The convolution procedure can be represented by:
qi = the flow hydrograph ordinates (m3/s)
Ii = excess rainfall hyetograph ordinates (m/s)
Ai = time-area histogram ordinates (m2)
i = number of isochrone area contributing to the outlet.
Equation 4.1 can be expanded for all subcatchment areas and all the ordinates as follows:
The above equations can be repeated until q12.
Note that I7A1 is zero.
As with the Rational Method, the whole catchment is taken to be contributing to the flow after T equals Tc.
The unrealistic assumption made in the Rational Method of uniform rainfall intensity over the whole catchment during the whole of Tc is avoided in the time–area method, where the catchment contributions are subdivided in time. The varying intensities within a storm are averaged over discrete periods according to the isochrone time interval selected.
This figure below shows the steps involved in the Time-Area method
Figure 4.2 shows the steps involved in the Time-Area method.