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Using QGIS, and the 'Raster > Analysis > Slope' tool, I could easily detect cliffs from my DEM.

I can identify all cliffs, and can color areas where slope is above a certain threshold. Since they are all vertical, they all have the same slope, and I cannot distinguish small cliffs (10m) from high ones (60m).

Is there another tool that would allow me to detect high cliffs from a DEM? I'm happy to use PostGIS if that's necessary.

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One approach is to create polygons from the cliff areas eg Raster Calculator with Slope > 60, then Polygonize.

Then, largely follow the steps outlined in this answer to split the polygons into roughly equal areas. This allows you to break up long/large cliff areas into smaller chunks.

Because cliff areas tend to be skinny, I found the centroids often lay outside the original polygons. So you can add a step after creating the centroids to use the Snap Geometries to Layer tool (snap the centroids back to the original random points). This will get you a point layer that is inside the cliff polygons - though the process will probably still work acceptably without this step.

Finally, use Zonal Statistics to calculate the range (top-bottom) for each area.

Here's an example with maximum cliff heights for each area in metres.

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If you are happy to just have one height for long clifflines, you can skip all of the middle steps, and go straight from Polygonize to Zonal Statistics.

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