Where the data mining method is vulnerable is if any of the series have spurious correlations, such as the bristlecones. The falback position on britlecones in Wahl and Ammann 2006 is that they may have a correlation to precipitation or some “climate field”- although they don’t try to provie this,

Thanks for the reply.

Looking at the 8 time series again they are surprisingly similar to each other and to the overall average. On the other hand, they don’t look anything like the charts of global mean temperature we all know if not love. But I guess you would expect them to correspond more closely to the weather at 58N, 111W which is possibly fairly different that the global average. What’s the nearest weather station with a reasonable history? How similar is the measured temperature history there to the time series you compute?

I’m fairly new to all this, so please forgive any dumb assumptions.

In fact, if you don’t like conclusions affected by one site, you can’t accept any study which gets different MWP-modern levels depending on whether they use Yamal or the Polar Urals Updata or whether bristlecones are in or out.

Then I’d weight each average by the inverse of the fractional number of series bits it contained, relative to the total, so that the noise levels reflected the amount of data actually present. Finally, I’d splice them all back together into one series. I haven’t done this, and recognize there may be a problem with the values of the averages at the splice-points. Maybe it would be necessary (but perhaps not proper) to adjust each section average so that the respective splice-points had the same absolute value. But if the method — or its like with adjusted splice-points — worked, the noise at each point should pretty faithfully reflect the quality of the data. Any model fitted through the data ought to then produce an r-value that was a pretty fair measure of the net uncertainty.

Correlations to annual gridcell temperature range from -0.29 to 0.02 and to JJA re -0.15 to 0.13.

I just took the average of available series. I wasn’t trying to do anything sophisticated here.

A. I would think averaging is pretty simple (when different numbers of series at different times). Just add the series that you have at any particular time and divide by number of data points.

TCO, you can get artefacts if you do that. The number of series suddenly jumps from one year to another, affecting the weightings, and if the series starting/ending starts or ends on a particularly high or low value it can lead to a nasty spike.

I don’t see (m)any artefacts in Steve’s average so I’m not sure if he did something to avoid this or whether it just happens to not be obvious.

Personally if I were averaging a number of time series which start and end at different points I would blur the edges of each set by a number of years by, say, introducing it at 10% per year. So if you have two series, one (a) starts at 1700 and one (b) at 1800, at 1799 I would have x = a, at 1800 I would have x = (a + (b*10%))/110%, at 1801 I would have x = (a + (b*20%))/120%, etc. until at 1809 you are up to a normal average. That should help limit the outliers created by the introduction.

Not being a statistician I don’t know whether this is a bad thing to do, but I think it makes sense.