Fooled by noise

I talked here about a post by Tamino who writes Open Mind, which discussed signal and noise, and how easy it was to get mislead by short-term random changes in the data of a time series.   Such considerations are why I often show extreme-adjusted or smoothed data, because these processes allow us to disentangle random fluctuations from the underlying trend.

He has written another post about this issue called Fooled by Noise.  I've summarised it below.


The chart below shows NASA's calculation of the global temperature anomaly. Observe how much the data fluctuate.  Hard to detect trends!  But some denialists maintain that global temperatures have started dropping again, over the last couple of years.  Of course, we can see similar downward spikes right through the last 140 years, only to be reversed later.  So how can we get a better handle on the data?

This chart shows the same data, except it's an annual average.  By taking a 12-month average, the random fluctuations are reduced.  Though the "spikiness" of the data has been reduced (i.e., the random fluctuations have been reduced) there are still some fluctuations, plus also some obvious longer waves or cycles.

The chart below shows even more smoothing.  It plots the 5 year averages of the monthly anomalies.  Note, now, how clear the trends are.  Global temperatures fell from circa 1880 to 1910, then rose steadily until the early 1940s, before levelling off until the late 70s.  The rise then resumed with a vengeance, and the most recent 5 year period shows a sharp jump.  The stabilisation of global temperatures from 1945 to 1975 despite rising levels of CO₂ is attributed to the equally rapid rise in the emissions of sulphur dioxide.  When acid rain was brought under control by scrubbing the smoke from factory and power stations flues of SO₂ in the late 70s, the underlying trend due to CO₂ was quickly revealed.  Note that you can't blame the most recent spike on El Niño.  The equally strong El Niño in 1998 barely tweaks the 5 year average.

The decadal averages are even clearer.  Once again El Niño is undetectable in the data.

You can apply the same analysis to the extent of Arctic sea ice.  Here is the annual chart, and below that is the chart of the decadal averages.

The moral of the story is that when denialists say "Arctic sea ice is recovering" or "global temperatures have stopped rising" what they are citing as evidence is unsmoothed data, still embodying random fluctuations.  We can only be sure global temperatures have peaked or the extent of Arctic sea ice has troughed when the decadal averages have turned, because these averages dramatically reduce random data errors, so we can see the true trends.  And they haven't: global temperatures are still rising and Arctic sea ice is still declining.  Nor would it be logical for them to do so,  except temporarily after a massive volcanic eruption, when sulphur dioxide is released into the atmosphere, lowering global temperatures. And as you can see from the decadal averages, previous eruptions cannot be seen in the data, though they do appear in the annual data, e.g., Mt Pinatubo in 1991.