Q = C.I.A / F
where Q is a peak flowrate in m3/s or L/s,
C is a dimensionless runoff coefficient,
I is a rainfall intensity (mm/h),
A is a catchment area (m3, ha or km2), and
F is a conversion factor for different units.
In English-speaking countries, I is usually in mm/h. For small-scale catchments, area A may be in m3, and Q is required in L/s, so that F is 3600. For medium scale work, A may be in ha and Q in m3/s, so that F should be 360, and for large catchments, A is in square kilometers and Q is in m3/s, with F being 3.6.
Flowrate or discharge, Q, is related to the intensity of the rainfall that causes it, and to the area of the catchment that collects runoff, with the C factor being used to cater for other effects such as slope and land-use. Although the method appears to be simple, there are a number of complications:
The intensity I must be selected for a particular time of concentration and average recurrence interval or annual exceedance probability using an intensity-frequency-duration relationship, a statistical description of the rainfall climate of the locality where the method is to be applied.
The rationale for assuming a storm duration equal to the time of concentration is that the greatest flowrate Q = C.I.A will occur at this time, as indicated below. However, there can be partial area effects of various kinds that cause the highest Q = C.I.A to be calculated at a time shorter than the time of concentration.
The big drawback of the rational method is that it only generates peak flowrates. This leads to problems and compromises in synchronisation when combining flows for a number of sub-catchments. It is also not possible to perform detention basin calculations, as full hydrographs specifying volumes of runoff are required. The Horton (ILSAX) hydrological model and others that produce full flow hydrographs avoid these problems, but will give different peak flows estimates to the rational method because they use different loss and routing models. It is generally not possible to calibrate Horton (ILSAX) or storage routing to match rational method peak flows over a range of ARIs and storm durations.
To address this problem DRAINS includes an extended rational method model that generates hydrographs consistent with the Australian Rainfall and Runoff 1987 flow peaks.
The use of the rational method is discouraged in Australian Rainfall and Runoff 2019, although there is very little discussion about this in Book 1 on scope and philosophy, Book 9 on runoff in urban areas, or any other parts. ARR Project 13, commissioned to aid the development of ARR 2019, was critical of the rational method, and the method has been criticised in presentations and papers by members of the ARR 2019 Team. This has provoked a response by Simpson.
The use of rational method procedures in rural areas has been replaced by the RFFE (regional flood frequency estimation) procedures set out in Chapter 3 of Book 3 of ARR 2019.
There is still widespread use of the model in urban catchments in urban locations, both in Australia and internationally. In the absence of a substantiated case against the rational method, DRAINS will continue to offer this model with 1987 and 2019 rainfall data.
References