What type of replacement door threshold do I need for a garage service door?
The one you have there was built into the door frame as a unit. You wouldn't find that exact part unless you contacted the manufacturer. 

I would simply see what your local hardware or home improvement store has on hand. The crest of the curve needs to mate well with your door's bottom seal or sweep. Other than that it's not terribly critical. You'll have to consult your inner engineer and figure it out.

Fit the new threshold to the floor and door plate as necessary. Clear silicone caulk is helpful at the ends and underneath.