Devil is in the details.
1. Modis500 was calibrated on a training dataset that used cities in excess of 100K.
2. Modis picks out “built” not urban. A golf course or city park will register as Rural, however their .1 degree slop factor should get that.
3. .1 degrees is roughly 10km at the equator but less as you go toward the poles. They need to fix that in the final paper and use a constant radius.
That work is a bitch,
4. Station location errors average over 2km, last I looked. This BEYOND reporting precision. So they often report the Wrong location to .1 degrees
5. The urban/rural differential depends upon the actual character of the rural land before it was urbanized. see Imhoff and Oke.
6. They didnt control for de urbanization. Some rural sites used to be urban, so you need historical population to eliminate that.
That’s off the top of my head