Practical use of analytically derived runoff models based on rainfall point processes

This work reports on the practical usage of the four stochastic rainfall‐runoff models introduced by Bierkens and Puente (1990). These models, which are lumped in space, were analytically derived combining two rainfall point process models with two simple runoff parameterizations. The rainfall models employ rectangular pulses with Poisson (PRP) and Neyman‐Scott (NSRP) arrivals, respectively. The runoff models route individual rainfall pulses via linear reservoirs. One runoff parameterization accounts for surface runoff by using a single linear reservoir (SLR). The other model considers both surface and groundwater runoff employing two linear reservoirs in parallel (PLR). All four representations were tested on two catchments located in the Netherlands and Colombia. Emphasis was placed on the models' ability to (1) give stable parameter values for data sets at alternative averaging (aggregation) lengths (consistency) and (2) preserve historical statistics at alternative averaging lengths when using parameters found from data at other averaging scales (robustness). Results show that the use of alternative rainfall models may have little effect on runoff performance. Specifically, the NSRP model resulted in more robust runoff behavior than the PRP model only when combined to the SLR parameterization. The type of model used to route individual rainfall pulses was found to be important. Runoff representations containing the PLR component were found more robust than those having the SLR model.