A little more about the supposed pause or decline!

I wrote a few days ago about the possibility that, as far as global warming is concerned, we’re now in a pause or a decline. To summarise that post, there is no evidence that we are in a pause or a decline. If you’d like to know more, you can read my earlier post or feel free to use the comments box.

The basic argument being used is that if one uses linear regression to analyse temperature anomaly data for the last 18 years or so, the error (2σ) in the trend is larger in magnitude than the trend. One can therefore not rule out (at the 95% level) that temperatures haven’t decreased since the mid-1990s. This is illustrated below. The data is GISSTEMP data and the solid line shows the best-fit trend for the period 1995 to 2013 (0.108oC per decade). The 2σ error in this trend is 0.114oC per decade and so the two dashed lines illustrate the steepest and shallowest trends based on this 2σ error. It’s clear that the shallowest line has a gradient that is negative and hence indicates that this period could have been a period of cooling.

GISSTEMP data from 1995 to 2013 together with a best-fit trend  (solid line) and two lines illustrating the steepese and shallowest trends (dashed lines) based on 2σ errors.

GISSTEMP data from 1995 to 2013 together with a best-fit trend (solid line) and two lines illustrating the steepest and shallowest trends (dashed lines) based on 2σ errors.

Okay, so it is indeed correct that at the 2σ level we can’t rule out cooling during the period 1995 to 2013. However, the likelihood of a particular trend being correct is not the same for all values. It is normally distributed. This means that it is more likely that the actual trend is close to the best-fit value than to one of the extremes. Using the form for the normal distribution, the probability of the actual trend, P(x), lying in the range dx is
P(x) dx = 1/[σ (2 π)1/2] e[-(x - μ)/(2 σ2)] dx,
where μ is the gradient of the best-fit line. If we consider the GISSTEMP data above and consider the 2σ range about the best-fit value (-0.006oC per decade to 0.222oC per decade) the distribution looks like that below.

Distribution of trends for the GISSTEMP data from 1995 to 2013 and considering only the range within 2σ of the best-fit value.

Distribution of trends for the GISSTEMP data from 1995 to 2013 and considering only the range within 2σ of the best-fit value.


As is clear from the above figure, there is a finite probability that the trend is negative (cooling). However, we can actually quantify this by integrating the above function from -0.006oC per decade to 0. If you do so, you get a value of 0.006 or 0.6%. In other words, there is a 0.6% chance that the trend lies between the value 2σ less than the best-fit value and 0. You can actually go one step further and ignore the 2σ range and simply determine the chance that the trend is negative (i.e., integrate from -∞ to 0). What you get (not surprisingly) is 2.9%. There is, therefore, a 2.9% chance that the actual trend in the GISSTEMP data from 1995 to 2013 is negative. There is consequently, a 97.1% chance that the actual trend is positive.

However, one could argue that it’s not about whether or not the trend is positive; it’s about whether it is positive and significant. What is significant? Well we can consider various values. Using the same figure for the distribution of trends, one can show that there is an 85% chance that the trend is greater than 0.05oC per decade and a 56% chance that it exceeds 0.1oC per decade. So, basically it is indeed correct that we can’t rule out that the period from 1995 to 2013 (based on GISSTEMP temperature anomaly data) hasn’t been a period of cooling. However, detailed analysis of the trend likelihoods indicates that there is only a 2.9% chance of this being the case, while there is an 85% chance that the actual trend exceeds 0.05oC per decade and a 56% chance that it exceeds 0.1oC per decade. I’m not a betting person but if forced to bet on whether or not the period between 1995 and 2013 has been one of cooling or warming (based on GISSTEMP data) I know which way I would bet.

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8 Responses to A little more about the supposed pause or decline!

  1. Interesting, thanks. Did you have some thoughts on the issue or were you simply making me aware of the article?

  2. izen says:

    @- ” There is consequently, a 97.1% chance that the actual trend is positive.”

    How curious that it so closely matches the percentage of the scientific consensus….
    Clearly a conspiracy!!!
    (grin)

  3. cvdanes says:

    There are possibilities, and there are probabilities. As you so aptly pointed out, it is possible that we are in a period of cooling, but not probable.

    Sadly, there are people in this debate who are paid large sums of money to confuse the distinction. Keep up the good work of helping to alleviate the confusion!

  4. Amazingly, I had not noticed that. Of course, there is now a risk that some will claim that I’ve chosen these numbers so as to achieve that result :-)

  5. Thanks. Trying to do my best.

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