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Stone (2000) revisited

February 5, 2019

This is just to tie up a loose end from a previous post in which I argued that a compilation of Be-10 and Al-26 concentrations in extremely old, low-erosion-rate surfaces from Antarctica indicated that the time-dependent, paleomagnetically-aware “LSDn” production rate scaling method of Lifton and others did a better job of production rate estimation than the non-time-dependent “St” scaling method of Lal (1991) as implemented by Stone (2000). Basically, the difference is the altitude dependence of the production rate. Tying up this loose end is an interesting exercise in data archaeology, and also highlights some evidence that either the Al-26 half-life or the Al-26/Be-10 production ratio may need some attention.

The issue in the previous post is just that in the St scaling method, the production rate increases more slowly with elevation in polar latitudes, with the result that many high-elevation Antarctic samples have measured Be-10 concentrations that are higher than saturation concentrations predicted by that scaling method. With LSDn scaling, predicted production rates at high altitudes are higher, so all the observed concentrations are near or below predicted saturation.

However, as I pointed out in the previous post, the 2000 paper already looked at available near-saturation data from Antarctica, and that paper concluded the opposite: that near-saturation measurements from Antarctica were consistent with the scaling method proposed in that paper. This was an important conclusion at the time, that was extremely persuasive in the adoption of lower production rate estimates and the abandonment of the standard atmosphere as a single global elevation-pressure conversion. However, lots of stuff has changed between the two comparisons. Errors in Be-10 measurement standardization were corrected by Nishiizumi and others (2007) and related work. The Be-10 half-life was remeasured, and remeasured again. Large amounts of new Be-10 and Al-26 production rate calibration data have been collected. Everything is different. So figuring out whether what the 2000 paper says is still valid is really complicated. But, let’s try anyway. It’s probably not worth the effort to explore the result of each individual one of those changes, but it’s possible to use the ICE-D:ANTARCTICA database and the latest version of the online exposure age calculator to look at the effect of the last 18 years of progress together. 18 years is a while, so hopefully there has actually been some progress.

First, a review of the original discussion. Here is the relevant figure from the 2000 paper.

This shows selected Be-10 and Al-26 data from Antarctica plotted on a two-isotope diagram. The simple exposure region — that is, the part of the diagram where it is physically possible for concentrations to lie given a single period of steady exposure at some surface erosion rate — is the region outlined by solid black lines. The point marking the right-hand boundary of this region is the saturation endpoint: concentrations cannot lie to the right of this point, or above the upper boundary of the region. Potentially, concentrations could lie below the region if sites had been ice-covered for a time, but the majority of these sites are from mountain summits that are unlikely to have experienced ice cover in the past. In the original paper, the point of this figure was to show that certain combinations of Be-10 production rates and scaling methods produced either unphysical results (like in the upper left panel where many concentrations lie above the simple exposure region) or unlikely ones (as in the upper right panel where all concentrations imply significant burial). On the other hand, the scaling approach proposed in the paper for Antarctic sites, shown in the lower left panel, produced plausible and physically possible results.

Now, if you believe my previous posting, changes in Be-10 standardization and production rate scaling in the subsequent 18 years have superseded these results: when we take these into account, the “St” scaling method actually forces concentrations to lie outside the simple exposure region. So, let’s try to reconstruct this diagram with our current best estimate of all this stuff.

Step 1 is to figure out which samples are involved. The 2000 paper doesn’t list sample names, but describes the sample set only as “Antarctic Be-10/Al-26 data from Nishiizumi et al. (1991), Ivy-Ochs et al. (1995), and Brook et al. (1995), selected to show the oldest exposure ages in each data set.” We can make a decent estimate of figuring out which samples these are using the ICE-D:ANTARCTICA database; choosing the highest-concentration samples from the three 1990’s papers yields this set of samples. We can then replicate  the figure from the 2000 paper using the following tools. One, the various scaling method implementations in version 3 of the online exposure age calculator described by Balco et al. (2008) and subsequently updated., specifically the “St” scaling method, which is an implementation of the method originally described in the 2000 paper, and the “LSDn” scaling method developed by Lifton and others in 2014-16. Two, the CRONUS “primary” production rate calibration data sets for Be-10 and Al-26. Three, the Be-10 and Al-26 standardization relationships used in the online exposure age calculator and tabulated here. With these ingredients and the “St” scaling method as implemented in the online exposure age calculator, the figure from the 2000 paper now looks like this:

The important change is now that at least two, and probably more, of the measurements exceed the saturation endpoint. They plot in the impossible region of the diagram to the right of the simple exposure region. So this answers one question: yes, trying to repeat the Stone (2000) calculation with the same data, but revised measurement standardizations and production rate calibration does, in fact, support the argument that this scaling method underpredicts elevation scaling at the poles. Primarily, what has happened here is that once everything has been corrected for measurement restandardization, new production rate calibration data imply a lower production rate than the best estimate at the time, so Be-10 concentrations are relatively higher in comparison to predicted saturation concentrations. Of course, we knew this already, but recalculating all these data is actually a fairly difficult test of whether the entire web of restandardization and recalibration is internally consistent. It seems to work, which is good.

For completeness, we should also try this with the latest “LSDn” scaling. Here is the result:

As discussed in the previous post, this scaling method predicts higher production rates, which pulls all the normalized Be-10 concentrations back to the left into the region of the possible. So from the perspective of Be-10 production rates, as discussed in the previous posting, this seems to show that LSDn scaling works: Be-10 concentrations are all at least a little bit below predicted saturation. However, both results, and in particular the LSDn result, are really interesting from the perspective of Al-26 production rates, because they imply that all these sites lie in the region of intermittent burial, below the simple exposure line, and thus have been covered by ice for significant parts of their exposure history. Of course, ice cover is not exactly unusual in Antarctica, but these samples, especially those from the Ivy-Ochs and Brook papers, are mostly from high-elevation mountaintop sites where ice cover is very unlikely to have occurred at any time. So this is consistent with the observation in the previous post that Al-26 concentrations throughout Antarctica are systematically lower with respect to predicted saturation than the corresponding Be-10 measurements, which probably indicates that something related to Al-26 is not as we expect. Note that we can’t fix this just by lowering production rates together (the difference between upper right and lower left panels in the original figure), because that would force Be-10 concentrations too far to the right — which tends to indicate that Be-10 is probably fine, and our problem likely has something to do with Al-26. Although of course it is hard to exactly reconstruct what happened to Al-26 measurements 20 years ago, there is not an obvious means by which Al-26 measurement standardization errors would cause this effect. In addition, we can look at more recently collected Al-26 data, for example recent unpublished measurements by Perry Spector at the Whitmore Mountains, and we get the same result. Here are some of the Whitmore Mountains data with LSDn scaling:

Same story. Be-10 concentrations at (or in this case maybe slightly beyond) the predicted saturation endpoint, but Al-26/Be-10 ratios significantly below that predicted for saturation. So if we can’t explain the problem with measurement standardization errors (and we’re pretty sure the Al-26 measurements were done right), this leaves two possibilities. First, the Al-26 half-life might be shorter than we think it is. This is possible: existing measurements of the Al-26 half-life might leave room for as much as a 3-5% inaccuracy, which could account for most of the apparent burial for these samples. If this is the answer it would imply an Al-26 half-life near 675 ka…but although this is technically within the uncertainty of some of the direct measurements of the half-life, it’s substantially lower than any of them. Second, we might be overestimating the Al-26/Be-10 production ratio, although fully accounting for apparent burial without changing the half-life would require the production ratio to be 6.3, which is lower than the mean ratio at moderate elevations allowed by currently available data, but not totally outside the range of the data. Certainly, though, the data set of near-saturation measurements from Antarctica are not at the moment consistent with proposals that the 26/10 production ratio is significantly higher than 6.75. But in any case, this seems to indicate that it’s probably worth taking another look at the highest Al-26 concentrations in Antarctica, perhaps making a systematic effort to remeasure Al-26/Be-10 ratios in the highest exposure-age samples, and maybe even looking into the Al-26 half-life.

Summary: recalculating the results in Stone (2000) to incorporate 18 years of work on measurement standardization and production rate calibration does, in fact, support the hypothesis that LSDn scaling performs better at scaling existing calibration data to high-elevation, high-latitude sites, at least for Be-10. It’s also relevant that we seem to actually be doing a decent job of systematically applying the improvements: adjusting 20-year-old data and calculations for all the subsequent changes in standardization and scaling seems to produce internally consistent results. That’s good. However, looking carefully at the data set of near-saturation measurements from Antarctica indicates that maybe the Al-26 half-life and the Al-26/Be-10 production ratio need some attention.

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