Rahmstorf et al. 2007 IPCC Error?

There appears to be an error in the influential paper by Rahmstorf et al. (2007). Rahmstorf et.al. (Science Brevia, 4 May 2007, p709 [1]) reports that the trend of the global mean of surface temperature and sea level raise concerns that the climate system “may be responding more quickly to climate change than our current generation of models indicates”. At least one major study, Interim Report of the Garnaut Review, relies on the paper for advocating prompt and extreme action on carbon emissions, one of its major conclusions (Section 2.4 Consequences of Climate Change, Observed Climate Change). But there seems to be a problem.

As previously reported here, the conclusions of Rahmstorf’s 7 (Rahmstorf, Cazenave, Church, Hansen, Keeling, Parker, and Somerville) rely on a trend line lying above the IPCC projections on their Figure 1, shown enlarged below. No statistical tests are performed, the basis for their claim is purely based on the visual aid. Their Figure 1 is below, with the key part of the image containing the IPCC projection enlarged.

Figures 1 and 2: Rahmstorf et al. (2007) Figure 1. Whole and enlarged.

Rahmstorf’s 7 state in the figure caption that “All trends are nonlinear trend lines and are computed with an embedding period of 11 years and a minimum roughness criterion at the end (Moore et.al. 2006 [2])”. On reading Moore’s paper, it would appear the nonlinear methodology used was Singular Spectrum Analysis (SSA). The Moore paper suggests the minimum roughness criterion (MRC) would follow the Mann 2004 [3] recipe of padding the end of the series with data reflected about the final value.

Figure 3 and 4: GISS temperature with SSA trend, unpadded and padded.

The peculiar property of MRC of “pinning” the trend line to the final end point of the series has been noted in a post “Mannomatic Smoothing and Pinned End-points” at ClimateAudit.

The comparison of MRC and non-MRC padded series is shown in figures captured from CaterpillarSSA. The first figure “unpadded.png” shows a SSA trend line that approximates the Rahmstorf figure result. The second figure “padded.png” shows the SSA trend line with an MRC padded GISS series, passing directly through the 2006 value. This is as it should be, as the MRC effectively ‘pins’ the trend line to the final value due to the symmetry about the final value.

Was a direct application of the SSA trend line used and not an MRC padded series as described?

If an MRC padded series had been used in the figure, it would have been end-pinned to the 2006 value, at the center of the IPCC projections. The figure would then not have conveyed the impression that temperatures are in the upper range of the IPCC projections, as claimed.

As it was in 2006, it appears that SSA without MRC padding produces a higher trend line than with MRC padding, necessary for supporting their claim.

An additional puzzling factor is the reference to MRC padding at all. Padding the end of the series is not actually necessary to ensure a SSA trend line is drawn to the end of the series values. Padding is only necessary in acausal filters such as moving averages that stop a window length short of the end of the series.

To date, attempts to contact Prof. Rahmstorf and clarify the actual methodology used have been unsuccessful.

References

[1]Stefan Rahmstorf, Anny Cazenave, John A. Church, James E. Hansen, Ralph F. Keeling, David E. Parker, and Richard C. J. Somerville. Recent Climate Observations Compared to Projections. Science, 316(5825):709–, 2007.

[2] A. Grinsted Moore, J.C. and S. Jevrejeva. New tools for analyzing time series relationships and trends. Eos, 86(24), 1995.

[3] M. E. Mann. On smoothing potentially non-stationary climate time series. Geophys. Res. Lett., 31:L07214, doi:10.1029/2004GL019569 2004.