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Let a hundred flowers bloom

August 1, 2016

This post is about the current proliferation of online exposure age calculators. Summary: good thing. Details: complicated.

Here is a short summary of the situation. Actually, it’s a long summary. But I can’t make it any shorter.

2008-v2. The initial online exposure age calculator at, also sometimes referred to by the deeply unfortunate and ill-conceived nickname “Balculator” after the first author of the accompanying paper, dates from 2008 and reflected current thinking at that time about how best to compute exposure ages. The initial funding for me to develop it (a Linux server and several months of postdoctoral salary) came from the then-just-beginning, NSF-funded “CRONUS-Earth” project, so it has also been widely known as the “CRONUS calculator;” however, as discussed below, this is no longer quite accurate. To avoid confusion in the rest of this post, I’ll refer to it here as “the 2008-v2 calculator,” because at the time it entered widespread use it was denoted by this version number, which is often reported in papers and other downstream uses.

Aspects of this calculator that have subsequently turned out to be important are twofold. First, it includes five different production rate scaling methods, two based on the work of Devendra Lal (“Lal-based schemes”) and the rest on later interpretation of more recent neutron monitor data (“neutron-monitor-based schemes”). This  probably excessive diversity was simply because at the time no one knew which one worked better. Second, reference production rates for Be-10 and Al-26 were based on a compilation of currently available calibration data (the “2008 global calibration data set”).

Between 2008-2015 there were several changes to this calculator that were the result of discoveries that various parameter values in version 2 were incorrect.

2008-v2.2. This revision (in 2009) made the important change that users were now required to enter information about isotope ratio standardizations used for Be and Al AMS measurements. The details of this are a giant can of worms that you can learn about here. Interestingly, this turned out to be a really effective example of incentive-based behavioral engineering in that users were successfully induced to solve a messy and unpleasant problem (standardization-related confusion) by being presented with an incentive to do so (the opportunity to outsource all the hard work of exposure age calculations to the online calculator). Also, a subsequent 2.2.1 revision changed a few parameter values, most notably the Be-10 decay constant, that had only minor effects.

2008-v2.2 with alternate production rate calibration data sets. Shortly after 2008, it became clear, from new production rate calibration data that were being generated, that the 2008 global calibration data set was simply wrong, predicting Be-10 and Al-26 production rates that were approximately 10% too high. The reasons for this are diverse and not entirely clear in some cases, but the overall result is quite clear. Although this was basically a non-issue for most applications of erosion rate calculations, it was a big issue for exposure-dating (for example, because the ages of the Younger Dryas and the Antarctic Cold Reversal differ by about 10%). To deal with this issue, I added features to the 2008-v2.2 calculator, mainly the capability to enter arbitrary production rate calibration data, use them to generate a best-fitting value of the reference production rate, and then use this production rate value to determine exposure ages at unknown-age sites. In addition, I carried out this exercise for a variety of published alternatives to the 2008 global calibration data set and made them available as distinct data entry pages. Thus, although the erroneous 2008 calibration data set was still presented as the default means of calculating exposure ages, the availability of other calibration data effectively solved this problem for most practical purposes.

This version (2008-v2.2 with various calibration data sets) has been widely used between ca. 2009 and the present.

Results of the CRONUS-Earth project.  Starting in 2014, results of the now-completed “CRONUS-Earth” project began to become available. Of these results, the ones most relevant to the issue of online exposure age calculators are as follows.

1. Calibration data. A lot more calibration data now exist, and they continue to indicate that the 2008 data set gives incorrect results.

2. Scaling schemes. It is now clear that the neutron-monitor-based scaling schemes are inaccurate, for reasons to do with how neutron monitors work. Nat Lifton and colleagues have put together a new class of scaling scheme based on particle transport models (“Sato-based schemes” after the author responsible for the particle transport modeling) that works better. Both Lal-based and Sato-based schemes appear to work indistinguishably well for most practical purposes, although they are not indistinguishable — they make different predictions for some situations.

3. Muons. We have better estimates of muon interaction cross-sections. This is only marginally relevant for surface exposure dating, but has a nonzero effect on erosion rate calculations.

Of these results, only (1) above has been dealt with at all in the 2008 calculator framework. Thus, at this point we have the situation where the 2008-v2.2 calculator includes incorrect default calibration data, scaling schemes that we know to be inaccurate, and muon interaction cross-sections that we know to be wrong. The calibration data issue can be fixed by use of alternate data sets, but not the others.

CRONUS-2016. In 2015-2016 (the accompanying paper is dated 2016), Shasta Marrero, Brian Borchers, and Rob Aumer put together a new online calculator, intended as one of the capstone products of the overall CRONUS project, that is here. Thus, this product is now the “CRONUS-Earth online exposure age calculator,” and, if one can learn from history, will presumably in future also be known as the “Shastalator” or “Marrerolator.”

One implication of this is that it appears that the 2008-v2.2 calculator is no longer the “CRONUS calculator.” Therefore, in homage to Prince, the 2008-v2.2 calculator will henceforth be known as “The online exposure age calculator formerly known as the CRONUS-Earth online exposure age calculator.”

The CRONUS-2016 calculator has the following features.

  1. Even more scaling schemes. Sato-based schemes (n = 2) have been added to the existing Lal-based (n = 2) and neutron monitor based (n = 3) schemes from 2008. Thus, n = 7.
  2. More complex code. More physical processes are represented in the code.
  3. More nuclides. It is possible to compute exposure ages not only for Be-10 and Al-26 measurements, but also C-14, He-3, and Cl-36.
  4. No shortcuts with respect to numerical precision. The 2008 code takes many numerical shortcuts to speed up calculations that maintain acceptable accuracy for surface exposure dating purposes, but sacrifice some capabilities, such as, for example, the ability to accurately calculate subsurface production rates. These shortcuts are not taken in the 2016 calculator.
  5. Default production rate calibration data derived from recent work.

Items 1-4 above were done for an important reason: the code that the online interface is running was designed also for quantitative testing of all known scaling schemes against all known calibration data (see this paper), and clearly in carrying out such an exercise it is important to take numerical imprecisions and unphysical shortcuts out of the picture. However, the downside of these features is that the code is quite slow; instead of immediate return of results via the web server as in the 2008-v2.2 calculator, the input page of the CRONUS-2016 calculator starts an often-fairly-time-consuming compute job on the server, which emails you the results at a later time when the job is complete.

2008-v2.3. At present, despite the existence of the CRONUS-2016 online calculator, there is still quite a lot of user demand for the 2008-v2.2 calculator, presumably for the following reasons. One, folks are used to it, so it is like a pair of nice fuzzy old socks. Two, it is faster than the CRONUS-2016 code. Three, it facilitates use of non-default calibration data. Possibly, four, it has a web service API. This is all fine, but as noted above, the 2008-v2.2 code perpetuates three major errors: incorrect default calibration data, incorrect scaling schemes, and incorrect muon interaction cross-sections. Thus, I have put together a version 2.3 that mitigates two of these. Specifically, the default production rate calibration data set is now the same (the “CRONUS primary data set” of Borchers and others, 2016) as is used in the CRONUS-2016 calculator, and the muon interaction cross-sections are also updated to reflect calibration data also from that paper. What’s not fixed is that the neutron-monitor-based scaling schemes (now obsolete) are still there, and the Sato-based scaling schemes are not there. However, if you can ignore the neutron-monitor-based scaling schemes, this update removes everything from the 2008-v2.2 code that we actually know to be incorrect. Thus, for most practical purposes the 2008-v2.3 calculators can be used for surface exposure dating with equivalent accuracy to the CRONUS-2016 calculators. Version 2.3 is now the default version at However, it will not be updated further, but, hopefully, instead replaced by:

v3. The v2.3 update doesn’t fix the scaling scheme issue, and in addition it would be nice if the 2008-v2.2 calculators could be used at least for the other primarily spallogenic nuclides (C-14, He-3, and Ne-21), even if not Cl-36 yet. To deal with these issues, there now exists a developmental version 3 of the online exposure age calculators formerly known as the CRONUS calculators, which is here. The design principle of the v3 calculator is to do only exposure-age and erosion-rate calculations for surface samples, but to do them as fast as possible while maintaining acceptable accuracy for these purposes. Thus, it includes a highly streamlined version of  Sato-based scaling that works by interpolation of precalculated gridded data and runs a couple of orders of magnitude faster than the code in the CRONUS-2016 calculator. Muon production systematics are also highly simplified. In addition, the v3 calculator ingests Be-10, Al-26, C-14, Ne-21, and He-3 data for various mineral targets (simultaneously, and also does the multiple-nuclide plots, which is fun). At the date of this writing, I believe it works correctly, but it hasn’t been extensively checked and one should expect that it will be modified fairly often in the near future.

The ICE-D database. One motivation for developing a fast v3 calculator is to facilitate the development of online databases of both exposure-age data and production rate calibration data, such as those here and here. As discussed in other posts, the idea of these databases is that they pretty much make the current approach to online exposure age calculators obsolete, because raw observational data such as nuclide concentrations lives behind the scenes in a database and exposure-age calculations happen dynamically and transparently when viewing the data. This completely deals with the problem of comparing published exposure-age data that were calculated inconsistently. But for it to work, the calculations have to be fast. Hence the need for v3. At present, the developmental v3 code is the back end for the ICE-D database.

Another goal of this database development is to improve how we deal with production rate calibration data. The idea of the ICE-D production rate calibration database is that it represents a compilation of up-to-date production rate calibration data that is generally believed to be complete and accurate, and can be available to whatever online calculator system wants to use it. This overall principle was one of the motivations for…

CREp. This is a new online exposure age calculator put together by Leo Martin, PH Blard, and their colleagues at CRPG in France, that is here. It includes Lal-based and Sato-based scaling schemes and has a large range of options for production rate calibration data sets that are derived from the ICE-D calibration database. This is a good step towards solving the data-assimilation problem for production rate calibration data (which continues to be steadily generated)…theoretically, as we add new data to the ICE-D database, it should be immediately available to the CREp online calculator. CREp also has by far the most attractive user interface (although unfortunately this is not a very high bar).

To summarize. The current situation features at least four different options for online exposure age calculations. One and two, the online calculators formerly known as the CRONUS calculators — the 2008-v2.3  and v3 calculators at Three, the CRONUS-2016 calculator. Four, CREp. Five, the ICE-D database, although as noted above that is just using the v3 code as the back end.

I think this is great.

I should note that there is not universal agreement on this being great. Some members of the CRONUS project envisioned something very different — that an eventual capstone result of the overall project would be a single online calculator that was used by all researchers everywhere as a de facto universal standard for exposure-age calculations. That is the vision described in this paper, which suggests the appointment of an international advisory committee to oversee a single online calculator and issue recommendations for best practices. I think this is a bad idea. In my view, the main value of the CRONUS project is that it generated a really large quantity of valuable information that is relevant to exposure-age calculations and production rate scaling. I think the best possible outcome of generating all this data is that a wide variety of people, whether associated with the original project or not, use it in whatever way they think is best to do whatever research they want to do, and to improve the state of the overall science. Ideally, instead of one committee-approved online calculator, we should have a whole bunch of online calculators that can compete based on their own merits. And that’s what seems to be happening. I think that’s really good.

However, this situation does create a couple of new problems.

One is more general. The question is, how are these things actually going to compete on their own merits? At present, certainly they can compete on the basis of ease of use and general attractiveness. However, really we would like for them to compete on the basis of some sort of quantitative performance metrics that reflect their speed, accuracy, and usefulness for whatever the needed application is. For this to happen, there needs to be some way to easily and transparently quantify the relative performance of different options. This is one important potential function of the ICE-D calibration database: to make the data needed for benchmarking and performance assessment of calculation methods in an easy and straightforward way. Actually making that process straightforward and transparent is more complicated, but at least that is a start.

The second problem is more specific. If I need to calculate some exposure ages right now, what do I do? The answer to this is fairly simple. It doesn’t matter very much which of the four options you use. There are only two things you need to remember. One, don’t use the neutron-monitor-based scaling schemes. Use the Lal- or Sato-based ones. These both work and are effectively equivalent for nearly all practical purposes. Two, which production rate calibration data set you use is much more important than which exposure age calculator you use. If you use the different calculators with the same calibration data, you should get indistinguishable (i.e., differing at less than measurement uncertainty) results in nearly all cases. Much more important, as always, is to completely record all the raw observations needed to compute the exposure ages in your papers, so that readers can recalculate the exposure ages themselves with different methods or calibration data as needed.


4 Comments leave one →
  1. shastamtn permalink
    August 1, 2016 20:19

    This is a great summary – it’s nice to see everything described so clearly. I completely agree that this is a good thing! Although I’m not so sure about the Shastalator…

  2. August 2, 2016 11:40

    Thank you Greg, Shasta, Nat, Leo and everyone else involved in developing the online calculators. At the recent Third Nordic Workshop on cosmogenic nuclide techniques Leo presented CREp. The initial reaction of the assembly was a mixture of “why create a free for all and confuse matters” to “this is great”. Eventually most folk agreed that the key is to provide readers all the necessary information for them to use alternative calculators if they so desire. One of the main positive outcomes of the web calculator development has been much improved documentation. As one of the culprits in earlier papers I appologise to those putting legacy databases together, and appreciate the opportunity afforded by ICE-D to improve the data. Derek

  3. August 3, 2016 16:59

    Great blog post and great work!
    I take the freedom to notify about where one can find a global compilation of glacial Be-10 and Al-26 exposure age data with input data (and comments on the source of the data) that can be used to recalculate exposure ages with various calculators (and production rate calibration data).
    /Jakob H


  1. Ten years of the online exposure age calculator formerly known as… | The bleeding edge of cosmogenic-nuclide geochemistry.

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