame to see someone throw their money away on a zero-possibility bet.     ;)

Here's the arithmetic to which Greg and southseas were referring...

8th May 2017 equates to Day 128

add 8 weeks (56 days) gives Day 184, which is July 3rd

Arctic sea ice / Re: Latest PIOMAS update (July)
« on: July 04, 2017, 07:41:07 PM »
...t should be more than possible for 2017 to keep pace with 2012.

That seems almost a certainty at this point. Only 2014 had a small enough decrease from this date onward that a repeat would fail to set a new record; a repetition of the behavior of any and every other year on the record would see a new one. (FWIW, the average July through minimum melt of the last ten seasons would render a 2017 September minimum of 3.18 thousand km3, or nearly 500 km3 below the 2012 record.) ...

Thanks Jim - I'll be sure to sleep better tonight. ;)
(Although the beer at the local quiz will probably have a part to play as well.)

Arctic sea ice / Re: The 2017 melting season
« on: July 04, 2017, 07:34:21 PM »
... Extensive regions of the Arctic Ocean have been seasonally ice free for years; the low albedo season overlaps poorly with insolation season ...
I fear for what will happen when the planet fails to dodge that particular bullet, as I suspect it will be another irreversible* tipping point.
(* At least in terms of timescales comparable to civilisation as we know it.)

Arctic sea ice / Re: IJIS
« on: July 02, 2017, 05:53:56 PM »
I agree - data must be tested. "Question all assumptions " is always a good motto. However, the response was to a post that suggested that the data was bent through malicious intent. I felt that would not do.

Yep. I'm going to do a further response to what you and Shared Humanity were saying.

However, as I'm being dragged out for some beer to (belatedly) celebrate having dodged the coffin for yet another orbit of Sol, that must, perforce, wait until tomorrow.

Arctic sea ice / Re: IJIS
« on: July 02, 2017, 04:28:39 PM »
This is the thread on which is posted the numeric data from JAXA. "It is what it is". Elsewhere are images and data from images and weather / SSTs , volume etc on what is now and may be in the near future. From that one might make interpretations on the future.
But data is just data. It does not express an opinion. It just is.

By and large, I completely agree with that sentiment. However, there are instances when the data can either be in error, or can be subject to misuse/misinterpretation.

On 2017 Melting Season thread, there was a recent comment which indirectly alluded to this.
This means one has to trust intuition of people who work in the field, personally, - more than usual.
 and sadly we can never know for sure what kind of errors (or even worse - bias) data processing made by other people may have.

Whilst we are waiting for the IJIS/JAXA/ADS site to complete its maintenance run, it may be educational to look at a form of data error which appears on ADS Vishop Version 2.

On the right hand side of their Extent Graphs page, there is a Graph Option selector. One of the options displays a simple line chart showing the progression of the annual average SIE. (The minimum and maximum values for each year can also be displayed.)

The first pair of charts below show the annual average SIE for both the Arctic and the Antarctic as they appear on ADS Vishop Ver 2. Something that should literally jump off the screen - at least for anyone familiar with the data - is the anomalous spike seemingly occurring in 1987 for both hemispheres. (A downward spike for the Arctic, and an upward spike for the Antarctic.)

However, the second pair of charts comparing the ADS and NSIDC annual average SIE makes this even clearer. Although the absolute values from ADS tend to be several hundred thousand sq kms lower than those from the NSIDC, the inter-annual variations exhibited by both usually track each other with a high level of agreement - except for 1987. (And, to a much lesser extent - no pun intended - in the 1980 Antarctic data.)

The "discrepancy" in 1987 is, of course, partially explained by the switch from alternate day to daily recording during July of that year. This change to recording frequency immediately introduces a weighting bias in favour of data gathered in the second half of the year. As the second half of each year encompasses the Arctic minimum and the Antarctic maximum, the averages thus calculated become skewed. In each case, the situation is exacerbated by further spurious data drops in January, April and December.

In the case of the 1980 data example, there are 4 data drops (each covering 3 or 4 measurement periods) spread from January through to April.

Using a simple linear interpolation, a proxy was created for the the missing data and for the incorrectly weighted data and more realistic annual averages were created for 1987 (both hemispheres) and for the Antarctic only in 1980. (NB A similar correction could have been applied in the Arctic, and this would have resulted in a better tracking there as well. However, I only carried out this correction for the Antarctic as the unadjusted averages actually went in different directions.)

The third pair of charts show how the ADS and NSIDC annual average SIE numbers would compare following such a data-infill exercise. The infill causes the Arctic annual average figure to rise by around 1 million sq kms, whilst the Antarctic equivalent falls by nearly 2 million sq kms.

The moral, if there is one, is that we can check up on certain aspects of the data ourselves. It just takes a bit of understanding, and a little bit of effort.

Arctic sea ice / Re: IJIS
« on: July 02, 2017, 08:55:38 AM »
Ho hum, looks like there will be a little more twitching...

Arctic sea ice / Re: The 2017 melting season
« on: June 30, 2017, 09:34:01 AM »
Another 88K drop today.

Actually closer to 92K, but what's 4K amongst friends?   ;)

Arctic sea ice / Re: The 2017 melting season
« on: June 28, 2017, 11:58:21 AM »
... I am not sure what kind of information one can extract from the thawing dd...

TDDs represent just one factor amongst many that combine chaotically to determine in the incredibly complex annual melt process. The Polar Science Centre at Washington University has this to say on the matter...

It could just be my interpretation, but I suspect that the TDD concept has a much more direct bearing on permafrost than on sea ice, as evinced by this NSIDC article...

... In the presence of ice the surface itself can never get above freezing can it? So if it is possible for this number to be higher than that must  it not reflect the air temperature at some hight above the surface?...

As Andreas T has already stated, it is important to think in terms of a thermal gradient - not just within the ice, but in a sort of "boundary layer" extending both above and below the ice surfaces.

In winter, the coldest part of the ice will be virtually at its surface, with the warmest part being that in contact with the underlying ocean. During the melt season, the situation changes markedly, resulting in a temperature inversion happening such that the coldest part of the ice is near its core.

Whilst you are correct in saying that the temperature at the ice surface (either the air-ice or ocean-ice boundary) is effectively clamped to the freezing point during the melt season, the thermal gradient (which enables the energy transfer conduit) continues into these extended boundary layers.

Arctic sea ice / Re: The 2017 melting season
« on: June 22, 2017, 06:24:53 PM »
... solstice up north is not much more insolation than a winter sun in mid-latitudes ...

NASA (to name but one source) would disagree

Around the time of the boreal summer solstice, average daily insolation at the NP exceeds that at the equator. (This effect is even more pronounced in Antarctica at the austral summer solstice, as that occurs only about 2 weeks before perigee. There's about 5 million kms difference in Earth's distance from the Sun between perigee and apogee.)

Arctic sea ice / Re: IJIS
« on: June 21, 2017, 11:58:04 PM »
... But Jaxa and NSIDC just tell us the result of the calculation. Perhaps they need to highlight the standard error for us dumbos.

I know this is the IJIS thread, but here's what NSIDC have to say about this subject on their FAQ page...

Arctic sea ice / Re: IJIS
« on: June 21, 2017, 08:56:45 AM »
9,817,660 km2(June 20, 2017)and 4th lowest measured for the date.

For those who haven't accessed the .csv and are pining for June 19th's value...
 9,891,859 sq kms

That comes out as 3rd lowest for both dates on the spreadsheet I use. The discrepancy between rankings may be due to the fact that 2012 was a Leap Year, and hence the Day Number for June 20th would have been 172 in 2012, but just 171 this year.

The exact position is somewhat immaterial, as just 39k covers the June 20th values for 2010, 2011, 2012 & 2017.

Arctic sea ice / Re: IJIS
« on: June 13, 2017, 07:40:03 PM »

If you are unfamiliar with the subtleties of the IJIS (now ADS) data, there is one point you should be aware of. The values appearing on the ADS site (and on their downloadable .csv files) are actually 2-day rolling averages. Hence, the nominal (i.e displayed) value for 12th June is, in fact, the arithmetic average of the measured values taken for the 11th and 12th.

I don't think that's how it works. 

The AMSR-E orbital period is 99 minutes, and only part of the region is imaged on each pass. When they say they calculate extent based on 2 days' data, it means they calculate it by aggregating data from all the satellite passes in the preceding 48 hours. Within this time frame, some pixels will have been imaged many times, others only a few times.

It's not as simple as imaging everything once a day and then averaging two days together. It also means you CAN'T work backwards and try and reverse-derive daily values from the provided data set.

Hi Peter,

I was responding to a query by arctic-watcher at #4349 as to the provenance of the ADS (aka IJIS) data. As that was only the 5th posting by arctic-watcher, and following the old adage about "don't try to run before you can walk", I tried to answer at what I considered to be the most appropriate level.

I fully appreciate that orbital periods generally don't line up with any 24 hour period, and that the coverage swathe paths most certainly do not tessellate, but rather overlap in a seriously convoluted fashion.

However, please try the following thought experiment...

The data from (say) Hour 0 to Hour 48 gets aggregated and presented as the extent for (say) Day X. The following day, the data from Hour 24 to Hour 72 gets aggregated and is presented as the extent for Day (X+1). The data garnered during Hour 24 to Hour 48 is common to both days, and therefore has no impact on the delta between Day X and Day (X+1)

The only thing that differs between the two days is that the data from Hour 0 to Hour 24 has been replaced by the corresponding data from Hour 48 to Hour 72.

Surely this is analogous to what happens on the NSIDC rolling 5-day Charctic? The extent there on the 11th June was 11.297 million sq kms, and this dropped the following day to 11.219 million sq kms. Consequently, we have a delta of 78 thousand sq kms between the two days. The June 11 Charctic value is the arithmetic average of the single-day values obtained between June 7 and June 11, whereas the June 12 Charctic is the average of the June 8 to June 12 dailies. The daily values from June 8 to June 11 are common to both, and the difference is purely due to the replacement of the June 7 daily with the June 12 daily.

Moving to the NSIDC single day values, June 7th came in at 11.455 million sq kms, with the June 12th equivalent having dropped to 11.069 million sq kms. The delta is now 386 thousand sq kms, which, allowing for rounding error, is 5 times the difference between the June 11 and June 12 rolling 5-day averages.

Working backwards from the Charctic numbers, although it is not feasible to reverse-engineer the precise one day values (unless given a seed value to start with), it is a trivial exercise to calculate what the delta between (say) Day Z and Day (Z+5) must have been.

If the ADS data was presented in two formats - as a single day value and as an aggregated 2-day value - then the difference between Day X and Day (X+1) on the aggregated 2-day format would be one half of the difference between Day (X-1) and Day (X+1) on the single day format.

Arctic sea ice / Re: IJIS
« on: June 13, 2017, 11:33:54 AM »
... where are you finding that info. before Espen posts it?  thanks

Jim has already provided the appropriate link, and, as gerontocrat also says, it is easy to access.

That system is now running on Version 2, but, from time to time, I find it more convenient to go back to the earlier version, which is here...

If you are unfamiliar with the subtleties of the IJIS (now ADS) data, there is one point you should be aware of. The values appearing on the ADS site (and on their downloadable .csv files) are actually 2-day rolling averages. Hence, the nominal (i.e displayed) value for 12th June is, in fact, the arithmetic average of the measured values taken for the 11th and 12th.

Consequently, what appears to be the drop between the displayed values for the 11th and 12th is actually one half of the measured difference between the 10th and the 12th.

When you access the link to either Ver1 or Ver2, it is worth scrolling down in order to familiarise yourself with some of the background material provided.

Arctic sea ice / Re: Latest PIOMAS update (June)
« on: June 05, 2017, 04:21:25 PM »
... Good to see you again, A-Team.
Welcome back A-Team! :) Great to see you here again!

Ditto to the above sentiments

Arctic sea ice / Re: The 2017 melting season
« on: June 05, 2017, 04:15:00 PM »
...  anyone willing to comment in more detail on latest PIOMAS data? Or are you guys just speechless seing it? Things are bad...

See Neven's latest post (dated June 4th) on the ASIB.

Arctic sea ice / Re: IJIS
« on: May 18, 2017, 04:27:45 PM »

Is this the largest drop for the day of the year?

From March 15 to 16, -112k
From April 04 to 05, -101k

However, the NSIDC daily went up 8k between the 14th & 15th May, so it will be interesting to see what happens (in about 4 hours time) when their daily figures get updated.

In case you meant drops for May 16 from any year, then the biggest drop was -105k from 2012.

Oops.  :-[

Re-reading the original question, I think my interpretation was incorrect.

I thought the questioner asked if the drop of 90,700 sq kms had been the largest to date for this year.

mea culpa   :-[

Yes, and we are now 4th lowest for the date. Might catch up with 2006 by the next few days. 2015 is a different task, might take over the second place by the first week in June when SIE stalled in 2015.

Yep, two days of -60K sq kms would put 2017 fractionally below 2006.

However, today's NSIDC daily only dropped by four thousand sq kms.

Arctic sea ice / Re: IJIS
« on: May 17, 2017, 10:00:07 AM »

Is this the largest drop for the day of the year?

From March 15 to 16, -112k
From April 04 to 05, -101k

However, the NSIDC daily went up 8k between the 14th & 15th May, so it will be interesting to see what happens (in about 4 hours time) when their daily figures get updated.

Consequences / Re: Global Surface Air Temperatures
« on: May 16, 2017, 12:20:06 AM »
... I don't think we should be surprised to see borderline El Niño conditions by late fall ...

As mentioned above, the April 2017 value was just 0.01o C below the equivalent value from 2010. However, the Nino3.4 Region values for the two years tell a completely different story.

Using NOAA's rolling 3-month threshold of +0.5o C, el Nino conditions held from JJA 2009 through to MAM 2010. On the other hand, after spending 8 months in negative territory (including a weak la Nina from JAS 2016 till NDJ) the 2017 FMA figure has just crept into positive territory.

It doesn't bode well.

Arctic sea ice / Re: IJIS
« on: May 15, 2017, 09:54:26 PM »
As there is not a great deal of movement on the IJIS/JAXA/ADS daily numbers at the moment, I thought I would re-post an updated version of the rolling-365 day average SIE chart which was posted near the end of January.

Three features of the data are readily apparent in the chart...

1) there is an unambiguous overall downward trend in annual average sea ice extent;

2) there is the appearance of an approximately 5-year cycle superimposed on the longer downward trend, and;

3) the downward spiral has recently been halted, albeit for what could be a brief period. (N.B. Once the data for the 16th, or possibly 17th, of May is at hand, the rolling average will be at its highest level since the end of 2016.)

The reasons behind points (1) and (3) are pretty straightforward, and therefore will be addressed first.

To all bar the inhabitants of Flatland, point (1) is clearly the direct consequence of the planetary energy imbalance due to the ~ 100ppm(v) rise in atmospheric CO2 levels since Charles Keeling started tracking these values nearly 60 years ago.

The current slight rise in the curve - point (3) - can be characterised as noise, but it is nonetheless possible to explain this in part. When any rolling 365-day average value is plotted, the "instantaneous" gradient of the curve is determined by a very simple inequality. Except for the vanishingly remote chance of Day X in any year having exactly the same value as Day X of the previous year, the inequality can exist in either of two, mutually exclusive, forms...

Day X(Year N) > Day X(Year N-1),
Day X(Year N) < Day X(Year N-1)

Whenever the Day X(Year N-1) value represents a genuine statistical outlier, then it is axiomatic that the Day X(Year N) value is generally likely to be less extreme, in other words, it is likely to demonstrate regression toward the mean.

That is exactly the situation we are seeing at present, and are going to be seeing for some time to come. When I did a snapshot on May 11th, this is what the rolling-365 day average would be seeing over the next 12 months...

181 days in which the Day X(Year N-1) value was the lowest on record
76 days in which the Day X(Year N-1) value was the 2nd lowest on record
72 days in which the Day X(Year N-1) value was the 3rd lowest on record

(NB Obviously the likelihood of regression to the mean taking place is affected by any developments in the shape of the overall trend.)

Graph 1 & 2 (below) are a matching pair which only differ in the Y-axis; the first shows the actual value of the rolling 365-day average extent, whilst its partner shows this as an anomaly from the Jan 2006 - December 2015 mean.

Graph 3 (bar chart) puts the above into a bit more context by also including overall means for the 1980's, 1990's, 2000's and 2010-2016. Column 5 shows the highest value for the rolling average attained over the last decade, and the remaining columns show the local minima recorded at the turning points in the first 2 graphs.

Moving onto point (2) - the putative approximately 5-year cycle superimposed upon the overall declining trend in sea ice extent. This is a topic that has been (and is being) discussed on the ASIB. My own view - for what little that is worth - was that the period under examination was far too short to determine if this was a genuine recurring pattern.

Given the current lack of activity in SIE numbers, I downloaded the .csv file from the ADS version 2 site - as this starts from 1979, rather than 2003 as per ADS version 1 - with the intention of extending the chart back by about 25 years. However, owing to the number of data drops during the early stages (and the fact that daily measurements  only began during 1987) it was easier to use the NSIDC monthly values as a reasonable proxy.

This is shown on graph 4, and, to my surprise, with the data stretched back to ~ 1980, there is still some semblance of a recurring pattern.

Given the approximately 5 year periodicity of this possibly cyclic phenomenon, it seemed like an idea to map - for starters - the Nino 3.4 anomalies. As with the SIE data, this was smoothed to give a rolling 12-month average, and was then lagged by 6, 12, 18, 24 and 30 month periods. This is shown as graph 5.

The Nino anomaly values are shown on a secondary Y-axis which has been inverted to display +ve anomalies as downward pointing excursions. It was hoped that by implementing this inversion, dips in the SIE might line up with el Nino events, but any such correlation escapes my Mk I eyeball. (Although, following the successful operation last year, I should perhaps call it a Mk II?)

Whilst graph 5 singularly fails to demonstrate any obvious correlation between el Nino/la Nina patterns and sea ice extent behaviour, it's been included in the hope that it may, nonetheless, give an idea to someone. Hopefully, at least two of the regular contributors to the ASIB might have some words offer, as we have differing views on the subject.

Arctic sea ice / Re: IJIS
« on: May 15, 2017, 05:12:40 PM »
Some decent drops the last two days but we are still 6th lowest and a whooping 800K behind 2016... Even 2004 had lower extent at this date of year.

2016 isn't a concern, if you ask me; given 2016's very low June decrease and the state of this year's ice, that 800k extent gap will disappear within the next 5-6 weeks. (Between May 31 and June 15, last year dropped by just 541k km2, while 2012 lost an amazing 1.347M--a "gap closing" of over 800k.)

My hunch is that 2017 will spend most of July and August in either first or second place.

Although 2017 might be currently "languishing" in 6th lowest position, when the data for May 14th gets factored in, the current SIE is only ~ 90k sq kms higher than the 3rd lowest for the date (2006), and ~ 180k sq kms higher than that recorded in 2015, which is the 2nd lowest for the date.

As at May 14, and just considering the period stretching from 2004 until now, 2012 has the 2nd highest SIE for the date in the IJIS/ADS database - and I think we all know what happened a bit later in that year.

Arctic sea ice / Re: IJIS
« on: May 11, 2017, 07:21:44 PM »
UPTICK in May?! :o How unusual is that?

There are a handful in the record. 2004 had a two day uptick of 19664 and 8586 on May 25 and 26.  There are a sprinkling of others but they are pretty rare.

As dnem said, May upticks are rare. I happen to have a spreadsheet based on the ADS Version 1 .csv (basically, this is from 2003 onwards) already set up to shown daily increments, and this reveals some even later upticks...

04 June 2016: +3,537
08 June 2015: +1,662
30 July  2013: +4,102

There are 4 more near the end of August, and then the colour scheme starts transitioning from red to black.

Arctic sea ice / Re: The 2017 melting season
« on: May 09, 2017, 12:47:01 PM »
I think I am going to move this to a separate thread
- The energy for raising 1.8 degrees 30 m of water is equivalent to that needed for bottom-melting approximately 0.75 m of ice!!!! (since raising 1C of a 80m-deep extent of water requires the same energy to melt 1m of the same extent of ice)

NB I will move my comment over to the appropriate thread once you have set it up.

I was going to mention that the density of ice is less than that of water, but you appear to have already included that in order to get to the 0.75 metre value.

(30/80) * 1.8 would just give 0.675 metres, but if the (relative) density was taken as ~ 0.9, that would give your figure of 0.75 metres.

I think your x80 multiplier would only be appropriate for fresh water. The SH of sea water varies somewhat with salinity, but is roughly 3.985, as opposed to the 4.186 value for pure water. {I am assuming you are using a value of around 333.5 as the enthalpy of fusion?}

However, that only represents a difference of ~ 5%, so it doesn't really help much in answering the question you raised.

Consequences / Re: Global Surface Air Temperatures
« on: May 06, 2017, 01:37:58 AM »
HadCrut annual comes with an estimated 2017 value, with a confidence range.

Top three stuff, new record possible.

Interesting that the very provisional "predicted" year-end value for HadCRUT is currently showing as the 4th consecutive record year...

2014 +0.575o C
2015 +0.760o C
2016 +0.773o C
2017 +0.820o C

As each of the three monthly anomaly values so far this year (+0.740o C ; +0.847o C ; +0.876o C ) was considerably cooler than the equivalent value(s) from 2016 (+0.906o C ; +1.070o C ; +1.069o C ), for this "projection/prediction" to be realised, the remainder of the year could get interesting.

To equal the 2016 temperature anomaly, the remaining 9 months of the year would need to average about 0.065o C warmer than that clocked up for April - December 2016 (which was ~ +0.694o C).

To get to the "predicted" value, the April - December average for this year would need to be about 0.125o C warmer than the equivalent from last year.

I would expect that the teams from the Met Office and the CRU are looking at the ENSO figures with some interest. NOAA figures put the July - December 2016 average anomaly in the 3.4 region at -0.71o C, but the Mar-April average this year is +0.3o C, and there currently seems to be about a 50% chance that an el Nino could develop later this year. (Although one would certainly expect some lag in the relationship.)

Consequences / Re: Global Surface Air Temperatures
« on: May 04, 2017, 01:20:55 AM »
Amidst the above talk about April, the UK Met Office and the University of East Anglia have finally managed to publish the March HadCRUT numbers. Coming in at +0.876o C, this was the 2nd warmest March and the 6th warmest of any month in the dataset.

The top 20 are...

1998/02   0.761   0.638   0.880   13
2007/01   0.834   0.692   0.981   10
2015/05   0.707   0.548   0.866   20
2015/06   0.740   0.594   0.886   14
2015/08   0.738   0.511   0.965   16
2015/09   0.792   0.599   0.986   11
2015/10   0.837   0.703   0.976   8
2015/11   0.836   0.720   0.955   9
2015/12   1.024   0.893   1.151   3
2016/01   0.906   0.753   1.061   5
2016/02   1.070   0.938   1.200   1
2016/03   1.069   0.923   1.208   2
2016/04   0.915   0.771   1.059   4
2016/06   0.731   0.585   0.877   17
2016/07   0.728   0.542   0.919   18
2016/08   0.770   0.549   0.994   12
2016/09   0.711   0.516   0.906   19
2017/01   0.740   0.577   0.906   14
2017/02   0.847   0.716   0.977   7
2017/03   0.876   0.733   1.018   6

Col 1 = Date; Col 2 = Anomaly, Cols 3 & 4 = Lower and Upper 95% Conf Range; Col 5 = Rank

One does not need to be excessively eagle-eyed to notice that 18 of these are from within the most recent 24 months.

Rather worryingly, things continue to warm up in the Nino 3.4 Region. The latest NOAA numbers are..

2016  11   25.96   26.88   -0.93
2016  12   26.08   26.80   -0.72
2017  01   26.24   26.61   -0.37
2017  02   26.63   26.80   -0.17
2017  03   27.49   27.32    0.17
2017  04   28.29   27.86    0.43

Cols 1 & 2 = Date; Col 3 = Actual Temp; Col 4 = Climatology; Col 5 = Anomaly

That's shaping up for the >= +0.5o C threshold for el Nino conditions by the end of May, although it would need to reach at least +0.75o C for the more meaningful rolling 3-month figure to reach the threshold. (N.B. Strictly speaking, the May value should need to reach +0.9o C, but, as NOAA only go down to the first decimal point when talking about the 3-month figure, that +0.75o C would suffice when rounding is taken into consideration.)

However, even if the MAM value reaches +0.5o C, the earliest that NOAA would declare a full el Nino would be if the rolling 3 month value stayed above threshold until the JAS period, i.e. five consecutive rolling 3-month figures.

Arctic sea ice / Re: The 2017 melting season
« on: May 02, 2017, 01:45:20 PM »
The NSIDC daily figures have just come in, and they show a rather abrupt loss of ~ 259k sq kms between 30th April and 1st May.

Is this a "1st of the month" effect?

Is it merely a form of "correction" caused by cells dropping out of the >15% threshold, after only losing ~100k over the last 8 or 9 days?

Or is Mr S*%t meeting Mr Fan?

Arctic sea ice / Re: IJIS
« on: May 02, 2017, 01:02:19 PM »
I suspect some rapid melt in the next 7 days around greenland

temps well over 0c forecast

Same as i, because not only of temp, also on thickness:

It will be interesting to see if this anticipated melting is sufficient to keep 2017 in amongst the "lowest 3 for the day" values.

Here is a variant on Deeenngee's chart at #4178, with data up to, and including, the 1st May (i.e. Day 121).

Tips on interpretation;

Only years with around ~90 (or more) entries in the "lowest 3" are shown.

Generally, each year has 5 columns...
Col 1: status at end of 2015
Col 2: status at end of 2016
Col 3: maximum still possible by end of 2017
Col 4: positions already achieved thus far in 2017 (i.e. "locked")
Col 5: positions held last year between NOW and 31st Dec 2016 (i.e. "vulnerable")

Therefore difference between Col 1 & Col 2 equates to positions lost last year, and the difference between Col 2 & Col 3 equates to positions lost since 1st Jan 2017.

Arctic sea ice / Re: Latest PIOMAS update (April)
« on: May 02, 2017, 12:28:33 PM »
Thank you Bill. Much appreciated.
First thing I noticed is that you and Random_Weather agree.
Your correlation between PIOMAS April numbers and NSIDC September numbers is R=0.342, which gives R^2=0.117 which is exactly what Random_Weather reported (thank you for that scatter plot RW!).
So PIOMAS in April is not a good predictor of September SIE

I've said it before, and will doubtless say it again.. D'Oh!!!!  :-[

Sorry for being so slow guys.

Can I just point out that I never said April PIOMAS figures had great skill at predicting the September SIE. The question originally was along the lines of did early month PIOMAS have more skill than early month SIE.

As Rob and I both wrote articles on the ASIB a few years ago discussing how weak (i.e non-existent) the April:September SIE relationship was, the bar was set pretty low to start with.

However, I still think that the April PIOMAS: September SIE correlation can correctly be described as "significant, but weak". Given such a tenuous relationship, it would never occur to me to do a September prediction predicated solely upon a single variable - and certainly not one involving SIE.

Arctic sea ice / Re: IJIS
« on: May 01, 2017, 01:59:16 PM »
For those experiencing "cold turkey" whilst ADS is having a little rest...

After spending the 8 days (covering the 22nd to 29th April) languishing in the 13.4xx million sq kms range, the NSIDC single day value plummeted all the way to 13.395 on the 30th.  ;)

Arctic sea ice / Re: The 2017 melting season
« on: May 01, 2017, 11:39:49 AM »
... Not many bergs or floes here in NZ. ... We did have some giant Bergs visit about ten years ago. Larsen remnants I believe they were believed to be ...

It's OT for this thread, but there could be some more en route to a place near you in the not too distant future...,1175.0.html

Shrek's had a haircut?  :'(

Antarctica / Re: Rift in Larsen C
« on: May 01, 2017, 11:28:08 AM »
I noticed what looks like a warm foehn wind forecast for the 10th, blowing off the ice shelf. Maybe that will help things along?

Depends on how you are using the word "help".  ;)

See this BBC article (or possibly "antarcticle"?) on the Larsen C and the impact of the Foehn effect thereupon...

The BBC probably used this BAS press release as their source...

Other BAS articles on the Foehn effect can be found...

Arctic sea ice / Re: IJIS
« on: April 30, 2017, 01:23:25 AM »
... NSIDC charctic ...Is this 5-day average? ...

Yes Rot, Tot, Otr, Rto, Ort, Tro, Tor

What appears on the charctic is the rolling 5-day average of this daily data series...

(No prizes for guessing what you get if you change the "north" to "south", and the "N_seaice" to "S_seaice" in that url.)

The above url is also the source for Feeltheburn's correct statement that the value on 28th April is the 4th lowest for that date. One can easily pull out the 3 lower instances by using the browser's "Find" functionality.

To quickly highlight just the 28th April dates, search for "04,  28", then start searching bottom upwards. (NOTE: the search string needs two spaces between the comma and the 2)


Arctic sea ice / Re: Latest PIOMAS update (April)
« on: April 30, 2017, 12:54:25 AM »
I agree with the comment from dosibl that this is getting into a statistics discussion, rather than a PIOMAS discussion.

However, if I am making a mistake in the way I try to use the available statistical functions, then I would be more than happy to be educated in their correct use. (Although that is always a difficult task where I'm concerned   :o) .

Therefore, can I just ask why R_W and Jai are NOT using a function such as CORREL?

I am pretty familiar with using the Coefficient of Determination (ie the R2 value) when one plots a traditional dependent variable versus independent variable chart, such as the decline of the September SIE through time, or the rise in global temperature anomaly through time.

When one then adds a trend line, the resultant R2 gives a measure of the unexplained variance. My understanding (again, this is always questionable) is that the fraction of the variance left unexplained is generally treated as being equal to { 1 - R2 }

I don't understand (and, yet again, that could be all down to my lack of in-depth knowledge) why you are choosing to use this metric when plotting two sets of residuals, instead of using a function such as CORREL - especially when it seems that CORREL has been specifically designed to calculate the correlation coefficient between two data series.

Perhaps we can iron this out using the forum's Messages functionality, rather than clogging the thread?

Arctic sea ice / Re: Latest PIOMAS update (April)
« on: April 29, 2017, 06:19:50 PM »
Just for a giggle, I did a quick correlation analysis between the PIOMAS September residuals and the NSIDC SIE September residuals.

The correlation is also going down over the last 2 decades.

Jai, here are the numbers I get when running CORREL on the PIOMAS September residuals and the NSIDC SIE September residuals...

1979-1998 +0.714
1997-2016 +0.808

I then thought you may have meant that the coefficient might have been dropping in a "jerky" fashion, so I locked the start year as 1979 and incremented the finish year...

1998   +0.714
1999   +0.715
2000   +0.717
2001   +0.741
2002   +0.733
2003   +0.736
2004   +0.738
2005   +0.734
2006   +0.734
2007   +0.751
2008   +0.750
2009   +0.745
2010   +0.735
2011   +0.744
2012   +0.773
2013   +0.755
2014   +0.760
2015   +0.758
2016   +0.755

Of course, as as been demonstrated before, it's not unheard of for me to pair up the wrong two columns.

I'll check my homework  ;)

Arctic sea ice / Re: The 2017 melting season
« on: April 29, 2017, 05:09:57 PM »
You made me feel young (very young) again!  :)

All part of the service  :-[

Arctic sea ice / Re: Latest PIOMAS update (April)
« on: April 29, 2017, 05:06:59 PM »
To make clear, April Volume residuals not saying anything about extent residuals in september, here for 1979-2016

You have plotted April PIOMAS residuals against September NSIDC SIE residuals, but I'm not sure what physical reality this is meant to represent. If I was looking for some correlation between the two data series, I would use a function such as Excel's CORREL.

There are 38 data pairs in the 1979-2016 range. On 11 occasions, each member of the pair is negative, and on 14 occasions, each pair member is positive.

I know this is an artificial example, but try thinking in terms of tossing two coins, and getting either 2 heads{2H}, or 2 tails{2T}. Using the cumulative binomial distribution, the chances of only getting {1H + 1T} on 13 (or less) occasions is less than 1.7%

The fact that there is this degree of agreement demonstrates that there IS a positive correlation, and the p-value derived from the correlation coefficient and the number of Degrees of Freedom subsequently demonstrates the level of statistical significance.

If you consider the direction of the slope on your diagram, you will see that this actually corresponds to a preponderance of the data pairs being either, both negative, or, both positive.

Arctic sea ice / Re: Latest PIOMAS update (April)
« on: April 29, 2017, 03:22:06 PM »
Just for a giggle, I did a quick correlation analysis between the PIOMAS September residuals and the NSIDC SIE September residuals. The value thus obtained for the correlation coefficient was +0.755

That value would be significant at the 99.9% level (p-value < 0.001) had there been only 16 data pairs, rather than the actual number, which was 38. Had there even been only 7 data pairs, such a correlation coefficient would have been significant at the 95% level.

Arctic sea ice / Re: The 2017 melting season
« on: April 29, 2017, 02:15:38 PM »
TotTor, oren, Terry, Rob,  {Oops, just noticed the fat-finger syndrome}

I think there has been some gibbering in Flatland recently concerning the amount of ice around Newfoundland. One suspects that this is export related, and that any such ice is basically "dead man walking".
The ice around Newfoundland is almost certainly the result of collapsing glaciers not sea ice. Its one area where an increase in 'sea ice' can be expected as glacier collapse in Greenland becomes more prevalent.

Yeah. My first response when I saw the comment(s) about ice in the Newfoundland region was that it was almost certainly a mixture of (a) detritus that had calved from a glacier front, and (b) an artefact caused by freshwater lensing as a result of melt.

However, there was also a remark about the thickness being at record level.

Having a totally useless memory, I cannot recall the article source. HOWEVER, I pretty sure it would have been something associated with a very recent entry on the "Arctic Image of the Day" thread. There was a photo (#835) on that thread of a grounded 'berg off the coast near Ferryland. It was just after seeing that image, that I read (somewhere) about there being sea ice of record thickness near Newfoundland.

Being in an unusually generous mood, I was prepared to accept the description as having some basis in fact - as opposed to the normal Flatland bollocks. As I mentioned in the original post, if that genuinely is sea ice - as opposed to glacial ice - then it has come from further north, and is on its way to a rather rapid phase change.

Perhaps I was being overly generous. (Perhaps there is no "perhaps" about it?)

Arctic sea ice / Re: The 2017 melting season
« on: April 29, 2017, 10:02:37 AM »
Tot, oren, Terry, Rob,

I think there has been some gibbering in Flatland recently concerning the amount of ice around Newfoundland. One suspects that this is export related, and that any such ice is basically "dead man walking".

Arctic sea ice / Re: Latest PIOMAS update (April)
« on: April 29, 2017, 09:56:26 AM »
Here you go, Rob...

April:September correlation coefficients for the period 1979-2016

Using NSIDC SIE monthly values only = -0.109

Using PIOMAS monthly values only = +0.650

Using PIOMAS April: NSIDC SIE September = +0.342

Given the Degrees of Freedom, that {PIOMAS April: NSIDC SIE September} correlation still has a p-value <0.05.

In other words, although the correlation could hardly be described as strong, it's still significant at the 95% confidence level.

{EDIT: Just to be fully explicit, the above correlations are based on the residuals left after each data series was detrended. In each case, the detrending was done by using a bog-standard linear trend line.}

Arctic sea ice / Re: Latest PIOMAS update (April)
« on: April 28, 2017, 08:11:01 PM »
However, using Excel's CORREL, the correlation coefficient between the PIOMAS mean March-April-May residuals and the September residuals (1979-2016) comes out at an interesting 0.65

R=0.65 is not bad at all for a March predictor of September SIE.
But what is the SD over the residuals ? And is it better than the SD of 550 k km^2 from the simple linear trend ?
Either way, we should probably take this discussion elsewhere.
You want to take it to the PIOMAS thread ?

Rob, here are the (hopefully) relevant numbers from my PIOMAS spreadsheet. Please let me know if I have managed to misinterpret your question.    :-[

March 1979-2016
Equation of linear trend: Y = -0.264X + 31.921
Mean value = 26.781
SD of residuals (after detrending using the above linear trend) = 1.049
Correlation Coefficient with Sept 1979-2016 = 0.638

April 1979-2016
Equation of linear trend: Y = -0.263X + 32.926
Mean value = 27.805
SD of residuals (after detrending using the above linear trend) = 1.010
Correlation Coefficient with Sept 1979-2016 = 0.650

Average across March, April and May 1979-2016
Equation of linear trend: Y = -0.270X + 32.478
Mean value = 27.209
SD of residuals (after detrending using the above linear trend) = 1.038
Correlation Coefficient with Sept 1979-2016 = 0.692

September 1979-2016
Equation of linear trend: Y = -0.324X + 17.482
Mean value = 11.170
SD of residuals (after detrending using the above linear trend) = 1.434

{With the exception of the coefficients, which are dimensionless natural numbers, all the other values shown above should be expressed in thousands of cubic kms.}

NB In my early post, I wrongly gave the Mar-May correlation with Sept as 0.650. This was a transcription error, and that value (0.650) is actually the April:September correlation coefficient. The averaged (March-May):September correlation comes out at 0.692, as shown immediately above.

Given the Degrees of Freedom for those correlation figures, the p-value for each would be < 0.001, and by a substantial margin.

I hardly need to tell you (although some others might not be as numerate) but there would need to be some appropriate form of normalisation required in order to compare the PIOMAS and NSIDC residuals. However, the fact that the September residuals are larger than those from near the maximum volume period, even before any normalisation based on mean values, is indicative of the increased level of "noise" surrounding the annual minimum.

Arctic sea ice / Re: Latest PIOMAS update (April)
« on: April 28, 2017, 12:22:53 AM »
This was originally posted on the 2017 Melting Season thread, but some parts are clearly of relevance to this PIOMAS thread...

Either way, and from the graphs posted earlier, it is clear that sea ice 'volume' is on a persistent and potentially catastrophic decline. 2017 is especially noteworthy, because of the current record low PIOMAS numbers.
We'll see what September 2017 brings us, but it seems clear that there is a good chance that we are about to find out if the Arctic summer melts ice 'volume' or if it melts 'extent'.

It's an interesting quandary, isn't it Rob?

I was playing about with the monthly figures for PIOMAS, NSIDC Area and NSIDC extent in order to see if I could tease out any clue as to which might be least susceptible to "noise". To do so, I used a simple linear regression in order to obtain a value for the trend, and then subsequently calculated the residuals.

I then compared the Standard Deviation of the residuals with the trend. It's obviously more than a bit crude and simplistic, but my thinking was the higher the value of this ratio, the less time it takes for the genuine underlying trend to emerge from any noise distortion (i.e. natural variability).

The September numbers were...

PIOMAS: Trend = -324 cubic kms per annum, SD of residuals = 1,434 cubic kms

NSIDC area: Trend = -79k sq kms per annum, SD of residuals = 441k sq kms

NSIDC extent: Trend = -87k sq kms per annum, SD of residuals = 550k sq kms

That produces ratios of...
PIOMAS 0.226
NSIDC area 0.18
NSIDC extent 0.159

A possibly more meaningful way of expressing these values might be in terms how many years worth of each trend equates to 2 times the relevant Standard Deviation (i.e. the old 95% confidence level). That comes out as 9 years, 11 years and 12 and a half years respectively.

Using that simplistic approach would suggest that PIOMAS will be the better indicator, as it makes an earlier emergence from the natural variability.

The PIOMAS Daily Arctic Ice Volume graph from Wipneus that you posted is excellent at showing how perilous the end-of-melt-season has become, but, looking at the March-April-May part, it also serves to show that we are still a long way from a totally ice free Arctic. On the 1979-2001 average, the value for the beginning of April is ~ 29,700 cubic kms. The equivalent 2017 value stands at ~ 20,4000 cubic kms - a drop of just over 9,000 cubic kms over a (notional) period of 27 years.

The attached diagrams below show PIOMAS projections for September and for the March-May average volume. If one projects a 2nd order polynomial trend line, the September figure effectively goes to zero in 5 years, but, with a linear projection, this is delayed until about 2032.

The maximum volume is typically attained in April, but with the March-May average and using a 2nd order polynomial fit, the trend does not go to zero until 2050. In fact, the March-May average would still be around 10,000 cubic kms in 20 years time. (Using a linear fit, this trend does not reach zero until almost the end of the 21st Century.)

Anyway, getting back to the melting season aspects, we both know how poor the correlation is for area/extent when the interval gets more than a couple of months. There are various references in the scientific literature to a decorrelation period of just 2 or 3 months for area/extent.

However, using Excel's CORREL, the correlation coefficient between the PIOMAS mean March-April-May residuals and the September residuals (1979-2016) comes out at an interesting 0.65

Rob, I know you asked a follow-up question, but I've been out virtually all day. I'm feeling zonked at the moment, but will provide an answer tomorrow.

There is one "significant" point that I should have mentioned in the original post. There were 38 pairs of values used to generate that correlation coefficient quoted just above. That means the system has, I think, 36 degrees of freedom. Using my old stats workbook, and given that d.f.=36, the generated correlation is established to hold at beyond the 0.001 significance level.

Arctic sea ice / Re: Latest PIOMAS update (April)
« on: April 27, 2017, 11:10:33 AM »
Rob, I hope I got the right place.  here is everything in somewhat chronological order.  Hope I got the overall gist of what was wanted . . .

Repost of what was original posted in "melting season".

Question:  I have used the PIOMAS volume and NSIDC area monthly averages to calculate thickness. 

As you already know dj, Wipneus has said that the NSIDC numbers have a "pole hole". This applies only to area, as they already incorporate the hole size into extent values. (i.e. it is taken as read that there is ice of >15% concentration at the pole hole hole.)

If one wishes to apply a correction to the area values, the relevant offsets are given here...

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