Modelling Arctic Sea Ice (part 1)

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

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

Despite being kosher, the first three of these time series contain too many nuts. That is to say errors of measurement and wildly fluctuating real world values give rise to outliers and rather noisy data. Noise can be a real problem when it comes to modelling and the first thing a statistician will do is examine and process outliers. Smoothing is a commonly used technique and there are all manner of ways we can go about this. My favoured method is to apply the T4253H filter.

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: