They sound like night terrors to me. Our youngest son was diagnosed with night terrors when he was very young, maybe 18 months or so. It's been so long it's hard for me to remember. I know he wasn't older than 2. Anyway, he's almost 8 now, and we're still waiting for him to outgrow them. :(
The only trigger we've figured out is him being over-tired, but he gets tons of sleep. He goes to sleep at 7:00, and gets up at 7:00. Occassionally he stays up late for a special occassion, and then he may or may not have a night terror the following night. It's hard to tell. His night terrors seem to come in waves, too. He'll go several months without one, and then he'll hit a rough patch and have 6 or 7 in one month. It's awful.
Talk to your pediatrician. There really isn't much you can do, though. The only comforting news is that the child doesn't have any recollection of them. I'm sorry you and your daughter are dealing with this.