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How well do we actually know sample elevations in Antarctica?

December 8, 2019

This is a guest post about verifying the elevations of samples collected in Antarctica for exposure dating purposes using a high-resolution DEM of the continent. Basically, what I’m doing is comparing the elevations reported in the literature of all samples in the ICE-D:ANTARCTICA database to the elevations of those same samples calculated from the high-resolution Reference Elevation Model of Antarctica (REMA). This is kind of a long post, but the main points are that (i) DEM-derived elevations agree reasonably well with reported elevations for most samples, but a large number of samples have misfits of 10s to 100s of meters; (ii) there is no obvious indication that folks are reporting elevations relative to the ellipsoid rather than the geoid, which is a good thing; (iii) misfits between reported and REMA-derived elevations decrease considerably starting in the early 2000s, presumably because portable GPS units had become widely available by then, and (iv)  large misfits of 10s to 100s of meters occur in both the pre-GPS era and the GPS era, and, in many cases, appear to be due to folks reporting incorrect or imprecise latitude and longitude coordinates.

I’m doing this exercise for two main reasons. First, elevation is the primary control on cosmogenic-nuclide production rates – production rates change by around 1% for every 10 m change in elevation – and so we’d really like to know whether elevations in the literature are actually correct. It’s reasonable to be a skeptic here because almost no one reports how they determined sample elevations, what their uncertainties are, and whether elevation uncertainty has been propagated into exposure-age uncertainty (probably not). In Antarctica, sample elevation is important for a second reason, which is that, provided that you also know the elevation of the local ice surface, you can often say something about how much ice thickness may have changed in the past.

I’m using REMA for this exercise, which is a DEM constructed from high-resolution stereo imagery shot by commercial satellites. Note, that I’ve re-referenced REMA from the WGS84 ellipsoid to the EGM96 geoid. Here’s how reported elevations compare to REMA elevations.

There’s actually a surprising amount of scatter. Given uncertainties in both REMA and in handheld GPS units (discussed below), I think about 10 m is as small as we can realistically hope the misfit to be for a given sample. However, of the 3300 samples in the database, only 61% have absolute misfits that are 10 m or less. 24% of samples have misfits less than 20 m and 5% have misfits that exceed 100 m. That’s big. An elevation error of 100 m would translate to a production rate error of roughly 10%.

At this point it’s reasonable to ask how much elevation error we expect from both field measurements and from REMA. Reported REMA elevation errors are generally less than 1 m for the open ice sheet but, not surprisingly, they are somewhat higher in rough terrain. The version of REMA that I’m using has 8 m horizontal resolution (a 2 m product is available, but the jump from 8 m to 2 m increases the hard-drive space needed for this exercise by a factor of 16). REMA errors for all samples (represented by vertical lines in the left panel above) have an average value of 2 m and a standard deviation of 7 m. So, I think we can safely say that, in almost all cases, the misfits of 10s to 100s of meters are not due to errors in REMA. For field-based elevation measurements, accuracy really depends on whether samples were collected in the pre-GPS era or the GPS era, as will be demonstrated later in this post. In the pre-GPS era, sample elevations were presumably estimated using topographic maps or barometric methods, and I would guess that these estimates have uncertainties of at least tens of meters in most cases. Since roughly the year 2000, most sample elevations have probably been determined with handheld GPS units. In this blog post, Greg compared measurements he made with an inexpensive handheld GPS unit to measurements with a fancy geodetic-grade one. He found normally distributed elevation residuals with a standard deviation of 7 m. So, to summarize, I think it’s safe to say that neither field GPS measurement error nor REMA error explains the large misfits of 10s to 100s of meters that we see.

Before moving on, it’s worth pointing out that the histogram in the right panel above is skewed significantly to the right. In other words, reported elevations are, on average, higher than REMA-derived elevations. We’ll come back to this later in the post.

Now let’s look at the spatial distribution of the misfit. In the figures below each 50 km box is colored by the average (upper panel) and standard deviation (lower panel) of the misfit of samples located in that box.

Interestingly, many of the blue squares in the upper panel are sites where either Mike Bentley, Jo Johnson, or John Stone (and academic descendants) have worked (e.g. Southern TAMs, Amundsen Sea Coast, Antarctic Peninsula, Pensacola Mtns., Lassiter Coast). You can also see that some of the largest misfits are clustered in certain areas such as the Shackleton Range, located east of the Filchner–Ronne Ice Shelf, and sites in Dronning Maud Land farther east along the coast. Note, however, that presenting the data in this way masks how many samples are actually contributing to each box. For example, in the case of the Shackleton Range, the three red boxes only contain five samples.

There are a few plausible factors that could be contributing to the large misfits. One possibility is that folks are reporting elevations relative to the ellipsoid rather than to the geoid. In Antarctica, depending on where you are, the difference between the ellipsoid and the geoid can be up to about 60 m. So, while this can’t explain the largest misfits, it is important to know whether or not sample elevations are being reported in a consistent fashion. The plot below shows the relationship between misfit and ellipsoid-geoid correction for all samples.

The distribution is skewed to the right (as noted above), but there is no obvious indication that folks are reporting elevations referenced to the ellipsoid rather than the geoid, which is a good thing.

A second possible explanation for the large misfits is that samples with large misfits were collected in the pre-GPS era. The figure below shows that this effect does, in fact, explain a lot of the misfit. In the lower panel, the misfit distribution for each year is represented by a box plot where the red line shows the median misfit, the bottom and top of the box represent the 25th and 75th percentiles, respectively, and the entire range of misfit is represented by the dashed line. We don’t actually know the collection date for all samples (or it is at least not compiled in the ICE-D:ANTARCTICA database), and, for those samples, I’m using the date of the earliest publications in which they are mentioned, which probably lags the collection date by a few years on average.

What’s cool about the lower panel is that you can actually see when folks started using precise GPS units in the field. Starting in the early 2000s the average misfit decreases to 6 m, which is about what we would expect given REMA errors and handheld GPS errors discussed above. 2019 is kind of an outlier, but as you can see in the upper panel, there are very few samples associated with that year (presumably more samples were actually collected in 2019 but have just not been published yet). Note that although GPS units were occasionally used in Antarctica to determine sample elevations at least as early as 1995, GPS signals for civilian use were intentionally degraded by the U.S. government until 2000 under a program known as “selective availability”, during which GPS-determined positions had uncertainty of 10s of meters.

It’s important to mention that the large difference between pre-GPS and GPS era misfits doesn’t necessarily mean that the elevation of samples collected in the pre-GPS era are wrong. Because REMA is queried at reported latitude and longitude coordinates, any error in these coordinates translates into elevation error in areas where there is significant vertical relief. So, it’s possible that the reported pre-GPS era elevations are actually correct, but that the samples are incorrectly located. This actually appears to be what’s going on for at least some samples.

Here’s an example of this effect from Dronning Maud Land. These samples were collected by a German expedition in 1995-1996. The samples are reported to have been collected from either the nunatak in the lower part of the image or from the nearby debris fields, however, as you can see, they appear to be located several kilometers away on the ice sheet.

Here’s another example of samples collected in 1999 from Migmatite Ridge in Marie Byrd Land. Five of the samples appear to be located hundreds of meters or more than a kilometer away from outcropping rock.

Interestingly, the problem of mis-located samples is not actually limited to samples collected in the pre-GPS era. Below is an example from the west side of the Antarctic Peninsula, where samples were collected from Overton Peak on Rothschild Island. Despite the fact that the collectors of these samples were using handheld GPS units in the field, six of their samples appear to have been collected in the middle of an ice shelf 15 km away from Overton Peak. Interestingly, these misplaced samples actually account for all of the samples with misfit in excess of 100 m from the year 2012.

Although the examples above show obviously misplaced samples, for most samples with large misfits it is not clear whether (i) the reported latitude and longitude coordinates are incorrect/imprecise, (ii) the reported elevations are incorrect, or (iii) both are wrong. Samples with large misfits commonly map to areas of outcropping rock, and, in these cases, it’s difficult to tell what the problem is. However, there is actually another piece of evidence in support of the idea that many of the large misfits are due to bad latitude and longitude coordinates. Recall the right panel in the first figure I showed. The distribution is skewed significantly to the right, which means that, on average, reported elevations are higher than REMA-derived elevations. Samples for exposure-dating purposes are more likely to be collected from topographic highs (summits, ridges, etc.) than from topographic depressions. That means that horizontal position error for a given sample will more often than not translate to a REMA-derived elevation that is lower than the sample’s true elevation, which is consistent with the skew in the distribution.

What’s interesting is that, if we assume that horizontal (rather than vertical) position error is the source of the bulk of the misfit, then samples are actually misplaced horizontally by much more than the 5-10 m typical of the accuracy of handheld GPS units. For example, if we look at all of the samples with misfits greater than 25 m, only 5% of these have reported elevations that can be found in REMA within 50 m of the reported latitude and longitude. For samples with misfits greater than 100 m, this value decreases to 0.6%.

So, to conclude, what have we learned from this exercise? Well, for one thing, the advent of the portable GPS unit was a big gift to cosmogenic-nuclide geochemists. However, even equipped with this technology, in some cases folks have still managed to report sample locations that are demonstrably incorrect in the vertical and/or the horizontal. Now that we are also equipped with an extremely high-resolution DEM of the entire continent, it’s probably a good idea to double check your elevation, latitude, and longitude measurements once you get back from the field.

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