Another Mathematically Honest Reconstruction
Posted by Jeff Condon on October 7, 2010
I learned a little more today. Behind the scenes, Steve McIntyre had a polite conversation with Dr. Ljungqvist who has recently performed a temperature reconstruction from proxies with remarkably similar results to Craig Loehle and Hu McCulloch’s work. Dr. Ljundqvist was kind enough to share the data with Steve. The internet made a bit of a stink about the fact that it visually matched Dr. Loehle’s much maligned work quite well. Climate science has learned to hate reconstructions with a medieval warm period so Tamino even took the time to try and trick (not the apparently good definition) people into thinking the match was dishonest.
Dr. Ljungqvist’s paper uses CPS method which Mann08 used and is known amongst tAV readers to create variance loss. Carrick and others were generous enough to provide a copy of the paper to me which has a description of the methods quoted below.
We use the common “composite-plus-scale”
method for creating our multi-proxy reconstruction
(von Storch et al. 2004; Lee et al. 2008). All
records with less than annual resolution were linearly
interpolated to have annual resolution before
the records were normalized to zero mean and
unit standard deviation, fitting the mean and variance
AD 1000–1900 and then we calculated 10-
year-mean values of the records. The arithmetic
mean of all 30 records was then calculated to form
a dimensionless index of Z-score units. This index
was scaled to fit the decadal mean and variance
over the period AD 1850–1989 in the variance adjusted
CRUTEM3+HadSST2 90–30°N instrumental
temperature record (Brohan et al. 2006;
Rayner et al. 2006) and adjusted to have a zero
equalling the 1961–1990 mean of this instrumental
record. The decadal correlation between proxy
and instrumental temperature is very high (r. 0.95,
r2 0.90) and the 2 standard deviation error bars
only amount to ±0.12°C in the calibration period
AD 1850–1989. As would be expected from different
sorts of proxy records deriving from different
regions, there is a certain standard deviation between
the decadal mean values of the records, as
seen in Figure 2. This should, however, not be of
concern for the accuracy of the reconstruction
since the coherency between the records is rather
stable in time back to c. AD 1000. The standard deviation
is somewhat larger in the first millennium
of the reconstruction, probably primarily because
of the decreasing number of proxies covering this
period, but even so this deviation is not much
higher than in the calibration period. To account
for changes in the standard deviation between the
records in the error bars, we have increased the
width of the confidence interval with the same
percentage as the standard deviation between the
records in a given decade exceeds the mean standard
deviation during the calibration period AD
CPS is a method where standard deviations of proxies were matched to temperature standard deviation. Other papers have used this method combined with data sorting or using the standard deviation only in the measured temperature period, and it creates hockey sticks from totally random data. Now on first reading of this paper and the authors comments, I assumed that this used a similar method, but it does not. Ljundqvist matched the variance of the entire timeseries to the variance of temperature rather than just the variance in the calibration period!! This is a very much reasonable method of calibration which is sometimes used in paleo.
This makes all the difference in the world.
Steve McIntyre shared the data with me by email along with extensive code verifying the correctness of the series but pointed out that some of the series are still top secret data or data not revealed by the original collectors. Therefore I will not be able to share the data for the below replication, but the original authors need to be encouraged to archive. I can say the proxies look exactly the same as all the rest I’ve seen, I’m getting familiar enough to pick the type of scribbles out just from looking at them. Sediment from borehole from treering from etc. I suppose SteveM and paleo’s consider that a minor thing but it’s news to me.
Anyway in starting this post, my intent was to replicate the reconstruction and take a look at variance loss. Ljundqvist left this quote in the vindication thread linked above.
Fredrik Charpentier Ljungqvist says:
September 28, 2010 at 7:16 am
A comment from the author:
Some remarks have been made suggesting that the amplitude of past temperature variability are deflated. It is indeed true and discuss in length in the article. The common regression methods do deflate the amplitude of changes in the reconstructed temperatures. This reconstruction shares this problem with all others.
Of course from the endless reconstructions we have all examined, it seemed quite reasonable coming from the author. Thanks to the sharing of the data, and the simple methods, I was able to reasonably well reproduce Ljungqvist result below .
It’s not a perfect replication but these are temperature proxies so the two are close enough for my liking. Some readers will recognize my standard lack of enthusiasm for more work beyond a certain point. My recon (black line) actually fits a little worse in the known temperature range. But consider this point:
All proxies are scaled in the Ljundqvist reconstruction by their entire length to match the variance of temperature.
All proxies are used, none thrown away by correlation sorting.
These two facts make it impossible to create a difference in variance loss between the calibration period and the historic period. They are scaled equally, all data is used!
In other words, this is a mathematically honest reconstruction!! It’s basically averaging!
What I don’t understand is the comment on variance loss by the author. I’m going to have to write him an email tomorrow. All combinations of timeseries are considered dimensional reduction and all cause varaince loss. But in this case, the loss is equal throughout the series. Perhaps he doesn’t realize how bad the problem is with recons like Mann08 or perhaps he doesn’t realize that we are criticizing a differential in varaince loss not the 100% statistically reasonable variance loss of averaging.
Now there is more to the story but this is enough for today. Just for a moment though, readers should consider this piece of evidence from the paper.
The decadal correlation between proxy and instrumental temperature is very high (r. 0.95, r2 0.90)
That is an amazingly good result for proxy data, especially when not preferentially sorted. Many of the series were pre-created to match temp but this result is not easily dismissed with a handwave. I’m going to have to look deeper into this paper (subpapers) to see if the reason for the incredible match to temperature can be understood. Wow.
Now we have two reconstructions, Craig Loehle’s and this one which use mathematically similar and reasonable methods. This says nothing about proxy quality but it is very much telling that two methods which address the differential variance loss match each other so well.