Very strong graphical evidence for the Pause. (Part 2)

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].

Graph 1 (1)

Here is the MTA graph for the second Pauseless reference interval, [January 1988 to December 2000].

Graph 2 (1)

Here is the MTA graph for the third interval, the one showing the Pause, [January 2001 to December 2013].

Graph 3 (1)

Here is the outline MTA graph which shows all 3 intervals, each with the same color as the previous graph for the interval.

Graph 4

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.

83 thoughts on “Very strong graphical evidence for the Pause. (Part 2)

  1. Something is fundamentally wrong with your graphs, or my understanding of them.
    As an example in Graph 1 you show that the 13 year trend for the entire data series is approximately 2, but you also show all of the calculable 12 year trends are less than 2.
    I don’t think it is mathematically possible for the overall trend to not be between Trend_12(max) and Trend_12(min).
    Mathematically that seems to be like saying the average of a bunch of numbers is X, but all of the numbers themselves are strictly less than X. That is not mathematically possible.

    • Mathematically that seems to be like saying the average of a bunch of numbers is X, but all of the numbers themselves are strictly less than X. That is not mathematically possible.

      That is an excellent question! Here are my thoughts. Going to the following, I got the slopes for 3 periods as follows:
      13 years:
      Temperature Anomaly trend
      Jan 2001 to Dec 2013 
      Rate: 0.516°C/Century;
      12 years:
      Temperature Anomaly trend
      Jan 2002 to Dec 2013 
      Rate: 0.354°C/Century;
      12 years:
      Temperature Anomaly trend
      Jan 2001 to Dec 2012 
      Rate: 0.402°C/Century;
      So the 13 year period had a higher slope than both 12 year periods, even though one 12 year period was at the start and the next in the end of the same 13 year period.
      The reason for this was that anomalies were climbing at the start of the 13 year period as well as at the end. So the 13 year period had the best of both worlds so to speak for a maximum value. But each 12 year period missed one of the spikes to give a lower slope.

      • @gregfreemyer – a good question.
        @Werner Brozek – a good answer
        In my first article, I looked at [January 1975 to December 1999] (length = 25 years). The range of warming rates for trend length = 22 years were very small (varying from +1.43 to +1.52 degC/century). But as the trend length increased to 23 years, the range of warming rates widened 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?
        My answer to these 2 question, using the “scatter” graph, and a graph of the temperature anomalies over the interval, was: 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.

      • Werner – Using a real satellite data curve published by UAH iin December 2015 I do not get positive anomalies from 2001 to 2013 as you do. The anomaly for that stretch is negative and has a slope of minus 1.5 degrees Celsius per century. Which data source gave you those positive slopes? As you know, the thing they fear most from a hiatus is that it invalidates their theory of greenhouse warming. A negative slope to them is even worse than a horizontal curve. During a hiatus the atmospheric carbon dioxide increases but temperature does not. The Arrhenius greenhouse theory they use requires that if carbon dioxide goes up temperature also must go up. Since it does not, the Arrhenius greenhouse theory is invalid and belongs in the waste basket of histor

      • Werner Brozek
        February 27, 2016 at 4:26 pm
        Which data source gave you those positive slopes?
        I was using what the author used: NOAA.
        Thanks, Werner. I would not accept the time of day if it came from NOAA. Here is how I found out about their involvement with fake warming. In 2008 I was studying satellite temperature curves when I noticed that a temperature section that had no warming according to satellites showed a distinct warming in ground-based temperature curves. I referred to this in comments and even put a warning about it into the preface of my book in 2010. All this was ignored and that fake warming is still part of the official temperature curve according to NOAA. Further research revealed that some ground-based temperature curves had identical computer noise incorporated into their publicly available temperature curves. Specifically, HadCRUT3, GISS, and NCDC (NOAA) data-sets suffered from sharp upward spikes. Satellite data do not have them. But they tie these three data-sets together for a purpose. And the purpose, most likely, is to hide their original differences from the fake temperature curve they just concocted. But why go to that trouble? Two reasons. First, existence of a hiatus is a deadly enemy of their greenhouse warming hypothesis. They knew that before anyone else. And second, they still do not control satellites but can change ground-based temperature curves at will, as they did here. According to NASA’s own records from 1997, there was no warming in the eighties and nineties, and if anything, the temperature curve may have had a slight negative trend. Arno

    • “I don’t think it is mathematically possible for the overall trend to not be between Trend_12(max) and Trend_12(min).”
      I thought that too, at first. But it is. I showed a case here.

      • All of my calculations are done with an Excel spreadsheet.
        I use the SLOPE function rather than the LINEST function, because I only need the slope of the regression line.
        The calculations are not difficult, but the large number of trends makes it challenging.

    • Can this method be used to move the start point back to establish the length of the Pause?

      If you mean the longest time for which there was a slope of 0, then the blue lines would indicate a pause of about 10.5 years at one point.
      We will see if the author agrees!

    • @A C Osborn – good question.
      Yes, I could move the start and end points to try and find the “best” start and end point. It would involve doing the analysis multiple times. But what is the “best” slowdown, there is normally a trade-off between the amount of slowdown, and the length of the slowdown (as I described above for “choosing the Pause interval”).
      Which is “better”, a short intense slowdown, or a long weak slowdown.
      I noted above that the warming rate for reference interval 2 appears to be decreasing slightly near the right end of the graph (as it approaches the Pause). This is just a guess at the moment, for why it slopes down slightly. But this may indicate that the Pause really starts slightly earlier than my Pause interval.
      I have currently only looked at slowdowns starting in January and ending in December (to keep things simple). However, a slowdown could start or end in any month. This obviously needs more work. Please send funding 🙂

      • @ Sheldon, 9:54 am, “Please send funding” , Thanks for the laugh and also thanks for the article. I am no expert but that one made sense to me and was easy to follow.

    • J L Alvarez:
      You ask

      Considering the temperatures since the last ice age, how does one define a pause?

      The IPCC provides two definitions of what it calls the “Hiatus”; viz,
      (a) a linear trend not distinguishably above zero
      (b) a linear trend that is significantly less than the predicted trend of the “CMIP5 ensemble mean trend”.
      The IPCC reports that the Hiatus exists according to both its definitions and report is confirmed by the above analysis of Sheldon Walker.
      The pertinent IPCC statements are in Box 9.2 on page 769 of Chapter 9 of IPCC the AR5 Working Group 1 (i.e. the most recent IPCC so-called science report) and is here. It says

      Box 9.2 | Climate Models and the Hiatus in Global Mean Surface Warming of the Past 15 Years
      Figure 9.8 demonstrates that 15-year-long hiatus periods are common in both the observed and CMIP5 historical GMST time series (see also Section 2.4.3, Figure 2.20; Easterling and Wehner, 2009; Liebmann et al., 2010). However, an analysis of the full suite of CMIP5 historical simulations (augmented for the period 2006–2012 by RCP4.5 simulations, Section 9.3.2) reveals that 111 out of 114 realizations show a GMST trend over 1998–2012 that is higher than the entire HadCRUT4 trend ensemble (Box 9.2 Figure 1a; CMIP5 ensemble mean trend is 0.21ºC per decade). This difference between simulated and observed trends could be caused by some combination of (a) internal climate variability, (b) missing or incorrect radiative forcing and (c) model response error. These potential sources of the difference, which are not mutually exclusive, are assessed below, as is the cause of the observed GMST trend hiatus.

      GMST trend is global mean surface temperature trend.
      A “hiatus” is a stop.
      And this was from the IPCC in that is tasked to provide information supportive of the AGW hypothesis and was published three years ago. The Hiatus (or Pause) is now over 18 years long.

      • “The IPCC provides two definitions of what it calls the “Hiatus”; viz,”
        Really? Where?
        There is nothing in the glossary. In Box 9.2 I see just two definition-like statements:
        “Depending on the observational data set, the GMST trend over 1998–2012 is estimated to be around one-third to one-half of the trend over 1951–2012 (Section 2.4.3, Table 2.7; Box 9.2 Figure 1a, c). For example, in HadCRUT4 the trend is 0.04oC per decade over 1998–2012, compared to 0.11oC per decade over 1951–2012. The reduction in observed GMST trend is most marked in Northern Hemisphere winter (Section 2.4.3; Cohen et al., 2012). Even with this “hiatus” in GMST trend, the decade of the 2000s has been the warmest in the instrumental record of GMST.”
        and more explicitly:
        “In summary, the observed recent warming hiatus, defined as the reduction in GMST trend during 1998–2012 as compared to the trend
        during 1951–2012, is attributable…”

        A reduced trend relative to other observation periods, not a zero trend, nor one relative to models.
        “A “hiatus” is a stop.”

      • Nick S.:
        I cited, referenced, linked to and quoted from the IPCC Box titled, “Climate Models and the Hiatus in Global Mean Surface Warming of the Past 15 Years
        Contrary to your astonishing assertion, a hiatus is a stop; e.g. the Oxford English Dictionary provides this definition.

        A pause or break in continuity in a sequence or activity:
        there was a brief hiatus in the war with France

        If you don’t like “stop” then use “pause”.
        Your assertion that you fail to see the two explanations of the “Hiatus” in the quotation I provided is merely another example of your lack of ability at reading comprehension.
        What do you think is the “Hiatus in Global Mean Surface Warming of the Past 15 Years” which the box was discussing if not the two points I identified in the quotation from the box?

      • Richard,
        “I cited, referenced, linked to and quoted from the IPCC Box”
        Yes, that is where I looked. You said, quite specifically:
        “The IPCC provides two definitions of what it calls the “Hiatus”; viz,
        (a) a linear trend not distinguishably above zero
        (b) a linear trend that is significantly less than the predicted trend of the “CMIP5 ensemble mean trend”.”

        The IPCC provides, not the dictionary provides. And I can’t see that anywhere, and I don’t believe the IPCC did provide that. Surely you can quote the words of that provision.
        “there was a brief hiatus in the war with France”
        but the war did not stop (at that time).

      • Nick S.:
        Everybody can see I have provided the necessary and complete quote:
        I repeat what I replied to you and you have ignored.
        “Your assertion that you fail to see the two explanations of the “Hiatus” in the quotation I provided is merely another example of your lack of ability at reading comprehension.
        What do you think is the “Hiatus in Global Mean Surface Warming of the Past 15 Years” which the box was discussing if not the two points I identified in the quotation from the box?”
        You seem to have missed my question perhaps also because of your lack of ability at reading comprehension. Maybe you will try to answer it now.

      • Richard,
        “What do you think is the “Hiatus in Global Mean Surface Warming of the Past 15 Years” which the box was discussing if not the two points I identified in the quotation from the box?””
        I think it is the actual definitions that they gave, and I quoted. I’ll say it again
        “In summary, the observed recent warming hiatus, defined as the reduction in GMST trend during 1998–2012 as compared to the trend during 1951–2012”
        The section you quoted makes no reference to a zero trend (your (a)). And though it does discuss a difference between CMIP5 and HADCRUT, it quite clearly is not calling that the hiatus, as the final sentence shows:
        “These potential sources of the difference, which are not mutually exclusive, are assessed below, as is the cause of the observed GMST trend hiatus”

      • NickS.:
        I stand by every word I wrote and I provided sufficient information to assess it.
        Your inability at reading comprehension is distorting your understanding of what the IPCC said: the words the IPCC used say what the IPCC meant and not whatever you wish they had said.
        In response to my repeatedly asking you

        What do you think is the “Hiatus in Global Mean Surface Warming of the Past 15 Years” which the box was discussing if not the two points I identified in the quotation from the box?

        You have written

        I think it is the actual definitions that they gave, and I quoted. I’ll say it again

        In summary, the observed recent warming hiatus, defined as the reduction in GMST trend during 1998–2012 as compared to the trend during 1951–2012

        NO! They actually wrote

        Depending on the observational data set, the GMST trend over 1998–2012 is estimated to be around one-third to one-half of the trend over 1951–2012

        Your suggestion of what they meant is merely a difference and it is not a hiatus unless the smaller trend is indistinguishable from zero. If they meant a reduction then they would have used the word reduction. They meant a hiatus because that is the word they used.
        What the IPCC did say about the two periods you mention says nothing about the ““Hiatus in Global Mean Surface Warming of the Past 15 Years” (i.e. 1997-2012). However, if the reduction of the trend over that period is “one-third to one-half” of the trend of the recent 61 years that includes those years then, clearly, there is large difference between the “observational data sets”. The IPCC does not state the inherent errors of those trends but they are clearly between “one-third to one-half” of the larger trend value. And they say the smaller trend value is a “hiatus” which can only mean they are saying the trend value for 1998–2012 is not distinguishable from zero.
        The IPCC phrase “GMST trend hiatus” means “GMST trend hiatus”: it does NOT mean ‘GMST trend reduction’.

    • The data comes from the NOAA global combined land and ocean temperature series.
      All values are calculated from the dates and temperature anomalies of the temperature series.

  2. Your technique is very interesting. It deals directly with the problem:
    “a trend is not a trend if it depends on the choice of endpoints”
    I would feel better about the graphs if the sample periods were all the same length. It could be the difference in “width” of the graphs is an artifact of the sample length, not of the underlying data.

    • oops – correction. I see your samples are all the same length, in which case the difference in the shapes is significant. It tells us very definitely that something fundamental has changed.

    • What the narrow shape of the 2001-2013 graph tells me is that temperature over this interval must have been much less extreme as compared to the previous intervals.
      I think you have found strong evidence that the climate system has become less extreme during the Pause Interval, that there has definitely been something quite different going on as compared to the previous intervals.
      Or that all the adjustments have really screwed up the data.

  3. 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?(/blockquote>
    Whilst I would accept that IF the overall warming rate has fallen to some 42% or better still some 27%, then there has been a slowdown in the rate of warming, I do not see how as a matter of the ordinary meaning of the word hiatus or pause a reduction in the rate of overall warming to those levels could properly be described as a pause or hiatus..
    For there to be a pause. there would have to be a protracted period when there was no statistically significant warming at all in the time series data.
    My understanding of your analysis is that is not what your analysis demonstrates.

    • opps!!!
      I have made a formatting error with the quoted text in the first paragraph. Paragraphs 2 to 4 are my comments on the quoted text.

    • In my opinion, the term “Slowdown” is the most accurate name for the event that I have described.
      The problem is that the terms “Pause” and “Hiatus” are the most common names used at the moment.
      How do we get people to use “Slowdown”?

      • How do we get people to use “Slowdown”?
        Hey, Sheldon, that’s a new one! ‘Slowdown’. I like your spin!
        Unfortunately for the alarmist Narrative, global warming has been stopped for many years. So let’s just use ‘stopped’.
        K? Thx, bye.

      • “Stopped” seems too strong. The climate (or the weather it’s made of) is never stopped.
        “Slowdown” seems too confident. The weather may reverse or accelerate or continue as is. We don’t know.
        I prefer “Enfeebled”.

      • M,
        I certainly respect what the situation seems to you, M. But when I observe that the trend stopped going up many years ago, it looks like it’s ‘stopped’ rising ever since. YMMV, of course. ☺

  4. “. A trend has 4 main attributes, a start date, an end date, a length, and a slope”

    There are only 3, not 4. the length is a function of the start and end date.

  5. “Could anybody deny the Pause, after seeing that evidence?”
    I think what your graphs mainly contrast is the lack of major features (peak or dip) in the 2001-2013 interval. Here is a time-series graph with a 12-month moving average added:
    It comes from this active gadget, which I’ll say more about. I’ve marked your 2001-2013 trend with the red and blue dots. The slope is indeed rather less (0.516°C/Century) than in some nearby regions. The argument about whether this is a “pause” or a “slowdown” seems to generate a lot of pointless argument.
    The other regions that you look at contain major ENSO features, like the 1998 peak or the 1985 dip. These generate large slope variations as you slide subintervals around, and are responsible for the larger spread of your plots there.
    I have my own style of MTA at that page. For the NOAA land/ocean since 1960, it looks like this:
    The x-axis is the end year of the interval, and the y-axis is the start. The color shows the trend. Fixed period trends lie along a SW-NE line; I’ve marked the 14-year line in white. If you follow it down, you can see that indeed it passes through a yellow and even green area in recent times, and further down orange (about 2 °C/Cen), and back to greenish. Stuff happens. I’ve marked a level of about 1.7 with grey, and 0 with brown, so you can pick out the actual negative trend regions. The typical feature for that is a blue blob near the hypotenuse (short trend) which represents the down slope side of a peak or dip, which diminishes as the trend region spreads, till you reach the brown border.
    Th right edge is current time, and you can see how all trends are increasing with the El Nino.
    The plot is active; you can click the triangle to show the trend with numeric data shown and the red/blue dots moved on the time series graph. You can also select different datasets, time periods and styles (eg significance masked).

  6. This method seems to oversample trends associated with the middle of the dataset as the moving window will catch the middle more often than the edges? This is particularly true when the trend sample length exceeds half the dataset length and the middle is part of every point on the scatter. How do we take that into account in interpretation of the results, or does it even matter? My thanks to you for sharing this interesting technique.

  7. Sheldon,
    An interesting way of looking at trends. What I am a bit worried about is that in these kinds of calculations, the points in the middle get used more often than the ones at the ends. In a way, they are weighted (much) more heavily. It then also follows that the choice of interval can influence the results by getting the “most desirable” points in the center of the interval. Maybe a sort of inverse weighting can help alleviate this problem?
    Best regards,

    • @MJB and @Frank de Jong
      I understand your concerns about oversampling the middle.
      The explanation that I am about to give is just off the top of my head, and needs more research. Because I plot all combinations of warming rate versus trend length, oversampling may cause an increased density of points in some parts of the graph. BUT, no incorrect point is plotted. So I can see the correct range of warming rates versus trend length pairs. And just as importantly, I can see the correct range where there are NO warming rate versus trend length pairs. This aspect is not affected by oversampling.

  8. Sheldon
    Your post title states, “Very strong graphical evidence for the Pause (Part 2)” .
    According to your Part 1 post, you constructed your analysis method (to include every conceivable trend) to thwart criticism that you were cherry picking trend start dates.
    As a Lukewarmer, I have two comments:
    (1) You are still subject to the “cherry picking” charge because you selected a’prior the start-end dates of the three regimes in your analysis.
    (2) But more importantly, your ad-hoc analysis method is mathematically incomprehensible, at least to me. Have you constructed hypothetical test cases based on a mix of trend (constant and linear) and natural variability of varying magnitudes … such that you can more clearly explicate your method and its significance.
    Good to keep thinking and challenging … and I thank you for that!!

    • @ DanMet’al
      Dan, you can not do ANY analysis at all, if you do not pick dates. The aim is to pick dates in a fair way. I described all of my choices. I wanted equal length intervals, and it would be rather pointless looking for a slowdown in an interval where I didn’t think that there was a slowdown. I had a very limited number of years to choose from, and I wanted the intervals to be as long as possible.
      I am happy with my date/interval choices. If you can suggest a better choice, please do.
      My analysis method is actually quite simple. If is based on simple linear regression. I just do lots of regressions, for every possible pair of points in the interval. That gives me every possible trend for the interval, and equally important, it shows me what trends are NOT possible for the interval.

      • Sheldon;
        My comments remain as originally presented: (1) you have cherry-picked the“regime start-stop date”, and (2) you have no awareness of any meaningful mathematical interpretation of your resultant curves ( e.g., how they depend on usual climate forcing and more extensive (el Nino/ AMO etc) climatic disruptions.
        As you posit, your analysis is quite simple … I ( posit your analysis is much too simple) … and proves nothing.
        But I admire your tenacity and interest in increasing your/our understanding … keep it up!!!

  9. @MJB, @Frank,
    I don’t think your concern about weighting is valid.
    Keep in mind that each trend is calculated separately and plotting as a separate, unique point. Critically, each point is independent of all other points on the graph.
    There would be a weighting problem if any one datum was used more than once in the calculation of any single point graphed in the scatter plot.
    What this method does is simply provide a visualization of ALL possible “cherry picked” intervals with a defined interval, revealing the consequence of cherry-picking any one particular interval in the time period of interest.
    This is enormously valuable. It addresses the “cherry-picking” objection completely. Prior to this method, there was no way to easily and efficiently address the argument. With this method, we can see clearly where trend intervals become more immune to cherry-picking effects, and can therefore counter such arguments factually.
    Also, there is other interesting signals that emerge from this analysis. In particular, the “quiet” nature of the pause period vs. the far more volatile signal in the warming periods. What does this mean? How might it correlate back to the forcing(s) causing the warming? Is it possible to show that CO2 forcing would behave one way (smooth and constant) vs. natural (sun, volcanoes, ocean patterns, cosmic rays, etc.) are naturally (pun intended) more volatile.
    If it turns out to hold every time that warming is always volatile and pauses are much quieter, then there’s something to be discovered there, and it may be a critical discovery.

    • @Dave Waller – very good points.
      There is still the issue of cherry-picking the start and end of the overall interval. However, as you point out, it handles the issue of cherry-picking within the interval completely.
      I will soon be analysing and comparing the intervals [January 1920 to December 1944] (warming when CO2 levels were low), with [January 1975 to December 1999] (warming when Co2 levels were high).
      A quick look at these intervals shows that the warming rate versus trend length graphs look very different. However, I can think of several things that might cause this. I imagine that data collection from 1920 to 1944 may be very limited compared to 1975 to 1999. The older temperature data may be “calculated” in a different way to the modern temperature data. Who knows what adjustments, interpolations, extrapolations, reconstructions, etc have been done, and did the modern and old temperature data get the same treatment.

      • Sheldon: In regard to my (and others) comment regarding “cherry picking of start/stop dates for the three regimes/episodes: Maybe you should consider taking random “longer” or “shorter” data sets; select 2,3, or four successive data subsets and redo your analysis. Expand your analysis to range from the 1920s to the 2015 time frame. After proper randomization … what do you get?
        Thanks Dan.
        It seem you picked your regimes after looking after the data …. that’s not the way to do it.
        But again … I respect the work you have put into your reported analysis!!

      • Dan,
        thank you for your suggestion. I will have a think about random “longer” or “shorter” data sets.
        You said, “It seems you picked your regimes after looking after the data …. that’s not the way to do it.”
        When I read that comment, it made me think about that joke about the drunk, who is searching for his lost car keys under a street light. A person offers to help, and says, “are you sure that you lost your keys here?”. The drunk says, “no, I dropped them across the road, but there is no light over there”.
        I searched for the Slowdown where I thought that it would be. Nobody else seems to have conclusively found it. It is very hard to prove that it is there if you don’t target it. If I didn’t target it directly, then I may not have found it.

      • If I didn’t target it directly, then I may not have found it.

        Suppose you were to do this with the whole RSS data set from its start in 1979 to date. You would find a number of places where the trend would be zero, including a place where the time is 18 years and 8 months.

  10. Sheldon, have you plotted the regression variance against interval? That would be an even better way to compare volatility between respective periods (warming, pause).

  11. It seems to me that the results say a lot about uncertainty. That is that the shorter the time interval the less likely it will be that it (the shorter intervals) will also at the same time characterize the long term trend. So to the far left of each graph is like the upper and lower bounds of the “uncertainty” in the long term trend and as it narrows to the right we get closer to the best estimate of the long term trend. I really like the technique. Nick Stokes’ is pretty cool too but gets a bit busy.

  12. I had done a similar analysis, for my own curiosity, with the UAH data last year. I found it much more informative to make the x axis be “center date” and plot all possible trend lengths centered about that date at that x location. All the information is the same, just choosing a different way to present your three dimensions of data on a two dimensional plot. I just found it more intuitive to have time be the x axis since we are used to asking the question of what is happening at a specific time.

    • @David Stienmier
      I agree with your comments. I am still experimenting with what to plot against what. As I said in the article, it is possible to plot any of the attributes (start date, end date, trend length, and slope) against any other.
      I like the warming rate versus trend length graphs because they are simple, and I think that people can understand them relatively easily.
      I have plotted warming rate against start date and end date, and I have thought about centre date (= (start date + end date) / 2).
      I am also thinking about using color to add another dimension to the graphs (e.g. plot points for different end dates in different colors, so that you can see “warming rate” versus “trend length” versus “end date”, all in one graph).

      • I think you have to choose what to plot against what based on what question you are trying to answer. I understood that one of the things you are trying to avoid is any possible (rational) accusation of cherry picking. By choosing an axis that requires you to then separate your data into chunks with arbitrary (chosen by you instead of calculated) start and end dates you set yourself up for accusations of cherry picking unless you also show all other start-end combinations. “Blocking” the data also eliminates all the trends that cross between blocks, thereby reducing you effective data set.
        If we constrain ourselves to having all charts show all data, with no arbitrary separations. Then it makes that to answer the question of “How was the earth warming/cooling in 2000-2010 compared to other times in the record” Then I should plot the trend values vs center date and compare. It might be useful to only compare trend length that are possible to calculate for the period in question, so if I want to look at 2005 I can only look at trends up to 22 years in length, so maybe limit the analysis to trends from 120 to 260 months for the entire set.
        Plots against trend length are very useful for identifying cycles. For example, in your first article you noticed the 22 year trends have a much narrower spread than other trend lengths (this would probably be even more noticeable if all the trends for the entire data set (1950-2015?) was plotted on the same graph). This indicates the presence of a ~22 or ~11 year cycle that is being filtered out by the effective 22 year moving average in the trend calculation for that trend length. If you have a long enough data set, and you didn’t break it up into hunks, you can start to make observations about such things. The 25 year hunks you broke it into in the first post aren’t long enough for more than a “huh, that’s curious” kind of statement (however 22 year cycles have been noticed in other analysis).
        Plots against trend length are also useful for pointing out things like you already have such as “be careful with short trends, they can say anything you want cause they are all over the place”
        In short form: If you want to avoid accusations of cherry picking then all available data should be on every plot with no arbitrary “blocking” of data. If you are tempted to block the data to answer a question, ask yourself if the question can instead be answered by looking at the data from an orthogonal direction.

  13. The method is interesting, but I cannot agree with the analysis.
    Taking the rightmost points as the trend = cherry picking (though not intentionally)+ needs no MTA at all.
    Instead we need the trend that does not depend on the chosen endpoints. Intuitively I would go for the horizontal parts of the mean trend (the first from right to left), that is:
    for graph 1: trendlength 10.5, value 1.35
    for graph 2: trendlength 11.5, value 1.65
    for graph 3: trendlength 11.5, value 0.30
    The mean values and their stdev can then be computed and the confidence intervals determined.

  14. 1) An anomaly is an observation that cannot be explained by a theory or mechanism.
    2) A paradox is an observation or analysis result that if correct disproves a theory or mechanism.
    It is a fact that there is cyclic warming and cooling in climate record. It is a fact there is from time to time massive abrupt cyclic change events in the paleo climate record.
    Atmospheric CO2 did change until hundreds of years after those temperature changes events and cycles and hence cannot be the cause of the past cyclic temperature change. CO2 level follows (sometimes millions of years after) planetary temperature changes.
    There is a cyclic mechanism that forces changes to the earth’s temperature (the temperature of both hemispheres changes in synchronism which rules out, in addition to a half dozen other independent observations/analysis results, as an explanation for what cause the changes solar insolation at 65N or ocean currents as the cause).
    Two satellite data sets supported hundreds of thousands of weather balloon temperature measurements show that the planet has not significantly warmed for 18 years. There is no logical reason to doubt those measures. It is a paradox that the earth has not significant warmed for 18 years at time in which atmospheric CO2 has increased year by year.
    Let’s call a spade a spade. It is pathetic that there is an in your face paradox that disproves AGW (No warming for more than 18 years) which many climate scientists and many in the media have ignored and do not understand the implications of.
    There is no AGW issue, there certainly is no CAGW issue.
    The satellite data sets are superior to the land based temperature measurements as they cover the entire earth (both oceans and land) and as they are not contaminated by the urban heat effect.
    As it is a fact that the climate war is currently going the land based temperature data has been manipulated (lowering past temperature data and raising current temperature data) to create a hockey stick. The climate war temperature data manipulation is an interesting side issue.
    The planet is starting to cool due to the interruption to the solar cycle. The solar cycle has been interrupted which is very, very, different than a slowdown in the solar cycle. If the past (paleo record) is a guide to the future the planet is going to abruptly cool. 95% of the warming in the last 150 years is due to solar cycle changes rather than the increase in atmospheric CO2.
    It is asserted, that you are taking the discussion off into left field. The problem is not that we need a new mathematical method to confirm the observational fact that the planet has not warmed for 18 years.
    We (so called skeptics and warmists) are stuck in a do loop where the discussion goes on and on and no progress is made. Something astonishing is happening to sun while we are having this pointless fight.
    Why is that so? Let’s talk about why this dang problem has not been solved.
    What do we know? Why in the world has no one written a summary of the observations that explains the logical implications of the observations compared to the logical implications of the competing theories.
    What are the logical implications of the observational fact that the planet has not warmed for 18 years? What are the competing theories for why the earth warmed in the last 150 years? Has the earth warmed before? What latitudes warmed before?
    What is the latitudinal warming paradox? Do you know what a paradox is? In private industry researchers would be fired for not addressing, not removing paradoxes. In private industry problems are not analyzed for ever. In private industry teams are changed or fired if problems are not solved.
    In private industry it is unthinkable that no one would have tried alternative theories to solve the problem. In private industry it is unthinkable that no one would have written a summary of all the observations noted paradoxes and anomalies with the standard theories.
    In pure sciences there are hundreds and hundreds of paradoxes. There has been for more than a decade ago sufficient observations/analysis to solve this problem (What causes the glacial/interglacial cycle, why did the planet warm in the last 150 years, what causes cyclic warming and cooling, will the planet warm or abruptly cool in the near future?) The paradoxes and anomalies go away when the correct theory is applied, with its different mechanisms.
    Big surprise things happen for physical reasons. There are no magic wands. Piles and piles of paradoxes and anomalies indicate there are multiple fundamental problems with the ‘standard’ theories. Most of the anomalies and paradoxes do not make it into the textbooks as they cannot be explained and they indicate the standard theories are rubbish.
    It does not matter how smart you are. You can never solve problem if you continue to apply a Zombie theory/theories and/or continue to build super complicate models that run on super computers based on a Zombie theories/mechanism. A Zombie theory is not part of the solution.
    It is a fact that for roughly 1/3 of the geological record levels of atmospheric CO2 are high and the planet is cold or the levels of CO2 are low and the planet is warm. CO2 and temperature does even correlate if the paleo record is examined for the entire term.
    Discussion of Process. Why this problem has not been solved. How it is possible look at the piles and piles of anomalies and paradoxes and solve the problem.
    There is in private industry (for example the process to investigate an airplane crash, the process to investigate and resolve maintenance, design, wear issues related to airplanes, and so on) a standard logical, structured very, very effective methodology that is used to solve physical problems. At any one time in the daytime there are roughly 500,000 people in airplanes traveling in the US.
    As the consequences of unresolved airplane maintenance and design issues are not acceptable, airplane maintenance and designed problems are solved as opposed not discussed for every and every. In pure science the incentive is publish papers and discuss a problem for every. In private industry planes that crash from time to time for no explained reasons is not acceptable.
    In private industry the excuse that the best theory we have cannot explain why the planes are crashing is not acceptable.

  15. One day, in the not so distant future, “The Pause” will become “The Plateau”.

    • Why do we persist in calling it a pause? That implies the long term trend continues to be warming, when in fact we have no idea what the current long-term (forward looking) trend is. Clearly, we have had a natural warming trend for the last few hundred years, but at any point in time we don’t know if the future trend will be cooling or warming or stays the same.

  16. The corollary of the observational fact that there has been no warming, no increase in temperature for the last 18 years is that the increase in atmospheric CO2 did not cause the warming in the last 150 years.
    There are piles and piles of other observations and analysis results that support the assertion that CO2 AGW is a Zombie theory. The principal reason why the CO2 AGW theory did not die is that planet did warm and the planet has not as yet significantly cooled. Significant cooling will end the climate wars.
    It is an observational fact that there are cycles of warming and cooling (sometimes abrupt cooling events) in the paleo record. It is an observational fact that there is concurrent with the cycles of warming and cooling changes in cosmogenic isotopes that are deposited in the ocean and on ice sheets. The cosmogenic isotopes changes are caused by changes in the solar cycle.
    The no brainer alternative hypothesis (alternative to CO2 AGW) as to what caused the warming in the last 150 years is solar cycle changes caused the warming. If solar changes caused the warming in the last 150 years, the warming is reversible.
    Comment: A period of no warming is different than slow warming where the rise in warming is less than predicted. If there was a gradually increase in planetary temperature the warmists could appeal to some mysterious mechanism that delayed the warming. The dozens of theories that proposed mysterious offsetting mechanisms that temporary cool the earth exactly offsetting the CO2 forcing have two issues:
    1) The offsetting mechanism has grow with time to explain fact that there is a plateau of no warming as opposed to a wiggly line that gradually increases.
    2) The second issue, the latitudinal warming paradox the fact that there has been almost no tropical warming and most of the warming has been in high latitude regions and that there has been more high latitude warming in the Northern hemisphere. This same peculiar pattern of warming has occurred before in the paleo record.
    To explain the non observed warming the aerosol cooling mechanism failed as the aerosol cooling mechanism should have cooled primarily the Northern hemisphere as this where the majority of the coal is burned and there is little mixing of the air of hemisphere to hemisphere. As noted however the Northern hemisphere is the region that experienced the most amount of warming, not the least amount of warming if aerosols were offsetting the CO2 warming mechanism.

    (kôr’ə-lěr’ē) A statement that follows with little or no proof required from an already proven statement. For example, it is a theorem in geometry that the angles opposite two congruent sides of a triangle are also congruent. A corollary to that statement is that an equilateral triangle is also equiangular.

    The following are peer reviewed papers that support the assertion that there are periods of millions of years when the planet is cold and atmospheric CO2 is high and vice versa.

    Evidence for decoupling of atmospheric CO2 and global climate during the Phanerozoic eon by J.Veizer*, Yves Godderis² & Louis M. Franceois²
    Atmospheric carbon dioxide concentrations are believed to drive climate changes from glacial to interglacial modes1, although geological1±3 and astronomical4±6 mechanisms have been invoked as ultimate causes.
    Additionally, it is unclear7,8 whether the changes between cold and warm modes should be regarded as a global phenomenon, affecting tropical and high-latitude temperatures alike9±13, or if they are better described as an expansion and contraction of the latitudinal climate zones, keeping equatorial temperatures approximately constant14±16.
    Here we present a reconstruction of tropical sea surface temperatures throughout the Phanerozoic eon (the past ,550 Myr) from our database17 of oxygen isotopes in calcite and aragonite shells.
    The data indicate large oscillations of tropical sea surface temperatures in phase with the cold and warm cycles, thus favouring the idea of climate variability as a global phenomenon.
    But our data conflict with a temperature reconstruction using an energy balance model that is forced by reconstructed atmospheric carbon dioxide concentrations18. The results can be reconciled if atmospheric carbon dioxide concentrations were not the principal driver of climate variability on geological timescales for at least one-third of the Phanerozoic eon, or if the reconstructed carbon dioxide concentrations are not reliable.

    “Atmospheric carbon dioxide levels for the last 500 million years
    The last 500 million years of the strontium-isotope record are shown to correlate significantly with the concurrent record of isotopic fractionation between inorganic and organic carbon after the effects of recycled sediment are removed from the strontium signal. The correlation is shown to result from the common dependence of both signals on weathering and magmatic processes. Because the long-term evolution of carbon dioxide levels depends similarly on weathering and magmatism, the relative fluctuations of CO2 levels are inferred from the shared fluctuations of the isotopic records. The resulting CO2 signal exhibits no systematic correspondence with the geologic record of climatic variations at tectonic time scales.”

    The observations do not support the assertion that the increase in atmospheric CO2 was the principal reason for the increase in planetary temperature.
    1) Latitudinal temperature anomaly paradox (Strike 1)
    The latitudinal temperature anomaly paradox is the fact that the latitudinal pattern of warming in the last 50 years does match the pattern of warming that would occur if the recent increase in planetary temperature was caused by the CO2 mechanism.
    The amount of CO2 gas warming observed is theoretically logarithmically proportional to the increase in atmospheric CO2 times the amount of long wave radiation that it emitted to space prior to the increase.
    As gases are evenly distributed in the atmosphere (ignoring very heavy or very light gases which biases the altitudinal distribution in the atmosphere), the potential for warming due to CO2 should be the same at all latitudes.
    The amount of warming is also proportional to amount of long waver radiation that is emitted to space prior to the increase in atmospheric CO2.
    Now we know that as the earth is a sphere the tropical region of the planet receives the most amount of short wave radiation and hence also emits the most amount long wave radiation. The tropical region of the planet should have hence warmed the most due to the increase in atmospheric CO2.
    There is in fact almost no warming in the tropical region of the planet. This observational fact supports the assertion that majority of the warming in the last 50 years was not caused by the increase in atmospheric CO2.
    2) The 18 year pause without warming (Strike 2)
    As atmospheric CO2 is increasing with time, the delta T (increase in planetary temperature due to the increase in CO2) should also be increasing with time. As we now that there has been a period of 18 years with no warming when atmospheric CO2 has increasing for each and every year we know that the majority of the warming in the last 50 years was not due to the increase in atmospheric CO2 and the IPCC general circulation model calculated warming due to CO2 is orders of magnitude too high.
    3) The tropical tropospheric 8km above the earth no hot spot Paradox (Strike 3 and the CAWG is disproved)
    The IPCC’s general circulation models predict that most amount of warming on the planet should occur in the tropics at 8k above the earth’s surface. The long wave radiation from warming at 8 km then warms the earth’s surface by of course radiation.
    At the earth’s surface there are more CO2 molecules and there is more water vapor. The amount of CO2 warming decreases as the number of molecules increases and as water long wave radiation overlaps with CO2, most amount of warming due to the increase in CO2 occurs at 8km above the surface of the planet where there is less water and less CO2 molecules. The CO2 effect is almost saturated at the surface of the planet.
    The signature of CO2 warming, the tropical tropospheric hot spot at 8km is not observed which is consistent with the observational fact that there has been almost no tropical region warming. The
    The following peer reviewed paper provides the strike 1 and strike 2 observational data and specifically states the observations support the assertion that majority of the warming in the last 30 years was not due to the increase in atmospheric CO2.

    Limits on CO2 Climate Forcing from Recent Temperature Data of Earth
    The atmospheric CO2 is slowly increasing with time [Keeling et al. (2004)]. The climate forcing according to the IPCC varies as ln (CO2) [IPCC (2001)] (The mathematical expression is given in section 4 below). The ΔT response would be expected to follow this function. A plot of ln (CO2) is found to be nearly linear in time over the interval 1979-2004. Thus ΔT from CO2 forcing should be nearly linear in time also.
    The atmospheric CO2 is well mixed and shows a variation with latitude which is less than 4% from pole to pole [Earth System Research Laboratory. 2008]. Thus one would expect that the latitude variation of ΔT from CO2 forcing to be also small. It is noted that low variability of trends with latitude is a result in some coupled atmosphere-ocean models. For example, the zonal-mean profiles of atmospheric temperature changes in models subject to “20CEN” forcing ( includes CO2 forcing) over 1979-1999 are discussed in Chap 5 of the U.S. Climate Change Science Program [Karl et al.2006]. The PCM model in Fig 5.7 shows little pole to pole variation in trends below altitudes corresponding to atmospheric pressures of 500hPa.
    If the climate forcing were only from CO2 one would expect from property #2 a small variation with latitude. However, it is noted that NoExtropics is 2 times that of the global and 4 times that of the Tropics. Thus one concludes that the climate forcing in the NoExtropics includes more than CO2 forcing. These non-CO2 effects include: land use [Peilke et al. 2007]; industrialization [McKitrick and Michaels (2007), Kalnay and Cai (2003), DeLaat and Maurellis (2006)]; high natural variability, and daily nocturnal effects [Walters et al. (2007)].
    An underlying temperature trend of 0.062±0.010ºK/decade was estimated from data in the tropical latitude band. Corrections to this trend value from solar and aerosols climate forcings are estimated to be a fraction of this value. The trend expected from CO2 climate forcing is 0.070g ºC/decade, where g is the gain due to any feedback. If the underlying trend is due to CO2 then g~1. Models giving values of g greater than 1 would need a negative climate forcing to partially cancel that from CO2. This negative forcing cannot be from aerosols.
    These conclusions are contrary to the IPCC [2007] statement: “[M]ost of the observed increase in global average temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations.

    A comparison of tropical temperature trends with model predictions
    We examine tropospheric temperature trends of 67 runs from 22 ‘Climate of the 20th Century’ model simulations and try to reconcile them with the best available updated observations (in the tropics during the satellite era). Model results and observed temperature trends are in disagreement in most of the tropical troposphere, being separated by more than twice the uncertainty of the model mean. In layers near 5 km, the modelled trend is 100 to 300% higher than observed, and, above 8 km, modelled and observed trends have opposite signs. These conclusions contrast strongly with those of recent publications based on essentially the same data.
    We have tested the proposition that greenhouse model simulations and trend observations can be reconciled. Our conclusion is that the present evidence, with the application of a robust statistical test, supports rejection of this proposition. (The use of tropical tropospheric temperature trends as a metric for this test is important, as this region represents the CEL and provides a clear signature of the trajectory of the climate system under enhanced greenhouse forcing.) On the whole, the evidence indicates that model trends in the troposphere are very likely inconsistent with observations that indicate that, since 1979, there is no significant long-term amplification factor relative to the surface. If these results continue to be supported, then future projections of temperature change, as depicted in the present suite of climate models, are likely too high.

  17. Interesting posts. And comments. Another way to investigate pauses is to plot temperature against CO2 concentrations instead of time. Another is to plot the running temperature trend per 100 ppm of CO2 on the normal x-axis time line (using UAH it’s currently 0.65C / 100 ppm- the lowest since 1996). See

  18. I hope this isn’t a dumb question. Why was data from NOAA used (which I thought was suspect due to “adjustments” of older temperatures), rather than data from UAH? I must say, despite the criticisms, it looked to me to be an excellent effort and should be applauded.

    • @3¢worth
      If I used UAH data, then no Alarmist would believe the results. They would simply ignore the results because they don’t trust the satellite data.
      Think about this. I have proved that there is a Slowdown in the data that Alarmists trusted the most. After all, it has been adjusted to get rid of the Slowdown. What could be more unsettling to an Alarmist, than finding a Slowdown in data that they thought was safe.

  19. A paradox is an observation that disproves a theory. People that continue to push a theory that has been proven incorrect by an observation are followers of cult science, people that have an agenda, people who are not interested in solving scientific problems only pushing their agenda.
    It is a fact that satellite data (two independent satellite data sets both of which are support by hundreds of thousands of balloon temperature measurements) that there has been no warming for more than 18 years at a time in which atmospheric CO2 has been rising year over year. This observational fact is paradox for the
    It is a fact that there has been widespread pathetic data GISS manipulation of the surface temperature data by NOAA which explains why there is roughly a 0.15C temperature difference (the difference between the satellite data increased overtime as the GISS data set was changed over time) current temperature satellite vs GISS.
    Manipulating data does not change the fact that the planet is about to abruptly cool. The data and analysis supports the assertion that the majority of the warming in the last 150 years was due to solar cycle changes rather than the increase in atmospheric CO2. If that assertion is correct, global warming is reversible.
    Observations continue to support the assertion that the solar cycle has been interrupted. There is an interesting explanation as to what is the physical reason for the delay in cooling as the solar cycle slowed down.
    Big surprise the paleo data unequivocally shows that the planet cyclically warms and cools with the cycles correlating with solar cycle changes. The past is a guide to the future.
    Scientific Explanation why there is almost no warming for a doubling of atmospheric and a how they did explanation of how the 1 dimension no feedback calculations where non-scientifically altered to create the AGW CO2 issue.
    The One Dimension, No Feedback Forcing Calculation’s Deliberate Incorrect (White Lies/Fibs)
    Comment: The so called 1 dimensional no feedback calculation shows ‘surface’ warming of 3.7 watts/m^2 or 1.2C. The following shows there is peer reviewed analysis that indicates that 1 dimensional no feedback calculation is too high by roughly a factor 16 due to white lie incorrect assumptions which are additive and both reduce the surface warming by a factor of four. The so called general circulation models (3 dimensional models referred to as GCM) have more than a 100 subject parameters that can be adjusted to give any answer possible. The 1 dimensional calculation is however the basis for the entire AGW charade.
    White Lie Assumptions
    A) Lapse Rate Fib
    The so called 1 dimensional, no feedback, forcing calculations for a doubling of atmospheric CO2 ignored the fact that the lapse rate decreases when atmospheric CO2 increases which reduces the forcing by a factor of four. The change in the lapse rate is due to the fact that hot air rises causing cold air to fall causing the phenomena which is called convection.
    B) Water Vapor Fib
    The 1 dimensional no feedback calculation CO2 forcing warming for a doubling of atmospheric CO2 was done with no water vapor in the atmosphere. As the planet is 70% covered with water there is a great deal of water vapor in the atmosphere. As the absorbtion spectrum of water and CO2 overlap, water vapor in the atmosphere reduces temperature increase due to the doubling of atmospheric CO2 also by a factor of four.
    Due to Fib A and Fib B, the warming due to doubling of atmospheric CO2, no feedbacks is 16 times smaller 0.075C rather than 1.2C which is so small the without feedback warming is the same as the with feedbacks warming.

    Collapse of the Anthropogenic Warming Theory of the IPCC

    4. Conclusions
    In physical reality, the surface climate sensitivity is 0.1~0.2K from the energy budget of the earth and the surface radiative forcing of 1.1W.m2 for 2xCO2. Since there is no positive feedback from water vapor and ice albedo at the surface, the zero feedback climate sensitivity CS (FAH) is also 0.1~0.2K. A 1K warming occurs in responding to the radiative forcing of 3.7W/m2 for 2xCO2 at the effective radiation height of 5km. This gives the slightly reduced lapse rate of 6.3K/km from 6.5K/km as shown in Fig.2.

    The modern anthropogenic global warming (AGW) theory began from the one dimensional radiative convective equilibrium model (1DRCM) studies with the fixed absolute and relative humidity utilizing the fixed lapse rate assumption of 6.5K/km (FLRA) for 1xCO2 and 2xCO2 [Manabe & Strickler, 1964; Manabe & Wetherald, 1967; Hansen et al., 1981]. Table 1 shows the obtained climate sensitivities for 2xCO2 in these studies, in which the climate sensitivity with the fixed absolute humidity CS (FAH) is 1.2~1.3K [Hansen et al., 1984].
    In the 1DRCM studies, the most basic assumption is the fixed lapse rate of 6.5K/km for 1xCO2 and 2xCO2. The lapse rate of 6.5K/km is defined for 1xCO2 in the U.S. Standard Atmosphere (1962) [Ramanathan & Coakley, 1978]. There is no guarantee, however, for the same lapse rate maintained in the perturbed atmosphere with 2xCO2 [Chylek & Kiehl, 1981; Sinha, 1995]. Therefore, the lapse rate for 2xCO2 is a parameter requiring a sensitivity analysis as shown in Fig.1.

    The followings are supporting data (William: In peer reviewed papers, published more than 20 years ago that support the assertion that convection cooling increases when there is an increase in greenhouse gases and support the assertion that a doubling of atmospheric CO2 will cause surface warming of less than 0.3C) for the Kimoto lapse rate theory above.
    (A) Kiehl & Ramanathan (1982) shows the following radiative forcing for 2xCO2.
    Radiative forcing at the tropopause: 3.7W/m2.
    Radiative forcing at the surface: 0.55~1.56W/m2 (averaged 1.1W/m2).
    This denies the FLRA giving the uniform warming throughout the troposphere in
    the 1DRCM and the 3DGCMs studies.
    (B) Newell & Dopplick (1979) obtained a climate sensitivity of 0.24K considering the
    evaporation cooling from the surface of the ocean.
    (C) Ramanathan (1981) shows the surface temperature increase of 0.17K with the
    direct heating of 1.2W/m2 for 2xCO2 at the surface.

    Transcript of a portion of Weart’s interview with Hansen.

    Weart: This was a radiative convective model, so where’s the convective part come in. Again, are you using somebody else’s…
    Hansen: That’s trivial. You just put in…
    Weart: … a lapse rate…
    Hansen: Yes. So it’s a fudge. (William it is not a ‘fudge’ its a white lie that is necessary or there would be CO2 AGW problem as it reduces the surface warming by a factor of 16) That’s why you have to have a 3-D model to do it properly. In the 1-D model, it’s just a fudge, and you can choose different lapse rates and you get somewhat different answers (William: Different answers that invalidate CAGW, the 3-D models have more than 100 parameters to play with so any answer is possible. The 1-D model is simple so it possible to see the fudging/shenanigans). So you try to pick something that has some physical justification (William: You pick what is necessary to create CAGW, the scam fails when the planet abruptly cools due to the abrupt solar change). But the best justification is probably trying to put in the fundamental equations into a 3-D model.

    In addition to ignoring the fact that ‘greenhouse’ gases increase convection which reduces surface warming by a factor of 4, the without ‘feedbacks’ calculation also ignored the fact the absorption spectrum of water vapor and CO2 overlap. As the earth is 70% covered with water there is a great deal of water vapor in the lower atmosphere particularly in the tropics.
    Redoing the double atmospheric CO2 level, no feedback calculation with a atmospheric model that takes into account the amount of water vapor in the atmosphere and the radiation effects of water/CO2 absorption overlap reduces the surface forcing for a doubling of atmospheric CO2 from 3.7 watts/meter^2 to 1.1 watts/meter^2 ( also reduces surface for a doubling of CO2 by a factor of four). The 1.1 watts/meter^2 increase in forcing will result in surface warming of ball park 0.1C to 0.2C which is so small, the no feedback case is the same as with feedback case.
    Check out figure 2 in this 1986 published paper that notes the 1 dimensional calculations were done for a dry atmosphere which is physically incorrect. The 1986 paper notes the surface forcing is reduced by a factor of four if it is redone with the estimated water vapor in the atmosphere.

    Radiative Heating Due to Increased CO2: The Role of H2O Continuum Absorption in the 18 mm region
    In the 18 mm region, the CO2 bands (William: CO2 spectral absorption band) are overlapped by the H2O pure rotational band and the H2O continuum band. The 12-18 mm H2O continuum absorption is neglected in most studies concerned with the climate effects of increased CO2.

    P.S. Reducing the surface warming for a doubling of atmospheric CO2 by a factor of 16 from 1.2C to 0.075C. Now as half of the warming should have all ready occurred, this means only 0.035C or less than 5% of the 0.8C warming in the last 150 years can be attributed to the increase in atmospheric CO2. The explanation of the remaining warming is due to solar cycle changes.

    • William Astley: Your long post above is very interesting, but mostly incorrect.
      Our data on temperature change isn’t reliable enough to accurately track changes of a few tenths of degC over several decades. A recent re-analysis of the various sources of SST data made most of the Pause disappear from the surface record, but not UAH/RSS (or the ARGO) records. Correcting undocumented discontinuities in the difference between neighboring pairs of surface stations (found almost once a decade for typical stations) adds 0.2 degC to 20th century warming. The methodology used by UAH and RSS to convert raw satellite data into troposphere temperature has undergone numerous revisions resulting in large changes in warming. None of this tells us that CAGW is or is not occurring – it tells us that the data isn’t unambiguous enough confirm or deny any hypothesis about climate change on a time-scale of one or two decades.
      Furthermore, variations in temperature can be both “forced” AND/OR “unforced”. The latter lacks obvious causation and is sometimes called “internal variability”. Unforced changes in surface temperature are the result of unpredictable fluctuations in the exchange between cold water from the deep ocean and warm surface water. (Fluid flow in notoriously chaotic.) El Nino, for example, warms GMST by slowing down the upwelling of cold water in the Eastern Equatorial Pacific and the downwelling of warm water in the Western Equatorial Pacific. Oscillations such as the AMO, PDO (and possibly MWP/LIA) could involve similar changes in heat exchange between the surface and the deep ocean, but they occur over such long periods of time that they have been poorly characterized by observation.
      The only way to distinguish between forced and unforced climate variability is with an AOGCM. Given the fact that models are consistently running hot, it is becoming clear that models either over-estimate climate sensitivity OR underestimate unforced variability. Without a reliable method to distinguish between forced and unforced warming, it is impossible to evaluate the CAGW hypothesis using small changes in temperature over a few decades.
      If the scientific method involves testing hypotheses with unambiguous observations or experiments; then CAGW is religion, not science. As you note, the climate sensitivity of an AOGCM is the net result of dozens of parameters that aren’t known with any certainty.
      If you want confirmation about the radiative forcing produced by rising GHGs, don’t examine temperature change for the whole planet. The theories and parameters describing the interactions between GHGs and radiation have been carefully studied in the laboratory for many decades. If another ice age arrived in the 21st century, it wouldn’t significantly change our estimate for the 3.7 W/m2 radiative forcing expected for doubled CO2! After all, glacials and interglacials begin before changes in CO2 are observed and occur with negligible change in global solar forcing. According to Milankovic, ice ages are caused by REGIONAL forcing (followed by large surface albedo feedback, GHG feedback and other feedbacks).
      Unfortunately, your comments on water vapor show confusion about the difference between a radiative imbalance at the TOA (or tropopause) and a radiative imbalance at the surface. A radiative imbalance at the TOA must eventually result in a change temperature somewhere in the atmosphere, surface or ocean, because: 1) energy is conserved (temperature is proportional to internal energy) and 2) radiation is the only significant pathway by which energy enters and leaves the planet. On the other hand, surface temperature is controlled by both radiation and convection. Convection (about 100 W/m2, mostly latent heat) involves fluxes comparable to net LW radiative cooling (390-333 W/m2) and warming from SWR reaching the surface (160 W/m2). Convection REDISTRIBUTES heat within the planetary system, but doesn’t change the total heat content of the planet. The abstract of the K&R (1982, not 1986) paper you linked says: “It is found that although the longwave SURFACE radiative heating due to increased CO2 is considerably reduced at low latitudes by H2O continuum absorption, where water vapor partial pressures are high, the radiative heating of the surface/troposphere system as a whole is minimally altered.” The water vapor continuum is caused by water vapor dimers and whose concentration varies with the square of the water vapor pressure. The critical TOA radiative balance isn’t effected much by continuum absorption, because most photons escaping to space are emitted from above the altitude where water vapor dimers are common. So the continuum is of minor importance to the planetary radiative balance. However, DLR passes the highest concentration of water vapor on its way to the surface. The continuum is important for getting the right value (about 1 W/m2 globally) for the (non-critical) surface radiative forcing for doubled CO2.
      Like Kimoto, I have long wondered why we should assume that the lapse rate will remain unchanged upon doubling CO2 – or unchanged until surface warming has increase humidity and thereby created lapse rate feedback. We don’t know why the earth’s average lapse rate is 6.5 K/km, so why should we assume it must remain unchanged? The maximum lapse rate that is stable to buoyancy-driven convection ranges from 4.9 K/km where humid tropical air is rising near the surface to 9.8 K/km where dry air begins to descend from the tropopause. The average environmental lapse rate, 6.5 K/km, is the result of turbulent mixing between rising and descending air masses.
      Unfortunately, Kimoto’s paper is badly flawed. He [mistakenly] calculates a “surface climate sensitivity” of 0.13 K/(W/m2) from the “natural greenhouse effect” (34 K) and what he calls “natural greenhouse energy” (333 W/m2 of DLR minus 78 W/m2 of SWR absorbed by the atmosphere). By multiplying the instantaneous increase in DLR from doubled CO2 (1.1 W/m2) by this “surface climate sensitivity”, Kimoto predicts a surface warming of only 0.14 K. Since Kimoto knows that a radiative imbalance of 3.7 W/m2 can only be eliminated by increasing the average temperature of the GHGs emitting photons to space by about 1 K (from 255 to 256 K), he deduces that the average lapse rate drop from 6.5 to 6.3 K/km. Unfortunately, spontaneous buoyancy-driven convection only occurs where rising air expands and cools, but still remains warmer and less dense than the surrounding air. The smaller the lapse rate; the less likely vertical convection is to develop. By predicting a lower lapse rate, Kimoto is also predicting a reduction in convective flux! Therefore surface temperature will not be determined solely by the increase in DLR produced by doubled CO2.
      Furthermore, instantaneously increasing DLR by 1.1 W/m2 should produce much more than 0.14 K of warming. Assuming that the convective flux doesn’t change, the surface needs to warm 0.20 K to emit an additional 1.1 W/m2 of upward flux. (A blackbody at 288.0 K emits 390.08 W/m2; at 288.2 K, 391.16 W/m2.) Since a blackbody at 277 K emits about 333 W/m2, average DLR photons reaching the surface are emitted from about 2 km above surface. The lower troposphere is in radiative-convective equilibrium with the surface and quickly warms by 0.2 K whenever the surface warms by 0.2 K (assuming constant lapse rate). The slightly warmer lower troposphere then emits slightly more DLR (1.10 + 0.87 W/m2), which further warms the surface (0.20 + 0.18 K). Repeating this process and summing the infinite series affords a total warming of about 2.0 K. If you want to get fancy, you can consider including the additional DLR from increased water vapor in the lower atmosphere and its reduction of the lapse rate. When Kimoto divides “natural greenhouse warming” by “natural greenhouse energy”, he obtains an answer with the correct units for climate sensitivity (K/W/m2), but the answer not derived from the relevant physics, especially convection.
      In reality, a surface radiative imbalance created by an increase in DLR can be corrected by: an increase in convection, a rise in surface temperature, or a combination of the two. From a surface energy balance perspective, climate sensitivity is lower when more of this surface forcing is carried upward by convection. Reducing the lapse rate (as Kimoto does) means less energy will be carried upward by convection. If a rise in CO2 is going to produce more convection, then one needs MORE warming at the surface than in the upper troposphere! Or, one needs an increase in absolute humidity, which reduces the maximum stable lapse rate.

  20. Sheldon,
    I did something similar a month or two ago but with RSS (also in Excel actually using the slope function). Excel is an excellent programming platform that a lot of people overlook or turn their nose up at but is powerful, quick and an easy learning curve with good output options. Keep meaning to learn R but it has such a steep learning curve! I did a similar mapping exercise of the positive (black) and negative (red) slopes from Dec 2015 backwards to Jan 1979. This was based on the period Jan 2016 to Dec 2022 being a repeat of earlier periods in RS series. Main thing is Dec-15 on left which is the real trend from then all the way back to Jan 1979. Periods where slope is negative go back to Jun2009, Nov2000 and May1997 any further back and it is all positive slopes.

  21. This is a fundamental flaw in reasoning to say that a trend has a linear progression. Take simple everyday example like the waveform of the sea for a day when there is little change in the roughness.
    There is a trend at any point but a separate trend for the tide going out and in. There is clearly no trend that expresses this using a linear analysis as the waves are cyclic and so is the tidal variation.
    Even if you took the tidal pattern as linear he only time like a broken clock the slope would be right would be once is any wave cycle.
    Climate data whether temperature or rainfall both can be proved to show a cyclic pattern so any linear analysis by definition is an oversimplification.

  22. 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.

  23. 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.

  24. 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?

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