Simple Statistical Evidence Why Hockey Stick Temp Graphs are Bent!!
Posted by Jeff Condon on September 29, 2008
This is a continuation of my posts on selective sorting of data and why it absolutely is a false representation of temperature. If this is your first time on this subject start at this link The Flaw in the Math Behind Every Hockey Stick
Paleoclimatology uses a statistical sorting technique to generate hockey stick graphs which demonstrate to the world that our current temperature has a higher upslope than any time in recent history. This is yet another demonstration of how that conclusion is false!! The data used in this post is random, a known temperature signal has been physically added with a + sign to the random data
As promised before but a bit late, I have worked on some red noise examples to explore how variations in signal noise affect the overall weighting of temperature in hockey stick style calibrations.
The first graph is similar to the weightings in my previous examples. Two random red noise series are plotted as grey and dark grey in the background they both quite randomly started at about -5. The blue line is actual temperature and has zero signal between 1900 and 2000 with a 1 degre hump at year 1250. The green and orange lines are the distortion in the temperature scale spaced 1 degree apart. The bottom orange line represents the true zero degree point on the graph the top orange is true 1 degree. The vertical scale compression is 42%.
The black line is the actual modifications which are created due to the sorting process whcih is as followsl.
1. Correlate all proxies to a linear uprise in temperature discarding any negative slopes
2. Scale and match all slopes to an assumed 0 to 1 degreee temperature rise between 1900 and 2000. (output = slope * original data + offset) — Slope and offset are modified for 0 to 1 degree.
3. Average high r^2 value proxies to 0.8 correlation.
The smoothness of the line results from a high number of red noise sereis, even the green and orange lines are just averages of noise values with offset temperatures included. So I clearly have enough data.
What happens when higher frequency noise series are used?
Higher noise means the red noise can shift more frequently across the graph and a key point is that this increases the average slope of the series. So I performed the same calculations with higher red noise.
This is what I expected to see. a very high compression of historic values compared to actual. The blue line is again 1 degree tall and represents the true temperature signal. I was again able to extract a strong hockey stick signal simply by sorting for my ‘favorite’ high correlation series. What is different though is the way the green and orange lines shift upward in recovery (from right to left behind the 1900 – 2000 calibration period) created by selective correlation. I refer to this as the recovery rate. The true signal ZERO temperature signal is perturbed and it recovers the further away from the disturbance.
This graph is very interesting to me because the black line settled on an exact value of 0.5. After the slope and offsets produced a very high compression of 13% of full scale. This is very high slope data however.
I decided to try very low slope data just for fun.
The green and orange lines are highly spaced out but what many of you might find interesting is that while this calculation again revealed a perfect 0 to 1 degree temperature rise in 1900 to 2000 it also produced an amplification of the historic signal of 242% !!
The recovery rate of the signal compared to the slope as well as the overall amplification of the historic pre-1900 data are dependant on the frequency of the data used!!
Not only is the temperature scale of every hockey stick proven completely wrong by this amazingly simple demonstration, the Mann 08 paper incorrectly combines proxies with different frequency (noise levels) to create historic temperature. EVERY PROXY TYPE MODIFIES THE AMPLIFICATION DIFFERENTLY.
What happens to the signal when there is an actual temperature we are looking for.
First lets see a placebo graph with a medium high r value and a compression of 18.2% with a historic offset of 0.5C and no temperature signal. This graph had no temperature signal in the last 100 years as indicated by the blue line. Typical proxies are shown in the background.
The 1250 year 1 degree signal we all know exists because I added it was added is flattened to nearly nothing in the same manner as above, a strong hockey stick upslope is created where we know none exists and a temperature offset at year 1000 of 0.5 degrees was also produced.
The blue line representing the added temperature signal to the random proxies has a 1 degree upslope from 1900 to 2000. Again the compression of historic values is exactly the same at 18.2% — very good news for correcting temperature scale. This value is easy to calculate for temperature proxies so future HS papers can utilize it to their advantage.
The offset of the zero degree line at year 1000 shifted downward from 0.5 degrees C to a 0.39 degree point.
I added a negative temperature to the graph at 1550 just to show the scale works. This has a scale factor slightly less than scale .5 and an offset from actual temp at 1000AD of 0.34 degrees C.
Finally due to popular request, I ran the exact settings of the above curve with a negative slope in my fake temperature proxies while still looking for a positive slope. This graph has the same settings as above but even I haven’t seen it yet.
The blue line is again the signal inserted into the data. Still I was able to create a hockey stick in the black line . The magnification of the historic data was 0.55% with an offset of 0.8 at year 1000.
Same graph with high freq red noise equal to graph 2.
Again, I created a hockey stick where there was none.
There are a few more series I can play with but one thing I can say for certain.