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Messages - Bill Fothergill

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Arctic sea ice / Re: IJIS
« on: August 26, 2017, 05:55:09 PM »
...  I think this (or something similar) is what Bill F. had in mind. (I assume rounding errors leads to the 102% cumulative probability.)  ...

Yep, spot on.

Being an old fart, my brain was unable to dredge up the term "cumulative probability" from what passes for a memory these days.

My excuse for this inexcusable behaviour is that this was something we did in Statistics (a subset of 3rd Year Maths) - and that was about 44 years ago.

Aw shit - that also probably explains why I can't run anywhere near as fast as I used to back then.  :'( :'( :'(

Arctic sea ice / Re: IJIS
« on: August 24, 2017, 02:19:59 PM »
That chart shows why the probabilities of various ranks are so strange (40+ % chance of 4th place or 6th place, but only a 4% chance of 5th place). 

In order to achieve 5th place, 2017 would need to squeeze in between the two blue dots under the "re" in "previous years".   Those dots are the minimums from 2011 and 2015, and there's not much space between them!  Much easier to come in 4th (lower extent than 2015) or 6th (higher extent than 2011).

Under such circumstances, it can often be far better to avoid the use of equalities, and instead plump for "greater than, or equal to".

Hence one would talk about there being...
an X% chance of being 4th or higher,  (NB Higher, in this context, means a larger ordinal number.)
a Y% chance of being 5th or higher,
a Z% chance of being 6th or higher,

In the case you are describing, the probability X would be appreciably larger than Y, but Y would be only marginally greater than Z. (The trivial case is, of course, that there is always a 100% chance of the year finishing 1st or higher - using "higher" to mean the same as mentioned above.)

At first glance it can seem as if one is trying to dodge a difficult question, but, when one has that kind of spread in the respective probabilities, it can make the situation easier to understand. (At least for those prepared to invest in the effort of a modicum of thought.)

Arctic sea ice / Re: Northwest Passage thread
« on: August 24, 2017, 11:11:24 AM »
Regarding the thickness of the ice shown in various photographs further up this thread, one should always try to remember that something in the order of 7/8ths is below the waterline.

The complex topography of the ice makes the determination of the freeboard:draught ratio something of a nightmare, as evinced in the following paper...

Arctic sea ice / Re: Northwest Passage thread
« on: August 24, 2017, 10:59:26 AM »
Jim H is not the only one with memory problems.  ;)

The two quotes shown below have triggered a memory, but only partially...

The trick, of course, is that as ice conditions enable more traffic, then numerous intermediate destinations will be utilised for trade and no doubt export of resources which can now be exploited.  This traffic may entail fewer all-the-way-through traverses, and more 'coastal' traffic between such origins/destinations.
However a ship-count metric is not directly relevant or 'impressive' when it comes to trying to inform the great unwashed about the critically sad state of the Arctic ice.


C3 is now at Gjoa Havn

On Jim's Great White Con blog sometime last year (I can't remember when) , one of the Flat Earth brigade made the claim that, as far back as 1929, no fewer than 3 ships from the Hudson Bay company had made the traverse in a single year.

It would have seemed an obvious thing to check with the HBC archives whether such a thing had indeed happened, but had somehow been kept secret from the rest of the world. However, as most here realise, genuine scepticism is in extremely short supply amongst self-styled climate change sceptics.

In response to my query, one of the HBC archivists very kindly - and quickly - came up with the answer. What had happened was that 3 ships did indeed overwinter around the Cambridge Bay/ Gjoa Havn region, but that was simply the limit point for their respective trading/supply routes.

Two of the ships (Fort James and Fort Macpherson) had started from different ends of the NWP in 1929, but each had made it no further than Gjoa Havn before overwintering and then reversing their course. The third ship (Baychimo) worked the Vancouver - Cambridge Bay route throughout the 1920's, and also happened to overwinter "near" the other two in 1929.

Yet another example of misinformation and deliberate twisting of the facts from the usual suspects.

Arctic sea ice / Re: The 2017 melting season
« on: August 23, 2017, 07:36:57 PM »
I always thought the 15 percent rule originated from the days of sail as a measure of when it would be dumb to venture further into the ice. But I have never found a confirmation of this.
I thought the same as you, i.e. anything more than 15%, and you don't even want to think about going there.

However, there is also another reason for that particular value. During one of my dialogues with the NSIDC team, I was given the following response...

"15% concentration is useful for some marine navigation. However, the contour was originally developed since this threshold provided the best agreement between passive microwave remote sensing on space-paced platforms and aerial overflight work in early studies (e.g. Cavalieri et al. 1991: Aircraft active and passive microwave validation of sea ice concentration from the Defense Meteorological Satellite Program Special Sensor Microwave Imager. Journal of Geophysical Research: Atmospheres, 96, 21989 – 22008, doi: 10.1029/91JC02335.)"

Arctic sea ice / Re: The 2017 melting season
« on: August 23, 2017, 10:23:52 AM »
Plea for help guys! I need to trace a link to one our our member discussing the current 15% or more measure for extent/area with NSIDC ? ...

G-W, I was one of the people in communication with the NSIDC on this subject. I've sent you a Personal Message with the relevant emails appended.

Arctic sea ice / Re: The 2017 melting season
« on: August 16, 2017, 12:26:39 PM » appears as if they mechanically break when pulverizing. This surface topology of ice objects is an important cue that points towards mechanical breakage as the primary, driving mechanism...

VAK, have you seen this paper which deals with the variation in mechanical strength with temperature?

One snippet from there reads as follows...

2.3.1. Effects of temperature

Generally, the strength of ice increases with decreasing temperature in both tension and compression, as shown in Fig. 1. This temperature effect on strength is more prominent in compression than in tension. Haynes reported that the compressive strength of ice increased by approximately a factor of 4 from 0◦C to −40◦C. However, he indicated that the tensile strength of ice increased by only a factor of 1.3 over the same temperature range. Schulson has suggested that the temperature dependence of compressive strength of ice is related to ice dislocation and grain boundary sliding phenomena that lead to temperature-dependent damage accumulation. . The much more limited temperature dependence of tensile strength is related to the localisation of stress-accommodating mechanisms at the tips of tensile flaws.

With increased temperatures, there is a concomitant reduction in the mechanical strength of the sea ice, and this would tend to lead towards, in your words, "pulverisation". As progressively more energy is getting stored in the oceans, it would seem reasonable to hypothesise that this "pulverisation" may show an increasing trend with each passing melt season.

Consequences / Re: Global Surface Air Temperatures
« on: August 16, 2017, 01:25:30 AM »
As Ken pointed out, the second lot of numbers I gave was HadSST3.1.1, not HadCRUT4.5. The latter tends to appear a couple of weeks after HadSST.

NOAA's NCEI numbers for July are due on the 17th.

BEST will be available when it's available.

(UAH ver 5 beta 6 had July as the 4th warmest for that month.)

Consequences / Re: Global Surface Air Temperatures
« on: August 15, 2017, 07:33:06 PM »
Bloody hell.

Gistemp LOTI has just been updated, and the July value is (marginally, and subject to subsequent review) the highest July value thus far. That I wasn't expecting!

The top six read as follows...

2017 +0.83oC
2016 +0.82oC
2015 +0.71oC
2011 +0.71oC
2009 +0.71oC
1998 +0.68oC

On the other hand, the HadSST3.1.1 dataset has 2017 merely in 4th highest place...

2016 +0.670oC
2015 +0.637oC
2014 +0.551oC
2017 +0.537oC
1998 +0.526oC
2009 +0.523oC

{N.B. That HadSST value for July 1998 was the highest value over the big 1997/98 el Nino, and I don't think it was topped by any monthly value until June 2014 came in at +0.563oC. In the most recent 38 month period (June 2014 - July 2017) only 9 months have failed to exceed the July 1998 value.}

Arctic sea ice / Re: The 2017 melting season
« on: August 15, 2017, 03:38:20 PM »
... In any event you she could also join a select list of ships that have been trapped by the ice in both the Arctic and Antarctic. :)

Apologies for going briefly OT, but one immediately thinks of the Fram. Tragically however, Erebus and Terror didn't fare so well when they headed north.

Antarctica / Re: Sea Ice Extent around Antarctica
« on: August 14, 2017, 09:29:00 PM »
@ gerontocrat

It will be interesting indeed to see how your projections regarding the max turn out.

During 2016, the max of 18.5 million sq kms occurred at the ridiculously early date of 29th August. It then dropped rapidly over a period of ~2 weeks, before spending the subsequent ~7 weeks in various of the lowest 4 positions. Of course, as we all know, it started to seriously separate from the rest early in November.

Looking at inter-annual differences on specific dates can be somewhat prone to cherry picking, but it can be educational to look at how the rolling 365-day average has differed from year to year.

As the latest available data is for the 13th August, here's how the rolling-365 shapes up on that date for each year from 2000 onward...

 Year      Average extent (in millions of sq kms)
2000      11.82
2001      11.79
2002      11.25
2003      11.75
2004      11.77
2005      11.63
2006      11.26
2007      11.51
2008      12.24
2009      11.93
2010      11.93
2011      11.56
2012      11.86
2013      12.25
2014      12.69
2015      12.69
2016      11.57
2017      10.53

That's a reduction of a frankly astonishing 2.16 million sq kms in the last 2 years. Hopefully next year will be nowhere near as bad! (To add a bit more context, the overall average from Jan 1979 to Dec 2016 was 11.714 million sq kms.)

Attached below is a zoomed view from ADS, and, with a bit of multiple-imaging and cropping, I've managed to highlight both 2016 and 2017. There is still a bit of "low hanging fruit" over the next 3 or 4 weeks, but, by then, the reduction rate in the rolling 365-day average should - hopefully - ease off.

The second attachment consists of two simple tables; the first shows the daily values on the 13th August for each year, and the second gives the daily values for the 25th October - a date approximately as far after the max as we currently are before it.

I really hope that the maximum will be considerably later than 2016, otherwise I'll seriously start to worry about the Antarctic as well.

Consequences / Re: Wildfires
« on: August 11, 2017, 03:52:48 PM »
.... The Wetcoast has received less than a mm of rain since June 18....

A typo to cheer me up!  ::)

That might not be a typo.

Permafrost / Re: Arctic Coastal Change
« on: August 10, 2017, 11:33:20 PM »
Have fun up there BFTV!

As regards the wildfires, Canada is not alone. I don't know how much access you have to the news channels, but even Greenland has been burning recently. (Brownland doesn't have quite that same ring to it, does it?)

Permafrost / Re: Arctic Methane Release
« on: August 10, 2017, 03:48:08 PM »
It can be quite a lengthy process finding the bit you're after in the IPCC publications. To save others the time, here is a relevant bit from Section 2.3.1 in the AR5 Synthesis Report...

"Carbon stored in the terrestrial biosphere is susceptible to loss to the atmosphere as a result of climate change, deforestation and ecosystem degradation (high confidence). The aspects of climate change with direct effects on stored terrestrial carbon include high temperatures, drought and windstorms; indirect effects include increased risk of fires, pest and disease outbreaks. Increased tree mortality and associated forest dieback is projected to occur in many regions over the 21st century (medium confidence), posing risks for carbon storage, biodiversity, wood production, water quality, amenity and economic activity. There is a high risk of substantial carbon and methane emissions as a result of permafrost thawing. {WGII SPM, 4.2–4.3, Figure 4-8, Box 4-2, Box 4-3, Box 4-4}"
{My emphasis added above.}

Woods Hole also issued a permafrost briefing note two years ago...

As a newcomer to this thread, apologies if either of the above have already been posted in preceding pages.

A few comments upthread, "reallybigbunny" posed a question about wildfires. I am particularly interested in the Greenland outbreak, some comments on which were started on the ASIB by Susan Anderson.

(NB I'm not suggesting Susan had anything to do with starting the fire.    ;))

I have emailed the Wildfire laboratory at Exeter University asking what impact the current peat-based fire might have upon permafrost locked carbon deposits. Will post any such response on this thread if/when it is forthcoming.

Antarctica / Re: Sea Ice Extent around Antarctica
« on: August 10, 2017, 02:31:24 PM »
Old gits with some background in electronics, such as myself, might remember the Signetics 555 timer, as it was almost ubiquitous in circuit design a few decades ago.

It was just that bit of weird arcane knowledge which caused me to do a quick double-take at the Antarctic tab in my JAXA/ADS extent tracker today. The rolling 365-day average has just dropped to  10.536 million sq kms, which displays on my spreadsheet as now being 555k sq kms lower than the previous lowest, which was set way back in August of 1980.
(How time[r]s have changed.  ;))

This current figure of 10.536 is still dropping at ~1.5k/day, and, considering that the 2016 Antarctic extent values didn't start to plummet until next month, it is definitely possible that, during September, the rolling-365 could end up more than 1 million sq kms below the 1980's average of 11.486 million sq kms.

The equivalent rolling-365 taken from the NSIDC dailies lags somewhat at "only" 408k sq kms lower than the erstwhile lowest ever NSIDC value from 1980; a difference of 147k sq kms between itself and the equivalent ADS reduction. However, the delta between the two sets of data has remained pretty constant for some time now.

The ADS rolling-365 equalled the 1980 record-low value on January 26th of this year; on the same date, the NSIDC equivalent was 138k higher than its 1980 figure.

The NSIDC rolling-365 attained parity with its equivalent 1980 record-low on March 26th, by which time the ADS number was 142k sq kms lower than its previous record low.

As mentioned above, the current amount by which the ADS record-low has been reduced now stands at 147k more than the equivalent NSIDC reduction. In other words, the delta between the two sets of data has changed by about 9k in a period of around 6 or 7 months.

So, the next time you hear one of the flat-earth brigade spew forth some drivel about "gains in Antarctic sea ice more or less cancel out losses in the Arctic", you'll be able to tell them precisely which orifice they're talking out of.   ;D

I was just about to hit the "Post" button, when the old Red Alert informed me that another comment had arrived whilst I was typing.

Apropos of gerontocrat's musing about the September value, it will also be very interesting to see what happens come November, as that is traditionally the time of the global sea ice maximum.

A few days ago, on another thread, I posted a chart showing the recent behaviour of the rolling-365 for global sea ice, and I've appended that below. (It has dropped another 7k sq kms in the intervening 5 days.)

As the current value is ~ 22.318 million sq kms, one cannot help but wonder when that might drop below 22? In the last 4 and a half months, it has lost ~ 318k sq kms, so it is not outwith the realms of possibility that we could see sub-22 by around Christmas time - just what we don't need as a present!

Arctic sea ice / Re: IJIS
« on: August 08, 2017, 10:50:52 AM »
Hi Espen,
I don't want to rock the boat much, since this is not a big deal.
But your greeting "Have a ice day!" should really be "Have an ice day!", not just for English grammar reasons, but also because it enforces the pun.
Well spotted Rob.

As it was clear what Espen meant, I have been simply reading his sign-off phrase as if the "n" was present.

This just goes to show the power of the written word, as exemplified in that well know aphorism...

"The penis; mightier than the S word"     ;) :-[

Arctic sea ice / Re: The 2017 melting season
« on: August 05, 2017, 03:38:42 PM »
Speaking of NSIDC SIE: with five to six weeks of decrease still to come, 2017's minimum is already lower than that recorded in every year from 1979 to 1998 (save for 1990 and 1995) plus 2001. It's also lower than the 1980s and 1990s average minimums.

Jim, did you experience a brief frisson of déjà vu as you were typing that?  See #3565  ;)

Arctic sea ice / Re: The 2017 melting season
« on: August 05, 2017, 03:00:04 PM »
Here's what the 4th August values look like on the NSIDC's 5-day Charctic.

2017 pretty much bisects 2012 & 2016, with 2007 (not shown) effectively identical to 2017 at today's date.

The other years shown are those in which the minimum has already been surpassed. (N.B. The minimums for the 1981-2010 median, and for both 1991 and 1998, are still fractionally below the 5-day value for August 4th 2017. However, as the daily values for Aug 3 and Aug 4 2017 are already well below these other entries, they will be "blown away" when tomorrow's numbers arrive.)

Arctic sea ice / Re: IJIS
« on: August 05, 2017, 02:04:31 PM »
I speculate that as melt progresses towards the north pole in the years to come, freeze onset dates might actually become slightly earlier rather than later.
The following chart shows the dates for IJIS extent minima. In general there seems to be no trend. More accuracy can be achieved by averaging around the minimum to avoid noise.
Oren, I realise that, in any given year, a polyna at higher latitude is likely to commence its autumnal refreeze at an earlier date than an equivalent polyna at a lower latitude. I can therefore see how one might expect that the gradual pole-ward retreat of peripheral ice, might indicate that refreezing could commence earlier.

This viewpoint, however, might fail to fully incorporate the ice/albedo positive feedback mechanism, which, as you know, results in greater heat storage within the body of the ocean. It is this cumulative build up in the heat content which would serve to delay refreeze.

During the period since I posted a link to that NASA article, I managed to find the paper I had mentally misplaced. (Something which is happening with alarming frequency as the years go by.)

The lead author was Julienne Stroeve - a name I'm certain you recognise - and here is an open access link to the AGU's Geophysical Research Letters article...

Another related paper would be this one, which has Walt Meier as the lead author...

In either article, doing a simple search on the term "delay" gets one quickly to the relevant sections.

However, you are completely correct in pointing out that there are significant differences when one looks at regions, rather than the Arctic as a whole. Quoting from Para 3.3 (Relationship Between Autumn Freezeup and Sea Surface Temperatures) in the Stroeve paper...

"While this is representative of the Arctic as a whole, there are regional differences. In the Chukchi, Beaufort, E. Siberian, Laptev, Kara, and Barents seas, the observed freezeup delay falls within the estimated value (Table S3), suggesting the delay in autumn freezeup is largely driven by the observed increases in SSTs in these regions. These SST increases, together with recent trends toward warmer air temperatures in September (Figure S8), result in a small difference in the air-ocean temperature difference, limiting the amount of latent heat released and a delay in sea ice formation.

Regions outside of the Arctic basin do not appear to show this same relationship however (i.e., Sea of Okhotsk, Bering, Hudson, and Baffin Bay, E. Greenland Sea). Instead large discrepancies between the observed changes in autumn freezeup and that estimated based on the change in SSTs are found, with the actual freezeup occurring between 1 week and 1 month earlier than estimated by equation (3). All these regions, except for Hudson Bay show earlier freezeup in 2000–2012 compared with that in 1982–1999, while SSTs have generally warmed. Trends toward cooler September air temperatures (Figure S8) in these regions may partly explain this discrepancy. While trends are toward warmer SSTs and higher OHC, the air-ocean temperature difference is becoming larger, allowing for the sea surface to release latent heat at a faster rate and for sublimation of sea ice to occur sooner. Ocean dynamics could also be playing an important role in the amount of sea ice found, particularly in the E. Greenland Sea.

In summary, while these preliminary results look promising, a need remains for more extensive research and better understanding of the processes affecting freezeup on a regional scale."

Arctic sea ice / Re: Year-round ice-free Arctic
« on: August 05, 2017, 01:16:20 PM »
Thinking it is a pity that this thread is entitled "Year-round ice-free Arctic". Probably because I think a lot about how it will go from a) now and b)year-round ice-free Arctic.

Will it be a case of a gradually extending blue ocean period or a case of last year's winter being repeated and an accelerating winter ice loss ? ...

There is an article on the Max Plank website which is complementary (without being unduly complimentary) to the Ametsoc article mentioned upthread.

It contains an interesting animation showing the modelled behaviour of Arctic sea ice for both  March and September. The March animation runs from 2050 to 2200, whilst its September equivalent goes from 1850 till 2100. (The reason for this temporal asymmetry should be obvious, especially after viewing.)

Arctic sea ice / Re: The 2017 melting season
« on: August 05, 2017, 12:54:31 PM »
As the "flat Earth" brigade still like to gibber about loss of sea ice in the Arctic being somehow balanced out by gains in the Antarctic ...

Arctic sea ice / Re: IJIS
« on: August 05, 2017, 10:01:54 AM »
Yeah and because theres so little ice now every year the min day gets earlier so the first week of september is the end in my book.

The available data might suggest otherwise.

Here is a link to a NASA article charting the variations in the onset of both melt and refreeze. I can't recall reading any paper which suggests either trend is likely to reverse. On the other hand, I do recall reading at least one paper which extrapolates this continuing divergence in the onset of melt and refreeze many decades into the future. (Needless to say, I can't put my hands on it at the moment.)   :-[ :-[ :-[

The relevant diagram from this NASA article is appended below.

Arctic sea ice / Re: Year-round ice-free Arctic
« on: August 04, 2017, 02:18:44 PM »
Whereas summer sea ice is too heterogeneous for large-scale rapid shifts in sea ice area to occur over a few years,
... Is the above highlighted quote the explanation (or part of it) ?

My guess is that the authors are thinking about the cumulative effect of (a) the gradual complete loss of MYI compounded by (b) the even more gradual regression in the date at which re-freeze begins.

Even if we lost all the MYI in the next couple of years, the date at which re-freeze commences isn't going to change much in the short term. The effect of this is that the new ice in some areas will still clock up significant Freezing Degree Days compared to those areas in which the refreeze didn't get going until (say) February.

I think that accounts for the heterogeneity which is being discussed in that quote.

As for this year's varying behaviour viz-a-viz volume & extent, I really wouldn't like to hazard a guess. There's always going to be a certain level of disconnect between these metrics.

I don't know if you noticed, but on the ASIB a couple of months ago, one of the contributors hypothesised that, since PIOMAS and NSIDC gave differing "projection down to zero ice" dates, then one or both had to be in error.

That seemed an astonishing failure to grasp basic maths: if the area is dropping, and the thickness is dropping, then it is axiomatic that the volume should be dropping even faster. Obviously it is physically impossible for matters to continue such that there is zero thickness whilst there is still area present, and vice-versa.

What will happen is that there will be a discontinuity (the rapidity of which will be interesting to learn) in the decline rates of the various metrics. I know you are familiar with all this, but I have appended three simple charts which I knocked up a while ago to demonstrate this effect to someone I know.

In each (extremely simple) case, I have assumed that the length, breadth and thickness of an ice mass each decrease in a perfect linear fashion.

Case (1) has these three values declining such that they would all go to zero in 10 years.

Cases (2) and (3) have the length & breadth (and, consequently, the area as well) decreasing at an unchanged rate. However, in Case (2), the rate of loss of thickness has been decreased, but has been increased for Case (3).

The format of the graphs may look somewhat unusual to some, so a quick explanation may be in order.

The primary Y-axis shows Area, whilst the secondary Y-axis displays volume. The X-axis is used to show thickness. However, as each data point on every data-series is one year apart, the separation of each data point can be considered as being a proxy for the passage of time.

In Case (1), there is no abrupt discontinuity, and the curves for each metric smoothly coalesce at the zero point. However, Case (2) demonstrates a discontinuity in the thickness metric, whilst Case (3) has a similar discontinuity for area.

As mentioned earlier, the physics of the actual ice loss will vary enormously from this simplistic mathematical representation. The losses will be anything but linear - and that's without introducing any noise into the situation.

Arctic sea ice / Re: Year-round ice-free Arctic
« on: August 04, 2017, 12:07:21 PM »
The subject of year-round ice-free Arctic surfaced in the ongoing Melt Season thread, and it is best we continue the discussion in this topic.

... Even with much higher temperatures, there will probably always be freeze in winter, that's why there will probably never exist zero ice all over the year...

What you are discussing is the transition of the Arctic Ocean from being perennially ice covered, through seasonally ice covered, and ending up in a perennially ice free condition.

One such study appeared last year in the Journal of the American Meteorological Society. Their findings, in a nutshell, were that the vast bulk of winter sea ice could be a thing of the past by as soon as ~2130.

I'll put more flesh on this later, but I'm off to sink a few pints.

Bill, excellent spotting about that paper! But i am sure their result is a vast underestimation. I am not familiar with the paper, but i could bet authors did not take the biosphere influence into much consideration when making their calculations. If so, then that is perhaps the biggest flaw of their work. Because, obviously, in real world, we _do_ have the biosphere. So far. Thank God for that, if i might add.

Following several beers, here is the additional flesh to which I alluded earlier...

Some time ago, I came across this Ametsoc article titled "On the Potential for Abrupt Arctic Winter Sea Ice Loss".

The authors used a variety of different models during their work, and largely assumed that CO2 emissions would roughly follow the scenario described by RCP8.5.

One of their most intriguing findings was that, once the conditions in the Arctic Ocean were right - i.e. warm enough - the transition from a seasonally ice free Arctic Ocean to one which is  perennially ice free could occur faster than the phase we are currently in: namely the transition from being perennially ice covered to being seasonally ice covered.

The first couple of paragraphs of their conclusions read as follows...

"We have found that in complex climate models the transition from a seasonally ice-covered Arctic to an ocean without any sea ice year-round occurs faster than the loss of summer sea ice under the same rate of warming. We attribute this effect to the seasonal asymmetry in the ice-thickness distribution. Whereas summer sea ice is too heterogeneous for large-scale rapid shifts in sea ice area to occur over a few years, Arctic winter sea ice is spread out more homogeneously. As long as the winters are cold enough, a thin and relatively homogeneous ice cover still forms each year. Once the water does not cool to the freezing temperature anymore in winter, the small loss of ice volume from one winter to the next is associated with a large ice-area loss. This explanation allows the possibility of abrupt change although it does not rely on any positive feedback because the freezing point constitutes a natural threshold.

Regarding the generality of this threshold mechanism, the loss of Arctic summer sea ice in the near future could provide an observational lower limit for the rate of Arctic winter sea ice loss, provided that global warming will continue with a similar rate. Because of the inherent uncertainties in the models, it is difficult to provide a quantitative estimate for the sensitivity of Arctic winter sea ice area. It is plausible that the models with the most sophisticated ice-thickness distribution yield the best estimate of the sensitivity of Arctic winter sea ice area, which is roughly 50% larger than the sensitivity of summer ice area (Fig. 3). We consider the distinctly abrupt Arctic winter ice loss in MPI-ESM and CSIRO to be less realistic due to their simple description of the subgrid-scale thickness distribution.

I didn't find the article particularly easy to assimilate (where are the Borg when you need them?) but nevertheless thought that the time was well spent.

One of the diagrams showing the rapidity of change which might occur in the March/April/May average next century is shown below.

By way of comparison, I followed this with simplistic projections based on 1979-2017 PIOMAS and NSIDC monthly averages for March. It is interesting to note that the possible transition period intimated in the study is roughly mid-way between a straight line PIOMAS projection and a 2nd-order polynomial projection of the NSIDC data.

Arctic sea ice / Re: The 2017 melting season
« on: August 01, 2017, 08:13:07 PM »
... Even with much higher temperatures, there will probably always be freeze in winter, that's why there will probably never exist zero ice all over the year...

What you are discussing is the transition of the Arctic Ocean from being perennially ice covered, through seasonally ice covered, and ending up in a perennially ice free condition.

One such study appeared last year in the Journal of the American Meteorological Society. Their findings, in a nutshell, were that the vast bulk of winter sea ice could be a thing of the past by as soon as ~2130.

I'll put more flesh on this later, but I'm off to sink a few pints.

Arctic sea ice / Re: The 2017 melting season
« on: August 01, 2017, 06:38:17 PM »
Regarding the highly dubious practice of looking at an extremely short time period (~ 10 years), Ned W has posted some excellent graphs on the Volume vs Extent thread.

There's been some discussion about "flattening" (or not) on the 2017 melt season thread, and up above on this thread as well.  To avoid "broken trends" here are LOESS smoothed versions of the September monthly volume and extent series...

I am somewhat reluctant to give them any publicity, but here is an example of the type of bollocks that the GWPF have come out with in the past. The title of the piece rather says it all...

What Whitehouse has done is precisely what Thawing Thunder mentioned upthread - hide the enormous 2007 extent loss by starting the "trend" measurement from that date. The 4 largest reductions in the record-lows for NSIDC September extent were...

0.59 million sq kms when 2005 replaced 2002 as the record holder
0.67 million sq kms when 1990 replaced 1985 as the record holder
0.69 million sq kms when 2012 replaced 2007 as the record holder
1.27 million sq kms when 2007 replaced 2005 as the record holder

In other words, the amount by which 2007 lowered the previous record was about the same as the next two biggest reductions combined. Starting from that date is the Arctic sea ice equivalent of taking surface temperatures from 1998.

Arctic sea ice / Re: Volume vs extent, by the numbers
« on: August 01, 2017, 06:13:31 PM »
Nice one, Ned.

I had just created virtually identical rolling 10-year graphs for September PIOMAS and September NSIDC extent, but you beat me to the draw.

Arctic sea ice / Re: The 2017 melting season
« on: July 31, 2017, 11:33:44 PM »
Since it's still July (just) here in sun-drenched England (or possibly just "drenched"), I thought I'd have a quick decko at NSIDC's 5-day Charctic can show how many annual minimums (since 1979) have already been beaten this early in the 2017 melt season...

1979, 1980, 1981, 1982, 1983
1986, 1987, 1988, 1989

Those digit counters are going to continue to fall (with apologies to The Who), and, in a few weeks time, it should start to become clear just how bad it's going to get.

Arctic sea ice / Re: The 2017 melting season
« on: July 31, 2017, 11:10:33 AM »
It would be better though if you'd actually link to the Greenland 2017 melt season thread so people can read what's being written there and write something themselves if they'd like.  :)
I need to figure out how to do that. Am I being thick?

I've sent you a message outlining the appropriate procedure. You are not being thick.

Arctic sea ice / Re: Volume vs extent, by the numbers
« on: July 29, 2017, 05:03:57 PM »
That is due to the "pole hole".  Between July 1987 and December 2007, the surface area of the pole hole was 0.31 million km2.  From January 2008 onward it is only 0.029 million km2:
Yep, and from Nov 78 until Jun 87 it was a whopping 1.19 million km2.

Every time I modify my NSIDC spreadsheet, I always end up having to recheck the pole hole size from here ...

(Some day, these values might actually lodge in my cranium - but I'm not holding my breath...)

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.

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