# How not to attribute climate change

In an earlier post, we discussed a review article by Frohlich et al. on solar activity and its relationship with our climate. We thought that paper was quite sound. This September saw a new article in the *Geophysical Research Letters* with the title «Phenomenological solar signature in 400 years of reconstructed Northern Hemisphere temperature record» by Scafetta & West (henceforth referred to as SW). This article has now been cited by US Senator James Inhofe in a senate hearing that took place on 25 September 2006 . SW find that solar forcing accounts for ~50% of 20C warming, but this conclusion relies on some rather primitive correlations and is sensitive to assumptions (see recent post by Gavin on attribution). We said before that peer review is a necessary but not sufficient condition. So what wrong with it…?

The greatest flaw, I think, lies in how their novel scale-by-scale transfer sensitivity model (they call it “SbS-TCSM”) is constructed. Coefficients, that they call *transfer functions*, are estimated by taking the difference between the mean temperature of the 18th and 17th centuries, and then dividing this by the difference in the averages of the total solar irradiances for the corresponding centuries. Thus:

Z = [ T(18th C.) – T(17th C.) ] / [ I(18th C.) – I(17th C.) ]

Here T(.) is the temperature average for the century while I(.) is the irradiance average. If the two terms, I(18th C.) & I(17th C.), in the denominator have very similar values, then the problem is ill-conditioned: small variations in the input values lead to large changes in the answers; which implies very large

error bounds. In my physics undergraduate course, we learned that one should stay away from analyses based on the difference between two large but almost equal numbers, especially when their accuracy is not exceptional. And using differences of two large and similar figures in a denominator is asking for trouble.

So when SW repeated the exercise for the differences between the 19th and 17th centuries, and for three different estimates of the total solar irradiance, the results gave a wide range of different values for the transfer functions: from 0.20 to 0.57! The problem is really that SW assume that *all* climatic fluctuations in the 17th to the 19th centuries to solar activity, and hence neglect factors (natural forcings) such as landscape changes (that the North America and Europe underwent large-scale de-forestation), volcanism (see IPCC TAR Fig 6-8), and internal variations due to chaotic dynamics. It is, however, possible to select two intervals over which the average total solar irradiance is the same but not so for the temperature. When the difference in the denominator of their equation is small (the changes in the total solar irradiance are small), then the model blows up because other factors also affect the temperature (i.e. the difference in temperature is not zero). Thus their model is likely to exaggerate the importance the solar activity.

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