By Steven Goddard
[see important addendum added to end of article ~ ctm]
[Note: The title and conclusion are wrong due to bias in the start/end point of the graph, the mistake was noted by Steven immediately after publication, and listed below as an addendum. I had never seen the article until after the correction was applied due to time difference in AU. My apologies to readers. I’ll leave it up (note altered title) as an example of what not to do when graphing trends, to illustrate that trends are very often slaves to endpoints. – Anthony]
JAXA Arctic Ice measurement just had its 8th birthday. They have been measuring Arctic ice extent since late June, 2002.
http://www.ijis.iarc.uaf.edu/en/home/seaice_extent.htm
We normally see year over year ice graphs displayed in the format above, with each year overlaid on top of previous years. The graph below just shows the standard representation of a time series, with the linest() trend.
As you can see, Arctic ice extent has been increasing by nearly 50,000 km² per year. Over the eight year record, that is an increase in average ice extent of about the size of California. More proof that the Arctic is melting down – as we are constantly reminded. Spreadsheet is here.
How do we explain this? There has been more ice during winter, paralleling the record winter snow in the Northern Hemisphere. Meanwhile in the Southern Hemisphere, ice extent is at a record high for the date.
Size matters, but I’m guessing that Nobel Prize winner Al Gore didn’t share this information with his masseuse.
Addendum:
I realized after publication that this analysis is biased by the time of year which the eighth anniversary occurred. While the linest() calculation uses eight complete cycles, it would produce different slopes depending on the date of the anniversary. For instance, had the anniversary occurred in March, the trend line would be less steep and perhaps negative.
This is always a problem with graphing any cyclical trend, but the short length of the record (8 years) makes it more problematic than what would be seen in a 30 year record.
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So, this is why Gore wont debate anyone?
Mann can refute all of this with one tree ring set.
I also noticed the mention of Al (the groper) Gores incident. He has also been redeemed by peer review.
If you apply linear regression to a pure sine wave over the range -pi to pi you get a positive slope. Similarly you get a smaller positive slope over the range -pi to 3 pi, and so on. And indeed you get a positive slope by applying linear regression to a sine wave over the range -pi to 15 pi which is a purely periodic function roughly corresponding to what you’ve drawn above. But clearly a sine wave wave isn’t showing a trend.
If you want to use linear regression to see if an oscillating function is increasing then you must choose your endpoints so that what happens over a single period has no effect on the slope. For a roughly sinusoidal function that means choosing endpoints to be either both maxima or both minima.
Do you still get a positive slope if you do this?
I can explain it in one word … chaos. Some day, soon I hope, some climate scientists will look it up.
Are you absolutely certain that trend line is correct?
Just eyeballing it, it doesn’t look right …
As the North Siberia is getting colder, its coastal ice will persist for longer. The question is if this will be long enough to offset temperature rise in the North East Canada and Greenland.
http://www.vukcevic.talktalk.net/NFC1.htm
Steve, you are getting a little desperate in your search for positive arctic sea ice news.
this one is beyond absurd. we know the 30 year trend. we know that the problem is summer extend.
this is simply too much of a spin!
Very interesting Steven! Keep standing tall.
I’m here every day, reading your interesting postings. A year ago I had not heard about WUWT, and had no idea what these guys were up to. I was busy doing my job.
We work trying to make this a better place. In the mean time the “greens” are at it behind the scene trying to tear it down. I am a software engineer.
That’s bad news for Al Baby: No massaging at Cancun.
Your JAXA AMSR-E chart above appears to have an arbitrary line added to indicate a 50,000 K2 per year increase. Looking at the annual means, the line should indicate a gradual downslope from 2002 to 2007 of approx 50,000 K2 then a return to normal through 2009. Untol 2010 has reached minimum levels, it is not factual to extend the averaging line beyond the end of year 2009 as it will give a false impression of increasing ice. As summer minimum is reached in the northern hemisphere, the line will need to be dropped and will very likely reach the same average point as the 10,000,000 mid line in 2002
Ian H
You are correct. Please read the addendum.
Steve,
This article should be retracted, and I think you know it. Not only is it biased on time of year, but in many other ways. A quick look at the JAXA graph shows, for example that 2003 had a greater extent in March, and was higher for this day (July 2) and every other day of the year. There is not one professional expert on Arctic Sea ice who would support your outrageous headline, and that’s not because they are “wild-eyed” warmists, but because your headline is misleading and flat wrong.
And here I was going to complement you on getting the slow down in melting right after Hudson Bay melted so fast…and then you come up with something as rediculous as this.
Since all warming is caused by CO2, how do they explain the increase of CO2 between March and October? Rational people would see that fluctuation may correlate with sunshine quantities.
@ctm:
Good to see your addendum. Quick work. Glad to help.
I am glad you added the addendum – a linear trend fitted to a cyclical function is mathematically dubious.
And the title of the post should be “Arctic Ice Increasing By 50,000 km2 Per Year according to JAXA records which began in 2002”
If you started in 1980, you might get a different answer.
In simple language, there actually is NOT a problem with graphing a cyclical trend. If you take for example the same number of measurments each year and on the same dates, it will be fine.
We are accustomed to seeing charts that have trend lines originatng in a cold month and ending in a month with a high upward anomaly.
R Gates,
You are probably correct. It is interesting that the last three years were among the top four for winter maximums, but the date bias is going to be too much of a distraction.
“I realized after publication that this analysis is biased…”
Wouldn’t it be wonderful if professional climate scientists admitted errors so readily? Okay, I’m dreaming.
SCIENCE
If you’re not making mistakes, you’re doing it wrong.
If your not correcting your mistakes, you’re doing it really wrong.
If you’re not accepting that you’ve made mistakes, you’re not doing it at all.
The trend line looks right. The summer minima are pretty short-lived as opposed to the winter maxima so they don’t pull it down that much.
R. Gates, sod, you can jump on me now. 😉
Or in other words: it’s not a symmetrical curve.
@ur momisugly Steve
Have you read this? If you have access to the full text could you write a review of it for us?
DirkH
The trend line is mathematically correct, but the trend is small enough that depending on the date of the anniversary could give entirely different results. R Gates is correct- my conclusion is flawed.
I say you need to retract this and redo it correctly, even if the slope should have been down.
Visually the “area above and below” the trend line each year just looks wrong. In theory it should be close to the same area above and below every year.
Ian H and R. Gates are correct,
If you can’t do the math, get out of the kitchen.
Although the decrease in ice extent has slowed the last couple of days, 2010 still has a 482,343 square kilometer lead on 2007.
The year of the record low, and with weather reports out of Siberia predicting temperatures into the 80s F, who knows what’s up.
That’s bigger than California.
bob
Do they have sea ice in the interior of Siberia?
If you can’t do geography, get out of the kitchen. Speaking of California, when it gets hot inland, what happens to temperatures on the coast?