Over the past few days, it has become clear to me that the entire issue of “flipping” or “upside-down-ness” of the Tiljander proxy is a red-herring.
Imagine a climate proxy, accurate over the last 2kyr, that shows (for example, let us suppose) a warm period around 1000 AD and which, undisturbed, would show the recent warming. Further suppose for definiteness that this proxy is of such a nature that increases in the proxy value represent increases in temperature. Imagine this proxy is contaminated with non-climatic signal over the last 200 years, enough that the climatic signal is overwhelmed. Suppose that this contamination is of such a nature that it leads to a strong decrease in the values of the proxy over the last 200 years. Such a proxy (call it A), fed into the Mea algorithm, will be flipped over (due to its negative correlation with recent instrumental temperature) and will contribute a net cold influence around 1000 AD. How much it contributes will depend on how well it correlates to recent times.
Now imagine a similar proxy, except the nature of the non-climatic contamination is such as to add a strong increase over the last 200 years. We’ll call it B. This time, the proxy won’t be flipped over, because its correlation to recent times will be positive. But the variance into the past will be strongly de-weighted (because we’ve just added an artificially large postiive trend). So it will imply not much change around AD 1000. But now we see this, we can see that the same problem applies to series A: unless, by bizarre co-incidence, the negative non-climate signal just happens to match the true positive instrumental signal, the variance in the past will be wrong. And since we’ve had to assume that the non-climate signal overwhelms the climate one, its likely that the recent variance will be too large, so the past will be de-weighted.
So in either case we can see that the real problem is the addition of the non-climate signal. The flipping is of little relevance.
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