Breakdown of Hockey Stick Distortions in CPS

Ok, just a quick post done at the suggesion of Craig Loehle.  He asked what would happen if we use CPS without r sorting.  This led to my breaking down the distortion into two modes.  One mode is the r correlation sort, which is well known to create a HS out of most anything yet is still used.  The second mode is created by data scaling.  This led to some revealing graphs.

See my previous post if you haven’t seen the background of this experiment.

Id Goes Mythbuster on Hockey Sticks- CPS

Same data as my last post 10,000 random series using CPS sorting.

First I put in the NH signal from before into the series.  Two posts ago I sorted the data by r value only without scaling and got this graph.

The original data is in blue,  I noticed the higher the r value the higher the distortion in original signal.  There is no distortion in magnitude of historic values using this method, only an amplification of recent values.

Then I used CPS methods to calibrate my artificial proxies and performed calibration and sorting of the data and got the graph below.

and for r>0.8

This method forced the fit of the hockey stick to the end of the graph yet demagnified the historic trend.  The higher correlation resulted in stronger demagnification of historic values.  The tail form0-200 is therefore  true temperature zero not the zero on the graph y axis.

Craig Loehle asked what would happen if I didn’t sort for r and just ran the calibration.

In this last case the scale is still demagnified by the CPS standard deviation scaling.  The process was like this.

Calculate Standard deviaton and mean for (red) calibration period in the above graph which represents in this case known temperature.

Calculate and match all series standard deviation and mean in the same calibration period to the standard deviatoin and mean of the calibration range data in the abover graph.

Average the proxies together.

The offset of the graph is the mean of the calibration period (1850-1995) times the magnification factor.  The net effect was to shift the zero down and the most negative numbers up.

What is happening is higher sloped proxies have a higher standard deviation on average.  If the proxies which = NH signal + red noise have more series with slopes higher than the calibration period the signal is demagnified.  If it was the other way around you get a magnification.