Re: Concrete Ukemi
I think it is important to know you can safely roll on any surface. It is important though you slowly build yourself up to roll on harder surfaces.
Being able to take good ukemi on mats is one thing but taking high falls on concrete is another. There are several folks I know, including myself, that are able to roll smoothly on hard surfaces as well as take breakfalls. We didn't do this overnight though.
Regarding rolling/breakfalling on grass/dirt. Providing there aren't any sticks, rocks, pinecones, etc....it is my preference over mats.