There's no real easy way. Q PROC and Q STG, might give you an idea. Also if you know what your client ingest was the night before, that would help too.
In an ideal environment, all your nightly backup would go to a disk pool, you then do your backup stgpool, and them migrate from disk to tape. So, when backup stgpool runs, everything in the disk pool needs to go to the copy pool. So the current occupancy of the disk pool is how much you need to copy, Q PROC will tell you how much has been copied already. However, if your diskpool fills up at night and overflows to tape, then all bets are off with that method.
However, if you know your clients backed up 2.8 TB for example the night before, then that's in theory how much BACKUP STGPOOL would need to copy.