Last week, I posted on the effect of ex post site selection on the Gulf of Alaska tree ring chronology used in Wilson et al 2016 (from Wiles et al 2014). An earlier incarnation of this chronology (in D’Arrigo et al 2016) had had a severe divergence problem, a problem that Wiles et al had purported to mitigate. However, their claimed mitigation depended on ex post selection of modern sites that were 800 km away from the original selection.

Even with this ex post selection, I could not replicate the supposed mitigation of the divergence problem, because Wiles et al had not archived all of their data: it appeared that their ex post result depended on still unarchived data. Subsequent to my post, Greg Wiles commendably archived the previously missing Wright Mountain (but, unfortunately, neglected to archive the update to Eyak Mountain leaving the data less incomplete but still incomplete.)

The new data confirms my suspicion that the “missing” Wright Mountain data was inhomogeneous: it turns out that the average Wright Mountain RW was 21% higher than the average RW value from other modern sites. Because Wiles et al used RCS with a single regional curve, the inclusion of this inhomogeneous data results in higher recent values. By itself, the Wright Mountain data doesn’t actually go up in the last half of the 20th century, but inclusion of the inhomogeneous data translates the chronology upwards relative to subfossil data. In the Calvinball world of RCS chronologies, the handling of inhomogeneous data is determined after the fact, with RCS chronologers seeming to be extremely alert to inhomogeneities that yield high medieval values (e.g. Polar Urals), but rather obtuse to inhomogeneities that yield high modern values, with decisions on site inhomogeneity always being made ex post. All too often, medieval-modern comparisons rest on Calvinball decisions, rather than the integrity of the data.

In today’s post, I’ll use the random effects techniques (consistently recommended at CA) to try to provide a structured consideration of this example.

Wiles, NLS and LMER Chronologies

Figure 1 below shows the Wiles et al chronology (top panel), the residual chronology from an nls model applied to available data, including the hot-off-the-press Wright Mountain data (middle panel) and the random effects chronology from an lmer model, also from available data (bottom panel). In each case, I’ve marked the 750-1400 average with a horizontal dashed line to facilitate medieval-modern comparison. All three series are obviously closely related, but notice the differences in the 20th century location in the three versions. More commentary below the figure.

Figure 1. Gulf of Alaska RCS versions. Top – Wiles et al 2014 (used in Wilson et al 2016); middle – nls on available data; bottom – lmer on available data. The 750-1400 average is marked with a horizontal dashed line.

Wiles et al stated that they used a single regional curve in their RCS calculation. In general, an RCS chronology calculated with a single regional curve can be closely replicated with a simple nls model. Obviously, the shape of the nls chronology (middle panel) is very similar to the shape of the Wiles chronology, with the only material difference being the 20th century level: in the nls chronology, the 20th century level is similar to the 750-1400 average, whereas the 20th century in the Wiles chronology result is above the 750-1400 average. I suspect that this difference is due to the effect of still unarchived Eyak Mountain data rather than methodology. If and when Wiles archives the balance of the Eyak Mountain data, I’ll re-visit this calculation.

However, of considerably more interest, in my opinion, are the results of the lmer chronology (bottom panel). As explained in a recent post here ^, the lmer statistical technique calculates a random effect for individual sites and for each year. This is my preferred technique for trying to disentangle the separate impact of site inhomogeneity and annual effect. It is a technique that directly relates to known statistical methodology. In this case, the inhomogeneity of the Wright Mountain data is accommodated through the random effect for individual sites.

The result here is interesting: while the high-frequency shape of the lmer chronology is virtually identical to the Wiles chronology, 20th century values, while higher than 19th century values, remain below the average of the medieval period. Conversely, the so-called mitigation of the divergence problem that was claimed by Wiles et al proves to be a mirage: it depends entirely on the inhomogeneity of the recently archived Wright Mountain data.



