Do the Math

Roger Pielke Sr. claims that northern hemisphere sea ice has not declined as fast as computer models predicted. Yet we’ve often heard the opposite, that northern hemisphere sea ice is declining faster than predicted by computer models. How does Pielke arrive at the opposite conclusion?

Pielke compares sea ice data from Cryosphere Today to predictions from a 1999 paper, Vinnikov et al. 1999 (Global Warming and Northern Hemisphere Sea Ice Extent, Science, 286, 1934-1937,doi:10.1126/science.286.5446.1934). Vinnikov et al. said this:

Both models predict continued substantial sea ice extent and thickness decreases in the next century.

Pielke gets quantitative:

In their paper (in Table 1) they have model predictions (in units of linear trend in 10^6 square kilometers per decade) listed for the GFDL climate model from 1978-1998 of -0.34 (and -0.19 using a “smoothed model output”) and for the Hadley Centre climate model -0.18 (and -0.16 using a “smoothed model output”).

A value of -0.18 is the loss of sea ice area of 180000 square kilometers per decade, for example.

He then displays a graph of sea ice area anomaly (not extent such as in Vinnikov et al. but the difference isn’t really important):

Here’s where it gets weird. Pielke says this:

Until later in 2007, the sea ice areal extent continued to decrease in a manner which, at least visually, is consistent with the Vinnikov et al 1999 predictions (although the actual values of areal coverage differ substantially between the observations and the predictions, perhaps as a result of their formulation to compute areal coverage).

However, since 2006, the reduction has stopped and even reversed.

I refer the reader to our advice on “Defense Against the Dark Arts.” His misdirection is revealed by Step 3: look at more than they show you, and be especially wary of time spans that are too brief and areas that are too small. In this case the “time spans that are too short” alarm is flashing red — not only has Pielke cherry-picked his starting point, he’s comparing a predicted long-term trend to an observed time span of far less than a decade. That’s foolish of him, and misleading to his readers.

But what Pielke himself should pay attention to is Step 2: study the data yourself. In this particular case we can put it another way, which is an important lesson for Roger Pielke: Do the Math.

Suppose we ignore the fact that “since 2006” is a ludicrous — some might suspect deliberately so — choice of time span. Let’s go ahead and estimate the trend in northern hemisphere sea ice area anomaly (Pielke’s own choice of data) since 2006 anyway, and compare it to the predictions from Vinnikov et al. 1999. In fact, let’s estimate the trend not just from 2006 to the present, but from every starting year since 1999 to the present:

We can do the same thing using actual extent data from the National Snow and Ice Data Center:

Note first that the estimated trend rate “since 2006” is in between the two predictions — which certainly doesn’t contradict Vinnikov et al. 1999. Note also that even to get that close to the predictions, you really have to cherry-pick — because if you start from a year that gives us a decent estimate of the trend, it’s declining much faster than these computer models predicted.

Note also that when you start “since 2006” or later, the error bars on the estimated rates are rather large. The trend for such short time spans is so uncertain, it really doesn’t give much information. Could it be that Roger Pielke is actually aware of that, but that he really doesn’t care about portraying sea ice changes correctly, he only cares about discrediting global warming science?

UPDATE UPDATE UPDATE

Roger Pielke has updated his post. He says I misrepresented him, and that

I do not disagree that the Arctic sea ice has been decreasing. My post was to compare the sea ice anomaly trends that were presented in the Vinnikov et al paper to real world observations updated to 2012. The figure in the Vinnikov et al 1999 paper shows a rather monotonic (but increasing over time) decrease in Arctic sea ice content with time. Tamino ignores what is obvious in even a visual comparison between the Vinnikov et al plot and the real world observations that the decline has stopped, at least for now.

So … first he says “However, since 2006, the reduction has stopped and even reversed.”

Then he says “I do not disagree that the Arctic sea ice has been decreasing.”

Then he says “the decline has stopped, at least for now.” His basis for this is “what is obvious in even a visual comparison.”

Hey Roger — what is obvious from numerical analysis is that the decline has not stopped. In fact even if you cherry-pick the starting time to get the lowest rate of decline, it’s still squarely in the range given by Vinnikov et al. DO THE MATH.

Roger seems to think I created a fantasy view of his post. The truth is, you can’t make this stuff up.