Previous investigations have shown that an estimate of the catchment r
esponse to a storm event can be obtained from a consideration of kinem
atic waves flowing over planar surfaces. For a singular plane, analyti
cal solutions have been presented previously for storm events with a c
onstant intensity of rainfall excess. However, these solutions have li
mited applicability owing to the non-uniform distribution of precipita
tion and, hence, rainfall excess in most real storm events. Analytical
and numerical solutions for a number of non-uniform patterns of rainf
all excess are presented. Solutions obtained show that the pattern of
rainfall excess has a considerable influence on the catchment response
. This influence is evident in the different time-to-peak of the resul
tant runoff hydrographs and in the hydrograph shape itself. Therefore,
the time of concentration is not a constant characteristic of the cat
chment which can be determined without consideration of the temporal p
attern of rainfall excess. Finally, the predicted hydrographs obtained
for variable rates of rainfall excess have higher peak flow rates tha
n that obtained for a constant intensity of rainfall excess.