Modelling Arctic Sea Ice (part 4)
Using a supplemented dataset incorporating NSDIC’s Sea Ice Index (SII) to explore the relationship with sea ice extent, sea surface & land surface temperate anomalies
So far in this series, which began back on 10th February, we’ve looked at cross-correlation function plots of:
Sea surface temperature (SST) with land surface temperature (LST)
Sea surface temperature with sea ice extent (SIE)
Land surface temperature with sea ice extent
Atmospheric CO2 with sea ice extent
Sunspot Number (SSN) with land surface temperature
Sunspot Number (SSN) with land surface temperature over the period 1900 - 2022 is arguably the most surprising result so far, so here is that slide again by way of refresher:
Positive-going bars peeking beyond the 95% upper confidence limit indicate a statistically significant positive correlation (SSN and LSA rising and falling together); negative-going bars peeking beyond the 95% lower confidence limit indicate a statistically significant negative correlation (SSN and LSA going in opposite directions). Bars at positive lags mean LSA is responding to SSN (i.e. a potentially causal relationship); bars at negative lags indicate LSA has changed before the SSN changes (i.e. not causal).
Hence 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 is not causal (positive bars at negative lags). Then there are those negative correlations at positive and negative lags that cloud the issue (see what I did there?).
What smacks us between the eyes is that regular wave-like pattern of up then down. 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. We’re talking solar!
The Whole Hog
We now need to complete the picture by looking at SSN with SST and SSN with SIE, and whilst I’ve got my crayons out we can go the whole hog and look at SSN with CO2. Here are those slides:
Now the interesting thing here is the correlation between sunspot number (SSN) and Sea surface temperature (SST) is stronger than that for land surface temperature (LSA), with a peak correlation of r = 0.392 being reached after a lag of three years, compared with a peak correlation of r = 0.277 for LSA. Though tricky to say we might guess that solar activity impacts more on Arctic waters than it does on land mass, but we shall be putting this hypothesis to the test in a short while.
Meanwhile, we see a statistically insignificant wobble for SSN and SIE, which suggests the primary effect is on Arctic waters and land masses that then go on to induce melting. This makes sense, as does the non-descript relationship between SSN and CO2. Nothing to see here, folks!
A Spanner Called ARIMA
So what about testing that hypothesis that the solar influence on Arctic sea ice extent is primarily a watery affair? This is where multivariate time series modelling using ARIMA comes in. We set SIE as our dependent variable then start adding the four independent variables of SST, LSA, CO2 and SSN one at a time and see where we end up.
Here’s how things turned out:
Only one of the four independent variables made it through as a statistically significant predictor of Arctic sea ice extent and that was T4253H smoothed mean Arctic sea surface temperature (p<0.001). Sorted. Warm water melting the ice it is then. All very sensible indeed but it’s nice that the numbers follow through.
Pudding
I always like to finish a meal with a pudding, so here is the performance of this simple ARIMA model in terms of crayoning:
Now that is what I call tidy! So tidy, in fact, that I decided not to add in predicted values and plot the 95% confidence envelope only. The orange lines mark the four years that popped out of the modelling process as outliers. We’ve detected two sudden declines and two sudden back-to-back increments – are the latter a sign of things to come?
Kettle On!