I want a method of generating LOD which can be used with a spherical dynamic heightfield dataset.

The basic idea is to start with a rough sphere as the base LOD and tesselate the tri's (split 1-into-4) based on the distance to the nearest of the 3 triangles vertices...

The heightmap only somes into play when nearing the surface of the planet - then the vertex height is purturbed by a fractal noise value base on the vertex location on the planet sphere.

I do high-level visibility test on each tri before I split it.

They seem to have a working spherical LOD renderer that looks pretty cool.

It should be possible to use Binary Triangle Trees for a spherical world, since if you start with a Tetrahedron which is connected to itself by proper neighbor pointers, it should work to split triangles in it just as you would in a flat mesh. Then you'd just need a mapping from 3-space vertex coordinates to your 2D height field, and you should be set. When you split a tri, you would need to position its new middle of hypotenuse point in 3D according to your mapping of height map to sphere, which would be a bit more work than in 2D where you can just directly make every vertex's Y coord the raw value from the height map under it.