1) If we know beforehand that there are no large variations in global temp during 1000-1860, we don’t need to reconstruct those temperatures. 1860-1900 average will do.

2) If there are large variations, with a sparse network of thermometers we would be unable to reconstruct the temperatures completely. This is due to the measurement noise that increases when the number of stations decreases. Averaging would help, but long averaging periods would average the high-freq signal components out as well. And we don’t know the frequency distribution of the temperature in the absence of human-CO2 (at this stage we can’t use the results of MBH99, the uncertainty levels would be a function of the results).

3) From this viewpoint, a good way to test the reconstuction would be to find a verification period with a strong, rapid increase or decrease in the temperature. Such as 1980-2005. If the verification period does not contain rapid variations, there is no penalty for taking a too strong average of the measurements.

]]>Positive spatial correlation just makes things worse, I guess (can’t get rid of variability by averaging). Positive temporal correlation means that there must be low-frequency variation in the temperatures, not helping either. i.i.d process with annual deviation of 0.15 C would be easier to reconstruct (in RMSE sense) with noisy observations than a positively correlated process with 0.15 C sd driving noise – the former has lower variability. Random constant process would be the easiest to reconstruct, but that’s apparently not very good model for annual global temperature. Maybe this is getting silly, I’ll read the refs in #19 before continuing..

]]>That would be one way to get an estimate. I was thinking about an oversimplified model: if the sd of annual averages of one temp station is 2 C, you need an average of 70 stations to get sd of 0.25 C, assuming that there is no correlation between the stations. If there is a positive correlation, more stations are needed (negative correlation between annual station averages would be interesting to see). Only way to get down to 0.25 C with fewer stations is to apply a dynamic model, but that’s another problem. We can’t predict the temperature of next year very well, implies that we don’t have exact dynamic model.

]]>Yes, English would be preferable. Besides TCO’s german is atrocious.

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