GPS Tracks: how is elevation gain calculated?

Positive elevation gain is one of the most important pieces of information in a GPS track, but calculating it is not as simple as it might seem. Discover why GPS elevations can contain noise, why different software can produce different results and how OkMap tries to obtain a reliable estimate of elevation gain.

Introduction

Positive elevation gain is one of the most commonly used pieces of information to describe the difficulty of a GPS track. It indicates the sum of elevation changes along uphill sections and is normally expressed in meters.

At first glance, the calculation may seem simple: it is enough to compare the elevation of each point in the track with that of the previous point and add up the positive changes. In practice, however, this approach can produce unrealistic results.

Elevations recorded by a GPS receiver are in fact subject to errors and fluctuations. Even when the actual route is almost flat, the elevation may increase and decrease slightly from one point to another. If all these variations were considered real, the calculated elevation gain could be significantly higher than the elevation gain actually covered.

For this reason, calculating elevation gain requires elevation data processing, and different software can obtain different values from the same GPS track.

Who is this article for?

Anyone who wants to understand how elevation gain is calculated from a GPS track.
Anyone who has encountered different values between software or devices.
Anyone who wants to understand the role of GPS noise in elevation data.
Anyone who uses OkMap to analyze hiking, cycling or outdoor tracks.

Topics covered

Why calculating elevation gain is not so simple.
Noise present in GPS elevations.
Why different software can produce different results.
How to reduce the influence of elevation noise.
The role of track optimization.
The approach used by OkMap.
The relationship between GPS elevations and DEM data.

Why calculating elevation gain is not so simple

A GPS track consists of a sequence of points, each of which may contain a geographic coordinate and an elevation.

Consider, for example, the following sequence of elevations:

100.0 m 100.8 m 100.2 m 101.0 m 100.5 m 101.2 m

The terrain could be substantially flat, while the variations recorded by the GPS produce a sequence of small climbs and descents.

A calculation that simply added up all the positive changes would also consider these fluctuations as positive elevation gain.

The problem is therefore to determine which elevation changes are significant enough to represent a real climb and which can instead be attributed to measurement noise.

There is no universal value that can always and rigorously distinguish between the two cases. The choice depends on data quality, point frequency, receiver characteristics and the processing method adopted by the software.

Why different software gives different results

It is quite common to import the same GPS track into different programs and obtain different positive elevation gain values.

This does not necessarily mean that one of the programs is making an error.

Software can in fact adopt different criteria for interpreting elevation changes. Some may apply thresholds or filters to eliminate the smallest fluctuations, others may use more complex algorithms to identify significant changes, while others may reprocess the elevations using an external elevation source.

Consequently, elevation gain is not an absolute property of the track independent of the processing method: the result also depends on how the elevation information is interpreted.

This explains why comparing the same track with different programs can produce significantly different values.

The role of GPS elevation quality

The quality of the elevations contained in a track depends on several factors.

quality and characteristics of the GPS receiver;
satellite reception conditions;
surrounding environment, such as the presence of mountains, trees or buildings;
frequency at which points are recorded;
method used by the device to determine elevation;
any processing of the elevations performed by the device before saving the track.

It is therefore possible for two tracks recorded along the same route to have slightly different elevation profiles.

Even a seemingly very detailed track is not necessarily more accurate from an elevation perspective: a high number of points can in fact make small elevation fluctuations even more apparent.

How can the effect of noise be reduced?

To obtain a more realistic elevation gain value, it is necessary to try to distinguish significant elevation changes from fluctuations caused by measurement error.

Different methods can be used. In general, they may include, for example:

elimination or attenuation of very small variations;
analysis of elevations over a certain distance rather than point by point;
comparison between previous and subsequent points;
identification of actual changes in the trend;
filtering or smoothing of the elevation series.

Each strategy has advantages and disadvantages. Excessively aggressive processing can eliminate real variations, while processing that is too permissive can count GPS noise as elevation gain.

The goal is therefore to find a compromise that preserves significant elevation changes while reducing the contribution of random fluctuations.

How OkMap calculates elevation gain

OkMap uses an algorithm specifically designed to try to distinguish real elevation changes from fluctuations caused by GPS measurement error.

The algorithm therefore does not automatically consider every difference between two consecutive elevations as a climb or descent. The elevation profile is analyzed also by considering the variations occurring around the point being examined, in order to reduce the likelihood that a small fluctuation will be interpreted as a real change in slope.

The goal is to obtain an elevation gain value that represents the actual profile of the route as closely as possible, avoiding the elevation noise in the track being added to the elevation gain actually covered.

The method was developed and experimentally tested on numerous GPS tracks and real routes, with particular attention to outdoor activities.

Naturally, no algorithm can reconstruct the actual elevation with absolute certainty from a noisy GPS measurement. The result should therefore be considered an estimate of elevation gain, not an absolute measurement.

GPS elevations and DEM elevations

An alternative way to obtain elevations is to use a DEM (Digital Elevation Model) instead of the elevations recorded in the GPX file.

In this case, each point of the track is assigned the elevation from the digital terrain model. This can be useful when GPS elevations are particularly noisy or when a consistent elevation source is desired for the entire track.

This solution also has limitations. Accuracy depends on the quality, resolution and coverage of the DEM used. In addition, the resulting value still depends on how the elevations are subsequently processed to determine the elevation gain.

To learn more about using DEMs in OkMap, see the articles DEM: Digital Elevation Models and SRTM, Copernicus and other DEMs: which one should you choose?.

Positive and negative elevation gain

The elevation processing method is used both to calculate positive and negative elevation gain.

Positive elevation gain is the sum of elevation changes considered to be uphill, while negative elevation change is the sum of changes considered to be downhill.

The two values do not necessarily have to be equal and can be influenced by the characteristics of the track and the method used to process the elevations.

It is also important not to confuse elevation gain with the difference between maximum and minimum elevation: the latter only measures the elevation range between the two extreme points and does not take into account any intermediate climbs and descents.

Why values can change after editing a track

Editing a GPS track can also affect the calculated elevation gain. Adding, removing or moving points changes the sequence of elevations used by the algorithm.

To obtain a more stable result, it is generally useful to optimize the track before calculating elevation gain, removing any spikes, point clusters and redundant points. An excessively dense track or one characterized by numerous elevation anomalies can in fact increase the contribution of GPS noise to the elevation gain calculation.

Reducing the number of points does not, however, mean indiscriminately removing information from the track. The goal is to maintain a sufficiently faithful representation of the route, mainly removing redundant points or those associated with anomalous variations. In this way, the algorithm can focus on genuinely significant elevation changes.

For this reason, after editing or optimizing a track, the elevation gain may be different from that calculated for the original track.

What does "correct elevation gain" mean?

There is not always a single value that can be considered mathematically correct.

For a real GPS track, we do not know the exact elevation of the terrain at every moment of the route. We have a series of measurements affected by errors and we must interpret them.

A good algorithm should therefore:

reduce the contribution of GPS noise;
preserve actual elevation changes;
avoid removing climbs and descents that were actually covered;
produce consistent results even for tracks with different characteristics.

Comparing different software should therefore take into account the processing method used, as well as the quality of the elevations contained in the track.

Practical tips

Use exactly the same GPX file when comparing elevation gain between different software.
Check that all programs are using the same elevation source.
Check whether the software uses the original GPX elevations or a DEM.
Consider the number and distribution of points in the track.
Before the analysis, consider optimizing the track by removing redundant points and obvious anomalies.
Do not necessarily expect different programs to return the same value.
To compare two algorithms, use several tracks rather than just a single route.

In particular, a difference between two values is not sufficient to determine which algorithm is more accurate. It would be necessary to compare the results with a sufficiently precise independent measurement of the actual route.

Common errors

Confusing the difference between maximum and minimum elevation with positive elevation gain.
Considering every small variation in GPS elevation as a real climb or descent.
Assuming that a track with a greater number of points necessarily produces more accurate elevation gain.
Comparing values obtained from different software without considering that they may use different criteria to process elevations.
Considering GPS elevations and elevations derived from a DEM to necessarily coincide.
Modifying or simplifying a track without considering that the modification may also affect the elevation gain calculation.

Frequently asked questions

Why can the elevation gain calculated from a GPS track differ between software?

Different software can use different criteria to process the elevation variations in a GPS track and reduce the influence of elevation noise. For this reason, the same track can produce different elevation gain values.

Is the difference between maximum and minimum elevation the positive elevation gain?

No. The difference between maximum and minimum elevation represents the elevation range between the two extremes of the route. Positive elevation gain, on the other hand, is the sum of the elevation changes considered as uphill along the entire track.

Why is it useful to optimize a track before calculating elevation gain?

Removing spikes, clusters and redundant points can reduce spurious elevation variations and therefore limit the contribution of GPS noise to the elevation gain calculation. However, optimization should not indiscriminately remove points that are necessary to represent the route correctly.

How does OkMap calculate elevation gain?

OkMap uses an algorithm developed to try to distinguish real elevation changes from fluctuations caused by GPS measurement error, analyzing the elevation profile and reducing the contribution of elevation noise as much as possible.

Summary

The positive elevation gain of a GPS track is not necessarily obtained by adding all the positive differences between consecutive elevations.

GPS elevations are in fact subject to noise and small fluctuations that can be incorrectly interpreted as climbs and descents. For this reason, software uses different algorithms to try to separate significant variations from measurement noise.

Consequently, different software can produce different elevation gain values from the same GPS track, without this necessarily meaning that one of the results is incorrect.

OkMap uses an algorithm developed to reduce the influence of GPS noise as much as possible and obtain a realistic estimate of the elevation gain of the route.

To learn more about how to read and interpret an elevation profile, also see the article How to read an elevation profile.

Want to apply these concepts with OkMap?

After reading the technical articles, you can learn more with the practical video tutorials or download OkMap Desktop and work directly with maps, GPX tracks and GPS data.

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