A grey box model describing the hydraulics in a creek : GREY-BOX MODEL FOR FLOW IN A CREEK

The Saint-Venant equation of mass balance is used here to derive a stochastic lumped model describing the dynamics of the flow in a river. The flow dynamics are described by the evolution of the cross-sectional area of the flow at two locations in the river. The unknown parameters of the model are estimated by combining the physical equations with a set of data.

This method is known as grey-box modelling. The data consist of water level measurements, taken every minute at two locations in a river, over a period of nine days. The data are sub-sampled to a sampling period of 15 minutes before further processing, and a maximum likelihood method is used to estimate the parameters of the model.Three different models were applied to the data set.

All three are linear reservoir models with an estimate of the dynamic lateral inflow as a function of precipitation. The first model is a single reservoir model, which proved to be too simple to adequately describe the effect of precipitation. The second model is also a single reservoir model, but the data from the downstream station were translated forward in time, corresponding to a time delay in the system (a retention time).

This model responds in a physically reasonable manner to precipitation, capturing very well the flow peaks caused by rain events. The third model is based on two reservoirs, and like the second model, it responds reasonably to precipitation. Its description of the dynamics seems quite good, though it does not capture the flow peaks quite as well as the second model.

However, it is shown, that this model statistically provides the best description of the system. Copyright © 2001 John Wiley & Sons, Ltd.