What’s the present trend in global surface air temperature? Good question.
We can estimate it from observed data, but there’s uncertainty in our estimate. Lots of uncertainty. One thing we’ll want to do is use recent data in order to get the recent trend, so let’s use data from some starting time to the present, and apply the best-known and most-used method, linear regression. The more recent the data on which we base our estimate (the later our starting time), the more it will be relevant to what’s happening now. But — the later our starting time, the less data we’ll have to work with so the more uncertain will be our estimate. That’s just the price we pay.
Let’s not cut corners on uncertainty. We’ll use the data from Cowtan & Way, and try all starting times from 1975 through 2005. We’ll estimate the standard error of our regression using the method of Foster & Rahmstorf (2011). We’ll also construct 95% confidence intervals, not using the “plus-or-minus two sigma” approximation which is rooted in the normal distribution, but using the t distribution because as we use smaller and smaller time spans the number of effective degrees of freedom decreases. This will give us larger uncertainty ranges (for 95% confidence intervals), as it should. Although for earlier start times the number of degrees of freedom will be large enough that the normal-distribution and t-distribution methods will be indistinguishably close, for later start times they will diverge.
We can then plot, for each starting time, the estimated rate of warming together with its 95% confidence interval. And here it is:
It should be borne in mind that the “raw statistical uncertainty” as shown by the 95% confidence ranges, are simply what meets the eye — there’s more uncertainty still. For instance, there are a lot of start years tested, so it’s far more than 5% likely that at least one of the given 95% ranges does not include the true value (see this). There is uncertainty in the data itself, both possible bias due to unknown factors and sheer uncertainty in the measured values even apart from bias. Therefore we should look upon the ranges shown in the graph as reliable but uncertain indicators of the true trend.
Yet despite those shortcomings, the given calculation includes enough consideration of uncertainty, treated in sufficiently rigorous fashion, to be a useful guide to what we can reliably say about the present trend in global average surface air temperature.
I would draw two main conclusions from this analysis. First, there really isn’t reliable evidence that the genuine trend (apart from the short-term fluctuations) is different from its value for 1975 to the present. Second, there really isn’t reliable evidence of a nonzero trend since 1997, in a purely statistical sense. These two conclusions might seem to some to be contradictory, but they’re not. Their difference serves to emphasize that for time spans less than about the 30 years which meteorology has settled on empirically, the uncertainty in trend estimates is big enough that we’re not able to distinguish between alternatives in a purely statistical sense.
One could argue that my last sentence isn’t right. After all, linear regression isn’t the last word in trend analysis, and one might make a strong case that a Bayesian approach would distinctly favor one conclusion over the other. But in my opinion, the impressive level of uncertainty in trend analysis over time spans of less than at least three decades, is the real take-home message from careful study of the data.
That may make some people uneasy — that there’s no ironclad smack-down of either claim just from basic analysis of bare numbers. But again, that’s the price we pay for making an honest attempt (albeit a necessarily incomplete one) at actual rigor. It’s truly great that being a statistician allows me to play in everyone’s backyard — but it comes at the price of occasionally having to be the voice of sobriety who throws cold water on others’ heat of passion.
Finally, for those interested in what I consider a good visual portrayal of the situation, here’s my now-”standard” display of the trend from 1975 through the end of 1999, projected into the future, with dashed lines 1 and 2 standard deviations (of the residuals) above and below the projected trend, compared to the data from 2000 to the present:
If that’s what you call a “pause,” then it’s not a very impressive one.