Elevation and slope calculation

Elevation and slope calculation. Accumulated positive slope and accumulated negative slope. GPS altimeters, barometric altimeters and DEM Digital Elevation Model

Surely, during an outing or after doing it, when we have that appreciated coffee or beer with colleagues, you have experienced this conversation: "I have 456m of slope..." "well, they give me 537...", "what wow man!!!, yes it's 425!!!".

Well yes, with obtaining the altitude, necessary to calculate the accumulated difference, there are always controversies and differences.

In this section we will try to explain the different methods that are normally used, both to obtain the altitude and other parameters related to hiking, biking, etc.

But before continuing, it is worth reviewing the three main systems used to determine the altitude of a point, these are: GPS altimeters, barometric altimeters and the DEM Digital Elevation Model.

We also recommend you take a look at the article "Altitude, Height and Elevation" in the "Additional information, curiosities and glossary of terms" section of this site

We also leave a link to this interesting blog article "Explorando Oruxmaps" in which the different methods in which the application is discussed and explained Oruxmaps shows the altitude and performs the calculation of the accumulated slopes:

https://tronpoonpo.blogspot.com/2023/01/algoritmo-de-elevacion.html

GPS receivers, GPS watches, and cycle computers commonly use two methods to measure altitude: GPS altitude measurement and barometric altimeters.

GPS altimeters

The most basic range devices use GPS altitude measurement. This consists of obtaining the altitude data by performing calculations based on the position of the receiver in the horizontal and vertical planes. In the horizontal plane, GPS precision is quite high, but not so much in the vertical plane, due to the different relative position of the satellites with respect to the GPS receiver (see the article “Global Positioning System” in the section “Additional information, curiosities and glossary of terms” of this site). Another problem that can arise is the lack of data due to loss of GPS coverage.

Barométric altimeters

Slightly higher-end devices usually have barometric altimeters for altitude measurement. Barometric altimeters are much more reliable than those measured by GPS and their operation is based on measuring the atmospheric pressure at the current position, which will be lower as the height increases, since it depends on the weight of the existing air column just below. over. The density of air and its pressure vary logarithmically with height, reducing approximately in half at 5000 meters, where it is approximately half an atmosphere, that is, half the pressure at sea level, which is one atmosphere.

The accuracy of the measurement of a barometric altimeter depends mainly on two factors, the first is the correct calibration at the starting point of the activity and the second, that the measurement may be affected by changes in atmospheric pressure that may cause changes in the weather. A drop in atmospheric pressure caused by a storm will be interpreted by the barometer as an increase in height. Other factors such as dirt clogging the sensor port may also affect it.

Digital Elevation Model (DEM)

The cartography supported by satellite measurements, has allowed to elaborate topographic maps with a high precision in the altitude data in each point of the terrain. Having a GPS receiver with DEM data mapping will allow you to accurately calculate the altitude of your location. The DEM is a raster, raster, or array of cells, each cell representing a unit of square area and containing a measured or estimated numerical altitude value that corresponds to that location. It can be included next to the map or be external. The precision of this system is limited on the one hand by the reliability of the DEM itself and on the other hand by the resolution of the mesh used. In maps, it is common to use DEM 200x200 meters, since higher resolutions (DEM 25x25 m, DEM 5x5 m) imply a greater amount of information and therefore a greater workload for the device, as well as greater requirements in terms of internal storage capacity.

It is possible to apply corrections to the altitude recorded by a GPS receiver using the DEM Digital Elevation Model. It is the usual method used by different platforms. In the case of Strava, instead of using DEM data, it uses data from the activities it has registered, obtaining an average of the altitude measurements of each of them. Every activity uploaded to the platform from a barometric altimeter device is used to develop the Strava elevation reference map.

Below is an example of how DEM resolution can affect elevation profile estimation.

In this first case we have traced a route using a DEM with a resolution of 10x10 m.

In this second case, the same route is shown on a DEM with a resolution of 30x30 m.