Have global surface temperatures not shown significant warming since the late 1990s?

Question

Those skeptical about the science of global warming have frequently alleged that the surface temperature record has "paused" since about 1998 and showed no significant warming trend (see this recent wattsupwiththat post as a representative example).

The mainstream climate science community has responded to this in several ways (see my italics in the quotes below highlighting the different claims).

Some deny that the pause exists or argue that recent extensions to the record show it to be a data error, see this news story from the Independent claiming:

A new study has found that global temperatures have not flat-lined over the past 15 years, as weather station records have been suggesting, but have in fact continued to rise as fast as previous decades, during which we have seen an unprecedented acceleration in global warming.

But other mainstream scientists accept the pause exists and seek explanations. A recent review in Nature starts with this admission:

For several years, scientists wrote off the stall as noise in the climate system: the natural variations in the atmosphere, oceans and biosphere that drive warm or cool spells around the globe. But the pause has persisted, sparking a minor crisis of confidence in the field. Although there have been jumps and dips, average atmospheric temperatures have risen little since 1998, in seeming defiance of projections of climate models and the ever-increasing emissions of greenhouse gases.

but continues

...Now, as the global-warming hiatus enters its sixteenth year, scientists are at last making headway in the case of the missing heat.

So some people don't believe there has been a pause and others are trying to explain the pause. My question is given the uncertainties have global surface temperatures shown no significant growth since about 1998?

Note for clarity I realise that most heat is not absorbed by the atmosphere and that climate change may well be continuing. That is relevant context but not the question. The question is about surface temperatures. So answer that first and provide context later.

Answer 1

The first thing to point out is that "no statistically significant warming" does not mean that there has been no warming, essentially it just means that there hasn't been enough warming to rule out the possibility that there has been no warming. If that sounds counter-intuitive, it is because it is, but that is the way frequentist statistical hypothesis testing works.

The way frequentist hypothesis tests work is broadly as follows: Say you have a hypothesis (H1) that you wish to support using a set of observations (X). Next you define a "null hypothesis" that is basically what you need to show to be false in order for your H1 to be true. For example, if you hypothesise that there has been some warming, then the obvious choice for H0 is that there has been no warming at all, i.e. the rate of warming is zero. You then calculate the p-value, which is the probability of observing a trend at least as large as that observed IF H0 is true. If the p-value is sufficiently small, say p < 0.05, this is taken as sufficient evidence that H0 is false so we say that "we reject the null hypothesis" or equivalently "the rate of warming is statistically significant" and otherwise "we fail to reject the null hypothesis" or "the rate of warming is not statistically significant".

Now the first point to notice here is that H0 should be the hypothesis you are arguing against. So for mainstream science, which suggests there will be warming due to the greenhouse effect, the natural H0 is that there is no warming. The "Skeptics" on the other hand hypothesise there is no warming, yet they are using that as their null hypothesis as well. This is a grave statistical error as it means that hypothesis testing no longer functions as a sanity check, as the skeptics are assuming that they are right and requiring evidence to prove them wrong. Mainstream science on the other hand are assuming that they are wrong (H0 is true) and asking if the observations refute H0 (implying, but not proving that H1 is true).

Now for the second point. If the trend is not statistically significant, there are at least two reasons: Firstly H0 actually is true, and secondly H0 is false, but there is insufficient data to demonstrate that it is wrong. Consider flipping a two-headed coin four times. The traditional test for the bias of a coin will fail to reject the null hypothesis as even getting four flips in a row will happen by chance with a fair coin more that 5% of the time. This is because the power of the test (the probability of rejecting the null hypothesis when it is actually false) is not very high.

This is the case for the "not statistically significant" observed trend we have now, given the expected size of the anthropogenic trend and the noise in the data (weather), the power of the test is so low that it is not at all surprising that the result is not statistically significant. Easterling and Wehner have demonstrated that the climate will occasionally show decadal (or more) periods with little or no trend, and that this is also found in model simulations.

To add to this, the hypothesis test assumes that you are looking at an n-year period chosen at random. If you cherry pick the start and end dates, the power is even lower, unless you compensate for the implicit multiple hypothesis testing.

The quote from the Independent does not show that it is a "data error"

A new study has found that global temperatures have not flat-lined over the past 15 years, as weather station records have been suggesting, but have in fact continued to rise as fast as previous decades, during which we have seen an unprecedented acceleration in global warming.

Saying that temperatures have not "flat-lined" is not incompatible with the rate of warming not being statistically significant, because the latter just means we cannot rule out the possibility that the underlying rate of warming is zero. The problem is that most journalists, and an even larger proportion of climate skeptic bloggers don't really understand hypothesis testing.

Saying that the rate of warming is the same as that before is not incompatible with the rate of warming being not statistically significant either for much the same reason.

The comment about acceleration needs a bit more evidence though.

The pause in warming is interesting, it is well explained as a result of the effects of ENSO (see the paper by Foster and Rahmsdorf), and it is providing an interesting area for research in climate variability. This does not however mean that the underlying rate of warming has changed, or that carbon dioxide is not a greenhouse gas etc. So the two views are not actually contradictory.

To give a direct answer to the question, whether the warming is significant or not depends on the dataset you look at, how you choose the period in question, your statistical assumptions (e.g. taking into account autocorrelation and multiple hypothesis testing due to choosing the period after looking at the data etc.). Even then, it doesn't necessarily mean much unless you also look at the statistical power of the test.

Answer 2

In this answer, I focus on the Cowtan and Way paper, which seems to be causing some of the dynamics of this debate (e.g., the The Independent article mentioned by you).

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I am assuming that when you speak of 'significant', you mean 'statistically significant'. There is another meaning to the word, and if you meant that, then this answer isn't very useful. I'm also assuming that you would like to take "no upward trend" as your null-hypothesis.

Given the amount of extrapolation done by Cowtan and Way, I suggest that their analysis is not suitable to answer your question in the negative [this is awkwardly phrased because you already have a 'not' in your question], but rather more aimed at providing a trend (i.e. point) estimate only. (Indeed there doesn't appear to be a claim about significance in either the abstract or the conclusion of the paper.)

However, in their paper (p. 11) they do provide us with:

Dataset          Trend +/- sigma
Hybrid s = 1.0   0.119 +/- 0.076

which might be used to answer your question in the positive (at least if this dataset/period is the only data admitted).

With some further assumptions, that translates to a p-value of about 6%. Given all the extrapolation going on, I'd suggest that objectively sigma should have been estimated higher, and therefore I'd suggest that the p-value is also higher. I don't know what significance level (to which the p-value should be compared) is conventional or justified in this area, but I wouldn't be surprised if it were 5% or less.

Summary: The Cowtan and Way paper isn't, and doesn't provide reason for us to be, conclusive either way with regards to your question. (That is: It can't give "significant" and it can't give "not significant".) If their data/period would be the only available, then their analysis would suggest: no significant upward trend.

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I have noted that such things are hotly debated. Perhaps it is good to state my position. I don't care. (And I don't follow this debate.)