Catchment Runoff Calculator

Two quite different questions are answered here. The Rational Method estimates a peak flow rate, on the reasoning that the maximum discharge at an outlet occurs once the whole catchment is contributing at the same instant, which requires a storm lasting at least the time of concentration. Its runoff coefficient C is a lumped ratio of peak runoff to rainfall intensity, taking values near 0.05 to 0.15 for woodland on sandy soil, 0.30 for pasture, 0.40 to 0.60 for suburban development and 0.85 to 0.95 for asphalt and roofs. Because the method assumes uniform rainfall and a constant C, drainage manuals restrict it to catchments of roughly 80 hectares or less. The Curve Number method instead estimates a runoff volume for a whole storm. Its single parameter, ranging from about 30 for deep sandy woodland to 98 for impervious pavement, converts to a maximum potential retention S in millimetres through S equal to 25400 divided by CN, minus 254. An initial abstraction taken as one fifth of S must be satisfied before any runoff appears, after which runoff depth equals the square of the rainfall excess divided by that excess plus S. Both approaches carry real limitations: the Curve Number contains no time information at all, so it cannot yield a peak on its own, and the ratio of initial abstraction to S was fitted to sparse early data, with later analyses of gauged watersheds suggesting a value nearer 0.05 fits better. A peak from one method and a volume from the other are not directly comparable, and antecedent soil moisture alone shifts Curve Number results substantially.

The rational approach is usually traced to Thomas James Mulvany, an Irish engineer who set out the concept of a time of concentration and the idea that peak discharge corresponds to whole-catchment contribution in an 1851 paper to the Institution of Civil Engineers of Ireland. It reached practical drainage design in the United States through Emil Kuichling, who applied it in 1889 to sizing sewers in Rochester, New York, and in Britain through the work of Lloyd-Davies in 1906, which is why the technique is still called the Lloyd-Davies method by some British engineers. Its persistence for well over a century owes much to needing only three inputs, all of which a designer can defend in front of a regulator. The Curve Number emerged from a very different tradition of measurement. From the 1930s the United States Department of Agriculture operated a network of small experimental watersheds, and the accumulated rainfall and runoff pairs were distilled by Victor Mockus and colleagues at the Soil Conservation Service into a single tabulated index combining soil hydrologic group, cover type and management practice. The method was published in Section 4 of the National Engineering Handbook in 1954 and revised repeatedly thereafter; Technical Release 55, issued in 1975 and revised in 1986, extended it to urban hydrology and became the standard reference for stormwater design. The agency was renamed the Natural Resources Conservation Service in 1994, and the current guidance appears as Part 630 of the handbook.