What is an elevation model? Laser data, point clouds and grids

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 elevation data is collected

The most precise elevation data comes from airborne laser scanning. An aircraft sweeps a laser that fires pulses and times how long each echo takes to come back. The result is a point cloud: millions of individual hits, each with a coordinate and a height, which are then classified as ground, vegetation, building or water.

The points are not equally dense everywhere. In Sweden's national laser survey, for example, the bare mountains were flown with sparser points than the rest of the country, simply because the fells 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. Every cell carries a height in a national height system, which we cover in the article on how a mountain's height is measured.

Laser or radar

Much of the world has never been laser scanned. Where it has not, there are global elevation models, usually built from satellite radar rather than airborne laser. Two things about them are worth knowing. The cells are larger, often around 30 metres. And they are generally a DSM: they measure the surface including forest, ice and snow, not the ground underneath.

That is why the same mountain can look sharp in one elevation model and soft in another. The difference is not in the mountain but in how it was measured.

What resolution actually means

This is where 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 is a scale of roughly 1:50,000, so one millimetre on the piece stands for about fifty metres on the ground.

With 30 metre cells you get just under two height values per millimetre in each direction. With one metre cells you get fifty. The difference shows in details like gullies and sharp edges, and much less in the overall shape of a broad massif.

Resolution is not the whole story, though. A coarse model can also simply be wrong. On a narrow, steep summit a 30 metre cell averages away a point that is only a few metres wide, and the top can come out tens of metres too low. You would never notice on a rounded fell. You notice immediately on a horn like the Matterhorn.

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 and the right underlying model. After, it is about making the surface hold light. We call that whole chain ALTIFORM, our own technology for turning elevation data into a relief you can recognise from across the room.

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 on the eastern side of the fell are exactly the kind of shape that disappears on a flat map.