## Tuesday, September 28, 2010

### Vindication of Craig Loehle

F.C. Ljungqvist has published a new climate reconstruction from the birth of Jesus Christ to the present:
Ljungqvist, F.C. 2010.
A new reconstruction of temperature variability in the extra-tropical northern hemisphere during the last two millenia.
Geografiska Annaler 92A(3):339-351.
Here for \$43, sorry (free abstract)
On Anthony Watts' blog, Craig Loehle argues that the paper is a vindication of his 2007 tree-less reconstruction in E&E. You don't need a 20-20 vision to see that the two (or three) are strikingly similar:

The data in TXT are here (FTP)

This is Lungqvist. Recall that the older Moberg (up) and Loehle (down) reconstructions looked like this:

In all the graphs, you see a pretty much linear warming up to the year 1000 AD or so (at least a few centuries before the year 1000 AD), followed by a linear cooling up to the year 1700 AD, followed by a linear warming up to the present. It's kind of interesting that the oscillating graphs are more similar to piecewise linear functions than the sines although the sines may look "more natural" to many of us.

None of the three graphs looks like a hockey stick. None of them paints the 20th century temperature dynamics as unprecedented.

There are some detailed differences between the three reconstructions, too. However, the agreement between Loehle and Ljungqvist in the years 900-2000 AD give r=0.85, a very high coefficient. It becomes worse if you try to go before the year 900. Of course, the further you go, the worse the agreement becomes.

However, fearmonger Grant Tamino Foster has raised an interesting objection. The first step in the comparison of the two graphs - that led Dr Loehle to conclude that a "vindication" has just been published - was that he shifted both graphs to have a vanishing long-term average.

Without a loss of generality, we may then talk about anomalies that are calculated as differences from the overall average temperature.

However, if you allow me to make Tamino's formulations more comprehensible, Tamino argues that the two temperature graphs should have been compared differently - namely by making their reconstructions of the "recent years" coincide (instead of making the long-term average coincide). These two procedures differ by a relative shift of the two graphs in the direction of the y-axis.

Tamino's objection sounds superficially reasonable because both Lungqvist and Loehle "know" what the temperatures did in the thermometer era, don't they? But is Tamino really right?

Even if he were right, it's clear that if you want to compare the detailed wiggles and time derivatives at various historical points in the past, it would be reasonable to try to match the graphs as closely as possible, so Loehle's step would be justified for this purpose, anyway. (You could also draw the derivatives and compare the graphs of the derivatives.)

But imagine that you really want to compare the whole reconstructions, and not just the character of the changes, by the most canonical "summed squared differences" method. If that's your goal, is Dr Loehle's first step justified?

This question may be asked differently: when you reconstruct the temperatures from the era of Jesus Christ, do you actually reconstruct the temperatures in °C at every point in the past, or do you just reconstruct these temperatures up to an unknown overall temperature shift?

Well, I think that the right answer is the latter. The reconstructions only reconstruct some kind of "temperature anomalies" (from the boreholes and other things you may imagine) but the overall additive shift in the y-direction remains unknown.

(Jeff Id has made a related point.)

So if you want to compare the anomalies reconstructed by the two reconstructions, and they're the only quantities that they really imply, you should minimize the deviation over possible relative temperature shifts in the y-direction - which is equivalent to requiring that the long-term averages of both graphs match.

I think that the idea that all the graphs of the reconstructions should be aligned in the instrumental period is - while not quite obviously flawed - an artifact of the hockey stick reasoning. Why?

Well, it's because if you use some non-thermometer data to reconstruct the past temperatures, your answers will differ from the actual temperatures. But what's important is that this is true even for the temperatures that you reconstruct in the instrumental period. So you must allow the errors of your reconstruction to be considered nonzero even in the instrumental period.

The hockey stick reasoning is equivalent to the denial the non-thermometer reconstructions may produce errors even in the thermometer era (and be sure that they do, especially if you look at the divergence problem etc.).

In this sense, I believe that Loehle's procedure of the comparison of the two reconstructions is valid even if you care about all the additive shifts that can actually be extracted from your reconstructions: one overall additive shift of the temperature is not reconstructed.

Of course, if you focus on some particular questions - such as the difference between the temperatures in the years 1000 AD and 2000 AD, and you compare these differences between Lungqvist and Loehle - you may get relatively large differences between the two reconstructions. However, this is a cherry-picked question. The years 1000 AD and 2000 AD have been cherry-picked.

If you want to compare the whole functions that follow from the reconstructions, you should sum the squared differences over the whole interval - but before you do so, you should first make the averages of both graphs to match because the overall additive shifts are not really implied by the procedures.

What do you think?

At any rate, I think it would be interesting to make pairwise comparisons between all these reconstructions - their correlations and other quantities. I don't have an easy access to all the data from the reconstructions so I can't turn this straightforward task into reality right now. Can you?