This is part of my critical review of the palaeoenvironmental evidence for the influence of solar activity on climate.

**Galloway, J.M., Wigston, A., Patterson, R.T., Swindles, G.T., Reinhardt, E. & Roe, H.M. (2013) Climate change and decadal to centennial-scale periodicities recorded in a late Holocene NE Pacific marine record: Examining the role of solar forcing. Palaeogeography, Palaeoclimatology, Palaeoecology**

*Cyclotella choctawhatcheeana* might not be the prettiest or most pronounceable of diatoms, but it is one of the most important taxa in Galloway et al, who publish a diatom stratigraphy from a fjord in British Columbia and use wavelets to find relationships between proxies and solar activity.

As with most attempts to find a solar signal in palaeoenvironmental data, the chronology is crucial. Galloway et al have nine radiocarbon dates from terrestrial macrofossils (wood fragments, twigs and cones) on their 12 m long core which spans 1100-4400 yr BP. This seems like a reasonable number of dates for this time window, and terrestrial macrofossils should give dates unaffected by marine reservoir effects. Unfortunately, four of the nine dates are rejected as outliers by the bacon age-depth modelling procedure. This is not good.

The reported median chronological uncertainty is ± 240 years (presumably 95% interval). The too-young date at 734 cm makes me suspect that there may be unresolved problems with this chronology and that the true uncertainty is much larger than that reported: bacon has chosen a set of five dates through which it can fit a model, it does not guarantee that these dates are correct.

The age-depth model also underestimates uncertainty as “no corrections were made for different sedimentary facies” and the core has a complex sedimentary stratigraphy with laminated sediments, massive sediments, sand lenses, and graded sediment interpreted as high-energy environment. It is simply implausible that all these facies have the same sedimentation rate, so the chronology will be wigglier than apparent from the fitted model. Making corrections for these different facies would require many times as many dates as the authors have available: this core is not conducive to generating a good age-depth model.

Galloway et al interpret that the massive sediment facies, which constitute 44% of the core, as being “deposited by transfer of sediments from fjord sides and/or by re-suspension of basin sediments initiated by localized failure of sediments on the walls of the fjord.” I would be immensely cautious analysing proxies from a core like this where the proportion of reworked material might be changing dramatically down core.

Galloway et al run their numerical analyses on the total diatom abundance, biogenic silica (representing diatoms and other siliceous microfossils) and grain size. With REDFIT, they find a host of significant frequencies in their proxies in the broad bands of frequencies in the reconstructed sunspot record from Solanki et al. (2004). For wavelet analysis, the data are interpolated to a regular interval. The length of the interval is not given, but this is critically important, it would be trivial to interpolate the data to 1 year resolution, which would hugely inflate the apparent number of observations in the wavelet analysis, and give an enormous risk of Type 1 errors, identifying noise as statistically significant patterns. The interpolation may not have been this extreme, but since the time axis on the wavelet plot goes down to 2 years, I do wonder what was done.

There follows a cross-wavelet analysis of the proxies against solar activity. Maraun and Kurths (2004) warn against using the wavelet cross-spectrum, recommending wavelet coherency instead.

“[wavelet cross spectrum] describes the common power of two processes without a normalization to the single [wavelet power spectrum]. This can produce misleading results, because one essentially multiplies the [continuous wavelet transformation]s of two time series. E.g. if one of the spectra is locally ﬂat and the other exhibits strong peaks, this can produce peaks in the cross spectrum, which may have nothing to do with any relation of the two time series. Thus, [wavelet cross spectrum] is not suitable for signiﬁcance testing the relation between two time series.”

What will the effect of the chronological uncertainty on the wavelet analysis be? Lenoir and Cruciﬁx (2012) [abstract only] have been working on this problem, and I’m keen to read what they find when they publish a paper.

The wavelet transforms of the individual proxies will be affected by chronological errors. If the age-depth model is simply offset from the true age, there is no problem — the wavelet transform will be correct, abet time shifted. If the estimated sedimentation rate is uniformly too high or low, the frequencies in the wavelet transform will be shifted, but otherwise correct. Real problems arise if the error in the apparent sedimentation rate varies, sometimes too low, sometimes too high. This will disrupt harmonic patterns in the data that are at the same scale as the changes in sedimentation rate.

When using wavelets to compare two time series, the problems get worse, as now the absolute age and mean sedimentation rate also matter. If the age is wrong, then the wrong parts of the time series will be compared, if the sedimentation rate is wrong, then the wrong frequencies will be compared (this is probably a secondary issue). Because wavelet transforms are smooth in time and frequency, small chronological errors might not matter too much, but if the chronological errors are large relative to the duration of peaks of high power, then the real relationship may be missed, and spurious ones found.

The problems are even worse for the phase relationship between the two time series. If there is a physical relationship between the proxies and solar activity, there should be a consistent or slowly varying phase relationship (Grinsted et al 2004). Phase relationships could be scrambled by chronological errors. In this core, the median chronological uncertainty is (at least) ± 240 yr, so the uncertainly on the phase due to the chronology alone when the period is 480 yr will be ± 180° (i.e any phase is possible). Shorter periods are likely to be completely scrambled and only for very long periods does the phase uncertainty become small.

**Conclusions**

Because of the chronological uncertainty, the complex sedimentation, and the lack of key details in the methods, Galloway et al does not provide credible evidence of a solar-palaeoenvironmental link.

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