Modelling Arctic Sea Ice (part 3)

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

In part 1 and part 2 of this series we noticed that the time series for mean annual Arctic land surface temperature anomaly (LSA) was rather knobbly. Periodic is the word I used and I suggested the period to be about 13 years, which is almost solar but not quite. This morning we are going to take a closer look at those knobbles and see if there is indeed a connection to solar cycles, so I suggest something funky to sip like a ginger and lemon tea.

I am going to start out by plotting the standardised scores for LSA along with standardised scores for the mean daily sunspot number for the period 1900 - 2022. These aren’t just any old sunspot numbers but the WDC-SILSO sunspot numbers held at the Royal Observatory of Belgium – you can grab these for yourself from this handy page.

Mean Daily Sunspot Number

For those not familiar with the mean daily sunspot number (SSN) I shall start by saying collecting and deriving this figure is the longest running scientific endeavour in the world. Here’s what Wiki has to say:

Astronomers have been observing the Sun recording information about sunspots since the advent of the telescope in 1609. However, the idea of compiling the information about the sunspot number from various observers originates in Rudolf Wolf in 1848 in Zürich, Switzerland. The produced series initially had his name, but now it is more commonly referred to as the international sunspot number series.

The international sunspot number series is still being produced today at the observatory of Brussels. The international number series shows an approximate periodicity of 11 years, the solar cycle, which was first found by Heinrich Schwabe in 1843, thus sometimes it is also referred to as the Schwabe cycle. The periodicity is not constant but varies roughly in the range 9.5 to 11 years. The international sunspot number series extends back to 1700 with annual values while daily values exist only since 1818.

What happens on the ground is a whole bunch of observatories will have a go at counting the number of sunspots each day and report their sighting to the WDC-SILSO database who then compute the mean value of all daily observations. Back in 1900 some 365 observatories provided a reading, whereas in 2022 some 14,273 observatories provided a reading, so the error associated with this measurement is very small indeed. The 365 (or 366) mean daily counts are then averaged over the year.

So let us have a look at those standardised scores not as they stand but as a first order differenced series. This sounds scary until you realise all we are doing is plotting out the year-to-year change in mean LSA and mean SSN instead of the absolute annual values. Why so? Because plotting out the differenced series removes any underlying long-term trend and leaves only the jiggling about knobbly bits, making it easier to compare two knobbly time series. Try this:

Isn’t that fascinating? There are times when a bump in land surface temperature follows a bump in solar activity, and there are times when a bump in land surface temperature precedes a bump in solar activity. All in all my eyeballs suggest there may be a connection since the jigging about has a similar feel. We better settle this using that spanner again…

A Spanner Called Cross Correlation

SIDE NOTE: Positive-going bars peeking beyond the 95% upper confidence limit indicate a statistically significant positive correlation (mean daily sunspot number variable of interest rising and falling together); negative-going bars peeking beyond the 95% lower confidence limit indicate a statistically significant negative correlation (mean daily sunspot number plus variable of interest going in opposite directions). Bars at positive lags mean the variable of interest is responding to mean daily sunspot number (i.e. potentially causal relationship); bars at negative lags the variable of interest has changed before the mean daily sunspot number changes (i.e. not causal).

Now ain’t that just fabulous? We’ve got evidence of a possible causal relationship between mean daily sunspot number and land surface temperature anomaly (positive bars at positive lags), but we’ve also got evidence suggesting this relationship cannot be causal (positive bars at negative lags). Then there are those negative correlations at positive and negative lags that confuse the issue. Brain ache or what?

Before anybody’s head explodes just drink in the whole picture. Can you see how regular the pattern of up then down is? If we measure the positive peak-to-positive peak distance we are talking 11 years plus or minus a couple of years. If we now measure the negative peak-to-negative peak distance we are still talking 11 years plus or minus a couple of years. This, ladles and jelly spoons, is evidence of the mean daily sunspot number and Arctic land surface temperature anomaly oscillating in and out of phase with a periodicity that matches the solar cycle of approximately 11 years.

Cross-correlation (a technique that is used in engineering) reveals that the temperature of the Arctic land mass is most definitely linked to the solar cycle but it isn’t rigidly locked to the solar cycle. Phase shifts are occurring (most likely due to lengthening and shortening of the cycle periods for both series) and these serve to muddy the water such that if we are not aware of this it would appear as if there is no relationship.

Pulling The Wool

Indeed so, for if I run a bivariate correlation of the differenced series depicted in the first slide I end-up with a total flop at  r = 0.034 (p=0.709, n=122). If I was an unscrupulous sort pushing a political agenda or bigging-up my academic career or flogging my latest book then I’d report this as hard factual evidence that the sun doesn’t play a role in determining Arctic land surface temperatures. I’d back this by pointing out that the total solar irradiance (TSI) of the sun has changed very little since the seventeenth century and present (0.05% - 0.1%) and changes very slowly on decadal and longer timescales so cannot possibly be the driver for the changes we’ve seen in land surface temperature over the last couple of decades. Except I’d be pulling the wool, and very few people would understand why.

What, How?

What we’re looking at here is a mechanism that is likely nothing to do with solar irradiance (visible and infra red light) and everything to do with the interplay of electric fields, magnetic fields, ionised particle streams (solar wind), cosmic rays, extreme ultraviolet, X-rays and gamma rays. There’s a whole bunch of stuff I shall be teasing out of NASA/NOAA wool later this year that reveal issues in how we go about measuring TSI and how the big players go about deliberately ignoring solar effects on climate, including the fudges embedded within CMIP6 that were supposed to tackle the phenomenon of solar particle forcing. Skeletons in the closet are numerous as we shall see in the coming months!

Kettle On!

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UPDATE:

Readers are understandably linking these findings with the work of Dr Henrik Svensmark. All I shall say at this point is that there is more cosmic connection to come! Herewith a list of links to introduce you to aspects of climate work with a cosmological rather than carbon perspective:

Svensmark The Cloud Mystery

Professor Henrik Svensmark 12-12-2015 Essen, Germany

Nir Shaviv & Henrik Svensmark - Welche Rolle hat die Sonne im Klimawandel gespielt?

Solar v Anthropogenic Causes of Global Warming - Dr Nir Shaviv

The Sun Also Warms: Dr. Willie Soon Shows the Sun-Climate Connection

The Chilling Stars: A Cosmic View of Climate Change - Dr Henrik Svensmark