Accuracy of Mountain Heights in Kananaskis Country?

A guest post from Gérard Lachapelle
What are the correct heights of mountains in Kananaskis Country? This is a question that many hikers using GPS devices ask when they obtain summit heights that are different from information online, sometime substantially. Being a geomatics engineer and having experienced the above problem for years on countless hikes, I decided to conduct a project to determine the height of selected summits this summer with the help of capable geomatics engineering students in our University of Calgary Department of Geomatics Engineering.

GNSS survey

GNSS survey on South Opal Ridge. Primary receiver at centre.

There are many reasons for these discrepancies. Handheld devices are low cost, hence have limited performance, although they are gradually being improved. Most newer devices include other global navigation satellite systems (GNSS), and are appropriately referred to as GNSS devices. They may include from two to four GNSS systems (GPS, Europe’s Galileo, Russia’s GLONASS and China’s Beidou).

Under open sky conditions when signals received from faraway satellites are still relatively strong, accuracy can be as good as a few metres.  However, trails going up mountains are not ideal due to forestry canopy and obstruction from topography, hence accuracy degrades. As a consequence, the elevation gain and height measured by such devices are not accurate. The addition of an integrated altimeter sensor is now common and helps to stabilize height reading and correct ascent values, which works well when atmospheric conditions are stable. Consequently the values for mountain heights from modern sport watches, hand-held GNSS devices and smartphones can vary by 10 to a few tens of metres from one hike to another.

Heights of features are usually given with respect to the average sea-level. But GNSS devices don’t determine heights with respect to sea-level, but with respect to a mathematical model of the earth, namely an ellipsoid. Determining average sea-level is a complex and continuous enterprise. Gradual improvements and changes in definitions have refined the results by up to a few decimetres. The difference between the elipsoid and sea-level can reach a few tens of metres in the Canadian Rockies, but the difference is now known with accuracy of 10 cm or better except in a few areas of extremely rugged topography.

Next, what is the summit of a mountain?  The top of the highest rock? What if someone moves that rock, resulting in a lower of height by 30 cm? In view of the above, it does not make sense to try to determine or quote a summit height with accuracy better than 1 metre. This might even be stretching it; think of the jagged edge of Ha Ling’s summit for example.

Nowadays, the most feasible method to determine summit heights with the best accuracy possible is to do a precise GNSS survey. This involves the use of highly sophisticated geodetic grade equipment, each unit worth 50 times that of a handheld unit, and complex methods, algorithms and software. Accuracy also depends on the time duration of measurements at a summit. Given all above error sources, we decided to record measurements for 30 minutes at the summits visited so far. The GNSS equipment we are using are rugged and self-contained 2 kg Trimble R10 units. The estimated GNSS height [above the ellipsoid] accuracy is typically of the order of 10 to 20 cm.  To this value, we must [quadratically] add the other error sources mentioned above, including the conversion to height above sea-level.

Trimble-R10

A close-up of the Trimble-R10 GNSS receiver.

We are confident that we are able to determine summit heights with accuracy of 1 m. Any measured quantity has technically to be assigned a statistical probability level. This 1 m value has a probability level of 1 sigma (65% confidence level). The height of summits visited so far are given below (updated July 31, 2018).

Note: Gérard Lachapelle is Professor Emeritus, Department of Geomatics Engineering, University of Calgary and an avid hiker.

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2 comments… add one
  • davebloggs Jul 9, 2018, 3:10 pm

    must have added some in the recent trail renovations

  • Gillean Daffern Jul 7, 2018, 11:37 am

    It is interesting to note that Ha Ling has gained a whopping 67 vertical m and is now an 8000 ft peak at 8117 m.

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