Modelling Arctic Sea Ice (part 2)
Modelling Arctic Sea Ice (part 2)
Using a supplemented dataset incorporating NSIDC’s Sea Ice Index (SII) to explore the relationship with sea ice extent, sea surface and land surface temperate anomalies
This morning we’re going to move along the bus and go all standardised scores (Z Scores). I remember meeting these scores for the first time as a statistical newbie bod in training back in the ‘80s and it seemed like total magic. For those not familiar with this statistical technique I shall summarise it by stating that it very cleverly removes the awkwardness of counting something in raw units without losing any of the flavour.
Let us suppose you’ve got data for sea ice extent that ranges from 6,000,000 sq km to 14,000,000 sq km and back over a period of 30 years, and you’ve got sea surface temperature that ranges from 3°C to 5°C and back over the same period. If you try and plot these on the same graph you’ll end up with a horizontal line representing sea ice up at a mean of 10,000,000 sq km with sea surface temperature indistinguishable from the zero axis down at the bottom. If we re-scale both series using the Z transform we get to see both in all their wiggly glory.
When it comes to statistical modelling the raw units of measure are not important; what is important is how things wiggle about and whether those wiggles correlate in some manner. Let us now look at slides of the four key variables (sea ice extent, sea surface temperature, land surface temperature, atmospheric CO2) converted to their Z-score format.
Sea Surface Temperature & Sea Ice Extent
As Arctic waters warm Arctic sea ice melts – simples! Except that there are some interesting features that suggest the situation is more complex than this. We may note that Arctic waters were warming from 1900 to 1960 with very little change in sea ice extent. This paradoxical fact in itself is cause enough for a decent ponder with a plate of something crunchy. The mysterious oceanic cooling around 1965 flies in the face of alarmism’s CO2 = warm earth mantra, but it does produce a lovely blip in sea ice extent in response. The period from 1975 onward gives alarmism the credibility it craves, with as strong a negative correlation as I ever did see! However, the last few data points throw a spanner in the works as we watch sea ice build and Arctic waters cool. In terms of bivariate correlation for the period 1900 - 2022 we looking at a relationship throwing out r = -0.869 (p<0.001, n=123).
Land Surface Temperature & Sea Ice Extent
As Arctic land stations warm Arctic sea ice melts – twice simples! Except once again there are some interesting features that suggest the situation is more complex than this, starting with the reluctance of sea ice to melt over the period 1900 – 1960. Alarmists really ought to explain to us why the Arctic land surface temperature anomaly didn’t budge between 1945 and 1986. Note the reversal from 2016 onward; are we about to enter an era of global cooling or are these blips? In terms of bivariate correlation for the period 1900 - 2022 we looking at a relationship throwing out r = -0.663 (p<0.001, n=123), though the feature that really catches my eye isn’t the underlying trend but the periodic oscillations of the land surface temperature anomaly - more on these in a future edition!
Atmospheric CO2 & Sea Ice Extent
We arrive at the best slide I can possibly conjure for alarmists both great and small. Here we have the Keeling curve superimposed in Z-score glory on Arctic sea ice extent for last 120+ years. Get in there Gore fans! From 1980 onward the negative relationship is well impressive (if we ignore the recent blip) but things ain’t so clear cut back from 1900 to 1950 when both CO2 and sea ice extent rose together. Whoops.
A crumbly comment if I may: are we looking at two distinct planetary phases that are giving rise to the illusion that CO2 is forcing global temperature? I say this because there is such a thing as Simpson’s Paradox. Wiki tells us that, ‘Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined’. What Wiki should also go on to say is that by combining disparate groups we can also generate an illusory trend.
Thus, if Earth was bobbing along in mode A from 1900 – 1950 and mode B from 1950 – 2022 then by irresponsibly combining these two phases it would appear as if CO2 was forcing temperature when it wasn’t. This notion wouldn’t preclude the fact that CO2 still acts as a greenhouse for - according to some serious-minded hyper experts - the global impact of CO2 will have saturated back when levels were below 200ppm. Saturation and Simpson might explain where we are today, with a science that is more troubled than it is settled.
If we now turn to eyeballing the correlation between these two series we find a rather peculiar result of r = -0.947, p<0.001. n=123). This indicates that atmospheric CO2 is a better indicator of Arctic sea ice extent than Arctic land surface temperature and sea surface temperature! This is clearly ludicrous and a physical impossibility. What is happening here methinks is that sea ice, like atmospheric CO2, is responding slowly to long-term climatic changes, making these two highly-damped mechanisms a perfect statistical match for each other. Think in terms of sea ice and CO2 as integrals of transient signals, an analogy being a baked1 potato getting warmer in a pulsing microwave.
A Spanner Called Cross Correlation
The three Z-score slides have given us a decent start to the day and some bones to chew on. What we need to do now is roll out that there brain-bending technique called cross correlation to see how these pairs of time series data bounce around with each other. Forget Strictly Come Dancing, this is strictly come cross-correlating!
Three slides…
You know the drill by now. Positive-going bars peeking beyond the 95% upper confidence limit indicate a statistically significant positive correlation (sea ice plus variable of interest rising and falling together); negative-going bars peeking beyond the 95% lower confidence limit indicate a statistically significant negative correlation (sea ice plus variable of interest going in opposite directions). Bars at positive lags mean sea ice is responding to the variable of interest; bars at negative lags mean sea ice has changed before the variable of interest changes. Let’s get stuck in, noting that alarmism dictates lots of negative-going bars at positive lags; anything else means the wheels have fallen off their theory.
Right then, we start straight in with negative-going bars at positive lags, which means Arctic sea ice over the period 1900 – 2022 was generally responding to sea surface temperature as we may expect (warmer seas = less ice). Nice one. I’d like to point out the bar at lag zero (ice instantly responding to sea surface temperature) and the bars at lags of one to three years. The latter suggest that energy transfer from Arctic seas to the ice mass can take up to three years. Dare I say cracking?
Lovely jubbly! Arctic sea ice is responding in a very similar manner to Arctic land surface temperature with an instant effect and evidence of energy transfer up to three years later. Cracking!
What the heck? Gone are the dynamic relationships that make sense and in their place we have a slab of negative correlation largely dumped down at monster negative lags of between -1 and -12 years. Thus, we observe that Arctic sea ice is negatively correlated with atmospheric CO2 as alarmism dictates, but there remains the rather awkward fact that sea ice is making its melt moves years before CO2 thinks about rising. This would suggest atmospheric CO2 levels are a response to stuff happening on the planet rather than a driver of stuff happening on the planet. Whoops again!
To be fair to alarmists there is a weeny bit of negative correlation at lags of zero and +1 years but these are likely to be inertia of a much more significant system of energy dynamics that is years in the making. Putting this in plain English I could say that CO2 is late to the party, and neither did it bring a bottle of wine.
Scrambled Eggs
Interestingly enough it is the temporal signature of the Arctic sea ice dance that has finally cracked my chicken or egg koan, which is rather ironic given the amount of Arctic-flavoured alarmism generated through the legacy media, who seem to think loss of ice and snow is a bad thing and a totally frozen planet a good thing. They should try living there with just a willy warmer.
Kettle On!
Not so much baked as steamed. I avoid nuked spuds, favouring ye olde oven!
Another very interesting piece of analysis. I have already learned more than I ever expected to know about immunology, virology, vaccinology and herbology/natural medicine over the last few years and I can definitely feel the beggining of a budding interest in statistical techniques and wizardry although the latter does seem more of a mystery to me from the starting line so I shall keep reading your pieces and hope some shoots of knowledge start to appear to guide me on my way.
My first thoughts, looking at your graphs, were that we can't assume that the ice is of uniform thickness and that maybe the first half of the 1900's just reduces the thickness and not the area, and once reduced, the rising temperatures then started affecting the extent. Rather like when I microwave frozen soup. The first half of the time is to do with melting the blob of iced soup, then the overall soup-heating comes after that. (I know you like kitchen analogies!)