When they say, for example, 2 inches of rain that is meant to represent 2 inches across the entire area of the rain storm, meaning every square foot of land and water is receiving 2 inches of rain. Depending on the area a significant percentage of that water can make it’s way into the river. So the river is getting 2 inches and then many more inches of rain water through run off from the land around the river.
They get not only the rain that falls into them directly, but also all the runoff from the nearby land which haven’t been soaked up by the soil. Soaking tends to take some time, so a short heavy rain quickly overwhelms it, and all the extra water on the surface speeds down into the nearest river/pond.
Their level depends not just on the rain that falls on them, but also all the water that falls on surrounding land and drains into them. Could be miles of land that all feed into that river or pond, through runoff over land and also water that seeps into the ground and ends up in that body of water.
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