Design and application of an adaptive time delay model for flow routing in prismatic trapezoidal geometry river reach

Simplified flow routing model is favourably used for control-based application because it does not only present acceptable results but also is computationally inexpensive. Recently, the Time Delay model (TD) with two parameters, time constant and time delay has been developed in order to approximate the river flow in a very wide rectangular profile. This paper presents an advancement we thereafter call Adaptive Time Delay model (ATD) that expands the application scope of the TD Model by simulating the flow using a prismatic trapezoidal geometry. Firstly, the mathematical representation of the ATD model and the linearized Saint Venant model (SVE) are defined. Secondly, the transfer functions of the ATD model and the complex hydraulic model (SVE) are obtained by Laplace transformation. Finally, the Taylor expansion technique is used to find cumulants of the two transfer functions, and consequently equating the cumulants to derive time constant and time delay of the ATD model as functions of the complex hydraulic model parameters. By applying the fourth order Runge Kutta numerical scheme the flow rate and water level at downstream reach end are simulated. The innovation of this research is that both water stage and flow rate are derived through optimization. The performance of the ATD Model is also presented and compared to the TD Model in a case study. The extension of the time delay model does not only issue more accurate results but also introduces more outcomes like flow rate, and relation curves between time delay and time constant with discharge that might be useful in flood forecasting and other purposes in water resources operation.