The characterization of floods has demonstrated the complexity of processes contributing to its generation and influencing the timing and magnitude of the basin flood hydrograph. Since the 1930s the science of hydrology has concentrated on the development of mathematical models to predict this flood hydrograph in catchments (deterministic hydrology). It started with the unit hydrograph model in 1932 of Sherman and Horton’s simplistic infiltration approach in 1933. Although further refined these two concepts were the only modelling approach for more than 30 years. They are still today the theoretical basis of the conceptual models in which the catchment is regarded as a system in which the input (precipitation) is transferred by a system function (unit hydrograph) to a runoff hydrograph at the outlet of the catchment. These rainfall-runoff models are also called “lumped models”.

In the 1970s the science of hydraulics joined the research field of runoff modelling. At the beginning they concentrate on the prediction of the changing magnitude, speed and shape of a flood wave as it propagates through rivers and channels (flood routing). They resolve the flow path by dividing the stream channel in profiles and applying the equations of motion^{(*1)}. Also at the end of the 1970s the Hillslope Hydrology^{(*2)} has provided new knowledge on the relationship between precipitation input and hillslope discharge output in terms of the spatial soil distribution and terrain contour. With the availability of powerful computers these physically based theoretical concepts (Physical Hydrology) have stimulated the development of a new generation of rainfall-runoff models, the physically based distributed models^{(*3)}.