Pause or No Pause

Has there been a “pause” in Global Warming since 1998?

I contend that there has not, but it really depends on how you define “pause”. My contention is that definitions which show a pause are not statistically useful.

[My analysis is based on NASA’s Global Land-Ocean Temperature Index which may be obtained from here and is described here. Other datasets exist which may show slightly different results. Data extracted on 13 Dec 2015 (so this does not include a full year of 2015 and my analysis stops at 2014)]

So let’s start with the obvious. When was the last time the temperature was at the level of 1998? Why in 2012. And because these data are noisy let’s be a little generous and ask instead: When was the last time the temperature was within .04°C of 1998? In 2013. Since the last year of full data was 2014 you might say “Hey, basically the temperature hasn’t changed at all since 1998.” and draw a flat line on the graph from 1998 to now (or at least to 2013).

But this is a statistically poor technique. I mean if you look at the scatter plot it’s pretty clear a horizontal line doesn’t fit the points well. It’s sort of saying “Let’s assume there is no trend and see what we get.” A much better way of proving a pause is to say “Let’s assume there is a trend and prove that that trend is zero.”

The data are noisy. You can’t just draw a line from start to end and say “This is what is happening.” The simplest way to extract a trend from noisy data is to apply a linear regression found by least squares — that is to find the line which minimizes the sum of squares of the errors — the error being the difference between what the regression line predicts for the temperature of a year and the actual temperature reading.

If there be no trend, if global warming have paused, then the slope of the line will be near zero. It won’t be exactly zero because the data are noisy.

If we look at each year since 1998 and generate a line based on the data from 1998 to that year then if warming were paused we’d expect that about half the lines would have a positive slope and half a negative one.

Slopes of the regression line for each year since 1998 in °C/year

2000: -.105	2001: -.024	2002: +.013	2003: +.020
2004: +.013	2005: +.021	2006: +.020	2007: +.019
2008: +.012	2009: +.012	2010: +.014	2011: +.012
2012: +.010	2013: +.010	2014: +.011

But that’s not what we see. Instead we see almost no lines with negative slope (and those all in the years immediately following 1998). Instead the slopes roughly average .012°C/year, or about the slope found between 1960 and 1984.

In other words, the data do NOT show a pause, they show an increase comparable to increase from before the 1990s. The naughties are not paused, they are not anomalous, they are in line with the average over the last half century. It is the nineties which are odd.

But there is another statistical mistake in the claim of a “pause”. This is something called “Data Mining”. The only reason anyone might think there was a pause is because 1998 was an extraordinarily hot year for the time. If you base your data in 1998 you have to wait for a long time for the trend to catch up to the noise.

But if you look at the next year, 1999, there is no way anyone could find a pause in the data. Since 1999 temperatures have simply increased. This, by the way, is data mining in the reverse direction since 1999 was (for the time) a particularly cold year.

Slopes of the regression line for each year since 1999 in °C/year

	2001: +.065	2002: +.076	2003: +.061
2004: +.038	2005: +.041	2006: +.034	2007: +.030
2008: +.020	2009: +.019	2010: +.020	2011: +.016
2012: +.014	2013: +.013	2014: +.014

Since we are only data-mining the start time if you wait long enough both trends will converge toward the same slope.

I have been told that the temperature change since 1998 is not statistically significant since it is less than two standard deviations. In a way, this is true, (ΔT(2014-1998): .11°C, σ: .067°C) but it ignores several things. First these years do not stand alone, they are a continuation a trend that started (at least) in 1960 and the change since 1960 is significant. And second 1998 is data-mining. If we pick 1999 as a base year then ΔT(2014-1999): .32°C, σ: .061°C, and the change is about 5σ which is very significant.

So I think the following graph is a much better way of looking at the data. There is no pause. Just three regions where the temperature increases, and in the two regions 1960-1984, 1999-2014 the temperature increases at about the same rate, while in one, 1986-1998, the temperature increases much faster.

Linear regression lines

1960-1984	T=.012*(year-1998)+14.355°C
1985-1998	T=.021*(year-1998)+14.488°C
1999-2014	T=.014*(year-1998)+14.492°C

My claim is that there has been no pause. Attempts to see a pause are based on two statistical mistakes, the first being data-mining, and the second being the belief that drawing line between two noisy datapoints is meaningful.

This analysis is based on statistics I learned in 10th grade. It isn’t hard.

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