Calibration Technique for 1-D Unsteady Flow Models

This paper presents a simple and efficient optimization technique for determining the continuous piecewise linear variation of the roughness parameter with discharge (or stage) for each reach of the river system bounded by gaging stations or major tributary confluences. The optimization technique is based on a modified Newton-Raphson gradient-type algorithm and the application of a decomposition principle that simplifies the treatment of complex river systems of dendritic (tree-type) configuration. The observed-computed stage hydrograph RMS errors coincident with the optimal roughness-discharge relationship range from essentially zero for ideal systems with no observational errors from 0.2 ft to 0.7 ft (0.06 to 0.21 m) for complex natural systems. The required computation time (IBM 360-195) is about 0.005 sec per time step per distance step when the optimization technique is coupled with a weighted four-point implicit finite difference approximation of the unsteady flow equations.