'After a rescue operation of more than an hour' in this sentence is called a prepositional phrase and tells us 'when' Yang Rongdi and her companions were saved. You could make it longer by saying 'After a rescue operation which lasted more than an hour, Yang Rongdi and her companions...' or you could put the prepostional phrase after the main clause which is 'Yang Rongdi and her companions were saved'. 'of more than an hour' tells us the length of time something lasts. You can say 'Now I have a lesson of one hour'. Although if the time is exact we would normally say 'a one hour lesson'.

a year's experience = sum total of experience meaning you are knowledgeable I have worked here. I have worked there. I have done this. I have done that. an operation of an hour = the duration of the operation. It's been going on for an hour. We've been doing it for hour. We've been working for an hour.