Elevation Profile Sampling Intervals

[Brian T]

On a recent hike, several participants noted the wide difference between elevation gains reported by their mobile apps compared with that published by a review of the hike. I ultimately determined that the difference was sampling intervals. It seems the apps were sampling and/or smoothing to effective 100′ intervals while the review was based on a 50′ interval.  The difference was about 1200′ over 18 miles, so not insignificant. And if I adjust the interval in CalTopo to include all track data (~12′ interval) the difference becomes more like 3500′ over those 18 miles.

It is a coastline paradox kind of problem. So what is the “best” interval? Do most apps tend to use 100′ as a generally assumed de facto standard? We use elevation gain when assessing the challenge and exertion of a hike, but that becomes difficult if there are different algorithms or interval standards being used. Is there some approach to this I am missing that makes it more obvious what the “optimum” interval would be to consistently and fairly express elevation expectations?

[Bill in Roswell]

Are you using barometric pressure devices or just GPS based elev devices? Best practice is to reset baro at the trailhead for accurate readings. Interval frequency set higher is more accurate. I suggest comparing barometric data (ABC watch) to GPS data (watch). Better yet, to handheld GPS data (Garmin Oregon). Note the GPS based elevation drift w sats available. Elev track w baro is more accurate.

Gaia/Caltopo are pro level data products developed by fed agencies originating w wildfire tracking/planning.

[Brian T]

Mechanism of collecting the data doesn’t matter here, this question isn’t about the specific accuracy of a single recorded data point but the interval frequency and what interval best represents elevation gain. Refer to the coastal paradox: the more “accurate” you measure the coast (or the elevation profile) the larger it becomes, approaching infinity even. So is 100′ better than 50′? Is 1′ better than 100′?

[Adrian Griffin]

On gpsvisualizer.com, there’s a good explanation of how sampling intervals and signal wandering affect the reported elevation gain of a track. Go to Help/FAQ and look at the tutorials. One solution might be to export the track and get trackpoint elevations from a DEM lookup. The only issue with this approach that it won’t capture ups and downs that are below the resolution of the DEM. This is often the case on a trail that was originally a game or user trail. These trails often go up and down 10 or 20 feet repeatedly instead of rising at a uniform grade like a planned, designed trail.

[Brian T]

The problem I am describing isn’t signal wandering (though I appreciate how that could /also/ be factor). This is a simple problem of data granularity. Again, it’s the coastline paradox problem:

https://en.wikipedia.org/wiki/Coastline_paradox

gpsvisualizer.com is a good and easy way to see it yourself. Just take one of your tracks, one with plenty of ups and downs, and load it into gpsvisualizer. Choose the option to replace your elevation data with DEM data and then calculate the cumulative elevation gain. Now adjust the trackpoint distance threshold, or even the elevation gain threshold and compare results. Try it with a variety of values to see how wildly the granularity of the data affects the calculation. These settings aren’t the same as simply changing sampling intervals on the DEM data like you might do in CalTopo but it demonstrates the same fundamental problem of data granularity affecting the calculation of cumulative gain.

[Chris R]

I work with Lidar data to study hydrology. Our current Lidar is sampled at a 1 metre interval, not so long ago it was sampled at 5m. Comparing the two datasets or resembling the data to average it over 3m instead of 1m to speed up model processing I notice the the tops have been knocked off the high points and bottoms of gullies raised up. This would mean that if you measured along the virtual ground surface the distance would be less using the wider sampling interval. To give an example of how far we’ve come though, around 10 years ago we were working with a DEM based on photogrammetric data sampled, at best every half mile. This is still the case for much of the Canadian backcountry unless it has been surveyed for a specific infrastructure or mining project.

[Rex Sanders]

Running joke from where I worked for 40 years:

Scientist: I need a digital coastline of California.
Data manager: We’ve got dozens, what are you looking for?
Scientist: (confused)

Not that long ago, the length, jaggedness, and “accuracy” of a digital coastline depended on how paper maps were digitized, by a human picking points on a digitizing table. Newer automagic air photo digitizing systems have the same problem. Don’t even get me started on tides, swash lines, relative sea-level rise & fall, and more.

What’s the best elevation profile sampling interval? Depends on what you want. Is knowing every 3 inch bump and dip in a trail important for some specific application? Do you need to match an existing trail profile?

Do you want to compare notes after a group hike? That’s probably a lowest-common-denominator problem, if you are lucky.

The standard-ish U.S. stair step height (~7 inches) would be easy to visualize. And almost impossible to measure with consumer-grade GPS devices. So device limits do come into play.

Traditional USGS topo maps had contour lines at different intervals depending on the map scale. Otherwise, contour lines in mountainous areas got too crowded to be visible. It was still a problem in extremely steep areas at any scale.

In short, there is no “best” interval for all purposes AFAIK.

— Rex

[Brian T]

That is a great story, Rex. And I am quickly coming to the same conclusion, that there isn’t really an answer to my question. I had hoped that for the purposes of using the information to convey the relative challenge of a hike, there was at least a de-facto convention being used.

At least now I can feel completely justified in changing my sampling down to the inch to claim heroic accomplishments of elevation crushing hikes.

[Rex Sanders]

At the other extreme, backpackers might be tempted to measure just the tops and bottoms of passes and peaks.

OK, here’s a perfectly valid profile of the 2,650 mile(*) Pacific Crest Trail:

How do YOU define a pass? Trails in the High Sierra are infamous for multiple so-called false passes before you reach the one that has a name. And there are plenty of trail descriptions that include something like “Un-named Pass, 5,280 feet.”

— Rex

* Trail lengths suffer exactly the same measurement paradox as coastlines. And the “real” length constantly changes, too, with trail re-routes in place of coastal erosion and deposition.

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