“Noisy” covariance matrices have been discussed here on many occasions in a variety of contexts, largely because the underlying strategy of Mannian methods is to calculate the covariance of everything to everything else and then calculate verification stats using methods that ignore the data mining that effectively takes place with huge covariance matrices. Steig et al 2009 is no exception.
The “justification” in Steig is as follows:
In essence, we use the spatial covariance structure of the surface temperature field to guide interpolation of the sparse but reliable 50-year-long records of 2-m temperature from occupied weather stations. Although it has been suggested that such interpolation is unreliable owing to the distances involved, [1. Turner, J. et al. Antarctic climate change during the last 50 years. Int. J. Climatol. 25, 279–294 (2005)] large spatial scales are not inherently problematic if there is high spatial coherence, as is the case in continental Antarctica [Schneider, D. P., Steig, E. J. & Comiso, J. Recent climate variability in Antarctica from satellite-derived temperature data. J. Clim. 17, 1569–1583 (2004)]
Which raises the obvious question: is there “high spatial coherence”? The citation for this (Schneider et al 2004) is unsurprisingly self-referential. Although the “active ingredient” in the pre-1980 reconstruction is the surface station record, Schneider et al 2004 provides no evidence for “high spatial coherence” in these records; instead, it discusses the AVHRR records.
I thought that it would be interesting to do a scatter plot of the distance between surface stations (here only the surface stations, not the AWS stations) against the inter-station correlation – the sort of low brow analysis that the Team abhors. Here is a location map of the stations. There are several Southern Ocean stations (e.g. Campbell Island, Macquarrie Island near NZ and Grytviken near Argentina), that are included in the data set.
Here is a scatter plot of correlations to distance, evidencing a strong decay with distance. There is a highly significant fit to a simple relationship based on exponential decay with distance (r^2 of 0.76 and t =71. (At this time, I’m not trying to assert that this is the form of a “true” relationship, only that it is very evident that there is a strong spatial decorrelation in the first 2000 km.)
fm=lm(cor~ I( exp(-dist/1000)-1) ,data=station);
Here is a histogram of correlations for distances above 2500 km, showing that they are distributed on both sides of zero – on balance slightly negative. It seems to me that it would be uphill to demonstrate that high correlations in this histogram are “significant” “teleconnections”, as opposed to the sorts of correlation turned up in a population of nearly 1000 autocorrelated series.
Above 2500 km, the covariance between surface stations all just looks like noise to me. The above decay of correlation with distance strongly argues in favor of the “null” model being stations with spatial autocorrelation decaying to 0 by 2500 km or so.
Note: In comments below, readers have argued that this is too negative a characterization, Ryan pointing to the clump of positive correlations around 6000 km. In light of these comments, I re-examined the data set and found that the clump of positive long distance correlations involve Campbell and Macquarrie Islands to Grytvyken and the Antarctic Peninsula stations; correlations to the Antarctic continent are slightly negative. For now, I’m just struck at the obvious decorrelation with distance. So far I’ve not carried out statistical analyses against a null model. You’d think that Steig et al would have done this sort of thing.
UPDATE Feb 24: Here’s a variation of the above graphic limiting stations to “continental” Antarctica. First here are the stations used:
Location map of surface stations used in correlation-distance plot below. 17 stations are excluded, of which 5 are islands in the Southern Ocean and 12 are in the northern part of the Peninsula.
Now here is the same scatter plot for correlation vs distance, which perhaps shows a more coherent decorrelation than with the island and far peninsula stations included.
Scatter Plot of Correlation vs Distance, 25 Stations.