Going Up ... and Down

We had an interesting question in our supporters forum this week about our GPS mapping application from our user ThinArthur. He asked:

Interested in your comments/thoughts on one of the perrennial challenges of computer mapping, namely ascent.

I uploaded a walk I did in South Wales today into a couple of different mapping tools I use. As ever all gave virtually identical distance (23.7m), but equally as predictably the ascents varied enormously as follows:

Walk Lakes: 668m
Anquet Maps: 965m
Garmin BaseCamp: 1123m

I think I half understand the difficulties and reasons behind the variation, but would welcome any obervations you may have.

Essentially the problem is that GPSs, although very good at giving accurate 2D fixes (especially with the aid of EGNOS if your GPS supports it) are nowhere near so good at working out your elevation with errors in the order of ±10-20m depending of what satellites it can see¹.

The other problem is that you get jitter. So if you're walking along dead flat ground then your elevation will apparently change.

So one possible reason for the variation in results that ThinArthur seeing is that some people rely on GPS elevation. This is a bad thing, mainly because of the jitter problem, and is likely to result in over-estimates of ascent/descent but if you're Garmin and writing for a worldwide audience then this may be what they're reduced to doing.

Ingleborough

Our solution to this is that we just ignore the elevation data your GPS gives us in a track. Instead we rely on Ordnance Survey's Land-Form PANORAMA® database which gives us the height of every point in the UK on a 50m x 50m grid to an apparent accuracy of 1m.

From that we can extrapolate to the elevation at points on the track with rather better accuracy than a GPS can.

However when we first starting doing this and were just adding all the changes together then the total ascent and descent were far higher than seemed likely. This for example is a walk we did up Ingleborough in the Yorkshire Dales a few years ago now before we got started with WalkLakes:

The start point of that walk is at about 170m. The summit of Ingleborough is 724m and the walk is pretty much up and down, there's very little in the way of intermediate down. This makes it a pretty good test case as you'd expect the ascent and descent to be around 600m. In reality we were getting figures of over 1000m. Even after revisiting the code and tweaking the way the figures were calculated we still were getting total ascent of 873m and descent of 714m which we're both implausibly high and oddly asymmetric.

But we worked out what was going on in the end - it turned out that even when using the OS database you still have to allow for jitter - and by the time we had finished allowing for that we got an ascent of 635m, which seemed a lot more plausible, as did other test cases we tried.

As for Anquet they're a UK based company so they may well be using the same data we are however as you can see from my example above unless you apply some correction you get an over-read in the order of 50%. Anquet's figure is about 50% higher than ours so I suspect they've probably not done what we do.

Having said all of that there is a fundamental problem which is that there is no "correct" answer to this. It's like asking how long the coastline of the UK is². All I can tell you is that when we were working on this we looked at a lot of tracks and routes and we were eventually getting figures that looked plausible to us ... and that's about as good as you can get really.

Photo of Ingleborough is by Andy Hawkins and is released under a CC-BY-SA 2.0 licence.

1. There's also another problem, which is that depending of which datum you use you get a different alleged elevation but most modern GPSs can cope with this. I've blogged about that here before in my post GPS and Elevation. However as ascent and descent are relative, not absolute, it doesn't matter when calculating those.
2. It's pretty much infinite if you count it down to grains of sand.

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