There's so many variables that it simply isn't possible to quantify exact distances. That's why we keep it simple - if you don't think you're going to get safely airborne then don't take the tow. Contributors to take-off performance include:
Altitude/Air density
Air Temperature
Humidity
Runway condition (eg.. grass vs tarmac)
Wind - strength, direction, gusting
Glider performance (+ how dirty the wings are)
Tug performance (+ how dirty it is)
Glider wing loading (carrying water balance, max auw)
Tug weight (+ vs max auw - e.g full vs empty)
Glider & Tug pilot competency
That said, the US Air Force did some detailed research in order to develop a set of operating minima for their operation from high altitude sites.