1. Measuring Topographic Exposure from Digital Elevation Models
Topographic exposure (‘topex’ for short) is a measure of the extent to which a site is sheltered by the surrounding terrain.
Topex can be calculated from a Digital Elevation Model such as this one.
Most GIS standard GIS software does not include a Topex function. Thus, topex is usually calculated using a custom-written script or program.
Elevation (metres)

2. Measuring Topographic Exposure from Digital Elevation Models
To explain how Topex is calculated, let us look at one ‘slice’ through this DEM
Our ‘slice’ from west to east is shown by the black line.
Let us imagine that we wish to calculate topex for the grid cell within the DEM marked with the red circle.
Elevation (metres)

3. Measuring Topographic Exposure from Digital Elevation Models
To the east, we can calculate the angle to the horizon using trigonometry. In this case, it’s 30 degrees.
We can also calculate the skyline angle to the west – in this case it’s 20 degrees.
Because this particular site is sheltered, the skyline angles are quite large.
30 degrees
20 degrees
West
East

4. Measuring Topographic Exposure from Digital Elevation Models
However, the skyline angles on an exposed ridge or open plain would be much lower.
For the ridge shown here, the angles are 0 degrees to the west and 5 degrees to the east.
So high topex values indicate sites that are sheltered from the wind, whilst low values indicate sites that are exposed to the wind.
5 degrees
0 degrees
West
East

5. Measuring Topographic Exposure from Digital Elevation Models
An overall topex score can be calculated from the skyline angles for the 8 major compass bearings (north, north-east, east, etc.)
All 8 angles can be added to give an overall topex score.
North NE NW E W SW S SE

6. Measuring Topographic Exposure from Digital Elevation Models
Overall topex scores (measured in degrees) for this site might look something like this illustration.
Note the sheltered valley bottoms with high topex scores appearing in red.
Note how plains and ridges have low topex scores and appear in blue / black.
Topex (degrees)