There is a recent post on Watts Up With That (WUWT) called are we in a pause or a decline (now includes at least April data). The answer, in my scientific opinion, is neither. I don’t quite know what argument is being made in this post but it seems to be that the author thinks we could fit a sine wave to the temperature data and hence the fit suggests we’re about to enter a cooling phase. Of course, even underneath this sine wave is an underlying warming trend, but there’s no mention of that in the post.
I was going to address one particular thing. The post goes on to say
For RSS the warming is not significant for over 23 years.
For RSS: +0.123 +/-0.131 C/decade at the two sigma level from 1990
For UAH the warming is not significant for over 19 years.
For UAH: 0.142 +/- 0.166 C/decade at the two sigma level from 1994
For Hadcrut3 the warming is not significant for over 19 years.
For Hadcrut3: 0.092 +/- 0.112 C/decade at the two sigma level from 1994
For Hadcrut4 the warming is not significant for over 18 years.
For Hadcrut4: 0.093 +/- 0.108 C/decade at the two sigma level from 1995
For GISS the warming is not significant for over 18 years.
For GISS: 0.103 +/- 0.111 C/decade at the two sigma level from 1995
For NOAA the warming is not significant for over 18 years.
For NOAA: 0.085 +/- 0.104 C/decade at the two sigma level from 1995.
Notice that the statement made is “not significant“. This statement is simply wrong. The above numbers are from linear regression of the various temperature anomaly data sets. In each case, the best-fit line has a trend of close to 0.1oC per decade. However, this data is quite noisy and so there is an uncertainty in the trend and what is presented above is the 2σ errors on the trend line. This means that there is a 95% chance that the actual trend lies between trend-error and trend+error.
That for all the intervals considered above (which aren’t the same for each dataset) the 2σ errors are larger (in magnitude) than the magnitude of the trend, means that we can’t rule out (at the 95% level) that there hasn’t been cooling. However, we also can’t rule out that the actual trend isn’t twice as big as the best-fit trend. If the author of this post thinks they can use this analysis to claim there’s been no warming, then I could use exactly the same argument to suggest that it’s been warming very rapidly. Neither is the correct interpretation of this analysis.
This analysis does not tell us that the warming is “not significant“, it tells us that it is “not statistically significant“. These are very different things. The term “significant” implies there has been no warming. The term “statistically significant” means that we can’t say, with certainty, what it is. The data, however, suggests that it is most likely close to 0.1oC per decade. This is also not surprising. You can go to the Skeptical Science trend calculator and see how many years of data are typically required for a statistically significant trend to be determined. It’s typically in excess of 10 years and often close to 20 years. That the trend for the last 18/19 years is not statistically significant does not mean that there is a good chance that there’s been no warming. It’s simply a consequence of the requirement that we need to consider sufficiently long time intervals if we wish to accurately determine the trend in the temperature anomaly data.
...and Then There's Physics 
I should have put this in the post, but you’ll notice that the first three data sets presented in the WUWT post consider 19 years of data, while the latter 3 consider 18 years of data. That’s because if you consider 19 for these datasets, the trend becomes statistically significant. For example, if we consider the last 19 years, the HADCRUT4 data has a linear trend of 0.119oC per decade with a 2σ error of 0.104oC per decade.
I think that the point of that post is that there is now a period of reasonable length which is “not statistically significant“. You’re right, there is a difference between “not significant” and “not statistically significant“, but the point you miss is that global warming is not keeping up with the rise in CO2 emissions. Even if the noise is masking a modest rise in temperature, it’s nowhere near the rise predicted by computer models.
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Indeed, but still within the range of the models. That, however, is not really the message that this WUWT post is presenting. It’s essentially claiming that it has either paused or is declining, neither of which is likely given the data. Also, the large temperature spike in 1998 clearly makes the trend from the mid-90s to today flatter than it would be without that spike. If one considers 1983 – 2013 you get a trend of 0.166 +-0.053oC per decade. There is a chance (although I would not claim that this is the case) that the underlying trend is between 0.15 and 0.2oC per decade, which would be quite significant. Maybe it is not, but we can’t rule that out and to assume that it is not is incorrect.
Something that I would add is that given that there has been period of reasonable length which is not statistically significant is not really all that relevant. You can try this yourself. Go to the skeptical science trend calculator and choose some random year (1995 for example). Then work back until you get a statistically significant warming trend. It will typically be longer than 10 years and often between 15 and 20. This is simply, in a sense, the nature of the data and because of the level of warming that is of interest.
The natural scatter in the data is between 0.1 and 0.2oC. This means that if you only consider 10 years worth of data, the error in the trend will typically be 0.2oC per decade. Therefore a 10 year period will only be statistically significant if the trend exceeds 0.2oC per decade. If you consider 15 years, the error will typically be 0.15oC per decade. Hence, the trend will only be statistically significant if it exceeds 0.15oC per decade. I would argue that we’re interested in knowing if the trend in the temperature anomaly data exceeds 0.1oC per decade. Hence, given the natural scatter in the data, we need to consider periods in excess of 15 years before we are likely to be able to determine a statistically significant trend. I appreciate that the WUWT post uses 18 and 19 years, but that’s still short enough that the error is large enough so that the trend is not statistically significant. Wait a year or two and that is unlikely to still be the case (unless you continue to move the start year).
You can also try the period 1977 to 1995 on the trend calculator. The flat trend is within two sigmas.
Indeed. There are numerous periods of 15 years or longer during which the trend is not statistically significant at the 2σ level.
The whole issue of statistical significance is all a little frustrating. It very much depends on your choice of significance. There are some science areas where 1σ is seen as good enough. Others (particle physics for example) where they require 5σ. The 2σ choice here is somewhat arbitrary (although not a bad choice). If, however, it had all been presented with 1σ errors, we might not be having this discussion. Although, the skeptic argument may then have been that 1σ isn’t rigorous enough.
If you use the exact same logic you use for the 2001 to 2013 period we can conclude there is no warming, it just isn’t statistically significant. But a good scientist goes beyond the raw statistics. The wide year-to-year variations in yearly data are largely due to ENSO , the Solar Cycle and volcanic eruptions, None of these are causing temperatures to be low. The Solar Cycle is actually near its peak. A good unbiased scientist can only conclude that temperatures are not rising despite growing GHG emissions.
Hmm, I think I see what you’re suggesting. If you do 2001 to 2013 you get -0.020 +- 0.166oC per decade. Hence one could conclude that there has been no warming (or, more correctly, no rise in global surface temperatures) since 2001. A good scientist would, however, see if they can see why this might be and might conclude, indeed, that this is partly due to the large ENSO event in the late 1990s. There is, however, a bit of an issue with what you suggest. ENSO events don’t generate energy, they simply move energy from the oceans to heat the surface. If the evolution of the global surface temperatures for the last decade is primarily due to a large ENSO event in the late 1990s, we would expect to see an associated drop in ocean heat content. Well, that doesn’t appear to be the case. That’s continued to rise.
What about solar? As far as I’m aware the Solar TSI peaked around 1980 and has been dropping slowly ever since. This is one of the reasons why some are convinced that very soon evidence for anthropogenic global warming (AGW) will become very strong since it’s becoming clearer that it can’t simply be solar variation.
Volcanoes, well not so sure about that. Last big one was in the early 90s, so not sure why it’s relevant to data in the 2000s.
What one could, therefore, conclude is that the large ENSO event in 1998 did indeed have a big effect on the surface temperature trend for the period 2001 to 2013. However, instead of the surface temperatures dropping back to what they were prior to this ENSO event, they remained a couple of tenths of a degree higher than they were prior to 1998. The trend might be flat, but the magnitude is higher and that is tricky to explain through ENSO, Solar and volcanoes. At some point one might therefore expect the surface temperatures to continue rising once the underlying trend catches up to the rise due to the ENSO event. We’ll have to wait and see, I guess, but – in my scientific opinion – the evidence against AGW is weak.
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Absolutely. I tried 1980 to 1997.
No statistically significant warming.
Just so you know, I agree that there is long term anthropogenic warming. I may be wrong, but I think many, if not most of the posters on WUWT and Anthony Watts himself agree with that. The question is about the rate of warming, how serious it is, and what actions should be taken.
I accept all of what you say above. ENSO events may have significant impacts which extend for several years and these may be large enough to totally offset any apparent global warming for a decade or more.
I note that there has not been an extended period of flat temperatures like the recent one for some time. However, if one looks at the period of about 1947 to 1977 there is a 30-year period where global temperatures did not increase while CO2 emissions grew swiftly at something like the current rate. In your view, is there any chance that this apparent pause in warming could have been caused by ocean currents?
A tricky question and I should acknowledge that I am not an expert at the details of climate science, simply a physical scientists who understands physics and data analysis (at least, understands them quite well). I’ll do my best to answer your question.
Indeed, I do think that natural effects can mask an underlying warming trend. If you look at the global surface temperature anomaly data, the ENSO event in 1998 increased the surface temperature anomaly by more than 0.2oC. Hence, one would expect the surface temperatures after that to be higher than they would be had that event not happened and if the anthropogenic warming trend was dominating. After that one would not only expect the trend to appear shallower, but might also expect the noise to be greater (because of a big spike in 1998) and hence it would take longer to determine a statistically significant warming trend.
The period from 1947 to 1977 is maybe a little trickier to understand. However if you look at solar irradiance data, it increased by more than 0.5 Wm-2 between 1900 and 1960 and has been decreasing slowly since the mid-1960s. If one considers the CO2 forcing for the period 1900 – 1977 it is was probably about 0.8 Wm-2 (this is from ΔF = 5.35 ln(C/Co) with C = 330 ppm and Co = 280 ppm). Therefore anthropogenic forcings didn’t dominate in the earlier half of this century. I don’t know if this is why there was a long pause from 1947 to 1977. It does seem, however, that natural variations could more easily mask the anthropogenic effect during this period.
Since 1977, anthropogenic forcing has increased by a further 1 Wm-2 while Solar irradiance has been dropping. Consequently, the calculations suggest that anthropogenic forcings are now dominating. If correct, this should become fairly obvious. If the warming trend becomes statistically significant in the next few years despite solar forcing decreasing is going to make it very difficult to explain it any other way.
I don’t know if that has answered your question. Maybe not, but that is really the limit of what I know and would be happy for others who know more to add their views.
I think focusing on surface temperatures is a mistake. Sure they’ve been relatively flat over the past decade, but they only represent about 2% of global warming. It can be hard to explain short-term surface temp changes because they’re so noisy and there are so many influences – ENSO, aerosols, solar cycles, deep ocean heat storage, etc.
But if you look at global heat content, the increase hasn’t slowed at all.
http://www.skepticalscience.com/graphics.php?g=65
The slowed surface warming seems most likely due mainly to accelerated deep ocean warming, which also appears unlikely to last very long.
Indeed, I completely agree. In fact if your read the last paragraph of an earlier post of mine, that was essentially the argument I was making. I may well have used your ocean heat content graphic somewhere without giving proper credit. Apologies if I have. The evidence for global warming is overwhelming and – in some sense – maybe I should ignore these posts on WUWT that focus on temperature anomaly data only, as that may make it appear as though using temperature anomaly data alone has some merit.
The point of this post was really to just make the argument that statistical significance and significance are not the same and that to claim that there has been no warming simply because the trend could have been flat (but probably wasn’t) is simply wrong.
I should add that you have a point about the deep ocean warming. It’s very possibly having an important influence in the current evolution of the surface temperature anomaly.
On this subject, people might be interested to see a graph that I posted at Skeptical Science at the beginning of this year:
http://www.skepticalscience.com/argument.php?p=5&t=237&&a=11#89115
Thanks. In fact I’ve seen that before but didn’t know who had produced it.