Guest essay by Sheldon Walker
A quick recap for anybody who missed my first article.
My first article can be found here.
I have developed a new technique for analysing global warming (and other things). It is called Multi Trend Analysis, or MTA. It analyses the data in a time interval, by calculating the trend between every possible pair of points in the interval. The trend includes all of the data points between each pair of points as well. This can involve a lot of trends. To analyse the interval [January 1975 to December 1999] involves 16,920 trends. A trend is basically a linear regression.
I have developed methods that allow large numbers of trends to be analysed quickly, and the results displayed either graphically or in a table. A trend has 4 main attributes, a start date, an end date, a length, and a slope (with global warming, the slope is the warming rate). In my first article, I displayed graphs of warming rate versus trend length, but any of the 4 main attributes can be graphed against any of the others.
Most people think that the graphs look good, but I am still investigating whether the graphs are actually useful for analysing global warming. They may end up just being eye candy, but I am hoping that they will prove to be useful for something.
After my first article, I decided to use MTA to try and prove that the Pause exists. I wanted to compare a graph of the interval where the Pause existed, against a graph of an interval where “The Pause” did not exist (a reference interval). If there was a significant difference, and it was the right kind of difference (e.g. a lower warming rate), then I would have good evidence that the Pause existed.
Picking the right intervals was important. From my previous investigations into the Pause, I knew that the core years were from 2002 to 2013. This is a 12 year interval with a very low warming rate. Moving the start date to 2001 increased the warming rate slightly, but gave a longer slightly weaker Pause. Moving the start date to 2000 increased the warming rate even more, but gave an even longer weaker Pause. Moving the finish date to 2014 also increased the warming rate, and moving the finish date to 2015 weakened “The Pause” considerably, because of the 2015 El Nino.
So I had a limited range of years for the Pause. I knew that there had been consistent warming since 1975, so my Pauseless interval had to start in or after 1975. From 1975 to 2015 there are 41 years. The first 25 years or so have definite warming, and the Pause started after that. It would be best if my Pauseless reference interval was the same size as my Pause interval, because I wanted to compare apples with apples. In the end, I decided to divide the 41 years into 3 * 13 + 2. This gave me two 13 year Pauseless reference intervals, one from [January 1975 to December 1987], and one from [January 1988 to December 2000], and one 13 year Pause interval from [January 2001 to December 2013]. This fitted nicely with my beliefs about the Pause, and gave me 2 reference periods to compare with. It would also be nice to compare the 2 reference intervals to each other, to see if they were consistent. I didn’t mind not using 2014, and 2015, because I knew that they weakened the Pause. I could worry about those 2 years later if I found evidence that the Pause did exist.
I did the MTA analysis, and graphed the results. Normally I don’t look at trends less than 10 years, because they are less stable. However, working with 13 years intervals only gave me trends from 10 years to 13 years. The graphs showed what I wanted to see, but they were a bit “thin”. I did the analysis again using a minimum trend length of 8 years, and got graphs that were much more robust.
I should mention quickly that all of the data comes from the NOAA global combined land and ocean temperature series. I will repeat my analysis with the other temperature series when I get time, but I thought that using NOAA first was appropriate, given that they have a reputation as “Pause Busters”.
I will first show the 3 full scatter graphs individually, one for each interval. These are good for examining the shape, checking the warming rates for different trend lengths, and getting a good idea about the overall warming rate. The rightmost point on each graph corresponds to a linear regression for the whole interval.
I will then show a single graph which contains the same 3 intervals, but plotted as outlines on a single graph. This is much better for comparing the different intervals with each other. The colour of an outline graph will be the same colour as the full scatter graph for the interval
Here is the MTA graph for the first Pauseless reference interval, [January 1975 to December 1987].
Here is the MTA graph for the second Pauseless reference interval, [January 1988 to December 2000].
Here is the MTA graph for the third interval, the one showing the Pause, [January 2001 to December 2013].
Here is the outline MTA graph which shows all 3 intervals, each with the same color as the previous graph for the interval.
I think that the results can be seen clearly from the graphs, but I will mention a few points from the outline graph.
Note that the 2 reference intervals are in quite good agreement. The first, the orange one, has an overall warming rate of just over 2 degC/century. The warming rate appears to be increasing slightly near the right end.
The second green reference interval has an overall warming rate of about 1.29 degC/century. The warming rate appears to be decreasing slightly near the right end (as it approaches the Pause).
The blue Pause interval has much less variability that the 2 reference intervals. The warming rate is mostly between 0 and 1 degC/century. it has an overall warming rate of about 0.54 degC/century, and appears to be increasing slightly at the end. Perhaps the end of 2013 showed a small increase in temperature, which then became larger in 2014 and 2015.
If we average the overall warming rates for the 2 reference intervals, we get about 1.65 degC/century. The Pause has an overall warming rate of less than 33% of the average of the 2 reference intervals.
To be more specific, the Pause has an overall warming rate of about 27% of reference interval 1, and less than 42% of reference interval 2. These percentages represent a large reduction in the warming rate, and justify the name “Slowdown”, or “Hiatus”, or “Pause”.
Could anybody deny the Pause, after seeing that evidence? I expect that there will be many “Pause deniers” who will stubbonly refuse to accept the proof that I have presented here. Of course, anybody can overturn my proof if they can find a significant error in it. That is the way that science works.
A final word about the future. The Pause has been weakened by the 2015 El Nino. That does not mean that it never existed. Anybody gloating over the Pause becoming weaker, should bear in mind that El Nino’s do not last forever. Once the El Nino’s temperature increase has gone, the Pause will probably strengthen. A La Nina may also give the Pause a boost. Do not underestimate the Pause, it may surprise you yet.
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Sheldon: This is another intriguing post. Like you, however, I wonder if it isn’t “eye-candy”.
My biggest concern is that all months don’t contribute equally to the graph. For example, in your Figure 1, the temperature change during Jan 1975 and December 1987 contribute to only one point in each column, or 60 data points. On the other hand, the temperature change during all 36 months between Jan 1980 and Dec 1982 contributes to every point on the graph (1830 points?). Furthermore, Dec 1987 is underweighted because of your decision to break the temperature record into segments between Dec 1987 and Jan 1988. This provides opportunities for distortion and cherry-picking. However, there may be a way to use your methodology in a way that doesn’t have these weaknesses.
Suppose one analyzes the entire 41-year period (1975-2015) using your technique with trends ranging from 41 years down to 8 years (or even as short as 2 years). In the resulting plot, we might expect to visually identify a cluster of points with cooling or little warming. Perhaps we might observe a “Pause” – a cluster of points with zero warming over periods ranging up to 12 years – while most points involve more rapid warming (at least 0.1 degC/decade). The next step would be to color code the points in this cluster by date, so that the time period responsible for this unusual cluster of negligible warming can be identified. By trial-and-error, one might discover that coloring dark blue all the points containing the entire period 2002-2010 – or some other period – does a reasonable job of distinguishing the “Pause” from the rest of the data. Perhaps additional insight could be obtained by coloring points medium blue when their trend is at least 80-99.9% derived from the 2002-2010 period.
It could be that there are too many overlapping points on the plot to clearly identify clusters with unusually low trends. Monthly temperature data is highly auto-correlated, so many points are redundant. Looking at quarterly, semi-annual or annual temperature data with less autocorrelation might make clusters more apparent.
One advantage of this approach is that the Pause would be “discovered” by a visual inspection of clustering within all trends – rather than being a hypothesis (out of a multitude of possible hypotheses) chosen at the beginning of the analysis.
A second advantage is that all periods would contribute equally to the output. Unlike Figure 1, 1987 would contribute as much data to the trend points as 1980-1982. And, if one looks at trends from periods as short as 2 years, even the earliest and latest years in the 1975-2015 period would have a chance to be recognized as being unusual. However, we expect to see many two-year periods with cooling – many of which did not come from 2002-2010. After demonstrating that short trends are noisy and contain no usual information, then it would probably would make sense to remove them from the graph and focus on long periods with little warming.
I made similar analysis back in 2011, nobody seemed to be impressed by it by then.
http://imgur.com/TI64K0n
Sheldon – you are screwed up with your description of warming from 1975 on. There is no La Nina event from 1975 to 1977. Fifties, sixties and early seventies are simply slow warming, part of recovery from the sharp World War II cooling that started with the winter of 1939/1940. I would have said it is a candidate for another pause if I knew what the temperature actually did what is shown because they keep revising it. Unfortunately, temperature records are so bad that some morons still show the first half of forties as a warming peak. That warm peak itself is the result of a steady warming from 1910 to 1940 whose origin is unknown. That being the case, they should not claim that AGW is responsible for the warming. Just to avoid having to answer this question, IPCC has decided to start counting observable anthropogenic influence with the year 1950. With that, their claim that AGW started with the beginning of the industrial age should be withdrawn. The recovery from the WWII cold spell speeded up about 1975 and by 1980 global temperature had reached the point where it was in 1940. Official temperature curves from IPCC show that temperature continues to rise beyond that point and then smoothly joins the twenty first century curve on the right.This is scientific fraud. That temperature curve does not go up but turns right, becomes horizontal, and continues in that direction until it encounters the wing of the super El Nino of 1998 at the beginning of 1997. This makes it a straight horizontal run of 18 years, the hiatus of the eighties and nineties. Showing the real temperature curve would interrupt this smooth upward curve with an ugly step carved out of this imaginary temperature rise. You will find the picture of this hiatus in Figure 15 of my book “What Warming?” In official temperature curves it is over-written by a fake “late twentieth century warming.” I was aware of this fakery when my book came out in 2010 and even put a warming about it into its preface. It was completely ignored. The fake warming has now been part of the official temperature curve since the late nineties, misleading scientists who want to study global temperature history. To complete the story, the satellite temperature measurements begin with the hiatus of the eighties and nineties and they end with the current twenty-first century hiatus. Between these two hiatuses is the super El Nino of 1998 and a short step warming that begins from the bottom of the La Nina of 1999. In three years it raises global temperature by a third of a degree Celsius and then stops. This is why twenty-first century temperatures are all higher than the eighties or nineties (except for the super El Nino). Hansen and other warmists have attributed this to carbon dioxide when its true cause is oceanic – the large amount of warm water carried across the ocean by the super El Nino of 1998. It is the only warming since the start of the satellite era in 1979. For determining the warmest year you must allow for the presence of this “unearned warming.” When this extra warming is allowed for both sides of the satellite curve become similar.
A couple of things. Since we are talking about heat transfer and fluid flow, shouldn’t the temperatures be in Kelvin? A freshman mistake in heat transfer and fluid flow is to use Celsius instead of Kelvin. Secondly, a thought. If more than half of the all the regressions show heating or cooling, wouldn’t that be the trend?