There are some cool large birds that hang around the field behind my house. I’ve noticed that they give off a screech before they dive, presumably to pick up a tasty morsel.
I know why birds sing, to mate and to alert other birds to birdy-type things. But isn’t it in a predator bird’s best interest to stay mum, in order not to warn the food that it’s coming?
Or am I misreading it - are they screeching to tell their pals where to find the food?
I’ve participated in a reasonably amount of falconry and have never heard a bird call when diving on prey. I believe the calls are basically to mark territory or to say “here I am” to a mate.
With limited exceptions (e.g. Harris Hawk), birds of prey are loners and don’t hunt cooperatively.
The screech you hear when they dive is added in post-production as movie shorthand for “this is a bad ass hawk about to kill something, isn’t it cool?” Note that it’s often the same screech, for a variety of birds.
Those big lights in baseball stadiums don’t THWUMP! when you turn them on, either. 
Ok cool. So if I am sitting in my yard and hear a hawk screech, it’s not actively hunting prey at the moment. It’s telling all the other hawks to fuck off?
But then doesn’t that also say to all the field mice “there’s a hawk here that has just declared this field as hunting territory, better fuck off”?
Or am I giving too much credit to the mice? 
The screeches I’ve heard from common buzzard and Osprey, which are the bird of preys I usually watch, seems to have to do with territorial claims and warnings.
There may also be some consideration to the fact that small mammels tend to freeze in place when scared rather then fleeing as a first response. So a screech would keep your meal from running away mid-dive.
If you’re a mouse, you have to assume that you’re in some hawk’s territory. So hearing the screech would get a response of, ‘yeah, I knew that.’
You’d also have to assume you’re in some owl’s territory, some cat’s territory, some fox’s . . . and so on. Not to mention that it would also be possible to be snagged by a poaching preditor that just happened to be passing through.
So a mouse isn’t going to be put off by territorial screeches. Have we established that hawks do not screech and dive? I’ve never seen one doing so, but I haven’t seen that many hawks diving.
I’ve heard that the redtail hawk’s call is popular for this, and that it’s usually the call you hear when a bald eagle is on the screen. Apparently the true cry of the bald eagle is not so impressive.