A little more Climate Change Analysis

There was an item on BBC news last night about the Met Office’s revisal of the the temperature trend for the next few years. They were predicting that the period between 2012 and 2016 would be higher than the long-term mean by 0.54oC, with a range of 0.36-0.72oC. It has now been revised to 0.43oC with a range of 0.28-0.59oC. What was a little frustrating was a comment made by David Shukman on the BBC news last night that this would mean 20 years of no significant warming. This is, I imagine, based on the claim that there has been no significant warming for the last 16 years.

As I pointed out in in an earlier post, there is a difference between the trend not being statistically significant and there being no significant warming. Given that the trend appears to be between 0.1 and 0.2oC per decade and the scatter in the anomaly data is about 0.1oc, the error in the trend over a period of about 15 years is likely to be about 0.15oC per decade. It will be similar to, or bigger than, the trend and hence, if one only consider a 15 year period, the trend will not be statistically significant. This doesn’t mean that there isn’t a warming trend. It just means that we can’t yet measure it. We would need to probably consider 20 years or longer to get a statistically significant result. In 4 years time, if we were to consider the previous 20 years, the error will be smaller than it currently is when we only consider 16 years of data, and the trend will probably be statistically significant. We don’t know this for sure, but we do know that 16 years is too short a time to determine a statistically significant trend.

I thought I would show this by considering the data that exists for the last 132 years. The data I’m using is the GISS Surface Temperature Analysis data from NASA. This gives the monthly temperature anomaly since 1880. Although I’ve written a code of my own to analyse this data, for this quick test I’ve used the Skeptical Science Trend Calculator. I’ve considered a series of 15 year intervals, starting in 1885 and progressing through to today. The values are shown in the table below. With the exception of 1985-2000, the trend in every interval is statistically insignificant. These are 2σ errors which means that there is a 95% chance that the trend lies between the (mean value – error) and the (mean value + error). Given that the error is bigger than the trend, we can’t rule out – over each of these 15 year time periods – that that the global surface temperature didn’t decrease. Even the 1985-2000 interval produces a trend that is only marginally significant.

ClimateChangeTable

Therefore if, at any time, we were only to consider the previous 15 years (I know this isn’t 16, but it’s close enough) we would always conclude that there is no statistically significant warming trend. The bottom row of the above table, however, shows the warming trend from 1880-2012. It is 0.064oC per decade with an error of 0.007oC per decade. This is clearly statistically significant. Below I repeat the figure that I included in my previous post which shows the anomaly data from 1880-2012 together with the best-fit trend line. It’s very clear that there has been warming since 1880 and that the mean surface temperature is about 0.85oC warmer today than it was in 1880 (which is the same as 0.064oC per decade over a period of 13 decades).
1880-2012TrendNoErrors

What I’m trying to get at here is firstly that just because something is not statistically significant, does not mean that it is not significant. It just means that we don’t yet know with any certainty. Secondly, if one is going to make claims about the significance of global warming one needs to use a time interval over which a statistically significant trend can be determined. If we only ever consider the past 16 years then the measured trend will always be statistically insignificant even if there is real, long-term, warming trend. It’s a very important issue and I’m more than happy to discuss and debate this with others. I’m just not willing to do so with those who misuse, or don’t understand, the data or the anaylsis.

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7 thoughts on “A little more Climate Change Analysis

  1. OMG! It’s happening faster than we thought! OK, maybe not quite that fast. It seems to have slowed down a bit or, depending who you ask, “paused”. We’re just having a bit of trouble detecting it right now. But that doesn’t mean it isn’t happening! What if it is? OMG!

    • Do you really think that we’re having trouble detecting it right now? Do you think it is possible to detect it right now? The whole point of this post was to show that you cannot make a statistically significant statement about the warming trend unless you consider a sufficiently long timescale (20 years or more). This isn’t opinion. It is simply a consequence of the difficulty of detecting a signal in data that is noisy.

      Over the period 1997 to 2012 the trend is 0.098 ± 0.143 oC per decade. All we can say is that this data suggests (with 95% certainty) that the warming trend has been between -0.045 and 0.241oC per decade. We can say with certainty that it is not as high as 0.3oC per decade and that it can’t be cooling faster than -0.1oC per decade. But, given the data we currently have, this would be roughly true for any 16 year period that we consider. This is also not an issue with the analysis of with the measurements. It is simply a consequence of this data being naturally variable.

      If you really think that it is somehow significant that we cannot detect a statistically significant warming signal in the data from the last 16 years, then you clearly have a poor understanding of data analysis.

      • “Do you really think that we’re having trouble detecting it right now?”

        I really think you’re having trouble detecting facetiousness.

        “Do you think it is possible to detect [global warming] right now?”

        Of course—do you deny it? Then explain why the ice is melting* and the divers beastes and fowles show ominous alterations in their behavior. Ewes with three horns express bloody milk. Just last week, during the rain of fire, a child was born already speaking, begging to be killed. The other day I swear I saw 50 million climate refugees, but by the time I got my camera out they were gone. You only have to look outside your window: inauspicious shit is happening everywhere.

        Isn’t it?

        *When I were a wee lad, ice would sublimate directly, as the Good Lord intended.

        “The whole point of this post was to show that you cannot make a statistically significant statement about the warming trend unless you consider a sufficiently long timescale (20 years or more).”

        Here’s a non-facetious question: where did the number 20 (or, to be climatically pedantic, 17) come from? Is it a natural constant?

        “But, given the data we currently have, this would be roughly true for any 16 year period that we consider.”

        Unless, of course, it was a period of rapid warming.

        And BTW, if you think it’s *not* significant that they can’t say whether there’s been any global warming over the last 16 years, then you have a poor understanding of popular psychology. This admission is going to weaken the alarmist cause, like it or not.

      • I’ve said this before, but I’m going to stop responding. Life’s too short and this is going nowhere. Given that I currently have an open comment policy, feel free to continue commenting if you wish to do so.

        I will, however, attempt to answer this one last question and will try to do so as completely and thoroughly as I can (your pedantry will probably win out though).

        Here’s a non-facetious question: where did the number 20 (or, to be climatically pedantic, 17) come from? Is it a natural constant?

        The temperature anomaly (GISSTEMP, NOAA, ….) has a natural variation of about 0.1oC. What we are interested in knowing is whether or not there is a warming trend of between 0.1 and 0.2oC decade. If we consider only a decade of data, the error in the trend (due to the natural variation) will be about 0.2oC per decade. Therefore we cannot make a strong statement about the warming trend if we consider only 10 years. If we consider 20 years, the error in the trend will be about 0.1oC per decade. We still can’t make a strong statement, but it will be more statistically significant. Given that we want to know if the trend is bigger than 0.1oC per decade we would want the error to be smaller than 0.1oC per decade which will require considering more than 20 years worth of data (the more we consider the smaller the error).

        If we could reduce the scatter in the anomaly data, we could reduce the error. Given that the scatter is probably natural, this probably isn’t possible.

      • Very helpful answer (though I think you will communicate even better if you drop the defensiveness).

        What, in your opinion, causes the “natural variation” and “natural scatter”?

        NB—these questions are merely of technical interest and are far less important than the ones I’ve asked you on the “Fake Skeptic Draws Fake Graph” article.

      • You’re giving me advice about how best to communicate. That’s rich. I think you’d communicate better if you weren’t so pedantic and pompous, but far be it from me to give advice to others.

        I don’t know what causes the natural variation. El Nino, La Nina, Solar variability, ….. Noone is suggesting that all variations in global surface temperature are due to the influence of man, just that there is good chance (better than 50%) that the upward trend in temperature over the last 30/40/50 years is primarily due to our releasing of large amounts of CO2 into the atmosphere.

        I really am doing a bad job of not responding. Maybe it’s my natural sense of optimism (which is slowly being beaten out of me).

  2. Pingback: Climate change – statistical significance | To the left of centre

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