I grow a short variety of carrots in buckets very successfully, Plant in succession and you can have them right up to Xmas. The containers don't have to be very large just more of them if you want to grow a lot. CXan't help you with parsnips, although builders suppliers do have a a large bucket shaped conainer that I've seen used for all sorts of jobs on a building site, and at the end of the day all tools etc are shoved in to it to take home ( a bit bigger than a standard bucket. I presume that you are not growing these for showing.) Bigal s