March Madness

The National Climate Data Center has updated their temperature data for individual states and for USA48 (a.k.a. the conterminous United States, a.k.a. the “lower 48”). The headlines are that this March was the hottest March on record nationally, and this year’s 1st quarter (January through March) was likewise the hottest on record. Much of the central U.S. was as much as 15 deg.F hotter than average this March:

L is for “linear”

A previous post addressed some issues with linear regression, “linear” meaning we’re fitting a straight line to some data. Let’s devote another post to scrutinizing the issue — so this post is all about the math, readers who aren’t that interested can rest assured we’ll get back to climate science soon.

It was mentioned in a comment that least-squares regression is BLUE. In this acronym, “B” is for “best” meaning “least-variance” — but for practical purposes it means (among other things) that if a linear trend is present, we have a better chance to detect it with fewer data points using least-squares than with any other linear unbiased estimator. “U” is for “unbiased,” meaning that the line we expect to get is the true trend line. Both of these are highly desirable qualities.

Finally, “L” is for “linear,” which in this context has nothing to do with the fact that our model trend is a straight line. It means that the best-fit line we get is a linear function of the input data. Therefore if we’re fitting data x as a linear function of time t, and it happens that the data x are the sum of two other data sets a and b, then the best-fit line to x is the sum of the best-fit line to a and the best-fit line to b. In some (perhaps even many) contexts that is a remarkably useful property.

Gutenberg-Richter

In a comment on the last post, it was mentioned that the frequency of earthquakes of any given magnitude or greater will be given by the Gutenberg-Richter law. It states that the expected number of earthquakes in a given region over a given span of time, of a given earthquake magnitude or greater, will be

,

where is the quake magnitude, and are constants, and is the expected number. For active regions, the constant usually has a value near 1.

Open Thread

For topics not related to other posts.

Deja Vu

A new study by scientists from the U.S. Geological Survey, not yet published but scheduled to be presented at the upcoming annual meeting of the Seismological Society of America, reports a dramatic increase in earthquakes of magnitude 3.0 or greater over a large area of the U.S. More interestingly, the report states that the increase is “almost certainly man-made,” and attributes it to oil and gas production.

Decadal Trend in Temperature

We all know that many things affect global temperature. Some, like greenhouse gases, cause long-term changes and can create significant trends. Others fluctuate but don’t really go anywhere over the long term, so they cause temperature fluctuations but don’t create long-term trends.

At least two such fluctuating influences have been identified. One is solar variation. The energy output of the sun is variable, especially showing a cyclic variation with the roughly 11-year solar cycle. Another is the el Nino Southern Oscillation (ENSO), which when high warms the planet and when low cools it. It too fluctuates up and down, but hasn’t exhibited long-term trends which could account for the trend we observe in global temperature. You might wonder, what has been the short-term impact of these two influences recently? Let’s look at their temperature influence over a recent 10-year period, from January 2002 through December 2011.

To robust, or not to robust? … that is the question

From time to time it is suggested that ordinary least squares, a.k.a. “OLS,” is inappropriate for some particular trend analysis. Sometimes this is a “word to the wise” because OLS actually is inappropriate (or at least, inferior to other choices). Sometimes (in tamino’s humble opinion) this is because an individual has seen situations in which OLS performs poorly, and is sufficiently impressed by robust regression as a substitute, to form the faulty opinion that it’s superior to OLS generally. For the record, this comment is not one of those cases.

In reality, OLS is the workhorse of trend analysis and there are very good reasons for that. It’s founded on some very simple, and very common, assumptions about the data, and if those assumptions hold true, OLS is the best method for linear trend detection and estimation. It can be dangerous to use the word “best” in a statistical analysis, but in this case I feel justified in doing so.

Of course that raises some nontrivial questions. What are those assumptions? When might they not hold true? How could we tell? What should we do if we can establish that the OLS assumptions aren’t valid?

How fake skeptics fool themselves, part infinity: Sea Ice version

Suppose you were suffering from a serious illness which attacked many of your internal organs. It’s likely to be fatal, so your wife is very concerned about the results of your latest medical tests. They indicate that your heart, lungs, and liver are degrading rapidly, but that your spleen has actually improved. In fact your spleen didn’t show any signs of degradation, even over the long term. So you go home and tell your wife, “Great news, honey! My spleen is in better shape than it was before!”

That wouldn’t really be an honest report of your overall health, would it?

But that’s exactly what Anthony Watts has graced us — or should I say, disgraced himself — with, in his latest post about sea ice at WUWT. He crows about how much sea ice there is in the Arctic, and how it has reached “near normal” levels (remind you of anything?). But if Arctic sea ice is disappearing in a “death spiral,” how could one possibly do so? Well, if your heart, lungs, and liver are degrading rapidly, how could you possibly report that your health has improved? Talk about your spleen!

It’s easy. First, look only at a brief moment of time, quite ignoring what really matters, the trend. Second, look only at a small region of the Arctic, quite ignoring, well, most of it. Be sure to pick the one region that happens to show signs of improvement at this particular moment. It’s a classic strategy called “cherry-picking.” As for an overall survey of the state of Arctic sea ice and its statistically significant trends — we can’t have that! It would show just how dire the situation is.

Which goes to show that Anthony Watts is no skeptic. When he finds some excuse — any excuse — to blind himself to the obvious (that Arctic sea ice has been and continues to be one of the most compelling signs of global warming) Watts has no skepticism to apply. Instead he’ll bring his usual level of infinite gullibility. Honestly, it’s pathetic.

But it’s the same strategy that almost every fake skeptic has used (or should I say, abused) and many of them make their modus operandi. And well they should, because if you want to deceive the naive (including yourself), it works.

What has really been happening to sea ice lately that can tell us about the recent course of global warming?

Mathturbation King

Nicola Scafetta has published yet another paper about his theory that the (probably tidal) influence of Jupiter and Saturn is responsible for long-term changes in solar output, and that these cycles are responsible for climate change on earth. You can read about it on WUWT. It doesn’t surprise me that the paper is due to be published in a journal which seems to me to be sinking further and further into disrepute, the Journal of Atmospheric and Solar-Terrestrial Physics. Nor does it surprise me that there’s really no physics in the paper, just mathturbation.

How Fake Skeptics Fool Themselves, part 3

Jeff Condon seems unhappy with me. Enough to blog about it. And Anthony Watts cross-posts. But what I’d really like to discuss is yet another way in which Condon fools himself about trends in sea ice.