Modelling Arctic Sea Ice (part 1)
Using a supplemented dataset incorporating NSDIC’s Sea Ice Index (SII) to explore the relationship with sea ice extent, sea surface and land surface temperate anomalies
Back in Arctic Sea Ice (part 6) I mentioned something about creating some “fabulous dishes”, and by this I mean some statistical models.
We ought to realise right up front that all models are wrong (not my words but those of statistical legend George Box), though George does qualify this by going on to say, “but some models are useful”.
In the fine art of cooking even over-baked flapjack has a useful function for it can be crumbled into ice cream, and so it is that I’m going to bake some goodies here today using just five variables:
- Mean Arctic Annual Sea Ice Extent (NSDIC SII supplemented by Vinnikov et al 1999)
- Mean Arctic Sea Surface Temperature (HADiSST v1.1)
- Mean Arctic Land Surface Temperature Anomaly (GHCNd, 16 station sample)
- Mean Annual Atmospheric CO2 Concentration (Mauna Loa in situ supplemented with IAC CMIP6 data)
You’ll need to re-read several earlier articles for background to these and how I went about stringing datasets together but for now all we need to realise is that this is top quality kosher data obtained from leading organisations.
Too Many Nuts
Dashing Away With The T4253H Smoothing Iron
For those not familiar the T4253H smoothing function the process kicks off with a running median of 4, which is centred by a running median of 2. It then re-smoothes these values by applying a running median of 5, a running median of 3, and ending with Hanning running weighted averages (span 3).
Residuals are computed by subtracting the smoothed series from the original series, and this whole process is then repeated on the computed residuals. Finally, the smoothed residuals are computed by subtracting the smoothed values obtained the first time through the process.
A bit of a head banger I admit, but there is a partially useful summary here with nowt to be found on Wiki!
At this stage it might do well for me to throw out three examples to show what sea surface temperature (SST), land surface temperature (LST) and Arctic sea ice extent (SIE) look like in the flesh and when subject to the smoothing iron:
That huge dip centred on 1967 is rather interesting. I presume this is real and not some artefact of data collection in which case I either need to find an explanation or create an indicator variable to flag up a very different period when it comes to time series modelling. The same goes for the lesser dips of 1918 and 1995.
What caught my eye here – aided by the T4253H smoothed orange wiggle – is just how periodic this data series is. I hadn’t appreciated this before, and it’s all rather curious because we don’t see this strong periodic pattern with sea surface temperature.
Using my eyeballs alone I’m guessing 12ish-year periodicity which isn’t far off the solar cycle of 10 – 13 years. H’mmmm, ok, so we better have a big think about this later on!
I think T4253H has done a spiffing job of this. We’ve smoothed out some noise whilst retaining the underlying character. The little kink upward at the end is noteworthy: is this the beginning of a new, ice-laden era or just a blip?
Sea & Land Tango
T4253H smoothing has clarified the situation so we may see just how well these two series correspond. In terms of overall correlation, the Pearson bivariate coefficient fetches up at r = 0.782 (p<0.001, n=123), which is good going for two variable variables!
We can also see that the huge dip around 1967 was observed both on land and sea, so is very likely a real thing.
One natty thing we can do at this stage is resort to cross-correlation analysis (CCA) to determine what sort of a dance these two major series do actually do.
My eyeballs pick out instances where land surface temperature (LST) leads sea surface temperature (SST), and instances where SST leads LST. This is where CCA comes in mighty handy, for it is a gem of a spanner for looking at periodic signals beating together over time. Here’s the CCA plot:
NOTE: If land surface temperature follows sea surface temperature and this relationship is positive then we’ll see a palisade of positive value red bars sticking up past the 95 percent confidence limit dashed line at positive lags.
Whereas if sea surface temperature follows land surface temperature and this relationship is positive then we’ll see a palisade of positive value red bars sticking up past the 95 percent confidence limit dashed line at negative lags.
If the relationship between the two variables is negative (sea surface warming whilst the land is cooling, and vice versa), then we’ll see negative-going red bars that push beyond the lower 95 percent confidence limit dashed line.
So now, what have we got here? We’ve got an upright bar at a positive lag of +1 year, indicating the land warms a year after Arctic seas warm, and we’ve got an upright bar at a negative lag of -1 year, indicating Arctic seas warm a year after the land warms.
However the biggest positive-going bar of all is plonked at lag zero, meaning the land and sea warm and cool together within the same season. Hopefully all that makes sense with things warming and cooling together, and with two-way energy transfer.
What will hurt our brains are those statistically significant negative-going bars down at a lag of -5 years and thereabouts. These indicate that either the land starts cooling five years before the seas start warming or the land starts warming five years before the seas start cooling. To say this is most curious is an understatement!
We might start to get a clearer idea of what is going on if we drink in the whole slide. I am sure we can all see the undulating pattern that incessantly flips from positive to negative. This situation arises when we have two oscillating variables with slightly differing periodicities such that they drift in and out of phase over time.
A good example is that wow-wow-wow effect (beat frequency) when tuning a guitar string to another and the frequency of the new string is getting close. Thus it isn’t a simple matter of warm Arctic seas warming the land or the land warming the seas; there’s a feedback mechanism and a degree of independence that produces a complex dynamic.
If you get your fingers to do the walking over this plot you’ll see the positive peak-to-peak lag offering 11 and 14 year beat cycles, with the negative peak-to-peak lag offering 12 and 13 year beat cycles.
This feels very solar, and I can see that I’m going to have to expand the study in a cosmic direction!
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Koen Vogel
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An interesting analysis, though after 6 previous posts I’m not really clear if your dataset is the modified dataset of your post 6 or the unmodified “top quality kosher data” sets. Land temperatures cannot lead or lag sea temperatures, as land retains no heat the way sea does, so I would suggest going with the lag=0 scenario. This is also very clear from the monthly average Arctic temperature anomalies (https://berkeleyearth.org/global-temperature-report-for-2020/; you need to scroll down a bit). thatn wax and wane with the seasons, and are mostly due to the Kara/Laptev sea anomaly, which shows an increase from 2016 to 2020 (https://arctic.noaa.gov/Report-Card/Report-Card-2020/ArtMID/7975/ArticleID/885/Sea-Surface-Temperature) which is not noticeable in your orange T4235H line. But an interesting rabbit hole to go down, as the Arctic is key to the climate change story.
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Koen Vogel
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I forgot to add something. Solar cycles are very well known (but poorly understood) from North American climate cycles (Herman & Goldberg, 1978). The reason you don’t see them in sea temperature is because the sea response is slow: it accumulates and sheds head over longer cycles. Land temperatures are more sensitive to solar cycles as they basically shed all their accumulated summer heat by winter (Arctic surface temperatures < 25 C in winter), and are therefore more influenced by Arctic ocean temperatures.
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Koen Vogel
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head = heat, and < 25 C = < -25 C
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Jerry Krause
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Hi Koen,
You wrote: “We can also see that the huge dip around 1967 was observed both on land and sea, so is very likely a real thing.” Isn’t all the data represented by this (not labeled) figure the REAL THING?
Especially that of the 1930s?
Have a good day
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Jerry Krause
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Hi Koen,
You wrote: “We can also see that the huge dip around 1967 was observed both on land and sea, so is very likely a real thing.” Isn’t all the data represented by this (not labeled) figure the REAL THING?
Especially that of the 1930s?
Have a good day
Reply
Jerry Krause
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Hi Koen and PSI Readers,
Fortunately my second complete did not post for I now see how confused I had been as I considered that Koen had started a new series about the Arctic Sea Ice.
So I will simply submit this comment to see if it will double post again. My question of the previous still needs an answer.
Have a good day
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Roald J. Larsen
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A lot of the data and charts used in the article is FAKE!
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Koen Vogel
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Can you elaborate?
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Jerry Krause
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Hi PSI Reaers,
Please ignore all my comments that I have written relative to Koen’s comments and this article. For I understand NOTHING of what I have read.
Have a good day.
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Koen Vogel
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Hi Jerry,
Too many cooks? Let me summarise what I get out of John Dee’s post for you, as it does bring some new views to light, and understanding the Arctic is key to understanding our current climate change. John takes some Arctic data, processes it somewhat to remove noise (smooth, edit?), analyses Land separately from Sea (common practice), and notes some differences, mainly that Land shows some solar cyclicity.(indicating a Natural Forcing is at work in IPCC terminology). The CCA analysis is a bit of specialism that is used to compare the Land and Sea time series, mainly to determine cause and effect: the cause has to precede the effect, the effect lags the cause. CCA shows a strong positive correlation for lag=0, which is somewhat frustrating viz a viz cause and effect, but it is widely accepted that ocean temperatures influence land temperatures and not vice versa. More heat energy can be stored in water than in air due to their different heat capacities. The strong positive correlations at -11 and +14 confirm the solar forcing: there is a good correlation between measurements separated by a -11 year lag, so e.g. data from 2023 and from 2012. This can be used to build a predictive model, which might be the next post.
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Herb Rose
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Hi Koen,
While land, water, and atmosphere are all absorbing energy from the sun, they are absorbing different wavelengths. Land absorbs visible light, water infrared, and the atmosphere (O2 & N2) ultraviolet. Both IR and visible light are emitted by the sun’s surface and do not vary much, the ultraviolet (and x-rays) absorbed by the atmosphere is produced in solar flares. When there is a solar minimum there is less UV energy being converted to IR by the O2 and N2 so there should be a greater effect on sea temperature than on land temperature.
Herb
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Koen Vogel
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Thanks for pointing that out.
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Jerry Krause
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Hi Koen,
Thank you for the attempt to clarify. I have one question: Why have I not anyone, except myself, referring to (https://follow.mosaic-expedition.org/) here at PSI?
Have a good day
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Jerry Krause
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Hi Koen,
Thank you for the attempt to clarify. I have one question: Why have I not anyone, except myself, referring to (https://follow.mosaic-expedition.org/) here at PSI?
Have a good day
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Jerry Krause
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Hi PSI Editors,
I have no idea of the cause of the double posting except I know everything was working perfectly at my end. I make this comment because I do make many errors as I make comments but I do NOT want to take credit for the double posting. Except I now question if the fact that I did compose the brief comment on a document which I copied and pasted at PSI. Which is what I will do with this comment.
Have a good day
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Jerry Krause
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Hi Koen,
Relative to the Mosaic-Expedition and Fridtjof Nansen’s much earlier expedition, I never read about any evidence that the these scientists ever considered that the centrifugal effect of the rotating earth might be the cause of the cracks which spontaneously and regularly formed in the ice during the Arctic winter.
Any thoughts about these FACTS. (cracks and rotating earth)
Have a good day
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Jerry Krause
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Hi Koen,
As I wait for a possible comment from you, I have been looking at the current information from these two links.
(https://www.accuweather.com/en/us/salem/97301/weather-radar/3301440)
(http://weather.uwyo.edu/upperair/sounding.html)
Do you look at what has been observed and is being reported at these links?
Are you familiar with this data? Have a good day
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Jerry Krause
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Hi Koen,
I admired my ignorance about what I had read and written and was moving on until you engaged me. Now as I call attention attention to actually measured meteorological data and significant scientific studies of the Arctic you seem to have moved on.
Of course, it is only my opinion that further conversations could (might) be productive.
Have a good day
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Jerry Krause
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“admired” was intended to be “admitted”
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MattH
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Hi Jerry..
I instinctively have some reservations about this article.
It states that a lot of “noise” has been smoothed or eliminated.
I interpret noise as being “data”.
Remove specific data to end up with results that suit one’s pet hypothesis. Maybe! Maybe not! I look forward to future real time observations.
Have a nice day.
Matt
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Jerry Krause
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Hi MattH,
What you wrote is a reason I was moving on. But what is known about the Arctic should not be ignored. Hence my reason that people like you and Koen should consider other information instead of moving on.
Have a good day
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MattH
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Hi Jerry. You are correct of course. There are only so many hours in the day and often we get distracted by extraneous subjects.
Have a nice day.
Matt
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