Trending trends

In this post I demonstrate my template that shows linear trends in data from any given point in time to the most recent month, (which is how I determine the starting point and length of The Pause.) It can be quickly seen how trends change over time and where these changes occur so they can be investigated. This can be used for any data at all, from monthly TLT anomalies to road fatalities. In future posts I will use this with Australian surface temperatures and rainfall. It does not replace, but supplements, normal time series graphs.
Up to now I have used monthly UAH temperature anomalies to study The Pause, but I have recently learnt that there can still be a weak seasonal signal, so from now on I will use 12 month running means of monthly anomalies. This leads to some changes in trends and the start of The Pause in some regions, notably Australia, but overall gives similar results. Importantly it reduces the impact of outlier individual months, especially at the start of the record and as each new month is added.
As well, my previous Pause criterion (a linear trend of less than +0.01 degree Celsius / 100 years) has been too strict. While UAH data are to two decimal places, the uncertainty range is +/- 0.1C. Accordingly, for 2016 my Pause criterion will be a trend of less than +0.1C per 100 years. (This is still far too lenient on Global Warming Enthusiasts- compared with trends above 1C per 100 years, anything below about +0.3C is an embarrassing slowdown.) Further, it is important to be transparent. All available data should be shown, not just those that create The Pause.
Finally I note, thanks to Christopher Monkton, that

In 2008, NOAA’s report on the State of the Global Climate, published as a supplement to the Bulletin of the American Meteorological Society, said: “The simulations rule out (at the 95% level) zero trends for intervals of 15 yr or more, suggesting that an observed absence of warming of this duration is needed to create a discrepancy with the expected present-day warming rate.”

A look at some of the graphs shown below will show why this is a valid statement. Certainly trends of 10 to 15 years give an indication of what has been happening, but I will agree that 15 years is about the length of time needed for trend values to settle without too much undue impact from the short term fluctuations in recent values.
Let’s begin.
Fig. 1: Running linear trend values in degrees Celsius per 100 years in Global UAH TLT anomalies from December 1978 to December 2015 (12 month means)

Trend whole
The plot shows the value of the linear trend from any given month to the most recent.
It should be plainly obvious that trends constructed from less than 10 years of data are spectacularly meaningless. This is weather.
The trend for the whole data series is about +1C/ 100 years.
The trend line crosses the zero value in 1997-98, so The Pause starts there.
Now I reduce the scale, and demonstrate how the graph may be interpreted.
Fig. 2: Running trend in degrees Celsius per 100 years in Global UAH TLT anomalies from December 1978 to December 2015 (12 month means)

Trend globe all

The trend for the entire record is +1.11C per 100 years.
A higher bounce in the trend indicates that earlier Temperatures were cooler relative to recent values, and a lower trend, a dip, the reverse. If recent temperatures are low enough compared with past values, the trend will reduce to zero or below, as it has above.
I have drawn a horizontal line showing +0.1 C, below which the trend cannot be distinguished from zero, unless it is below -0.1, in which case it is definitely negative.
The trend line crosses +0.1C in 1997. I have drawn in a horizontal black line from 2015 back to this point showing the length of The Pause. I can now refer to my spreadsheet table to find the exact month for the commencement of The Pause- April 1997- and graph it.
Fig. 3: UAH v6.0 anomalies for the Globe in blue, with data since April 1997 in orange.

Globe graphs all

The Pause is highly dependent on the El Nino generated 1998-99 spike. However showing the whole record makes the following plateau plainly obvious.
Now, what about the mysterious disappearing Northern Hemisphere Pause? In graphs of 12 month means, it’s back!
Fig. 4: Running trend in degrees Celsius per 100 years in Northern Hemisphere UAH TLT anomalies from December 1978 to December 2015 (12 month means)

Trend NH all

Of course, this is very much dependent on values in the next few months, as it will probably disappear again!
You will note the series of bumps and dips in the trend values. The small upward bounces coincide with cooling events such as La Ninas or explosive volcanoes, while the dips coincide with warming events such as El Ninos.
So, we have a Northern Hemisphere Pause again, if only briefly, and Global Warming Enthusiasts will surely accuse me of cherry picking. But remember, values will continue to be applied to the right hand end.
Fig. 5: UAH v6.0 anomalies for the Northern Hemisphere with the whole series in blue, and with data since October 1997 in orange.

NH graphs all

The next graph illustrates how using 12 month means can alter the Pause length. Monthly data had Australia’s Pause lasting for 18 years and 1 month, but this has shortened to 15 years and 3 months (which still meets NOAA criteria).
Fig. 6: Running trend in degrees Celsius per 100 years in Australian UAH TLT anomalies from December 1978 to December 2015 (12 month means)

Trend Aust

As the next graph shows, the Australian Pause starts from near the bottom of a La Nina cooling. No cherry picking there.
Fig. 7: Australian crawl: UAH v6.0 anomalies for Australia with the whole series in blue, and with data since October 2000 in orange.

Aust graphs all

I’ll conclude with a warning that as each month’s data point is appended, the trend graph will change (unlike temperature graphs where all past data points are fixed.) Don’t be confused by this- we are simply re-calculating linear trends.


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4 Responses to “Trending trends”

  1. MikeR Says:

    Hi Ken,

    I have been using back trend graphs using the same approach as yours for the past couple of years and it has become increasingly obvious that the global pause was in big trouble.

    I was mystified as to how you were going to cope with the probable and imminent demise of the UAH global hiatus, but the above has provide some clarity. You have embarked on two approaches neither of which will be likely to save the day.

    But before discussing your attempts I think we need to discuss the raw UAH V6 data. it is becoming clearer month by month that the low hanging cherries are going to become scarcer and scarcer. It only requires a value of 0.52 or greater for the UAH temperature for January 2016 for the global pause to join the recently deceased N.H. pause. In all probability this pause is unlikely to reappear, even after a possible subsequent LA-Nina , unless belatedly the mini ice age turns up or a volcano erupts at the appropriate time.

    The value of 0.52 or greater for January is a distinct possibly as during both the last two significant El-Nina event (1997/98 and 2009/10), the January UAH temperature was significantly greater than for December (0.23 greater for 1999/98 and 0.38 for 2009/10). Even if this does not eventuate for January, the global pause will be terminated by February for just two successive values of 0.35. The global pause is now in a critical condition in intensive care and may never recover.

    Accordingly if the other regional UAH data also follows the trend of the past major El- Ninos then they too will succumb, one by one. The only survivors after a further 6 months or so, interestingly enough, could be Australia and the South Pole.

    Back to your methodology to delay or hide the rise.
    Firstly the standard practice of claiming ‘so and so months’ of no global warming is usually updated month by month by adding in the latest value of the UAH temperature to the series and then fitting the data.

    If you apply a 12 month running average before fitting , this, of course, reduces the effect of the last few months that are currently rising steeply as the current El-Nino takes hold.

    To elaborate, this sleight of hand is accomplished by averaging the last few warming months with the preceding cooler months, that make up the remainder of the 12 month interval. As this lowers the right end boundary values of the graph the this naturally forces the trend line to a lower (in this case negative value). To illustrate the raw UAH data for the norther hemisphere for the last 3 months are 0.64,0.43 and 0.51. In contrast 12 month smoothing of the UAH data gives 0.33, 0.34 and 0.37!

    If the impact of El-Nino upon UAH plays out as per usual then this the method that resurrects the N.H. hiatus from oblivion by this approach only gives it a month or two of grace before it disappears from view. This t would most likely only delay the inevitable, I guess this tactic could be effective if an El-Cichon or Pinatubo like volcano eruption occurs in the mean time. It’s been twenty five years since the last major volcanic event that impacted UAH so we may be due for one but I wouldn’t be holding my breath.

    A more reasonable approach to smoothing data is to use Loess smoothing. This has two advantages over the running average. Firstly it is significantly less prone to over smoothing at the boundaries. In contrast to the 12 point smoothing the values for the corresponding Loess smoothing for the past 3 months are 0.45,0.48 and 0.51 which much more closely corresponds to reality.

    The other issue with 12 month running average smoothing is that it will either be centred on the data and not generate values for the first 5 (or 6) months and the last (6 or 5) months or it will be delayed by 6 months with the first 6 months ignored (or left unsmoothed).

    For those who would like to check this for themselves an addin for Excel for Loess smoothing can be found at . Ken, I recommend it highly.

    The other ruse employed as a delaying tactic is to change the rules of the game by raising the bar to an arbitrary +0.01 degrees per decade instead of just using zero as the limit between warming and a hiatus, as was the case before this goal post was suddenly moved. This will give you another month or so of leeway to hope for something out of the ordinary to occur. Even another adhoc raising to 0.03 degrees per decade will be unlikely to save the day in the long run.

    As they say “it is difficult to make predictions, especially about the future” . In that vein my predictions over the next few months , based upon the past El Ninos, may not come to pass in which case the egg will be all over my face. I will gladly wear it as it will be provide a glimmer of evidence that climate change is just a beat up and I have been taken for a ride by the 97%. I indeed hope for all of us that this is the case .

  2. kenskingdom Says:

    I will cope with the ‘probable and imminent demise’ of the pause in the same manner as I have always done- let the record speak for itself. You may not have noticed but all along I have been saying that the Pause is likely to shrink or disappear entirely as the effects of the El Nino are felt. I have also mentioned how it amuses me that Global Warming Enthusiasts cling to a cause of natural variation- the El Nino- to get them out of trouble with the gap between expectations and reality. Thank you for the continued amusement.
    I thought I explained pretty clearly in the first couple of paragraphs my change in methodology: a trend of +0.1C / 100 years cannot be distinguished from zero so can become the benchmark from here on. As well, monthly anomalies can and do have seasonal auto-correlation, which can be safely removed with a 12 month running mean. This is not a ruse, sleight of hand, or any other sort of trick, but is intended to improve the analysis. I haven’t changed anything in previous posts, they are still public and these changes are publicly documented. If the Pause shrinks, disappears, or continues, so be it, I report that. You will note that my slightly changed method has reduced the Pause in Australia by years. Further, how do you imagine 2015 was proclaimed the hottest recorded unless the previous 12 months were averaged?
    Que sera, sera.
    (And stand by for another “glimmer of evidence that climate change is just a beat up and (you) have been taken for a ride by the 97%”.)

  3. MikeR Says:

    My major concern was that 12 month averaging was suppressing the latest temperatures. Why not use the Loess smoothing which accomplishes the same without this problem?

    By the way 12 month moving averaging of any kind does massively increase the serial correlation and makes the uncertainties in trends even more ridiculous. It is last thing that you would want to do to the data.

    A good explanation of why this is not a good idea at all can be found at . Note the discussion of the moving average model and also Causes of Autocorrelation point 3..

  4. MikeR Says:

    Just to clarify with regard to your last statement ” how do you imagine 2015 was proclaimed the hottest recorded unless the previous 12 months were averaged?”. Yes this average over 12 months obviously gives a single annual figure. The annual year to year figures may exhibit some natural serial correlation but you would expect it to to be limited as we are comparing averages that are a year apart and the autocorrelation for temperatures 12 months apart are always much smaller than the month to month autocorrelation values

    In comparison, for the running average you get 12 successive values that are correlated at a monthly level and also correlated with the other 11 monthly values that are part of the average for that particular month. Therein lies the problem of using this approach.

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