The objective of the paper is to interpret data on water level variation in a river affected by overflow from a sewer system during rain. The simplest possible, hydraulic description is combined with stochastic methods for data analysis and model parameter estimation. This combination of deterministic and stochastic interpretation is called grey box modelling.
As a deterministic description the linear reservoir approximation is used. A series of linear reservoirs in sufficient number will approximate a plug flow reactor. The choice of number is an empirical expression of the longitudinal dispersion in the river. This approximation is expected to be a sufficiently good approximation as a tool for the ultimate aim: the description of pollutant transport in the river.
The grey box modelling involves a statistical tool for estimation of the parameters in the deterministic model. The advantage is that the parameters have physical meaning, as opposed to many other statistically estimated, empirical parameters. The identifiability of each parameter, the uncertainty of the parameter estimation and the overall uncertainty of the simulation are determined.