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David Middleton's comment
06-15-2011, 09:04 PM
Post: #1
David Middleton's comment

Quote:David Middleton says:
April 12, 2010 at 2:55 pm

Peter Hearnden (14:14:44) :

This is a non story that, I can only assume, is here to provide today’s opportunity for harumpfing.

Those lines just show the linear trend over a variety of times. I don’t think here anyone can (or will) show either that the trends are wrong, or show where anyone (other than Anthony (who I assume has written this piece)) asserts these trends or graphs ‘prove’ anything.

It’s not a matter of trends being right or wrong… It’s a matter of the significance and meaningfulness of the trends.

A linear trend-line through one leg of a sine wave will have a very high R^2 (high statistical significance) but it is totally meaningless; because the sine wave is a harmonic function.

A plot of the HadCRUT3 temperature series since 1995 certainly seems to show a warming trend…

HadCRUT3 1995-2009

However, this trend is not “statistically significant.” The correlation coefficient (or r-squared) value is only 0.13. This means that only 13% of the data fit the linear trend.

Since 1998, the data show no trend at all…

HadCRUT3 1998-2009

Since 2003, HadCRUT3 shows a statistically insignificant cooling trend…

HadCRUT3 2003-2009

One of the “problems” with the way climate data are handled is in the obsession with applying linear trend lines to non-linear data.

A Sine wave has no real linear trend…

Sine Wave (From Wood For Trees)

But… What happens if my data represent only a portion of a Sin wave pattern?

A partial Sine wave apparently has a very significant secular trend.

The r-squared of a linear trend line of this partial Sine wave is 0.88… 88% of the data fit the trend line. This implies a very strong secular trend; yet, we know that in reality Sine waves do not have secular trends.

If we take the entire HadCRUT3 series and apply a linear trend line, we get an apparent secular trend…

HadCRUT3 Temperature Anomaly 1850-2009

The r-squared is 0.55… 55% of the data fit the secular trend. This implies that there is a real long-term warming trend.

What happens to that secular trend if we expand our time series like we did with the Sine wave?

The apparent secular trend vanishes in a puff of mathematics…

Moberg et al., 2005 Climate Reconstruction

How can such a clear secular trend vanish like that? The answer is easy. Each “up hill” and each “down hill” leg of a Sine wave has a very strong secular trend. Unless you have enough data to see several cycles, you don’t know if you are looking at a long-term trend or an incomplete cycle.

If we take the HadCRUT3 series and compare the the period from 1912-1945 to the period from 1975-2009, we find that they are statistically indistinguishable…

HadCRUT3 1912-1945 vs. 1975-2009

We also find that Moberg’s Medieval Warm Period reconstruction is very similar to the HadCRUT3 series…

HadCRUT3 vs. Moberg Medieval Warm Period Reconstruction

Using the GISP2 ice core data from central Greenland we can see that over the last 50,000 years, there have been statistically significant warming trends…

GISP2: 50 kya to 1855 AD

GISP2: 1540 AD to 1855 AD

GISP2: 1778 AD to 1855 AD

And there have been cooling trends of varying statistical significance…

GISP2: 10 kya to 1855 AD

GISP2: 3.3 kya to 1855 AD

What does all of this mean?

It means that the Earth’s climate is cyclical. It means that the climate changes we’ve experienced over the last 150 years are not anomalous in any way, shape, fashion or form. And itr means that linear trend lines can be very misleading when applied to less than one full wave length of a quasi-harmonic function.

It is our attitude toward free thought and free expression that will determine our fate. There must be no limit on the range of temperate discussion, no limits on thought. No subject must be taboo. No censor must preside at our assemblies.

–William O. Douglas, U.S. Supreme Court Justice, 1952
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David Middleton's comment - Sunsettommy - 06-15-2011 09:04 PM

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