In well-known hydrologic response theories like the IUH, it has been established that for a specific catchment and a constant rainfall, there exists a 'critical rainfall duration' resulting in the maximum discharge for that catchment, which is usually known as concentration time.
The next step is to associate a return period with the constant rainfall. This allows us to demonstrate that given a precipitation with an assigned return period, there is a critical rainfall duration that yields the highest possible discharge in that river section.This is what has been accomplished in Rigon et al., 2011 (but the research dates back to early 00, which is another interesting story). BTW, In the paper, we have also shown that this time is less or equal to the concentration time.
The above argument may lead to the misconception that the “maximum discharge” for the catchment cannot be exceeded (keep in mind that the concept of maximum discharge obtainable is incomplete when you do not mention a return period). Consider doubling the duration of the rainfall while keeping the intensity fixed. The first impulse results in the highest discharge with the assigned return period. Yet, it also has a discharge tail that, depending on the catchment's features, can last quite long. When the second impulse of precipitation arrives with the same intensity, it adds to the recession of the first impulse, usually increasing the discharge beyond the maximum discharge obtained with a single impulse.
In certain cases, like in the kinematic hydrograph model (uniform IUH) the rise of the new impulse discharge may precisely compensate for the decreasing recession of the older impulse, resulting in a constant discharge. However, this is not the general scenario, as simple calculations can show and sticking with this idea can be erroneous. Typically in fact, and especially when there is a marked contrast between the response time of the surface and subsurface storm flow waves, the recession discharge generated of the first impulse decreases more slowly than the increase in the new impulse discharge, effectively acting as additional rainfall. This effect is equivalent to increase the intensity of the effective rainfall to a return period which can be estimated through inverse modelling. In other words, two subsequent rainfall impulses, each with an assigned return period, are equivalent to a precipitation event with a higher return period. While the IUH theory establishes a precise equality between the return period of rainfall and discharge for a single impulse, the two return periods of discharges and rainfall become decoupled when multiple rainfall impulses occur.
