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Alternative calibration data sets

October 25, 2013

For the first time in a couple of years, there are some new modifications to the online exposure age and erosion rate calculators. This post describes the what, the why, and the how of these modifications, not necessarily in that order.

What? I’ve added input pages that permit calculating exposure ages using production rate calibration data sets that have been published after, and are different from, the 2008 calibration data set used in the calculators by default.

Why? Basically, the as-published-in-2008 version of the online exposure age calculators estimates the Be-10 production rate from a set of geological calibration data that includes what we believed to be all the production rate calibration data that were available at the time and that could be traced to an identifiable Be-10 measurement standard (the “2008 global calibration data set,” or “GCDS,” although this should not be confused with GCDS). Given the 07KNSTD Be-10 measurement standardization and the scaling scheme of Stone (2000), this calibration data set implied a reference spallogenic Be-10 production rate (1013.25 hPa, high latitude) of somewhere near 4.5 atoms Be-10/g quartz/year.

In the past few years, a number of researchers showed that this calibration data set generated exposure ages that were inconsistent with radiocarbon ages at a variety of field sites, mostly involving Late Glacial and early Holocene ice-marginal landforms. These inconsistencies are generally at the 10% level and thus not demonstrably significant given the relatively large (10%) stated uncertainties in the reference production rates described from the 2008 GCDS. However, in all cases these apparent exposure ages were younger than permitted by the radiocarbon age constraints, thus giving the general idea that the 2008 production rate estimates yielded systematically incorrect results in a fairly large range of important exposure-dating applications. This observation gave rise to the idea that it might be a better idea to not use the 2008 GCDS for many of these exposure-dating projects, but instead to generate a “local” calibration site by both radiocarbon dating and exposure dating a landform of similar location and age to the unknown-age landforms of interest. That is, if you want to date LGM moraines in New Zealand, work hard to find one LGM-age moraine that can be dated by both methods, infer average LGM-to-present Be-10 production rates from these data, and then use these production rate estimates to exposure-date other moraines in the region. In other words, treat cosmogenic-nuclide exposure-dating less like an absolutely calibrated independent dating method and more like a relative dating method pinned to the radiocarbon time scale. The key advantage of this approach is that you are minimizing production rate scaling — you are inferring production rates from sites that are close in paleomagnetic field characteristics, elevation, and age to the unknown-age sites you want to date. Thus, you are less subject to production rate scaling uncertainties than if you were extrapolating production rates inferred from a globally distributed set of calibration data to parts of location-age space that are not well represented by the calibration sites.

A number of studies have now espoused this “adopt a local calibration site” approach. Here are some examples:

Balco, G., Briner, J., Finkel, R.C., Rayburn, J.A., Ridge, J.C., Schaefer, J.M., 2009, Regional beryllium-10 production rate calibration for northeastern North America. Quaternary Geochronology 4, pp. 93-107.

Putnam, A.E. et al., 2010. In situ cosmogenic Be-10 production-rate calibration from the Southern Alps, New Zealand. Quaternary Geochronology 5, pp. 392.409.

Fenton, C. and 7 others, 2011. Regional Be-10 production rate calibration for the past 12 ka deduced from the radiocarbon-dated Grøtlandura and Russenes rock avalanches at 69° N, Norway. Quaternary Geochronology 6, pp. 437-452.

Kaplan, M. and nine others, 2011. In-situ cosmogenic Be-10 production rate at Lago Argentino, Patagonia: implications for late-glacial climate chronology. Earth and Planetary Science Letters, v. 309, pp. 21-32.

Goehring, B., and 6 others, 2012. Late Glacial and Holocene Be-10 production rates for western Norway. Journal of Quaternary Science, v. 27, pp. 89-96.

Briner et al., 2012, Constraining Holocene Be-10 production rates in Greenland. Journal of Quaternary Science, v. 27, pp. 2-6.

Young N.E., Schaefer J.M., Briner J.P., Goehring B.M., 2013. A Be-10 production rate calibration for the Arctic. Journal of Quaternary Science, v. 28, pp. 515-526.

So this approach is now pretty widely used. Overall I think this is an important and useful development — among other things, it’s resulted in a lot of progress in unscrambling the relative timing of climate changes and glacier advances in the Southern Hemisphere (see the Kaplan paper above for a summary of this). Conclusions about climate-glacier interactions in this region derived from exposure-age data are a lot more credible when one can also show that they are clearly consistent with radiocarbon chronologies for events that occurred at the same time.

More on “what”: To change the subject entirely, one of the overall principles we’ve used in deciding when to update the online exposure age calculator is that updates to constants, calculation methods, production rate calibration, etc., should reflect only published data. The upside of this policy is that everything that goes in is documented and traceable to published and publicly available data. The downside is that it takes a while for the calculator to catch up with new things that we learn. Thus, for a while it’s been the case that exposure ages generated by the online calculator (using the default 2008 GCDS) are demonstrably wrong (i.e., inconsistent with radiocarbon age constraints) in many cases. A few years ago I put some alternate data input pages on the “developmental” page of the calculator website that would allow calculation of exposure ages using alternative calibration data sets that were, at the time, unpublished. Now, of course, they’ve been published for a couple of years, so there is no point calling them “developmental” any more. Thus, there is now a link from the front page of the online calculator to a page that enables use of alternative published calibration data sets to compute exposure ages. These input pages use the same MATLAB code and calculation methods, but reference production rates are derived from different calibration data.

How? One important thing about these pages is that they list the reference (1013.25 hPa, high latitude) Be-10 production rates calculated from each of the calibration data sets. These differ by varying amounts from the reference production rates listed in the publications that describe the various calibration data sets; these differences are mostly at the < 1% to 3% level. Thus, the following describes where these differences come from. They exist because the calculation methods used by these authors to calculate reference production rates from measured Be-10 concentrations at sites of known age are not exactly the same as the calculation method used to compute exposure ages in the online calculators. Thus, I’ve recalculated reference production rates from the calibration data using the exposure-age calculation code that is actually in use in the online calculator. This insures internal consistency between calibration data and ages at unknown sites. Basically, the workflow is as follows:  take measured Be-10 concentrations at calibration sites, assume a reference production rate, and use this information with the MATLAB code that is used in the online calculators to calculate apparent exposure ages for the calibration samples. Determine the difference between these apparent exposure ages and the independently determined true exposure ages of the calibration samples. Adjust the reference production rate until this difference is minimized.

Most of the papers listed above used MATLAB code that is closely related to the code used in the online calculators to do this, so I generate reference production rate estimates that are close to within rounding error of those reported in the relevant publications. The main exception is the study of Fenton et al., who used a different age calculation method (cosmocalc). Thus, the production rate estimates quoted in their paper should only be used to compute exposure ages if you are also using cosmocalc to compute the ages — if you are using the online calculator code to compute exposure ages, then different values for the reference production rate are implied. The basic principle, as always, is to use the same calculation method in both directions — from calibration data to reference production rate and then from reference production rate to exposure ages of unknown samples.

And a conclusion: One conclusion that falls out of putting all this together is that all these studies wind up with the same reference production rate. According to the scaling scheme of Stone (2000),

Reference Be-10 production rate
due to spallation
 Who? Where? (atoms/g/yr) +/-
Balco et al. Northeastern North America 3.93 0.19
Putnam et al. New Zealand 3.84 0.08
Fenton et al. northern Norway 3.77 0.19
Kaplan et al. Patagonia 3.79 0.13
Goehring et al. west-central Norway 4.07 0.16
Young et al. Baffin Bay 3.93 0.15

To get the total reference Be-10 production rate, add 0.18 atoms/g/yr due to muon interactions. Basically, these are the same.



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