On physical & data driven model of irrigation channels

The St. Venant equations are commonly used for prediction and control design for irrigation channels. Despite widespread use, their accuracy are largely unknown which is surprising, taking into account the large amount of practically oriented research which uses the St. Venant equations as a starting point. Hence, a natural question is therefore whether the St. Venant equations are capable of describing the relevant dynamics of an irrigation channel accurately?

A data set from the Haughton Main Channel in Northern Queensland is shown in Figure 1.

Figure 1: Water level, head over upstream and downstream gate position

In order to examine the accuracy of the St. Venant equations, the water level to the right of the vertical line in Figure 1 is simulated using the best known and most used finite difference method, the Preissmann scheme. The simulated water level is compared against the measured water level. The unknown parameters in the St. Venant equations and the boundary conditions are estimated using the first 200 data points in Figure 1, and the accuracy of the St. Venant equations with estimated and physical parameters is compared.

Furthermore, previous works showed that simple mathematical models that describe the dynamics of the channel adequately can be obtained using system identification methods based on operational data from the channel (see System Identification). The St. Venant equations are hyperbolic partial differential equations and much more complex than the system identification models, and it is an open question whether the St. Venant equations are significantly more accurate than the system identification models to justify their use. We therefore also compare the performance of the models based on the St. Venant equations and the system identification models. The results are shown in Figure 2.

Figure 2: The measured and the simulated water levels using the St. Venant equations and the system identification models.

The results show that the St. Venant equations can adequately capture the dynamics of real open water channels. However, third order nonlinear system identification models are as accurate as the St. Venant equations with estimated parameters and much simpler to use. Of course, if there is no operational data from the channel available then the St. Venant equations must be used. The St. Venant equations also give the water levels at the intermediate points along the channel, while the identification models only give the downstream water level. However, the downstream water level is all that is needed if the model is going to be used for control purposes. If there are operational data available, the system identification models are as accurate as the St. Venant equations with estimated parameters, and they are preferred since they are much easier to use for control design and prediction purposes.

For more information see

Ooi S.K., M.P.M. Krutzen, and E. Weyer (2003). "On physical and data driven modelling of irrigation channels." Control Engineering Practice, Article In Press, 2003.

Ooi S.K., M.P.M. Krutzen, and E. Weyer (2003). "On physical and data driven modelling of irrigation channels." Proceedings of the 13th IFAC Symposium of System Identification, pp. 1975-1980, Rotterdam, The Netherlands, 2003.