Detention Storage from a Routing Step

This is conservation of mass with nothing else added: what comes in and does not go out is stored. Five cubic metres a second arriving against two leaving means three accumulating, and over an hour that is 10,800 m³ of water sitting in the pond. It looks too simple to be worth a page, and yet it is the entire basis of level-pool routing and of every detention pond sizing calculation in a stormwater report.

What makes routing more than arithmetic is that the outflow is not a free choice. It is set by the outlet structure and by the water level, so $Q_{out}$ is a function of the storage itself. That coupling is why the storage-indication method exists: you tabulate $2S/\Delta t + Q_{out}$ against stage, and the continuity equation and the outlet rating curve are then solved together, step by step, without iteration. Do it on a spreadsheet with a ten minute step and a real hydrograph and the pond design falls out.

Two things go wrong in practice. The time step has to be short relative to the rise of the hydrograph, and a step longer than about a fifth of the time to peak will systematically under-predict the peak stage, which is the wrong direction to be wrong in. And the storage a pond actually has is not the storage on the drawing: sediment accumulation, a permanent pool, and freeboard reserved for safety all subtract from it. Ontario practice adds a further wrinkle worth knowing, in that ponds are often sized for water quality on a small frequent storm and for quantity control on a rare one, and the two requirements can want different outlet configurations entirely.