In the last post I graphed the average temperature for 2015 so far with the annual averages prior to that. It’s certainly not the clearest way to show things, and someone who doesn’t read the text and pay close attention could get the wrong impression. It was also pointed out that there may be seasonal differences in the way temperature has changed; maybe January through April has behaved differently than other times of the year. Finally, the inherent scatter in a 4-month average is bound to be higher than that in an annual average.
In an attempt to present things more clearly, here are a few more views of where we are. We’ll begin with year-long averages for all the data points, but to include the most recent data let’s end each year with April. Here is the average temperature for each May-through-April period since 1880:
Another popular choice, and in my opinion a very good one, is to plot 12-month moving averages. In those terms here is where we are:
Let’s also take a look at the seasonality issue. I took the data since 1970 for each month separately, and fit a smooth (modified lowess) to get some clue about how different times of the year may have differed. Here are the smooths themselves, one for each month, and for one of the months I have highlighted the result, plotting it in red and with a thicker line:
The one in red, which looks distinctly different from the others, is the month of February.
As I have often emphasized, fitting a smooth isn’t the same as testing for a genuine change in the trend. But it is suggestive, so let’s isolate February data and try to fit an alternative model other than a straight line. I fit a piece-wise linear function to imitate the behavior of change-point analysis, and the best fit was for a change in 2000:
Considered as an isolated statistical test, this would pass statistical significance and demonstrate that the February trend has not been constant. But when one takes into account all the possible start years one can try, as well as the twelve different months that one could choose, it turns out that the result is not significant.
So, we can’t really claim to have demonstrated a trend change in February. That doesn’t mean there hasn’t been one, just that there’s not yet enough evidence to say so definitively.
What this means is that although it is certainly the case that February temperature has shown a different short-term pattern than the other months, the difference hasn’t yet been great enough or long-lasting enough to rise to the level of trend. While it certainly does look like its trend has changed, with so many places to look it was likely all along that we would find one which looked that much like a trend change.
I will also mention that this conclusion is based on studying only global temperature data in isolation.