Over at “American Thinker”, Randall Hoven has a post about the Arctic ice caps and, specifically, the difference between the “area” and “extent” values for the size of these. The problems start with the interpretation of a graph much like this:
Now, you probably noticed the substantial discontinuity in the “area” during 1987. This is even more apparent if you look purely at the difference between extent and area:
I’ve also plotted the difference between the extent and area for the entire period (taken from the bootstrap data):
Now, Randall includes an “Important Note” from raw data which explains that:
Important Note: The “extent” column includes the area near the pole not imaged by the sensor. It is assumed to be entirely ice covered with at least 15% concentration. However, the “area” column excludes the area not imaged by the sensor. This area is 1.19 million square kilometres for SMMR (from the beginning of the series through June 1987) and 0.31 million square kilometres for SSM/I (from July 1987 to present). Therefore, there is a discontinuity in the “area” data values in this file at the June/July 1987 boundary.
So the discontinuity exists because, from the start to mid-1987, data is taken from the SMMR, which did not have any data for 1.19 million square kilometres in the polar regions (a “pole hole”), whereas it was then replaced by the SSM/I instrument, which only missed 0.31 million square kilometres. As the “area” figure does not account for this, and as at least most of that area will be covered in sea ice, there will be almost 0.88 million square kilometres of extra sea ice from the middle of 1987 onwards, purely due to the instrument change. So from mid-1987, the area figure includes the ice from an additional area 0.88 million square kilometres. So, obviously, if I remove this difference, the discontinuity disappears:
Looking at this, there is still substantial variation in the difference between “extent” and “area” figures. Randall asks why:
What were the differences? From the above words from the NSIDC, you would think that the differences would be constant offsets (1.19 million sq km from 1979 through June of 1987, and 0.31 million since). But the actual differences in the data file were not constant at all; they varied between 1.93 and 3.42 million sq km.
Notice, however – it shows up particularly clearly with the complete data set – that these differences are clearly changing on an annual cycle (plus some variation – weather). And there’s no reason to assume that “extent” and “area” are measuring exactly the same thing. So, if we check how the NSIDC define these terms, we learn:
In computing the total ice-covered area and ice extent with both the NASA Team and Bootstrap Algorithms, pixels must have an ice concentration of 15 percent or greater to be included. Total ice-covered area is defined as the area of each pixel with at least 15 percent ice concentration multiplied by the ice fraction in the pixel (0.15 to 1.00). Total ice extent is computed by summing the number of pixels with at least 15 percent ice concentration multiplied by the area per pixel, thus the entire area of any pixel with at least 15 percent ice concentration is considered to contribute to the total ice extent.
These, obviously, are different figures, as in each pixel “area” is weighted by its concentration, and this would presumably be higher in winter – which is exactly what we see in the differences. Randall, on the other hand, resolves the issue by completely ignoring it.
Going back to the March data, before adjusting for the “pole hole”, like Randall, I find it actually has a slight positive trend:
However, after adding the pole hole region, I get a much stronger downwards trend in the quantity of sea ice:
Now, I’ll emphasise that this isn’t (necessarily) accurate, some (unknown to me) portion of the pole hole might not contain sea ice during March. That data obviously exists, but I don’t have the time at the moment to try and analyse it.
And all of this means that the rest of Randall’s conclusions are invalid, being that they are based on a false premise.
Actually, the rate of growth is statistically insignificant, meaning that a statistician would say that it is neither growing nor shrinking; it just bobs up and down randomly. More good news: no coming ice age, either.
No, there is definitely a significant trend.
You see that “extent” always shows more shrinkage than “area” does. In the months of maximum sea ice, February and March, the area trend is upward. And for winter months generally, December through May, any trend in area is statistically insignificant. For summer months, July through October, the trend is downward and statistically significant.
But these calculations are all based on extremely biased data for the start of the period, and so are all wrong.
Katie Couric should have used the month of September as her example. In three decades, the Arctic sea ice “extent” shrank by 34%. She could make such claims while stating, truthfully, that the data come from NSIDC/NOAA and the trend is statistically significant. It’s science.
Despite the sarcasm dripping from this sentence, yes, it is science. The Arctic ice is melting. Without the “pole hole”, September looks like this:
As you can see, my trend line isn’t a very good fit to this data, and, as Randall says, any decrease seems to be in just the last few years. After adding in the pole, however, things look a lot different:
Again, the red line represents “area,” the only thing actually measured. A downward trend is evident to the eyeball. But look closely and that downward trend is fairly recent — say, since 2000. Indeed, the calculated trend was slightly upward through 2001. That is, the entire decline is explained by measurements since 2002, a timespan of just eight years.
But the older data was biased, so the downward trend was actually for the whole period, and somewhat stronger, to boot.
To understand the trend, you need to understand the data you’re looking at. Or, as the readme file for the data Randall Hoven looked at put it: “we recommend that you read the complete documentation in detail before working with the data”. Had Randall done that, and checked the meanings of “area” and “extent” before writing this piece, he could have saved himself a lot of bother and embarrassment.
Randall starts his conclusion like this:
This little Northern Hemisphere sea ice example captures so much of the climate change tempest in microcosm.
And that’s very true. Someone looking at data then didn’t understand, analysing it improperly, and reaching strong but extremely false conclusions as a result. And then, even when corrected on the misunderstanding, continuing to believe those conclusions.
See, as I was writing this post, Randall posted a correction on his site. It turns out that he’d found the definitions of area and extent (technically, he still got the definition of area slightly wrong, but it’s not as bad). However, although pointing out these problems with his main article, he tries to recover the point with this:
If we add the “pole hole” back to the measured “area,” we would get a downward trend in area due to the change in pole hole size in 1987. If we assume that the pole hole is 100% ice, then the downward trend in March would be 2.2% per decade. But if we assume that the pole hole is only 15% ice (the low end of what is assumed), then the downward trend is only 0.1% per decade, which is not statistically significant. (The corresponding downward trend for “extent” was 2.6% per decade.)
It is true that whatever downward trend there is for March is due only to these adjustments (assumed pole hole size and concentration). And whether that trend is statistically significant depends on ice concentration in the “pole hole,” an assumed value.
For a start, it seems to me to be a fairly reasonable assumption that the ice content of the pole hole is towards the high end of the range – after all, that’s the bit of the Arctic closest to the North Pole. And the thing is, that assumption is a pretty darn testable one. All you have to do is go to the North Pole and look. Come to think of it, I’d be willing to bet that someone already has.