This post is about elevation measurements for exposure-dating samples, and how accurate they need to be. Basically, the main thing that controls cosmogenic-nuclide production rates is site elevation, or, more precisely, atmospheric pressure — at higher elevation, there is less atmosphere between you and the extraterrestrial cosmic-ray flux, so the production rate is higher. Thus, to compute the cosmogenic-nuclide production rate at a sample site, the first thing we need to know is the elevation. Once we know the elevation, we can convert it to a mean atmospheric pressure using a model for how the atmospheric pressure varies with elevation, and then compute the production rate.

Note that there are two places to potentially screw up here. The second one — converting an elevation to a mean atmospheric pressure during the exposure duration of the sample — is actually a fairly complicated problem and is the subject of another post, as well as a fairly large number of papers. However, the first one — accurately measuring the elevation — ought to be pretty simple. In general, determining your elevation is a fairly well-established technology that people have been working on for centuries. So even if we can’t be completely sure that we’ve done the elevation-atmospheric pressure conversion very precisely, we ought to be able to be fairly confident that we’re not making things worse by also making inaccurate elevation measurements. So the rest of this post covers (i) exactly how precise we need elevation measurements to be, and (ii) various ways to accomplish or not accomplish that goal.

So how precise do we need elevation measurements to be? The basic rule of thumb is that 10 m of elevation change is approximately a 1% change in the production rate, but this is a bit variable with elevation. Specifically, if we choose, for example, the production rate scaling method and Antarctic atmosphere model from Stone, 2000 (other scaling methods and atmosphere models are equivalent for all practical purposes from this perspective), here is how much effect a 10 m change in elevation has on the production rate:

It’s about 1% per 10 m at sea level and less at higher elevation. What this means is that accurate elevation measurement is actually fairly important. In most cases, the total uncertainty in estimating production rates for purposes of exposure-dating is around 5% or 6%, and 1% is a decent-sized fraction of that. If having a 10-m uncertainty in measuring elevation is adding an additional 1% uncertainty to your production rate estimate, that certainly seems like something to try to avoid. Basically, the point of all this is that we would like to be able to measure elevations with better than 10 m precision. Preferably quite a lot better.

In the modern era, the default and simplest way to measure your elevation is just with the same inexpensive handheld GPS unit, which is probably a Garmin that you bought a few years ago for about \$150, that you are already using to record the position of your sample. Most handheld GPS units indicate their estimated horizontal positioning accuracy in real time, and in most situations it’s generally somewhere in the range of 3-6  m. Note, however, that this condition dates back only to approximately the year 2000. Prior to that time, the GPS satellite network, which of course was operated by the U.S. Department of Defense, included a feature with the Orwellian name of “Selective Availability” that intentionally degraded GPS performance for non-military users. So handheld GPS data from that era are much less accurate, with horizontal precision in the tens-of-meters range.

Unfortunately, in nearly all cases the vertical accuracy of a GPS position is not nearly as good as its horizontal accuracy.  This is just because GPS satellites are mostly not right over your head, but well away from the zenith at shallow angles toward the horizon. In this geometry your vertical  position is more sensitive to range errors than your horizontal position. A rough rule of thumb is that vertical position errors are usually about twice horizontal ones, so if your handheld GPS is indicating 3-6 m horizontal precision, that is something like 6-12 m vertical precision. Here is an example from data that I collected during a couple of exposure-dating projects in Antarctica. What these figures show are histograms of differences between elevations measured with a Garmin consumer handheld GPS (\$170; an older version of this) and elevations of the same sites measured with a pair of fancy, differentially-corrected, post-processed, dual-frequency Trimble survey GPS units (probably \$40K, but should have decimeter precision).

If we throw out the obvious wild outliers in both of these data sets (more about them later), these residuals are approximately normally distributed with a standard deviation of 7 m, which is actually a little better than we expect from the twice-horizontal-precision rule of thumb. So in general, this is pretty good: with our \$170 low-hassle solution we can keep production rate inaccuracy due to errors in elevation measurements below 1%.

There are, however, a couple of other important points about these data. One, they both show an offset in which the handheld measurement is systematically approx. 4 m above the DGPS measurement. These are in different years so we can’t ascribe it to weird satellite availability. I suspect this may reflect my error in converting between ellipsoid and geoid heights (more about this later) for the two sets of measurements: I am not an expert in GPS data reduction and it might be that this is how you can tell that. Alternatively, it could have something to do with the handheld GPS unit having a less sophisticated atmospheric correction than used in the DGPS post-processing.

Two, there are some pretty serious outliers in the 20-30 m range — sometimes the measurement is very wrong. Of course, you expect some of these from any random process, but I suspect that what happened here is just that I didn’t leave the handheld GPS turned on for long enough to collect an accurate position. These data are from Antarctica, which is (i) remote, and (ii) cold. Item (i) means you are highly motivated to conserve battery power because you have only a finite supply of AA batteries in your camp, and item (ii) means you are highly motivated to complete the measurement quickly and put your mittens back on. Both factors would tend to favor not leaving the unit turned on long enough to collect sufficient data. But these are significant outliers that could affect an exposure age by 3%. That’s nearly 1/3 of the Younger Dryas.

In my opinion, the summary of all this is that modern inexpensive handheld GPS units are, basically, just barely good enough for measuring elevations of exposure-dating samples. Assuming  I am right about the outliers in the data set above just being due to my carelessness, if you are careful, you should be able to keep production rate uncertainties stemming from this source to approximately 0.5-0.7%. That’s not bad.

The next question, then, is how to do better. There are several strategies for this. One is just to buy a more expensive dual-frequency GPS that can be differentially corrected. As Trimble has a near-monopoly on this market, the first issue here is that this is expensive. Still, a suitable unit can usually be borrowed from most university geoscience departments. However, this solution creates a number of new problems. One is weight — if your fieldwork is foot-supported, you have just added a lot of weight to your pack. Another is power — most of these units require daily recharging (or heavy gel-cells). Again, a potential problem for remote fieldwork. A third potential problem is that if you are operating someplace very remote (like Antarctica, again), you will not be within range of stationary GPS stations that can be used for differential correction, so you will need to not only carry a rover unit with you to the sample sites, but also establish a temporary base station at your camp with a second unit. A fourth is that you need to learn enough about GPS data processing to not make errors in the processing that are much worse than you would have made with the inexpensive unit. This is a serious consideration. A final problem is that collecting enough data with a Trimble DGPS unit to eventually yield submeter vertical precision takes a while — generally on the order of 30 minutes per site. Doing this at each site would seriously limit the number of samples that could be collected in a day.

A completely different strategy is to measure sample elevations using a barometer or barometric altimeter. This is very old-school and, at this point, kind of in the realm of retro hipster hobbies, but has a couple of big advantages, mainly that barometers designed for this purpose are extremely sensitive — they can register less than 1 m of elevation change — and quite lightweight. Some don’t even require batteries. The problem, of course, is that barometric pressure is constantly changing independently of elevation due to meteorological effects, so collecting good barometric elevation data requires care and thought, and, in some cases, a stationary base-station barometer as well. However, if you are working in any area of the continental US that is covered by a USGS 7.5′ topographic map, you can very accurately estimate the elevation of your sample sites by barometric traverse between sample sites and elevation benchmarks or survey points noted on the map. Of course, in this example in most cases you will find that you could have just plotted your horizontal GPS position on the map and read off the contour elevation to get the same result.

Leaving aside the special case where you have a USGS map (or, even better, a SwissTopo map that is almost so complete that your individual boulder is already marked), you can sometimes significantly improve on the 7-m accuracy of handheld units without incurring serious pack weight problems, by establishing temporary benchmarks with a Trimble DGPS and then using the barometric altimeter to survey elevations of sample sites in relation to the temporary benchmarks. I’ve used this strategy for many years in Antarctica and found it to yield total vertical positioning uncertainty somewhere in the 1.5-2.5 m range, depending on how closely spaced the benchmarks and sample sites are. This strategy does require a fancy GPS unit, but it is fast (because you only need to do a couple of 30-min occupations per day) and light (because you can minimize carrying around the heavy antenna and batteries). This is generally my preferred approach when possible — it’s not a prohibitive amount of work, but it reduces production rate errors associated with elevation measurements to essentially negligible levels.

Summarizing the discussion up to now, a decent-quality handheld GPS is just barely good enough for exposure dating in that errors in elevations measured using this method transfer to 0.5-0.7% errors in production rate estimates. Note that I’m pretty sure your iPhone is substantially worse, just due to the antenna size and geometry, but I have not attempted to verify that. If you can, though, you should do better, either with a more elaborate GPS unit or some combination of DGPS benchmarks and barometric survey.

There is, however, one final topic on the subject of GPS measurements of sample elevations, that is important. What we actually want to measure for exposure dating is the elevation of a sample with respect to sea level. Elevation-atmospheric pressure models are indexed to the bottom of the atmosphere, which is sea level, so we need to know how far above sea level we are. However, for GPS data reduction it is common to work not in a sea-level reference frame but in an ellipsoidal reference frame in which the Earth is represented by a simplified ellipsoid rather than the somewhat lumpy shape of the actual surface of the ocean (generally referred to as the geoid). This is not the place to launch into a full discussion of the differences between ellipsoid and geoid elevations (good places for this are here or here), but the point is that they are different. In some parts of the Earth they are quite different: here is a map (from this site) showing the difference between sea level (in this case represented by the EGM2008 geoid model) and the WGS84 ellipsoid, which is commonly used in GPS data reduction:

The details are beyond the scope of this post, but the point is that a GPS elevation computed with respect to an ellipsoid is not a sea level elevation, and can be tens of meters different from the correct sea level elevation. I am pretty sure there are a lot of errors in the exposure-dating literature where ellipsoid heights have been incorrectly reported instead of sea level heights. Be careful.