Loss-of-Natural-Storage Detention Volume

This formula gives a first, conservative estimate of the volume a detention or retention pond must hold to bring the runoff from a developed area back to what it was before development. The Federal Highway Administration's urban drainage manual (HEC-22, fourth edition, equations 10.1 and 10.2) writes it this way. The idea is as simple as it looks: the volume is $V_s = \alpha A Q_s$, the drainage area $A$ times the extra depth of runoff $Q_s = Q_a - Q_b$ (the post-development depth less the pre-development depth), with $\alpha$ only converting units.

The runoff depth is a depth, the volume of runoff spread evenly over the whole watershed, although the manual calls it a volume; that is why multiplying by the area gives a real volume. The constant $\alpha$ only converts units: 3,630 cubic feet per acre-inch (43,560 square feet in an acre divided by 12 inches in a foot), or 10 cubic metres per hectare-millimetre (10,000 square metres in a hectare divided by 1,000 millimetres in a metre). The unit pickers apply it. Take $Q_a$ and $Q_b$ from the NRCS curve number runoff equation, or from the Rational Method.

The page's example is the manual's Example 10.1. A drainage area of 5.7 acres has a post-development runoff depth of 0.33 in and a pre-development depth of 0.18 in, so the extra depth is 0.15 in, and $V_s$ is 3,630 × 5.7 × 0.15, which the manual prints as 3,100 ft³ (88 m³). The exact value is 3,103.65 ft³ (87.9 m³); the manual keeps two significant figures. A metric case: 4 ha with depths of 12 mm and 5 mm gives 10 × 4 × 7 = 280 m³.

Treat the result as a starting figure. The manual says the method is conservative for detention volumes and better suited to retention volumes, and that it gives a preliminary figure only: its other methods can be run and compared before a design volume is chosen. The answer scales directly with the area and with the difference of the two runoff depths, so any error in either depth carries straight into the volume. Once a volume has been chosen, the detention storage mass balance is the next step, routing a hydrograph through the pond.