An elevation model is not an image. It is a table.
That is probably the single most useful thing to understand about digital terrain. The picture above, with its shadows and contour lines, is an interpretation. Underneath it there are only numbers: for every point in a grid, a height in metres. The same table can be drawn as a map, as a 3D view or as a physical surface. The shape is identical; only the presentation differs.
Ground or surface: DTM and DSM
Two abbreviations keep coming up, and they mean different things.
A DSM, digital surface model, describes the topmost thing present at a location. Tree canopies, roofs, power lines. A DTM, digital terrain model, describes the ground itself once all of that has been filtered out. On bare mountain the difference is close to zero. In a spruce forest it is twenty metres.
For a mountain you normally want the ground. Otherwise a stand of pine sits bulging on the slope and hides the shape you were after.
How Swedish elevation data is collected
Lantmäteriet's elevation data comes from airborne laser scanning. An aircraft sweeps a laser that emits pulses and measures the time until the echo returns. The result is a point cloud, millions of individual hits with a coordinate and a height, which are then classified: ground, vegetation, building, water.
The product Laserdata NH was collected between 2009 and 2019 at a point density of 0.5 to 1 point per square metre, dropping to 0.25 points per square metre in bare mountain areas. It is sparser in the mountains than further south, simply because the mountains are large and relatively smooth.
An even grid is then computed from the point cloud. The grid is the elevation model proper, and it is what you can calculate with. Coordinates sit in SWEREF 99 TM and heights in RH 2000, which we covered in the article on how a mountain's height is measured.
Outside Sweden it gets coarser
Laser-scanned countries are a privilege. Sweden, Norway and Denmark have it. Large parts of the world do not.
There, global models are used instead. The most common open one is called Copernicus DEM and is freely available at 30 metre resolution. It is not based on laser but on radar, collected by the TanDEM-X satellite pair between 2011 and 2015. And it is a DSM, that is, the surface including vegetation.
That is why a Swedish summit can be rendered more sharply than an Italian volcano. The difference lies not in our interest in the place but in which agency has flown over it.
What resolution actually means
Here it gets concrete, and slightly surprising.
One of our square reliefs is 25 centimetres across and typically covers an area around ten to twelve kilometres wide. That gives a scale of roughly 1:50,000. One millimetre on the piece therefore corresponds to about fifty metres on the ground.
With 30 metre elevation data you get just over two data points per millimetre. With Swedish metre data you get fifty. The difference shows in features like ravines and sharp edges, but it does not show at all in the overall shape of the mountain. The limit is more often set by how finely the material can be formed than by how fine the data is.
It is also the reason a coarser global model is perfectly adequate for a large massif, but not for a single valley where you want to see every fold.
From table to something you can touch
The translation itself is then surprisingly direct: every cell in the grid becomes a point on a surface, the surface gets a base, and the result is a solid body that can be printed. The hard work sits before and after. Before, it is about choosing the right window. After, it is about making the surface hold light.
If you want to see what a window looks like before it becomes physical, try it yourself in FRMD by You, where you mark an area on the map and get a preview of the terrain. And to see how a finished surface looks in reality, the Helags piece is a good example: the steep face and the glacier niche beneath it are exactly the kind of shape that disappears on a flat map.