A colour based comparison of the temperature series used by Hausfather et al. 2017

Guest essay by Sheldon Walker

It can be difficult to accurately estimate the warming rates of a temperature series, from a graph of temperature versus time. A global warming contour map makes this task easy, by colour coding all of the trends in the temperature series.

Global warming contour maps will be displayed for each of the 6 temperature series used in “Assessing recent warming using instrumentally homogeneous sea surface temperature records” by Zeke Hausfather, Kevin Cowtan, David C. Clarke, Peter Jacobs, Mark Richardson, and Robert Rohde.

The 6 temperature series are:

  1. Satellite radiometer record from 1997
  2. Buoy only record from 1997
  3. COBE-SST (Japanese record) from 1997
  4. HadSST3 from 1997
  5. ERSSTv3b from 1997
  6. ERSSTv4 from 1997

A detailed analysis of the contour maps will not be done in this article. The idea is for people to do their own analysis by looking at the contour maps. Some general comments will be made to assist people in understanding how a global warming contour map works. For example, how to work out if a temperature series has had a recent slowdown or pause.

First, the legend for global warming contour maps is displayed. This is used to convert a colour into a warming rate range, or a warming rate range into a colour. The same legend is used for all global warming contour maps.

clip_image002

Now the global warming contour maps for each of the 6 temperature series:

1) Satellite radiometer record from 1997

clip_image004

2) Buoy only record from 1997

clip_image006

3) COBE-SST (Japanese record) from 1997

clip_image008

4) HadSST3 from 1997

clip_image010

5) ERSSTv3b from 1997

clip_image012

6) ERSSTv4 from 1997

clip_image014

The first thing that should be noticed when looking at the 6 contour maps, is how similar they all are. Given that all of the temperature series are attempting to measure the same thing, it is reasonable to expect some similarity. But the contour maps are so similar, that you need to look closely to tell them apart.

It is worth comparing ERSSTv3b carefully with ERSSTv4. This will show you what effect “Karlization” has had on the ERSST temperature series (also used by GISTEMP).

If I had to separate these 6 contour maps based on whatever differences that there are between them, then I would group:

  • the ERSSTv4 series,
  • the Buoy only series, and
  • the Satellite radiometer series, (this one could be in either group)

in one group.

And

  • the COBE-SST (Japanese record)
  • the HadSST3 series, and
  • the ERSSTv3b series

in the other group.

This grouping is based on the size of the mid-green (pause or cooling) area near the centre of each contour map. The first group has a smaller mid-green area, and the second group has a larger mid-green area.

A quick comment on slowdowns and pauses. Has the recent slowdown or pause been removed?

Let me just say that:

  1. the light-green colour represents a warming rate of 0.0 to +1.0 degC/century, and
  2. the mid-green colour represents a warming rate of -1.0 to 0.0 degC/century (this is either a full pause (warming rate = zero) or cooling (warming rate < zero)

Have a look at any of the global warming contour maps above.

If you can’t see any green, then I suggest that you get your colour vision checked.

References:

Assessing recent warming using instrumentally homogeneous sea surface temperature records” by Zeke Hausfather, Kevin Cowtan, David C. Clarke, Peter Jacobs, Mark Richardson, and Robert Rohde. Science Advances  04 Jan 2017: Vol. 3, no. 1, e1601207 DOI: 10.1126/sciadv.1601207

The datasets: data available here in a ZIP file (17KB)

Advertisements

87 thoughts on “A colour based comparison of the temperature series used by Hausfather et al. 2017

      • Pick a point, i.e. 2000 on the x axis and 6 years on the y. That color depicts the average rate of warming from 1997-2003. The colors below represent shorter data periods used for the average rate of warming, so basically the bottom of the triangle shows warming/cooling at that moment and the top of the triangle shows the overall trend.

    • I preferred the old method of putting the Good Foods on one side, and the Bad Foods on the other side. Easier to follow.

  1. And tomorrow, we will all be given a demonstration on how to join the dots to make a picture followed by “colouring by numbers”.

    You bloody beauty!

  2. I need some help interpreting the y axis in trend length (years?) and x axis in years? What is the information you are trying to depict? How long the trend has been ongoing for that year?

    • I think this is simpler than it may appear at first . . the x axis is dealing with the length of time any given general trend lasted, and hence the tip of the triangle is the only place that speaks to the total trend over the entire time-span being portrayed. Down at the bottom we see short bursts of warming or cooling, which can be combined over any span of time to readout the general trend over that span, directly over the midpoint, at a height equal to the span being considered. In graph-speak, it’s “smoothing” the ups and downs as one looks higher up, and hence at a longer time-span under consideration . .

  3. It might be called for here to explain how these contour maps work. It is not very intuitive, and many people do not understand them at all.

    • What you’re looking at is a map of all possible trends that can be computed over the period. The Y axis is the length of the trend being calculated which is plotted on the X axis based on the middle year of that trend. The full length of the data can only have one trend right? You’re using all the data. That’s the apex of the triangle. If you plot trends that are one month less than the total number of data points then you can only have two trends (of contiguous data). One starting on the first month of the data and one starting on the second. That’s the second row. And so on till you get to the bottom row which would be trends of two months in length. That’s why there’s a lot of them. As you get towards the shorter trends you can see how they get more and more variable as the variation in month to month weather overtakes the trend. The longer trends show less variation because adding a month affects the trend less and less as it becomes a smaller part of the dataset.

      • I understand it. I was referring to other people who have expressed confusion regarding how to interpret the contour maps.

  4. Suggesting no pause via adjusted data is ludicrous. If Argo data alone is examined there was still a pause. As done by Xue 2012 in A Comparative Analysis of Upper-Ocean Heat Content Variability from an Ensemble of Operational Ocean Reanalyses they reported “there is a consensus that the global ocean increased from 1984 to 1992 followed by a short cooling episode in 1992/93, and then increased from 1994 to 2003/04, followed by flattening or a decrease.” In other words Argo data shows a pause since 2003.

    Second Hausfather is shooting is fellow alarmists. There were over 40 papers explaining the pause. For example Trenberth explained the pause by arguing the heat that should be warming the atmosphere was being stored in the ocean. Now if there was no pause, then there was not extra heat being stored, and Trenberth’s analysis was bogus.

    • The study is also flawed because the data set ends at the 2015 El Nino peak. MSM (think WaPO) are touting this a proving no pause. We will see about that at the end of 2017. The temperature drop since the El Nino peak (new 10 months ago) is the sharpest on record, even sharper than 1999. This stuff could backfire bigtime in a few months.

      • The study also starts at a low point, Jan 1997. That is the equivalent of drawing a line from the peak of the 1997/98 El Nino to Dec 2016 and then crowing about the decline in global temps. It is the perfect example of a meaningless cherry pick.

      • wrong

        The study makes TWO POINTS

        A) Karls Adjusted series is VINDICATED by yhe latest un-adjusted Satellite data as well as other data sets.
        B) The Slowdown or pause was not as great as some folks think

        FURTHER

        The paper was submitted in March of 2016. That is wehn I started to warn you about your claims that karl was a fraud. you didnt listen

        FINALLY, the conclusions dont change now that we have data through Nov, and wont change with Dec data… and wont change ….period because karl did an fair enough job.

      • @goldminor

        “That is the equivalent of drawing a line from the peak of the 1997/98 El Nino to Dec 2016 and then crowing about the decline in global temps.”

        All of Sheldon Walker’s contour graphs show a warming trend over that period.

      • Steve, you are ignoring the very valid point that the data starts at a low point and ends at a high point. No one will be feigning surprise when the satellite data and karlized data continue to diverge.

    • Forty papers and still no answer – what a shame after putting so many technicians on a single problem. Can’t really call them scientists because they were charged with coming up with a specific result. As to Trenberth, I read his paper and found that in four years they lost 80 percent pf global warming and no one has yet found it.. If I had been a reviewer I would have sent him back to study those Argo buoys until he understood them. But anything can happen when buddy review takes over.

  5. I’d LOVE to see a global map based on historical temps from say, 500AD to the present.

    You know- detailing the Medieval climate optimum cooling at the little ice age – then the year without summer – then whammo – the rebound in temps as we come out of the little ice age- revealing that yes – temperatures are CYCLICAL and WERE in fact higher 1000 years ago . . .

  6. How many authors to ‘chart some data’?

    Zeke Hausfather, Kevin Cowtan, David C. Clarke, Peter Jacobs, Mark Richardson, and Robert Rohde

  7. I still say a study of climate over such a short period of time does what to increase the knowledge of climate science other than to say it was hot yesterday .

  8. Suggestion to author: Would it be possible to incorporate a ‘blink’ comparator between a couple of the plots?

    Give the eye and the mind a chance to do an intuitive, quasi pixel by pixel compare.

  9. @ Everybody:
    They do take some getting used to, that is for sure.

    PLOT 1
    Example 1: The whole plot
    Start date: 1997 (x axis)
    Length: 19 (y axis) Go to the top.
    Color is yellow, follow the triangle diagonal down, see the end date is 2016
    Example 2: The first 12 years.
    Start 1997, follow the diagonal up to the 12 year line
    Color is green, follow a line parallel to the right diagonal to the end date, 2009
    Example 3: cut a path
    Start at the summit (yellow), diagonals left and right lead you to the start and end dates.
    from the summit, drop straight down 6 years to 13 year length (into the green), follow lines parallel to the left and right diagonals to find the start and end years, 2000, 2013.

    I hope this explanation helps, they are confusing at first.

  10. Maybe I’m overlooking some magic, but I fail to see what advantage these charts have over plain ol’ line graphs, other than the pretty paisley. Also, these charts have the disadvantage of not conveying the actual measurement at any given time. I see little value in charting thousands of linear regressions; I can get those simply by eyeballing slopes in a line graph. All I can conclude from these charts is, given the coarseness of the color scale, over the long term, the rate is somewhere between +0.75 and +2.0 C/century and has increased recently.

    • An effort to show all the possible imbedded period slopes. Problem here is the entire period is meaningless since it stops near the peak of an El Nino that has nothing to do with AGW. So the assertion that the study vindicates Karlization of much longer records is bogus. So studying the minutia of its cherry picked period for propaganda purposes is not very rewarding. The tool is cool, and best saved for important things.

      • Right ristvan, they should wait and analyze the data again after 2016 or 2017. The pretty colors are a distraction from the fact they omitted 2016 data, thus emphasizing a big El Nino year.

  11. This may help people to understand the graphs.

    Every trend has a start date, an end date, and a warming rate (the warming rate = the slope of the trend).

    From the start date and end date you can calculate the trend length.
    trend length = end date minus start date

    From the start date and end date you can also calculate the middle date of the trend.
    middle date = (start date + end date) / 2

    The middle date is used for the graph, rather than the start date or end date, because it gives the graph certain desirable properties. Like being able to see when something happened.

    It is possible to plot a global warming contour map using the start date. This puts all trends with the same start date on the same vertical line. This makes it easy to see when something started, but hard to see when something ended.

    It is also possible to plot a global warming contour map using the end date. This puts all trends with the same end date on the same vertical line. This makes it easy to see when something ended, but hard to see when something started.

    The warming rate is colour coded using the legend, and plotted at X = middle date, and Y = Trend length.

    So short trends are plotted lower on the graph, and longer trends are plotted higher on the graph.

    Things which happened earlier (defined by the middle date), are plotted nearer to the left side of the graph. And things which happened later, are plotted nearer to the right side of the graph.

    There are 2 time dimensions:
    1) when the trend happened, and
    2) how long the trend is.
    When something happened, is plotted on the X axis. How long the trend is, is plotted on the Y axis.

    • As said upthread and on previous posts, a cool tool. Inter sting new data visualization. The problem is not the tool, it is the paper to which the tool is applied.

    • And knowing what the trend was a decade ago with no reference to the value from which the trend arose is valuable why?

    • A colour bar on the right with the “average colour” of the trends of the corresponding length could be nice. The shorter trends change to much to give useful information so an average may be more informative.

  12. Seems to me the records are telling us the longest trend is for global warming somewhere between 1 to 2 c over a century
    Within that it seems the buoy series trend is within the 1to 2 c range
    Does this mean ocean temperatures have risen more than the atmosphere ?
    Or maybe I cant interpret the charts either
    What are the ERRSST series ?

  13. I think these plots suggest what happens if you include 2016 data. The latest, which I assume here is end 2015, is found at the North-East edge of the triangles. There is no indication that the colors heading NE are in the direction of reduced trend.

    The other thing is “But the contour maps are so similar, that you need to look closely to tell them apart.”. Yes, that was the point of the paper. And the “Karlization” does a little warming, but not much. Entended for another twenty years, and it would be less again.

    I see that Fig 5 is incorrectly titled ERSSTv3a.

    • Nick, that cannot be a correct inference as the now 10 month since peak T decline is the sharpest on record. Change the regression end data, you will change the slope. The longer, the more. Put differently, the ‘missing’ lower right 2016 corner is dark blue, and that changes the rest.

      • Hi ristvan,
        one of the attributes of a global warming contour map, is that what has been plotted NEVER changes when you add more years. So adding 2016 to these graphs, just adds new bits to the right side of the triangle, and leaves all of the existing parts the same as they are now. None of the trends in these contour maps uses dates after 2015, so they stay the same no matter many years of data you add.

      • ristvan,
        Sheldon is right, of course. What happens as you add more data, you add new strips to that NE edge. Existing dots don’t change.

        But what affects trends on getting new data is not so much slope, but whether the new values lie above or below the trend line. And the thing about this “sharpest on record” decline is that 2016 is still going to be a record hot year.The individual months lie well above long term trend lines, so each new one increases the trend. I’ll quote again the table of trends (C/cen) starting from June 1997, depending on whether you stop at end 2015 or Nov 2016. Going through 2016 makes the trends a lot higher:

        dataset       End 12/15  End 11/16
        NOAA SST       1.099     1.316
        HADSST3        0.763     1.026
        
      • Nick Stokes is smarter than I am but I’m smart enough to see that he is right. The trend line is still rising at the end of 2016

      • Yes, he is right. For now. But, the effects of the Nino are not gone yet. Patience, folks. There are no conclusions as yet to draw.

      • What do you mean the trend is still positive, even Ray Charles can see the blue at the end on all but the satellite graph, and I’m sure that has already changed. The cooling will likely continue but whether it will be one of those small 3-4 month cooling trends or a multi year cooling is yet to be seen. I think rather than “change the rest,” ristvan meant change the overall trend at the top of the pyramid. I think it’s quite obvious that the overall trend will likely decrease a little but whether it becomes statistically insignificant again remains to be seen.

      • As for “warmest year evah” it only took 18 years to beat the last one, when do you think 2016 will be beat?

    • Stokes,

      Karlization is an unconventional and non-rigorous approach to concatenating data series. One should never adjust superior data to agree with inferior data!

      As to Karlization only doing “a little warming,” that is in the eye of the beholder. About 0.12 deg C warming was accomplished by indefensible adjustments, while the MSM and warmunists are crowing about a 0.02 deg C anomaly in 2016 defining the warmest year in recorded history.

      If I were in the position of advocating the proof of “warming as usual,” I’d be sure that my data adjustments were above reproach.

    • If the last couple of years have been the warmest “evah” by 0.04 and 0.02 degrees, that is very little warming. So Karlization that does “a little warming, but not much” could make all the difference in the narrative. Comments?

  14. If you find a trend with middle date = MD, and trend length = TL, then you can calculate the start and end date using:

    start date = MD – (TL / 2)

    end date = MD + (TL / 2)

    for example, if middle date = 2007 and trend length = 10 years

    then start date = 2007 – (10 / 2) = 2002

    and end date = 2007 + (10 / 2) = 2012

  15. THis gal is really confused. Keynesian stimulus is why we have a boom and bust economy in the first place. It does not create real wealth in the long run. ANd BTW, many of the numbers ARE faked, whether she knows or likes it or not. And the 20,000 Dow? ENTIRELY an artifact of the FED creating money out of nothing to benefit their friends on Wall St. Stop counterfieting money and many of the resulting counterfiet businesses will go away, the DOW go down. Which will happen anyway as what they created is simply not sustainable.

    • Once again, the bug in the WordPress comments implementation intersects with a ripple in the space-time continuum. In this case the ripple created a wormhole to an alternate universe where, apparently, Anthony blogs about matters of economics and finance.
      In the middle of an economics comment thread, an inexplicable comment about the physics of radiation and climatology suddenly appears.
      *sigh*

      • Four score and seven years ago our forefathers brought forth… yikes another wormhole brought us honest Abe. Now what would he say about AGW?

    • Navnek, hey we’re all confused. But I can stand only one confusing issue at a time. The economy/stock market (and associated politics) is child’s play compared to climate issues, and I feel better being confused by climate.

      Donald Trump is confused too, and if he’d only admit it I’d feel still better.

  16. It is interesting that each year sees a periodic warming and cooling trend which means that the entire mass of the planet is changing across a range of +/- 5C during the course of each year. Other measurements I’ve seen show the peak to peak seasonal change in the N hemisphere is larger than in the S such that the global average has the signature of the N hemisphere. The rate of change defies claims that the climate responds very slowly to other kinds of change, for example, changing CO2 levels.

  17. What so important about the start date of 1997. Otherwise it opens up the criticism of cherry picking Data.

    • “What so important about the start date of 1997. Otherwise it opens up the criticism of cherry picking Data.”

      It’s the year just before a massive El Nino, so people have claimed a pause or slowdown started at that point.

    • I think that Bellman is right.

      The satellite data goes back to 1979, but the recent Berkeley Earth paper is seeking to demonstrate that there was no pause whereas prior to the recent 2015/16 El Nino it was accepted that there had been a pause or at any rate a significant slow down in the rate of warming going back about 18 years (or so).

      The game is now on to try and eradicate the pause from the record, but IF La Nina conditions develop in 2017, this attempt is likely to prove futile and the pause will then likely reappear and will be more than 20 years in duration.

      I am not saying that a La Nina will develop in 2017, but IF it does, it will almost certainly be the case that the pause will make a reappearance and once more raise its ugly head.

  18. I do enjoy this unique representation. It’s value is limited but they are pictures/colors that tell the story a different way.

    Sorry to interrupt the rainbow world of global temperature graphing but the big weather story right now is the massive precip event taking shape on the West Coast of the USA. We can use rainbow precip colors to represent the huge totals expected.

    Here is the latest NWS QPF(quantitative precipitation forecast) for the next 7 days:

    http://www.wpc.ncep.noaa.gov/qpf/p168i.gif?1483659753

    This product is updated 2 times daily and it’s currently Thursday Evening. It will be fairly similar on Friday, before the event(s), which will come in several waves. It will be much different(with lesser amounts) if you are looking at it in several days, as precip goes from predicted to measured.

    This is why its a big deal. Drought in California:
    http://droughtmonitor.unl.edu/

    There will be places in central California that currently have exceptional drought that have their best precip measured in 1 week in many years. Reservoirs near record lows will get some needed water. Many locations will see 5 inches of rain with isolated spots getting much more than that. Snow in the highest elevations will be measured in yards. These heavy amounts will also effect northern California.

    Hefty but less precip will fall farther north(Oregon/Washington), where they are in less need of the water//snow but it still will help boost moisture reserves.

    Of course too much will fall in some places, causing mud slides, flooding and other issues. Nothing new for the state of California.
    California extreme precipitation symposium:
    http://www.cepsym.org/

    How far south will the heavy precip fall?

    Good question. Probably not far enough to substantively help San Diego. Los Angeles has the best shot at an inch of rain early on Monday. Here’s the NWS link for LA:
    http://www.wrh.noaa.gov/lox/

    The forecast totals and locations will be adjusted a bit in the next few days but the pattern and powerful Pacific jet stream aimed at the West Coast makes this a sure thing.

    Anthony, you might want to move this post to another location.

  19. Interesting but poorly chosen limits. Much interesting data is cut off by using a triangular format that adds nothing to understanding the data set. For example, I would have liked to have seen the data for the 2015/2016 El Nino, to see how it peaked and its aftermath. All that is cut off by the right side of the triangle. They had the data but simply thought it either too much trouble or not worth showing. On the left side of the triangle the 1997 La Nina is misplaced to the right by three years and so is the super El Nino of 1998 which follows it. Everything to the left of that triangle is missing and it should not be because the data are there. There exists an ENSO cluster of five El Nino peaks. It covers the interval between 1979 and 1997. It would have been interesting to relate the temperature changes to the periodicity of ENSO. These ENSO oscillations appeared on a background of no warming – a hiatus lasting 18 years. Unfortunately, the global temperature chart that Hausfather et al. would have had to use was a version transmogrified into a non-existent global warming by the cooperation of GISS, NCDC(NOAA) and the Met Office, before 2010. The aim of this data falsification was apparently a desire to wipe out the hiatus of the eighties and nineties. See figure 15 in my book “What Warming?” Fortunately, they do not yet control satellites and the real shape of the eighties and nineties temperature curve is still shown in satellite temperature archives.

  20. Thank you. This makes it very easy to interpret what those contour maps are demonstrating. And yes, the effect of unjustifiable Karlization is readily visible.

  21. Mods

    i have posted a couple of comments that have disappeared. Presumably they have gone into moderation. But they should be uncontentious and do not contain any dodgy wording.

    Please will you look out for these.

    many thanks.

  22. Two suggestions for the graphs:

    1. Why not cut the bottom five years of it? If we are looking for middle to long term trend, the trends over only a few years are not relevant. Also all the “extreme” trends (both cooling and warming) colors are seen on the bottom and are not relevant. This would allows to groups trends into smaller categories (instead of “from 0 to 1 deg/century”, having “from 0 to 0.5 deg/century, for example) Obviously the categories must stay bigger than the uncertainty (note that you didn’t give us any uncertainty on your data)

    2. I would prefer to see one of the category centered on 0deg/100y, for example “from -0.5 to 0.5 deg/100y”, instead of “from 0 to 1 deg/100y”, because this creates a “no warming nor cooling” category, while your current ranges are only “warming” or “cooling”.

  23. I’m 72 years old. Before I die, I would like to see one revision study, just ONE, where the temperature record actually is adjusted downward. Is that even possible, or is it just that every “improvement” in data analysis necessarily leads to an upward revision? I’ve studied this subject for years. What am I missing?

    Is it possible that such a study could be funded in today’s research world, a world in which Kevin Trenberth can be proven wrong about the pause (“there really wasn’t one”) but whose credibility is actually enhanced?

    As much as Donald Trump worries me, I am hopeful that science can evolve so that the study I want to see would be conducted by a traditional scientific source, who might even admit that a departure from the consensus is something other than denialism?

    Nick Stokes, TonyL, come on, you’re reasonable people. Is the above even possible, or is the status quo just the way science works?

  24. 2PetitsVerres on January 6, 2017 at 3:23 am

    … note that you didn’t give us any uncertainty on your data

    This is exactly what I miss here – and everywhere S. Walker presents his childish toy.

    If you want a more professional approach, 2PetitsVerres, you might visit really useful trend viewers like
    – Nick Stokes’ Trend Viewer
    https://moyhu.blogspot.de/p/temperature-trend-viewer.html
    – Kevin Cowtan’s Trend Computer
    http://www.ysbl.york.ac.uk/~cowtan/applets/trend/trend.html

    Nick for example had a beautiful idea: that of weakening colors upon an increasing loss of significance.
    Here is for example a trend & significance chart for HadSST3 from 1997 till 2016:

    Kevin has a thoroughly different approach I appreciate as much as Nick’s, because I’m often enough rather interested in singular observations than in a twodimensional trend view.

    Below you see two RSS3.3 TLT trend charts, one for 1979-2016:

    and one for 2009-2016:

    You immediately see here that especially for time series originating from satellite observations, the 2σ increases exponentially with the trend period getting shorter.

    That you see best when you compute, for e.g. a monthly time series, each linear estimate with its 2σ month by month, and plot the resulting monthly trend time series with the increasing 2σ around it.

    So in my opinion, one could give Nick’s tool as additional parameter a 2σ level above which trends become totally insignificant, what then would be expressed by the tool as white areas in the trend charts.

  25. Great graphs, showing any trend over x years for any year. Just one suggestion: as the contrast visually between yellows/reds and greens/blues is quite marked, would it not be better to make the 1st green band in the legend -1.0 to 0? This would allow immediate interpretation between heating and cooling.

    Many thanks for this presentation of data.

  26. [-> mod]

    I have nothing against any comment being refused whatever the reason: I’m a guest here, not more.

    But
    – to give a [snipped -mod] hint would be fair;
    – refusing to publish even a second one-line comment indicating that I’m missing the bigger preceeding one? Watts that? Strange, unusual behavior.

  27. Sheldon: If you are going to compare these triangles, perhaps you should create triangles representing the DIFFERENCE between the trends in these records. That way we could see that the buoy trend is similar to ERSST4 during some period, but perhaps not during all periods. etc.

    The triangle with the greatest amount of area with the color that represents a zero difference would be the best match.

    If you included confidence intervals, all differences might be insignificant.

Comments are closed.