Is there a reason why a linear trend is shown for the NH sea ice extent, where a second order
polynomial fit trend is shown on the Arctic Sea Ice Escalator graphic?
The dark black, grey and bright red curves are second order
polynomial fitted trends produced by Excel - they are not predictions, but they do indicate the current direction the trends are taking.
The above Excel chart includes 2nd order
polynomial fitted trends of the 15 - year average growth rates.
Not exact matches
The solid line is is simply a
fit 4th degree
polynomial I imposed in the a spirit of parsimony to illustrate
trend in a general way.
Leaving that aside, and also leaving aside the issues with
fitting a 10th order
polynomial to such «data» (lots of degrees of freedom...) what is becoming apparent to me is that there is a cyclical
trend that can be linked to physical processes such as the PDO / AMO, as well as a long - term linear
trend.
Let's remove the very - long - term
trend by subtracting a cubic
polynomial fit, leaving this:
a higher order
polynomial fit is NOT an «advanced» method of
fitting a
trend.
As I explained before, there is no justification for using anything other than a linear
trend to
fit the UAH data — the correlation coefficients show no significant improvement as a result of putting in the additional
fitting parameters for a
polynomial trend.
If to justify your values you need to use a fourth order
polynomial, as is shown on the
trend you present, you have to show that there is a significant improvement in the correlation coefficient between the
trend and the data by using three additional
fitting parameters.
I also learned that given enough fudge factors and enough
polynomials, I can make an equation
fit any smooth
trend that you can come up with... to a certain point.
The chart's
fitted trends (2nd order
polynomial) reveal the earlier period with a closing warming rate that is accelerating away from the modern
fitted trend.
That is, they first
fit a
polynomial of order two to the data, remove this
trend, and study the deviations from the
trend.
This band width was signal was normalized and the
trend removed by
fitting an order 2
polynomial trend line to the band width data.