A Linear Model for Irrigation Canals Operating in Real Time Applied in ASCE Test Cases

In the context of irrigation canal flow, numerical models developed to accurately estimate canal behavior based on gate trajectories are often highly complex. Consequently, hardware limitations make it significantly more challenging to implement these models locally at gate devices. In this regard, one of the most significant contributions of this paper is the concept of the hydraulic influence matrix (HIM) and its application as a linear model to estimate the water surface flow in irrigation canals, integrated within an irrigation canal controller to facilitate real-time operations. The HIM model provides a significant advantage by quickly and accurately computing water level and velocity perturbations in open-flow canals. This capability empowers watermasters to apply this linear free-surface model in both unsteady and steady flow conditions, enabling real-time applications in control algorithms. The HIM model was validated by comparing water-level estimates under various perturbations with results from software using the full Saint-Venant equations. The test involved introducing a 10% perturbation in gate movement over a specified time period in two different test cases, resulting in a flow discharge increase of more than 10% in each test case. The results showed maximum absolute errors below 7 cm and 0.2 cm, relative errors of 0.7% and 0.023%, root mean square errors ranging from 2.4 to 0.07 cm, and Nash–Sutcliffe efficiency values of approximately 0.95 in the first and second test cases, respectively, when compared to the full Saint-Venant equations. This highlights the high precision of the HIM model, even when subjected to significant disturbances. However, larger gate movement disturbances (exceeding 10%) should be planned in advance rather than managed in real time.