Calibration of Riverbed Roughness

Abstract

Singular value decomposition is used to calibrate the Manning's roughness coefficients in a one-dimensional unsteady flow model of the Upper Niagara River. The method is used to solve for the parameters after formulating the calibration problem as a generalized linear inverse problem. Singular value decomposition is useful in solving underdetermined, overdetermined or even-determined problems, and can provide information to compute matrices describing parameter resolution, covariance, and correlation. This information is useful in identifying the important parameter groups in the model. Calibration is repeated with different numbers of parameter groups to determine the variation of the output error and uncertainty of the parameters with the parameter dimension. For purposes of comparison, the model with a selected group of parameters is calibrated using the Gauss-Newton method and minimax methods. The study shows the relationship of the parameters to the geometric layout of the river and the gauging stations.