## Tuesday, January 03, 2012

### Entertaining Roy Spencer's Fit to His Temperature Data

The UAH temperature anomaly for the lower troposphere is +0.127°C, the 12th-warmest December in the 33 years of their records. The year 2011 is the 9th-warmest year, and the coldest year since 2004.

The last 10 years (120 months) are 0.21°C warmer than the preceding 10 years (120 months).

As he does every month, Roy Spencer includes a 3rd-order polynomial fit for the data, "for entertainment purposes only":

Why 3rd-order? Perhaps because here's what the 6th-order fit looks like:

Notice that little hike upward there at the end.... And actually a 6th-order fit has a better correlation coefficient than does the 3rd-order fit:
R(3rd-order fit) = 0.3901
R(6th-order fit) = 0.3951

What does Spencer's fit "predict" for the future?

Jan 2050: -5.8°C
Jan 2100: -50.2°C

Those are some entertaining "predictions" -- the "planet" at the end of this century "will have" an average temperature of "-33°F." Naturally the commenters at WUWT are excited about Spencer's fit because they think it's starting to show a downward trend.

By the way, the 10-year slope of the UAH global LT data is 0.032 ± 0.049 °C/decade. Notice it's not negative.

Aren't statistics fun? They can say so many different things, all at the same time....

Belette said...

> a 6th-order fit has a better correlation coefficient than does the 3rd-order fit

But you expect that anyway; you're allowing more parameters, so you get a better fit.

There is a proper statistic-y way of accounting for this, but I forget it. DC will know :-)

bob said...

funny. i always thought it would be more "entertaining" to use a linear fit

Belette said...

It is not quite the thing I was thinking of, but http://tamino.wordpress.com/2012/01/09/steps/ discusses the same issue: that more params leads to a better fit, but may not be a better model. See AIC, there.