Why is time of concentration used to calculate storm water flows? why is it important

the storm water flows can be calculated by multiplying the impremeable catchment area by the rainfall intensity. i understand all of this, but why use the time of concentration to determine a rainfall intensity from an IDF curve (intensity duration frequency curve). why is it that the time of concentration is assumed to be the duration of the rainfall? i realise that this is worded badly but i would be greatful of an answer, thank you

A long and narrow watershed will have a different hydrograph than a short square one. It takes longer for the raindrop falling on the extreme upper edge of the basin to run down to the bottom than the drop landing in the middle. So the drop from the center runs off before the ones at the end get to the concentration point. The water does not just all of a sudden concentrate at the bottom. How this is handled depends on how sophisticated your modeling is. Some methods you just throw in a factor, some more detailed studies you break each branch up and have seperate times and shapes for each little stream, you use a hydrograph that is known for the area, a rainfall pattern etc.

PS In other words, say your rainfall amount is 1 inch. If you just take 1" x Area you get the total volume. However, this volume does not all run past the concentration point at once. It happens over a time period. Steep streams move together quickly and have a sharp peak flow in a short time where flat rivers take a long time and have wide shallow hydrographs that occur over a long time.

Likewise it does not just rain the volume all at once. It happens over time. The rain starts slow then increases to a peak and then tapers off. In your method you are applying this pattern to come up with a peak instanneous flow at the bottom of the basin. Like the rain the flow starts low and goes up to a peak and then goes down.