The difference between present perfect to express an amount of work finished up to the present moment (I've read three books )and the present perfect continuous to express the duration of the current activity (She's been reading for three hours).
So "It has rained since this morning." means the rain has stopped at the time of speaking.
It has rained since this morning.
It has been raining since this morning.
Do you see any difference in meaning?
I read somewhere (have been + ing) means it will probably continue raining in the future.
It has been raining since this morning. It started raining this morning and it is still raining now.
It has rained since this morning. It didn't rain this morning, but since then it has rained, it may or may not be raining now.