In the graphs below I show the relationship in scatter plots with a smooth spline best fit of the Gergis 28 proxy distance separation and series correlations and the same relationship for 55 Australasia temperature stations using GHCN adjusted mean temperatures. It is obvious that the relationship that is present in the station data breaks down for the proxies. While the breakdown points to the problem of using the proxy responses in the same sense of temperature responses at the stations, another problem encountered due to this lack of relationship of distance to series correlation is that arising from using that relationship to reduce the sampling error where the spatial coverage is sparse as it is with Gergis 2016.

The Gergis 2016 temperature reconstruction, like other reconstructions as I recall, does not attempt to deal with the sampling and measurement error. I have made some simplistic estimates of these errors for Gergis 2016 and have found that the resulting confidence intervals for a standardized proxy composite become sufficiently large to make the reconstruction rather meaningless with regards to claims about an unprecedented warming for the modern era. I am wondering if any readers of these posts here can recall published temperature reconstructions that dealt in detail with measurement and sampling errors in constructing confidence intervals for their series. I also recall that using sampling and measurement errors for temperature series from temperature stations and ocean satellite, buoy and ship data is a rather recent development.

]]>It is based on a study by Paul E. Smaldino, Richard McElreath published in the “Royal Society Open Science” http://rsos.royalsocietypublishing.org/content/3/9/160384 ]]>

My analysis was based on the 51 proxies that Gergis (G51) used as a pool for post fact selection and on the smoothing that can be used for the Gergis 28 proxies (G28) composite that passed the authors post fact tortured selection process. There were 2 or 3 proxy for which I had to search the locations. I think I have those locations correct but I am not certain.

In my approach for the G51 I used all the common data points for the years 1880-2001 for the standardized proxy series (centered and scaled) and the HadCRUT4 temperature series extracted from KNMI for the corresponding 5X5 grid where the proxy was located. On these data I did both correlations and trend differences for the proxy versus grid data. The confidence intervals (CIs) were adjusted for ar1 autocorrelation by ARMA modeling the linearly regressed residuals for ar1 and standard deviation of the ARMA residuals and using that model to determine the CIs with 1000 simulations for each proxy and corresponding grid series in the case of correlation and for the proxy minus grid difference series for the trend differences. The correlation results reported below in the table are for detrended series and the trend differences were derived by calculating the linearly regressed trend that resulted from the proxy minus HadCRUT4 grid series.

I used HadCRUT4 because it is the latest HadCRUT temperature series available. The 5×5 grids were used to provide a reasonable amount of temperature data without missing data intervals from the common points with the proxy data. I used annual data because that is the temperature that should be of interest when looking at historical versus modern era differences. If there is not a very high correlation of seasonal temperatures to annual temperatures for the entire reconstruction period then the reconstruction becomes much less useful. I used a longer time period for lessening the uncertainties of the results. I added a trend difference measurement since while high frequency annual (or seasonal) correlations might indicate something about that correspondence it is really the trend or low frequency correspondence that we are most interested in when comparing modern to historic temperature changes.

The results in the table show that a statistically significant correlation of detrended proxy to detrended grid data has little to no predictive power to those pairs having the same trends for these same common data points within the bounds of statistical significance. When using longer time periods for comparison of proxy/grid pairs it appears that more of the proxy response to grid temperature relationships are the reverse of what would be expected for that type of proxy. I put an asterisk by those relationships that show a significant correlation but with the wrong sign. From a close observation of the table it can be seen that there are other proxy/grid pair correlations and trends that show the wrong sign and had no statistical relationship. Tree rings, speleotherm, luminescent and ice core accumulations proxies should have a positive response to temperature while coral and ice core d18O proxies should have a negative response. I should also point out here that for the Vostok and Talos corresponding 5X5 grids I used the CW Infilled HadCRUT4 temperature series in order to get a reasonable number of common data points. I would think that if a scientist were doing serious work attempting to find valid proxies that could be used in developing a priori criteria for selecting proxies based on some hard physical basis that a more detailed look at those proxies that pass both the detrended and trend difference tests might be in order. That work though would have to remain as preliminary tests for finding a proper a prior criteria and not the basis for post fact selection.

My final analysis involved the sensitivity of how the composite series of the G28 post fact selected proxies can appear depending on some simple changes to the smoothing function used. In the 4 graphs presented below I used the smooth spline function from R to smooth the G28 composite using df=7 and spar values of 1.0, 0.75, 0.50 and 0.25. It is rather obvious that the unprecedented view of the modern warming period can be greatly affected by choice of a smoothing parameter. I should note here that the proxy responses to temperature were adjusted given the expected orientation as noted above.

]]>I recall being surprised that the G12 authors didn’t catch those oversights in their Table 1, as the proxies which are outside of the defined region (0-50S,110-180E) are so prominent in Figure 1. But it was only typo; it would not have made any difference to the analysis, because correlations were only calculated between the proxy records and the regional average, not to any local series. ]]>

https://www.ncdc.noaa.gov/data-access/paleoclimatology-data/datasets

The correlation results changed for Rarotonga, Rarotonga.3R and Bunaken and I have included those changes in the corrected table linked below. The overall numbers of significant correlations between proxies and the 10 station near neighbors for the series and detrended series did not change.

]]>The trend error was estimated by determining the best fitting ar1 model for the SSA trend residuals of each series and using the ar1 coefficient and the standard deviation of the modeled residuals to do simulations that resulted in calculating 1000 realizations of composited SSA derived trend line of all 27 proxies. From those realizations the 2.5%, 50.0% and 97.5% probabilities were determined and used to construct a graph with the trend line of the composite and the 95% confidence intervals over the entire reconstruction period from 1000-2001. That graph is shown in the link below.

The sampling error was determined using an adaption of the approach of P. Jones in the paper: “Estimating Sampling Errors in Large Scale Temperature Averages” http://www.st-andrews.ac.uk/~rjsw/PalaeoPDFs/Jonesetal1997.pdf

That approach uses estimations of the average of the paired correlations of stations series(proxy locations and series) and the average standard deviation of the series of all the station series (proxy series) for the area of interest. That information is combined with number of stations (proxy locations) to calculate a standard error for sampling over the entire area. If the area is well covered by stations (proxy locations) the average paired correlation can used in the following equation:

SE^2=Sibar^2*rbar(1-rbar)/(1+(n-1)*rbar where SE is the standard error for sampling the area, Sibar is the average of the standard deviations of the individual series and rbar is the average of the paired series correlations.

If the location of the individual series does not cover the area well – as is the case of the Gergis proxies and the Australasia area – the Jones paper gives an alternative method for determining rbar from the equation:

rbar=(x0/X)*(1-e^(-X/x0)) where x0 is the correlation decay length and X is the farthest distance for possible separation of series locations (the diagonal of a rectangular area). x0 is determined from a plot of the correlations versus the separation distance of proxy pairs and where the trend line reaches a correlation value of 0.368. Unfortunately for the Gergis proxy case there is very little dependency of proxy series paired correlations on distance and the decay length would actually be a negative distance of approximately 1000 km. The graph depicting that relationship is show in the link below.

That leaves my only alternative for obtaining an estimation of the sampling error for the Gergis 27 proxies in that large bounded Australasia area (0S-50S and 180E-110E) to limiting the number of locations, n, where the stations are located in close proximity to one another or outside the bounded area. The value of n for this purpose is reduced by 3 for the 2 Vostok ice proxies and the Palmyra proxy for this purpose for being outside the boundary as well as by 2 for the 2 Rarotonga and 2 Fiji proxies which are collocated. While it is noted that the n will vary downward from a maximum n where all proxies have common dates with the year of the Gergis 27 composite, the maximum n is reduced from 27 to 22 by this first step. A second step is to assume collocation of the stations that are separated by less than one-half degree in latitude and longitude. That would include the pair Mt Read and Buckley’s Chance and the triple consisting of North Island LIBI Composite 1 and 2, and Takapari. The maximum number for n here goes to 19. The link below gives a table showing the locations of the proxies in the Australasia boundary and that my use of effective values of n is conservative given the clumping together of the proxy locations.

The proxy composite trend line and the trend plus sampling error 95% CIs are shown in graphical form in the link below. I have not been able to do a proxy measurement error, but I do have some ideas on approaching that problem and when I feel I have a good handle on it I could add that error to sampling and trend error to obtain something perhaps close to a total uncertainty range for the trend lines. Currently I feel that the proxy measurement errors could be quite large with tree ring proxies – if one can consider the differences between cores from the same tree as a measurement error.

In conclusion, even when the construction of a temperature reconstruction is **incorrectly allowed to select proxies post facto**, the uncertainties when properly included can obliterate any opportunity to show the modern warming period being revealed in the post facto selected proxy responses as unprecedented.

**Steve: sometimes specialists believe that growth is responding to temperatures of the previous season – for actual reasons, not just data mining. There weren’t that many studies and the specialist authors were involved, so Gergis could have consulted the specialists ex ante, rather than data mining.
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