Concur with quid, V2 is a compromise value.
Screen height is all about obstacle clearance and nothing to do with ground effect. The rules on airport licensing are tied into screen height - they require a certain clearway, that co-ordinates with the take-off requirements (plus obviously a fairly hefty safety factor).
When I did my aero degree, we did a lot of work on take-off performance, but I can't say I recall ground effect ever being taken into account at-all. In my personal experience, ground effect is very much a function of crosswind, surface conditions, etc. (this is personal, I've never read this in a textbook) and it's not safe to take-it into account.
G