This post is about the distribution of production rate calibration data, and whether it’s good enough or not.

The basic background here is that “production rate calibration data” are measurements of cosmogenic-nuclide concentrations from sites where we already know the exposure age of a surface from some sort of independent geochronology. In the simplest possible case, the way surface exposure dating works is that we go and measure the concentration of some cosmic-ray-produced nuclide (call this N, with units of atoms/g) in a rock surface . If we know what the production rate (P, units of atoms/g/yr) is, we can just divide N by P to get the exposure age of the surface in years (call it t). This works great if you know what P is. We can use physical first principles and measurements of the modern cosmic-ray flux to put together “scaling methods” or “scaling models ” that describe how P should vary with elevation and position in the Earth’s magnetic field. Then, to use a scaling model to estimate the actual value of a production rate at a particular location, we need to calibrate the scaling model to actual measurements of the production rate, and, as noted above, we do this by measuring nuclide concentrations in surfaces where we already know the exposure age: we measure N and divide by t to get P.

So to summarize, if we want to estimate production rates everywhere globally, we do that by formulating a scaling model and then fitting the scaling model to measured production rate calibration data. This also allows us to evaluate scaling models by asking whether they fit the calibration data, or not. Because production rates vary by a lot (factors of 10 or more) within the part of the Earth where we’d like to be able to do exposure dating (at pretty much all latitudes from sea level up to about 4-5 km elevation), it is evident that to accurately calibrate a scaling model, and to accurately test whether a scaling model either works at all or works better than another scaling model, we want to have calibration data from the entire range of scaling space, that is, that span a large range in both latitude and elevation. We’d also like to have calibration data that span a large range of true exposure ages (in order to test time-dependent scaling models), but I’ll take that as a secondary issue for now and save it for some other time.

So the question is, do we have production rate calibration data that span the entire useful part of production rate scaling space? We certainly have a lot of production rate calibration data: the ICE-D:CALIBRATION database at this writing includes 72 distinct sites where we have Be-10, Al-26, or He-3 production rate calibration data. There are also a lot of additional sites where we have C-14 or Cl-36 calibration data; we’ll leave that for now on the basis that these nuclides are less commonly measured. Mostly this proliferation of calibration data is the result of a greatly increased rate of calibration data collection during the past few years, both as part of the CRONUS-Earth and CRONUS-EU projects and by other groups. The following image, which is taken from the front page of that database, shows the distribution of the Be-10, Al-26, and He-3 data geographically and in scaling space.

In the world map, the size of the circles indicates the number of different samples collected at each site. Although the world map reveals the interesting phenomenon that there are exactly zero production rate calibration measurements for these nuclides in the entire continent of Asia, the three lower panels are more relevant in answering the question of how well the calibration data are distributed in scaling space. From left to right, they show the distribution in latitude (a simple proxy for position in the magnetic field) and elevation for Be-10 (red), Al-26 (green), and He-3 (gray) calibration data. In these plots, the size of the circle reflects how many measurements of the respective nuclides were made at each site.

This shows that the available calibration data do span a wide range in latitude. They do span a wide range in elevation. But their distribution across scaling space is not even close to uniform. Rather, with the exception of a couple of He-3 calibration sites near sea level at low latitude, latitude and elevation are highly correlated for these sites, such that they nearly all lie in a fairly narrow zone of scaling space that is at high elevation at low latitude, and at low elevation at high latitude. The opposite corners of scaling space — high-elevation-high-latitude and low-elevation-low-latitude — are nearly empty.

To figure out why, consult the following figure from a well-known 1990 article in Scientific American by George Denton and Wally Broecker.

This shows the latitudinal distribution of the global snowline, which essentially controls where glaciers exist. Naturally, it’s lower at the poles and higher in the tropics, where it’s warmer. The highest snowlines are actually in the subtropics due to the relative aridity there compared to the equator, but that’s beside the point for now. The red line is the modern snowline; the blue line is the (lower) snowline during the last glacial maximum.

The distribution of global snowlines is a thoroughly well-discussed phenomenon and this diagram, or something like it, appears lots of other places. Here is a nice example from a Russian glacier atlas that shows the same thing for South America (north is to left):

The point here is that the majority of production rate calibration data are from glacial deposits — they’re sites where glacial moraines with boulders on them have been independently radiocarbon-dated. Thus, the very non-uniform distribution of calibration data in scaling space just reflects the fact that most calibration data are from glacial deposits formed during or after the LGM, and these deposits, by nature, are lower in polar regions and higher in tropical regions. Here are the locations of Be-10 and Al-26 calibration data pasted onto the Denton-Broecker diagram:

Although a lot of the Northern Hemisphere calibration sites are well below mountain snowlines because they are associated with ice-marginal deposits of the Laurentide and Greenland ice sheets (and there are a few sites that aren’t associated with glaciers or ice sheets at all), the calibration data basically follow the LGM snowline, because that’s where you find LGM and late-glacial moraines. Again, the main exceptions are in the He-3 data set (not shown here; see above), where there are a few sites that consist of dated lava flows or other volcanics at low elevation and low latitude.

So, in fact, the production rate calibration data that we have, although fairly abundant now, are not, in fact, very evenly distributed across scaling space. The next question is, do we care? For us to care, two things need to be true.

First, we have to want to exposure-date something that is not near the Pleistocene snowline, e.g., something that is at high latitude and high elevation, or low latitude and low elevation. Do we want to do this? Consider what is by far the most common application of exposure-dating, which is, of course, dating glacial deposits. Like calibration data, glacial deposits tend to be near the global snowline, so we  might not be worried about this. To find out whether we are worried, let’s look at the distribution of where glacial geochronologists actually collect exposure-age data.

This shows the latitude-elevation distribution of exposure-age data associated with glacial deposits from both the ICE-D:ANTARCTICA database (green dots; includes measurements of many different nuclides) and a prototype of a similar database aimed at global exposure-age data for alpine glacier moraines (gray dots; includes Be-10 and Al-26 data from a future ICE-D:ALPINE database). As expected, most of these data that aren’t in Antarctica are clustered around and a bit below Pleistocene snowlines:

Now add Be-10 and Al-26 calibration data to these data (without the Denton/Broecker diagram):

For the most part, the places where we want to actually apply exposure-dating to glacial deposits are located very close in scaling space to the calibration data that we have. That’s good. In most glacier-chronology situations, we don’t have to worry about extrapolating production rate estimates away from the calibration data. However, there are some exceptions. Of course, if we’re trying to exposure-date something that’s not a glacier — landslides, fault scarps, shoreline features, whatever — we could be anywhere in scaling space and could require large extrapolations. But even in the more restricted province of glacier chronology, the most glaring mismatch in this figure (there are others less glaring) is that there are a lot of situations where we want to date glacial deposits that are at relatively high elevations, 2000-3000 m, near both poles…but we don’t have any calibration data at all at high elevations near the poles. So the first requirement for whether or not we care about the restricted distribution of calibration data is, in fact, met. We definitely want to exposure-date things in parts of scaling space that are empty of calibration data.

The second criterion for whether or not we should be worried about uncertainty in extrapolating production rates from where they are well constrained by calibration data near the global snowline to locations that are not near the global snowline is as follows. We have scaling models that predict the variation in production rates everywhere in scaling space, not just near the calibration data. However, we can’t test whether they are correct in areas where we don’t have calibration data. So the question is, do we know that the scaling models are accurate in unsampled parts of scaling space, in particular at high latitude near the poles? Obviously, we can’t answer this question by comparing predictions to calibration data, because we don’t have any calibration data in that area. One alternative, but much less satisfying, way to answer the question is to ask whether different scaling models predict the same production rates for this region, or not. If they do, we might not be that worried; if they don’t, we might be more worried. Here is a comparison of production rate estimates for high latitude derived using the two most au courant scaling methods: that based on the work of Devendra Lal (the “St” scaling method in current jargon) and that based on the work of Nat Lifton and Tatsuhiko Sato (“LSDn”):

Here I have calibrated both scaling methods using the CRONUS-Earth “primary” calibration data set for Be-10, and plotted the resulting predictions for high latitude (zero cutoff rigidity, mean Holocene solar modulation parameter). Left panel shows the predicted production rates (at high latitude using an Antarctic atmosphere approximation) for the St (blue) and LSDn (red) scaling models; right panel shows the ratio of the two production rates. At low elevation, both scaling models predict production rates that are within a few percent of each other (because they are both pinned to calibration data at relatively low elevations at relatively high latitudes), but the predictions diverge at higher elevations. At 3000 m in Antarctica, LSDn scaling predicts ca. 15% higher production rates than St scaling (note that this is the same phenomenon discussed in this blog posting about saturated surfaces in Antarctica). This is a pretty big difference. As noted in the other blog entry about saturated surfaces, we can potentially use near-saturation Be-10 and Al-26 measurements from Antarctica to in part overcome the lack of independently dated calibration data in this part of scaling space. This exercise, I argue, indicates that LSDn scaling is accurate, and St scaling is not, for high latitude and high elevation. We could also potentially address this issue using samples that are saturated with respect to in-situ-produced cosmogenic C-14 in quartz, although this was attempted by Borchers and others and was inconclusive. Overall, however, this situation could be very much improved with new production rate calibration data from high elevation near the poles.

Summary: the existing set of production rate calibration data, although very far from uniformly distributed in scaling space, is pretty good if you are interested in using cosmogenic-nuclide exposure dating for glacier chronology, with one exception. The exception is that we could really use more calibration data from high elevation near the poles. This is actually a lot harder than it sounds, because there is, for the most part, not much in the way of organic life forms living at high elevation near the poles. By extension, there is not much available for radiocarbon dating, which makes it rather hard to independently date landforms. But this is clearly a problem that could use some creative ideas about how to overcome it.