2012-03-11 18:47:05The Skeptical Science Temperature Trend Calculator
Kevin C


Here's a first attempt at a blog post to go with the trend uncertainty calculator:


And here is the calculator itself at it's temporary location on my website:


2012-03-11 19:44:38


"The first graph is from the NASA GISTEMP temperature record, while the second uses the corrected data of Foster and Rahmstorf (2011) which removes some of the short term variations."

In what sense is this "corrected" data more likely to be more correct?

2012-03-11 23:59:56
Mark Richardson

Minor comment: shouldn't your uncertainty be reported to the same decimal precision as the output? e.g. from 1950-2012 GISTemp I get 0.133 +- 0.0199 oC/decade as the trend.

Iirc, that should be reported as either 0.133 +- 0.020 oC or 0.1330 +- 0.0199 oC/decade (I don't know enough about the statistics of trends to say how many significant figures you can quote to).

2012-03-12 01:23:17
Kevin C


Neal: Yes, adjusted would be a better term. Will change. I also need to make it clear that the trend calculation is nothing to do with the F&R adjusted temperature data, I'm just using it as an illustration (despite the fact that the uncertainty method is described in the same paper).

MarkR: Good point. But a real nuisance to code. In general computer programs spit out far to many digits and leave it to the scientists to sort out before they publish. However I might be able to hard-code something given that I know the sort of numbers we're dealing with.

2012-03-14 15:27:17
Sarah Green

I love the calculator.

The explanation is good. It's very long and detailed, and I suspect many people will just start playing with the data and not read the details. The tool is cool enough that people should be encouraged to play with it first and learn as they go.

I was going to suggest a quick and dirty brief introduction for them. Actually, you could bring the "what you can do" part up to the front and let people play first, then link to the explanations below. e.g. "statistically significant cooling trend" links to an explanation of how to tell if it is significant, etc.

And/or you could run through some specific examples. e.g. "the NOAA data looks like cooling between 1940 and 1960; is it significant?"

I spotted one typo: "spurious shirt term trends" but didn't hunt for other.

2012-03-15 02:17:56
Dana Nuccitelli

Yeah it might be better to introduce the calculator and what you can do up front, and then follow with the statistical details.  It's a good post though.

2012-03-15 04:03:07
Kevin C


Thanks Sarah and Dana. Good observation. Will reorder as suggested.

2012-03-15 09:07:11
Andy S


This is great. Thanks! I learned something.


it can equally well mean that there calculation has been performed  perhaps  "the"?

And some comments.

As you'll see, I'm no statistician, so forgive me if I get things wrong here. I'm just pointing out some things that struck me as odd or unclear after a quick reading.

The problem is that every observation contains errors. Perhaps you should clarify what you mean by "errors" for the general audience. Do you mean "mistakes", "noise", "non-linear, short-term natural variations" or "uncertainty of measurement". I note that later you refer to all of these factors in the text that follows but it's not immediately clear what's an "error" and what's not. [My old physics teacher used to say: "Gentlemen, there are two types of error, measurement errors, which always occur, and blunders, which must never occur"]

 that all the data are independent observations. I know you explain this in the paragraph that follows but it might be less confusing to the reader stumbling across this if you explain immediately that the temperature in one month depends to some degree on the preceeding (and also the following) months because there are short term cycles and patterns. The observations themselves are independent of one another (the thermometers have no memory) but the actual temperatures measured are not.

It is still possible to obtain an estimate of the trend uncertainty, but more sophisticated methods must be used. Why don't you say something like: "cyclic, short-term effects can be estimated and partly filtered out", which might be more understandable? I may have this wrong, since I haven't read F&R yet (though I should) but I doubt if most of your readers will, either.

 the true trend is likely to lie within this region approximately 95% of the time. That region is not a "trend" (ie, a gradient, "m" in y=mx+c) but the region in which 95% of the trend lines (mx+c) would fall.

a tool to allow temperature trends to be calculated with uncertainties. Perhaps better would be to say "a tool that allows trends and their uncertainties to be calculated."

2012-03-17 02:06:38
Dana Nuccitelli

How soon can we get the calculator on SkS and get this post published, Kevin?  I've got 2 posts in the works where I'd like to use the calculator, so the sooner the better.

2012-03-17 19:12:17
Kevin C


It's up and running, and I've updated the post to incorporate Sarah's suggestions and most of Andy's.

I'd be happier if a few people would look over it once more, but I think it's about ready.

2012-03-18 03:29:47
Andy S

The "click here" buttons at the top don't display properly on an iPad. Apart from that, thumbs up!
2012-03-18 07:31:54
Kevin C


Thanks Andy, done the typos, and changed how the buttons are generated - hopefully that will fix it for ipad.

I've retested in situ on Firefox and IE8, and the current version has been tested on my site on Opera 11, Chrome 17, Firefox 8 and Safari.

I've just got a niggling doubt about IE9. Does anyone have it to hand? If it doesn't work, can you try switching to standards mode?


2012-03-18 09:38:53
Sarah Green

a few tiny bits more:

Can you include a static image of the graph at the top to attract eyes and encourge clicking on the links?

Is it possible to have the default start/end dates pre-filled for each dataset?

How about asking people to compare to the sks escalator graph?

Can beta, sigma, etc at the bottom of the graph be linked to the text section explaining them?

beta doesn't change when the units change (per yr, decade, etc).

Remove unecessary sentences:

"Hopefully this material will help you to identify which is meant."

"One purpose of this article and the accompanying tools is to help you to do that."


Uncertainty decreases for with more data


"As the sampling period gets longer, any error in the trend leads to a greater and greater divergence between the estimated and true trend." .. Makes it sound like longer times increase errors.

2012-03-18 09:43:58
Sarah Green

You might want to include this bit from your text at the bottom of the graph page:

The data section gives the trend and uncertainty, together with some raw data. β is the trend. σw is the (wrong) OLS estimate of the standard uncertainty, ν is the ratio of the number of observations to the number of independent degrees of freedom, and σc is the corrected standard uncertainty.

Use "raw" unstead of "wrong" for σw. Wrong will confuse the average reader, especially when it's used to calculate the "right" value.

2012-03-18 19:36:14
Kevin C


Done all the changes to the article. I can't change the graph pages now - only John can do that, but I'll start a list of things to change when he next has time.

2012-03-18 20:43:18One suggestion
John Cook

Kevin, if you're cool with it, I'd like to put a green box at the bottom of the actual calculator page, saying something like "The Skeptical Science Temperature Trend Calculator was created by Kevin C." perhaps adding a "click here for more info" linking to this blog post. If you're happy with that, let me know if you'd like any specific text there plus any links you'd like to include.

Re updating any of the scripts, just email me the new file for now, until Bob and I have the new development system set up.

And congrats, very cool tool and SkS is very lucky to have it! :-)

2012-03-19 01:04:35
Kevin C


Thanks! The one showstopper at the moment is IE9 testing. Will email you about it.

2012-03-19 03:10:01
Tom Curtis


Using HadCRUT3v data (I presume), the trend from 1998 to 2011 differs significantly from the IPCC predicted trend of 0.2 C per decade.  In contrast, you need to go back to 1994 for the trend to differ significantly from zero.  The deniers will have a field day with this, and we are setting ourselves up for it.

Can I strongly recommend that we do not make this post until version 4 of HadCRUT comes out.

2012-03-19 06:02:56
Dana Nuccitelli

They can already do that with WfT, Tom.  Anyway, I think we need to worry less about what the deniers are going to do.  They're mostly just talking amonst themselves.

2012-03-19 08:36:10
Kevin C


Dana: The difference is that we are announcing that the difference is statistically significant, something most of the deniers don't know how to work out for themselves.

Tom: We've known this since November, when it prompted me to start work on the problems in HadCrut3. (I think my first thread here was called something like 'Planning for the HadCrut3 train wreck'.)

That's the other reason why I want to push forward with my first HadCrut3 problems post, which I might be able to do now without relying on anything except published data. I might be able to get it done for the back end of next week, depending on family health. The HadCrut3 post could spin off the trend calculator post nicely. I can certainly see an argument for the trend calculator waiting to go out just before the HadCrut3 post. The HadCrut3 post can then start with the question 'Why does HadCrut3 show a statistically significant deviation from the IPCC prediction?'. And the answer? Because it is wrong.

OK, you can't make a judgement without seeing the HadCrut3 post. It's really simple:

1. The land coverage of HadCrut has been declining for a couple of decades. Worse, the proportion of land in total HadCrut3 sample has been dropping. The Earth has ~29% land. But by the end of the 00's land temperature measurements made up only 22% of the HadCrut3 data. (Graph from the HadCrut data files, if it is good enough, or from my higher resolution gridded calcs if not.)

2.  The oceans are warming slower than the land. Therefore, the SST anomaly is lower than the land station anomaly. And the difference has been most significant since ~2000. (Graph from GISTEMP)

What would happen if you were to do a survey of average heights, but your sample group consisted of only 30% men and 70% women? You'd underestimate the mean height.
What happens if you do multiple surveys to measure how fast people are getting taller over time, but with a declining proportion of men in each subsequent survery?

Yes, it really is that simple and that wrong! (This accounts for just under half the bias in HadCrut3, but it is the bit which is really blatant, and not widely talked about. The other half is the high latitute sampling which we all know about.)

Bob is looking at the IE9 problem with John - he knows more about it than me. Not sure how long that will take to deal with.

2012-03-19 22:58:26
Tom Curtis


Kevin C, if we hold of launching the trend calculator until a day or so from posting your HadCRU post (which I am looking forward to), that would be a good move.  Ideally they should be posted on the same day with cross links so that anybody going to the trend calculator gets an immediate link to the explanation.

What we should not do is launch the trend calculator without that explanation immediately to hand, or without HadCRUT4 data to hand.  In that regard, would it be too much trouble to add CRUTEM3 and CRUTEM4 to your land indices, given that both are now available?

I like your height analogy.  It makes the issue very clear.

2012-03-20 03:22:04
Kevin C


Sounds like HadCrut4 may be coming pretty soon anyway. So it may become 'Why HadCrut3 was wrong'. I'll write it anyway - the precise order doesn't matter, and it does let us get the trend calculator out.

As soon as HadCrut4 comes out, I'll add it. Should take 10 mins and an email to John.

I'm loathe to add CRUTEM3 or 4, because they use the weird 'mean of NH+SH' method which means that they are not comparable to anything else, which confuses people. Alternatively, adding my own land-area average from the gridded CRUTEM3/4 which is comparable to the others, would probably confuse people even more.