# 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: