Continuing with my analyses of the Kaufmann Arctic 2K proxies(A2K), I have concentrated on the tree ring proxies and primarily since it is those proxies that have, as a group, the best correlations within the group and with the instrumental record. What I want to show here is that these proxies look very different in the decadal and centennial range of trends. Further the proxies appear differently in the frequency domain. I found the best measure of what I want to show can be derived from the use of Singular Spectrum analysis. I used the ssa function from R (library Rssa) with a window of 10 years for the 14 A2K tree ring proxies and a 100 year window for the composite of all 14 TR proxies. The analysis uses eigenvectors to decompose the series into cyclical, secular trend and residual white/red noise. My interest here was to plot the 14 proxy and composite series with the secular trend and then ARMA model the resulting white/red noise residuals. The result of those analyses are in the links below.

It is rather obvious that these proxies, while having reasonably high correlations on a pair wise basis, look very different under the closer scrutiny that SSA provides. I have searched for similar use of SSA analyzing tree ring proxies, or other types of proxies for that matter and have found the first link below referring to 0.4 to 0.8 degree longer term oscillations in various type proxy series – including tree rings. They conclude that those oscillations can be translated to historical temperature oscillations, but that holds only if it assumed the proxies are responding to a temperature signal. The second link below talks about SSA and composite tree ring lower and higher frequency cycles but that does not address the issue I raised here about differences amongst proxies. The third link below studies once again a composite and thus does not discuss the issue of differences in individual proxies. I need to do more literature searching in looking for the question I have posed in my analysis here.

]]>The eyes in the skies

Cool the fever of lies.

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In my continuing effort to better understand the temperature proxies used in the more prominent published reconstructions and in the context of the basic flaw of directly or indirectly selecting proxies based on the ex post fact measured correlation with the modern instrumental record, I have recently been studying the Kaufman Arctic 2K (A2K) reconstruction individual proxies.

I have compared the proxy correlations with temperature and pair wise amongst the individual proxies. It is easy to show that even the reasonably high and significant correlations between proxy and temperature series that exists for a small portion of the proxies does not necessarily produce a relationship whereby one could confidently expect that high correlation to be a useful indicator of decadal or longer trends. It is these trends that after all are the critically important use made of the proxies in reconstructions.

For the Arctic zone reconstructed in A2K the local temperature changes can vary over a wide range. I have compared the difference between the temperature series from close neighbor temperature stations and compared that difference to the difference I see in similarly situated proxies of the same types. In most cases the difference in the decadal structure of the proximate proxy series is greater than for the series of proximate temperature stations, however the variation of series from nearby stations remained a bit troubling for me.

In the end I decided to use data from the best behaved proxy with regards to higher correlations with temperature (at a nearby station) and other like proxies. The proxy I selected was the Grudd tree ring proxy. Tree ring proxies are in turn calculated using many data points from the measurements of individual trees and thus one has many individual proxy responses from the same location and with the reasonable assumption that the temperature changes over time are the same for all these trees. The Grudd tree ring data used in the A2K reconstruction were taken from the ITRDB linked here:

http://hurricane.ncdc.noaa.gov/pls/paleox/f?p=518:7:0::NO:::

ftp://ftp.ncdc.noaa.gov/pub/data/paleo/treering/measurements/europe/swed334.rwl

It should be noted that the tree ring data that I used in my analysis are derived as noted here from the Grudd meta data:

“Biological trends in the data were removed with autoregressive standardization (ARS) to emphasize year-to-year variability, and with regional curve standardization (RCS) to emphasize variability on timescales from decades to centuries.”

I have plotted all the individual tree ring series and found that on visual examination the basic structure of these series from the same time period could have 3 or 4 patterns with decadal differences in trends. What was a bit surprising was that the composite calculation using all the available tree data for a given year yielded a composite with relatively narrow confidence intervals. I started looking at 150 year periods and when I saw what appeared a very regular cycle in the data I took all the Grudd tree data from year 9 to year 1999 and did a spectral analysis using the ssa function in R (library Rssa) to decompose the composite time series. The results are summarized in the first link below and show two prominent and significant cycles (as determined by the spec.pgram function in R) at approximately 250 and 60 years. The residuals are white/red noise that can be best modeled by ARMA(5,0) (see the second link below which also shows the number of individual trees used in the analysis).

Now, I would not accept the conjecture ,without independent evidence, that these Grudd tree rings are responding faithfully to temperature and doing it consistently over time, but if, apparently like the authors of these reconstructions do, it is surprising that no mention is made in the literature that I have searched about this cyclical pattern in the Grudd data. It presents a picture of the climate in that part of the Arctic as being very predictably made up of repeating cycles and white/red noise and without evidence of the effects of AGW. Alternative views of the data might lead to conjecture about the cycles being an artifact of the standardization processes used on the tree ring data. A quick review of the literature on temperature cycles brings forth the Atlantic multidecadal oscillation which supposedly oscillates between 60-70 years. There are some rather far out there conjectures on a 250 year solar cycle but nothing reported seriously in the literature.

I want to next do the same kind of analyses on the other tree ring proxies used in the A2K reconstruction.

]]>Many thanks, Kenneth, for your reply and explanation. The world of climatology is replete with conundrums, some of which I suspect are due to the beliefs/wishes of investigators rather than clear thinking and unbiased exposition of observational science.

Yes, now that you point it out, I understand that the high correlation pairs are probably a result of fairly close relative positions. Seems obvious now!

Something that I have not yet found out is how many observations are involved in typical correlations. This is because I have not attempted to access the original numbers. For me it would be a considerable task, I think. Should they all have effectively the same numbers of observations, it would be possible to construct probability contours, which might just be enlightening.

In my trials, taking the Arctic 2K data in the link as being the considered outcome of McKay and Kaufman, I find it very difficult to believe that they had not noticed that since 1922 there has been no measurable increase in their data. Have you an opinion on this?

Steve: they reported that their 1941-1970 period had higher values than their 1971-2000 period.

Robin, please note that the pair wise correlations of station to station locations are very dependent on the longitudinal separation of the station locations. Using the same proximate pair wise locations of the proxies to estimate a correlation one would expect that those station and proxy correlations should in turn have some reasonable correlation if we assume the proxies were responding reasonably well to temperature. That the correlation is not significant should tell us something about the proxy response. Further that we can see a higher correlation from proxy to proxy location where the temperature stations at the same locations have a low correlation indicates how easy it is to obtain a spurious correlation.

The upper right region of the graph consists mainly of pairs from some tree ring and dO18 proxies. I am currently doing some analyses on the best performing proxies with regards to correlation to local temperature. I am not sure I understand what you mean about time dependence but a significant and reasonably high correlation between temperature and proxy or proxy and proxy can be misleading in terms of what one sees when comparing the series of the temperature record and proxy response over an extended period of time. Those series can diverge from one another over decadal periods of time and yet have higher and significant correlations. That becomes problematic when looking at warming/cooling trends in comparing the modern and historical periods.

I am currently thinking about analyzing these proxy to instrumental data by using difference series and then looking for breakpoints and trends in the difference series.

I just wish that those doing temperature reconstructions would take a more detailed look at these relationships. I am sure they are capable of doing these analyses better than I.

]]>Over time I have formed the view that ordinary linear correlation coefficients are seldom really useful in the context of climate, though correlation plots may give a useful impression of the associations between pairs of variables. What may be missing is that other vital component of climate data, the fourth dimension, time. These diagrams are I think, integrations over the time of the observations, and to me it seems probable that one would expect most correlations to be rather small. The data of most interest are surely those in the top right quadrant, and I’d guess that Kenneth has looked pretty closely at at these.

I wondered about the development of contours on the plot, indicating specific boundaries of significance level. These would presumably be a series of roughly arc-shaped lines at varying distances from the origin. Would this have some interpretative value?

Something else I’ve noticed is that the values of the data appear to be at discrete intervals along both axes. Am I right in this? This is only curiosity of course! It has no practical significance.

]]>OK , that makes sense. They should have used a word like distinct or separate or nonoverlapping.

]]>With these above difference in mind, I looked at 2 stations in close proximity to each of the 57 individual proxy locations in the 2K Arctic reconstruction using the GISS adjusted mean temperatures from KNMI. I did pair wise correlations for the period 1880-2007 for one of the station series for each proxy in Group 1 and the same for the other station series for each proxy in Group 2. I then compared those pair wise station series correlations with those for the proxy pair wise series from the same locations. In effect the pair wise comparisons between proxy pairs are now taking into account the location differences. One would expect from an array of 57 valid temperature proxies to see a reasonable correlation of these station to station and proxy to proxy correlations. The results were not encouraging, however, with the Group 1 correlation of the station to station and proxy to proxy correlations having a correlation of r=0.017 with a p.value=0.56 for 1107 station to station and proxy to proxy data points. Group 2 showed nearly an identical result with r=-0.017 and p.value=0.55 for 1108 data points. The scatter plots for both Group 1 and 2 are linked/shown below.

It should be noted that the station and proxy data did not necessarily cover all the years between 1880-2007, but the average correlation was with 68 years of data. A correlation with less than 5 years was not made. Also to make the estimate conservative I used the absolute value of the correlations in order to avoid the issue of assigning the correct sign for a proxy.

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