NUMERICAL TECHNIQUES FOR ESTIMATING BEST-DISTRIBUTED MANNINGS ROUGHNESS COEFFICIENTS FOR OPEN ESTUARIAL RIVER SYSTEMS

A finite difference version of the Levenberg‐Marquardt method for nonlinear least squares problems has been extended to include inverse problems in distributed estuarial hydraulic systems. The objective in solving the inverse problems was to establish a numerical simulation procedure for estimating best‐distributed Manning's roughness coefficients from sets of observed tide heights. As an illustration, spatially varying Manning's roughness coefficients for the Upper Delaware River Estuary system were determined for several representative sets of tide height data for the period October 1973 to June 1974. The roughness coefficients were modeled as polynomial functions of distance. Manning's n was thus found generally to vary inversely with distance from the head of tide at Trenton to Wilmington. The spatially distributed tidal‐averaged Reynolds number Re was used to correlate Manning's n and Darcy‐Weisbach's f. The resultant n‐Re relationships displayed three distinct hydrodynamic flow regimes characterized as having turbulence. Both n and f were found to be independent of Re for Re > 1.52 × 106 but inversely related to Re for Re < 1.2 × 106. Among the numerical techniques used to simulate tidal hydraulic transients it was found that a ‘hopscotch’ finite difference method yielded the best compromise between computational economy and overall accuracy. Copyright 1978 by the American Geophysical Union.