Much has been written about the Karl et al “pause buster” paper published this past summer, this essay suggests Karl et al actually shot themselves in the foot with the paper

Guest essay by Sheldon Walker

In this article we will:

1) look at an interesting new technique for analyzing global warming

2) use the new technique to analyze the time interval [January 1950 to December 1999]

3) use the results of 2) to show why Karl et al got it wrong, in their paper about “The Pause”

Most people are familiar with the use of linear regression in global warming.

Pick a start time, pick an end time, and calculate the slope of the regression line from the dates and temperature anomalies in the data series. What could possibly go wrong?

One of the common accusations made with global warming, is that the start time and/or end time were cherry-picked to give a particular result.

Accusations are also made that the length of the trend was too short to give a significant result (e.g. trends less than 10 years, or even trends less than 30 years).

What if there was a technique that we could use to get around these accusations?

To overcome the problem of cherry-picking, we use all possible start and end times from the time interval being investigated.

To overcome the problem of short trends, we only look at trends which are at least 10 years in length.

For example, imagine that we were interested in the time interval from [January 1975 to December 1999]. This interval is 24 years and 11 months in length. We divide [January 1975 to December 1999] up into EVERY possible trend of at least 10 years.

When I say EVERY possible trend of at least 10 years, I mean EVERY possible trend of at least 10 years. For the time interval [January 1975 to December 1999] there are 16,920 possible trends, and this method uses them ALL.

Example trends from [January 1975 to December 1999]:

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10 year trends: e.g. January 1975 to January 1985

10 year trends: e.g. February 1976 to February 1986

10 year and 1 month trends: e.g. February 1980 to March 1990

10 year and 2 month trends: e.g. January 1985 to March 1995

20 year trends: e.g. September 1979 to September 1999

20 year and 3 month trends: e.g. September 1979 to December 1999

24 year trends: e.g. June 1975 to June 1999

24 year and 5 month trends: e.g. May 1975 to October 1999

24 year and 11 month trends: e.g. January 1975 to December 1999 (the entire interval)

plus the other 16,911 trends.

This might appear to be overwhelming, but with Excel and a modern computer, it can be calculated quite easily.

There are several ways to present the results. The simplest way is to plot a “scatter” graph of the warming rate versus the trend length.

What does the graph of every possible combination of warming rate and trend length for [January 1975 to December 1999], look like? Have a look at Graph 1.

This graph holds a lot of valuable information, but it needs a little interpretation.

For example, how does the warming rate change with the trend length.

From the graph:

The warming rate for 10 year trends varies from -0.20 to +2.80 degC/century

The warming rate for 15 year trends varies from +0.65 to +2.20 degC/century

The warming rate for 20 year trends varies from +1.02 to +1.61 degC/century

The warming rate for 24 year and 11 month trends doesn’t vary at all, because there is only one, which is for the entire period, and it equals +1.71 degC/century

These results probably agree quite well with most people’s expectations. One lesson is, be wary of 10 years trends. You can get just about any warming rate that you want from a 10 year trend. Note than in certain circumstances a 10 year trend can be meaningful, but in general, 10 years trends are all over the place.

In general, warming rates become more stable with increasing trend length. But not always. Look at the warming rates for trend length = 22 years. There is a very small range of warming rates varying from +1.43 to +1.52 degC/century. But as the trend length increases to 23 years, the range of warming rates widens considerably. Why?

Also, after having a fairly stable warming rate of about +1.48 degC/century at trend length 22 years, the interval ends up with a warming rate of +1.71 degC/century for the entire interval. What made the warming rate suddenly increase by over 15%, as the trend length increased by just 3 years?

I am going to guess the answer to these 2 question, using the “scatter” graph, and a graph of the temperature anomalies over the interval. If you disagree with my quick guess then let me know what you think the answer is. At the start of the interval there is a La Nina type event from about 1975 to 1977. At the other end of the interval there is the large 1998 El Nino from about 1997 to 1999. As the trend length gets long enough to be influenced by both of these at the same time, the slope of the regression line is increased by the El Nino at one end, and also increased by the La Nina at the other end. So as the trend length exceeds 22 years, there is a double boost to the warming rate, which the “scatter” graph shows quite nicely.

Looking at the “scatter” graph for a single time interval, is only one possible use for this technique. Comparing the “scatter” graphs from different time intervals is another exciting possibility. It is this method that I will use to prove that Karl et al got it wrong in their paper about “The Pause” (“Possible artifacts of data biases in the recent global surface warming hiatus”).

To start, have look at Graph 2. This is similar to Graph 1, but shows every possible combination of warming rate and trend length for a different time interval, this time [January 1950 to December 1974]. This graph looks a bit like the one for [January 1975 to December 1999], but it is also a bit different.

To make it easier to compare these scatter graphs, I will put them onto the same graph. This means that one of the graphs hides some of the other graph, where they overlap. If necessary, this can be improved by plotting only the perimeters of each graph, but I am more interested in where the graphs don’t overlap at the moment, so we will ignore the overlap for now.

See Graph 3 – All combinations of warming rate and trend length that exist in the periods [1975 to 1999] and [1950 to 1974], for trends of at least 10 years.

Now it is easier to appreciate the differences between the 2 graphs. They are sort of similar in shape, but the green curve is translated down from the orange curve. Why is this? Looking at the warming rate for the entire interval for each graph gives the answer.

The orange curve has a 24 year and 11 month trend of +1.71 degC/century. A rate of global warming which is NOT low.

The green curve has a 24 year and 11 month trend of +0.28 degC/century. There is not much global warming in this interval.

Note how there is no overlap between the 2 graphs for trend lengths greater than about 15 years. This reinforces the idea that these 2 time intervals have very different warming rate profiles.

Now, the BIG question. If you add together these 2 periods, [1950 to 1974] and [1975 to 1999], and calculate the warming rate for the combined interval [1950 to 1999], what would the warming rate be? I have done this, and a linear regression over the combined interval has a warming rate of +1.12 degC/century. OK, but what does this value of +1.12 degC/century actually represent.

It is NOT the warming rate for normal anthropogenic global warming.

It is NOT the warming rate for when there is NO anthropogenic global warming.

It is an artificial average rate of warming, for an interval when anthropogenic global warming was present for about 1/2 the time, and absent for about 1/2 the time.

Unfortunately, Karl et al used this value as their “normal” anthropogenic warming rate, and based on this value, they concluded that the warming rate for [2000 to 2014] did NOT support the notion of a global warming “hiatus”.

Recapping quickly on the Karl et al paper:

Karl et al adjusted the NOAA data to account for the 0.12 degC average difference between buoy and ship SSTs. This “correction” had an impact on temperature trends, with the largest impact being on trends from 2000 to 2014 (which is where “The Pause” was meant to be).

So Karl et al calculated the new warming rates for [1950 to 1999] and [2000 to 2014]. They got:

Warming rate [1950 to 1999] = +1.13 degC/century

Warming rate [2000 to 2014] = +1.16 degC/century

Karl et al concluded that since the warming rate from [2000 to 2014] was virtually indistinguishable from the warming rate from [1950 to 1999], it does NOT support the notion of a global warming “hiatus”.

I am NOT questioning the adjustments that Karl et al made to Sea Surface Temperatures (SSTs). I am not qualified to dispute these adjustments, so I will use the adjusted NOAA data as it stands. Special note – I am using the NOAA data. If I find a “Pause” in the NOAA data, then they can not accuse me of using the wrong data.

I am also NOT disputing the calculation results from Karl et al. I get very similar results to theirs.

My issue is with the use of the Warming rate for [1950 to 1999]. Karl et al said this:

“Our new analysis now shows the trend over the period 1950-1999, a time widely agreed as having significant anthropogenic global warming (1), is 0.113°C dec−1, which is virtually indistinguishable with the trend over the period 2000-2014 (0.116°C dec−1).”

Now [1975 to 1999] is an interval having significant anthropogenic global warming.

But [1950 to 1974] is an interval having very little anthropogenic global warming.

By joining these 2 intervals together to form [1950 to 1999], Karl et al have created an interval that basically has half strength anthropogenic global warming (half with warming, and half without warming). But Karl et al used this value as their “normal” anthropogenic warming rate, when they compared it to [2000 to 2014].

If the warming rate for [2000 to 2014] matches the warming rate for [1950 to 1999] (which it does), then that means that [2000 to 2014] also has half strength anthropogenic global warming.

There are 2 simple ways to explain how [2000 to 2014] could have half strength anthropogenic global warming.

1) The period [2000 to 2014] could consist of 2 parts, one part which has anthropogenic global warming, and one part which does NOT have anthropogenic global warming (like [1950 to 1999]). But I do not think that this is the case.

2) The more reasonable explanation is that the period [2000 to 2014] has a lower warming rate than “normal” anthropogenic global warming. The warming rate would be about 50% of the “normal” warming rate. This could be called a “Slowdown”, a “Hiatus”, or a “Pause”. Whichever name you prefer, the data shows that it exists.

So Karl et al, while trying to convince everybody that there is NO Pause, have actually provided strong evidence that “The Pause” does exist (once their error concerning [1950 to 1999] is corrected).

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In part 2 of this article, I will analyse [2000 to 2015] using the new technique described in this article.

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