Why is one sun angle barely better than noise?

Almost every lidar image you have ever seen is a hillshade. The software puts an imaginary sun at a compass bearing and an elevation, and shades each cell by how much light it would catch. It is a rendering choice, and it decides what you can see.

The problem is geometric and it is not subtle. A bank running east to west, lit from the east, casts almost no shadow. It is there in the height data and it is invisible in the picture. Turn the sun 90 degrees and it appears. Turn it back and it is gone again.

What we measured

We took 4 tiles of Dorset downland, 4 square kilometres in total, and rendered each one from eight azimuths at 45 degree intervals, sun elevation 30 degrees, vertical exaggeration 3, then ran the same blob detector over each rendering on a 12 metre grid.

Best angle: 20.2%. Worst: 14.5%. Mean: 17.2%. Pick a sun angle without thinking about it, which is what most people do because it is the software default, and on this ground you saw about a sixth of what the eight angles found between them.

Now the part that makes the number smaller

Here is where this page earns its place. That 17.2% is a real measurement and it means less than it appears to.

Suppose the eight renderings shared no signal at all. Suppose each one found its own set of things and none of them overlapped. The union would be the sum, and each individual azimuth would then account for exactly one eighth of it. One eighth is 12.5%. So 12.5% is what pure noise scores on this metric, by construction.

We could have published the 17.2% on its own. It is true, it is ours, and it sounds like a finding. Reported without the floor it invites you to conclude that a single azimuth misses 83% of the archaeology, which is not what it shows.

What it shows is that the number is roughly a third of the way from noise to certainty, and that the experiment cannot tell you which third. Separating "different angles reveal different real features" from "different angles reveal different noise" needs ground truth, and that is a separate run.

What to do about it

• Never survey from a single azimuth. It is the cheapest mistake on this list to avoid.
• Multi-directional hillshade, or a sky-view factor, or a local relief model. All three remove the lighting choice rather than making a better one.
• If you must publish a hillshade, publish the azimuth and elevation with it. A reader cannot judge what is missing without knowing where the sun was.