Estimation of roughness profile in trapezoidal open channels

In the well-known de Saint Venant equations, the bed roughness-coefficient cannot be measured directly and therefore needs to be estimated. The estimation process is referred to as "parameter identification," which is a mathematical process based on using the difference between the solution of the model equations and the measured system response. This paper introduces an approach for solving the parameter identification problem in the de Saint Venant equations. The method proposed herein is widely used in gas dynamics; however, it has not been used before for unsteady problem identification of open channel flow parameters. Although the proposed solution procedure will be applied herein to the bed roughness-coefficient, it can be used for other parameters, e.g., cross-sectional area, bed width, etc. Starting with an initial guess of the roughness coefficient, the algorithm iteratively improves the guesses in the direction of the gradient of the least square criterion. The gradient is obtained by means of a variational approach, while the conditions of the criterion minimum are identified by the general method of indefinite Lagrangian multipliers.