Water leaking behind gutters
That is a lot of water pouring out of your soffit. 

To find roof leaks, we use a garden hose and start at the eave and work our way up the roof. 

Often we discover it’s not the roof membrane, (especially if there’s no roof penetrations like roof jacks, skylights, etc.), but rather the joint between the roof and an upper wall. It’s easy to accumulate a significant amount of water if it hits a wall, runs down the wall and then under the roof membrane. The water will run down the roof sheathing until it finds a gap...then flows out.